Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1176,4,Mod(1,1176)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1176, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 0, 0]))
N = Newforms(chi, 4, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1176.1");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1176 = 2^{3} \cdot 3 \cdot 7^{2} \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 1176.a (trivial) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | yes |
Analytic conductor: | \(69.3862461668\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{4} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} - 2x^{3} - 152x^{2} - 177x + 2922 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{11}]\) |
Coefficient ring index: | \( 2^{3}\cdot 7 \) |
Twist minimal: | no (minimal twist has level 168) |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.2 | ||
Root | \(-8.69515\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1176.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | 3.00000 | 0.577350 | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 0.128591 | 0.0115015 | 0.00575077 | − | 0.999983i | \(-0.498169\pi\) | ||||
0.00575077 | + | 0.999983i | \(0.498169\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 0 | 0 | ||||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 9.00000 | 0.333333 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 54.0066 | 1.48033 | 0.740163 | − | 0.672427i | \(-0.234748\pi\) | ||||
0.740163 | + | 0.672427i | \(0.234748\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −50.2350 | −1.07175 | −0.535873 | − | 0.844299i | \(-0.680017\pi\) | ||||
−0.535873 | + | 0.844299i | \(0.680017\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0.385773 | 0.00664042 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −131.487 | −1.87590 | −0.937951 | − | 0.346767i | \(-0.887279\pi\) | ||||
−0.937951 | + | 0.346767i | \(0.887279\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 91.5094 | 1.10493 | 0.552466 | − | 0.833536i | \(-0.313687\pi\) | ||||
0.552466 | + | 0.833536i | \(0.313687\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 179.487 | 1.62720 | 0.813602 | − | 0.581423i | \(-0.197504\pi\) | ||||
0.813602 | + | 0.581423i | \(0.197504\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −124.983 | −0.999868 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 27.0000 | 0.192450 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −69.8961 | −0.447565 | −0.223782 | − | 0.974639i | \(-0.571841\pi\) | ||||
−0.223782 | + | 0.974639i | \(0.571841\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 326.847 | 1.89366 | 0.946829 | − | 0.321736i | \(-0.104266\pi\) | ||||
0.946829 | + | 0.321736i | \(0.104266\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 162.020 | 0.854667 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 301.698 | 1.34051 | 0.670254 | − | 0.742132i | \(-0.266185\pi\) | ||||
0.670254 | + | 0.742132i | \(0.266185\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −150.705 | −0.618773 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 296.048 | 1.12768 | 0.563840 | − | 0.825884i | \(-0.309324\pi\) | ||||
0.563840 | + | 0.825884i | \(0.309324\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −144.302 | −0.511764 | −0.255882 | − | 0.966708i | \(-0.582366\pi\) | ||||
−0.255882 | + | 0.966708i | \(0.582366\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 1.15732 | 0.00383385 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −360.085 | −1.11753 | −0.558764 | − | 0.829326i | \(-0.688724\pi\) | ||||
−0.558764 | + | 0.829326i | \(0.688724\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 0 | 0 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −394.462 | −1.08305 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 1.83513 | 0.00475613 | 0.00237807 | − | 0.999997i | \(-0.499243\pi\) | ||||
0.00237807 | + | 0.999997i | \(0.499243\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 6.94477 | 0.0170260 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 274.528 | 0.637932 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −53.2386 | −0.117476 | −0.0587379 | − | 0.998273i | \(-0.518708\pi\) | ||||
−0.0587379 | + | 0.998273i | \(0.518708\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −108.121 | −0.226942 | −0.113471 | − | 0.993541i | \(-0.536197\pi\) | ||||
−0.113471 | + | 0.993541i | \(0.536197\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −6.45978 | −0.0123267 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 842.007 | 1.53534 | 0.767668 | − | 0.640848i | \(-0.221417\pi\) | ||||
0.767668 | + | 0.640848i | \(0.221417\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 538.462 | 0.939466 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −241.111 | −0.403023 | −0.201511 | − | 0.979486i | \(-0.564585\pi\) | ||||
−0.201511 | + | 0.979486i | \(0.564585\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −206.983 | −0.331857 | −0.165929 | − | 0.986138i | \(-0.553062\pi\) | ||||
−0.165929 | + | 0.986138i | \(0.553062\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −374.950 | −0.577274 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 559.962 | 0.797477 | 0.398738 | − | 0.917065i | \(-0.369448\pi\) | ||||
0.398738 | + | 0.917065i | \(0.369448\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 81.0000 | 0.111111 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 986.652 | 1.30481 | 0.652404 | − | 0.757871i | \(-0.273760\pi\) | ||||
0.652404 | + | 0.757871i | \(0.273760\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −16.9081 | −0.0215758 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −209.688 | −0.258402 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −443.366 | −0.528053 | −0.264026 | − | 0.964515i | \(-0.585051\pi\) | ||||
−0.264026 | + | 0.964515i | \(0.585051\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 980.541 | 1.09330 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 11.7673 | 0.0127084 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −740.815 | −0.775447 | −0.387723 | − | 0.921776i | \(-0.626738\pi\) | ||||
