Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [3549,2,Mod(1,3549)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(3549, 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("3549.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 3549 = 3 \cdot 7 \cdot 13^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 3549.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: | \(28.3389076774\) |
Analytic rank: | \(0\) |
Dimension: | \(9\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{9} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{9} - x^{8} - 11x^{7} + 8x^{6} + 37x^{5} - 18x^{4} - 41x^{3} + 12x^{2} + 6x - 1 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.8 | ||
Root | \(-1.60159\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 3549.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 1.60159 | 1.13250 | 0.566248 | − | 0.824235i | \(-0.308394\pi\) | ||||
0.566248 | + | 0.824235i | \(0.308394\pi\) | |||||||
\(3\) | −1.00000 | −0.577350 | ||||||||
\(4\) | 0.565099 | 0.282549 | ||||||||
\(5\) | 2.27787 | 1.01870 | 0.509348 | − | 0.860560i | \(-0.329887\pi\) | ||||
0.509348 | + | 0.860560i | \(0.329887\pi\) | |||||||
\(6\) | −1.60159 | −0.653847 | ||||||||
\(7\) | 1.00000 | 0.377964 | ||||||||
\(8\) | −2.29813 | −0.812511 | ||||||||
\(9\) | 1.00000 | 0.333333 | ||||||||
\(10\) | 3.64823 | 1.15367 | ||||||||
\(11\) | 2.53947 | 0.765678 | 0.382839 | − | 0.923815i | \(-0.374946\pi\) | ||||
0.382839 | + | 0.923815i | \(0.374946\pi\) | |||||||
\(12\) | −0.565099 | −0.163130 | ||||||||
\(13\) | 0 | 0 | ||||||||
\(14\) | 1.60159 | 0.428044 | ||||||||
\(15\) | −2.27787 | −0.588145 | ||||||||
\(16\) | −4.81086 | −1.20272 | ||||||||
\(17\) | −4.05395 | −0.983228 | −0.491614 | − | 0.870813i | \(-0.663593\pi\) | ||||
−0.491614 | + | 0.870813i | \(0.663593\pi\) | |||||||
\(18\) | 1.60159 | 0.377499 | ||||||||
\(19\) | 7.93457 | 1.82032 | 0.910158 | − | 0.414261i | \(-0.135960\pi\) | ||||
0.910158 | + | 0.414261i | \(0.135960\pi\) | |||||||
\(20\) | 1.28722 | 0.287832 | ||||||||
\(21\) | −1.00000 | −0.218218 | ||||||||
\(22\) | 4.06719 | 0.867128 | ||||||||
\(23\) | 0.458029 | 0.0955057 | 0.0477529 | − | 0.998859i | \(-0.484794\pi\) | ||||
0.0477529 | + | 0.998859i | \(0.484794\pi\) | |||||||
\(24\) | 2.29813 | 0.469103 | ||||||||
\(25\) | 0.188713 | 0.0377425 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −1.00000 | −0.192450 | ||||||||
\(28\) | 0.565099 | 0.106794 | ||||||||
\(29\) | 6.01106 | 1.11623 | 0.558113 | − | 0.829765i | \(-0.311526\pi\) | ||||
0.558113 | + | 0.829765i | \(0.311526\pi\) | |||||||
\(30\) | −3.64823 | −0.666072 | ||||||||
\(31\) | −0.340678 | −0.0611875 | −0.0305938 | − | 0.999532i | \(-0.509740\pi\) | ||||
−0.0305938 | + | 0.999532i | \(0.509740\pi\) | |||||||
\(32\) | −3.10879 | −0.549561 | ||||||||
\(33\) | −2.53947 | −0.442064 | ||||||||
\(34\) | −6.49278 | −1.11350 | ||||||||
\(35\) | 2.27787 | 0.385031 | ||||||||
\(36\) | 0.565099 | 0.0941831 | ||||||||
\(37\) | 4.74702 | 0.780405 | 0.390202 | − | 0.920729i | \(-0.372405\pi\) | ||||
0.390202 | + | 0.920729i | \(0.372405\pi\) | |||||||
\(38\) | 12.7080 | 2.06150 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | −5.23485 | −0.827702 | ||||||||
\(41\) | 8.88028 | 1.38687 | 0.693433 | − | 0.720521i | \(-0.256097\pi\) | ||||
0.693433 | + | 0.720521i | \(0.256097\pi\) | |||||||
\(42\) | −1.60159 | −0.247131 | ||||||||
\(43\) | −2.14282 | −0.326777 | −0.163389 | − | 0.986562i | \(-0.552242\pi\) | ||||
−0.163389 | + | 0.986562i | \(0.552242\pi\) | |||||||
\(44\) | 1.43505 | 0.216342 | ||||||||
\(45\) | 2.27787 | 0.339565 | ||||||||
\(46\) | 0.733576 | 0.108160 | ||||||||
\(47\) | −7.16883 | −1.04568 | −0.522841 | − | 0.852430i | \(-0.675128\pi\) | ||||
−0.522841 | + | 0.852430i | \(0.675128\pi\) | |||||||
\(48\) | 4.81086 | 0.694388 | ||||||||
\(49\) | 1.00000 | 0.142857 | ||||||||
\(50\) | 0.302241 | 0.0427433 | ||||||||
\(51\) | 4.05395 | 0.567667 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 3.30421 | 0.453868 | 0.226934 | − | 0.973910i | \(-0.427130\pi\) | ||||
0.226934 | + | 0.973910i | \(0.427130\pi\) | |||||||
\(54\) | −1.60159 | −0.217949 | ||||||||
\(55\) | 5.78459 | 0.779993 | ||||||||
\(56\) | −2.29813 | −0.307100 | ||||||||
\(57\) | −7.93457 | −1.05096 | ||||||||
\(58\) | 9.62727 | 1.26412 | ||||||||
\(59\) | 4.30373 | 0.560298 | 0.280149 | − | 0.959957i | \(-0.409616\pi\) | ||||
0.280149 | + | 0.959957i | \(0.409616\pi\) | |||||||
\(60\) | −1.28722 | −0.166180 | ||||||||
\(61\) | −11.4865 | −1.47069 | −0.735347 | − | 0.677691i | \(-0.762981\pi\) | ||||
−0.735347 | + | 0.677691i | \(0.762981\pi\) | |||||||
\(62\) | −0.545627 | −0.0692947 | ||||||||
\(63\) | 1.00000 | 0.125988 | ||||||||
\(64\) | 4.64271 | 0.580339 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | −4.06719 | −0.500637 | ||||||||
\(67\) | 10.4979 | 1.28252 | 0.641258 | − | 0.767325i | \(-0.278413\pi\) | ||||
0.641258 | + | 0.767325i | \(0.278413\pi\) | |||||||
\(68\) | −2.29088 | −0.277810 | ||||||||
\(69\) | −0.458029 | −0.0551402 | ||||||||
\(70\) | 3.64823 | 0.436047 | ||||||||
\(71\) | 4.25291 | 0.504727 | 0.252364 | − | 0.967633i | \(-0.418792\pi\) | ||||
0.252364 | + | 0.967633i | \(0.418792\pi\) | |||||||
\(72\) | −2.29813 | −0.270837 | ||||||||
\(73\) | 1.59136 | 0.186255 | 0.0931273 | − | 0.995654i | \(-0.470314\pi\) | ||||
0.0931273 | + | 0.995654i | \(0.470314\pi\) | |||||||
\(74\) | 7.60279 | 0.883806 | ||||||||
\(75\) | −0.188713 | −0.0217907 | ||||||||
\(76\) | 4.48382 | 0.514329 | ||||||||
\(77\) | 2.53947 | 0.289399 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −9.42077 | −1.05992 | −0.529960 | − | 0.848023i | \(-0.677793\pi\) | ||||
−0.529960 | + | 0.848023i | \(0.677793\pi\) | |||||||
\(80\) | −10.9585 | −1.22520 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | 14.2226 | 1.57062 | ||||||||
\(83\) | 1.87743 | 0.206074 | 0.103037 | − | 0.994678i | \(-0.467144\pi\) | ||||
0.103037 | + | 0.994678i | \(0.467144\pi\) | |||||||
\(84\) | −0.565099 | −0.0616573 | ||||||||
\(85\) | −9.23439 | −1.00161 | ||||||||
\(86\) | −3.43193 | −0.370074 | ||||||||
\(87\) | −6.01106 | −0.644453 | ||||||||
\(88\) | −5.83602 | −0.622121 | ||||||||
\(89\) | 17.9934 | 1.90730 | 0.953648 | − | 0.300923i | \(-0.0972948\pi\) | ||||
0.953648 | + | 0.300923i | \(0.0972948\pi\) | |||||||
\(90\) | 3.64823 | 0.384557 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | 0.258832 | 0.0269851 | ||||||||
\(93\) | 0.340678 | 0.0353266 | ||||||||
\(94\) | −11.4815 | −1.18423 | ||||||||
\(95\) | 18.0740 | 1.85435 | ||||||||
\(96\) | 3.10879 | 0.317289 | ||||||||
\(97\) | 18.9563 | 1.92472 | 0.962359 | − | 0.271780i | \(-0.0876123\pi\) | ||||
0.962359 | + | 0.271780i | \(0.0876123\pi\) | |||||||
\(98\) | 1.60159 | 0.161785 | ||||||||
\(99\) | 2.53947 | 0.255226 | ||||||||
\(100\) | 0.106641 | 0.0106641 | ||||||||
\(101\) | −4.02671 | −0.400672 | −0.200336 | − | 0.979727i | \(-0.564203\pi\) | ||||
−0.200336 | + | 0.979727i | \(0.564203\pi\) | |||||||
\(102\) | 6.49278 | 0.642881 | ||||||||
\(103\) | −11.3431 | −1.11767 | −0.558835 | − | 0.829279i | \(-0.688751\pi\) | ||||
