Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [4018,2,Mod(1,4018)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(4018, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([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("4018.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 4018 = 2 \cdot 7^{2} \cdot 41 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 4018.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: | \(32.0838915322\) |
Analytic rank: | \(1\) |
Dimension: | \(4\) |
Coefficient field: | 4.4.113481.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} - 2x^{3} - 9x^{2} + 3x + 12 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{11}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 574) |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.2 | ||
Root | \(3.90611\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 4018.1 |
$q$-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 | ||||||||
\(3\) | 1.00000 | 0.577350 | 0.288675 | − | 0.957427i | \(-0.406785\pi\) | ||||
0.288675 | + | 0.957427i | \(0.406785\pi\) | |||||||
\(4\) | 1.00000 | 0.500000 | ||||||||
\(5\) | 0.705371 | 0.315451 | 0.157726 | − | 0.987483i | \(-0.449584\pi\) | ||||
0.157726 | + | 0.987483i | \(0.449584\pi\) | |||||||
\(6\) | −1.00000 | −0.408248 | ||||||||
\(7\) | 0 | 0 | ||||||||
\(8\) | −1.00000 | −0.353553 | ||||||||
\(9\) | −2.00000 | −0.666667 | ||||||||
\(10\) | −0.705371 | −0.223058 | ||||||||
\(11\) | 6.35160 | 1.91508 | 0.957539 | − | 0.288303i | \(-0.0930910\pi\) | ||||
0.957539 | + | 0.288303i | \(0.0930910\pi\) | |||||||
\(12\) | 1.00000 | 0.288675 | ||||||||
\(13\) | −3.15086 | −0.873890 | −0.436945 | − | 0.899488i | \(-0.643940\pi\) | ||||
−0.436945 | + | 0.899488i | \(0.643940\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0.705371 | 0.182126 | ||||||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | 6.10685 | 1.48113 | 0.740565 | − | 0.671985i | \(-0.234558\pi\) | ||||
0.740565 | + | 0.671985i | \(0.234558\pi\) | |||||||
\(18\) | 2.00000 | 0.471405 | ||||||||
\(19\) | −3.36674 | −0.772383 | −0.386191 | − | 0.922419i | \(-0.626210\pi\) | ||||
−0.386191 | + | 0.922419i | \(0.626210\pi\) | |||||||
\(20\) | 0.705371 | 0.157726 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −6.35160 | −1.35416 | ||||||||
\(23\) | −5.61148 | −1.17007 | −0.585037 | − | 0.811006i | \(-0.698920\pi\) | ||||
−0.585037 | + | 0.811006i | \(0.698920\pi\) | |||||||
\(24\) | −1.00000 | −0.204124 | ||||||||
\(25\) | −4.50245 | −0.900490 | ||||||||
\(26\) | 3.15086 | 0.617934 | ||||||||
\(27\) | −5.00000 | −0.962250 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −7.44549 | −1.38259 | −0.691296 | − | 0.722572i | \(-0.742960\pi\) | ||||
−0.691296 | + | 0.722572i | \(0.742960\pi\) | |||||||
\(30\) | −0.705371 | −0.128782 | ||||||||
\(31\) | −8.66137 | −1.55563 | −0.777814 | − | 0.628495i | \(-0.783671\pi\) | ||||
−0.777814 | + | 0.628495i | \(0.783671\pi\) | |||||||
\(32\) | −1.00000 | −0.176777 | ||||||||
\(33\) | 6.35160 | 1.10567 | ||||||||
\(34\) | −6.10685 | −1.04732 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | −2.00000 | −0.333333 | ||||||||
\(37\) | −9.71834 | −1.59768 | −0.798842 | − | 0.601541i | \(-0.794554\pi\) | ||||
−0.798842 | + | 0.601541i | \(0.794554\pi\) | |||||||
\(38\) | 3.36674 | 0.546157 | ||||||||
\(39\) | −3.15086 | −0.504541 | ||||||||
\(40\) | −0.705371 | −0.111529 | ||||||||
\(41\) | −1.00000 | −0.156174 | ||||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −1.74011 | −0.265365 | −0.132682 | − | 0.991159i | \(-0.542359\pi\) | ||||
−0.132682 | + | 0.991159i | \(0.542359\pi\) | |||||||
\(44\) | 6.35160 | 0.957539 | ||||||||
\(45\) | −1.41074 | −0.210301 | ||||||||
\(46\) | 5.61148 | 0.827368 | ||||||||
\(47\) | 0.460627 | 0.0671893 | 0.0335946 | − | 0.999436i | \(-0.489304\pi\) | ||||
0.0335946 | + | 0.999436i | \(0.489304\pi\) | |||||||
\(48\) | 1.00000 | 0.144338 | ||||||||
\(49\) | 0 | 0 | ||||||||
\(50\) | 4.50245 | 0.636743 | ||||||||
\(51\) | 6.10685 | 0.855130 | ||||||||
\(52\) | −3.15086 | −0.436945 | ||||||||
\(53\) | −1.90611 | −0.261825 | −0.130912 | − | 0.991394i | \(-0.541791\pi\) | ||||
−0.130912 | + | 0.991394i | \(0.541791\pi\) | |||||||
\(54\) | 5.00000 | 0.680414 | ||||||||
\(55\) | 4.48023 | 0.604114 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −3.36674 | −0.445935 | ||||||||
\(58\) | 7.44549 | 0.977640 | ||||||||
\(59\) | −7.97822 | −1.03868 | −0.519338 | − | 0.854569i | \(-0.673821\pi\) | ||||
−0.519338 | + | 0.854569i | \(0.673821\pi\) | |||||||
\(60\) | 0.705371 | 0.0910629 | ||||||||
\(61\) | 0.805142 | 0.103088 | 0.0515439 | − | 0.998671i | \(-0.483586\pi\) | ||||
0.0515439 | + | 0.998671i | \(0.483586\pi\) | |||||||
\(62\) | 8.66137 | 1.09999 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | −2.22252 | −0.275670 | ||||||||
\(66\) | −6.35160 | −0.781828 | ||||||||
\(67\) | 9.05697 | 1.10648 | 0.553242 | − | 0.833020i | \(-0.313390\pi\) | ||||
0.553242 | + | 0.833020i | \(0.313390\pi\) | |||||||
\(68\) | 6.10685 | 0.740565 | ||||||||
\(69\) | −5.61148 | −0.675543 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 13.9039 | 1.65009 | 0.825047 | − | 0.565064i | \(-0.191149\pi\) | ||||
0.825047 | + | 0.565064i | \(0.191149\pi\) | |||||||
\(72\) | 2.00000 | 0.235702 | ||||||||
\(73\) | −1.63326 | −0.191159 | −0.0955794 | − | 0.995422i | \(-0.530470\pi\) | ||||
−0.0955794 | + | 0.995422i | \(0.530470\pi\) | |||||||
\(74\) | 9.71834 | 1.12973 | ||||||||
\(75\) | −4.50245 | −0.519898 | ||||||||
\(76\) | −3.36674 | −0.386191 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 3.15086 | 0.356764 | ||||||||
\(79\) | −4.14377 | −0.466211 | −0.233105 | − | 0.972451i | \(-0.574889\pi\) | ||||
−0.233105 | + | 0.972451i | \(0.574889\pi\) | |||||||
\(80\) | 0.705371 | 0.0788628 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | 1.00000 | 0.110432 | ||||||||
\(83\) | 14.1198 | 1.54985 | 0.774926 | − | 0.632052i | \(-0.217787\pi\) | ||||
0.774926 | + | 0.632052i | \(0.217787\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 4.30759 | 0.467224 | ||||||||
\(86\) | 1.74011 | 0.187641 | ||||||||
\(87\) | −7.44549 | −0.798240 | ||||||||
\(88\) | −6.35160 | −0.677082 | ||||||||
\(89\) | −2.36674 | −0.250874 | −0.125437 | − | 0.992102i | \(-0.540033\pi\) | ||||
−0.125437 | + | 0.992102i | \(0.540033\pi\) | |||||||
\(90\) | 1.41074 | 0.148705 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | −5.61148 | −0.585037 | ||||||||
\(93\) | −8.66137 | −0.898142 | ||||||||
\(94\) | −0.460627 | −0.0475100 | ||||||||
\(95\) | −2.37480 | −0.243649 | ||||||||
\(96\) | −1.00000 | −0.102062 | ||||||||
\(97\) | 3.34451 | 0.339584 | 0.169792 | − | 0.985480i | \(-0.445690\pi\) | ||||
0.169792 | + | 0.985480i | \(0.445690\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −12.7032 | −1.27672 | ||||||||
\(100\) | −4.50245 | −0.450245 | ||||||||
\(101\) | 1.51759 | 0.151006 | 0.0755031 | − | 0.997146i | \(-0.475944\pi\) | ||||
0.0755031 | + | 0.997146i | \(0.475944\pi\) | |||||||
\(102\) | −6.10685 | −0.604669 | ||||||||
\(103\) | −15.4655 | −1.52386 | −0.761932 | − | 0.647657i | \(-0.775749\pi\) | ||||
