Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [3344,2,Mod(1,3344)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(3344, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 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("3344.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 3344 = 2^{4} \cdot 11 \cdot 19 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 3344.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: | \(26.7019744359\) |
Analytic rank: | \(0\) |
Dimension: | \(6\) |
Coefficient field: | 6.6.106392688.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: |
\( x^{6} - 2x^{5} - 9x^{4} + 12x^{3} + 25x^{2} - 10x - 16 \)
|
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 1672) |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.2 | ||
Root | \(2.50058\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 3344.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | −1.50058 | −0.866358 | −0.433179 | − | 0.901308i | \(-0.642608\pi\) | ||||
−0.433179 | + | 0.901308i | \(0.642608\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −2.88388 | −1.28971 | −0.644856 | − | 0.764304i | \(-0.723082\pi\) | ||||
−0.644856 | + | 0.764304i | \(0.723082\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −1.88388 | −0.712040 | −0.356020 | − | 0.934478i | \(-0.615867\pi\) | ||||
−0.356020 | + | 0.934478i | \(0.615867\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −0.748274 | −0.249425 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 1.00000 | 0.301511 | ||||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −1.08333 | −0.300461 | −0.150231 | − | 0.988651i | \(-0.548002\pi\) | ||||
−0.150231 | + | 0.988651i | \(0.548002\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 4.32748 | 1.11735 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −4.80304 | −1.16491 | −0.582454 | − | 0.812864i | \(-0.697907\pi\) | ||||
−0.582454 | + | 0.812864i | \(0.697907\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −1.00000 | −0.229416 | ||||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 2.82691 | 0.616882 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −8.51652 | −1.77582 | −0.887909 | − | 0.460020i | \(-0.847842\pi\) | ||||
−0.887909 | + | 0.460020i | \(0.847842\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 3.31677 | 0.663355 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 5.62457 | 1.08245 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −7.97528 | −1.48097 | −0.740486 | − | 0.672071i | \(-0.765405\pi\) | ||||
−0.740486 | + | 0.672071i | \(0.765405\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 4.32748 | 0.777239 | 0.388619 | − | 0.921398i | \(-0.372952\pi\) | ||||
0.388619 | + | 0.921398i | \(0.372952\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −1.50058 | −0.261217 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 5.43289 | 0.918326 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −7.21003 | −1.18532 | −0.592661 | − | 0.805452i | \(-0.701923\pi\) | ||||
−0.592661 | + | 0.805452i | \(0.701923\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 1.62562 | 0.260307 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −8.45503 | −1.32045 | −0.660227 | − | 0.751066i | \(-0.729540\pi\) | ||||
−0.660227 | + | 0.751066i | \(0.729540\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −3.83075 | −0.584184 | −0.292092 | − | 0.956390i | \(-0.594351\pi\) | ||||
−0.292092 | + | 0.956390i | \(0.594351\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 2.15793 | 0.321686 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −4.50575 | −0.657232 | −0.328616 | − | 0.944464i | \(-0.606582\pi\) | ||||
−0.328616 | + | 0.944464i | \(0.606582\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −3.45099 | −0.492999 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 7.20732 | 1.00923 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −6.88436 | −0.945640 | −0.472820 | − | 0.881159i | \(-0.656764\pi\) | ||||
−0.472820 | + | 0.881159i | \(0.656764\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −2.88388 | −0.388863 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 1.50058 | 0.198756 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −1.50998 | −0.196583 | −0.0982913 | − | 0.995158i | \(-0.531338\pi\) | ||||
−0.0982913 | + | 0.995158i | \(0.531338\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 3.50460 | 0.448718 | 0.224359 | − | 0.974507i | \(-0.427971\pi\) | ||||
0.224359 | + | 0.974507i | \(0.427971\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 1.40966 | 0.177600 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 3.12419 | 0.387508 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 7.29221 | 0.890885 | 0.445442 | − | 0.895311i | \(-0.353046\pi\) | ||||
0.445442 | + | 0.895311i | \(0.353046\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 12.7797 | 1.53849 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 7.56562 | 0.897874 | 0.448937 | − | 0.893563i | \(-0.351803\pi\) | ||||
0.448937 | + | 0.893563i | \(0.351803\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 9.30612 | 1.08920 | 0.544600 | − | 0.838696i | \(-0.316682\pi\) | ||||
0.544600 | + | 0.838696i | \(0.316682\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −4.97707 | −0.574702 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −1.88388 | −0.214688 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −0.234538 | −0.0263876 | −0.0131938 | − | 0.999913i | \(-0.504200\pi\) | ||||
−0.0131938 | + | 0.999913i | \(0.504200\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −6.19527 | −0.688363 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 4.64910 | 0.510305 | 0.255153 | − | 0.966901i | \(-0.417874\pi\) | ||||
0.255153 | + | 0.966901i | \(0.417874\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 13.8514 | 1.50239 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 11.9675 | 1.28305 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −7.24132 | −0.767578 | −0.383789 | − | 0.923421i | \(-0.625381\pi\) | ||||
−0.383789 | + | 0.923421i | \(0.625381\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 2.04086 | 0.213940 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −6.49371 | −0.673367 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 2.88388 | 0.295880 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −8.05525 | −0.817886 | −0.408943 | − | 0.912560i | \(-0.634103\pi\) | ||||
−0.408943 | + | 0.912560i | \(0.634103\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −0.748274 | −0.0752043 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −6.06788 | −0.603777 | −0.301888 | − | 0.953343i | \(-0.597617\pi\) | ||||
