Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [8001,2,Mod(1,8001)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(8001, 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("8001.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 8001 = 3^{2} \cdot 7 \cdot 127 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 8001.a (trivial) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | yes |
Analytic conductor: | \(63.8883066572\) |
Analytic rank: | \(0\) |
Dimension: | \(28\) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.18 | ||
Character | \(\chi\) | \(=\) | 8001.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0.662421 | 0.468403 | 0.234201 | − | 0.972188i | \(-0.424753\pi\) | ||||
0.234201 | + | 0.972188i | \(0.424753\pi\) | |||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | −1.56120 | −0.780599 | ||||||||
\(5\) | 3.26980 | 1.46230 | 0.731150 | − | 0.682216i | \(-0.238984\pi\) | ||||
0.731150 | + | 0.682216i | \(0.238984\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −1.00000 | −0.377964 | ||||||||
\(8\) | −2.35901 | −0.834037 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 2.16599 | 0.684945 | ||||||||
\(11\) | −1.50096 | −0.452557 | −0.226279 | − | 0.974063i | \(-0.572656\pi\) | ||||
−0.226279 | + | 0.974063i | \(0.572656\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −4.27180 | −1.18478 | −0.592392 | − | 0.805650i | \(-0.701816\pi\) | ||||
−0.592392 | + | 0.805650i | \(0.701816\pi\) | |||||||
\(14\) | −0.662421 | −0.177040 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 1.55974 | 0.389934 | ||||||||
\(17\) | 2.42284 | 0.587625 | 0.293813 | − | 0.955863i | \(-0.405076\pi\) | ||||
0.293813 | + | 0.955863i | \(0.405076\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −3.39105 | −0.777961 | −0.388981 | − | 0.921246i | \(-0.627173\pi\) | ||||
−0.388981 | + | 0.921246i | \(0.627173\pi\) | |||||||
\(20\) | −5.10481 | −1.14147 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −0.994269 | −0.211979 | ||||||||
\(23\) | 4.67878 | 0.975594 | 0.487797 | − | 0.872957i | \(-0.337801\pi\) | ||||
0.487797 | + | 0.872957i | \(0.337801\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 5.69162 | 1.13832 | ||||||||
\(26\) | −2.82973 | −0.554956 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 1.56120 | 0.295039 | ||||||||
\(29\) | 2.49283 | 0.462907 | 0.231454 | − | 0.972846i | \(-0.425652\pi\) | ||||
0.231454 | + | 0.972846i | \(0.425652\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 5.16438 | 0.927551 | 0.463775 | − | 0.885953i | \(-0.346494\pi\) | ||||
0.463775 | + | 0.885953i | \(0.346494\pi\) | |||||||
\(32\) | 5.75123 | 1.01668 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 1.60494 | 0.275245 | ||||||||
\(35\) | −3.26980 | −0.552698 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −9.93232 | −1.63286 | −0.816432 | − | 0.577442i | \(-0.804051\pi\) | ||||
−0.816432 | + | 0.577442i | \(0.804051\pi\) | |||||||
\(38\) | −2.24631 | −0.364399 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | −7.71351 | −1.21961 | ||||||||
\(41\) | 1.42938 | 0.223232 | 0.111616 | − | 0.993751i | \(-0.464397\pi\) | ||||
0.111616 | + | 0.993751i | \(0.464397\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 0.721457 | 0.110021 | 0.0550106 | − | 0.998486i | \(-0.482481\pi\) | ||||
0.0550106 | + | 0.998486i | \(0.482481\pi\) | |||||||
\(44\) | 2.34330 | 0.353266 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 3.09932 | 0.456971 | ||||||||
\(47\) | −2.25922 | −0.329541 | −0.164770 | − | 0.986332i | \(-0.552688\pi\) | ||||
−0.164770 | + | 0.986332i | \(0.552688\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 1.00000 | 0.142857 | ||||||||
\(50\) | 3.77025 | 0.533194 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 6.66913 | 0.924841 | ||||||||
\(53\) | 1.84702 | 0.253707 | 0.126854 | − | 0.991921i | \(-0.459512\pi\) | ||||
0.126854 | + | 0.991921i | \(0.459512\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −4.90785 | −0.661775 | ||||||||
\(56\) | 2.35901 | 0.315236 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 1.65131 | 0.216827 | ||||||||
\(59\) | 3.44025 | 0.447883 | 0.223941 | − | 0.974603i | \(-0.428108\pi\) | ||||
0.223941 | + | 0.974603i | \(0.428108\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −1.15426 | −0.147788 | −0.0738942 | − | 0.997266i | \(-0.523543\pi\) | ||||
−0.0738942 | + | 0.997266i | \(0.523543\pi\) | |||||||
\(62\) | 3.42100 | 0.434467 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0.690263 | 0.0862829 | ||||||||
\(65\) | −13.9679 | −1.73251 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −14.4075 | −1.76016 | −0.880079 | − | 0.474827i | \(-0.842511\pi\) | ||||
−0.880079 | + | 0.474827i | \(0.842511\pi\) | |||||||
\(68\) | −3.78254 | −0.458700 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | −2.16599 | −0.258885 | ||||||||
\(71\) | 11.7156 | 1.39038 | 0.695192 | − | 0.718824i | \(-0.255319\pi\) | ||||
0.695192 | + | 0.718824i | \(0.255319\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 3.97876 | 0.465679 | 0.232839 | − | 0.972515i | \(-0.425198\pi\) | ||||
0.232839 | + | 0.972515i | \(0.425198\pi\) | |||||||
\(74\) | −6.57938 | −0.764837 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 5.29411 | 0.607276 | ||||||||
\(77\) | 1.50096 | 0.171050 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −3.64679 | −0.410295 | −0.205148 | − | 0.978731i | \(-0.565767\pi\) | ||||
−0.205148 | + | 0.978731i | \(0.565767\pi\) | |||||||
\(80\) | 5.10003 | 0.570201 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 0.946851 | 0.104562 | ||||||||
\(83\) | 12.5424 | 1.37671 | 0.688353 | − | 0.725375i | \(-0.258334\pi\) | ||||
0.688353 | + | 0.725375i | \(0.258334\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 7.92222 | 0.859285 | ||||||||
\(86\) | 0.477908 | 0.0515342 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 3.54079 | 0.377449 | ||||||||
\(89\) | 13.9694 | 1.48075 | 0.740376 | − | 0.672193i | \(-0.234648\pi\) | ||||
0.740376 | + | 0.672193i | \(0.234648\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 4.27180 | 0.447806 | ||||||||
\(92\) | −7.30451 | −0.761548 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | −1.49655 | −0.154358 | ||||||||
\(95\) | −11.0881 | −1.13761 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −9.82688 | −0.997769 | −0.498884 | − | 0.866669i | \(-0.666257\pi\) | ||||
−0.498884 | + | 0.866669i | \(0.666257\pi\) | |||||||
\(98\) | 0.662421 | 0.0669146 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | −8.88575 | −0.888575 | ||||||||
\(101\) | 2.11397 | 0.210348 | 0.105174 | − | 0.994454i | \(-0.466460\pi\) | ||||
0.105174 | + | 0.994454i | \(0.466460\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 7.93085 | 0.781450 | 0.390725 | − | 0.920507i | \(-0.372224\pi\) | ||||
0.390725 | + | 0.920507i | \(0.372224\pi\) | |||||||
