Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [4016,2,Mod(1,4016)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(4016, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("4016.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 4016 = 2^{4} \cdot 251 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 4016.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: | \(32.0679214517\) |
Analytic rank: | \(1\) |
Dimension: | \(6\) |
Coefficient field: | 6.6.60853001.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{6} - 3x^{5} - 8x^{4} + 15x^{3} + 20x^{2} - 12x - 5 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 502) |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.4 | ||
Root | \(-0.303212\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 4016.1 |
$q$-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 | ||||||||
\(3\) | 1.63228 | 0.942400 | 0.471200 | − | 0.882026i | \(-0.343821\pi\) | ||||
0.471200 | + | 0.882026i | \(0.343821\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 2.87032 | 1.28364 | 0.641822 | − | 0.766854i | \(-0.278179\pi\) | ||||
0.641822 | + | 0.766854i | \(0.278179\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −4.63886 | −1.75332 | −0.876662 | − | 0.481107i | \(-0.840235\pi\) | ||||
−0.876662 | + | 0.481107i | \(0.840235\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −0.335646 | −0.111882 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 2.30164 | 0.693970 | 0.346985 | − | 0.937871i | \(-0.387206\pi\) | ||||
0.346985 | + | 0.937871i | \(0.387206\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −5.47674 | −1.51897 | −0.759487 | − | 0.650522i | \(-0.774550\pi\) | ||||
−0.759487 | + | 0.650522i | \(0.774550\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 4.68517 | 1.20971 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 3.36682 | 0.816574 | 0.408287 | − | 0.912854i | \(-0.366126\pi\) | ||||
0.408287 | + | 0.912854i | \(0.366126\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −6.90916 | −1.58507 | −0.792535 | − | 0.609826i | \(-0.791239\pi\) | ||||
−0.792535 | + | 0.609826i | \(0.791239\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −7.57194 | −1.65233 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 0.413133 | 0.0861442 | 0.0430721 | − | 0.999072i | \(-0.486285\pi\) | ||||
0.0430721 | + | 0.999072i | \(0.486285\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 3.23871 | 0.647742 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −5.44472 | −1.04784 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 3.71261 | 0.689414 | 0.344707 | − | 0.938710i | \(-0.387978\pi\) | ||||
0.344707 | + | 0.938710i | \(0.387978\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 4.81396 | 0.864613 | 0.432306 | − | 0.901727i | \(-0.357700\pi\) | ||||
0.432306 | + | 0.901727i | \(0.357700\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 3.75693 | 0.653997 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −13.3150 | −2.25064 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −9.04384 | −1.48680 | −0.743399 | − | 0.668848i | \(-0.766788\pi\) | ||||
−0.743399 | + | 0.668848i | \(0.766788\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −8.93960 | −1.43148 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −1.24070 | −0.193765 | −0.0968826 | − | 0.995296i | \(-0.530887\pi\) | ||||
−0.0968826 | + | 0.995296i | \(0.530887\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −5.17421 | −0.789059 | −0.394530 | − | 0.918883i | \(-0.629092\pi\) | ||||
−0.394530 | + | 0.918883i | \(0.629092\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −0.963410 | −0.143617 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −3.72748 | −0.543709 | −0.271855 | − | 0.962338i | \(-0.587637\pi\) | ||||
−0.271855 | + | 0.962338i | \(0.587637\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 14.5190 | 2.07414 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 5.49561 | 0.769539 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −4.50833 | −0.619267 | −0.309633 | − | 0.950856i | \(-0.600206\pi\) | ||||
−0.309633 | + | 0.950856i | \(0.600206\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 6.60642 | 0.890810 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −11.2777 | −1.49377 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 10.3879 | 1.35239 | 0.676194 | − | 0.736723i | \(-0.263628\pi\) | ||||
0.676194 | + | 0.736723i | \(0.263628\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −7.69836 | −0.985674 | −0.492837 | − | 0.870122i | \(-0.664040\pi\) | ||||
−0.492837 | + | 0.870122i | \(0.664040\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 1.55701 | 0.196165 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −15.7200 | −1.94982 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 12.5478 | 1.53295 | 0.766477 | − | 0.642272i | \(-0.222008\pi\) | ||||
0.766477 | + | 0.642272i | \(0.222008\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0.674351 | 0.0811823 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −16.5669 | −1.96613 | −0.983064 | − | 0.183260i | \(-0.941335\pi\) | ||||
−0.983064 | + | 0.183260i | \(0.941335\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −8.59665 | −1.00616 | −0.503081 | − | 0.864239i | \(-0.667800\pi\) | ||||
−0.503081 | + | 0.864239i | \(0.667800\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 5.28650 | 0.610432 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −10.6770 | −1.21675 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −0.0752223 | −0.00846317 | −0.00423159 | − | 0.999991i | \(-0.501347\pi\) | ||||
−0.00423159 | + | 0.999991i | \(0.501347\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −7.88040 | −0.875600 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −9.54676 | −1.04789 | −0.523946 | − | 0.851751i | \(-0.675541\pi\) | ||||
−0.523946 | + | 0.851751i | \(0.675541\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 9.66383 | 1.04819 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 6.06003 | 0.649704 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −17.0363 | −1.80585 | −0.902924 | − | 0.429801i | \(-0.858584\pi\) | ||||
−0.902924 | + | 0.429801i | \(0.858584\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 25.4058 | 2.66325 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 7.85776 | 0.814811 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −19.8315 | −2.03467 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 16.0360 | 1.62821 | 0.814103 | − | 0.580721i | \(-0.197229\pi\) | ||||
0.814103 | + | 0.580721i | \(0.197229\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −0.772535 | −0.0776427 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −11.7563 | −1.16980 | −0.584900 | − | 0.811105i | \(-0.698866\pi\) | ||||
