Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [8002,2,Mod(1,8002)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(8002, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("8002.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 8002 = 2 \cdot 4001 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 8002.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: | \(63.8962916974\) |
Analytic rank: | \(0\) |
Dimension: | \(77\) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.19 | ||
Character | \(\chi\) | \(=\) | 8002.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.00000 | −0.707107 | ||||||||
\(3\) | −1.65847 | −0.957519 | −0.478760 | − | 0.877946i | \(-0.658913\pi\) | ||||
−0.478760 | + | 0.877946i | \(0.658913\pi\) | |||||||
\(4\) | 1.00000 | 0.500000 | ||||||||
\(5\) | −0.802626 | −0.358945 | −0.179473 | − | 0.983763i | \(-0.557439\pi\) | ||||
−0.179473 | + | 0.983763i | \(0.557439\pi\) | |||||||
\(6\) | 1.65847 | 0.677068 | ||||||||
\(7\) | −0.0977002 | −0.0369272 | −0.0184636 | − | 0.999830i | \(-0.505877\pi\) | ||||
−0.0184636 | + | 0.999830i | \(0.505877\pi\) | |||||||
\(8\) | −1.00000 | −0.353553 | ||||||||
\(9\) | −0.249472 | −0.0831572 | ||||||||
\(10\) | 0.802626 | 0.253813 | ||||||||
\(11\) | −4.28508 | −1.29200 | −0.646000 | − | 0.763338i | \(-0.723559\pi\) | ||||
−0.646000 | + | 0.763338i | \(0.723559\pi\) | |||||||
\(12\) | −1.65847 | −0.478760 | ||||||||
\(13\) | −5.88772 | −1.63296 | −0.816480 | − | 0.577374i | \(-0.804078\pi\) | ||||
−0.816480 | + | 0.577374i | \(0.804078\pi\) | |||||||
\(14\) | 0.0977002 | 0.0261115 | ||||||||
\(15\) | 1.33113 | 0.343697 | ||||||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | 4.10249 | 0.994999 | 0.497500 | − | 0.867464i | \(-0.334252\pi\) | ||||
0.497500 | + | 0.867464i | \(0.334252\pi\) | |||||||
\(18\) | 0.249472 | 0.0588011 | ||||||||
\(19\) | 4.88102 | 1.11978 | 0.559892 | − | 0.828566i | \(-0.310843\pi\) | ||||
0.559892 | + | 0.828566i | \(0.310843\pi\) | |||||||
\(20\) | −0.802626 | −0.179473 | ||||||||
\(21\) | 0.162033 | 0.0353585 | ||||||||
\(22\) | 4.28508 | 0.913582 | ||||||||
\(23\) | −7.15578 | −1.49208 | −0.746042 | − | 0.665899i | \(-0.768048\pi\) | ||||
−0.746042 | + | 0.665899i | \(0.768048\pi\) | |||||||
\(24\) | 1.65847 | 0.338534 | ||||||||
\(25\) | −4.35579 | −0.871158 | ||||||||
\(26\) | 5.88772 | 1.15468 | ||||||||
\(27\) | 5.38916 | 1.03714 | ||||||||
\(28\) | −0.0977002 | −0.0184636 | ||||||||
\(29\) | 6.43182 | 1.19436 | 0.597179 | − | 0.802108i | \(-0.296288\pi\) | ||||
0.597179 | + | 0.802108i | \(0.296288\pi\) | |||||||
\(30\) | −1.33113 | −0.243031 | ||||||||
\(31\) | −4.30233 | −0.772721 | −0.386360 | − | 0.922348i | \(-0.626268\pi\) | ||||
−0.386360 | + | 0.922348i | \(0.626268\pi\) | |||||||
\(32\) | −1.00000 | −0.176777 | ||||||||
\(33\) | 7.10668 | 1.23711 | ||||||||
\(34\) | −4.10249 | −0.703571 | ||||||||
\(35\) | 0.0784167 | 0.0132548 | ||||||||
\(36\) | −0.249472 | −0.0415786 | ||||||||
\(37\) | −0.738173 | −0.121355 | −0.0606775 | − | 0.998157i | \(-0.519326\pi\) | ||||
−0.0606775 | + | 0.998157i | \(0.519326\pi\) | |||||||
\(38\) | −4.88102 | −0.791806 | ||||||||
\(39\) | 9.76462 | 1.56359 | ||||||||
\(40\) | 0.802626 | 0.126906 | ||||||||
\(41\) | −9.15637 | −1.42999 | −0.714993 | − | 0.699132i | \(-0.753570\pi\) | ||||
−0.714993 | + | 0.699132i | \(0.753570\pi\) | |||||||
\(42\) | −0.162033 | −0.0250022 | ||||||||
\(43\) | −3.11395 | −0.474873 | −0.237437 | − | 0.971403i | \(-0.576307\pi\) | ||||
−0.237437 | + | 0.971403i | \(0.576307\pi\) | |||||||
\(44\) | −4.28508 | −0.646000 | ||||||||
\(45\) | 0.200233 | 0.0298489 | ||||||||
\(46\) | 7.15578 | 1.05506 | ||||||||
\(47\) | 7.49518 | 1.09328 | 0.546642 | − | 0.837366i | \(-0.315906\pi\) | ||||
0.546642 | + | 0.837366i | \(0.315906\pi\) | |||||||
\(48\) | −1.65847 | −0.239380 | ||||||||
\(49\) | −6.99045 | −0.998636 | ||||||||
\(50\) | 4.35579 | 0.616002 | ||||||||
\(51\) | −6.80386 | −0.952731 | ||||||||
\(52\) | −5.88772 | −0.816480 | ||||||||
\(53\) | −8.00141 | −1.09908 | −0.549539 | − | 0.835468i | \(-0.685197\pi\) | ||||
−0.549539 | + | 0.835468i | \(0.685197\pi\) | |||||||
\(54\) | −5.38916 | −0.733371 | ||||||||
\(55\) | 3.43932 | 0.463757 | ||||||||
\(56\) | 0.0977002 | 0.0130557 | ||||||||
\(57\) | −8.09504 | −1.07221 | ||||||||
\(58\) | −6.43182 | −0.844539 | ||||||||
\(59\) | −8.80842 | −1.14676 | −0.573379 | − | 0.819290i | \(-0.694368\pi\) | ||||
−0.573379 | + | 0.819290i | \(0.694368\pi\) | |||||||
\(60\) | 1.33113 | 0.171849 | ||||||||
\(61\) | −2.70949 | −0.346915 | −0.173458 | − | 0.984841i | \(-0.555494\pi\) | ||||
−0.173458 | + | 0.984841i | \(0.555494\pi\) | |||||||
\(62\) | 4.30233 | 0.546396 | ||||||||
\(63\) | 0.0243734 | 0.00307076 | ||||||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | 4.72564 | 0.586143 | ||||||||
\(66\) | −7.10668 | −0.874772 | ||||||||
\(67\) | −10.2707 | −1.25476 | −0.627380 | − | 0.778713i | \(-0.715873\pi\) | ||||
−0.627380 | + | 0.778713i | \(0.715873\pi\) | |||||||
\(68\) | 4.10249 | 0.497500 | ||||||||
\(69\) | 11.8677 | 1.42870 | ||||||||
\(70\) | −0.0784167 | −0.00937259 | ||||||||
\(71\) | −10.3343 | −1.22646 | −0.613229 | − | 0.789905i | \(-0.710130\pi\) | ||||
−0.613229 | + | 0.789905i | \(0.710130\pi\) | |||||||
\(72\) | 0.249472 | 0.0294005 | ||||||||
\(73\) | 0.0428290 | 0.00501276 | 0.00250638 | − | 0.999997i | \(-0.499202\pi\) | ||||
0.00250638 | + | 0.999997i | \(0.499202\pi\) | |||||||
\(74\) | 0.738173 | 0.0858109 | ||||||||
\(75\) | 7.22396 | 0.834151 | ||||||||
\(76\) | 4.88102 | 0.559892 | ||||||||
\(77\) | 0.418653 | 0.0477099 | ||||||||
\(78\) | −9.76462 | −1.10563 | ||||||||
\(79\) | 3.97141 | 0.446818 | 0.223409 | − | 0.974725i | \(-0.428281\pi\) | ||||
0.223409 | + | 0.974725i | \(0.428281\pi\) | |||||||
\(80\) | −0.802626 | −0.0897363 | ||||||||
\(81\) | −8.18935 | −0.909928 | ||||||||
\(82\) | 9.15637 | 1.01115 | ||||||||
\(83\) | 6.86346 | 0.753362 | 0.376681 | − | 0.926343i | \(-0.377065\pi\) | ||||
0.376681 | + | 0.926343i | \(0.377065\pi\) | |||||||
\(84\) | 0.162033 | 0.0176792 | ||||||||
\(85\) | −3.29276 | −0.357150 | ||||||||
\(86\) | 3.11395 | 0.335786 | ||||||||
\(87\) | −10.6670 | −1.14362 | ||||||||
\(88\) | 4.28508 | 0.456791 | ||||||||
\(89\) | −5.35914 | −0.568067 | −0.284034 | − | 0.958814i | \(-0.591673\pi\) | ||||
−0.284034 | + | 0.958814i | \(0.591673\pi\) | |||||||
\(90\) | −0.200233 | −0.0211064 | ||||||||
\(91\) | 0.575231 | 0.0603006 | ||||||||
\(92\) | −7.15578 | −0.746042 | ||||||||
\(93\) | 7.13529 | 0.739895 | ||||||||
\(94\) | −7.49518 | −0.773069 | ||||||||
\(95\) | −3.91764 | −0.401941 | ||||||||
\(96\) | 1.65847 | 0.169267 | ||||||||
\(97\) | −4.07812 | −0.414071 | −0.207035 | − | 0.978333i | \(-0.566381\pi\) | ||||
−0.207035 | + | 0.978333i | \(0.566381\pi\) | |||||||
\(98\) | 6.99045 | 0.706143 | ||||||||
\(99\) | 1.06901 | 0.107439 | ||||||||
\(100\) | −4.35579 | −0.435579 | ||||||||
\(101\) | −5.49159 | −0.546434 | −0.273217 | − | 0.961952i | \(-0.588088\pi\) | ||||
−0.273217 | + | 0.961952i | \(0.588088\pi\) | |||||||
\(102\) | 6.80386 | 0.673682 | ||||||||
\(103\) | −17.9063 | −1.76436 | −0.882180 | − | 0.470913i | \(-0.843925\pi\) | ||||
−0.882180 | + | 0.470913i | \(0.843925\pi\) | |||||||
\(104\) | 5.88772 | 0.577339 | ||||||||