−0.301888 | + | 0.953343i | \(0.597617\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −13.7616 | −1.35597 | −0.677987 | − | 0.735074i | \(-0.737147\pi\) | ||||
−0.677987 | + | 0.735074i | \(0.737147\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −8.15246 | −0.795599 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 3.53873 | 0.342102 | 0.171051 | − | 0.985262i | \(-0.445284\pi\) | ||||
0.171051 | + | 0.985262i | \(0.445284\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 5.68927 | 0.544933 | 0.272467 | − | 0.962165i | \(-0.412161\pi\) | ||||
0.272467 | + | 0.962165i | \(0.412161\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 10.8192 | 1.02691 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −5.78942 | −0.544623 | −0.272311 | − | 0.962209i | \(-0.587788\pi\) | ||||
−0.272311 | + | 0.962209i | \(0.587788\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 24.5606 | 2.29029 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0.810626 | 0.0749424 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 9.04835 | 0.829461 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 1.00000 | 0.0909091 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 12.6874 | 1.14399 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 4.85423 | 0.434175 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −9.09017 | −0.806622 | −0.403311 | − | 0.915063i | \(-0.632141\pi\) | ||||
−0.403311 | + | 0.915063i | \(0.632141\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 5.74833 | 0.506112 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 19.8530 | 1.73457 | 0.867283 | − | 0.497815i | \(-0.165864\pi\) | ||||
0.867283 | + | 0.497815i | \(0.165864\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 1.88388 | 0.163353 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −16.2206 | −1.39605 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 15.0136 | 1.28269 | 0.641347 | − | 0.767251i | \(-0.278376\pi\) | ||||
0.641347 | + | 0.767251i | \(0.278376\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −8.10427 | −0.687395 | −0.343698 | − | 0.939080i | \(-0.611679\pi\) | ||||
−0.343698 | + | 0.939080i | \(0.611679\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 6.76122 | 0.569398 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −1.08333 | −0.0905924 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 22.9998 | 1.91003 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 5.17847 | 0.427113 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 13.1339 | 1.07597 | 0.537986 | − | 0.842954i | \(-0.319185\pi\) | ||||
0.537986 | + | 0.842954i | \(0.319185\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 1.79627 | 0.146178 | 0.0730892 | − | 0.997325i | \(-0.476714\pi\) | ||||
0.0730892 | + | 0.997325i | \(0.476714\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 3.59399 | 0.290557 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −12.4799 | −1.00241 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 16.9881 | 1.35580 | 0.677898 | − | 0.735156i | \(-0.262891\pi\) | ||||
0.677898 | + | 0.735156i | \(0.262891\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 10.3305 | 0.819263 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 16.0441 | 1.26445 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 11.1884 | 0.876341 | 0.438170 | − | 0.898892i | \(-0.355627\pi\) | ||||
0.438170 | + | 0.898892i | \(0.355627\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 4.32748 | 0.336894 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −15.2962 | −1.18366 | −0.591828 | − | 0.806064i | \(-0.701593\pi\) | ||||
−0.591828 | + | 0.806064i | \(0.701593\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −11.8264 | −0.909723 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0.748274 | 0.0572219 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −10.0067 | −0.760798 | −0.380399 | − | 0.924822i | \(-0.624213\pi\) | ||||
−0.380399 | + | 0.924822i | \(0.624213\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −6.24841 | −0.472335 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 2.26584 | 0.170311 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 6.93780 | 0.518555 | 0.259278 | − | 0.965803i | \(-0.416516\pi\) | ||||
0.259278 | + | 0.965803i | \(0.416516\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 13.8801 | 1.03170 | 0.515851 | − | 0.856678i | \(-0.327476\pi\) | ||||
0.515851 | + | 0.856678i | \(0.327476\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −5.25892 | −0.388751 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 20.7929 | 1.52872 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −4.80304 | −0.351233 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −10.5960 | −0.770747 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 2.46370 | 0.178267 | 0.0891335 | − | 0.996020i | \(-0.471590\pi\) | ||||
0.0891335 | + | 0.996020i | \(0.471590\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 11.6753 | 0.840409 | 0.420204 | − | 0.907430i | \(-0.361958\pi\) | ||||
0.420204 | + | 0.907430i | \(0.361958\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −4.68808 | −0.335721 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −19.0357 | −1.35624 | −0.678119 | − | 0.734952i | \(-0.737205\pi\) | ||||
−0.678119 | + | 0.734952i | \(0.737205\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −6.26600 | −0.444185 | −0.222092 | − | 0.975026i | \(-0.571289\pi\) | ||||
−0.222092 | + | 0.975026i | \(0.571289\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −10.9425 | −0.771825 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 15.0245 | 1.05451 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 24.3833 | 1.70300 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 6.37269 | 0.442932 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −1.00000 | −0.0691714 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 20.8366 | 1.43445 | 0.717226 | − | 0.696840i | \(-0.245411\pi\) | ||||
0.717226 | + | 0.696840i | \(0.245411\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −11.3528 | −0.777880 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 11.0474 | 0.753429 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −8.15246 | −0.553425 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −13.9645 | −0.943636 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 5.20327 | 0.350010 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −27.9736 | −1.87325 | −0.936624 | − | 0.350337i | \(-0.886067\pi\) | ||||
