Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [7098,2,Mod(1,7098)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(7098, 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("7098.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 7098 = 2 \cdot 3 \cdot 7 \cdot 13^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 7098.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: | \(56.6778153547\) |
Analytic rank: | \(1\) |
Dimension: | \(6\) |
Coefficient field: | 6.6.48406561.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{6} - 3x^{5} - 17x^{4} + 39x^{3} + 111x^{2} - 131x - 281 \) |
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 | 1.2 | ||
Root | \(3.10863\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 7098.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.00000 | −0.707107 | ||||||||
\(3\) | 1.00000 | 0.577350 | ||||||||
\(4\) | 1.00000 | 0.500000 | ||||||||
\(5\) | −3.10863 | −1.39022 | −0.695111 | − | 0.718902i | \(-0.744645\pi\) | ||||
−0.695111 | + | 0.718902i | \(0.744645\pi\) | |||||||
\(6\) | −1.00000 | −0.408248 | ||||||||
\(7\) | −1.00000 | −0.377964 | ||||||||
\(8\) | −1.00000 | −0.353553 | ||||||||
\(9\) | 1.00000 | 0.333333 | ||||||||
\(10\) | 3.10863 | 0.983036 | ||||||||
\(11\) | −1.55496 | −0.468838 | −0.234419 | − | 0.972136i | \(-0.575319\pi\) | ||||
−0.234419 | + | 0.972136i | \(0.575319\pi\) | |||||||
\(12\) | 1.00000 | 0.288675 | ||||||||
\(13\) | 0 | 0 | ||||||||
\(14\) | 1.00000 | 0.267261 | ||||||||
\(15\) | −3.10863 | −0.802645 | ||||||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | −1.24698 | −0.302437 | −0.151218 | − | 0.988500i | \(-0.548320\pi\) | ||||
−0.151218 | + | 0.988500i | \(0.548320\pi\) | |||||||
\(18\) | −1.00000 | −0.235702 | ||||||||
\(19\) | 4.73805 | 1.08698 | 0.543492 | − | 0.839414i | \(-0.317102\pi\) | ||||
0.543492 | + | 0.839414i | \(0.317102\pi\) | |||||||
\(20\) | −3.10863 | −0.695111 | ||||||||
\(21\) | −1.00000 | −0.218218 | ||||||||
\(22\) | 1.55496 | 0.331518 | ||||||||
\(23\) | 5.10817 | 1.06513 | 0.532564 | − | 0.846390i | \(-0.321229\pi\) | ||||
0.532564 | + | 0.846390i | \(0.321229\pi\) | |||||||
\(24\) | −1.00000 | −0.204124 | ||||||||
\(25\) | 4.66359 | 0.932718 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 1.00000 | 0.192450 | ||||||||
\(28\) | −1.00000 | −0.188982 | ||||||||
\(29\) | −1.05926 | −0.196699 | −0.0983494 | − | 0.995152i | \(-0.531356\pi\) | ||||
−0.0983494 | + | 0.995152i | \(0.531356\pi\) | |||||||
\(30\) | 3.10863 | 0.567556 | ||||||||
\(31\) | 2.46553 | 0.442822 | 0.221411 | − | 0.975181i | \(-0.428934\pi\) | ||||
0.221411 | + | 0.975181i | \(0.428934\pi\) | |||||||
\(32\) | −1.00000 | −0.176777 | ||||||||
\(33\) | −1.55496 | −0.270683 | ||||||||
\(34\) | 1.24698 | 0.213855 | ||||||||
\(35\) | 3.10863 | 0.525455 | ||||||||
\(36\) | 1.00000 | 0.166667 | ||||||||
\(37\) | −7.92429 | −1.30274 | −0.651372 | − | 0.758758i | \(-0.725806\pi\) | ||||
−0.651372 | + | 0.758758i | \(0.725806\pi\) | |||||||
\(38\) | −4.73805 | −0.768614 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 3.10863 | 0.491518 | ||||||||
\(41\) | −2.71654 | −0.424252 | −0.212126 | − | 0.977242i | \(-0.568039\pi\) | ||||
−0.212126 | + | 0.977242i | \(0.568039\pi\) | |||||||
\(42\) | 1.00000 | 0.154303 | ||||||||
\(43\) | −2.63128 | −0.401266 | −0.200633 | − | 0.979666i | \(-0.564300\pi\) | ||||
−0.200633 | + | 0.979666i | \(0.564300\pi\) | |||||||
\(44\) | −1.55496 | −0.234419 | ||||||||
\(45\) | −3.10863 | −0.463407 | ||||||||
\(46\) | −5.10817 | −0.753159 | ||||||||
\(47\) | −5.06412 | −0.738678 | −0.369339 | − | 0.929295i | \(-0.620416\pi\) | ||||
−0.369339 | + | 0.929295i | \(0.620416\pi\) | |||||||
\(48\) | 1.00000 | 0.144338 | ||||||||
\(49\) | 1.00000 | 0.142857 | ||||||||
\(50\) | −4.66359 | −0.659531 | ||||||||
\(51\) | −1.24698 | −0.174612 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −7.09392 | −0.974425 | −0.487212 | − | 0.873284i | \(-0.661986\pi\) | ||||
−0.487212 | + | 0.873284i | \(0.661986\pi\) | |||||||
\(54\) | −1.00000 | −0.136083 | ||||||||
\(55\) | 4.83379 | 0.651788 | ||||||||
\(56\) | 1.00000 | 0.133631 | ||||||||
\(57\) | 4.73805 | 0.627570 | ||||||||
\(58\) | 1.05926 | 0.139087 | ||||||||
\(59\) | 3.41870 | 0.445077 | 0.222539 | − | 0.974924i | \(-0.428566\pi\) | ||||
0.222539 | + | 0.974924i | \(0.428566\pi\) | |||||||
\(60\) | −3.10863 | −0.401323 | ||||||||
\(61\) | 13.2814 | 1.70051 | 0.850254 | − | 0.526373i | \(-0.176448\pi\) | ||||
0.850254 | + | 0.526373i | \(0.176448\pi\) | |||||||
\(62\) | −2.46553 | −0.313122 | ||||||||
\(63\) | −1.00000 | −0.125988 | ||||||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 1.55496 | 0.191402 | ||||||||
\(67\) | 8.48684 | 1.03683 | 0.518416 | − | 0.855128i | \(-0.326522\pi\) | ||||
0.518416 | + | 0.855128i | \(0.326522\pi\) | |||||||
\(68\) | −1.24698 | −0.151218 | ||||||||
\(69\) | 5.10817 | 0.614952 | ||||||||
\(70\) | −3.10863 | −0.371553 | ||||||||
\(71\) | 5.31350 | 0.630596 | 0.315298 | − | 0.948993i | \(-0.397896\pi\) | ||||
0.315298 | + | 0.948993i | \(0.397896\pi\) | |||||||
\(72\) | −1.00000 | −0.117851 | ||||||||
\(73\) | −9.45056 | −1.10610 | −0.553052 | − | 0.833147i | \(-0.686537\pi\) | ||||
−0.553052 | + | 0.833147i | \(0.686537\pi\) | |||||||
\(74\) | 7.92429 | 0.921180 | ||||||||
\(75\) | 4.66359 | 0.538505 | ||||||||
\(76\) | 4.73805 | 0.543492 | ||||||||
\(77\) | 1.55496 | 0.177204 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 11.1942 | 1.25945 | 0.629725 | − | 0.776818i | \(-0.283167\pi\) | ||||
0.629725 | + | 0.776818i | \(0.283167\pi\) | |||||||
\(80\) | −3.10863 | −0.347556 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | 2.71654 | 0.299991 | ||||||||
\(83\) | 4.40061 | 0.483030 | 0.241515 | − | 0.970397i | \(-0.422356\pi\) | ||||
0.241515 | + | 0.970397i | \(0.422356\pi\) | |||||||
\(84\) | −1.00000 | −0.109109 | ||||||||
\(85\) | 3.87640 | 0.420455 | ||||||||
\(86\) | 2.63128 | 0.283738 | ||||||||
\(87\) | −1.05926 | −0.113564 | ||||||||
\(88\) | 1.55496 | 0.165759 | ||||||||
\(89\) | −5.76399 | −0.610982 | −0.305491 | − | 0.952195i | \(-0.598821\pi\) | ||||
−0.305491 | + | 0.952195i | \(0.598821\pi\) | |||||||
\(90\) | 3.10863 | 0.327679 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | 5.10817 | 0.532564 | ||||||||
\(93\) | 2.46553 | 0.255663 | ||||||||
\(94\) | 5.06412 | 0.522325 | ||||||||
\(95\) | −14.7289 | −1.51115 | ||||||||
\(96\) | −1.00000 | −0.102062 | ||||||||
\(97\) | −10.8007 | −1.09664 | −0.548322 | − | 0.836267i | \(-0.684733\pi\) | ||||
−0.548322 | + | 0.836267i | \(0.684733\pi\) | |||||||
\(98\) | −1.00000 | −0.101015 | ||||||||
\(99\) | −1.55496 | −0.156279 | ||||||||
\(100\) | 4.66359 | 0.466359 | ||||||||
\(101\) | 8.82958 | 0.878576 | 0.439288 | − | 0.898346i | \(-0.355231\pi\) | ||||
0.439288 | + | 0.898346i | \(0.355231\pi\) | |||||||
\(102\) | 1.24698 | 0.123469 | ||||||||
\(103\) | 1.89793 | 0.187009 | 0.0935044 | − | 0.995619i | \(-0.470193\pi\) | ||||
0.0935044 | + | 0.995619i | \(0.470193\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 3.10863 | 0.303371 | ||||||||
\(106\) | 7.09392 | 0.689022 | ||||||||
