Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [847,2,Mod(1,847)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(847, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("847.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 847 = 7 \cdot 11^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 847.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: | \(6.76332905120\) |
Analytic rank: | \(1\) |
Dimension: | \(4\) |
Coefficient field: | 4.4.2525.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} - 2x^{3} - 4x^{2} + 5x + 5 \) |
Coefficient ring: | \(\Z[a_1, a_2]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 77) |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.3 | ||
Root | \(1.77748\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 847.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 1.77748 | 1.25687 | 0.628436 | − | 0.777862i | \(-0.283696\pi\) | ||||
0.628436 | + | 0.777862i | \(0.283696\pi\) | |||||||
\(3\) | 0.618034 | 0.356822 | 0.178411 | − | 0.983956i | \(-0.442904\pi\) | ||||
0.178411 | + | 0.983956i | \(0.442904\pi\) | |||||||
\(4\) | 1.15945 | 0.579725 | ||||||||
\(5\) | −2.77748 | −1.24213 | −0.621064 | − | 0.783760i | \(-0.713299\pi\) | ||||
−0.621064 | + | 0.783760i | \(0.713299\pi\) | |||||||
\(6\) | 1.09855 | 0.448479 | ||||||||
\(7\) | −1.00000 | −0.377964 | ||||||||
\(8\) | −1.49406 | −0.528231 | ||||||||
\(9\) | −2.61803 | −0.872678 | ||||||||
\(10\) | −4.93693 | −1.56120 | ||||||||
\(11\) | 0 | 0 | ||||||||
\(12\) | 0.716580 | 0.206859 | ||||||||
\(13\) | −4.29348 | −1.19080 | −0.595398 | − | 0.803431i | \(-0.703006\pi\) | ||||
−0.595398 | + | 0.803431i | \(0.703006\pi\) | |||||||
\(14\) | −1.77748 | −0.475053 | ||||||||
\(15\) | −1.71658 | −0.443219 | ||||||||
\(16\) | −4.97458 | −1.24364 | ||||||||
\(17\) | −2.75556 | −0.668321 | −0.334160 | − | 0.942516i | \(-0.608453\pi\) | ||||
−0.334160 | + | 0.942516i | \(0.608453\pi\) | |||||||
\(18\) | −4.65351 | −1.09684 | ||||||||
\(19\) | 1.93910 | 0.444859 | 0.222429 | − | 0.974949i | \(-0.428601\pi\) | ||||
0.222429 | + | 0.974949i | \(0.428601\pi\) | |||||||
\(20\) | −3.22035 | −0.720093 | ||||||||
\(21\) | −0.618034 | −0.134866 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 4.37009 | 0.911228 | 0.455614 | − | 0.890178i | \(-0.349420\pi\) | ||||
0.455614 | + | 0.890178i | \(0.349420\pi\) | |||||||
\(24\) | −0.923382 | −0.188485 | ||||||||
\(25\) | 2.71442 | 0.542884 | ||||||||
\(26\) | −7.63159 | −1.49668 | ||||||||
\(27\) | −3.47214 | −0.668213 | ||||||||
\(28\) | −1.15945 | −0.219116 | ||||||||
\(29\) | 8.62809 | 1.60220 | 0.801098 | − | 0.598533i | \(-0.204250\pi\) | ||||
0.801098 | + | 0.598533i | \(0.204250\pi\) | |||||||
\(30\) | −3.05119 | −0.557069 | ||||||||
\(31\) | −0.200588 | −0.0360266 | −0.0180133 | − | 0.999838i | \(-0.505734\pi\) | ||||
−0.0180133 | + | 0.999838i | \(0.505734\pi\) | |||||||
\(32\) | −5.85410 | −1.03487 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | −4.89796 | −0.839993 | ||||||||
\(35\) | 2.77748 | 0.469481 | ||||||||
\(36\) | −3.03548 | −0.505913 | ||||||||
\(37\) | 1.03548 | 0.170232 | 0.0851159 | − | 0.996371i | \(-0.472874\pi\) | ||||
0.0851159 | + | 0.996371i | \(0.472874\pi\) | |||||||
\(38\) | 3.44671 | 0.559130 | ||||||||
\(39\) | −2.65351 | −0.424902 | ||||||||
\(40\) | 4.14974 | 0.656131 | ||||||||
\(41\) | 9.60616 | 1.50023 | 0.750115 | − | 0.661307i | \(-0.229998\pi\) | ||||
0.750115 | + | 0.661307i | \(0.229998\pi\) | |||||||
\(42\) | −1.09855 | −0.169509 | ||||||||
\(43\) | −4.70820 | −0.717994 | −0.358997 | − | 0.933339i | \(-0.616881\pi\) | ||||
−0.358997 | + | 0.933339i | \(0.616881\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 7.27155 | 1.08398 | ||||||||
\(46\) | 7.76777 | 1.14530 | ||||||||
\(47\) | −13.0455 | −1.90289 | −0.951443 | − | 0.307823i | \(-0.900399\pi\) | ||||
−0.951443 | + | 0.307823i | \(0.900399\pi\) | |||||||
\(48\) | −3.07446 | −0.443760 | ||||||||
\(49\) | 1.00000 | 0.142857 | ||||||||
\(50\) | 4.82484 | 0.682335 | ||||||||
\(51\) | −1.70303 | −0.238472 | ||||||||
\(52\) | −4.97807 | −0.690334 | ||||||||
\(53\) | −3.90012 | −0.535723 | −0.267861 | − | 0.963457i | \(-0.586317\pi\) | ||||
−0.267861 | + | 0.963457i | \(0.586317\pi\) | |||||||
\(54\) | −6.17167 | −0.839857 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 1.49406 | 0.199653 | ||||||||
\(57\) | 1.19843 | 0.158736 | ||||||||
\(58\) | 15.3363 | 2.01375 | ||||||||
\(59\) | −8.55713 | −1.11404 | −0.557022 | − | 0.830498i | \(-0.688056\pi\) | ||||
−0.557022 | + | 0.830498i | \(0.688056\pi\) | |||||||
\(60\) | −1.99029 | −0.256945 | ||||||||
\(61\) | −0.988609 | −0.126578 | −0.0632892 | − | 0.997995i | \(-0.520159\pi\) | ||||
−0.0632892 | + | 0.997995i | \(0.520159\pi\) | |||||||
\(62\) | −0.356542 | −0.0452808 | ||||||||
\(63\) | 2.61803 | 0.329841 | ||||||||
\(64\) | −0.456423 | −0.0570529 | ||||||||
\(65\) | 11.9251 | 1.47912 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −5.41745 | −0.661846 | −0.330923 | − | 0.943658i | \(-0.607360\pi\) | ||||
−0.330923 | + | 0.943658i | \(0.607360\pi\) | |||||||
\(68\) | −3.19493 | −0.387442 | ||||||||
\(69\) | 2.70087 | 0.325146 | ||||||||
\(70\) | 4.93693 | 0.590077 | ||||||||
\(71\) | −2.01705 | −0.239380 | −0.119690 | − | 0.992811i | \(-0.538190\pi\) | ||||
−0.119690 | + | 0.992811i | \(0.538190\pi\) | |||||||
\(72\) | 3.91151 | 0.460976 | ||||||||
\(73\) | −9.97108 | −1.16703 | −0.583513 | − | 0.812104i | \(-0.698322\pi\) | ||||
−0.583513 | + | 0.812104i | \(0.698322\pi\) | |||||||
\(74\) | 1.84055 | 0.213960 | ||||||||
\(75\) | 1.67760 | 0.193713 | ||||||||
\(76\) | 2.24828 | 0.257896 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | −4.71658 | −0.534047 | ||||||||
\(79\) | 6.29348 | 0.708071 | 0.354036 | − | 0.935232i | \(-0.384809\pi\) | ||||
0.354036 | + | 0.935232i | \(0.384809\pi\) | |||||||
\(80\) | 13.8168 | 1.54477 | ||||||||
\(81\) | 5.70820 | 0.634245 | ||||||||
\(82\) | 17.0748 | 1.88560 | ||||||||
\(83\) | −1.72146 | −0.188955 | −0.0944773 | − | 0.995527i | \(-0.530118\pi\) | ||||
−0.0944773 | + | 0.995527i | \(0.530118\pi\) | |||||||
\(84\) | −0.716580 | −0.0781853 | ||||||||
\(85\) | 7.65351 | 0.830140 | ||||||||
\(86\) | −8.36876 | −0.902426 | ||||||||
\(87\) | 5.33245 | 0.571699 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −15.3035 | −1.62217 | −0.811086 | − | 0.584928i | \(-0.801123\pi\) | ||||
−0.811086 | + | 0.584928i | \(0.801123\pi\) | |||||||
\(90\) | 12.9251 | 1.36242 | ||||||||
\(91\) | 4.29348 | 0.450079 | ||||||||
\(92\) | 5.06691 | 0.528262 | ||||||||
\(93\) | −0.123970 | −0.0128551 | ||||||||
\(94\) | −23.1882 | −2.39168 | ||||||||
\(95\) | −5.38581 | −0.552572 | ||||||||
\(96\) | −3.61803 | −0.369264 | ||||||||
\(97\) | 11.6162 | 1.17945 | 0.589724 | − | 0.807605i | \(-0.299236\pi\) | ||||
0.589724 | + | 0.807605i | \(0.299236\pi\) | |||||||
\(98\) | 1.77748 | 0.179553 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 3.14723 | 0.314723 | ||||||||
\(101\) | 3.41179 | 0.339486 | 0.169743 | − | 0.985488i | \(-0.445706\pi\) | ||||
0.169743 | + | 0.985488i | \(0.445706\pi\) | |||||||
\(102\) | −3.02710 | −0.299728 | ||||||||
\(103\) | −18.1826 | −1.79158 | −0.895791 | − | 0.444475i | \(-0.853390\pi\) | ||||
−0.895791 | + | 0.444475i | \(0.853390\pi\) | |||||||
\(104\) | 6.41473 | 0.629016 | ||||||||
\(105\) | 1.71658 | 0.167521 | ||||||||
\(106\) | −6.93240 | −0.673334 | ||||||||
