Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [8020,2,Mod(1,8020)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(8020, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("8020.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 8020 = 2^{2} \cdot 5 \cdot 401 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 8020.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: | \(64.0400224211\) |
Analytic rank: | \(1\) |
Dimension: | \(29\) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.15 | ||
Character | \(\chi\) | \(=\) | 8020.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | −0.107530 | −0.0620828 | −0.0310414 | − | 0.999518i | \(-0.509882\pi\) | ||||
−0.0310414 | + | 0.999518i | \(0.509882\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 1.00000 | 0.447214 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 2.68164 | 1.01357 | 0.506783 | − | 0.862074i | \(-0.330834\pi\) | ||||
0.506783 | + | 0.862074i | \(0.330834\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −2.98844 | −0.996146 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 4.61949 | 1.39283 | 0.696414 | − | 0.717640i | \(-0.254778\pi\) | ||||
0.696414 | + | 0.717640i | \(0.254778\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −2.28176 | −0.632845 | −0.316423 | − | 0.948618i | \(-0.602482\pi\) | ||||
−0.316423 | + | 0.948618i | \(0.602482\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −0.107530 | −0.0277643 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 1.13181 | 0.274504 | 0.137252 | − | 0.990536i | \(-0.456173\pi\) | ||||
0.137252 | + | 0.990536i | \(0.456173\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −2.01120 | −0.461401 | −0.230700 | − | 0.973025i | \(-0.574102\pi\) | ||||
−0.230700 | + | 0.973025i | \(0.574102\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −0.288359 | −0.0629250 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −6.89522 | −1.43775 | −0.718876 | − | 0.695138i | \(-0.755343\pi\) | ||||
−0.718876 | + | 0.695138i | \(0.755343\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 1.00000 | 0.200000 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0.643940 | 0.123926 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −3.21723 | −0.597424 | −0.298712 | − | 0.954343i | \(-0.596557\pi\) | ||||
−0.298712 | + | 0.954343i | \(0.596557\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 3.50595 | 0.629688 | 0.314844 | − | 0.949143i | \(-0.398048\pi\) | ||||
0.314844 | + | 0.949143i | \(0.398048\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −0.496736 | −0.0864707 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 2.68164 | 0.453281 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −2.91993 | −0.480034 | −0.240017 | − | 0.970769i | \(-0.577153\pi\) | ||||
−0.240017 | + | 0.970769i | \(0.577153\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0.245358 | 0.0392888 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −9.50402 | −1.48428 | −0.742139 | − | 0.670246i | \(-0.766189\pi\) | ||||
−0.742139 | + | 0.670246i | \(0.766189\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −5.26560 | −0.802996 | −0.401498 | − | 0.915860i | \(-0.631510\pi\) | ||||
−0.401498 | + | 0.915860i | \(0.631510\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −2.98844 | −0.445490 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −11.2358 | −1.63890 | −0.819451 | − | 0.573149i | \(-0.805722\pi\) | ||||
−0.819451 | + | 0.573149i | \(0.805722\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 0.191216 | 0.0273166 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −0.121704 | −0.0170420 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 2.54571 | 0.349680 | 0.174840 | − | 0.984597i | \(-0.444059\pi\) | ||||
0.174840 | + | 0.984597i | \(0.444059\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 4.61949 | 0.622892 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0.216265 | 0.0286450 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −13.4719 | −1.75389 | −0.876946 | − | 0.480589i | \(-0.840423\pi\) | ||||
−0.876946 | + | 0.480589i | \(0.840423\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 8.98971 | 1.15101 | 0.575507 | − | 0.817797i | \(-0.304805\pi\) | ||||
0.575507 | + | 0.817797i | \(0.304805\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −8.01393 | −1.00966 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −2.28176 | −0.283017 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −10.4558 | −1.27738 | −0.638688 | − | 0.769466i | \(-0.720522\pi\) | ||||
−0.638688 | + | 0.769466i | \(0.720522\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0.741446 | 0.0892596 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 0.519620 | 0.0616676 | 0.0308338 | − | 0.999525i | \(-0.490184\pi\) | ||||
0.0308338 | + | 0.999525i | \(0.490184\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −0.240208 | −0.0281142 | −0.0140571 | − | 0.999901i | \(-0.504475\pi\) | ||||
−0.0140571 | + | 0.999901i | \(0.504475\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −0.107530 | −0.0124166 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 12.3878 | 1.41172 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 13.3375 | 1.50059 | 0.750294 | − | 0.661105i | \(-0.229912\pi\) | ||||
0.750294 | + | 0.661105i | \(0.229912\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 8.89607 | 0.988452 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 0.442286 | 0.0485472 | 0.0242736 | − | 0.999705i | \(-0.492273\pi\) | ||||
0.0242736 | + | 0.999705i | \(0.492273\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 1.13181 | 0.122762 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0.345950 | 0.0370897 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −18.4216 | −1.95268 | −0.976341 | − | 0.216236i | \(-0.930622\pi\) | ||||
−0.976341 | + | 0.216236i | \(0.930622\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −6.11886 | −0.641431 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −0.376997 | −0.0390927 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −2.01120 | −0.206345 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 14.0002 | 1.42151 | 0.710754 | − | 0.703441i | \(-0.248354\pi\) | ||||
0.710754 | + | 0.703441i | \(0.248354\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −13.8051 | −1.38746 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −4.39922 | −0.437739 | −0.218869 | − | 0.975754i | \(-0.570237\pi\) | ||||
−0.218869 | + | 0.975754i | \(0.570237\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −16.2889 | −1.60499 | −0.802495 | − | 0.596659i | \(-0.796495\pi\) | ||||
