Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [3150,3,Mod(449,3150)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(3150, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1, 1, 0]))
N = Newforms(chi, 3, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("3150.449");
S:= CuspForms(chi, 3);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 3150 = 2 \cdot 3^{2} \cdot 5^{2} \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 3 \) |
Character orbit: | \([\chi]\) | \(=\) | 3150.c (of order \(2\), degree \(1\), not minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(85.8312832735\) |
Analytic rank: | \(0\) |
Dimension: | \(16\) |
Coefficient field: | 16.0.9671731157401600000000.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{16} + 7x^{12} + 753x^{8} + 112x^{4} + 256 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{13}]\) |
Coefficient ring index: | \( 2^{28}\cdot 3^{4} \) |
Twist minimal: | no (minimal twist has level 630) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 449.10 | ||
Root | \(0.941471 - 2.08559i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 3150.449 |
Dual form | 3150.3.c.d.449.15 |
$q$-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 \(\left(\mathbb{Z}/3150\mathbb{Z}\right)^\times\).
\(n\) | \(127\) | \(451\) | \(2801\) |
\(\chi(n)\) | \(-1\) | \(1\) | \(-1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 1.41421 | 0.707107 | ||||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 2.00000 | 0.500000 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | − 2.64575i | − 0.377964i | ||||||||
\(8\) | 2.82843 | 0.353553 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 2.32744i | 0.211586i | 0.994388 | + | 0.105793i | \(0.0337381\pi\) | ||||
−0.994388 | + | 0.105793i | \(0.966262\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 10.6912i | 0.822397i | 0.911546 | + | 0.411198i | \(0.134890\pi\) | ||||
−0.911546 | + | 0.411198i | \(0.865110\pi\) | |||||||
\(14\) | − 3.74166i | − 0.267261i | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 4.00000 | 0.250000 | ||||||||
\(17\) | 2.70514 | 0.159126 | 0.0795628 | − | 0.996830i | \(-0.474648\pi\) | ||||
0.0795628 | + | 0.996830i | \(0.474648\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −11.0962 | −0.584009 | −0.292005 | − | 0.956417i | \(-0.594322\pi\) | ||||
−0.292005 | + | 0.956417i | \(0.594322\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 3.29150i | 0.149614i | ||||||||
\(23\) | −34.7065 | −1.50898 | −0.754490 | − | 0.656312i | \(-0.772116\pi\) | ||||
−0.754490 | + | 0.656312i | \(0.772116\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 15.1196i | 0.581522i | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | − 5.29150i | − 0.188982i | ||||||||
\(29\) | − 5.82252i | − 0.200777i | −0.994948 | − | 0.100388i | \(-0.967992\pi\) | ||||
0.994948 | − | 0.100388i | \(-0.0320085\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −15.2705 | −0.492598 | −0.246299 | − | 0.969194i | \(-0.579214\pi\) | ||||
−0.246299 | + | 0.969194i | \(0.579214\pi\) | |||||||
\(32\) | 5.65685 | 0.176777 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 3.82564 | 0.112519 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 0.900842i | 0.0243471i | 0.999926 | + | 0.0121735i | \(0.00387505\pi\) | ||||
−0.999926 | + | 0.0121735i | \(0.996125\pi\) | |||||||
\(38\) | −15.6924 | −0.412957 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 31.6661i | 0.772344i | 0.922427 | + | 0.386172i | \(0.126203\pi\) | ||||
−0.922427 | + | 0.386172i | \(0.873797\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 13.0752i | 0.304074i | 0.988375 | + | 0.152037i | \(0.0485834\pi\) | ||||
−0.988375 | + | 0.152037i | \(0.951417\pi\) | |||||||
\(44\) | 4.65489i | 0.105793i | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −49.0825 | −1.06701 | ||||||||
\(47\) | 17.1532 | 0.364961 | 0.182480 | − | 0.983209i | \(-0.441587\pi\) | ||||
0.182480 | + | 0.983209i | \(0.441587\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −7.00000 | −0.142857 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 21.3823i | 0.411198i | ||||||||
\(53\) | −68.1864 | −1.28654 | −0.643268 | − | 0.765641i | \(-0.722422\pi\) | ||||
−0.643268 | + | 0.765641i | \(0.722422\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | − 7.48331i | − 0.133631i | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | − 8.23429i | − 0.141970i | ||||||||
\(59\) | − 34.3712i | − 0.582563i | −0.956637 | − | 0.291282i | \(-0.905918\pi\) | ||||
0.956637 | − | 0.291282i | \(-0.0940816\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −81.5400 | −1.33672 | −0.668360 | − | 0.743838i | \(-0.733004\pi\) | ||||
−0.668360 | + | 0.743838i | \(0.733004\pi\) | |||||||
\(62\) | −21.5958 | −0.348319 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 8.00000 | 0.125000 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 46.2125i | 0.689739i | 0.938651 | + | 0.344869i | \(0.112077\pi\) | ||||
−0.938651 | + | 0.344869i | \(0.887923\pi\) | |||||||
\(68\) | 5.41027 | 0.0795628 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 61.3258i | 0.863744i | 0.901935 | + | 0.431872i | \(0.142147\pi\) | ||||
−0.901935 | + | 0.431872i | \(0.857853\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | − 20.5408i | − 0.281380i | −0.990054 | − | 0.140690i | \(-0.955068\pi\) | ||||
0.990054 | − | 0.140690i | \(-0.0449321\pi\) | |||||||
\(74\) | 1.27398i | 0.0172160i | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −22.1923 | −0.292005 | ||||||||
\(77\) | 6.15784 | 0.0799719 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −78.0870 | −0.988443 | −0.494222 | − | 0.869336i | \(-0.664547\pi\) | ||||
−0.494222 | + | 0.869336i | \(0.664547\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 44.7826i | 0.546129i | ||||||||
\(83\) | 28.7135 | 0.345945 | 0.172973 | − | 0.984927i | \(-0.444663\pi\) | ||||
0.172973 | + | 0.984927i | \(0.444663\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 18.4911i | 0.215013i | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 6.58301i | 0.0748069i | ||||||||
\(89\) | − 136.885i | − 1.53804i | −0.639227 | − | 0.769019i | \(-0.720745\pi\) | ||||
0.639227 | − | 0.769019i | \(-0.279255\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 28.2861 | 0.310837 | ||||||||
\(92\) | −69.4131 | −0.754490 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 24.2582 | 0.258066 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | − 10.0195i | − 0.103294i | −0.998665 | − | 0.0516470i | \(-0.983553\pi\) | ||||
