Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [8550,2,Mod(1,8550)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(8550, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("8550.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 8550 = 2 \cdot 3^{2} \cdot 5^{2} \cdot 19 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 8550.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: | \(68.2720937282\) |
Analytic rank: | \(0\) |
Dimension: | \(3\) |
Coefficient field: | 3.3.788.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{3} - x^{2} - 7x - 3 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.3 | ||
Root | \(-1.87740\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 8550.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 1.00000 | 0.707107 | ||||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 1.00000 | 0.500000 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 2.87740 | 1.08756 | 0.543778 | − | 0.839229i | \(-0.316993\pi\) | ||||
0.543778 | + | 0.839229i | \(0.316993\pi\) | |||||||
\(8\) | 1.00000 | 0.353553 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 2.40205 | 0.724245 | 0.362122 | − | 0.932131i | \(-0.382052\pi\) | ||||
0.362122 | + | 0.932131i | \(0.382052\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 0.597951 | 0.165842 | 0.0829209 | − | 0.996556i | \(-0.473575\pi\) | ||||
0.0829209 | + | 0.996556i | \(0.473575\pi\) | |||||||
\(14\) | 2.87740 | 0.769018 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | 2.87740 | 0.697873 | 0.348936 | − | 0.937146i | \(-0.386543\pi\) | ||||
0.348936 | + | 0.937146i | \(0.386543\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −1.00000 | −0.229416 | ||||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 2.40205 | 0.512118 | ||||||||
\(23\) | 7.03426 | 1.46674 | 0.733372 | − | 0.679827i | \(-0.237945\pi\) | ||||
0.733372 | + | 0.679827i | \(0.237945\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 0.597951 | 0.117268 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 2.87740 | 0.543778 | ||||||||
\(29\) | −6.43631 | −1.19519 | −0.597596 | − | 0.801797i | \(-0.703877\pi\) | ||||
−0.597596 | + | 0.801797i | \(0.703877\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −2.75481 | −0.494778 | −0.247389 | − | 0.968916i | \(-0.579573\pi\) | ||||
−0.247389 | + | 0.968916i | \(0.579573\pi\) | |||||||
\(32\) | 1.00000 | 0.176777 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 2.87740 | 0.493471 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 2.80410 | 0.460991 | 0.230495 | − | 0.973073i | \(-0.425965\pi\) | ||||
0.230495 | + | 0.973073i | \(0.425965\pi\) | |||||||
\(38\) | −1.00000 | −0.162221 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 6.27945 | 0.980686 | 0.490343 | − | 0.871530i | \(-0.336872\pi\) | ||||
0.490343 | + | 0.871530i | \(0.336872\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 11.7158 | 1.78664 | 0.893318 | − | 0.449424i | \(-0.148371\pi\) | ||||
0.893318 | + | 0.449424i | \(0.148371\pi\) | |||||||
\(44\) | 2.40205 | 0.362122 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 7.03426 | 1.03715 | ||||||||
\(47\) | −3.08355 | −0.449782 | −0.224891 | − | 0.974384i | \(-0.572203\pi\) | ||||
−0.224891 | + | 0.974384i | \(0.572203\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 1.27945 | 0.182779 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0.597951 | 0.0829209 | ||||||||
\(53\) | −4.96095 | −0.681439 | −0.340720 | − | 0.940165i | \(-0.610671\pi\) | ||||
−0.340720 | + | 0.940165i | \(0.610671\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 2.87740 | 0.384509 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | −6.43631 | −0.845129 | ||||||||
\(59\) | −1.15686 | −0.150610 | −0.0753049 | − | 0.997161i | \(-0.523993\pi\) | ||||
−0.0753049 | + | 0.997161i | \(0.523993\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 6.96095 | 0.891259 | 0.445629 | − | 0.895218i | \(-0.352980\pi\) | ||||
0.445629 | + | 0.895218i | \(0.352980\pi\) | |||||||
\(62\) | −2.75481 | −0.349861 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −10.9952 | −1.34328 | −0.671640 | − | 0.740878i | \(-0.734410\pi\) | ||||
−0.671640 | + | 0.740878i | \(0.734410\pi\) | |||||||
\(68\) | 2.87740 | 0.348936 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 6.07331 | 0.720769 | 0.360384 | − | 0.932804i | \(-0.382646\pi\) | ||||
0.360384 | + | 0.932804i | \(0.382646\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −3.83836 | −0.449246 | −0.224623 | − | 0.974446i | \(-0.572115\pi\) | ||||
−0.224623 | + | 0.974446i | \(0.572115\pi\) | |||||||
\(74\) | 2.80410 | 0.325970 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −1.00000 | −0.114708 | ||||||||
\(77\) | 6.91166 | 0.787657 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −5.95071 | −0.669507 | −0.334754 | − | 0.942306i | \(-0.608653\pi\) | ||||
−0.334754 | + | 0.942306i | \(0.608653\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 6.27945 | 0.693450 | ||||||||
\(83\) | −4.68150 | −0.513861 | −0.256931 | − | 0.966430i | \(-0.582711\pi\) | ||||
−0.256931 | + | 0.966430i | \(0.582711\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 11.7158 | 1.26334 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 2.40205 | 0.256059 | ||||||||
\(89\) | 11.8384 | 1.25486 | 0.627432 | − | 0.778672i | \(-0.284106\pi\) | ||||
0.627432 | + | 0.778672i | \(0.284106\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 1.72055 | 0.180362 | ||||||||
\(92\) | 7.03426 | 0.733372 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | −3.08355 | −0.318044 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −8.63221 | −0.876468 | −0.438234 | − | 0.898861i | \(-0.644396\pi\) | ||||
−0.438234 | + | 0.898861i | \(0.644396\pi\) | |||||||
\(98\) | 1.27945 | 0.129244 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 8.59795 | 0.855528 | 0.427764 | − | 0.903890i | \(-0.359301\pi\) | ||||
0.427764 | + | 0.903890i | \(0.359301\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 3.52464 | 0.347294 | 0.173647 | − | 0.984808i | \(-0.444445\pi\) | ||||
0.173647 | + | 0.984808i | \(0.444445\pi\) | |||||||
