Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [2394,2,Mod(1,2394)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(2394, 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("2394.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 2394 = 2 \cdot 3^{2} \cdot 7 \cdot 19 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 2394.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: | \(19.1161862439\) |
Analytic rank: | \(0\) |
Dimension: | \(3\) |
Coefficient field: | 3.3.469.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{3} - x^{2} - 5x + 4 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 266) |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.3 | ||
Root | \(2.39138\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 2394.1 |
$q$-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 | ||||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 1.00000 | 0.500000 | ||||||||
\(5\) | 0.391382 | 0.175032 | 0.0875158 | − | 0.996163i | \(-0.472107\pi\) | ||||
0.0875158 | + | 0.996163i | \(0.472107\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −1.00000 | −0.377964 | ||||||||
\(8\) | −1.00000 | −0.353553 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | −0.391382 | −0.123766 | ||||||||
\(11\) | −3.06406 | −0.923847 | −0.461924 | − | 0.886920i | \(-0.652841\pi\) | ||||
−0.461924 | + | 0.886920i | \(0.652841\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 2.78276 | 0.771800 | 0.385900 | − | 0.922541i | \(-0.373891\pi\) | ||||
0.385900 | + | 0.922541i | \(0.373891\pi\) | |||||||
\(14\) | 1.00000 | 0.267261 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | 6.22018 | 1.50862 | 0.754308 | − | 0.656521i | \(-0.227972\pi\) | ||||
0.754308 | + | 0.656521i | \(0.227972\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −1.00000 | −0.229416 | ||||||||
\(20\) | 0.391382 | 0.0875158 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 3.06406 | 0.653259 | ||||||||
\(23\) | 4.78276 | 0.997275 | 0.498638 | − | 0.866811i | \(-0.333834\pi\) | ||||
0.498638 | + | 0.866811i | \(0.333834\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −4.84682 | −0.969364 | ||||||||
\(26\) | −2.78276 | −0.545745 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | −1.00000 | −0.188982 | ||||||||
\(29\) | −7.82880 | −1.45377 | −0.726886 | − | 0.686758i | \(-0.759033\pi\) | ||||
−0.726886 | + | 0.686758i | \(0.759033\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 1.34535 | 0.241631 | 0.120816 | − | 0.992675i | \(-0.461449\pi\) | ||||
0.120816 | + | 0.992675i | \(0.461449\pi\) | |||||||
\(32\) | −1.00000 | −0.176777 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | −6.22018 | −1.06675 | ||||||||
\(35\) | −0.391382 | −0.0661557 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −3.82880 | −0.629451 | −0.314726 | − | 0.949183i | \(-0.601912\pi\) | ||||
−0.314726 | + | 0.949183i | \(0.601912\pi\) | |||||||
\(38\) | 1.00000 | 0.162221 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | −0.391382 | −0.0618830 | ||||||||
\(41\) | 4.39138 | 0.685819 | 0.342909 | − | 0.939368i | \(-0.388588\pi\) | ||||
0.342909 | + | 0.939368i | \(0.388588\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 5.82880 | 0.888884 | 0.444442 | − | 0.895808i | \(-0.353402\pi\) | ||||
0.444442 | + | 0.895808i | \(0.353402\pi\) | |||||||
\(44\) | −3.06406 | −0.461924 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −4.78276 | −0.705180 | ||||||||
\(47\) | 5.71871 | 0.834160 | 0.417080 | − | 0.908870i | \(-0.363054\pi\) | ||||
0.417080 | + | 0.908870i | \(0.363054\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 1.00000 | 0.142857 | ||||||||
\(50\) | 4.84682 | 0.685444 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 2.78276 | 0.385900 | ||||||||
\(53\) | −7.15613 | −0.982970 | −0.491485 | − | 0.870886i | \(-0.663546\pi\) | ||||
−0.491485 | + | 0.870886i | \(0.663546\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −1.19922 | −0.161702 | ||||||||
\(56\) | 1.00000 | 0.133631 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 7.82880 | 1.02797 | ||||||||
\(59\) | 7.17415 | 0.933994 | 0.466997 | − | 0.884259i | \(-0.345336\pi\) | ||||
0.466997 | + | 0.884259i | \(0.345336\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 8.50147 | 1.08850 | 0.544251 | − | 0.838922i | \(-0.316814\pi\) | ||||
0.544251 | + | 0.838922i | \(0.316814\pi\) | |||||||
\(62\) | −1.34535 | −0.170859 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | 1.08913 | 0.135089 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 12.2202 | 1.49293 | 0.746467 | − | 0.665423i | \(-0.231749\pi\) | ||||
0.746467 | + | 0.665423i | \(0.231749\pi\) | |||||||
\(68\) | 6.22018 | 0.754308 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0.391382 | 0.0467791 | ||||||||
\(71\) | −0.935945 | −0.111076 | −0.0555381 | − | 0.998457i | \(-0.517687\pi\) | ||||
−0.0555381 | + | 0.998457i | \(0.517687\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −4.12811 | −0.483159 | −0.241579 | − | 0.970381i | \(-0.577665\pi\) | ||||
−0.241579 | + | 0.970381i | \(0.577665\pi\) | |||||||
\(74\) | 3.82880 | 0.445089 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −1.00000 | −0.114708 | ||||||||
\(77\) | 3.06406 | 0.349181 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 2.95396 | 0.332347 | 0.166173 | − | 0.986097i | \(-0.446859\pi\) | ||||
0.166173 | + | 0.986097i | \(0.446859\pi\) | |||||||
\(80\) | 0.391382 | 0.0437579 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | −4.39138 | −0.484947 | ||||||||
\(83\) | 13.5655 | 1.48901 | 0.744505 | − | 0.667617i | \(-0.232685\pi\) | ||||
0.744505 | + | 0.667617i | \(0.232685\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 2.43447 | 0.264055 | ||||||||
\(86\) | −5.82880 | −0.628536 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 3.06406 | 0.326629 | ||||||||
\(89\) | −1.06406 | −0.112790 | −0.0563948 | − | 0.998409i | \(-0.517961\pi\) | ||||
−0.0563948 | + | 0.998409i | \(0.517961\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −2.78276 | −0.291713 | ||||||||
\(92\) | 4.78276 | 0.498638 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | −5.71871 | −0.589840 | ||||||||
\(95\) | −0.391382 | −0.0401550 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 4.50147 | 0.457055 | 0.228528 | − | 0.973537i | \(-0.426609\pi\) | ||||
0.228528 | + | 0.973537i | \(0.426609\pi\) | |||||||
\(98\) | −1.00000 | −0.101015 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | −4.84682 | −0.484682 | ||||||||
\(101\) | −17.1311 | −1.70460 | −0.852302 | − | 0.523050i | \(-0.824794\pi\) | ||||
−0.852302 | + | 0.523050i | \(0.824794\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −2.09207 | −0.206138 | −0.103069 | − | 0.994674i | \(-0.532866\pi\) | ||||
−0.103069 | + | 0.994674i | \(0.532866\pi\) | |||||||
\(104\) | −2.78276 | −0.272873 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 7.15613 | 0.695065 | ||||||||