\(107\) | −3.58727 | −0.346795 | −0.173397 | − | 0.984852i | \(-0.555474\pi\) | ||||
−0.173397 | + | 0.984852i | \(0.555474\pi\) | |||||||
\(108\) | 1.00000 | 0.0962250 | ||||||||
\(109\) | 20.3167 | 1.94599 | 0.972995 | − | 0.230826i | \(-0.0741428\pi\) | ||||
0.972995 | + | 0.230826i | \(0.0741428\pi\) | |||||||
\(110\) | −4.83379 | −0.460884 | ||||||||
\(111\) | −7.92429 | −0.752140 | ||||||||
\(112\) | −1.00000 | −0.0944911 | ||||||||
\(113\) | −6.85060 | −0.644450 | −0.322225 | − | 0.946663i | \(-0.604431\pi\) | ||||
−0.322225 | + | 0.946663i | \(0.604431\pi\) | |||||||
\(114\) | −4.73805 | −0.443759 | ||||||||
\(115\) | −15.8794 | −1.48076 | ||||||||
\(116\) | −1.05926 | −0.0983494 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | −3.41870 | −0.314717 | ||||||||
\(119\) | 1.24698 | 0.114310 | ||||||||
\(120\) | 3.10863 | 0.283778 | ||||||||
\(121\) | −8.58211 | −0.780191 | ||||||||
\(122\) | −13.2814 | −1.20244 | ||||||||
\(123\) | −2.71654 | −0.244942 | ||||||||
\(124\) | 2.46553 | 0.221411 | ||||||||
\(125\) | 1.04578 | 0.0935370 | ||||||||
\(126\) | 1.00000 | 0.0890871 | ||||||||
\(127\) | 8.46378 | 0.751039 | 0.375520 | − | 0.926814i | \(-0.377464\pi\) | ||||
0.375520 | + | 0.926814i | \(0.377464\pi\) | |||||||
\(128\) | −1.00000 | −0.0883883 | ||||||||
\(129\) | −2.63128 | −0.231671 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −5.07860 | −0.443719 | −0.221860 | − | 0.975079i | \(-0.571213\pi\) | ||||
−0.221860 | + | 0.975079i | \(0.571213\pi\) | |||||||
\(132\) | −1.55496 | −0.135342 | ||||||||
\(133\) | −4.73805 | −0.410841 | ||||||||
\(134\) | −8.48684 | −0.733151 | ||||||||
\(135\) | −3.10863 | −0.267548 | ||||||||
\(136\) | 1.24698 | 0.106928 | ||||||||
\(137\) | −20.8764 | −1.78359 | −0.891795 | − | 0.452440i | \(-0.850554\pi\) | ||||
−0.891795 | + | 0.452440i | \(0.850554\pi\) | |||||||
\(138\) | −5.10817 | −0.434837 | ||||||||
\(139\) | 17.7255 | 1.50346 | 0.751729 | − | 0.659472i | \(-0.229220\pi\) | ||||
0.751729 | + | 0.659472i | \(0.229220\pi\) | |||||||
\(140\) | 3.10863 | 0.262727 | ||||||||
\(141\) | −5.06412 | −0.426476 | ||||||||
\(142\) | −5.31350 | −0.445899 | ||||||||
\(143\) | 0 | 0 | ||||||||
\(144\) | 1.00000 | 0.0833333 | ||||||||
\(145\) | 3.29284 | 0.273455 | ||||||||
\(146\) | 9.45056 | 0.782134 | ||||||||
\(147\) | 1.00000 | 0.0824786 | ||||||||
\(148\) | −7.92429 | −0.651372 | ||||||||
\(149\) | −0.829877 | −0.0679862 | −0.0339931 | − | 0.999422i | \(-0.510822\pi\) | ||||
−0.0339931 | + | 0.999422i | \(0.510822\pi\) | |||||||
\(150\) | −4.66359 | −0.380780 | ||||||||
\(151\) | 3.39170 | 0.276012 | 0.138006 | − | 0.990431i | \(-0.455931\pi\) | ||||
0.138006 | + | 0.990431i | \(0.455931\pi\) | |||||||
\(152\) | −4.73805 | −0.384307 | ||||||||
\(153\) | −1.24698 | −0.100812 | ||||||||
\(154\) | −1.55496 | −0.125302 | ||||||||
\(155\) | −7.66442 | −0.615621 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −23.7381 | −1.89450 | −0.947251 | − | 0.320492i | \(-0.896152\pi\) | ||||
−0.947251 | + | 0.320492i | \(0.896152\pi\) | |||||||
\(158\) | −11.1942 | −0.890566 | ||||||||
\(159\) | −7.09392 | −0.562584 | ||||||||
\(160\) | 3.10863 | 0.245759 | ||||||||
\(161\) | −5.10817 | −0.402580 | ||||||||
\(162\) | −1.00000 | −0.0785674 | ||||||||
\(163\) | 6.35482 | 0.497748 | 0.248874 | − | 0.968536i | \(-0.419940\pi\) | ||||
0.248874 | + | 0.968536i | \(0.419940\pi\) | |||||||
\(164\) | −2.71654 | −0.212126 | ||||||||
\(165\) | 4.83379 | 0.376310 | ||||||||
\(166\) | −4.40061 | −0.341554 | ||||||||
\(167\) | 7.50114 | 0.580456 | 0.290228 | − | 0.956958i | \(-0.406269\pi\) | ||||
0.290228 | + | 0.956958i | \(0.406269\pi\) | |||||||
\(168\) | 1.00000 | 0.0771517 | ||||||||
\(169\) | 0 | 0 | ||||||||
\(170\) | −3.87640 | −0.297306 | ||||||||
\(171\) | 4.73805 | 0.362328 | ||||||||
\(172\) | −2.63128 | −0.200633 | ||||||||
\(173\) | −16.1881 | −1.23076 | −0.615378 | − | 0.788232i | \(-0.710997\pi\) | ||||
−0.615378 | + | 0.788232i | \(0.710997\pi\) | |||||||
\(174\) | 1.05926 | 0.0803020 | ||||||||
\(175\) | −4.66359 | −0.352534 | ||||||||
\(176\) | −1.55496 | −0.117209 | ||||||||
\(177\) | 3.41870 | 0.256966 | ||||||||
\(178\) | 5.76399 | 0.432030 | ||||||||
\(179\) | 1.95421 | 0.146064 | 0.0730322 | − | 0.997330i | \(-0.476732\pi\) | ||||
0.0730322 | + | 0.997330i | \(0.476732\pi\) | |||||||
\(180\) | −3.10863 | −0.231704 | ||||||||
\(181\) | −1.81969 | −0.135256 | −0.0676281 | − | 0.997711i | \(-0.521543\pi\) | ||||
−0.0676281 | + | 0.997711i | \(0.521543\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 13.2814 | 0.981788 | ||||||||
\(184\) | −5.10817 | −0.376580 | ||||||||
\(185\) | 24.6337 | 1.81110 | ||||||||
\(186\) | −2.46553 | −0.180781 | ||||||||
\(187\) | 1.93900 | 0.141794 | ||||||||
\(188\) | −5.06412 | −0.369339 | ||||||||
\(189\) | −1.00000 | −0.0727393 | ||||||||
\(190\) | 14.7289 | 1.06854 | ||||||||
\(191\) | −23.3210 | −1.68745 | −0.843723 | − | 0.536779i | \(-0.819641\pi\) | ||||
−0.843723 | + | 0.536779i | \(0.819641\pi\) | |||||||
\(192\) | 1.00000 | 0.0721688 | ||||||||
\(193\) | −7.99277 | −0.575332 | −0.287666 | − | 0.957731i | \(-0.592879\pi\) | ||||
−0.287666 | + | 0.957731i | \(0.592879\pi\) | |||||||
\(194\) | 10.8007 | 0.775444 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 1.00000 | 0.0714286 | ||||||||
\(197\) | 2.24858 | 0.160205 | 0.0801024 | − | 0.996787i | \(-0.474475\pi\) | ||||
0.0801024 | + | 0.996787i | \(0.474475\pi\) | |||||||
\(198\) | 1.55496 | 0.110506 | ||||||||
\(199\) | −25.4768 | −1.80600 | −0.903001 | − | 0.429638i | \(-0.858641\pi\) | ||||
−0.903001 | + | 0.429638i | \(0.858641\pi\) | |||||||
\(200\) | −4.66359 | −0.329766 | ||||||||
\(201\) | 8.48684 | 0.598615 | ||||||||
\(202\) | −8.82958 | −0.621247 | ||||||||
\(203\) | 1.05926 | 0.0743452 | ||||||||
\(204\) | −1.24698 | −0.0873060 | ||||||||
\(205\) | 8.44471 | 0.589804 | ||||||||
\(206\) | −1.89793 | −0.132235 | ||||||||
\(207\) | 5.10817 | 0.355043 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −7.36747 | −0.509619 | ||||||||
\(210\) | −3.10863 | −0.214516 | ||||||||
\(211\) | 2.01914 | 0.139003 | 0.0695016 | − | 0.997582i | \(-0.477859\pi\) | ||||
0.0695016 | + | 0.997582i | \(0.477859\pi\) | |||||||
\(212\) | −7.09392 | −0.487212 | ||||||||
\(213\) | 5.31350 | 0.364075 | ||||||||
\(214\) | 3.58727 | 0.245221 | ||||||||
\(215\) | 8.17967 | 0.557849 | ||||||||
\(216\) | −1.00000 | −0.0680414 | ||||||||
\(217\) | −2.46553 | −0.167371 | ||||||||
\(218\) | −20.3167 | −1.37602 | ||||||||
\(219\) | −9.45056 | −0.638610 | ||||||||
\(220\) | 4.83379 | 0.325894 | ||||||||
\(221\) | 0 | 0 | ||||||||
\(222\) | 7.92429 | 0.531843 | ||||||||
\(223\) | 13.1491 | 0.880532 | 0.440266 | − | 0.897867i | \(-0.354884\pi\) | ||||
0.440266 | + | 0.897867i | \(0.354884\pi\) | |||||||
\(224\) | 1.00000 | 0.0668153 | ||||||||
\(225\) | 4.66359 | 0.310906 | ||||||||
\(226\) | 6.85060 | 0.455695 | ||||||||
\(227\) | −1.90722 | −0.126587 | −0.0632935 | − | 0.997995i | \(-0.520160\pi\) | ||||
−0.0632935 | + | 0.997995i | \(0.520160\pi\) | |||||||
\(228\) | 4.73805 | 0.313785 | ||||||||
\(229\) | 1.32344 | 0.0874554 | 0.0437277 | − | 0.999043i | \(-0.486077\pi\) | ||||