−0.584900 | + | 0.811105i | \(0.698866\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 11.1363 | 1.09729 | 0.548647 | − | 0.836054i | \(-0.315143\pi\) | ||||
0.548647 | + | 0.836054i | \(0.315143\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −21.7339 | −2.12101 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 3.44009 | 0.332566 | 0.166283 | − | 0.986078i | \(-0.446823\pi\) | ||||
0.166283 | + | 0.986078i | \(0.446823\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −9.11018 | −0.872597 | −0.436298 | − | 0.899802i | \(-0.643711\pi\) | ||||
−0.436298 | + | 0.899802i | \(0.643711\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −14.7621 | −1.40116 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −6.31389 | −0.593961 | −0.296980 | − | 0.954884i | \(-0.595980\pi\) | ||||
−0.296980 | + | 0.954884i | \(0.595980\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 1.18582 | 0.110579 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 1.83825 | 0.169946 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −15.6182 | −1.43172 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −5.70247 | −0.518406 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −2.02518 | −0.182604 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −5.05546 | −0.452174 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −0.0794803 | −0.00705274 | −0.00352637 | − | 0.999994i | \(-0.501122\pi\) | ||||
−0.00352637 | + | 0.999994i | \(0.501122\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −8.44578 | −0.743609 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −2.53326 | −0.221332 | −0.110666 | − | 0.993858i | \(-0.535298\pi\) | ||||
−0.110666 | + | 0.993858i | \(0.535298\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 32.0506 | 2.77914 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −15.6281 | −1.34505 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 9.81927 | 0.838917 | 0.419459 | − | 0.907774i | \(-0.362220\pi\) | ||||
0.419459 | + | 0.907774i | \(0.362220\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −9.23340 | −0.783167 | −0.391584 | − | 0.920143i | \(-0.628073\pi\) | ||||
−0.391584 | + | 0.920143i | \(0.628073\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −6.08431 | −0.512392 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −12.6055 | −1.05412 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 10.6564 | 0.884962 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 23.6992 | 1.95467 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 12.9714 | 1.06266 | 0.531329 | − | 0.847166i | \(-0.321693\pi\) | ||||
0.531329 | + | 0.847166i | \(0.321693\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −20.6481 | −1.68032 | −0.840158 | − | 0.542342i | \(-0.817538\pi\) | ||||
−0.840158 | + | 0.542342i | \(0.817538\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −1.13006 | −0.0913599 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 13.8176 | 1.10986 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −9.18457 | −0.733008 | −0.366504 | − | 0.930416i | \(-0.619445\pi\) | ||||
−0.366504 | + | 0.930416i | \(0.619445\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −7.35888 | −0.583597 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −1.91647 | −0.151039 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 16.9288 | 1.32597 | 0.662984 | − | 0.748633i | \(-0.269290\pi\) | ||||
0.662984 | + | 0.748633i | \(0.269290\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 10.7836 | 0.839500 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 1.88414 | 0.145799 | 0.0728996 | − | 0.997339i | \(-0.476775\pi\) | ||||
0.0728996 | + | 0.997339i | \(0.476775\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 16.9947 | 1.30728 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 2.31903 | 0.177341 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −0.363353 | −0.0276252 | −0.0138126 | − | 0.999905i | \(-0.504397\pi\) | ||||
−0.0138126 | + | 0.999905i | \(0.504397\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −15.0239 | −1.13570 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 16.9560 | 1.27449 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 0.946542 | 0.0707479 | 0.0353739 | − | 0.999374i | \(-0.488738\pi\) | ||||
0.0353739 | + | 0.999374i | \(0.488738\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −15.6678 | −1.16458 | −0.582288 | − | 0.812983i | \(-0.697842\pi\) | ||||
−0.582288 | + | 0.812983i | \(0.697842\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −12.5659 | −0.928900 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −25.9587 | −1.90852 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 7.74920 | 0.566677 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 25.2573 | 1.83720 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 13.2104 | 0.955873 | 0.477937 | − | 0.878394i | \(-0.341385\pi\) | ||||
0.477937 | + | 0.878394i | \(0.341385\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 5.29266 | 0.380974 | 0.190487 | − | 0.981690i | \(-0.438993\pi\) | ||||
0.190487 | + | 0.981690i | \(0.438993\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −25.6595 | −1.83751 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 23.2327 | 1.65526 | 0.827631 | − | 0.561272i | \(-0.189688\pi\) | ||||
0.827631 | + | 0.561272i | \(0.189688\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 9.79983 | 0.694691 | 0.347346 | − | 0.937737i | \(-0.387083\pi\) | ||||
0.347346 | + | 0.937737i | \(0.387083\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 20.4815 | 1.44466 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −17.2223 | −1.20877 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −3.56121 | −0.248726 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −0.138667 | −0.00963799 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −15.9024 | −1.09999 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −9.74926 | −0.671167 | −0.335583 | − | 0.942011i | \(-0.608933\pi\) | ||||
−0.335583 | + | 0.942011i | \(0.608933\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −27.0419 | −1.85288 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −14.8516 | −1.01287 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −22.3313 | −1.51595 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −14.0322 | −0.948207 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −18.4392 | −1.24035 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 4.06139 | 0.271971 | 0.135985 | − | 0.990711i | \(-0.456580\pi\) | ||||
