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: | \(1\) |
Dimension: | \(32\) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.11 | ||
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −0.959867 | −0.678728 | −0.339364 | − | 0.940655i | \(-0.610212\pi\) | ||||
−0.339364 | + | 0.940655i | \(0.610212\pi\) | |||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | −1.07866 | −0.539328 | ||||||||
\(5\) | −2.40466 | −1.07540 | −0.537698 | − | 0.843138i | \(-0.680706\pi\) | ||||
−0.537698 | + | 0.843138i | \(0.680706\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −1.00000 | −0.377964 | ||||||||
\(8\) | 2.95510 | 1.04479 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 2.30815 | 0.729901 | ||||||||
\(11\) | −4.25741 | −1.28366 | −0.641829 | − | 0.766848i | \(-0.721824\pi\) | ||||
−0.641829 | + | 0.766848i | \(0.721824\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 3.54385 | 0.982886 | 0.491443 | − | 0.870910i | \(-0.336470\pi\) | ||||
0.491443 | + | 0.870910i | \(0.336470\pi\) | |||||||
\(14\) | 0.959867 | 0.256535 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −0.679190 | −0.169797 | ||||||||
\(17\) | −0.302404 | −0.0733436 | −0.0366718 | − | 0.999327i | \(-0.511676\pi\) | ||||
−0.0366718 | + | 0.999327i | \(0.511676\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −6.75953 | −1.55074 | −0.775371 | − | 0.631506i | \(-0.782437\pi\) | ||||
−0.775371 | + | 0.631506i | \(0.782437\pi\) | |||||||
\(20\) | 2.59380 | 0.579991 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 4.08655 | 0.871255 | ||||||||
\(23\) | 6.51256 | 1.35796 | 0.678981 | − | 0.734155i | \(-0.262422\pi\) | ||||
0.678981 | + | 0.734155i | \(0.262422\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 0.782373 | 0.156475 | ||||||||
\(26\) | −3.40162 | −0.667113 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 1.07866 | 0.203847 | ||||||||
\(29\) | 3.90770 | 0.725641 | 0.362820 | − | 0.931859i | \(-0.381814\pi\) | ||||
0.362820 | + | 0.931859i | \(0.381814\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −5.48700 | −0.985495 | −0.492748 | − | 0.870172i | \(-0.664007\pi\) | ||||
−0.492748 | + | 0.870172i | \(0.664007\pi\) | |||||||
\(32\) | −5.25827 | −0.929539 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0.290267 | 0.0497804 | ||||||||
\(35\) | 2.40466 | 0.406461 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −6.55479 | −1.07760 | −0.538800 | − | 0.842434i | \(-0.681122\pi\) | ||||
−0.538800 | + | 0.842434i | \(0.681122\pi\) | |||||||
\(38\) | 6.48825 | 1.05253 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | −7.10600 | −1.12356 | ||||||||
\(41\) | 2.17456 | 0.339609 | 0.169805 | − | 0.985478i | \(-0.445686\pi\) | ||||
0.169805 | + | 0.985478i | \(0.445686\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 9.47361 | 1.44471 | 0.722356 | − | 0.691521i | \(-0.243059\pi\) | ||||
0.722356 | + | 0.691521i | \(0.243059\pi\) | |||||||
\(44\) | 4.59228 | 0.692313 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −6.25119 | −0.921688 | ||||||||
\(47\) | 1.43429 | 0.209212 | 0.104606 | − | 0.994514i | \(-0.466642\pi\) | ||||
0.104606 | + | 0.994514i | \(0.466642\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 1.00000 | 0.142857 | ||||||||
\(50\) | −0.750974 | −0.106204 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | −3.82259 | −0.530098 | ||||||||
\(53\) | 10.5740 | 1.45246 | 0.726228 | − | 0.687454i | \(-0.241272\pi\) | ||||
0.726228 | + | 0.687454i | \(0.241272\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 10.2376 | 1.38044 | ||||||||
\(56\) | −2.95510 | −0.394892 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | −3.75087 | −0.492513 | ||||||||
\(59\) | −7.97145 | −1.03779 | −0.518897 | − | 0.854837i | \(-0.673657\pi\) | ||||
−0.518897 | + | 0.854837i | \(0.673657\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 1.05914 | 0.135608 | 0.0678042 | − | 0.997699i | \(-0.478401\pi\) | ||||
0.0678042 | + | 0.997699i | \(0.478401\pi\) | |||||||
\(62\) | 5.26679 | 0.668883 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 6.40561 | 0.800702 | ||||||||
\(65\) | −8.52173 | −1.05699 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −4.72133 | −0.576802 | −0.288401 | − | 0.957510i | \(-0.593124\pi\) | ||||
−0.288401 | + | 0.957510i | \(0.593124\pi\) | |||||||
\(68\) | 0.326189 | 0.0395563 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | −2.30815 | −0.275877 | ||||||||
\(71\) | 6.25244 | 0.742028 | 0.371014 | − | 0.928627i | \(-0.379010\pi\) | ||||
0.371014 | + | 0.928627i | \(0.379010\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −11.4772 | −1.34330 | −0.671652 | − | 0.740867i | \(-0.734415\pi\) | ||||
−0.671652 | + | 0.740867i | \(0.734415\pi\) | |||||||
\(74\) | 6.29172 | 0.731398 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 7.29120 | 0.836358 | ||||||||
\(77\) | 4.25741 | 0.485177 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 4.55627 | 0.512620 | 0.256310 | − | 0.966595i | \(-0.417493\pi\) | ||||
0.256310 | + | 0.966595i | \(0.417493\pi\) | |||||||
\(80\) | 1.63322 | 0.182599 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | −2.08729 | −0.230502 | ||||||||
\(83\) | 10.1365 | 1.11263 | 0.556315 | − | 0.830972i | \(-0.312215\pi\) | ||||
0.556315 | + | 0.830972i | \(0.312215\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0.727177 | 0.0788734 | ||||||||
\(86\) | −9.09340 | −0.980567 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | −12.5811 | −1.34115 | ||||||||
\(89\) | 8.24382 | 0.873844 | 0.436922 | − | 0.899499i | \(-0.356069\pi\) | ||||
0.436922 | + | 0.899499i | \(0.356069\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −3.54385 | −0.371496 | ||||||||
\(92\) | −7.02481 | −0.732387 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | −1.37672 | −0.141998 | ||||||||
\(95\) | 16.2543 | 1.66766 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 1.74407 | 0.177084 | 0.0885419 | − | 0.996072i | \(-0.471779\pi\) | ||||
0.0885419 | + | 0.996072i | \(0.471779\pi\) | |||||||
\(98\) | −0.959867 | −0.0969612 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | −0.843912 | −0.0843912 | ||||||||
\(101\) | −3.61578 | −0.359783 | −0.179892 | − | 0.983686i | \(-0.557575\pi\) | ||||
−0.179892 | + | 0.983686i | \(0.557575\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 5.92884 | 0.584186 | 0.292093 | − | 0.956390i | \(-0.405648\pi\) | ||||
0.292093 | + | 0.956390i | \(0.405648\pi\) | |||||||
\(104\) | 10.4724 | 1.02690 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −10.1497 | −0.985823 | ||||||||
\(107\) | 6.45523 | 0.624050 | 0.312025 | − | 0.950074i | \(-0.398993\pi\) | ||||
0.312025 | + | 0.950074i | \(0.398993\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 20.5285 | 1.96628 | 0.983138 | − | 0.182865i | \(-0.0585371\pi\) | ||||