−0.387723 | + | 0.921776i | \(0.626738\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 486.059 | 0.493442 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 743.777 | 0.732758 | 0.366379 | − | 0.930466i | \(-0.380597\pi\) | ||||
0.366379 | + | 0.930466i | \(0.380597\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 104.651 | 0.100112 | 0.0500559 | − | 0.998746i | \(-0.484060\pi\) | ||||
0.0500559 | + | 0.998746i | \(0.484060\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 513.700 | 0.464124 | 0.232062 | − | 0.972701i | \(-0.425453\pi\) | ||||
0.232062 | + | 0.972701i | \(0.425453\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 975.038 | 0.856805 | 0.428402 | − | 0.903588i | \(-0.359077\pi\) | ||||
0.428402 | + | 0.903588i | \(0.359077\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 905.093 | 0.773942 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 1926.07 | 1.60345 | 0.801723 | − | 0.597696i | \(-0.203917\pi\) | ||||
0.801723 | + | 0.597696i | \(0.203917\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 23.0805 | 0.0187153 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −452.115 | −0.357248 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 1585.71 | 1.19137 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 888.143 | 0.651066 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −32.1457 | −0.0230016 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −1125.95 | −0.786709 | −0.393355 | − | 0.919387i | \(-0.628686\pi\) | ||||
−0.393355 | + | 0.919387i | \(0.628686\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −432.906 | −0.295467 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 1493.24 | 0.995918 | 0.497959 | − | 0.867201i | \(-0.334083\pi\) | ||||
0.497959 | + | 0.867201i | \(0.334083\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 3.47196 | 0.00221347 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 1460.77 | 0.910965 | 0.455483 | − | 0.890245i | \(-0.349467\pi\) | ||||
0.455483 | + | 0.890245i | \(0.349467\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 2225.85 | 1.35823 | 0.679116 | − | 0.734031i | \(-0.262363\pi\) | ||||
0.679116 | + | 0.734031i | \(0.262363\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −1080.26 | −0.645206 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −2713.02 | −1.58653 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −8.98802 | −0.00514769 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 394.681 | 0.217003 | 0.108502 | − | 0.994096i | \(-0.465395\pi\) | ||||
0.108502 | + | 0.994096i | \(0.465395\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −3124.20 | −1.68373 | −0.841867 | − | 0.539685i | \(-0.818543\pi\) | ||||
−0.841867 | + | 0.539685i | \(0.818543\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −1183.39 | −0.625301 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 42.0296 | 0.0217800 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −3600.71 | −1.83037 | −0.915183 | − | 0.403038i | \(-0.867954\pi\) | ||||
−0.915183 | + | 0.403038i | \(0.867954\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 5.50540 | 0.00274596 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 1974.02 | 0.948573 | 0.474287 | − | 0.880370i | \(-0.342706\pi\) | ||||
0.474287 | + | 0.880370i | \(0.342706\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 20.8343 | 0.00982999 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 1067.09 | 0.494453 | 0.247227 | − | 0.968958i | \(-0.420481\pi\) | ||||
0.247227 | + | 0.968958i | \(0.420481\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 326.559 | 0.148638 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 823.584 | 0.368310 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −274.655 | −0.120703 | −0.0603515 | − | 0.998177i | \(-0.519222\pi\) | ||||
−0.0603515 | + | 0.998177i | \(0.519222\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −159.716 | −0.0678247 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 554.332 | 0.231468 | 0.115734 | − | 0.993280i | \(-0.463078\pi\) | ||||
0.115734 | + | 0.993280i | \(0.463078\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −685.436 | −0.281481 | −0.140741 | − | 0.990047i | \(-0.544948\pi\) | ||||
−0.140741 | + | 0.990047i | \(0.544948\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −324.363 | −0.131025 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 38.7956 | 0.0154179 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −7101.18 | −2.77695 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 4898.87 | 1.85586 | 0.927932 | − | 0.372750i | \(-0.121585\pi\) | ||||
0.927932 | + | 0.372750i | \(0.121585\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 3140.26 | 1.17120 | 0.585598 | − | 0.810601i | \(-0.300860\pi\) | ||||
0.585598 | + | 0.810601i | \(0.300860\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −19.3793 | −0.00711684 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −227.412 | −0.0822460 | −0.0411230 | − | 0.999154i | \(-0.513094\pi\) | ||||
−0.0411230 | + | 0.999154i | \(0.513094\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −1214.50 | −0.432631 | −0.216316 | − | 0.976323i | \(-0.569404\pi\) | ||||
−0.216316 | + | 0.976323i | \(0.569404\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 2526.02 | 0.886427 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 38.0691 | 0.0129700 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 1615.39 | 0.542401 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 4942.11 | 1.63566 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 5116.07 | 1.66922 | 0.834608 | − | 0.550844i | \(-0.185694\pi\) | ||||
0.834608 | + | 0.550844i | \(0.185694\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −723.333 | −0.232685 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −18.5560 | −0.00588608 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −620.950 | −0.191598 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 6605.27 | 2.01049 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 119.384 | 0.0358499 | 0.0179250 | − | 0.999839i | \(-0.494294\pi\) | ||||