−0.558835 | + | 0.829279i | \(0.688751\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −2.27787 | −0.222298 | ||||||||
\(106\) | 5.29200 | 0.514004 | ||||||||
\(107\) | −15.8563 | −1.53289 | −0.766444 | − | 0.642311i | \(-0.777976\pi\) | ||||
−0.766444 | + | 0.642311i | \(0.777976\pi\) | |||||||
\(108\) | −0.565099 | −0.0543767 | ||||||||
\(109\) | 13.1406 | 1.25864 | 0.629320 | − | 0.777146i | \(-0.283334\pi\) | ||||
0.629320 | + | 0.777146i | \(0.283334\pi\) | |||||||
\(110\) | 9.26455 | 0.883340 | ||||||||
\(111\) | −4.74702 | −0.450567 | ||||||||
\(112\) | −4.81086 | −0.454584 | ||||||||
\(113\) | 0.392747 | 0.0369465 | 0.0184733 | − | 0.999829i | \(-0.494119\pi\) | ||||
0.0184733 | + | 0.999829i | \(0.494119\pi\) | |||||||
\(114\) | −12.7080 | −1.19021 | ||||||||
\(115\) | 1.04333 | 0.0972913 | ||||||||
\(116\) | 3.39684 | 0.315389 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 6.89282 | 0.634535 | ||||||||
\(119\) | −4.05395 | −0.371625 | ||||||||
\(120\) | 5.23485 | 0.477874 | ||||||||
\(121\) | −4.55111 | −0.413737 | ||||||||
\(122\) | −18.3967 | −1.66556 | ||||||||
\(123\) | −8.88028 | −0.800708 | ||||||||
\(124\) | −0.192517 | −0.0172885 | ||||||||
\(125\) | −10.9595 | −0.980248 | ||||||||
\(126\) | 1.60159 | 0.142681 | ||||||||
\(127\) | 15.9958 | 1.41940 | 0.709701 | − | 0.704503i | \(-0.248830\pi\) | ||||
0.709701 | + | 0.704503i | \(0.248830\pi\) | |||||||
\(128\) | 13.6533 | 1.20679 | ||||||||
\(129\) | 2.14282 | 0.188665 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 16.6090 | 1.45113 | 0.725567 | − | 0.688151i | \(-0.241577\pi\) | ||||
0.725567 | + | 0.688151i | \(0.241577\pi\) | |||||||
\(132\) | −1.43505 | −0.124905 | ||||||||
\(133\) | 7.93457 | 0.688015 | ||||||||
\(134\) | 16.8133 | 1.45245 | ||||||||
\(135\) | −2.27787 | −0.196048 | ||||||||
\(136\) | 9.31650 | 0.798883 | ||||||||
\(137\) | −1.57748 | −0.134773 | −0.0673865 | − | 0.997727i | \(-0.521466\pi\) | ||||
−0.0673865 | + | 0.997727i | \(0.521466\pi\) | |||||||
\(138\) | −0.733576 | −0.0624462 | ||||||||
\(139\) | 12.0257 | 1.02000 | 0.510001 | − | 0.860174i | \(-0.329645\pi\) | ||||
0.510001 | + | 0.860174i | \(0.329645\pi\) | |||||||
\(140\) | 1.28722 | 0.108790 | ||||||||
\(141\) | 7.16883 | 0.603724 | ||||||||
\(142\) | 6.81142 | 0.571602 | ||||||||
\(143\) | 0 | 0 | ||||||||
\(144\) | −4.81086 | −0.400905 | ||||||||
\(145\) | 13.6924 | 1.13710 | ||||||||
\(146\) | 2.54871 | 0.210933 | ||||||||
\(147\) | −1.00000 | −0.0824786 | ||||||||
\(148\) | 2.68253 | 0.220503 | ||||||||
\(149\) | −24.1801 | −1.98091 | −0.990456 | − | 0.137827i | \(-0.955988\pi\) | ||||
−0.990456 | + | 0.137827i | \(0.955988\pi\) | |||||||
\(150\) | −0.302241 | −0.0246779 | ||||||||
\(151\) | −8.98472 | −0.731167 | −0.365583 | − | 0.930779i | \(-0.619130\pi\) | ||||
−0.365583 | + | 0.930779i | \(0.619130\pi\) | |||||||
\(152\) | −18.2347 | −1.47903 | ||||||||
\(153\) | −4.05395 | −0.327743 | ||||||||
\(154\) | 4.06719 | 0.327744 | ||||||||
\(155\) | −0.776021 | −0.0623315 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −2.71212 | −0.216451 | −0.108225 | − | 0.994126i | \(-0.534517\pi\) | ||||
−0.108225 | + | 0.994126i | \(0.534517\pi\) | |||||||
\(158\) | −15.0882 | −1.20036 | ||||||||
\(159\) | −3.30421 | −0.262041 | ||||||||
\(160\) | −7.08142 | −0.559836 | ||||||||
\(161\) | 0.458029 | 0.0360978 | ||||||||
\(162\) | 1.60159 | 0.125833 | ||||||||
\(163\) | −17.3562 | −1.35944 | −0.679722 | − | 0.733470i | \(-0.737899\pi\) | ||||
−0.679722 | + | 0.733470i | \(0.737899\pi\) | |||||||
\(164\) | 5.01823 | 0.391858 | ||||||||
\(165\) | −5.78459 | −0.450329 | ||||||||
\(166\) | 3.00687 | 0.233379 | ||||||||
\(167\) | 12.7077 | 0.983349 | 0.491674 | − | 0.870779i | \(-0.336385\pi\) | ||||
0.491674 | + | 0.870779i | \(0.336385\pi\) | |||||||
\(168\) | 2.29813 | 0.177304 | ||||||||
\(169\) | 0 | 0 | ||||||||
\(170\) | −14.7897 | −1.13432 | ||||||||
\(171\) | 7.93457 | 0.606772 | ||||||||
\(172\) | −1.21091 | −0.0923307 | ||||||||
\(173\) | 1.35443 | 0.102975 | 0.0514876 | − | 0.998674i | \(-0.483604\pi\) | ||||
0.0514876 | + | 0.998674i | \(0.483604\pi\) | |||||||
\(174\) | −9.62727 | −0.729842 | ||||||||
\(175\) | 0.188713 | 0.0142653 | ||||||||
\(176\) | −12.2170 | −0.920892 | ||||||||
\(177\) | −4.30373 | −0.323488 | ||||||||
\(178\) | 28.8181 | 2.16001 | ||||||||
\(179\) | 21.0691 | 1.57478 | 0.787390 | − | 0.616456i | \(-0.211432\pi\) | ||||
0.787390 | + | 0.616456i | \(0.211432\pi\) | |||||||
\(180\) | 1.28722 | 0.0959440 | ||||||||
\(181\) | −0.269780 | −0.0200526 | −0.0100263 | − | 0.999950i | \(-0.503192\pi\) | ||||
−0.0100263 | + | 0.999950i | \(0.503192\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 11.4865 | 0.849106 | ||||||||
\(184\) | −1.05261 | −0.0775994 | ||||||||
\(185\) | 10.8131 | 0.794995 | ||||||||
\(186\) | 0.545627 | 0.0400073 | ||||||||
\(187\) | −10.2949 | −0.752836 | ||||||||
\(188\) | −4.05110 | −0.295457 | ||||||||
\(189\) | −1.00000 | −0.0727393 | ||||||||
\(190\) | 28.9471 | 2.10005 | ||||||||
\(191\) | −6.28281 | −0.454608 | −0.227304 | − | 0.973824i | \(-0.572991\pi\) | ||||
−0.227304 | + | 0.973824i | \(0.572991\pi\) | |||||||
\(192\) | −4.64271 | −0.335059 | ||||||||
\(193\) | 19.3154 | 1.39035 | 0.695177 | − | 0.718839i | \(-0.255326\pi\) | ||||
0.695177 | + | 0.718839i | \(0.255326\pi\) | |||||||
\(194\) | 30.3602 | 2.17974 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0.565099 | 0.0403642 | ||||||||
\(197\) | −21.0050 | −1.49654 | −0.748272 | − | 0.663392i | \(-0.769116\pi\) | ||||
−0.748272 | + | 0.663392i | \(0.769116\pi\) | |||||||
\(198\) | 4.06719 | 0.289043 | ||||||||
\(199\) | 17.0312 | 1.20731 | 0.603653 | − | 0.797247i | \(-0.293711\pi\) | ||||
0.603653 | + | 0.797247i | \(0.293711\pi\) | |||||||
\(200\) | −0.433686 | −0.0306662 | ||||||||
\(201\) | −10.4979 | −0.740461 | ||||||||
\(202\) | −6.44914 | −0.453760 | ||||||||
\(203\) | 6.01106 | 0.421894 | ||||||||
\(204\) | 2.29088 | 0.160394 | ||||||||
\(205\) | 20.2282 | 1.41280 | ||||||||
\(206\) | −18.1670 | −1.26576 | ||||||||
\(207\) | 0.458029 | 0.0318352 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 20.1496 | 1.39378 | ||||||||
\(210\) | −3.64823 | −0.251752 | ||||||||
\(211\) | −10.0436 | −0.691428 | −0.345714 | − | 0.938340i | \(-0.612363\pi\) | ||||
−0.345714 | + | 0.938340i | \(0.612363\pi\) | |||||||
\(212\) | 1.86721 | 0.128240 | ||||||||
\(213\) | −4.25291 | −0.291404 | ||||||||
\(214\) | −25.3954 | −1.73599 | ||||||||
\(215\) | −4.88108 | −0.332887 | ||||||||
\(216\) | 2.29813 | 0.156368 | ||||||||
\(217\) | −0.340678 | −0.0231267 | ||||||||
\(218\) | 21.0459 | 1.42541 | ||||||||
\(219\) | −1.59136 | −0.107534 | ||||||||
\(220\) | 3.26886 | 0.220387 | ||||||||
\(221\) | 0 | 0 | ||||||||
\(222\) | −7.60279 | −0.510266 | ||||||||
\(223\) | 1.30689 | 0.0875156 | 0.0437578 | − | 0.999042i | \(-0.486067\pi\) | ||||
0.0437578 | + | 0.999042i | \(0.486067\pi\) | |||||||
\(224\) | −3.10879 | −0.207714 | ||||||||
\(225\) | 0.188713 | 0.0125808 | ||||||||
\(226\) | 0.629020 | 0.0418418 | ||||||||
\(227\) | 7.31823 | 0.485728 | 0.242864 | − | 0.970060i | \(-0.421913\pi\) | ||||
0.242864 | + | 0.970060i | \(0.421913\pi\) | |||||||