0.998665 | − | 0.0516470i | \(-0.0164471\pi\) | |||||||
\(98\) | −9.89949 | −0.101015 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | − 37.1254i | − 0.367578i | −0.982966 | − | 0.183789i | \(-0.941164\pi\) | ||||
0.982966 | − | 0.183789i | \(-0.0588364\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 107.296i | 1.04171i | 0.853645 | + | 0.520856i | \(0.174387\pi\) | ||||
−0.853645 | + | 0.520856i | \(0.825613\pi\) | |||||||
\(104\) | 30.2392i | 0.290761i | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −96.4301 | −0.909718 | ||||||||
\(107\) | −142.217 | −1.32913 | −0.664564 | − | 0.747232i | \(-0.731383\pi\) | ||||
−0.664564 | + | 0.747232i | \(0.731383\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 47.5626 | 0.436355 | 0.218177 | − | 0.975909i | \(-0.429989\pi\) | ||||
0.218177 | + | 0.975909i | \(0.429989\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | − 10.5830i | − 0.0944911i | ||||||||
\(113\) | 103.302 | 0.914173 | 0.457087 | − | 0.889422i | \(-0.348893\pi\) | ||||
0.457087 | + | 0.889422i | \(0.348893\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | − 11.6450i | − 0.100388i | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | − 48.6082i | − 0.411934i | ||||||||
\(119\) | − 7.15712i | − 0.0601438i | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 115.583 | 0.955231 | ||||||||
\(122\) | −115.315 | −0.945204 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | −30.5411 | −0.246299 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 104.802i | 0.825216i | 0.910909 | + | 0.412608i | \(0.135382\pi\) | ||||
−0.910909 | + | 0.412608i | \(0.864618\pi\) | |||||||
\(128\) | 11.3137 | 0.0883883 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 168.925i | 1.28951i | 0.764390 | + | 0.644754i | \(0.223040\pi\) | ||||
−0.764390 | + | 0.644754i | \(0.776960\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 29.3577i | 0.220735i | ||||||||
\(134\) | 65.3543i | 0.487719i | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 7.65128 | 0.0562594 | ||||||||
\(137\) | −110.555 | −0.806973 | −0.403486 | − | 0.914986i | \(-0.632202\pi\) | ||||
−0.403486 | + | 0.914986i | \(0.632202\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −223.453 | −1.60758 | −0.803788 | − | 0.594916i | \(-0.797185\pi\) | ||||
−0.803788 | + | 0.594916i | \(0.797185\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 86.7278i | 0.610759i | ||||||||
\(143\) | −24.8831 | −0.174007 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | − 29.0490i | − 0.198966i | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 1.80168i | 0.0121735i | ||||||||
\(149\) | 80.4313i | 0.539808i | 0.962887 | + | 0.269904i | \(0.0869919\pi\) | ||||
−0.962887 | + | 0.269904i | \(0.913008\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −138.258 | −0.915613 | −0.457807 | − | 0.889052i | \(-0.651365\pi\) | ||||
−0.457807 | + | 0.889052i | \(0.651365\pi\) | |||||||
\(152\) | −31.3847 | −0.206478 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 8.70850 | 0.0565487 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | − 1.50532i | − 0.00958802i | −0.999989 | − | 0.00479401i | \(-0.998474\pi\) | ||||
0.999989 | − | 0.00479401i | \(-0.00152599\pi\) | |||||||
\(158\) | −110.432 | −0.698935 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 91.8249i | 0.570341i | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 222.982i | 1.36799i | 0.729488 | + | 0.683993i | \(0.239758\pi\) | ||||
−0.729488 | + | 0.683993i | \(0.760242\pi\) | |||||||
\(164\) | 63.3322i | 0.386172i | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 40.6070 | 0.244620 | ||||||||
\(167\) | −120.483 | −0.721455 | −0.360728 | − | 0.932671i | \(-0.617472\pi\) | ||||
−0.360728 | + | 0.932671i | \(0.617472\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 54.6992 | 0.323664 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 26.1504i | 0.152037i | ||||||||
\(173\) | −100.276 | −0.579631 | −0.289816 | − | 0.957082i | \(-0.593594\pi\) | ||||
−0.289816 | + | 0.957082i | \(0.593594\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 9.30978i | 0.0528965i | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | − 193.585i | − 1.08756i | ||||||||
\(179\) | − 91.4566i | − 0.510931i | −0.966818 | − | 0.255465i | \(-0.917771\pi\) | ||||
0.966818 | − | 0.255465i | \(-0.0822287\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 130.398 | 0.720429 | 0.360214 | − | 0.932870i | \(-0.382704\pi\) | ||||
0.360214 | + | 0.932870i | \(0.382704\pi\) | |||||||
\(182\) | 40.0026 | 0.219795 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | −98.1649 | −0.533505 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 6.29605i | 0.0336687i | ||||||||
\(188\) | 34.3063 | 0.182480 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | − 118.977i | − 0.622916i | −0.950260 | − | 0.311458i | \(-0.899183\pi\) | ||||
0.950260 | − | 0.311458i | \(-0.100817\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 202.816i | 1.05086i | 0.850837 | + | 0.525430i | \(0.176096\pi\) | ||||
−0.850837 | + | 0.525430i | \(0.823904\pi\) | |||||||
\(194\) | − 14.1697i | − 0.0730399i | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −14.0000 | −0.0714286 | ||||||||
\(197\) | −295.867 | −1.50186 | −0.750932 | − | 0.660379i | \(-0.770396\pi\) | ||||
−0.750932 | + | 0.660379i | \(0.770396\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −303.023 | −1.52273 | −0.761365 | − | 0.648323i | \(-0.775471\pi\) | ||||
−0.761365 | + | 0.648323i | \(0.775471\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | − 52.5033i | − 0.259917i | ||||||||
\(203\) | −15.4049 | −0.0758864 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 151.740i | 0.736601i | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 42.7646i | 0.205599i | ||||||||
\(209\) | − 25.8257i | − 0.123568i | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 234.073 | 1.10935 | 0.554676 | − | 0.832067i | \(-0.312842\pi\) | ||||
0.554676 | + | 0.832067i | \(0.312842\pi\) | |||||||
\(212\) | −136.373 | −0.643268 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | −201.125 | −0.939835 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 40.4020i | 0.186184i | ||||||||
\(218\) | 67.2637 | 0.308549 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 28.9210i | 0.130864i | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 301.026i | 1.34989i | 0.737867 | + | 0.674946i | \(0.235833\pi\) | ||||