0.0179250 | + | 0.999839i | \(0.494294\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −1124.85 | −0.333289 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 1992.00 | 0.582439 | 0.291220 | − | 0.956656i | \(-0.405939\pi\) | ||||
0.291220 | + | 0.956656i | \(0.405939\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 703.476 | 0.203000 | 0.101500 | − | 0.994836i | \(-0.467636\pi\) | ||||
0.101500 | + | 0.994836i | \(0.467636\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 961.783 | 0.270423 | 0.135211 | − | 0.990817i | \(-0.456829\pi\) | ||||
0.135211 | + | 0.990817i | \(0.456829\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −46.3038 | −0.0128533 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 1679.89 | 0.460423 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −4464.71 | −1.20836 | −0.604179 | − | 0.796848i | \(-0.706499\pi\) | ||||
−0.604179 | + | 0.796848i | \(0.706499\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −435.311 | −0.116352 | −0.0581761 | − | 0.998306i | \(-0.518528\pi\) | ||||
−0.0581761 | + | 0.998306i | \(0.518528\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 243.000 | 0.0641500 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −4596.98 | −1.18421 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 2959.95 | 0.753331 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 863.003 | 0.217021 | 0.108510 | − | 0.994095i | \(-0.465392\pi\) | ||||
0.108510 | + | 0.994095i | \(0.465392\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 9693.49 | 2.40879 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −50.7243 | −0.0124568 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −536.693 | −0.130264 | −0.0651322 | − | 0.997877i | \(-0.520747\pi\) | ||||
−0.0651322 | + | 0.997877i | \(0.520747\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −629.065 | −0.149188 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 371.908 | 0.0871971 | 0.0435986 | − | 0.999049i | \(-0.486118\pi\) | ||||
0.0435986 | + | 0.999049i | \(0.486118\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0.235982 | 5.47029e−5 0 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −1330.10 | −0.304871 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −4505.61 | −1.02123 | −0.510616 | − | 0.859809i | \(-0.670583\pi\) | ||||
−0.510616 | + | 0.859809i | \(0.670583\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −396.115 | −0.0887908 | −0.0443954 | − | 0.999014i | \(-0.514136\pi\) | ||||
−0.0443954 | + | 0.999014i | \(0.514136\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −6749.93 | −1.48013 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −6508.74 | −1.41181 | −0.705907 | − | 0.708305i | \(-0.749460\pi\) | ||||
−0.705907 | + | 0.708305i | \(0.749460\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 2941.62 | 0.631220 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 2785.80 | 0.591413 | 0.295707 | − | 0.955279i | \(-0.404445\pi\) | ||||
0.295707 | + | 0.955279i | \(0.404445\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 0.611846 | 0.000128518 0 | 6.42588e−5 | − | 1.00000i | \(-0.499980\pi\) | ||||
6.42588e−5 | 1.00000i | \(0.499980\pi\) | ||||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 35.3019 | 0.00733720 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 12375.9 | 2.51901 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −2222.44 | −0.447704 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −4145.98 | −0.826657 | −0.413329 | − | 0.910582i | \(-0.635634\pi\) | ||||
−0.413329 | + | 0.910582i | \(0.635634\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −6.84601 | −0.00135115 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 1458.18 | 0.284889 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −9016.55 | −1.74395 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 2231.33 | 0.423058 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −13.9034 | −0.00261019 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 1960.53 | 0.364473 | 0.182236 | − | 0.983255i | \(-0.441666\pi\) | ||||
0.182236 | + | 0.983255i | \(0.441666\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 313.952 | 0.0577996 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 5207.57 | 0.949499 | 0.474749 | − | 0.880121i | \(-0.342539\pi\) | ||||
0.474749 | + | 0.880121i | \(0.342539\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −3991.71 | −0.720846 | −0.360423 | − | 0.932789i | \(-0.617368\pi\) | ||||
−0.360423 | + | 0.932789i | \(0.617368\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 1805.04 | 0.319814 | 0.159907 | − | 0.987132i | \(-0.448881\pi\) | ||||
0.159907 | + | 0.987132i | \(0.448881\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −3774.85 | −0.662543 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 1541.10 | 0.267962 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −12032.3 | −2.07274 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 6278.55 | 1.07160 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 2925.11 | 0.494676 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 6906.18 | 1.14682 | 0.573411 | − | 0.819268i | \(-0.305620\pi\) | ||||
0.573411 | + | 0.819268i | \(0.305620\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 2715.28 | 0.446836 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 108.275 | 0.0176587 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −6081.36 | −0.983006 | −0.491503 | − | 0.870876i | \(-0.663552\pi\) | ||||
−0.491503 | + | 0.870876i | \(0.663552\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 5778.21 | 0.925750 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 17651.9 | 2.80323 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 0 | 0 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 69.2414 | 0.0108053 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −7787.02 | −1.20469 | −0.602347 | − | 0.798234i | \(-0.705768\pi\) | ||||
−0.602347 | + | 0.798234i | \(0.705768\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −1928.25 | −0.295751 | −0.147875 | − | 0.989006i | \(-0.547243\pi\) | ||||