−0.802495 | + | 0.596659i | \(0.796495\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −0.288359 | −0.0281409 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −2.52153 | −0.243765 | −0.121883 | − | 0.992545i | \(-0.538893\pi\) | ||||
−0.121883 | + | 0.992545i | \(0.538893\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −0.284536 | −0.0272536 | −0.0136268 | − | 0.999907i | \(-0.504338\pi\) | ||||
−0.0136268 | + | 0.999907i | \(0.504338\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0.313982 | 0.0298018 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 14.6911 | 1.38203 | 0.691013 | − | 0.722842i | \(-0.257165\pi\) | ||||
0.691013 | + | 0.722842i | \(0.257165\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −6.89522 | −0.642983 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 6.81888 | 0.630406 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 3.03511 | 0.278228 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 10.3397 | 0.939973 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 1.02197 | 0.0921481 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 1.00000 | 0.0894427 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −16.4713 | −1.46159 | −0.730794 | − | 0.682598i | \(-0.760850\pi\) | ||||
−0.730794 | + | 0.682598i | \(0.760850\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 0.566212 | 0.0498522 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 12.9557 | 1.13194 | 0.565971 | − | 0.824425i | \(-0.308501\pi\) | ||||
0.565971 | + | 0.824425i | \(0.308501\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −5.39332 | −0.467660 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0.643940 | 0.0554215 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 2.17677 | 0.185974 | 0.0929871 | − | 0.995667i | \(-0.470358\pi\) | ||||
0.0929871 | + | 0.995667i | \(0.470358\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 2.77707 | 0.235548 | 0.117774 | − | 0.993040i | \(-0.462424\pi\) | ||||
0.117774 | + | 0.993040i | \(0.462424\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 1.20819 | 0.101748 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −10.5406 | −0.881445 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −3.21723 | −0.267176 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −0.0205616 | −0.00169589 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −20.9646 | −1.71749 | −0.858743 | − | 0.512407i | \(-0.828754\pi\) | ||||
−0.858743 | + | 0.512407i | \(0.828754\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 11.4288 | 0.930061 | 0.465030 | − | 0.885295i | \(-0.346043\pi\) | ||||
0.465030 | + | 0.885295i | \(0.346043\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −3.38234 | −0.273446 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 3.50595 | 0.281605 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −17.9659 | −1.43384 | −0.716918 | − | 0.697158i | \(-0.754448\pi\) | ||||
−0.716918 | + | 0.697158i | \(0.754448\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −0.273741 | −0.0217091 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −18.4905 | −1.45726 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −3.45117 | −0.270316 | −0.135158 | − | 0.990824i | \(-0.543154\pi\) | ||||
−0.135158 | + | 0.990824i | \(0.543154\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −0.496736 | −0.0386709 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 3.50747 | 0.271416 | 0.135708 | − | 0.990749i | \(-0.456669\pi\) | ||||
0.135708 | + | 0.990749i | \(0.456669\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −7.79359 | −0.599507 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 6.01034 | 0.459622 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 8.46228 | 0.643375 | 0.321688 | − | 0.946846i | \(-0.395750\pi\) | ||||
0.321688 | + | 0.946846i | \(0.395750\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 2.68164 | 0.202713 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 1.44864 | 0.108886 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 0.447045 | 0.0334137 | 0.0167068 | − | 0.999860i | \(-0.494682\pi\) | ||||
0.0167068 | + | 0.999860i | \(0.494682\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 12.8317 | 0.953770 | 0.476885 | − | 0.878966i | \(-0.341766\pi\) | ||||
0.476885 | + | 0.878966i | \(0.341766\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −0.966667 | −0.0714581 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −2.91993 | −0.214678 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 5.22838 | 0.382337 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 1.72682 | 0.125607 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −0.116074 | −0.00839880 | −0.00419940 | − | 0.999991i | \(-0.501337\pi\) | ||||
−0.00419940 | + | 0.999991i | \(0.501337\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −18.7963 | −1.35299 | −0.676495 | − | 0.736447i | \(-0.736502\pi\) | ||||
−0.676495 | + | 0.736447i | \(0.736502\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0.245358 | 0.0175705 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 9.96109 | 0.709699 | 0.354849 | − | 0.934924i | \(-0.384532\pi\) | ||||
0.354849 | + | 0.934924i | \(0.384532\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −21.4699 | −1.52196 | −0.760981 | − | 0.648774i | \(-0.775282\pi\) | ||||
−0.760981 | + | 0.648774i | \(0.775282\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 1.12431 | 0.0793030 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −8.62745 | −0.605529 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −9.50402 | −0.663790 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 20.6059 | 1.43221 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −9.29071 | −0.642652 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −4.57433 | −0.314910 | −0.157455 | − | 0.987526i | \(-0.550329\pi\) | ||||
−0.157455 | + | 0.987526i | \(0.550329\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −0.0558750 | −0.00382849 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −5.26560 | −0.359111 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 9.40172 | 0.638230 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 0.0258297 | 0.00174541 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −2.58251 | −0.173719 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 25.9396 | 1.73705 | 0.868523 | − | 0.495649i | \(-0.165070\pi\) | ||||
0.868523 | + | 0.495649i | \(0.165070\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −2.98844 | −0.199229 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 12.9032 | 0.856414 | 0.428207 | − | 0.903681i | \(-0.359145\pi\) | ||||