0.135985 | + | 0.990711i | \(0.456580\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −1.08706 | −0.0724707 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 3.73589 | 0.247960 | 0.123980 | − | 0.992285i | \(-0.460434\pi\) | ||||
0.123980 | + | 0.992285i | \(0.460434\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −15.0833 | −0.996731 | −0.498366 | − | 0.866967i | \(-0.666066\pi\) | ||||
−0.498366 | + | 0.866967i | \(0.666066\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −17.4279 | −1.14667 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 16.6564 | 1.09119 | 0.545597 | − | 0.838047i | \(-0.316303\pi\) | ||||
0.545597 | + | 0.838047i | \(0.316303\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −10.6991 | −0.697929 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −0.122784 | −0.00797569 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 8.31383 | 0.537777 | 0.268888 | − | 0.963171i | \(-0.413344\pi\) | ||||
0.268888 | + | 0.963171i | \(0.413344\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 3.76545 | 0.242554 | 0.121277 | − | 0.992619i | \(-0.461301\pi\) | ||||
0.121277 | + | 0.992619i | \(0.461301\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 3.47111 | 0.222672 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 41.6741 | 2.66246 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 37.8397 | 2.40768 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −15.5830 | −0.987534 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 1.00000 | 0.0631194 | ||||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 0.950883 | 0.0597815 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 15.7741 | 0.987814 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 17.0430 | 1.06311 | 0.531555 | − | 0.847024i | \(-0.321608\pi\) | ||||
0.531555 | + | 0.847024i | \(0.321608\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 41.9531 | 2.60684 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −1.24612 | −0.0771330 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −8.78669 | −0.541810 | −0.270905 | − | 0.962606i | \(-0.587323\pi\) | ||||
−0.270905 | + | 0.962606i | \(0.587323\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −12.9403 | −0.794918 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −27.8081 | −1.70183 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 15.4573 | 0.942448 | 0.471224 | − | 0.882013i | \(-0.343812\pi\) | ||||
0.471224 | + | 0.882013i | \(0.343812\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 6.89090 | 0.418592 | 0.209296 | − | 0.977852i | \(-0.432883\pi\) | ||||
0.209296 | + | 0.977852i | \(0.432883\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 41.4695 | 2.50985 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 7.45434 | 0.449513 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −8.15544 | −0.490013 | −0.245006 | − | 0.969521i | \(-0.578790\pi\) | ||||
−0.245006 | + | 0.969521i | \(0.578790\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −1.61579 | −0.0967346 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 4.16579 | 0.248510 | 0.124255 | − | 0.992250i | \(-0.460346\pi\) | ||||
0.124255 | + | 0.992250i | \(0.460346\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 11.1550 | 0.663097 | 0.331548 | − | 0.943438i | \(-0.392429\pi\) | ||||
0.331548 | + | 0.943438i | \(0.392429\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −32.3706 | −1.91747 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 5.75545 | 0.339733 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −5.66453 | −0.333207 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 26.1753 | 1.53442 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 18.4528 | 1.07802 | 0.539011 | − | 0.842299i | \(-0.318798\pi\) | ||||
0.539011 | + | 0.842299i | \(0.318798\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 29.8165 | 1.73599 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −12.5318 | −0.727168 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −2.26262 | −0.130851 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 24.0024 | 1.38348 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −19.1897 | −1.10242 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −22.0967 | −1.26525 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 12.9615 | 0.739750 | 0.369875 | − | 0.929082i | \(-0.379401\pi\) | ||||
0.369875 | + | 0.929082i | \(0.379401\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 18.1776 | 1.03409 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −18.8328 | −1.06791 | −0.533955 | − | 0.845513i | \(-0.679295\pi\) | ||||
−0.533955 | + | 0.845513i | \(0.679295\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 17.7906 | 1.00558 | 0.502791 | − | 0.864408i | \(-0.332307\pi\) | ||||
0.502791 | + | 0.864408i | \(0.332307\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 4.46912 | 0.251807 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 33.0228 | 1.85474 | 0.927372 | − | 0.374141i | \(-0.122063\pi\) | ||||
0.927372 | + | 0.374141i | \(0.122063\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 8.54508 | 0.478432 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 5.61521 | 0.313410 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −23.2619 | −1.29433 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −17.7376 | −0.983903 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −14.8704 | −0.822335 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 17.2913 | 0.953298 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 18.1365 | 0.996873 | 0.498436 | − | 0.866926i | \(-0.333908\pi\) | ||||
0.498436 | + | 0.866926i | \(0.333908\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 3.03553 | 0.166346 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 36.0160 | 1.96777 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 25.0332 | 1.36365 | 0.681823 | − | 0.731517i | \(-0.261187\pi\) | ||||
0.681823 | + | 0.731517i | \(0.261187\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −10.3061 | −0.559749 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 11.0800 | 0.600015 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −34.8796 | −1.88332 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 1.93560 | 0.104209 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −34.9223 | −1.87473 | −0.937363 | − | 0.348353i | \(-0.886741\pi\) | ||||
−0.937363 | + | 0.348353i | \(0.886741\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −15.6814 | −0.839408 | −0.419704 | − | 0.907661i | \(-0.637866\pi\) | ||||