−0.147875 | + | 0.989006i | \(0.547243\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −1356.35 | −0.206258 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −3404.27 | −0.513289 | −0.256645 | − | 0.966506i | \(-0.582617\pi\) | ||||
−0.256645 | + | 0.966506i | \(0.582617\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −31.0047 | −0.00463538 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 4417.05 | 0.649368 | 0.324684 | − | 0.945823i | \(-0.394742\pi\) | ||||
0.324684 | + | 0.945823i | \(0.394742\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 1514.97 | 0.220873 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 4757.13 | 0.687837 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −26.6162 | −0.00381687 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −5076.65 | −0.722068 | −0.361034 | − | 0.932553i | \(-0.617576\pi\) | ||||
−0.361034 | + | 0.932553i | \(0.617576\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 2664.43 | 0.375893 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −6876.64 | −0.954582 | −0.477291 | − | 0.878745i | \(-0.658381\pi\) | ||||
−0.477291 | + | 0.878745i | \(0.658381\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −96.4370 | −0.0132800 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 3511.23 | 0.479676 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −9285.61 | −1.25850 | −0.629248 | − | 0.777205i | \(-0.716637\pi\) | ||||
−0.629248 | + | 0.777205i | \(0.716637\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −3377.85 | −0.454207 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −7681.65 | −1.02484 | −0.512420 | − | 0.858735i | \(-0.671251\pi\) | ||||
−0.512420 | + | 0.858735i | \(0.671251\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −1298.72 | −0.170588 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 8627.72 | 1.12453 | 0.562266 | − | 0.826956i | \(-0.309930\pi\) | ||||
0.562266 | + | 0.826956i | \(0.309930\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −23600.3 | −3.05247 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 4479.73 | 0.574993 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 72.0062 | 0.00917221 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 5735.61 | 0.725094 | 0.362547 | − | 0.931966i | \(-0.381907\pi\) | ||||
0.362547 | + | 0.931966i | \(0.381907\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −7217.79 | −0.898850 | −0.449425 | − | 0.893318i | \(-0.648371\pi\) | ||||
−0.449425 | + | 0.893318i | \(0.648371\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −16419.2 | −2.02952 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 10.4159 | 0.00127795 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 16293.7 | 1.98439 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −10802.9 | −1.30604 | −0.653019 | − | 0.757341i | \(-0.726498\pi\) | ||||
−0.653019 | + | 0.757341i | \(0.726498\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 4382.32 | 0.525946 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 126.875 | 0.0150073 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 6677.55 | 0.784175 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 13257.1 | 1.54571 | 0.772856 | − | 0.634582i | \(-0.218828\pi\) | ||||
0.772856 | + | 0.634582i | \(0.218828\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −6252.11 | −0.723774 | −0.361887 | − | 0.932222i | \(-0.617867\pi\) | ||||
−0.361887 | + | 0.932222i | \(0.617867\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −3240.77 | −0.372510 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 16433.7 | 1.87565 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −8139.07 | −0.915986 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 4949.08 | 0.553106 | 0.276553 | − | 0.960999i | \(-0.410808\pi\) | ||||
0.276553 | + | 0.960999i | \(0.410808\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −16602.8 | −1.84267 | −0.921337 | − | 0.388764i | \(-0.872902\pi\) | ||||
−0.921337 | + | 0.388764i | \(0.872902\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −26.9641 | −0.00297202 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 16424.8 | 1.79795 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −4708.38 | −0.511887 | −0.255944 | − | 0.966692i | \(-0.582386\pi\) | ||||
−0.255944 | + | 0.966692i | \(0.582386\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −1700.44 | −0.182370 | −0.0911852 | − | 0.995834i | \(-0.529066\pi\) | ||||
−0.0911852 | + | 0.995834i | \(0.529066\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −57.0129 | −0.00607342 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 1184.04 | 0.125287 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 10050.2 | 1.05635 | 0.528173 | − | 0.849137i | \(-0.322877\pi\) | ||||
0.528173 | + | 0.849137i | \(0.322877\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 15988.5 | 1.66933 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −9372.60 | −0.972104 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −10991.9 | −1.12512 | −0.562560 | − | 0.826757i | \(-0.690183\pi\) | ||||
−0.562560 | + | 0.826757i | \(0.690183\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −3550.16 | −0.361018 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −548.440 | −0.0554086 | −0.0277043 | − | 0.999616i | \(-0.508820\pi\) | ||||
−0.0277043 | + | 0.999616i | \(0.508820\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 4028.04 | 0.404317 | 0.202159 | − | 0.979353i | \(-0.435204\pi\) | ||||
0.202159 | + | 0.979353i | \(0.435204\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 126.089 | 0.0125747 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 2070.69 | 0.205182 | 0.102591 | − | 0.994724i | \(-0.467287\pi\) | ||||
0.102591 | + | 0.994724i | \(0.467287\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −10802.1 | −1.05676 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −7793.26 | −0.757579 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −11437.2 | −1.10479 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 16.5162 | 0.00158538 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −178.785 | −0.0170541 | −0.00852704 | − | 0.999964i | \(-0.502714\pi\) | ||||