0.428207 | + | 0.903681i | \(0.359145\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 17.8607 | 1.18027 | 0.590134 | − | 0.807305i | \(-0.299075\pi\) | ||||
0.590134 | + | 0.807305i | \(0.299075\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −1.33207 | −0.0876437 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 15.9492 | 1.04487 | 0.522433 | − | 0.852680i | \(-0.325024\pi\) | ||||
0.522433 | + | 0.852680i | \(0.325024\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −11.2358 | −0.732940 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −1.43419 | −0.0931606 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −2.47618 | −0.160171 | −0.0800855 | − | 0.996788i | \(-0.525519\pi\) | ||||
−0.0800855 | + | 0.996788i | \(0.525519\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 18.8558 | 1.21461 | 0.607304 | − | 0.794470i | \(-0.292251\pi\) | ||||
0.607304 | + | 0.794470i | \(0.292251\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −2.88842 | −0.185292 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 0.191216 | 0.0122164 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 4.58906 | 0.291995 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −0.0475592 | −0.00301394 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 2.57469 | 0.162513 | 0.0812567 | − | 0.996693i | \(-0.474107\pi\) | ||||
0.0812567 | + | 0.996693i | \(0.474107\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −31.8524 | −2.00254 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −0.121704 | −0.00762140 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 18.2155 | 1.13625 | 0.568126 | − | 0.822941i | \(-0.307668\pi\) | ||||
0.568126 | + | 0.822941i | \(0.307668\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −7.83022 | −0.486546 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 9.61448 | 0.595121 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 6.91213 | 0.426220 | 0.213110 | − | 0.977028i | \(-0.431641\pi\) | ||||
0.213110 | + | 0.977028i | \(0.431641\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 2.54571 | 0.156382 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 1.98088 | 0.121228 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −7.08625 | −0.432056 | −0.216028 | − | 0.976387i | \(-0.569310\pi\) | ||||
−0.216028 | + | 0.976387i | \(0.569310\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 19.2813 | 1.17125 | 0.585627 | − | 0.810581i | \(-0.300848\pi\) | ||||
0.585627 | + | 0.810581i | \(0.300848\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0.657964 | 0.0398218 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 4.61949 | 0.278566 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −21.9048 | −1.31613 | −0.658067 | − | 0.752959i | \(-0.728626\pi\) | ||||
−0.658067 | + | 0.752959i | \(0.728626\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −10.4773 | −0.627261 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 5.29023 | 0.315589 | 0.157794 | − | 0.987472i | \(-0.449562\pi\) | ||||
0.157794 | + | 0.987472i | \(0.449562\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −0.738913 | −0.0439238 | −0.0219619 | − | 0.999759i | \(-0.506991\pi\) | ||||
−0.0219619 | + | 0.999759i | \(0.506991\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0.216265 | 0.0128104 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −25.4864 | −1.50441 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −15.7190 | −0.924648 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −1.50545 | −0.0882511 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 21.8949 | 1.27911 | 0.639556 | − | 0.768745i | \(-0.279118\pi\) | ||||
0.639556 | + | 0.768745i | \(0.279118\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −13.4719 | −0.784364 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 2.97467 | 0.172608 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 15.7332 | 0.909875 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −14.1205 | −0.813890 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0.473050 | 0.0271760 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 8.98971 | 0.514749 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 9.42666 | 0.538008 | 0.269004 | − | 0.963139i | \(-0.413306\pi\) | ||||
0.269004 | + | 0.963139i | \(0.413306\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 1.75155 | 0.0996422 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −6.26994 | −0.355536 | −0.177768 | − | 0.984072i | \(-0.556888\pi\) | ||||
−0.177768 | + | 0.984072i | \(0.556888\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −8.85701 | −0.500628 | −0.250314 | − | 0.968165i | \(-0.580534\pi\) | ||||
−0.250314 | + | 0.968165i | \(0.580534\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −8.01393 | −0.451534 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −12.1420 | −0.681962 | −0.340981 | − | 0.940070i | \(-0.610759\pi\) | ||||
−0.340981 | + | 0.940070i | \(0.610759\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −14.8619 | −0.832109 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0.271141 | 0.0151336 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −2.27629 | −0.126656 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −2.28176 | −0.126569 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 0.0305963 | 0.00169198 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −30.1303 | −1.66114 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −34.4670 | −1.89448 | −0.947238 | − | 0.320532i | \(-0.896138\pi\) | ||||
−0.947238 | + | 0.320532i | \(0.896138\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 8.72603 | 0.478184 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −10.4558 | −0.571260 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 22.1900 | 1.20877 | 0.604385 | − | 0.796693i | \(-0.293419\pi\) | ||||
0.604385 | + | 0.796693i | \(0.293419\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −1.57975 | −0.0858000 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 16.1957 | 0.877047 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −18.2587 | −0.985879 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0.741446 | 0.0399181 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −13.3192 | −0.715011 | −0.357506 | − | 0.933911i | \(-0.616373\pi\) | ||||
−0.357506 | + | 0.933911i | \(0.616373\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −21.0432 | −1.12641 | −0.563207 | − | 0.826316i | \(-0.690433\pi\) | ||||
−0.563207 | + | 0.826316i | \(0.690433\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −1.46931 | −0.0784261 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −31.0319 | −1.65166 | −0.825831 | − | 0.563917i | \(-0.809294\pi\) | ||||