\(107\) | 14.0921 | 1.36233 | 0.681166 | − | 0.732129i | \(-0.261473\pi\) | ||||
0.681166 | + | 0.732129i | \(0.261473\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 15.1561 | 1.45169 | 0.725847 | − | 0.687856i | \(-0.241448\pi\) | ||||
0.725847 | + | 0.687856i | \(0.241448\pi\) | |||||||
\(110\) | 1.19922 | 0.114341 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | −1.00000 | −0.0944911 | ||||||||
\(113\) | −19.7857 | −1.86128 | −0.930642 | − | 0.365932i | \(-0.880750\pi\) | ||||
−0.930642 | + | 0.365932i | \(0.880750\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 1.87189 | 0.174555 | ||||||||
\(116\) | −7.82880 | −0.726886 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | −7.17415 | −0.660434 | ||||||||
\(119\) | −6.22018 | −0.570203 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −1.61157 | −0.146506 | ||||||||
\(122\) | −8.50147 | −0.769687 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 1.34535 | 0.120816 | ||||||||
\(125\) | −3.85387 | −0.344701 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 2.50147 | 0.221970 | 0.110985 | − | 0.993822i | \(-0.464599\pi\) | ||||
0.110985 | + | 0.993822i | \(0.464599\pi\) | |||||||
\(128\) | −1.00000 | −0.0883883 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | −1.08913 | −0.0955226 | ||||||||
\(131\) | 15.4374 | 1.34877 | 0.674387 | − | 0.738378i | \(-0.264408\pi\) | ||||
0.674387 | + | 0.738378i | \(0.264408\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 1.00000 | 0.0867110 | ||||||||
\(134\) | −12.2202 | −1.05566 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −6.22018 | −0.533376 | ||||||||
\(137\) | −13.9209 | −1.18934 | −0.594670 | − | 0.803970i | \(-0.702717\pi\) | ||||
−0.594670 | + | 0.803970i | \(0.702717\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 10.8748 | 0.922392 | 0.461196 | − | 0.887298i | \(-0.347421\pi\) | ||||
0.461196 | + | 0.887298i | \(0.347421\pi\) | |||||||
\(140\) | −0.391382 | −0.0330778 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0.935945 | 0.0785428 | ||||||||
\(143\) | −8.52654 | −0.713025 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −3.06406 | −0.254456 | ||||||||
\(146\) | 4.12811 | 0.341645 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | −3.82880 | −0.314726 | ||||||||
\(149\) | 1.77982 | 0.145808 | 0.0729041 | − | 0.997339i | \(-0.476773\pi\) | ||||
0.0729041 | + | 0.997339i | \(0.476773\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 5.30931 | 0.432065 | 0.216033 | − | 0.976386i | \(-0.430688\pi\) | ||||
0.216033 | + | 0.976386i | \(0.430688\pi\) | |||||||
\(152\) | 1.00000 | 0.0811107 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | −3.06406 | −0.246909 | ||||||||
\(155\) | 0.526544 | 0.0422931 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 15.3763 | 1.22716 | 0.613582 | − | 0.789631i | \(-0.289728\pi\) | ||||
0.613582 | + | 0.789631i | \(0.289728\pi\) | |||||||
\(158\) | −2.95396 | −0.235005 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | −0.391382 | −0.0309415 | ||||||||
\(161\) | −4.78276 | −0.376935 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 17.9389 | 1.40508 | 0.702541 | − | 0.711643i | \(-0.252049\pi\) | ||||
0.702541 | + | 0.711643i | \(0.252049\pi\) | |||||||
\(164\) | 4.39138 | 0.342909 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −13.5655 | −1.05289 | ||||||||
\(167\) | 13.5295 | 1.04694 | 0.523472 | − | 0.852043i | \(-0.324637\pi\) | ||||
0.523472 | + | 0.852043i | \(0.324637\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −5.25622 | −0.404325 | ||||||||
\(170\) | −2.43447 | −0.186715 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 5.82880 | 0.444442 | ||||||||
\(173\) | 8.12811 | 0.617969 | 0.308984 | − | 0.951067i | \(-0.400011\pi\) | ||||
0.308984 | + | 0.951067i | \(0.400011\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 4.84682 | 0.366385 | ||||||||
\(176\) | −3.06406 | −0.230962 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 1.06406 | 0.0797543 | ||||||||
\(179\) | 11.4735 | 0.857566 | 0.428783 | − | 0.903407i | \(-0.358942\pi\) | ||||
0.428783 | + | 0.903407i | \(0.358942\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 16.3123 | 1.21248 | 0.606240 | − | 0.795282i | \(-0.292677\pi\) | ||||
0.606240 | + | 0.795282i | \(0.292677\pi\) | |||||||
\(182\) | 2.78276 | 0.206272 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | −4.78276 | −0.352590 | ||||||||
\(185\) | −1.49853 | −0.110174 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −19.0590 | −1.39373 | ||||||||
\(188\) | 5.71871 | 0.417080 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0.391382 | 0.0283939 | ||||||||
\(191\) | 15.4735 | 1.11962 | 0.559810 | − | 0.828621i | \(-0.310874\pi\) | ||||
0.559810 | + | 0.828621i | \(0.310874\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 7.00295 | 0.504083 | 0.252042 | − | 0.967716i | \(-0.418898\pi\) | ||||
0.252042 | + | 0.967716i | \(0.418898\pi\) | |||||||
\(194\) | −4.50147 | −0.323187 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 1.00000 | 0.0714286 | ||||||||
\(197\) | 10.4404 | 0.743845 | 0.371923 | − | 0.928264i | \(-0.378699\pi\) | ||||
0.371923 | + | 0.928264i | \(0.378699\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −6.83175 | −0.484290 | −0.242145 | − | 0.970240i | \(-0.577851\pi\) | ||||
−0.242145 | + | 0.970240i | \(0.577851\pi\) | |||||||
\(200\) | 4.84682 | 0.342722 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 17.1311 | 1.20534 | ||||||||
\(203\) | 7.82880 | 0.549474 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 1.71871 | 0.120040 | ||||||||
\(206\) | 2.09207 | 0.145762 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 2.78276 | 0.192950 | ||||||||
\(209\) | 3.06406 | 0.211945 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −9.30931 | −0.640879 | −0.320440 | − | 0.947269i | \(-0.603831\pi\) | ||||
−0.320440 | + | 0.947269i | \(0.603831\pi\) | |||||||
\(212\) | −7.15613 | −0.491485 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | −14.0921 | −0.963314 | ||||||||
\(215\) | 2.28129 | 0.155583 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −1.34535 | −0.0913280 | ||||||||
\(218\) | −15.1561 | −1.02650 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | −1.19922 | −0.0808512 | ||||||||
\(221\) | 17.3093 | 1.16435 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −2.31226 | −0.154840 | −0.0774201 | − | 0.996999i | \(-0.524668\pi\) | ||||
−0.0774201 | + | 0.996999i | \(0.524668\pi\) | |||||||
\(224\) | 1.00000 | 0.0668153 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 19.7857 | 1.31613 | ||||||||
\(227\) | −12.4404 | −0.825696 | −0.412848 | − | 0.910800i | \(-0.635466\pi\) | ||||
−0.412848 | + | 0.910800i | \(0.635466\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 15.6086 | 1.03145 | 0.515723 | − | 0.856755i | \(-0.327523\pi\) | ||||
0.515723 | + | 0.856755i | \(0.327523\pi\) | |||||||