\(105\) | −0.130052 | −0.0126918 | ||||||||
\(106\) | 8.00141 | 0.777166 | ||||||||
\(107\) | −11.2606 | −1.08860 | −0.544301 | − | 0.838890i | \(-0.683205\pi\) | ||||
−0.544301 | + | 0.838890i | \(0.683205\pi\) | |||||||
\(108\) | 5.38916 | 0.518572 | ||||||||
\(109\) | −6.84529 | −0.655660 | −0.327830 | − | 0.944737i | \(-0.606317\pi\) | ||||
−0.327830 | + | 0.944737i | \(0.606317\pi\) | |||||||
\(110\) | −3.43932 | −0.327926 | ||||||||
\(111\) | 1.22424 | 0.116200 | ||||||||
\(112\) | −0.0977002 | −0.00923180 | ||||||||
\(113\) | 10.7483 | 1.01112 | 0.505558 | − | 0.862792i | \(-0.331286\pi\) | ||||
0.505558 | + | 0.862792i | \(0.331286\pi\) | |||||||
\(114\) | 8.09504 | 0.758170 | ||||||||
\(115\) | 5.74342 | 0.535577 | ||||||||
\(116\) | 6.43182 | 0.597179 | ||||||||
\(117\) | 1.46882 | 0.135792 | ||||||||
\(118\) | 8.80842 | 0.810881 | ||||||||
\(119\) | −0.400814 | −0.0367425 | ||||||||
\(120\) | −1.33113 | −0.121515 | ||||||||
\(121\) | 7.36190 | 0.669263 | ||||||||
\(122\) | 2.70949 | 0.245306 | ||||||||
\(123\) | 15.1856 | 1.36924 | ||||||||
\(124\) | −4.30233 | −0.386360 | ||||||||
\(125\) | 7.50920 | 0.671644 | ||||||||
\(126\) | −0.0243734 | −0.00217136 | ||||||||
\(127\) | −7.85976 | −0.697441 | −0.348721 | − | 0.937227i | \(-0.613384\pi\) | ||||
−0.348721 | + | 0.937227i | \(0.613384\pi\) | |||||||
\(128\) | −1.00000 | −0.0883883 | ||||||||
\(129\) | 5.16440 | 0.454700 | ||||||||
\(130\) | −4.72564 | −0.414466 | ||||||||
\(131\) | −20.3039 | −1.77396 | −0.886981 | − | 0.461806i | \(-0.847202\pi\) | ||||
−0.886981 | + | 0.461806i | \(0.847202\pi\) | |||||||
\(132\) | 7.10668 | 0.618557 | ||||||||
\(133\) | −0.476877 | −0.0413505 | ||||||||
\(134\) | 10.2707 | 0.887250 | ||||||||
\(135\) | −4.32548 | −0.372278 | ||||||||
\(136\) | −4.10249 | −0.351785 | ||||||||
\(137\) | 11.7342 | 1.00252 | 0.501262 | − | 0.865296i | \(-0.332869\pi\) | ||||
0.501262 | + | 0.865296i | \(0.332869\pi\) | |||||||
\(138\) | −11.8677 | −1.01024 | ||||||||
\(139\) | 3.26959 | 0.277323 | 0.138661 | − | 0.990340i | \(-0.455720\pi\) | ||||
0.138661 | + | 0.990340i | \(0.455720\pi\) | |||||||
\(140\) | 0.0784167 | 0.00662742 | ||||||||
\(141\) | −12.4305 | −1.04684 | ||||||||
\(142\) | 10.3343 | 0.867237 | ||||||||
\(143\) | 25.2293 | 2.10978 | ||||||||
\(144\) | −0.249472 | −0.0207893 | ||||||||
\(145\) | −5.16235 | −0.428710 | ||||||||
\(146\) | −0.0428290 | −0.00354455 | ||||||||
\(147\) | 11.5935 | 0.956213 | ||||||||
\(148\) | −0.738173 | −0.0606775 | ||||||||
\(149\) | 4.82312 | 0.395126 | 0.197563 | − | 0.980290i | \(-0.436697\pi\) | ||||
0.197563 | + | 0.980290i | \(0.436697\pi\) | |||||||
\(150\) | −7.22396 | −0.589834 | ||||||||
\(151\) | 12.8253 | 1.04371 | 0.521854 | − | 0.853035i | \(-0.325241\pi\) | ||||
0.521854 | + | 0.853035i | \(0.325241\pi\) | |||||||
\(152\) | −4.88102 | −0.395903 | ||||||||
\(153\) | −1.02345 | −0.0827414 | ||||||||
\(154\) | −0.418653 | −0.0337360 | ||||||||
\(155\) | 3.45316 | 0.277365 | ||||||||
\(156\) | 9.76462 | 0.781795 | ||||||||
\(157\) | −0.792102 | −0.0632166 | −0.0316083 | − | 0.999500i | \(-0.510063\pi\) | ||||
−0.0316083 | + | 0.999500i | \(0.510063\pi\) | |||||||
\(158\) | −3.97141 | −0.315948 | ||||||||
\(159\) | 13.2701 | 1.05239 | ||||||||
\(160\) | 0.802626 | 0.0634532 | ||||||||
\(161\) | 0.699121 | 0.0550985 | ||||||||
\(162\) | 8.18935 | 0.643416 | ||||||||
\(163\) | 11.2416 | 0.880513 | 0.440256 | − | 0.897872i | \(-0.354888\pi\) | ||||
0.440256 | + | 0.897872i | \(0.354888\pi\) | |||||||
\(164\) | −9.15637 | −0.714993 | ||||||||
\(165\) | −5.70401 | −0.444056 | ||||||||
\(166\) | −6.86346 | −0.532708 | ||||||||
\(167\) | −11.1276 | −0.861082 | −0.430541 | − | 0.902571i | \(-0.641677\pi\) | ||||
−0.430541 | + | 0.902571i | \(0.641677\pi\) | |||||||
\(168\) | −0.162033 | −0.0125011 | ||||||||
\(169\) | 21.6653 | 1.66656 | ||||||||
\(170\) | 3.29276 | 0.252543 | ||||||||
\(171\) | −1.21768 | −0.0931181 | ||||||||
\(172\) | −3.11395 | −0.237437 | ||||||||
\(173\) | −3.93491 | −0.299166 | −0.149583 | − | 0.988749i | \(-0.547793\pi\) | ||||
−0.149583 | + | 0.988749i | \(0.547793\pi\) | |||||||
\(174\) | 10.6670 | 0.808662 | ||||||||
\(175\) | 0.425562 | 0.0321694 | ||||||||
\(176\) | −4.28508 | −0.323000 | ||||||||
\(177\) | 14.6085 | 1.09804 | ||||||||
\(178\) | 5.35914 | 0.401684 | ||||||||
\(179\) | −9.10842 | −0.680795 | −0.340398 | − | 0.940282i | \(-0.610562\pi\) | ||||
−0.340398 | + | 0.940282i | \(0.610562\pi\) | |||||||
\(180\) | 0.200233 | 0.0149245 | ||||||||
\(181\) | −9.30241 | −0.691443 | −0.345721 | − | 0.938337i | \(-0.612366\pi\) | ||||
−0.345721 | + | 0.938337i | \(0.612366\pi\) | |||||||
\(182\) | −0.575231 | −0.0426390 | ||||||||
\(183\) | 4.49362 | 0.332178 | ||||||||
\(184\) | 7.15578 | 0.527531 | ||||||||
\(185\) | 0.592477 | 0.0435598 | ||||||||
\(186\) | −7.13529 | −0.523185 | ||||||||
\(187\) | −17.5795 | −1.28554 | ||||||||
\(188\) | 7.49518 | 0.546642 | ||||||||
\(189\) | −0.526522 | −0.0382988 | ||||||||
\(190\) | 3.91764 | 0.284215 | ||||||||
\(191\) | 13.3414 | 0.965349 | 0.482674 | − | 0.875800i | \(-0.339665\pi\) | ||||
0.482674 | + | 0.875800i | \(0.339665\pi\) | |||||||
\(192\) | −1.65847 | −0.119690 | ||||||||
\(193\) | 4.90829 | 0.353307 | 0.176653 | − | 0.984273i | \(-0.443473\pi\) | ||||
0.176653 | + | 0.984273i | \(0.443473\pi\) | |||||||
\(194\) | 4.07812 | 0.292792 | ||||||||
\(195\) | −7.83734 | −0.561244 | ||||||||
\(196\) | −6.99045 | −0.499318 | ||||||||
\(197\) | 1.64123 | 0.116933 | 0.0584663 | − | 0.998289i | \(-0.481379\pi\) | ||||
0.0584663 | + | 0.998289i | \(0.481379\pi\) | |||||||
\(198\) | −1.06901 | −0.0759710 | ||||||||
\(199\) | −4.52532 | −0.320791 | −0.160396 | − | 0.987053i | \(-0.551277\pi\) | ||||
−0.160396 | + | 0.987053i | \(0.551277\pi\) | |||||||
\(200\) | 4.35579 | 0.308001 | ||||||||
\(201\) | 17.0336 | 1.20146 | ||||||||
\(202\) | 5.49159 | 0.386387 | ||||||||
\(203\) | −0.628390 | −0.0441043 | ||||||||
\(204\) | −6.80386 | −0.476365 | ||||||||
\(205\) | 7.34915 | 0.513287 | ||||||||
\(206\) | 17.9063 | 1.24759 | ||||||||
\(207\) | 1.78517 | 0.124078 | ||||||||
\(208\) | −5.88772 | −0.408240 | ||||||||
\(209\) | −20.9156 | −1.44676 | ||||||||
\(210\) | 0.130052 | 0.00897444 | ||||||||
\(211\) | −0.227580 | −0.0156672 | −0.00783361 | − | 0.999969i | \(-0.502494\pi\) | ||||
−0.00783361 | + | 0.999969i | \(0.502494\pi\) | |||||||
\(212\) | −8.00141 | −0.549539 | ||||||||
\(213\) | 17.1392 | 1.17436 | ||||||||
\(214\) | 11.2606 | 0.769758 | ||||||||
\(215\) | 2.49934 | 0.170454 | ||||||||
\(216\) | −5.38916 | −0.366686 | ||||||||
\(217\) | 0.420338 | 0.0285344 | ||||||||
\(218\) | 6.84529 | 0.463622 | ||||||||
\(219\) | −0.0710307 | −0.00479981 | ||||||||
\(220\) | 3.43932 | 0.231879 | ||||||||
\(221\) | −24.1543 | −1.62479 | ||||||||
\(222\) | −1.22424 | −0.0821656 | ||||||||
\(223\) | 13.0588 | 0.874483 | 0.437241 | − | 0.899344i | \(-0.355956\pi\) | ||||
0.437241 | + | 0.899344i | \(0.355956\pi\) | |||||||
\(224\) | 0.0977002 | 0.00652787 | ||||||||
\(225\) | 1.08665 | 0.0724431 | ||||||||
\(226\) | −10.7483 | −0.714968 | ||||||||
\(227\) | 12.3681 | 0.820898 | 0.410449 | − | 0.911884i | \(-0.365372\pi\) | ||||
0.410449 | + | 0.911884i | \(0.365372\pi\) | |||||||
\(228\) | −8.09504 | −0.536107 | ||||||||