\(107\) | 3.24746 | 0.313944 | 0.156972 | − | 0.987603i | \(-0.449827\pi\) | ||||
0.156972 | + | 0.987603i | \(0.449827\pi\) | |||||||
\(108\) | −4.02577 | −0.387380 | ||||||||
\(109\) | 12.6912 | 1.21559 | 0.607796 | − | 0.794093i | \(-0.292054\pi\) | ||||
0.607796 | + | 0.794093i | \(0.292054\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0.639962 | 0.0607425 | ||||||||
\(112\) | 4.97458 | 0.470053 | ||||||||
\(113\) | −18.4480 | −1.73545 | −0.867723 | − | 0.497048i | \(-0.834417\pi\) | ||||
−0.867723 | + | 0.497048i | \(0.834417\pi\) | |||||||
\(114\) | 2.13018 | 0.199510 | ||||||||
\(115\) | −12.1379 | −1.13186 | ||||||||
\(116\) | 10.0038 | 0.928833 | ||||||||
\(117\) | 11.2405 | 1.03918 | ||||||||
\(118\) | −15.2102 | −1.40021 | ||||||||
\(119\) | 2.75556 | 0.252601 | ||||||||
\(120\) | 2.56468 | 0.234122 | ||||||||
\(121\) | 0 | 0 | ||||||||
\(122\) | −1.75724 | −0.159093 | ||||||||
\(123\) | 5.93693 | 0.535315 | ||||||||
\(124\) | −0.232572 | −0.0208855 | ||||||||
\(125\) | 6.34817 | 0.567797 | ||||||||
\(126\) | 4.65351 | 0.414568 | ||||||||
\(127\) | 19.5093 | 1.73117 | 0.865585 | − | 0.500762i | \(-0.166947\pi\) | ||||
0.865585 | + | 0.500762i | \(0.166947\pi\) | |||||||
\(128\) | 10.8969 | 0.963161 | ||||||||
\(129\) | −2.90983 | −0.256196 | ||||||||
\(130\) | 21.1966 | 1.85907 | ||||||||
\(131\) | −6.89796 | −0.602677 | −0.301339 | − | 0.953517i | \(-0.597433\pi\) | ||||
−0.301339 | + | 0.953517i | \(0.597433\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −1.93910 | −0.168141 | ||||||||
\(134\) | −9.62943 | −0.831856 | ||||||||
\(135\) | 9.64380 | 0.830006 | ||||||||
\(136\) | 4.11698 | 0.353028 | ||||||||
\(137\) | −2.61070 | −0.223047 | −0.111523 | − | 0.993762i | \(-0.535573\pi\) | ||||
−0.111523 | + | 0.993762i | \(0.535573\pi\) | |||||||
\(138\) | 4.80075 | 0.408667 | ||||||||
\(139\) | −1.00134 | −0.0849322 | −0.0424661 | − | 0.999098i | \(-0.513521\pi\) | ||||
−0.0424661 | + | 0.999098i | \(0.513521\pi\) | |||||||
\(140\) | 3.22035 | 0.272170 | ||||||||
\(141\) | −8.06258 | −0.678992 | ||||||||
\(142\) | −3.58527 | −0.300869 | ||||||||
\(143\) | 0 | 0 | ||||||||
\(144\) | 13.0236 | 1.08530 | ||||||||
\(145\) | −23.9644 | −1.99013 | ||||||||
\(146\) | −17.7234 | −1.46680 | ||||||||
\(147\) | 0.618034 | 0.0509746 | ||||||||
\(148\) | 1.20059 | 0.0986877 | ||||||||
\(149\) | −14.8948 | −1.22023 | −0.610113 | − | 0.792314i | \(-0.708876\pi\) | ||||
−0.610113 | + | 0.792314i | \(0.708876\pi\) | |||||||
\(150\) | 2.98191 | 0.243472 | ||||||||
\(151\) | 15.8046 | 1.28616 | 0.643080 | − | 0.765799i | \(-0.277656\pi\) | ||||
0.643080 | + | 0.765799i | \(0.277656\pi\) | |||||||
\(152\) | −2.89713 | −0.234988 | ||||||||
\(153\) | 7.21414 | 0.583229 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 0.557129 | 0.0447497 | ||||||||
\(156\) | −3.07662 | −0.246327 | ||||||||
\(157\) | 4.59123 | 0.366420 | 0.183210 | − | 0.983074i | \(-0.441351\pi\) | ||||
0.183210 | + | 0.983074i | \(0.441351\pi\) | |||||||
\(158\) | 11.1866 | 0.889955 | ||||||||
\(159\) | −2.41041 | −0.191158 | ||||||||
\(160\) | 16.2597 | 1.28544 | ||||||||
\(161\) | −4.37009 | −0.344412 | ||||||||
\(162\) | 10.1462 | 0.797164 | ||||||||
\(163\) | 8.03764 | 0.629557 | 0.314778 | − | 0.949165i | \(-0.398070\pi\) | ||||
0.314778 | + | 0.949165i | \(0.398070\pi\) | |||||||
\(164\) | 11.1379 | 0.869721 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −3.05987 | −0.237492 | ||||||||
\(167\) | −13.4069 | −1.03746 | −0.518729 | − | 0.854939i | \(-0.673595\pi\) | ||||
−0.518729 | + | 0.854939i | \(0.673595\pi\) | |||||||
\(168\) | 0.923382 | 0.0712405 | ||||||||
\(169\) | 5.43394 | 0.417995 | ||||||||
\(170\) | 13.6040 | 1.04338 | ||||||||
\(171\) | −5.07662 | −0.388219 | ||||||||
\(172\) | −5.45893 | −0.416239 | ||||||||
\(173\) | −20.5821 | −1.56483 | −0.782413 | − | 0.622760i | \(-0.786011\pi\) | ||||
−0.782413 | + | 0.622760i | \(0.786011\pi\) | |||||||
\(174\) | 9.47835 | 0.718552 | ||||||||
\(175\) | −2.71442 | −0.205191 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −5.28860 | −0.397515 | ||||||||
\(178\) | −27.2018 | −2.03886 | ||||||||
\(179\) | −3.71520 | −0.277687 | −0.138843 | − | 0.990314i | \(-0.544338\pi\) | ||||
−0.138843 | + | 0.990314i | \(0.544338\pi\) | |||||||
\(180\) | 8.43100 | 0.628410 | ||||||||
\(181\) | 4.77183 | 0.354687 | 0.177344 | − | 0.984149i | \(-0.443250\pi\) | ||||
0.177344 | + | 0.984149i | \(0.443250\pi\) | |||||||
\(182\) | 7.63159 | 0.565691 | ||||||||
\(183\) | −0.610994 | −0.0451660 | ||||||||
\(184\) | −6.52920 | −0.481339 | ||||||||
\(185\) | −2.87603 | −0.211450 | ||||||||
\(186\) | −0.220355 | −0.0161572 | ||||||||
\(187\) | 0 | 0 | ||||||||
\(188\) | −15.1257 | −1.10315 | ||||||||
\(189\) | 3.47214 | 0.252561 | ||||||||
\(190\) | −9.57319 | −0.694512 | ||||||||
\(191\) | −0.829158 | −0.0599958 | −0.0299979 | − | 0.999550i | \(-0.509550\pi\) | ||||
−0.0299979 | + | 0.999550i | \(0.509550\pi\) | |||||||
\(192\) | −0.282085 | −0.0203577 | ||||||||
\(193\) | −6.73803 | −0.485014 | −0.242507 | − | 0.970150i | \(-0.577970\pi\) | ||||
−0.242507 | + | 0.970150i | \(0.577970\pi\) | |||||||
\(194\) | 20.6476 | 1.48241 | ||||||||
\(195\) | 7.37009 | 0.527783 | ||||||||
\(196\) | 1.15945 | 0.0828179 | ||||||||
\(197\) | −10.9216 | −0.778129 | −0.389065 | − | 0.921210i | \(-0.627202\pi\) | ||||
−0.389065 | + | 0.921210i | \(0.627202\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 20.9746 | 1.48685 | 0.743424 | − | 0.668820i | \(-0.233200\pi\) | ||||
0.743424 | + | 0.668820i | \(0.233200\pi\) | |||||||
\(200\) | −4.05552 | −0.286768 | ||||||||
\(201\) | −3.34817 | −0.236161 | ||||||||
\(202\) | 6.06440 | 0.426690 | ||||||||
\(203\) | −8.62809 | −0.605573 | ||||||||
\(204\) | −1.97458 | −0.138248 | ||||||||
\(205\) | −26.6810 | −1.86348 | ||||||||
\(206\) | −32.3192 | −2.25179 | ||||||||
\(207\) | −11.4411 | −0.795208 | ||||||||
\(208\) | 21.3582 | 1.48093 | ||||||||
\(209\) | 0 | 0 | ||||||||
\(210\) | 3.05119 | 0.210552 | ||||||||
\(211\) | −6.02361 | −0.414682 | −0.207341 | − | 0.978269i | \(-0.566481\pi\) | ||||
−0.207341 | + | 0.978269i | \(0.566481\pi\) | |||||||
\(212\) | −4.52199 | −0.310572 | ||||||||
\(213\) | −1.24660 | −0.0854159 | ||||||||
\(214\) | 5.77231 | 0.394587 | ||||||||
\(215\) | 13.0770 | 0.891841 | ||||||||
\(216\) | 5.18759 | 0.352971 | ||||||||
\(217\) | 0.200588 | 0.0136168 | ||||||||
\(218\) | 22.5583 | 1.52784 | ||||||||
\(219\) | −6.16247 | −0.416421 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 11.8309 | 0.795833 | ||||||||
\(222\) | 1.13752 | 0.0763455 | ||||||||
\(223\) | −4.62507 | −0.309718 | −0.154859 | − | 0.987937i | \(-0.549492\pi\) | ||||
−0.154859 | + | 0.987937i | \(0.549492\pi\) | |||||||
\(224\) | 5.85410 | 0.391144 | ||||||||
\(225\) | −7.10644 | −0.473763 | ||||||||
\(226\) | −32.7911 | −2.18123 | ||||||||
\(227\) | 17.3003 | 1.14826 | 0.574132 | − | 0.818763i | \(-0.305340\pi\) | ||||
0.574132 | + | 0.818763i | \(0.305340\pi\) | |||||||
\(228\) | 1.38952 | 0.0920230 | ||||||||
\(229\) | −4.42612 | −0.292486 | −0.146243 | − | 0.989249i | \(-0.546718\pi\) | ||||
−0.146243 | + | 0.989249i | \(0.546718\pi\) | |||||||
\(230\) | −21.5749 | −1.42260 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −12.8909 | −0.846330 | ||||||||
\(233\) | −10.5330 | −0.690042 | −0.345021 | − | 0.938595i | \(-0.612128\pi\) | ||||
−0.345021 | + | 0.938595i | \(0.612128\pi\) | |||||||
\(234\) | 19.9798 | 1.30612 | ||||||||