0.983138 | + | 0.182865i | \(0.0585371\pi\) | |||||||
\(110\) | −9.82675 | −0.936943 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0.679190 | 0.0641774 | ||||||||
\(113\) | −15.2547 | −1.43504 | −0.717520 | − | 0.696538i | \(-0.754723\pi\) | ||||
−0.717520 | + | 0.696538i | \(0.754723\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −15.6605 | −1.46035 | ||||||||
\(116\) | −4.21506 | −0.391358 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 7.65153 | 0.704380 | ||||||||
\(119\) | 0.302404 | 0.0277213 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 7.12556 | 0.647778 | ||||||||
\(122\) | −1.01663 | −0.0920412 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 5.91859 | 0.531505 | ||||||||
\(125\) | 10.1419 | 0.907123 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −1.00000 | −0.0887357 | ||||||||
\(128\) | 4.36800 | 0.386080 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 8.17973 | 0.717410 | ||||||||
\(131\) | −5.94653 | −0.519551 | −0.259775 | − | 0.965669i | \(-0.583648\pi\) | ||||
−0.259775 | + | 0.965669i | \(0.583648\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 6.75953 | 0.586125 | ||||||||
\(134\) | 4.53185 | 0.391492 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −0.893633 | −0.0766284 | ||||||||
\(137\) | 1.37243 | 0.117255 | 0.0586273 | − | 0.998280i | \(-0.481328\pi\) | ||||
0.0586273 | + | 0.998280i | \(0.481328\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 3.13422 | 0.265841 | 0.132921 | − | 0.991127i | \(-0.457564\pi\) | ||||
0.132921 | + | 0.991127i | \(0.457564\pi\) | |||||||
\(140\) | −2.59380 | −0.219216 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | −6.00151 | −0.503635 | ||||||||
\(143\) | −15.0876 | −1.26169 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −9.39666 | −0.780351 | ||||||||
\(146\) | 11.0166 | 0.911738 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 7.07036 | 0.581180 | ||||||||
\(149\) | 13.3703 | 1.09534 | 0.547670 | − | 0.836694i | \(-0.315515\pi\) | ||||
0.547670 | + | 0.836694i | \(0.315515\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −10.2915 | −0.837513 | −0.418757 | − | 0.908098i | \(-0.637534\pi\) | ||||
−0.418757 | + | 0.908098i | \(0.637534\pi\) | |||||||
\(152\) | −19.9751 | −1.62019 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | −4.08655 | −0.329303 | ||||||||
\(155\) | 13.1944 | 1.05980 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 7.70342 | 0.614800 | 0.307400 | − | 0.951580i | \(-0.400541\pi\) | ||||
0.307400 | + | 0.951580i | \(0.400541\pi\) | |||||||
\(158\) | −4.37341 | −0.347930 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 12.6443 | 0.999622 | ||||||||
\(161\) | −6.51256 | −0.513262 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 6.54115 | 0.512342 | 0.256171 | − | 0.966631i | \(-0.417539\pi\) | ||||
0.256171 | + | 0.966631i | \(0.417539\pi\) | |||||||
\(164\) | −2.34560 | −0.183161 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −9.72973 | −0.755173 | ||||||||
\(167\) | 2.06466 | 0.159769 | 0.0798843 | − | 0.996804i | \(-0.474545\pi\) | ||||
0.0798843 | + | 0.996804i | \(0.474545\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −0.441156 | −0.0339351 | ||||||||
\(170\) | −0.697993 | −0.0535336 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | −10.2188 | −0.779174 | ||||||||
\(173\) | −11.0221 | −0.837991 | −0.418996 | − | 0.907988i | \(-0.637618\pi\) | ||||
−0.418996 | + | 0.907988i | \(0.637618\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −0.782373 | −0.0591419 | ||||||||
\(176\) | 2.89159 | 0.217962 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | −7.91297 | −0.593102 | ||||||||
\(179\) | 23.6676 | 1.76900 | 0.884501 | − | 0.466537i | \(-0.154499\pi\) | ||||
0.884501 | + | 0.466537i | \(0.154499\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −15.1437 | −1.12563 | −0.562813 | − | 0.826584i | \(-0.690281\pi\) | ||||
−0.562813 | + | 0.826584i | \(0.690281\pi\) | |||||||
\(182\) | 3.40162 | 0.252145 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 19.2453 | 1.41878 | ||||||||
\(185\) | 15.7620 | 1.15885 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 1.28746 | 0.0941482 | ||||||||
\(188\) | −1.54710 | −0.112834 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | −15.6020 | −1.13189 | ||||||||
\(191\) | 11.4808 | 0.830722 | 0.415361 | − | 0.909657i | \(-0.363655\pi\) | ||||
0.415361 | + | 0.909657i | \(0.363655\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −8.41906 | −0.606017 | −0.303009 | − | 0.952988i | \(-0.597991\pi\) | ||||
−0.303009 | + | 0.952988i | \(0.597991\pi\) | |||||||
\(194\) | −1.67408 | −0.120192 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −1.07866 | −0.0770468 | ||||||||
\(197\) | 6.10162 | 0.434723 | 0.217361 | − | 0.976091i | \(-0.430255\pi\) | ||||
0.217361 | + | 0.976091i | \(0.430255\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −10.7103 | −0.759231 | −0.379616 | − | 0.925144i | \(-0.623944\pi\) | ||||
−0.379616 | + | 0.925144i | \(0.623944\pi\) | |||||||
\(200\) | 2.31199 | 0.163482 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 3.47066 | 0.244195 | ||||||||
\(203\) | −3.90770 | −0.274266 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −5.22907 | −0.365214 | ||||||||
\(206\) | −5.69089 | −0.396503 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | −2.40694 | −0.166891 | ||||||||
\(209\) | 28.7781 | 1.99062 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −13.8349 | −0.952436 | −0.476218 | − | 0.879327i | \(-0.657993\pi\) | ||||
−0.476218 | + | 0.879327i | \(0.657993\pi\) | |||||||
\(212\) | −11.4057 | −0.783350 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | −6.19616 | −0.423561 | ||||||||
\(215\) | −22.7808 | −1.55364 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 5.48700 | 0.372482 | ||||||||
\(218\) | −19.7046 | −1.33457 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | −11.0429 | −0.744510 | ||||||||
\(221\) | −1.07167 | −0.0720884 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −5.00800 | −0.335360 | −0.167680 | − | 0.985841i | \(-0.553628\pi\) | ||||
−0.167680 | + | 0.985841i | \(0.553628\pi\) | |||||||
\(224\) | 5.25827 | 0.351333 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 14.6425 | 0.974002 | ||||||||
\(227\) | −23.4386 | −1.55567 | −0.777837 | − | 0.628467i | \(-0.783683\pi\) | ||||
−0.777837 | + | 0.628467i | \(0.783683\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −3.95298 | −0.261220 | −0.130610 | − | 0.991434i | \(-0.541694\pi\) | ||||
−0.130610 | + | 0.991434i | \(0.541694\pi\) | |||||||
\(230\) | 15.0320 | 0.991179 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 11.5476 | 0.758139 | ||||||||
\(233\) | 1.27357 | 0.0834346 | 0.0417173 | − | 0.999129i | \(-0.486717\pi\) | ||||