−0.737867 | + | 0.674946i | \(0.764167\pi\) | |||||||
\(224\) | − 14.9666i | − 0.0668153i | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 146.090 | 0.646418 | ||||||||
\(227\) | 97.7782 | 0.430741 | 0.215371 | − | 0.976532i | \(-0.430904\pi\) | ||||
0.215371 | + | 0.976532i | \(0.430904\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −71.7468 | −0.313305 | −0.156652 | − | 0.987654i | \(-0.550070\pi\) | ||||
−0.156652 | + | 0.987654i | \(0.550070\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | − 16.4686i | − 0.0709852i | ||||||||
\(233\) | 321.396 | 1.37938 | 0.689691 | − | 0.724104i | \(-0.257747\pi\) | ||||
0.689691 | + | 0.724104i | \(0.257747\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | − 68.7424i | − 0.291282i | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | − 10.1217i | − 0.0425281i | ||||||||
\(239\) | − 37.4949i | − 0.156882i | −0.996919 | − | 0.0784411i | \(-0.975006\pi\) | ||||
0.996919 | − | 0.0784411i | \(-0.0249943\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −153.379 | −0.636427 | −0.318213 | − | 0.948019i | \(-0.603083\pi\) | ||||
−0.318213 | + | 0.948019i | \(0.603083\pi\) | |||||||
\(242\) | 163.459 | 0.675451 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | −163.080 | −0.668360 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | − 118.631i | − 0.480287i | ||||||||
\(248\) | −43.1916 | −0.174160 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 121.515i | 0.484122i | 0.970261 | + | 0.242061i | \(0.0778234\pi\) | ||||
−0.970261 | + | 0.242061i | \(0.922177\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | − 80.7775i | − 0.319279i | ||||||||
\(254\) | 148.213i | 0.583516i | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 16.0000 | 0.0625000 | ||||||||
\(257\) | −387.420 | −1.50747 | −0.753736 | − | 0.657177i | \(-0.771750\pi\) | ||||
−0.753736 | + | 0.657177i | \(0.771750\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 2.38340 | 0.00920233 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 238.897i | 0.911819i | ||||||||
\(263\) | 229.701 | 0.873387 | 0.436694 | − | 0.899610i | \(-0.356149\pi\) | ||||
0.436694 | + | 0.899610i | \(0.356149\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 41.5181i | 0.156083i | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 92.4250i | 0.344869i | ||||||||
\(269\) | − 406.720i | − 1.51197i | −0.654588 | − | 0.755986i | \(-0.727158\pi\) | ||||
0.654588 | − | 0.755986i | \(-0.272842\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 139.965 | 0.516474 | 0.258237 | − | 0.966082i | \(-0.416858\pi\) | ||||
0.258237 | + | 0.966082i | \(0.416858\pi\) | |||||||
\(272\) | 10.8205 | 0.0397814 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −156.349 | −0.570616 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 476.481i | 1.72015i | 0.510170 | + | 0.860074i | \(0.329583\pi\) | ||||
−0.510170 | + | 0.860074i | \(0.670417\pi\) | |||||||
\(278\) | −316.010 | −1.13673 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | − 292.967i | − 1.04259i | −0.853377 | − | 0.521294i | \(-0.825450\pi\) | ||||
0.853377 | − | 0.521294i | \(-0.174550\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | − 157.100i | − 0.555124i | −0.960708 | − | 0.277562i | \(-0.910474\pi\) | ||||
0.960708 | − | 0.277562i | \(-0.0895264\pi\) | |||||||
\(284\) | 122.652i | 0.431872i | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −35.1900 | −0.123042 | ||||||||
\(287\) | 83.7806 | 0.291918 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −281.682 | −0.974679 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | − 41.0815i | − 0.140690i | ||||||||
\(293\) | 30.3825 | 0.103695 | 0.0518473 | − | 0.998655i | \(-0.483489\pi\) | ||||
0.0518473 | + | 0.998655i | \(0.483489\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 2.54797i | 0.00860799i | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 113.747i | 0.381702i | ||||||||
\(299\) | − 371.053i | − 1.24098i | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 34.5937 | 0.114929 | ||||||||
\(302\) | −195.526 | −0.647436 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | −44.3847 | −0.146002 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | − 348.067i | − 1.13377i | −0.823797 | − | 0.566885i | \(-0.808149\pi\) | ||||
0.823797 | − | 0.566885i | \(-0.191851\pi\) | |||||||
\(308\) | 12.3157 | 0.0399860 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 23.3072i | 0.0749427i | 0.999298 | + | 0.0374713i | \(0.0119303\pi\) | ||||
−0.999298 | + | 0.0374713i | \(0.988070\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | − 543.057i | − 1.73501i | −0.497431 | − | 0.867504i | \(-0.665723\pi\) | ||||
0.497431 | − | 0.867504i | \(-0.334277\pi\) | |||||||
\(314\) | − 2.12884i | − 0.00677975i | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −156.174 | −0.494222 | ||||||||
\(317\) | −434.349 | −1.37019 | −0.685093 | − | 0.728456i | \(-0.740238\pi\) | ||||
−0.685093 | + | 0.728456i | \(0.740238\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 13.5516 | 0.0424815 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 129.860i | 0.403292i | ||||||||
\(323\) | −30.0167 | −0.0929308 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 315.344i | 0.967313i | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 89.5652i | 0.273065i | ||||||||
\(329\) | − 45.3830i | − 0.137942i | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 88.4517 | 0.267226 | 0.133613 | − | 0.991034i | \(-0.457342\pi\) | ||||
0.133613 | + | 0.991034i | \(0.457342\pi\) | |||||||
\(332\) | 57.4269 | 0.172973 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | −170.389 | −0.510146 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 421.409i | 1.25047i | 0.780436 | + | 0.625235i | \(0.214997\pi\) | ||||
−0.780436 | + | 0.625235i | \(0.785003\pi\) | |||||||
\(338\) | 77.3563 | 0.228865 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | − 35.5413i | − 0.104227i | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 18.5203i | 0.0539949i | ||||||||
\(344\) | 36.9823i | 0.107507i | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −141.812 | −0.409861 | ||||||||
\(347\) | 86.4624 | 0.249171 | 0.124586 | − | 0.992209i | \(-0.460240\pi\) | ||||
0.124586 | + | 0.992209i | \(0.460240\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 17.8784 | 0.0512275 | 0.0256138 | − | 0.999672i | \(-0.491846\pi\) | ||||
