Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [8048,2,Mod(1,8048)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(8048, 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("8048.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 8048 = 2^{4} \cdot 503 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 8048.a (trivial) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | yes |
Analytic conductor: | \(64.2636035467\) |
Analytic rank: | \(0\) |
Dimension: | \(21\) |
Twist minimal: | no (minimal twist has level 2012) |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.14 | ||
Character | \(\chi\) | \(=\) | 8048.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | 1.70783 | 0.986019 | 0.493009 | − | 0.870024i | \(-0.335897\pi\) | ||||
0.493009 | + | 0.870024i | \(0.335897\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −2.09685 | −0.937741 | −0.468870 | − | 0.883267i | \(-0.655339\pi\) | ||||
−0.468870 | + | 0.883267i | \(0.655339\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −2.97923 | −1.12604 | −0.563022 | − | 0.826442i | \(-0.690361\pi\) | ||||
−0.563022 | + | 0.826442i | \(0.690361\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −0.0833023 | −0.0277674 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −0.460249 | −0.138770 | −0.0693851 | − | 0.997590i | \(-0.522104\pi\) | ||||
−0.0693851 | + | 0.997590i | \(0.522104\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −1.42418 | −0.394996 | −0.197498 | − | 0.980303i | \(-0.563282\pi\) | ||||
−0.197498 | + | 0.980303i | \(0.563282\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −3.58108 | −0.924630 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 0.812462 | 0.197051 | 0.0985255 | − | 0.995135i | \(-0.468587\pi\) | ||||
0.0985255 | + | 0.995135i | \(0.468587\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 1.75227 | 0.401999 | 0.200999 | − | 0.979591i | \(-0.435581\pi\) | ||||
0.200999 | + | 0.979591i | \(0.435581\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −5.08803 | −1.11030 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −5.11790 | −1.06716 | −0.533578 | − | 0.845751i | \(-0.679153\pi\) | ||||
−0.533578 | + | 0.845751i | \(0.679153\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −0.603213 | −0.120643 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −5.26577 | −1.01340 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −2.72020 | −0.505128 | −0.252564 | − | 0.967580i | \(-0.581274\pi\) | ||||
−0.252564 | + | 0.967580i | \(0.581274\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 4.50450 | 0.809033 | 0.404516 | − | 0.914531i | \(-0.367440\pi\) | ||||
0.404516 | + | 0.914531i | \(0.367440\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −0.786029 | −0.136830 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 6.24701 | 1.05594 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 4.97175 | 0.817350 | 0.408675 | − | 0.912680i | \(-0.365991\pi\) | ||||
0.408675 | + | 0.912680i | \(0.365991\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −2.43226 | −0.389473 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 9.10730 | 1.42232 | 0.711161 | − | 0.703030i | \(-0.248170\pi\) | ||||
0.711161 | + | 0.703030i | \(0.248170\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 4.89067 | 0.745820 | 0.372910 | − | 0.927868i | \(-0.378360\pi\) | ||||
0.372910 | + | 0.927868i | \(0.378360\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0.174673 | 0.0260387 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −12.9392 | −1.88738 | −0.943688 | − | 0.330838i | \(-0.892669\pi\) | ||||
−0.943688 | + | 0.330838i | \(0.892669\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 1.87583 | 0.267975 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 1.38755 | 0.194296 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −11.4519 | −1.57304 | −0.786519 | − | 0.617566i | \(-0.788119\pi\) | ||||
−0.786519 | + | 0.617566i | \(0.788119\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0.965074 | 0.130131 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 2.99259 | 0.396378 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 13.7014 | 1.78377 | 0.891884 | − | 0.452264i | \(-0.149383\pi\) | ||||
0.891884 | + | 0.452264i | \(0.149383\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −11.0181 | −1.41073 | −0.705363 | − | 0.708846i | \(-0.749216\pi\) | ||||
−0.705363 | + | 0.708846i | \(0.749216\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0.248177 | 0.0312674 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 2.98629 | 0.370403 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −6.13144 | −0.749075 | −0.374538 | − | 0.927212i | \(-0.622199\pi\) | ||||
−0.374538 | + | 0.927212i | \(0.622199\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −8.74052 | −1.05224 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −2.61426 | −0.310255 | −0.155128 | − | 0.987894i | \(-0.549579\pi\) | ||||
−0.155128 | + | 0.987894i | \(0.549579\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 6.63903 | 0.777040 | 0.388520 | − | 0.921440i | \(-0.372986\pi\) | ||||
0.388520 | + | 0.921440i | \(0.372986\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −1.03019 | −0.118956 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 1.37119 | 0.156261 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 14.9513 | 1.68215 | 0.841075 | − | 0.540919i | \(-0.181924\pi\) | ||||
0.841075 | + | 0.540919i | \(0.181924\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −8.74315 | −0.971462 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 13.5873 | 1.49141 | 0.745703 | − | 0.666279i | \(-0.232114\pi\) | ||||
0.745703 | + | 0.666279i | \(0.232114\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −1.70361 | −0.184783 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −4.64565 | −0.498066 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −9.40221 | −0.996632 | −0.498316 | − | 0.866995i | \(-0.666048\pi\) | ||||
−0.498316 | + | 0.866995i | \(0.666048\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 4.24295 | 0.444782 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 7.69294 | 0.797721 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −3.67425 | −0.376971 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −0.130292 | −0.0132291 | −0.00661457 | − | 0.999978i | \(-0.502105\pi\) | ||||
−0.00661457 | + | 0.999978i | \(0.502105\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0.0383398 | 0.00385330 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 18.4834 | 1.83917 | 0.919585 | − | 0.392891i | \(-0.128525\pi\) | ||||