\(104\) | 0.597951 | 0.0586340 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −4.96095 | −0.481850 | ||||||||
\(107\) | −8.10757 | −0.783788 | −0.391894 | − | 0.920010i | \(-0.628180\pi\) | ||||
−0.391894 | + | 0.920010i | \(0.628180\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −4.24519 | −0.406616 | −0.203308 | − | 0.979115i | \(-0.565169\pi\) | ||||
−0.203308 | + | 0.979115i | \(0.565169\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 2.87740 | 0.271889 | ||||||||
\(113\) | 10.3973 | 0.978092 | 0.489046 | − | 0.872258i | \(-0.337345\pi\) | ||||
0.489046 | + | 0.872258i | \(0.337345\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | −6.43631 | −0.597596 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | −1.15686 | −0.106497 | ||||||||
\(119\) | 8.27945 | 0.758976 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −5.23016 | −0.475469 | ||||||||
\(122\) | 6.96095 | 0.630215 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | −2.75481 | −0.247389 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 9.31371 | 0.826458 | 0.413229 | − | 0.910627i | \(-0.364401\pi\) | ||||
0.413229 | + | 0.910627i | \(0.364401\pi\) | |||||||
\(128\) | 1.00000 | 0.0883883 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −4.19112 | −0.366179 | −0.183090 | − | 0.983096i | \(-0.558610\pi\) | ||||
−0.183090 | + | 0.983096i | \(0.558610\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −2.87740 | −0.249503 | ||||||||
\(134\) | −10.9952 | −0.949842 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 2.87740 | 0.246735 | ||||||||
\(137\) | 13.3630 | 1.14168 | 0.570839 | − | 0.821062i | \(-0.306618\pi\) | ||||
0.570839 | + | 0.821062i | \(0.306618\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −14.1076 | −1.19659 | −0.598294 | − | 0.801277i | \(-0.704155\pi\) | ||||
−0.598294 | + | 0.801277i | \(0.704155\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 6.07331 | 0.509661 | ||||||||
\(143\) | 1.43631 | 0.120110 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | −3.83836 | −0.317665 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 2.80410 | 0.230495 | ||||||||
\(149\) | 15.2644 | 1.25051 | 0.625255 | − | 0.780420i | \(-0.284995\pi\) | ||||
0.625255 | + | 0.780420i | \(0.284995\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 12.9850 | 1.05670 | 0.528351 | − | 0.849026i | \(-0.322811\pi\) | ||||
0.528351 | + | 0.849026i | \(0.322811\pi\) | |||||||
\(152\) | −1.00000 | −0.0811107 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 6.91166 | 0.556958 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −6.52464 | −0.520723 | −0.260362 | − | 0.965511i | \(-0.583842\pi\) | ||||
−0.260362 | + | 0.965511i | \(0.583842\pi\) | |||||||
\(158\) | −5.95071 | −0.473413 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 20.2404 | 1.59517 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 6.00000 | 0.469956 | 0.234978 | − | 0.972001i | \(-0.424498\pi\) | ||||
0.234978 | + | 0.972001i | \(0.424498\pi\) | |||||||
\(164\) | 6.27945 | 0.490343 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −4.68150 | −0.363355 | ||||||||
\(167\) | −15.6767 | −1.21310 | −0.606550 | − | 0.795045i | \(-0.707447\pi\) | ||||
−0.606550 | + | 0.795045i | \(0.707447\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −12.6425 | −0.972496 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 11.7158 | 0.893318 | ||||||||
\(173\) | −17.9459 | −1.36440 | −0.682202 | − | 0.731164i | \(-0.738977\pi\) | ||||
−0.682202 | + | 0.731164i | \(0.738977\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 2.40205 | 0.181061 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 11.8384 | 0.887322 | ||||||||
\(179\) | −2.70552 | −0.202220 | −0.101110 | − | 0.994875i | \(-0.532239\pi\) | ||||
−0.101110 | + | 0.994875i | \(0.532239\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −12.2747 | −0.912369 | −0.456184 | − | 0.889885i | \(-0.650784\pi\) | ||||
−0.456184 | + | 0.889885i | \(0.650784\pi\) | |||||||
\(182\) | 1.72055 | 0.127535 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 7.03426 | 0.518573 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 6.91166 | 0.505431 | ||||||||
\(188\) | −3.08355 | −0.224891 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 9.80410 | 0.709400 | 0.354700 | − | 0.934980i | \(-0.384583\pi\) | ||||
0.354700 | + | 0.934980i | \(0.384583\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 22.7993 | 1.64113 | 0.820565 | − | 0.571553i | \(-0.193659\pi\) | ||||
0.820565 | + | 0.571553i | \(0.193659\pi\) | |||||||
\(194\) | −8.63221 | −0.619757 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 1.27945 | 0.0913895 | ||||||||
\(197\) | −0.352759 | −0.0251330 | −0.0125665 | − | 0.999921i | \(-0.504000\pi\) | ||||
−0.0125665 | + | 0.999921i | \(0.504000\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −24.7260 | −1.75278 | −0.876390 | − | 0.481602i | \(-0.840055\pi\) | ||||
−0.876390 | + | 0.481602i | \(0.840055\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 8.59795 | 0.604950 | ||||||||
\(203\) | −18.5199 | −1.29984 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 3.52464 | 0.245574 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0.597951 | 0.0414605 | ||||||||
\(209\) | −2.40205 | −0.166153 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −25.3432 | −1.74470 | −0.872348 | − | 0.488885i | \(-0.837404\pi\) | ||||
−0.872348 | + | 0.488885i | \(0.837404\pi\) | |||||||
\(212\) | −4.96095 | −0.340720 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | −8.10757 | −0.554222 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −7.92669 | −0.538099 | ||||||||
\(218\) | −4.24519 | −0.287521 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 1.72055 | 0.115737 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −15.9069 | −1.06520 | −0.532602 | − | 0.846366i | \(-0.678786\pi\) | ||||
−0.532602 | + | 0.846366i | \(0.678786\pi\) | |||||||
\(224\) | 2.87740 | 0.192255 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 10.3973 | 0.691616 | ||||||||
\(227\) | 18.5589 | 1.23180 | 0.615899 | − | 0.787825i | \(-0.288793\pi\) | ||||
0.615899 | + | 0.787825i | \(0.288793\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 16.7500 | 1.10687 | 0.553436 | − | 0.832892i | \(-0.313316\pi\) | ||||