\(104\) | 10.0772 | 0.988154 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 1.22350 | 0.118837 | ||||||||
\(107\) | 9.27389 | 0.896541 | 0.448271 | − | 0.893898i | \(-0.352040\pi\) | ||||
0.448271 | + | 0.893898i | \(0.352040\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 8.91701 | 0.854095 | 0.427048 | − | 0.904229i | \(-0.359554\pi\) | ||||
0.427048 | + | 0.904229i | \(0.359554\pi\) | |||||||
\(110\) | −3.25106 | −0.309977 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | −1.55974 | −0.147381 | ||||||||
\(113\) | 14.8106 | 1.39326 | 0.696632 | − | 0.717428i | \(-0.254681\pi\) | ||||
0.696632 | + | 0.717428i | \(0.254681\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 15.2987 | 1.42661 | ||||||||
\(116\) | −3.89181 | −0.361345 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 2.27890 | 0.209789 | ||||||||
\(119\) | −2.42284 | −0.222102 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −8.74711 | −0.795192 | ||||||||
\(122\) | −0.764609 | −0.0692244 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | −8.06263 | −0.724045 | ||||||||
\(125\) | 2.26146 | 0.202271 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 1.00000 | 0.0887357 | ||||||||
\(128\) | −11.0452 | −0.976268 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | −9.25266 | −0.811512 | ||||||||
\(131\) | 7.10395 | 0.620675 | 0.310337 | − | 0.950626i | \(-0.399558\pi\) | ||||
0.310337 | + | 0.950626i | \(0.399558\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 3.39105 | 0.294042 | ||||||||
\(134\) | −9.54384 | −0.824462 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −5.71551 | −0.490101 | ||||||||
\(137\) | 8.96915 | 0.766286 | 0.383143 | − | 0.923689i | \(-0.374842\pi\) | ||||
0.383143 | + | 0.923689i | \(0.374842\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 3.30357 | 0.280205 | 0.140102 | − | 0.990137i | \(-0.455257\pi\) | ||||
0.140102 | + | 0.990137i | \(0.455257\pi\) | |||||||
\(140\) | 5.10481 | 0.431435 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 7.76065 | 0.651259 | ||||||||
\(143\) | 6.41181 | 0.536182 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 8.15108 | 0.676910 | ||||||||
\(146\) | 2.63562 | 0.218125 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 15.5063 | 1.27461 | ||||||||
\(149\) | 6.69098 | 0.548147 | 0.274073 | − | 0.961709i | \(-0.411629\pi\) | ||||
0.274073 | + | 0.961709i | \(0.411629\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 15.4206 | 1.25491 | 0.627455 | − | 0.778653i | \(-0.284097\pi\) | ||||
0.627455 | + | 0.778653i | \(0.284097\pi\) | |||||||
\(152\) | 7.99954 | 0.648848 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0.994269 | 0.0801205 | ||||||||
\(155\) | 16.8865 | 1.35636 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −8.27724 | −0.660596 | −0.330298 | − | 0.943877i | \(-0.607149\pi\) | ||||
−0.330298 | + | 0.943877i | \(0.607149\pi\) | |||||||
\(158\) | −2.41571 | −0.192183 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 18.8054 | 1.48670 | ||||||||
\(161\) | −4.67878 | −0.368740 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 4.67491 | 0.366167 | 0.183084 | − | 0.983097i | \(-0.441392\pi\) | ||||
0.183084 | + | 0.983097i | \(0.441392\pi\) | |||||||
\(164\) | −2.23154 | −0.174254 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 8.30835 | 0.644853 | ||||||||
\(167\) | 10.9392 | 0.846498 | 0.423249 | − | 0.906014i | \(-0.360890\pi\) | ||||
0.423249 | + | 0.906014i | \(0.360890\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 5.24827 | 0.403713 | ||||||||
\(170\) | 5.24784 | 0.402491 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | −1.12634 | −0.0858824 | ||||||||
\(173\) | −6.16889 | −0.469012 | −0.234506 | − | 0.972115i | \(-0.575347\pi\) | ||||
−0.234506 | + | 0.972115i | \(0.575347\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −5.69162 | −0.430246 | ||||||||
\(176\) | −2.34110 | −0.176467 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 9.25362 | 0.693588 | ||||||||
\(179\) | 8.30227 | 0.620541 | 0.310270 | − | 0.950648i | \(-0.399580\pi\) | ||||
0.310270 | + | 0.950648i | \(0.399580\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 1.49944 | 0.111453 | 0.0557263 | − | 0.998446i | \(-0.482253\pi\) | ||||
0.0557263 | + | 0.998446i | \(0.482253\pi\) | |||||||
\(182\) | 2.82973 | 0.209754 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | −11.0373 | −0.813681 | ||||||||
\(185\) | −32.4768 | −2.38774 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −3.63659 | −0.265934 | ||||||||
\(188\) | 3.52709 | 0.257239 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | −7.34498 | −0.532861 | ||||||||
\(191\) | −0.767209 | −0.0555133 | −0.0277566 | − | 0.999615i | \(-0.508836\pi\) | ||||
−0.0277566 | + | 0.999615i | \(0.508836\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −11.3034 | −0.813636 | −0.406818 | − | 0.913509i | \(-0.633362\pi\) | ||||
−0.406818 | + | 0.913509i | \(0.633362\pi\) | |||||||
\(194\) | −6.50953 | −0.467357 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −1.56120 | −0.111514 | ||||||||
\(197\) | 14.1865 | 1.01074 | 0.505371 | − | 0.862902i | \(-0.331355\pi\) | ||||
0.505371 | + | 0.862902i | \(0.331355\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 4.78068 | 0.338893 | 0.169447 | − | 0.985539i | \(-0.445802\pi\) | ||||
0.169447 | + | 0.985539i | \(0.445802\pi\) | |||||||
\(200\) | −13.4266 | −0.949404 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 1.40034 | 0.0985276 | ||||||||
\(203\) | −2.49283 | −0.174963 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 4.67379 | 0.326432 | ||||||||
\(206\) | 5.25357 | 0.366033 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | −6.66288 | −0.461988 | ||||||||
\(209\) | 5.08984 | 0.352072 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −1.56528 | −0.107759 | −0.0538793 | − | 0.998547i | \(-0.517159\pi\) | ||||
−0.0538793 | + | 0.998547i | \(0.517159\pi\) | |||||||
\(212\) | −2.88356 | −0.198044 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 6.14322 | 0.419942 | ||||||||
\(215\) | 2.35902 | 0.160884 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −5.16438 | −0.350581 | ||||||||
\(218\) | 5.90682 | 0.400060 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 7.66213 | 0.516581 | ||||||||
\(221\) | −10.3499 | −0.696209 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −5.42472 | −0.363266 | −0.181633 | − | 0.983366i | \(-0.558138\pi\) | ||||
−0.181633 | + | 0.983366i | \(0.558138\pi\) | |||||||
\(224\) | −5.75123 | −0.384270 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 9.81086 | 0.652609 | ||||||||
\(227\) | −13.4870 | −0.895167 | −0.447583 | − | 0.894242i | \(-0.647715\pi\) | ||||
−0.447583 | + | 0.894242i | \(0.647715\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 26.6212 | 1.75918 | 0.879590 | − | 0.475732i | \(-0.157817\pi\) | ||||