0.0417173 | + | 0.999129i | \(0.486717\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −3.44897 | −0.224986 | ||||||||
\(236\) | 8.59845 | 0.559712 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | −0.290267 | −0.0188152 | ||||||||
\(239\) | 8.13559 | 0.526248 | 0.263124 | − | 0.964762i | \(-0.415247\pi\) | ||||
0.263124 | + | 0.964762i | \(0.415247\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 19.4833 | 1.25503 | 0.627513 | − | 0.778606i | \(-0.284073\pi\) | ||||
0.627513 | + | 0.778606i | \(0.284073\pi\) | |||||||
\(242\) | −6.83959 | −0.439665 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | −1.14244 | −0.0731374 | ||||||||
\(245\) | −2.40466 | −0.153628 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −23.9547 | −1.52420 | ||||||||
\(248\) | −16.2146 | −1.02963 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | −9.73491 | −0.615690 | ||||||||
\(251\) | 2.25176 | 0.142130 | 0.0710650 | − | 0.997472i | \(-0.477360\pi\) | ||||
0.0710650 | + | 0.997472i | \(0.477360\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −27.7267 | −1.74316 | ||||||||
\(254\) | 0.959867 | 0.0602274 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −17.0039 | −1.06275 | ||||||||
\(257\) | 15.5072 | 0.967310 | 0.483655 | − | 0.875259i | \(-0.339309\pi\) | ||||
0.483655 | + | 0.875259i | \(0.339309\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 6.55479 | 0.407295 | ||||||||
\(260\) | 9.19202 | 0.570065 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 5.70787 | 0.352634 | ||||||||
\(263\) | 3.83687 | 0.236591 | 0.118296 | − | 0.992978i | \(-0.462257\pi\) | ||||
0.118296 | + | 0.992978i | \(0.462257\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −25.4269 | −1.56196 | ||||||||
\(266\) | −6.48825 | −0.397820 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 5.09269 | 0.311086 | ||||||||
\(269\) | 15.6381 | 0.953470 | 0.476735 | − | 0.879047i | \(-0.341820\pi\) | ||||
0.476735 | + | 0.879047i | \(0.341820\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 23.4561 | 1.42485 | 0.712427 | − | 0.701746i | \(-0.247596\pi\) | ||||
0.712427 | + | 0.701746i | \(0.247596\pi\) | |||||||
\(272\) | 0.205389 | 0.0124536 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −1.31735 | −0.0795840 | ||||||||
\(275\) | −3.33089 | −0.200860 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 26.8299 | 1.61205 | 0.806025 | − | 0.591881i | \(-0.201615\pi\) | ||||
0.806025 | + | 0.591881i | \(0.201615\pi\) | |||||||
\(278\) | −3.00844 | −0.180434 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 7.10600 | 0.424665 | ||||||||
\(281\) | −20.9721 | −1.25109 | −0.625545 | − | 0.780188i | \(-0.715123\pi\) | ||||
−0.625545 | + | 0.780188i | \(0.715123\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −16.5527 | −0.983959 | −0.491979 | − | 0.870607i | \(-0.663726\pi\) | ||||
−0.491979 | + | 0.870607i | \(0.663726\pi\) | |||||||
\(284\) | −6.74423 | −0.400196 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 14.4821 | 0.856344 | ||||||||
\(287\) | −2.17456 | −0.128360 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −16.9086 | −0.994621 | ||||||||
\(290\) | 9.01955 | 0.529646 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 12.3799 | 0.724481 | ||||||||
\(293\) | −16.6113 | −0.970443 | −0.485221 | − | 0.874391i | \(-0.661261\pi\) | ||||
−0.485221 | + | 0.874391i | \(0.661261\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 19.1686 | 1.11604 | ||||||||
\(296\) | −19.3701 | −1.12586 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | −12.8337 | −0.743439 | ||||||||
\(299\) | 23.0795 | 1.33472 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −9.47361 | −0.546050 | ||||||||
\(302\) | 9.87850 | 0.568444 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 4.59100 | 0.263312 | ||||||||
\(305\) | −2.54686 | −0.145833 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −25.6493 | −1.46388 | −0.731942 | − | 0.681367i | \(-0.761386\pi\) | ||||
−0.731942 | + | 0.681367i | \(0.761386\pi\) | |||||||
\(308\) | −4.59228 | −0.261670 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | −12.6648 | −0.719314 | ||||||||
\(311\) | 6.28790 | 0.356554 | 0.178277 | − | 0.983980i | \(-0.442948\pi\) | ||||
0.178277 | + | 0.983980i | \(0.442948\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −24.0220 | −1.35781 | −0.678903 | − | 0.734228i | \(-0.737544\pi\) | ||||
−0.678903 | + | 0.734228i | \(0.737544\pi\) | |||||||
\(314\) | −7.39425 | −0.417282 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −4.91464 | −0.276470 | ||||||||
\(317\) | −11.7159 | −0.658031 | −0.329016 | − | 0.944324i | \(-0.606717\pi\) | ||||
−0.329016 | + | 0.944324i | \(0.606717\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −16.6367 | −0.931475 | ||||||||
\(320\) | −15.4033 | −0.861071 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 6.25119 | 0.348365 | ||||||||
\(323\) | 2.04411 | 0.113737 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 2.77261 | 0.153797 | ||||||||
\(326\) | −6.27863 | −0.347741 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 6.42604 | 0.354819 | ||||||||
\(329\) | −1.43429 | −0.0790748 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −14.4126 | −0.792187 | −0.396094 | − | 0.918210i | \(-0.629634\pi\) | ||||
−0.396094 | + | 0.918210i | \(0.629634\pi\) | |||||||
\(332\) | −10.9338 | −0.600072 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | −1.98180 | −0.108439 | ||||||||
\(335\) | 11.3532 | 0.620290 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −14.1181 | −0.769061 | −0.384531 | − | 0.923112i | \(-0.625637\pi\) | ||||
−0.384531 | + | 0.923112i | \(0.625637\pi\) | |||||||
\(338\) | 0.423451 | 0.0230327 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | −0.784373 | −0.0425386 | ||||||||
\(341\) | 23.3604 | 1.26504 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −1.00000 | −0.0539949 | ||||||||
\(344\) | 27.9955 | 1.50941 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 10.5797 | 0.568768 | ||||||||
\(347\) | −28.8833 | −1.55053 | −0.775267 | − | 0.631633i | \(-0.782385\pi\) | ||||
−0.775267 | + | 0.631633i | \(0.782385\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 24.3596 | 1.30394 | 0.651971 | − | 0.758244i | \(-0.273943\pi\) | ||||
0.651971 | + | 0.758244i | \(0.273943\pi\) | |||||||
\(350\) | 0.750974 | 0.0401413 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 22.3866 | 1.19321 | ||||||||
\(353\) | 22.1309 | 1.17791 | 0.588955 | − | 0.808166i | \(-0.299539\pi\) | ||||
0.588955 | + | 0.808166i | \(0.299539\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −15.0350 | −0.797973 | ||||||||
\(356\) | −8.89225 | −0.471288 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −22.7178 | −1.20067 | ||||||||
\(359\) | 34.4554 | 1.81848 | 0.909242 | − | 0.416268i | \(-0.136662\pi\) | ||||