−0.761932 | + | 0.647657i | \(0.775749\pi\) | |||||||
\(104\) | 3.15086 | 0.308967 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 1.90611 | 0.185138 | ||||||||
\(107\) | 0.567479 | 0.0548603 | 0.0274302 | − | 0.999624i | \(-0.491268\pi\) | ||||
0.0274302 | + | 0.999624i | \(0.491268\pi\) | |||||||
\(108\) | −5.00000 | −0.481125 | ||||||||
\(109\) | −3.96526 | −0.379803 | −0.189901 | − | 0.981803i | \(-0.560817\pi\) | ||||
−0.189901 | + | 0.981803i | \(0.560817\pi\) | |||||||
\(110\) | −4.48023 | −0.427173 | ||||||||
\(111\) | −9.71834 | −0.922424 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −10.9061 | −1.02596 | −0.512980 | − | 0.858400i | \(-0.671459\pi\) | ||||
−0.512980 | + | 0.858400i | \(0.671459\pi\) | |||||||
\(114\) | 3.36674 | 0.315324 | ||||||||
\(115\) | −3.95817 | −0.369102 | ||||||||
\(116\) | −7.44549 | −0.691296 | ||||||||
\(117\) | 6.30171 | 0.582593 | ||||||||
\(118\) | 7.97822 | 0.734455 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | −0.705371 | −0.0643912 | ||||||||
\(121\) | 29.3428 | 2.66753 | ||||||||
\(122\) | −0.805142 | −0.0728941 | ||||||||
\(123\) | −1.00000 | −0.0901670 | ||||||||
\(124\) | −8.66137 | −0.777814 | ||||||||
\(125\) | −6.70275 | −0.599512 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −4.38852 | −0.389418 | −0.194709 | − | 0.980861i | \(-0.562376\pi\) | ||||
−0.194709 | + | 0.980861i | \(0.562376\pi\) | |||||||
\(128\) | −1.00000 | −0.0883883 | ||||||||
\(129\) | −1.74011 | −0.153209 | ||||||||
\(130\) | 2.22252 | 0.194928 | ||||||||
\(131\) | 13.6533 | 1.19290 | 0.596448 | − | 0.802652i | \(-0.296578\pi\) | ||||
0.596448 | + | 0.802652i | \(0.296578\pi\) | |||||||
\(132\) | 6.35160 | 0.552836 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | −9.05697 | −0.782403 | ||||||||
\(135\) | −3.52685 | −0.303543 | ||||||||
\(136\) | −6.10685 | −0.523658 | ||||||||
\(137\) | 5.58262 | 0.476955 | 0.238478 | − | 0.971148i | \(-0.423352\pi\) | ||||
0.238478 | + | 0.971148i | \(0.423352\pi\) | |||||||
\(138\) | 5.61148 | 0.477681 | ||||||||
\(139\) | 9.58120 | 0.812667 | 0.406333 | − | 0.913725i | \(-0.366807\pi\) | ||||
0.406333 | + | 0.913725i | \(0.366807\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0.460627 | 0.0387918 | ||||||||
\(142\) | −13.9039 | −1.16679 | ||||||||
\(143\) | −20.0130 | −1.67357 | ||||||||
\(144\) | −2.00000 | −0.166667 | ||||||||
\(145\) | −5.25183 | −0.436140 | ||||||||
\(146\) | 1.63326 | 0.135170 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | −9.71834 | −0.798842 | ||||||||
\(149\) | −22.9387 | −1.87921 | −0.939605 | − | 0.342261i | \(-0.888807\pi\) | ||||
−0.939605 | + | 0.342261i | \(0.888807\pi\) | |||||||
\(150\) | 4.50245 | 0.367624 | ||||||||
\(151\) | −18.5083 | −1.50619 | −0.753093 | − | 0.657914i | \(-0.771439\pi\) | ||||
−0.753093 | + | 0.657914i | \(0.771439\pi\) | |||||||
\(152\) | 3.36674 | 0.273079 | ||||||||
\(153\) | −12.2137 | −0.987420 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −6.10947 | −0.490725 | ||||||||
\(156\) | −3.15086 | −0.252270 | ||||||||
\(157\) | −2.79708 | −0.223231 | −0.111616 | − | 0.993751i | \(-0.535603\pi\) | ||||
−0.111616 | + | 0.993751i | \(0.535603\pi\) | |||||||
\(158\) | 4.14377 | 0.329661 | ||||||||
\(159\) | −1.90611 | −0.151164 | ||||||||
\(160\) | −0.705371 | −0.0557644 | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | −1.00000 | −0.0785674 | ||||||||
\(163\) | −17.0976 | −1.33919 | −0.669593 | − | 0.742728i | \(-0.733532\pi\) | ||||
−0.669593 | + | 0.742728i | \(0.733532\pi\) | |||||||
\(164\) | −1.00000 | −0.0780869 | ||||||||
\(165\) | 4.48023 | 0.348785 | ||||||||
\(166\) | −14.1198 | −1.09591 | ||||||||
\(167\) | 14.2946 | 1.10615 | 0.553076 | − | 0.833131i | \(-0.313454\pi\) | ||||
0.553076 | + | 0.833131i | \(0.313454\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −3.07211 | −0.236316 | ||||||||
\(170\) | −4.30759 | −0.330377 | ||||||||
\(171\) | 6.73348 | 0.514922 | ||||||||
\(172\) | −1.74011 | −0.132682 | ||||||||
\(173\) | 24.3066 | 1.84800 | 0.923999 | − | 0.382395i | \(-0.124901\pi\) | ||||
0.923999 | + | 0.382395i | \(0.124901\pi\) | |||||||
\(174\) | 7.44549 | 0.564441 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 6.35160 | 0.478770 | ||||||||
\(177\) | −7.97822 | −0.599680 | ||||||||
\(178\) | 2.36674 | 0.177395 | ||||||||
\(179\) | 4.51759 | 0.337661 | 0.168830 | − | 0.985645i | \(-0.446001\pi\) | ||||
0.168830 | + | 0.985645i | \(0.446001\pi\) | |||||||
\(180\) | −1.41074 | −0.105150 | ||||||||
\(181\) | −4.88389 | −0.363017 | −0.181508 | − | 0.983389i | \(-0.558098\pi\) | ||||
−0.181508 | + | 0.983389i | \(0.558098\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0.805142 | 0.0595178 | ||||||||
\(184\) | 5.61148 | 0.413684 | ||||||||
\(185\) | −6.85503 | −0.503992 | ||||||||
\(186\) | 8.66137 | 0.635082 | ||||||||
\(187\) | 38.7883 | 2.83648 | ||||||||
\(188\) | 0.460627 | 0.0335946 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 2.37480 | 0.172286 | ||||||||
\(191\) | −5.64623 | −0.408547 | −0.204273 | − | 0.978914i | \(-0.565483\pi\) | ||||
−0.204273 | + | 0.978914i | \(0.565483\pi\) | |||||||
\(192\) | 1.00000 | 0.0721688 | ||||||||
\(193\) | 0.0997710 | 0.00718168 | 0.00359084 | − | 0.999994i | \(-0.498857\pi\) | ||||
0.00359084 | + | 0.999994i | \(0.498857\pi\) | |||||||
\(194\) | −3.34451 | −0.240122 | ||||||||
\(195\) | −2.22252 | −0.159158 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −6.20738 | −0.442257 | −0.221129 | − | 0.975245i | \(-0.570974\pi\) | ||||
−0.221129 | + | 0.975245i | \(0.570974\pi\) | |||||||
\(198\) | 12.7032 | 0.902777 | ||||||||
\(199\) | −5.09171 | −0.360942 | −0.180471 | − | 0.983580i | \(-0.557762\pi\) | ||||
−0.180471 | + | 0.983580i | \(0.557762\pi\) | |||||||
\(200\) | 4.50245 | 0.318371 | ||||||||
\(201\) | 9.05697 | 0.638829 | ||||||||
\(202\) | −1.51759 | −0.106778 | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | 6.10685 | 0.427565 | ||||||||
\(205\) | −0.705371 | −0.0492652 | ||||||||
\(206\) | 15.4655 | 1.07753 | ||||||||
\(207\) | 11.2230 | 0.780050 | ||||||||
\(208\) | −3.15086 | −0.218473 | ||||||||
\(209\) | −21.3842 | −1.47917 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 20.6604 | 1.42232 | 0.711160 | − | 0.703030i | \(-0.248170\pi\) | ||||
0.711160 | + | 0.703030i | \(0.248170\pi\) | |||||||
\(212\) | −1.90611 | −0.130912 | ||||||||
\(213\) | 13.9039 | 0.952682 | ||||||||
\(214\) | −0.567479 | −0.0387921 | ||||||||
\(215\) | −1.22743 | −0.0837097 | ||||||||
\(216\) | 5.00000 | 0.340207 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | 3.96526 | 0.268561 | ||||||||
\(219\) | −1.63326 | −0.110366 | ||||||||
\(220\) | 4.48023 | 0.302057 | ||||||||
\(221\) | −19.2418 | −1.29434 | ||||||||
\(222\) | 9.71834 | 0.652252 | ||||||||
\(223\) | 3.48023 | 0.233053 | 0.116527 | − | 0.993188i | \(-0.462824\pi\) | ||||
0.116527 | + | 0.993188i | \(0.462824\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 9.00490 | 0.600327 | ||||||||
\(226\) | 10.9061 | 0.725464 | ||||||||
\(227\) | −22.0179 | −1.46138 | −0.730689 | − | 0.682711i | \(-0.760801\pi\) | ||||
−0.730689 | + | 0.682711i | \(0.760801\pi\) | |||||||