−0.936624 | + | 0.350337i | \(0.886067\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −2.48185 | −0.165457 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 25.1395 | 1.66857 | 0.834283 | − | 0.551337i | \(-0.185882\pi\) | ||||
0.834283 | + | 0.551337i | \(0.185882\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 21.9050 | 1.44752 | 0.723762 | − | 0.690050i | \(-0.242411\pi\) | ||||
0.723762 | + | 0.690050i | \(0.242411\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 2.82691 | 0.185997 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −16.1431 | −1.05757 | −0.528783 | − | 0.848757i | \(-0.677352\pi\) | ||||
−0.528783 | + | 0.848757i | \(0.677352\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 12.9941 | 0.847639 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0.351942 | 0.0228611 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −0.996425 | −0.0644534 | −0.0322267 | − | 0.999481i | \(-0.510260\pi\) | ||||
−0.0322267 | + | 0.999481i | \(0.510260\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −22.6038 | −1.45604 | −0.728020 | − | 0.685556i | \(-0.759559\pi\) | ||||
−0.728020 | + | 0.685556i | \(0.759559\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −7.57724 | −0.486080 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 9.95225 | 0.635826 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 1.08333 | 0.0689305 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −6.97633 | −0.442107 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −23.7686 | −1.50026 | −0.750131 | − | 0.661290i | \(-0.770009\pi\) | ||||
−0.750131 | + | 0.661290i | \(0.770009\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −8.51652 | −0.535429 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −20.7851 | −1.30161 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −1.27407 | −0.0794741 | −0.0397371 | − | 0.999210i | \(-0.512652\pi\) | ||||
−0.0397371 | + | 0.999210i | \(0.512652\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 13.5828 | 0.843997 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 5.96769 | 0.369391 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −12.7381 | −0.785466 | −0.392733 | − | 0.919652i | \(-0.628470\pi\) | ||||
−0.392733 | + | 0.919652i | \(0.628470\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 19.8537 | 1.21960 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 10.8661 | 0.664997 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −7.92406 | −0.483139 | −0.241569 | − | 0.970384i | \(-0.577662\pi\) | ||||
−0.241569 | + | 0.970384i | \(0.577662\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −2.18100 | −0.132486 | −0.0662431 | − | 0.997804i | \(-0.521101\pi\) | ||||
−0.0662431 | + | 0.997804i | \(0.521101\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −3.06247 | −0.185349 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 3.31677 | 0.200009 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −13.3873 | −0.804364 | −0.402182 | − | 0.915560i | \(-0.631748\pi\) | ||||
−0.402182 | + | 0.915560i | \(0.631748\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −3.23814 | −0.193862 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 22.5787 | 1.34693 | 0.673465 | − | 0.739219i | \(-0.264805\pi\) | ||||
0.673465 | + | 0.739219i | \(0.264805\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −14.1317 | −0.840044 | −0.420022 | − | 0.907514i | \(-0.637978\pi\) | ||||
−0.420022 | + | 0.907514i | \(0.637978\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −4.32748 | −0.256338 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 15.9283 | 0.940217 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 6.06917 | 0.357010 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 12.0875 | 0.708582 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −12.0224 | −0.702355 | −0.351178 | − | 0.936309i | \(-0.614219\pi\) | ||||
−0.351178 | + | 0.936309i | \(0.614219\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 4.35460 | 0.253535 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 5.62457 | 0.326370 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 9.22619 | 0.533564 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 7.21668 | 0.415963 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 9.10531 | 0.523087 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −10.1069 | −0.578717 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −25.2989 | −1.44388 | −0.721941 | − | 0.691954i | \(-0.756750\pi\) | ||||
−0.721941 | + | 0.691954i | \(0.756750\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 20.6504 | 1.17476 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −16.6945 | −0.946657 | −0.473328 | − | 0.880886i | \(-0.656948\pi\) | ||||
−0.473328 | + | 0.880886i | \(0.656948\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −8.39640 | −0.474593 | −0.237296 | − | 0.971437i | \(-0.576261\pi\) | ||||
−0.237296 | + | 0.971437i | \(0.576261\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −4.06529 | −0.229053 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 10.9712 | 0.616206 | 0.308103 | − | 0.951353i | \(-0.400306\pi\) | ||||
0.308103 | + | 0.951353i | \(0.400306\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −7.97528 | −0.446530 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −5.31013 | −0.296382 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 4.80304 | 0.267248 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −3.59315 | −0.199312 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −8.53718 | −0.472107 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 8.48831 | 0.467976 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 18.8667 | 1.03701 | 0.518504 | − | 0.855075i | \(-0.326489\pi\) | ||||
0.518504 | + | 0.855075i | \(0.326489\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 5.39508 | 0.295648 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −21.0299 | −1.14898 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 18.4177 | 1.00327 | 0.501637 | − | 0.865078i | \(-0.332731\pi\) | ||||
0.501637 | + | 0.865078i | \(0.332731\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 8.68746 | 0.471838 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 4.32748 | 0.234346 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 19.6884 | 1.06308 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −36.8551 | −1.98421 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 5.74801 | 0.308570 | 0.154285 | − | 0.988026i | \(-0.450693\pi\) | ||||
0.154285 | + | 0.988026i | \(0.450693\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −34.4243 | −1.84269 | −0.921346 | − | 0.388744i | \(-0.872909\pi\) | ||||