0.919585 | + | 0.392891i | \(0.128525\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 15.2790 | 1.50548 | 0.752742 | − | 0.658316i | \(-0.228731\pi\) | ||||
0.752742 | + | 0.658316i | \(0.228731\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 10.6689 | 1.04117 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 15.3367 | 1.48265 | 0.741326 | − | 0.671145i | \(-0.234197\pi\) | ||||
0.741326 | + | 0.671145i | \(0.234197\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −3.74293 | −0.358508 | −0.179254 | − | 0.983803i | \(-0.557368\pi\) | ||||
−0.179254 | + | 0.983803i | \(0.557368\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 8.49092 | 0.805923 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 0.129695 | 0.0122006 | 0.00610032 | − | 0.999981i | \(-0.498058\pi\) | ||||
0.00610032 | + | 0.999981i | \(0.498058\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 10.7315 | 1.00072 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0.118637 | 0.0109680 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −2.42051 | −0.221888 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −10.7882 | −0.980743 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 15.5538 | 1.40244 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 11.7491 | 1.05087 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 10.7478 | 0.953713 | 0.476857 | − | 0.878981i | \(-0.341776\pi\) | ||||
0.476857 | + | 0.878981i | \(0.341776\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 8.35245 | 0.735392 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −16.5826 | −1.44883 | −0.724413 | − | 0.689366i | \(-0.757889\pi\) | ||||
−0.724413 | + | 0.689366i | \(0.757889\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −5.22043 | −0.452668 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 11.0415 | 0.950304 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −15.0310 | −1.28418 | −0.642091 | − | 0.766628i | \(-0.721933\pi\) | ||||
−0.642091 | + | 0.766628i | \(0.721933\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 10.7004 | 0.907599 | 0.453799 | − | 0.891104i | \(-0.350068\pi\) | ||||
0.453799 | + | 0.891104i | \(0.350068\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −22.0980 | −1.86099 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 0.655476 | 0.0548137 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 5.70385 | 0.473679 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 3.20360 | 0.264228 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −5.50784 | −0.451220 | −0.225610 | − | 0.974218i | \(-0.572437\pi\) | ||||
−0.225610 | + | 0.974218i | \(0.572437\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 23.8320 | 1.93942 | 0.969712 | − | 0.244251i | \(-0.0785420\pi\) | ||||
0.969712 | + | 0.244251i | \(0.0785420\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −0.0676800 | −0.00547160 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −9.44527 | −0.758663 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −10.1181 | −0.807514 | −0.403757 | − | 0.914866i | \(-0.632296\pi\) | ||||
−0.403757 | + | 0.914866i | \(0.632296\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −19.5579 | −1.55105 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 15.2474 | 1.20166 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −5.94785 | −0.465872 | −0.232936 | − | 0.972492i | \(-0.574833\pi\) | ||||
−0.232936 | + | 0.972492i | \(0.574833\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 1.64819 | 0.128311 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 15.4869 | 1.19841 | 0.599207 | − | 0.800594i | \(-0.295483\pi\) | ||||
0.599207 | + | 0.800594i | \(0.295483\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −10.9717 | −0.843978 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −0.145968 | −0.0111625 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 15.2597 | 1.16017 | 0.580085 | − | 0.814556i | \(-0.303019\pi\) | ||||
0.580085 | + | 0.814556i | \(0.303019\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 1.79711 | 0.135849 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 23.3997 | 1.75883 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 10.5306 | 0.787092 | 0.393546 | − | 0.919305i | \(-0.371248\pi\) | ||||
0.393546 | + | 0.919305i | \(0.371248\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 14.2605 | 1.05997 | 0.529987 | − | 0.848006i | \(-0.322197\pi\) | ||||
0.529987 | + | 0.848006i | \(0.322197\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −18.8171 | −1.39100 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −10.4250 | −0.766463 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −0.373935 | −0.0273448 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 15.6879 | 1.14113 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −22.1766 | −1.60464 | −0.802321 | − | 0.596892i | \(-0.796402\pi\) | ||||
−0.802321 | + | 0.596892i | \(0.796402\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −4.65576 | −0.335129 | −0.167565 | − | 0.985861i | \(-0.553590\pi\) | ||||
−0.167565 | + | 0.985861i | \(0.553590\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 5.10008 | 0.365225 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −13.5952 | −0.968619 | −0.484309 | − | 0.874897i | \(-0.660929\pi\) | ||||
−0.484309 | + | 0.874897i | \(0.660929\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −7.69902 | −0.545769 | −0.272884 | − | 0.962047i | \(-0.587978\pi\) | ||||
−0.272884 | + | 0.962047i | \(0.587978\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −10.4715 | −0.738602 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 8.10410 | 0.568796 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −19.0967 | −1.33377 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0.426333 | 0.0296322 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −0.806481 | −0.0557855 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −2.74256 | −0.188806 | −0.0944029 | − | 0.995534i | \(-0.530094\pi\) | ||||
−0.0944029 | + | 0.995534i | \(0.530094\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −4.46472 | −0.305917 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −10.2550 | −0.699385 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −13.4200 | −0.911006 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 11.3384 | 0.766176 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −1.15709 | −0.0778343 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 18.1118 | 1.21285 | 0.606427 | − | 0.795139i | \(-0.292602\pi\) | ||||
0.606427 | + | 0.795139i | \(0.292602\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0.0502490 | 0.00334994 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 21.6597 | 1.43760 | 0.718802 | − | 0.695214i | \(-0.244691\pi\) | ||||