−0.00852704 | + | 0.999964i | \(0.502714\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −15155.8 | −1.43668 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −95.2622 | −0.00891883 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −16597.0 | −1.54431 | −0.772156 | − | 0.635433i | \(-0.780822\pi\) | ||||
−0.772156 | + | 0.635433i | \(0.780822\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 5922.07 | 0.547659 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −4547.22 | −0.417949 | −0.208975 | − | 0.977921i | \(-0.567013\pi\) | ||||
−0.208975 | + | 0.977921i | \(0.567013\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 9190.45 | 0.839588 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 62.5029 | 0.00567535 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 1025.97 | 0.0920414 | 0.0460207 | − | 0.998940i | \(-0.485346\pi\) | ||||
0.0460207 | + | 0.998940i | \(0.485346\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 3201.26 | 0.285473 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 6745.26 | 0.597925 | 0.298962 | − | 0.954265i | \(-0.403359\pi\) | ||||
0.298962 | + | 0.954265i | \(0.403359\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 95.6431 | 0.00842785 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 979.676 | 0.0858164 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −6001.02 | −0.522575 | −0.261287 | − | 0.965261i | \(-0.584147\pi\) | ||||
−0.261287 | + | 0.965261i | \(0.584147\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 2470.75 | 0.212644 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 13.4571 | 0.00115144 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −19447.0 | −1.65431 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −823.964 | −0.0696879 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 4695.21 | 0.394820 | 0.197410 | − | 0.980321i | \(-0.436747\pi\) | ||||
0.197410 | + | 0.980321i | \(0.436747\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 771.767 | 0.0645258 | 0.0322629 | − | 0.999479i | \(-0.489729\pi\) | ||||
0.0322629 | + | 0.999479i | \(0.489729\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −42976.2 | −3.55232 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 20048.7 | 1.64779 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −479.147 | −0.0391586 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −14872.0 | −1.20859 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 66.0573 | 0.00533814 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 1663.00 | 0.133638 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 3385.66 | 0.269059 | 0.134529 | − | 0.990910i | \(-0.457048\pi\) | ||||
0.134529 | + | 0.990910i | \(0.457048\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −2056.31 | −0.162513 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 125.381 | 0.00985457 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 4988.75 | 0.389952 | 0.194976 | − | 0.980808i | \(-0.437537\pi\) | ||||
0.194976 | + | 0.980808i | \(0.437537\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −973.090 | −0.0756475 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −6396.15 | −0.494529 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 116.387 | 0.00890153 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −20207.3 | −1.53718 | −0.768591 | − | 0.639740i | \(-0.779042\pi\) | ||||
−0.768591 | + | 0.639740i | \(0.779042\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 7249.02 | 0.548481 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −21303.5 | −1.60327 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −11690.4 | −0.875118 | −0.437559 | − | 0.899190i | \(-0.644157\pi\) | ||||
−0.437559 | + | 0.899190i | \(0.644157\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 247.675 | 0.0184421 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −17928.9 | −1.32095 | −0.660473 | − | 0.750849i | \(-0.729644\pi\) | ||||
−0.660473 | + | 0.750849i | \(0.729644\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −15673.7 | −1.14873 | −0.574364 | − | 0.818600i | \(-0.694751\pi\) | ||||
−0.574364 | + | 0.818600i | \(0.694751\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 14696.6 | 1.07148 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −22432.9 | −1.62699 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −13653.0 | −0.985064 | −0.492532 | − | 0.870294i | \(-0.663929\pi\) | ||||
−0.492532 | + | 0.870294i | \(0.663929\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 9420.78 | 0.676191 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 99.1093 | 0.00704063 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −58.1380 | −0.00410891 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −18021.5 | −1.26717 | −0.633583 | − | 0.773675i | \(-0.718417\pi\) | ||||
−0.633583 | + | 0.773675i | \(0.718417\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 29909.6 | 2.09236 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −682.237 | −0.0474847 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 21137.3 | 1.46375 | 0.731877 | − | 0.681437i | \(-0.238645\pi\) | ||||
0.731877 | + | 0.681437i | \(0.238645\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −3643.50 | −0.249780 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 9369.59 | 0.639117 | 0.319559 | − | 0.947567i | \(-0.396465\pi\) | ||||
0.319559 | + | 0.947567i | \(0.396465\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −22750.0 | −1.54408 | −0.772040 | − | 0.635573i | \(-0.780764\pi\) | ||||
−0.772040 | + | 0.635573i | \(0.780764\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 7578.06 | 0.511779 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 203.908 | 0.0137026 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −5973.65 | −0.399445 | −0.199722 | − | 0.979853i | \(-0.564004\pi\) | ||||
−0.199722 | + | 0.979853i | \(0.564004\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 18088.9 | 1.19771 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −23347.4 | −1.53832 | −0.769162 | − | 0.639054i | \(-0.779326\pi\) | ||||