0.879590 | + | 0.475732i | \(0.157817\pi\) | |||||||
\(230\) | 10.1342 | 0.668228 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −5.88062 | −0.386082 | ||||||||
\(233\) | 12.2959 | 0.805528 | 0.402764 | − | 0.915304i | \(-0.368049\pi\) | ||||
0.402764 | + | 0.915304i | \(0.368049\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −7.38720 | −0.481888 | ||||||||
\(236\) | −5.37092 | −0.349617 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | −1.60494 | −0.104033 | ||||||||
\(239\) | 21.7254 | 1.40530 | 0.702651 | − | 0.711535i | \(-0.252000\pi\) | ||||
0.702651 | + | 0.711535i | \(0.252000\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 24.2273 | 1.56062 | 0.780308 | − | 0.625396i | \(-0.215062\pi\) | ||||
0.780308 | + | 0.625396i | \(0.215062\pi\) | |||||||
\(242\) | −5.79427 | −0.372470 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 1.80203 | 0.115363 | ||||||||
\(245\) | 3.26980 | 0.208900 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 14.4859 | 0.921716 | ||||||||
\(248\) | −12.1829 | −0.773612 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 1.49804 | 0.0947444 | ||||||||
\(251\) | 12.6868 | 0.800784 | 0.400392 | − | 0.916344i | \(-0.368874\pi\) | ||||
0.400392 | + | 0.916344i | \(0.368874\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −7.02268 | −0.441512 | ||||||||
\(254\) | 0.662421 | 0.0415640 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −8.69711 | −0.543569 | ||||||||
\(257\) | −9.00660 | −0.561816 | −0.280908 | − | 0.959735i | \(-0.590636\pi\) | ||||
−0.280908 | + | 0.959735i | \(0.590636\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 9.93232 | 0.617164 | ||||||||
\(260\) | 21.8067 | 1.35240 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 4.70581 | 0.290726 | ||||||||
\(263\) | 0.569700 | 0.0351292 | 0.0175646 | − | 0.999846i | \(-0.494409\pi\) | ||||
0.0175646 | + | 0.999846i | \(0.494409\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 6.03938 | 0.370996 | ||||||||
\(266\) | 2.24631 | 0.137730 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 22.4930 | 1.37398 | ||||||||
\(269\) | −8.24294 | −0.502581 | −0.251290 | − | 0.967912i | \(-0.580855\pi\) | ||||
−0.251290 | + | 0.967912i | \(0.580855\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −13.0643 | −0.793597 | −0.396799 | − | 0.917906i | \(-0.629879\pi\) | ||||
−0.396799 | + | 0.917906i | \(0.629879\pi\) | |||||||
\(272\) | 3.77899 | 0.229135 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 5.94136 | 0.358930 | ||||||||
\(275\) | −8.54291 | −0.515157 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −26.0311 | −1.56406 | −0.782029 | − | 0.623242i | \(-0.785815\pi\) | ||||
−0.782029 | + | 0.623242i | \(0.785815\pi\) | |||||||
\(278\) | 2.18835 | 0.131249 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 7.71351 | 0.460970 | ||||||||
\(281\) | −9.62664 | −0.574277 | −0.287139 | − | 0.957889i | \(-0.592704\pi\) | ||||
−0.287139 | + | 0.957889i | \(0.592704\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −6.55517 | −0.389664 | −0.194832 | − | 0.980837i | \(-0.562416\pi\) | ||||
−0.194832 | + | 0.980837i | \(0.562416\pi\) | |||||||
\(284\) | −18.2903 | −1.08533 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 4.24732 | 0.251149 | ||||||||
\(287\) | −1.42938 | −0.0843736 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −11.1298 | −0.654696 | ||||||||
\(290\) | 5.39944 | 0.317066 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | −6.21164 | −0.363508 | ||||||||
\(293\) | −18.1387 | −1.05968 | −0.529838 | − | 0.848099i | \(-0.677747\pi\) | ||||
−0.529838 | + | 0.848099i | \(0.677747\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 11.2490 | 0.654940 | ||||||||
\(296\) | 23.4305 | 1.36187 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 4.43225 | 0.256753 | ||||||||
\(299\) | −19.9868 | −1.15587 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −0.721457 | −0.0415841 | ||||||||
\(302\) | 10.2149 | 0.587803 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | −5.28915 | −0.303353 | ||||||||
\(305\) | −3.77422 | −0.216111 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −19.1900 | −1.09523 | −0.547615 | − | 0.836731i | \(-0.684464\pi\) | ||||
−0.547615 | + | 0.836731i | \(0.684464\pi\) | |||||||
\(308\) | −2.34330 | −0.133522 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 11.1860 | 0.635322 | ||||||||
\(311\) | −7.90235 | −0.448101 | −0.224051 | − | 0.974577i | \(-0.571928\pi\) | ||||
−0.224051 | + | 0.974577i | \(0.571928\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −0.379749 | −0.0214647 | −0.0107324 | − | 0.999942i | \(-0.503416\pi\) | ||||
−0.0107324 | + | 0.999942i | \(0.503416\pi\) | |||||||
\(314\) | −5.48302 | −0.309425 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 5.69336 | 0.320276 | ||||||||
\(317\) | 4.64692 | 0.260997 | 0.130499 | − | 0.991448i | \(-0.458342\pi\) | ||||
0.130499 | + | 0.991448i | \(0.458342\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −3.74165 | −0.209492 | ||||||||
\(320\) | 2.25703 | 0.126172 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | −3.09932 | −0.172719 | ||||||||
\(323\) | −8.21598 | −0.457150 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −24.3135 | −1.34867 | ||||||||
\(326\) | 3.09676 | 0.171514 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | −3.37192 | −0.186183 | ||||||||
\(329\) | 2.25922 | 0.124555 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −2.44366 | −0.134316 | −0.0671578 | − | 0.997742i | \(-0.521393\pi\) | ||||
−0.0671578 | + | 0.997742i | \(0.521393\pi\) | |||||||
\(332\) | −19.5812 | −1.07466 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 7.24633 | 0.396502 | ||||||||
\(335\) | −47.1098 | −2.57388 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 27.6343 | 1.50533 | 0.752667 | − | 0.658402i | \(-0.228767\pi\) | ||||
0.752667 | + | 0.658402i | \(0.228767\pi\) | |||||||
\(338\) | 3.47657 | 0.189100 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | −12.3682 | −0.670757 | ||||||||
\(341\) | −7.75154 | −0.419770 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −1.00000 | −0.0539949 | ||||||||
\(344\) | −1.70193 | −0.0917617 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −4.08640 | −0.219686 | ||||||||
\(347\) | 33.0149 | 1.77233 | 0.886167 | − | 0.463366i | \(-0.153358\pi\) | ||||
0.886167 | + | 0.463366i | \(0.153358\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 14.2869 | 0.764763 | 0.382381 | − | 0.924005i | \(-0.375104\pi\) | ||||
0.382381 | + | 0.924005i | \(0.375104\pi\) | |||||||
\(350\) | −3.77025 | −0.201528 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | −8.63237 | −0.460107 | ||||||||
\(353\) | −27.1604 | −1.44560 | −0.722800 | − | 0.691057i | \(-0.757145\pi\) | ||||
−0.722800 | + | 0.691057i | \(0.757145\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 38.3077 | 2.03316 | ||||||||