0.0256138 | + | 0.999672i | \(0.491846\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 13.1660i | 0.0374034i | ||||||||
\(353\) | −118.434 | −0.335506 | −0.167753 | − | 0.985829i | \(-0.553651\pi\) | ||||
−0.167753 | + | 0.985829i | \(0.553651\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | − 273.771i | − 0.769019i | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | − 129.339i | − 0.361283i | ||||||||
\(359\) | − 112.800i | − 0.314207i | −0.987582 | − | 0.157104i | \(-0.949784\pi\) | ||||
0.987582 | − | 0.157104i | \(-0.0502156\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −237.875 | −0.658933 | ||||||||
\(362\) | 184.410 | 0.509420 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 56.5723 | 0.155418 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 604.221i | 1.64638i | 0.567767 | + | 0.823189i | \(0.307807\pi\) | ||||
−0.567767 | + | 0.823189i | \(0.692193\pi\) | |||||||
\(368\) | −138.826 | −0.377245 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 180.404i | 0.486265i | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 133.363i | 0.357542i | 0.983891 | + | 0.178771i | \(0.0572120\pi\) | ||||
−0.983891 | + | 0.178771i | \(0.942788\pi\) | |||||||
\(374\) | 8.90396i | 0.0238074i | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 48.5165 | 0.129033 | ||||||||
\(377\) | 62.2495 | 0.165118 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 278.552 | 0.734966 | 0.367483 | − | 0.930030i | \(-0.380220\pi\) | ||||
0.367483 | + | 0.930030i | \(0.380220\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | − 168.259i | − 0.440468i | ||||||||
\(383\) | −447.329 | −1.16796 | −0.583981 | − | 0.811767i | \(-0.698506\pi\) | ||||
−0.583981 | + | 0.811767i | \(0.698506\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 286.825i | 0.743071i | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | − 20.0390i | − 0.0516470i | ||||||||
\(389\) | 51.7707i | 0.133087i | 0.997784 | + | 0.0665433i | \(0.0211971\pi\) | ||||
−0.997784 | + | 0.0665433i | \(0.978803\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −93.8859 | −0.240117 | ||||||||
\(392\) | −19.7990 | −0.0505076 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | −418.420 | −1.06198 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 386.835i | 0.974395i | 0.873292 | + | 0.487197i | \(0.161981\pi\) | ||||
−0.873292 | + | 0.487197i | \(0.838019\pi\) | |||||||
\(398\) | −428.540 | −1.07673 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | − 611.141i | − 1.52404i | −0.647552 | − | 0.762021i | \(-0.724207\pi\) | ||||
0.647552 | − | 0.762021i | \(-0.275793\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | − 163.260i | − 0.405111i | ||||||||
\(404\) | − 74.2508i | − 0.183789i | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −21.7859 | −0.0536598 | ||||||||
\(407\) | −2.09666 | −0.00515150 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 320.232 | 0.782964 | 0.391482 | − | 0.920186i | \(-0.371962\pi\) | ||||
0.391482 | + | 0.920186i | \(0.371962\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 214.592i | 0.520856i | ||||||||
\(413\) | −90.9377 | −0.220188 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 60.4783i | 0.145381i | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | − 36.5231i | − 0.0873758i | ||||||||
\(419\) | − 467.521i | − 1.11580i | −0.829908 | − | 0.557901i | \(-0.811607\pi\) | ||||
0.829908 | − | 0.557901i | \(-0.188393\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 176.598 | 0.419473 | 0.209736 | − | 0.977758i | \(-0.432739\pi\) | ||||
0.209736 | + | 0.977758i | \(0.432739\pi\) | |||||||
\(422\) | 331.030 | 0.784430 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | −192.860 | −0.454859 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 215.734i | 0.505233i | ||||||||
\(428\) | −284.433 | −0.664564 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | − 159.316i | − 0.369643i | −0.982772 | − | 0.184821i | \(-0.940829\pi\) | ||||
0.982772 | − | 0.184821i | \(-0.0591707\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 310.841i | 0.717879i | 0.933361 | + | 0.358939i | \(0.116861\pi\) | ||||
−0.933361 | + | 0.358939i | \(0.883139\pi\) | |||||||
\(434\) | 57.1371i | 0.131652i | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 95.1253 | 0.218177 | ||||||||
\(437\) | 385.110 | 0.881258 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 802.810 | 1.82872 | 0.914362 | − | 0.404897i | \(-0.132693\pi\) | ||||
0.914362 | + | 0.404897i | \(0.132693\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 40.9005i | 0.0925351i | ||||||||
\(443\) | 656.281 | 1.48145 | 0.740724 | − | 0.671810i | \(-0.234483\pi\) | ||||
0.740724 | + | 0.671810i | \(0.234483\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 425.715i | 0.954518i | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | − 21.1660i | − 0.0472456i | ||||||||
\(449\) | − 366.837i | − 0.817010i | −0.912756 | − | 0.408505i | \(-0.866050\pi\) | ||||
0.912756 | − | 0.408505i | \(-0.133950\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −73.7010 | −0.163417 | ||||||||
\(452\) | 206.603 | 0.457087 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 138.279 | 0.304580 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 637.661i | 1.39532i | 0.716429 | + | 0.697660i | \(0.245775\pi\) | ||||
−0.716429 | + | 0.697660i | \(0.754225\pi\) | |||||||
\(458\) | −101.465 | −0.221540 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | − 591.806i | − 1.28374i | −0.766811 | − | 0.641872i | \(-0.778158\pi\) | ||||
0.766811 | − | 0.641872i | \(-0.221842\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 899.898i | 1.94362i | 0.235756 | + | 0.971812i | \(0.424243\pi\) | ||||
−0.235756 | + | 0.971812i | \(0.575757\pi\) | |||||||
\(464\) | − 23.2901i | − 0.0501941i | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 454.522 | 0.975370 | ||||||||
\(467\) | −418.700 | −0.896574 | −0.448287 | − | 0.893890i | \(-0.647966\pi\) | ||||
−0.448287 | + | 0.893890i | \(0.647966\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 122.267 | 0.260697 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | − 97.2165i | − 0.205967i | ||||||||
\(473\) | −30.4318 | −0.0643378 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | − 14.3142i | − 0.0300719i | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | − 53.0257i | − 0.110932i | ||||||||
\(479\) | − 631.947i | − 1.31930i | −0.751571 | − | 0.659652i | \(-0.770704\pi\) | ||||