0.553436 | + | 0.832892i | \(0.313316\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −6.43631 | −0.422564 | ||||||||
\(233\) | −13.0240 | −0.853232 | −0.426616 | − | 0.904433i | \(-0.640294\pi\) | ||||
−0.426616 | + | 0.904433i | \(0.640294\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | −1.15686 | −0.0753049 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 8.27945 | 0.536677 | ||||||||
\(239\) | 23.9357 | 1.54827 | 0.774135 | − | 0.633020i | \(-0.218185\pi\) | ||||
0.774135 | + | 0.633020i | \(0.218185\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 14.3870 | 0.926749 | 0.463375 | − | 0.886162i | \(-0.346638\pi\) | ||||
0.463375 | + | 0.886162i | \(0.346638\pi\) | |||||||
\(242\) | −5.23016 | −0.336208 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 6.96095 | 0.445629 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −0.597951 | −0.0380467 | ||||||||
\(248\) | −2.75481 | −0.174930 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 20.7398 | 1.30908 | 0.654542 | − | 0.756026i | \(-0.272862\pi\) | ||||
0.654542 | + | 0.756026i | \(0.272862\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 16.8966 | 1.06228 | ||||||||
\(254\) | 9.31371 | 0.584394 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | 17.0343 | 1.06257 | 0.531284 | − | 0.847194i | \(-0.321710\pi\) | ||||
0.531284 | + | 0.847194i | \(0.321710\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 8.06852 | 0.501353 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | −4.19112 | −0.258928 | ||||||||
\(263\) | −13.5246 | −0.833965 | −0.416983 | − | 0.908914i | \(-0.636912\pi\) | ||||
−0.416983 | + | 0.908914i | \(0.636912\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | −2.87740 | −0.176425 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | −10.9952 | −0.671640 | ||||||||
\(269\) | 0.804097 | 0.0490267 | 0.0245133 | − | 0.999700i | \(-0.492196\pi\) | ||||
0.0245133 | + | 0.999700i | \(0.492196\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 25.1911 | 1.53025 | 0.765126 | − | 0.643881i | \(-0.222677\pi\) | ||||
0.765126 | + | 0.643881i | \(0.222677\pi\) | |||||||
\(272\) | 2.87740 | 0.174468 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 13.3630 | 0.807288 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −16.3035 | −0.979581 | −0.489790 | − | 0.871840i | \(-0.662927\pi\) | ||||
−0.489790 | + | 0.871840i | \(0.662927\pi\) | |||||||
\(278\) | −14.1076 | −0.846116 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 14.1959 | 0.846857 | 0.423428 | − | 0.905930i | \(-0.360827\pi\) | ||||
0.423428 | + | 0.905930i | \(0.360827\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 6.95071 | 0.413177 | 0.206588 | − | 0.978428i | \(-0.433764\pi\) | ||||
0.206588 | + | 0.978428i | \(0.433764\pi\) | |||||||
\(284\) | 6.07331 | 0.360384 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 1.43631 | 0.0849307 | ||||||||
\(287\) | 18.0685 | 1.06655 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −8.72055 | −0.512973 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | −3.83836 | −0.224623 | ||||||||
\(293\) | −16.3035 | −0.952459 | −0.476229 | − | 0.879321i | \(-0.657997\pi\) | ||||
−0.476229 | + | 0.879321i | \(0.657997\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 2.80410 | 0.162985 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 15.2644 | 0.884244 | ||||||||
\(299\) | 4.20615 | 0.243248 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 33.7110 | 1.94307 | ||||||||
\(302\) | 12.9850 | 0.747201 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | −1.00000 | −0.0573539 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −5.73079 | −0.327073 | −0.163537 | − | 0.986537i | \(-0.552290\pi\) | ||||
−0.163537 | + | 0.986537i | \(0.552290\pi\) | |||||||
\(308\) | 6.91166 | 0.393829 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −3.23016 | −0.183166 | −0.0915829 | − | 0.995797i | \(-0.529193\pi\) | ||||
−0.0915829 | + | 0.995797i | \(0.529193\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 12.2987 | 0.695163 | 0.347581 | − | 0.937650i | \(-0.387003\pi\) | ||||
0.347581 | + | 0.937650i | \(0.387003\pi\) | |||||||
\(314\) | −6.52464 | −0.368207 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −5.95071 | −0.334754 | ||||||||
\(317\) | 13.5637 | 0.761813 | 0.380906 | − | 0.924614i | \(-0.375612\pi\) | ||||
0.380906 | + | 0.924614i | \(0.375612\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −15.4603 | −0.865612 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 20.2404 | 1.12795 | ||||||||
\(323\) | −2.87740 | −0.160103 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 6.00000 | 0.332309 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 6.27945 | 0.346725 | ||||||||
\(329\) | −8.87262 | −0.489163 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 22.9952 | 1.26393 | 0.631966 | − | 0.774996i | \(-0.282248\pi\) | ||||
0.631966 | + | 0.774996i | \(0.282248\pi\) | |||||||
\(332\) | −4.68150 | −0.256931 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | −15.6767 | −0.857792 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −15.2644 | −0.831506 | −0.415753 | − | 0.909478i | \(-0.636482\pi\) | ||||
−0.415753 | + | 0.909478i | \(0.636482\pi\) | |||||||
\(338\) | −12.6425 | −0.687659 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −6.61718 | −0.358340 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −16.4603 | −0.888774 | ||||||||
\(344\) | 11.7158 | 0.631671 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −17.9459 | −0.964779 | ||||||||
\(347\) | 8.41229 | 0.451595 | 0.225798 | − | 0.974174i | \(-0.427501\pi\) | ||||
0.225798 | + | 0.974174i | \(0.427501\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 27.7993 | 1.48806 | 0.744031 | − | 0.668145i | \(-0.232911\pi\) | ||||
0.744031 | + | 0.668145i | \(0.232911\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 2.40205 | 0.128030 | ||||||||
\(353\) | 11.3582 | 0.604537 | 0.302268 | − | 0.953223i | \(-0.402256\pi\) | ||||
0.302268 | + | 0.953223i | \(0.402256\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 11.8384 | 0.627432 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −2.70552 | −0.142991 | ||||||||