\(229\) | −27.7355 | −1.83281 | −0.916406 | − | 0.400251i | \(-0.868923\pi\) | ||||
−0.916406 | + | 0.400251i | \(0.868923\pi\) | |||||||
\(230\) | −5.74342 | −0.378710 | ||||||||
\(231\) | −0.694324 | −0.0456832 | ||||||||
\(232\) | −6.43182 | −0.422270 | ||||||||
\(233\) | 16.0290 | 1.05010 | 0.525048 | − | 0.851073i | \(-0.324047\pi\) | ||||
0.525048 | + | 0.851073i | \(0.324047\pi\) | |||||||
\(234\) | −1.46882 | −0.0960198 | ||||||||
\(235\) | −6.01583 | −0.392429 | ||||||||
\(236\) | −8.80842 | −0.573379 | ||||||||
\(237\) | −6.58646 | −0.427837 | ||||||||
\(238\) | 0.400814 | 0.0259809 | ||||||||
\(239\) | 19.1279 | 1.23728 | 0.618640 | − | 0.785674i | \(-0.287684\pi\) | ||||
0.618640 | + | 0.785674i | \(0.287684\pi\) | |||||||
\(240\) | 1.33113 | 0.0859243 | ||||||||
\(241\) | −26.5054 | −1.70737 | −0.853683 | − | 0.520794i | \(-0.825636\pi\) | ||||
−0.853683 | + | 0.520794i | \(0.825636\pi\) | |||||||
\(242\) | −7.36190 | −0.473241 | ||||||||
\(243\) | −2.58567 | −0.165871 | ||||||||
\(244\) | −2.70949 | −0.173458 | ||||||||
\(245\) | 5.61072 | 0.358456 | ||||||||
\(246\) | −15.1856 | −0.968198 | ||||||||
\(247\) | −28.7381 | −1.82856 | ||||||||
\(248\) | 4.30233 | 0.273198 | ||||||||
\(249\) | −11.3828 | −0.721359 | ||||||||
\(250\) | −7.50920 | −0.474924 | ||||||||
\(251\) | 10.3539 | 0.653535 | 0.326767 | − | 0.945105i | \(-0.394041\pi\) | ||||
0.326767 | + | 0.945105i | \(0.394041\pi\) | |||||||
\(252\) | 0.0243734 | 0.00153538 | ||||||||
\(253\) | 30.6631 | 1.92777 | ||||||||
\(254\) | 7.85976 | 0.493165 | ||||||||
\(255\) | 5.46096 | 0.341978 | ||||||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | 1.73524 | 0.108242 | 0.0541208 | − | 0.998534i | \(-0.482764\pi\) | ||||
0.0541208 | + | 0.998534i | \(0.482764\pi\) | |||||||
\(258\) | −5.16440 | −0.321521 | ||||||||
\(259\) | 0.0721197 | 0.00448130 | ||||||||
\(260\) | 4.72564 | 0.293072 | ||||||||
\(261\) | −1.60456 | −0.0993196 | ||||||||
\(262\) | 20.3039 | 1.25438 | ||||||||
\(263\) | 8.81690 | 0.543673 | 0.271837 | − | 0.962343i | \(-0.412369\pi\) | ||||
0.271837 | + | 0.962343i | \(0.412369\pi\) | |||||||
\(264\) | −7.10668 | −0.437386 | ||||||||
\(265\) | 6.42214 | 0.394509 | ||||||||
\(266\) | 0.476877 | 0.0292392 | ||||||||
\(267\) | 8.88798 | 0.543935 | ||||||||
\(268\) | −10.2707 | −0.627380 | ||||||||
\(269\) | 3.26925 | 0.199330 | 0.0996649 | − | 0.995021i | \(-0.468223\pi\) | ||||
0.0996649 | + | 0.995021i | \(0.468223\pi\) | |||||||
\(270\) | 4.32548 | 0.263240 | ||||||||
\(271\) | −23.0568 | −1.40060 | −0.700301 | − | 0.713848i | \(-0.746951\pi\) | ||||
−0.700301 | + | 0.713848i | \(0.746951\pi\) | |||||||
\(272\) | 4.10249 | 0.248750 | ||||||||
\(273\) | −0.954005 | −0.0577390 | ||||||||
\(274\) | −11.7342 | −0.708891 | ||||||||
\(275\) | 18.6649 | 1.12554 | ||||||||
\(276\) | 11.8677 | 0.714349 | ||||||||
\(277\) | −20.6326 | −1.23969 | −0.619846 | − | 0.784723i | \(-0.712805\pi\) | ||||
−0.619846 | + | 0.784723i | \(0.712805\pi\) | |||||||
\(278\) | −3.26959 | −0.196097 | ||||||||
\(279\) | 1.07331 | 0.0642573 | ||||||||
\(280\) | −0.0784167 | −0.00468630 | ||||||||
\(281\) | −28.5470 | −1.70297 | −0.851486 | − | 0.524377i | \(-0.824298\pi\) | ||||
−0.851486 | + | 0.524377i | \(0.824298\pi\) | |||||||
\(282\) | 12.4305 | 0.740228 | ||||||||
\(283\) | 12.6676 | 0.753012 | 0.376506 | − | 0.926414i | \(-0.377126\pi\) | ||||
0.376506 | + | 0.926414i | \(0.377126\pi\) | |||||||
\(284\) | −10.3343 | −0.613229 | ||||||||
\(285\) | 6.49729 | 0.384866 | ||||||||
\(286\) | −25.2293 | −1.49184 | ||||||||
\(287\) | 0.894579 | 0.0528053 | ||||||||
\(288\) | 0.249472 | 0.0147003 | ||||||||
\(289\) | −0.169596 | −0.00997623 | ||||||||
\(290\) | 5.16235 | 0.303143 | ||||||||
\(291\) | 6.76345 | 0.396480 | ||||||||
\(292\) | 0.0428290 | 0.00250638 | ||||||||
\(293\) | −16.3219 | −0.953533 | −0.476767 | − | 0.879030i | \(-0.658191\pi\) | ||||
−0.476767 | + | 0.879030i | \(0.658191\pi\) | |||||||
\(294\) | −11.5935 | −0.676145 | ||||||||
\(295\) | 7.06987 | 0.411624 | ||||||||
\(296\) | 0.738173 | 0.0429055 | ||||||||
\(297\) | −23.0930 | −1.33999 | ||||||||
\(298\) | −4.82312 | −0.279396 | ||||||||
\(299\) | 42.1312 | 2.43651 | ||||||||
\(300\) | 7.22396 | 0.417075 | ||||||||
\(301\) | 0.304234 | 0.0175357 | ||||||||
\(302\) | −12.8253 | −0.738013 | ||||||||
\(303\) | 9.10765 | 0.523221 | ||||||||
\(304\) | 4.88102 | 0.279946 | ||||||||
\(305\) | 2.17471 | 0.124524 | ||||||||
\(306\) | 1.02345 | 0.0585070 | ||||||||
\(307\) | 11.0823 | 0.632502 | 0.316251 | − | 0.948676i | \(-0.397576\pi\) | ||||
0.316251 | + | 0.948676i | \(0.397576\pi\) | |||||||
\(308\) | 0.418653 | 0.0238550 | ||||||||
\(309\) | 29.6971 | 1.68941 | ||||||||
\(310\) | −3.45316 | −0.196126 | ||||||||
\(311\) | 29.0299 | 1.64614 | 0.823068 | − | 0.567943i | \(-0.192260\pi\) | ||||
0.823068 | + | 0.567943i | \(0.192260\pi\) | |||||||
\(312\) | −9.76462 | −0.552813 | ||||||||
\(313\) | −6.07292 | −0.343262 | −0.171631 | − | 0.985161i | \(-0.554904\pi\) | ||||
−0.171631 | + | 0.985161i | \(0.554904\pi\) | |||||||
\(314\) | 0.792102 | 0.0447009 | ||||||||
\(315\) | −0.0195628 | −0.00110224 | ||||||||
\(316\) | 3.97141 | 0.223409 | ||||||||
\(317\) | −9.81771 | −0.551417 | −0.275709 | − | 0.961241i | \(-0.588912\pi\) | ||||
−0.275709 | + | 0.961241i | \(0.588912\pi\) | |||||||
\(318\) | −13.2701 | −0.744151 | ||||||||
\(319\) | −27.5608 | −1.54311 | ||||||||
\(320\) | −0.802626 | −0.0448682 | ||||||||
\(321\) | 18.6754 | 1.04236 | ||||||||
\(322\) | −0.699121 | −0.0389605 | ||||||||
\(323\) | 20.0243 | 1.11418 | ||||||||
\(324\) | −8.18935 | −0.454964 | ||||||||
\(325\) | 25.6457 | 1.42257 | ||||||||
\(326\) | −11.2416 | −0.622617 | ||||||||
\(327\) | 11.3527 | 0.627807 | ||||||||
\(328\) | 9.15637 | 0.505576 | ||||||||
\(329\) | −0.732281 | −0.0403719 | ||||||||
\(330\) | 5.70401 | 0.313995 | ||||||||
\(331\) | −31.5144 | −1.73219 | −0.866094 | − | 0.499882i | \(-0.833377\pi\) | ||||
−0.866094 | + | 0.499882i | \(0.833377\pi\) | |||||||
\(332\) | 6.86346 | 0.376681 | ||||||||
\(333\) | 0.184153 | 0.0100915 | ||||||||
\(334\) | 11.1276 | 0.608877 | ||||||||
\(335\) | 8.24350 | 0.450391 | ||||||||
\(336\) | 0.162033 | 0.00883962 | ||||||||
\(337\) | 2.34590 | 0.127790 | 0.0638948 | − | 0.997957i | \(-0.479648\pi\) | ||||
0.0638948 | + | 0.997957i | \(0.479648\pi\) | |||||||
\(338\) | −21.6653 | −1.17843 | ||||||||
\(339\) | −17.8258 | −0.968164 | ||||||||
\(340\) | −3.29276 | −0.178575 | ||||||||
\(341\) | 18.4358 | 0.998355 | ||||||||
\(342\) | 1.21768 | 0.0658444 | ||||||||
\(343\) | 1.36687 | 0.0738040 | ||||||||
\(344\) | 3.11395 | 0.167893 | ||||||||
\(345\) | −9.52530 | −0.512825 | ||||||||
\(346\) | 3.93491 | 0.211542 | ||||||||
\(347\) | −16.3252 | −0.876380 | −0.438190 | − | 0.898882i | \(-0.644380\pi\) | ||||
−0.438190 | + | 0.898882i | \(0.644380\pi\) | |||||||
\(348\) | −10.6670 | −0.571811 | ||||||||
\(349\) | 33.6684 | 1.80223 | 0.901114 | − | 0.433581i | \(-0.142750\pi\) | ||||
0.901114 | + | 0.433581i | \(0.142750\pi\) | |||||||
\(350\) | −0.425562 | −0.0227472 | ||||||||
\(351\) | −31.7299 | −1.69361 | ||||||||
\(352\) | 4.28508 | 0.228395 | ||||||||
\(353\) | −12.2203 | −0.650419 | −0.325209 | − | 0.945642i | \(-0.605435\pi\) | ||||