\(228\) | −3.36674 | −0.222968 | ||||||||
\(229\) | −4.45212 | −0.294205 | −0.147102 | − | 0.989121i | \(-0.546995\pi\) | ||||
−0.147102 | + | 0.989121i | \(0.546995\pi\) | |||||||
\(230\) | 3.95817 | 0.260994 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 7.44549 | 0.488820 | ||||||||
\(233\) | −25.5235 | −1.67210 | −0.836049 | − | 0.548654i | \(-0.815140\pi\) | ||||
−0.836049 | + | 0.548654i | \(0.815140\pi\) | |||||||
\(234\) | −6.30171 | −0.411956 | ||||||||
\(235\) | 0.324912 | 0.0211949 | ||||||||
\(236\) | −7.97822 | −0.519338 | ||||||||
\(237\) | −4.14377 | −0.269167 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −4.01960 | −0.260006 | −0.130003 | − | 0.991514i | \(-0.541499\pi\) | ||||
−0.130003 | + | 0.991514i | \(0.541499\pi\) | |||||||
\(240\) | 0.705371 | 0.0455315 | ||||||||
\(241\) | −2.58926 | −0.166789 | −0.0833944 | − | 0.996517i | \(-0.526576\pi\) | ||||
−0.0833944 | + | 0.996517i | \(0.526576\pi\) | |||||||
\(242\) | −29.3428 | −1.88623 | ||||||||
\(243\) | 16.0000 | 1.02640 | ||||||||
\(244\) | 0.805142 | 0.0515439 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 1.00000 | 0.0637577 | ||||||||
\(247\) | 10.6081 | 0.674978 | ||||||||
\(248\) | 8.66137 | 0.549997 | ||||||||
\(249\) | 14.1198 | 0.894807 | ||||||||
\(250\) | 6.70275 | 0.423919 | ||||||||
\(251\) | 4.89805 | 0.309162 | 0.154581 | − | 0.987980i | \(-0.450597\pi\) | ||||
0.154581 | + | 0.987980i | \(0.450597\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −35.6419 | −2.24079 | ||||||||
\(254\) | 4.38852 | 0.275360 | ||||||||
\(255\) | 4.30759 | 0.269752 | ||||||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | −19.7687 | −1.23314 | −0.616568 | − | 0.787302i | \(-0.711477\pi\) | ||||
−0.616568 | + | 0.787302i | \(0.711477\pi\) | |||||||
\(258\) | 1.74011 | 0.108335 | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | −2.22252 | −0.137835 | ||||||||
\(261\) | 14.8910 | 0.921728 | ||||||||
\(262\) | −13.6533 | −0.843504 | ||||||||
\(263\) | 8.36674 | 0.515915 | 0.257958 | − | 0.966156i | \(-0.416951\pi\) | ||||
0.257958 | + | 0.966156i | \(0.416951\pi\) | |||||||
\(264\) | −6.35160 | −0.390914 | ||||||||
\(265\) | −1.34451 | −0.0825929 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −2.36674 | −0.144842 | ||||||||
\(268\) | 9.05697 | 0.553242 | ||||||||
\(269\) | 21.7694 | 1.32730 | 0.663652 | − | 0.748041i | \(-0.269005\pi\) | ||||
0.663652 | + | 0.748041i | \(0.269005\pi\) | |||||||
\(270\) | 3.52685 | 0.214637 | ||||||||
\(271\) | 18.7623 | 1.13973 | 0.569865 | − | 0.821738i | \(-0.306995\pi\) | ||||
0.569865 | + | 0.821738i | \(0.306995\pi\) | |||||||
\(272\) | 6.10685 | 0.370282 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −5.58262 | −0.337258 | ||||||||
\(275\) | −28.5978 | −1.72451 | ||||||||
\(276\) | −5.61148 | −0.337772 | ||||||||
\(277\) | −9.46183 | −0.568506 | −0.284253 | − | 0.958749i | \(-0.591746\pi\) | ||||
−0.284253 | + | 0.958749i | \(0.591746\pi\) | |||||||
\(278\) | −9.58120 | −0.574642 | ||||||||
\(279\) | 17.3227 | 1.03709 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 4.16338 | 0.248366 | 0.124183 | − | 0.992259i | \(-0.460369\pi\) | ||||
0.124183 | + | 0.992259i | \(0.460369\pi\) | |||||||
\(282\) | −0.460627 | −0.0274299 | ||||||||
\(283\) | 27.4844 | 1.63378 | 0.816888 | − | 0.576796i | \(-0.195697\pi\) | ||||
0.816888 | + | 0.576796i | \(0.195697\pi\) | |||||||
\(284\) | 13.9039 | 0.825047 | ||||||||
\(285\) | −2.37480 | −0.140671 | ||||||||
\(286\) | 20.0130 | 1.18339 | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | 2.00000 | 0.117851 | ||||||||
\(289\) | 20.2937 | 1.19374 | ||||||||
\(290\) | 5.25183 | 0.308398 | ||||||||
\(291\) | 3.34451 | 0.196059 | ||||||||
\(292\) | −1.63326 | −0.0955794 | ||||||||
\(293\) | −31.9044 | −1.86387 | −0.931937 | − | 0.362621i | \(-0.881882\pi\) | ||||
−0.931937 | + | 0.362621i | \(0.881882\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −5.62760 | −0.327652 | ||||||||
\(296\) | 9.71834 | 0.564867 | ||||||||
\(297\) | −31.7580 | −1.84279 | ||||||||
\(298\) | 22.9387 | 1.32880 | ||||||||
\(299\) | 17.6810 | 1.02252 | ||||||||
\(300\) | −4.50245 | −0.259949 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | 18.5083 | 1.06504 | ||||||||
\(303\) | 1.51759 | 0.0871835 | ||||||||
\(304\) | −3.36674 | −0.193096 | ||||||||
\(305\) | 0.567923 | 0.0325192 | ||||||||
\(306\) | 12.2137 | 0.698211 | ||||||||
\(307\) | −31.8800 | −1.81949 | −0.909743 | − | 0.415171i | \(-0.863722\pi\) | ||||
−0.909743 | + | 0.415171i | \(0.863722\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −15.4655 | −0.879803 | ||||||||
\(310\) | 6.10947 | 0.346995 | ||||||||
\(311\) | −7.77040 | −0.440619 | −0.220309 | − | 0.975430i | \(-0.570707\pi\) | ||||
−0.220309 | + | 0.975430i | \(0.570707\pi\) | |||||||
\(312\) | 3.15086 | 0.178382 | ||||||||
\(313\) | −1.63914 | −0.0926499 | −0.0463250 | − | 0.998926i | \(-0.514751\pi\) | ||||
−0.0463250 | + | 0.998926i | \(0.514751\pi\) | |||||||
\(314\) | 2.79708 | 0.157848 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −4.14377 | −0.233105 | ||||||||
\(317\) | 12.1790 | 0.684039 | 0.342019 | − | 0.939693i | \(-0.388889\pi\) | ||||
0.342019 | + | 0.939693i | \(0.388889\pi\) | |||||||
\(318\) | 1.90611 | 0.106889 | ||||||||
\(319\) | −47.2907 | −2.64777 | ||||||||
\(320\) | 0.705371 | 0.0394314 | ||||||||
\(321\) | 0.567479 | 0.0316736 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −20.5602 | −1.14400 | ||||||||
\(324\) | 1.00000 | 0.0555556 | ||||||||
\(325\) | 14.1866 | 0.786930 | ||||||||
\(326\) | 17.0976 | 0.946948 | ||||||||
\(327\) | −3.96526 | −0.219279 | ||||||||
\(328\) | 1.00000 | 0.0552158 | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | −4.48023 | −0.246628 | ||||||||
\(331\) | 9.81102 | 0.539263 | 0.269631 | − | 0.962964i | \(-0.413098\pi\) | ||||
0.269631 | + | 0.962964i | \(0.413098\pi\) | |||||||
\(332\) | 14.1198 | 0.774926 | ||||||||
\(333\) | 19.4367 | 1.06512 | ||||||||
\(334\) | −14.2946 | −0.782167 | ||||||||
\(335\) | 6.38852 | 0.349042 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −6.87017 | −0.374242 | −0.187121 | − | 0.982337i | \(-0.559916\pi\) | ||||
−0.187121 | + | 0.982337i | \(0.559916\pi\) | |||||||
\(338\) | 3.07211 | 0.167101 | ||||||||
\(339\) | −10.9061 | −0.592339 | ||||||||
\(340\) | 4.30759 | 0.233612 | ||||||||
\(341\) | −55.0135 | −2.97915 | ||||||||
\(342\) | −6.73348 | −0.364105 | ||||||||
\(343\) | 0 | 0 | ||||||||
\(344\) | 1.74011 | 0.0938207 | ||||||||
\(345\) | −3.95817 | −0.213101 | ||||||||
\(346\) | −24.3066 | −1.30673 | ||||||||
\(347\) | −21.8127 | −1.17097 | −0.585483 | − | 0.810685i | \(-0.699095\pi\) | ||||
−0.585483 | + | 0.810685i | \(0.699095\pi\) | |||||||
\(348\) | −7.44549 | −0.399120 | ||||||||
\(349\) | 27.4844 | 1.47121 | 0.735603 | − | 0.677413i | \(-0.236899\pi\) | ||||
0.735603 | + | 0.677413i | \(0.236899\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 15.7543 | 0.840901 | ||||||||
\(352\) | −6.35160 | −0.338541 | ||||||||
\(353\) | 16.8051 | 0.894447 | 0.447224 | − | 0.894422i | \(-0.352413\pi\) | ||||
0.447224 | + | 0.894422i | \(0.352413\pi\) | |||||||