\(359\) | 8.91645 | 0.470592 | 0.235296 | − | 0.971924i | \(-0.424394\pi\) | ||||
0.235296 | + | 0.971924i | \(0.424394\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 1.00000 | 0.0526316 | ||||||||
\(362\) | −12.2747 | −0.645142 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 1.72055 | 0.0901812 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −2.07331 | −0.108226 | −0.0541129 | − | 0.998535i | \(-0.517233\pi\) | ||||
−0.0541129 | + | 0.998535i | \(0.517233\pi\) | |||||||
\(368\) | 7.03426 | 0.366686 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −14.2747 | −0.741104 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −4.51986 | −0.234029 | −0.117015 | − | 0.993130i | \(-0.537332\pi\) | ||||
−0.117015 | + | 0.993130i | \(0.537332\pi\) | |||||||
\(374\) | 6.91166 | 0.357394 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −3.08355 | −0.159022 | ||||||||
\(377\) | −3.84860 | −0.198213 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −7.29448 | −0.374692 | −0.187346 | − | 0.982294i | \(-0.559989\pi\) | ||||
−0.187346 | + | 0.982294i | \(0.559989\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 9.80410 | 0.501621 | ||||||||
\(383\) | −25.6034 | −1.30827 | −0.654136 | − | 0.756377i | \(-0.726968\pi\) | ||||
−0.654136 | + | 0.756377i | \(0.726968\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 22.7993 | 1.16045 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | −8.63221 | −0.438234 | ||||||||
\(389\) | −7.36300 | −0.373319 | −0.186660 | − | 0.982425i | \(-0.559766\pi\) | ||||
−0.186660 | + | 0.982425i | \(0.559766\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 20.2404 | 1.02360 | ||||||||
\(392\) | 1.27945 | 0.0646221 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | −0.352759 | −0.0177717 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −11.4994 | −0.577137 | −0.288568 | − | 0.957459i | \(-0.593179\pi\) | ||||
−0.288568 | + | 0.957459i | \(0.593179\pi\) | |||||||
\(398\) | −24.7260 | −1.23940 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −7.95071 | −0.397040 | −0.198520 | − | 0.980097i | \(-0.563613\pi\) | ||||
−0.198520 | + | 0.980097i | \(0.563613\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −1.64724 | −0.0820549 | ||||||||
\(404\) | 8.59795 | 0.427764 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −18.5199 | −0.919125 | ||||||||
\(407\) | 6.73558 | 0.333870 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 9.19590 | 0.454708 | 0.227354 | − | 0.973812i | \(-0.426993\pi\) | ||||
0.227354 | + | 0.973812i | \(0.426993\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 3.52464 | 0.173647 | ||||||||
\(413\) | −3.32874 | −0.163797 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 0.597951 | 0.0293170 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | −2.40205 | −0.117488 | ||||||||
\(419\) | 11.3630 | 0.555119 | 0.277559 | − | 0.960708i | \(-0.410474\pi\) | ||||
0.277559 | + | 0.960708i | \(0.410474\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −13.5781 | −0.661758 | −0.330879 | − | 0.943673i | \(-0.607345\pi\) | ||||
−0.330879 | + | 0.943673i | \(0.607345\pi\) | |||||||
\(422\) | −25.3432 | −1.23369 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | −4.96095 | −0.240925 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 20.0295 | 0.969294 | ||||||||
\(428\) | −8.10757 | −0.391894 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 25.6562 | 1.23582 | 0.617909 | − | 0.786250i | \(-0.287980\pi\) | ||||
0.617909 | + | 0.786250i | \(0.287980\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −31.8966 | −1.53285 | −0.766427 | − | 0.642331i | \(-0.777967\pi\) | ||||
−0.766427 | + | 0.642331i | \(0.777967\pi\) | |||||||
\(434\) | −7.92669 | −0.380493 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −4.24519 | −0.203308 | ||||||||
\(437\) | −7.03426 | −0.336494 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −15.9712 | −0.762264 | −0.381132 | − | 0.924521i | \(-0.624466\pi\) | ||||
−0.381132 | + | 0.924521i | \(0.624466\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 1.72055 | 0.0818381 | ||||||||
\(443\) | −24.6815 | −1.17265 | −0.586327 | − | 0.810075i | \(-0.699427\pi\) | ||||
−0.586327 | + | 0.810075i | \(0.699427\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | −15.9069 | −0.753212 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 2.87740 | 0.135945 | ||||||||
\(449\) | −13.1028 | −0.618358 | −0.309179 | − | 0.951004i | \(-0.600054\pi\) | ||||
−0.309179 | + | 0.951004i | \(0.600054\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 15.0835 | 0.710257 | ||||||||
\(452\) | 10.3973 | 0.489046 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 18.5589 | 0.871013 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −3.18213 | −0.148854 | −0.0744269 | − | 0.997226i | \(-0.523713\pi\) | ||||
−0.0744269 | + | 0.997226i | \(0.523713\pi\) | |||||||
\(458\) | 16.7500 | 0.782677 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 28.5589 | 1.33012 | 0.665060 | − | 0.746790i | \(-0.268406\pi\) | ||||
0.665060 | + | 0.746790i | \(0.268406\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −5.82333 | −0.270633 | −0.135316 | − | 0.990802i | \(-0.543205\pi\) | ||||
−0.135316 | + | 0.990802i | \(0.543205\pi\) | |||||||
\(464\) | −6.43631 | −0.298798 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −13.0240 | −0.603326 | ||||||||
\(467\) | 39.0980 | 1.80924 | 0.904620 | − | 0.426220i | \(-0.140155\pi\) | ||||
0.904620 | + | 0.426220i | \(0.140155\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −31.6377 | −1.46089 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | −1.15686 | −0.0532486 | ||||||||
\(473\) | 28.1418 | 1.29396 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 8.27945 | 0.379488 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 23.9357 | 1.09479 | ||||||||
\(479\) | −9.35755 | −0.427557 | −0.213779 | − | 0.976882i | \(-0.568577\pi\) | ||||
−0.213779 | + | 0.976882i | \(0.568577\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 1.67671 | 0.0764516 | ||||||||