−0.419704 | + | 0.907661i | \(0.637866\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 29.8193 | 1.59164 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 10.6859 | 0.568753 | 0.284377 | − | 0.958713i | \(-0.408213\pi\) | ||||
0.284377 | + | 0.958713i | \(0.408213\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −47.5522 | −2.52381 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −25.4933 | −1.34925 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −34.6653 | −1.82956 | −0.914782 | − | 0.403947i | \(-0.867638\pi\) | ||||
−0.914782 | + | 0.403947i | \(0.867638\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 28.7365 | 1.51245 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −9.30805 | −0.488546 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −24.6751 | −1.29155 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 1.47086 | 0.0767783 | 0.0383891 | − | 0.999263i | \(-0.487777\pi\) | ||||
0.0383891 | + | 0.999263i | \(0.487777\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0.416437 | 0.0216788 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 20.9135 | 1.08578 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 18.1346 | 0.938976 | 0.469488 | − | 0.882939i | \(-0.344439\pi\) | ||||
0.469488 | + | 0.882939i | \(0.344439\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −8.25195 | −0.426129 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −20.3330 | −1.04720 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −20.5720 | −1.05671 | −0.528355 | − | 0.849023i | \(-0.677191\pi\) | ||||
−0.528355 | + | 0.849023i | \(0.677191\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −0.129734 | −0.00664650 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 23.3434 | 1.19279 | 0.596397 | − | 0.802690i | \(-0.296598\pi\) | ||||
0.596397 | + | 0.802690i | \(0.296598\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −30.6463 | −1.56188 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 1.73670 | 0.0882815 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −7.03637 | −0.356758 | −0.178379 | − | 0.983962i | \(-0.557085\pi\) | ||||
−0.178379 | + | 0.983962i | \(0.557085\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 1.39094 | 0.0703431 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −4.13500 | −0.208583 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −0.215912 | −0.0108637 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 36.5747 | 1.83563 | 0.917817 | − | 0.397005i | \(-0.129950\pi\) | ||||
0.917817 | + | 0.397005i | \(0.129950\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 52.3157 | 2.61906 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −32.3014 | −1.61306 | −0.806528 | − | 0.591196i | \(-0.798656\pi\) | ||||
−0.806528 | + | 0.591196i | \(0.798656\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −26.3648 | −1.31332 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −22.6192 | −1.12396 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −20.8156 | −1.03179 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 8.42789 | 0.416733 | 0.208366 | − | 0.978051i | \(-0.433185\pi\) | ||||
0.208366 | + | 0.978051i | \(0.433185\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 16.0279 | 0.790596 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −48.1880 | −2.37117 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −27.4022 | −1.34512 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −15.0715 | −0.738057 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 4.41936 | 0.215900 | 0.107950 | − | 0.994156i | \(-0.465571\pi\) | ||||
0.107950 | + | 0.994156i | \(0.465571\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −30.4368 | −1.48340 | −0.741699 | − | 0.670733i | \(-0.765980\pi\) | ||||
−0.741699 | + | 0.670733i | \(0.765980\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 1.25112 | 0.0608313 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 10.9042 | 0.528929 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 35.7116 | 1.72821 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −20.5757 | −0.993405 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −34.9690 | −1.68440 | −0.842200 | − | 0.539165i | \(-0.818740\pi\) | ||||
−0.842200 | + | 0.539165i | \(0.818740\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −19.7229 | −0.947821 | −0.473910 | − | 0.880573i | \(-0.657158\pi\) | ||||
−0.473910 | + | 0.880573i | \(0.657158\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 17.3942 | 0.833988 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −2.85440 | −0.136545 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 25.5127 | 1.21765 | 0.608827 | − | 0.793303i | \(-0.291640\pi\) | ||||
0.608827 | + | 0.793303i | \(0.291640\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −4.87325 | −0.232059 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −37.1938 | −1.76713 | −0.883566 | − | 0.468308i | \(-0.844864\pi\) | ||||
−0.883566 | + | 0.468308i | \(0.844864\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −48.8996 | −2.31807 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 21.1730 | 1.00145 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −3.32128 | −0.156741 | −0.0783705 | − | 0.996924i | \(-0.524972\pi\) | ||||
−0.0783705 | + | 0.996924i | \(0.524972\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −2.85565 | −0.134467 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −33.7035 | −1.58353 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 72.9227 | 3.41867 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 9.90999 | 0.463570 | 0.231785 | − | 0.972767i | \(-0.425543\pi\) | ||||
0.231785 | + | 0.972767i | \(0.425543\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −18.3314 | −0.855637 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −11.4921 | −0.535242 | −0.267621 | − | 0.963524i | \(-0.586238\pi\) | ||||
−0.267621 | + | 0.963524i | \(0.586238\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −41.3658 | −1.92243 | −0.961216 | − | 0.275797i | \(-0.911058\pi\) | ||||
−0.961216 | + | 0.275797i | \(0.911058\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 22.5542 | 1.04593 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −12.7058 | −0.587956 | −0.293978 | − | 0.955812i | \(-0.594979\pi\) | ||||
−0.293978 | + | 0.955812i | \(0.594979\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −58.2073 | −2.68776 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −14.9918 | −0.690787 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −11.9091 | −0.547583 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −22.3768 | −1.02672 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 1.51320 | 0.0692848 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 34.6466 | 1.58304 | 0.791522 | − | 0.611141i | \(-0.209289\pi\) | ||||