0.0437277 | + | 0.999043i | \(0.486077\pi\) | |||||||
\(230\) | 15.8794 | 1.04706 | ||||||||
\(231\) | 1.55496 | 0.102309 | ||||||||
\(232\) | 1.05926 | 0.0695435 | ||||||||
\(233\) | −23.7561 | −1.55631 | −0.778157 | − | 0.628069i | \(-0.783845\pi\) | ||||
−0.778157 | + | 0.628069i | \(0.783845\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 15.7425 | 1.02693 | ||||||||
\(236\) | 3.41870 | 0.222539 | ||||||||
\(237\) | 11.1942 | 0.727144 | ||||||||
\(238\) | −1.24698 | −0.0808297 | ||||||||
\(239\) | −27.3308 | −1.76789 | −0.883943 | − | 0.467595i | \(-0.845121\pi\) | ||||
−0.883943 | + | 0.467595i | \(0.845121\pi\) | |||||||
\(240\) | −3.10863 | −0.200661 | ||||||||
\(241\) | −2.68328 | −0.172846 | −0.0864228 | − | 0.996259i | \(-0.527544\pi\) | ||||
−0.0864228 | + | 0.996259i | \(0.527544\pi\) | |||||||
\(242\) | 8.58211 | 0.551679 | ||||||||
\(243\) | 1.00000 | 0.0641500 | ||||||||
\(244\) | 13.2814 | 0.850254 | ||||||||
\(245\) | −3.10863 | −0.198603 | ||||||||
\(246\) | 2.71654 | 0.173200 | ||||||||
\(247\) | 0 | 0 | ||||||||
\(248\) | −2.46553 | −0.156561 | ||||||||
\(249\) | 4.40061 | 0.278877 | ||||||||
\(250\) | −1.04578 | −0.0661407 | ||||||||
\(251\) | −30.8962 | −1.95015 | −0.975077 | − | 0.221867i | \(-0.928785\pi\) | ||||
−0.975077 | + | 0.221867i | \(0.928785\pi\) | |||||||
\(252\) | −1.00000 | −0.0629941 | ||||||||
\(253\) | −7.94300 | −0.499372 | ||||||||
\(254\) | −8.46378 | −0.531065 | ||||||||
\(255\) | 3.87640 | 0.242750 | ||||||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | 27.6822 | 1.72677 | 0.863385 | − | 0.504546i | \(-0.168340\pi\) | ||||
0.863385 | + | 0.504546i | \(0.168340\pi\) | |||||||
\(258\) | 2.63128 | 0.163816 | ||||||||
\(259\) | 7.92429 | 0.492391 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −1.05926 | −0.0655663 | ||||||||
\(262\) | 5.07860 | 0.313757 | ||||||||
\(263\) | 21.8601 | 1.34795 | 0.673975 | − | 0.738754i | \(-0.264586\pi\) | ||||
0.673975 | + | 0.738754i | \(0.264586\pi\) | |||||||
\(264\) | 1.55496 | 0.0957011 | ||||||||
\(265\) | 22.0524 | 1.35467 | ||||||||
\(266\) | 4.73805 | 0.290509 | ||||||||
\(267\) | −5.76399 | −0.352751 | ||||||||
\(268\) | 8.48684 | 0.518416 | ||||||||
\(269\) | −17.0766 | −1.04118 | −0.520590 | − | 0.853807i | \(-0.674288\pi\) | ||||
−0.520590 | + | 0.853807i | \(0.674288\pi\) | |||||||
\(270\) | 3.10863 | 0.189185 | ||||||||
\(271\) | −27.8718 | −1.69309 | −0.846547 | − | 0.532315i | \(-0.821322\pi\) | ||||
−0.846547 | + | 0.532315i | \(0.821322\pi\) | |||||||
\(272\) | −1.24698 | −0.0756092 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 20.8764 | 1.26119 | ||||||||
\(275\) | −7.25169 | −0.437293 | ||||||||
\(276\) | 5.10817 | 0.307476 | ||||||||
\(277\) | −31.9253 | −1.91820 | −0.959102 | − | 0.283061i | \(-0.908650\pi\) | ||||
−0.959102 | + | 0.283061i | \(0.908650\pi\) | |||||||
\(278\) | −17.7255 | −1.06311 | ||||||||
\(279\) | 2.46553 | 0.147607 | ||||||||
\(280\) | −3.10863 | −0.185776 | ||||||||
\(281\) | 11.3692 | 0.678229 | 0.339114 | − | 0.940745i | \(-0.389873\pi\) | ||||
0.339114 | + | 0.940745i | \(0.389873\pi\) | |||||||
\(282\) | 5.06412 | 0.301564 | ||||||||
\(283\) | −16.6264 | −0.988334 | −0.494167 | − | 0.869367i | \(-0.664527\pi\) | ||||
−0.494167 | + | 0.869367i | \(0.664527\pi\) | |||||||
\(284\) | 5.31350 | 0.315298 | ||||||||
\(285\) | −14.7289 | −0.872462 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 2.71654 | 0.160352 | ||||||||
\(288\) | −1.00000 | −0.0589256 | ||||||||
\(289\) | −15.4450 | −0.908532 | ||||||||
\(290\) | −3.29284 | −0.193362 | ||||||||
\(291\) | −10.8007 | −0.633147 | ||||||||
\(292\) | −9.45056 | −0.553052 | ||||||||
\(293\) | 5.41358 | 0.316265 | 0.158132 | − | 0.987418i | \(-0.449453\pi\) | ||||
0.158132 | + | 0.987418i | \(0.449453\pi\) | |||||||
\(294\) | −1.00000 | −0.0583212 | ||||||||
\(295\) | −10.6275 | −0.618757 | ||||||||
\(296\) | 7.92429 | 0.460590 | ||||||||
\(297\) | −1.55496 | −0.0902278 | ||||||||
\(298\) | 0.829877 | 0.0480735 | ||||||||
\(299\) | 0 | 0 | ||||||||
\(300\) | 4.66359 | 0.269252 | ||||||||
\(301\) | 2.63128 | 0.151664 | ||||||||
\(302\) | −3.39170 | −0.195170 | ||||||||
\(303\) | 8.82958 | 0.507246 | ||||||||
\(304\) | 4.73805 | 0.271746 | ||||||||
\(305\) | −41.2869 | −2.36408 | ||||||||
\(306\) | 1.24698 | 0.0712851 | ||||||||
\(307\) | −6.53538 | −0.372994 | −0.186497 | − | 0.982456i | \(-0.559713\pi\) | ||||
−0.186497 | + | 0.982456i | \(0.559713\pi\) | |||||||
\(308\) | 1.55496 | 0.0886020 | ||||||||
\(309\) | 1.89793 | 0.107970 | ||||||||
\(310\) | 7.66442 | 0.435310 | ||||||||
\(311\) | −27.7921 | −1.57595 | −0.787973 | − | 0.615710i | \(-0.788869\pi\) | ||||
−0.787973 | + | 0.615710i | \(0.788869\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −4.35209 | −0.245995 | −0.122997 | − | 0.992407i | \(-0.539251\pi\) | ||||
−0.122997 | + | 0.992407i | \(0.539251\pi\) | |||||||
\(314\) | 23.7381 | 1.33962 | ||||||||
\(315\) | 3.10863 | 0.175152 | ||||||||
\(316\) | 11.1942 | 0.629725 | ||||||||
\(317\) | −12.5835 | −0.706761 | −0.353381 | − | 0.935480i | \(-0.614968\pi\) | ||||
−0.353381 | + | 0.935480i | \(0.614968\pi\) | |||||||
\(318\) | 7.09392 | 0.397807 | ||||||||
\(319\) | 1.64710 | 0.0922198 | ||||||||
\(320\) | −3.10863 | −0.173778 | ||||||||
\(321\) | −3.58727 | −0.200222 | ||||||||
\(322\) | 5.10817 | 0.284667 | ||||||||
\(323\) | −5.90825 | −0.328744 | ||||||||
\(324\) | 1.00000 | 0.0555556 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | −6.35482 | −0.351961 | ||||||||
\(327\) | 20.3167 | 1.12352 | ||||||||
\(328\) | 2.71654 | 0.149996 | ||||||||
\(329\) | 5.06412 | 0.279194 | ||||||||
\(330\) | −4.83379 | −0.266091 | ||||||||
\(331\) | −19.8866 | −1.09307 | −0.546533 | − | 0.837437i | \(-0.684053\pi\) | ||||
−0.546533 | + | 0.837437i | \(0.684053\pi\) | |||||||
\(332\) | 4.40061 | 0.241515 | ||||||||
\(333\) | −7.92429 | −0.434248 | ||||||||
\(334\) | −7.50114 | −0.410444 | ||||||||
\(335\) | −26.3825 | −1.44143 | ||||||||
\(336\) | −1.00000 | −0.0545545 | ||||||||
\(337\) | 0.500733 | 0.0272767 | 0.0136383 | − | 0.999907i | \(-0.495659\pi\) | ||||
0.0136383 | + | 0.999907i | \(0.495659\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −6.85060 | −0.372074 | ||||||||
\(340\) | 3.87640 | 0.210227 | ||||||||
\(341\) | −3.83379 | −0.207611 | ||||||||
\(342\) | −4.73805 | −0.256205 | ||||||||
\(343\) | −1.00000 | −0.0539949 | ||||||||
\(344\) | 2.63128 | 0.141869 | ||||||||
\(345\) | −15.8794 | −0.854920 | ||||||||
\(346\) | 16.1881 | 0.870276 | ||||||||
\(347\) | −24.7464 | −1.32846 | −0.664229 | − | 0.747530i | \(-0.731240\pi\) | ||||
−0.664229 | + | 0.747530i | \(0.731240\pi\) | |||||||
\(348\) | −1.05926 | −0.0567821 | ||||||||
\(349\) | 4.30578 | 0.230483 | 0.115241 | − | 0.993338i | \(-0.463236\pi\) | ||||
0.115241 | + | 0.993338i | \(0.463236\pi\) | |||||||
\(350\) | 4.66359 | 0.249279 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 1.55496 | 0.0828795 | ||||||||
\(353\) | 4.18501 | 0.222746 | 0.111373 | − | 0.993779i | \(-0.464475\pi\) | ||||
0.111373 | + | 0.993779i | \(0.464475\pi\) | |||||||
\(354\) | −3.41870 | −0.181702 | ||||||||