\(230\) | −1.87189 | −0.123429 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 7.82880 | 0.513986 | ||||||||
\(233\) | 5.28424 | 0.346182 | 0.173091 | − | 0.984906i | \(-0.444625\pi\) | ||||
0.173091 | + | 0.984906i | \(0.444625\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 2.23820 | 0.146004 | ||||||||
\(236\) | 7.17415 | 0.466997 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 6.22018 | 0.403195 | ||||||||
\(239\) | −1.87189 | −0.121082 | −0.0605412 | − | 0.998166i | \(-0.519283\pi\) | ||||
−0.0605412 | + | 0.998166i | \(0.519283\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −22.4835 | −1.44829 | −0.724143 | − | 0.689649i | \(-0.757765\pi\) | ||||
−0.724143 | + | 0.689649i | \(0.757765\pi\) | |||||||
\(242\) | 1.61157 | 0.103595 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 8.50147 | 0.544251 | ||||||||
\(245\) | 0.391382 | 0.0250045 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −2.78276 | −0.177063 | ||||||||
\(248\) | −1.34535 | −0.0854295 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 3.85387 | 0.243740 | ||||||||
\(251\) | −11.6936 | −0.738096 | −0.369048 | − | 0.929410i | \(-0.620316\pi\) | ||||
−0.369048 | + | 0.929410i | \(0.620316\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −14.6547 | −0.921330 | ||||||||
\(254\) | −2.50147 | −0.156956 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | 2.82585 | 0.176272 | 0.0881359 | − | 0.996108i | \(-0.471909\pi\) | ||||
0.0881359 | + | 0.996108i | \(0.471909\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 3.82880 | 0.237910 | ||||||||
\(260\) | 1.08913 | 0.0675447 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | −15.4374 | −0.953727 | ||||||||
\(263\) | 29.4433 | 1.81555 | 0.907776 | − | 0.419455i | \(-0.137779\pi\) | ||||
0.907776 | + | 0.419455i | \(0.137779\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −2.80078 | −0.172051 | ||||||||
\(266\) | −1.00000 | −0.0613139 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 12.2202 | 0.746467 | ||||||||
\(269\) | 10.4404 | 0.636560 | 0.318280 | − | 0.947997i | \(-0.396895\pi\) | ||||
0.318280 | + | 0.947997i | \(0.396895\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −4.29931 | −0.261164 | −0.130582 | − | 0.991437i | \(-0.541685\pi\) | ||||
−0.130582 | + | 0.991437i | \(0.541685\pi\) | |||||||
\(272\) | 6.22018 | 0.377154 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 13.9209 | 0.840991 | ||||||||
\(275\) | 14.8509 | 0.895544 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −28.7526 | −1.72758 | −0.863789 | − | 0.503854i | \(-0.831915\pi\) | ||||
−0.863789 | + | 0.503854i | \(0.831915\pi\) | |||||||
\(278\) | −10.8748 | −0.652229 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0.391382 | 0.0233896 | ||||||||
\(281\) | 20.6547 | 1.23215 | 0.616077 | − | 0.787686i | \(-0.288721\pi\) | ||||
0.616077 | + | 0.787686i | \(0.288721\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −9.30931 | −0.553381 | −0.276690 | − | 0.960959i | \(-0.589238\pi\) | ||||
−0.276690 | + | 0.960959i | \(0.589238\pi\) | |||||||
\(284\) | −0.935945 | −0.0555381 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 8.52654 | 0.504185 | ||||||||
\(287\) | −4.39138 | −0.259215 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 21.6907 | 1.27592 | ||||||||
\(290\) | 3.06406 | 0.179928 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | −4.12811 | −0.241579 | ||||||||
\(293\) | −1.65760 | −0.0968382 | −0.0484191 | − | 0.998827i | \(-0.515418\pi\) | ||||
−0.0484191 | + | 0.998827i | \(0.515418\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 2.80783 | 0.163478 | ||||||||
\(296\) | 3.82880 | 0.222545 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | −1.77982 | −0.103102 | ||||||||
\(299\) | 13.3093 | 0.769697 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −5.82880 | −0.335967 | ||||||||
\(302\) | −5.30931 | −0.305516 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | −1.00000 | −0.0573539 | ||||||||
\(305\) | 3.32733 | 0.190522 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −31.0880 | −1.77428 | −0.887142 | − | 0.461496i | \(-0.847313\pi\) | ||||
−0.887142 | + | 0.461496i | \(0.847313\pi\) | |||||||
\(308\) | 3.06406 | 0.174591 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | −0.526544 | −0.0299057 | ||||||||
\(311\) | −11.8468 | −0.671772 | −0.335886 | − | 0.941903i | \(-0.609036\pi\) | ||||
−0.335886 | + | 0.941903i | \(0.609036\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 34.6606 | 1.95913 | 0.979565 | − | 0.201127i | \(-0.0644605\pi\) | ||||
0.979565 | + | 0.201127i | \(0.0644605\pi\) | |||||||
\(314\) | −15.3763 | −0.867736 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 2.95396 | 0.166173 | ||||||||
\(317\) | 16.4654 | 0.924791 | 0.462396 | − | 0.886674i | \(-0.346990\pi\) | ||||
0.462396 | + | 0.886674i | \(0.346990\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 23.9879 | 1.34306 | ||||||||
\(320\) | 0.391382 | 0.0218789 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 4.78276 | 0.266533 | ||||||||
\(323\) | −6.22018 | −0.346100 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −13.4876 | −0.748155 | ||||||||
\(326\) | −17.9389 | −0.993543 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | −4.39138 | −0.242474 | ||||||||
\(329\) | −5.71871 | −0.315283 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −3.09502 | −0.170118 | −0.0850589 | − | 0.996376i | \(-0.527108\pi\) | ||||
−0.0850589 | + | 0.996376i | \(0.527108\pi\) | |||||||
\(332\) | 13.5655 | 0.744505 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | −13.5295 | −0.740301 | ||||||||
\(335\) | 4.78276 | 0.261310 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −24.5324 | −1.33637 | −0.668184 | − | 0.743996i | \(-0.732928\pi\) | ||||
−0.668184 | + | 0.743996i | \(0.732928\pi\) | |||||||
\(338\) | 5.25622 | 0.285901 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 2.43447 | 0.132028 | ||||||||
\(341\) | −4.12221 | −0.223230 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −1.00000 | −0.0539949 | ||||||||
\(344\) | −5.82880 | −0.314268 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −8.12811 | −0.436970 | ||||||||
\(347\) | −5.56553 | −0.298773 | −0.149387 | − | 0.988779i | \(-0.547730\pi\) | ||||
−0.149387 | + | 0.988779i | \(0.547730\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 25.1311 | 1.34523 | 0.672617 | − | 0.739990i | \(-0.265170\pi\) | ||||
0.672617 | + | 0.739990i | \(0.265170\pi\) | |||||||
\(350\) | −4.84682 | −0.259073 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 3.06406 | 0.163315 | ||||||||
\(353\) | 3.52949 | 0.187856 | 0.0939280 | − | 0.995579i | \(-0.470058\pi\) | ||||
0.0939280 | + | 0.995579i | \(0.470058\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −0.366312 | −0.0194418 | ||||||||
\(356\) | −1.06406 | −0.0563948 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −11.4735 | −0.606391 | ||||||||