0.751571 | − | 0.659652i | \(-0.229296\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −9.63104 | −0.0200230 | ||||||||
\(482\) | −216.910 | −0.450022 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 231.166 | 0.477616 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 241.105i | 0.495081i | 0.968877 | + | 0.247541i | \(0.0796224\pi\) | ||||
−0.968877 | + | 0.247541i | \(0.920378\pi\) | |||||||
\(488\) | −230.630 | −0.472602 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 176.708i | 0.359893i | 0.983676 | + | 0.179947i | \(0.0575925\pi\) | ||||
−0.983676 | + | 0.179947i | \(0.942407\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | − 15.7507i | − 0.0319487i | ||||||||
\(494\) | − 167.769i | − 0.339614i | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −61.0821 | −0.123149 | ||||||||
\(497\) | 162.253 | 0.326464 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −431.360 | −0.864449 | −0.432224 | − | 0.901766i | \(-0.642271\pi\) | ||||
−0.432224 | + | 0.901766i | \(0.642271\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 171.848i | 0.342326i | ||||||||
\(503\) | 138.491 | 0.275330 | 0.137665 | − | 0.990479i | \(-0.456040\pi\) | ||||
0.137665 | + | 0.990479i | \(0.456040\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | − 114.237i | − 0.225764i | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 209.605i | 0.412608i | ||||||||
\(509\) | − 693.349i | − 1.36218i | −0.732201 | − | 0.681089i | \(-0.761507\pi\) | ||||
0.732201 | − | 0.681089i | \(-0.238493\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −54.3457 | −0.106352 | ||||||||
\(512\) | 22.6274 | 0.0441942 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | −547.895 | −1.06594 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 39.9230i | 0.0772206i | ||||||||
\(518\) | 3.37064 | 0.00650703 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | − 74.9273i | − 0.143814i | −0.997411 | − | 0.0719072i | \(-0.977091\pi\) | ||||
0.997411 | − | 0.0719072i | \(-0.0229086\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | − 62.8549i | − 0.120182i | −0.998193 | − | 0.0600908i | \(-0.980861\pi\) | ||||
0.998193 | − | 0.0600908i | \(-0.0191390\pi\) | |||||||
\(524\) | 337.851i | 0.644754i | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 324.846 | 0.617578 | ||||||||
\(527\) | −41.3089 | −0.0783849 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 675.544 | 1.27702 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 58.7154i | 0.110367i | ||||||||
\(533\) | −338.547 | −0.635173 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 130.709i | 0.243859i | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | − 575.190i | − 1.06913i | ||||||||
\(539\) | − 16.2921i | − 0.0302265i | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 510.104 | 0.942890 | 0.471445 | − | 0.881895i | \(-0.343733\pi\) | ||||
0.471445 | + | 0.881895i | \(0.343733\pi\) | |||||||
\(542\) | 197.940 | 0.365203 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 15.3026 | 0.0281297 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | − 587.829i | − 1.07464i | −0.843378 | − | 0.537320i | \(-0.819437\pi\) | ||||
0.843378 | − | 0.537320i | \(-0.180563\pi\) | |||||||
\(548\) | −221.111 | −0.403486 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 64.6077i | 0.117255i | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 206.599i | 0.373596i | ||||||||
\(554\) | 673.846i | 1.21633i | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −446.906 | −0.803788 | ||||||||
\(557\) | 730.298 | 1.31113 | 0.655564 | − | 0.755140i | \(-0.272431\pi\) | ||||
0.655564 | + | 0.755140i | \(0.272431\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −139.789 | −0.250070 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | − 414.318i | − 0.737220i | ||||||||
\(563\) | 36.0516 | 0.0640349 | 0.0320174 | − | 0.999487i | \(-0.489807\pi\) | ||||
0.0320174 | + | 0.999487i | \(0.489807\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | − 222.173i | − 0.392532i | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 173.456i | 0.305379i | ||||||||
\(569\) | 903.457i | 1.58780i | 0.608050 | + | 0.793899i | \(0.291952\pi\) | ||||
−0.608050 | + | 0.793899i | \(0.708048\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 167.817 | 0.293899 | 0.146950 | − | 0.989144i | \(-0.453054\pi\) | ||||
0.146950 | + | 0.989144i | \(0.453054\pi\) | |||||||
\(572\) | −49.7661 | −0.0870037 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 118.484 | 0.206417 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 405.888i | 0.703445i | 0.936104 | + | 0.351722i | \(0.114404\pi\) | ||||
−0.936104 | + | 0.351722i | \(0.885596\pi\) | |||||||
\(578\) | −398.359 | −0.689202 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | − 75.9687i | − 0.130755i | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | − 158.700i | − 0.272213i | ||||||||
\(584\) | − 58.0980i | − 0.0994829i | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 42.9674 | 0.0733231 | ||||||||
\(587\) | −202.539 | −0.345041 | −0.172520 | − | 0.985006i | \(-0.555191\pi\) | ||||
−0.172520 | + | 0.985006i | \(0.555191\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 169.444 | 0.287682 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 3.60337i | 0.00608677i | ||||||||
\(593\) | 1080.22 | 1.82162 | 0.910812 | − | 0.412821i | \(-0.135457\pi\) | ||||
0.910812 | + | 0.412821i | \(0.135457\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 160.863i | 0.269904i | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | − 524.748i | − 0.877505i | ||||||||
\(599\) | − 110.028i | − 0.183687i | −0.995773 | − | 0.0918434i | \(-0.970724\pi\) | ||||
0.995773 | − | 0.0918434i | \(-0.0292759\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −667.302 | −1.11032 | −0.555160 | − | 0.831744i | \(-0.687343\pi\) | ||||
−0.555160 | + | 0.831744i | \(0.687343\pi\) | |||||||
\(602\) | 48.9229 | 0.0812673 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | −276.515 | −0.457807 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | − 354.193i | − 0.583514i | −0.956492 | − | 0.291757i | \(-0.905760\pi\) | ||||
0.956492 | − | 0.291757i | \(-0.0942399\pi\) | |||||||
\(608\) | −62.7694 | −0.103239 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 183.387i | 0.300143i | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | − 374.939i | − 0.611646i | −0.952088 | − | 0.305823i | \(-0.901068\pi\) | ||||