0.909242 | + | 0.416268i | \(0.136662\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 26.6912 | 1.40480 | ||||||||
\(362\) | 14.5360 | 0.763994 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 3.82259 | 0.200358 | ||||||||
\(365\) | 27.5987 | 1.44458 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −29.6470 | −1.54756 | −0.773780 | − | 0.633455i | \(-0.781636\pi\) | ||||
−0.773780 | + | 0.633455i | \(0.781636\pi\) | |||||||
\(368\) | −4.42326 | −0.230579 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | −15.1294 | −0.786542 | ||||||||
\(371\) | −10.5740 | −0.548977 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −24.6924 | −1.27852 | −0.639262 | − | 0.768989i | \(-0.720760\pi\) | ||||
−0.639262 | + | 0.768989i | \(0.720760\pi\) | |||||||
\(374\) | −1.23579 | −0.0639010 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 4.23846 | 0.218582 | ||||||||
\(377\) | 13.8483 | 0.713222 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −37.1608 | −1.90882 | −0.954412 | − | 0.298493i | \(-0.903516\pi\) | ||||
−0.954412 | + | 0.298493i | \(0.903516\pi\) | |||||||
\(380\) | −17.5328 | −0.899416 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | −11.0200 | −0.563834 | ||||||||
\(383\) | 16.4370 | 0.839894 | 0.419947 | − | 0.907549i | \(-0.362049\pi\) | ||||
0.419947 | + | 0.907549i | \(0.362049\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −10.2376 | −0.521757 | ||||||||
\(386\) | 8.08118 | 0.411321 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | −1.88125 | −0.0955062 | ||||||||
\(389\) | 3.32747 | 0.168709 | 0.0843547 | − | 0.996436i | \(-0.473117\pi\) | ||||
0.0843547 | + | 0.996436i | \(0.473117\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −1.96942 | −0.0995979 | ||||||||
\(392\) | 2.95510 | 0.149255 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | −5.85675 | −0.295059 | ||||||||
\(395\) | −10.9563 | −0.551269 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 4.88603 | 0.245223 | 0.122611 | − | 0.992455i | \(-0.460873\pi\) | ||||
0.122611 | + | 0.992455i | \(0.460873\pi\) | |||||||
\(398\) | 10.2804 | 0.515312 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −0.531380 | −0.0265690 | ||||||||
\(401\) | −18.0905 | −0.903396 | −0.451698 | − | 0.892171i | \(-0.649182\pi\) | ||||
−0.451698 | + | 0.892171i | \(0.649182\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −19.4451 | −0.968629 | ||||||||
\(404\) | 3.90018 | 0.194041 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 3.75087 | 0.186152 | ||||||||
\(407\) | 27.9064 | 1.38327 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 13.1826 | 0.651837 | 0.325918 | − | 0.945398i | \(-0.394327\pi\) | ||||
0.325918 | + | 0.945398i | \(0.394327\pi\) | |||||||
\(410\) | 5.01921 | 0.247881 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | −6.39518 | −0.315068 | ||||||||
\(413\) | 7.97145 | 0.392249 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −24.3749 | −1.19652 | ||||||||
\(416\) | −18.6345 | −0.913631 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | −27.6231 | −1.35109 | ||||||||
\(419\) | −33.2567 | −1.62470 | −0.812348 | − | 0.583173i | \(-0.801811\pi\) | ||||
−0.812348 | + | 0.583173i | \(0.801811\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −4.43830 | −0.216309 | −0.108155 | − | 0.994134i | \(-0.534494\pi\) | ||||
−0.108155 | + | 0.994134i | \(0.534494\pi\) | |||||||
\(422\) | 13.2797 | 0.646445 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 31.2473 | 1.51750 | ||||||||
\(425\) | −0.236592 | −0.0114764 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −1.05914 | −0.0512552 | ||||||||
\(428\) | −6.96297 | −0.336568 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 21.8665 | 1.05450 | ||||||||
\(431\) | −19.7379 | −0.950743 | −0.475371 | − | 0.879785i | \(-0.657686\pi\) | ||||
−0.475371 | + | 0.879785i | \(0.657686\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 29.6295 | 1.42390 | 0.711952 | − | 0.702228i | \(-0.247811\pi\) | ||||
0.711952 | + | 0.702228i | \(0.247811\pi\) | |||||||
\(434\) | −5.26679 | −0.252814 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −22.1432 | −1.06047 | ||||||||
\(437\) | −44.0218 | −2.10585 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −41.2017 | −1.96645 | −0.983224 | − | 0.182403i | \(-0.941612\pi\) | ||||
−0.983224 | + | 0.182403i | \(0.941612\pi\) | |||||||
\(440\) | 30.2532 | 1.44226 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 1.02866 | 0.0489285 | ||||||||
\(443\) | −24.9988 | −1.18773 | −0.593863 | − | 0.804566i | \(-0.702398\pi\) | ||||
−0.593863 | + | 0.804566i | \(0.702398\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −19.8236 | −0.939727 | ||||||||
\(446\) | 4.80701 | 0.227619 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | −6.40561 | −0.302637 | ||||||||
\(449\) | 4.39785 | 0.207548 | 0.103774 | − | 0.994601i | \(-0.466908\pi\) | ||||
0.103774 | + | 0.994601i | \(0.466908\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −9.25800 | −0.435942 | ||||||||
\(452\) | 16.4545 | 0.773957 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 22.4979 | 1.05588 | ||||||||
\(455\) | 8.52173 | 0.399505 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 13.3749 | 0.625653 | 0.312826 | − | 0.949810i | \(-0.398724\pi\) | ||||
0.312826 | + | 0.949810i | \(0.398724\pi\) | |||||||
\(458\) | 3.79433 | 0.177298 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 16.8923 | 0.787606 | ||||||||
\(461\) | −10.2563 | −0.477685 | −0.238842 | − | 0.971058i | \(-0.576768\pi\) | ||||
−0.238842 | + | 0.971058i | \(0.576768\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −16.2905 | −0.757084 | −0.378542 | − | 0.925584i | \(-0.623575\pi\) | ||||
−0.378542 | + | 0.925584i | \(0.623575\pi\) | |||||||
\(464\) | −2.65407 | −0.123212 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −1.22246 | −0.0566294 | ||||||||
\(467\) | −8.99794 | −0.416375 | −0.208188 | − | 0.978089i | \(-0.566756\pi\) | ||||
−0.208188 | + | 0.978089i | \(0.566756\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 4.72133 | 0.218011 | ||||||||
\(470\) | 3.31055 | 0.152704 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | −23.5564 | −1.08427 | ||||||||
\(473\) | −40.3331 | −1.85452 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −5.28847 | −0.242652 | ||||||||
\(476\) | −0.326189 | −0.0149509 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | −7.80908 | −0.357179 | ||||||||
\(479\) | −14.2639 | −0.651733 | −0.325866 | − | 0.945416i | \(-0.605656\pi\) | ||||
−0.325866 | + | 0.945416i | \(0.605656\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −23.2292 | −1.05916 | ||||||||
\(482\) | −18.7013 | −0.851822 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −7.68603 | −0.349365 | ||||||||