0.718802 | + | 0.695214i | \(0.244691\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 11.2116 | 0.740882 | 0.370441 | − | 0.928856i | \(-0.379207\pi\) | ||||
0.370441 | + | 0.928856i | \(0.379207\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 2.34176 | 0.154077 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 20.0828 | 1.31567 | 0.657833 | − | 0.753164i | \(-0.271473\pi\) | ||||
0.657833 | + | 0.753164i | \(0.271473\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 27.1316 | 1.76987 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 25.5343 | 1.65863 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −7.52919 | −0.487023 | −0.243511 | − | 0.969898i | \(-0.578299\pi\) | ||||
−0.243511 | + | 0.969898i | \(0.578299\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 24.6424 | 1.58736 | 0.793680 | − | 0.608336i | \(-0.208163\pi\) | ||||
0.793680 | + | 0.608336i | \(0.208163\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 0.865450 | 0.0555187 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −3.93333 | −0.251291 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −2.49555 | −0.158788 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 23.2049 | 1.47055 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −12.5017 | −0.789099 | −0.394550 | − | 0.918875i | \(-0.629099\pi\) | ||||
−0.394550 | + | 0.918875i | \(0.629099\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 2.35551 | 0.148089 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −2.90949 | −0.182199 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 22.0515 | 1.37553 | 0.687767 | − | 0.725931i | \(-0.258591\pi\) | ||||
0.687767 | + | 0.725931i | \(0.258591\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −14.8120 | −0.920373 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0.226599 | 0.0140261 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 6.00997 | 0.370591 | 0.185295 | − | 0.982683i | \(-0.440676\pi\) | ||||
0.185295 | + | 0.982683i | \(0.440676\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 24.0129 | 1.47510 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −16.0574 | −0.982698 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −10.2196 | −0.623099 | −0.311550 | − | 0.950230i | \(-0.600848\pi\) | ||||
−0.311550 | + | 0.950230i | \(0.600848\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 6.05847 | 0.368026 | 0.184013 | − | 0.982924i | \(-0.441091\pi\) | ||||
0.184013 | + | 0.982924i | \(0.441091\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 7.24626 | 0.438564 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 0.277628 | 0.0167416 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 7.11430 | 0.427457 | 0.213728 | − | 0.976893i | \(-0.431439\pi\) | ||||
0.213728 | + | 0.976893i | \(0.431439\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −0.375235 | −0.0224648 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −1.82364 | −0.108789 | −0.0543945 | − | 0.998520i | \(-0.517323\pi\) | ||||
−0.0543945 | + | 0.998520i | \(0.517323\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 4.96688 | 0.295250 | 0.147625 | − | 0.989043i | \(-0.452837\pi\) | ||||
0.147625 | + | 0.989043i | \(0.452837\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −6.27502 | −0.371700 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −27.1328 | −1.60160 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −16.3399 | −0.961171 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −0.222517 | −0.0130442 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −5.01252 | −0.292834 | −0.146417 | − | 0.989223i | \(-0.546774\pi\) | ||||
−0.146417 | + | 0.989223i | \(0.546774\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −28.7298 | −1.67271 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 2.42356 | 0.140630 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 7.28879 | 0.421522 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −14.5704 | −0.839826 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 31.5666 | 1.81346 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 23.1034 | 1.32290 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −3.74187 | −0.213560 | −0.106780 | − | 0.994283i | \(-0.534054\pi\) | ||||
−0.106780 | + | 0.994283i | \(0.534054\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 26.0940 | 1.48444 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −26.0308 | −1.47607 | −0.738035 | − | 0.674763i | \(-0.764246\pi\) | ||||
−0.738035 | + | 0.674763i | \(0.764246\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 1.79685 | 0.101564 | 0.0507819 | − | 0.998710i | \(-0.483829\pi\) | ||||
0.0507819 | + | 0.998710i | \(0.483829\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −0.520390 | −0.0293207 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 16.2137 | 0.910652 | 0.455326 | − | 0.890325i | \(-0.349523\pi\) | ||||
0.455326 | + | 0.890325i | \(0.349523\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 1.25197 | 0.0700968 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 26.1925 | 1.46192 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 1.42366 | 0.0792143 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 0.859082 | 0.0476533 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −6.39231 | −0.353495 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 38.5489 | 2.12527 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 29.6755 | 1.63111 | 0.815556 | − | 0.578678i | \(-0.196431\pi\) | ||||
0.815556 | + | 0.578678i | \(0.196431\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −0.414158 | −0.0226957 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 12.8567 | 0.702438 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 28.6237 | 1.55923 | 0.779617 | − | 0.626256i | \(-0.215414\pi\) | ||||
0.779617 | + | 0.626256i | \(0.215414\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0.221497 | 0.0120301 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −2.07319 | −0.112270 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 15.2661 | 0.824292 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 18.3276 | 0.986724 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 18.3802 | 0.986703 | 0.493352 | − | 0.869830i | \(-0.335772\pi\) | ||||
0.493352 | + | 0.869830i | \(0.335772\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −10.3441 | −0.553706 | −0.276853 | − | 0.960912i | \(-0.589291\pi\) | ||||