\(235\) | 36.2338 | 2.36363 | ||||||||
\(236\) | −9.92157 | −0.645839 | ||||||||
\(237\) | 3.88958 | 0.252656 | ||||||||
\(238\) | 4.89796 | 0.317487 | ||||||||
\(239\) | −9.75646 | −0.631093 | −0.315546 | − | 0.948910i | \(-0.602188\pi\) | ||||
−0.315546 | + | 0.948910i | \(0.602188\pi\) | |||||||
\(240\) | 8.53926 | 0.551207 | ||||||||
\(241\) | 12.5501 | 0.808422 | 0.404211 | − | 0.914666i | \(-0.367546\pi\) | ||||
0.404211 | + | 0.914666i | \(0.367546\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 13.9443 | 0.894525 | ||||||||
\(244\) | −1.14624 | −0.0733807 | ||||||||
\(245\) | −2.77748 | −0.177447 | ||||||||
\(246\) | 10.5528 | 0.672822 | ||||||||
\(247\) | −8.32546 | −0.529736 | ||||||||
\(248\) | 0.299691 | 0.0190304 | ||||||||
\(249\) | −1.06392 | −0.0674232 | ||||||||
\(250\) | 11.2838 | 0.713648 | ||||||||
\(251\) | −10.9912 | −0.693758 | −0.346879 | − | 0.937910i | \(-0.612759\pi\) | ||||
−0.346879 | + | 0.937910i | \(0.612759\pi\) | |||||||
\(252\) | 3.03548 | 0.191217 | ||||||||
\(253\) | 0 | 0 | ||||||||
\(254\) | 34.6775 | 2.17586 | ||||||||
\(255\) | 4.73013 | 0.296212 | ||||||||
\(256\) | 20.2819 | 1.26762 | ||||||||
\(257\) | 5.33280 | 0.332651 | 0.166325 | − | 0.986071i | \(-0.446810\pi\) | ||||
0.166325 | + | 0.986071i | \(0.446810\pi\) | |||||||
\(258\) | −5.17218 | −0.322006 | ||||||||
\(259\) | −1.03548 | −0.0643416 | ||||||||
\(260\) | 13.8265 | 0.857484 | ||||||||
\(261\) | −22.5886 | −1.39820 | ||||||||
\(262\) | −12.2610 | −0.757488 | ||||||||
\(263\) | −8.18034 | −0.504421 | −0.252211 | − | 0.967672i | \(-0.581158\pi\) | ||||
−0.252211 | + | 0.967672i | \(0.581158\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 10.8325 | 0.665436 | ||||||||
\(266\) | −3.44671 | −0.211331 | ||||||||
\(267\) | −9.45810 | −0.578826 | ||||||||
\(268\) | −6.28126 | −0.383689 | ||||||||
\(269\) | 12.8439 | 0.783107 | 0.391554 | − | 0.920155i | \(-0.371938\pi\) | ||||
0.391554 | + | 0.920155i | \(0.371938\pi\) | |||||||
\(270\) | 17.1417 | 1.04321 | ||||||||
\(271\) | −22.0472 | −1.33927 | −0.669636 | − | 0.742689i | \(-0.733550\pi\) | ||||
−0.669636 | + | 0.742689i | \(0.733550\pi\) | |||||||
\(272\) | 13.7077 | 0.831153 | ||||||||
\(273\) | 2.65351 | 0.160598 | ||||||||
\(274\) | −4.64047 | −0.280341 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 3.13152 | 0.188495 | ||||||||
\(277\) | 24.0770 | 1.44664 | 0.723322 | − | 0.690511i | \(-0.242614\pi\) | ||||
0.723322 | + | 0.690511i | \(0.242614\pi\) | |||||||
\(278\) | −1.77986 | −0.106749 | ||||||||
\(279\) | 0.525146 | 0.0314396 | ||||||||
\(280\) | −4.14974 | −0.247994 | ||||||||
\(281\) | 15.4418 | 0.921182 | 0.460591 | − | 0.887612i | \(-0.347637\pi\) | ||||
0.460591 | + | 0.887612i | \(0.347637\pi\) | |||||||
\(282\) | −14.3311 | −0.853406 | ||||||||
\(283\) | −3.35732 | −0.199572 | −0.0997860 | − | 0.995009i | \(-0.531816\pi\) | ||||
−0.0997860 | + | 0.995009i | \(0.531816\pi\) | |||||||
\(284\) | −2.33867 | −0.138774 | ||||||||
\(285\) | −3.32861 | −0.197170 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −9.60616 | −0.567034 | ||||||||
\(288\) | 15.3262 | 0.903107 | ||||||||
\(289\) | −9.40691 | −0.553348 | ||||||||
\(290\) | −42.5963 | −2.50134 | ||||||||
\(291\) | 7.17922 | 0.420853 | ||||||||
\(292\) | −11.5610 | −0.676555 | ||||||||
\(293\) | 6.83705 | 0.399425 | 0.199712 | − | 0.979855i | \(-0.435999\pi\) | ||||
0.199712 | + | 0.979855i | \(0.435999\pi\) | |||||||
\(294\) | 1.09855 | 0.0640685 | ||||||||
\(295\) | 23.7673 | 1.38379 | ||||||||
\(296\) | −1.54707 | −0.0899218 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | −26.4752 | −1.53367 | ||||||||
\(299\) | −18.7629 | −1.08509 | ||||||||
\(300\) | 1.94510 | 0.112300 | ||||||||
\(301\) | 4.70820 | 0.271376 | ||||||||
\(302\) | 28.0924 | 1.61654 | ||||||||
\(303\) | 2.10860 | 0.121136 | ||||||||
\(304\) | −9.64618 | −0.553246 | ||||||||
\(305\) | 2.74585 | 0.157227 | ||||||||
\(306\) | 12.8230 | 0.733043 | ||||||||
\(307\) | −11.7970 | −0.673293 | −0.336646 | − | 0.941631i | \(-0.609293\pi\) | ||||
−0.336646 | + | 0.941631i | \(0.609293\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −11.2375 | −0.639276 | ||||||||
\(310\) | 0.990289 | 0.0562446 | ||||||||
\(311\) | 25.3139 | 1.43542 | 0.717709 | − | 0.696343i | \(-0.245191\pi\) | ||||
0.717709 | + | 0.696343i | \(0.245191\pi\) | |||||||
\(312\) | 3.96452 | 0.224447 | ||||||||
\(313\) | −19.6543 | −1.11093 | −0.555464 | − | 0.831540i | \(-0.687460\pi\) | ||||
−0.555464 | + | 0.831540i | \(0.687460\pi\) | |||||||
\(314\) | 8.16083 | 0.460542 | ||||||||
\(315\) | −7.27155 | −0.409705 | ||||||||
\(316\) | 7.29697 | 0.410487 | ||||||||
\(317\) | 3.61056 | 0.202789 | 0.101395 | − | 0.994846i | \(-0.467670\pi\) | ||||
0.101395 | + | 0.994846i | \(0.467670\pi\) | |||||||
\(318\) | −4.28446 | −0.240261 | ||||||||
\(319\) | 0 | 0 | ||||||||
\(320\) | 1.26771 | 0.0708670 | ||||||||
\(321\) | 2.00704 | 0.112022 | ||||||||
\(322\) | −7.76777 | −0.432881 | ||||||||
\(323\) | −5.34329 | −0.297308 | ||||||||
\(324\) | 6.61838 | 0.367688 | ||||||||
\(325\) | −11.6543 | −0.646464 | ||||||||
\(326\) | 14.2868 | 0.791272 | ||||||||
\(327\) | 7.84357 | 0.433750 | ||||||||
\(328\) | −14.3522 | −0.792469 | ||||||||
\(329\) | 13.0455 | 0.719224 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −26.5335 | −1.45841 | −0.729205 | − | 0.684295i | \(-0.760110\pi\) | ||||
−0.729205 | + | 0.684295i | \(0.760110\pi\) | |||||||
\(332\) | −1.99595 | −0.109542 | ||||||||
\(333\) | −2.71092 | −0.148558 | ||||||||
\(334\) | −23.8306 | −1.30395 | ||||||||
\(335\) | 15.0469 | 0.822098 | ||||||||
\(336\) | 3.07446 | 0.167725 | ||||||||
\(337\) | −0.685979 | −0.0373676 | −0.0186838 | − | 0.999825i | \(-0.505948\pi\) | ||||
−0.0186838 | + | 0.999825i | \(0.505948\pi\) | |||||||
\(338\) | 9.65874 | 0.525366 | ||||||||
\(339\) | −11.4015 | −0.619246 | ||||||||
\(340\) | 8.87387 | 0.481253 | ||||||||
\(341\) | 0 | 0 | ||||||||
\(342\) | −9.02361 | −0.487941 | ||||||||
\(343\) | −1.00000 | −0.0539949 | ||||||||
\(344\) | 7.03436 | 0.379267 | ||||||||
\(345\) | −7.50161 | −0.403873 | ||||||||
\(346\) | −36.5843 | −1.96678 | ||||||||
\(347\) | 21.5055 | 1.15447 | 0.577237 | − | 0.816577i | \(-0.304131\pi\) | ||||
0.577237 | + | 0.816577i | \(0.304131\pi\) | |||||||
\(348\) | 6.18271 | 0.331428 | ||||||||
\(349\) | 19.4429 | 1.04075 | 0.520377 | − | 0.853937i | \(-0.325792\pi\) | ||||
0.520377 | + | 0.853937i | \(0.325792\pi\) | |||||||
\(350\) | −4.82484 | −0.257898 | ||||||||
\(351\) | 14.9075 | 0.795705 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −20.9307 | −1.11403 | −0.557015 | − | 0.830502i | \(-0.688053\pi\) | ||||
−0.557015 | + | 0.830502i | \(0.688053\pi\) | |||||||
\(354\) | −9.40040 | −0.499625 | ||||||||
\(355\) | 5.60232 | 0.297340 | ||||||||
\(356\) | −17.7437 | −0.940413 | ||||||||
\(357\) | 1.70303 | 0.0901338 | ||||||||
\(358\) | −6.60370 | −0.349017 | ||||||||
\(359\) | 9.77127 | 0.515708 | 0.257854 | − | 0.966184i | \(-0.416985\pi\) | ||||
0.257854 | + | 0.966184i | \(0.416985\pi\) | |||||||
\(360\) | −10.8642 | −0.572591 | ||||||||
\(361\) | −15.2399 | −0.802100 | ||||||||
\(362\) | 8.48185 | 0.445796 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 4.97807 | 0.260922 | ||||||||
\(365\) | 27.6945 | 1.44960 | ||||||||
\(366\) | −1.08603 | −0.0567678 | ||||||||
\(367\) | 9.89969 | 0.516759 | 0.258380 | − | 0.966043i | \(-0.416811\pi\) | ||||