−0.325209 | + | 0.945642i | \(0.605435\pi\) | |||||||
\(354\) | −14.6085 | −0.776434 | ||||||||
\(355\) | 8.29460 | 0.440232 | ||||||||
\(356\) | −5.35914 | −0.284034 | ||||||||
\(357\) | 0.664738 | 0.0351817 | ||||||||
\(358\) | 9.10842 | 0.481395 | ||||||||
\(359\) | −0.786973 | −0.0415348 | −0.0207674 | − | 0.999784i | \(-0.506611\pi\) | ||||
−0.0207674 | + | 0.999784i | \(0.506611\pi\) | |||||||
\(360\) | −0.200233 | −0.0105532 | ||||||||
\(361\) | 4.82438 | 0.253915 | ||||||||
\(362\) | 9.30241 | 0.488924 | ||||||||
\(363\) | −12.2095 | −0.640833 | ||||||||
\(364\) | 0.575231 | 0.0301503 | ||||||||
\(365\) | −0.0343757 | −0.00179931 | ||||||||
\(366\) | −4.49362 | −0.234885 | ||||||||
\(367\) | 15.6163 | 0.815164 | 0.407582 | − | 0.913169i | \(-0.366372\pi\) | ||||
0.407582 | + | 0.913169i | \(0.366372\pi\) | |||||||
\(368\) | −7.15578 | −0.373021 | ||||||||
\(369\) | 2.28426 | 0.118914 | ||||||||
\(370\) | −0.592477 | −0.0308014 | ||||||||
\(371\) | 0.781739 | 0.0405859 | ||||||||
\(372\) | 7.13529 | 0.369947 | ||||||||
\(373\) | 2.46615 | 0.127692 | 0.0638461 | − | 0.997960i | \(-0.479663\pi\) | ||||
0.0638461 | + | 0.997960i | \(0.479663\pi\) | |||||||
\(374\) | 17.5795 | 0.909013 | ||||||||
\(375\) | −12.4538 | −0.643112 | ||||||||
\(376\) | −7.49518 | −0.386535 | ||||||||
\(377\) | −37.8688 | −1.95034 | ||||||||
\(378\) | 0.526522 | 0.0270813 | ||||||||
\(379\) | −2.86090 | −0.146954 | −0.0734772 | − | 0.997297i | \(-0.523410\pi\) | ||||
−0.0734772 | + | 0.997297i | \(0.523410\pi\) | |||||||
\(380\) | −3.91764 | −0.200971 | ||||||||
\(381\) | 13.0352 | 0.667813 | ||||||||
\(382\) | −13.3414 | −0.682605 | ||||||||
\(383\) | 27.7756 | 1.41927 | 0.709634 | − | 0.704570i | \(-0.248860\pi\) | ||||
0.709634 | + | 0.704570i | \(0.248860\pi\) | |||||||
\(384\) | 1.65847 | 0.0846335 | ||||||||
\(385\) | −0.336022 | −0.0171253 | ||||||||
\(386\) | −4.90829 | −0.249826 | ||||||||
\(387\) | 0.776843 | 0.0394891 | ||||||||
\(388\) | −4.07812 | −0.207035 | ||||||||
\(389\) | −19.4925 | −0.988311 | −0.494156 | − | 0.869374i | \(-0.664523\pi\) | ||||
−0.494156 | + | 0.869374i | \(0.664523\pi\) | |||||||
\(390\) | 7.83734 | 0.396859 | ||||||||
\(391\) | −29.3565 | −1.48462 | ||||||||
\(392\) | 6.99045 | 0.353071 | ||||||||
\(393\) | 33.6735 | 1.69860 | ||||||||
\(394\) | −1.64123 | −0.0826838 | ||||||||
\(395\) | −3.18755 | −0.160383 | ||||||||
\(396\) | 1.06901 | 0.0537196 | ||||||||
\(397\) | −5.27141 | −0.264564 | −0.132282 | − | 0.991212i | \(-0.542231\pi\) | ||||
−0.132282 | + | 0.991212i | \(0.542231\pi\) | |||||||
\(398\) | 4.52532 | 0.226834 | ||||||||
\(399\) | 0.790887 | 0.0395939 | ||||||||
\(400\) | −4.35579 | −0.217790 | ||||||||
\(401\) | 17.5397 | 0.875889 | 0.437944 | − | 0.899002i | \(-0.355707\pi\) | ||||
0.437944 | + | 0.899002i | \(0.355707\pi\) | |||||||
\(402\) | −17.0336 | −0.849559 | ||||||||
\(403\) | 25.3309 | 1.26182 | ||||||||
\(404\) | −5.49159 | −0.273217 | ||||||||
\(405\) | 6.57299 | 0.326614 | ||||||||
\(406\) | 0.628390 | 0.0311865 | ||||||||
\(407\) | 3.16313 | 0.156791 | ||||||||
\(408\) | 6.80386 | 0.336841 | ||||||||
\(409\) | −19.6791 | −0.973067 | −0.486533 | − | 0.873662i | \(-0.661739\pi\) | ||||
−0.486533 | + | 0.873662i | \(0.661739\pi\) | |||||||
\(410\) | −7.34915 | −0.362948 | ||||||||
\(411\) | −19.4609 | −0.959935 | ||||||||
\(412\) | −17.9063 | −0.882180 | ||||||||
\(413\) | 0.860584 | 0.0423466 | ||||||||
\(414\) | −1.78517 | −0.0877361 | ||||||||
\(415\) | −5.50879 | −0.270416 | ||||||||
\(416\) | 5.88772 | 0.288669 | ||||||||
\(417\) | −5.42252 | −0.265542 | ||||||||
\(418\) | 20.9156 | 1.02301 | ||||||||
\(419\) | 39.5113 | 1.93025 | 0.965126 | − | 0.261786i | \(-0.0843116\pi\) | ||||
0.965126 | + | 0.261786i | \(0.0843116\pi\) | |||||||
\(420\) | −0.130052 | −0.00634588 | ||||||||
\(421\) | −6.83947 | −0.333335 | −0.166668 | − | 0.986013i | \(-0.553301\pi\) | ||||
−0.166668 | + | 0.986013i | \(0.553301\pi\) | |||||||
\(422\) | 0.227580 | 0.0110784 | ||||||||
\(423\) | −1.86984 | −0.0909146 | ||||||||
\(424\) | 8.00141 | 0.388583 | ||||||||
\(425\) | −17.8696 | −0.866802 | ||||||||
\(426\) | −17.1392 | −0.830396 | ||||||||
\(427\) | 0.264718 | 0.0128106 | ||||||||
\(428\) | −11.2606 | −0.544301 | ||||||||
\(429\) | −41.8422 | −2.02016 | ||||||||
\(430\) | −2.49934 | −0.120529 | ||||||||
\(431\) | −15.8031 | −0.761210 | −0.380605 | − | 0.924738i | \(-0.624284\pi\) | ||||
−0.380605 | + | 0.924738i | \(0.624284\pi\) | |||||||
\(432\) | 5.38916 | 0.259286 | ||||||||
\(433\) | −22.3223 | −1.07274 | −0.536370 | − | 0.843983i | \(-0.680205\pi\) | ||||
−0.536370 | + | 0.843983i | \(0.680205\pi\) | |||||||
\(434\) | −0.420338 | −0.0201769 | ||||||||
\(435\) | 8.56160 | 0.410498 | ||||||||
\(436\) | −6.84529 | −0.327830 | ||||||||
\(437\) | −34.9275 | −1.67081 | ||||||||
\(438\) | 0.0710307 | 0.00339398 | ||||||||
\(439\) | −7.48827 | −0.357396 | −0.178698 | − | 0.983904i | \(-0.557188\pi\) | ||||
−0.178698 | + | 0.983904i | \(0.557188\pi\) | |||||||
\(440\) | −3.43932 | −0.163963 | ||||||||
\(441\) | 1.74392 | 0.0830439 | ||||||||
\(442\) | 24.1543 | 1.14890 | ||||||||
\(443\) | −8.30280 | −0.394478 | −0.197239 | − | 0.980355i | \(-0.563197\pi\) | ||||
−0.197239 | + | 0.980355i | \(0.563197\pi\) | |||||||
\(444\) | 1.22424 | 0.0580998 | ||||||||
\(445\) | 4.30138 | 0.203905 | ||||||||
\(446\) | −13.0588 | −0.618353 | ||||||||
\(447\) | −7.99901 | −0.378340 | ||||||||
\(448\) | −0.0977002 | −0.00461590 | ||||||||
\(449\) | 22.7332 | 1.07285 | 0.536423 | − | 0.843949i | \(-0.319775\pi\) | ||||
0.536423 | + | 0.843949i | \(0.319775\pi\) | |||||||
\(450\) | −1.08665 | −0.0512250 | ||||||||
\(451\) | 39.2358 | 1.84754 | ||||||||
\(452\) | 10.7483 | 0.505558 | ||||||||
\(453\) | −21.2704 | −0.999371 | ||||||||
\(454\) | −12.3681 | −0.580462 | ||||||||
\(455\) | −0.461696 | −0.0216446 | ||||||||
\(456\) | 8.09504 | 0.379085 | ||||||||
\(457\) | 15.6497 | 0.732064 | 0.366032 | − | 0.930602i | \(-0.380716\pi\) | ||||
0.366032 | + | 0.930602i | \(0.380716\pi\) | |||||||
\(458\) | 27.7355 | 1.29599 | ||||||||
\(459\) | 22.1089 | 1.03196 | ||||||||
\(460\) | 5.74342 | 0.267788 | ||||||||
\(461\) | −21.2303 | −0.988792 | −0.494396 | − | 0.869237i | \(-0.664611\pi\) | ||||
−0.494396 | + | 0.869237i | \(0.664611\pi\) | |||||||
\(462\) | 0.694324 | 0.0323029 | ||||||||
\(463\) | 26.7309 | 1.24229 | 0.621145 | − | 0.783696i | \(-0.286668\pi\) | ||||
0.621145 | + | 0.783696i | \(0.286668\pi\) | |||||||
\(464\) | 6.43182 | 0.298590 | ||||||||
\(465\) | −5.72697 | −0.265582 | ||||||||
\(466\) | −16.0290 | −0.742530 | ||||||||
\(467\) | 9.39671 | 0.434828 | 0.217414 | − | 0.976079i | \(-0.430238\pi\) | ||||
0.217414 | + | 0.976079i | \(0.430238\pi\) | |||||||
\(468\) | 1.46882 | 0.0678962 | ||||||||
\(469\) | 1.00345 | 0.0463348 | ||||||||
\(470\) | 6.01583 | 0.277490 | ||||||||
\(471\) | 1.31368 | 0.0605311 | ||||||||
\(472\) | 8.80842 | 0.405440 | ||||||||
\(473\) | 13.3435 | 0.613536 | ||||||||
\(474\) | 6.58646 | 0.302526 | ||||||||
\(475\) | −21.2607 | −0.975509 | ||||||||
\(476\) | −0.400814 | −0.0183713 | ||||||||
\(477\) | 1.99613 | 0.0913963 | ||||||||
\(478\) | −19.1279 | −0.874890 | ||||||||
\(479\) | −10.0603 | −0.459667 | −0.229833 | − | 0.973230i | \(-0.573818\pi\) | ||||