\(485\) | −4.19390 | −0.190435 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −10.7755 | −0.488284 | −0.244142 | − | 0.969740i | \(-0.578506\pi\) | ||||
−0.244142 | + | 0.969740i | \(0.578506\pi\) | |||||||
\(488\) | 3.12985 | 0.141682 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 2.30815 | 0.104272 | ||||||||
\(491\) | −6.80357 | −0.307041 | −0.153520 | − | 0.988145i | \(-0.549061\pi\) | ||||
−0.153520 | + | 0.988145i | \(0.549061\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −1.18170 | −0.0532211 | ||||||||
\(494\) | 22.9933 | 1.03452 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 3.72672 | 0.167335 | ||||||||
\(497\) | −6.25244 | −0.280460 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −30.2923 | −1.35607 | −0.678035 | − | 0.735030i | \(-0.737168\pi\) | ||||
−0.678035 | + | 0.735030i | \(0.737168\pi\) | |||||||
\(500\) | −10.9397 | −0.489237 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | −2.16139 | −0.0964677 | ||||||||
\(503\) | 14.4114 | 0.642571 | 0.321286 | − | 0.946982i | \(-0.395885\pi\) | ||||
0.321286 | + | 0.946982i | \(0.395885\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 8.69470 | 0.386909 | ||||||||
\(506\) | 26.6139 | 1.18313 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 1.07866 | 0.0478576 | ||||||||
\(509\) | −0.467272 | −0.0207115 | −0.0103557 | − | 0.999946i | \(-0.503296\pi\) | ||||
−0.0103557 | + | 0.999946i | \(0.503296\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 11.4772 | 0.507721 | ||||||||
\(512\) | 7.58551 | 0.335235 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | −14.8848 | −0.656541 | ||||||||
\(515\) | −14.2568 | −0.628230 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −6.10635 | −0.268557 | ||||||||
\(518\) | −6.29172 | −0.276442 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | −25.1826 | −1.10433 | ||||||||
\(521\) | −34.7244 | −1.52130 | −0.760651 | − | 0.649160i | \(-0.775120\pi\) | ||||
−0.760651 | + | 0.649160i | \(0.775120\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −9.13868 | −0.399607 | −0.199803 | − | 0.979836i | \(-0.564030\pi\) | ||||
−0.199803 | + | 0.979836i | \(0.564030\pi\) | |||||||
\(524\) | 6.41426 | 0.280208 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −3.68288 | −0.160581 | ||||||||
\(527\) | 1.65929 | 0.0722798 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 19.4134 | 0.844063 | ||||||||
\(530\) | 24.4065 | 1.06015 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | −7.29120 | −0.316114 | ||||||||
\(533\) | 7.70631 | 0.333797 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −15.5226 | −0.671101 | ||||||||
\(536\) | −13.9520 | −0.602635 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | −15.0105 | −0.647147 | ||||||||
\(539\) | −4.25741 | −0.183380 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 8.80281 | 0.378462 | 0.189231 | − | 0.981933i | \(-0.439400\pi\) | ||||
0.189231 | + | 0.981933i | \(0.439400\pi\) | |||||||
\(542\) | −22.5147 | −0.967089 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 1.59012 | 0.0681758 | ||||||||
\(545\) | −49.3641 | −2.11452 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 2.47099 | 0.105652 | 0.0528258 | − | 0.998604i | \(-0.483177\pi\) | ||||
0.0528258 | + | 0.998604i | \(0.483177\pi\) | |||||||
\(548\) | −1.48038 | −0.0632386 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 3.19721 | 0.136329 | ||||||||
\(551\) | −26.4142 | −1.12528 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −4.55627 | −0.193752 | ||||||||
\(554\) | −25.7531 | −1.09414 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −3.38075 | −0.143376 | ||||||||
\(557\) | 32.2057 | 1.36460 | 0.682299 | − | 0.731073i | \(-0.260980\pi\) | ||||
0.682299 | + | 0.731073i | \(0.260980\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 33.5730 | 1.41999 | ||||||||
\(560\) | −1.63322 | −0.0690161 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 20.1304 | 0.849150 | ||||||||
\(563\) | 13.9684 | 0.588696 | 0.294348 | − | 0.955698i | \(-0.404898\pi\) | ||||
0.294348 | + | 0.955698i | \(0.404898\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 36.6823 | 1.54323 | ||||||||
\(566\) | 15.8884 | 0.667841 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 18.4766 | 0.775260 | ||||||||
\(569\) | −18.2780 | −0.766252 | −0.383126 | − | 0.923696i | \(-0.625153\pi\) | ||||
−0.383126 | + | 0.923696i | \(0.625153\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 40.3925 | 1.69037 | 0.845187 | − | 0.534470i | \(-0.179489\pi\) | ||||
0.845187 | + | 0.534470i | \(0.179489\pi\) | |||||||
\(572\) | 16.2743 | 0.680464 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 2.08729 | 0.0871217 | ||||||||
\(575\) | 5.09525 | 0.212487 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 4.42495 | 0.184213 | 0.0921065 | − | 0.995749i | \(-0.470640\pi\) | ||||
0.0921065 | + | 0.995749i | \(0.470640\pi\) | |||||||
\(578\) | 16.2300 | 0.675077 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 10.1358 | 0.420865 | ||||||||
\(581\) | −10.1365 | −0.420534 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −45.0180 | −1.86446 | ||||||||
\(584\) | −33.9162 | −1.40346 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 15.9446 | 0.658667 | ||||||||
\(587\) | −22.3504 | −0.922500 | −0.461250 | − | 0.887270i | \(-0.652599\pi\) | ||||
−0.461250 | + | 0.887270i | \(0.652599\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 37.0896 | 1.52825 | ||||||||
\(590\) | −18.3993 | −0.757487 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 4.45194 | 0.182974 | ||||||||
\(593\) | −39.1966 | −1.60961 | −0.804805 | − | 0.593539i | \(-0.797730\pi\) | ||||
−0.804805 | + | 0.593539i | \(0.797730\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −0.727177 | −0.0298113 | ||||||||
\(596\) | −14.4220 | −0.590748 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | −22.1533 | −0.905914 | ||||||||
\(599\) | −20.9632 | −0.856534 | −0.428267 | − | 0.903652i | \(-0.640876\pi\) | ||||
−0.428267 | + | 0.903652i | \(0.640876\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 39.3899 | 1.60675 | 0.803375 | − | 0.595474i | \(-0.203036\pi\) | ||||
0.803375 | + | 0.595474i | \(0.203036\pi\) | |||||||
\(602\) | 9.09340 | 0.370620 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 11.1010 | 0.451694 | ||||||||
\(605\) | −17.1345 | −0.696618 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −6.62814 | −0.269028 | −0.134514 | − | 0.990912i | \(-0.542947\pi\) | ||||
−0.134514 | + | 0.990912i | \(0.542947\pi\) | |||||||
\(608\) | 35.5434 | 1.44148 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 2.44464 | 0.0989807 | ||||||||
\(611\) | 5.08289 | 0.205632 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −22.9071 | −0.925210 | −0.462605 | − | 0.886565i | \(-0.653085\pi\) | ||||
−0.462605 | + | 0.886565i | \(0.653085\pi\) | |||||||