\(359\) | −24.9669 | −1.31770 | −0.658852 | − | 0.752273i | \(-0.728958\pi\) | ||||
−0.658852 | + | 0.752273i | \(0.728958\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 1.00000 | 0.0526316 | ||||||||
\(362\) | −16.3123 | −0.857353 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | −2.78276 | −0.145857 | ||||||||
\(365\) | −1.61567 | −0.0845680 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −15.2842 | −0.797831 | −0.398915 | − | 0.916988i | \(-0.630613\pi\) | ||||
−0.398915 | + | 0.916988i | \(0.630613\pi\) | |||||||
\(368\) | 4.78276 | 0.249319 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 1.49853 | 0.0779046 | ||||||||
\(371\) | 7.15613 | 0.371528 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −17.0519 | −0.882916 | −0.441458 | − | 0.897282i | \(-0.645539\pi\) | ||||
−0.441458 | + | 0.897282i | \(0.645539\pi\) | |||||||
\(374\) | 19.0590 | 0.985517 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −5.71871 | −0.294920 | ||||||||
\(377\) | −21.7857 | −1.12202 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 17.0029 | 0.873383 | 0.436691 | − | 0.899611i | \(-0.356150\pi\) | ||||
0.436691 | + | 0.899611i | \(0.356150\pi\) | |||||||
\(380\) | −0.391382 | −0.0200775 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | −15.4735 | −0.791691 | ||||||||
\(383\) | −29.2231 | −1.49323 | −0.746616 | − | 0.665255i | \(-0.768323\pi\) | ||||
−0.746616 | + | 0.665255i | \(0.768323\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 1.19922 | 0.0611178 | ||||||||
\(386\) | −7.00295 | −0.356441 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 4.50147 | 0.228528 | ||||||||
\(389\) | 26.4404 | 1.34058 | 0.670290 | − | 0.742099i | \(-0.266170\pi\) | ||||
0.670290 | + | 0.742099i | \(0.266170\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 29.7497 | 1.50451 | ||||||||
\(392\) | −1.00000 | −0.0505076 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | −10.4404 | −0.525978 | ||||||||
\(395\) | 1.15613 | 0.0581712 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 18.5074 | 0.928858 | 0.464429 | − | 0.885610i | \(-0.346260\pi\) | ||||
0.464429 | + | 0.885610i | \(0.346260\pi\) | |||||||
\(398\) | 6.83175 | 0.342445 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −4.84682 | −0.242341 | ||||||||
\(401\) | 32.2261 | 1.60929 | 0.804647 | − | 0.593754i | \(-0.202355\pi\) | ||||
0.804647 | + | 0.593754i | \(0.202355\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 3.74378 | 0.186491 | ||||||||
\(404\) | −17.1311 | −0.852302 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −7.82880 | −0.388537 | ||||||||
\(407\) | 11.7317 | 0.581517 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 19.3763 | 0.958097 | 0.479049 | − | 0.877788i | \(-0.340982\pi\) | ||||
0.479049 | + | 0.877788i | \(0.340982\pi\) | |||||||
\(410\) | −1.71871 | −0.0848810 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | −2.09207 | −0.103069 | ||||||||
\(413\) | −7.17415 | −0.353017 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 5.30931 | 0.260624 | ||||||||
\(416\) | −2.78276 | −0.136436 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | −3.06406 | −0.149868 | ||||||||
\(419\) | −27.5354 | −1.34519 | −0.672596 | − | 0.740010i | \(-0.734821\pi\) | ||||
−0.672596 | + | 0.740010i | \(0.734821\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −16.4345 | −0.800967 | −0.400484 | − | 0.916304i | \(-0.631158\pi\) | ||||
−0.400484 | + | 0.916304i | \(0.631158\pi\) | |||||||
\(422\) | 9.30931 | 0.453170 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 7.15613 | 0.347532 | ||||||||
\(425\) | −30.1481 | −1.46240 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −8.50147 | −0.411415 | ||||||||
\(428\) | 14.0921 | 0.681166 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | −2.28129 | −0.110014 | ||||||||
\(431\) | −40.9979 | −1.97480 | −0.987399 | − | 0.158249i | \(-0.949415\pi\) | ||||
−0.987399 | + | 0.158249i | \(0.949415\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −22.4835 | −1.08049 | −0.540243 | − | 0.841509i | \(-0.681668\pi\) | ||||
−0.540243 | + | 0.841509i | \(0.681668\pi\) | |||||||
\(434\) | 1.34535 | 0.0645786 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 15.1561 | 0.725847 | ||||||||
\(437\) | −4.78276 | −0.228791 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −18.9109 | −0.902567 | −0.451283 | − | 0.892381i | \(-0.649034\pi\) | ||||
−0.451283 | + | 0.892381i | \(0.649034\pi\) | |||||||
\(440\) | 1.19922 | 0.0571704 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | −17.3093 | −0.823320 | ||||||||
\(443\) | 10.0850 | 0.479154 | 0.239577 | − | 0.970877i | \(-0.422991\pi\) | ||||
0.239577 | + | 0.970877i | \(0.422991\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −0.416452 | −0.0197417 | ||||||||
\(446\) | 2.31226 | 0.109489 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | −1.00000 | −0.0472456 | ||||||||
\(449\) | −17.9138 | −0.845406 | −0.422703 | − | 0.906268i | \(-0.638919\pi\) | ||||
−0.422703 | + | 0.906268i | \(0.638919\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −13.4554 | −0.633592 | ||||||||
\(452\) | −19.7857 | −0.930642 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 12.4404 | 0.583855 | ||||||||
\(455\) | −1.08913 | −0.0510590 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 23.8527 | 1.11578 | 0.557892 | − | 0.829914i | \(-0.311611\pi\) | ||||
0.557892 | + | 0.829914i | \(0.311611\pi\) | |||||||
\(458\) | −15.6086 | −0.729343 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 1.87189 | 0.0872773 | ||||||||
\(461\) | −22.2512 | −1.03634 | −0.518170 | − | 0.855278i | \(-0.673386\pi\) | ||||
−0.518170 | + | 0.855278i | \(0.673386\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 27.8778 | 1.29559 | 0.647795 | − | 0.761814i | \(-0.275691\pi\) | ||||
0.647795 | + | 0.761814i | \(0.275691\pi\) | |||||||
\(464\) | −7.82880 | −0.363443 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −5.28424 | −0.244788 | ||||||||
\(467\) | 24.0980 | 1.11512 | 0.557561 | − | 0.830136i | \(-0.311737\pi\) | ||||
0.557561 | + | 0.830136i | \(0.311737\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −12.2202 | −0.564276 | ||||||||
\(470\) | −2.23820 | −0.103241 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | −7.17415 | −0.330217 | ||||||||
\(473\) | −17.8598 | −0.821193 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 4.84682 | 0.222387 | ||||||||
\(476\) | −6.22018 | −0.285102 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 1.87189 | 0.0856182 | ||||||||
\(479\) | 8.92382 | 0.407740 | 0.203870 | − | 0.978998i | \(-0.434648\pi\) | ||||
0.203870 | + | 0.978998i | \(0.434648\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −10.6547 | −0.485810 | ||||||||
\(482\) | 22.4835 | 1.02409 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −1.61157 | −0.0732530 | ||||||||
\(485\) | 1.76180 | 0.0799991 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −41.0578 | −1.86051 | −0.930254 | − | 0.366916i | \(-0.880414\pi\) | ||||