\(482\) | 14.3870 | 0.655311 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −5.23016 | −0.237735 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 10.2452 | 0.464254 | 0.232127 | − | 0.972685i | \(-0.425432\pi\) | ||||
0.232127 | + | 0.972685i | \(0.425432\pi\) | |||||||
\(488\) | 6.96095 | 0.315108 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −5.34252 | −0.241104 | −0.120552 | − | 0.992707i | \(-0.538467\pi\) | ||||
−0.120552 | + | 0.992707i | \(0.538467\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −18.5199 | −0.834092 | ||||||||
\(494\) | −0.597951 | −0.0269031 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −2.75481 | −0.123695 | ||||||||
\(497\) | 17.4754 | 0.783877 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −2.25418 | −0.100911 | −0.0504555 | − | 0.998726i | \(-0.516067\pi\) | ||||
−0.0504555 | + | 0.998726i | \(0.516067\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 20.7398 | 0.925662 | ||||||||
\(503\) | −16.0000 | −0.713405 | −0.356702 | − | 0.934218i | \(-0.616099\pi\) | ||||
−0.356702 | + | 0.934218i | \(0.616099\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 16.8966 | 0.751147 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 9.31371 | 0.413229 | ||||||||
\(509\) | −7.49937 | −0.332404 | −0.166202 | − | 0.986092i | \(-0.553150\pi\) | ||||
−0.166202 | + | 0.986092i | \(0.553150\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −11.0445 | −0.488580 | ||||||||
\(512\) | 1.00000 | 0.0441942 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 17.0343 | 0.751349 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −7.40684 | −0.325752 | ||||||||
\(518\) | 8.06852 | 0.354510 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 27.7740 | 1.21680 | 0.608401 | − | 0.793630i | \(-0.291811\pi\) | ||||
0.608401 | + | 0.793630i | \(0.291811\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −9.19590 | −0.402109 | −0.201054 | − | 0.979580i | \(-0.564437\pi\) | ||||
−0.201054 | + | 0.979580i | \(0.564437\pi\) | |||||||
\(524\) | −4.19112 | −0.183090 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −13.5246 | −0.589703 | ||||||||
\(527\) | −7.92669 | −0.345292 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 26.4808 | 1.15134 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | −2.87740 | −0.124751 | ||||||||
\(533\) | 3.75481 | 0.162639 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | −10.9952 | −0.474921 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 0.804097 | 0.0346671 | ||||||||
\(539\) | 3.07331 | 0.132377 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 7.46511 | 0.320950 | 0.160475 | − | 0.987040i | \(-0.448697\pi\) | ||||
0.160475 | + | 0.987040i | \(0.448697\pi\) | |||||||
\(542\) | 25.1911 | 1.08205 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 2.87740 | 0.123368 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −8.96095 | −0.383143 | −0.191571 | − | 0.981479i | \(-0.561358\pi\) | ||||
−0.191571 | + | 0.981479i | \(0.561358\pi\) | |||||||
\(548\) | 13.3630 | 0.570839 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 6.43631 | 0.274196 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −17.1226 | −0.728127 | ||||||||
\(554\) | −16.3035 | −0.692668 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −14.1076 | −0.598294 | ||||||||
\(557\) | −20.1761 | −0.854888 | −0.427444 | − | 0.904042i | \(-0.640586\pi\) | ||||
−0.427444 | + | 0.904042i | \(0.640586\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 7.00546 | 0.296299 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 14.1959 | 0.598818 | ||||||||
\(563\) | 12.3732 | 0.521470 | 0.260735 | − | 0.965410i | \(-0.416035\pi\) | ||||
0.260735 | + | 0.965410i | \(0.416035\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 6.95071 | 0.292160 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 6.07331 | 0.254830 | ||||||||
\(569\) | −7.68629 | −0.322226 | −0.161113 | − | 0.986936i | \(-0.551508\pi\) | ||||
−0.161113 | + | 0.986936i | \(0.551508\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 0.843144 | 0.0352845 | 0.0176422 | − | 0.999844i | \(-0.494384\pi\) | ||||
0.0176422 | + | 0.999844i | \(0.494384\pi\) | |||||||
\(572\) | 1.43631 | 0.0600551 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 18.0685 | 0.754165 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −0.539675 | −0.0224670 | −0.0112335 | − | 0.999937i | \(-0.503576\pi\) | ||||
−0.0112335 | + | 0.999937i | \(0.503576\pi\) | |||||||
\(578\) | −8.72055 | −0.362727 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −13.4706 | −0.558853 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −11.9165 | −0.493529 | ||||||||
\(584\) | −3.83836 | −0.158832 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −16.3035 | −0.673490 | ||||||||
\(587\) | 36.0925 | 1.48970 | 0.744849 | − | 0.667233i | \(-0.232521\pi\) | ||||
0.744849 | + | 0.667233i | \(0.232521\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 2.75481 | 0.113510 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 2.80410 | 0.115248 | ||||||||
\(593\) | −39.1082 | −1.60598 | −0.802991 | − | 0.595991i | \(-0.796760\pi\) | ||||
−0.802991 | + | 0.595991i | \(0.796760\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 15.2644 | 0.625255 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 4.20615 | 0.172002 | ||||||||
\(599\) | 21.4267 | 0.875473 | 0.437736 | − | 0.899103i | \(-0.355780\pi\) | ||||
0.437736 | + | 0.899103i | \(0.355780\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −25.8486 | −1.05439 | −0.527193 | − | 0.849745i | \(-0.676756\pi\) | ||||
−0.527193 | + | 0.849745i | \(0.676756\pi\) | |||||||
\(602\) | 33.7110 | 1.37396 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 12.9850 | 0.528351 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 40.0535 | 1.62572 | 0.812860 | − | 0.582458i | \(-0.197909\pi\) | ||||
0.812860 | + | 0.582458i | \(0.197909\pi\) | |||||||
\(608\) | −1.00000 | −0.0405554 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −1.84381 | −0.0745927 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −0.323286 | −0.0130574 | −0.00652870 | − | 0.999979i | \(-0.502078\pi\) | ||||
−0.00652870 | + | 0.999979i | \(0.502078\pi\) | |||||||
