Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [2842,2,Mod(1,2842)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(2842, 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("2842.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 2842 = 2 \cdot 7^{2} \cdot 29 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 2842.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: | \(22.6934842544\) |
Analytic rank: | \(0\) |
Dimension: | \(5\) |
Coefficient field: | 5.5.1019601.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: |
\( x^{5} - 10x^{3} - x^{2} + 24x + 7 \)
|
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 406) |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.5 | ||
Root | \(2.37936\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 2842.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 1.00000 | 0.707107 | ||||||||
\(3\) | 3.23497 | 1.86771 | 0.933854 | − | 0.357653i | \(-0.116423\pi\) | ||||
0.933854 | + | 0.357653i | \(0.116423\pi\) | |||||||
\(4\) | 1.00000 | 0.500000 | ||||||||
\(5\) | 1.14439 | 0.511789 | 0.255894 | − | 0.966705i | \(-0.417630\pi\) | ||||
0.255894 | + | 0.966705i | \(0.417630\pi\) | |||||||
\(6\) | 3.23497 | 1.32067 | ||||||||
\(7\) | 0 | 0 | ||||||||
\(8\) | 1.00000 | 0.353553 | ||||||||
\(9\) | 7.46501 | 2.48834 | ||||||||
\(10\) | 1.14439 | 0.361889 | ||||||||
\(11\) | −0.850683 | −0.256491 | −0.128245 | − | 0.991742i | \(-0.540934\pi\) | ||||
−0.128245 | + | 0.991742i | \(0.540934\pi\) | |||||||
\(12\) | 3.23497 | 0.933854 | ||||||||
\(13\) | 3.66136 | 1.01548 | 0.507739 | − | 0.861511i | \(-0.330481\pi\) | ||||
0.507739 | + | 0.861511i | \(0.330481\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 3.70208 | 0.955872 | ||||||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | 0.194248 | 0.0471121 | 0.0235561 | − | 0.999723i | \(-0.492501\pi\) | ||||
0.0235561 | + | 0.999723i | \(0.492501\pi\) | |||||||
\(18\) | 7.46501 | 1.75952 | ||||||||
\(19\) | −6.99369 | −1.60446 | −0.802231 | − | 0.597014i | \(-0.796354\pi\) | ||||
−0.802231 | + | 0.597014i | \(0.796354\pi\) | |||||||
\(20\) | 1.14439 | 0.255894 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −0.850683 | −0.181366 | ||||||||
\(23\) | −3.46219 | −0.721916 | −0.360958 | − | 0.932582i | \(-0.617550\pi\) | ||||
−0.360958 | + | 0.932582i | \(0.617550\pi\) | |||||||
\(24\) | 3.23497 | 0.660335 | ||||||||
\(25\) | −3.69036 | −0.738072 | ||||||||
\(26\) | 3.66136 | 0.718051 | ||||||||
\(27\) | 14.4442 | 2.77978 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −1.00000 | −0.185695 | ||||||||
\(30\) | 3.70208 | 0.675904 | ||||||||
\(31\) | −3.97423 | −0.713792 | −0.356896 | − | 0.934144i | \(-0.616165\pi\) | ||||
−0.356896 | + | 0.934144i | \(0.616165\pi\) | |||||||
\(32\) | 1.00000 | 0.176777 | ||||||||
\(33\) | −2.75193 | −0.479050 | ||||||||
\(34\) | 0.194248 | 0.0333133 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 7.46501 | 1.24417 | ||||||||
\(37\) | 7.20919 | 1.18518 | 0.592592 | − | 0.805503i | \(-0.298105\pi\) | ||||
0.592592 | + | 0.805503i | \(0.298105\pi\) | |||||||
\(38\) | −6.99369 | −1.13453 | ||||||||
\(39\) | 11.8444 | 1.89662 | ||||||||
\(40\) | 1.14439 | 0.180945 | ||||||||
\(41\) | 4.04493 | 0.631712 | 0.315856 | − | 0.948807i | \(-0.397708\pi\) | ||||
0.315856 | + | 0.948807i | \(0.397708\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 9.77788 | 1.49111 | 0.745556 | − | 0.666443i | \(-0.232184\pi\) | ||||
0.745556 | + | 0.666443i | \(0.232184\pi\) | |||||||
\(44\) | −0.850683 | −0.128245 | ||||||||
\(45\) | 8.54291 | 1.27350 | ||||||||
\(46\) | −3.46219 | −0.510472 | ||||||||
\(47\) | 0.0538211 | 0.00785061 | 0.00392531 | − | 0.999992i | \(-0.498751\pi\) | ||||
0.00392531 | + | 0.999992i | \(0.498751\pi\) | |||||||
\(48\) | 3.23497 | 0.466927 | ||||||||
\(49\) | 0 | 0 | ||||||||
\(50\) | −3.69036 | −0.521896 | ||||||||
\(51\) | 0.628386 | 0.0879917 | ||||||||
\(52\) | 3.66136 | 0.507739 | ||||||||
\(53\) | −2.67097 | −0.366886 | −0.183443 | − | 0.983030i | \(-0.558724\pi\) | ||||
−0.183443 | + | 0.983030i | \(0.558724\pi\) | |||||||
\(54\) | 14.4442 | 1.96560 | ||||||||
\(55\) | −0.973516 | −0.131269 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −22.6244 | −2.99667 | ||||||||
\(58\) | −1.00000 | −0.131306 | ||||||||
\(59\) | −8.04354 | −1.04718 | −0.523590 | − | 0.851970i | \(-0.675408\pi\) | ||||
−0.523590 | + | 0.851970i | \(0.675408\pi\) | |||||||
\(60\) | 3.70208 | 0.477936 | ||||||||
\(61\) | −5.08144 | −0.650611 | −0.325306 | − | 0.945609i | \(-0.605467\pi\) | ||||
−0.325306 | + | 0.945609i | \(0.605467\pi\) | |||||||
\(62\) | −3.97423 | −0.504727 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | 4.19004 | 0.519710 | ||||||||
\(66\) | −2.75193 | −0.338739 | ||||||||
\(67\) | −11.6003 | −1.41720 | −0.708599 | − | 0.705611i | \(-0.750673\pi\) | ||||
−0.708599 | + | 0.705611i | \(0.750673\pi\) | |||||||
\(68\) | 0.194248 | 0.0235561 | ||||||||
\(69\) | −11.2001 | −1.34833 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −11.2825 | −1.33898 | −0.669492 | − | 0.742819i | \(-0.733488\pi\) | ||||
−0.669492 | + | 0.742819i | \(0.733488\pi\) | |||||||
\(72\) | 7.46501 | 0.879760 | ||||||||
\(73\) | −7.31077 | −0.855661 | −0.427830 | − | 0.903859i | \(-0.640722\pi\) | ||||
−0.427830 | + | 0.903859i | \(0.640722\pi\) | |||||||
\(74\) | 7.20919 | 0.838052 | ||||||||
\(75\) | −11.9382 | −1.37850 | ||||||||
\(76\) | −6.99369 | −0.802231 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 11.8444 | 1.34111 | ||||||||
\(79\) | −13.3564 | −1.50271 | −0.751357 | − | 0.659896i | \(-0.770600\pi\) | ||||
−0.751357 | + | 0.659896i | \(0.770600\pi\) | |||||||
\(80\) | 1.14439 | 0.127947 | ||||||||
\(81\) | 24.3314 | 2.70348 | ||||||||
\(82\) | 4.04493 | 0.446688 | ||||||||
\(83\) | 9.04564 | 0.992888 | 0.496444 | − | 0.868069i | \(-0.334639\pi\) | ||||
0.496444 | + | 0.868069i | \(0.334639\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0.222296 | 0.0241114 | ||||||||
\(86\) | 9.77788 | 1.05438 | ||||||||
\(87\) | −3.23497 | −0.346825 | ||||||||
\(88\) | −0.850683 | −0.0906831 | ||||||||
\(89\) | 14.2305 | 1.50843 | 0.754216 | − | 0.656626i | \(-0.228017\pi\) | ||||
0.754216 | + | 0.656626i | \(0.228017\pi\) | |||||||
\(90\) | 8.54291 | 0.900502 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | −3.46219 | −0.360958 | ||||||||
\(93\) | −12.8565 | −1.33316 | ||||||||
\(94\) | 0.0538211 | 0.00555122 | ||||||||
\(95\) | −8.00353 | −0.821145 | ||||||||
\(96\) | 3.23497 | 0.330167 | ||||||||
\(97\) | 18.7779 | 1.90660 | 0.953302 | − | 0.302017i | \(-0.0976601\pi\) | ||||
0.953302 | + | 0.302017i | \(0.0976601\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −6.35036 | −0.638235 | ||||||||
\(100\) | −3.69036 | −0.369036 | ||||||||
\(101\) | 13.7194 | 1.36513 | 0.682564 | − | 0.730826i | \(-0.260865\pi\) | ||||
0.682564 | + | 0.730826i | \(0.260865\pi\) | |||||||
\(102\) | 0.628386 | 0.0622195 | ||||||||
\(103\) | 1.18115 | 0.116382 | 0.0581909 | − | 0.998305i | \(-0.481467\pi\) | ||||
0.0581909 | + | 0.998305i | \(0.481467\pi\) | |||||||