−0.229833 | + | 0.973230i | \(0.573818\pi\) | |||||||
\(480\) | −1.33113 | −0.0607576 | ||||||||
\(481\) | 4.34616 | 0.198168 | ||||||||
\(482\) | 26.5054 | 1.20729 | ||||||||
\(483\) | −1.15947 | −0.0527578 | ||||||||
\(484\) | 7.36190 | 0.334632 | ||||||||
\(485\) | 3.27321 | 0.148629 | ||||||||
\(486\) | 2.58567 | 0.117288 | ||||||||
\(487\) | −11.1698 | −0.506150 | −0.253075 | − | 0.967447i | \(-0.581442\pi\) | ||||
−0.253075 | + | 0.967447i | \(0.581442\pi\) | |||||||
\(488\) | 2.70949 | 0.122653 | ||||||||
\(489\) | −18.6439 | −0.843108 | ||||||||
\(490\) | −5.61072 | −0.253467 | ||||||||
\(491\) | 16.0088 | 0.722467 | 0.361233 | − | 0.932475i | \(-0.382356\pi\) | ||||
0.361233 | + | 0.932475i | \(0.382356\pi\) | |||||||
\(492\) | 15.1856 | 0.684619 | ||||||||
\(493\) | 26.3865 | 1.18839 | ||||||||
\(494\) | 28.7381 | 1.29299 | ||||||||
\(495\) | −0.858012 | −0.0385648 | ||||||||
\(496\) | −4.30233 | −0.193180 | ||||||||
\(497\) | 1.00967 | 0.0452897 | ||||||||
\(498\) | 11.3828 | 0.510078 | ||||||||
\(499\) | 7.49915 | 0.335708 | 0.167854 | − | 0.985812i | \(-0.446316\pi\) | ||||
0.167854 | + | 0.985812i | \(0.446316\pi\) | |||||||
\(500\) | 7.50920 | 0.335822 | ||||||||
\(501\) | 18.4549 | 0.824503 | ||||||||
\(502\) | −10.3539 | −0.462119 | ||||||||
\(503\) | 8.50531 | 0.379233 | 0.189616 | − | 0.981858i | \(-0.439276\pi\) | ||||
0.189616 | + | 0.981858i | \(0.439276\pi\) | |||||||
\(504\) | −0.0243734 | −0.00108568 | ||||||||
\(505\) | 4.40770 | 0.196140 | ||||||||
\(506\) | −30.6631 | −1.36314 | ||||||||
\(507\) | −35.9312 | −1.59576 | ||||||||
\(508\) | −7.85976 | −0.348721 | ||||||||
\(509\) | −14.9416 | −0.662273 | −0.331137 | − | 0.943583i | \(-0.607432\pi\) | ||||
−0.331137 | + | 0.943583i | \(0.607432\pi\) | |||||||
\(510\) | −5.46096 | −0.241815 | ||||||||
\(511\) | −0.00418440 | −0.000185107 0 | ||||||||
\(512\) | −1.00000 | −0.0441942 | ||||||||
\(513\) | 26.3046 | 1.16138 | ||||||||
\(514\) | −1.73524 | −0.0765383 | ||||||||
\(515\) | 14.3721 | 0.633309 | ||||||||
\(516\) | 5.16440 | 0.227350 | ||||||||
\(517\) | −32.1174 | −1.41252 | ||||||||
\(518\) | −0.0721197 | −0.00316876 | ||||||||
\(519\) | 6.52594 | 0.286457 | ||||||||
\(520\) | −4.72564 | −0.207233 | ||||||||
\(521\) | 18.1638 | 0.795768 | 0.397884 | − | 0.917436i | \(-0.369745\pi\) | ||||
0.397884 | + | 0.917436i | \(0.369745\pi\) | |||||||
\(522\) | 1.60456 | 0.0702296 | ||||||||
\(523\) | −3.89656 | −0.170385 | −0.0851924 | − | 0.996365i | \(-0.527150\pi\) | ||||
−0.0851924 | + | 0.996365i | \(0.527150\pi\) | |||||||
\(524\) | −20.3039 | −0.886981 | ||||||||
\(525\) | −0.705782 | −0.0308028 | ||||||||
\(526\) | −8.81690 | −0.384435 | ||||||||
\(527\) | −17.6502 | −0.768857 | ||||||||
\(528\) | 7.10668 | 0.309279 | ||||||||
\(529\) | 28.2052 | 1.22631 | ||||||||
\(530\) | −6.42214 | −0.278960 | ||||||||
\(531\) | 2.19745 | 0.0953613 | ||||||||
\(532\) | −0.476877 | −0.0206752 | ||||||||
\(533\) | 53.9102 | 2.33511 | ||||||||
\(534\) | −8.88798 | −0.384620 | ||||||||
\(535\) | 9.03805 | 0.390749 | ||||||||
\(536\) | 10.2707 | 0.443625 | ||||||||
\(537\) | 15.1061 | 0.651875 | ||||||||
\(538\) | −3.26925 | −0.140947 | ||||||||
\(539\) | 29.9546 | 1.29024 | ||||||||
\(540\) | −4.32548 | −0.186139 | ||||||||
\(541\) | 29.6054 | 1.27283 | 0.636417 | − | 0.771345i | \(-0.280416\pi\) | ||||
0.636417 | + | 0.771345i | \(0.280416\pi\) | |||||||
\(542\) | 23.0568 | 0.990375 | ||||||||
\(543\) | 15.4278 | 0.662070 | ||||||||
\(544\) | −4.10249 | −0.175893 | ||||||||
\(545\) | 5.49421 | 0.235346 | ||||||||
\(546\) | 0.954005 | 0.0408276 | ||||||||
\(547\) | 27.6682 | 1.18301 | 0.591503 | − | 0.806303i | \(-0.298535\pi\) | ||||
0.591503 | + | 0.806303i | \(0.298535\pi\) | |||||||
\(548\) | 11.7342 | 0.501262 | ||||||||
\(549\) | 0.675942 | 0.0288485 | ||||||||
\(550\) | −18.6649 | −0.795874 | ||||||||
\(551\) | 31.3939 | 1.33742 | ||||||||
\(552\) | −11.8677 | −0.505121 | ||||||||
\(553\) | −0.388007 | −0.0164997 | ||||||||
\(554\) | 20.6326 | 0.876595 | ||||||||
\(555\) | −0.982607 | −0.0417093 | ||||||||
\(556\) | 3.26959 | 0.138661 | ||||||||
\(557\) | 30.9459 | 1.31122 | 0.655610 | − | 0.755100i | \(-0.272412\pi\) | ||||
0.655610 | + | 0.755100i | \(0.272412\pi\) | |||||||
\(558\) | −1.07331 | −0.0454368 | ||||||||
\(559\) | 18.3341 | 0.775449 | ||||||||
\(560\) | 0.0784167 | 0.00331371 | ||||||||
\(561\) | 29.1551 | 1.23093 | ||||||||
\(562\) | 28.5470 | 1.20418 | ||||||||
\(563\) | 28.5625 | 1.20377 | 0.601883 | − | 0.798584i | \(-0.294417\pi\) | ||||
0.601883 | + | 0.798584i | \(0.294417\pi\) | |||||||
\(564\) | −12.4305 | −0.523420 | ||||||||
\(565\) | −8.62688 | −0.362936 | ||||||||
\(566\) | −12.6676 | −0.532460 | ||||||||
\(567\) | 0.800101 | 0.0336011 | ||||||||
\(568\) | 10.3343 | 0.433619 | ||||||||
\(569\) | 41.8278 | 1.75351 | 0.876757 | − | 0.480934i | \(-0.159702\pi\) | ||||
0.876757 | + | 0.480934i | \(0.159702\pi\) | |||||||
\(570\) | −6.49729 | −0.272142 | ||||||||
\(571\) | −30.5524 | −1.27858 | −0.639289 | − | 0.768967i | \(-0.720771\pi\) | ||||
−0.639289 | + | 0.768967i | \(0.720771\pi\) | |||||||
\(572\) | 25.2293 | 1.05489 | ||||||||
\(573\) | −22.1263 | −0.924340 | ||||||||
\(574\) | −0.894579 | −0.0373390 | ||||||||
\(575\) | 31.1691 | 1.29984 | ||||||||
\(576\) | −0.249472 | −0.0103947 | ||||||||
\(577\) | −15.9307 | −0.663203 | −0.331602 | − | 0.943419i | \(-0.607589\pi\) | ||||
−0.331602 | + | 0.943419i | \(0.607589\pi\) | |||||||
\(578\) | 0.169596 | 0.00705426 | ||||||||
\(579\) | −8.14026 | −0.338298 | ||||||||
\(580\) | −5.16235 | −0.214355 | ||||||||
\(581\) | −0.670561 | −0.0278196 | ||||||||
\(582\) | −6.76345 | −0.280354 | ||||||||
\(583\) | 34.2867 | 1.42001 | ||||||||
\(584\) | −0.0428290 | −0.00177228 | ||||||||
\(585\) | −1.17891 | −0.0487421 | ||||||||
\(586\) | 16.3219 | 0.674250 | ||||||||
\(587\) | 6.09090 | 0.251398 | 0.125699 | − | 0.992068i | \(-0.459883\pi\) | ||||
0.125699 | + | 0.992068i | \(0.459883\pi\) | |||||||
\(588\) | 11.5935 | 0.478107 | ||||||||
\(589\) | −20.9998 | −0.865280 | ||||||||
\(590\) | −7.06987 | −0.291062 | ||||||||
\(591\) | −2.72193 | −0.111965 | ||||||||
\(592\) | −0.738173 | −0.0303387 | ||||||||
\(593\) | −42.0285 | −1.72590 | −0.862952 | − | 0.505285i | \(-0.831387\pi\) | ||||
−0.862952 | + | 0.505285i | \(0.831387\pi\) | |||||||
\(594\) | 23.0930 | 0.947516 | ||||||||
\(595\) | 0.321704 | 0.0131886 | ||||||||
\(596\) | 4.82312 | 0.197563 | ||||||||
\(597\) | 7.50512 | 0.307164 | ||||||||
\(598\) | −42.1312 | −1.72287 | ||||||||
\(599\) | 15.7289 | 0.642666 | 0.321333 | − | 0.946966i | \(-0.395869\pi\) | ||||
0.321333 | + | 0.946966i | \(0.395869\pi\) | |||||||
\(600\) | −7.22396 | −0.294917 | ||||||||
\(601\) | −41.2478 | −1.68253 | −0.841266 | − | 0.540621i | \(-0.818189\pi\) | ||||
−0.841266 | + | 0.540621i | \(0.818189\pi\) | |||||||
\(602\) | −0.304234 | −0.0123996 | ||||||||
\(603\) | 2.56224 | 0.104342 | ||||||||
\(604\) | 12.8253 | 0.521854 | ||||||||
\(605\) | −5.90885 | −0.240229 | ||||||||
\(606\) | −9.10765 | −0.369973 | ||||||||
\(607\) | −5.31367 | −0.215675 | −0.107838 | − | 0.994169i | \(-0.534393\pi\) | ||||
−0.107838 | + | 0.994169i | \(0.534393\pi\) | |||||||
\(608\) | −4.88102 | −0.197952 | ||||||||
\(609\) | 1.04217 | 0.0422307 | ||||||||
\(610\) | −2.17471 | −0.0880515 | ||||||||