0.258380 | + | 0.966043i | \(0.416811\pi\) | |||||||
\(368\) | −21.7394 | −1.13324 | ||||||||
\(369\) | −25.1493 | −1.30922 | ||||||||
\(370\) | −5.11210 | −0.265765 | ||||||||
\(371\) | 3.90012 | 0.202484 | ||||||||
\(372\) | −0.143737 | −0.00745242 | ||||||||
\(373\) | −4.27475 | −0.221338 | −0.110669 | − | 0.993857i | \(-0.535299\pi\) | ||||
−0.110669 | + | 0.993857i | \(0.535299\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 3.92338 | 0.202603 | ||||||||
\(376\) | 19.4909 | 1.00516 | ||||||||
\(377\) | −37.0445 | −1.90789 | ||||||||
\(378\) | 6.17167 | 0.317436 | ||||||||
\(379\) | 4.32594 | 0.222209 | 0.111104 | − | 0.993809i | \(-0.464561\pi\) | ||||
0.111104 | + | 0.993809i | \(0.464561\pi\) | |||||||
\(380\) | −6.24458 | −0.320340 | ||||||||
\(381\) | 12.0574 | 0.617720 | ||||||||
\(382\) | −1.47382 | −0.0754070 | ||||||||
\(383\) | −1.32210 | −0.0675561 | −0.0337781 | − | 0.999429i | \(-0.510754\pi\) | ||||
−0.0337781 | + | 0.999429i | \(0.510754\pi\) | |||||||
\(384\) | 6.73467 | 0.343677 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −11.9767 | −0.609600 | ||||||||
\(387\) | 12.3262 | 0.626578 | ||||||||
\(388\) | 13.4684 | 0.683756 | ||||||||
\(389\) | −38.5092 | −1.95249 | −0.976246 | − | 0.216665i | \(-0.930482\pi\) | ||||
−0.976246 | + | 0.216665i | \(0.930482\pi\) | |||||||
\(390\) | 13.1002 | 0.663356 | ||||||||
\(391\) | −12.0420 | −0.608992 | ||||||||
\(392\) | −1.49406 | −0.0754616 | ||||||||
\(393\) | −4.26317 | −0.215049 | ||||||||
\(394\) | −19.4129 | −0.978008 | ||||||||
\(395\) | −17.4800 | −0.879516 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −0.410109 | −0.0205828 | −0.0102914 | − | 0.999947i | \(-0.503276\pi\) | ||||
−0.0102914 | + | 0.999947i | \(0.503276\pi\) | |||||||
\(398\) | 37.2820 | 1.86878 | ||||||||
\(399\) | −1.19843 | −0.0599964 | ||||||||
\(400\) | −13.5031 | −0.675154 | ||||||||
\(401\) | −1.56684 | −0.0782443 | −0.0391221 | − | 0.999234i | \(-0.512456\pi\) | ||||
−0.0391221 | + | 0.999234i | \(0.512456\pi\) | |||||||
\(402\) | −5.95131 | −0.296824 | ||||||||
\(403\) | 0.861219 | 0.0429004 | ||||||||
\(404\) | 3.95580 | 0.196808 | ||||||||
\(405\) | −15.8544 | −0.787814 | ||||||||
\(406\) | −15.3363 | −0.761127 | ||||||||
\(407\) | 0 | 0 | ||||||||
\(408\) | 2.54443 | 0.125968 | ||||||||
\(409\) | −6.77852 | −0.335176 | −0.167588 | − | 0.985857i | \(-0.553598\pi\) | ||||
−0.167588 | + | 0.985857i | \(0.553598\pi\) | |||||||
\(410\) | −47.4250 | −2.34215 | ||||||||
\(411\) | −1.61350 | −0.0795880 | ||||||||
\(412\) | −21.0818 | −1.03863 | ||||||||
\(413\) | 8.55713 | 0.421069 | ||||||||
\(414\) | −20.3363 | −0.999474 | ||||||||
\(415\) | 4.78133 | 0.234706 | ||||||||
\(416\) | 25.1344 | 1.23232 | ||||||||
\(417\) | −0.618859 | −0.0303057 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 28.7218 | 1.40315 | 0.701577 | − | 0.712594i | \(-0.252480\pi\) | ||||
0.701577 | + | 0.712594i | \(0.252480\pi\) | |||||||
\(420\) | 1.99029 | 0.0971161 | ||||||||
\(421\) | 12.2256 | 0.595838 | 0.297919 | − | 0.954591i | \(-0.403707\pi\) | ||||
0.297919 | + | 0.954591i | \(0.403707\pi\) | |||||||
\(422\) | −10.7069 | −0.521202 | ||||||||
\(423\) | 34.1537 | 1.66061 | ||||||||
\(424\) | 5.82703 | 0.282985 | ||||||||
\(425\) | −7.47973 | −0.362820 | ||||||||
\(426\) | −2.21582 | −0.107357 | ||||||||
\(427\) | 0.988609 | 0.0478421 | ||||||||
\(428\) | 3.76527 | 0.182001 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 23.2441 | 1.12093 | ||||||||
\(431\) | 3.69129 | 0.177803 | 0.0889016 | − | 0.996040i | \(-0.471664\pi\) | ||||
0.0889016 | + | 0.996040i | \(0.471664\pi\) | |||||||
\(432\) | 17.2724 | 0.831019 | ||||||||
\(433\) | 29.0749 | 1.39725 | 0.698625 | − | 0.715488i | \(-0.253796\pi\) | ||||
0.698625 | + | 0.715488i | \(0.253796\pi\) | |||||||
\(434\) | 0.356542 | 0.0171145 | ||||||||
\(435\) | −14.8108 | −0.710124 | ||||||||
\(436\) | 14.7148 | 0.704709 | ||||||||
\(437\) | 8.47403 | 0.405368 | ||||||||
\(438\) | −10.9537 | −0.523387 | ||||||||
\(439\) | −14.2017 | −0.677811 | −0.338905 | − | 0.940820i | \(-0.610057\pi\) | ||||
−0.338905 | + | 0.940820i | \(0.610057\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −2.61803 | −0.124668 | ||||||||
\(442\) | 21.0293 | 1.00026 | ||||||||
\(443\) | 27.2356 | 1.29400 | 0.647001 | − | 0.762489i | \(-0.276023\pi\) | ||||
0.647001 | + | 0.762489i | \(0.276023\pi\) | |||||||
\(444\) | 0.742004 | 0.0352140 | ||||||||
\(445\) | 42.5053 | 2.01495 | ||||||||
\(446\) | −8.22100 | −0.389275 | ||||||||
\(447\) | −9.20547 | −0.435404 | ||||||||
\(448\) | 0.456423 | 0.0215640 | ||||||||
\(449\) | −41.9159 | −1.97813 | −0.989067 | − | 0.147467i | \(-0.952888\pi\) | ||||
−0.989067 | + | 0.147467i | \(0.952888\pi\) | |||||||
\(450\) | −12.6316 | −0.595459 | ||||||||
\(451\) | 0 | 0 | ||||||||
\(452\) | −21.3896 | −1.00608 | ||||||||
\(453\) | 9.76777 | 0.458930 | ||||||||
\(454\) | 30.7511 | 1.44322 | ||||||||
\(455\) | −11.9251 | −0.559056 | ||||||||
\(456\) | −1.79053 | −0.0838491 | ||||||||
\(457\) | 19.4977 | 0.912063 | 0.456032 | − | 0.889964i | \(-0.349270\pi\) | ||||
0.456032 | + | 0.889964i | \(0.349270\pi\) | |||||||
\(458\) | −7.86736 | −0.367617 | ||||||||
\(459\) | 9.56767 | 0.446580 | ||||||||
\(460\) | −14.0733 | −0.656169 | ||||||||
\(461\) | 12.2251 | 0.569380 | 0.284690 | − | 0.958620i | \(-0.408109\pi\) | ||||
0.284690 | + | 0.958620i | \(0.408109\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 13.8550 | 0.643894 | 0.321947 | − | 0.946758i | \(-0.395663\pi\) | ||||
0.321947 | + | 0.946758i | \(0.395663\pi\) | |||||||
\(464\) | −42.9211 | −1.99256 | ||||||||
\(465\) | 0.344325 | 0.0159677 | ||||||||
\(466\) | −18.7223 | −0.867294 | ||||||||
\(467\) | −16.4207 | −0.759861 | −0.379930 | − | 0.925015i | \(-0.624052\pi\) | ||||
−0.379930 | + | 0.925015i | \(0.624052\pi\) | |||||||
\(468\) | 13.0328 | 0.602440 | ||||||||
\(469\) | 5.41745 | 0.250154 | ||||||||
\(470\) | 64.4050 | 2.97078 | ||||||||
\(471\) | 2.83753 | 0.130747 | ||||||||
\(472\) | 12.7849 | 0.588473 | ||||||||
\(473\) | 0 | 0 | ||||||||
\(474\) | 6.91367 | 0.317555 | ||||||||
\(475\) | 5.26352 | 0.241507 | ||||||||
\(476\) | 3.19493 | 0.146439 | ||||||||
\(477\) | 10.2106 | 0.467513 | ||||||||
\(478\) | −17.3420 | −0.793202 | ||||||||
\(479\) | −24.7914 | −1.13275 | −0.566374 | − | 0.824149i | \(-0.691654\pi\) | ||||
−0.566374 | + | 0.824149i | \(0.691654\pi\) | |||||||
\(480\) | 10.0490 | 0.458673 | ||||||||
\(481\) | −4.44581 | −0.202711 | ||||||||
\(482\) | 22.3076 | 1.01608 | ||||||||
\(483\) | −2.70087 | −0.122894 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −32.2639 | −1.46503 | ||||||||
\(486\) | 24.7857 | 1.12430 | ||||||||
\(487\) | −14.3342 | −0.649544 | −0.324772 | − | 0.945792i | \(-0.605288\pi\) | ||||
−0.324772 | + | 0.945792i | \(0.605288\pi\) | |||||||
\(488\) | 1.47704 | 0.0668627 | ||||||||
\(489\) | 4.96754 | 0.224640 | ||||||||
\(490\) | −4.93693 | −0.223028 | ||||||||
\(491\) | −22.0193 | −0.993719 | −0.496859 | − | 0.867831i | \(-0.665514\pi\) | ||||
−0.496859 | + | 0.867831i | \(0.665514\pi\) | |||||||
\(492\) | 6.88358 | 0.310336 | ||||||||
\(493\) | −23.7752 | −1.07078 | ||||||||
\(494\) | −14.7984 | −0.665810 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0.997839 | 0.0448043 | ||||||||
\(497\) | 2.01705 | 0.0904770 | ||||||||
\(498\) | −1.89110 | −0.0847423 | ||||||||
\(499\) | −25.3117 | −1.13311 | −0.566554 | − | 0.824024i | \(-0.691724\pi\) | ||||