\(355\) | −16.5177 | −0.876668 | ||||||||
\(356\) | −5.76399 | −0.305491 | ||||||||
\(357\) | 1.24698 | 0.0659972 | ||||||||
\(358\) | −1.95421 | −0.103283 | ||||||||
\(359\) | 6.33135 | 0.334156 | 0.167078 | − | 0.985944i | \(-0.446567\pi\) | ||||
0.167078 | + | 0.985944i | \(0.446567\pi\) | |||||||
\(360\) | 3.10863 | 0.163839 | ||||||||
\(361\) | 3.44914 | 0.181533 | ||||||||
\(362\) | 1.81969 | 0.0956406 | ||||||||
\(363\) | −8.58211 | −0.450444 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 29.3783 | 1.53773 | ||||||||
\(366\) | −13.2814 | −0.694229 | ||||||||
\(367\) | 19.8935 | 1.03843 | 0.519216 | − | 0.854643i | \(-0.326224\pi\) | ||||
0.519216 | + | 0.854643i | \(0.326224\pi\) | |||||||
\(368\) | 5.10817 | 0.266282 | ||||||||
\(369\) | −2.71654 | −0.141417 | ||||||||
\(370\) | −24.6337 | −1.28064 | ||||||||
\(371\) | 7.09392 | 0.368298 | ||||||||
\(372\) | 2.46553 | 0.127832 | ||||||||
\(373\) | −35.9969 | −1.86385 | −0.931923 | − | 0.362655i | \(-0.881870\pi\) | ||||
−0.931923 | + | 0.362655i | \(0.881870\pi\) | |||||||
\(374\) | −1.93900 | −0.100263 | ||||||||
\(375\) | 1.04578 | 0.0540036 | ||||||||
\(376\) | 5.06412 | 0.261162 | ||||||||
\(377\) | 0 | 0 | ||||||||
\(378\) | 1.00000 | 0.0514344 | ||||||||
\(379\) | −29.5252 | −1.51661 | −0.758304 | − | 0.651901i | \(-0.773972\pi\) | ||||
−0.758304 | + | 0.651901i | \(0.773972\pi\) | |||||||
\(380\) | −14.7289 | −0.755574 | ||||||||
\(381\) | 8.46378 | 0.433613 | ||||||||
\(382\) | 23.3210 | 1.19320 | ||||||||
\(383\) | 0.770083 | 0.0393494 | 0.0196747 | − | 0.999806i | \(-0.493737\pi\) | ||||
0.0196747 | + | 0.999806i | \(0.493737\pi\) | |||||||
\(384\) | −1.00000 | −0.0510310 | ||||||||
\(385\) | −4.83379 | −0.246353 | ||||||||
\(386\) | 7.99277 | 0.406821 | ||||||||
\(387\) | −2.63128 | −0.133755 | ||||||||
\(388\) | −10.8007 | −0.548322 | ||||||||
\(389\) | 18.6621 | 0.946208 | 0.473104 | − | 0.881006i | \(-0.343133\pi\) | ||||
0.473104 | + | 0.881006i | \(0.343133\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −6.36979 | −0.322134 | ||||||||
\(392\) | −1.00000 | −0.0505076 | ||||||||
\(393\) | −5.07860 | −0.256181 | ||||||||
\(394\) | −2.24858 | −0.113282 | ||||||||
\(395\) | −34.7988 | −1.75092 | ||||||||
\(396\) | −1.55496 | −0.0781396 | ||||||||
\(397\) | −17.7403 | −0.890360 | −0.445180 | − | 0.895441i | \(-0.646860\pi\) | ||||
−0.445180 | + | 0.895441i | \(0.646860\pi\) | |||||||
\(398\) | 25.4768 | 1.27704 | ||||||||
\(399\) | −4.73805 | −0.237199 | ||||||||
\(400\) | 4.66359 | 0.233179 | ||||||||
\(401\) | −18.1461 | −0.906172 | −0.453086 | − | 0.891467i | \(-0.649677\pi\) | ||||
−0.453086 | + | 0.891467i | \(0.649677\pi\) | |||||||
\(402\) | −8.48684 | −0.423285 | ||||||||
\(403\) | 0 | 0 | ||||||||
\(404\) | 8.82958 | 0.439288 | ||||||||
\(405\) | −3.10863 | −0.154469 | ||||||||
\(406\) | −1.05926 | −0.0525700 | ||||||||
\(407\) | 12.3219 | 0.610776 | ||||||||
\(408\) | 1.24698 | 0.0617347 | ||||||||
\(409\) | −0.936649 | −0.0463143 | −0.0231572 | − | 0.999732i | \(-0.507372\pi\) | ||||
−0.0231572 | + | 0.999732i | \(0.507372\pi\) | |||||||
\(410\) | −8.44471 | −0.417054 | ||||||||
\(411\) | −20.8764 | −1.02976 | ||||||||
\(412\) | 1.89793 | 0.0935044 | ||||||||
\(413\) | −3.41870 | −0.168223 | ||||||||
\(414\) | −5.10817 | −0.251053 | ||||||||
\(415\) | −13.6799 | −0.671519 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 17.7255 | 0.868022 | ||||||||
\(418\) | 7.36747 | 0.360355 | ||||||||
\(419\) | −10.0234 | −0.489675 | −0.244838 | − | 0.969564i | \(-0.578735\pi\) | ||||
−0.244838 | + | 0.969564i | \(0.578735\pi\) | |||||||
\(420\) | 3.10863 | 0.151686 | ||||||||
\(421\) | 19.7171 | 0.960951 | 0.480475 | − | 0.877008i | \(-0.340464\pi\) | ||||
0.480475 | + | 0.877008i | \(0.340464\pi\) | |||||||
\(422\) | −2.01914 | −0.0982902 | ||||||||
\(423\) | −5.06412 | −0.246226 | ||||||||
\(424\) | 7.09392 | 0.344511 | ||||||||
\(425\) | −5.81540 | −0.282088 | ||||||||
\(426\) | −5.31350 | −0.257440 | ||||||||
\(427\) | −13.2814 | −0.642731 | ||||||||
\(428\) | −3.58727 | −0.173397 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | −8.17967 | −0.394459 | ||||||||
\(431\) | 31.5252 | 1.51852 | 0.759259 | − | 0.650789i | \(-0.225562\pi\) | ||||
0.759259 | + | 0.650789i | \(0.225562\pi\) | |||||||
\(432\) | 1.00000 | 0.0481125 | ||||||||
\(433\) | 19.6284 | 0.943281 | 0.471641 | − | 0.881791i | \(-0.343662\pi\) | ||||
0.471641 | + | 0.881791i | \(0.343662\pi\) | |||||||
\(434\) | 2.46553 | 0.118349 | ||||||||
\(435\) | 3.29284 | 0.157879 | ||||||||
\(436\) | 20.3167 | 0.972995 | ||||||||
\(437\) | 24.2028 | 1.15778 | ||||||||
\(438\) | 9.45056 | 0.451565 | ||||||||
\(439\) | 34.8525 | 1.66342 | 0.831708 | − | 0.555213i | \(-0.187363\pi\) | ||||
0.831708 | + | 0.555213i | \(0.187363\pi\) | |||||||
\(440\) | −4.83379 | −0.230442 | ||||||||
\(441\) | 1.00000 | 0.0476190 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −9.65305 | −0.458630 | −0.229315 | − | 0.973352i | \(-0.573649\pi\) | ||||
−0.229315 | + | 0.973352i | \(0.573649\pi\) | |||||||
\(444\) | −7.92429 | −0.376070 | ||||||||
\(445\) | 17.9181 | 0.849401 | ||||||||
\(446\) | −13.1491 | −0.622630 | ||||||||
\(447\) | −0.829877 | −0.0392518 | ||||||||
\(448\) | −1.00000 | −0.0472456 | ||||||||
\(449\) | −15.2830 | −0.721249 | −0.360625 | − | 0.932711i | \(-0.617436\pi\) | ||||
−0.360625 | + | 0.932711i | \(0.617436\pi\) | |||||||
\(450\) | −4.66359 | −0.219844 | ||||||||
\(451\) | 4.22410 | 0.198905 | ||||||||
\(452\) | −6.85060 | −0.322225 | ||||||||
\(453\) | 3.39170 | 0.159356 | ||||||||
\(454\) | 1.90722 | 0.0895105 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | −4.73805 | −0.221880 | ||||||||
\(457\) | −16.0318 | −0.749937 | −0.374968 | − | 0.927038i | \(-0.622346\pi\) | ||||
−0.374968 | + | 0.927038i | \(0.622346\pi\) | |||||||
\(458\) | −1.32344 | −0.0618403 | ||||||||
\(459\) | −1.24698 | −0.0582040 | ||||||||
\(460\) | −15.8794 | −0.740382 | ||||||||
\(461\) | −28.6119 | −1.33259 | −0.666294 | − | 0.745689i | \(-0.732121\pi\) | ||||
−0.666294 | + | 0.745689i | \(0.732121\pi\) | |||||||
\(462\) | −1.55496 | −0.0723432 | ||||||||
\(463\) | 35.8620 | 1.66665 | 0.833325 | − | 0.552783i | \(-0.186434\pi\) | ||||
0.833325 | + | 0.552783i | \(0.186434\pi\) | |||||||
\(464\) | −1.05926 | −0.0491747 | ||||||||
\(465\) | −7.66442 | −0.355429 | ||||||||
\(466\) | 23.7561 | 1.10048 | ||||||||
\(467\) | −14.9263 | −0.690708 | −0.345354 | − | 0.938473i | \(-0.612241\pi\) | ||||
−0.345354 | + | 0.938473i | \(0.612241\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −8.48684 | −0.391886 | ||||||||
\(470\) | −15.7425 | −0.726147 | ||||||||
\(471\) | −23.7381 | −1.09379 | ||||||||
\(472\) | −3.41870 | −0.157359 | ||||||||
\(473\) | 4.09153 | 0.188129 | ||||||||
\(474\) | −11.1942 | −0.514169 | ||||||||
\(475\) | 22.0963 | 1.01385 | ||||||||
\(476\) | 1.24698 | 0.0571552 | ||||||||
\(477\) | −7.09392 | −0.324808 | ||||||||
\(478\) | 27.3308 | 1.25008 | ||||||||
\(479\) | 14.4348 | 0.659541 | 0.329771 | − | 0.944061i | \(-0.393029\pi\) | ||||
0.329771 | + | 0.944061i | \(0.393029\pi\) | |||||||
\(480\) | 3.10863 | 0.141889 | ||||||||