−0.921346 | + | 0.388744i | \(0.872909\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −6.09325 | −0.325234 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 8.11721 | 0.432035 | 0.216018 | − | 0.976389i | \(-0.430693\pi\) | ||||
0.216018 | + | 0.976389i | \(0.430693\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −21.8184 | −1.15800 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −13.5777 | −0.718610 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 23.0264 | 1.21529 | 0.607645 | − | 0.794209i | \(-0.292114\pi\) | ||||
0.607645 | + | 0.794209i | \(0.292114\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 1.00000 | 0.0526316 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −1.50058 | −0.0787598 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −26.8378 | −1.40475 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −21.1810 | −1.10564 | −0.552821 | − | 0.833300i | \(-0.686449\pi\) | ||||
−0.552821 | + | 0.833300i | \(0.686449\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 6.32668 | 0.329354 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 12.9693 | 0.673334 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 7.78939 | 0.403320 | 0.201660 | − | 0.979456i | \(-0.435366\pi\) | ||||
0.201660 | + | 0.979456i | \(0.435366\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −7.28413 | −0.376151 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 8.63985 | 0.444975 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 16.7545 | 0.860619 | 0.430309 | − | 0.902681i | \(-0.358404\pi\) | ||||
0.430309 | + | 0.902681i | \(0.358404\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 13.6405 | 0.698823 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 23.7500 | 1.21357 | 0.606785 | − | 0.794866i | \(-0.292459\pi\) | ||||
0.606785 | + | 0.794866i | \(0.292459\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 5.43289 | 0.276886 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 2.86645 | 0.145710 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 0.00246725 | 0.000125095 0 | 6.25473e−5 | − | 1.00000i | \(-0.499980\pi\) | ||||
6.25473e−5 | 1.00000i | \(0.499980\pi\) | ||||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 40.9052 | 2.06866 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −29.7910 | −1.50276 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 0.676380 | 0.0340324 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 35.4514 | 1.77926 | 0.889628 | − | 0.456687i | \(-0.150964\pi\) | ||||
0.889628 | + | 0.456687i | \(0.150964\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −2.82691 | −0.141522 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −14.6214 | −0.730157 | −0.365078 | − | 0.930977i | \(-0.618958\pi\) | ||||
−0.365078 | + | 0.930977i | \(0.618958\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −4.68808 | −0.233530 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 17.8664 | 0.887789 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −7.21003 | −0.357388 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −6.49695 | −0.321254 | −0.160627 | − | 0.987015i | \(-0.551352\pi\) | ||||
−0.160627 | + | 0.987015i | \(0.551352\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −22.5290 | −1.11127 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 2.84462 | 0.139975 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −13.4075 | −0.658146 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 12.1611 | 0.595530 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −26.1834 | −1.27914 | −0.639571 | − | 0.768732i | \(-0.720888\pi\) | ||||
−0.639571 | + | 0.768732i | \(0.720888\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −5.45746 | −0.265980 | −0.132990 | − | 0.991117i | \(-0.542458\pi\) | ||||
−0.132990 | + | 0.991117i | \(0.542458\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 3.37154 | 0.163930 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −15.9306 | −0.772747 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −6.60226 | −0.319506 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 1.62562 | 0.0784854 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −18.2241 | −0.877823 | −0.438912 | − | 0.898530i | \(-0.644636\pi\) | ||||
−0.438912 | + | 0.898530i | \(0.644636\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −13.9249 | −0.669188 | −0.334594 | − | 0.942362i | \(-0.608599\pi\) | ||||
−0.334594 | + | 0.942362i | \(0.608599\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −34.5129 | −1.65477 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 8.51652 | 0.407400 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 4.64620 | 0.221751 | 0.110876 | − | 0.993834i | \(-0.464634\pi\) | ||||
0.110876 | + | 0.993834i | \(0.464634\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 2.58229 | 0.122966 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −26.6366 | −1.26554 | −0.632771 | − | 0.774339i | \(-0.718083\pi\) | ||||
−0.632771 | + | 0.774339i | \(0.718083\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 20.8831 | 0.989954 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −19.7084 | −0.932176 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 30.5263 | 1.44063 | 0.720314 | − | 0.693649i | \(-0.243998\pi\) | ||||
0.720314 | + | 0.693649i | \(0.243998\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −8.45503 | −0.398132 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −2.69544 | −0.126643 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −5.88560 | −0.275921 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −24.1980 | −1.13194 | −0.565968 | − | 0.824427i | \(-0.691497\pi\) | ||||
−0.565968 | + | 0.824427i | \(0.691497\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −27.0150 | −1.26095 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 16.1065 | 0.750153 | 0.375076 | − | 0.926994i | \(-0.377616\pi\) | ||||
0.375076 | + | 0.926994i | \(0.377616\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 29.7887 | 1.38440 | 0.692200 | − | 0.721705i | \(-0.256641\pi\) | ||||
0.692200 | + | 0.721705i | \(0.256641\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 18.7271 | 0.868448 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −33.9385 | −1.57049 | −0.785244 | − | 0.619187i | \(-0.787462\pi\) | ||||
−0.785244 | + | 0.619187i | \(0.787462\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −13.7377 | −0.634346 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −25.4919 | −1.17460 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −3.83075 | −0.176138 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −3.31677 | −0.152184 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 5.15139 | 0.235866 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 3.50720 | 0.160248 | 0.0801241 | − | 0.996785i | \(-0.474468\pi\) | ||||