−0.276853 | + | 0.960912i | \(0.589291\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 7.49939 | 0.400288 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 10.9746 | 0.584121 | 0.292060 | − | 0.956400i | \(-0.405659\pi\) | ||||
0.292060 | + | 0.956400i | \(0.405659\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 5.48171 | 0.290939 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −4.13384 | −0.218786 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −17.0847 | −0.901696 | −0.450848 | − | 0.892601i | \(-0.648878\pi\) | ||||
−0.450848 | + | 0.892601i | \(0.648878\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −15.9295 | −0.838397 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −18.4244 | −0.967031 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −13.9211 | −0.728662 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 11.5399 | 0.602377 | 0.301188 | − | 0.953565i | \(-0.402617\pi\) | ||||
0.301188 | + | 0.953565i | \(0.402617\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −0.758659 | −0.0394942 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 34.1179 | 1.77131 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 19.0705 | 0.987435 | 0.493718 | − | 0.869622i | \(-0.335638\pi\) | ||||
0.493718 | + | 0.869622i | \(0.335638\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 20.0655 | 1.03618 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 3.87404 | 0.199523 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −7.12746 | −0.366113 | −0.183057 | − | 0.983102i | \(-0.558599\pi\) | ||||
−0.183057 | + | 0.983102i | \(0.558599\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 18.3555 | 0.940379 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 31.2764 | 1.59815 | 0.799074 | − | 0.601232i | \(-0.205323\pi\) | ||||
0.799074 | + | 0.601232i | \(0.205323\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −2.87518 | −0.146533 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −0.407404 | −0.0207095 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 4.17824 | 0.211845 | 0.105923 | − | 0.994374i | \(-0.466220\pi\) | ||||
0.105923 | + | 0.994374i | \(0.466220\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −4.15810 | −0.210284 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −28.3203 | −1.42857 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −31.3506 | −1.57742 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −20.8948 | −1.04868 | −0.524340 | − | 0.851509i | \(-0.675688\pi\) | ||||
−0.524340 | + | 0.851509i | \(0.675688\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −8.91562 | −0.446339 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −5.39620 | −0.269473 | −0.134737 | − | 0.990881i | \(-0.543019\pi\) | ||||
−0.134737 | + | 0.990881i | \(0.543019\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −6.41521 | −0.319564 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 18.3331 | 0.910979 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −2.28824 | −0.113424 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −20.2177 | −0.999700 | −0.499850 | − | 0.866112i | \(-0.666612\pi\) | ||||
−0.499850 | + | 0.866112i | \(0.666612\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −25.6704 | −1.26623 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −40.8196 | −2.00860 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −28.4907 | −1.39855 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 18.2746 | 0.894909 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 35.2717 | 1.72314 | 0.861569 | − | 0.507641i | \(-0.169482\pi\) | ||||
0.861569 | + | 0.507641i | \(0.169482\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −34.3101 | −1.67217 | −0.836086 | − | 0.548599i | \(-0.815162\pi\) | ||||
−0.836086 | + | 0.548599i | \(0.815162\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 1.07786 | 0.0524076 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −0.490088 | −0.0237728 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 32.8256 | 1.58854 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 1.11944 | 0.0540473 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −15.8509 | −0.763513 | −0.381756 | − | 0.924263i | \(-0.624681\pi\) | ||||
−0.381756 | + | 0.924263i | \(0.624681\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −4.03995 | −0.194148 | −0.0970739 | − | 0.995277i | \(-0.530948\pi\) | ||||
−0.0970739 | + | 0.995277i | \(0.530948\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 9.74123 | 0.467056 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −8.96795 | −0.428995 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −39.1240 | −1.86729 | −0.933644 | − | 0.358202i | \(-0.883390\pi\) | ||||
−0.933644 | + | 0.358202i | \(0.883390\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −0.156261 | −0.00744098 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −28.3101 | −1.34505 | −0.672527 | − | 0.740073i | \(-0.734791\pi\) | ||||
−0.672527 | + | 0.740073i | \(0.734791\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 19.7150 | 0.934582 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −9.40647 | −0.444911 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −23.7418 | −1.12044 | −0.560221 | − | 0.828343i | \(-0.689284\pi\) | ||||
−0.560221 | + | 0.828343i | \(0.689284\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −4.19163 | −0.197376 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 40.7012 | 1.91231 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −8.89684 | −0.417091 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 35.3209 | 1.65224 | 0.826121 | − | 0.563492i | \(-0.190542\pi\) | ||||
0.826121 | + | 0.563492i | \(0.190542\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −4.27824 | −0.199691 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 13.1074 | 0.610471 | 0.305235 | − | 0.952277i | \(-0.401265\pi\) | ||||
0.305235 | + | 0.952277i | \(0.401265\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 40.1611 | 1.86644 | 0.933221 | − | 0.359302i | \(-0.116985\pi\) | ||||
0.933221 | + | 0.359302i | \(0.116985\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −16.1310 | −0.748055 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −14.7735 | −0.683637 | −0.341818 | − | 0.939766i | \(-0.611043\pi\) | ||||
−0.341818 | + | 0.939766i | \(0.611043\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 18.2670 | 0.843491 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −17.2801 | −0.796224 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −2.25092 | −0.103498 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −1.05699 | −0.0484982 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0.953969 | 0.0436793 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −25.4093 | −1.16098 | −0.580489 | − | 0.814268i | \(-0.697139\pi\) | ||||