\(228\) | −4.48382 | −0.296948 | ||||||||
\(229\) | −16.5282 | −1.09221 | −0.546107 | − | 0.837715i | \(-0.683891\pi\) | ||||
−0.546107 | + | 0.837715i | \(0.683891\pi\) | |||||||
\(230\) | 1.67099 | 0.110182 | ||||||||
\(231\) | −2.53947 | −0.167085 | ||||||||
\(232\) | −13.8142 | −0.906946 | ||||||||
\(233\) | 5.48450 | 0.359302 | 0.179651 | − | 0.983730i | \(-0.442503\pi\) | ||||
0.179651 | + | 0.983730i | \(0.442503\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −16.3297 | −1.06523 | ||||||||
\(236\) | 2.43203 | 0.158312 | ||||||||
\(237\) | 9.42077 | 0.611945 | ||||||||
\(238\) | −6.49278 | −0.420864 | ||||||||
\(239\) | 17.8572 | 1.15509 | 0.577543 | − | 0.816360i | \(-0.304012\pi\) | ||||
0.577543 | + | 0.816360i | \(0.304012\pi\) | |||||||
\(240\) | 10.9585 | 0.707371 | ||||||||
\(241\) | 23.1081 | 1.48852 | 0.744262 | − | 0.667887i | \(-0.232801\pi\) | ||||
0.744262 | + | 0.667887i | \(0.232801\pi\) | |||||||
\(242\) | −7.28903 | −0.468556 | ||||||||
\(243\) | −1.00000 | −0.0641500 | ||||||||
\(244\) | −6.49100 | −0.415544 | ||||||||
\(245\) | 2.27787 | 0.145528 | ||||||||
\(246\) | −14.2226 | −0.906799 | ||||||||
\(247\) | 0 | 0 | ||||||||
\(248\) | 0.782921 | 0.0497155 | ||||||||
\(249\) | −1.87743 | −0.118977 | ||||||||
\(250\) | −17.5527 | −1.11013 | ||||||||
\(251\) | 11.7442 | 0.741290 | 0.370645 | − | 0.928775i | \(-0.379137\pi\) | ||||
0.370645 | + | 0.928775i | \(0.379137\pi\) | |||||||
\(252\) | 0.565099 | 0.0355979 | ||||||||
\(253\) | 1.16315 | 0.0731266 | ||||||||
\(254\) | 25.6188 | 1.60747 | ||||||||
\(255\) | 9.23439 | 0.578280 | ||||||||
\(256\) | 12.5816 | 0.786350 | ||||||||
\(257\) | −9.53811 | −0.594971 | −0.297486 | − | 0.954726i | \(-0.596148\pi\) | ||||
−0.297486 | + | 0.954726i | \(0.596148\pi\) | |||||||
\(258\) | 3.43193 | 0.213662 | ||||||||
\(259\) | 4.74702 | 0.294965 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 6.01106 | 0.372075 | ||||||||
\(262\) | 26.6008 | 1.64341 | ||||||||
\(263\) | −5.26624 | −0.324730 | −0.162365 | − | 0.986731i | \(-0.551912\pi\) | ||||
−0.162365 | + | 0.986731i | \(0.551912\pi\) | |||||||
\(264\) | 5.83602 | 0.359182 | ||||||||
\(265\) | 7.52658 | 0.462354 | ||||||||
\(266\) | 12.7080 | 0.779175 | ||||||||
\(267\) | −17.9934 | −1.10118 | ||||||||
\(268\) | 5.93232 | 0.362374 | ||||||||
\(269\) | 0.602644 | 0.0367438 | 0.0183719 | − | 0.999831i | \(-0.494152\pi\) | ||||
0.0183719 | + | 0.999831i | \(0.494152\pi\) | |||||||
\(270\) | −3.64823 | −0.222024 | ||||||||
\(271\) | −5.69585 | −0.345998 | −0.172999 | − | 0.984922i | \(-0.555346\pi\) | ||||
−0.172999 | + | 0.984922i | \(0.555346\pi\) | |||||||
\(272\) | 19.5030 | 1.18254 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −2.52648 | −0.152630 | ||||||||
\(275\) | 0.479229 | 0.0288986 | ||||||||
\(276\) | −0.258832 | −0.0155798 | ||||||||
\(277\) | −8.00692 | −0.481089 | −0.240545 | − | 0.970638i | \(-0.577326\pi\) | ||||
−0.240545 | + | 0.970638i | \(0.577326\pi\) | |||||||
\(278\) | 19.2602 | 1.15515 | ||||||||
\(279\) | −0.340678 | −0.0203958 | ||||||||
\(280\) | −5.23485 | −0.312842 | ||||||||
\(281\) | −3.01814 | −0.180047 | −0.0900236 | − | 0.995940i | \(-0.528694\pi\) | ||||
−0.0900236 | + | 0.995940i | \(0.528694\pi\) | |||||||
\(282\) | 11.4815 | 0.683716 | ||||||||
\(283\) | 8.91703 | 0.530062 | 0.265031 | − | 0.964240i | \(-0.414618\pi\) | ||||
0.265031 | + | 0.964240i | \(0.414618\pi\) | |||||||
\(284\) | 2.40331 | 0.142610 | ||||||||
\(285\) | −18.0740 | −1.07061 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 8.88028 | 0.524186 | ||||||||
\(288\) | −3.10879 | −0.183187 | ||||||||
\(289\) | −0.565477 | −0.0332633 | ||||||||
\(290\) | 21.9297 | 1.28776 | ||||||||
\(291\) | −18.9563 | −1.11124 | ||||||||
\(292\) | 0.899276 | 0.0526261 | ||||||||
\(293\) | −5.32016 | −0.310807 | −0.155403 | − | 0.987851i | \(-0.549668\pi\) | ||||
−0.155403 | + | 0.987851i | \(0.549668\pi\) | |||||||
\(294\) | −1.60159 | −0.0934068 | ||||||||
\(295\) | 9.80335 | 0.570773 | ||||||||
\(296\) | −10.9092 | −0.634087 | ||||||||
\(297\) | −2.53947 | −0.147355 | ||||||||
\(298\) | −38.7267 | −2.24338 | ||||||||
\(299\) | 0 | 0 | ||||||||
\(300\) | −0.106641 | −0.00615694 | ||||||||
\(301\) | −2.14282 | −0.123510 | ||||||||
\(302\) | −14.3899 | −0.828044 | ||||||||
\(303\) | 4.02671 | 0.231328 | ||||||||
\(304\) | −38.1721 | −2.18932 | ||||||||
\(305\) | −26.1648 | −1.49819 | ||||||||
\(306\) | −6.49278 | −0.371167 | ||||||||
\(307\) | −3.65245 | −0.208457 | −0.104228 | − | 0.994553i | \(-0.533237\pi\) | ||||
−0.104228 | + | 0.994553i | \(0.533237\pi\) | |||||||
\(308\) | 1.43505 | 0.0817695 | ||||||||
\(309\) | 11.3431 | 0.645287 | ||||||||
\(310\) | −1.24287 | −0.0705903 | ||||||||
\(311\) | 4.97775 | 0.282262 | 0.141131 | − | 0.989991i | \(-0.454926\pi\) | ||||
0.141131 | + | 0.989991i | \(0.454926\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −30.8020 | −1.74103 | −0.870516 | − | 0.492140i | \(-0.836215\pi\) | ||||
−0.870516 | + | 0.492140i | \(0.836215\pi\) | |||||||
\(314\) | −4.34371 | −0.245130 | ||||||||
\(315\) | 2.27787 | 0.128344 | ||||||||
\(316\) | −5.32367 | −0.299480 | ||||||||
\(317\) | −22.5252 | −1.26514 | −0.632570 | − | 0.774503i | \(-0.718000\pi\) | ||||
−0.632570 | + | 0.774503i | \(0.718000\pi\) | |||||||
\(318\) | −5.29200 | −0.296761 | ||||||||
\(319\) | 15.2649 | 0.854670 | ||||||||
\(320\) | 10.5755 | 0.591190 | ||||||||
\(321\) | 15.8563 | 0.885013 | ||||||||
\(322\) | 0.733576 | 0.0408806 | ||||||||
\(323\) | −32.1664 | −1.78979 | ||||||||
\(324\) | 0.565099 | 0.0313944 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | −27.7976 | −1.53957 | ||||||||
\(327\) | −13.1406 | −0.726676 | ||||||||
\(328\) | −20.4080 | −1.12684 | ||||||||
\(329\) | −7.16883 | −0.395230 | ||||||||
\(330\) | −9.26455 | −0.509997 | ||||||||
\(331\) | 4.73222 | 0.260106 | 0.130053 | − | 0.991507i | \(-0.458485\pi\) | ||||
0.130053 | + | 0.991507i | \(0.458485\pi\) | |||||||
\(332\) | 1.06093 | 0.0582262 | ||||||||
\(333\) | 4.74702 | 0.260135 | ||||||||
\(334\) | 20.3525 | 1.11364 | ||||||||
\(335\) | 23.9128 | 1.30650 | ||||||||
\(336\) | 4.81086 | 0.262454 | ||||||||
\(337\) | −27.2574 | −1.48480 | −0.742402 | − | 0.669955i | \(-0.766313\pi\) | ||||
−0.742402 | + | 0.669955i | \(0.766313\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −0.392747 | −0.0213311 | ||||||||
\(340\) | −5.21834 | −0.283004 | ||||||||
\(341\) | −0.865140 | −0.0468499 | ||||||||
\(342\) | 12.7080 | 0.687168 | ||||||||
\(343\) | 1.00000 | 0.0539949 | ||||||||
\(344\) | 4.92447 | 0.265510 | ||||||||
\(345\) | −1.04333 | −0.0561712 | ||||||||
\(346\) | 2.16924 | 0.116619 | ||||||||
\(347\) | −34.5372 | −1.85406 | −0.927028 | − | 0.374993i | \(-0.877645\pi\) | ||||
−0.927028 | + | 0.374993i | \(0.877645\pi\) | |||||||
\(348\) | −3.39684 | −0.182090 | ||||||||
\(349\) | −25.5552 | −1.36794 | −0.683969 | − | 0.729511i | \(-0.739748\pi\) | ||||
−0.683969 | + | 0.729511i | \(0.739748\pi\) | |||||||
\(350\) | 0.302241 | 0.0161554 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | −7.89465 | −0.420787 | ||||||||
\(353\) | −26.8466 | −1.42890 | −0.714450 | − | 0.699686i | \(-0.753323\pi\) | ||||