\(611\) | −44.1295 | −1.78529 | ||||||||
\(612\) | −1.02345 | −0.0413707 | ||||||||
\(613\) | −7.97335 | −0.322041 | −0.161020 | − | 0.986951i | \(-0.551478\pi\) | ||||
−0.161020 | + | 0.986951i | \(0.551478\pi\) | |||||||
\(614\) | −11.0823 | −0.447246 | ||||||||
\(615\) | −12.1883 | −0.491482 | ||||||||
\(616\) | −0.418653 | −0.0168680 | ||||||||
\(617\) | −4.90797 | −0.197587 | −0.0987937 | − | 0.995108i | \(-0.531498\pi\) | ||||
−0.0987937 | + | 0.995108i | \(0.531498\pi\) | |||||||
\(618\) | −29.6971 | −1.19459 | ||||||||
\(619\) | −21.0560 | −0.846311 | −0.423155 | − | 0.906057i | \(-0.639078\pi\) | ||||
−0.423155 | + | 0.906057i | \(0.639078\pi\) | |||||||
\(620\) | 3.45316 | 0.138682 | ||||||||
\(621\) | −38.5636 | −1.54751 | ||||||||
\(622\) | −29.0299 | −1.16399 | ||||||||
\(623\) | 0.523589 | 0.0209771 | ||||||||
\(624\) | 9.76462 | 0.390898 | ||||||||
\(625\) | 15.7519 | 0.630075 | ||||||||
\(626\) | 6.07292 | 0.242723 | ||||||||
\(627\) | 34.6879 | 1.38530 | ||||||||
\(628\) | −0.792102 | −0.0316083 | ||||||||
\(629\) | −3.02835 | −0.120748 | ||||||||
\(630\) | 0.0195628 | 0.000779399 0 | ||||||||
\(631\) | 30.3314 | 1.20747 | 0.603737 | − | 0.797184i | \(-0.293678\pi\) | ||||
0.603737 | + | 0.797184i | \(0.293678\pi\) | |||||||
\(632\) | −3.97141 | −0.157974 | ||||||||
\(633\) | 0.377434 | 0.0150017 | ||||||||
\(634\) | 9.81771 | 0.389911 | ||||||||
\(635\) | 6.30845 | 0.250343 | ||||||||
\(636\) | 13.2701 | 0.526194 | ||||||||
\(637\) | 41.1578 | 1.63073 | ||||||||
\(638\) | 27.5608 | 1.09114 | ||||||||
\(639\) | 2.57812 | 0.101989 | ||||||||
\(640\) | 0.802626 | 0.0317266 | ||||||||
\(641\) | 45.8922 | 1.81263 | 0.906317 | − | 0.422599i | \(-0.138882\pi\) | ||||
0.906317 | + | 0.422599i | \(0.138882\pi\) | |||||||
\(642\) | −18.6754 | −0.737058 | ||||||||
\(643\) | −11.0864 | −0.437204 | −0.218602 | − | 0.975814i | \(-0.570150\pi\) | ||||
−0.218602 | + | 0.975814i | \(0.570150\pi\) | |||||||
\(644\) | 0.699121 | 0.0275492 | ||||||||
\(645\) | −4.14508 | −0.163212 | ||||||||
\(646\) | −20.0243 | −0.787847 | ||||||||
\(647\) | 33.8818 | 1.33203 | 0.666015 | − | 0.745938i | \(-0.267999\pi\) | ||||
0.666015 | + | 0.745938i | \(0.267999\pi\) | |||||||
\(648\) | 8.18935 | 0.321708 | ||||||||
\(649\) | 37.7448 | 1.48161 | ||||||||
\(650\) | −25.6457 | −1.00591 | ||||||||
\(651\) | −0.697119 | −0.0273222 | ||||||||
\(652\) | 11.2416 | 0.440256 | ||||||||
\(653\) | 7.10147 | 0.277902 | 0.138951 | − | 0.990299i | \(-0.455627\pi\) | ||||
0.138951 | + | 0.990299i | \(0.455627\pi\) | |||||||
\(654\) | −11.3527 | −0.443927 | ||||||||
\(655\) | 16.2965 | 0.636755 | ||||||||
\(656\) | −9.15637 | −0.357496 | ||||||||
\(657\) | −0.0106846 | −0.000416847 0 | ||||||||
\(658\) | 0.732281 | 0.0285473 | ||||||||
\(659\) | 12.3793 | 0.482228 | 0.241114 | − | 0.970497i | \(-0.422487\pi\) | ||||
0.241114 | + | 0.970497i | \(0.422487\pi\) | |||||||
\(660\) | −5.70401 | −0.222028 | ||||||||
\(661\) | 36.6294 | 1.42472 | 0.712359 | − | 0.701815i | \(-0.247627\pi\) | ||||
0.712359 | + | 0.701815i | \(0.247627\pi\) | |||||||
\(662\) | 31.5144 | 1.22484 | ||||||||
\(663\) | 40.0592 | 1.55577 | ||||||||
\(664\) | −6.86346 | −0.266354 | ||||||||
\(665\) | 0.382754 | 0.0148426 | ||||||||
\(666\) | −0.184153 | −0.00713580 | ||||||||
\(667\) | −46.0247 | −1.78208 | ||||||||
\(668\) | −11.1276 | −0.430541 | ||||||||
\(669\) | −21.6577 | −0.837334 | ||||||||
\(670\) | −8.24350 | −0.318474 | ||||||||
\(671\) | 11.6104 | 0.448214 | ||||||||
\(672\) | −0.162033 | −0.00625056 | ||||||||
\(673\) | 43.8692 | 1.69103 | 0.845517 | − | 0.533948i | \(-0.179292\pi\) | ||||
0.845517 | + | 0.533948i | \(0.179292\pi\) | |||||||
\(674\) | −2.34590 | −0.0903609 | ||||||||
\(675\) | −23.4740 | −0.903516 | ||||||||
\(676\) | 21.6653 | 0.833279 | ||||||||
\(677\) | −0.191652 | −0.00736577 | −0.00368288 | − | 0.999993i | \(-0.501172\pi\) | ||||
−0.00368288 | + | 0.999993i | \(0.501172\pi\) | |||||||
\(678\) | 17.8258 | 0.684595 | ||||||||
\(679\) | 0.398433 | 0.0152905 | ||||||||
\(680\) | 3.29276 | 0.126272 | ||||||||
\(681\) | −20.5121 | −0.786025 | ||||||||
\(682\) | −18.4358 | −0.705944 | ||||||||
\(683\) | 23.0823 | 0.883221 | 0.441611 | − | 0.897207i | \(-0.354407\pi\) | ||||
0.441611 | + | 0.897207i | \(0.354407\pi\) | |||||||
\(684\) | −1.21768 | −0.0465591 | ||||||||
\(685\) | −9.41820 | −0.359851 | ||||||||
\(686\) | −1.36687 | −0.0521873 | ||||||||
\(687\) | 45.9985 | 1.75495 | ||||||||
\(688\) | −3.11395 | −0.118718 | ||||||||
\(689\) | 47.1101 | 1.79475 | ||||||||
\(690\) | 9.52530 | 0.362622 | ||||||||
\(691\) | −14.5510 | −0.553544 | −0.276772 | − | 0.960936i | \(-0.589265\pi\) | ||||
−0.276772 | + | 0.960936i | \(0.589265\pi\) | |||||||
\(692\) | −3.93491 | −0.149583 | ||||||||
\(693\) | −0.104442 | −0.00396743 | ||||||||
\(694\) | 16.3252 | 0.619694 | ||||||||
\(695\) | −2.62426 | −0.0995438 | ||||||||
\(696\) | 10.6670 | 0.404331 | ||||||||
\(697\) | −37.5639 | −1.42283 | ||||||||
\(698\) | −33.6684 | −1.27437 | ||||||||
\(699\) | −26.5837 | −1.00549 | ||||||||
\(700\) | 0.425562 | 0.0160847 | ||||||||
\(701\) | −4.85468 | −0.183359 | −0.0916794 | − | 0.995789i | \(-0.529224\pi\) | ||||
−0.0916794 | + | 0.995789i | \(0.529224\pi\) | |||||||
\(702\) | 31.7299 | 1.19757 | ||||||||
\(703\) | −3.60304 | −0.135891 | ||||||||
\(704\) | −4.28508 | −0.161500 | ||||||||
\(705\) | 9.97708 | 0.375759 | ||||||||
\(706\) | 12.2203 | 0.459915 | ||||||||
\(707\) | 0.536530 | 0.0201783 | ||||||||
\(708\) | 14.6085 | 0.549022 | ||||||||
\(709\) | 51.6131 | 1.93837 | 0.969186 | − | 0.246330i | \(-0.0792248\pi\) | ||||
0.969186 | + | 0.246330i | \(0.0792248\pi\) | |||||||
\(710\) | −8.29460 | −0.311291 | ||||||||
\(711\) | −0.990754 | −0.0371562 | ||||||||
\(712\) | 5.35914 | 0.200842 | ||||||||
\(713\) | 30.7865 | 1.15296 | ||||||||
\(714\) | −0.664738 | −0.0248772 | ||||||||
\(715\) | −20.2497 | −0.757297 | ||||||||
\(716\) | −9.10842 | −0.340398 | ||||||||
\(717\) | −31.7231 | −1.18472 | ||||||||
\(718\) | 0.786973 | 0.0293696 | ||||||||
\(719\) | 22.4510 | 0.837280 | 0.418640 | − | 0.908152i | \(-0.362507\pi\) | ||||
0.418640 | + | 0.908152i | \(0.362507\pi\) | |||||||
\(720\) | 0.200233 | 0.00746223 | ||||||||
\(721\) | 1.74945 | 0.0651529 | ||||||||
\(722\) | −4.82438 | −0.179545 | ||||||||
\(723\) | 43.9585 | 1.63483 | ||||||||
\(724\) | −9.30241 | −0.345721 | ||||||||
\(725\) | −28.0157 | −1.04048 | ||||||||
\(726\) | 12.2095 | 0.453137 | ||||||||
\(727\) | 29.2295 | 1.08406 | 0.542031 | − | 0.840359i | \(-0.317656\pi\) | ||||
0.542031 | + | 0.840359i | \(0.317656\pi\) | |||||||
\(728\) | −0.575231 | −0.0213195 | ||||||||
\(729\) | 28.8563 | 1.06875 | ||||||||
\(730\) | 0.0343757 | 0.00127230 | ||||||||
\(731\) | −12.7749 | −0.472498 | ||||||||
\(732\) | 4.49362 | 0.166089 | ||||||||
\(733\) | 49.8269 | 1.84040 | 0.920200 | − | 0.391450i | \(-0.128026\pi\) | ||||
0.920200 | + | 0.391450i | \(0.128026\pi\) | |||||||
\(734\) | −15.6163 | −0.576408 | ||||||||
\(735\) | −9.30522 | −0.343228 | ||||||||
\(736\) | 7.15578 | 0.263766 | ||||||||
\(737\) | 44.0106 | 1.62115 | ||||||||
\(738\) | −2.28426 | −0.0840846 | ||||||||
\(739\) | −53.0377 | −1.95102 | −0.975511 | − | 0.219949i | \(-0.929411\pi\) | ||||
−0.975511 | + | 0.219949i | \(0.929411\pi\) | |||||||