−0.930254 | + | 0.366916i | \(0.880414\pi\) | |||||||
\(488\) | −8.50147 | −0.384844 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | −0.391382 | −0.0176809 | ||||||||
\(491\) | 20.8807 | 0.942334 | 0.471167 | − | 0.882044i | \(-0.343833\pi\) | ||||
0.471167 | + | 0.882044i | \(0.343833\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −48.6966 | −2.19318 | ||||||||
\(494\) | 2.78276 | 0.125203 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 1.34535 | 0.0604078 | ||||||||
\(497\) | 0.935945 | 0.0419829 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 12.8619 | 0.575777 | 0.287889 | − | 0.957664i | \(-0.407047\pi\) | ||||
0.287889 | + | 0.957664i | \(0.407047\pi\) | |||||||
\(500\) | −3.85387 | −0.172350 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 11.6936 | 0.521913 | ||||||||
\(503\) | 22.9179 | 1.02186 | 0.510930 | − | 0.859622i | \(-0.329301\pi\) | ||||
0.510930 | + | 0.859622i | \(0.329301\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −6.70479 | −0.298359 | ||||||||
\(506\) | 14.6547 | 0.651479 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 2.50147 | 0.110985 | ||||||||
\(509\) | 17.6936 | 0.784257 | 0.392128 | − | 0.919910i | \(-0.371739\pi\) | ||||
0.392128 | + | 0.919910i | \(0.371739\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 4.12811 | 0.182617 | ||||||||
\(512\) | −1.00000 | −0.0441942 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | −2.82585 | −0.124643 | ||||||||
\(515\) | −0.818801 | −0.0360807 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −17.5224 | −0.770636 | ||||||||
\(518\) | −3.82880 | −0.168228 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | −1.08913 | −0.0477613 | ||||||||
\(521\) | 13.3152 | 0.583350 | 0.291675 | − | 0.956518i | \(-0.405787\pi\) | ||||
0.291675 | + | 0.956518i | \(0.405787\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −44.4404 | −1.94324 | −0.971621 | − | 0.236544i | \(-0.923985\pi\) | ||||
−0.971621 | + | 0.236544i | \(0.923985\pi\) | |||||||
\(524\) | 15.4374 | 0.674387 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −29.4433 | −1.28379 | ||||||||
\(527\) | 8.36830 | 0.364529 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −0.125161 | −0.00544179 | ||||||||
\(530\) | 2.80078 | 0.121658 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 1.00000 | 0.0433555 | ||||||||
\(533\) | 12.2202 | 0.529315 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 5.51539 | 0.238451 | ||||||||
\(536\) | −12.2202 | −0.527832 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | −10.4404 | −0.450116 | ||||||||
\(539\) | −3.06406 | −0.131978 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 18.5626 | 0.798068 | 0.399034 | − | 0.916936i | \(-0.369346\pi\) | ||||
0.399034 | + | 0.916936i | \(0.369346\pi\) | |||||||
\(542\) | 4.29931 | 0.184671 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | −6.22018 | −0.266688 | ||||||||
\(545\) | 5.93184 | 0.254092 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −26.2762 | −1.12349 | −0.561745 | − | 0.827310i | \(-0.689870\pi\) | ||||
−0.561745 | + | 0.827310i | \(0.689870\pi\) | |||||||
\(548\) | −13.9209 | −0.594670 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | −14.8509 | −0.633245 | ||||||||
\(551\) | 7.82880 | 0.333518 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −2.95396 | −0.125615 | ||||||||
\(554\) | 28.7526 | 1.22158 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 10.8748 | 0.461196 | ||||||||
\(557\) | −32.6045 | −1.38150 | −0.690749 | − | 0.723095i | \(-0.742719\pi\) | ||||
−0.690749 | + | 0.723095i | \(0.742719\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 16.2202 | 0.686041 | ||||||||
\(560\) | −0.391382 | −0.0165389 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | −20.6547 | −0.871264 | ||||||||
\(563\) | −35.4182 | −1.49270 | −0.746351 | − | 0.665553i | \(-0.768196\pi\) | ||||
−0.746351 | + | 0.665553i | \(0.768196\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −7.74378 | −0.325783 | ||||||||
\(566\) | 9.30931 | 0.391299 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0.935945 | 0.0392714 | ||||||||
\(569\) | 13.6936 | 0.574067 | 0.287034 | − | 0.957921i | \(-0.407331\pi\) | ||||
0.287034 | + | 0.957921i | \(0.407331\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −17.9389 | −0.750719 | −0.375360 | − | 0.926879i | \(-0.622481\pi\) | ||||
−0.375360 | + | 0.926879i | \(0.622481\pi\) | |||||||
\(572\) | −8.52654 | −0.356513 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 4.39138 | 0.183293 | ||||||||
\(575\) | −23.1812 | −0.966723 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −45.3873 | −1.88950 | −0.944749 | − | 0.327796i | \(-0.893694\pi\) | ||||
−0.944749 | + | 0.327796i | \(0.893694\pi\) | |||||||
\(578\) | −21.6907 | −0.902214 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | −3.06406 | −0.127228 | ||||||||
\(581\) | −13.5655 | −0.562793 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 21.9268 | 0.908114 | ||||||||
\(584\) | 4.12811 | 0.170822 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 1.65760 | 0.0684750 | ||||||||
\(587\) | 34.3483 | 1.41771 | 0.708853 | − | 0.705356i | \(-0.249213\pi\) | ||||
0.708853 | + | 0.705356i | \(0.249213\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −1.34535 | −0.0554340 | ||||||||
\(590\) | −2.80783 | −0.115597 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | −3.82880 | −0.157363 | ||||||||
\(593\) | −6.56258 | −0.269493 | −0.134746 | − | 0.990880i | \(-0.543022\pi\) | ||||
−0.134746 | + | 0.990880i | \(0.543022\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −2.43447 | −0.0998036 | ||||||||
\(596\) | 1.77982 | 0.0729041 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | −13.3093 | −0.544258 | ||||||||
\(599\) | 8.62958 | 0.352595 | 0.176298 | − | 0.984337i | \(-0.443588\pi\) | ||||
0.176298 | + | 0.984337i | \(0.443588\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 10.4404 | 0.425872 | 0.212936 | − | 0.977066i | \(-0.431697\pi\) | ||||
0.212936 | + | 0.977066i | \(0.431697\pi\) | |||||||
\(602\) | 5.82880 | 0.237564 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 5.30931 | 0.216033 | ||||||||
\(605\) | −0.630739 | −0.0256432 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −1.43152 | −0.0581037 | −0.0290518 | − | 0.999578i | \(-0.509249\pi\) | ||||
−0.0290518 | + | 0.999578i | \(0.509249\pi\) | |||||||
\(608\) | 1.00000 | 0.0405554 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | −3.32733 | −0.134720 | ||||||||
\(611\) | 15.9138 | 0.643804 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −41.0950 | −1.65981 | −0.829906 | − | 0.557903i | \(-0.811606\pi\) | ||||
−0.829906 | + | 0.557903i | \(0.811606\pi\) | |||||||
\(614\) | 31.0880 | 1.25461 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −3.06406 | −0.123454 | ||||||||
\(617\) | −27.1440 | −1.09278 | −0.546388 | − | 0.837532i | \(-0.683998\pi\) | ||||