0.0801241 | + | 0.996785i | \(0.474468\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 7.81083 | 0.356143 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −24.0754 | −1.09547 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 23.2304 | 1.05484 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −32.6977 | −1.48168 | −0.740838 | − | 0.671684i | \(-0.765571\pi\) | ||||
−0.740838 | + | 0.671684i | \(0.765571\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −16.7890 | −0.759225 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 29.9128 | 1.34995 | 0.674973 | − | 0.737842i | \(-0.264155\pi\) | ||||
0.674973 | + | 0.737842i | \(0.264155\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 38.3056 | 1.72520 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 2.15793 | 0.0969919 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −14.2527 | −0.639323 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 23.2622 | 1.04136 | 0.520680 | − | 0.853752i | \(-0.325679\pi\) | ||||
0.520680 | + | 0.853752i | \(0.325679\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 22.9531 | 1.02547 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −7.52711 | −0.335617 | −0.167809 | − | 0.985820i | \(-0.553669\pi\) | ||||
−0.167809 | + | 0.985820i | \(0.553669\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 17.4991 | 0.778698 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 17.7464 | 0.788145 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −24.4275 | −1.08273 | −0.541365 | − | 0.840788i | \(-0.682092\pi\) | ||||
−0.541365 | + | 0.840788i | \(0.682092\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −17.5316 | −0.775554 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −5.62457 | −0.248331 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 39.6869 | 1.74881 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −4.50575 | −0.198163 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 15.0159 | 0.659123 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −39.7937 | −1.74339 | −0.871697 | − | 0.490045i | \(-0.836980\pi\) | ||||
−0.871697 | + | 0.490045i | \(0.836980\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 13.4389 | 0.587640 | 0.293820 | − | 0.955861i | \(-0.405073\pi\) | ||||
0.293820 | + | 0.955861i | \(0.405073\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 9.37621 | 0.409211 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −20.7851 | −0.905411 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 49.5311 | 2.15353 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 1.12988 | 0.0490325 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 9.15958 | 0.396745 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −10.2053 | −0.441212 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −10.4107 | −0.449254 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −3.45099 | −0.148645 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 1.49194 | 0.0641437 | 0.0320719 | − | 0.999486i | \(-0.489789\pi\) | ||||
0.0320719 | + | 0.999486i | \(0.489789\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −20.8282 | −0.893823 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −16.4072 | −0.702807 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 10.2877 | 0.439869 | 0.219934 | − | 0.975515i | \(-0.429416\pi\) | ||||
0.219934 | + | 0.975515i | \(0.429416\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −2.62240 | −0.111921 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 7.97528 | 0.339758 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 0.441842 | 0.0187890 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −31.2013 | −1.32442 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −39.2207 | −1.66184 | −0.830918 | − | 0.556395i | \(-0.812184\pi\) | ||||
−0.830918 | + | 0.556395i | \(0.812184\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 4.14996 | 0.175525 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 7.20732 | 0.304293 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −40.1331 | −1.69141 | −0.845705 | − | 0.533650i | \(-0.820820\pi\) | ||||
−0.845705 | + | 0.533650i | \(0.820820\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 16.6960 | 0.702406 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 11.6711 | 0.490142 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −33.6336 | −1.40999 | −0.704997 | − | 0.709210i | \(-0.749052\pi\) | ||||
−0.704997 | + | 0.709210i | \(0.749052\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 1.25726 | 0.0526145 | 0.0263073 | − | 0.999654i | \(-0.491625\pi\) | ||||
0.0263073 | + | 0.999654i | \(0.491625\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −3.69697 | −0.154443 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −28.2474 | −1.17800 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 47.2793 | 1.96826 | 0.984132 | − | 0.177437i | \(-0.0567806\pi\) | ||||
0.984132 | + | 0.177437i | \(0.0567806\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −17.5197 | −0.728094 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −8.75836 | −0.363358 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −6.88436 | −0.285121 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −2.33775 | −0.0966540 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −29.6527 | −1.22390 | −0.611950 | − | 0.790897i | \(-0.709615\pi\) | ||||
−0.611950 | + | 0.790897i | \(0.709615\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −4.32748 | −0.178311 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 28.5645 | 1.17499 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 24.3518 | 1.00001 | 0.500003 | − | 0.866023i | \(-0.333332\pi\) | ||||
0.500003 | + | 0.866023i | \(0.333332\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −26.0944 | −1.06977 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 9.40260 | 0.384823 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −30.3821 | −1.24138 | −0.620690 | − | 0.784056i | \(-0.713148\pi\) | ||||
−0.620690 | + | 0.784056i | \(0.713148\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −9.07411 | −0.370140 | −0.185070 | − | 0.982725i | \(-0.559251\pi\) | ||||
−0.185070 | + | 0.982725i | \(0.559251\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −5.45657 | −0.222209 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −2.88388 | −0.117246 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 35.6353 | 1.44639 | 0.723196 | − | 0.690643i | \(-0.242672\pi\) | ||||