−0.714450 | + | 0.699686i | \(0.753323\pi\) | |||||||
\(354\) | −6.89282 | −0.366349 | ||||||||
\(355\) | 9.68759 | 0.514164 | ||||||||
\(356\) | 10.1680 | 0.538906 | ||||||||
\(357\) | 4.05395 | 0.214558 | ||||||||
\(358\) | 33.7441 | 1.78343 | ||||||||
\(359\) | −23.6724 | −1.24938 | −0.624690 | − | 0.780873i | \(-0.714775\pi\) | ||||
−0.624690 | + | 0.780873i | \(0.714775\pi\) | |||||||
\(360\) | −5.23485 | −0.275901 | ||||||||
\(361\) | 43.9575 | 2.31355 | ||||||||
\(362\) | −0.432077 | −0.0227095 | ||||||||
\(363\) | 4.55111 | 0.238871 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 3.62492 | 0.189737 | ||||||||
\(366\) | 18.3967 | 0.961610 | ||||||||
\(367\) | 11.5392 | 0.602341 | 0.301171 | − | 0.953570i | \(-0.402623\pi\) | ||||
0.301171 | + | 0.953570i | \(0.402623\pi\) | |||||||
\(368\) | −2.20352 | −0.114866 | ||||||||
\(369\) | 8.88028 | 0.462289 | ||||||||
\(370\) | 17.3182 | 0.900330 | ||||||||
\(371\) | 3.30421 | 0.171546 | ||||||||
\(372\) | 0.192517 | 0.00998152 | ||||||||
\(373\) | 1.52172 | 0.0787916 | 0.0393958 | − | 0.999224i | \(-0.487457\pi\) | ||||
0.0393958 | + | 0.999224i | \(0.487457\pi\) | |||||||
\(374\) | −16.4882 | −0.852584 | ||||||||
\(375\) | 10.9595 | 0.565947 | ||||||||
\(376\) | 16.4749 | 0.849627 | ||||||||
\(377\) | 0 | 0 | ||||||||
\(378\) | −1.60159 | −0.0823770 | ||||||||
\(379\) | −34.4586 | −1.77002 | −0.885010 | − | 0.465571i | \(-0.845849\pi\) | ||||
−0.885010 | + | 0.465571i | \(0.845849\pi\) | |||||||
\(380\) | 10.2136 | 0.523945 | ||||||||
\(381\) | −15.9958 | −0.819492 | ||||||||
\(382\) | −10.0625 | −0.514842 | ||||||||
\(383\) | −3.91678 | −0.200138 | −0.100069 | − | 0.994980i | \(-0.531906\pi\) | ||||
−0.100069 | + | 0.994980i | \(0.531906\pi\) | |||||||
\(384\) | −13.6533 | −0.696742 | ||||||||
\(385\) | 5.78459 | 0.294810 | ||||||||
\(386\) | 30.9354 | 1.57457 | ||||||||
\(387\) | −2.14282 | −0.108926 | ||||||||
\(388\) | 10.7122 | 0.543828 | ||||||||
\(389\) | −31.0836 | −1.57600 | −0.788002 | − | 0.615673i | \(-0.788884\pi\) | ||||
−0.788002 | + | 0.615673i | \(0.788884\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −1.85683 | −0.0939039 | ||||||||
\(392\) | −2.29813 | −0.116073 | ||||||||
\(393\) | −16.6090 | −0.837813 | ||||||||
\(394\) | −33.6414 | −1.69483 | ||||||||
\(395\) | −21.4593 | −1.07974 | ||||||||
\(396\) | 1.43505 | 0.0721139 | ||||||||
\(397\) | −9.75019 | −0.489348 | −0.244674 | − | 0.969605i | \(-0.578681\pi\) | ||||
−0.244674 | + | 0.969605i | \(0.578681\pi\) | |||||||
\(398\) | 27.2770 | 1.36727 | ||||||||
\(399\) | −7.93457 | −0.397226 | ||||||||
\(400\) | −0.907870 | −0.0453935 | ||||||||
\(401\) | −2.38904 | −0.119303 | −0.0596515 | − | 0.998219i | \(-0.518999\pi\) | ||||
−0.0596515 | + | 0.998219i | \(0.518999\pi\) | |||||||
\(402\) | −16.8133 | −0.838570 | ||||||||
\(403\) | 0 | 0 | ||||||||
\(404\) | −2.27549 | −0.113210 | ||||||||
\(405\) | 2.27787 | 0.113188 | ||||||||
\(406\) | 9.62727 | 0.477793 | ||||||||
\(407\) | 12.0549 | 0.597539 | ||||||||
\(408\) | −9.31650 | −0.461235 | ||||||||
\(409\) | 19.0527 | 0.942094 | 0.471047 | − | 0.882108i | \(-0.343876\pi\) | ||||
0.471047 | + | 0.882108i | \(0.343876\pi\) | |||||||
\(410\) | 32.3973 | 1.59999 | ||||||||
\(411\) | 1.57748 | 0.0778113 | ||||||||
\(412\) | −6.40997 | −0.315797 | ||||||||
\(413\) | 4.30373 | 0.211773 | ||||||||
\(414\) | 0.733576 | 0.0360533 | ||||||||
\(415\) | 4.27654 | 0.209927 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −12.0257 | −0.588899 | ||||||||
\(418\) | 32.2714 | 1.57845 | ||||||||
\(419\) | 19.6916 | 0.961998 | 0.480999 | − | 0.876721i | \(-0.340274\pi\) | ||||
0.480999 | + | 0.876721i | \(0.340274\pi\) | |||||||
\(420\) | −1.28722 | −0.0628101 | ||||||||
\(421\) | −25.2278 | −1.22953 | −0.614765 | − | 0.788711i | \(-0.710749\pi\) | ||||
−0.614765 | + | 0.788711i | \(0.710749\pi\) | |||||||
\(422\) | −16.0857 | −0.783040 | ||||||||
\(423\) | −7.16883 | −0.348560 | ||||||||
\(424\) | −7.59350 | −0.368773 | ||||||||
\(425\) | −0.765032 | −0.0371095 | ||||||||
\(426\) | −6.81142 | −0.330014 | ||||||||
\(427\) | −11.4865 | −0.555870 | ||||||||
\(428\) | −8.96038 | −0.433117 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | −7.81750 | −0.376993 | ||||||||
\(431\) | 7.87972 | 0.379553 | 0.189776 | − | 0.981827i | \(-0.439224\pi\) | ||||
0.189776 | + | 0.981827i | \(0.439224\pi\) | |||||||
\(432\) | 4.81086 | 0.231463 | ||||||||
\(433\) | −24.8346 | −1.19348 | −0.596738 | − | 0.802436i | \(-0.703537\pi\) | ||||
−0.596738 | + | 0.802436i | \(0.703537\pi\) | |||||||
\(434\) | −0.545627 | −0.0261909 | ||||||||
\(435\) | −13.6924 | −0.656502 | ||||||||
\(436\) | 7.42573 | 0.355628 | ||||||||
\(437\) | 3.63427 | 0.173851 | ||||||||
\(438\) | −2.54871 | −0.121782 | ||||||||
\(439\) | −19.0971 | −0.911457 | −0.455728 | − | 0.890119i | \(-0.650621\pi\) | ||||
−0.455728 | + | 0.890119i | \(0.650621\pi\) | |||||||
\(440\) | −13.2937 | −0.633753 | ||||||||
\(441\) | 1.00000 | 0.0476190 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 39.1199 | 1.85864 | 0.929320 | − | 0.369275i | \(-0.120394\pi\) | ||||
0.929320 | + | 0.369275i | \(0.120394\pi\) | |||||||
\(444\) | −2.68253 | −0.127307 | ||||||||
\(445\) | 40.9867 | 1.94296 | ||||||||
\(446\) | 2.09310 | 0.0991112 | ||||||||
\(447\) | 24.1801 | 1.14368 | ||||||||
\(448\) | 4.64271 | 0.219348 | ||||||||
\(449\) | 2.38383 | 0.112500 | 0.0562500 | − | 0.998417i | \(-0.482086\pi\) | ||||
0.0562500 | + | 0.998417i | \(0.482086\pi\) | |||||||
\(450\) | 0.302241 | 0.0142478 | ||||||||
\(451\) | 22.5512 | 1.06189 | ||||||||
\(452\) | 0.221941 | 0.0104392 | ||||||||
\(453\) | 8.98472 | 0.422139 | ||||||||
\(454\) | 11.7208 | 0.550085 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 18.2347 | 0.853916 | ||||||||
\(457\) | −14.9656 | −0.700061 | −0.350031 | − | 0.936738i | \(-0.613829\pi\) | ||||
−0.350031 | + | 0.936738i | \(0.613829\pi\) | |||||||
\(458\) | −26.4714 | −1.23693 | ||||||||
\(459\) | 4.05395 | 0.189222 | ||||||||
\(460\) | 0.589586 | 0.0274896 | ||||||||
\(461\) | 33.0078 | 1.53733 | 0.768664 | − | 0.639653i | \(-0.220922\pi\) | ||||
0.768664 | + | 0.639653i | \(0.220922\pi\) | |||||||
\(462\) | −4.06719 | −0.189223 | ||||||||
\(463\) | 34.2144 | 1.59008 | 0.795039 | − | 0.606559i | \(-0.207450\pi\) | ||||
0.795039 | + | 0.606559i | \(0.207450\pi\) | |||||||
\(464\) | −28.9184 | −1.34250 | ||||||||
\(465\) | 0.776021 | 0.0359871 | ||||||||
\(466\) | 8.78393 | 0.406908 | ||||||||
\(467\) | −25.2750 | −1.16959 | −0.584795 | − | 0.811181i | \(-0.698825\pi\) | ||||
−0.584795 | + | 0.811181i | \(0.698825\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 10.4979 | 0.484746 | ||||||||
\(470\) | −26.1535 | −1.20637 | ||||||||
\(471\) | 2.71212 | 0.124968 | ||||||||
\(472\) | −9.89051 | −0.455248 | ||||||||
\(473\) | −5.44162 | −0.250206 | ||||||||
\(474\) | 15.0882 | 0.693026 | ||||||||
\(475\) | 1.49735 | 0.0687033 | ||||||||
\(476\) | −2.29088 | −0.105002 | ||||||||
\(477\) | 3.30421 | 0.151289 | ||||||||
\(478\) | 28.5999 | 1.30813 | ||||||||
\(479\) | −37.4251 | −1.70999 | −0.854997 | − | 0.518633i | \(-0.826441\pi\) | ||||
−0.854997 | + | 0.518633i | \(0.826441\pi\) | |||||||