−0.825831 | + | 0.563917i | \(0.809294\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0.519620 | 0.0275786 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −0.326367 | −0.0172732 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 34.8907 | 1.84146 | 0.920729 | − | 0.390202i | \(-0.127595\pi\) | ||||
0.920729 | + | 0.390202i | \(0.127595\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −14.9551 | −0.787110 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −1.11183 | −0.0583561 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −0.240208 | −0.0125731 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 2.86494 | 0.149549 | 0.0747744 | − | 0.997200i | \(-0.476176\pi\) | ||||
0.0747744 | + | 0.997200i | \(0.476176\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 28.4022 | 1.47856 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 6.82668 | 0.354424 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −16.4919 | −0.853917 | −0.426958 | − | 0.904271i | \(-0.640415\pi\) | ||||
−0.426958 | + | 0.904271i | \(0.640415\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −0.107530 | −0.00555285 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 7.34092 | 0.378077 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 8.14872 | 0.418572 | 0.209286 | − | 0.977855i | \(-0.432886\pi\) | ||||
0.209286 | + | 0.977855i | \(0.432886\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 1.77116 | 0.0907395 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −17.9974 | −0.919625 | −0.459813 | − | 0.888016i | \(-0.652083\pi\) | ||||
−0.459813 | + | 0.888016i | \(0.652083\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 12.3878 | 0.631342 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 15.7359 | 0.799901 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 3.93065 | 0.199292 | 0.0996460 | − | 0.995023i | \(-0.468229\pi\) | ||||
0.0996460 | + | 0.995023i | \(0.468229\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −7.80407 | −0.394669 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −1.39313 | −0.0702741 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 13.3375 | 0.671083 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −32.4096 | −1.62659 | −0.813295 | − | 0.581852i | \(-0.802328\pi\) | ||||
−0.813295 | + | 0.581852i | \(0.802328\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0.579946 | 0.0290336 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −1.00000 | −0.0499376 | ||||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −7.99973 | −0.398495 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 8.89607 | 0.442049 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −13.4886 | −0.668605 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 19.3544 | 0.957012 | 0.478506 | − | 0.878084i | \(-0.341179\pi\) | ||||
0.478506 | + | 0.878084i | \(0.341179\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −0.234069 | −0.0115458 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −36.1268 | −1.77769 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 0.442286 | 0.0217110 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −0.298620 | −0.0146235 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 27.5338 | 1.34512 | 0.672558 | − | 0.740045i | \(-0.265196\pi\) | ||||
0.672558 | + | 0.740045i | \(0.265196\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 17.1646 | 0.836549 | 0.418275 | − | 0.908321i | \(-0.362635\pi\) | ||||
0.418275 | + | 0.908321i | \(0.362635\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 33.5773 | 1.63259 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 1.13181 | 0.0549008 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 24.1072 | 1.16663 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 1.13343 | 0.0547225 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −16.6915 | −0.804002 | −0.402001 | − | 0.915639i | \(-0.631685\pi\) | ||||
−0.402001 | + | 0.915639i | \(0.631685\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −20.9644 | −1.00748 | −0.503742 | − | 0.863854i | \(-0.668044\pi\) | ||||
−0.503742 | + | 0.863854i | \(0.668044\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0.345950 | 0.0165870 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 13.8677 | 0.663380 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 15.9033 | 0.759023 | 0.379511 | − | 0.925187i | \(-0.376092\pi\) | ||||
0.379511 | + | 0.925187i | \(0.376092\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −0.571438 | −0.0272114 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 4.62494 | 0.219737 | 0.109869 | − | 0.993946i | \(-0.464957\pi\) | ||||
0.109869 | + | 0.993946i | \(0.464957\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −18.4216 | −0.873266 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 2.25433 | 0.106626 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −25.4521 | −1.20116 | −0.600579 | − | 0.799566i | \(-0.705063\pi\) | ||||
−0.600579 | + | 0.799566i | \(0.705063\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −43.9037 | −2.06735 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −1.22894 | −0.0577407 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −6.11886 | −0.286857 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 3.36936 | 0.157612 | 0.0788060 | − | 0.996890i | \(-0.474889\pi\) | ||||
0.0788060 | + | 0.996890i | \(0.474889\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0.728817 | 0.0340182 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −16.5242 | −0.769608 | −0.384804 | − | 0.922998i | \(-0.625731\pi\) | ||||
−0.384804 | + | 0.922998i | \(0.625731\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 2.64568 | 0.122955 | 0.0614775 | − | 0.998108i | \(-0.480419\pi\) | ||||
0.0614775 | + | 0.998108i | \(0.480419\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −0.376997 | −0.0174828 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −26.7230 | −1.23659 | −0.618297 | − | 0.785945i | \(-0.712177\pi\) | ||||
−0.618297 | + | 0.785945i | \(0.712177\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −28.0387 | −1.29471 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 1.93188 | 0.0890165 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −24.3244 | −1.11844 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −2.01120 | −0.0922801 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −7.60769 | −0.348332 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 0.974638 | 0.0445323 | 0.0222662 | − | 0.999752i | \(-0.492912\pi\) | ||||