\(356\) | −21.8090 | −1.15587 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 5.49960 | 0.290663 | ||||||||
\(359\) | 27.3202 | 1.44190 | 0.720952 | − | 0.692984i | \(-0.243705\pi\) | ||||
0.720952 | + | 0.692984i | \(0.243705\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −7.50076 | −0.394777 | ||||||||
\(362\) | 0.993262 | 0.0522047 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | −6.66913 | −0.349557 | ||||||||
\(365\) | 13.0098 | 0.680963 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 24.1868 | 1.26254 | 0.631271 | − | 0.775562i | \(-0.282534\pi\) | ||||
0.631271 | + | 0.775562i | \(0.282534\pi\) | |||||||
\(368\) | 7.29767 | 0.380417 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | −21.5133 | −1.11842 | ||||||||
\(371\) | −1.84702 | −0.0958923 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 16.7437 | 0.866958 | 0.433479 | − | 0.901164i | \(-0.357286\pi\) | ||||
0.433479 | + | 0.901164i | \(0.357286\pi\) | |||||||
\(374\) | −2.40896 | −0.124564 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 5.32953 | 0.274849 | ||||||||
\(377\) | −10.6489 | −0.548445 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 33.7897 | 1.73566 | 0.867830 | − | 0.496861i | \(-0.165514\pi\) | ||||
0.867830 | + | 0.496861i | \(0.165514\pi\) | |||||||
\(380\) | 17.3107 | 0.888020 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | −0.508215 | −0.0260026 | ||||||||
\(383\) | −12.8406 | −0.656125 | −0.328063 | − | 0.944656i | \(-0.606396\pi\) | ||||
−0.328063 | + | 0.944656i | \(0.606396\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 4.90785 | 0.250127 | ||||||||
\(386\) | −7.48761 | −0.381109 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 15.3417 | 0.778857 | ||||||||
\(389\) | −1.62314 | −0.0822967 | −0.0411484 | − | 0.999153i | \(-0.513102\pi\) | ||||
−0.0411484 | + | 0.999153i | \(0.513102\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 11.3359 | 0.573284 | ||||||||
\(392\) | −2.35901 | −0.119148 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 9.39741 | 0.473435 | ||||||||
\(395\) | −11.9243 | −0.599975 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 0.0450194 | 0.00225946 | 0.00112973 | − | 0.999999i | \(-0.499640\pi\) | ||||
0.00112973 | + | 0.999999i | \(0.499640\pi\) | |||||||
\(398\) | 3.16682 | 0.158738 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 8.87743 | 0.443871 | ||||||||
\(401\) | 11.0217 | 0.550398 | 0.275199 | − | 0.961387i | \(-0.411256\pi\) | ||||
0.275199 | + | 0.961387i | \(0.411256\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −22.0612 | −1.09895 | ||||||||
\(404\) | −3.30033 | −0.164197 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −1.65131 | −0.0819529 | ||||||||
\(407\) | 14.9080 | 0.738964 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 28.1749 | 1.39316 | 0.696580 | − | 0.717479i | \(-0.254704\pi\) | ||||
0.696580 | + | 0.717479i | \(0.254704\pi\) | |||||||
\(410\) | 3.09602 | 0.152901 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | −12.3816 | −0.609999 | ||||||||
\(413\) | −3.44025 | −0.169284 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 41.0112 | 2.01316 | ||||||||
\(416\) | −24.5681 | −1.20455 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 3.37162 | 0.164911 | ||||||||
\(419\) | 7.08817 | 0.346280 | 0.173140 | − | 0.984897i | \(-0.444609\pi\) | ||||
0.173140 | + | 0.984897i | \(0.444609\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −3.66854 | −0.178794 | −0.0893969 | − | 0.995996i | \(-0.528494\pi\) | ||||
−0.0893969 | + | 0.995996i | \(0.528494\pi\) | |||||||
\(422\) | −1.03688 | −0.0504744 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | −4.35714 | −0.211601 | ||||||||
\(425\) | 13.7899 | 0.668908 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 1.15426 | 0.0558587 | ||||||||
\(428\) | −14.4784 | −0.699839 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 1.56267 | 0.0753585 | ||||||||
\(431\) | −40.0756 | −1.93037 | −0.965187 | − | 0.261561i | \(-0.915763\pi\) | ||||
−0.965187 | + | 0.261561i | \(0.915763\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 5.97880 | 0.287323 | 0.143661 | − | 0.989627i | \(-0.454112\pi\) | ||||
0.143661 | + | 0.989627i | \(0.454112\pi\) | |||||||
\(434\) | −3.42100 | −0.164213 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −13.9212 | −0.666706 | ||||||||
\(437\) | −15.8660 | −0.758974 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 16.8939 | 0.806302 | 0.403151 | − | 0.915134i | \(-0.367915\pi\) | ||||
0.403151 | + | 0.915134i | \(0.367915\pi\) | |||||||
\(440\) | 11.5777 | 0.551945 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | −6.85599 | −0.326106 | ||||||||
\(443\) | 18.8237 | 0.894341 | 0.447171 | − | 0.894449i | \(-0.352432\pi\) | ||||
0.447171 | + | 0.894449i | \(0.352432\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 45.6772 | 2.16530 | ||||||||
\(446\) | −3.59345 | −0.170155 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | −0.690263 | −0.0326119 | ||||||||
\(449\) | −12.7387 | −0.601177 | −0.300588 | − | 0.953754i | \(-0.597183\pi\) | ||||
−0.300588 | + | 0.953754i | \(0.597183\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −2.14544 | −0.101025 | ||||||||
\(452\) | −23.1223 | −1.08758 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | −8.93411 | −0.419298 | ||||||||
\(455\) | 13.9679 | 0.654828 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 38.4582 | 1.79900 | 0.899500 | − | 0.436920i | \(-0.143931\pi\) | ||||
0.899500 | + | 0.436920i | \(0.143931\pi\) | |||||||
\(458\) | 17.6345 | 0.824005 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | −23.8843 | −1.11361 | ||||||||
\(461\) | 12.2755 | 0.571728 | 0.285864 | − | 0.958270i | \(-0.407719\pi\) | ||||
0.285864 | + | 0.958270i | \(0.407719\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 23.8693 | 1.10930 | 0.554649 | − | 0.832084i | \(-0.312853\pi\) | ||||
0.554649 | + | 0.832084i | \(0.312853\pi\) | |||||||
\(464\) | 3.88816 | 0.180503 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 8.14504 | 0.377311 | ||||||||
\(467\) | −11.5335 | −0.533708 | −0.266854 | − | 0.963737i | \(-0.585984\pi\) | ||||
−0.266854 | + | 0.963737i | \(0.585984\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 14.4075 | 0.665277 | ||||||||
\(470\) | −4.89344 | −0.225718 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | −8.11560 | −0.373551 | ||||||||
\(473\) | −1.08288 | −0.0497908 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −19.3006 | −0.885572 | ||||||||
\(476\) | 3.78254 | 0.173372 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 14.3914 | 0.658247 | ||||||||
\(479\) | 41.2351 | 1.88408 | 0.942041 | − | 0.335498i | \(-0.108905\pi\) | ||||
0.942041 | + | 0.335498i | \(0.108905\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 42.4289 | 1.93459 | ||||||||