−0.769162 | + | 0.639054i | \(0.779326\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 114.207 | 0.00748826 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 28199.1 | 1.83996 | 0.919979 | − | 0.391968i | \(-0.128206\pi\) | ||||
0.919979 | + | 0.391968i | \(0.128206\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −2975.56 | −0.193211 | −0.0966057 | − | 0.995323i | \(-0.530799\pi\) | ||||
−0.0966057 | + | 0.995323i | \(0.530799\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 4846.16 | 0.313155 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 15618.8 | 0.999603 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 14826.3 | 0.944348 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −39669.4 | −2.51466 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −2631.33 | −0.166009 | −0.0830044 | − | 0.996549i | \(-0.526452\pi\) | ||||
−0.0830044 | + | 0.996549i | \(0.526452\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 15348.2 | 0.963723 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −144.787 | −0.00904837 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −2170.00 | −0.134341 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 14494.2 | 0.893117 | 0.446559 | − | 0.894754i | \(-0.352649\pi\) | ||||
0.446559 | + | 0.894754i | \(0.352649\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −15176.0 | −0.930767 | −0.465383 | − | 0.885109i | \(-0.654084\pi\) | ||||
−0.465383 | + | 0.885109i | \(0.654084\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −55.6679 | −0.00339833 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −7569.18 | −0.459931 | −0.229965 | − | 0.973199i | \(-0.573861\pi\) | ||||
−0.229965 | + | 0.973199i | \(0.573861\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −2875.23 | −0.173903 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −13933.5 | −0.835007 | −0.417504 | − | 0.908675i | \(-0.637095\pi\) | ||||
−0.417504 | + | 0.908675i | \(0.637095\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 192.018 | 0.0114546 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −1862.85 | −0.110619 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −17015.5 | −1.00581 | −0.502904 | − | 0.864342i | \(-0.667735\pi\) | ||||
−0.502904 | + | 0.864342i | \(0.667735\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −16535.4 | −0.972999 | −0.486500 | − | 0.873681i | \(-0.661726\pi\) | ||||
−0.486500 | + | 0.873681i | \(0.661726\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 19815.8 | 1.16076 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −12545.5 | −0.728279 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 358.152 | 0.0206980 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −5839.25 | −0.335949 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 4571.05 | 0.261814 | 0.130907 | − | 0.991395i | \(-0.458211\pi\) | ||||
0.130907 | + | 0.991395i | \(0.458211\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −3374.55 | −0.192425 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 26284.5 | 1.49217 | 0.746083 | − | 0.665853i | \(-0.231932\pi\) | ||||
0.746083 | + | 0.665853i | \(0.231932\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 5976.00 | 0.336271 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 6797.22 | 0.380803 | 0.190402 | − | 0.981706i | \(-0.439021\pi\) | ||||
0.190402 | + | 0.981706i | \(0.439021\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 187.842 | 0.0104775 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 2110.43 | 0.117202 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −92.1880 | −0.00509737 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 27758.7 | 1.52821 | 0.764103 | − | 0.645094i | \(-0.223182\pi\) | ||||
0.764103 | + | 0.645094i | \(0.223182\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 286.225 | 0.0156218 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −38926.5 | −2.11542 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 2885.35 | 0.156129 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −21638.3 | −1.16586 | −0.582929 | − | 0.812523i | \(-0.698093\pi\) | ||||
−0.582929 | + | 0.812523i | \(0.698093\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 27608.2 | 1.48117 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −138.911 | −0.00742086 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −16288.7 | −0.862815 | −0.431408 | − | 0.902157i | \(-0.641983\pi\) | ||||
−0.431408 | + | 0.902157i | \(0.641983\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 5039.66 | 0.265826 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 58664.8 | 3.08137 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −348.871 | −0.0182476 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −13394.1 | −0.697646 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −3391.74 | −0.175926 | −0.0879628 | − | 0.996124i | \(-0.528036\pi\) | ||||
−0.0879628 | + | 0.996124i | \(0.528036\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −1305.93 | −0.0671760 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 8735.86 | 0.447506 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 23158.7 | 1.18144 | 0.590722 | − | 0.806875i | \(-0.298843\pi\) | ||||
0.590722 | + | 0.806875i | \(0.298843\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 729.000 | 0.0370370 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 18973.9 | 0.960020 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −27629.2 | −1.39223 | −0.696116 | − | 0.717929i | \(-0.745090\pi\) | ||||
−0.696116 | + | 0.717929i | \(0.745090\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 45473.9 | 2.27280 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −9461.65 | −0.470978 | −0.235489 | − | 0.971877i | \(-0.575669\pi\) | ||||
−0.235489 | + | 0.971877i | \(0.575669\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −13790.9 | −0.683701 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −14316.9 | −0.706913 | −0.353457 | − | 0.935451i | \(-0.614994\pi\) | ||||
−0.353457 | + | 0.935451i | \(0.614994\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 50.7524 | 0.00249587 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 8879.86 | 0.434936 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −7486.07 | −0.363742 | −0.181871 | − | 0.983322i | \(-0.558215\pi\) | ||||