\(480\) | 7.08142 | 0.323221 | ||||||||
\(481\) | 0 | 0 | ||||||||
\(482\) | 37.0098 | 1.68575 | ||||||||
\(483\) | −0.458029 | −0.0208411 | ||||||||
\(484\) | −2.57183 | −0.116901 | ||||||||
\(485\) | 43.1800 | 1.96070 | ||||||||
\(486\) | −1.60159 | −0.0726497 | ||||||||
\(487\) | −30.3596 | −1.37572 | −0.687862 | − | 0.725842i | \(-0.741451\pi\) | ||||
−0.687862 | + | 0.725842i | \(0.741451\pi\) | |||||||
\(488\) | 26.3974 | 1.19495 | ||||||||
\(489\) | 17.3562 | 0.784875 | ||||||||
\(490\) | 3.64823 | 0.164810 | ||||||||
\(491\) | −5.62758 | −0.253969 | −0.126984 | − | 0.991905i | \(-0.540530\pi\) | ||||
−0.126984 | + | 0.991905i | \(0.540530\pi\) | |||||||
\(492\) | −5.01823 | −0.226239 | ||||||||
\(493\) | −24.3686 | −1.09750 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 5.78459 | 0.259998 | ||||||||
\(496\) | 1.63895 | 0.0735912 | ||||||||
\(497\) | 4.25291 | 0.190769 | ||||||||
\(498\) | −3.00687 | −0.134741 | ||||||||
\(499\) | 34.1534 | 1.52892 | 0.764459 | − | 0.644673i | \(-0.223006\pi\) | ||||
0.764459 | + | 0.644673i | \(0.223006\pi\) | |||||||
\(500\) | −6.19321 | −0.276969 | ||||||||
\(501\) | −12.7077 | −0.567737 | ||||||||
\(502\) | 18.8095 | 0.839509 | ||||||||
\(503\) | 10.4426 | 0.465612 | 0.232806 | − | 0.972523i | \(-0.425209\pi\) | ||||
0.232806 | + | 0.972523i | \(0.425209\pi\) | |||||||
\(504\) | −2.29813 | −0.102367 | ||||||||
\(505\) | −9.17233 | −0.408163 | ||||||||
\(506\) | 1.86289 | 0.0828157 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 9.03923 | 0.401051 | ||||||||
\(509\) | 18.2623 | 0.809463 | 0.404732 | − | 0.914436i | \(-0.367365\pi\) | ||||
0.404732 | + | 0.914436i | \(0.367365\pi\) | |||||||
\(510\) | 14.7897 | 0.654901 | ||||||||
\(511\) | 1.59136 | 0.0703976 | ||||||||
\(512\) | −7.15601 | −0.316254 | ||||||||
\(513\) | −7.93457 | −0.350320 | ||||||||
\(514\) | −15.2762 | −0.673803 | ||||||||
\(515\) | −25.8382 | −1.13857 | ||||||||
\(516\) | 1.21091 | 0.0533071 | ||||||||
\(517\) | −18.2050 | −0.800655 | ||||||||
\(518\) | 7.60279 | 0.334047 | ||||||||
\(519\) | −1.35443 | −0.0594527 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 34.9086 | 1.52937 | 0.764687 | − | 0.644401i | \(-0.222893\pi\) | ||||
0.764687 | + | 0.644401i | \(0.222893\pi\) | |||||||
\(522\) | 9.62727 | 0.421374 | ||||||||
\(523\) | −4.61292 | −0.201709 | −0.100854 | − | 0.994901i | \(-0.532158\pi\) | ||||
−0.100854 | + | 0.994901i | \(0.532158\pi\) | |||||||
\(524\) | 9.38572 | 0.410017 | ||||||||
\(525\) | −0.188713 | −0.00823609 | ||||||||
\(526\) | −8.43437 | −0.367756 | ||||||||
\(527\) | 1.38109 | 0.0601613 | ||||||||
\(528\) | 12.2170 | 0.531677 | ||||||||
\(529\) | −22.7902 | −0.990879 | ||||||||
\(530\) | 12.0545 | 0.523614 | ||||||||
\(531\) | 4.30373 | 0.186766 | ||||||||
\(532\) | 4.48382 | 0.194398 | ||||||||
\(533\) | 0 | 0 | ||||||||
\(534\) | −28.8181 | −1.24708 | ||||||||
\(535\) | −36.1187 | −1.56155 | ||||||||
\(536\) | −24.1254 | −1.04206 | ||||||||
\(537\) | −21.0691 | −0.909199 | ||||||||
\(538\) | 0.965190 | 0.0416123 | ||||||||
\(539\) | 2.53947 | 0.109383 | ||||||||
\(540\) | −1.28722 | −0.0553933 | ||||||||
\(541\) | −31.6729 | −1.36172 | −0.680862 | − | 0.732412i | \(-0.738395\pi\) | ||||
−0.680862 | + | 0.732412i | \(0.738395\pi\) | |||||||
\(542\) | −9.12243 | −0.391842 | ||||||||
\(543\) | 0.269780 | 0.0115774 | ||||||||
\(544\) | 12.6029 | 0.540343 | ||||||||
\(545\) | 29.9326 | 1.28217 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 21.6899 | 0.927393 | 0.463697 | − | 0.885994i | \(-0.346523\pi\) | ||||
0.463697 | + | 0.885994i | \(0.346523\pi\) | |||||||
\(548\) | −0.891431 | −0.0380800 | ||||||||
\(549\) | −11.4865 | −0.490231 | ||||||||
\(550\) | 0.767530 | 0.0327276 | ||||||||
\(551\) | 47.6952 | 2.03188 | ||||||||
\(552\) | 1.05261 | 0.0448020 | ||||||||
\(553\) | −9.42077 | −0.400612 | ||||||||
\(554\) | −12.8238 | −0.544832 | ||||||||
\(555\) | −10.8131 | −0.458991 | ||||||||
\(556\) | 6.79568 | 0.288201 | ||||||||
\(557\) | −32.4871 | −1.37652 | −0.688262 | − | 0.725462i | \(-0.741626\pi\) | ||||
−0.688262 | + | 0.725462i | \(0.741626\pi\) | |||||||
\(558\) | −0.545627 | −0.0230982 | ||||||||
\(559\) | 0 | 0 | ||||||||
\(560\) | −10.9585 | −0.463083 | ||||||||
\(561\) | 10.2949 | 0.434650 | ||||||||
\(562\) | −4.83383 | −0.203903 | ||||||||
\(563\) | −13.0529 | −0.550115 | −0.275058 | − | 0.961428i | \(-0.588697\pi\) | ||||
−0.275058 | + | 0.961428i | \(0.588697\pi\) | |||||||
\(564\) | 4.05110 | 0.170582 | ||||||||
\(565\) | 0.894628 | 0.0376373 | ||||||||
\(566\) | 14.2814 | 0.600294 | ||||||||
\(567\) | 1.00000 | 0.0419961 | ||||||||
\(568\) | −9.77372 | −0.410096 | ||||||||
\(569\) | −15.3184 | −0.642182 | −0.321091 | − | 0.947048i | \(-0.604049\pi\) | ||||
−0.321091 | + | 0.947048i | \(0.604049\pi\) | |||||||
\(570\) | −28.9471 | −1.21246 | ||||||||
\(571\) | −44.0404 | −1.84303 | −0.921517 | − | 0.388337i | \(-0.873050\pi\) | ||||
−0.921517 | + | 0.388337i | \(0.873050\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 6.28281 | 0.262468 | ||||||||
\(574\) | 14.2226 | 0.593639 | ||||||||
\(575\) | 0.0864359 | 0.00360463 | ||||||||
\(576\) | 4.64271 | 0.193446 | ||||||||
\(577\) | 13.7961 | 0.574338 | 0.287169 | − | 0.957880i | \(-0.407286\pi\) | ||||
0.287169 | + | 0.957880i | \(0.407286\pi\) | |||||||
\(578\) | −0.905663 | −0.0376706 | ||||||||
\(579\) | −19.3154 | −0.802721 | ||||||||
\(580\) | 7.73758 | 0.321286 | ||||||||
\(581\) | 1.87743 | 0.0778888 | ||||||||
\(582\) | −30.3602 | −1.25847 | ||||||||
\(583\) | 8.39093 | 0.347517 | ||||||||
\(584\) | −3.65715 | −0.151334 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −8.52072 | −0.351988 | ||||||||
\(587\) | 29.7424 | 1.22760 | 0.613801 | − | 0.789461i | \(-0.289640\pi\) | ||||
0.613801 | + | 0.789461i | \(0.289640\pi\) | |||||||
\(588\) | −0.565099 | −0.0233043 | ||||||||
\(589\) | −2.70313 | −0.111381 | ||||||||
\(590\) | 15.7010 | 0.646399 | ||||||||
\(591\) | 21.0050 | 0.864030 | ||||||||
\(592\) | −22.8372 | −0.938605 | ||||||||
\(593\) | 26.2248 | 1.07692 | 0.538461 | − | 0.842650i | \(-0.319006\pi\) | ||||
0.538461 | + | 0.842650i | \(0.319006\pi\) | |||||||
\(594\) | −4.06719 | −0.166879 | ||||||||
\(595\) | −9.23439 | −0.378573 | ||||||||
\(596\) | −13.6642 | −0.559706 | ||||||||
\(597\) | −17.0312 | −0.697039 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −7.80961 | −0.319092 | −0.159546 | − | 0.987191i | \(-0.551003\pi\) | ||||
−0.159546 | + | 0.987191i | \(0.551003\pi\) | |||||||
\(600\) | 0.433686 | 0.0177051 | ||||||||
\(601\) | 13.4938 | 0.550422 | 0.275211 | − | 0.961384i | \(-0.411252\pi\) | ||||
0.275211 | + | 0.961384i | \(0.411252\pi\) | |||||||
\(602\) | −3.43193 | −0.139875 | ||||||||
\(603\) | 10.4979 | 0.427506 | ||||||||
\(604\) | −5.07726 | −0.206591 | ||||||||
\(605\) | −10.3669 | −0.421473 | ||||||||
\(606\) | 6.44914 | 0.261978 | ||||||||
\(607\) | −18.5539 | −0.753078 | −0.376539 | − | 0.926401i | \(-0.622886\pi\) | ||||
−0.376539 | + | 0.926401i | \(0.622886\pi\) | |||||||
\(608\) | −24.6669 | −1.00037 | ||||||||
\(609\) | −6.01106 | −0.243580 | ||||||||
\(610\) | −41.9053 | −1.69670 | ||||||||