−0.580489 | + | 0.814268i | \(0.697139\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −7.08065 | −0.322850 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 26.0400 | 1.18486 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 0.273203 | 0.0124055 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −36.4903 | −1.65353 | −0.826767 | − | 0.562544i | \(-0.809823\pi\) | ||||
−0.826767 | + | 0.562544i | \(0.809823\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −10.1579 | −0.459358 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 11.1497 | 0.503180 | 0.251590 | − | 0.967834i | \(-0.419047\pi\) | ||||
0.251590 | + | 0.967834i | \(0.419047\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −2.21006 | −0.0995360 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −0.0803929 | −0.00361339 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 7.78848 | 0.349361 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 8.21934 | 0.367948 | 0.183974 | − | 0.982931i | \(-0.441104\pi\) | ||||
0.183974 | + | 0.982931i | \(0.441104\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 26.4491 | 1.18166 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −1.00000 | −0.0445878 | ||||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −38.7570 | −1.72466 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −18.7379 | −0.832178 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −0.298382 | −0.0132256 | −0.00661278 | − | 0.999978i | \(-0.502105\pi\) | ||||
−0.00661278 | + | 0.999978i | \(0.502105\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −19.7792 | −0.874981 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −9.22706 | −0.407385 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −32.0378 | −1.41175 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 5.95525 | 0.261912 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 26.0610 | 1.14395 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −3.97801 | −0.174280 | −0.0871399 | − | 0.996196i | \(-0.527773\pi\) | ||||
−0.0871399 | + | 0.996196i | \(0.527773\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −7.66014 | −0.334954 | −0.167477 | − | 0.985876i | \(-0.553562\pi\) | ||||
−0.167477 | + | 0.985876i | \(0.553562\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 3.06917 | 0.133950 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 3.65974 | 0.159421 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 3.19288 | 0.138821 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −1.14136 | −0.0495307 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −12.9704 | −0.561811 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −32.1587 | −1.39034 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 17.9845 | 0.776087 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −0.863347 | −0.0371870 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 19.7723 | 0.850076 | 0.425038 | − | 0.905175i | \(-0.360261\pi\) | ||||
0.425038 | + | 0.905175i | \(0.360261\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 24.3545 | 1.04515 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 7.84838 | 0.336187 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −10.4650 | −0.447453 | −0.223726 | − | 0.974652i | \(-0.571822\pi\) | ||||
−0.223726 | + | 0.974652i | \(0.571822\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 0.917835 | 0.0391723 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −4.76653 | −0.203061 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −44.5433 | −1.89417 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −17.8042 | −0.755746 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 4.53652 | 0.192218 | 0.0961092 | − | 0.995371i | \(-0.469360\pi\) | ||||
0.0961092 | + | 0.995371i | \(0.469360\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −6.96517 | −0.294596 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −0.638619 | −0.0269625 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 10.9857 | 0.462993 | 0.231497 | − | 0.972836i | \(-0.425638\pi\) | ||||
0.231497 | + | 0.972836i | \(0.425638\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −0.271950 | −0.0114410 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 26.0479 | 1.09391 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 9.17445 | 0.384613 | 0.192306 | − | 0.981335i | \(-0.438403\pi\) | ||||
0.192306 | + | 0.981335i | \(0.438403\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −20.9159 | −0.875304 | −0.437652 | − | 0.899144i | \(-0.644190\pi\) | ||||
−0.437652 | + | 0.899144i | \(0.644190\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −37.8740 | −1.58221 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 3.08718 | 0.128744 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 14.9036 | 0.620445 | 0.310223 | − | 0.950664i | \(-0.399596\pi\) | ||||
0.310223 | + | 0.950664i | \(0.399596\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −7.95127 | −0.330444 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −40.4799 | −1.67939 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 5.27072 | 0.218291 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −0.248765 | −0.0102852 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 36.1420 | 1.49174 | 0.745869 | − | 0.666092i | \(-0.232034\pi\) | ||||
0.745869 | + | 0.666092i | \(0.232034\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 7.89311 | 0.325230 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −23.2184 | −0.955076 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 34.6875 | 1.42445 | 0.712223 | − | 0.701953i | \(-0.247688\pi\) | ||||
0.712223 | + | 0.701953i | \(0.247688\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 5.07546 | 0.208074 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −13.1486 | −0.538138 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 34.4028 | 1.40566 | 0.702829 | − | 0.711359i | \(-0.251920\pi\) | ||||
0.702829 | + | 0.711359i | \(0.251920\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 36.0776 | 1.47164 | 0.735818 | − | 0.677179i | \(-0.236798\pi\) | ||||
0.735818 | + | 0.677179i | \(0.236798\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0.510763 | 0.0207999 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 22.6212 | 0.919682 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 22.6603 | 0.919755 | 0.459877 | − | 0.887982i | \(-0.347893\pi\) | ||||