−0.566554 | + | 0.824024i | \(0.691724\pi\) | |||||||
\(500\) | 7.36038 | 0.329166 | ||||||||
\(501\) | −8.28593 | −0.370188 | ||||||||
\(502\) | −19.5367 | −0.871964 | ||||||||
\(503\) | −26.0214 | −1.16024 | −0.580119 | − | 0.814531i | \(-0.696994\pi\) | ||||
−0.580119 | + | 0.814531i | \(0.696994\pi\) | |||||||
\(504\) | −3.91151 | −0.174233 | ||||||||
\(505\) | −9.47619 | −0.421685 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 3.35836 | 0.149150 | ||||||||
\(508\) | 22.6201 | 1.00360 | ||||||||
\(509\) | 38.1269 | 1.68994 | 0.844972 | − | 0.534810i | \(-0.179617\pi\) | ||||
0.844972 | + | 0.534810i | \(0.179617\pi\) | |||||||
\(510\) | 8.40773 | 0.372301 | ||||||||
\(511\) | 9.97108 | 0.441095 | ||||||||
\(512\) | 14.2570 | 0.630077 | ||||||||
\(513\) | −6.73280 | −0.297261 | ||||||||
\(514\) | 9.47896 | 0.418099 | ||||||||
\(515\) | 50.5018 | 2.22538 | ||||||||
\(516\) | −3.37380 | −0.148523 | ||||||||
\(517\) | 0 | 0 | ||||||||
\(518\) | −1.84055 | −0.0808691 | ||||||||
\(519\) | −12.7204 | −0.558364 | ||||||||
\(520\) | −17.8168 | −0.781319 | ||||||||
\(521\) | −26.0420 | −1.14092 | −0.570460 | − | 0.821325i | \(-0.693235\pi\) | ||||
−0.570460 | + | 0.821325i | \(0.693235\pi\) | |||||||
\(522\) | −40.1509 | −1.75736 | ||||||||
\(523\) | 19.1230 | 0.836189 | 0.418095 | − | 0.908403i | \(-0.362698\pi\) | ||||
0.418095 | + | 0.908403i | \(0.362698\pi\) | |||||||
\(524\) | −7.99784 | −0.349387 | ||||||||
\(525\) | −1.67760 | −0.0732166 | ||||||||
\(526\) | −14.5404 | −0.633993 | ||||||||
\(527\) | 0.552731 | 0.0240773 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −3.90228 | −0.169664 | ||||||||
\(530\) | 19.2546 | 0.836368 | ||||||||
\(531\) | 22.4029 | 0.972201 | ||||||||
\(532\) | −2.24828 | −0.0974755 | ||||||||
\(533\) | −41.2438 | −1.78647 | ||||||||
\(534\) | −16.8116 | −0.727510 | ||||||||
\(535\) | −9.01977 | −0.389959 | ||||||||
\(536\) | 8.09401 | 0.349608 | ||||||||
\(537\) | −2.29612 | −0.0990848 | ||||||||
\(538\) | 22.8298 | 0.984265 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 11.1815 | 0.481176 | ||||||||
\(541\) | 10.8860 | 0.468027 | 0.234014 | − | 0.972233i | \(-0.424814\pi\) | ||||
0.234014 | + | 0.972233i | \(0.424814\pi\) | |||||||
\(542\) | −39.1886 | −1.68329 | ||||||||
\(543\) | 2.94915 | 0.126560 | ||||||||
\(544\) | 16.1313 | 0.691624 | ||||||||
\(545\) | −35.2495 | −1.50992 | ||||||||
\(546\) | 4.71658 | 0.201851 | ||||||||
\(547\) | −12.9091 | −0.551951 | −0.275976 | − | 0.961165i | \(-0.589001\pi\) | ||||
−0.275976 | + | 0.961165i | \(0.589001\pi\) | |||||||
\(548\) | −3.02697 | −0.129306 | ||||||||
\(549\) | 2.58821 | 0.110462 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 16.7307 | 0.712751 | ||||||||
\(552\) | −4.03527 | −0.171752 | ||||||||
\(553\) | −6.29348 | −0.267626 | ||||||||
\(554\) | 42.7964 | 1.81825 | ||||||||
\(555\) | −1.77748 | −0.0754500 | ||||||||
\(556\) | −1.16100 | −0.0492373 | ||||||||
\(557\) | −0.762626 | −0.0323135 | −0.0161567 | − | 0.999869i | \(-0.505143\pi\) | ||||
−0.0161567 | + | 0.999869i | \(0.505143\pi\) | |||||||
\(558\) | 0.933438 | 0.0395156 | ||||||||
\(559\) | 20.2146 | 0.854985 | ||||||||
\(560\) | −13.8168 | −0.583867 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 27.4476 | 1.15781 | ||||||||
\(563\) | −22.2281 | −0.936803 | −0.468402 | − | 0.883516i | \(-0.655170\pi\) | ||||
−0.468402 | + | 0.883516i | \(0.655170\pi\) | |||||||
\(564\) | −9.34817 | −0.393629 | ||||||||
\(565\) | 51.2392 | 2.15565 | ||||||||
\(566\) | −5.96758 | −0.250836 | ||||||||
\(567\) | −5.70820 | −0.239722 | ||||||||
\(568\) | 3.01360 | 0.126448 | ||||||||
\(569\) | −20.5131 | −0.859955 | −0.429978 | − | 0.902839i | \(-0.641479\pi\) | ||||
−0.429978 | + | 0.902839i | \(0.641479\pi\) | |||||||
\(570\) | −5.91656 | −0.247817 | ||||||||
\(571\) | −19.5654 | −0.818785 | −0.409393 | − | 0.912358i | \(-0.634259\pi\) | ||||
−0.409393 | + | 0.912358i | \(0.634259\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −0.512448 | −0.0214078 | ||||||||
\(574\) | −17.0748 | −0.712688 | ||||||||
\(575\) | 11.8623 | 0.494691 | ||||||||
\(576\) | 1.19493 | 0.0497888 | ||||||||
\(577\) | −19.5716 | −0.814776 | −0.407388 | − | 0.913255i | \(-0.633560\pi\) | ||||
−0.407388 | + | 0.913255i | \(0.633560\pi\) | |||||||
\(578\) | −16.7206 | −0.695487 | ||||||||
\(579\) | −4.16433 | −0.173064 | ||||||||
\(580\) | −27.7855 | −1.15373 | ||||||||
\(581\) | 1.72146 | 0.0714182 | ||||||||
\(582\) | 12.7609 | 0.528958 | ||||||||
\(583\) | 0 | 0 | ||||||||
\(584\) | 14.8974 | 0.616460 | ||||||||
\(585\) | −31.2202 | −1.29080 | ||||||||
\(586\) | 12.1528 | 0.502026 | ||||||||
\(587\) | 1.57068 | 0.0648290 | 0.0324145 | − | 0.999475i | \(-0.489680\pi\) | ||||
0.0324145 | + | 0.999475i | \(0.489680\pi\) | |||||||
\(588\) | 0.716580 | 0.0295512 | ||||||||
\(589\) | −0.388959 | −0.0160268 | ||||||||
\(590\) | 42.2460 | 1.73924 | ||||||||
\(591\) | −6.74990 | −0.277654 | ||||||||
\(592\) | −5.15107 | −0.211708 | ||||||||
\(593\) | −30.1230 | −1.23700 | −0.618502 | − | 0.785783i | \(-0.712260\pi\) | ||||
−0.618502 | + | 0.785783i | \(0.712260\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −7.65351 | −0.313763 | ||||||||
\(596\) | −17.2697 | −0.707396 | ||||||||
\(597\) | 12.9630 | 0.530540 | ||||||||
\(598\) | −33.3507 | −1.36381 | ||||||||
\(599\) | 5.77792 | 0.236079 | 0.118040 | − | 0.993009i | \(-0.462339\pi\) | ||||
0.118040 | + | 0.993009i | \(0.462339\pi\) | |||||||
\(600\) | −2.50645 | −0.102325 | ||||||||
\(601\) | 45.5645 | 1.85862 | 0.929308 | − | 0.369305i | \(-0.120404\pi\) | ||||
0.929308 | + | 0.369305i | \(0.120404\pi\) | |||||||
\(602\) | 8.36876 | 0.341085 | ||||||||
\(603\) | 14.1831 | 0.577579 | ||||||||
\(604\) | 18.3246 | 0.745619 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 3.74801 | 0.152252 | ||||||||
\(607\) | 34.7211 | 1.40928 | 0.704642 | − | 0.709563i | \(-0.251108\pi\) | ||||
0.704642 | + | 0.709563i | \(0.251108\pi\) | |||||||
\(608\) | −11.3517 | −0.460371 | ||||||||
\(609\) | −5.33245 | −0.216082 | ||||||||
\(610\) | 4.88070 | 0.197614 | ||||||||
\(611\) | 56.0107 | 2.26595 | ||||||||
\(612\) | 8.36444 | 0.338112 | ||||||||
\(613\) | −24.1423 | −0.975097 | −0.487548 | − | 0.873096i | \(-0.662109\pi\) | ||||
−0.487548 | + | 0.873096i | \(0.662109\pi\) | |||||||
\(614\) | −20.9690 | −0.846242 | ||||||||
\(615\) | −16.4897 | −0.664931 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −13.4967 | −0.543358 | −0.271679 | − | 0.962388i | \(-0.587579\pi\) | ||||
−0.271679 | + | 0.962388i | \(0.587579\pi\) | |||||||
\(618\) | −19.9744 | −0.803488 | ||||||||
\(619\) | −43.4856 | −1.74783 | −0.873917 | − | 0.486074i | \(-0.838428\pi\) | ||||
−0.873917 | + | 0.486074i | \(0.838428\pi\) | |||||||
\(620\) | 0.645964 | 0.0259425 | ||||||||
\(621\) | −15.1736 | −0.608894 | ||||||||
\(622\) | 44.9950 | 1.80414 | ||||||||
\(623\) | 15.3035 | 0.613123 | ||||||||
\(624\) | 13.2001 | 0.528427 | ||||||||
\(625\) | −31.2040 | −1.24816 | ||||||||
\(626\) | −34.9353 | −1.39629 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 5.32330 | 0.212423 | ||||||||
\(629\) | −2.85332 | −0.113769 | ||||||||
\(630\) | −12.9251 | −0.514947 | ||||||||
\(631\) | 6.42012 | 0.255581 | 0.127790 | − | 0.991801i | \(-0.459212\pi\) | ||||
0.127790 | + | 0.991801i | \(0.459212\pi\) | |||||||
\(632\) | −9.40286 | −0.374026 | ||||||||
\(633\) | −3.72279 | −0.147968 | ||||||||