\(611\) | 0 | 0 | ||||||||
\(612\) | −2.29088 | −0.0926035 | ||||||||
\(613\) | −12.9374 | −0.522536 | −0.261268 | − | 0.965266i | \(-0.584141\pi\) | ||||
−0.261268 | + | 0.965266i | \(0.584141\pi\) | |||||||
\(614\) | −5.84974 | −0.236076 | ||||||||
\(615\) | −20.2282 | −0.815678 | ||||||||
\(616\) | −5.83602 | −0.235140 | ||||||||
\(617\) | −33.2636 | −1.33914 | −0.669571 | − | 0.742748i | \(-0.733522\pi\) | ||||
−0.669571 | + | 0.742748i | \(0.733522\pi\) | |||||||
\(618\) | 18.1670 | 0.730785 | ||||||||
\(619\) | −18.8470 | −0.757523 | −0.378762 | − | 0.925494i | \(-0.623650\pi\) | ||||
−0.378762 | + | 0.925494i | \(0.623650\pi\) | |||||||
\(620\) | −0.438529 | −0.0176117 | ||||||||
\(621\) | −0.458029 | −0.0183801 | ||||||||
\(622\) | 7.97233 | 0.319661 | ||||||||
\(623\) | 17.9934 | 0.720890 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −25.9080 | −1.03632 | ||||||||
\(626\) | −49.3323 | −1.97171 | ||||||||
\(627\) | −20.1496 | −0.804697 | ||||||||
\(628\) | −1.53262 | −0.0611581 | ||||||||
\(629\) | −19.2442 | −0.767315 | ||||||||
\(630\) | 3.64823 | 0.145349 | ||||||||
\(631\) | −25.5434 | −1.01687 | −0.508433 | − | 0.861101i | \(-0.669775\pi\) | ||||
−0.508433 | + | 0.861101i | \(0.669775\pi\) | |||||||
\(632\) | 21.6501 | 0.861196 | ||||||||
\(633\) | 10.0436 | 0.399196 | ||||||||
\(634\) | −36.0762 | −1.43277 | ||||||||
\(635\) | 36.4365 | 1.44594 | ||||||||
\(636\) | −1.86721 | −0.0740395 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | 24.4481 | 0.967911 | ||||||||
\(639\) | 4.25291 | 0.168242 | ||||||||
\(640\) | 31.1005 | 1.22936 | ||||||||
\(641\) | 14.6984 | 0.580552 | 0.290276 | − | 0.956943i | \(-0.406253\pi\) | ||||
0.290276 | + | 0.956943i | \(0.406253\pi\) | |||||||
\(642\) | 25.3954 | 1.00227 | ||||||||
\(643\) | −8.13670 | −0.320880 | −0.160440 | − | 0.987046i | \(-0.551291\pi\) | ||||
−0.160440 | + | 0.987046i | \(0.551291\pi\) | |||||||
\(644\) | 0.258832 | 0.0101994 | ||||||||
\(645\) | 4.88108 | 0.192192 | ||||||||
\(646\) | −51.5174 | −2.02693 | ||||||||
\(647\) | −17.9914 | −0.707315 | −0.353658 | − | 0.935375i | \(-0.615062\pi\) | ||||
−0.353658 | + | 0.935375i | \(0.615062\pi\) | |||||||
\(648\) | −2.29813 | −0.0902790 | ||||||||
\(649\) | 10.9292 | 0.429008 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0.340678 | 0.0133522 | ||||||||
\(652\) | −9.80798 | −0.384110 | ||||||||
\(653\) | −9.74392 | −0.381309 | −0.190654 | − | 0.981657i | \(-0.561061\pi\) | ||||
−0.190654 | + | 0.981657i | \(0.561061\pi\) | |||||||
\(654\) | −21.0459 | −0.822958 | ||||||||
\(655\) | 37.8332 | 1.47827 | ||||||||
\(656\) | −42.7218 | −1.66801 | ||||||||
\(657\) | 1.59136 | 0.0620849 | ||||||||
\(658\) | −11.4815 | −0.447597 | ||||||||
\(659\) | 39.8534 | 1.55247 | 0.776234 | − | 0.630445i | \(-0.217128\pi\) | ||||
0.776234 | + | 0.630445i | \(0.217128\pi\) | |||||||
\(660\) | −3.26886 | −0.127240 | ||||||||
\(661\) | −4.70505 | −0.183005 | −0.0915025 | − | 0.995805i | \(-0.529167\pi\) | ||||
−0.0915025 | + | 0.995805i | \(0.529167\pi\) | |||||||
\(662\) | 7.57908 | 0.294570 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | −4.31457 | −0.167438 | ||||||||
\(665\) | 18.0740 | 0.700878 | ||||||||
\(666\) | 7.60279 | 0.294602 | ||||||||
\(667\) | 2.75324 | 0.106606 | ||||||||
\(668\) | 7.18109 | 0.277845 | ||||||||
\(669\) | −1.30689 | −0.0505272 | ||||||||
\(670\) | 38.2985 | 1.47960 | ||||||||
\(671\) | −29.1696 | −1.12608 | ||||||||
\(672\) | 3.10879 | 0.119924 | ||||||||
\(673\) | −51.1974 | −1.97351 | −0.986757 | − | 0.162205i | \(-0.948139\pi\) | ||||
−0.986757 | + | 0.162205i | \(0.948139\pi\) | |||||||
\(674\) | −43.6552 | −1.68154 | ||||||||
\(675\) | −0.188713 | −0.00726355 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −6.98340 | −0.268394 | −0.134197 | − | 0.990955i | \(-0.542845\pi\) | ||||
−0.134197 | + | 0.990955i | \(0.542845\pi\) | |||||||
\(678\) | −0.629020 | −0.0241574 | ||||||||
\(679\) | 18.9563 | 0.727475 | ||||||||
\(680\) | 21.2218 | 0.813819 | ||||||||
\(681\) | −7.31823 | −0.280435 | ||||||||
\(682\) | −1.38560 | −0.0530574 | ||||||||
\(683\) | 14.7082 | 0.562793 | 0.281396 | − | 0.959592i | \(-0.409202\pi\) | ||||
0.281396 | + | 0.959592i | \(0.409202\pi\) | |||||||
\(684\) | 4.48382 | 0.171443 | ||||||||
\(685\) | −3.59330 | −0.137293 | ||||||||
\(686\) | 1.60159 | 0.0611491 | ||||||||
\(687\) | 16.5282 | 0.630590 | ||||||||
\(688\) | 10.3088 | 0.393020 | ||||||||
\(689\) | 0 | 0 | ||||||||
\(690\) | −1.67099 | −0.0636137 | ||||||||
\(691\) | 45.3789 | 1.72629 | 0.863147 | − | 0.504953i | \(-0.168490\pi\) | ||||
0.863147 | + | 0.504953i | \(0.168490\pi\) | |||||||
\(692\) | 0.765385 | 0.0290956 | ||||||||
\(693\) | 2.53947 | 0.0964663 | ||||||||
\(694\) | −55.3146 | −2.09971 | ||||||||
\(695\) | 27.3929 | 1.03907 | ||||||||
\(696\) | 13.8142 | 0.523625 | ||||||||
\(697\) | −36.0002 | −1.36361 | ||||||||
\(698\) | −40.9290 | −1.54918 | ||||||||
\(699\) | −5.48450 | −0.207443 | ||||||||
\(700\) | 0.106641 | 0.00403066 | ||||||||
\(701\) | −16.8794 | −0.637525 | −0.318763 | − | 0.947835i | \(-0.603267\pi\) | ||||
−0.318763 | + | 0.947835i | \(0.603267\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 37.6656 | 1.42058 | ||||||||
\(704\) | 11.7900 | 0.444353 | ||||||||
\(705\) | 16.3297 | 0.615012 | ||||||||
\(706\) | −42.9973 | −1.61823 | ||||||||
\(707\) | −4.02671 | −0.151440 | ||||||||
\(708\) | −2.43203 | −0.0914014 | ||||||||
\(709\) | −41.2478 | −1.54909 | −0.774547 | − | 0.632516i | \(-0.782022\pi\) | ||||
−0.774547 | + | 0.632516i | \(0.782022\pi\) | |||||||
\(710\) | 15.5156 | 0.582289 | ||||||||
\(711\) | −9.42077 | −0.353307 | ||||||||
\(712\) | −41.3511 | −1.54970 | ||||||||
\(713\) | −0.156040 | −0.00584376 | ||||||||
\(714\) | 6.49278 | 0.242986 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 11.9061 | 0.444953 | ||||||||
\(717\) | −17.8572 | −0.666889 | ||||||||
\(718\) | −37.9135 | −1.41492 | ||||||||
\(719\) | 14.8928 | 0.555409 | 0.277704 | − | 0.960667i | \(-0.410426\pi\) | ||||
0.277704 | + | 0.960667i | \(0.410426\pi\) | |||||||
\(720\) | −10.9585 | −0.408401 | ||||||||
\(721\) | −11.3431 | −0.422439 | ||||||||
\(722\) | 70.4020 | 2.62009 | ||||||||
\(723\) | −23.1081 | −0.859400 | ||||||||
\(724\) | −0.152452 | −0.00566584 | ||||||||
\(725\) | 1.13436 | 0.0421292 | ||||||||
\(726\) | 7.28903 | 0.270521 | ||||||||
\(727\) | 31.4330 | 1.16578 | 0.582892 | − | 0.812550i | \(-0.301921\pi\) | ||||
0.582892 | + | 0.812550i | \(0.301921\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | 5.80564 | 0.214876 | ||||||||
\(731\) | 8.68689 | 0.321296 | ||||||||
\(732\) | 6.49100 | 0.239914 | ||||||||
\(733\) | −5.22860 | −0.193123 | −0.0965613 | − | 0.995327i | \(-0.530784\pi\) | ||||
−0.0965613 | + | 0.995327i | \(0.530784\pi\) | |||||||
\(734\) | 18.4811 | 0.682150 | ||||||||
\(735\) | −2.27787 | −0.0840207 | ||||||||
\(736\) | −1.42391 | −0.0524862 | ||||||||
\(737\) | 26.6589 | 0.981995 | ||||||||
\(738\) | 14.2226 | 0.523541 | ||||||||
\(739\) | −23.0653 | −0.848469 | −0.424235 | − | 0.905552i | \(-0.639457\pi\) | ||||
−0.424235 | + | 0.905552i | \(0.639457\pi\) | |||||||