\(740\) | 0.592477 | 0.0217799 | ||||||||
\(741\) | 47.6613 | 1.75088 | ||||||||
\(742\) | −0.781739 | −0.0286986 | ||||||||
\(743\) | −14.1535 | −0.519240 | −0.259620 | − | 0.965711i | \(-0.583597\pi\) | ||||
−0.259620 | + | 0.965711i | \(0.583597\pi\) | |||||||
\(744\) | −7.13529 | −0.261592 | ||||||||
\(745\) | −3.87116 | −0.141828 | ||||||||
\(746\) | −2.46615 | −0.0902921 | ||||||||
\(747\) | −1.71224 | −0.0626475 | ||||||||
\(748\) | −17.5795 | −0.642769 | ||||||||
\(749\) | 1.10016 | 0.0401990 | ||||||||
\(750\) | 12.4538 | 0.454749 | ||||||||
\(751\) | −38.0657 | −1.38904 | −0.694519 | − | 0.719474i | \(-0.744383\pi\) | ||||
−0.694519 | + | 0.719474i | \(0.744383\pi\) | |||||||
\(752\) | 7.49518 | 0.273321 | ||||||||
\(753\) | −17.1717 | −0.625772 | ||||||||
\(754\) | 37.8688 | 1.37910 | ||||||||
\(755\) | −10.2939 | −0.374634 | ||||||||
\(756\) | −0.526522 | −0.0191494 | ||||||||
\(757\) | 0.760696 | 0.0276480 | 0.0138240 | − | 0.999904i | \(-0.495600\pi\) | ||||
0.0138240 | + | 0.999904i | \(0.495600\pi\) | |||||||
\(758\) | 2.86090 | 0.103912 | ||||||||
\(759\) | −50.8539 | −1.84588 | ||||||||
\(760\) | 3.91764 | 0.142108 | ||||||||
\(761\) | 47.3777 | 1.71744 | 0.858720 | − | 0.512446i | \(-0.171260\pi\) | ||||
0.858720 | + | 0.512446i | \(0.171260\pi\) | |||||||
\(762\) | −13.0352 | −0.472215 | ||||||||
\(763\) | 0.668786 | 0.0242117 | ||||||||
\(764\) | 13.3414 | 0.482674 | ||||||||
\(765\) | 0.821452 | 0.0296996 | ||||||||
\(766\) | −27.7756 | −1.00357 | ||||||||
\(767\) | 51.8615 | 1.87261 | ||||||||
\(768\) | −1.65847 | −0.0598449 | ||||||||
\(769\) | −31.3581 | −1.13080 | −0.565401 | − | 0.824816i | \(-0.691279\pi\) | ||||
−0.565401 | + | 0.824816i | \(0.691279\pi\) | |||||||
\(770\) | 0.336022 | 0.0121094 | ||||||||
\(771\) | −2.87785 | −0.103643 | ||||||||
\(772\) | 4.90829 | 0.176653 | ||||||||
\(773\) | 12.3595 | 0.444540 | 0.222270 | − | 0.974985i | \(-0.428653\pi\) | ||||
0.222270 | + | 0.974985i | \(0.428653\pi\) | |||||||
\(774\) | −0.776843 | −0.0279230 | ||||||||
\(775\) | 18.7400 | 0.673162 | ||||||||
\(776\) | 4.07812 | 0.146396 | ||||||||
\(777\) | −0.119608 | −0.00429093 | ||||||||
\(778\) | 19.4925 | 0.698841 | ||||||||
\(779\) | −44.6925 | −1.60127 | ||||||||
\(780\) | −7.83734 | −0.280622 | ||||||||
\(781\) | 44.2834 | 1.58458 | ||||||||
\(782\) | 29.3565 | 1.04979 | ||||||||
\(783\) | 34.6621 | 1.23872 | ||||||||
\(784\) | −6.99045 | −0.249659 | ||||||||
\(785\) | 0.635762 | 0.0226913 | ||||||||
\(786\) | −33.6735 | −1.20109 | ||||||||
\(787\) | −52.5595 | −1.87354 | −0.936771 | − | 0.349942i | \(-0.886201\pi\) | ||||
−0.936771 | + | 0.349942i | \(0.886201\pi\) | |||||||
\(788\) | 1.64123 | 0.0584663 | ||||||||
\(789\) | −14.6226 | −0.520577 | ||||||||
\(790\) | 3.18755 | 0.113408 | ||||||||
\(791\) | −1.05011 | −0.0373377 | ||||||||
\(792\) | −1.06901 | −0.0379855 | ||||||||
\(793\) | 15.9527 | 0.566499 | ||||||||
\(794\) | 5.27141 | 0.187075 | ||||||||
\(795\) | −10.6509 | −0.377750 | ||||||||
\(796\) | −4.52532 | −0.160396 | ||||||||
\(797\) | −22.6091 | −0.800856 | −0.400428 | − | 0.916328i | \(-0.631139\pi\) | ||||
−0.400428 | + | 0.916328i | \(0.631139\pi\) | |||||||
\(798\) | −0.790887 | −0.0279971 | ||||||||
\(799\) | 30.7489 | 1.08782 | ||||||||
\(800\) | 4.35579 | 0.154000 | ||||||||
\(801\) | 1.33695 | 0.0472389 | ||||||||
\(802\) | −17.5397 | −0.619347 | ||||||||
\(803\) | −0.183526 | −0.00647648 | ||||||||
\(804\) | 17.0336 | 0.600729 | ||||||||
\(805\) | −0.561133 | −0.0197773 | ||||||||
\(806\) | −25.3309 | −0.892243 | ||||||||
\(807\) | −5.42196 | −0.190862 | ||||||||
\(808\) | 5.49159 | 0.193194 | ||||||||
\(809\) | −39.0578 | −1.37320 | −0.686599 | − | 0.727036i | \(-0.740897\pi\) | ||||
−0.686599 | + | 0.727036i | \(0.740897\pi\) | |||||||
\(810\) | −6.57299 | −0.230951 | ||||||||
\(811\) | 21.7603 | 0.764109 | 0.382054 | − | 0.924140i | \(-0.375217\pi\) | ||||
0.382054 | + | 0.924140i | \(0.375217\pi\) | |||||||
\(812\) | −0.628390 | −0.0220522 | ||||||||
\(813\) | 38.2391 | 1.34110 | ||||||||
\(814\) | −3.16313 | −0.110868 | ||||||||
\(815\) | −9.02283 | −0.316056 | ||||||||
\(816\) | −6.80386 | −0.238183 | ||||||||
\(817\) | −15.1993 | −0.531755 | ||||||||
\(818\) | 19.6791 | 0.688062 | ||||||||
\(819\) | −0.143504 | −0.00501444 | ||||||||
\(820\) | 7.34915 | 0.256643 | ||||||||
\(821\) | −45.5228 | −1.58876 | −0.794379 | − | 0.607423i | \(-0.792203\pi\) | ||||
−0.794379 | + | 0.607423i | \(0.792203\pi\) | |||||||
\(822\) | 19.4609 | 0.678777 | ||||||||
\(823\) | −17.6042 | −0.613643 | −0.306822 | − | 0.951767i | \(-0.599266\pi\) | ||||
−0.306822 | + | 0.951767i | \(0.599266\pi\) | |||||||
\(824\) | 17.9063 | 0.623795 | ||||||||
\(825\) | −30.9552 | −1.07772 | ||||||||
\(826\) | −0.860584 | −0.0299436 | ||||||||
\(827\) | 50.3123 | 1.74953 | 0.874765 | − | 0.484547i | \(-0.161015\pi\) | ||||
0.874765 | + | 0.484547i | \(0.161015\pi\) | |||||||
\(828\) | 1.78517 | 0.0620388 | ||||||||
\(829\) | 47.1262 | 1.63676 | 0.818381 | − | 0.574676i | \(-0.194872\pi\) | ||||
0.818381 | + | 0.574676i | \(0.194872\pi\) | |||||||
\(830\) | 5.50879 | 0.191213 | ||||||||
\(831\) | 34.2186 | 1.18703 | ||||||||
\(832\) | −5.88772 | −0.204120 | ||||||||
\(833\) | −28.6783 | −0.993643 | ||||||||
\(834\) | 5.42252 | 0.187767 | ||||||||
\(835\) | 8.93133 | 0.309082 | ||||||||
\(836\) | −20.9156 | −0.723380 | ||||||||
\(837\) | −23.1859 | −0.801423 | ||||||||
\(838\) | −39.5113 | −1.36489 | ||||||||
\(839\) | 9.19789 | 0.317546 | 0.158773 | − | 0.987315i | \(-0.449246\pi\) | ||||
0.158773 | + | 0.987315i | \(0.449246\pi\) | |||||||
\(840\) | 0.130052 | 0.00448722 | ||||||||
\(841\) | 12.3683 | 0.426493 | ||||||||
\(842\) | 6.83947 | 0.235704 | ||||||||
\(843\) | 47.3444 | 1.63063 | ||||||||
\(844\) | −0.227580 | −0.00783361 | ||||||||
\(845\) | −17.3891 | −0.598203 | ||||||||
\(846\) | 1.86984 | 0.0642863 | ||||||||
\(847\) | −0.719259 | −0.0247140 | ||||||||
\(848\) | −8.00141 | −0.274770 | ||||||||
\(849\) | −21.0089 | −0.721023 | ||||||||
\(850\) | 17.8696 | 0.612921 | ||||||||
\(851\) | 5.28221 | 0.181072 | ||||||||
\(852\) | 17.1392 | 0.587179 | ||||||||
\(853\) | −21.1509 | −0.724193 | −0.362097 | − | 0.932141i | \(-0.617939\pi\) | ||||
−0.362097 | + | 0.932141i | \(0.617939\pi\) | |||||||
\(854\) | −0.264718 | −0.00905847 | ||||||||
\(855\) | 0.977340 | 0.0334243 | ||||||||
\(856\) | 11.2606 | 0.384879 | ||||||||
\(857\) | 17.7553 | 0.606511 | 0.303255 | − | 0.952909i | \(-0.401926\pi\) | ||||
0.303255 | + | 0.952909i | \(0.401926\pi\) | |||||||
\(858\) | 41.8422 | 1.42847 | ||||||||
\(859\) | −47.0523 | −1.60540 | −0.802702 | − | 0.596381i | \(-0.796605\pi\) | ||||
−0.802702 | + | 0.596381i | \(0.796605\pi\) | |||||||
\(860\) | 2.49934 | 0.0852268 | ||||||||
\(861\) | −1.48363 | −0.0505621 | ||||||||
\(862\) | 15.8031 | 0.538257 | ||||||||
\(863\) | −4.78579 | −0.162910 | −0.0814551 | − | 0.996677i | \(-0.525957\pi\) | ||||
−0.0814551 | + | 0.996677i | \(0.525957\pi\) | |||||||
\(864\) | −5.38916 | −0.183343 | ||||||||
\(865\) | 3.15826 | 0.107384 | ||||||||
\(866\) | 22.3223 | 0.758542 | ||||||||
\(867\) | 0.281270 | 0.00955243 | ||||||||
\(868\) | 0.420338 | 0.0142672 | ||||||||
\(869\) | −17.0178 | −0.577289 | ||||||||
\(870\) | −8.56160 | −0.290266 | ||||||||