\(614\) | 24.6199 | 0.993579 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 12.5811 | 0.506906 | ||||||||
\(617\) | −40.6908 | −1.63815 | −0.819076 | − | 0.573685i | \(-0.805513\pi\) | ||||
−0.819076 | + | 0.573685i | \(0.805513\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −24.2607 | −0.975118 | −0.487559 | − | 0.873090i | \(-0.662113\pi\) | ||||
−0.487559 | + | 0.873090i | \(0.662113\pi\) | |||||||
\(620\) | −14.2322 | −0.571578 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | −6.03554 | −0.242003 | ||||||||
\(623\) | −8.24382 | −0.330282 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −28.2998 | −1.13199 | ||||||||
\(626\) | 23.0579 | 0.921581 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | −8.30933 | −0.331579 | ||||||||
\(629\) | 1.98219 | 0.0790351 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −36.8846 | −1.46835 | −0.734177 | − | 0.678959i | \(-0.762432\pi\) | ||||
−0.734177 | + | 0.678959i | \(0.762432\pi\) | |||||||
\(632\) | 13.4642 | 0.535578 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 11.2457 | 0.446624 | ||||||||
\(635\) | 2.40466 | 0.0954259 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 3.54385 | 0.140412 | ||||||||
\(638\) | 15.9690 | 0.632218 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | −10.5035 | −0.415189 | ||||||||
\(641\) | −37.0112 | −1.46186 | −0.730928 | − | 0.682455i | \(-0.760912\pi\) | ||||
−0.730928 | + | 0.682455i | \(0.760912\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −19.7735 | −0.779790 | −0.389895 | − | 0.920859i | \(-0.627489\pi\) | ||||
−0.389895 | + | 0.920859i | \(0.627489\pi\) | |||||||
\(644\) | 7.02481 | 0.276816 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −1.96207 | −0.0771966 | ||||||||
\(647\) | −8.97670 | −0.352910 | −0.176455 | − | 0.984309i | \(-0.556463\pi\) | ||||
−0.176455 | + | 0.984309i | \(0.556463\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 33.9378 | 1.33217 | ||||||||
\(650\) | −2.66134 | −0.104386 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −7.05565 | −0.276321 | ||||||||
\(653\) | 11.3033 | 0.442331 | 0.221166 | − | 0.975236i | \(-0.429014\pi\) | ||||
0.221166 | + | 0.975236i | \(0.429014\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 14.2994 | 0.558722 | ||||||||
\(656\) | −1.47694 | −0.0576648 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 1.37672 | 0.0536703 | ||||||||
\(659\) | 44.1617 | 1.72029 | 0.860147 | − | 0.510046i | \(-0.170371\pi\) | ||||
0.860147 | + | 0.510046i | \(0.170371\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 35.8877 | 1.39587 | 0.697936 | − | 0.716160i | \(-0.254102\pi\) | ||||
0.697936 | + | 0.716160i | \(0.254102\pi\) | |||||||
\(662\) | 13.8342 | 0.537680 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 29.9545 | 1.16246 | ||||||||
\(665\) | −16.2543 | −0.630316 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 25.4491 | 0.985393 | ||||||||
\(668\) | −2.22706 | −0.0861676 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | −10.8975 | −0.421009 | ||||||||
\(671\) | −4.50918 | −0.174075 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 30.0012 | 1.15646 | 0.578230 | − | 0.815873i | \(-0.303743\pi\) | ||||
0.578230 | + | 0.815873i | \(0.303743\pi\) | |||||||
\(674\) | 13.5515 | 0.521984 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0.475856 | 0.0183022 | ||||||||
\(677\) | −12.7361 | −0.489488 | −0.244744 | − | 0.969588i | \(-0.578704\pi\) | ||||
−0.244744 | + | 0.969588i | \(0.578704\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −1.74407 | −0.0669314 | ||||||||
\(680\) | 2.14888 | 0.0824058 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | −22.4229 | −0.858618 | ||||||||
\(683\) | 21.9682 | 0.840591 | 0.420295 | − | 0.907387i | \(-0.361926\pi\) | ||||
0.420295 | + | 0.907387i | \(0.361926\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −3.30022 | −0.126095 | ||||||||
\(686\) | 0.959867 | 0.0366479 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | −6.43438 | −0.245308 | ||||||||
\(689\) | 37.4728 | 1.42760 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 34.3489 | 1.30669 | 0.653347 | − | 0.757058i | \(-0.273364\pi\) | ||||
0.653347 | + | 0.757058i | \(0.273364\pi\) | |||||||
\(692\) | 11.8890 | 0.451952 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 27.7241 | 1.05239 | ||||||||
\(695\) | −7.53673 | −0.285884 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −0.657595 | −0.0249082 | ||||||||
\(698\) | −23.3820 | −0.885022 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0.843912 | 0.0318969 | ||||||||
\(701\) | 44.3643 | 1.67562 | 0.837809 | − | 0.545963i | \(-0.183836\pi\) | ||||
0.837809 | + | 0.545963i | \(0.183836\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 44.3073 | 1.67108 | ||||||||
\(704\) | −27.2713 | −1.02783 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −21.2427 | −0.799481 | ||||||||
\(707\) | 3.61578 | 0.135985 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 26.5449 | 0.996913 | 0.498457 | − | 0.866915i | \(-0.333900\pi\) | ||||
0.498457 | + | 0.866915i | \(0.333900\pi\) | |||||||
\(710\) | 14.4316 | 0.541607 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 24.3613 | 0.912979 | ||||||||
\(713\) | −35.7345 | −1.33827 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 36.2805 | 1.35681 | ||||||||
\(716\) | −25.5292 | −0.954073 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | −33.0725 | −1.23426 | ||||||||
\(719\) | 29.8919 | 1.11478 | 0.557389 | − | 0.830251i | \(-0.311803\pi\) | ||||
0.557389 | + | 0.830251i | \(0.311803\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −5.92884 | −0.220801 | ||||||||
\(722\) | −25.6200 | −0.953478 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 16.3349 | 0.607081 | ||||||||
\(725\) | 3.05728 | 0.113544 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −42.0562 | −1.55978 | −0.779889 | − | 0.625918i | \(-0.784725\pi\) | ||||
−0.779889 | + | 0.625918i | \(0.784725\pi\) | |||||||
\(728\) | −10.4724 | −0.388134 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | −26.4911 | −0.980478 | ||||||||
\(731\) | −2.86485 | −0.105960 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 11.2662 | 0.416128 | 0.208064 | − | 0.978115i | \(-0.433284\pi\) | ||||
0.208064 | + | 0.978115i | \(0.433284\pi\) | |||||||
\(734\) | 28.4571 | 1.05037 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −34.2448 | −1.26228 | ||||||||
\(737\) | 20.1006 | 0.740417 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 30.3213 | 1.11539 | 0.557694 | − | 0.830046i | \(-0.311686\pi\) | ||||
0.557694 | + | 0.830046i | \(0.311686\pi\) | |||||||
\(740\) | −17.0018 | −0.624998 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 10.1497 | 0.372606 | ||||||||