\(740\) | 6.11047 | 0.224626 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 5.29200 | 0.194275 | ||||||||
\(743\) | −0.991530 | −0.0363757 | −0.0181878 | − | 0.999835i | \(-0.505790\pi\) | ||||
−0.0181878 | + | 0.999835i | \(0.505790\pi\) | |||||||
\(744\) | −0.782921 | −0.0287033 | ||||||||
\(745\) | −55.0793 | −2.01795 | ||||||||
\(746\) | 2.43717 | 0.0892312 | ||||||||
\(747\) | 1.87743 | 0.0686915 | ||||||||
\(748\) | −5.81762 | −0.212713 | ||||||||
\(749\) | −15.8563 | −0.579377 | ||||||||
\(750\) | 17.5527 | 0.640933 | ||||||||
\(751\) | 29.7806 | 1.08671 | 0.543356 | − | 0.839503i | \(-0.317154\pi\) | ||||
0.543356 | + | 0.839503i | \(0.317154\pi\) | |||||||
\(752\) | 34.4882 | 1.25766 | ||||||||
\(753\) | −11.7442 | −0.427984 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −20.4661 | −0.744837 | ||||||||
\(756\) | −0.565099 | −0.0205524 | ||||||||
\(757\) | −9.12624 | −0.331699 | −0.165849 | − | 0.986151i | \(-0.553037\pi\) | ||||
−0.165849 | + | 0.986151i | \(0.553037\pi\) | |||||||
\(758\) | −55.1887 | −2.00454 | ||||||||
\(759\) | −1.16315 | −0.0422197 | ||||||||
\(760\) | −41.5363 | −1.50668 | ||||||||
\(761\) | −14.2507 | −0.516586 | −0.258293 | − | 0.966067i | \(-0.583160\pi\) | ||||
−0.258293 | + | 0.966067i | \(0.583160\pi\) | |||||||
\(762\) | −25.6188 | −0.928072 | ||||||||
\(763\) | 13.1406 | 0.475721 | ||||||||
\(764\) | −3.55041 | −0.128449 | ||||||||
\(765\) | −9.23439 | −0.333870 | ||||||||
\(766\) | −6.27309 | −0.226656 | ||||||||
\(767\) | 0 | 0 | ||||||||
\(768\) | −12.5816 | −0.454000 | ||||||||
\(769\) | −43.0440 | −1.55221 | −0.776103 | − | 0.630606i | \(-0.782807\pi\) | ||||
−0.776103 | + | 0.630606i | \(0.782807\pi\) | |||||||
\(770\) | 9.26455 | 0.333871 | ||||||||
\(771\) | 9.53811 | 0.343507 | ||||||||
\(772\) | 10.9151 | 0.392844 | ||||||||
\(773\) | −30.5971 | −1.10050 | −0.550251 | − | 0.834999i | \(-0.685468\pi\) | ||||
−0.550251 | + | 0.834999i | \(0.685468\pi\) | |||||||
\(774\) | −3.43193 | −0.123358 | ||||||||
\(775\) | −0.0642902 | −0.00230937 | ||||||||
\(776\) | −43.5639 | −1.56385 | ||||||||
\(777\) | −4.74702 | −0.170298 | ||||||||
\(778\) | −49.7833 | −1.78482 | ||||||||
\(779\) | 70.4612 | 2.52453 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 10.8001 | 0.386458 | ||||||||
\(782\) | −2.97388 | −0.106346 | ||||||||
\(783\) | −6.01106 | −0.214818 | ||||||||
\(784\) | −4.81086 | −0.171816 | ||||||||
\(785\) | −6.17787 | −0.220498 | ||||||||
\(786\) | −26.6008 | −0.948820 | ||||||||
\(787\) | −23.2516 | −0.828830 | −0.414415 | − | 0.910088i | \(-0.636014\pi\) | ||||
−0.414415 | + | 0.910088i | \(0.636014\pi\) | |||||||
\(788\) | −11.8699 | −0.422848 | ||||||||
\(789\) | 5.26624 | 0.187483 | ||||||||
\(790\) | −34.3691 | −1.22280 | ||||||||
\(791\) | 0.392747 | 0.0139645 | ||||||||
\(792\) | −5.83602 | −0.207374 | ||||||||
\(793\) | 0 | 0 | ||||||||
\(794\) | −15.6158 | −0.554185 | ||||||||
\(795\) | −7.52658 | −0.266940 | ||||||||
\(796\) | 9.62428 | 0.341124 | ||||||||
\(797\) | −48.7696 | −1.72751 | −0.863754 | − | 0.503914i | \(-0.831893\pi\) | ||||
−0.863754 | + | 0.503914i | \(0.831893\pi\) | |||||||
\(798\) | −12.7080 | −0.449857 | ||||||||
\(799\) | 29.0621 | 1.02814 | ||||||||
\(800\) | −0.586667 | −0.0207418 | ||||||||
\(801\) | 17.9934 | 0.635766 | ||||||||
\(802\) | −3.82627 | −0.135110 | ||||||||
\(803\) | 4.04120 | 0.142611 | ||||||||
\(804\) | −5.93232 | −0.209217 | ||||||||
\(805\) | 1.04333 | 0.0367727 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −0.602644 | −0.0212141 | ||||||||
\(808\) | 9.25388 | 0.325550 | ||||||||
\(809\) | −4.26862 | −0.150077 | −0.0750383 | − | 0.997181i | \(-0.523908\pi\) | ||||
−0.0750383 | + | 0.997181i | \(0.523908\pi\) | |||||||
\(810\) | 3.64823 | 0.128186 | ||||||||
\(811\) | 16.1267 | 0.566287 | 0.283143 | − | 0.959078i | \(-0.408623\pi\) | ||||
0.283143 | + | 0.959078i | \(0.408623\pi\) | |||||||
\(812\) | 3.39684 | 0.119206 | ||||||||
\(813\) | 5.69585 | 0.199762 | ||||||||
\(814\) | 19.3070 | 0.676711 | ||||||||
\(815\) | −39.5353 | −1.38486 | ||||||||
\(816\) | −19.5030 | −0.682741 | ||||||||
\(817\) | −17.0024 | −0.594838 | ||||||||
\(818\) | 30.5146 | 1.06692 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 11.4309 | 0.399185 | ||||||||
\(821\) | 42.1403 | 1.47071 | 0.735354 | − | 0.677684i | \(-0.237016\pi\) | ||||
0.735354 | + | 0.677684i | \(0.237016\pi\) | |||||||
\(822\) | 2.52648 | 0.0881210 | ||||||||
\(823\) | 34.5376 | 1.20391 | 0.601953 | − | 0.798531i | \(-0.294389\pi\) | ||||
0.601953 | + | 0.798531i | \(0.294389\pi\) | |||||||
\(824\) | 26.0679 | 0.908118 | ||||||||
\(825\) | −0.479229 | −0.0166846 | ||||||||
\(826\) | 6.89282 | 0.239832 | ||||||||
\(827\) | 43.7311 | 1.52068 | 0.760340 | − | 0.649525i | \(-0.225032\pi\) | ||||
0.760340 | + | 0.649525i | \(0.225032\pi\) | |||||||
\(828\) | 0.258832 | 0.00899503 | ||||||||
\(829\) | −0.927355 | −0.0322084 | −0.0161042 | − | 0.999870i | \(-0.505126\pi\) | ||||
−0.0161042 | + | 0.999870i | \(0.505126\pi\) | |||||||
\(830\) | 6.84928 | 0.237742 | ||||||||
\(831\) | 8.00692 | 0.277757 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −4.05395 | −0.140461 | ||||||||
\(834\) | −19.2602 | −0.666926 | ||||||||
\(835\) | 28.9465 | 1.00173 | ||||||||
\(836\) | 11.3865 | 0.393811 | ||||||||
\(837\) | 0.340678 | 0.0117755 | ||||||||
\(838\) | 31.5379 | 1.08946 | ||||||||
\(839\) | 24.1448 | 0.833571 | 0.416785 | − | 0.909005i | \(-0.363157\pi\) | ||||
0.416785 | + | 0.909005i | \(0.363157\pi\) | |||||||
\(840\) | 5.23485 | 0.180619 | ||||||||
\(841\) | 7.13286 | 0.245961 | ||||||||
\(842\) | −40.4047 | −1.39244 | ||||||||
\(843\) | 3.01814 | 0.103950 | ||||||||
\(844\) | −5.67561 | −0.195363 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | −11.4815 | −0.394744 | ||||||||
\(847\) | −4.55111 | −0.156378 | ||||||||
\(848\) | −15.8961 | −0.545874 | ||||||||
\(849\) | −8.91703 | −0.306032 | ||||||||
\(850\) | −1.22527 | −0.0420264 | ||||||||
\(851\) | 2.17427 | 0.0745331 | ||||||||
\(852\) | −2.40331 | −0.0823361 | ||||||||
\(853\) | 54.7857 | 1.87583 | 0.937914 | − | 0.346868i | \(-0.112755\pi\) | ||||
0.937914 | + | 0.346868i | \(0.112755\pi\) | |||||||
\(854\) | −18.3967 | −0.629521 | ||||||||
\(855\) | 18.0740 | 0.618117 | ||||||||
\(856\) | 36.4398 | 1.24549 | ||||||||
\(857\) | 2.79688 | 0.0955396 | 0.0477698 | − | 0.998858i | \(-0.484789\pi\) | ||||
0.0477698 | + | 0.998858i | \(0.484789\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −37.7430 | −1.28778 | −0.643888 | − | 0.765120i | \(-0.722680\pi\) | ||||
−0.643888 | + | 0.765120i | \(0.722680\pi\) | |||||||
\(860\) | −2.75829 | −0.0940569 | ||||||||
\(861\) | −8.88028 | −0.302639 | ||||||||
\(862\) | 12.6201 | 0.429843 | ||||||||
\(863\) | 25.0401 | 0.852376 | 0.426188 | − | 0.904635i | \(-0.359856\pi\) | ||||
0.426188 | + | 0.904635i | \(0.359856\pi\) | |||||||
\(864\) | 3.10879 | 0.105763 | ||||||||
\(865\) | 3.08521 | 0.104900 | ||||||||
\(866\) | −39.7749 | −1.35161 | ||||||||
\(867\) | 0.565477 | 0.0192046 | ||||||||
\(868\) | −0.192517 | −0.00653444 | ||||||||
\(869\) | −23.9237 | −0.811557 | ||||||||
\(870\) | −21.9297 | −0.743487 | ||||||||
\(871\) | 0 | 0 | ||||||||