\(481\) | 0 | 0 | ||||||||
\(482\) | 2.68328 | 0.122220 | ||||||||
\(483\) | −5.10817 | −0.232430 | ||||||||
\(484\) | −8.58211 | −0.390096 | ||||||||
\(485\) | 33.5754 | 1.52458 | ||||||||
\(486\) | −1.00000 | −0.0453609 | ||||||||
\(487\) | 24.8740 | 1.12715 | 0.563575 | − | 0.826065i | \(-0.309425\pi\) | ||||
0.563575 | + | 0.826065i | \(0.309425\pi\) | |||||||
\(488\) | −13.2814 | −0.601220 | ||||||||
\(489\) | 6.35482 | 0.287375 | ||||||||
\(490\) | 3.10863 | 0.140434 | ||||||||
\(491\) | −10.6142 | −0.479014 | −0.239507 | − | 0.970895i | \(-0.576986\pi\) | ||||
−0.239507 | + | 0.970895i | \(0.576986\pi\) | |||||||
\(492\) | −2.71654 | −0.122471 | ||||||||
\(493\) | 1.32087 | 0.0594890 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 4.83379 | 0.217263 | ||||||||
\(496\) | 2.46553 | 0.110705 | ||||||||
\(497\) | −5.31350 | −0.238343 | ||||||||
\(498\) | −4.40061 | −0.197196 | ||||||||
\(499\) | −0.950418 | −0.0425465 | −0.0212733 | − | 0.999774i | \(-0.506772\pi\) | ||||
−0.0212733 | + | 0.999774i | \(0.506772\pi\) | |||||||
\(500\) | 1.04578 | 0.0467685 | ||||||||
\(501\) | 7.50114 | 0.335126 | ||||||||
\(502\) | 30.8962 | 1.37897 | ||||||||
\(503\) | 34.9853 | 1.55992 | 0.779958 | − | 0.625832i | \(-0.215240\pi\) | ||||
0.779958 | + | 0.625832i | \(0.215240\pi\) | |||||||
\(504\) | 1.00000 | 0.0445435 | ||||||||
\(505\) | −27.4479 | −1.22142 | ||||||||
\(506\) | 7.94300 | 0.353109 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 8.46378 | 0.375520 | ||||||||
\(509\) | −26.0425 | −1.15431 | −0.577157 | − | 0.816634i | \(-0.695838\pi\) | ||||
−0.577157 | + | 0.816634i | \(0.695838\pi\) | |||||||
\(510\) | −3.87640 | −0.171650 | ||||||||
\(511\) | 9.45056 | 0.418068 | ||||||||
\(512\) | −1.00000 | −0.0441942 | ||||||||
\(513\) | 4.73805 | 0.209190 | ||||||||
\(514\) | −27.6822 | −1.22101 | ||||||||
\(515\) | −5.89997 | −0.259984 | ||||||||
\(516\) | −2.63128 | −0.115836 | ||||||||
\(517\) | 7.87450 | 0.346320 | ||||||||
\(518\) | −7.92429 | −0.348173 | ||||||||
\(519\) | −16.1881 | −0.710578 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 39.0890 | 1.71252 | 0.856261 | − | 0.516544i | \(-0.172782\pi\) | ||||
0.856261 | + | 0.516544i | \(0.172782\pi\) | |||||||
\(522\) | 1.05926 | 0.0463624 | ||||||||
\(523\) | −6.41000 | −0.280290 | −0.140145 | − | 0.990131i | \(-0.544757\pi\) | ||||
−0.140145 | + | 0.990131i | \(0.544757\pi\) | |||||||
\(524\) | −5.07860 | −0.221860 | ||||||||
\(525\) | −4.66359 | −0.203536 | ||||||||
\(526\) | −21.8601 | −0.953144 | ||||||||
\(527\) | −3.07446 | −0.133926 | ||||||||
\(528\) | −1.55496 | −0.0676709 | ||||||||
\(529\) | 3.09343 | 0.134497 | ||||||||
\(530\) | −22.0524 | −0.957894 | ||||||||
\(531\) | 3.41870 | 0.148359 | ||||||||
\(532\) | −4.73805 | −0.205421 | ||||||||
\(533\) | 0 | 0 | ||||||||
\(534\) | 5.76399 | 0.249432 | ||||||||
\(535\) | 11.1515 | 0.482122 | ||||||||
\(536\) | −8.48684 | −0.366576 | ||||||||
\(537\) | 1.95421 | 0.0843303 | ||||||||
\(538\) | 17.0766 | 0.736225 | ||||||||
\(539\) | −1.55496 | −0.0669768 | ||||||||
\(540\) | −3.10863 | −0.133774 | ||||||||
\(541\) | −20.7891 | −0.893792 | −0.446896 | − | 0.894586i | \(-0.647471\pi\) | ||||
−0.446896 | + | 0.894586i | \(0.647471\pi\) | |||||||
\(542\) | 27.8718 | 1.19720 | ||||||||
\(543\) | −1.81969 | −0.0780902 | ||||||||
\(544\) | 1.24698 | 0.0534638 | ||||||||
\(545\) | −63.1572 | −2.70536 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 12.9402 | 0.553284 | 0.276642 | − | 0.960973i | \(-0.410778\pi\) | ||||
0.276642 | + | 0.960973i | \(0.410778\pi\) | |||||||
\(548\) | −20.8764 | −0.891795 | ||||||||
\(549\) | 13.2814 | 0.566836 | ||||||||
\(550\) | 7.25169 | 0.309213 | ||||||||
\(551\) | −5.01881 | −0.213808 | ||||||||
\(552\) | −5.10817 | −0.217418 | ||||||||
\(553\) | −11.1942 | −0.476028 | ||||||||
\(554\) | 31.9253 | 1.35637 | ||||||||
\(555\) | 24.6337 | 1.04564 | ||||||||
\(556\) | 17.7255 | 0.751729 | ||||||||
\(557\) | 24.0823 | 1.02040 | 0.510200 | − | 0.860056i | \(-0.329571\pi\) | ||||
0.510200 | + | 0.860056i | \(0.329571\pi\) | |||||||
\(558\) | −2.46553 | −0.104374 | ||||||||
\(559\) | 0 | 0 | ||||||||
\(560\) | 3.10863 | 0.131364 | ||||||||
\(561\) | 1.93900 | 0.0818647 | ||||||||
\(562\) | −11.3692 | −0.479580 | ||||||||
\(563\) | −27.0146 | −1.13853 | −0.569266 | − | 0.822154i | \(-0.692772\pi\) | ||||
−0.569266 | + | 0.822154i | \(0.692772\pi\) | |||||||
\(564\) | −5.06412 | −0.213238 | ||||||||
\(565\) | 21.2960 | 0.895929 | ||||||||
\(566\) | 16.6264 | 0.698858 | ||||||||
\(567\) | −1.00000 | −0.0419961 | ||||||||
\(568\) | −5.31350 | −0.222949 | ||||||||
\(569\) | −17.1952 | −0.720859 | −0.360429 | − | 0.932787i | \(-0.617370\pi\) | ||||
−0.360429 | + | 0.932787i | \(0.617370\pi\) | |||||||
\(570\) | 14.7289 | 0.616924 | ||||||||
\(571\) | −21.5316 | −0.901071 | −0.450536 | − | 0.892758i | \(-0.648767\pi\) | ||||
−0.450536 | + | 0.892758i | \(0.648767\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −23.3210 | −0.974247 | ||||||||
\(574\) | −2.71654 | −0.113386 | ||||||||
\(575\) | 23.8224 | 0.993464 | ||||||||
\(576\) | 1.00000 | 0.0416667 | ||||||||
\(577\) | 30.2104 | 1.25767 | 0.628837 | − | 0.777537i | \(-0.283531\pi\) | ||||
0.628837 | + | 0.777537i | \(0.283531\pi\) | |||||||
\(578\) | 15.4450 | 0.642429 | ||||||||
\(579\) | −7.99277 | −0.332168 | ||||||||
\(580\) | 3.29284 | 0.136728 | ||||||||
\(581\) | −4.40061 | −0.182568 | ||||||||
\(582\) | 10.8007 | 0.447703 | ||||||||
\(583\) | 11.0307 | 0.456847 | ||||||||
\(584\) | 9.45056 | 0.391067 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −5.41358 | −0.223633 | ||||||||
\(587\) | 39.7362 | 1.64009 | 0.820045 | − | 0.572299i | \(-0.193948\pi\) | ||||
0.820045 | + | 0.572299i | \(0.193948\pi\) | |||||||
\(588\) | 1.00000 | 0.0412393 | ||||||||
\(589\) | 11.6818 | 0.481340 | ||||||||
\(590\) | 10.6275 | 0.437527 | ||||||||
\(591\) | 2.24858 | 0.0924943 | ||||||||
\(592\) | −7.92429 | −0.325686 | ||||||||
\(593\) | −37.1150 | −1.52413 | −0.762066 | − | 0.647499i | \(-0.775815\pi\) | ||||
−0.762066 | + | 0.647499i | \(0.775815\pi\) | |||||||
\(594\) | 1.55496 | 0.0638007 | ||||||||
\(595\) | −3.87640 | −0.158917 | ||||||||
\(596\) | −0.829877 | −0.0339931 | ||||||||
\(597\) | −25.4768 | −1.04270 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 10.5957 | 0.432928 | 0.216464 | − | 0.976291i | \(-0.430548\pi\) | ||||
0.216464 | + | 0.976291i | \(0.430548\pi\) | |||||||
\(600\) | −4.66359 | −0.190390 | ||||||||
\(601\) | 0.577212 | 0.0235450 | 0.0117725 | − | 0.999931i | \(-0.496253\pi\) | ||||
0.0117725 | + | 0.999931i | \(0.496253\pi\) | |||||||
\(602\) | −2.63128 | −0.107243 | ||||||||
\(603\) | 8.48684 | 0.345611 | ||||||||
\(604\) | 3.39170 | 0.138006 | ||||||||
\(605\) | 26.6786 | 1.08464 | ||||||||
\(606\) | −8.82958 | −0.358677 | ||||||||
\(607\) | 3.75798 | 0.152532 | 0.0762659 | − | 0.997088i | \(-0.475700\pi\) | ||||
0.0762659 | + | 0.997088i | \(0.475700\pi\) | |||||||
\(608\) | −4.73805 | −0.192153 | ||||||||
\(609\) | 1.05926 | 0.0429232 | ||||||||
\(610\) | 41.2869 | 1.67166 | ||||||||
\(611\) | 0 | 0 | ||||||||