0.723196 | + | 0.690643i | \(0.242672\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −22.5454 | −0.913585 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 4.88121 | 0.197473 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −17.3009 | −0.698777 | −0.349388 | − | 0.936978i | \(-0.613611\pi\) | ||||
−0.349388 | + | 0.936978i | \(0.613611\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −36.5890 | −1.47541 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −15.7903 | −0.635695 | −0.317847 | − | 0.948142i | \(-0.602960\pi\) | ||||
−0.317847 | + | 0.948142i | \(0.602960\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 20.2011 | 0.811950 | 0.405975 | − | 0.913884i | \(-0.366932\pi\) | ||||
0.405975 | + | 0.913884i | \(0.366932\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −47.9017 | −1.92223 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 13.6418 | 0.546547 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −30.5829 | −1.22332 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 1.50058 | 0.0599272 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 34.6300 | 1.38079 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −1.49437 | −0.0594900 | −0.0297450 | − | 0.999558i | \(-0.509470\pi\) | ||||
−0.0297450 | + | 0.999558i | \(0.509470\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −31.2669 | −1.24275 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 26.2150 | 1.04031 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 3.73855 | 0.148127 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −5.66116 | −0.223952 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 18.8967 | 0.746377 | 0.373188 | − | 0.927756i | \(-0.378265\pi\) | ||||
0.373188 | + | 0.927756i | \(0.378265\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 28.4030 | 1.12011 | 0.560053 | − | 0.828457i | \(-0.310781\pi\) | ||||
0.560053 | + | 0.828457i | \(0.310781\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −16.5775 | −0.652739 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 21.5350 | 0.846630 | 0.423315 | − | 0.905983i | \(-0.360866\pi\) | ||||
0.423315 | + | 0.905983i | \(0.360866\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −1.50998 | −0.0592719 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 12.2334 | 0.479464 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 16.2729 | 0.636808 | 0.318404 | − | 0.947955i | \(-0.396853\pi\) | ||||
0.318404 | + | 0.947955i | \(0.396853\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −57.2538 | −2.23709 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −6.96353 | −0.271673 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −4.66279 | −0.181637 | −0.0908183 | − | 0.995867i | \(-0.528948\pi\) | ||||
−0.0908183 | + | 0.995867i | \(0.528948\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −23.1724 | −0.901304 | −0.450652 | − | 0.892700i | \(-0.648808\pi\) | ||||
−0.450652 | + | 0.892700i | \(0.648808\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −7.80789 | −0.303233 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −5.43289 | −0.210678 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 67.9216 | 2.62994 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 41.9764 | 1.62290 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 3.50460 | 0.135294 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 46.2401 | 1.78242 | 0.891212 | − | 0.453588i | \(-0.149856\pi\) | ||||
0.891212 | + | 0.453588i | \(0.149856\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 18.6554 | 0.718047 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −33.6361 | −1.29274 | −0.646370 | − | 0.763024i | \(-0.723714\pi\) | ||||
−0.646370 | + | 0.763024i | \(0.723714\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 15.1751 | 0.582368 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −37.7237 | −1.44557 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 4.79055 | 0.183305 | 0.0916526 | − | 0.995791i | \(-0.470785\pi\) | ||||
0.0916526 | + | 0.995791i | \(0.470785\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −43.2973 | −1.65430 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −32.8701 | −1.25407 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 7.45803 | 0.284128 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 16.4497 | 0.625777 | 0.312888 | − | 0.949790i | \(-0.398703\pi\) | ||||
0.312888 | + | 0.949790i | \(0.398703\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 1.40966 | 0.0535485 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 23.3718 | 0.886541 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 40.6098 | 1.53821 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 24.2239 | 0.916231 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −32.6582 | −1.23348 | −0.616742 | − | 0.787165i | \(-0.711548\pi\) | ||||
−0.616742 | + | 0.787165i | \(0.711548\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 7.21003 | 0.271931 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −19.4986 | −0.734359 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 11.4312 | 0.429913 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −14.2212 | −0.534090 | −0.267045 | − | 0.963684i | \(-0.586047\pi\) | ||||
−0.267045 | + | 0.963684i | \(0.586047\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0.175499 | 0.00658172 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −36.8551 | −1.38023 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 3.12419 | 0.116838 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 1.49521 | 0.0558397 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −26.9647 | −1.00561 | −0.502807 | − | 0.864399i | \(-0.667699\pi\) | ||||
−0.502807 | + | 0.864399i | \(0.667699\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 25.9253 | 0.965508 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 33.9187 | 1.26145 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −26.4522 | −0.982410 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 21.4897 | 0.797008 | 0.398504 | − | 0.917167i | \(-0.369529\pi\) | ||||
0.398504 | + | 0.917167i | \(0.369529\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 29.9560 | 1.10948 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 18.3992 | 0.680521 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −49.5639 | −1.83069 | −0.915343 | − | 0.402676i | \(-0.868080\pi\) | ||||
−0.915343 | + | 0.402676i | \(0.868080\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | −14.9341 | −0.550852 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 7.29221 | 0.268612 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −32.5018 | −1.19560 | −0.597800 | − | 0.801646i | \(-0.703958\pi\) | ||||