\(354\) | 7.97822 | 0.424038 | ||||||||
\(355\) | 9.80743 | 0.520524 | ||||||||
\(356\) | −2.36674 | −0.125437 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −4.51759 | −0.238762 | ||||||||
\(359\) | −7.93497 | −0.418792 | −0.209396 | − | 0.977831i | \(-0.567150\pi\) | ||||
−0.209396 | + | 0.977831i | \(0.567150\pi\) | |||||||
\(360\) | 1.41074 | 0.0743526 | ||||||||
\(361\) | −7.66507 | −0.403425 | ||||||||
\(362\) | 4.88389 | 0.256691 | ||||||||
\(363\) | 29.3428 | 1.54010 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −1.15205 | −0.0603013 | ||||||||
\(366\) | −0.805142 | −0.0420854 | ||||||||
\(367\) | 26.6743 | 1.39239 | 0.696194 | − | 0.717853i | \(-0.254875\pi\) | ||||
0.696194 | + | 0.717853i | \(0.254875\pi\) | |||||||
\(368\) | −5.61148 | −0.292519 | ||||||||
\(369\) | 2.00000 | 0.104116 | ||||||||
\(370\) | 6.85503 | 0.356376 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | −8.66137 | −0.449071 | ||||||||
\(373\) | −20.3080 | −1.05151 | −0.525755 | − | 0.850636i | \(-0.676217\pi\) | ||||
−0.525755 | + | 0.850636i | \(0.676217\pi\) | |||||||
\(374\) | −38.7883 | −2.00569 | ||||||||
\(375\) | −6.70275 | −0.346129 | ||||||||
\(376\) | −0.460627 | −0.0237550 | ||||||||
\(377\) | 23.4596 | 1.20823 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −8.53840 | −0.438588 | −0.219294 | − | 0.975659i | \(-0.570375\pi\) | ||||
−0.219294 | + | 0.975659i | \(0.570375\pi\) | |||||||
\(380\) | −2.37480 | −0.121825 | ||||||||
\(381\) | −4.38852 | −0.224831 | ||||||||
\(382\) | 5.64623 | 0.288886 | ||||||||
\(383\) | 9.59896 | 0.490484 | 0.245242 | − | 0.969462i | \(-0.421133\pi\) | ||||
0.245242 | + | 0.969462i | \(0.421133\pi\) | |||||||
\(384\) | −1.00000 | −0.0510310 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −0.0997710 | −0.00507821 | ||||||||
\(387\) | 3.48023 | 0.176910 | ||||||||
\(388\) | 3.34451 | 0.169792 | ||||||||
\(389\) | −20.2203 | −1.02521 | −0.512606 | − | 0.858624i | \(-0.671320\pi\) | ||||
−0.512606 | + | 0.858624i | \(0.671320\pi\) | |||||||
\(390\) | 2.22252 | 0.112542 | ||||||||
\(391\) | −34.2685 | −1.73303 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 13.6533 | 0.688718 | ||||||||
\(394\) | 6.20738 | 0.312723 | ||||||||
\(395\) | −2.92290 | −0.147067 | ||||||||
\(396\) | −12.7032 | −0.638359 | ||||||||
\(397\) | −0.193659 | −0.00971948 | −0.00485974 | − | 0.999988i | \(-0.501547\pi\) | ||||
−0.00485974 | + | 0.999988i | \(0.501547\pi\) | |||||||
\(398\) | 5.09171 | 0.255224 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −4.50245 | −0.225123 | ||||||||
\(401\) | −12.3831 | −0.618381 | −0.309191 | − | 0.951000i | \(-0.600058\pi\) | ||||
−0.309191 | + | 0.951000i | \(0.600058\pi\) | |||||||
\(402\) | −9.05697 | −0.451720 | ||||||||
\(403\) | 27.2907 | 1.35945 | ||||||||
\(404\) | 1.51759 | 0.0755031 | ||||||||
\(405\) | 0.705371 | 0.0350501 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −61.7269 | −3.05969 | ||||||||
\(408\) | −6.10685 | −0.302334 | ||||||||
\(409\) | 34.1754 | 1.68986 | 0.844931 | − | 0.534875i | \(-0.179641\pi\) | ||||
0.844931 | + | 0.534875i | \(0.179641\pi\) | |||||||
\(410\) | 0.705371 | 0.0348358 | ||||||||
\(411\) | 5.58262 | 0.275370 | ||||||||
\(412\) | −15.4655 | −0.761932 | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | −11.2230 | −0.551579 | ||||||||
\(415\) | 9.95970 | 0.488903 | ||||||||
\(416\) | 3.15086 | 0.154483 | ||||||||
\(417\) | 9.58120 | 0.469193 | ||||||||
\(418\) | 21.3842 | 1.04593 | ||||||||
\(419\) | 1.35040 | 0.0659712 | 0.0329856 | − | 0.999456i | \(-0.489498\pi\) | ||||
0.0329856 | + | 0.999456i | \(0.489498\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −8.41445 | −0.410095 | −0.205048 | − | 0.978752i | \(-0.565735\pi\) | ||||
−0.205048 | + | 0.978752i | \(0.565735\pi\) | |||||||
\(422\) | −20.6604 | −1.00573 | ||||||||
\(423\) | −0.921253 | −0.0447929 | ||||||||
\(424\) | 1.90611 | 0.0925690 | ||||||||
\(425\) | −27.4958 | −1.33374 | ||||||||
\(426\) | −13.9039 | −0.673648 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | 0.567479 | 0.0274302 | ||||||||
\(429\) | −20.0130 | −0.966235 | ||||||||
\(430\) | 1.22743 | 0.0591917 | ||||||||
\(431\) | −21.7834 | −1.04927 | −0.524634 | − | 0.851328i | \(-0.675798\pi\) | ||||
−0.524634 | + | 0.851328i | \(0.675798\pi\) | |||||||
\(432\) | −5.00000 | −0.240563 | ||||||||
\(433\) | 37.8892 | 1.82084 | 0.910420 | − | 0.413685i | \(-0.135758\pi\) | ||||
0.910420 | + | 0.413685i | \(0.135758\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −5.25183 | −0.251806 | ||||||||
\(436\) | −3.96526 | −0.189901 | ||||||||
\(437\) | 18.8924 | 0.903746 | ||||||||
\(438\) | 1.63326 | 0.0780403 | ||||||||
\(439\) | 2.66212 | 0.127056 | 0.0635281 | − | 0.997980i | \(-0.479765\pi\) | ||||
0.0635281 | + | 0.997980i | \(0.479765\pi\) | |||||||
\(440\) | −4.48023 | −0.213587 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 19.2418 | 0.915240 | ||||||||
\(443\) | −32.2555 | −1.53251 | −0.766253 | − | 0.642539i | \(-0.777881\pi\) | ||||
−0.766253 | + | 0.642539i | \(0.777881\pi\) | |||||||
\(444\) | −9.71834 | −0.461212 | ||||||||
\(445\) | −1.66943 | −0.0791384 | ||||||||
\(446\) | −3.48023 | −0.164794 | ||||||||
\(447\) | −22.9387 | −1.08496 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 3.73794 | 0.176404 | 0.0882021 | − | 0.996103i | \(-0.471888\pi\) | ||||
0.0882021 | + | 0.996103i | \(0.471888\pi\) | |||||||
\(450\) | −9.00490 | −0.424495 | ||||||||
\(451\) | −6.35160 | −0.299085 | ||||||||
\(452\) | −10.9061 | −0.512980 | ||||||||
\(453\) | −18.5083 | −0.869597 | ||||||||
\(454\) | 22.0179 | 1.03335 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 3.36674 | 0.157662 | ||||||||
\(457\) | 23.4526 | 1.09706 | 0.548532 | − | 0.836129i | \(-0.315187\pi\) | ||||
0.548532 | + | 0.836129i | \(0.315187\pi\) | |||||||
\(458\) | 4.45212 | 0.208034 | ||||||||
\(459\) | −30.5343 | −1.42522 | ||||||||
\(460\) | −3.95817 | −0.184551 | ||||||||
\(461\) | 30.4499 | 1.41820 | 0.709098 | − | 0.705110i | \(-0.249103\pi\) | ||||
0.709098 | + | 0.705110i | \(0.249103\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 21.5180 | 1.00003 | 0.500014 | − | 0.866017i | \(-0.333328\pi\) | ||||
0.500014 | + | 0.866017i | \(0.333328\pi\) | |||||||
\(464\) | −7.44549 | −0.345648 | ||||||||
\(465\) | −6.10947 | −0.283320 | ||||||||
\(466\) | 25.5235 | 1.18235 | ||||||||
\(467\) | −21.6951 | −1.00393 | −0.501966 | − | 0.864888i | \(-0.667390\pi\) | ||||
−0.501966 | + | 0.864888i | \(0.667390\pi\) | |||||||
\(468\) | 6.30171 | 0.291297 | ||||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | −0.324912 | −0.0149871 | ||||||||
\(471\) | −2.79708 | −0.128883 | ||||||||
\(472\) | 7.97822 | 0.367227 | ||||||||
\(473\) | −11.0525 | −0.508195 | ||||||||
\(474\) | 4.14377 | 0.190330 | ||||||||
\(475\) | 15.1586 | 0.695523 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 3.81222 | 0.174550 | ||||||||
\(478\) | 4.01960 | 0.183852 | ||||||||
\(479\) | 23.8171 | 1.08823 | 0.544116 | − | 0.839010i | \(-0.316865\pi\) | ||||
0.544116 | + | 0.839010i | \(0.316865\pi\) | |||||||
\(480\) | −0.705371 | −0.0321956 | ||||||||