\(634\) | 6.41771 | 0.254880 | ||||||||
\(635\) | −54.1868 | −2.15034 | ||||||||
\(636\) | −2.79475 | −0.110819 | ||||||||
\(637\) | −4.29348 | −0.170114 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 5.28070 | 0.208901 | ||||||||
\(640\) | −30.2660 | −1.19637 | ||||||||
\(641\) | −6.39600 | −0.252627 | −0.126313 | − | 0.991990i | \(-0.540314\pi\) | ||||
−0.126313 | + | 0.991990i | \(0.540314\pi\) | |||||||
\(642\) | 3.56748 | 0.140797 | ||||||||
\(643\) | 0.652660 | 0.0257384 | 0.0128692 | − | 0.999917i | \(-0.495903\pi\) | ||||
0.0128692 | + | 0.999917i | \(0.495903\pi\) | |||||||
\(644\) | −5.06691 | −0.199664 | ||||||||
\(645\) | 8.08201 | 0.318229 | ||||||||
\(646\) | −9.49761 | −0.373678 | ||||||||
\(647\) | 17.9621 | 0.706165 | 0.353082 | − | 0.935592i | \(-0.385134\pi\) | ||||
0.353082 | + | 0.935592i | \(0.385134\pi\) | |||||||
\(648\) | −8.52842 | −0.335028 | ||||||||
\(649\) | 0 | 0 | ||||||||
\(650\) | −20.7153 | −0.812522 | ||||||||
\(651\) | 0.123970 | 0.00485877 | ||||||||
\(652\) | 9.31925 | 0.364970 | ||||||||
\(653\) | −16.9181 | −0.662055 | −0.331028 | − | 0.943621i | \(-0.607395\pi\) | ||||
−0.331028 | + | 0.943621i | \(0.607395\pi\) | |||||||
\(654\) | 13.9418 | 0.545168 | ||||||||
\(655\) | 19.1590 | 0.748603 | ||||||||
\(656\) | −47.7866 | −1.86575 | ||||||||
\(657\) | 26.1046 | 1.01844 | ||||||||
\(658\) | 23.1882 | 0.903972 | ||||||||
\(659\) | 23.6249 | 0.920297 | 0.460148 | − | 0.887842i | \(-0.347796\pi\) | ||||
0.460148 | + | 0.887842i | \(0.347796\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −20.9819 | −0.816103 | −0.408051 | − | 0.912959i | \(-0.633792\pi\) | ||||
−0.408051 | + | 0.912959i | \(0.633792\pi\) | |||||||
\(662\) | −47.1628 | −1.83303 | ||||||||
\(663\) | 7.31191 | 0.283971 | ||||||||
\(664\) | 2.57197 | 0.0998118 | ||||||||
\(665\) | 5.38581 | 0.208853 | ||||||||
\(666\) | −4.81862 | −0.186718 | ||||||||
\(667\) | 37.7056 | 1.45997 | ||||||||
\(668\) | −15.5446 | −0.601440 | ||||||||
\(669\) | −2.85845 | −0.110514 | ||||||||
\(670\) | 26.7456 | 1.03327 | ||||||||
\(671\) | 0 | 0 | ||||||||
\(672\) | 3.61803 | 0.139569 | ||||||||
\(673\) | 12.0986 | 0.466368 | 0.233184 | − | 0.972433i | \(-0.425086\pi\) | ||||
0.233184 | + | 0.972433i | \(0.425086\pi\) | |||||||
\(674\) | −1.21932 | −0.0469663 | ||||||||
\(675\) | −9.42483 | −0.362762 | ||||||||
\(676\) | 6.30038 | 0.242322 | ||||||||
\(677\) | −9.42988 | −0.362420 | −0.181210 | − | 0.983444i | \(-0.558001\pi\) | ||||
−0.181210 | + | 0.983444i | \(0.558001\pi\) | |||||||
\(678\) | −20.2660 | −0.778312 | ||||||||
\(679\) | −11.6162 | −0.445790 | ||||||||
\(680\) | −11.4348 | −0.438506 | ||||||||
\(681\) | 10.6922 | 0.409726 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −15.2986 | −0.585385 | −0.292692 | − | 0.956207i | \(-0.594551\pi\) | ||||
−0.292692 | + | 0.956207i | \(0.594551\pi\) | |||||||
\(684\) | −5.88609 | −0.225060 | ||||||||
\(685\) | 7.25117 | 0.277053 | ||||||||
\(686\) | −1.77748 | −0.0678647 | ||||||||
\(687\) | −2.73549 | −0.104366 | ||||||||
\(688\) | 23.4213 | 0.892929 | ||||||||
\(689\) | 16.7451 | 0.637936 | ||||||||
\(690\) | −13.3340 | −0.507617 | ||||||||
\(691\) | 22.8193 | 0.868086 | 0.434043 | − | 0.900892i | \(-0.357087\pi\) | ||||
0.434043 | + | 0.900892i | \(0.357087\pi\) | |||||||
\(692\) | −23.8639 | −0.907169 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 38.2256 | 1.45102 | ||||||||
\(695\) | 2.78119 | 0.105497 | ||||||||
\(696\) | −7.96703 | −0.301989 | ||||||||
\(697\) | −26.4703 | −1.00263 | ||||||||
\(698\) | 34.5594 | 1.30809 | ||||||||
\(699\) | −6.50978 | −0.246222 | ||||||||
\(700\) | −3.14723 | −0.118954 | ||||||||
\(701\) | −32.3242 | −1.22087 | −0.610433 | − | 0.792068i | \(-0.709005\pi\) | ||||
−0.610433 | + | 0.792068i | \(0.709005\pi\) | |||||||
\(702\) | 26.4979 | 1.00010 | ||||||||
\(703\) | 2.00789 | 0.0757292 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 22.3937 | 0.843396 | ||||||||
\(706\) | −37.2040 | −1.40019 | ||||||||
\(707\) | −3.41179 | −0.128314 | ||||||||
\(708\) | −6.13186 | −0.230450 | ||||||||
\(709\) | 14.5598 | 0.546804 | 0.273402 | − | 0.961900i | \(-0.411851\pi\) | ||||
0.273402 | + | 0.961900i | \(0.411851\pi\) | |||||||
\(710\) | 9.95804 | 0.373718 | ||||||||
\(711\) | −16.4765 | −0.617918 | ||||||||
\(712\) | 22.8645 | 0.856882 | ||||||||
\(713\) | −0.876587 | −0.0328285 | ||||||||
\(714\) | 3.02710 | 0.113287 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | −4.30759 | −0.160982 | ||||||||
\(717\) | −6.02982 | −0.225188 | ||||||||
\(718\) | 17.3683 | 0.648178 | ||||||||
\(719\) | 44.8602 | 1.67300 | 0.836501 | − | 0.547965i | \(-0.184597\pi\) | ||||
0.836501 | + | 0.547965i | \(0.184597\pi\) | |||||||
\(720\) | −36.1729 | −1.34808 | ||||||||
\(721\) | 18.1826 | 0.677155 | ||||||||
\(722\) | −27.0887 | −1.00814 | ||||||||
\(723\) | 7.75638 | 0.288463 | ||||||||
\(724\) | 5.53270 | 0.205621 | ||||||||
\(725\) | 23.4202 | 0.869806 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 28.3582 | 1.05175 | 0.525874 | − | 0.850562i | \(-0.323738\pi\) | ||||
0.525874 | + | 0.850562i | \(0.323738\pi\) | |||||||
\(728\) | −6.41473 | −0.237746 | ||||||||
\(729\) | −8.50658 | −0.315058 | ||||||||
\(730\) | 49.2266 | 1.82196 | ||||||||
\(731\) | 12.9737 | 0.479850 | ||||||||
\(732\) | −0.708417 | −0.0261838 | ||||||||
\(733\) | 6.25696 | 0.231106 | 0.115553 | − | 0.993301i | \(-0.463136\pi\) | ||||
0.115553 | + | 0.993301i | \(0.463136\pi\) | |||||||
\(734\) | 17.5965 | 0.649500 | ||||||||
\(735\) | −1.71658 | −0.0633170 | ||||||||
\(736\) | −25.5830 | −0.943001 | ||||||||
\(737\) | 0 | 0 | ||||||||
\(738\) | −44.7024 | −1.64552 | ||||||||
\(739\) | 9.35201 | 0.344019 | 0.172010 | − | 0.985095i | \(-0.444974\pi\) | ||||
0.172010 | + | 0.985095i | \(0.444974\pi\) | |||||||
\(740\) | −3.33461 | −0.122583 | ||||||||
\(741\) | −5.14542 | −0.189022 | ||||||||
\(742\) | 6.93240 | 0.254496 | ||||||||
\(743\) | 25.2066 | 0.924740 | 0.462370 | − | 0.886687i | \(-0.346999\pi\) | ||||
0.462370 | + | 0.886687i | \(0.346999\pi\) | |||||||
\(744\) | 0.185219 | 0.00679047 | ||||||||
\(745\) | 41.3700 | 1.51568 | ||||||||
\(746\) | −7.59830 | −0.278193 | ||||||||
\(747\) | 4.50684 | 0.164897 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −3.24746 | −0.118660 | ||||||||
\(750\) | 6.97375 | 0.254645 | ||||||||
\(751\) | −34.7493 | −1.26802 | −0.634010 | − | 0.773325i | \(-0.718592\pi\) | ||||
−0.634010 | + | 0.773325i | \(0.718592\pi\) | |||||||
\(752\) | 64.8960 | 2.36651 | ||||||||
\(753\) | −6.79293 | −0.247548 | ||||||||
\(754\) | −65.8460 | −2.39797 | ||||||||
\(755\) | −43.8970 | −1.59758 | ||||||||
\(756\) | 4.02577 | 0.146416 | ||||||||
\(757\) | 34.7960 | 1.26468 | 0.632341 | − | 0.774690i | \(-0.282094\pi\) | ||||
0.632341 | + | 0.774690i | \(0.282094\pi\) | |||||||
\(758\) | 7.68929 | 0.279288 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 8.04674 | 0.291886 | ||||||||
\(761\) | −12.2255 | −0.443172 | −0.221586 | − | 0.975141i | \(-0.571123\pi\) | ||||
−0.221586 | + | 0.975141i | \(0.571123\pi\) | |||||||
\(762\) | 21.4319 | 0.776394 | ||||||||
\(763\) | −12.6912 | −0.459451 | ||||||||
\(764\) | −0.961368 | −0.0347811 | ||||||||
\(765\) | −20.0372 | −0.724445 | ||||||||
\(766\) | −2.35001 | −0.0849094 | ||||||||
\(767\) | 36.7398 | 1.32660 | ||||||||
\(768\) | 12.5349 | 0.452315 | ||||||||
\(769\) | −2.61946 | −0.0944603 | −0.0472301 | − | 0.998884i | \(-0.515039\pi\) | ||||