\(104\) | 3.66136 | 0.359026 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −2.67097 | −0.259428 | ||||||||
\(107\) | −1.79224 | −0.173263 | −0.0866313 | − | 0.996240i | \(-0.527610\pi\) | ||||
−0.0866313 | + | 0.996240i | \(0.527610\pi\) | |||||||
\(108\) | 14.4442 | 1.38989 | ||||||||
\(109\) | 3.64190 | 0.348830 | 0.174415 | − | 0.984672i | \(-0.444197\pi\) | ||||
0.174415 | + | 0.984672i | \(0.444197\pi\) | |||||||
\(110\) | −0.973516 | −0.0928211 | ||||||||
\(111\) | 23.3215 | 2.21358 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −17.7718 | −1.67183 | −0.835915 | − | 0.548859i | \(-0.815063\pi\) | ||||
−0.835915 | + | 0.548859i | \(0.815063\pi\) | |||||||
\(114\) | −22.6244 | −2.11896 | ||||||||
\(115\) | −3.96211 | −0.369468 | ||||||||
\(116\) | −1.00000 | −0.0928477 | ||||||||
\(117\) | 27.3321 | 2.52685 | ||||||||
\(118\) | −8.04354 | −0.740468 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 3.70208 | 0.337952 | ||||||||
\(121\) | −10.2763 | −0.934213 | ||||||||
\(122\) | −5.08144 | −0.460052 | ||||||||
\(123\) | 13.0852 | 1.17985 | ||||||||
\(124\) | −3.97423 | −0.356896 | ||||||||
\(125\) | −9.94520 | −0.889526 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −11.5789 | −1.02746 | −0.513732 | − | 0.857950i | \(-0.671738\pi\) | ||||
−0.513732 | + | 0.857950i | \(0.671738\pi\) | |||||||
\(128\) | 1.00000 | 0.0883883 | ||||||||
\(129\) | 31.6311 | 2.78496 | ||||||||
\(130\) | 4.19004 | 0.367490 | ||||||||
\(131\) | −16.1976 | −1.41519 | −0.707593 | − | 0.706620i | \(-0.750219\pi\) | ||||
−0.707593 | + | 0.706620i | \(0.750219\pi\) | |||||||
\(132\) | −2.75193 | −0.239525 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | −11.6003 | −1.00211 | ||||||||
\(135\) | 16.5298 | 1.42266 | ||||||||
\(136\) | 0.194248 | 0.0166566 | ||||||||
\(137\) | −12.7842 | −1.09223 | −0.546116 | − | 0.837710i | \(-0.683894\pi\) | ||||
−0.546116 | + | 0.837710i | \(0.683894\pi\) | |||||||
\(138\) | −11.2001 | −0.953412 | ||||||||
\(139\) | 0.170575 | 0.0144679 | 0.00723397 | − | 0.999974i | \(-0.497697\pi\) | ||||
0.00723397 | + | 0.999974i | \(0.497697\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0.174109 | 0.0146627 | ||||||||
\(142\) | −11.2825 | −0.946804 | ||||||||
\(143\) | −3.11465 | −0.260460 | ||||||||
\(144\) | 7.46501 | 0.622084 | ||||||||
\(145\) | −1.14439 | −0.0950367 | ||||||||
\(146\) | −7.31077 | −0.605044 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 7.20919 | 0.592592 | ||||||||
\(149\) | 14.0440 | 1.15053 | 0.575263 | − | 0.817969i | \(-0.304900\pi\) | ||||
0.575263 | + | 0.817969i | \(0.304900\pi\) | |||||||
\(150\) | −11.9382 | −0.974750 | ||||||||
\(151\) | 12.1976 | 0.992623 | 0.496311 | − | 0.868145i | \(-0.334687\pi\) | ||||
0.496311 | + | 0.868145i | \(0.334687\pi\) | |||||||
\(152\) | −6.99369 | −0.567263 | ||||||||
\(153\) | 1.45006 | 0.117231 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −4.54808 | −0.365311 | ||||||||
\(156\) | 11.8444 | 0.948309 | ||||||||
\(157\) | 14.3897 | 1.14842 | 0.574212 | − | 0.818707i | \(-0.305309\pi\) | ||||
0.574212 | + | 0.818707i | \(0.305309\pi\) | |||||||
\(158\) | −13.3564 | −1.06258 | ||||||||
\(159\) | −8.64051 | −0.685237 | ||||||||
\(160\) | 1.14439 | 0.0904723 | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | 24.3314 | 1.91165 | ||||||||
\(163\) | 16.7674 | 1.31332 | 0.656660 | − | 0.754186i | \(-0.271969\pi\) | ||||
0.656660 | + | 0.754186i | \(0.271969\pi\) | |||||||
\(164\) | 4.04493 | 0.315856 | ||||||||
\(165\) | −3.14929 | −0.245172 | ||||||||
\(166\) | 9.04564 | 0.702078 | ||||||||
\(167\) | −10.6555 | −0.824544 | −0.412272 | − | 0.911061i | \(-0.635265\pi\) | ||||
−0.412272 | + | 0.911061i | \(0.635265\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 0.405541 | 0.0311955 | ||||||||
\(170\) | 0.222296 | 0.0170494 | ||||||||
\(171\) | −52.2080 | −3.99244 | ||||||||
\(172\) | 9.77788 | 0.745556 | ||||||||
\(173\) | 17.9251 | 1.36282 | 0.681409 | − | 0.731902i | \(-0.261367\pi\) | ||||
0.681409 | + | 0.731902i | \(0.261367\pi\) | |||||||
\(174\) | −3.23497 | −0.245242 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | −0.850683 | −0.0641226 | ||||||||
\(177\) | −26.0206 | −1.95583 | ||||||||
\(178\) | 14.2305 | 1.06662 | ||||||||
\(179\) | 5.28920 | 0.395333 | 0.197667 | − | 0.980269i | \(-0.436664\pi\) | ||||
0.197667 | + | 0.980269i | \(0.436664\pi\) | |||||||
\(180\) | 8.54291 | 0.636751 | ||||||||
\(181\) | 13.1711 | 0.978997 | 0.489498 | − | 0.872004i | \(-0.337180\pi\) | ||||
0.489498 | + | 0.872004i | \(0.337180\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −16.4383 | −1.21515 | ||||||||
\(184\) | −3.46219 | −0.255236 | ||||||||
\(185\) | 8.25016 | 0.606564 | ||||||||
\(186\) | −12.8565 | −0.942684 | ||||||||
\(187\) | −0.165244 | −0.0120838 | ||||||||
\(188\) | 0.0538211 | 0.00392531 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | −8.00353 | −0.580637 | ||||||||
\(191\) | 9.90869 | 0.716968 | 0.358484 | − | 0.933536i | \(-0.383294\pi\) | ||||
0.358484 | + | 0.933536i | \(0.383294\pi\) | |||||||
\(192\) | 3.23497 | 0.233464 | ||||||||
\(193\) | −17.3950 | −1.25212 | −0.626061 | − | 0.779774i | \(-0.715334\pi\) | ||||
−0.626061 | + | 0.779774i | \(0.715334\pi\) | |||||||
\(194\) | 18.7779 | 1.34817 | ||||||||
\(195\) | 13.5546 | 0.970667 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 17.5961 | 1.25367 | 0.626834 | − | 0.779153i | \(-0.284350\pi\) | ||||
0.626834 | + | 0.779153i | \(0.284350\pi\) | |||||||
\(198\) | −6.35036 | −0.451300 | ||||||||
\(199\) | 11.2846 | 0.799943 | 0.399972 | − | 0.916528i | \(-0.369020\pi\) | ||||
0.399972 | + | 0.916528i | \(0.369020\pi\) | |||||||
\(200\) | −3.69036 | −0.260948 | ||||||||
\(201\) | −37.5265 | −2.64691 | ||||||||
\(202\) | 13.7194 | 0.965291 | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | 0.628386 | 0.0439958 | ||||||||
\(205\) | 4.62899 | 0.323303 | ||||||||
\(206\) | 1.18115 | 0.0822943 | ||||||||
\(207\) | −25.8453 | −1.79637 | ||||||||
\(208\) | 3.66136 | 0.253869 | ||||||||
\(209\) | 5.94941 | 0.411529 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −9.87572 | −0.679873 | −0.339936 | − | 0.940448i | \(-0.610406\pi\) | ||||
−0.339936 | + | 0.940448i | \(0.610406\pi\) | |||||||
\(212\) | −2.67097 | −0.183443 | ||||||||
\(213\) | −36.4984 | −2.50083 | ||||||||
\(214\) | −1.79224 | −0.122515 | ||||||||
\(215\) | 11.1897 | 0.763134 | ||||||||
\(216\) | 14.4442 | 0.982801 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | 3.64190 | 0.246660 | ||||||||
\(219\) | −23.6501 | −1.59813 | ||||||||
\(220\) | −0.973516 | −0.0656345 | ||||||||
\(221\) | 0.711212 | 0.0478413 | ||||||||
\(222\) | 23.3215 | 1.56524 | ||||||||
\(223\) | −16.5982 | −1.11150 | −0.555748 | − | 0.831351i | \(-0.687568\pi\) | ||||
−0.555748 | + | 0.831351i | \(0.687568\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −27.5486 | −1.83657 | ||||||||
\(226\) | −17.7718 | −1.18216 | ||||||||
\(227\) | 17.9930 | 1.19424 | 0.597120 | − | 0.802152i | \(-0.296312\pi\) | ||||
0.597120 | + | 0.802152i | \(0.296312\pi\) | |||||||
\(228\) | −22.6244 | −1.49833 | ||||||||
\(229\) | −2.03821 | −0.134689 | −0.0673444 | − | 0.997730i | \(-0.521453\pi\) | ||||