\(614\) | −5.73079 | −0.231276 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 6.91166 | 0.278479 | ||||||||
\(617\) | 35.0397 | 1.41065 | 0.705323 | − | 0.708886i | \(-0.250802\pi\) | ||||
0.705323 | + | 0.708886i | \(0.250802\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −2.13763 | −0.0859184 | −0.0429592 | − | 0.999077i | \(-0.513679\pi\) | ||||
−0.0429592 | + | 0.999077i | \(0.513679\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | −3.23016 | −0.129518 | ||||||||
\(623\) | 34.0637 | 1.36473 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 12.2987 | 0.491554 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | −6.52464 | −0.260362 | ||||||||
\(629\) | 8.06852 | 0.321713 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −4.23562 | −0.168617 | −0.0843087 | − | 0.996440i | \(-0.526868\pi\) | ||||
−0.0843087 | + | 0.996440i | \(0.526868\pi\) | |||||||
\(632\) | −5.95071 | −0.236707 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 13.5637 | 0.538683 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 0.765050 | 0.0303124 | ||||||||
\(638\) | −15.4603 | −0.612080 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 16.5932 | 0.655391 | 0.327695 | − | 0.944783i | \(-0.393728\pi\) | ||||
0.327695 | + | 0.944783i | \(0.393728\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 33.5301 | 1.32230 | 0.661149 | − | 0.750255i | \(-0.270069\pi\) | ||||
0.661149 | + | 0.750255i | \(0.270069\pi\) | |||||||
\(644\) | 20.2404 | 0.797584 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −2.87740 | −0.113210 | ||||||||
\(647\) | −32.7891 | −1.28907 | −0.644536 | − | 0.764574i | \(-0.722949\pi\) | ||||
−0.644536 | + | 0.764574i | \(0.722949\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −2.77882 | −0.109078 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 6.00000 | 0.234978 | ||||||||
\(653\) | 18.6274 | 0.728947 | 0.364474 | − | 0.931214i | \(-0.381249\pi\) | ||||
0.364474 | + | 0.931214i | \(0.381249\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 6.27945 | 0.245171 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | −8.87262 | −0.345891 | ||||||||
\(659\) | −14.4213 | −0.561773 | −0.280887 | − | 0.959741i | \(-0.590628\pi\) | ||||
−0.280887 | + | 0.959741i | \(0.590628\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 12.3822 | 0.481613 | 0.240806 | − | 0.970573i | \(-0.422588\pi\) | ||||
0.240806 | + | 0.970573i | \(0.422588\pi\) | |||||||
\(662\) | 22.9952 | 0.893734 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | −4.68150 | −0.181677 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −45.2747 | −1.75304 | ||||||||
\(668\) | −15.6767 | −0.606550 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 16.7205 | 0.645490 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −17.8281 | −0.687223 | −0.343612 | − | 0.939112i | \(-0.611650\pi\) | ||||
−0.343612 | + | 0.939112i | \(0.611650\pi\) | |||||||
\(674\) | −15.2644 | −0.587964 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −12.6425 | −0.486248 | ||||||||
\(677\) | −43.6364 | −1.67708 | −0.838542 | − | 0.544837i | \(-0.816591\pi\) | ||||
−0.838542 | + | 0.544837i | \(0.816591\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −24.8384 | −0.953209 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | −6.61718 | −0.253385 | ||||||||
\(683\) | −16.6665 | −0.637725 | −0.318862 | − | 0.947801i | \(-0.603301\pi\) | ||||
−0.318862 | + | 0.947801i | \(0.603301\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | −16.4603 | −0.628458 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 11.7158 | 0.446659 | ||||||||
\(689\) | −2.96641 | −0.113011 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −11.1364 | −0.423647 | −0.211824 | − | 0.977308i | \(-0.567940\pi\) | ||||
−0.211824 | + | 0.977308i | \(0.567940\pi\) | |||||||
\(692\) | −17.9459 | −0.682202 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 8.41229 | 0.319326 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 18.0685 | 0.684394 | ||||||||
\(698\) | 27.7993 | 1.05222 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 24.1671 | 0.912779 | 0.456389 | − | 0.889780i | \(-0.349142\pi\) | ||||
0.456389 | + | 0.889780i | \(0.349142\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −2.80410 | −0.105759 | ||||||||
\(704\) | 2.40205 | 0.0905306 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 11.3582 | 0.427472 | ||||||||
\(707\) | 24.7398 | 0.930435 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 5.95550 | 0.223663 | 0.111832 | − | 0.993727i | \(-0.464328\pi\) | ||||
0.111832 | + | 0.993727i | \(0.464328\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 11.8384 | 0.443661 | ||||||||
\(713\) | −19.3780 | −0.725713 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | −2.70552 | −0.101110 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 8.91645 | 0.332759 | ||||||||
\(719\) | −28.5000 | −1.06287 | −0.531436 | − | 0.847098i | \(-0.678347\pi\) | ||||
−0.531436 | + | 0.847098i | \(0.678347\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 10.1418 | 0.377701 | ||||||||
\(722\) | 1.00000 | 0.0372161 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | −12.2747 | −0.456184 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −44.4808 | −1.64970 | −0.824851 | − | 0.565350i | \(-0.808741\pi\) | ||||
−0.824851 | + | 0.565350i | \(0.808741\pi\) | |||||||
\(728\) | 1.72055 | 0.0637677 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 33.7110 | 1.24685 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −17.3390 | −0.640430 | −0.320215 | − | 0.947345i | \(-0.603755\pi\) | ||||
−0.320215 | + | 0.947345i | \(0.603755\pi\) | |||||||
\(734\) | −2.07331 | −0.0765271 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 7.03426 | 0.259286 | ||||||||
\(737\) | −26.4110 | −0.972863 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −24.7055 | −0.908807 | −0.454404 | − | 0.890796i | \(-0.650148\pi\) | ||||
−0.454404 | + | 0.890796i | \(0.650148\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | −14.2747 | −0.524039 | ||||||||
\(743\) | 36.6959 | 1.34624 | 0.673122 | − | 0.739532i | \(-0.264953\pi\) | ||||