−0.0472301 | + | 0.998884i | \(0.515039\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 3.29585 | 0.118697 | ||||||||
\(772\) | −7.81241 | −0.281175 | ||||||||
\(773\) | −0.212804 | −0.00765405 | −0.00382702 | − | 0.999993i | \(-0.501218\pi\) | ||||
−0.00382702 | + | 0.999993i | \(0.501218\pi\) | |||||||
\(774\) | 21.9097 | 0.787528 | ||||||||
\(775\) | −0.544479 | −0.0195583 | ||||||||
\(776\) | −17.3554 | −0.623022 | ||||||||
\(777\) | −0.639962 | −0.0229585 | ||||||||
\(778\) | −68.4494 | −2.45403 | ||||||||
\(779\) | 18.6273 | 0.667391 | ||||||||
\(780\) | 8.54526 | 0.305969 | ||||||||
\(781\) | 0 | 0 | ||||||||
\(782\) | −21.4045 | −0.765425 | ||||||||
\(783\) | −29.9579 | −1.07061 | ||||||||
\(784\) | −4.97458 | −0.177663 | ||||||||
\(785\) | −12.7521 | −0.455141 | ||||||||
\(786\) | −7.57772 | −0.270288 | ||||||||
\(787\) | 29.1375 | 1.03864 | 0.519320 | − | 0.854580i | \(-0.326185\pi\) | ||||
0.519320 | + | 0.854580i | \(0.326185\pi\) | |||||||
\(788\) | −12.6630 | −0.451101 | ||||||||
\(789\) | −5.05573 | −0.179989 | ||||||||
\(790\) | −31.0705 | −1.10544 | ||||||||
\(791\) | 18.4480 | 0.655937 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 4.24457 | 0.150729 | ||||||||
\(794\) | −0.728962 | −0.0258699 | ||||||||
\(795\) | 6.69486 | 0.237442 | ||||||||
\(796\) | 24.3190 | 0.861963 | ||||||||
\(797\) | 32.2284 | 1.14159 | 0.570794 | − | 0.821093i | \(-0.306635\pi\) | ||||
0.570794 | + | 0.821093i | \(0.306635\pi\) | |||||||
\(798\) | −2.13018 | −0.0754077 | ||||||||
\(799\) | 35.9477 | 1.27174 | ||||||||
\(800\) | −15.8905 | −0.561813 | ||||||||
\(801\) | 40.0652 | 1.41563 | ||||||||
\(802\) | −2.78503 | −0.0983430 | ||||||||
\(803\) | 0 | 0 | ||||||||
\(804\) | −3.88203 | −0.136909 | ||||||||
\(805\) | 12.1379 | 0.427804 | ||||||||
\(806\) | 1.53080 | 0.0539202 | ||||||||
\(807\) | 7.93797 | 0.279430 | ||||||||
\(808\) | −5.09743 | −0.179327 | ||||||||
\(809\) | −29.3461 | −1.03175 | −0.515877 | − | 0.856663i | \(-0.672534\pi\) | ||||
−0.515877 | + | 0.856663i | \(0.672534\pi\) | |||||||
\(810\) | −28.1810 | −0.990180 | ||||||||
\(811\) | 1.03940 | 0.0364982 | 0.0182491 | − | 0.999833i | \(-0.494191\pi\) | ||||
0.0182491 | + | 0.999833i | \(0.494191\pi\) | |||||||
\(812\) | −10.0038 | −0.351066 | ||||||||
\(813\) | −13.6259 | −0.477882 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −22.3244 | −0.781990 | ||||||||
\(816\) | 8.47184 | 0.296574 | ||||||||
\(817\) | −9.12966 | −0.319406 | ||||||||
\(818\) | −12.0487 | −0.421274 | ||||||||
\(819\) | −11.2405 | −0.392774 | ||||||||
\(820\) | −30.9352 | −1.08031 | ||||||||
\(821\) | 28.5323 | 0.995786 | 0.497893 | − | 0.867239i | \(-0.334107\pi\) | ||||
0.497893 | + | 0.867239i | \(0.334107\pi\) | |||||||
\(822\) | −2.86797 | −0.100032 | ||||||||
\(823\) | 26.6577 | 0.929227 | 0.464614 | − | 0.885513i | \(-0.346193\pi\) | ||||
0.464614 | + | 0.885513i | \(0.346193\pi\) | |||||||
\(824\) | 27.1659 | 0.946370 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 15.2102 | 0.529229 | ||||||||
\(827\) | 1.71964 | 0.0597978 | 0.0298989 | − | 0.999553i | \(-0.490481\pi\) | ||||
0.0298989 | + | 0.999553i | \(0.490481\pi\) | |||||||
\(828\) | −13.2653 | −0.461002 | ||||||||
\(829\) | 27.9605 | 0.971107 | 0.485554 | − | 0.874207i | \(-0.338618\pi\) | ||||
0.485554 | + | 0.874207i | \(0.338618\pi\) | |||||||
\(830\) | 8.49873 | 0.294995 | ||||||||
\(831\) | 14.8804 | 0.516195 | ||||||||
\(832\) | 1.95964 | 0.0679383 | ||||||||
\(833\) | −2.75556 | −0.0954744 | ||||||||
\(834\) | −1.10001 | −0.0380903 | ||||||||
\(835\) | 37.2375 | 1.28866 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0.696468 | 0.0240735 | ||||||||
\(838\) | 51.0526 | 1.76358 | ||||||||
\(839\) | 35.8624 | 1.23811 | 0.619054 | − | 0.785348i | \(-0.287516\pi\) | ||||
0.619054 | + | 0.785348i | \(0.287516\pi\) | |||||||
\(840\) | −2.56468 | −0.0884899 | ||||||||
\(841\) | 45.4439 | 1.56703 | ||||||||
\(842\) | 21.7308 | 0.748892 | ||||||||
\(843\) | 9.54358 | 0.328698 | ||||||||
\(844\) | −6.98407 | −0.240402 | ||||||||
\(845\) | −15.0927 | −0.519204 | ||||||||
\(846\) | 60.7076 | 2.08717 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | 19.4014 | 0.666248 | ||||||||
\(849\) | −2.07494 | −0.0712117 | ||||||||
\(850\) | −13.2951 | −0.456018 | ||||||||
\(851\) | 4.52515 | 0.155120 | ||||||||
\(852\) | −1.44538 | −0.0495178 | ||||||||
\(853\) | −15.1427 | −0.518478 | −0.259239 | − | 0.965813i | \(-0.583472\pi\) | ||||
−0.259239 | + | 0.965813i | \(0.583472\pi\) | |||||||
\(854\) | 1.75724 | 0.0601314 | ||||||||
\(855\) | 14.1002 | 0.482218 | ||||||||
\(856\) | −4.85191 | −0.165835 | ||||||||
\(857\) | 25.3267 | 0.865142 | 0.432571 | − | 0.901600i | \(-0.357606\pi\) | ||||
0.432571 | + | 0.901600i | \(0.357606\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 41.5291 | 1.41696 | 0.708478 | − | 0.705733i | \(-0.249382\pi\) | ||||
0.708478 | + | 0.705733i | \(0.249382\pi\) | |||||||
\(860\) | 15.1621 | 0.517023 | ||||||||
\(861\) | −5.93693 | −0.202330 | ||||||||
\(862\) | 6.56121 | 0.223476 | ||||||||
\(863\) | −24.0504 | −0.818684 | −0.409342 | − | 0.912381i | \(-0.634242\pi\) | ||||
−0.409342 | + | 0.912381i | \(0.634242\pi\) | |||||||
\(864\) | 20.3262 | 0.691513 | ||||||||
\(865\) | 57.1664 | 1.94372 | ||||||||
\(866\) | 51.6801 | 1.75616 | ||||||||
\(867\) | −5.81379 | −0.197447 | ||||||||
\(868\) | 0.232572 | 0.00789399 | ||||||||
\(869\) | 0 | 0 | ||||||||
\(870\) | −26.3260 | −0.892534 | ||||||||
\(871\) | 23.2597 | 0.788124 | ||||||||
\(872\) | −18.9614 | −0.642114 | ||||||||
\(873\) | −30.4117 | −1.02928 | ||||||||
\(874\) | 15.0625 | 0.509495 | ||||||||
\(875\) | −6.34817 | −0.214607 | ||||||||
\(876\) | −7.14507 | −0.241410 | ||||||||
\(877\) | 33.8052 | 1.14152 | 0.570760 | − | 0.821117i | \(-0.306649\pi\) | ||||
0.570760 | + | 0.821117i | \(0.306649\pi\) | |||||||
\(878\) | −25.2433 | −0.851921 | ||||||||
\(879\) | 4.22553 | 0.142524 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −36.8296 | −1.24082 | −0.620410 | − | 0.784278i | \(-0.713034\pi\) | ||||
−0.620410 | + | 0.784278i | \(0.713034\pi\) | |||||||
\(882\) | −4.65351 | −0.156692 | ||||||||
\(883\) | 53.4103 | 1.79740 | 0.898701 | − | 0.438563i | \(-0.144512\pi\) | ||||
0.898701 | + | 0.438563i | \(0.144512\pi\) | |||||||
\(884\) | 13.7174 | 0.461365 | ||||||||
\(885\) | 14.6890 | 0.493765 | ||||||||
\(886\) | 48.4108 | 1.62639 | ||||||||
\(887\) | 11.4616 | 0.384843 | 0.192421 | − | 0.981312i | \(-0.438366\pi\) | ||||
0.192421 | + | 0.981312i | \(0.438366\pi\) | |||||||
\(888\) | −0.956144 | −0.0320861 | ||||||||
\(889\) | −19.5093 | −0.654321 | ||||||||
\(890\) | 75.5525 | 2.53253 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | −5.36254 | −0.179551 | ||||||||
\(893\) | −25.2965 | −0.846516 | ||||||||
\(894\) | −16.3626 | −0.547246 | ||||||||
\(895\) | 10.3189 | 0.344923 | ||||||||
\(896\) | −10.8969 | −0.364041 | ||||||||
\(897\) | −11.5961 | −0.387183 | ||||||||
\(898\) | −74.5049 | −2.48626 | ||||||||
\(899\) | −1.73069 | −0.0577217 | ||||||||
\(900\) | −8.23956 | −0.274652 | ||||||||
\(901\) | 10.7470 | 0.358034 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 2.90983 | 0.0968331 | ||||||||
\(904\) | 27.5626 | 0.916717 | ||||||||
\(905\) | −13.2537 | −0.440567 | ||||||||
\(906\) | 17.3621 | 0.576816 | ||||||||
\(907\) | 57.0582 | 1.89459 | 0.947293 | − | 0.320369i | \(-0.103807\pi\) | ||||