0.952088 | − | 0.305823i | \(-0.0989315\pi\) | |||||||
\(614\) | − 492.241i | − 0.801696i | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 17.4170 | 0.0282743 | ||||||||
\(617\) | 157.220 | 0.254814 | 0.127407 | − | 0.991850i | \(-0.459335\pi\) | ||||
0.127407 | + | 0.991850i | \(0.459335\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −977.265 | −1.57878 | −0.789390 | − | 0.613892i | \(-0.789603\pi\) | ||||
−0.789390 | + | 0.613892i | \(0.789603\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 32.9613i | 0.0529925i | ||||||||
\(623\) | −362.164 | −0.581323 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | − 767.999i | − 1.22684i | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | − 3.01064i | − 0.00479401i | ||||||||
\(629\) | 2.43690i | 0.00387424i | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 624.635 | 0.989912 | 0.494956 | − | 0.868918i | \(-0.335184\pi\) | ||||
0.494956 | + | 0.868918i | \(0.335184\pi\) | |||||||
\(632\) | −220.863 | −0.349467 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | −614.262 | −0.968867 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | − 74.8381i | − 0.117485i | ||||||||
\(638\) | 19.1648 | 0.0300389 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | − 535.603i | − 0.835574i | −0.908545 | − | 0.417787i | \(-0.862806\pi\) | ||||
0.908545 | − | 0.417787i | \(-0.137194\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 974.527i | 1.51559i | 0.652490 | + | 0.757797i | \(0.273724\pi\) | ||||
−0.652490 | + | 0.757797i | \(0.726276\pi\) | |||||||
\(644\) | 183.650i | 0.285170i | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −42.4500 | −0.0657120 | ||||||||
\(647\) | 132.916 | 0.205435 | 0.102717 | − | 0.994711i | \(-0.467246\pi\) | ||||
0.102717 | + | 0.994711i | \(0.467246\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 79.9971 | 0.123262 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 445.964i | 0.683993i | ||||||||
\(653\) | −45.5996 | −0.0698310 | −0.0349155 | − | 0.999390i | \(-0.511116\pi\) | ||||
−0.0349155 | + | 0.999390i | \(0.511116\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 126.664i | 0.193086i | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | − 64.1813i | − 0.0975399i | ||||||||
\(659\) | 124.398i | 0.188769i | 0.995536 | + | 0.0943843i | \(0.0300882\pi\) | ||||
−0.995536 | + | 0.0943843i | \(0.969912\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 514.066 | 0.777710 | 0.388855 | − | 0.921299i | \(-0.372871\pi\) | ||||
0.388855 | + | 0.921299i | \(0.372871\pi\) | |||||||
\(662\) | 125.090 | 0.188957 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 81.2139 | 0.122310 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 202.079i | 0.302968i | ||||||||
\(668\) | −240.966 | −0.360728 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | − 189.780i | − 0.282831i | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 441.681i | 0.656287i | 0.944628 | + | 0.328144i | \(0.106423\pi\) | ||||
−0.944628 | + | 0.328144i | \(0.893577\pi\) | |||||||
\(674\) | 595.962i | 0.884216i | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 109.398 | 0.161832 | ||||||||
\(677\) | 103.462 | 0.152825 | 0.0764124 | − | 0.997076i | \(-0.475653\pi\) | ||||
0.0764124 | + | 0.997076i | \(0.475653\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −26.5091 | −0.0390414 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | − 50.2630i | − 0.0736994i | ||||||||
\(683\) | 576.481 | 0.844042 | 0.422021 | − | 0.906586i | \(-0.361321\pi\) | ||||
0.422021 | + | 0.906586i | \(0.361321\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 26.1916i | 0.0381802i | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 52.3008i | 0.0760186i | ||||||||
\(689\) | − 728.991i | − 1.05804i | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −546.270 | −0.790549 | −0.395275 | − | 0.918563i | \(-0.629351\pi\) | ||||
−0.395275 | + | 0.918563i | \(0.629351\pi\) | |||||||
\(692\) | −200.552 | −0.289816 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 122.276 | 0.176191 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 85.6611i | 0.122900i | ||||||||
\(698\) | 25.2839 | 0.0362233 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | − 248.599i | − 0.354634i | −0.984154 | − | 0.177317i | \(-0.943258\pi\) | ||||
0.984154 | − | 0.177317i | \(-0.0567419\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | − 9.99590i | − 0.0142189i | ||||||||
\(704\) | 18.6196i | 0.0264482i | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −167.491 | −0.237239 | ||||||||
\(707\) | −98.2246 | −0.138932 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 463.405 | 0.653604 | 0.326802 | − | 0.945093i | \(-0.394029\pi\) | ||||
0.326802 | + | 0.945093i | \(0.394029\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | − 387.170i | − 0.543778i | ||||||||
\(713\) | 529.987 | 0.743320 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | − 182.913i | − 0.255465i | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | − 159.524i | − 0.222178i | ||||||||
\(719\) | 5.86223i | 0.00815330i | 0.999992 | + | 0.00407665i | \(0.00129764\pi\) | ||||
−0.999992 | + | 0.00407665i | \(0.998702\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 283.879 | 0.393730 | ||||||||
\(722\) | −336.406 | −0.465936 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 260.795 | 0.360214 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | − 840.247i | − 1.15577i | −0.816117 | − | 0.577887i | \(-0.803877\pi\) | ||||
0.816117 | − | 0.577887i | \(-0.196123\pi\) | |||||||
\(728\) | 80.0053 | 0.109897 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 35.3702i | 0.0483860i | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | − 227.202i | − 0.309962i | −0.987917 | − | 0.154981i | \(-0.950468\pi\) | ||||
0.987917 | − | 0.154981i | \(-0.0495316\pi\) | |||||||
\(734\) | 854.497i | 1.16417i | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −196.330 | −0.266752 | ||||||||
\(737\) | −107.557 | −0.145939 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 649.346 | 0.878682 | 0.439341 | − | 0.898320i | \(-0.355212\pi\) | ||||
0.439341 | + | 0.898320i | \(0.355212\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 255.130i | 0.343841i | ||||||||
\(743\) | −681.019 | −0.916580 | −0.458290 | − | 0.888803i | \(-0.651538\pi\) | ||||