−0.0673444 | + | 0.997730i | \(0.521453\pi\) | |||||||
\(230\) | −3.96211 | −0.261253 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −1.00000 | −0.0656532 | ||||||||
\(233\) | −16.4989 | −1.08088 | −0.540441 | − | 0.841382i | \(-0.681742\pi\) | ||||
−0.540441 | + | 0.841382i | \(0.681742\pi\) | |||||||
\(234\) | 27.3321 | 1.78675 | ||||||||
\(235\) | 0.0615925 | 0.00401785 | ||||||||
\(236\) | −8.04354 | −0.523590 | ||||||||
\(237\) | −43.2075 | −2.80663 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 18.7414 | 1.21228 | 0.606141 | − | 0.795357i | \(-0.292717\pi\) | ||||
0.606141 | + | 0.795357i | \(0.292717\pi\) | |||||||
\(240\) | 3.70208 | 0.238968 | ||||||||
\(241\) | 17.8781 | 1.15163 | 0.575813 | − | 0.817581i | \(-0.304685\pi\) | ||||
0.575813 | + | 0.817581i | \(0.304685\pi\) | |||||||
\(242\) | −10.2763 | −0.660588 | ||||||||
\(243\) | 35.3786 | 2.26954 | ||||||||
\(244\) | −5.08144 | −0.325306 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 13.0852 | 0.834283 | ||||||||
\(247\) | −25.6064 | −1.62930 | ||||||||
\(248\) | −3.97423 | −0.252364 | ||||||||
\(249\) | 29.2624 | 1.85443 | ||||||||
\(250\) | −9.94520 | −0.628990 | ||||||||
\(251\) | −1.69249 | −0.106829 | −0.0534144 | − | 0.998572i | \(-0.517010\pi\) | ||||
−0.0534144 | + | 0.998572i | \(0.517010\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 2.94522 | 0.185165 | ||||||||
\(254\) | −11.5789 | −0.726527 | ||||||||
\(255\) | 0.719122 | 0.0450331 | ||||||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | 3.55324 | 0.221645 | 0.110822 | − | 0.993840i | \(-0.464652\pi\) | ||||
0.110822 | + | 0.993840i | \(0.464652\pi\) | |||||||
\(258\) | 31.6311 | 1.96927 | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | 4.19004 | 0.259855 | ||||||||
\(261\) | −7.46501 | −0.462073 | ||||||||
\(262\) | −16.1976 | −1.00069 | ||||||||
\(263\) | −18.3627 | −1.13229 | −0.566147 | − | 0.824304i | \(-0.691567\pi\) | ||||
−0.566147 | + | 0.824304i | \(0.691567\pi\) | |||||||
\(264\) | −2.75193 | −0.169370 | ||||||||
\(265\) | −3.05665 | −0.187768 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 46.0353 | 2.81731 | ||||||||
\(268\) | −11.6003 | −0.708599 | ||||||||
\(269\) | 18.1820 | 1.10858 | 0.554289 | − | 0.832324i | \(-0.312990\pi\) | ||||
0.554289 | + | 0.832324i | \(0.312990\pi\) | |||||||
\(270\) | 16.5298 | 1.00597 | ||||||||
\(271\) | −7.30703 | −0.443871 | −0.221935 | − | 0.975061i | \(-0.571237\pi\) | ||||
−0.221935 | + | 0.975061i | \(0.571237\pi\) | |||||||
\(272\) | 0.194248 | 0.0117780 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −12.7842 | −0.772324 | ||||||||
\(275\) | 3.13933 | 0.189309 | ||||||||
\(276\) | −11.2001 | −0.674164 | ||||||||
\(277\) | −16.6420 | −0.999918 | −0.499959 | − | 0.866049i | \(-0.666652\pi\) | ||||
−0.499959 | + | 0.866049i | \(0.666652\pi\) | |||||||
\(278\) | 0.170575 | 0.0102304 | ||||||||
\(279\) | −29.6676 | −1.77616 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 13.2562 | 0.790800 | 0.395400 | − | 0.918509i | \(-0.370606\pi\) | ||||
0.395400 | + | 0.918509i | \(0.370606\pi\) | |||||||
\(282\) | 0.174109 | 0.0103681 | ||||||||
\(283\) | −15.2786 | −0.908217 | −0.454109 | − | 0.890946i | \(-0.650042\pi\) | ||||
−0.454109 | + | 0.890946i | \(0.650042\pi\) | |||||||
\(284\) | −11.2825 | −0.669492 | ||||||||
\(285\) | −25.8912 | −1.53366 | ||||||||
\(286\) | −3.11465 | −0.184173 | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | 7.46501 | 0.439880 | ||||||||
\(289\) | −16.9623 | −0.997780 | ||||||||
\(290\) | −1.14439 | −0.0672011 | ||||||||
\(291\) | 60.7458 | 3.56098 | ||||||||
\(292\) | −7.31077 | −0.427830 | ||||||||
\(293\) | −15.5191 | −0.906637 | −0.453318 | − | 0.891349i | \(-0.649760\pi\) | ||||
−0.453318 | + | 0.891349i | \(0.649760\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −9.20498 | −0.535935 | ||||||||
\(296\) | 7.20919 | 0.419026 | ||||||||
\(297\) | −12.2874 | −0.712987 | ||||||||
\(298\) | 14.0440 | 0.813544 | ||||||||
\(299\) | −12.6763 | −0.733090 | ||||||||
\(300\) | −11.9382 | −0.689252 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | 12.1976 | 0.701890 | ||||||||
\(303\) | 44.3817 | 2.54966 | ||||||||
\(304\) | −6.99369 | −0.401116 | ||||||||
\(305\) | −5.81517 | −0.332975 | ||||||||
\(306\) | 1.45006 | 0.0828947 | ||||||||
\(307\) | 3.14277 | 0.179368 | 0.0896838 | − | 0.995970i | \(-0.471414\pi\) | ||||
0.0896838 | + | 0.995970i | \(0.471414\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 3.82097 | 0.217367 | ||||||||
\(310\) | −4.54808 | −0.258314 | ||||||||
\(311\) | 24.2160 | 1.37316 | 0.686581 | − | 0.727053i | \(-0.259111\pi\) | ||||
0.686581 | + | 0.727053i | \(0.259111\pi\) | |||||||
\(312\) | 11.8444 | 0.670555 | ||||||||
\(313\) | −10.3528 | −0.585175 | −0.292588 | − | 0.956239i | \(-0.594516\pi\) | ||||
−0.292588 | + | 0.956239i | \(0.594516\pi\) | |||||||
\(314\) | 14.3897 | 0.812058 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −13.3564 | −0.751357 | ||||||||
\(317\) | −34.5329 | −1.93956 | −0.969780 | − | 0.243983i | \(-0.921546\pi\) | ||||
−0.969780 | + | 0.243983i | \(0.921546\pi\) | |||||||
\(318\) | −8.64051 | −0.484536 | ||||||||
\(319\) | 0.850683 | 0.0476291 | ||||||||
\(320\) | 1.14439 | 0.0639736 | ||||||||
\(321\) | −5.79784 | −0.323604 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −1.35851 | −0.0755896 | ||||||||
\(324\) | 24.3314 | 1.35174 | ||||||||
\(325\) | −13.5117 | −0.749496 | ||||||||
\(326\) | 16.7674 | 0.928658 | ||||||||
\(327\) | 11.7814 | 0.651514 | ||||||||
\(328\) | 4.04493 | 0.223344 | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | −3.14929 | −0.173363 | ||||||||
\(331\) | 5.10043 | 0.280345 | 0.140173 | − | 0.990127i | \(-0.455234\pi\) | ||||
0.140173 | + | 0.990127i | \(0.455234\pi\) | |||||||
\(332\) | 9.04564 | 0.496444 | ||||||||
\(333\) | 53.8167 | 2.94914 | ||||||||
\(334\) | −10.6555 | −0.583041 | ||||||||
\(335\) | −13.2753 | −0.725306 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 24.7613 | 1.34884 | 0.674418 | − | 0.738350i | \(-0.264394\pi\) | ||||
0.674418 | + | 0.738350i | \(0.264394\pi\) | |||||||
\(338\) | 0.405541 | 0.0220585 | ||||||||
\(339\) | −57.4912 | −3.12249 | ||||||||
\(340\) | 0.222296 | 0.0120557 | ||||||||
\(341\) | 3.38081 | 0.183081 | ||||||||
\(342\) | −52.2080 | −2.82308 | ||||||||
\(343\) | 0 | 0 | ||||||||
\(344\) | 9.77788 | 0.527188 | ||||||||
\(345\) | −12.8173 | −0.690059 | ||||||||
\(346\) | 17.9251 | 0.963658 | ||||||||
\(347\) | 6.42032 | 0.344661 | 0.172331 | − | 0.985039i | \(-0.444870\pi\) | ||||
0.172331 | + | 0.985039i | \(0.444870\pi\) | |||||||
\(348\) | −3.23497 | −0.173412 | ||||||||
\(349\) | −2.54039 | −0.135984 | −0.0679920 | − | 0.997686i | \(-0.521659\pi\) | ||||
−0.0679920 | + | 0.997686i | \(0.521659\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 52.8852 | 2.82281 | ||||||||
\(352\) | −0.850683 | −0.0453415 | ||||||||
\(353\) | −1.20628 | −0.0642038 | −0.0321019 | − | 0.999485i | \(-0.510220\pi\) | ||||
−0.0321019 | + | 0.999485i | \(0.510220\pi\) | |||||||
\(354\) | −26.0206 | −1.38298 | ||||||||