−0.546388 | + | 0.837532i | \(0.683998\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 1.83585 | 0.0737892 | 0.0368946 | − | 0.999319i | \(-0.488253\pi\) | ||||
0.0368946 | + | 0.999319i | \(0.488253\pi\) | |||||||
\(620\) | 0.526544 | 0.0211465 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 11.8468 | 0.475014 | ||||||||
\(623\) | 1.06406 | 0.0426305 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 22.7258 | 0.909030 | ||||||||
\(626\) | −34.6606 | −1.38531 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 15.3763 | 0.613582 | ||||||||
\(629\) | −23.8159 | −0.949600 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 43.5714 | 1.73455 | 0.867276 | − | 0.497828i | \(-0.165869\pi\) | ||||
0.867276 | + | 0.497828i | \(0.165869\pi\) | |||||||
\(632\) | −2.95396 | −0.117502 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | −16.4654 | −0.653926 | ||||||||
\(635\) | 0.979033 | 0.0388517 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 2.78276 | 0.110257 | ||||||||
\(638\) | −23.9879 | −0.949689 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | −0.391382 | −0.0154707 | ||||||||
\(641\) | −43.6275 | −1.72318 | −0.861591 | − | 0.507604i | \(-0.830531\pi\) | ||||
−0.861591 | + | 0.507604i | \(0.830531\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 14.6907 | 0.579344 | 0.289672 | − | 0.957126i | \(-0.406454\pi\) | ||||
0.289672 | + | 0.957126i | \(0.406454\pi\) | |||||||
\(644\) | −4.78276 | −0.188467 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 6.22018 | 0.244730 | ||||||||
\(647\) | −19.6145 | −0.771126 | −0.385563 | − | 0.922681i | \(-0.625993\pi\) | ||||
−0.385563 | + | 0.922681i | \(0.625993\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −21.9820 | −0.862868 | ||||||||
\(650\) | 13.4876 | 0.529026 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 17.9389 | 0.702541 | ||||||||
\(653\) | −42.1700 | −1.65024 | −0.825121 | − | 0.564957i | \(-0.808893\pi\) | ||||
−0.825121 | + | 0.564957i | \(0.808893\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 6.04193 | 0.236078 | ||||||||
\(656\) | 4.39138 | 0.171455 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 5.71871 | 0.222939 | ||||||||
\(659\) | −34.1900 | −1.33186 | −0.665928 | − | 0.746016i | \(-0.731964\pi\) | ||||
−0.665928 | + | 0.746016i | \(0.731964\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −31.1370 | −1.21109 | −0.605544 | − | 0.795812i | \(-0.707044\pi\) | ||||
−0.605544 | + | 0.795812i | \(0.707044\pi\) | |||||||
\(662\) | 3.09502 | 0.120291 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | −13.5655 | −0.526445 | ||||||||
\(665\) | 0.391382 | 0.0151772 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −37.4433 | −1.44981 | ||||||||
\(668\) | 13.5295 | 0.523472 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | −4.78276 | −0.184774 | ||||||||
\(671\) | −26.0490 | −1.00561 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −48.6045 | −1.87357 | −0.936783 | − | 0.349910i | \(-0.886212\pi\) | ||||
−0.936783 | + | 0.349910i | \(0.886212\pi\) | |||||||
\(674\) | 24.5324 | 0.944954 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −5.25622 | −0.202162 | ||||||||
\(677\) | −9.81585 | −0.377254 | −0.188627 | − | 0.982049i | \(-0.560404\pi\) | ||||
−0.188627 | + | 0.982049i | \(0.560404\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −4.50147 | −0.172751 | ||||||||
\(680\) | −2.43447 | −0.0933577 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 4.12221 | 0.157848 | ||||||||
\(683\) | 12.6606 | 0.484443 | 0.242221 | − | 0.970221i | \(-0.422124\pi\) | ||||
0.242221 | + | 0.970221i | \(0.422124\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −5.44839 | −0.208172 | ||||||||
\(686\) | 1.00000 | 0.0381802 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 5.82880 | 0.222221 | ||||||||
\(689\) | −19.9138 | −0.758656 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 45.4073 | 1.72737 | 0.863687 | − | 0.504028i | \(-0.168149\pi\) | ||||
0.863687 | + | 0.504028i | \(0.168149\pi\) | |||||||
\(692\) | 8.12811 | 0.308984 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 5.56553 | 0.211265 | ||||||||
\(695\) | 4.25622 | 0.161448 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 27.3152 | 1.03464 | ||||||||
\(698\) | −25.1311 | −0.951225 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 4.84682 | 0.183193 | ||||||||
\(701\) | 11.1871 | 0.422531 | 0.211265 | − | 0.977429i | \(-0.432242\pi\) | ||||
0.211265 | + | 0.977429i | \(0.432242\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 3.82880 | 0.144406 | ||||||||
\(704\) | −3.06406 | −0.115481 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −3.52949 | −0.132834 | ||||||||
\(707\) | 17.1311 | 0.644280 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 13.4014 | 0.503300 | 0.251650 | − | 0.967818i | \(-0.419027\pi\) | ||||
0.251650 | + | 0.967818i | \(0.419027\pi\) | |||||||
\(710\) | 0.366312 | 0.0137475 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 1.06406 | 0.0398771 | ||||||||
\(713\) | 6.43447 | 0.240973 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −3.33714 | −0.124802 | ||||||||
\(716\) | 11.4735 | 0.428783 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 24.9669 | 0.931757 | ||||||||
\(719\) | 16.0000 | 0.596699 | 0.298350 | − | 0.954457i | \(-0.403564\pi\) | ||||
0.298350 | + | 0.954457i | \(0.403564\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 2.09207 | 0.0779129 | ||||||||
\(722\) | −1.00000 | −0.0372161 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 16.3123 | 0.606240 | ||||||||
\(725\) | 37.9448 | 1.40923 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −42.4153 | −1.57310 | −0.786548 | − | 0.617529i | \(-0.788134\pi\) | ||||
−0.786548 | + | 0.617529i | \(0.788134\pi\) | |||||||
\(728\) | 2.78276 | 0.103136 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 1.61567 | 0.0597986 | ||||||||
\(731\) | 36.2562 | 1.34098 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −43.9628 | −1.62380 | −0.811902 | − | 0.583794i | \(-0.801568\pi\) | ||||
−0.811902 | + | 0.583794i | \(0.801568\pi\) | |||||||
\(734\) | 15.2842 | 0.564152 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −4.78276 | −0.176295 | ||||||||
\(737\) | −37.4433 | −1.37924 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 1.57258 | 0.0578483 | 0.0289242 | − | 0.999582i | \(-0.490792\pi\) | ||||
0.0289242 | + | 0.999582i | \(0.490792\pi\) | |||||||
\(740\) | −1.49853 | −0.0550869 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | −7.15613 | −0.262710 | ||||||||
\(743\) | −37.0460 | −1.35909 | −0.679544 | − | 0.733635i | \(-0.737822\pi\) | ||||
−0.679544 | + | 0.733635i | \(0.737822\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 0.696589 | 0.0255210 | ||||||||
\(746\) | 17.0519 | 0.624316 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | −19.0590 | −0.696866 | ||||||||