0.791522 | + | 0.611141i | \(0.209289\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 49.5308 | 2.25841 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −3.12822 | −0.142339 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 46.0283 | 2.09004 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −29.4549 | −1.33473 | −0.667364 | − | 0.744732i | \(-0.732577\pi\) | ||||
−0.667364 | + | 0.744732i | \(0.732577\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 27.6327 | 1.24959 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −10.6479 | −0.480534 | −0.240267 | − | 0.970707i | \(-0.577235\pi\) | ||||
−0.240267 | + | 0.970707i | \(0.577235\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 12.4997 | 0.562957 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −2.21742 | −0.0996656 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 76.8515 | 3.44726 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 41.0716 | 1.83862 | 0.919310 | − | 0.393535i | \(-0.128748\pi\) | ||||
0.919310 | + | 0.393535i | \(0.128748\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 3.07546 | 0.137401 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −14.2097 | −0.633581 | −0.316791 | − | 0.948495i | \(-0.602605\pi\) | ||||
−0.316791 | + | 0.948495i | \(0.602605\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −33.7444 | −1.50161 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 27.7402 | 1.23198 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −12.2017 | −0.540829 | −0.270415 | − | 0.962744i | \(-0.587161\pi\) | ||||
−0.270415 | + | 0.962744i | \(0.587161\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 39.8786 | 1.76413 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 37.6185 | 1.66090 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 31.9647 | 1.40853 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −8.57931 | −0.377318 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −0.593095 | −0.0260340 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 9.30863 | 0.407818 | 0.203909 | − | 0.978990i | \(-0.434635\pi\) | ||||
0.203909 | + | 0.978990i | \(0.434635\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −21.9797 | −0.961107 | −0.480554 | − | 0.876965i | \(-0.659564\pi\) | ||||
−0.480554 | + | 0.876965i | \(0.659564\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | −24.5233 | −1.07029 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 16.2077 | 0.706020 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −22.8293 | −0.992579 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −3.48666 | −0.151308 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 6.79501 | 0.294324 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 9.87414 | 0.426897 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 1.54503 | 0.0666728 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 33.4175 | 1.43939 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −32.7094 | −1.40629 | −0.703144 | − | 0.711048i | \(-0.748221\pi\) | ||||
−0.703144 | + | 0.711048i | \(0.748221\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −25.5743 | −1.09750 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −26.1491 | −1.12010 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 12.0570 | 0.515518 | 0.257759 | − | 0.966209i | \(-0.417016\pi\) | ||||
0.257759 | + | 0.966209i | \(0.417016\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 2.58393 | 0.110279 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −25.6510 | −1.09277 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 0.348946 | 0.0148387 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −42.3720 | −1.79859 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −36.8171 | −1.55999 | −0.779996 | − | 0.625785i | \(-0.784779\pi\) | ||||
−0.779996 | + | 0.625785i | \(0.784779\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 28.3378 | 1.19856 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 12.6489 | 0.534037 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −0.368628 | −0.0155358 | −0.00776791 | − | 0.999970i | \(-0.502473\pi\) | ||||
−0.00776791 | + | 0.999970i | \(0.502473\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −18.1229 | −0.762434 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 36.5561 | 1.53521 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 24.0359 | 1.00764 | 0.503819 | − | 0.863809i | \(-0.331928\pi\) | ||||
0.503819 | + | 0.863809i | \(0.331928\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 22.5164 | 0.942282 | 0.471141 | − | 0.882058i | \(-0.343842\pi\) | ||||
0.471141 | + | 0.882058i | \(0.343842\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 21.5632 | 0.900815 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 1.33802 | 0.0557992 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 2.72462 | 0.113427 | 0.0567137 | − | 0.998390i | \(-0.481938\pi\) | ||||
0.0567137 | + | 0.998390i | \(0.481938\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 8.63912 | 0.359030 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 44.2861 | 1.83730 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −10.3765 | −0.429753 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 5.27635 | 0.218150 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −18.2284 | −0.752365 | −0.376182 | − | 0.926546i | \(-0.622763\pi\) | ||||
−0.376182 | + | 0.926546i | \(0.622763\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −33.2604 | −1.37047 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 37.9224 | 1.55992 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 11.1564 | 0.458140 | 0.229070 | − | 0.973410i | \(-0.426431\pi\) | ||||
0.229070 | + | 0.973410i | \(0.426431\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −44.8292 | −1.83782 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 15.9961 | 0.654677 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 1.81180 | 0.0740281 | 0.0370140 | − | 0.999315i | \(-0.488215\pi\) | ||||
0.0370140 | + | 0.999315i | \(0.488215\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −12.9149 | −0.526810 | −0.263405 | − | 0.964685i | \(-0.584846\pi\) | ||||
−0.263405 | + | 0.964685i | \(0.584846\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −4.21161 | −0.171510 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −16.3679 | −0.665449 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −30.1082 | −1.22205 | −0.611026 | − | 0.791610i | \(-0.709243\pi\) | ||||