\(612\) | −1.24698 | −0.0504062 | ||||||||
\(613\) | −8.92496 | −0.360476 | −0.180238 | − | 0.983623i | \(-0.557687\pi\) | ||||
−0.180238 | + | 0.983623i | \(0.557687\pi\) | |||||||
\(614\) | 6.53538 | 0.263746 | ||||||||
\(615\) | 8.44471 | 0.340524 | ||||||||
\(616\) | −1.55496 | −0.0626510 | ||||||||
\(617\) | 8.90864 | 0.358648 | 0.179324 | − | 0.983790i | \(-0.442609\pi\) | ||||
0.179324 | + | 0.983790i | \(0.442609\pi\) | |||||||
\(618\) | −1.89793 | −0.0763460 | ||||||||
\(619\) | 8.63105 | 0.346911 | 0.173456 | − | 0.984842i | \(-0.444507\pi\) | ||||
0.173456 | + | 0.984842i | \(0.444507\pi\) | |||||||
\(620\) | −7.66442 | −0.307810 | ||||||||
\(621\) | 5.10817 | 0.204984 | ||||||||
\(622\) | 27.7921 | 1.11436 | ||||||||
\(623\) | 5.76399 | 0.230930 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −26.5689 | −1.06276 | ||||||||
\(626\) | 4.35209 | 0.173945 | ||||||||
\(627\) | −7.36747 | −0.294229 | ||||||||
\(628\) | −23.7381 | −0.947251 | ||||||||
\(629\) | 9.88142 | 0.393998 | ||||||||
\(630\) | −3.10863 | −0.123851 | ||||||||
\(631\) | 22.0935 | 0.879528 | 0.439764 | − | 0.898113i | \(-0.355062\pi\) | ||||
0.439764 | + | 0.898113i | \(0.355062\pi\) | |||||||
\(632\) | −11.1942 | −0.445283 | ||||||||
\(633\) | 2.01914 | 0.0802536 | ||||||||
\(634\) | 12.5835 | 0.499756 | ||||||||
\(635\) | −26.3108 | −1.04411 | ||||||||
\(636\) | −7.09392 | −0.281292 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | −1.64710 | −0.0652092 | ||||||||
\(639\) | 5.31350 | 0.210199 | ||||||||
\(640\) | 3.10863 | 0.122879 | ||||||||
\(641\) | 10.0871 | 0.398416 | 0.199208 | − | 0.979957i | \(-0.436163\pi\) | ||||
0.199208 | + | 0.979957i | \(0.436163\pi\) | |||||||
\(642\) | 3.58727 | 0.141578 | ||||||||
\(643\) | −8.84091 | −0.348652 | −0.174326 | − | 0.984688i | \(-0.555775\pi\) | ||||
−0.174326 | + | 0.984688i | \(0.555775\pi\) | |||||||
\(644\) | −5.10817 | −0.201290 | ||||||||
\(645\) | 8.17967 | 0.322074 | ||||||||
\(646\) | 5.90825 | 0.232457 | ||||||||
\(647\) | 1.73856 | 0.0683497 | 0.0341748 | − | 0.999416i | \(-0.489120\pi\) | ||||
0.0341748 | + | 0.999416i | \(0.489120\pi\) | |||||||
\(648\) | −1.00000 | −0.0392837 | ||||||||
\(649\) | −5.31594 | −0.208669 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −2.46553 | −0.0966316 | ||||||||
\(652\) | 6.35482 | 0.248874 | ||||||||
\(653\) | −45.8052 | −1.79250 | −0.896248 | − | 0.443554i | \(-0.853717\pi\) | ||||
−0.896248 | + | 0.443554i | \(0.853717\pi\) | |||||||
\(654\) | −20.3167 | −0.794447 | ||||||||
\(655\) | 15.7875 | 0.616868 | ||||||||
\(656\) | −2.71654 | −0.106063 | ||||||||
\(657\) | −9.45056 | −0.368701 | ||||||||
\(658\) | −5.06412 | −0.197420 | ||||||||
\(659\) | 11.7599 | 0.458099 | 0.229050 | − | 0.973415i | \(-0.426438\pi\) | ||||
0.229050 | + | 0.973415i | \(0.426438\pi\) | |||||||
\(660\) | 4.83379 | 0.188155 | ||||||||
\(661\) | 13.5257 | 0.526089 | 0.263044 | − | 0.964784i | \(-0.415273\pi\) | ||||
0.263044 | + | 0.964784i | \(0.415273\pi\) | |||||||
\(662\) | 19.8866 | 0.772915 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | −4.40061 | −0.170777 | ||||||||
\(665\) | 14.7289 | 0.571161 | ||||||||
\(666\) | 7.92429 | 0.307060 | ||||||||
\(667\) | −5.41086 | −0.209509 | ||||||||
\(668\) | 7.50114 | 0.290228 | ||||||||
\(669\) | 13.1491 | 0.508375 | ||||||||
\(670\) | 26.3825 | 1.01924 | ||||||||
\(671\) | −20.6520 | −0.797262 | ||||||||
\(672\) | 1.00000 | 0.0385758 | ||||||||
\(673\) | 12.0762 | 0.465505 | 0.232752 | − | 0.972536i | \(-0.425227\pi\) | ||||
0.232752 | + | 0.972536i | \(0.425227\pi\) | |||||||
\(674\) | −0.500733 | −0.0192875 | ||||||||
\(675\) | 4.66359 | 0.179502 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 4.22192 | 0.162262 | 0.0811308 | − | 0.996703i | \(-0.474147\pi\) | ||||
0.0811308 | + | 0.996703i | \(0.474147\pi\) | |||||||
\(678\) | 6.85060 | 0.263096 | ||||||||
\(679\) | 10.8007 | 0.414492 | ||||||||
\(680\) | −3.87640 | −0.148653 | ||||||||
\(681\) | −1.90722 | −0.0730850 | ||||||||
\(682\) | 3.83379 | 0.146803 | ||||||||
\(683\) | −46.8330 | −1.79201 | −0.896007 | − | 0.444039i | \(-0.853545\pi\) | ||||
−0.896007 | + | 0.444039i | \(0.853545\pi\) | |||||||
\(684\) | 4.73805 | 0.181164 | ||||||||
\(685\) | 64.8970 | 2.47959 | ||||||||
\(686\) | 1.00000 | 0.0381802 | ||||||||
\(687\) | 1.32344 | 0.0504924 | ||||||||
\(688\) | −2.63128 | −0.100316 | ||||||||
\(689\) | 0 | 0 | ||||||||
\(690\) | 15.8794 | 0.604519 | ||||||||
\(691\) | 19.2883 | 0.733762 | 0.366881 | − | 0.930268i | \(-0.380426\pi\) | ||||
0.366881 | + | 0.930268i | \(0.380426\pi\) | |||||||
\(692\) | −16.1881 | −0.615378 | ||||||||
\(693\) | 1.55496 | 0.0590680 | ||||||||
\(694\) | 24.7464 | 0.939361 | ||||||||
\(695\) | −55.1021 | −2.09014 | ||||||||
\(696\) | 1.05926 | 0.0401510 | ||||||||
\(697\) | 3.38747 | 0.128309 | ||||||||
\(698\) | −4.30578 | −0.162976 | ||||||||
\(699\) | −23.7561 | −0.898539 | ||||||||
\(700\) | −4.66359 | −0.176267 | ||||||||
\(701\) | −16.9306 | −0.639459 | −0.319729 | − | 0.947509i | \(-0.603592\pi\) | ||||
−0.319729 | + | 0.947509i | \(0.603592\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −37.5457 | −1.41606 | ||||||||
\(704\) | −1.55496 | −0.0586047 | ||||||||
\(705\) | 15.7425 | 0.592897 | ||||||||
\(706\) | −4.18501 | −0.157505 | ||||||||
\(707\) | −8.82958 | −0.332070 | ||||||||
\(708\) | 3.41870 | 0.128483 | ||||||||
\(709\) | 7.93895 | 0.298153 | 0.149077 | − | 0.988826i | \(-0.452370\pi\) | ||||
0.149077 | + | 0.988826i | \(0.452370\pi\) | |||||||
\(710\) | 16.5177 | 0.619898 | ||||||||
\(711\) | 11.1942 | 0.419817 | ||||||||
\(712\) | 5.76399 | 0.216015 | ||||||||
\(713\) | 12.5943 | 0.471662 | ||||||||
\(714\) | −1.24698 | −0.0466670 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 1.95421 | 0.0730322 | ||||||||
\(717\) | −27.3308 | −1.02069 | ||||||||
\(718\) | −6.33135 | −0.236284 | ||||||||
\(719\) | 31.5702 | 1.17737 | 0.588684 | − | 0.808363i | \(-0.299646\pi\) | ||||
0.588684 | + | 0.808363i | \(0.299646\pi\) | |||||||
\(720\) | −3.10863 | −0.115852 | ||||||||
\(721\) | −1.89793 | −0.0706827 | ||||||||
\(722\) | −3.44914 | −0.128364 | ||||||||
\(723\) | −2.68328 | −0.0997924 | ||||||||
\(724\) | −1.81969 | −0.0676281 | ||||||||
\(725\) | −4.93993 | −0.183465 | ||||||||
\(726\) | 8.58211 | 0.318512 | ||||||||
\(727\) | 10.8589 | 0.402733 | 0.201367 | − | 0.979516i | \(-0.435462\pi\) | ||||
0.201367 | + | 0.979516i | \(0.435462\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | −29.3783 | −1.08734 | ||||||||
\(731\) | 3.28115 | 0.121358 | ||||||||
\(732\) | 13.2814 | 0.490894 | ||||||||
\(733\) | −2.22682 | −0.0822495 | −0.0411247 | − | 0.999154i | \(-0.513094\pi\) | ||||
−0.0411247 | + | 0.999154i | \(0.513094\pi\) | |||||||
\(734\) | −19.8935 | −0.734282 | ||||||||
\(735\) | −3.10863 | −0.114664 | ||||||||
\(736\) | −5.10817 | −0.188290 | ||||||||
\(737\) | −13.1967 | −0.486106 | ||||||||
\(738\) | 2.71654 | 0.0999971 | ||||||||
\(739\) | −39.5399 | −1.45450 | −0.727249 | − | 0.686374i | \(-0.759201\pi\) | ||||
−0.727249 | + | 0.686374i | \(0.759201\pi\) | |||||||
\(740\) | 24.6337 | 0.905552 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | −7.09392 | −0.260426 | ||||||||