\(749\) | −14.0921 | −0.514913 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 15.7367 | 0.574241 | 0.287121 | − | 0.957894i | \(-0.407302\pi\) | ||||
0.287121 | + | 0.957894i | \(0.407302\pi\) | |||||||
\(752\) | 5.71871 | 0.208540 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 21.7857 | 0.793389 | ||||||||
\(755\) | 2.07797 | 0.0756251 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 33.3512 | 1.21217 | 0.606086 | − | 0.795399i | \(-0.292739\pi\) | ||||
0.606086 | + | 0.795399i | \(0.292739\pi\) | |||||||
\(758\) | −17.0029 | −0.617575 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0.391382 | 0.0141969 | ||||||||
\(761\) | −20.0059 | −0.725213 | −0.362607 | − | 0.931942i | \(-0.618113\pi\) | ||||
−0.362607 | + | 0.931942i | \(0.618113\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −15.1561 | −0.548689 | ||||||||
\(764\) | 15.4735 | 0.559810 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 29.2231 | 1.05587 | ||||||||
\(767\) | 19.9640 | 0.720857 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 55.0029 | 1.98346 | 0.991729 | − | 0.128353i | \(-0.0409691\pi\) | ||||
0.991729 | + | 0.128353i | \(0.0409691\pi\) | |||||||
\(770\) | −1.19922 | −0.0432168 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 7.00295 | 0.252042 | ||||||||
\(773\) | −32.7526 | −1.17803 | −0.589015 | − | 0.808122i | \(-0.700484\pi\) | ||||
−0.589015 | + | 0.808122i | \(0.700484\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −6.52065 | −0.234229 | ||||||||
\(776\) | −4.50147 | −0.161594 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −26.4404 | −0.947933 | ||||||||
\(779\) | −4.39138 | −0.157338 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 2.86779 | 0.102617 | ||||||||
\(782\) | −29.7497 | −1.06385 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 1.00000 | 0.0357143 | ||||||||
\(785\) | 6.01802 | 0.214792 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 16.2993 | 0.581008 | 0.290504 | − | 0.956874i | \(-0.406177\pi\) | ||||
0.290504 | + | 0.956874i | \(0.406177\pi\) | |||||||
\(788\) | 10.4404 | 0.371923 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | −1.15613 | −0.0411332 | ||||||||
\(791\) | 19.7857 | 0.703499 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 23.6576 | 0.840106 | ||||||||
\(794\) | −18.5074 | −0.656802 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −6.83175 | −0.242145 | ||||||||
\(797\) | −9.50949 | −0.336843 | −0.168422 | − | 0.985715i | \(-0.553867\pi\) | ||||
−0.168422 | + | 0.985715i | \(0.553867\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 35.5714 | 1.25843 | ||||||||
\(800\) | 4.84682 | 0.171361 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | −32.2261 | −1.13794 | ||||||||
\(803\) | 12.6488 | 0.446365 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −1.87189 | −0.0659754 | ||||||||
\(806\) | −3.74378 | −0.131869 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 17.1311 | 0.602669 | ||||||||
\(809\) | 20.0129 | 0.703618 | 0.351809 | − | 0.936072i | \(-0.385567\pi\) | ||||
0.351809 | + | 0.936072i | \(0.385567\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 49.8527 | 1.75057 | 0.875283 | − | 0.483611i | \(-0.160675\pi\) | ||||
0.875283 | + | 0.483611i | \(0.160675\pi\) | |||||||
\(812\) | 7.82880 | 0.274737 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | −11.7317 | −0.411194 | ||||||||
\(815\) | 7.02097 | 0.245934 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −5.82880 | −0.203924 | ||||||||
\(818\) | −19.3763 | −0.677477 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 1.71871 | 0.0600199 | ||||||||
\(821\) | 2.68479 | 0.0936999 | 0.0468500 | − | 0.998902i | \(-0.485082\pi\) | ||||
0.0468500 | + | 0.998902i | \(0.485082\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −28.4764 | −0.992625 | −0.496313 | − | 0.868144i | \(-0.665313\pi\) | ||||
−0.496313 | + | 0.868144i | \(0.665313\pi\) | |||||||
\(824\) | 2.09207 | 0.0728809 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 7.17415 | 0.249621 | ||||||||
\(827\) | 29.0390 | 1.00978 | 0.504892 | − | 0.863182i | \(-0.331532\pi\) | ||||
0.504892 | + | 0.863182i | \(0.331532\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −19.7136 | −0.684683 | −0.342342 | − | 0.939576i | \(-0.611220\pi\) | ||||
−0.342342 | + | 0.939576i | \(0.611220\pi\) | |||||||
\(830\) | −5.30931 | −0.184289 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 2.78276 | 0.0964750 | ||||||||
\(833\) | 6.22018 | 0.215517 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 5.29521 | 0.183248 | ||||||||
\(836\) | 3.06406 | 0.105973 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 27.5354 | 0.951194 | ||||||||
\(839\) | 18.9109 | 0.652876 | 0.326438 | − | 0.945219i | \(-0.394152\pi\) | ||||
0.326438 | + | 0.945219i | \(0.394152\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 32.2901 | 1.11345 | ||||||||
\(842\) | 16.4345 | 0.566369 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | −9.30931 | −0.320440 | ||||||||
\(845\) | −2.05719 | −0.0707696 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 1.61157 | 0.0553741 | ||||||||
\(848\) | −7.15613 | −0.245742 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 30.1481 | 1.03407 | ||||||||
\(851\) | −18.3123 | −0.627736 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −23.7928 | −0.814649 | −0.407324 | − | 0.913284i | \(-0.633538\pi\) | ||||
−0.407324 | + | 0.913284i | \(0.633538\pi\) | |||||||
\(854\) | 8.50147 | 0.290914 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −14.0921 | −0.481657 | ||||||||
\(857\) | −10.0000 | −0.341593 | −0.170797 | − | 0.985306i | \(-0.554634\pi\) | ||||
−0.170797 | + | 0.985306i | \(0.554634\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −12.9669 | −0.442425 | −0.221213 | − | 0.975226i | \(-0.571001\pi\) | ||||
−0.221213 | + | 0.975226i | \(0.571001\pi\) | |||||||
\(860\) | 2.28129 | 0.0777914 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 40.9979 | 1.39639 | ||||||||
\(863\) | −23.0519 | −0.784697 | −0.392348 | − | 0.919817i | \(-0.628337\pi\) | ||||
−0.392348 | + | 0.919817i | \(0.628337\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 3.18120 | 0.108164 | ||||||||
\(866\) | 22.4835 | 0.764019 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | −1.34535 | −0.0456640 | ||||||||
\(869\) | −9.05111 | −0.307038 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 34.0059 | 1.15225 | ||||||||
\(872\) | −15.1561 | −0.513251 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 4.78276 | 0.161779 | ||||||||
\(875\) | 3.85387 | 0.130285 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 17.8468 | 0.602644 | 0.301322 | − | 0.953522i | \(-0.402572\pi\) | ||||
0.301322 | + | 0.953522i | \(0.402572\pi\) | |||||||
\(878\) | 18.9109 | 0.638211 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | −1.19922 | −0.0404256 | ||||||||
\(881\) | −6.71069 | −0.226089 | −0.113044 | − | 0.993590i | \(-0.536060\pi\) | ||||