0.947293 | + | 0.320369i | \(0.103807\pi\) | |||||||
\(908\) | 20.0589 | 0.665677 | ||||||||
\(909\) | −8.93218 | −0.296262 | ||||||||
\(910\) | −21.1966 | −0.702661 | ||||||||
\(911\) | 6.67566 | 0.221175 | 0.110587 | − | 0.993866i | \(-0.464727\pi\) | ||||
0.110587 | + | 0.993866i | \(0.464727\pi\) | |||||||
\(912\) | −5.96167 | −0.197410 | ||||||||
\(913\) | 0 | 0 | ||||||||
\(914\) | 34.6568 | 1.14635 | ||||||||
\(915\) | 1.69703 | 0.0561019 | ||||||||
\(916\) | −5.13186 | −0.169562 | ||||||||
\(917\) | 6.89796 | 0.227791 | ||||||||
\(918\) | 17.0064 | 0.561294 | ||||||||
\(919\) | −29.1339 | −0.961038 | −0.480519 | − | 0.876984i | \(-0.659552\pi\) | ||||
−0.480519 | + | 0.876984i | \(0.659552\pi\) | |||||||
\(920\) | 18.1347 | 0.597885 | ||||||||
\(921\) | −7.29097 | −0.240246 | ||||||||
\(922\) | 21.7299 | 0.715637 | ||||||||
\(923\) | 8.66015 | 0.285052 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 2.81073 | 0.0924161 | ||||||||
\(926\) | 24.6270 | 0.809292 | ||||||||
\(927\) | 47.6026 | 1.56347 | ||||||||
\(928\) | −50.5097 | −1.65806 | ||||||||
\(929\) | 2.34472 | 0.0769277 | 0.0384638 | − | 0.999260i | \(-0.487754\pi\) | ||||
0.0384638 | + | 0.999260i | \(0.487754\pi\) | |||||||
\(930\) | 0.612032 | 0.0200693 | ||||||||
\(931\) | 1.93910 | 0.0635513 | ||||||||
\(932\) | −12.2125 | −0.400035 | ||||||||
\(933\) | 15.6448 | 0.512189 | ||||||||
\(934\) | −29.1876 | −0.955047 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | −16.7940 | −0.548928 | ||||||||
\(937\) | 8.78780 | 0.287085 | 0.143542 | − | 0.989644i | \(-0.454151\pi\) | ||||
0.143542 | + | 0.989644i | \(0.454151\pi\) | |||||||
\(938\) | 9.62943 | 0.314412 | ||||||||
\(939\) | −12.1470 | −0.396404 | ||||||||
\(940\) | 42.0113 | 1.37026 | ||||||||
\(941\) | 8.88871 | 0.289764 | 0.144882 | − | 0.989449i | \(-0.453720\pi\) | ||||
0.144882 | + | 0.989449i | \(0.453720\pi\) | |||||||
\(942\) | 5.04367 | 0.164332 | ||||||||
\(943\) | 41.9798 | 1.36705 | ||||||||
\(944\) | 42.5681 | 1.38547 | ||||||||
\(945\) | −9.64380 | −0.313713 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −7.86275 | −0.255505 | −0.127752 | − | 0.991806i | \(-0.540776\pi\) | ||||
−0.127752 | + | 0.991806i | \(0.540776\pi\) | |||||||
\(948\) | 4.50978 | 0.146471 | ||||||||
\(949\) | 42.8106 | 1.38969 | ||||||||
\(950\) | 9.35582 | 0.303543 | ||||||||
\(951\) | 2.23145 | 0.0723597 | ||||||||
\(952\) | −4.11698 | −0.133432 | ||||||||
\(953\) | −17.4644 | −0.565727 | −0.282864 | − | 0.959160i | \(-0.591284\pi\) | ||||
−0.282864 | + | 0.959160i | \(0.591284\pi\) | |||||||
\(954\) | 18.1493 | 0.587604 | ||||||||
\(955\) | 2.30297 | 0.0745225 | ||||||||
\(956\) | −11.3121 | −0.365860 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | −44.0663 | −1.42372 | ||||||||
\(959\) | 2.61070 | 0.0843038 | ||||||||
\(960\) | 0.783486 | 0.0252869 | ||||||||
\(961\) | −30.9598 | −0.998702 | ||||||||
\(962\) | −7.90236 | −0.254782 | ||||||||
\(963\) | −8.50196 | −0.273972 | ||||||||
\(964\) | 14.5512 | 0.468663 | ||||||||
\(965\) | 18.7148 | 0.602450 | ||||||||
\(966\) | −4.80075 | −0.154462 | ||||||||
\(967\) | −45.6122 | −1.46679 | −0.733395 | − | 0.679802i | \(-0.762066\pi\) | ||||
−0.733395 | + | 0.679802i | \(0.762066\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −3.30233 | −0.106086 | ||||||||
\(970\) | −57.3485 | −1.84135 | ||||||||
\(971\) | 2.38378 | 0.0764992 | 0.0382496 | − | 0.999268i | \(-0.487822\pi\) | ||||
0.0382496 | + | 0.999268i | \(0.487822\pi\) | |||||||
\(972\) | 16.1677 | 0.518579 | ||||||||
\(973\) | 1.00134 | 0.0321013 | ||||||||
\(974\) | −25.4788 | −0.816393 | ||||||||
\(975\) | −7.20275 | −0.230673 | ||||||||
\(976\) | 4.91791 | 0.157418 | ||||||||
\(977\) | −19.2662 | −0.616380 | −0.308190 | − | 0.951325i | \(-0.599723\pi\) | ||||
−0.308190 | + | 0.951325i | \(0.599723\pi\) | |||||||
\(978\) | 8.82972 | 0.282343 | ||||||||
\(979\) | 0 | 0 | ||||||||
\(980\) | −3.22035 | −0.102870 | ||||||||
\(981\) | −33.2259 | −1.06082 | ||||||||
\(982\) | −39.1390 | −1.24898 | ||||||||
\(983\) | −16.2256 | −0.517517 | −0.258759 | − | 0.965942i | \(-0.583313\pi\) | ||||
−0.258759 | + | 0.965942i | \(0.583313\pi\) | |||||||
\(984\) | −8.87016 | −0.282770 | ||||||||
\(985\) | 30.3345 | 0.966537 | ||||||||
\(986\) | −42.2600 | −1.34583 | ||||||||
\(987\) | 8.06258 | 0.256635 | ||||||||
\(988\) | −9.65296 | −0.307101 | ||||||||
\(989\) | −20.5753 | −0.654256 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −50.5214 | −1.60487 | −0.802433 | − | 0.596743i | \(-0.796461\pi\) | ||||
−0.802433 | + | 0.596743i | \(0.796461\pi\) | |||||||
\(992\) | 1.17426 | 0.0372828 | ||||||||
\(993\) | −16.3986 | −0.520393 | ||||||||
\(994\) | 3.58527 | 0.113718 | ||||||||
\(995\) | −58.2566 | −1.84686 | ||||||||
\(996\) | −1.23356 | −0.0390869 | ||||||||
\(997\) | −45.0206 | −1.42582 | −0.712909 | − | 0.701257i | \(-0.752623\pi\) | ||||
−0.712909 | + | 0.701257i | \(0.752623\pi\) | |||||||
\(998\) | −44.9912 | −1.42417 | ||||||||
\(999\) | −3.59533 | −0.113751 |
(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 | 847.2.a.l.1.3 | 4 | ||
3.2 | odd | 2 | 7623.2.a.ch.1.2 | 4 | |||
7.6 | odd | 2 | 5929.2.a.bi.1.3 | 4 | |||
11.2 | odd | 10 | 847.2.f.s.323.2 | 8 | |||
11.3 | even | 5 | 77.2.f.a.64.2 | ✓ | 8 | ||
11.4 | even | 5 | 77.2.f.a.71.2 | yes | 8 | ||
11.5 | even | 5 | 847.2.f.p.729.1 | 8 | |||
11.6 | odd | 10 | 847.2.f.s.729.2 | 8 | |||
11.7 | odd | 10 | 847.2.f.q.148.1 | 8 | |||
11.8 | odd | 10 | 847.2.f.q.372.1 | 8 | |||
11.9 | even | 5 | 847.2.f.p.323.1 | 8 | |||
11.10 | odd | 2 | 847.2.a.k.1.2 | 4 | |||
33.14 | odd | 10 | 693.2.m.g.64.1 | 8 | |||
33.26 | odd | 10 | 693.2.m.g.379.1 | 8 | |||
33.32 | even | 2 | 7623.2.a.co.1.3 | 4 | |||
77.3 | odd | 30 | 539.2.q.b.471.2 | 16 | |||
77.4 | even | 15 | 539.2.q.c.324.1 | 16 | |||
77.25 | even | 15 | 539.2.q.c.471.2 | 16 | |||
77.26 | odd | 30 | 539.2.q.b.214.2 | 16 | |||
77.37 | even | 15 | 539.2.q.c.214.2 | 16 | |||
77.47 | odd | 30 | 539.2.q.b.361.1 | 16 | |||
77.48 | odd | 10 | 539.2.f.d.148.2 | 8 | |||
77.58 | even | 15 | 539.2.q.c.361.1 | 16 | |||
77.59 | odd | 30 | 539.2.q.b.324.1 | 16 | |||
77.69 | odd | 10 | 539.2.f.d.295.2 | 8 | |||
77.76 | even | 2 | 5929.2.a.bb.1.2 | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
77.2.f.a.64.2 | ✓ | 8 | 11.3 | even | 5 | ||
77.2.f.a.71.2 | yes | 8 | 11.4 | even | 5 | ||
539.2.f.d.148.2 | 8 | 77.48 | odd | 10 | |||
539.2.f.d.295.2 | 8 | 77.69 | odd | 10 | |||
539.2.q.b.214.2 | 16 | 77.26 | odd | 30 | |||
539.2.q.b.324.1 | 16 | 77.59 | odd | 30 | |||
539.2.q.b.361.1 | 16 | 77.47 | odd | 30 | |||
539.2.q.b.471.2 | 16 | 77.3 | odd | 30 | |||
539.2.q.c.214.2 | 16 | 77.37 | even | 15 | |||
539.2.q.c.324.1 | 16 | 77.4 | even | 15 | |||
539.2.q.c.361.1 | 16 | 77.58 | even | 15 | |||
539.2.q.c.471.2 | 16 | 77.25 | even | 15 | |||
693.2.m.g.64.1 | 8 | 33.14 | odd | 10 | |||
693.2.m.g.379.1 | 8 | 33.26 | odd | 10 | |||
847.2.a.k.1.2 | 4 | 11.10 | odd | 2 | |||
847.2.a.l.1.3 | 4 | 1.1 | even | 1 | trivial | ||
847.2.f.p.323.1 | 8 | 11.9 | even | 5 | |||
847.2.f.p.729.1 | 8 | 11.5 | even | 5 | |||
847.2.f.q.148.1 | 8 | 11.7 | odd | 10 | |||
847.2.f.q.372.1 | 8 | 11.8 | odd | 10 | |||
847.2.f.s.323.2 | 8 | 11.2 | odd | 10 | |||
847.2.f.s.729.2 | 8 | 11.6 | odd | 10 | |||
5929.2.a.bb.1.2 | 4 | 77.76 | even | 2 | |||
5929.2.a.bi.1.3 | 4 | 7.6 | odd | 2 | |||
7623.2.a.ch.1.2 | 4 | 3.2 | odd | 2 | |||
7623.2.a.co.1.3 | 4 | 33.32 | even | 2 |