0.0222662 | + | 0.999752i | \(0.492912\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 6.66257 | 0.303787 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 1.98830 | 0.0904706 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 14.0002 | 0.635718 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −4.20800 | −0.190683 | −0.0953414 | − | 0.995445i | \(-0.530394\pi\) | ||||
−0.0953414 | + | 0.995445i | \(0.530394\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 0.371106 | 0.0167820 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −8.07946 | −0.364621 | −0.182310 | − | 0.983241i | \(-0.558358\pi\) | ||||
−0.182310 | + | 0.983241i | \(0.558358\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −3.64129 | −0.163995 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −13.8051 | −0.620491 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 1.39344 | 0.0625042 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 2.57209 | 0.115142 | 0.0575712 | − | 0.998341i | \(-0.481664\pi\) | ||||
0.0575712 | + | 0.998341i | \(0.481664\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −0.377160 | −0.0168503 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −14.3804 | −0.641190 | −0.320595 | − | 0.947216i | \(-0.603883\pi\) | ||||
−0.320595 | + | 0.947216i | \(0.603883\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −4.39922 | −0.195763 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0.838048 | 0.0372190 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 19.1946 | 0.850783 | 0.425392 | − | 0.905009i | \(-0.360136\pi\) | ||||
0.425392 | + | 0.905009i | \(0.360136\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −0.644152 | −0.0284956 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −1.29509 | −0.0571796 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −16.2889 | −0.717774 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −51.9035 | −2.28271 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −0.909953 | −0.0399425 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −13.1825 | −0.577536 | −0.288768 | − | 0.957399i | \(-0.593246\pi\) | ||||
−0.288768 | + | 0.957399i | \(0.593246\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 13.7109 | 0.599536 | 0.299768 | − | 0.954012i | \(-0.403091\pi\) | ||||
0.299768 | + | 0.954012i | \(0.403091\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | −0.288359 | −0.0125850 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 3.96807 | 0.172852 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 24.5440 | 1.06713 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 40.2599 | 1.74713 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 21.6859 | 0.939319 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −2.52153 | −0.109015 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −0.0480709 | −0.00207441 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 0.883323 | 0.0380474 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 13.1710 | 0.566267 | 0.283134 | − | 0.959080i | \(-0.408626\pi\) | ||||
0.283134 | + | 0.959080i | \(0.408626\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −1.37979 | −0.0592126 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −0.284536 | −0.0121882 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 44.9432 | 1.92163 | 0.960816 | − | 0.277187i | \(-0.0894021\pi\) | ||||
0.960816 | + | 0.277187i | \(0.0894021\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −26.8652 | −1.14658 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 6.47048 | 0.275652 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 35.7665 | 1.52094 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0.313982 | 0.0133278 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −27.6421 | −1.17123 | −0.585616 | − | 0.810589i | \(-0.699147\pi\) | ||||
−0.585616 | + | 0.810589i | \(0.699147\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 12.0148 | 0.508172 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −0.562210 | −0.0237365 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −2.80614 | −0.118265 | −0.0591324 | − | 0.998250i | \(-0.518833\pi\) | ||||
−0.0591324 | + | 0.998250i | \(0.518833\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 14.6911 | 0.618061 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 23.8561 | 1.00186 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 12.9648 | 0.543515 | 0.271757 | − | 0.962366i | \(-0.412395\pi\) | ||||
0.271757 | + | 0.962366i | \(0.412395\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −9.21349 | −0.385572 | −0.192786 | − | 0.981241i | \(-0.561752\pi\) | ||||
−0.192786 | + | 0.981241i | \(0.561752\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0.0124815 | 0.000521421 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −6.89522 | −0.287551 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 31.3358 | 1.30453 | 0.652264 | − | 0.757992i | \(-0.273819\pi\) | ||||
0.652264 | + | 0.757992i | \(0.273819\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 2.02118 | 0.0839973 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 1.18605 | 0.0492058 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 11.7599 | 0.487044 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 6.81888 | 0.281926 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −26.3550 | −1.08779 | −0.543894 | − | 0.839154i | \(-0.683051\pi\) | ||||
−0.543894 | + | 0.839154i | \(0.683051\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −7.05117 | −0.290538 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −1.07112 | −0.0440600 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 20.6956 | 0.849866 | 0.424933 | − | 0.905225i | \(-0.360298\pi\) | ||||
0.424933 | + | 0.905225i | \(0.360298\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 3.03511 | 0.124427 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 2.30867 | 0.0944876 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −19.8701 | −0.811871 | −0.405936 | − | 0.913902i | \(-0.633054\pi\) | ||||
−0.405936 | + | 0.913902i | \(0.633054\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −29.4627 | −1.20181 | −0.600905 | − | 0.799320i | \(-0.705193\pi\) | ||||
−0.600905 | + | 0.799320i | \(0.705193\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 31.2464 | 1.27245 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 10.3397 | 0.420369 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −23.3291 | −0.946897 | −0.473448 | − | 0.880822i | \(-0.656991\pi\) | ||||