−0.597800 | + | 0.801646i | \(0.703958\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −1.62562 | −0.0597185 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −23.7010 | −0.869506 | −0.434753 | − | 0.900550i | \(-0.643164\pi\) | ||||
−0.434753 | + | 0.900550i | \(0.643164\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −37.8766 | −1.38769 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −3.47880 | −0.127283 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −6.66654 | −0.243590 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 40.5798 | 1.48078 | 0.740388 | − | 0.672179i | \(-0.234642\pi\) | ||||
0.740388 | + | 0.672179i | \(0.234642\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 35.6666 | 1.29976 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −5.18023 | −0.188528 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −29.9224 | −1.08755 | −0.543773 | − | 0.839232i | \(-0.683005\pi\) | ||||
−0.543773 | + | 0.839232i | \(0.683005\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 12.7797 | 0.463873 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −23.8651 | −0.865108 | −0.432554 | − | 0.901608i | \(-0.642388\pi\) | ||||
−0.432554 | + | 0.901608i | \(0.642388\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −10.7179 | −0.388015 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −10.3646 | −0.374734 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 1.63580 | 0.0590655 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 35.3464 | 1.27463 | 0.637313 | − | 0.770605i | \(-0.280046\pi\) | ||||
0.637313 | + | 0.770605i | \(0.280046\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 1.91183 | 0.0688530 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −48.9820 | −1.76176 | −0.880880 | − | 0.473340i | \(-0.843048\pi\) | ||||
−0.880880 | + | 0.473340i | \(0.843048\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 14.3533 | 0.515585 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −20.3821 | −0.731203 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 8.45503 | 0.302933 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 7.56562 | 0.270719 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −44.8575 | −1.60308 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −48.9916 | −1.74859 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 8.01895 | 0.285845 | 0.142922 | − | 0.989734i | \(-0.454350\pi\) | ||||
0.142922 | + | 0.989734i | \(0.454350\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 19.1145 | 0.680495 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 10.9066 | 0.387793 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −3.79664 | −0.134822 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −29.7920 | −1.05661 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −22.9829 | −0.814096 | −0.407048 | − | 0.913407i | \(-0.633442\pi\) | ||||
−0.407048 | + | 0.913407i | \(0.633442\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 21.6413 | 0.765614 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 5.41849 | 0.191453 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 9.30612 | 0.328406 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −46.2693 | −1.63078 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 11.8907 | 0.418571 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 23.7249 | 0.834122 | 0.417061 | − | 0.908878i | \(-0.363060\pi\) | ||||
0.417061 | + | 0.908878i | \(0.363060\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −15.1527 | −0.532083 | −0.266042 | − | 0.963962i | \(-0.585716\pi\) | ||||
−0.266042 | + | 0.963962i | \(0.585716\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 3.27275 | 0.114780 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −32.2659 | −1.13023 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 3.83075 | 0.134021 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −1.52712 | −0.0533620 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −39.3391 | −1.37295 | −0.686473 | − | 0.727155i | \(-0.740842\pi\) | ||||
−0.686473 | + | 0.727155i | \(0.740842\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 8.43831 | 0.294141 | 0.147071 | − | 0.989126i | \(-0.453016\pi\) | ||||
0.147071 | + | 0.989126i | \(0.453016\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −4.97707 | −0.173279 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 9.58576 | 0.333330 | 0.166665 | − | 0.986014i | \(-0.446700\pi\) | ||||
0.166665 | + | 0.986014i | \(0.446700\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −12.3387 | −0.428540 | −0.214270 | − | 0.976775i | \(-0.568737\pi\) | ||||
−0.214270 | + | 0.976775i | \(0.568737\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 20.0886 | 0.696867 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 16.5752 | 0.574298 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 44.1124 | 1.52657 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 24.3402 | 0.841321 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −19.5182 | −0.673844 | −0.336922 | − | 0.941533i | \(-0.609386\pi\) | ||||
−0.336922 | + | 0.941533i | \(0.609386\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 34.6051 | 1.19328 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −33.8810 | −1.16692 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 34.1059 | 1.17328 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −1.88388 | −0.0647309 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 21.2057 | 0.727778 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 61.4044 | 2.10491 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −32.0583 | −1.09766 | −0.548828 | − | 0.835935i | \(-0.684926\pi\) | ||||
−0.548828 | + | 0.835935i | \(0.684926\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −2.15793 | −0.0737997 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 3.94409 | 0.134728 | 0.0673639 | − | 0.997728i | \(-0.478541\pi\) | ||||
0.0673639 | + | 0.997728i | \(0.478541\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −19.0054 | −0.648455 | −0.324227 | − | 0.945979i | \(-0.605104\pi\) | ||||
−0.324227 | + | 0.945979i | \(0.605104\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −23.9016 | −0.814564 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 14.9638 | 0.509373 | 0.254687 | − | 0.967024i | \(-0.418028\pi\) | ||||
0.254687 | + | 0.967024i | \(0.418028\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 28.8582 | 0.981210 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −9.10725 | −0.309298 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −0.234538 | −0.00795616 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −7.89985 | −0.267676 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 6.02753 | 0.204001 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −9.14479 | −0.309150 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −49.9928 | −1.68814 | −0.844068 | − | 0.536237i | \(-0.819846\pi\) | ||||