\(482\) | 16.0487 | 0.730996 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 13.6560 | 0.620726 | ||||||||
\(485\) | −32.1320 | −1.45904 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −25.0962 | −1.13722 | −0.568608 | − | 0.822608i | \(-0.692518\pi\) | ||||
−0.568608 | + | 0.822608i | \(0.692518\pi\) | |||||||
\(488\) | 2.72292 | 0.123261 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 2.16599 | 0.0978493 | ||||||||
\(491\) | −30.7343 | −1.38702 | −0.693509 | − | 0.720448i | \(-0.743936\pi\) | ||||
−0.693509 | + | 0.720448i | \(0.743936\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 6.03974 | 0.272016 | ||||||||
\(494\) | 9.59577 | 0.431734 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 8.05508 | 0.361684 | ||||||||
\(497\) | −11.7156 | −0.525516 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 37.8270 | 1.69337 | 0.846684 | − | 0.532097i | \(-0.178596\pi\) | ||||
0.846684 | + | 0.532097i | \(0.178596\pi\) | |||||||
\(500\) | −3.53059 | −0.157893 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 8.40400 | 0.375089 | ||||||||
\(503\) | 1.91290 | 0.0852921 | 0.0426461 | − | 0.999090i | \(-0.486421\pi\) | ||||
0.0426461 | + | 0.999090i | \(0.486421\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 6.91227 | 0.307592 | ||||||||
\(506\) | −4.65197 | −0.206805 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | −1.56120 | −0.0692670 | ||||||||
\(509\) | −31.9035 | −1.41410 | −0.707049 | − | 0.707164i | \(-0.749974\pi\) | ||||
−0.707049 | + | 0.707164i | \(0.749974\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −3.97876 | −0.176010 | ||||||||
\(512\) | 16.3293 | 0.721659 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | −5.96616 | −0.263156 | ||||||||
\(515\) | 25.9323 | 1.14272 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 3.39100 | 0.149136 | ||||||||
\(518\) | 6.57938 | 0.289081 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 32.9506 | 1.44498 | ||||||||
\(521\) | −40.7782 | −1.78652 | −0.893262 | − | 0.449536i | \(-0.851589\pi\) | ||||
−0.893262 | + | 0.449536i | \(0.851589\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −6.54698 | −0.286280 | −0.143140 | − | 0.989702i | \(-0.545720\pi\) | ||||
−0.143140 | + | 0.989702i | \(0.545720\pi\) | |||||||
\(524\) | −11.0907 | −0.484498 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0.377382 | 0.0164546 | ||||||||
\(527\) | 12.5125 | 0.545052 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −1.10899 | −0.0482169 | ||||||||
\(530\) | 4.00061 | 0.173776 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | −5.29411 | −0.229529 | ||||||||
\(533\) | −6.10602 | −0.264481 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 30.3238 | 1.31101 | ||||||||
\(536\) | 33.9875 | 1.46804 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | −5.46030 | −0.235410 | ||||||||
\(539\) | −1.50096 | −0.0646510 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −14.3882 | −0.618595 | −0.309297 | − | 0.950965i | \(-0.600094\pi\) | ||||
−0.309297 | + | 0.950965i | \(0.600094\pi\) | |||||||
\(542\) | −8.65404 | −0.371723 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 13.9343 | 0.597429 | ||||||||
\(545\) | 29.1569 | 1.24894 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −38.8696 | −1.66194 | −0.830972 | − | 0.556314i | \(-0.812215\pi\) | ||||
−0.830972 | + | 0.556314i | \(0.812215\pi\) | |||||||
\(548\) | −14.0026 | −0.598163 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | −5.65900 | −0.241301 | ||||||||
\(551\) | −8.45333 | −0.360124 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 3.64679 | 0.155077 | ||||||||
\(554\) | −17.2436 | −0.732609 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −5.15752 | −0.218728 | ||||||||
\(557\) | 4.06639 | 0.172299 | 0.0861493 | − | 0.996282i | \(-0.472544\pi\) | ||||
0.0861493 | + | 0.996282i | \(0.472544\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −3.08192 | −0.130351 | ||||||||
\(560\) | −5.10003 | −0.215516 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | −6.37689 | −0.268993 | ||||||||
\(563\) | 4.72486 | 0.199129 | 0.0995646 | − | 0.995031i | \(-0.468255\pi\) | ||||
0.0995646 | + | 0.995031i | \(0.468255\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 48.4278 | 2.03737 | ||||||||
\(566\) | −4.34228 | −0.182520 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −27.6372 | −1.15963 | ||||||||
\(569\) | 6.56790 | 0.275341 | 0.137670 | − | 0.990478i | \(-0.456039\pi\) | ||||
0.137670 | + | 0.990478i | \(0.456039\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 9.73369 | 0.407342 | 0.203671 | − | 0.979039i | \(-0.434713\pi\) | ||||
0.203671 | + | 0.979039i | \(0.434713\pi\) | |||||||
\(572\) | −10.0101 | −0.418543 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | −0.946851 | −0.0395208 | ||||||||
\(575\) | 26.6299 | 1.11054 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 8.68524 | 0.361571 | 0.180786 | − | 0.983523i | \(-0.442136\pi\) | ||||
0.180786 | + | 0.983523i | \(0.442136\pi\) | |||||||
\(578\) | −7.37264 | −0.306661 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | −12.7254 | −0.528395 | ||||||||
\(581\) | −12.5424 | −0.520346 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −2.77230 | −0.114817 | ||||||||
\(584\) | −9.38595 | −0.388393 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −12.0155 | −0.496355 | ||||||||
\(587\) | 28.0699 | 1.15857 | 0.579285 | − | 0.815125i | \(-0.303332\pi\) | ||||
0.579285 | + | 0.815125i | \(0.303332\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −17.5127 | −0.721598 | ||||||||
\(590\) | 7.45155 | 0.306775 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | −15.4918 | −0.636709 | ||||||||
\(593\) | −17.6643 | −0.725385 | −0.362693 | − | 0.931909i | \(-0.618142\pi\) | ||||
−0.362693 | + | 0.931909i | \(0.618142\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −7.92222 | −0.324779 | ||||||||
\(596\) | −10.4459 | −0.427883 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | −13.2397 | −0.541411 | ||||||||
\(599\) | −19.1441 | −0.782205 | −0.391102 | − | 0.920347i | \(-0.627906\pi\) | ||||
−0.391102 | + | 0.920347i | \(0.627906\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −39.2226 | −1.59992 | −0.799961 | − | 0.600052i | \(-0.795147\pi\) | ||||
−0.799961 | + | 0.600052i | \(0.795147\pi\) | |||||||
\(602\) | −0.477908 | −0.0194781 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | −24.0746 | −0.979581 | ||||||||
\(605\) | −28.6013 | −1.16281 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 0.762927 | 0.0309662 | 0.0154831 | − | 0.999880i | \(-0.495071\pi\) | ||||
0.0154831 | + | 0.999880i | \(0.495071\pi\) | |||||||
\(608\) | −19.5027 | −0.790940 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | −2.50012 | −0.101227 | ||||||||