\(481\) | 30.6211 | 1.39620 | ||||||||
\(482\) | 2.58926 | 0.117938 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 29.3428 | 1.33376 | ||||||||
\(485\) | 2.35912 | 0.107122 | ||||||||
\(486\) | −16.0000 | −0.725775 | ||||||||
\(487\) | 9.97387 | 0.451959 | 0.225980 | − | 0.974132i | \(-0.427442\pi\) | ||||
0.225980 | + | 0.974132i | \(0.427442\pi\) | |||||||
\(488\) | −0.805142 | −0.0364470 | ||||||||
\(489\) | −17.0976 | −0.773180 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 32.0807 | 1.44778 | 0.723891 | − | 0.689914i | \(-0.242352\pi\) | ||||
0.723891 | + | 0.689914i | \(0.242352\pi\) | |||||||
\(492\) | −1.00000 | −0.0450835 | ||||||||
\(493\) | −45.4685 | −2.04780 | ||||||||
\(494\) | −10.6081 | −0.477281 | ||||||||
\(495\) | −8.96046 | −0.402743 | ||||||||
\(496\) | −8.66137 | −0.388907 | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | −14.1198 | −0.632724 | ||||||||
\(499\) | −18.3361 | −0.820839 | −0.410419 | − | 0.911897i | \(-0.634618\pi\) | ||||
−0.410419 | + | 0.911897i | \(0.634618\pi\) | |||||||
\(500\) | −6.70275 | −0.299756 | ||||||||
\(501\) | 14.2946 | 0.638637 | ||||||||
\(502\) | −4.89805 | −0.218611 | ||||||||
\(503\) | −40.9654 | −1.82656 | −0.913278 | − | 0.407338i | \(-0.866457\pi\) | ||||
−0.913278 | + | 0.407338i | \(0.866457\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 1.07047 | 0.0476351 | ||||||||
\(506\) | 35.6419 | 1.58447 | ||||||||
\(507\) | −3.07211 | −0.136437 | ||||||||
\(508\) | −4.38852 | −0.194709 | ||||||||
\(509\) | 1.61856 | 0.0717416 | 0.0358708 | − | 0.999356i | \(-0.488580\pi\) | ||||
0.0358708 | + | 0.999356i | \(0.488580\pi\) | |||||||
\(510\) | −4.30759 | −0.190743 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | −1.00000 | −0.0441942 | ||||||||
\(513\) | 16.8337 | 0.743226 | ||||||||
\(514\) | 19.7687 | 0.871958 | ||||||||
\(515\) | −10.9089 | −0.480705 | ||||||||
\(516\) | −1.74011 | −0.0766043 | ||||||||
\(517\) | 2.92571 | 0.128673 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 24.3066 | 1.06694 | ||||||||
\(520\) | 2.22252 | 0.0974640 | ||||||||
\(521\) | 29.6734 | 1.30001 | 0.650007 | − | 0.759929i | \(-0.274766\pi\) | ||||
0.650007 | + | 0.759929i | \(0.274766\pi\) | |||||||
\(522\) | −14.8910 | −0.651760 | ||||||||
\(523\) | −7.03692 | −0.307703 | −0.153852 | − | 0.988094i | \(-0.549168\pi\) | ||||
−0.153852 | + | 0.988094i | \(0.549168\pi\) | |||||||
\(524\) | 13.6533 | 0.596448 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −8.36674 | −0.364807 | ||||||||
\(527\) | −52.8937 | −2.30409 | ||||||||
\(528\) | 6.35160 | 0.276418 | ||||||||
\(529\) | 8.48873 | 0.369075 | ||||||||
\(530\) | 1.34451 | 0.0584020 | ||||||||
\(531\) | 15.9564 | 0.692451 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 3.15086 | 0.136479 | ||||||||
\(534\) | 2.36674 | 0.102419 | ||||||||
\(535\) | 0.400283 | 0.0173058 | ||||||||
\(536\) | −9.05697 | −0.391201 | ||||||||
\(537\) | 4.51759 | 0.194949 | ||||||||
\(538\) | −21.7694 | −0.938546 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | −3.52685 | −0.151772 | ||||||||
\(541\) | 8.77966 | 0.377467 | 0.188733 | − | 0.982028i | \(-0.439562\pi\) | ||||
0.188733 | + | 0.982028i | \(0.439562\pi\) | |||||||
\(542\) | −18.7623 | −0.805911 | ||||||||
\(543\) | −4.88389 | −0.209588 | ||||||||
\(544\) | −6.10685 | −0.261829 | ||||||||
\(545\) | −2.79697 | −0.119809 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −7.78074 | −0.332680 | −0.166340 | − | 0.986068i | \(-0.553195\pi\) | ||||
−0.166340 | + | 0.986068i | \(0.553195\pi\) | |||||||
\(548\) | 5.58262 | 0.238478 | ||||||||
\(549\) | −1.61028 | −0.0687252 | ||||||||
\(550\) | 28.5978 | 1.21941 | ||||||||
\(551\) | 25.0670 | 1.06789 | ||||||||
\(552\) | 5.61148 | 0.238841 | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | 9.46183 | 0.401994 | ||||||||
\(555\) | −6.85503 | −0.290980 | ||||||||
\(556\) | 9.58120 | 0.406333 | ||||||||
\(557\) | −11.6232 | −0.492493 | −0.246246 | − | 0.969207i | \(-0.579197\pi\) | ||||
−0.246246 | + | 0.969207i | \(0.579197\pi\) | |||||||
\(558\) | −17.3227 | −0.733330 | ||||||||
\(559\) | 5.48285 | 0.231900 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 38.7883 | 1.63764 | ||||||||
\(562\) | −4.16338 | −0.175621 | ||||||||
\(563\) | −4.55234 | −0.191858 | −0.0959291 | − | 0.995388i | \(-0.530582\pi\) | ||||
−0.0959291 | + | 0.995388i | \(0.530582\pi\) | |||||||
\(564\) | 0.460627 | 0.0193959 | ||||||||
\(565\) | −7.69285 | −0.323641 | ||||||||
\(566\) | −27.4844 | −1.15525 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −13.9039 | −0.583396 | ||||||||
\(569\) | 22.2499 | 0.932763 | 0.466382 | − | 0.884584i | \(-0.345557\pi\) | ||||
0.466382 | + | 0.884584i | \(0.345557\pi\) | |||||||
\(570\) | 2.37480 | 0.0994693 | ||||||||
\(571\) | −11.6555 | −0.487767 | −0.243883 | − | 0.969805i | \(-0.578421\pi\) | ||||
−0.243883 | + | 0.969805i | \(0.578421\pi\) | |||||||
\(572\) | −20.0130 | −0.836784 | ||||||||
\(573\) | −5.64623 | −0.235874 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 25.2654 | 1.05364 | ||||||||
\(576\) | −2.00000 | −0.0833333 | ||||||||
\(577\) | −12.4769 | −0.519418 | −0.259709 | − | 0.965687i | \(-0.583627\pi\) | ||||
−0.259709 | + | 0.965687i | \(0.583627\pi\) | |||||||
\(578\) | −20.2937 | −0.844105 | ||||||||
\(579\) | 0.0997710 | 0.00414634 | ||||||||
\(580\) | −5.25183 | −0.218070 | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | −3.34451 | −0.138635 | ||||||||
\(583\) | −12.1069 | −0.501415 | ||||||||
\(584\) | 1.63326 | 0.0675849 | ||||||||
\(585\) | 4.44504 | 0.183780 | ||||||||
\(586\) | 31.9044 | 1.31796 | ||||||||
\(587\) | 3.04651 | 0.125743 | 0.0628715 | − | 0.998022i | \(-0.479974\pi\) | ||||
0.0628715 | + | 0.998022i | \(0.479974\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 29.1606 | 1.20154 | ||||||||
\(590\) | 5.62760 | 0.231685 | ||||||||
\(591\) | −6.20738 | −0.255337 | ||||||||
\(592\) | −9.71834 | −0.399421 | ||||||||
\(593\) | 24.9228 | 1.02346 | 0.511728 | − | 0.859148i | \(-0.329006\pi\) | ||||
0.511728 | + | 0.859148i | \(0.329006\pi\) | |||||||
\(594\) | 31.7580 | 1.30305 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | −22.9387 | −0.939605 | ||||||||
\(597\) | −5.09171 | −0.208390 | ||||||||
\(598\) | −17.6810 | −0.723029 | ||||||||
\(599\) | −12.0315 | −0.491593 | −0.245797 | − | 0.969321i | \(-0.579050\pi\) | ||||
−0.245797 | + | 0.969321i | \(0.579050\pi\) | |||||||
\(600\) | 4.50245 | 0.183812 | ||||||||
\(601\) | −16.2511 | −0.662895 | −0.331447 | − | 0.943474i | \(-0.607537\pi\) | ||||
−0.331447 | + | 0.943474i | \(0.607537\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −18.1139 | −0.737656 | ||||||||
\(604\) | −18.5083 | −0.753093 | ||||||||
\(605\) | 20.6975 | 0.841474 | ||||||||
\(606\) | −1.51759 | −0.0616480 | ||||||||
\(607\) | −35.2392 | −1.43031 | −0.715157 | − | 0.698964i | \(-0.753645\pi\) | ||||
−0.715157 | + | 0.698964i | \(0.753645\pi\) | |||||||
\(608\) | 3.36674 | 0.136539 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | −0.567923 | −0.0229945 | ||||||||
\(611\) | −1.45137 | −0.0587161 | ||||||||
\(612\) | −12.2137 | −0.493710 | ||||||||