−0.473448 | + | 0.880822i | \(0.656991\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0.927714 | 0.0375929 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 25.6372 | 1.03717 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 27.8120 | 1.12332 | 0.561659 | − | 0.827369i | \(-0.310163\pi\) | ||||
0.561659 | + | 0.827369i | \(0.310163\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 1.02197 | 0.0412099 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 14.7170 | 0.592482 | 0.296241 | − | 0.955113i | \(-0.404267\pi\) | ||||
0.296241 | + | 0.955113i | \(0.404267\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −10.3808 | −0.417240 | −0.208620 | − | 0.977997i | \(-0.566897\pi\) | ||||
−0.208620 | + | 0.977997i | \(0.566897\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −4.44010 | −0.178175 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −49.4001 | −1.97917 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 1.00000 | 0.0400000 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0.999035 | 0.0398976 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −3.30480 | −0.131771 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −27.0178 | −1.07556 | −0.537780 | − | 0.843085i | \(-0.680737\pi\) | ||||
−0.537780 | + | 0.843085i | \(0.680737\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 0.491880 | 0.0195505 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −16.4713 | −0.653642 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −0.436309 | −0.0172872 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −1.55285 | −0.0614299 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −14.0534 | −0.555078 | −0.277539 | − | 0.960714i | \(-0.589519\pi\) | ||||
−0.277539 | + | 0.960714i | \(0.589519\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 22.7023 | 0.895291 | 0.447646 | − | 0.894211i | \(-0.352263\pi\) | ||||
0.447646 | + | 0.894211i | \(0.352263\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0.566212 | 0.0222946 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 27.4245 | 1.07817 | 0.539084 | − | 0.842252i | \(-0.318771\pi\) | ||||
0.539084 | + | 0.842252i | \(0.318771\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −62.2333 | −2.44287 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −1.01097 | −0.0396231 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 39.5648 | 1.54829 | 0.774146 | − | 0.633008i | \(-0.218180\pi\) | ||||
0.774146 | + | 0.633008i | \(0.218180\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 12.9557 | 0.506220 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 0.717846 | 0.0280058 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −15.7371 | −0.613032 | −0.306516 | − | 0.951865i | \(-0.599163\pi\) | ||||
−0.306516 | + | 0.951865i | \(0.599163\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −22.1069 | −0.859859 | −0.429929 | − | 0.902863i | \(-0.641462\pi\) | ||||
−0.429929 | + | 0.902863i | \(0.641462\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0.277699 | 0.0107849 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −5.39332 | −0.209144 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 22.1835 | 0.858948 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −2.78930 | −0.107841 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 41.5279 | 1.60317 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −29.2498 | −1.12750 | −0.563749 | − | 0.825946i | \(-0.690641\pi\) | ||||
−0.563749 | + | 0.825946i | \(0.690641\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0.643940 | 0.0247852 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −27.5421 | −1.05853 | −0.529264 | − | 0.848457i | \(-0.677532\pi\) | ||||
−0.529264 | + | 0.848457i | \(0.677532\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 37.5436 | 1.44079 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −1.38749 | −0.0531686 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −19.6018 | −0.750040 | −0.375020 | − | 0.927017i | \(-0.622364\pi\) | ||||
−0.375020 | + | 0.927017i | \(0.622364\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 2.17677 | 0.0831702 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −1.92057 | −0.0732743 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −5.80868 | −0.221293 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 34.4657 | 1.31114 | 0.655568 | − | 0.755136i | \(-0.272429\pi\) | ||||
0.655568 | + | 0.755136i | \(0.272429\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −37.0203 | −1.40628 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 2.77707 | 0.105340 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −10.7567 | −0.407440 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −1.71502 | −0.0648682 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −13.7043 | −0.517604 | −0.258802 | − | 0.965930i | \(-0.583328\pi\) | ||||
−0.258802 | + | 0.965930i | \(0.583328\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 5.87256 | 0.221488 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 1.20819 | 0.0455029 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −11.7971 | −0.443677 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 16.8716 | 0.633627 | 0.316813 | − | 0.948488i | \(-0.397387\pi\) | ||||
0.316813 | + | 0.948488i | \(0.397387\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −39.8583 | −1.49480 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −24.1743 | −0.905335 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −10.5406 | −0.394194 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 0.266265 | 0.00994385 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −21.6476 | −0.807318 | −0.403659 | − | 0.914909i | \(-0.632262\pi\) | ||||
−0.403659 | + | 0.914909i | \(0.632262\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −43.6810 | −1.62676 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −2.02757 | −0.0754062 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −3.21723 | −0.119485 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −9.41647 | −0.349237 | −0.174619 | − | 0.984636i | \(-0.555869\pi\) | ||||
−0.174619 | + | 0.984636i | \(0.555869\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −26.3776 | −0.976949 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −5.95965 | −0.220426 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −13.1814 | −0.486867 | −0.243433 | − | 0.969918i | \(-0.578274\pi\) | ||||
−0.243433 | + | 0.969918i | \(0.578274\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | −0.0205616 | −0.000758426 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −48.3003 | −1.77917 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 47.8664 | 1.76079 | 0.880396 | − | 0.474239i | \(-0.157277\pi\) | ||||