\(355\) | −12.9116 | −0.685276 | ||||||||
\(356\) | 14.2305 | 0.754216 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 5.28920 | 0.279543 | ||||||||
\(359\) | 0.315996 | 0.0166777 | 0.00833883 | − | 0.999965i | \(-0.497346\pi\) | ||||
0.00833883 | + | 0.999965i | \(0.497346\pi\) | |||||||
\(360\) | 8.54291 | 0.450251 | ||||||||
\(361\) | 29.9117 | 1.57430 | ||||||||
\(362\) | 13.1711 | 0.692255 | ||||||||
\(363\) | −33.2436 | −1.74484 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −8.36640 | −0.437917 | ||||||||
\(366\) | −16.4383 | −0.859243 | ||||||||
\(367\) | 24.2997 | 1.26843 | 0.634217 | − | 0.773155i | \(-0.281322\pi\) | ||||
0.634217 | + | 0.773155i | \(0.281322\pi\) | |||||||
\(368\) | −3.46219 | −0.180479 | ||||||||
\(369\) | 30.1955 | 1.57191 | ||||||||
\(370\) | 8.25016 | 0.428905 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | −12.8565 | −0.666578 | ||||||||
\(373\) | −9.98510 | −0.517009 | −0.258504 | − | 0.966010i | \(-0.583230\pi\) | ||||
−0.258504 | + | 0.966010i | \(0.583230\pi\) | |||||||
\(374\) | −0.165244 | −0.00854454 | ||||||||
\(375\) | −32.1724 | −1.66137 | ||||||||
\(376\) | 0.0538211 | 0.00277561 | ||||||||
\(377\) | −3.66136 | −0.188570 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −13.0891 | −0.672343 | −0.336172 | − | 0.941801i | \(-0.609132\pi\) | ||||
−0.336172 | + | 0.941801i | \(0.609132\pi\) | |||||||
\(380\) | −8.00353 | −0.410573 | ||||||||
\(381\) | −37.4575 | −1.91901 | ||||||||
\(382\) | 9.90869 | 0.506973 | ||||||||
\(383\) | −2.96390 | −0.151448 | −0.0757241 | − | 0.997129i | \(-0.524127\pi\) | ||||
−0.0757241 | + | 0.997129i | \(0.524127\pi\) | |||||||
\(384\) | 3.23497 | 0.165084 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −17.3950 | −0.885384 | ||||||||
\(387\) | 72.9920 | 3.71039 | ||||||||
\(388\) | 18.7779 | 0.953302 | ||||||||
\(389\) | −34.9114 | −1.77008 | −0.885040 | − | 0.465514i | \(-0.845869\pi\) | ||||
−0.885040 | + | 0.465514i | \(0.845869\pi\) | |||||||
\(390\) | 13.5546 | 0.686365 | ||||||||
\(391\) | −0.672523 | −0.0340110 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −52.3985 | −2.64316 | ||||||||
\(394\) | 17.5961 | 0.886477 | ||||||||
\(395\) | −15.2850 | −0.769072 | ||||||||
\(396\) | −6.35036 | −0.319117 | ||||||||
\(397\) | 15.4156 | 0.773685 | 0.386842 | − | 0.922146i | \(-0.373566\pi\) | ||||
0.386842 | + | 0.922146i | \(0.373566\pi\) | |||||||
\(398\) | 11.2846 | 0.565645 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −3.69036 | −0.184518 | ||||||||
\(401\) | 38.0366 | 1.89946 | 0.949728 | − | 0.313077i | \(-0.101360\pi\) | ||||
0.949728 | + | 0.313077i | \(0.101360\pi\) | |||||||
\(402\) | −37.5265 | −1.87165 | ||||||||
\(403\) | −14.5511 | −0.724840 | ||||||||
\(404\) | 13.7194 | 0.682564 | ||||||||
\(405\) | 27.8447 | 1.38361 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −6.13274 | −0.303989 | ||||||||
\(408\) | 0.628386 | 0.0311098 | ||||||||
\(409\) | −29.2856 | −1.44808 | −0.724041 | − | 0.689757i | \(-0.757717\pi\) | ||||
−0.724041 | + | 0.689757i | \(0.757717\pi\) | |||||||
\(410\) | 4.62899 | 0.228610 | ||||||||
\(411\) | −41.3566 | −2.03997 | ||||||||
\(412\) | 1.18115 | 0.0581909 | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | −25.8453 | −1.27023 | ||||||||
\(415\) | 10.3518 | 0.508149 | ||||||||
\(416\) | 3.66136 | 0.179513 | ||||||||
\(417\) | 0.551803 | 0.0270219 | ||||||||
\(418\) | 5.94941 | 0.290995 | ||||||||
\(419\) | −6.29412 | −0.307488 | −0.153744 | − | 0.988111i | \(-0.549133\pi\) | ||||
−0.153744 | + | 0.988111i | \(0.549133\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 2.94479 | 0.143520 | 0.0717602 | − | 0.997422i | \(-0.477138\pi\) | ||||
0.0717602 | + | 0.997422i | \(0.477138\pi\) | |||||||
\(422\) | −9.87572 | −0.480743 | ||||||||
\(423\) | 0.401775 | 0.0195350 | ||||||||
\(424\) | −2.67097 | −0.129714 | ||||||||
\(425\) | −0.716846 | −0.0347721 | ||||||||
\(426\) | −36.4984 | −1.76836 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | −1.79224 | −0.0866313 | ||||||||
\(429\) | −10.0758 | −0.486464 | ||||||||
\(430\) | 11.1897 | 0.539617 | ||||||||
\(431\) | 5.45942 | 0.262971 | 0.131486 | − | 0.991318i | \(-0.458025\pi\) | ||||
0.131486 | + | 0.991318i | \(0.458025\pi\) | |||||||
\(432\) | 14.4442 | 0.694945 | ||||||||
\(433\) | −16.9899 | −0.816482 | −0.408241 | − | 0.912874i | \(-0.633858\pi\) | ||||
−0.408241 | + | 0.912874i | \(0.633858\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −3.70208 | −0.177501 | ||||||||
\(436\) | 3.64190 | 0.174415 | ||||||||
\(437\) | 24.2135 | 1.15829 | ||||||||
\(438\) | −23.6501 | −1.13005 | ||||||||
\(439\) | −22.6419 | −1.08064 | −0.540321 | − | 0.841459i | \(-0.681697\pi\) | ||||
−0.540321 | + | 0.841459i | \(0.681697\pi\) | |||||||
\(440\) | −0.973516 | −0.0464106 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0.711212 | 0.0338289 | ||||||||
\(443\) | −17.1387 | −0.814285 | −0.407143 | − | 0.913365i | \(-0.633475\pi\) | ||||
−0.407143 | + | 0.913365i | \(0.633475\pi\) | |||||||
\(444\) | 23.3215 | 1.10679 | ||||||||
\(445\) | 16.2853 | 0.771998 | ||||||||
\(446\) | −16.5982 | −0.785946 | ||||||||
\(447\) | 45.4317 | 2.14885 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −12.1802 | −0.574818 | −0.287409 | − | 0.957808i | \(-0.592794\pi\) | ||||
−0.287409 | + | 0.957808i | \(0.592794\pi\) | |||||||
\(450\) | −27.5486 | −1.29865 | ||||||||
\(451\) | −3.44095 | −0.162028 | ||||||||
\(452\) | −17.7718 | −0.835915 | ||||||||
\(453\) | 39.4587 | 1.85393 | ||||||||
\(454\) | 17.9930 | 0.844455 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | −22.6244 | −1.05948 | ||||||||
\(457\) | 31.5102 | 1.47398 | 0.736991 | − | 0.675902i | \(-0.236246\pi\) | ||||
0.736991 | + | 0.675902i | \(0.236246\pi\) | |||||||
\(458\) | −2.03821 | −0.0952394 | ||||||||
\(459\) | 2.80575 | 0.130961 | ||||||||
\(460\) | −3.96211 | −0.184734 | ||||||||
\(461\) | −6.40796 | −0.298448 | −0.149224 | − | 0.988803i | \(-0.547678\pi\) | ||||
−0.149224 | + | 0.988803i | \(0.547678\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −0.902939 | −0.0419632 | −0.0209816 | − | 0.999780i | \(-0.506679\pi\) | ||||
−0.0209816 | + | 0.999780i | \(0.506679\pi\) | |||||||
\(464\) | −1.00000 | −0.0464238 | ||||||||
\(465\) | −14.7129 | −0.682294 | ||||||||
\(466\) | −16.4989 | −0.764299 | ||||||||
\(467\) | −36.4112 | −1.68491 | −0.842454 | − | 0.538768i | \(-0.818890\pi\) | ||||
−0.842454 | + | 0.538768i | \(0.818890\pi\) | |||||||
\(468\) | 27.3321 | 1.26343 | ||||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | 0.0615925 | 0.00284105 | ||||||||
\(471\) | 46.5502 | 2.14492 | ||||||||
\(472\) | −8.04354 | −0.370234 | ||||||||
\(473\) | −8.31787 | −0.382456 | ||||||||
\(474\) | −43.2075 | −1.98459 | ||||||||
\(475\) | 25.8092 | 1.18421 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −19.9388 | −0.912937 | ||||||||
\(478\) | 18.7414 | 0.857213 | ||||||||
\(479\) | 31.4283 | 1.43600 | 0.717998 | − | 0.696045i | \(-0.245059\pi\) | ||||
0.717998 | + | 0.696045i | \(0.245059\pi\) | |||||||
\(480\) | 3.70208 | 0.168976 | ||||||||
\(481\) | 26.3954 | 1.20353 | ||||||||