\(613\) | −4.51879 | −0.182512 | −0.0912562 | − | 0.995827i | \(-0.529088\pi\) | ||||
−0.0912562 | + | 0.995827i | \(0.529088\pi\) | |||||||
\(614\) | 31.8800 | 1.28657 | ||||||||
\(615\) | −0.705371 | −0.0284433 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −33.6700 | −1.35550 | −0.677751 | − | 0.735291i | \(-0.737045\pi\) | ||||
−0.677751 | + | 0.735291i | \(0.737045\pi\) | |||||||
\(618\) | 15.4655 | 0.622115 | ||||||||
\(619\) | 29.3831 | 1.18101 | 0.590503 | − | 0.807036i | \(-0.298929\pi\) | ||||
0.590503 | + | 0.807036i | \(0.298929\pi\) | |||||||
\(620\) | −6.10947 | −0.245362 | ||||||||
\(621\) | 28.0574 | 1.12591 | ||||||||
\(622\) | 7.77040 | 0.311565 | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | −3.15086 | −0.126135 | ||||||||
\(625\) | 17.7843 | 0.711374 | ||||||||
\(626\) | 1.63914 | 0.0655134 | ||||||||
\(627\) | −21.3842 | −0.854001 | ||||||||
\(628\) | −2.79708 | −0.111616 | ||||||||
\(629\) | −59.3484 | −2.36638 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 12.0218 | 0.478579 | 0.239290 | − | 0.970948i | \(-0.423085\pi\) | ||||
0.239290 | + | 0.970948i | \(0.423085\pi\) | |||||||
\(632\) | 4.14377 | 0.164830 | ||||||||
\(633\) | 20.6604 | 0.821177 | ||||||||
\(634\) | −12.1790 | −0.483688 | ||||||||
\(635\) | −3.09553 | −0.122842 | ||||||||
\(636\) | −1.90611 | −0.0755822 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | 47.2907 | 1.87226 | ||||||||
\(639\) | −27.8079 | −1.10006 | ||||||||
\(640\) | −0.705371 | −0.0278822 | ||||||||
\(641\) | −20.5778 | −0.812775 | −0.406388 | − | 0.913701i | \(-0.633212\pi\) | ||||
−0.406388 | + | 0.913701i | \(0.633212\pi\) | |||||||
\(642\) | −0.567479 | −0.0223966 | ||||||||
\(643\) | −23.8607 | −0.940974 | −0.470487 | − | 0.882407i | \(-0.655922\pi\) | ||||
−0.470487 | + | 0.882407i | \(0.655922\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −1.22743 | −0.0483298 | ||||||||
\(646\) | 20.5602 | 0.808929 | ||||||||
\(647\) | −14.6152 | −0.574582 | −0.287291 | − | 0.957843i | \(-0.592755\pi\) | ||||
−0.287291 | + | 0.957843i | \(0.592755\pi\) | |||||||
\(648\) | −1.00000 | −0.0392837 | ||||||||
\(649\) | −50.6744 | −1.98915 | ||||||||
\(650\) | −14.1866 | −0.556443 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −17.0976 | −0.669593 | ||||||||
\(653\) | 20.9546 | 0.820016 | 0.410008 | − | 0.912082i | \(-0.365526\pi\) | ||||
0.410008 | + | 0.912082i | \(0.365526\pi\) | |||||||
\(654\) | 3.96526 | 0.155054 | ||||||||
\(655\) | 9.63064 | 0.376300 | ||||||||
\(656\) | −1.00000 | −0.0390434 | ||||||||
\(657\) | 3.26652 | 0.127439 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 21.6289 | 0.842543 | 0.421271 | − | 0.906935i | \(-0.361584\pi\) | ||||
0.421271 | + | 0.906935i | \(0.361584\pi\) | |||||||
\(660\) | 4.48023 | 0.174393 | ||||||||
\(661\) | −41.5128 | −1.61466 | −0.807330 | − | 0.590100i | \(-0.799088\pi\) | ||||
−0.807330 | + | 0.590100i | \(0.799088\pi\) | |||||||
\(662\) | −9.81102 | −0.381316 | ||||||||
\(663\) | −19.2418 | −0.747290 | ||||||||
\(664\) | −14.1198 | −0.547955 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | −19.4367 | −0.753156 | ||||||||
\(667\) | 41.7802 | 1.61774 | ||||||||
\(668\) | 14.2946 | 0.553076 | ||||||||
\(669\) | 3.48023 | 0.134553 | ||||||||
\(670\) | −6.38852 | −0.246810 | ||||||||
\(671\) | 5.11393 | 0.197421 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 20.2858 | 0.781961 | 0.390980 | − | 0.920399i | \(-0.372136\pi\) | ||||
0.390980 | + | 0.920399i | \(0.372136\pi\) | |||||||
\(674\) | 6.87017 | 0.264629 | ||||||||
\(675\) | 22.5123 | 0.866497 | ||||||||
\(676\) | −3.07211 | −0.118158 | ||||||||
\(677\) | 21.8507 | 0.839790 | 0.419895 | − | 0.907573i | \(-0.362067\pi\) | ||||
0.419895 | + | 0.907573i | \(0.362067\pi\) | |||||||
\(678\) | 10.9061 | 0.418847 | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | −4.30759 | −0.165189 | ||||||||
\(681\) | −22.0179 | −0.843727 | ||||||||
\(682\) | 55.0135 | 2.10658 | ||||||||
\(683\) | −6.06034 | −0.231893 | −0.115946 | − | 0.993255i | \(-0.536990\pi\) | ||||
−0.115946 | + | 0.993255i | \(0.536990\pi\) | |||||||
\(684\) | 6.73348 | 0.257461 | ||||||||
\(685\) | 3.93782 | 0.150456 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −4.45212 | −0.169859 | ||||||||
\(688\) | −1.74011 | −0.0663412 | ||||||||
\(689\) | 6.00588 | 0.228806 | ||||||||
\(690\) | 3.95817 | 0.150685 | ||||||||
\(691\) | −26.9765 | −1.02623 | −0.513117 | − | 0.858319i | \(-0.671509\pi\) | ||||
−0.513117 | + | 0.858319i | \(0.671509\pi\) | |||||||
\(692\) | 24.3066 | 0.923999 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 21.8127 | 0.827998 | ||||||||
\(695\) | 6.75830 | 0.256357 | ||||||||
\(696\) | 7.44549 | 0.282220 | ||||||||
\(697\) | −6.10685 | −0.231314 | ||||||||
\(698\) | −27.4844 | −1.04030 | ||||||||
\(699\) | −25.5235 | −0.965387 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −2.93051 | −0.110684 | −0.0553420 | − | 0.998467i | \(-0.517625\pi\) | ||||
−0.0553420 | + | 0.998467i | \(0.517625\pi\) | |||||||
\(702\) | −15.7543 | −0.594607 | ||||||||
\(703\) | 32.7191 | 1.23402 | ||||||||
\(704\) | 6.35160 | 0.239385 | ||||||||
\(705\) | 0.324912 | 0.0122369 | ||||||||
\(706\) | −16.8051 | −0.632470 | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | −7.97822 | −0.299840 | ||||||||
\(709\) | 19.0075 | 0.713843 | 0.356921 | − | 0.934134i | \(-0.383826\pi\) | ||||
0.356921 | + | 0.934134i | \(0.383826\pi\) | |||||||
\(710\) | −9.80743 | −0.368066 | ||||||||
\(711\) | 8.28755 | 0.310807 | ||||||||
\(712\) | 2.36674 | 0.0886973 | ||||||||
\(713\) | 48.6031 | 1.82020 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −14.1166 | −0.527929 | ||||||||
\(716\) | 4.51759 | 0.168830 | ||||||||
\(717\) | −4.01960 | −0.150115 | ||||||||
\(718\) | 7.93497 | 0.296131 | ||||||||
\(719\) | −42.0367 | −1.56770 | −0.783852 | − | 0.620947i | \(-0.786748\pi\) | ||||
−0.783852 | + | 0.620947i | \(0.786748\pi\) | |||||||
\(720\) | −1.41074 | −0.0525752 | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | 7.66507 | 0.285264 | ||||||||
\(723\) | −2.58926 | −0.0962956 | ||||||||
\(724\) | −4.88389 | −0.181508 | ||||||||
\(725\) | 33.5229 | 1.24501 | ||||||||
\(726\) | −29.3428 | −1.08901 | ||||||||
\(727\) | 21.2242 | 0.787161 | 0.393580 | − | 0.919290i | \(-0.371236\pi\) | ||||
0.393580 | + | 0.919290i | \(0.371236\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 13.0000 | 0.481481 | ||||||||
\(730\) | 1.15205 | 0.0426395 | ||||||||
\(731\) | −10.6266 | −0.393040 | ||||||||
\(732\) | 0.805142 | 0.0297589 | ||||||||
\(733\) | −32.5951 | −1.20393 | −0.601965 | − | 0.798523i | \(-0.705615\pi\) | ||||
−0.601965 | + | 0.798523i | \(0.705615\pi\) | |||||||
\(734\) | −26.6743 | −0.984568 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 5.61148 | 0.206842 | ||||||||
\(737\) | 57.5262 | 2.11900 | ||||||||
\(738\) | −2.00000 | −0.0736210 | ||||||||
\(739\) | 10.4710 | 0.385181 | 0.192590 | − | 0.981279i | \(-0.438311\pi\) | ||||
0.192590 | + | 0.981279i | \(0.438311\pi\) | |||||||
\(740\) | −6.85503 | −0.251996 | ||||||||