0.459877 | + | 0.887982i | \(0.347893\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 13.8405 | 0.560844 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 18.4277 | 0.745505 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −21.3813 | −0.863581 | −0.431790 | − | 0.901974i | \(-0.642118\pi\) | ||||
−0.431790 | + | 0.901974i | \(0.642118\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −32.6139 | −1.31512 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −16.0936 | −0.647906 | −0.323953 | − | 0.946073i | \(-0.605012\pi\) | ||||
−0.323953 | + | 0.946073i | \(0.605012\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −36.9907 | −1.48678 | −0.743392 | − | 0.668856i | \(-0.766784\pi\) | ||||
−0.743392 | + | 0.668856i | \(0.766784\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 26.9497 | 1.08145 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 28.0114 | 1.12225 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −21.6201 | −0.864803 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −1.37734 | −0.0550055 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 4.03936 | 0.161060 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 30.3302 | 1.20743 | 0.603714 | − | 0.797201i | \(-0.293687\pi\) | ||||
0.603714 | + | 0.797201i | \(0.293687\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −4.68384 | −0.186166 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −22.5365 | −0.894335 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −2.67151 | −0.105849 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0.217774 | 0.00861499 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 25.8295 | 1.02020 | 0.510102 | − | 0.860114i | \(-0.329608\pi\) | ||||
0.510102 | + | 0.860114i | \(0.329608\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −40.8285 | −1.61012 | −0.805060 | − | 0.593194i | \(-0.797867\pi\) | ||||
−0.805060 | + | 0.593194i | \(0.797867\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −17.5138 | −0.689607 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 22.0342 | 0.866253 | 0.433127 | − | 0.901333i | \(-0.357410\pi\) | ||||
0.433127 | + | 0.901333i | \(0.357410\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −6.30605 | −0.247534 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −22.9191 | −0.898269 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −37.4987 | −1.46744 | −0.733718 | − | 0.679454i | \(-0.762217\pi\) | ||||
−0.733718 | + | 0.679454i | \(0.762217\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 34.7712 | 1.35862 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −0.553047 | −0.0215764 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −39.1034 | −1.52325 | −0.761626 | − | 0.648017i | \(-0.775599\pi\) | ||||
−0.761626 | + | 0.648017i | \(0.775599\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 12.6533 | 0.492155 | 0.246077 | − | 0.969250i | \(-0.420858\pi\) | ||||
0.246077 | + | 0.969250i | \(0.420858\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −1.97612 | −0.0767461 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 10.9465 | 0.424485 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 13.9217 | 0.539050 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 30.9319 | 1.19590 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 5.07108 | 0.195767 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −16.9888 | −0.654872 | −0.327436 | − | 0.944873i | \(-0.606185\pi\) | ||||
−0.327436 | + | 0.944873i | \(0.606185\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 3.17638 | 0.122259 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −40.1360 | −1.54255 | −0.771277 | − | 0.636500i | \(-0.780382\pi\) | ||||
−0.771277 | + | 0.636500i | \(0.780382\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 0.388170 | 0.0148966 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 36.9912 | 1.41750 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 17.0463 | 0.652257 | 0.326129 | − | 0.945325i | \(-0.394256\pi\) | ||||
0.326129 | + | 0.945325i | \(0.394256\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 31.5177 | 1.20423 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 19.1475 | 0.730523 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 16.3095 | 0.621343 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −8.37553 | −0.318620 | −0.159310 | − | 0.987229i | \(-0.550927\pi\) | ||||
−0.159310 | + | 0.987229i | \(0.550927\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −0.114223 | −0.00433898 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −22.4372 | −0.851092 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 7.39934 | 0.280270 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 34.2980 | 1.29727 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −22.7434 | −0.859006 | −0.429503 | − | 0.903065i | \(-0.641311\pi\) | ||||
−0.429503 | + | 0.903065i | \(0.641311\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 8.71186 | 0.328574 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 46.3362 | 1.74512 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −55.0664 | −2.07099 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −43.5337 | −1.63494 | −0.817471 | − | 0.575970i | \(-0.804624\pi\) | ||||
−0.817471 | + | 0.575970i | \(0.804624\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −1.24548 | −0.0467090 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −23.0536 | −0.863364 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −1.37444 | −0.0514010 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −12.8586 | −0.480214 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −20.1699 | −0.752212 | −0.376106 | − | 0.926577i | \(-0.622737\pi\) | ||||
−0.376106 | + | 0.926577i | \(0.622737\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −45.5197 | −1.69524 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 42.0852 | 1.56517 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 1.64086 | 0.0609400 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −21.8244 | −0.809424 | −0.404712 | − | 0.914444i | \(-0.632628\pi\) | ||||
−0.404712 | + | 0.914444i | \(0.632628\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 27.7075 | 1.02620 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 3.97348 | 0.146965 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −36.3457 | −1.34246 | −0.671229 | − | 0.741250i | \(-0.734233\pi\) | ||||
−0.671229 | + | 0.741250i | \(0.734233\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | −6.71747 | −0.247778 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 2.82199 | 0.103949 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 31.7359 | 1.16742 | 0.583712 | − | 0.811961i | \(-0.301600\pi\) | ||||