−0.181871 | + | 0.983322i | \(0.558215\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 2589.01 | 0.125297 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −401.744 | −0.0193655 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −17416.8 | −0.836227 | −0.418114 | − | 0.908395i | \(-0.637309\pi\) | ||||
−0.418114 | + | 0.908395i | \(0.637309\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 29080.5 | 1.39072 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −33231.0 | −1.58295 | −0.791474 | − | 0.611203i | \(-0.790686\pi\) | ||||
−0.791474 | + | 0.611203i | \(0.790686\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −152.173 | −0.00719192 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 2674.44 | 0.125904 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 13714.2 | 0.643103 | 0.321552 | − | 0.946892i | \(-0.395796\pi\) | ||||
0.321552 | + | 0.946892i | \(0.395796\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −1610.08 | −0.0752082 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 15209.3 | 0.707685 | 0.353842 | − | 0.935305i | \(-0.384875\pi\) | ||||
0.353842 | + | 0.935305i | \(0.384875\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −40850.5 | −1.89341 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 27091.1 | 1.24601 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −13021.6 | −0.596605 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −1887.20 | −0.0861339 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −463.019 | −0.0210520 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −13221.5 | −0.598850 | −0.299425 | − | 0.954120i | \(-0.596795\pi\) | ||||
−0.299425 | + | 0.954120i | \(0.596795\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 1115.72 | 0.0503433 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 5431.47 | 0.243224 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0.707946 | 3.15827e−5 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 13373.9 | 0.594387 | 0.297194 | − | 0.954817i | \(-0.403949\pi\) | ||||
0.297194 | + | 0.954817i | \(0.403949\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 47346.6 | 2.09637 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −3990.29 | −0.176018 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −11178.5 | −0.491257 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −13516.8 | −0.589609 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −11229.3 | −0.488011 | −0.244005 | − | 0.969774i | \(-0.578461\pi\) | ||||
−0.244005 | + | 0.969774i | \(0.578461\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −4301.42 | −0.186243 | −0.0931215 | − | 0.995655i | \(-0.529685\pi\) | ||||
−0.0931215 | + | 0.995655i | \(0.529685\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −1188.35 | −0.0512634 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 253.842 | 0.0109101 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −13205.0 | −0.565464 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −40910.6 | −1.73909 | −0.869543 | − | 0.493857i | \(-0.835587\pi\) | ||||
−0.869543 | + | 0.493857i | \(0.835587\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 28043.2 | 1.18776 | 0.593879 | − | 0.804554i | \(-0.297596\pi\) | ||||
0.593879 | + | 0.804554i | \(0.297596\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −20249.8 | −0.854554 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 17598.9 | 0.739993 | 0.369996 | − | 0.929033i | \(-0.379359\pi\) | ||||
0.369996 | + | 0.929033i | \(0.379359\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −14565.5 | −0.610231 | −0.305116 | − | 0.952315i | \(-0.598695\pi\) | ||||
−0.305116 | + | 0.952315i | \(0.598695\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −19526.2 | −0.815111 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 137.218 | 0.00568697 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 8824.86 | 0.364435 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 711.056 | 0.0292591 | 0.0146295 | − | 0.999893i | \(-0.495343\pi\) | ||||
0.0146295 | + | 0.999893i | \(0.495343\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −19503.5 | −0.799686 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 8357.41 | 0.341453 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 41.9925 | 0.00170957 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 1.83554 | 7.41996e−5 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 54150.9 | 2.18128 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −7459.48 | −0.299423 | −0.149712 | − | 0.988730i | \(-0.547834\pi\) | ||||
−0.149712 | + | 0.988730i | \(0.547834\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 105.906 | 0.00423614 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 3560.92 | 0.141936 | 0.0709678 | − | 0.997479i | \(-0.477391\pi\) | ||||
0.0709678 | + | 0.997479i | \(0.477391\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 13519.1 | 0.536981 | 0.268491 | − | 0.963282i | \(-0.413475\pi\) | ||||
0.268491 | + | 0.963282i | \(0.413475\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 20395.9 | 0.804502 | 0.402251 | − | 0.915530i | \(-0.368228\pi\) | ||||
0.402251 | + | 0.915530i | \(0.368228\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −35.3182 | −0.00138827 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 37127.7 | 1.45435 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 30241.6 | 1.18053 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −42298.3 | −1.64549 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −6667.33 | −0.258482 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 7197.26 | 0.277120 | 0.138560 | − | 0.990354i | \(-0.455753\pi\) | ||||
0.138560 | + | 0.990354i | \(0.455753\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −12437.9 | −0.477271 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 11588.3 | 0.443156 | 0.221578 | − | 0.975143i | \(-0.428879\pi\) | ||||
0.221578 | + | 0.975143i | \(0.428879\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 21959.0 | 0.836898 | 0.418449 | − | 0.908240i | \(-0.362574\pi\) | ||||