\(611\) | 9.65093 | 0.390435 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −21.3445 | −0.862097 | −0.431048 | − | 0.902329i | \(-0.641856\pi\) | ||||
−0.431048 | + | 0.902329i | \(0.641856\pi\) | |||||||
\(614\) | −12.7118 | −0.513008 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −3.54079 | −0.142662 | ||||||||
\(617\) | 16.2462 | 0.654046 | 0.327023 | − | 0.945016i | \(-0.393954\pi\) | ||||
0.327023 | + | 0.945016i | \(0.393954\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 25.6478 | 1.03087 | 0.515436 | − | 0.856928i | \(-0.327630\pi\) | ||||
0.515436 | + | 0.856928i | \(0.327630\pi\) | |||||||
\(620\) | −26.3632 | −1.05877 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | −5.23469 | −0.209892 | ||||||||
\(623\) | −13.9694 | −0.559672 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −21.0636 | −0.842542 | ||||||||
\(626\) | −0.251554 | −0.0100541 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 12.9224 | 0.515660 | ||||||||
\(629\) | −24.0644 | −0.959512 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −4.71692 | −0.187777 | −0.0938887 | − | 0.995583i | \(-0.529930\pi\) | ||||
−0.0938887 | + | 0.995583i | \(0.529930\pi\) | |||||||
\(632\) | 8.60282 | 0.342202 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 3.07822 | 0.122252 | ||||||||
\(635\) | 3.26980 | 0.129758 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −4.27180 | −0.169255 | ||||||||
\(638\) | −2.47855 | −0.0981266 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | −36.1157 | −1.42760 | ||||||||
\(641\) | −1.83451 | −0.0724588 | −0.0362294 | − | 0.999344i | \(-0.511535\pi\) | ||||
−0.0362294 | + | 0.999344i | \(0.511535\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −29.1448 | −1.14936 | −0.574679 | − | 0.818379i | \(-0.694873\pi\) | ||||
−0.574679 | + | 0.818379i | \(0.694873\pi\) | |||||||
\(644\) | 7.30451 | 0.287838 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −5.44244 | −0.214130 | ||||||||
\(647\) | 20.8372 | 0.819197 | 0.409598 | − | 0.912266i | \(-0.365669\pi\) | ||||
0.409598 | + | 0.912266i | \(0.365669\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −5.16369 | −0.202693 | ||||||||
\(650\) | −16.1058 | −0.631720 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −7.29846 | −0.285830 | ||||||||
\(653\) | −13.0640 | −0.511235 | −0.255617 | − | 0.966778i | \(-0.582279\pi\) | ||||
−0.255617 | + | 0.966778i | \(0.582279\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 23.2285 | 0.907613 | ||||||||
\(656\) | 2.22945 | 0.0870456 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 1.49655 | 0.0583418 | ||||||||
\(659\) | −9.10837 | −0.354812 | −0.177406 | − | 0.984138i | \(-0.556770\pi\) | ||||
−0.177406 | + | 0.984138i | \(0.556770\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 11.0180 | 0.428549 | 0.214274 | − | 0.976774i | \(-0.431261\pi\) | ||||
0.214274 | + | 0.976774i | \(0.431261\pi\) | |||||||
\(662\) | −1.61873 | −0.0629137 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | −29.5877 | −1.14822 | ||||||||
\(665\) | 11.0881 | 0.429977 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 11.6634 | 0.451610 | ||||||||
\(668\) | −17.0782 | −0.660775 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | −31.2065 | −1.20561 | ||||||||
\(671\) | 1.73251 | 0.0668827 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 20.0887 | 0.774362 | 0.387181 | − | 0.922004i | \(-0.373449\pi\) | ||||
0.387181 | + | 0.922004i | \(0.373449\pi\) | |||||||
\(674\) | 18.3055 | 0.705102 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −8.19359 | −0.315138 | ||||||||
\(677\) | 40.4365 | 1.55410 | 0.777051 | − | 0.629438i | \(-0.216715\pi\) | ||||
0.777051 | + | 0.629438i | \(0.216715\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 9.82688 | 0.377121 | ||||||||
\(680\) | −18.6886 | −0.716676 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | −5.13479 | −0.196621 | ||||||||
\(683\) | 29.3606 | 1.12345 | 0.561727 | − | 0.827323i | \(-0.310137\pi\) | ||||
0.561727 | + | 0.827323i | \(0.310137\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 29.3274 | 1.12054 | ||||||||
\(686\) | −0.662421 | −0.0252914 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 1.12528 | 0.0429010 | ||||||||
\(689\) | −7.89008 | −0.300588 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −46.0332 | −1.75118 | −0.875592 | − | 0.483051i | \(-0.839528\pi\) | ||||
−0.875592 | + | 0.483051i | \(0.839528\pi\) | |||||||
\(692\) | 9.63086 | 0.366110 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 21.8698 | 0.830166 | ||||||||
\(695\) | 10.8020 | 0.409744 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 3.46316 | 0.131177 | ||||||||
\(698\) | 9.46397 | 0.358217 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 8.88575 | 0.335850 | ||||||||
\(701\) | 17.3356 | 0.654756 | 0.327378 | − | 0.944893i | \(-0.393835\pi\) | ||||
0.327378 | + | 0.944893i | \(0.393835\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 33.6810 | 1.27030 | ||||||||
\(704\) | −1.03606 | −0.0390479 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −17.9916 | −0.677123 | ||||||||
\(707\) | −2.11397 | −0.0795041 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 11.4015 | 0.428194 | 0.214097 | − | 0.976812i | \(-0.431319\pi\) | ||||
0.214097 | + | 0.976812i | \(0.431319\pi\) | |||||||
\(710\) | 25.3758 | 0.952337 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | −32.9540 | −1.23500 | ||||||||
\(713\) | 24.1630 | 0.904913 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 20.9654 | 0.784060 | ||||||||
\(716\) | −12.9615 | −0.484393 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 18.0975 | 0.675392 | ||||||||
\(719\) | 10.3304 | 0.385258 | 0.192629 | − | 0.981272i | \(-0.438299\pi\) | ||||
0.192629 | + | 0.981272i | \(0.438299\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −7.93085 | −0.295360 | ||||||||
\(722\) | −4.96866 | −0.184914 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | −2.34092 | −0.0869998 | ||||||||
\(725\) | 14.1883 | 0.526939 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 39.8392 | 1.47755 | 0.738777 | − | 0.673950i | \(-0.235404\pi\) | ||||
0.738777 | + | 0.673950i | \(0.235404\pi\) | |||||||
\(728\) | −10.0772 | −0.373487 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 8.61795 | 0.318965 | ||||||||
\(731\) | 1.74798 | 0.0646512 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 6.61936 | 0.244492 | 0.122246 | − | 0.992500i | \(-0.460990\pi\) | ||||
0.122246 | + | 0.992500i | \(0.460990\pi\) | |||||||
\(734\) | 16.0219 | 0.591378 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 26.9087 | 0.991870 | ||||||||
\(737\) | 21.6251 | 0.796572 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 2.68575 | 0.0987971 | 0.0493985 | − | 0.998779i | \(-0.484270\pi\) | ||||
0.0493985 | + | 0.998779i | \(0.484270\pi\) | |||||||
\(740\) | 50.7026 | 1.86387 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | −1.22350 | −0.0449162 | ||||||||