\(743\) | 35.0085 | 1.28434 | 0.642169 | − | 0.766563i | \(-0.278035\pi\) | ||||
0.642169 | + | 0.766563i | \(0.278035\pi\) | |||||||
\(744\) | −2.46553 | −0.0903906 | ||||||||
\(745\) | 2.57978 | 0.0945159 | ||||||||
\(746\) | 35.9969 | 1.31794 | ||||||||
\(747\) | 4.40061 | 0.161010 | ||||||||
\(748\) | 1.93900 | 0.0708969 | ||||||||
\(749\) | 3.58727 | 0.131076 | ||||||||
\(750\) | −1.04578 | −0.0381863 | ||||||||
\(751\) | 3.08816 | 0.112689 | 0.0563443 | − | 0.998411i | \(-0.482056\pi\) | ||||
0.0563443 | + | 0.998411i | \(0.482056\pi\) | |||||||
\(752\) | −5.06412 | −0.184670 | ||||||||
\(753\) | −30.8962 | −1.12592 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −10.5435 | −0.383719 | ||||||||
\(756\) | −1.00000 | −0.0363696 | ||||||||
\(757\) | −31.1069 | −1.13060 | −0.565300 | − | 0.824885i | \(-0.691240\pi\) | ||||
−0.565300 | + | 0.824885i | \(0.691240\pi\) | |||||||
\(758\) | 29.5252 | 1.07240 | ||||||||
\(759\) | −7.94300 | −0.288312 | ||||||||
\(760\) | 14.7289 | 0.534272 | ||||||||
\(761\) | −34.3881 | −1.24657 | −0.623284 | − | 0.781996i | \(-0.714202\pi\) | ||||
−0.623284 | + | 0.781996i | \(0.714202\pi\) | |||||||
\(762\) | −8.46378 | −0.306611 | ||||||||
\(763\) | −20.3167 | −0.735515 | ||||||||
\(764\) | −23.3210 | −0.843723 | ||||||||
\(765\) | 3.87640 | 0.140152 | ||||||||
\(766\) | −0.770083 | −0.0278242 | ||||||||
\(767\) | 0 | 0 | ||||||||
\(768\) | 1.00000 | 0.0360844 | ||||||||
\(769\) | −28.7352 | −1.03622 | −0.518109 | − | 0.855314i | \(-0.673364\pi\) | ||||
−0.518109 | + | 0.855314i | \(0.673364\pi\) | |||||||
\(770\) | 4.83379 | 0.174198 | ||||||||
\(771\) | 27.6822 | 0.996951 | ||||||||
\(772\) | −7.99277 | −0.287666 | ||||||||
\(773\) | 43.0766 | 1.54936 | 0.774679 | − | 0.632354i | \(-0.217911\pi\) | ||||
0.774679 | + | 0.632354i | \(0.217911\pi\) | |||||||
\(774\) | 2.63128 | 0.0945793 | ||||||||
\(775\) | 11.4982 | 0.413028 | ||||||||
\(776\) | 10.8007 | 0.387722 | ||||||||
\(777\) | 7.92429 | 0.284282 | ||||||||
\(778\) | −18.6621 | −0.669070 | ||||||||
\(779\) | −12.8711 | −0.461155 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −8.26226 | −0.295647 | ||||||||
\(782\) | 6.36979 | 0.227783 | ||||||||
\(783\) | −1.05926 | −0.0378547 | ||||||||
\(784\) | 1.00000 | 0.0357143 | ||||||||
\(785\) | 73.7929 | 2.63378 | ||||||||
\(786\) | 5.07860 | 0.181148 | ||||||||
\(787\) | 12.5432 | 0.447117 | 0.223558 | − | 0.974691i | \(-0.428233\pi\) | ||||
0.223558 | + | 0.974691i | \(0.428233\pi\) | |||||||
\(788\) | 2.24858 | 0.0801024 | ||||||||
\(789\) | 21.8601 | 0.778239 | ||||||||
\(790\) | 34.7988 | 1.23808 | ||||||||
\(791\) | 6.85060 | 0.243579 | ||||||||
\(792\) | 1.55496 | 0.0552530 | ||||||||
\(793\) | 0 | 0 | ||||||||
\(794\) | 17.7403 | 0.629580 | ||||||||
\(795\) | 22.0524 | 0.782117 | ||||||||
\(796\) | −25.4768 | −0.903001 | ||||||||
\(797\) | 35.9473 | 1.27332 | 0.636659 | − | 0.771146i | \(-0.280316\pi\) | ||||
0.636659 | + | 0.771146i | \(0.280316\pi\) | |||||||
\(798\) | 4.73805 | 0.167725 | ||||||||
\(799\) | 6.31486 | 0.223404 | ||||||||
\(800\) | −4.66359 | −0.164883 | ||||||||
\(801\) | −5.76399 | −0.203661 | ||||||||
\(802\) | 18.1461 | 0.640761 | ||||||||
\(803\) | 14.6952 | 0.518583 | ||||||||
\(804\) | 8.48684 | 0.299308 | ||||||||
\(805\) | 15.8794 | 0.559676 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −17.0766 | −0.601125 | ||||||||
\(808\) | −8.82958 | −0.310623 | ||||||||
\(809\) | 38.3283 | 1.34755 | 0.673776 | − | 0.738936i | \(-0.264671\pi\) | ||||
0.673776 | + | 0.738936i | \(0.264671\pi\) | |||||||
\(810\) | 3.10863 | 0.109226 | ||||||||
\(811\) | 55.4449 | 1.94693 | 0.973466 | − | 0.228831i | \(-0.0734903\pi\) | ||||
0.973466 | + | 0.228831i | \(0.0734903\pi\) | |||||||
\(812\) | 1.05926 | 0.0371726 | ||||||||
\(813\) | −27.8718 | −0.977508 | ||||||||
\(814\) | −12.3219 | −0.431884 | ||||||||
\(815\) | −19.7548 | −0.691980 | ||||||||
\(816\) | −1.24698 | −0.0436530 | ||||||||
\(817\) | −12.4671 | −0.436170 | ||||||||
\(818\) | 0.936649 | 0.0327492 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 8.44471 | 0.294902 | ||||||||
\(821\) | −30.7208 | −1.07216 | −0.536082 | − | 0.844166i | \(-0.680096\pi\) | ||||
−0.536082 | + | 0.844166i | \(0.680096\pi\) | |||||||
\(822\) | 20.8764 | 0.728148 | ||||||||
\(823\) | −29.4586 | −1.02686 | −0.513431 | − | 0.858131i | \(-0.671626\pi\) | ||||
−0.513431 | + | 0.858131i | \(0.671626\pi\) | |||||||
\(824\) | −1.89793 | −0.0661176 | ||||||||
\(825\) | −7.25169 | −0.252471 | ||||||||
\(826\) | 3.41870 | 0.118952 | ||||||||
\(827\) | −39.5955 | −1.37687 | −0.688435 | − | 0.725298i | \(-0.741702\pi\) | ||||
−0.688435 | + | 0.725298i | \(0.741702\pi\) | |||||||
\(828\) | 5.10817 | 0.177521 | ||||||||
\(829\) | 52.6258 | 1.82777 | 0.913884 | − | 0.405975i | \(-0.133068\pi\) | ||||
0.913884 | + | 0.405975i | \(0.133068\pi\) | |||||||
\(830\) | 13.6799 | 0.474836 | ||||||||
\(831\) | −31.9253 | −1.10748 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −1.24698 | −0.0432053 | ||||||||
\(834\) | −17.7255 | −0.613784 | ||||||||
\(835\) | −23.3183 | −0.806962 | ||||||||
\(836\) | −7.36747 | −0.254809 | ||||||||
\(837\) | 2.46553 | 0.0852211 | ||||||||
\(838\) | 10.0234 | 0.346253 | ||||||||
\(839\) | 31.0141 | 1.07073 | 0.535363 | − | 0.844622i | \(-0.320175\pi\) | ||||
0.535363 | + | 0.844622i | \(0.320175\pi\) | |||||||
\(840\) | −3.10863 | −0.107258 | ||||||||
\(841\) | −27.8780 | −0.961310 | ||||||||
\(842\) | −19.7171 | −0.679495 | ||||||||
\(843\) | 11.3692 | 0.391576 | ||||||||
\(844\) | 2.01914 | 0.0695016 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 5.06412 | 0.174108 | ||||||||
\(847\) | 8.58211 | 0.294885 | ||||||||
\(848\) | −7.09392 | −0.243606 | ||||||||
\(849\) | −16.6264 | −0.570615 | ||||||||
\(850\) | 5.81540 | 0.199467 | ||||||||
\(851\) | −40.4786 | −1.38759 | ||||||||
\(852\) | 5.31350 | 0.182037 | ||||||||
\(853\) | −55.8464 | −1.91214 | −0.956072 | − | 0.293133i | \(-0.905302\pi\) | ||||
−0.956072 | + | 0.293133i | \(0.905302\pi\) | |||||||
\(854\) | 13.2814 | 0.454480 | ||||||||
\(855\) | −14.7289 | −0.503716 | ||||||||
\(856\) | 3.58727 | 0.122610 | ||||||||
\(857\) | 26.7950 | 0.915299 | 0.457650 | − | 0.889133i | \(-0.348691\pi\) | ||||
0.457650 | + | 0.889133i | \(0.348691\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 13.5325 | 0.461724 | 0.230862 | − | 0.972986i | \(-0.425845\pi\) | ||||
0.230862 | + | 0.972986i | \(0.425845\pi\) | |||||||
\(860\) | 8.17967 | 0.278924 | ||||||||
\(861\) | 2.71654 | 0.0925793 | ||||||||
\(862\) | −31.5252 | −1.07375 | ||||||||
\(863\) | −34.8946 | −1.18783 | −0.593914 | − | 0.804529i | \(-0.702418\pi\) | ||||
−0.593914 | + | 0.804529i | \(0.702418\pi\) | |||||||
\(864\) | −1.00000 | −0.0340207 | ||||||||
\(865\) | 50.3228 | 1.71103 | ||||||||
\(866\) | −19.6284 | −0.667000 | ||||||||
\(867\) | −15.4450 | −0.524541 | ||||||||
\(868\) | −2.46553 | −0.0836855 | ||||||||
\(869\) | −17.4066 | −0.590478 | ||||||||
\(870\) | −3.29284 | −0.111638 | ||||||||
\(871\) | 0 | 0 | ||||||||
\(872\) | −20.3167 | −0.688011 | ||||||||
\(873\) | −10.8007 | −0.365548 | ||||||||