0.673122 | + | 0.739532i | \(0.264953\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | −4.51986 | −0.165484 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 6.91166 | 0.252715 | ||||||||
\(749\) | −23.3287 | −0.852414 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 7.85759 | 0.286727 | 0.143364 | − | 0.989670i | \(-0.454208\pi\) | ||||
0.143364 | + | 0.989670i | \(0.454208\pi\) | |||||||
\(752\) | −3.08355 | −0.112445 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | −3.84860 | −0.140158 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −38.6034 | −1.40306 | −0.701532 | − | 0.712638i | \(-0.747500\pi\) | ||||
−0.701532 | + | 0.712638i | \(0.747500\pi\) | |||||||
\(758\) | −7.29448 | −0.264948 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −2.02527 | −0.0734161 | −0.0367080 | − | 0.999326i | \(-0.511687\pi\) | ||||
−0.0367080 | + | 0.999326i | \(0.511687\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −12.2151 | −0.442217 | ||||||||
\(764\) | 9.80410 | 0.354700 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −25.6034 | −0.925089 | ||||||||
\(767\) | −0.691744 | −0.0249774 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 37.7302 | 1.36059 | 0.680293 | − | 0.732940i | \(-0.261853\pi\) | ||||
0.680293 | + | 0.732940i | \(0.261853\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 22.7993 | 0.820565 | ||||||||
\(773\) | 22.3617 | 0.804296 | 0.402148 | − | 0.915575i | \(-0.368264\pi\) | ||||
0.402148 | + | 0.915575i | \(0.368264\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | −8.63221 | −0.309878 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −7.36300 | −0.263976 | ||||||||
\(779\) | −6.27945 | −0.224985 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 14.5884 | 0.522013 | ||||||||
\(782\) | 20.2404 | 0.723795 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 1.27945 | 0.0456947 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −23.5336 | −0.838883 | −0.419442 | − | 0.907782i | \(-0.637774\pi\) | ||||
−0.419442 | + | 0.907782i | \(0.637774\pi\) | |||||||
\(788\) | −0.352759 | −0.0125665 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 29.9171 | 1.06373 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 4.16231 | 0.147808 | ||||||||
\(794\) | −11.4994 | −0.408097 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −24.7260 | −0.876390 | ||||||||
\(797\) | 18.3275 | 0.649193 | 0.324596 | − | 0.945853i | \(-0.394772\pi\) | ||||
0.324596 | + | 0.945853i | \(0.394772\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −8.87262 | −0.313891 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | −7.95071 | −0.280749 | ||||||||
\(803\) | −9.21992 | −0.325364 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | −1.64724 | −0.0580216 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 8.59795 | 0.302475 | ||||||||
\(809\) | 53.6719 | 1.88700 | 0.943502 | − | 0.331366i | \(-0.107510\pi\) | ||||
0.943502 | + | 0.331366i | \(0.107510\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −0.548662 | −0.0192661 | −0.00963306 | − | 0.999954i | \(-0.503066\pi\) | ||||
−0.00963306 | + | 0.999954i | \(0.503066\pi\) | |||||||
\(812\) | −18.5199 | −0.649920 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 6.73558 | 0.236082 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −11.7158 | −0.409883 | ||||||||
\(818\) | 9.19590 | 0.321527 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −17.4706 | −0.609727 | −0.304864 | − | 0.952396i | \(-0.598611\pi\) | ||||
−0.304864 | + | 0.952396i | \(0.598611\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 19.0192 | 0.662969 | 0.331484 | − | 0.943461i | \(-0.392451\pi\) | ||||
0.331484 | + | 0.943461i | \(0.392451\pi\) | |||||||
\(824\) | 3.52464 | 0.122787 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −3.32874 | −0.115822 | ||||||||
\(827\) | −36.4898 | −1.26887 | −0.634437 | − | 0.772974i | \(-0.718768\pi\) | ||||
−0.634437 | + | 0.772974i | \(0.718768\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −21.4911 | −0.746415 | −0.373208 | − | 0.927748i | \(-0.621742\pi\) | ||||
−0.373208 | + | 0.927748i | \(0.621742\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0.597951 | 0.0207302 | ||||||||
\(833\) | 3.68150 | 0.127556 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | −2.40205 | −0.0830766 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 11.3630 | 0.392528 | ||||||||
\(839\) | −20.4856 | −0.707241 | −0.353621 | − | 0.935389i | \(-0.615050\pi\) | ||||
−0.353621 | + | 0.935389i | \(0.615050\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 12.4261 | 0.428485 | ||||||||
\(842\) | −13.5781 | −0.467933 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | −25.3432 | −0.872348 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −15.0493 | −0.517100 | ||||||||
\(848\) | −4.96095 | −0.170360 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 19.7247 | 0.676156 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −40.8726 | −1.39945 | −0.699726 | − | 0.714411i | \(-0.746695\pi\) | ||||
−0.699726 | + | 0.714411i | \(0.746695\pi\) | |||||||
\(854\) | 20.0295 | 0.685394 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −8.10757 | −0.277111 | ||||||||
\(857\) | 19.2782 | 0.658531 | 0.329265 | − | 0.944237i | \(-0.393199\pi\) | ||||
0.329265 | + | 0.944237i | \(0.393199\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −43.1863 | −1.47350 | −0.736749 | − | 0.676166i | \(-0.763640\pi\) | ||||
−0.736749 | + | 0.676166i | \(0.763640\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 25.6562 | 0.873855 | ||||||||
\(863\) | −24.3137 | −0.827648 | −0.413824 | − | 0.910357i | \(-0.635807\pi\) | ||||
−0.413824 | + | 0.910357i | \(0.635807\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | −31.8966 | −1.08389 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | −7.92669 | −0.269050 | ||||||||
\(869\) | −14.2939 | −0.484887 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −6.57460 | −0.222772 | ||||||||
\(872\) | −4.24519 | −0.143760 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | −7.03426 | −0.237937 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −35.8438 | −1.21036 | −0.605180 | − | 0.796089i | \(-0.706899\pi\) | ||||