\(741\) | 10.6081 | 0.389699 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −46.2600 | −1.69711 | −0.848557 | − | 0.529104i | \(-0.822528\pi\) | ||||
−0.848557 | + | 0.529104i | \(0.822528\pi\) | |||||||
\(744\) | 8.66137 | 0.317541 | ||||||||
\(745\) | −16.1803 | −0.592799 | ||||||||
\(746\) | 20.3080 | 0.743530 | ||||||||
\(747\) | −28.2396 | −1.03323 | ||||||||
\(748\) | 38.7883 | 1.41824 | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 6.70275 | 0.244750 | ||||||||
\(751\) | 48.3037 | 1.76263 | 0.881313 | − | 0.472533i | \(-0.156660\pi\) | ||||
0.881313 | + | 0.472533i | \(0.156660\pi\) | |||||||
\(752\) | 0.460627 | 0.0167973 | ||||||||
\(753\) | 4.89805 | 0.178495 | ||||||||
\(754\) | −23.4596 | −0.854350 | ||||||||
\(755\) | −13.0552 | −0.475129 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 36.4118 | 1.32341 | 0.661705 | − | 0.749764i | \(-0.269833\pi\) | ||||
0.661705 | + | 0.749764i | \(0.269833\pi\) | |||||||
\(758\) | 8.53840 | 0.310128 | ||||||||
\(759\) | −35.6419 | −1.29372 | ||||||||
\(760\) | 2.37480 | 0.0861430 | ||||||||
\(761\) | 27.7486 | 1.00589 | 0.502943 | − | 0.864319i | \(-0.332250\pi\) | ||||
0.502943 | + | 0.864319i | \(0.332250\pi\) | |||||||
\(762\) | 4.38852 | 0.158979 | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | −5.64623 | −0.204273 | ||||||||
\(765\) | −8.61519 | −0.311483 | ||||||||
\(766\) | −9.59896 | −0.346825 | ||||||||
\(767\) | 25.1382 | 0.907689 | ||||||||
\(768\) | 1.00000 | 0.0360844 | ||||||||
\(769\) | −44.3428 | −1.59904 | −0.799521 | − | 0.600638i | \(-0.794913\pi\) | ||||
−0.799521 | + | 0.600638i | \(0.794913\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −19.7687 | −0.711951 | ||||||||
\(772\) | 0.0997710 | 0.00359084 | ||||||||
\(773\) | 6.81178 | 0.245003 | 0.122501 | − | 0.992468i | \(-0.460908\pi\) | ||||
0.122501 | + | 0.992468i | \(0.460908\pi\) | |||||||
\(774\) | −3.48023 | −0.125094 | ||||||||
\(775\) | 38.9974 | 1.40083 | ||||||||
\(776\) | −3.34451 | −0.120061 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 20.2203 | 0.724934 | ||||||||
\(779\) | 3.36674 | 0.120626 | ||||||||
\(780\) | −2.22252 | −0.0795790 | ||||||||
\(781\) | 88.3122 | 3.16006 | ||||||||
\(782\) | 34.2685 | 1.22544 | ||||||||
\(783\) | 37.2274 | 1.33040 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −1.97298 | −0.0704186 | ||||||||
\(786\) | −13.6533 | −0.486997 | ||||||||
\(787\) | 11.7460 | 0.418700 | 0.209350 | − | 0.977841i | \(-0.432865\pi\) | ||||
0.209350 | + | 0.977841i | \(0.432865\pi\) | |||||||
\(788\) | −6.20738 | −0.221129 | ||||||||
\(789\) | 8.36674 | 0.297864 | ||||||||
\(790\) | 2.92290 | 0.103992 | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | 12.7032 | 0.451388 | ||||||||
\(793\) | −2.53688 | −0.0900874 | ||||||||
\(794\) | 0.193659 | 0.00687271 | ||||||||
\(795\) | −1.34451 | −0.0476850 | ||||||||
\(796\) | −5.09171 | −0.180471 | ||||||||
\(797\) | 27.0623 | 0.958596 | 0.479298 | − | 0.877652i | \(-0.340891\pi\) | ||||
0.479298 | + | 0.877652i | \(0.340891\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 2.81298 | 0.0995160 | ||||||||
\(800\) | 4.50245 | 0.159186 | ||||||||
\(801\) | 4.73348 | 0.167249 | ||||||||
\(802\) | 12.3831 | 0.437262 | ||||||||
\(803\) | −10.3738 | −0.366084 | ||||||||
\(804\) | 9.05697 | 0.319415 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | −27.2907 | −0.961275 | ||||||||
\(807\) | 21.7694 | 0.766320 | ||||||||
\(808\) | −1.51759 | −0.0533888 | ||||||||
\(809\) | 15.7460 | 0.553600 | 0.276800 | − | 0.960928i | \(-0.410726\pi\) | ||||
0.276800 | + | 0.960928i | \(0.410726\pi\) | |||||||
\(810\) | −0.705371 | −0.0247842 | ||||||||
\(811\) | −44.6629 | −1.56833 | −0.784163 | − | 0.620555i | \(-0.786908\pi\) | ||||
−0.784163 | + | 0.620555i | \(0.786908\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 18.7623 | 0.658024 | ||||||||
\(814\) | 61.7269 | 2.16353 | ||||||||
\(815\) | −12.0601 | −0.422448 | ||||||||
\(816\) | 6.10685 | 0.213783 | ||||||||
\(817\) | 5.85851 | 0.204963 | ||||||||
\(818\) | −34.1754 | −1.19491 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −0.705371 | −0.0246326 | ||||||||
\(821\) | −51.5369 | −1.79865 | −0.899325 | − | 0.437281i | \(-0.855941\pi\) | ||||
−0.899325 | + | 0.437281i | \(0.855941\pi\) | |||||||
\(822\) | −5.58262 | −0.194716 | ||||||||
\(823\) | −11.1778 | −0.389632 | −0.194816 | − | 0.980840i | \(-0.562411\pi\) | ||||
−0.194816 | + | 0.980840i | \(0.562411\pi\) | |||||||
\(824\) | 15.4655 | 0.538767 | ||||||||
\(825\) | −28.5978 | −0.995646 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −41.7242 | −1.45089 | −0.725447 | − | 0.688278i | \(-0.758367\pi\) | ||||
−0.725447 | + | 0.688278i | \(0.758367\pi\) | |||||||
\(828\) | 11.2230 | 0.390025 | ||||||||
\(829\) | 43.5350 | 1.51203 | 0.756017 | − | 0.654552i | \(-0.227143\pi\) | ||||
0.756017 | + | 0.654552i | \(0.227143\pi\) | |||||||
\(830\) | −9.95970 | −0.345706 | ||||||||
\(831\) | −9.46183 | −0.328227 | ||||||||
\(832\) | −3.15086 | −0.109236 | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | −9.58120 | −0.331770 | ||||||||
\(835\) | 10.0830 | 0.348937 | ||||||||
\(836\) | −21.3842 | −0.739587 | ||||||||
\(837\) | 43.3068 | 1.49690 | ||||||||
\(838\) | −1.35040 | −0.0466487 | ||||||||
\(839\) | 7.37708 | 0.254685 | 0.127343 | − | 0.991859i | \(-0.459355\pi\) | ||||
0.127343 | + | 0.991859i | \(0.459355\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 26.4352 | 0.911560 | ||||||||
\(842\) | 8.41445 | 0.289981 | ||||||||
\(843\) | 4.16338 | 0.143394 | ||||||||
\(844\) | 20.6604 | 0.711160 | ||||||||
\(845\) | −2.16697 | −0.0745462 | ||||||||
\(846\) | 0.921253 | 0.0316733 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | −1.90611 | −0.0654561 | ||||||||
\(849\) | 27.4844 | 0.943261 | ||||||||
\(850\) | 27.4958 | 0.943099 | ||||||||
\(851\) | 54.5343 | 1.86941 | ||||||||
\(852\) | 13.9039 | 0.476341 | ||||||||
\(853\) | −15.6119 | −0.534542 | −0.267271 | − | 0.963621i | \(-0.586122\pi\) | ||||
−0.267271 | + | 0.963621i | \(0.586122\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 4.74960 | 0.162433 | ||||||||
\(856\) | −0.567479 | −0.0193960 | ||||||||
\(857\) | −50.8608 | −1.73737 | −0.868686 | − | 0.495363i | \(-0.835035\pi\) | ||||
−0.868686 | + | 0.495363i | \(0.835035\pi\) | |||||||
\(858\) | 20.0130 | 0.683231 | ||||||||
\(859\) | 48.5069 | 1.65503 | 0.827517 | − | 0.561440i | \(-0.189753\pi\) | ||||
0.827517 | + | 0.561440i | \(0.189753\pi\) | |||||||
\(860\) | −1.22743 | −0.0418549 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 21.7834 | 0.741944 | ||||||||
\(863\) | 6.79828 | 0.231416 | 0.115708 | − | 0.993283i | \(-0.463086\pi\) | ||||
0.115708 | + | 0.993283i | \(0.463086\pi\) | |||||||
\(864\) | 5.00000 | 0.170103 | ||||||||
\(865\) | 17.1452 | 0.582953 | ||||||||
\(866\) | −37.8892 | −1.28753 | ||||||||
\(867\) | 20.2937 | 0.689209 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −26.3196 | −0.892831 | ||||||||
\(870\) | 5.25183 | 0.178054 | ||||||||
\(871\) | −28.5372 | −0.966946 | ||||||||
\(872\) | 3.96526 | 0.134281 | ||||||||
\(873\) | −6.68903 | −0.226389 | ||||||||
\(874\) | −18.8924 | −0.639045 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | −1.63326 | −0.0551828 | ||||||||