\(482\) | 17.8781 | 0.814323 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −10.2763 | −0.467106 | ||||||||
\(485\) | 21.4893 | 0.975778 | ||||||||
\(486\) | 35.3786 | 1.60481 | ||||||||
\(487\) | 14.4460 | 0.654609 | 0.327304 | − | 0.944919i | \(-0.393860\pi\) | ||||
0.327304 | + | 0.944919i | \(0.393860\pi\) | |||||||
\(488\) | −5.08144 | −0.230026 | ||||||||
\(489\) | 54.2418 | 2.45290 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 29.2405 | 1.31961 | 0.659803 | − | 0.751439i | \(-0.270640\pi\) | ||||
0.659803 | + | 0.751439i | \(0.270640\pi\) | |||||||
\(492\) | 13.0852 | 0.589927 | ||||||||
\(493\) | −0.194248 | −0.00874850 | ||||||||
\(494\) | −25.6064 | −1.15209 | ||||||||
\(495\) | −7.26731 | −0.326641 | ||||||||
\(496\) | −3.97423 | −0.178448 | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | 29.2624 | 1.31128 | ||||||||
\(499\) | 28.4905 | 1.27541 | 0.637704 | − | 0.770282i | \(-0.279884\pi\) | ||||
0.637704 | + | 0.770282i | \(0.279884\pi\) | |||||||
\(500\) | −9.94520 | −0.444763 | ||||||||
\(501\) | −34.4700 | −1.54001 | ||||||||
\(502\) | −1.69249 | −0.0755393 | ||||||||
\(503\) | 19.9091 | 0.887701 | 0.443850 | − | 0.896101i | \(-0.353612\pi\) | ||||
0.443850 | + | 0.896101i | \(0.353612\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 15.7004 | 0.698657 | ||||||||
\(506\) | 2.94522 | 0.130931 | ||||||||
\(507\) | 1.31191 | 0.0582641 | ||||||||
\(508\) | −11.5789 | −0.513732 | ||||||||
\(509\) | 3.57199 | 0.158326 | 0.0791628 | − | 0.996862i | \(-0.474775\pi\) | ||||
0.0791628 | + | 0.996862i | \(0.474775\pi\) | |||||||
\(510\) | 0.719122 | 0.0318432 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | 1.00000 | 0.0441942 | ||||||||
\(513\) | −101.018 | −4.46005 | ||||||||
\(514\) | 3.55324 | 0.156727 | ||||||||
\(515\) | 1.35170 | 0.0595628 | ||||||||
\(516\) | 31.6311 | 1.39248 | ||||||||
\(517\) | −0.0457847 | −0.00201361 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 57.9871 | 2.54535 | ||||||||
\(520\) | 4.19004 | 0.183745 | ||||||||
\(521\) | −9.36877 | −0.410453 | −0.205227 | − | 0.978714i | \(-0.565793\pi\) | ||||
−0.205227 | + | 0.978714i | \(0.565793\pi\) | |||||||
\(522\) | −7.46501 | −0.326735 | ||||||||
\(523\) | −13.6159 | −0.595381 | −0.297690 | − | 0.954662i | \(-0.596216\pi\) | ||||
−0.297690 | + | 0.954662i | \(0.596216\pi\) | |||||||
\(524\) | −16.1976 | −0.707593 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −18.3627 | −0.800653 | ||||||||
\(527\) | −0.771986 | −0.0336283 | ||||||||
\(528\) | −2.75193 | −0.119762 | ||||||||
\(529\) | −11.0133 | −0.478838 | ||||||||
\(530\) | −3.05665 | −0.132772 | ||||||||
\(531\) | −60.0451 | −2.60574 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 14.8099 | 0.641490 | ||||||||
\(534\) | 46.0353 | 1.99214 | ||||||||
\(535\) | −2.05103 | −0.0886738 | ||||||||
\(536\) | −11.6003 | −0.501055 | ||||||||
\(537\) | 17.1104 | 0.738367 | ||||||||
\(538\) | 18.1820 | 0.783883 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 16.5298 | 0.711330 | ||||||||
\(541\) | 10.6970 | 0.459901 | 0.229951 | − | 0.973202i | \(-0.426144\pi\) | ||||
0.229951 | + | 0.973202i | \(0.426144\pi\) | |||||||
\(542\) | −7.30703 | −0.313864 | ||||||||
\(543\) | 42.6079 | 1.82848 | ||||||||
\(544\) | 0.194248 | 0.00832832 | ||||||||
\(545\) | 4.16776 | 0.178527 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −23.6925 | −1.01302 | −0.506509 | − | 0.862235i | \(-0.669064\pi\) | ||||
−0.506509 | + | 0.862235i | \(0.669064\pi\) | |||||||
\(548\) | −12.7842 | −0.546116 | ||||||||
\(549\) | −37.9330 | −1.61894 | ||||||||
\(550\) | 3.13933 | 0.133861 | ||||||||
\(551\) | 6.99369 | 0.297941 | ||||||||
\(552\) | −11.2001 | −0.476706 | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | −16.6420 | −0.707049 | ||||||||
\(555\) | 26.6890 | 1.13288 | ||||||||
\(556\) | 0.170575 | 0.00723397 | ||||||||
\(557\) | 12.2781 | 0.520242 | 0.260121 | − | 0.965576i | \(-0.416238\pi\) | ||||
0.260121 | + | 0.965576i | \(0.416238\pi\) | |||||||
\(558\) | −29.6676 | −1.25593 | ||||||||
\(559\) | 35.8003 | 1.51419 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −0.534558 | −0.0225690 | ||||||||
\(562\) | 13.2562 | 0.559180 | ||||||||
\(563\) | 37.3831 | 1.57551 | 0.787755 | − | 0.615989i | \(-0.211244\pi\) | ||||
0.787755 | + | 0.615989i | \(0.211244\pi\) | |||||||
\(564\) | 0.174109 | 0.00733133 | ||||||||
\(565\) | −20.3379 | −0.855624 | ||||||||
\(566\) | −15.2786 | −0.642207 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −11.2825 | −0.473402 | ||||||||
\(569\) | −14.2478 | −0.597300 | −0.298650 | − | 0.954363i | \(-0.596536\pi\) | ||||
−0.298650 | + | 0.954363i | \(0.596536\pi\) | |||||||
\(570\) | −25.8912 | −1.08446 | ||||||||
\(571\) | −6.59865 | −0.276145 | −0.138072 | − | 0.990422i | \(-0.544091\pi\) | ||||
−0.138072 | + | 0.990422i | \(0.544091\pi\) | |||||||
\(572\) | −3.11465 | −0.130230 | ||||||||
\(573\) | 32.0543 | 1.33909 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 12.7767 | 0.532826 | ||||||||
\(576\) | 7.46501 | 0.311042 | ||||||||
\(577\) | −21.0911 | −0.878032 | −0.439016 | − | 0.898479i | \(-0.644673\pi\) | ||||
−0.439016 | + | 0.898479i | \(0.644673\pi\) | |||||||
\(578\) | −16.9623 | −0.705537 | ||||||||
\(579\) | −56.2723 | −2.33860 | ||||||||
\(580\) | −1.14439 | −0.0475184 | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | 60.7458 | 2.51800 | ||||||||
\(583\) | 2.27215 | 0.0941029 | ||||||||
\(584\) | −7.31077 | −0.302522 | ||||||||
\(585\) | 31.2787 | 1.29321 | ||||||||
\(586\) | −15.5191 | −0.641089 | ||||||||
\(587\) | 23.5851 | 0.973459 | 0.486730 | − | 0.873553i | \(-0.338190\pi\) | ||||
0.486730 | + | 0.873553i | \(0.338190\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 27.7945 | 1.14525 | ||||||||
\(590\) | −9.20498 | −0.378963 | ||||||||
\(591\) | 56.9227 | 2.34149 | ||||||||
\(592\) | 7.20919 | 0.296296 | ||||||||
\(593\) | −24.8808 | −1.02173 | −0.510865 | − | 0.859661i | \(-0.670675\pi\) | ||||
−0.510865 | + | 0.859661i | \(0.670675\pi\) | |||||||
\(594\) | −12.2874 | −0.504158 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 14.0440 | 0.575263 | ||||||||
\(597\) | 36.5053 | 1.49406 | ||||||||
\(598\) | −12.6763 | −0.518373 | ||||||||
\(599\) | 4.77907 | 0.195268 | 0.0976338 | − | 0.995222i | \(-0.468873\pi\) | ||||
0.0976338 | + | 0.995222i | \(0.468873\pi\) | |||||||
\(600\) | −11.9382 | −0.487375 | ||||||||
\(601\) | −44.3292 | −1.80823 | −0.904113 | − | 0.427292i | \(-0.859467\pi\) | ||||
−0.904113 | + | 0.427292i | \(0.859467\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −86.5961 | −3.52647 | ||||||||
\(604\) | 12.1976 | 0.496311 | ||||||||
\(605\) | −11.7602 | −0.478119 | ||||||||
\(606\) | 44.3817 | 1.80288 | ||||||||
\(607\) | 42.8992 | 1.74123 | 0.870613 | − | 0.491968i | \(-0.163722\pi\) | ||||
0.870613 | + | 0.491968i | \(0.163722\pi\) | |||||||
\(608\) | −6.99369 | −0.283632 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | −5.81517 | −0.235449 | ||||||||
\(611\) | 0.197058 | 0.00797212 | ||||||||
\(612\) | 1.45006 | 0.0586154 | ||||||||
\(613\) | 26.0405 | 1.05177 | 0.525884 | − | 0.850557i | \(-0.323735\pi\) | ||||