\(743\) | −39.3851 | −1.44490 | −0.722450 | − | 0.691423i | \(-0.756984\pi\) | ||||
−0.722450 | + | 0.691423i | \(0.756984\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −32.1511 | −1.17792 | ||||||||
\(746\) | 23.7014 | 0.867771 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | −1.38872 | −0.0507767 | ||||||||
\(749\) | −6.45523 | −0.235869 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 1.95873 | 0.0714751 | 0.0357375 | − | 0.999361i | \(-0.488622\pi\) | ||||
0.0357375 | + | 0.999361i | \(0.488622\pi\) | |||||||
\(752\) | −0.974153 | −0.0355237 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | −13.2925 | −0.484084 | ||||||||
\(755\) | 24.7476 | 0.900658 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 29.2998 | 1.06492 | 0.532460 | − | 0.846455i | \(-0.321268\pi\) | ||||
0.532460 | + | 0.846455i | \(0.321268\pi\) | |||||||
\(758\) | 35.6694 | 1.29557 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 48.0332 | 1.74235 | ||||||||
\(761\) | −2.27331 | −0.0824075 | −0.0412038 | − | 0.999151i | \(-0.513119\pi\) | ||||
−0.0412038 | + | 0.999151i | \(0.513119\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −20.5285 | −0.743183 | ||||||||
\(764\) | −12.3838 | −0.448031 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −15.7774 | −0.570060 | ||||||||
\(767\) | −28.2496 | −1.02003 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −37.8564 | −1.36514 | −0.682568 | − | 0.730822i | \(-0.739137\pi\) | ||||
−0.682568 | + | 0.730822i | \(0.739137\pi\) | |||||||
\(770\) | 9.82675 | 0.354131 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 9.08127 | 0.326842 | ||||||||
\(773\) | 31.5316 | 1.13411 | 0.567056 | − | 0.823679i | \(-0.308082\pi\) | ||||
0.567056 | + | 0.823679i | \(0.308082\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −4.29289 | −0.154205 | ||||||||
\(776\) | 5.15391 | 0.185015 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −3.19393 | −0.114508 | ||||||||
\(779\) | −14.6990 | −0.526646 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −26.6192 | −0.952510 | ||||||||
\(782\) | 1.89038 | 0.0675999 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | −0.679190 | −0.0242568 | ||||||||
\(785\) | −18.5241 | −0.661152 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −5.10263 | −0.181889 | −0.0909446 | − | 0.995856i | \(-0.528989\pi\) | ||||
−0.0909446 | + | 0.995856i | \(0.528989\pi\) | |||||||
\(788\) | −6.58155 | −0.234458 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 10.5165 | 0.374162 | ||||||||
\(791\) | 15.2547 | 0.542394 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 3.75341 | 0.133288 | ||||||||
\(794\) | −4.68994 | −0.166440 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 11.5527 | 0.409475 | ||||||||
\(797\) | −20.3107 | −0.719441 | −0.359720 | − | 0.933060i | \(-0.617128\pi\) | ||||
−0.359720 | + | 0.933060i | \(0.617128\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −0.433733 | −0.0153444 | ||||||||
\(800\) | −4.11393 | −0.145449 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 17.3645 | 0.613161 | ||||||||
\(803\) | 48.8631 | 1.72434 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 15.6605 | 0.551959 | ||||||||
\(806\) | 18.6647 | 0.657436 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | −10.6850 | −0.375896 | ||||||||
\(809\) | −41.8654 | −1.47191 | −0.735955 | − | 0.677030i | \(-0.763267\pi\) | ||||
−0.735955 | + | 0.677030i | \(0.763267\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 1.27580 | 0.0447992 | 0.0223996 | − | 0.999749i | \(-0.492869\pi\) | ||||
0.0223996 | + | 0.999749i | \(0.492869\pi\) | |||||||
\(812\) | 4.21506 | 0.147920 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | −26.7865 | −0.938865 | ||||||||
\(815\) | −15.7292 | −0.550970 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −64.0371 | −2.24038 | ||||||||
\(818\) | −12.6535 | −0.442420 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 5.64037 | 0.196970 | ||||||||
\(821\) | 41.2734 | 1.44045 | 0.720226 | − | 0.693740i | \(-0.244038\pi\) | ||||
0.720226 | + | 0.693740i | \(0.244038\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 37.3455 | 1.30178 | 0.650891 | − | 0.759171i | \(-0.274396\pi\) | ||||
0.650891 | + | 0.759171i | \(0.274396\pi\) | |||||||
\(824\) | 17.5203 | 0.610349 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −7.65153 | −0.266231 | ||||||||
\(827\) | −5.74511 | −0.199777 | −0.0998886 | − | 0.994999i | \(-0.531849\pi\) | ||||
−0.0998886 | + | 0.994999i | \(0.531849\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 46.6365 | 1.61975 | 0.809876 | − | 0.586601i | \(-0.199534\pi\) | ||||
0.809876 | + | 0.586601i | \(0.199534\pi\) | |||||||
\(830\) | 23.3966 | 0.812110 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 22.7005 | 0.786999 | ||||||||
\(833\) | −0.302404 | −0.0104777 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −4.96481 | −0.171814 | ||||||||
\(836\) | −31.0417 | −1.07360 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 31.9220 | 1.10273 | ||||||||
\(839\) | 31.6074 | 1.09121 | 0.545605 | − | 0.838043i | \(-0.316300\pi\) | ||||
0.545605 | + | 0.838043i | \(0.316300\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −13.7299 | −0.473446 | ||||||||
\(842\) | 4.26017 | 0.146815 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 14.9231 | 0.513675 | ||||||||
\(845\) | 1.06083 | 0.0364937 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −7.12556 | −0.244837 | ||||||||
\(848\) | −7.18178 | −0.246623 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0.227097 | 0.00778937 | ||||||||
\(851\) | −42.6885 | −1.46334 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −35.7198 | −1.22302 | −0.611512 | − | 0.791235i | \(-0.709438\pi\) | ||||
−0.611512 | + | 0.791235i | \(0.709438\pi\) | |||||||
\(854\) | 1.01663 | 0.0347883 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 19.0758 | 0.651999 | ||||||||
\(857\) | −11.5668 | −0.395113 | −0.197556 | − | 0.980292i | \(-0.563301\pi\) | ||||
−0.197556 | + | 0.980292i | \(0.563301\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −34.8509 | −1.18910 | −0.594549 | − | 0.804059i | \(-0.702669\pi\) | ||||
−0.594549 | + | 0.804059i | \(0.702669\pi\) | |||||||
\(860\) | 24.5726 | 0.837920 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 18.9458 | 0.645296 | ||||||||
\(863\) | 11.4883 | 0.391068 | 0.195534 | − | 0.980697i | \(-0.437356\pi\) | ||||
0.195534 | + | 0.980697i | \(0.437356\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 26.5043 | 0.901172 | ||||||||
\(866\) | −28.4404 | −0.966444 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | −5.91859 | −0.200890 | ||||||||
\(869\) | −19.3979 | −0.658029 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −16.7317 | −0.566931 | ||||||||
\(872\) | 60.6638 | 2.05434 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 42.2551 | 1.42930 | ||||||||