0.583712 | + | 0.811961i | \(0.301600\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −4.26198 | −0.156568 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 20.3640 | 0.747081 | 0.373541 | − | 0.927614i | \(-0.378144\pi\) | ||||
0.373541 | + | 0.927614i | \(0.378144\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 11.5491 | 0.423127 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −1.13186 | −0.0414125 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −45.6915 | −1.66953 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −36.0390 | −1.31508 | −0.657540 | − | 0.753419i | \(-0.728403\pi\) | ||||
−0.657540 | + | 0.753419i | \(0.728403\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −21.3508 | −0.778066 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −49.9723 | −1.81868 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 4.02544 | 0.146307 | 0.0731535 | − | 0.997321i | \(-0.476694\pi\) | ||||
0.0731535 | + | 0.997321i | \(0.476694\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 4.02282 | 0.146019 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −13.0849 | −0.474327 | −0.237164 | − | 0.971470i | \(-0.576218\pi\) | ||||
−0.237164 | + | 0.971470i | \(0.576218\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 11.1511 | 0.403696 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0.141915 | 0.00513094 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −19.5132 | −0.704581 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 50.7230 | 1.82912 | 0.914559 | − | 0.404453i | \(-0.132538\pi\) | ||||
0.914559 | + | 0.404453i | \(0.132538\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 37.6603 | 1.35630 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 15.6122 | 0.561532 | 0.280766 | − | 0.959776i | \(-0.409411\pi\) | ||||
0.280766 | + | 0.959776i | \(0.409411\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −2.71717 | −0.0976038 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −25.2964 | −0.907504 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 15.9585 | 0.571771 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 1.20321 | 0.0430542 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 14.3239 | 0.511896 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 21.2162 | 0.757239 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 39.5500 | 1.40980 | 0.704902 | − | 0.709305i | \(-0.250991\pi\) | ||||
0.704902 | + | 0.709305i | \(0.250991\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 10.2640 | 0.365409 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −0.386390 | −0.0137385 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 15.6918 | 0.557231 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 41.0101 | 1.45448 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −13.1211 | −0.464775 | −0.232387 | − | 0.972623i | \(-0.574654\pi\) | ||||
−0.232387 | + | 0.972623i | \(0.574654\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −10.5126 | −0.371909 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0.783226 | 0.0276739 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −3.05561 | −0.107830 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −31.9716 | −1.12685 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −17.4534 | −0.614387 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −16.4507 | −0.578377 | −0.289189 | − | 0.957272i | \(-0.593385\pi\) | ||||
−0.289189 | + | 0.957272i | \(0.593385\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 14.8064 | 0.519924 | 0.259962 | − | 0.965619i | \(-0.416290\pi\) | ||||
0.259962 | + | 0.965619i | \(0.416290\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 10.3469 | 0.362881 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 12.4718 | 0.436867 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 8.56978 | 0.299819 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −0.353448 | −0.0123505 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −32.4419 | −1.13223 | −0.566115 | − | 0.824326i | \(-0.691554\pi\) | ||||
−0.566115 | + | 0.824326i | \(0.691554\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −8.00269 | −0.278956 | −0.139478 | − | 0.990225i | \(-0.544543\pi\) | ||||
−0.139478 | + | 0.990225i | \(0.544543\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0.474143 | 0.0165075 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −7.38956 | −0.256960 | −0.128480 | − | 0.991712i | \(-0.541010\pi\) | ||||
−0.128480 | + | 0.991712i | \(0.541010\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 31.6209 | 1.09824 | 0.549119 | − | 0.835744i | \(-0.314963\pi\) | ||||
0.549119 | + | 0.835744i | \(0.314963\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 12.1500 | 0.421480 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 1.52404 | 0.0528048 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −32.4738 | −1.12380 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −23.7197 | −0.819872 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −13.6131 | −0.469976 | −0.234988 | − | 0.971998i | \(-0.575505\pi\) | ||||
−0.234988 | + | 0.971998i | \(0.575505\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −21.6005 | −0.744846 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −3.11447 | −0.107268 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 23.0061 | 0.791433 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 32.1405 | 1.10436 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 8.48260 | 0.291122 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −25.4449 | −0.872240 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 2.34684 | 0.0803542 | 0.0401771 | − | 0.999193i | \(-0.487208\pi\) | ||||
0.0401771 | + | 0.999193i | \(0.487208\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0.306074 | 0.0104675 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −48.2762 | −1.64909 | −0.824543 | − | 0.565800i | \(-0.808567\pi\) | ||||
−0.824543 | + | 0.565800i | \(0.808567\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −5.17193 | −0.176464 | −0.0882319 | − | 0.996100i | \(-0.528122\pi\) | ||||
−0.0882319 | + | 0.996100i | \(0.528122\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −46.3383 | −1.57920 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −30.4408 | −1.03622 | −0.518108 | − | 0.855315i | \(-0.673363\pi\) | ||||
−0.518108 | + | 0.855315i | \(0.673363\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −31.9972 | −1.08794 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −27.9058 | −0.947732 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −6.88131 | −0.233432 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 8.73226 | 0.295881 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 0.0108536 | 0.000367339 0 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −35.0033 | −1.18333 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −11.4687 | −0.387271 | −0.193635 | − | 0.981074i | \(-0.562028\pi\) | ||||