0.880396 | + | 0.474239i | \(0.157277\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −0.493464 | −0.0181279 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −8.05550 | −0.295528 | −0.147764 | − | 0.989023i | \(-0.547208\pi\) | ||||
−0.147764 | + | 0.989023i | \(0.547208\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −20.9646 | −0.768083 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −1.32174 | −0.0483601 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −6.76184 | −0.247072 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 45.8484 | 1.67303 | 0.836515 | − | 0.547943i | \(-0.184589\pi\) | ||||
0.836515 | + | 0.547943i | \(0.184589\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −0.276858 | −0.0100893 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 11.4288 | 0.415936 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −36.0645 | −1.31079 | −0.655394 | − | 0.755287i | \(-0.727497\pi\) | ||||
−0.655394 | + | 0.755287i | \(0.727497\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 3.42510 | 0.124323 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −20.6287 | −0.747789 | −0.373895 | − | 0.927471i | \(-0.621978\pi\) | ||||
−0.373895 | + | 0.927471i | \(0.621978\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −0.763025 | −0.0276234 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −3.38234 | −0.122289 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 30.7396 | 1.10994 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −13.0496 | −0.470580 | −0.235290 | − | 0.971925i | \(-0.575604\pi\) | ||||
−0.235290 | + | 0.971925i | \(0.575604\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −1.95872 | −0.0705417 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −47.3700 | −1.70378 | −0.851891 | − | 0.523720i | \(-0.824544\pi\) | ||||
−0.851891 | + | 0.523720i | \(0.824544\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 3.50595 | 0.125938 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0.841987 | 0.0302061 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 19.1145 | 0.684847 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 2.40038 | 0.0858924 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −2.07170 | −0.0740365 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −17.9659 | −0.641231 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −42.4249 | −1.51228 | −0.756141 | − | 0.654408i | \(-0.772918\pi\) | ||||
−0.756141 | + | 0.654408i | \(0.772918\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −0.743265 | −0.0264609 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 39.3964 | 1.40077 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −20.5123 | −0.728414 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −0.273741 | −0.00970860 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −40.7859 | −1.44471 | −0.722355 | − | 0.691523i | \(-0.756940\pi\) | ||||
−0.722355 | + | 0.691523i | \(0.756940\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −12.7167 | −0.449885 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 55.0517 | 1.94516 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −1.10964 | −0.0391583 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −18.4905 | −0.651705 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0.761988 | 0.0268232 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −29.5501 | −1.03893 | −0.519463 | − | 0.854493i | \(-0.673868\pi\) | ||||
−0.519463 | + | 0.854493i | \(0.673868\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 2.77441 | 0.0974228 | 0.0487114 | − | 0.998813i | \(-0.484489\pi\) | ||||
0.0487114 | + | 0.998813i | \(0.484489\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −2.07332 | −0.0727146 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −3.45117 | −0.120889 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 10.5902 | 0.370503 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 18.2858 | 0.638958 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −2.07217 | −0.0723191 | −0.0361595 | − | 0.999346i | \(-0.511512\pi\) | ||||
−0.0361595 | + | 0.999346i | \(0.511512\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −34.5578 | −1.20461 | −0.602304 | − | 0.798267i | \(-0.705751\pi\) | ||||
−0.602304 | + | 0.798267i | \(0.705751\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −0.496736 | −0.0172941 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 13.4854 | 0.468935 | 0.234467 | − | 0.972124i | \(-0.424665\pi\) | ||||
0.234467 | + | 0.972124i | \(0.424665\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −18.1037 | −0.628768 | −0.314384 | − | 0.949296i | \(-0.601798\pi\) | ||||
−0.314384 | + | 0.949296i | \(0.601798\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 2.35544 | 0.0817092 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 0.216421 | 0.00749853 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 3.50747 | 0.121381 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 2.25762 | 0.0780348 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 13.4443 | 0.464149 | 0.232074 | − | 0.972698i | \(-0.425449\pi\) | ||||
0.232074 | + | 0.972698i | \(0.425449\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −18.6495 | −0.643085 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −0.568861 | −0.0195926 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −7.79359 | −0.268108 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 27.7274 | 0.952725 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 0.0794557 | 0.00272691 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 20.1336 | 0.690170 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 37.0538 | 1.26870 | 0.634348 | − | 0.773047i | \(-0.281268\pi\) | ||||
0.634348 | + | 0.773047i | \(0.281268\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 6.01034 | 0.205549 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −57.7654 | −1.97323 | −0.986615 | − | 0.163068i | \(-0.947861\pi\) | ||||
−0.986615 | + | 0.163068i | \(0.947861\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 55.2127 | 1.88383 | 0.941916 | − | 0.335848i | \(-0.109023\pi\) | ||||
0.941916 | + | 0.335848i | \(0.109023\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 2.74057 | 0.0933982 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 23.7506 | 0.808480 | 0.404240 | − | 0.914653i | \(-0.367536\pi\) | ||||