\(871\) | 60.4708 | 2.04897 | ||||||||
\(872\) | 6.84529 | 0.231811 | ||||||||
\(873\) | 1.01738 | 0.0344330 | ||||||||
\(874\) | 34.9275 | 1.18144 | ||||||||
\(875\) | −0.733651 | −0.0248019 | ||||||||
\(876\) | −0.0710307 | −0.00239991 | ||||||||
\(877\) | −20.8922 | −0.705480 | −0.352740 | − | 0.935721i | \(-0.614750\pi\) | ||||
−0.352740 | + | 0.935721i | \(0.614750\pi\) | |||||||
\(878\) | 7.48827 | 0.252717 | ||||||||
\(879\) | 27.0693 | 0.913026 | ||||||||
\(880\) | 3.43932 | 0.115939 | ||||||||
\(881\) | −47.5976 | −1.60360 | −0.801802 | − | 0.597590i | \(-0.796125\pi\) | ||||
−0.801802 | + | 0.597590i | \(0.796125\pi\) | |||||||
\(882\) | −1.74392 | −0.0587209 | ||||||||
\(883\) | −35.4578 | −1.19325 | −0.596625 | − | 0.802520i | \(-0.703492\pi\) | ||||
−0.596625 | + | 0.802520i | \(0.703492\pi\) | |||||||
\(884\) | −24.1543 | −0.812397 | ||||||||
\(885\) | −11.7252 | −0.394138 | ||||||||
\(886\) | 8.30280 | 0.278938 | ||||||||
\(887\) | 37.9632 | 1.27468 | 0.637340 | − | 0.770582i | \(-0.280035\pi\) | ||||
0.637340 | + | 0.770582i | \(0.280035\pi\) | |||||||
\(888\) | −1.22424 | −0.0410828 | ||||||||
\(889\) | 0.767900 | 0.0257546 | ||||||||
\(890\) | −4.30138 | −0.144183 | ||||||||
\(891\) | 35.0920 | 1.17563 | ||||||||
\(892\) | 13.0588 | 0.437241 | ||||||||
\(893\) | 36.5842 | 1.22424 | ||||||||
\(894\) | 7.99901 | 0.267527 | ||||||||
\(895\) | 7.31066 | 0.244368 | ||||||||
\(896\) | 0.0977002 | 0.00326393 | ||||||||
\(897\) | −69.8735 | −2.33301 | ||||||||
\(898\) | −22.7332 | −0.758616 | ||||||||
\(899\) | −27.6718 | −0.922906 | ||||||||
\(900\) | 1.08665 | 0.0362216 | ||||||||
\(901\) | −32.8257 | −1.09358 | ||||||||
\(902\) | −39.2358 | −1.30641 | ||||||||
\(903\) | −0.504563 | −0.0167908 | ||||||||
\(904\) | −10.7483 | −0.357484 | ||||||||
\(905\) | 7.46636 | 0.248190 | ||||||||
\(906\) | 21.2704 | 0.706662 | ||||||||
\(907\) | 21.0148 | 0.697786 | 0.348893 | − | 0.937163i | \(-0.386558\pi\) | ||||
0.348893 | + | 0.937163i | \(0.386558\pi\) | |||||||
\(908\) | 12.3681 | 0.410449 | ||||||||
\(909\) | 1.37000 | 0.0454399 | ||||||||
\(910\) | 0.461696 | 0.0153051 | ||||||||
\(911\) | −31.4707 | −1.04267 | −0.521335 | − | 0.853352i | \(-0.674566\pi\) | ||||
−0.521335 | + | 0.853352i | \(0.674566\pi\) | |||||||
\(912\) | −8.09504 | −0.268053 | ||||||||
\(913\) | −29.4104 | −0.973344 | ||||||||
\(914\) | −15.6497 | −0.517647 | ||||||||
\(915\) | −3.60670 | −0.119234 | ||||||||
\(916\) | −27.7355 | −0.916406 | ||||||||
\(917\) | 1.98370 | 0.0655074 | ||||||||
\(918\) | −22.1089 | −0.729704 | ||||||||
\(919\) | 32.3594 | 1.06744 | 0.533719 | − | 0.845662i | \(-0.320794\pi\) | ||||
0.533719 | + | 0.845662i | \(0.320794\pi\) | |||||||
\(920\) | −5.74342 | −0.189355 | ||||||||
\(921\) | −18.3797 | −0.605632 | ||||||||
\(922\) | 21.2303 | 0.699181 | ||||||||
\(923\) | 60.8456 | 2.00276 | ||||||||
\(924\) | −0.694324 | −0.0228416 | ||||||||
\(925\) | 3.21533 | 0.105719 | ||||||||
\(926\) | −26.7309 | −0.878432 | ||||||||
\(927\) | 4.46711 | 0.146719 | ||||||||
\(928\) | −6.43182 | −0.211135 | ||||||||
\(929\) | 20.2891 | 0.665664 | 0.332832 | − | 0.942986i | \(-0.391996\pi\) | ||||
0.332832 | + | 0.942986i | \(0.391996\pi\) | |||||||
\(930\) | 5.72697 | 0.187795 | ||||||||
\(931\) | −34.1206 | −1.11826 | ||||||||
\(932\) | 16.0290 | 0.525048 | ||||||||
\(933\) | −48.1453 | −1.57621 | ||||||||
\(934\) | −9.39671 | −0.307470 | ||||||||
\(935\) | 14.1098 | 0.461438 | ||||||||
\(936\) | −1.46882 | −0.0480099 | ||||||||
\(937\) | −25.6601 | −0.838280 | −0.419140 | − | 0.907922i | \(-0.637668\pi\) | ||||
−0.419140 | + | 0.907922i | \(0.637668\pi\) | |||||||
\(938\) | −1.00345 | −0.0327636 | ||||||||
\(939\) | 10.0718 | 0.328680 | ||||||||
\(940\) | −6.01583 | −0.196215 | ||||||||
\(941\) | −25.2864 | −0.824313 | −0.412157 | − | 0.911113i | \(-0.635224\pi\) | ||||
−0.412157 | + | 0.911113i | \(0.635224\pi\) | |||||||
\(942\) | −1.31368 | −0.0428019 | ||||||||
\(943\) | 65.5210 | 2.13366 | ||||||||
\(944\) | −8.80842 | −0.286690 | ||||||||
\(945\) | 0.422600 | 0.0137472 | ||||||||
\(946\) | −13.3435 | −0.433835 | ||||||||
\(947\) | −9.96278 | −0.323747 | −0.161873 | − | 0.986812i | \(-0.551754\pi\) | ||||
−0.161873 | + | 0.986812i | \(0.551754\pi\) | |||||||
\(948\) | −6.58646 | −0.213918 | ||||||||
\(949\) | −0.252165 | −0.00818563 | ||||||||
\(950\) | 21.2607 | 0.689789 | ||||||||
\(951\) | 16.2824 | 0.527993 | ||||||||
\(952\) | 0.400814 | 0.0129904 | ||||||||
\(953\) | −45.2388 | −1.46543 | −0.732715 | − | 0.680536i | \(-0.761747\pi\) | ||||
−0.732715 | + | 0.680536i | \(0.761747\pi\) | |||||||
\(954\) | −1.99613 | −0.0646270 | ||||||||
\(955\) | −10.7081 | −0.346508 | ||||||||
\(956\) | 19.1279 | 0.618640 | ||||||||
\(957\) | 45.7089 | 1.47756 | ||||||||
\(958\) | 10.0603 | 0.325033 | ||||||||
\(959\) | −1.14644 | −0.0370204 | ||||||||
\(960\) | 1.33113 | 0.0429621 | ||||||||
\(961\) | −12.4900 | −0.402903 | ||||||||
\(962\) | −4.34616 | −0.140126 | ||||||||
\(963\) | 2.80920 | 0.0905252 | ||||||||
\(964\) | −26.5054 | −0.853683 | ||||||||
\(965\) | −3.93952 | −0.126818 | ||||||||
\(966\) | 1.15947 | 0.0373054 | ||||||||
\(967\) | 45.5246 | 1.46397 | 0.731987 | − | 0.681319i | \(-0.238593\pi\) | ||||
0.731987 | + | 0.681319i | \(0.238593\pi\) | |||||||
\(968\) | −7.36190 | −0.236620 | ||||||||
\(969\) | −33.2098 | −1.06685 | ||||||||
\(970\) | −3.27321 | −0.105096 | ||||||||
\(971\) | −12.0528 | −0.386792 | −0.193396 | − | 0.981121i | \(-0.561950\pi\) | ||||
−0.193396 | + | 0.981121i | \(0.561950\pi\) | |||||||
\(972\) | −2.58567 | −0.0829353 | ||||||||
\(973\) | −0.319440 | −0.0102408 | ||||||||
\(974\) | 11.1698 | 0.357902 | ||||||||
\(975\) | −42.5326 | −1.36213 | ||||||||
\(976\) | −2.70949 | −0.0867288 | ||||||||
\(977\) | 40.3367 | 1.29049 | 0.645243 | − | 0.763977i | \(-0.276756\pi\) | ||||
0.645243 | + | 0.763977i | \(0.276756\pi\) | |||||||
\(978\) | 18.6439 | 0.596167 | ||||||||
\(979\) | 22.9643 | 0.733943 | ||||||||
\(980\) | 5.61072 | 0.179228 | ||||||||
\(981\) | 1.70771 | 0.0545229 | ||||||||
\(982\) | −16.0088 | −0.510861 | ||||||||
\(983\) | 0.920216 | 0.0293503 | 0.0146752 | − | 0.999892i | \(-0.495329\pi\) | ||||
0.0146752 | + | 0.999892i | \(0.495329\pi\) | |||||||
\(984\) | −15.1856 | −0.484099 | ||||||||
\(985\) | −1.31729 | −0.0419724 | ||||||||
\(986\) | −26.3865 | −0.840316 | ||||||||
\(987\) | 1.21447 | 0.0386569 | ||||||||
\(988\) | −28.7381 | −0.914281 | ||||||||
\(989\) | 22.2828 | 0.708550 | ||||||||
\(990\) | 0.858012 | 0.0272694 | ||||||||
\(991\) | 28.7618 | 0.913650 | 0.456825 | − | 0.889557i | \(-0.348987\pi\) | ||||
0.456825 | + | 0.889557i | \(0.348987\pi\) | |||||||
\(992\) | 4.30233 | 0.136599 | ||||||||
\(993\) | 52.2657 | 1.65860 | ||||||||
\(994\) | −1.00967 | −0.0320246 | ||||||||
\(995\) | 3.63214 | 0.115147 | ||||||||
\(996\) | −11.3828 | −0.360679 | ||||||||
\(997\) | −46.0569 | −1.45864 | −0.729318 | − | 0.684175i | \(-0.760163\pi\) | ||||
−0.729318 | + | 0.684175i | \(0.760163\pi\) | |||||||
\(998\) | −7.49915 | −0.237381 | ||||||||
\(999\) | −3.97813 | −0.125863 |
(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 | 8002.2.a.e.1.19 | ✓ | 77 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
8002.2.a.e.1.19 | ✓ | 77 | 1.1 | even | 1 | trivial |