−0.611026 | + | 0.791610i | \(0.709243\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −28.1116 | −1.13914 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 20.4145 | 0.825881 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 23.1449 | 0.934814 | 0.467407 | − | 0.884042i | \(-0.345188\pi\) | ||||
0.467407 | + | 0.884042i | \(0.345188\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −5.81291 | −0.234399 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 16.0919 | 0.647837 | 0.323919 | − | 0.946085i | \(-0.395000\pi\) | ||||
0.323919 | + | 0.946085i | \(0.395000\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −15.4108 | −0.619413 | −0.309706 | − | 0.950832i | \(-0.600231\pi\) | ||||
−0.309706 | + | 0.950832i | \(0.600231\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −2.24940 | −0.0902652 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 79.0291 | 3.16624 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −30.7043 | −1.22817 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −25.9572 | −1.03663 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −30.4490 | −1.21408 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 14.0058 | 0.557561 | 0.278780 | − | 0.960355i | \(-0.410070\pi\) | ||||
0.278780 | + | 0.960355i | \(0.410070\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −15.9136 | −0.632507 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −0.228134 | −0.00905320 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −79.5168 | −3.15057 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 5.56061 | 0.219974 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −17.1361 | −0.676836 | −0.338418 | − | 0.940996i | \(-0.609892\pi\) | ||||
−0.338418 | + | 0.940996i | \(0.609892\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 31.5872 | 1.24568 | 0.622839 | − | 0.782350i | \(-0.285979\pi\) | ||||
0.622839 | + | 0.782350i | \(0.285979\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −24.2421 | −0.954530 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 28.6672 | 1.12702 | 0.563512 | − | 0.826108i | \(-0.309450\pi\) | ||||
0.563512 | + | 0.826108i | \(0.309450\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 23.9092 | 0.938517 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −36.4510 | −1.42863 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −11.6536 | −0.456042 | −0.228021 | − | 0.973656i | \(-0.573226\pi\) | ||||
−0.228021 | + | 0.973656i | \(0.573226\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −7.27125 | −0.284111 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 2.88543 | 0.112571 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −31.9217 | −1.24349 | −0.621747 | − | 0.783218i | \(-0.713577\pi\) | ||||
−0.621747 | + | 0.783218i | \(0.713577\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 30.7329 | 1.19537 | 0.597685 | − | 0.801731i | \(-0.296087\pi\) | ||||
0.597685 | + | 0.801731i | \(0.296087\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −30.0980 | −1.16891 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 91.9954 | 3.56743 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 1.53380 | 0.0593890 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 6.62935 | 0.256305 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −17.7188 | −0.684028 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 0.990387 | 0.0381766 | 0.0190883 | − | 0.999818i | \(-0.493924\pi\) | ||||
0.0190883 | + | 0.999818i | \(0.493924\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −17.6339 | −0.678728 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −3.16119 | −0.121494 | −0.0607471 | − | 0.998153i | \(-0.519348\pi\) | ||||
−0.0607471 | + | 0.998153i | \(0.519348\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −74.3886 | −2.85477 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 6.09803 | 0.233677 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 38.1167 | 1.45850 | 0.729248 | − | 0.684250i | \(-0.239870\pi\) | ||||
0.729248 | + | 0.684250i | \(0.239870\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 28.1844 | 1.07687 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −24.6202 | −0.939320 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 24.6910 | 0.940651 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −30.3637 | −1.15509 | −0.577546 | − | 0.816358i | \(-0.695989\pi\) | ||||
−0.577546 | + | 0.816358i | \(0.695989\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 3.58368 | 0.136133 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −26.5028 | −1.00531 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −4.17722 | −0.158224 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 27.1879 | 1.02834 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 21.5013 | 0.812091 | 0.406046 | − | 0.913853i | \(-0.366907\pi\) | ||||
0.406046 | + | 0.913853i | \(0.366907\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 62.4854 | 2.35668 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −17.4639 | −0.657729 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 54.5360 | 2.05104 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 22.1149 | 0.830542 | 0.415271 | − | 0.909698i | \(-0.363687\pi\) | ||||
0.415271 | + | 0.909698i | \(0.363687\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0.0252481 | 0.000946877 0 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 1.98881 | 0.0744814 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −36.1817 | −1.35312 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 13.5705 | 0.506801 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −34.6275 | −1.29139 | −0.645694 | − | 0.763596i | \(-0.723432\pi\) | ||||
−0.645694 | + | 0.763596i | \(0.723432\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −51.6598 | −1.92391 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 6.14629 | 0.228583 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 12.0241 | 0.446562 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 10.6479 | 0.394907 | 0.197454 | − | 0.980312i | \(-0.436733\pi\) | ||||
0.197454 | + | 0.980312i | \(0.436733\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 29.3071 | 1.08545 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −17.4206 | −0.644325 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −1.67308 | −0.0617966 | −0.0308983 | − | 0.999523i | \(-0.509837\pi\) | ||||
−0.0308983 | + | 0.999523i | \(0.509837\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 68.0241 | 2.50911 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 28.8804 | 1.06382 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 23.8919 | 0.878878 | 0.439439 | − | 0.898272i | \(-0.355177\pi\) | ||||