0.525884 | + | 0.850557i | \(0.323735\pi\) | |||||||
\(614\) | 3.14277 | 0.126832 | ||||||||
\(615\) | 14.9746 | 0.603836 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −38.2301 | −1.53909 | −0.769543 | − | 0.638595i | \(-0.779516\pi\) | ||||
−0.769543 | + | 0.638595i | \(0.779516\pi\) | |||||||
\(618\) | 3.82097 | 0.153702 | ||||||||
\(619\) | 33.8413 | 1.36020 | 0.680098 | − | 0.733122i | \(-0.261937\pi\) | ||||
0.680098 | + | 0.733122i | \(0.261937\pi\) | |||||||
\(620\) | −4.54808 | −0.182655 | ||||||||
\(621\) | −50.0084 | −2.00677 | ||||||||
\(622\) | 24.2160 | 0.970973 | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | 11.8444 | 0.474154 | ||||||||
\(625\) | 7.07059 | 0.282823 | ||||||||
\(626\) | −10.3528 | −0.413781 | ||||||||
\(627\) | 19.2461 | 0.768617 | ||||||||
\(628\) | 14.3897 | 0.574212 | ||||||||
\(629\) | 1.40037 | 0.0558365 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −36.3237 | −1.44602 | −0.723012 | − | 0.690835i | \(-0.757243\pi\) | ||||
−0.723012 | + | 0.690835i | \(0.757243\pi\) | |||||||
\(632\) | −13.3564 | −0.531290 | ||||||||
\(633\) | −31.9476 | −1.26980 | ||||||||
\(634\) | −34.5329 | −1.37148 | ||||||||
\(635\) | −13.2509 | −0.525845 | ||||||||
\(636\) | −8.64051 | −0.342618 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | 0.850683 | 0.0336789 | ||||||||
\(639\) | −84.2238 | −3.33184 | ||||||||
\(640\) | 1.14439 | 0.0452361 | ||||||||
\(641\) | −5.01376 | −0.198031 | −0.0990157 | − | 0.995086i | \(-0.531569\pi\) | ||||
−0.0990157 | + | 0.995086i | \(0.531569\pi\) | |||||||
\(642\) | −5.79784 | −0.228823 | ||||||||
\(643\) | −21.6758 | −0.854811 | −0.427406 | − | 0.904060i | \(-0.640572\pi\) | ||||
−0.427406 | + | 0.904060i | \(0.640572\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 36.1985 | 1.42531 | ||||||||
\(646\) | −1.35851 | −0.0534499 | ||||||||
\(647\) | −23.0945 | −0.907940 | −0.453970 | − | 0.891017i | \(-0.649993\pi\) | ||||
−0.453970 | + | 0.891017i | \(0.649993\pi\) | |||||||
\(648\) | 24.3314 | 0.955826 | ||||||||
\(649\) | 6.84250 | 0.268592 | ||||||||
\(650\) | −13.5117 | −0.529974 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 16.7674 | 0.656660 | ||||||||
\(653\) | −33.9240 | −1.32755 | −0.663774 | − | 0.747933i | \(-0.731046\pi\) | ||||
−0.663774 | + | 0.747933i | \(0.731046\pi\) | |||||||
\(654\) | 11.7814 | 0.460690 | ||||||||
\(655\) | −18.5364 | −0.724276 | ||||||||
\(656\) | 4.04493 | 0.157928 | ||||||||
\(657\) | −54.5750 | −2.12917 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −5.52520 | −0.215231 | −0.107616 | − | 0.994193i | \(-0.534322\pi\) | ||||
−0.107616 | + | 0.994193i | \(0.534322\pi\) | |||||||
\(660\) | −3.14929 | −0.122586 | ||||||||
\(661\) | −1.62365 | −0.0631527 | −0.0315763 | − | 0.999501i | \(-0.510053\pi\) | ||||
−0.0315763 | + | 0.999501i | \(0.510053\pi\) | |||||||
\(662\) | 5.10043 | 0.198234 | ||||||||
\(663\) | 2.30075 | 0.0893536 | ||||||||
\(664\) | 9.04564 | 0.351039 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 53.8167 | 2.08536 | ||||||||
\(667\) | 3.46219 | 0.134056 | ||||||||
\(668\) | −10.6555 | −0.412272 | ||||||||
\(669\) | −53.6945 | −2.07595 | ||||||||
\(670\) | −13.2753 | −0.512869 | ||||||||
\(671\) | 4.32269 | 0.166876 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −1.69886 | −0.0654862 | −0.0327431 | − | 0.999464i | \(-0.510424\pi\) | ||||
−0.0327431 | + | 0.999464i | \(0.510424\pi\) | |||||||
\(674\) | 24.7613 | 0.953771 | ||||||||
\(675\) | −53.3042 | −2.05168 | ||||||||
\(676\) | 0.405541 | 0.0155977 | ||||||||
\(677\) | 20.7277 | 0.796628 | 0.398314 | − | 0.917249i | \(-0.369595\pi\) | ||||
0.398314 | + | 0.917249i | \(0.369595\pi\) | |||||||
\(678\) | −57.4912 | −2.20794 | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | 0.222296 | 0.00852468 | ||||||||
\(681\) | 58.2068 | 2.23049 | ||||||||
\(682\) | 3.38081 | 0.129458 | ||||||||
\(683\) | −30.3817 | −1.16252 | −0.581261 | − | 0.813717i | \(-0.697441\pi\) | ||||
−0.581261 | + | 0.813717i | \(0.697441\pi\) | |||||||
\(684\) | −52.2080 | −1.99622 | ||||||||
\(685\) | −14.6302 | −0.558991 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −6.59355 | −0.251560 | ||||||||
\(688\) | 9.77788 | 0.372778 | ||||||||
\(689\) | −9.77939 | −0.372565 | ||||||||
\(690\) | −12.8173 | −0.487945 | ||||||||
\(691\) | −4.62046 | −0.175771 | −0.0878853 | − | 0.996131i | \(-0.528011\pi\) | ||||
−0.0878853 | + | 0.996131i | \(0.528011\pi\) | |||||||
\(692\) | 17.9251 | 0.681409 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 6.42032 | 0.243712 | ||||||||
\(695\) | 0.195204 | 0.00740453 | ||||||||
\(696\) | −3.23497 | −0.122621 | ||||||||
\(697\) | 0.785720 | 0.0297613 | ||||||||
\(698\) | −2.54039 | −0.0961553 | ||||||||
\(699\) | −53.3735 | −2.01877 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 36.9179 | 1.39437 | 0.697186 | − | 0.716890i | \(-0.254435\pi\) | ||||
0.697186 | + | 0.716890i | \(0.254435\pi\) | |||||||
\(702\) | 52.8852 | 1.99602 | ||||||||
\(703\) | −50.4189 | −1.90158 | ||||||||
\(704\) | −0.850683 | −0.0320613 | ||||||||
\(705\) | 0.199250 | 0.00750418 | ||||||||
\(706\) | −1.20628 | −0.0453989 | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | −26.0206 | −0.977914 | ||||||||
\(709\) | −32.0742 | −1.20457 | −0.602286 | − | 0.798281i | \(-0.705743\pi\) | ||||
−0.602286 | + | 0.798281i | \(0.705743\pi\) | |||||||
\(710\) | −12.9116 | −0.484564 | ||||||||
\(711\) | −99.7058 | −3.73926 | ||||||||
\(712\) | 14.2305 | 0.533311 | ||||||||
\(713\) | 13.7595 | 0.515298 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −3.56439 | −0.133301 | ||||||||
\(716\) | 5.28920 | 0.197667 | ||||||||
\(717\) | 60.6279 | 2.26419 | ||||||||
\(718\) | 0.315996 | 0.0117929 | ||||||||
\(719\) | 35.8354 | 1.33644 | 0.668218 | − | 0.743966i | \(-0.267057\pi\) | ||||
0.668218 | + | 0.743966i | \(0.267057\pi\) | |||||||
\(720\) | 8.54291 | 0.318376 | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | 29.9117 | 1.11320 | ||||||||
\(723\) | 57.8349 | 2.15090 | ||||||||
\(724\) | 13.1711 | 0.489498 | ||||||||
\(725\) | 3.69036 | 0.137057 | ||||||||
\(726\) | −33.2436 | −1.23379 | ||||||||
\(727\) | −12.8401 | −0.476215 | −0.238107 | − | 0.971239i | \(-0.576527\pi\) | ||||
−0.238107 | + | 0.971239i | \(0.576527\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 41.4546 | 1.53536 | ||||||||
\(730\) | −8.36640 | −0.309654 | ||||||||
\(731\) | 1.89934 | 0.0702495 | ||||||||
\(732\) | −16.4383 | −0.607576 | ||||||||
\(733\) | −9.13293 | −0.337332 | −0.168666 | − | 0.985673i | \(-0.553946\pi\) | ||||
−0.168666 | + | 0.985673i | \(0.553946\pi\) | |||||||
\(734\) | 24.2997 | 0.896919 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −3.46219 | −0.127618 | ||||||||
\(737\) | 9.86815 | 0.363498 | ||||||||
\(738\) | 30.1955 | 1.11151 | ||||||||
\(739\) | 6.32454 | 0.232652 | 0.116326 | − | 0.993211i | \(-0.462888\pi\) | ||||
0.116326 | + | 0.993211i | \(0.462888\pi\) | |||||||
\(740\) | 8.25016 | 0.303282 | ||||||||
\(741\) | −82.8358 | −3.04305 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 32.2973 | 1.18487 | 0.592436 | − | 0.805618i | \(-0.298166\pi\) | ||||