−0.844068 | + | 0.536237i | \(0.819846\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 18.0405 | 0.608491 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −45.5061 | −1.53314 | −0.766570 | − | 0.642160i | \(-0.778038\pi\) | ||||
−0.766570 | + | 0.642160i | \(0.778038\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −16.3052 | −0.548715 | −0.274357 | − | 0.961628i | \(-0.588465\pi\) | ||||
−0.274357 | + | 0.961628i | \(0.588465\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −6.53441 | −0.219652 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 26.9400 | 0.904556 | 0.452278 | − | 0.891877i | \(-0.350611\pi\) | ||||
0.452278 | + | 0.891877i | \(0.350611\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 17.1248 | 0.574347 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −6.19527 | −0.207549 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 4.50575 | 0.150779 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −20.0078 | −0.668786 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −13.8446 | −0.462257 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −34.5129 | −1.15107 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 33.0659 | 1.10158 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −10.8292 | −0.360372 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −40.0287 | −1.33060 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −34.1279 | −1.13320 | −0.566600 | − | 0.823993i | \(-0.691742\pi\) | ||||
−0.566600 | + | 0.823993i | \(0.691742\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 4.54044 | 0.150597 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −47.0120 | −1.55758 | −0.778789 | − | 0.627286i | \(-0.784166\pi\) | ||||
−0.778789 | + | 0.627286i | \(0.784166\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 4.64910 | 0.153863 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 15.1661 | 0.501376 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −37.4007 | −1.23508 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 30.5621 | 1.00815 | 0.504075 | − | 0.863660i | \(-0.331833\pi\) | ||||
0.504075 | + | 0.863660i | \(0.331833\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 37.9629 | 1.25092 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −8.19605 | −0.269776 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −23.9140 | −0.786289 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 10.2975 | 0.338213 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −28.7378 | −0.942855 | −0.471428 | − | 0.881905i | \(-0.656261\pi\) | ||||
−0.471428 | + | 0.881905i | \(0.656261\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 3.45099 | 0.113102 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 25.0513 | 0.820143 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 13.8514 | 0.452989 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −39.3706 | −1.28618 | −0.643091 | − | 0.765789i | \(-0.722348\pi\) | ||||
−0.643091 | + | 0.765789i | \(0.722348\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 12.5994 | 0.411167 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 26.0169 | 0.848127 | 0.424064 | − | 0.905632i | \(-0.360603\pi\) | ||||
0.424064 | + | 0.905632i | \(0.360603\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 72.0075 | 2.34489 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 30.5577 | 0.994041 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 48.2165 | 1.56683 | 0.783413 | − | 0.621502i | \(-0.213477\pi\) | ||||
0.783413 | + | 0.621502i | \(0.213477\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −10.0816 | −0.327262 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −16.4632 | −0.533855 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 20.4822 | 0.663483 | 0.331741 | − | 0.943370i | \(-0.392364\pi\) | ||||
0.331741 | + | 0.943370i | \(0.392364\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −7.10502 | −0.229913 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 11.9675 | 0.386855 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −28.2838 | −0.913330 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −12.2729 | −0.395900 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −2.64794 | −0.0853286 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −33.6703 | −1.08388 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −21.7691 | −0.700046 | −0.350023 | − | 0.936741i | \(-0.613826\pi\) | ||||
−0.350023 | + | 0.936741i | \(0.613826\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −7.20732 | −0.231532 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −18.5628 | −0.595708 | −0.297854 | − | 0.954611i | \(-0.596271\pi\) | ||||
−0.297854 | + | 0.954611i | \(0.596271\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 15.2675 | 0.489453 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 5.39180 | 0.172676 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 10.8339 | 0.346607 | 0.173303 | − | 0.984868i | \(-0.444556\pi\) | ||||
0.173303 | + | 0.984868i | \(0.444556\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −7.24132 | −0.231434 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −4.25713 | −0.135920 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 11.6111 | 0.370336 | 0.185168 | − | 0.982707i | \(-0.440717\pi\) | ||||
0.185168 | + | 0.982707i | \(0.440717\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 54.8967 | 1.74916 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −12.7373 | −0.405434 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 32.6247 | 1.03740 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 34.1635 | 1.08524 | 0.542620 | − | 0.839978i | \(-0.317432\pi\) | ||||
0.542620 | + | 0.839978i | \(0.317432\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −28.3109 | −0.898421 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 18.0704 | 0.572870 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −13.4776 | −0.426838 | −0.213419 | − | 0.976961i | \(-0.568460\pi\) | ||||
−0.213419 | + | 0.976961i | \(0.568460\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −40.5533 | −1.28305 |
(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 | 3344.2.a.z.1.2 | 6 | ||
4.3 | odd | 2 | 1672.2.a.i.1.5 | ✓ | 6 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1672.2.a.i.1.5 | ✓ | 6 | 4.3 | odd | 2 | ||
3344.2.a.z.1.2 | 6 | 1.1 | even | 1 | trivial |