0.439439 | + | 0.898272i | \(0.355177\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 61.7651 | 2.26900 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −42.4663 | −1.55794 | −0.778968 | − | 0.627064i | \(-0.784257\pi\) | ||||
−0.778968 | + | 0.627064i | \(0.784257\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 37.2320 | 1.36407 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 3.20433 | 0.117240 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −15.9581 | −0.583096 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −23.8577 | −0.870581 | −0.435290 | − | 0.900290i | \(-0.643354\pi\) | ||||
−0.435290 | + | 0.900290i | \(0.643354\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 1.63228 | 0.0594838 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −59.2664 | −2.15693 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −1.16655 | −0.0423989 | −0.0211994 | − | 0.999775i | \(-0.506748\pi\) | ||||
−0.0211994 | + | 0.999775i | \(0.506748\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 1.55211 | 0.0563381 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −2.91355 | −0.105616 | −0.0528080 | − | 0.998605i | \(-0.516817\pi\) | ||||
−0.0528080 | + | 0.998605i | \(0.516817\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 42.2608 | 1.52994 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −3.24363 | −0.117274 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −56.8918 | −2.05424 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 8.81372 | 0.317831 | 0.158915 | − | 0.987292i | \(-0.449200\pi\) | ||||
0.158915 | + | 0.987292i | \(0.449200\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 27.8190 | 1.00188 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −11.8965 | −0.427887 | −0.213943 | − | 0.976846i | \(-0.568631\pi\) | ||||
−0.213943 | + | 0.976846i | \(0.568631\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 15.5910 | 0.560046 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 68.4794 | 2.45669 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 8.57221 | 0.307131 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −38.1310 | −1.36443 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −20.2141 | −0.722394 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −26.3626 | −0.940921 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 33.8613 | 1.20703 | 0.603513 | − | 0.797353i | \(-0.293767\pi\) | ||||
0.603513 | + | 0.797353i | \(0.293767\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −14.3424 | −0.510602 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 29.2892 | 1.04141 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 42.1619 | 1.49721 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −21.1223 | −0.749131 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −13.0031 | −0.460595 | −0.230298 | − | 0.973120i | \(-0.573970\pi\) | ||||
−0.230298 | + | 0.973120i | \(0.573970\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −12.5498 | −0.443979 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 5.71818 | 0.202042 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −19.7864 | −0.698246 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −5.50086 | −0.193880 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 25.2307 | 0.888163 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −35.6551 | −1.25357 | −0.626784 | − | 0.779193i | \(-0.715629\pi\) | ||||
−0.626784 | + | 0.779193i | \(0.715629\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −46.9020 | −1.64695 | −0.823476 | − | 0.567350i | \(-0.807969\pi\) | ||||
−0.823476 | + | 0.567350i | \(0.807969\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 11.2479 | 0.394482 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 48.5911 | 1.70207 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 35.7494 | 1.25071 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −8.52736 | −0.297970 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 19.4661 | 0.679373 | 0.339687 | − | 0.940539i | \(-0.389679\pi\) | ||||
0.339687 | + | 0.940539i | \(0.389679\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −25.7226 | −0.896632 | −0.448316 | − | 0.893875i | \(-0.647976\pi\) | ||||
−0.448316 | + | 0.893875i | \(0.647976\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 12.1676 | 0.423621 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 46.3912 | 1.61318 | 0.806590 | − | 0.591111i | \(-0.201311\pi\) | ||||
0.806590 | + | 0.591111i | \(0.201311\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −31.5959 | −1.09737 | −0.548685 | − | 0.836029i | \(-0.684871\pi\) | ||||
−0.548685 | + | 0.836029i | \(0.684871\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −13.3120 | −0.461788 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 48.8829 | 1.69369 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 5.40808 | 0.187154 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −26.2107 | −0.905974 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 40.4925 | 1.39796 | 0.698978 | − | 0.715144i | \(-0.253639\pi\) | ||||
0.698978 | + | 0.715144i | \(0.253639\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −15.2165 | −0.524709 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 6.79975 | 0.234196 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 48.7801 | 1.67809 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 26.4529 | 0.908933 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 18.2082 | 0.624902 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −3.73631 | −0.128079 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 34.7367 | 1.18936 | 0.594681 | − | 0.803962i | \(-0.297278\pi\) | ||||
0.594681 | + | 0.803962i | \(0.297278\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 6.65635 | 0.227642 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −11.1365 | −0.380417 | −0.190208 | − | 0.981744i | \(-0.560916\pi\) | ||||
−0.190208 | + | 0.981744i | \(0.560916\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 28.9208 | 0.986764 | 0.493382 | − | 0.869813i | \(-0.335760\pi\) | ||||
0.493382 | + | 0.869813i | \(0.335760\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 9.39453 | 0.320165 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −1.14400 | −0.0389421 | −0.0194711 | − | 0.999810i | \(-0.506198\pi\) | ||||
−0.0194711 | + | 0.999810i | \(0.506198\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −1.04294 | −0.0354609 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −9.24612 | −0.314015 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −0.173134 | −0.00587319 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −68.7208 | −2.32852 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −5.38241 | −0.182167 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 23.4516 | 0.792807 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 41.4237 | 1.39878 | 0.699390 | − | 0.714740i | \(-0.253455\pi\) | ||||