−0.458290 | + | 0.888803i | \(0.651538\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 188.604i | 0.252820i | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 12.5921i | 0.0168344i | ||||||||
\(749\) | 376.270i | 0.502363i | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 507.471 | 0.675727 | 0.337863 | − | 0.941195i | \(-0.390296\pi\) | ||||
0.337863 | + | 0.941195i | \(0.390296\pi\) | |||||||
\(752\) | 68.6127 | 0.0912402 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 88.0340 | 0.116756 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | − 1503.28i | − 1.98585i | −0.118764 | − | 0.992923i | \(-0.537893\pi\) | ||||
0.118764 | − | 0.992923i | \(-0.462107\pi\) | |||||||
\(758\) | 393.932 | 0.519699 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | − 71.4488i | − 0.0938880i | −0.998898 | − | 0.0469440i | \(-0.985052\pi\) | ||||
0.998898 | − | 0.0469440i | \(-0.0149482\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | − 125.839i | − 0.164927i | ||||||||
\(764\) | − 237.954i | − 0.311458i | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −632.619 | −0.825874 | ||||||||
\(767\) | 367.468 | 0.479098 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 1276.97 | 1.66055 | 0.830277 | − | 0.557352i | \(-0.188182\pi\) | ||||
0.830277 | + | 0.557352i | \(0.188182\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 405.632i | 0.525430i | ||||||||
\(773\) | 1105.18 | 1.42973 | 0.714866 | − | 0.699261i | \(-0.246488\pi\) | ||||
0.714866 | + | 0.699261i | \(0.246488\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | − 28.3395i | − 0.0365199i | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 73.2149i | 0.0941065i | ||||||||
\(779\) | − 351.372i | − 0.451056i | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −142.732 | −0.182756 | ||||||||
\(782\) | −132.775 | −0.169789 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | −28.0000 | −0.0357143 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | − 1158.39i | − 1.47191i | −0.677029 | − | 0.735956i | \(-0.736733\pi\) | ||||
0.677029 | − | 0.735956i | \(-0.263267\pi\) | |||||||
\(788\) | −591.735 | −0.750932 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | − 273.310i | − 0.345525i | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | − 871.757i | − 1.09931i | ||||||||
\(794\) | 547.067i | 0.689001i | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −606.047 | −0.761365 | ||||||||
\(797\) | 387.467 | 0.486157 | 0.243078 | − | 0.970007i | \(-0.421843\pi\) | ||||
0.243078 | + | 0.970007i | \(0.421843\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 46.4016 | 0.0580747 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | − 864.284i | − 1.07766i | ||||||||
\(803\) | 47.8074 | 0.0595360 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | − 230.884i | − 0.286457i | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | − 105.007i | − 0.129959i | ||||||||
\(809\) | 1535.11i | 1.89754i | 0.315964 | + | 0.948771i | \(0.397672\pi\) | ||||
−0.315964 | + | 0.948771i | \(0.602328\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 564.588 | 0.696163 | 0.348082 | − | 0.937464i | \(-0.386833\pi\) | ||||
0.348082 | + | 0.937464i | \(0.386833\pi\) | |||||||
\(812\) | −30.8099 | −0.0379432 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | −2.96512 | −0.00364266 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | − 145.085i | − 0.177582i | ||||||||
\(818\) | 452.877 | 0.553639 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | − 1060.19i | − 1.29134i | −0.763615 | − | 0.645672i | \(-0.776577\pi\) | ||||
0.763615 | − | 0.645672i | \(-0.223423\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 933.052i | 1.13372i | 0.823814 | + | 0.566860i | \(0.191842\pi\) | ||||
−0.823814 | + | 0.566860i | \(0.808158\pi\) | |||||||
\(824\) | 303.480i | 0.368300i | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −128.605 | −0.155697 | ||||||||
\(827\) | −597.367 | −0.722330 | −0.361165 | − | 0.932502i | \(-0.617621\pi\) | ||||
−0.361165 | + | 0.932502i | \(0.617621\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −1178.19 | −1.42122 | −0.710609 | − | 0.703587i | \(-0.751580\pi\) | ||||
−0.710609 | + | 0.703587i | \(0.751580\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 85.5292i | 0.102800i | ||||||||
\(833\) | −18.9360 | −0.0227322 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | − 51.6514i | − 0.0617840i | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | − 661.174i | − 0.788991i | ||||||||
\(839\) | 693.857i | 0.827005i | 0.910503 | + | 0.413503i | \(0.135695\pi\) | ||||
−0.910503 | + | 0.413503i | \(0.864305\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 807.098 | 0.959689 | ||||||||
\(842\) | 249.747 | 0.296612 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 468.146 | 0.554676 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | − 305.804i | − 0.361044i | ||||||||
\(848\) | −272.745 | −0.321634 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | − 31.2651i | − 0.0367393i | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 166.782i | 0.195524i | 0.995210 | + | 0.0977619i | \(0.0311683\pi\) | ||||
−0.995210 | + | 0.0977619i | \(0.968832\pi\) | |||||||
\(854\) | 305.095i | 0.357254i | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −402.249 | −0.469917 | ||||||||
\(857\) | 658.616 | 0.768514 | 0.384257 | − | 0.923226i | \(-0.374458\pi\) | ||||
0.384257 | + | 0.923226i | \(0.374458\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 1267.25 | 1.47527 | 0.737633 | − | 0.675202i | \(-0.235943\pi\) | ||||
0.737633 | + | 0.675202i | \(0.235943\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | − 225.307i | − 0.261377i | ||||||||
\(863\) | 961.019 | 1.11358 | 0.556790 | − | 0.830654i | \(-0.312033\pi\) | ||||
0.556790 | + | 0.830654i | \(0.312033\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 439.596i | 0.507617i | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 80.8041i | 0.0930922i | ||||||||
\(869\) | − 181.743i | − 0.209141i | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −494.065 | −0.567239 | ||||||||
\(872\) | 134.527 | 0.154275 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 544.627 | 0.623144 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 33.2355i | 0.0378968i | 0.999820 | + | 0.0189484i | \(0.00603182\pi\) | ||||
−0.999820 | + | 0.0189484i | \(0.993968\pi\) | |||||||
\(878\) | 1135.34 | 1.29310 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 88.5981i | 0.100565i | 0.998735 | + | 0.0502827i | \(0.0160122\pi\) | ||||