−0.113044 | + | 0.993590i | \(0.536060\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 13.3144 | 0.448064 | 0.224032 | − | 0.974582i | \(-0.428078\pi\) | ||||
0.224032 | + | 0.974582i | \(0.428078\pi\) | |||||||
\(884\) | 17.3093 | 0.582175 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −10.0850 | −0.338813 | ||||||||
\(887\) | −17.2733 | −0.579980 | −0.289990 | − | 0.957030i | \(-0.593652\pi\) | ||||
−0.289990 | + | 0.957030i | \(0.593652\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −2.50147 | −0.0838968 | ||||||||
\(890\) | 0.416452 | 0.0139595 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | −2.31226 | −0.0774201 | ||||||||
\(893\) | −5.71871 | −0.191369 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 4.49051 | 0.150101 | ||||||||
\(896\) | 1.00000 | 0.0334077 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 17.9138 | 0.597792 | ||||||||
\(899\) | −10.5324 | −0.351277 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −44.5124 | −1.48292 | ||||||||
\(902\) | 13.4554 | 0.448017 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 19.7857 | 0.658063 | ||||||||
\(905\) | 6.38433 | 0.212222 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 6.99705 | 0.232333 | 0.116167 | − | 0.993230i | \(-0.462939\pi\) | ||||
0.116167 | + | 0.993230i | \(0.462939\pi\) | |||||||
\(908\) | −12.4404 | −0.412848 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 1.08913 | 0.0361041 | ||||||||
\(911\) | −24.1050 | −0.798635 | −0.399318 | − | 0.916813i | \(-0.630753\pi\) | ||||
−0.399318 | + | 0.916813i | \(0.630753\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −41.5655 | −1.37562 | ||||||||
\(914\) | −23.8527 | −0.788978 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 15.6086 | 0.515723 | ||||||||
\(917\) | −15.4374 | −0.509789 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −55.3011 | −1.82422 | −0.912108 | − | 0.409951i | \(-0.865546\pi\) | ||||
−0.912108 | + | 0.409951i | \(0.865546\pi\) | |||||||
\(920\) | −1.87189 | −0.0617144 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 22.2512 | 0.732803 | ||||||||
\(923\) | −2.60451 | −0.0857286 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 18.5575 | 0.610167 | ||||||||
\(926\) | −27.8778 | −0.916121 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 7.82880 | 0.256993 | ||||||||
\(929\) | −4.60451 | −0.151069 | −0.0755346 | − | 0.997143i | \(-0.524066\pi\) | ||||
−0.0755346 | + | 0.997143i | \(0.524066\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −1.00000 | −0.0327737 | ||||||||
\(932\) | 5.28424 | 0.173091 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | −24.0980 | −0.788510 | ||||||||
\(935\) | −7.45935 | −0.243947 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 45.7195 | 1.49359 | 0.746796 | − | 0.665053i | \(-0.231591\pi\) | ||||
0.746796 | + | 0.665053i | \(0.231591\pi\) | |||||||
\(938\) | 12.2202 | 0.399003 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 2.23820 | 0.0730021 | ||||||||
\(941\) | −32.5324 | −1.06053 | −0.530264 | − | 0.847833i | \(-0.677907\pi\) | ||||
−0.530264 | + | 0.847833i | \(0.677907\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 21.0029 | 0.683950 | ||||||||
\(944\) | 7.17415 | 0.233499 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 17.8598 | 0.580671 | ||||||||
\(947\) | 35.0641 | 1.13943 | 0.569714 | − | 0.821843i | \(-0.307054\pi\) | ||||
0.569714 | + | 0.821843i | \(0.307054\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −11.4876 | −0.372902 | ||||||||
\(950\) | −4.84682 | −0.157252 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 6.22018 | 0.201597 | ||||||||
\(953\) | −15.9941 | −0.518100 | −0.259050 | − | 0.965864i | \(-0.583409\pi\) | ||||
−0.259050 | + | 0.965864i | \(0.583409\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 6.05604 | 0.195969 | ||||||||
\(956\) | −1.87189 | −0.0605412 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | −8.92382 | −0.288316 | ||||||||
\(959\) | 13.9209 | 0.449529 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −29.1900 | −0.941614 | ||||||||
\(962\) | 10.6547 | 0.343520 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | −22.4835 | −0.724143 | ||||||||
\(965\) | 2.74083 | 0.0882305 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 16.0721 | 0.516843 | 0.258422 | − | 0.966032i | \(-0.416798\pi\) | ||||
0.258422 | + | 0.966032i | \(0.416798\pi\) | |||||||
\(968\) | 1.61157 | 0.0517977 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | −1.76180 | −0.0565679 | ||||||||
\(971\) | −34.6715 | −1.11266 | −0.556331 | − | 0.830961i | \(-0.687791\pi\) | ||||
−0.556331 | + | 0.830961i | \(0.687791\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −10.8748 | −0.348631 | ||||||||
\(974\) | 41.0578 | 1.31558 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 8.50147 | 0.272126 | ||||||||
\(977\) | 12.5685 | 0.402101 | 0.201051 | − | 0.979581i | \(-0.435564\pi\) | ||||
0.201051 | + | 0.979581i | \(0.435564\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 3.26032 | 0.104200 | ||||||||
\(980\) | 0.391382 | 0.0125023 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | −20.8807 | −0.666331 | ||||||||
\(983\) | −1.56553 | −0.0499326 | −0.0249663 | − | 0.999688i | \(-0.507948\pi\) | ||||
−0.0249663 | + | 0.999688i | \(0.507948\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 4.08618 | 0.130196 | ||||||||
\(986\) | 48.6966 | 1.55082 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −2.78276 | −0.0885315 | ||||||||
\(989\) | 27.8778 | 0.886462 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −42.6355 | −1.35436 | −0.677180 | − | 0.735817i | \(-0.736798\pi\) | ||||
−0.677180 | + | 0.735817i | \(0.736798\pi\) | |||||||
\(992\) | −1.34535 | −0.0427148 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | −0.935945 | −0.0296864 | ||||||||
\(995\) | −2.67383 | −0.0847660 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 61.2721 | 1.94051 | 0.970254 | − | 0.242090i | \(-0.0778330\pi\) | ||||
0.970254 | + | 0.242090i | \(0.0778330\pi\) | |||||||
\(998\) | −12.8619 | −0.407136 | ||||||||
\(999\) | 0 | 0 |
(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 | 2394.2.a.ba.1.3 | 3 | ||
3.2 | odd | 2 | 266.2.a.d.1.3 | ✓ | 3 | ||
12.11 | even | 2 | 2128.2.a.s.1.1 | 3 | |||
15.14 | odd | 2 | 6650.2.a.cd.1.1 | 3 | |||
21.20 | even | 2 | 1862.2.a.r.1.1 | 3 | |||
24.5 | odd | 2 | 8512.2.a.bm.1.1 | 3 | |||
24.11 | even | 2 | 8512.2.a.bj.1.3 | 3 | |||
57.56 | even | 2 | 5054.2.a.r.1.1 | 3 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
266.2.a.d.1.3 | ✓ | 3 | 3.2 | odd | 2 | ||
1862.2.a.r.1.1 | 3 | 21.20 | even | 2 | |||
2128.2.a.s.1.1 | 3 | 12.11 | even | 2 | |||
2394.2.a.ba.1.3 | 3 | 1.1 | even | 1 | trivial | ||
5054.2.a.r.1.1 | 3 | 57.56 | even | 2 | |||
6650.2.a.cd.1.1 | 3 | 15.14 | odd | 2 | |||
8512.2.a.bj.1.3 | 3 | 24.11 | even | 2 | |||
8512.2.a.bm.1.1 | 3 | 24.5 | odd | 2 |