0.699390 | + | 0.714740i | \(0.253455\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 30.1202 | 1.01593 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −24.6217 | −0.829525 | −0.414762 | − | 0.909930i | \(-0.636135\pi\) | ||||
−0.414762 | + | 0.909930i | \(0.636135\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 25.0682 | 0.843611 | 0.421805 | − | 0.906686i | \(-0.361397\pi\) | ||||
0.421805 | + | 0.906686i | \(0.361397\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 48.6691 | 1.63599 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 4.77843 | 0.160444 | 0.0802221 | − | 0.996777i | \(-0.474437\pi\) | ||||
0.0802221 | + | 0.996777i | \(0.474437\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 0.368698 | 0.0123657 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −18.1378 | −0.607640 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 25.7538 | 0.861817 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 2.71687 | 0.0908151 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −3.69325 | −0.123314 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 17.8723 | 0.596076 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −15.1787 | −0.505677 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 39.1788 | 1.30379 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −44.9714 | −1.49490 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 7.15637 | 0.237623 | 0.118812 | − | 0.992917i | \(-0.462092\pi\) | ||||
0.118812 | + | 0.992917i | \(0.462092\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 3.94597 | 0.130880 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 31.4930 | 1.04341 | 0.521705 | − | 0.853126i | \(-0.325296\pi\) | ||||
0.521705 | + | 0.853126i | \(0.325296\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −21.9732 | −0.727206 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −36.0682 | −1.19238 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 11.7514 | 0.388066 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −5.78404 | −0.190798 | −0.0953989 | − | 0.995439i | \(-0.530413\pi\) | ||||
−0.0953989 | + | 0.995439i | \(0.530413\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 21.1568 | 0.697140 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 90.7326 | 2.98650 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −29.2904 | −0.963062 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −3.73786 | −0.122767 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −11.8961 | −0.390299 | −0.195149 | − | 0.980774i | \(-0.562519\pi\) | ||||
−0.195149 | + | 0.980774i | \(0.562519\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −100.314 | −3.28766 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −30.7405 | −1.00640 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 22.2426 | 0.727412 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 11.2316 | 0.366922 | 0.183461 | − | 0.983027i | \(-0.441270\pi\) | ||||
0.183461 | + | 0.983027i | \(0.441270\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 29.0393 | 0.947660 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −32.7463 | −1.06750 | −0.533749 | − | 0.845643i | \(-0.679217\pi\) | ||||
−0.533749 | + | 0.845643i | \(0.679217\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −0.512576 | −0.0166918 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 72.4964 | 2.35831 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −2.88535 | −0.0937613 | −0.0468807 | − | 0.998900i | \(-0.514928\pi\) | ||||
−0.0468807 | + | 0.998900i | \(0.514928\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 47.0816 | 1.52833 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 53.9026 | 1.74791 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −21.4667 | −0.695375 | −0.347688 | − | 0.937610i | \(-0.613033\pi\) | ||||
−0.347688 | + | 0.937610i | \(0.613033\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 37.9181 | 1.22700 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 13.9480 | 0.450875 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −45.5502 | −1.47089 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −7.82578 | −0.252444 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −1.15465 | −0.0372082 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 15.1916 | 0.489035 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 0.0340542 | 0.00109511 | 0.000547555 | − | 1.00000i | \(-0.499826\pi\) | ||||
0.000547555 | 1.00000i | \(0.499826\pi\) | ||||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −37.9700 | −1.21977 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −4.96680 | −0.159392 | −0.0796962 | − | 0.996819i | \(-0.525395\pi\) | ||||
−0.0796962 | + | 0.996819i | \(0.525395\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 42.8325 | 1.37315 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −28.9528 | −0.927231 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 26.6350 | 0.852129 | 0.426064 | − | 0.904693i | \(-0.359900\pi\) | ||||
0.426064 | + | 0.904693i | \(0.359900\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −39.2115 | −1.25320 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 3.05779 | 0.0976279 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −20.5273 | −0.654718 | −0.327359 | − | 0.944900i | \(-0.606159\pi\) | ||||
−0.327359 | + | 0.944900i | \(0.606159\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 66.6852 | 2.12477 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 28.2243 | 0.898389 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −2.13764 | −0.0679729 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −45.8505 | −1.45649 | −0.728245 | − | 0.685317i | \(-0.759664\pi\) | ||||
−0.728245 | + | 0.685317i | \(0.759664\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 29.6040 | 0.939453 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 28.1286 | 0.891736 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −40.6335 | −1.28688 | −0.643438 | − | 0.765498i | \(-0.722493\pi\) | ||||
−0.643438 | + | 0.765498i | \(0.722493\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 49.2412 | 1.55792 |
(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 | 4016.2.a.f.1.4 | 6 | ||
4.3 | odd | 2 | 502.2.a.e.1.3 | ✓ | 6 | ||
12.11 | even | 2 | 4518.2.a.x.1.1 | 6 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
502.2.a.e.1.3 | ✓ | 6 | 4.3 | odd | 2 | ||
4016.2.a.f.1.4 | 6 | 1.1 | even | 1 | trivial | ||
4518.2.a.x.1.1 | 6 | 12.11 | even | 2 |