−0.998735 | + | 0.0502827i | \(0.983988\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | − 477.823i | − 0.541135i | −0.962701 | − | 0.270568i | \(-0.912789\pi\) | ||||
0.962701 | − | 0.270568i | \(-0.0872114\pi\) | |||||||
\(884\) | 57.8421i | 0.0654322i | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 928.122 | 1.04754 | ||||||||
\(887\) | −1317.14 | −1.48493 | −0.742467 | − | 0.669882i | \(-0.766345\pi\) | ||||
−0.742467 | + | 0.669882i | \(0.766345\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 277.281 | 0.311902 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 602.052i | 0.674946i | ||||||||
\(893\) | −190.334 | −0.213141 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | − 29.9333i | − 0.0334077i | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | − 518.786i | − 0.577713i | ||||||||
\(899\) | 88.9130i | 0.0989021i | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −184.453 | −0.204721 | ||||||||
\(902\) | −104.229 | −0.115553 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 292.181 | 0.323209 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | − 201.813i | − 0.222506i | −0.993792 | − | 0.111253i | \(-0.964514\pi\) | ||||
0.993792 | − | 0.111253i | \(-0.0354863\pi\) | |||||||
\(908\) | 195.556 | 0.215371 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 1188.08i | 1.30415i | 0.758153 | + | 0.652076i | \(0.226102\pi\) | ||||
−0.758153 | + | 0.652076i | \(0.773898\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 66.8290i | 0.0731971i | ||||||||
\(914\) | 901.789i | 0.986640i | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −143.494 | −0.156652 | ||||||||
\(917\) | 446.935 | 0.487388 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −982.856 | −1.06948 | −0.534742 | − | 0.845015i | \(-0.679591\pi\) | ||||
−0.534742 | + | 0.845015i | \(0.679591\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | − 836.941i | − 0.907745i | ||||||||
\(923\) | −655.644 | −0.710340 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 1272.65i | 1.37435i | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | − 32.9371i | − 0.0354926i | ||||||||
\(929\) | − 630.846i | − 0.679060i | −0.940595 | − | 0.339530i | \(-0.889732\pi\) | ||||
0.940595 | − | 0.339530i | \(-0.110268\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 77.6732 | 0.0834299 | ||||||||
\(932\) | 642.792 | 0.689691 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | −592.131 | −0.633974 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | − 1036.23i | − 1.10591i | −0.833212 | − | 0.552953i | \(-0.813501\pi\) | ||||
0.833212 | − | 0.552953i | \(-0.186499\pi\) | |||||||
\(938\) | 172.911 | 0.184340 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 326.428i | 0.346894i | 0.984843 | + | 0.173447i | \(0.0554906\pi\) | ||||
−0.984843 | + | 0.173447i | \(0.944509\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | − 1099.02i | − 1.16545i | ||||||||
\(944\) | − 137.485i | − 0.145641i | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −43.0371 | −0.0454937 | ||||||||
\(947\) | 1020.01 | 1.07709 | 0.538547 | − | 0.842595i | \(-0.318973\pi\) | ||||
0.538547 | + | 0.842595i | \(0.318973\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 219.604 | 0.231406 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | − 20.2434i | − 0.0212641i | ||||||||
\(953\) | 268.365 | 0.281600 | 0.140800 | − | 0.990038i | \(-0.455032\pi\) | ||||
0.140800 | + | 0.990038i | \(0.455032\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | − 74.9897i | − 0.0784411i | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | − 893.708i | − 0.932889i | ||||||||
\(959\) | 292.502i | 0.305007i | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −727.811 | −0.757347 | ||||||||
\(962\) | −13.6203 | −0.0141584 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | −306.758 | −0.318213 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | − 963.369i | − 0.996245i | −0.867107 | − | 0.498123i | \(-0.834023\pi\) | ||||
0.867107 | − | 0.498123i | \(-0.165977\pi\) | |||||||
\(968\) | 326.918 | 0.337725 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | − 321.620i | − 0.331225i | −0.986191 | − | 0.165613i | \(-0.947040\pi\) | ||||
0.986191 | − | 0.165613i | \(-0.0529601\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 591.201i | 0.607607i | ||||||||
\(974\) | 340.974i | 0.350075i | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −326.160 | −0.334180 | ||||||||
\(977\) | 1124.21 | 1.15068 | 0.575339 | − | 0.817915i | \(-0.304870\pi\) | ||||
0.575339 | + | 0.817915i | \(0.304870\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 318.593 | 0.325427 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 249.902i | 0.254483i | ||||||||
\(983\) | 844.372 | 0.858974 | 0.429487 | − | 0.903073i | \(-0.358694\pi\) | ||||
0.429487 | + | 0.903073i | \(0.358694\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | − 22.2749i | − 0.0225911i | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | − 237.262i | − 0.240144i | ||||||||
\(989\) | − 453.795i | − 0.458842i | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −1038.57 | −1.04801 | −0.524003 | − | 0.851717i | \(-0.675562\pi\) | ||||
−0.524003 | + | 0.851717i | \(0.675562\pi\) | |||||||
\(992\) | −86.3832 | −0.0870798 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 229.460 | 0.230845 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | − 1050.74i | − 1.05390i | −0.849896 | − | 0.526950i | \(-0.823336\pi\) | ||||
0.849896 | − | 0.526950i | \(-0.176664\pi\) | |||||||
\(998\) | −610.035 | −0.611258 | ||||||||
\(999\) | 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 | 3150.3.c.d.449.10 | 16 | ||
3.2 | odd | 2 | inner | 3150.3.c.d.449.4 | 16 | ||
5.2 | odd | 4 | 630.3.e.a.71.8 | yes | 8 | ||
5.3 | odd | 4 | 3150.3.e.i.701.1 | 8 | |||
5.4 | even | 2 | inner | 3150.3.c.d.449.5 | 16 | ||
15.2 | even | 4 | 630.3.e.a.71.2 | ✓ | 8 | ||
15.8 | even | 4 | 3150.3.e.i.701.5 | 8 | |||
15.14 | odd | 2 | inner | 3150.3.c.d.449.15 | 16 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
630.3.e.a.71.2 | ✓ | 8 | 15.2 | even | 4 | ||
630.3.e.a.71.8 | yes | 8 | 5.2 | odd | 4 | ||
3150.3.c.d.449.4 | 16 | 3.2 | odd | 2 | inner | ||
3150.3.c.d.449.5 | 16 | 5.4 | even | 2 | inner | ||
3150.3.c.d.449.10 | 16 | 1.1 | even | 1 | trivial | ||
3150.3.c.d.449.15 | 16 | 15.14 | odd | 2 | inner | ||
3150.3.e.i.701.1 | 8 | 5.3 | odd | 4 | |||
3150.3.e.i.701.5 | 8 | 15.8 | even | 4 |