\(872\) | −30.1987 | −1.02266 | ||||||||
\(873\) | 18.9563 | 0.641573 | ||||||||
\(874\) | 5.82062 | 0.196885 | ||||||||
\(875\) | −10.9595 | −0.370499 | ||||||||
\(876\) | −0.899276 | −0.0303837 | ||||||||
\(877\) | −32.5220 | −1.09819 | −0.549095 | − | 0.835760i | \(-0.685027\pi\) | ||||
−0.549095 | + | 0.835760i | \(0.685027\pi\) | |||||||
\(878\) | −30.5858 | −1.03222 | ||||||||
\(879\) | 5.32016 | 0.179444 | ||||||||
\(880\) | −27.8288 | −0.938110 | ||||||||
\(881\) | 27.6515 | 0.931604 | 0.465802 | − | 0.884889i | \(-0.345766\pi\) | ||||
0.465802 | + | 0.884889i | \(0.345766\pi\) | |||||||
\(882\) | 1.60159 | 0.0539284 | ||||||||
\(883\) | 18.0601 | 0.607771 | 0.303885 | − | 0.952709i | \(-0.401716\pi\) | ||||
0.303885 | + | 0.952709i | \(0.401716\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −9.80335 | −0.329536 | ||||||||
\(886\) | 62.6541 | 2.10490 | ||||||||
\(887\) | 44.6426 | 1.49895 | 0.749476 | − | 0.662032i | \(-0.230306\pi\) | ||||
0.749476 | + | 0.662032i | \(0.230306\pi\) | |||||||
\(888\) | 10.9092 | 0.366090 | ||||||||
\(889\) | 15.9958 | 0.536483 | ||||||||
\(890\) | 65.6440 | 2.20039 | ||||||||
\(891\) | 2.53947 | 0.0850753 | ||||||||
\(892\) | 0.738520 | 0.0247275 | ||||||||
\(893\) | −56.8816 | −1.90347 | ||||||||
\(894\) | 38.7267 | 1.29521 | ||||||||
\(895\) | 47.9928 | 1.60422 | ||||||||
\(896\) | 13.6533 | 0.456125 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 3.81793 | 0.127406 | ||||||||
\(899\) | −2.04783 | −0.0682991 | ||||||||
\(900\) | 0.106641 | 0.00355471 | ||||||||
\(901\) | −13.3951 | −0.446256 | ||||||||
\(902\) | 36.1178 | 1.20259 | ||||||||
\(903\) | 2.14282 | 0.0713086 | ||||||||
\(904\) | −0.902582 | −0.0300194 | ||||||||
\(905\) | −0.614524 | −0.0204275 | ||||||||
\(906\) | 14.3899 | 0.478071 | ||||||||
\(907\) | −26.3976 | −0.876517 | −0.438259 | − | 0.898849i | \(-0.644405\pi\) | ||||
−0.438259 | + | 0.898849i | \(0.644405\pi\) | |||||||
\(908\) | 4.13552 | 0.137242 | ||||||||
\(909\) | −4.02671 | −0.133557 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 4.45669 | 0.147657 | 0.0738283 | − | 0.997271i | \(-0.476478\pi\) | ||||
0.0738283 | + | 0.997271i | \(0.476478\pi\) | |||||||
\(912\) | 38.1721 | 1.26401 | ||||||||
\(913\) | 4.76766 | 0.157787 | ||||||||
\(914\) | −23.9688 | −0.792817 | ||||||||
\(915\) | 26.1648 | 0.864981 | ||||||||
\(916\) | −9.34006 | −0.308604 | ||||||||
\(917\) | 16.6090 | 0.548477 | ||||||||
\(918\) | 6.49278 | 0.214294 | ||||||||
\(919\) | −6.71089 | −0.221372 | −0.110686 | − | 0.993855i | \(-0.535305\pi\) | ||||
−0.110686 | + | 0.993855i | \(0.535305\pi\) | |||||||
\(920\) | −2.39771 | −0.0790502 | ||||||||
\(921\) | 3.65245 | 0.120352 | ||||||||
\(922\) | 52.8651 | 1.74102 | ||||||||
\(923\) | 0 | 0 | ||||||||
\(924\) | −1.43505 | −0.0472097 | ||||||||
\(925\) | 0.895822 | 0.0294544 | ||||||||
\(926\) | 54.7975 | 1.80076 | ||||||||
\(927\) | −11.3431 | −0.372556 | ||||||||
\(928\) | −18.6871 | −0.613434 | ||||||||
\(929\) | −28.2471 | −0.926759 | −0.463379 | − | 0.886160i | \(-0.653363\pi\) | ||||
−0.463379 | + | 0.886160i | \(0.653363\pi\) | |||||||
\(930\) | 1.24287 | 0.0407553 | ||||||||
\(931\) | 7.93457 | 0.260045 | ||||||||
\(932\) | 3.09928 | 0.101520 | ||||||||
\(933\) | −4.97775 | −0.162964 | ||||||||
\(934\) | −40.4803 | −1.32456 | ||||||||
\(935\) | −23.4504 | −0.766911 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −33.0728 | −1.08044 | −0.540220 | − | 0.841524i | \(-0.681659\pi\) | ||||
−0.540220 | + | 0.841524i | \(0.681659\pi\) | |||||||
\(938\) | 16.8133 | 0.548973 | ||||||||
\(939\) | 30.8020 | 1.00519 | ||||||||
\(940\) | −9.22789 | −0.300981 | ||||||||
\(941\) | 40.0527 | 1.30568 | 0.652840 | − | 0.757495i | \(-0.273577\pi\) | ||||
0.652840 | + | 0.757495i | \(0.273577\pi\) | |||||||
\(942\) | 4.34371 | 0.141526 | ||||||||
\(943\) | 4.06743 | 0.132454 | ||||||||
\(944\) | −20.7046 | −0.673879 | ||||||||
\(945\) | −2.27787 | −0.0740993 | ||||||||
\(946\) | −8.71526 | −0.283358 | ||||||||
\(947\) | 52.8629 | 1.71781 | 0.858907 | − | 0.512132i | \(-0.171144\pi\) | ||||
0.858907 | + | 0.512132i | \(0.171144\pi\) | |||||||
\(948\) | 5.32367 | 0.172905 | ||||||||
\(949\) | 0 | 0 | ||||||||
\(950\) | 2.39815 | 0.0778063 | ||||||||
\(951\) | 22.5252 | 0.730429 | ||||||||
\(952\) | 9.31650 | 0.301949 | ||||||||
\(953\) | −47.6352 | −1.54306 | −0.771528 | − | 0.636196i | \(-0.780507\pi\) | ||||
−0.771528 | + | 0.636196i | \(0.780507\pi\) | |||||||
\(954\) | 5.29200 | 0.171335 | ||||||||
\(955\) | −14.3114 | −0.463108 | ||||||||
\(956\) | 10.0911 | 0.326369 | ||||||||
\(957\) | −15.2649 | −0.493444 | ||||||||
\(958\) | −59.9397 | −1.93656 | ||||||||
\(959\) | −1.57748 | −0.0509394 | ||||||||
\(960\) | −10.5755 | −0.341324 | ||||||||
\(961\) | −30.8839 | −0.996256 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −15.8563 | −0.510963 | ||||||||
\(964\) | 13.0584 | 0.420582 | ||||||||
\(965\) | 43.9981 | 1.41635 | ||||||||
\(966\) | −0.733576 | −0.0236024 | ||||||||
\(967\) | −34.0050 | −1.09353 | −0.546764 | − | 0.837287i | \(-0.684140\pi\) | ||||
−0.546764 | + | 0.837287i | \(0.684140\pi\) | |||||||
\(968\) | 10.4590 | 0.336166 | ||||||||
\(969\) | 32.1664 | 1.03333 | ||||||||
\(970\) | 69.1568 | 2.22049 | ||||||||
\(971\) | −1.28177 | −0.0411338 | −0.0205669 | − | 0.999788i | \(-0.506547\pi\) | ||||
−0.0205669 | + | 0.999788i | \(0.506547\pi\) | |||||||
\(972\) | −0.565099 | −0.0181256 | ||||||||
\(973\) | 12.0257 | 0.385525 | ||||||||
\(974\) | −48.6237 | −1.55800 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 55.2599 | 1.76883 | ||||||||
\(977\) | 53.5945 | 1.71464 | 0.857320 | − | 0.514783i | \(-0.172128\pi\) | ||||
0.857320 | + | 0.514783i | \(0.172128\pi\) | |||||||
\(978\) | 27.7976 | 0.888869 | ||||||||
\(979\) | 45.6936 | 1.46037 | ||||||||
\(980\) | 1.28722 | 0.0411189 | ||||||||
\(981\) | 13.1406 | 0.419547 | ||||||||
\(982\) | −9.01309 | −0.287619 | ||||||||
\(983\) | 12.2091 | 0.389410 | 0.194705 | − | 0.980862i | \(-0.437625\pi\) | ||||
0.194705 | + | 0.980862i | \(0.437625\pi\) | |||||||
\(984\) | 20.4080 | 0.650583 | ||||||||
\(985\) | −47.8468 | −1.52452 | ||||||||
\(986\) | −39.0285 | −1.24292 | ||||||||
\(987\) | 7.16883 | 0.228186 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −0.981475 | −0.0312091 | ||||||||
\(990\) | 9.26455 | 0.294447 | ||||||||
\(991\) | −7.83719 | −0.248957 | −0.124478 | − | 0.992222i | \(-0.539726\pi\) | ||||
−0.124478 | + | 0.992222i | \(0.539726\pi\) | |||||||
\(992\) | 1.05909 | 0.0336263 | ||||||||
\(993\) | −4.73222 | −0.150172 | ||||||||
\(994\) | 6.81142 | 0.216045 | ||||||||
\(995\) | 38.7948 | 1.22988 | ||||||||
\(996\) | −1.06093 | −0.0336169 | ||||||||
\(997\) | 57.3019 | 1.81477 | 0.907385 | − | 0.420302i | \(-0.138076\pi\) | ||||
0.907385 | + | 0.420302i | \(0.138076\pi\) | |||||||
\(998\) | 54.6999 | 1.73149 | ||||||||
\(999\) | −4.74702 | −0.150189 |
(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 | 3549.2.a.be.1.8 | ✓ | 9 | |
13.12 | even | 2 | 3549.2.a.bf.1.2 | yes | 9 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
3549.2.a.be.1.8 | ✓ | 9 | 1.1 | even | 1 | trivial | |
3549.2.a.bf.1.2 | yes | 9 | 13.12 | even | 2 |