0.404240 | + | 0.914653i | \(0.367536\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 8.46228 | 0.287726 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 1.69027 | 0.0574047 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 61.6125 | 2.09006 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 23.8575 | 0.808381 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −41.8388 | −1.41603 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 2.68164 | 0.0906561 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 24.7407 | 0.835434 | 0.417717 | − | 0.908577i | \(-0.362830\pi\) | ||||
0.417717 | + | 0.908577i | \(0.362830\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −2.35436 | −0.0794107 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −12.0942 | −0.407463 | −0.203731 | − | 0.979027i | \(-0.565307\pi\) | ||||
−0.203731 | + | 0.979027i | \(0.565307\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 3.44520 | 0.115940 | 0.0579702 | − | 0.998318i | \(-0.481537\pi\) | ||||
0.0579702 | + | 0.998318i | \(0.481537\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 1.44864 | 0.0486955 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 16.3037 | 0.547425 | 0.273712 | − | 0.961812i | \(-0.411748\pi\) | ||||
0.273712 | + | 0.961812i | \(0.411748\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −44.1701 | −1.48142 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 41.0953 | 1.37674 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 22.5973 | 0.756191 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 0.447045 | 0.0149431 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −1.69180 | −0.0564875 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −11.2794 | −0.376190 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 2.88126 | 0.0959885 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 1.51838 | 0.0505285 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 12.8317 | 0.426539 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 21.6352 | 0.718384 | 0.359192 | − | 0.933264i | \(-0.383052\pi\) | ||||
0.359192 | + | 0.933264i | \(0.383052\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 13.1468 | 0.436051 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 29.4463 | 0.975600 | 0.487800 | − | 0.872956i | \(-0.337800\pi\) | ||||
0.487800 | + | 0.872956i | \(0.337800\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 2.04314 | 0.0676179 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −0.966667 | −0.0319570 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 34.7425 | 1.14730 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 38.7772 | 1.27914 | 0.639570 | − | 0.768733i | \(-0.279112\pi\) | ||||
0.639570 | + | 0.768733i | \(0.279112\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −1.01365 | −0.0334010 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −1.18565 | −0.0390260 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −2.91993 | −0.0960067 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 48.6783 | 1.59880 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 11.0566 | 0.362754 | 0.181377 | − | 0.983414i | \(-0.441945\pi\) | ||||
0.181377 | + | 0.983414i | \(0.441945\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −0.384574 | −0.0126039 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 0.674210 | 0.0220726 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 5.22838 | 0.170986 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 13.5811 | 0.443674 | 0.221837 | − | 0.975084i | \(-0.428795\pi\) | ||||
0.221837 | + | 0.975084i | \(0.428795\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0.952399 | 0.0310804 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 1.55187 | 0.0505895 | 0.0252947 | − | 0.999680i | \(-0.491948\pi\) | ||||
0.0252947 | + | 0.999680i | \(0.491948\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 65.5323 | 2.13403 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 1.72682 | 0.0561734 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 27.8176 | 0.903951 | 0.451975 | − | 0.892030i | \(-0.350719\pi\) | ||||
0.451975 | + | 0.892030i | \(0.350719\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 0.548096 | 0.0177919 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 1.30563 | 0.0423381 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −41.8854 | −1.35680 | −0.678401 | − | 0.734692i | \(-0.737327\pi\) | ||||
−0.678401 | + | 0.734692i | \(0.737327\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −0.116074 | −0.00375606 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 1.59811 | 0.0516596 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 5.83733 | 0.188497 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −18.7083 | −0.603493 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 7.53543 | 0.242826 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −18.7963 | −0.605076 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 0.112018 | 0.00360225 | 0.00180112 | − | 0.999998i | \(-0.499427\pi\) | ||||
0.00180112 | + | 0.999998i | \(0.499427\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0.244771 | 0.00786317 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −45.4862 | −1.45972 | −0.729860 | − | 0.683596i | \(-0.760415\pi\) | ||||
−0.729860 | + | 0.683596i | \(0.760415\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 7.44713 | 0.238744 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0.245358 | 0.00785776 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −40.5369 | −1.29689 | −0.648446 | − | 0.761261i | \(-0.724581\pi\) | ||||
−0.648446 | + | 0.761261i | \(0.724581\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −85.0983 | −2.71975 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0.850319 | 0.0271486 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −37.3299 | −1.19064 | −0.595319 | − | 0.803489i | \(-0.702975\pi\) | ||||
−0.595319 | + | 0.803489i | \(0.702975\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 9.96109 | 0.317387 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 3.23992 | 0.103128 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 36.3074 | 1.15451 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 37.6416 | 1.19573 | 0.597863 | − | 0.801598i | \(-0.296017\pi\) | ||||
0.597863 | + | 0.801598i | \(0.296017\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 3.70625 | 0.117614 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −21.4699 | −0.680642 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −32.0529 | −1.01512 | −0.507562 | − | 0.861615i | \(-0.669453\pi\) | ||||
−0.507562 | + | 0.861615i | \(0.669453\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −1.88026 | −0.0594888 |
(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 | 8020.2.a.d.1.15 | ✓ | 29 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
8020.2.a.d.1.15 | ✓ | 29 | 1.1 | even | 1 | trivial |