−0.605180 | + | 0.796089i | \(0.706899\pi\) | |||||||
\(878\) | −15.9712 | −0.539002 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −11.8233 | −0.398338 | −0.199169 | − | 0.979965i | \(-0.563824\pi\) | ||||
−0.199169 | + | 0.979965i | \(0.563824\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −39.3925 | −1.32566 | −0.662831 | − | 0.748769i | \(-0.730645\pi\) | ||||
−0.662831 | + | 0.748769i | \(0.730645\pi\) | |||||||
\(884\) | 1.72055 | 0.0578683 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −24.6815 | −0.829191 | ||||||||
\(887\) | −4.90268 | −0.164616 | −0.0823079 | − | 0.996607i | \(-0.526229\pi\) | ||||
−0.0823079 | + | 0.996607i | \(0.526229\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 26.7993 | 0.898820 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | −15.9069 | −0.532602 | ||||||||
\(893\) | 3.08355 | 0.103187 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 2.87740 | 0.0961273 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | −13.1028 | −0.437245 | ||||||||
\(899\) | 17.7308 | 0.591355 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −14.2747 | −0.475558 | ||||||||
\(902\) | 15.0835 | 0.502227 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 10.3973 | 0.345808 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 21.0740 | 0.699750 | 0.349875 | − | 0.936796i | \(-0.386224\pi\) | ||||
0.349875 | + | 0.936796i | \(0.386224\pi\) | |||||||
\(908\) | 18.5589 | 0.615899 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −40.4508 | −1.34019 | −0.670097 | − | 0.742274i | \(-0.733747\pi\) | ||||
−0.670097 | + | 0.742274i | \(0.733747\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −11.2452 | −0.372162 | ||||||||
\(914\) | −3.18213 | −0.105255 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 16.7500 | 0.553436 | ||||||||
\(917\) | −12.0595 | −0.398241 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 17.7020 | 0.583935 | 0.291967 | − | 0.956428i | \(-0.405690\pi\) | ||||
0.291967 | + | 0.956428i | \(0.405690\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 28.5589 | 0.940537 | ||||||||
\(923\) | 3.63154 | 0.119534 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | −5.82333 | −0.191366 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | −6.43631 | −0.211282 | ||||||||
\(929\) | 39.4796 | 1.29528 | 0.647641 | − | 0.761946i | \(-0.275756\pi\) | ||||
0.647641 | + | 0.761946i | \(0.275756\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −1.27945 | −0.0419324 | ||||||||
\(932\) | −13.0240 | −0.426616 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 39.0980 | 1.27933 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −22.7055 | −0.741757 | −0.370878 | − | 0.928681i | \(-0.620943\pi\) | ||||
−0.370878 | + | 0.928681i | \(0.620943\pi\) | |||||||
\(938\) | −31.6377 | −1.03301 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −47.9802 | −1.56411 | −0.782055 | − | 0.623210i | \(-0.785828\pi\) | ||||
−0.782055 | + | 0.623210i | \(0.785828\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 44.1713 | 1.43842 | ||||||||
\(944\) | −1.15686 | −0.0376525 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 28.1418 | 0.914970 | ||||||||
\(947\) | 56.1275 | 1.82390 | 0.911949 | − | 0.410304i | \(-0.134577\pi\) | ||||
0.911949 | + | 0.410304i | \(0.134577\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −2.29515 | −0.0745038 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 8.27945 | 0.268339 | ||||||||
\(953\) | 9.87262 | 0.319805 | 0.159903 | − | 0.987133i | \(-0.448882\pi\) | ||||
0.159903 | + | 0.987133i | \(0.448882\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 23.9357 | 0.774135 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | −9.35755 | −0.302329 | ||||||||
\(959\) | 38.4508 | 1.24164 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −23.4110 | −0.755195 | ||||||||
\(962\) | 1.67671 | 0.0540594 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 14.3870 | 0.463375 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 8.70552 | 0.279951 | 0.139975 | − | 0.990155i | \(-0.455298\pi\) | ||||
0.139975 | + | 0.990155i | \(0.455298\pi\) | |||||||
\(968\) | −5.23016 | −0.168104 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −3.41162 | −0.109484 | −0.0547421 | − | 0.998501i | \(-0.517434\pi\) | ||||
−0.0547421 | + | 0.998501i | \(0.517434\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −40.5932 | −1.30136 | ||||||||
\(974\) | 10.2452 | 0.328277 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 6.96095 | 0.222815 | ||||||||
\(977\) | −11.6220 | −0.371820 | −0.185910 | − | 0.982567i | \(-0.559523\pi\) | ||||
−0.185910 | + | 0.982567i | \(0.559523\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 28.4363 | 0.908828 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | −5.34252 | −0.170487 | ||||||||
\(983\) | −32.6912 | −1.04269 | −0.521343 | − | 0.853347i | \(-0.674569\pi\) | ||||
−0.521343 | + | 0.853347i | \(0.674569\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | −18.5199 | −0.589792 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −0.597951 | −0.0190234 | ||||||||
\(989\) | 82.4117 | 2.62054 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 46.9562 | 1.49161 | 0.745806 | − | 0.666163i | \(-0.232065\pi\) | ||||
0.745806 | + | 0.666163i | \(0.232065\pi\) | |||||||
\(992\) | −2.75481 | −0.0874652 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 17.4754 | 0.554285 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −53.3227 | −1.68875 | −0.844373 | − | 0.535755i | \(-0.820027\pi\) | ||||
−0.844373 | + | 0.535755i | \(0.820027\pi\) | |||||||
\(998\) | −2.25418 | −0.0713548 | ||||||||
\(999\) | 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 | 8550.2.a.ct.1.3 | yes | 3 | |
3.2 | odd | 2 | 8550.2.a.ch.1.3 | yes | 3 | ||
5.4 | even | 2 | 8550.2.a.cc.1.1 | ✓ | 3 | ||
15.14 | odd | 2 | 8550.2.a.cm.1.1 | yes | 3 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
8550.2.a.cc.1.1 | ✓ | 3 | 5.4 | even | 2 | ||
8550.2.a.ch.1.3 | yes | 3 | 3.2 | odd | 2 | ||
8550.2.a.cm.1.1 | yes | 3 | 15.14 | odd | 2 | ||
8550.2.a.ct.1.3 | yes | 3 | 1.1 | even | 1 | trivial |