0.592436 | + | 0.805618i | \(0.298166\pi\) | |||||||
\(744\) | −12.8565 | −0.471342 | ||||||||
\(745\) | 16.0718 | 0.588826 | ||||||||
\(746\) | −9.98510 | −0.365581 | ||||||||
\(747\) | 67.5258 | 2.47064 | ||||||||
\(748\) | −0.165244 | −0.00604190 | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | −32.1724 | −1.17477 | ||||||||
\(751\) | 19.8619 | 0.724771 | 0.362385 | − | 0.932028i | \(-0.381962\pi\) | ||||
0.362385 | + | 0.932028i | \(0.381962\pi\) | |||||||
\(752\) | 0.0538211 | 0.00196265 | ||||||||
\(753\) | −5.47514 | −0.199525 | ||||||||
\(754\) | −3.66136 | −0.133339 | ||||||||
\(755\) | 13.9588 | 0.508013 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 24.1136 | 0.876425 | 0.438213 | − | 0.898871i | \(-0.355612\pi\) | ||||
0.438213 | + | 0.898871i | \(0.355612\pi\) | |||||||
\(758\) | −13.0891 | −0.475419 | ||||||||
\(759\) | 9.52770 | 0.345834 | ||||||||
\(760\) | −8.00353 | −0.290319 | ||||||||
\(761\) | 39.6245 | 1.43639 | 0.718194 | − | 0.695843i | \(-0.244969\pi\) | ||||
0.718194 | + | 0.695843i | \(0.244969\pi\) | |||||||
\(762\) | −37.4575 | −1.35694 | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | 9.90869 | 0.358484 | ||||||||
\(765\) | 1.65945 | 0.0599974 | ||||||||
\(766\) | −2.96390 | −0.107090 | ||||||||
\(767\) | −29.4503 | −1.06339 | ||||||||
\(768\) | 3.23497 | 0.116732 | ||||||||
\(769\) | −11.8143 | −0.426034 | −0.213017 | − | 0.977049i | \(-0.568329\pi\) | ||||
−0.213017 | + | 0.977049i | \(0.568329\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 11.4946 | 0.413968 | ||||||||
\(772\) | −17.3950 | −0.626061 | ||||||||
\(773\) | 18.0208 | 0.648164 | 0.324082 | − | 0.946029i | \(-0.394945\pi\) | ||||
0.324082 | + | 0.946029i | \(0.394945\pi\) | |||||||
\(774\) | 72.9920 | 2.62364 | ||||||||
\(775\) | 14.6663 | 0.526830 | ||||||||
\(776\) | 18.7779 | 0.674087 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −34.9114 | −1.25164 | ||||||||
\(779\) | −28.2890 | −1.01356 | ||||||||
\(780\) | 13.5546 | 0.485334 | ||||||||
\(781\) | 9.59781 | 0.343437 | ||||||||
\(782\) | −0.672523 | −0.0240494 | ||||||||
\(783\) | −14.4442 | −0.516192 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 16.4675 | 0.587750 | ||||||||
\(786\) | −52.3985 | −1.86899 | ||||||||
\(787\) | −7.31843 | −0.260874 | −0.130437 | − | 0.991457i | \(-0.541638\pi\) | ||||
−0.130437 | + | 0.991457i | \(0.541638\pi\) | |||||||
\(788\) | 17.5961 | 0.626834 | ||||||||
\(789\) | −59.4028 | −2.11480 | ||||||||
\(790\) | −15.2850 | −0.543816 | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | −6.35036 | −0.225650 | ||||||||
\(793\) | −18.6050 | −0.660682 | ||||||||
\(794\) | 15.4156 | 0.547078 | ||||||||
\(795\) | −9.88815 | −0.350696 | ||||||||
\(796\) | 11.2846 | 0.399972 | ||||||||
\(797\) | 53.5394 | 1.89646 | 0.948232 | − | 0.317578i | \(-0.102869\pi\) | ||||
0.948232 | + | 0.317578i | \(0.102869\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 0.0104546 | 0.000369859 0 | ||||||||
\(800\) | −3.69036 | −0.130474 | ||||||||
\(801\) | 106.231 | 3.75349 | ||||||||
\(802\) | 38.0366 | 1.34312 | ||||||||
\(803\) | 6.21915 | 0.219469 | ||||||||
\(804\) | −37.5265 | −1.32346 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | −14.5511 | −0.512540 | ||||||||
\(807\) | 58.8183 | 2.07050 | ||||||||
\(808\) | 13.7194 | 0.482646 | ||||||||
\(809\) | 8.89326 | 0.312670 | 0.156335 | − | 0.987704i | \(-0.450032\pi\) | ||||
0.156335 | + | 0.987704i | \(0.450032\pi\) | |||||||
\(810\) | 27.8447 | 0.978361 | ||||||||
\(811\) | 4.11053 | 0.144340 | 0.0721701 | − | 0.997392i | \(-0.477008\pi\) | ||||
0.0721701 | + | 0.997392i | \(0.477008\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −23.6380 | −0.829021 | ||||||||
\(814\) | −6.13274 | −0.214952 | ||||||||
\(815\) | 19.1885 | 0.672142 | ||||||||
\(816\) | 0.628386 | 0.0219979 | ||||||||
\(817\) | −68.3834 | −2.39243 | ||||||||
\(818\) | −29.2856 | −1.02395 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 4.62899 | 0.161652 | ||||||||
\(821\) | 14.2064 | 0.495806 | 0.247903 | − | 0.968785i | \(-0.420259\pi\) | ||||
0.247903 | + | 0.968785i | \(0.420259\pi\) | |||||||
\(822\) | −41.3566 | −1.44248 | ||||||||
\(823\) | 18.8402 | 0.656728 | 0.328364 | − | 0.944551i | \(-0.393503\pi\) | ||||
0.328364 | + | 0.944551i | \(0.393503\pi\) | |||||||
\(824\) | 1.18115 | 0.0411472 | ||||||||
\(825\) | 10.1556 | 0.353573 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 7.13405 | 0.248075 | 0.124038 | − | 0.992278i | \(-0.460416\pi\) | ||||
0.124038 | + | 0.992278i | \(0.460416\pi\) | |||||||
\(828\) | −25.8453 | −0.898185 | ||||||||
\(829\) | 1.21203 | 0.0420956 | 0.0210478 | − | 0.999778i | \(-0.493300\pi\) | ||||
0.0210478 | + | 0.999778i | \(0.493300\pi\) | |||||||
\(830\) | 10.3518 | 0.359315 | ||||||||
\(831\) | −53.8362 | −1.86756 | ||||||||
\(832\) | 3.66136 | 0.126935 | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | 0.551803 | 0.0191074 | ||||||||
\(835\) | −12.1940 | −0.421992 | ||||||||
\(836\) | 5.94941 | 0.205765 | ||||||||
\(837\) | −57.4044 | −1.98419 | ||||||||
\(838\) | −6.29412 | −0.217427 | ||||||||
\(839\) | 13.0004 | 0.448823 | 0.224412 | − | 0.974494i | \(-0.427954\pi\) | ||||
0.224412 | + | 0.974494i | \(0.427954\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 1.00000 | 0.0344828 | ||||||||
\(842\) | 2.94479 | 0.101484 | ||||||||
\(843\) | 42.8834 | 1.47698 | ||||||||
\(844\) | −9.87572 | −0.339936 | ||||||||
\(845\) | 0.464099 | 0.0159655 | ||||||||
\(846\) | 0.401775 | 0.0138133 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | −2.67097 | −0.0917216 | ||||||||
\(849\) | −49.4257 | −1.69629 | ||||||||
\(850\) | −0.716846 | −0.0245876 | ||||||||
\(851\) | −24.9596 | −0.855603 | ||||||||
\(852\) | −36.4984 | −1.25042 | ||||||||
\(853\) | 23.8201 | 0.815584 | 0.407792 | − | 0.913075i | \(-0.366299\pi\) | ||||
0.407792 | + | 0.913075i | \(0.366299\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −59.7465 | −2.04329 | ||||||||
\(856\) | −1.79224 | −0.0612576 | ||||||||
\(857\) | −7.27140 | −0.248386 | −0.124193 | − | 0.992258i | \(-0.539634\pi\) | ||||
−0.124193 | + | 0.992258i | \(0.539634\pi\) | |||||||
\(858\) | −10.0758 | −0.343982 | ||||||||
\(859\) | 9.83263 | 0.335485 | 0.167742 | − | 0.985831i | \(-0.446352\pi\) | ||||
0.167742 | + | 0.985831i | \(0.446352\pi\) | |||||||
\(860\) | 11.1897 | 0.381567 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 5.45942 | 0.185949 | ||||||||
\(863\) | 21.9413 | 0.746890 | 0.373445 | − | 0.927652i | \(-0.378176\pi\) | ||||
0.373445 | + | 0.927652i | \(0.378176\pi\) | |||||||
\(864\) | 14.4442 | 0.491400 | ||||||||
\(865\) | 20.5134 | 0.697475 | ||||||||
\(866\) | −16.9899 | −0.577340 | ||||||||
\(867\) | −54.8724 | −1.86356 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 11.3621 | 0.385432 | ||||||||
\(870\) | −3.70208 | −0.125512 | ||||||||
\(871\) | −42.4727 | −1.43913 | ||||||||
\(872\) | 3.64190 | 0.123330 | ||||||||
\(873\) | 140.177 | 4.74427 | ||||||||
\(874\) | 24.2135 | 0.819032 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | −23.6501 | −0.799063 | ||||||||