\(874\) | −24.2028 | −0.818672 | ||||||||
\(875\) | −1.04578 | −0.0353537 | ||||||||
\(876\) | −9.45056 | −0.319305 | ||||||||
\(877\) | −51.7834 | −1.74860 | −0.874300 | − | 0.485386i | \(-0.838679\pi\) | ||||
−0.874300 | + | 0.485386i | \(0.838679\pi\) | |||||||
\(878\) | −34.8525 | −1.17621 | ||||||||
\(879\) | 5.41358 | 0.182596 | ||||||||
\(880\) | 4.83379 | 0.162947 | ||||||||
\(881\) | −2.60278 | −0.0876900 | −0.0438450 | − | 0.999038i | \(-0.513961\pi\) | ||||
−0.0438450 | + | 0.999038i | \(0.513961\pi\) | |||||||
\(882\) | −1.00000 | −0.0336718 | ||||||||
\(883\) | −38.5127 | −1.29605 | −0.648027 | − | 0.761617i | \(-0.724406\pi\) | ||||
−0.648027 | + | 0.761617i | \(0.724406\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −10.6275 | −0.357239 | ||||||||
\(886\) | 9.65305 | 0.324300 | ||||||||
\(887\) | 15.6703 | 0.526156 | 0.263078 | − | 0.964775i | \(-0.415262\pi\) | ||||
0.263078 | + | 0.964775i | \(0.415262\pi\) | |||||||
\(888\) | 7.92429 | 0.265922 | ||||||||
\(889\) | −8.46378 | −0.283866 | ||||||||
\(890\) | −17.9181 | −0.600617 | ||||||||
\(891\) | −1.55496 | −0.0520931 | ||||||||
\(892\) | 13.1491 | 0.440266 | ||||||||
\(893\) | −23.9941 | −0.802931 | ||||||||
\(894\) | 0.829877 | 0.0277552 | ||||||||
\(895\) | −6.07491 | −0.203062 | ||||||||
\(896\) | 1.00000 | 0.0334077 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 15.2830 | 0.510000 | ||||||||
\(899\) | −2.61162 | −0.0871025 | ||||||||
\(900\) | 4.66359 | 0.155453 | ||||||||
\(901\) | 8.84597 | 0.294702 | ||||||||
\(902\) | −4.22410 | −0.140647 | ||||||||
\(903\) | 2.63128 | 0.0875634 | ||||||||
\(904\) | 6.85060 | 0.227848 | ||||||||
\(905\) | 5.65673 | 0.188036 | ||||||||
\(906\) | −3.39170 | −0.112682 | ||||||||
\(907\) | −30.6745 | −1.01853 | −0.509265 | − | 0.860610i | \(-0.670083\pi\) | ||||
−0.509265 | + | 0.860610i | \(0.670083\pi\) | |||||||
\(908\) | −1.90722 | −0.0632935 | ||||||||
\(909\) | 8.82958 | 0.292859 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 32.8588 | 1.08866 | 0.544331 | − | 0.838870i | \(-0.316784\pi\) | ||||
0.544331 | + | 0.838870i | \(0.316784\pi\) | |||||||
\(912\) | 4.73805 | 0.156893 | ||||||||
\(913\) | −6.84277 | −0.226463 | ||||||||
\(914\) | 16.0318 | 0.530285 | ||||||||
\(915\) | −41.2869 | −1.36490 | ||||||||
\(916\) | 1.32344 | 0.0437277 | ||||||||
\(917\) | 5.07860 | 0.167710 | ||||||||
\(918\) | 1.24698 | 0.0411565 | ||||||||
\(919\) | −10.6383 | −0.350925 | −0.175462 | − | 0.984486i | \(-0.556142\pi\) | ||||
−0.175462 | + | 0.984486i | \(0.556142\pi\) | |||||||
\(920\) | 15.8794 | 0.523529 | ||||||||
\(921\) | −6.53538 | −0.215348 | ||||||||
\(922\) | 28.6119 | 0.942282 | ||||||||
\(923\) | 0 | 0 | ||||||||
\(924\) | 1.55496 | 0.0511544 | ||||||||
\(925\) | −36.9556 | −1.21509 | ||||||||
\(926\) | −35.8620 | −1.17850 | ||||||||
\(927\) | 1.89793 | 0.0623363 | ||||||||
\(928\) | 1.05926 | 0.0347718 | ||||||||
\(929\) | −3.54100 | −0.116176 | −0.0580882 | − | 0.998311i | \(-0.518500\pi\) | ||||
−0.0580882 | + | 0.998311i | \(0.518500\pi\) | |||||||
\(930\) | 7.66442 | 0.251326 | ||||||||
\(931\) | 4.73805 | 0.155283 | ||||||||
\(932\) | −23.7561 | −0.778157 | ||||||||
\(933\) | −27.7921 | −0.909873 | ||||||||
\(934\) | 14.9263 | 0.488404 | ||||||||
\(935\) | −6.02764 | −0.197125 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −15.5489 | −0.507959 | −0.253980 | − | 0.967210i | \(-0.581740\pi\) | ||||
−0.253980 | + | 0.967210i | \(0.581740\pi\) | |||||||
\(938\) | 8.48684 | 0.277105 | ||||||||
\(939\) | −4.35209 | −0.142025 | ||||||||
\(940\) | 15.7425 | 0.513464 | ||||||||
\(941\) | −34.3011 | −1.11818 | −0.559092 | − | 0.829106i | \(-0.688850\pi\) | ||||
−0.559092 | + | 0.829106i | \(0.688850\pi\) | |||||||
\(942\) | 23.7381 | 0.773427 | ||||||||
\(943\) | −13.8765 | −0.451882 | ||||||||
\(944\) | 3.41870 | 0.111269 | ||||||||
\(945\) | 3.10863 | 0.101124 | ||||||||
\(946\) | −4.09153 | −0.133027 | ||||||||
\(947\) | 45.7712 | 1.48737 | 0.743683 | − | 0.668533i | \(-0.233077\pi\) | ||||
0.743683 | + | 0.668533i | \(0.233077\pi\) | |||||||
\(948\) | 11.1942 | 0.363572 | ||||||||
\(949\) | 0 | 0 | ||||||||
\(950\) | −22.0963 | −0.716900 | ||||||||
\(951\) | −12.5835 | −0.408049 | ||||||||
\(952\) | −1.24698 | −0.0404148 | ||||||||
\(953\) | 38.1938 | 1.23722 | 0.618609 | − | 0.785699i | \(-0.287697\pi\) | ||||
0.618609 | + | 0.785699i | \(0.287697\pi\) | |||||||
\(954\) | 7.09392 | 0.229674 | ||||||||
\(955\) | 72.4963 | 2.34592 | ||||||||
\(956\) | −27.3308 | −0.883943 | ||||||||
\(957\) | 1.64710 | 0.0532431 | ||||||||
\(958\) | −14.4348 | −0.466366 | ||||||||
\(959\) | 20.8764 | 0.674134 | ||||||||
\(960\) | −3.10863 | −0.100331 | ||||||||
\(961\) | −24.9212 | −0.803909 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −3.58727 | −0.115598 | ||||||||
\(964\) | −2.68328 | −0.0864228 | ||||||||
\(965\) | 24.8466 | 0.799839 | ||||||||
\(966\) | 5.10817 | 0.164353 | ||||||||
\(967\) | 1.46535 | 0.0471223 | 0.0235612 | − | 0.999722i | \(-0.492500\pi\) | ||||
0.0235612 | + | 0.999722i | \(0.492500\pi\) | |||||||
\(968\) | 8.58211 | 0.275839 | ||||||||
\(969\) | −5.90825 | −0.189800 | ||||||||
\(970\) | −33.5754 | −1.07804 | ||||||||
\(971\) | −15.1475 | −0.486106 | −0.243053 | − | 0.970013i | \(-0.578149\pi\) | ||||
−0.243053 | + | 0.970013i | \(0.578149\pi\) | |||||||
\(972\) | 1.00000 | 0.0320750 | ||||||||
\(973\) | −17.7255 | −0.568254 | ||||||||
\(974\) | −24.8740 | −0.797016 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 13.2814 | 0.425127 | ||||||||
\(977\) | −30.6974 | −0.982098 | −0.491049 | − | 0.871132i | \(-0.663386\pi\) | ||||
−0.491049 | + | 0.871132i | \(0.663386\pi\) | |||||||
\(978\) | −6.35482 | −0.203205 | ||||||||
\(979\) | 8.96277 | 0.286451 | ||||||||
\(980\) | −3.10863 | −0.0993016 | ||||||||
\(981\) | 20.3167 | 0.648663 | ||||||||
\(982\) | 10.6142 | 0.338714 | ||||||||
\(983\) | −13.4997 | −0.430574 | −0.215287 | − | 0.976551i | \(-0.569069\pi\) | ||||
−0.215287 | + | 0.976551i | \(0.569069\pi\) | |||||||
\(984\) | 2.71654 | 0.0866000 | ||||||||
\(985\) | −6.99001 | −0.222720 | ||||||||
\(986\) | −1.32087 | −0.0420651 | ||||||||
\(987\) | 5.06412 | 0.161193 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −13.4410 | −0.427400 | ||||||||
\(990\) | −4.83379 | −0.153628 | ||||||||
\(991\) | −39.7612 | −1.26306 | −0.631529 | − | 0.775352i | \(-0.717572\pi\) | ||||
−0.631529 | + | 0.775352i | \(0.717572\pi\) | |||||||
\(992\) | −2.46553 | −0.0782806 | ||||||||
\(993\) | −19.8866 | −0.631082 | ||||||||
\(994\) | 5.31350 | 0.168534 | ||||||||
\(995\) | 79.1980 | 2.51075 | ||||||||
\(996\) | 4.40061 | 0.139439 | ||||||||
\(997\) | 5.54069 | 0.175475 | 0.0877377 | − | 0.996144i | \(-0.472036\pi\) | ||||
0.0877377 | + | 0.996144i | \(0.472036\pi\) | |||||||
\(998\) | 0.950418 | 0.0300849 | ||||||||
\(999\) | −7.92429 | −0.250713 |
(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 | 7098.2.a.cr.1.2 | ✓ | 6 | |
13.12 | even | 2 | 7098.2.a.ct.1.5 | yes | 6 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
7098.2.a.cr.1.2 | ✓ | 6 | 1.1 | even | 1 | trivial | |
7098.2.a.ct.1.5 | yes | 6 | 13.12 | even | 2 |