\(875\) | −10.1419 | −0.342860 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −7.92650 | −0.267659 | −0.133829 | − | 0.991004i | \(-0.542727\pi\) | ||||
−0.133829 | + | 0.991004i | \(0.542727\pi\) | |||||||
\(878\) | 39.5481 | 1.33468 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | −6.95328 | −0.234395 | ||||||||
\(881\) | −31.4350 | −1.05907 | −0.529536 | − | 0.848287i | \(-0.677634\pi\) | ||||
−0.529536 | + | 0.848287i | \(0.677634\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 1.77775 | 0.0598260 | 0.0299130 | − | 0.999553i | \(-0.490477\pi\) | ||||
0.0299130 | + | 0.999553i | \(0.490477\pi\) | |||||||
\(884\) | 1.15596 | 0.0388793 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 23.9955 | 0.806144 | ||||||||
\(887\) | 10.3134 | 0.346292 | 0.173146 | − | 0.984896i | \(-0.444607\pi\) | ||||
0.173146 | + | 0.984896i | \(0.444607\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 1.00000 | 0.0335389 | ||||||||
\(890\) | 19.0280 | 0.637819 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 5.40191 | 0.180869 | ||||||||
\(893\) | −9.69510 | −0.324434 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −56.9126 | −1.90238 | ||||||||
\(896\) | −4.36800 | −0.145925 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | −4.22135 | −0.140868 | ||||||||
\(899\) | −21.4415 | −0.715115 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −3.19763 | −0.106528 | ||||||||
\(902\) | 8.88644 | 0.295886 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −45.0791 | −1.49931 | ||||||||
\(905\) | 36.4155 | 1.21049 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 2.28463 | 0.0758598 | 0.0379299 | − | 0.999280i | \(-0.487924\pi\) | ||||
0.0379299 | + | 0.999280i | \(0.487924\pi\) | |||||||
\(908\) | 25.2822 | 0.839018 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | −8.17973 | −0.271155 | ||||||||
\(911\) | −5.90967 | −0.195796 | −0.0978980 | − | 0.995196i | \(-0.531212\pi\) | ||||
−0.0978980 | + | 0.995196i | \(0.531212\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −43.1554 | −1.42824 | ||||||||
\(914\) | −12.8381 | −0.424648 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 4.26390 | 0.140883 | ||||||||
\(917\) | 5.94653 | 0.196372 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −45.1535 | −1.48947 | −0.744737 | − | 0.667358i | \(-0.767425\pi\) | ||||
−0.744737 | + | 0.667358i | \(0.767425\pi\) | |||||||
\(920\) | −46.2783 | −1.52575 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 9.84471 | 0.324218 | ||||||||
\(923\) | 22.1577 | 0.729329 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −5.12829 | −0.168617 | ||||||||
\(926\) | 15.6367 | 0.513855 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | −20.5477 | −0.674511 | ||||||||
\(929\) | 43.7874 | 1.43662 | 0.718309 | − | 0.695724i | \(-0.244916\pi\) | ||||
0.718309 | + | 0.695724i | \(0.244916\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −6.75953 | −0.221535 | ||||||||
\(932\) | −1.37375 | −0.0449986 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 8.63683 | 0.282606 | ||||||||
\(935\) | −3.09589 | −0.101246 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 39.0370 | 1.27528 | 0.637642 | − | 0.770333i | \(-0.279910\pi\) | ||||
0.637642 | + | 0.770333i | \(0.279910\pi\) | |||||||
\(938\) | −4.53185 | −0.147970 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 3.72025 | 0.121341 | ||||||||
\(941\) | 15.5982 | 0.508488 | 0.254244 | − | 0.967140i | \(-0.418173\pi\) | ||||
0.254244 | + | 0.967140i | \(0.418173\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 14.1620 | 0.461177 | ||||||||
\(944\) | 5.41413 | 0.176215 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 38.7144 | 1.25871 | ||||||||
\(947\) | −51.9065 | −1.68673 | −0.843367 | − | 0.537338i | \(-0.819430\pi\) | ||||
−0.843367 | + | 0.537338i | \(0.819430\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −40.6734 | −1.32031 | ||||||||
\(950\) | 5.07623 | 0.164695 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0.893633 | 0.0289628 | ||||||||
\(953\) | −9.02726 | −0.292422 | −0.146211 | − | 0.989253i | \(-0.546708\pi\) | ||||
−0.146211 | + | 0.989253i | \(0.546708\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −27.6074 | −0.893354 | ||||||||
\(956\) | −8.77550 | −0.283820 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 13.6914 | 0.442349 | ||||||||
\(959\) | −1.37243 | −0.0443180 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −0.892778 | −0.0287993 | ||||||||
\(962\) | 22.2969 | 0.718881 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | −21.0157 | −0.676871 | ||||||||
\(965\) | 20.2449 | 0.651708 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 6.81098 | 0.219027 | 0.109513 | − | 0.993985i | \(-0.465071\pi\) | ||||
0.109513 | + | 0.993985i | \(0.465071\pi\) | |||||||
\(968\) | 21.0567 | 0.676789 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 4.02558 | 0.129254 | ||||||||
\(971\) | 24.2046 | 0.776764 | 0.388382 | − | 0.921499i | \(-0.373034\pi\) | ||||
0.388382 | + | 0.921499i | \(0.373034\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −3.13422 | −0.100479 | ||||||||
\(974\) | 10.3430 | 0.331412 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −0.719354 | −0.0230260 | ||||||||
\(977\) | −25.4883 | −0.815443 | −0.407722 | − | 0.913106i | \(-0.633677\pi\) | ||||
−0.407722 | + | 0.913106i | \(0.633677\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −35.0974 | −1.12172 | ||||||||
\(980\) | 2.59380 | 0.0828558 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 6.53052 | 0.208397 | ||||||||
\(983\) | −21.3210 | −0.680035 | −0.340017 | − | 0.940419i | \(-0.610433\pi\) | ||||
−0.340017 | + | 0.940419i | \(0.610433\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −14.6723 | −0.467499 | ||||||||
\(986\) | 1.13428 | 0.0361227 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 25.8389 | 0.822045 | ||||||||
\(989\) | 61.6975 | 1.96187 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 54.5238 | 1.73200 | 0.866002 | − | 0.500040i | \(-0.166681\pi\) | ||||
0.866002 | + | 0.500040i | \(0.166681\pi\) | |||||||
\(992\) | 28.8521 | 0.916056 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 6.00151 | 0.190356 | ||||||||
\(995\) | 25.7545 | 0.816473 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −54.8655 | −1.73761 | −0.868804 | − | 0.495155i | \(-0.835111\pi\) | ||||
−0.868804 | + | 0.495155i | \(0.835111\pi\) | |||||||
\(998\) | 29.0766 | 0.920403 | ||||||||
\(999\) | 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.z.1.11 | ✓ | 32 | |
3.2 | odd | 2 | inner | 8001.2.a.z.1.22 | yes | 32 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
8001.2.a.z.1.11 | ✓ | 32 | 1.1 | even | 1 | trivial | |
8001.2.a.z.1.22 | yes | 32 | 3.2 | odd | 2 | inner |