\(877\) | 36.5659 | 1.23474 | 0.617372 | − | 0.786672i | \(-0.288197\pi\) | ||||
0.617372 | + | 0.786672i | \(0.288197\pi\) | |||||||
\(878\) | −22.6419 | −0.764129 | ||||||||
\(879\) | −50.2039 | −1.69333 | ||||||||
\(880\) | −0.973516 | −0.0328172 | ||||||||
\(881\) | −33.4505 | −1.12698 | −0.563489 | − | 0.826124i | \(-0.690541\pi\) | ||||
−0.563489 | + | 0.826124i | \(0.690541\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −23.9555 | −0.806166 | −0.403083 | − | 0.915163i | \(-0.632061\pi\) | ||||
−0.403083 | + | 0.915163i | \(0.632061\pi\) | |||||||
\(884\) | 0.711212 | 0.0239207 | ||||||||
\(885\) | −29.7778 | −1.00097 | ||||||||
\(886\) | −17.1387 | −0.575787 | ||||||||
\(887\) | 7.39554 | 0.248318 | 0.124159 | − | 0.992262i | \(-0.460377\pi\) | ||||
0.124159 | + | 0.992262i | \(0.460377\pi\) | |||||||
\(888\) | 23.3215 | 0.782618 | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | 16.2853 | 0.545885 | ||||||||
\(891\) | −20.6983 | −0.693418 | ||||||||
\(892\) | −16.5982 | −0.555748 | ||||||||
\(893\) | −0.376408 | −0.0125960 | ||||||||
\(894\) | 45.4317 | 1.51946 | ||||||||
\(895\) | 6.05292 | 0.202327 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −41.0074 | −1.36920 | ||||||||
\(898\) | −12.1802 | −0.406457 | ||||||||
\(899\) | 3.97423 | 0.132548 | ||||||||
\(900\) | −27.5486 | −0.918286 | ||||||||
\(901\) | −0.518832 | −0.0172848 | ||||||||
\(902\) | −3.44095 | −0.114571 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −17.7718 | −0.591081 | ||||||||
\(905\) | 15.0729 | 0.501039 | ||||||||
\(906\) | 39.4587 | 1.31093 | ||||||||
\(907\) | 28.5892 | 0.949289 | 0.474644 | − | 0.880178i | \(-0.342577\pi\) | ||||
0.474644 | + | 0.880178i | \(0.342577\pi\) | |||||||
\(908\) | 17.9930 | 0.597120 | ||||||||
\(909\) | 102.415 | 3.39690 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −15.2600 | −0.505587 | −0.252793 | − | 0.967520i | \(-0.581349\pi\) | ||||
−0.252793 | + | 0.967520i | \(0.581349\pi\) | |||||||
\(912\) | −22.6244 | −0.749167 | ||||||||
\(913\) | −7.69497 | −0.254666 | ||||||||
\(914\) | 31.5102 | 1.04226 | ||||||||
\(915\) | −18.8119 | −0.621901 | ||||||||
\(916\) | −2.03821 | −0.0673444 | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 2.80575 | 0.0926036 | ||||||||
\(919\) | −22.3019 | −0.735673 | −0.367836 | − | 0.929891i | \(-0.619901\pi\) | ||||
−0.367836 | + | 0.929891i | \(0.619901\pi\) | |||||||
\(920\) | −3.96211 | −0.130627 | ||||||||
\(921\) | 10.1668 | 0.335006 | ||||||||
\(922\) | −6.40796 | −0.211035 | ||||||||
\(923\) | −41.3092 | −1.35971 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −26.6045 | −0.874752 | ||||||||
\(926\) | −0.902939 | −0.0296724 | ||||||||
\(927\) | 8.81727 | 0.289597 | ||||||||
\(928\) | −1.00000 | −0.0328266 | ||||||||
\(929\) | −44.9700 | −1.47542 | −0.737710 | − | 0.675118i | \(-0.764093\pi\) | ||||
−0.737710 | + | 0.675118i | \(0.764093\pi\) | |||||||
\(930\) | −14.7129 | −0.482455 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | −16.4989 | −0.540441 | ||||||||
\(933\) | 78.3379 | 2.56467 | ||||||||
\(934\) | −36.4112 | −1.19141 | ||||||||
\(935\) | −0.189104 | −0.00618435 | ||||||||
\(936\) | 27.3321 | 0.893377 | ||||||||
\(937\) | 20.6347 | 0.674105 | 0.337053 | − | 0.941486i | \(-0.390570\pi\) | ||||
0.337053 | + | 0.941486i | \(0.390570\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −33.4910 | −1.09294 | ||||||||
\(940\) | 0.0615925 | 0.00200893 | ||||||||
\(941\) | 33.2588 | 1.08421 | 0.542103 | − | 0.840312i | \(-0.317628\pi\) | ||||
0.542103 | + | 0.840312i | \(0.317628\pi\) | |||||||
\(942\) | 46.5502 | 1.51669 | ||||||||
\(943\) | −14.0043 | −0.456043 | ||||||||
\(944\) | −8.04354 | −0.261795 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −8.31787 | −0.270437 | ||||||||
\(947\) | 0.0959893 | 0.00311923 | 0.00155962 | − | 0.999999i | \(-0.499504\pi\) | ||||
0.00155962 | + | 0.999999i | \(0.499504\pi\) | |||||||
\(948\) | −43.2075 | −1.40332 | ||||||||
\(949\) | −26.7673 | −0.868905 | ||||||||
\(950\) | 25.8092 | 0.837362 | ||||||||
\(951\) | −111.713 | −3.62253 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −11.4213 | −0.369974 | −0.184987 | − | 0.982741i | \(-0.559224\pi\) | ||||
−0.184987 | + | 0.982741i | \(0.559224\pi\) | |||||||
\(954\) | −19.9388 | −0.645544 | ||||||||
\(955\) | 11.3394 | 0.366936 | ||||||||
\(956\) | 18.7414 | 0.606141 | ||||||||
\(957\) | 2.75193 | 0.0889573 | ||||||||
\(958\) | 31.4283 | 1.01540 | ||||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | 3.70208 | 0.119484 | ||||||||
\(961\) | −15.2055 | −0.490501 | ||||||||
\(962\) | 26.3954 | 0.851023 | ||||||||
\(963\) | −13.3791 | −0.431136 | ||||||||
\(964\) | 17.8781 | 0.575813 | ||||||||
\(965\) | −19.9068 | −0.640822 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −9.43755 | −0.303491 | −0.151746 | − | 0.988420i | \(-0.548489\pi\) | ||||
−0.151746 | + | 0.988420i | \(0.548489\pi\) | |||||||
\(968\) | −10.2763 | −0.330294 | ||||||||
\(969\) | −4.39474 | −0.141179 | ||||||||
\(970\) | 21.4893 | 0.689980 | ||||||||
\(971\) | −18.5280 | −0.594592 | −0.297296 | − | 0.954785i | \(-0.596085\pi\) | ||||
−0.297296 | + | 0.954785i | \(0.596085\pi\) | |||||||
\(972\) | 35.3786 | 1.13477 | ||||||||
\(973\) | 0 | 0 | ||||||||
\(974\) | 14.4460 | 0.462878 | ||||||||
\(975\) | −43.7100 | −1.39984 | ||||||||
\(976\) | −5.08144 | −0.162653 | ||||||||
\(977\) | −40.6766 | −1.30136 | −0.650680 | − | 0.759352i | \(-0.725516\pi\) | ||||
−0.650680 | + | 0.759352i | \(0.725516\pi\) | |||||||
\(978\) | 54.2418 | 1.73446 | ||||||||
\(979\) | −12.1057 | −0.386899 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 27.1868 | 0.868008 | ||||||||
\(982\) | 29.2405 | 0.933102 | ||||||||
\(983\) | 52.6149 | 1.67816 | 0.839078 | − | 0.544012i | \(-0.183095\pi\) | ||||
0.839078 | + | 0.544012i | \(0.183095\pi\) | |||||||
\(984\) | 13.0852 | 0.417142 | ||||||||
\(985\) | 20.1368 | 0.641613 | ||||||||
\(986\) | −0.194248 | −0.00618612 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −25.6064 | −0.814648 | ||||||||
\(989\) | −33.8528 | −1.07646 | ||||||||
\(990\) | −7.26731 | −0.230970 | ||||||||
\(991\) | −24.7835 | −0.787273 | −0.393637 | − | 0.919266i | \(-0.628783\pi\) | ||||
−0.393637 | + | 0.919266i | \(0.628783\pi\) | |||||||
\(992\) | −3.97423 | −0.126182 | ||||||||
\(993\) | 16.4997 | 0.523603 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 12.9140 | 0.409402 | ||||||||
\(996\) | 29.2624 | 0.927213 | ||||||||
\(997\) | 16.1891 | 0.512713 | 0.256356 | − | 0.966582i | \(-0.417478\pi\) | ||||
0.256356 | + | 0.966582i | \(0.417478\pi\) | |||||||
\(998\) | 28.4905 | 0.901850 | ||||||||
\(999\) | 104.131 | 3.29455 |
(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 | 2842.2.a.z.1.5 | 5 | ||
7.2 | even | 3 | 406.2.e.a.291.1 | yes | 10 | ||
7.4 | even | 3 | 406.2.e.a.233.1 | ✓ | 10 | ||
7.6 | odd | 2 | 2842.2.a.x.1.1 | 5 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
406.2.e.a.233.1 | ✓ | 10 | 7.4 | even | 3 | ||
406.2.e.a.291.1 | yes | 10 | 7.2 | even | 3 | ||
2842.2.a.x.1.1 | 5 | 7.6 | odd | 2 | |||
2842.2.a.z.1.5 | 5 | 1.1 | even | 1 | trivial |