0.418449 | + | 0.908240i | \(0.362574\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −20.5380 | −0.000780088 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 12518.9 | 0.473894 | 0.236947 | − | 0.971523i | \(-0.423853\pi\) | ||||
0.236947 | + | 0.971523i | \(0.423853\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 4374.53 | 0.164481 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −32951.2 | −1.23479 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 71.2822 | 0.00266224 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −27049.6 | −1.00687 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −22845.3 | −0.847535 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −241.297 | −0.00892204 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −88.1410 | −0.00323747 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 28270.0 | 1.03494 | 0.517470 | − | 0.855701i | \(-0.326874\pi\) | ||||
0.517470 | + | 0.855701i | \(0.326874\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 6693.99 | 0.244253 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −7908.58 | −0.287621 | −0.143811 | − | 0.989605i | \(-0.545936\pi\) | ||||
−0.143811 | + | 0.989605i | \(0.545936\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 53285.7 | 1.93154 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −41.7102 | −0.00150699 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 31450.6 | 1.12890 | 0.564451 | − | 0.825467i | \(-0.309088\pi\) | ||||
0.564451 | + | 0.825467i | \(0.309088\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 5881.58 | 0.210428 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 12112.2 | 0.431938 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −37707.2 | −1.34033 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 941.855 | 0.0333706 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −3469.19 | −0.122519 | −0.0612596 | − | 0.998122i | \(-0.519512\pi\) | ||||
−0.0612596 | + | 0.998122i | \(0.519512\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 15622.7 | 0.548193 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −913.148 | −0.0319392 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 50935.7 | 1.77588 | 0.887939 | − | 0.459962i | \(-0.152137\pi\) | ||||
0.887939 | + | 0.459962i | \(0.152137\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −11975.1 | −0.416181 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 47894.9 | 1.65922 | 0.829612 | − | 0.558341i | \(-0.188562\pi\) | ||||
0.829612 | + | 0.558341i | \(0.188562\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 53136.7 | 1.83496 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 10538.9 | 0.361634 | 0.180817 | − | 0.983517i | \(-0.442126\pi\) | ||||
0.180817 | + | 0.983517i | \(0.442126\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 10397.8 | 0.355667 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 5415.11 | 0.184645 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 31123.5 | 1.05791 | 0.528955 | − | 0.848650i | \(-0.322584\pi\) | ||||
0.528955 | + | 0.848650i | \(0.322584\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 629.951 | 0.0213453 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −11324.6 | −0.382519 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 77037.9 | 2.58594 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 4623.30 | 0.154708 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 403.810 | 0.0134706 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −1626.14 | −0.0540776 | −0.0270388 | − | 0.999634i | \(-0.508608\pi\) | ||||
−0.0270388 | + | 0.999634i | \(0.508608\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −36096.9 | −1.19670 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 35500.1 | 1.17328 | 0.586638 | − | 0.809849i | \(-0.300451\pi\) | ||||
0.586638 | + | 0.809849i | \(0.300451\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 0 | 0 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 18835.6 | 0.618691 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 26570.2 | 0.870068 | 0.435034 | − | 0.900414i | \(-0.356736\pi\) | ||||
0.435034 | + | 0.900414i | \(0.356736\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −23944.7 | −0.781691 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 8775.34 | 0.285602 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −53851.6 | −1.74730 | −0.873652 | − | 0.486552i | \(-0.838254\pi\) | ||||
−0.873652 | + | 0.486552i | \(0.838254\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −29.2432 | −0.000945955 0 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −25900.4 | −0.832745 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 2829.75 | 0.0907063 | 0.0453531 | − | 0.998971i | \(-0.485559\pi\) | ||||
0.0453531 | + | 0.998971i | \(0.485559\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 20718.6 | 0.662118 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −156.174 | −0.00497593 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 12904.3 | 0.409912 | 0.204956 | − | 0.978771i | \(-0.434295\pi\) | ||||
0.204956 | + | 0.978771i | \(0.434295\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 8145.83 | 0.257981 |
(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 | 1176.4.a.bd.1.2 | 4 | ||
4.3 | odd | 2 | 2352.4.a.cm.1.2 | 4 | |||
7.2 | even | 3 | 168.4.q.f.25.3 | ✓ | 8 | ||
7.4 | even | 3 | 168.4.q.f.121.3 | yes | 8 | ||
7.6 | odd | 2 | 1176.4.a.ba.1.3 | 4 | |||
21.2 | odd | 6 | 504.4.s.j.361.2 | 8 | |||
21.11 | odd | 6 | 504.4.s.j.289.2 | 8 | |||
28.11 | odd | 6 | 336.4.q.m.289.3 | 8 | |||
28.23 | odd | 6 | 336.4.q.m.193.3 | 8 | |||
28.27 | even | 2 | 2352.4.a.cp.1.3 | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
168.4.q.f.25.3 | ✓ | 8 | 7.2 | even | 3 | ||
168.4.q.f.121.3 | yes | 8 | 7.4 | even | 3 | ||
336.4.q.m.193.3 | 8 | 28.23 | odd | 6 | |||
336.4.q.m.289.3 | 8 | 28.11 | odd | 6 | |||
504.4.s.j.289.2 | 8 | 21.11 | odd | 6 | |||
504.4.s.j.361.2 | 8 | 21.2 | odd | 6 | |||
1176.4.a.ba.1.3 | 4 | 7.6 | odd | 2 | |||
1176.4.a.bd.1.2 | 4 | 1.1 | even | 1 | trivial | ||
2352.4.a.cm.1.2 | 4 | 4.3 | odd | 2 | |||
2352.4.a.cp.1.3 | 4 | 28.27 | even | 2 |