−0.193635 | + | 0.981074i | \(0.562028\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −8.56055 | −0.288740 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −1.15396 | −0.0388778 | −0.0194389 | − | 0.999811i | \(-0.506188\pi\) | ||||
−0.0194389 | + | 0.999811i | \(0.506188\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 47.1677 | 1.58732 | 0.793659 | − | 0.608363i | \(-0.208173\pi\) | ||||
0.793659 | + | 0.608363i | \(0.208173\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −49.0657 | −1.64933 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −9.97150 | −0.334810 | −0.167405 | − | 0.985888i | \(-0.553539\pi\) | ||||
−0.167405 | + | 0.985888i | \(0.553539\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −32.0202 | −1.07392 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 4.02403 | 0.134810 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −22.6730 | −0.758722 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −22.0810 | −0.738088 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 12.4480 | 0.415628 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −12.2531 | −0.408665 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −9.30423 | −0.309969 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −24.8839 | −0.828084 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −29.9021 | −0.993980 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 26.3908 | 0.876291 | 0.438145 | − | 0.898904i | \(-0.355635\pi\) | ||||
0.438145 | + | 0.898904i | \(0.355635\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −1.53971 | −0.0510690 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 33.8813 | 1.12254 | 0.561268 | − | 0.827634i | \(-0.310314\pi\) | ||||
0.561268 | + | 0.827634i | \(0.310314\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −6.25356 | −0.206963 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 39.4567 | 1.30440 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 49.4033 | 1.63144 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 20.9457 | 0.690936 | 0.345468 | − | 0.938431i | \(-0.387720\pi\) | ||||
0.345468 | + | 0.938431i | \(0.387720\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −6.39049 | −0.210574 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 3.72316 | 0.122549 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −2.99902 | −0.0986073 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −1.27278 | −0.0418034 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −20.7936 | −0.682215 | −0.341107 | − | 0.940024i | \(-0.610802\pi\) | ||||
−0.341107 | + | 0.940024i | \(0.610802\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 3.28696 | 0.107726 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −44.4562 | −1.45543 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 0.784086 | 0.0256424 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 5.65325 | 0.184683 | 0.0923417 | − | 0.995727i | \(-0.470565\pi\) | ||||
0.0923417 | + | 0.995727i | \(0.470565\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 3.06872 | 0.100144 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −15.8425 | −0.516451 | −0.258226 | − | 0.966085i | \(-0.583138\pi\) | ||||
−0.258226 | + | 0.966085i | \(0.583138\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −46.6102 | −1.51784 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | −32.8953 | −1.07008 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −57.9813 | −1.88414 | −0.942070 | − | 0.335416i | \(-0.891123\pi\) | ||||
−0.942070 | + | 0.335416i | \(0.891123\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −9.45516 | −0.306927 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 27.6903 | 0.897920 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 51.8726 | 1.68032 | 0.840159 | − | 0.542340i | \(-0.182461\pi\) | ||||
0.840159 | + | 0.542340i | \(0.182461\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 46.5010 | 1.50474 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 2.13815 | 0.0691167 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 44.7808 | 1.44605 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −10.7095 | −0.345466 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −1.27758 | −0.0411694 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 9.76244 | 0.314264 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −6.21398 | −0.199828 | −0.0999141 | − | 0.994996i | \(-0.531857\pi\) | ||||
−0.0999141 | + | 0.994996i | \(0.531857\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 2.43137 | 0.0781068 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −16.8227 | −0.539868 | −0.269934 | − | 0.962879i | \(-0.587002\pi\) | ||||
−0.269934 | + | 0.962879i | \(0.587002\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −31.8791 | −1.02200 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 1.46717 | 0.0469870 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 29.7655 | 0.952282 | 0.476141 | − | 0.879369i | \(-0.342035\pi\) | ||||
0.476141 | + | 0.879369i | \(0.342035\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 4.32736 | 0.138303 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0.311795 | 0.00995485 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −6.08958 | −0.194227 | −0.0971137 | − | 0.995273i | \(-0.530961\pi\) | ||||
−0.0971137 | + | 0.995273i | \(0.530961\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 28.5071 | 0.908313 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 65.8351 | 2.09555 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −25.0299 | −0.795906 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −14.0190 | −0.445328 | −0.222664 | − | 0.974895i | \(-0.571475\pi\) | ||||
−0.222664 | + | 0.974895i | \(0.571475\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 50.6808 | 1.60831 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 16.1437 | 0.511790 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −10.7255 | −0.339681 | −0.169840 | − | 0.985472i | \(-0.554325\pi\) | ||||
−0.169840 | + | 0.985472i | \(0.554325\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −26.1801 | −0.828301 |
(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 | 8048.2.a.t.1.14 | 21 | ||
4.3 | odd | 2 | 2012.2.a.a.1.8 | ✓ | 21 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
2012.2.a.a.1.8 | ✓ | 21 | 4.3 | odd | 2 | ||
8048.2.a.t.1.14 | 21 | 1.1 | even | 1 | trivial |