\(743\) | −0.915186 | −0.0335749 | −0.0167875 | − | 0.999859i | \(-0.505344\pi\) | ||||
−0.0167875 | + | 0.999859i | \(0.505344\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 21.8782 | 0.801555 | ||||||||
\(746\) | 11.0914 | 0.406085 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 5.67744 | 0.207588 | ||||||||
\(749\) | −9.27389 | −0.338861 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 24.3489 | 0.888505 | 0.444252 | − | 0.895902i | \(-0.353469\pi\) | ||||
0.444252 | + | 0.895902i | \(0.353469\pi\) | |||||||
\(752\) | −3.52379 | −0.128499 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | −7.05404 | −0.256893 | ||||||||
\(755\) | 50.4223 | 1.83505 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −42.8153 | −1.55615 | −0.778074 | − | 0.628173i | \(-0.783803\pi\) | ||||
−0.778074 | + | 0.628173i | \(0.783803\pi\) | |||||||
\(758\) | 22.3830 | 0.812987 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 26.1569 | 0.948812 | ||||||||
\(761\) | 21.3773 | 0.774927 | 0.387463 | − | 0.921885i | \(-0.373351\pi\) | ||||
0.387463 | + | 0.921885i | \(0.373351\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −8.91701 | −0.322818 | ||||||||
\(764\) | 1.19776 | 0.0433336 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −8.50590 | −0.307331 | ||||||||
\(767\) | −14.6961 | −0.530645 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −8.30249 | −0.299395 | −0.149698 | − | 0.988732i | \(-0.547830\pi\) | ||||
−0.149698 | + | 0.988732i | \(0.547830\pi\) | |||||||
\(770\) | 3.25106 | 0.117160 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 17.6468 | 0.635124 | ||||||||
\(773\) | −24.0880 | −0.866384 | −0.433192 | − | 0.901302i | \(-0.642613\pi\) | ||||
−0.433192 | + | 0.901302i | \(0.642613\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 29.3937 | 1.05585 | ||||||||
\(776\) | 23.1817 | 0.832176 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −1.07521 | −0.0385480 | ||||||||
\(779\) | −4.84710 | −0.173665 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −17.5846 | −0.629228 | ||||||||
\(782\) | 7.50917 | 0.268527 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 1.55974 | 0.0557049 | ||||||||
\(785\) | −27.0650 | −0.965990 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 29.2925 | 1.04416 | 0.522082 | − | 0.852895i | \(-0.325156\pi\) | ||||
0.522082 | + | 0.852895i | \(0.325156\pi\) | |||||||
\(788\) | −22.1479 | −0.788985 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | −7.89889 | −0.281030 | ||||||||
\(791\) | −14.8106 | −0.526605 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 4.93078 | 0.175097 | ||||||||
\(794\) | 0.0298218 | 0.00105834 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −7.46358 | −0.264540 | ||||||||
\(797\) | 14.0851 | 0.498919 | 0.249460 | − | 0.968385i | \(-0.419747\pi\) | ||||
0.249460 | + | 0.968385i | \(0.419747\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −5.47373 | −0.193647 | ||||||||
\(800\) | 32.7338 | 1.15731 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 7.30102 | 0.257808 | ||||||||
\(803\) | −5.97197 | −0.210746 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −15.2987 | −0.539208 | ||||||||
\(806\) | −14.6138 | −0.514750 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | −4.98689 | −0.175438 | ||||||||
\(809\) | 15.5617 | 0.547121 | 0.273561 | − | 0.961855i | \(-0.411799\pi\) | ||||
0.273561 | + | 0.961855i | \(0.411799\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −34.6939 | −1.21827 | −0.609133 | − | 0.793068i | \(-0.708483\pi\) | ||||
−0.609133 | + | 0.793068i | \(0.708483\pi\) | |||||||
\(812\) | 3.89181 | 0.136576 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 9.87540 | 0.346133 | ||||||||
\(815\) | 15.2860 | 0.535447 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −2.44650 | −0.0855922 | ||||||||
\(818\) | 18.6637 | 0.652560 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −7.29671 | −0.254812 | ||||||||
\(821\) | −53.7305 | −1.87521 | −0.937604 | − | 0.347705i | \(-0.886961\pi\) | ||||
−0.937604 | + | 0.347705i | \(0.886961\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 31.8700 | 1.11092 | 0.555458 | − | 0.831544i | \(-0.312543\pi\) | ||||
0.555458 | + | 0.831544i | \(0.312543\pi\) | |||||||
\(824\) | −18.7090 | −0.651759 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −2.27890 | −0.0792930 | ||||||||
\(827\) | 47.6852 | 1.65818 | 0.829089 | − | 0.559117i | \(-0.188860\pi\) | ||||
0.829089 | + | 0.559117i | \(0.188860\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −21.6153 | −0.750731 | −0.375365 | − | 0.926877i | \(-0.622483\pi\) | ||||
−0.375365 | + | 0.926877i | \(0.622483\pi\) | |||||||
\(830\) | 27.1667 | 0.942969 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | −2.94867 | −0.102227 | ||||||||
\(833\) | 2.42284 | 0.0839465 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 35.7689 | 1.23783 | ||||||||
\(836\) | −7.94625 | −0.274827 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 4.69536 | 0.162198 | ||||||||
\(839\) | 27.1939 | 0.938838 | 0.469419 | − | 0.882976i | \(-0.344463\pi\) | ||||
0.469419 | + | 0.882976i | \(0.344463\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −22.7858 | −0.785717 | ||||||||
\(842\) | −2.43012 | −0.0837475 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 2.44372 | 0.0841162 | ||||||||
\(845\) | 17.1608 | 0.590350 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 8.74711 | 0.300554 | ||||||||
\(848\) | 2.88086 | 0.0989291 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 9.13472 | 0.313318 | ||||||||
\(851\) | −46.4712 | −1.59301 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 3.03848 | 0.104035 | 0.0520177 | − | 0.998646i | \(-0.483435\pi\) | ||||
0.0520177 | + | 0.998646i | \(0.483435\pi\) | |||||||
\(854\) | 0.764609 | 0.0261644 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −21.8772 | −0.747748 | ||||||||
\(857\) | −29.6832 | −1.01396 | −0.506979 | − | 0.861959i | \(-0.669238\pi\) | ||||
−0.506979 | + | 0.861959i | \(0.669238\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −44.7450 | −1.52668 | −0.763339 | − | 0.645998i | \(-0.776442\pi\) | ||||
−0.763339 | + | 0.645998i | \(0.776442\pi\) | |||||||
\(860\) | −3.68290 | −0.125586 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −26.5469 | −0.904192 | ||||||||
\(863\) | −32.0831 | −1.09212 | −0.546060 | − | 0.837746i | \(-0.683873\pi\) | ||||
−0.546060 | + | 0.837746i | \(0.683873\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −20.1711 | −0.685837 | ||||||||
\(866\) | 3.96048 | 0.134583 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 8.06263 | 0.273663 | ||||||||
\(869\) | 5.47369 | 0.185682 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 61.5460 | 2.08541 | ||||||||