\(877\) | 23.2469 | 0.784993 | 0.392496 | − | 0.919754i | \(-0.371612\pi\) | ||||
0.392496 | + | 0.919754i | \(0.371612\pi\) | |||||||
\(878\) | −2.66212 | −0.0898423 | ||||||||
\(879\) | −31.9044 | −1.07611 | ||||||||
\(880\) | 4.48023 | 0.151028 | ||||||||
\(881\) | 11.1834 | 0.376779 | 0.188390 | − | 0.982094i | \(-0.439673\pi\) | ||||
0.188390 | + | 0.982094i | \(0.439673\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 0.523033 | 0.0176015 | 0.00880073 | − | 0.999961i | \(-0.497199\pi\) | ||||
0.00880073 | + | 0.999961i | \(0.497199\pi\) | |||||||
\(884\) | −19.2418 | −0.647172 | ||||||||
\(885\) | −5.62760 | −0.189170 | ||||||||
\(886\) | 32.2555 | 1.08365 | ||||||||
\(887\) | 21.4819 | 0.721291 | 0.360645 | − | 0.932703i | \(-0.382556\pi\) | ||||
0.360645 | + | 0.932703i | \(0.382556\pi\) | |||||||
\(888\) | 9.71834 | 0.326126 | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | 1.66943 | 0.0559593 | ||||||||
\(891\) | 6.35160 | 0.212786 | ||||||||
\(892\) | 3.48023 | 0.116527 | ||||||||
\(893\) | −1.55081 | −0.0518958 | ||||||||
\(894\) | 22.9387 | 0.767184 | ||||||||
\(895\) | 3.18658 | 0.106516 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 17.6810 | 0.590350 | ||||||||
\(898\) | −3.73794 | −0.124737 | ||||||||
\(899\) | 64.4881 | 2.15080 | ||||||||
\(900\) | 9.00490 | 0.300163 | ||||||||
\(901\) | −11.6403 | −0.387796 | ||||||||
\(902\) | 6.35160 | 0.211485 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 10.9061 | 0.362732 | ||||||||
\(905\) | −3.44495 | −0.114514 | ||||||||
\(906\) | 18.5083 | 0.614898 | ||||||||
\(907\) | −20.1872 | −0.670306 | −0.335153 | − | 0.942164i | \(-0.608788\pi\) | ||||
−0.335153 | + | 0.942164i | \(0.608788\pi\) | |||||||
\(908\) | −22.0179 | −0.730689 | ||||||||
\(909\) | −3.03519 | −0.100671 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 26.2352 | 0.869210 | 0.434605 | − | 0.900621i | \(-0.356888\pi\) | ||||
0.434605 | + | 0.900621i | \(0.356888\pi\) | |||||||
\(912\) | −3.36674 | −0.111484 | ||||||||
\(913\) | 89.6834 | 2.96809 | ||||||||
\(914\) | −23.4526 | −0.775742 | ||||||||
\(915\) | 0.567923 | 0.0187750 | ||||||||
\(916\) | −4.45212 | −0.147102 | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 30.5343 | 1.00778 | ||||||||
\(919\) | −7.17896 | −0.236812 | −0.118406 | − | 0.992965i | \(-0.537778\pi\) | ||||
−0.118406 | + | 0.992965i | \(0.537778\pi\) | |||||||
\(920\) | 3.95817 | 0.130497 | ||||||||
\(921\) | −31.8800 | −1.05048 | ||||||||
\(922\) | −30.4499 | −1.00282 | ||||||||
\(923\) | −43.8093 | −1.44200 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 43.7563 | 1.43870 | ||||||||
\(926\) | −21.5180 | −0.707127 | ||||||||
\(927\) | 30.9311 | 1.01591 | ||||||||
\(928\) | 7.44549 | 0.244410 | ||||||||
\(929\) | 21.3531 | 0.700573 | 0.350287 | − | 0.936643i | \(-0.386084\pi\) | ||||
0.350287 | + | 0.936643i | \(0.386084\pi\) | |||||||
\(930\) | 6.10947 | 0.200338 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | −25.5235 | −0.836049 | ||||||||
\(933\) | −7.77040 | −0.254391 | ||||||||
\(934\) | 21.6951 | 0.709886 | ||||||||
\(935\) | 27.3601 | 0.894771 | ||||||||
\(936\) | −6.30171 | −0.205978 | ||||||||
\(937\) | 6.77257 | 0.221250 | 0.110625 | − | 0.993862i | \(-0.464715\pi\) | ||||
0.110625 | + | 0.993862i | \(0.464715\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −1.63914 | −0.0534915 | ||||||||
\(940\) | 0.324912 | 0.0105975 | ||||||||
\(941\) | 41.6050 | 1.35628 | 0.678141 | − | 0.734932i | \(-0.262786\pi\) | ||||
0.678141 | + | 0.734932i | \(0.262786\pi\) | |||||||
\(942\) | 2.79708 | 0.0911339 | ||||||||
\(943\) | 5.61148 | 0.182735 | ||||||||
\(944\) | −7.97822 | −0.259669 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 11.0525 | 0.359348 | ||||||||
\(947\) | −35.4052 | −1.15051 | −0.575257 | − | 0.817973i | \(-0.695098\pi\) | ||||
−0.575257 | + | 0.817973i | \(0.695098\pi\) | |||||||
\(948\) | −4.14377 | −0.134584 | ||||||||
\(949\) | 5.14617 | 0.167052 | ||||||||
\(950\) | −15.1586 | −0.491809 | ||||||||
\(951\) | 12.1790 | 0.394930 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 38.9079 | 1.26035 | 0.630175 | − | 0.776453i | \(-0.282983\pi\) | ||||
0.630175 | + | 0.776453i | \(0.282983\pi\) | |||||||
\(954\) | −3.81222 | −0.123425 | ||||||||
\(955\) | −3.98268 | −0.128877 | ||||||||
\(956\) | −4.01960 | −0.130003 | ||||||||
\(957\) | −47.2907 | −1.52869 | ||||||||
\(958\) | −23.8171 | −0.769496 | ||||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | 0.705371 | 0.0227657 | ||||||||
\(961\) | 44.0193 | 1.41998 | ||||||||
\(962\) | −30.6211 | −0.987263 | ||||||||
\(963\) | −1.13496 | −0.0365735 | ||||||||
\(964\) | −2.58926 | −0.0833944 | ||||||||
\(965\) | 0.0703756 | 0.00226547 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 24.7339 | 0.795389 | 0.397695 | − | 0.917518i | \(-0.369810\pi\) | ||||
0.397695 | + | 0.917518i | \(0.369810\pi\) | |||||||
\(968\) | −29.3428 | −0.943113 | ||||||||
\(969\) | −20.5602 | −0.660488 | ||||||||
\(970\) | −2.35912 | −0.0757469 | ||||||||
\(971\) | −6.89066 | −0.221132 | −0.110566 | − | 0.993869i | \(-0.535266\pi\) | ||||
−0.110566 | + | 0.993869i | \(0.535266\pi\) | |||||||
\(972\) | 16.0000 | 0.513200 | ||||||||
\(973\) | 0 | 0 | ||||||||
\(974\) | −9.97387 | −0.319583 | ||||||||
\(975\) | 14.1866 | 0.454334 | ||||||||
\(976\) | 0.805142 | 0.0257720 | ||||||||
\(977\) | −23.4458 | −0.750098 | −0.375049 | − | 0.927005i | \(-0.622374\pi\) | ||||
−0.375049 | + | 0.927005i | \(0.622374\pi\) | |||||||
\(978\) | 17.0976 | 0.546721 | ||||||||
\(979\) | −15.0326 | −0.480443 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 7.93051 | 0.253202 | ||||||||
\(982\) | −32.0807 | −1.02374 | ||||||||
\(983\) | 1.24443 | 0.0396912 | 0.0198456 | − | 0.999803i | \(-0.493683\pi\) | ||||
0.0198456 | + | 0.999803i | \(0.493683\pi\) | |||||||
\(984\) | 1.00000 | 0.0318788 | ||||||||
\(985\) | −4.37850 | −0.139511 | ||||||||
\(986\) | 45.4685 | 1.44801 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 10.6081 | 0.337489 | ||||||||
\(989\) | 9.76462 | 0.310497 | ||||||||
\(990\) | 8.96046 | 0.284782 | ||||||||
\(991\) | −2.64480 | −0.0840150 | −0.0420075 | − | 0.999117i | \(-0.513375\pi\) | ||||
−0.0420075 | + | 0.999117i | \(0.513375\pi\) | |||||||
\(992\) | 8.66137 | 0.274999 | ||||||||
\(993\) | 9.81102 | 0.311343 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −3.59154 | −0.113860 | ||||||||
\(996\) | 14.1198 | 0.447404 | ||||||||
\(997\) | 17.9479 | 0.568417 | 0.284208 | − | 0.958763i | \(-0.408269\pi\) | ||||
0.284208 | + | 0.958763i | \(0.408269\pi\) | |||||||
\(998\) | 18.3361 | 0.580420 | ||||||||
\(999\) | 48.5917 | 1.53737 |
(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 | 4018.2.a.bk.1.2 | 4 | ||
7.2 | even | 3 | 574.2.e.f.165.3 | ✓ | 8 | ||
7.4 | even | 3 | 574.2.e.f.247.3 | yes | 8 | ||
7.6 | odd | 2 | 4018.2.a.bi.1.3 | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
574.2.e.f.165.3 | ✓ | 8 | 7.2 | even | 3 | ||
574.2.e.f.247.3 | yes | 8 | 7.4 | even | 3 | ||
4018.2.a.bi.1.3 | 4 | 7.6 | odd | 2 | |||
4018.2.a.bk.1.2 | 4 | 1.1 | even | 1 | trivial |