\(872\) | −21.0354 | −0.712347 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | −10.5100 | −0.355505 | ||||||||
\(875\) | −2.26146 | −0.0764514 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −42.1566 | −1.42353 | −0.711763 | − | 0.702420i | \(-0.752103\pi\) | ||||
−0.711763 | + | 0.702420i | \(0.752103\pi\) | |||||||
\(878\) | 11.1909 | 0.377674 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | −7.65495 | −0.258048 | ||||||||
\(881\) | 3.01953 | 0.101731 | 0.0508653 | − | 0.998706i | \(-0.483802\pi\) | ||||
0.0508653 | + | 0.998706i | \(0.483802\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −48.2690 | −1.62438 | −0.812190 | − | 0.583393i | \(-0.801725\pi\) | ||||
−0.812190 | + | 0.583393i | \(0.801725\pi\) | |||||||
\(884\) | 16.1582 | 0.543460 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 12.4692 | 0.418912 | ||||||||
\(887\) | −17.5918 | −0.590676 | −0.295338 | − | 0.955393i | \(-0.595432\pi\) | ||||
−0.295338 | + | 0.955393i | \(0.595432\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −1.00000 | −0.0335389 | ||||||||
\(890\) | 30.2575 | 1.01423 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 8.46906 | 0.283565 | ||||||||
\(893\) | 7.66113 | 0.256370 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 27.1468 | 0.907417 | ||||||||
\(896\) | 11.0452 | 0.368995 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | −8.43839 | −0.281593 | ||||||||
\(899\) | 12.8739 | 0.429370 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 4.47503 | 0.149085 | ||||||||
\(902\) | −1.42119 | −0.0473204 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −34.9384 | −1.16203 | ||||||||
\(905\) | 4.90288 | 0.162977 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −4.41456 | −0.146583 | −0.0732915 | − | 0.997311i | \(-0.523350\pi\) | ||||
−0.0732915 | + | 0.997311i | \(0.523350\pi\) | |||||||
\(908\) | 21.0560 | 0.698766 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 9.25266 | 0.306723 | ||||||||
\(911\) | −21.8078 | −0.722525 | −0.361263 | − | 0.932464i | \(-0.617654\pi\) | ||||
−0.361263 | + | 0.932464i | \(0.617654\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −18.8257 | −0.623038 | ||||||||
\(914\) | 25.4756 | 0.842656 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −41.5610 | −1.37321 | ||||||||
\(917\) | −7.10395 | −0.234593 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 44.9714 | 1.48347 | 0.741735 | − | 0.670693i | \(-0.234003\pi\) | ||||
0.741735 | + | 0.670693i | \(0.234003\pi\) | |||||||
\(920\) | −36.0898 | −1.18985 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 8.13157 | 0.267799 | ||||||||
\(923\) | −50.0466 | −1.64730 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −56.5310 | −1.85873 | ||||||||
\(926\) | 15.8115 | 0.519598 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 14.3369 | 0.470630 | ||||||||
\(929\) | 6.22681 | 0.204295 | 0.102147 | − | 0.994769i | \(-0.467429\pi\) | ||||
0.102147 | + | 0.994769i | \(0.467429\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −3.39105 | −0.111137 | ||||||||
\(932\) | −19.1963 | −0.628795 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | −7.64005 | −0.249990 | ||||||||
\(935\) | −11.8909 | −0.388876 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 29.3666 | 0.959365 | 0.479683 | − | 0.877442i | \(-0.340752\pi\) | ||||
0.479683 | + | 0.877442i | \(0.340752\pi\) | |||||||
\(938\) | 9.54384 | 0.311618 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 11.5329 | 0.376161 | ||||||||
\(941\) | −20.1629 | −0.657290 | −0.328645 | − | 0.944453i | \(-0.606592\pi\) | ||||
−0.328645 | + | 0.944453i | \(0.606592\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 6.68776 | 0.217783 | ||||||||
\(944\) | 5.36589 | 0.174645 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −0.717322 | −0.0233222 | ||||||||
\(947\) | −5.62411 | −0.182759 | −0.0913796 | − | 0.995816i | \(-0.529128\pi\) | ||||
−0.0913796 | + | 0.995816i | \(0.529128\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −16.9965 | −0.551729 | ||||||||
\(950\) | −12.7851 | −0.414804 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 5.71551 | 0.185241 | ||||||||
\(953\) | 42.2249 | 1.36780 | 0.683899 | − | 0.729577i | \(-0.260283\pi\) | ||||
0.683899 | + | 0.729577i | \(0.260283\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −2.50862 | −0.0811771 | ||||||||
\(956\) | −33.9177 | −1.09698 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 27.3150 | 0.882509 | ||||||||
\(959\) | −8.96915 | −0.289629 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −4.32913 | −0.139649 | ||||||||
\(962\) | 28.1058 | 0.906167 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | −37.8236 | −1.21822 | ||||||||
\(965\) | −36.9599 | −1.18978 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 6.32562 | 0.203418 | 0.101709 | − | 0.994814i | \(-0.467569\pi\) | ||||
0.101709 | + | 0.994814i | \(0.467569\pi\) | |||||||
\(968\) | 20.6346 | 0.663220 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | −21.2849 | −0.683417 | ||||||||
\(971\) | 55.0518 | 1.76670 | 0.883348 | − | 0.468717i | \(-0.155284\pi\) | ||||
0.883348 | + | 0.468717i | \(0.155284\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −3.30357 | −0.105907 | ||||||||
\(974\) | −16.6242 | −0.532675 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −1.80035 | −0.0576277 | ||||||||
\(977\) | −1.20715 | −0.0386200 | −0.0193100 | − | 0.999814i | \(-0.506147\pi\) | ||||
−0.0193100 | + | 0.999814i | \(0.506147\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −20.9675 | −0.670125 | ||||||||
\(980\) | −5.10481 | −0.163067 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | −20.3590 | −0.649683 | ||||||||
\(983\) | −5.96804 | −0.190351 | −0.0951755 | − | 0.995461i | \(-0.530341\pi\) | ||||
−0.0951755 | + | 0.995461i | \(0.530341\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 46.3869 | 1.47801 | ||||||||
\(986\) | 4.00085 | 0.127413 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −22.6154 | −0.719491 | ||||||||
\(989\) | 3.37554 | 0.107336 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 16.4137 | 0.521398 | 0.260699 | − | 0.965420i | \(-0.416047\pi\) | ||||
0.260699 | + | 0.965420i | \(0.416047\pi\) | |||||||
\(992\) | 29.7016 | 0.943025 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | −7.76065 | −0.246153 | ||||||||
\(995\) | 15.6319 | 0.495564 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −3.64536 | −0.115450 | −0.0577249 | − | 0.998333i | \(-0.518385\pi\) | ||||
−0.0577249 | + | 0.998333i | \(0.518385\pi\) | |||||||
\(998\) | 25.0574 | 0.793177 | ||||||||
\(999\) | 0 | 0 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 8001.2.a.y.1.18 | yes | 28 | |
3.2 | odd | 2 | inner | 8001.2.a.y.1.11 | ✓ | 28 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
8001.2.a.y.1.11 | ✓ | 28 | 3.2 | odd | 2 | inner | |
8001.2.a.y.1.18 | yes | 28 | 1.1 | even | 1 | trivial |