Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [8032,2,Mod(1,8032)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(8032, 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("8032.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 8032 = 2^{5} \cdot 251 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 8032.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: | \(64.1358429035\) |
Analytic rank: | \(1\) |
Dimension: | \(30\) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.2 | ||
Character | \(\chi\) | \(=\) | 8032.1 |
$q$-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 | ||||||||
\(3\) | −3.13996 | −1.81285 | −0.906427 | − | 0.422362i | \(-0.861201\pi\) | ||||
−0.906427 | + | 0.422362i | \(0.861201\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −2.26457 | −1.01275 | −0.506373 | − | 0.862315i | \(-0.669014\pi\) | ||||
−0.506373 | + | 0.862315i | \(0.669014\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 2.38671 | 0.902090 | 0.451045 | − | 0.892501i | \(-0.351051\pi\) | ||||
0.451045 | + | 0.892501i | \(0.351051\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 6.85933 | 2.28644 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −2.83190 | −0.853850 | −0.426925 | − | 0.904287i | \(-0.640403\pi\) | ||||
−0.426925 | + | 0.904287i | \(0.640403\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 5.60226 | 1.55379 | 0.776893 | − | 0.629632i | \(-0.216795\pi\) | ||||
0.776893 | + | 0.629632i | \(0.216795\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 7.11065 | 1.83596 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 1.36097 | 0.330083 | 0.165042 | − | 0.986287i | \(-0.447224\pi\) | ||||
0.165042 | + | 0.986287i | \(0.447224\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −2.30596 | −0.529023 | −0.264512 | − | 0.964383i | \(-0.585211\pi\) | ||||
−0.264512 | + | 0.964383i | \(0.585211\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −7.49415 | −1.63536 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 0.856792 | 0.178653 | 0.0893267 | − | 0.996002i | \(-0.471528\pi\) | ||||
0.0893267 | + | 0.996002i | \(0.471528\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 0.128269 | 0.0256539 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −12.1181 | −2.33213 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 1.86972 | 0.347199 | 0.173599 | − | 0.984816i | \(-0.444460\pi\) | ||||
0.173599 | + | 0.984816i | \(0.444460\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −4.41452 | −0.792872 | −0.396436 | − | 0.918062i | \(-0.629753\pi\) | ||||
−0.396436 | + | 0.918062i | \(0.629753\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 8.89204 | 1.54791 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −5.40486 | −0.913588 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −1.21387 | −0.199559 | −0.0997793 | − | 0.995010i | \(-0.531814\pi\) | ||||
−0.0997793 | + | 0.995010i | \(0.531814\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −17.5908 | −2.81679 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 0.904775 | 0.141302 | 0.0706510 | − | 0.997501i | \(-0.477492\pi\) | ||||
0.0706510 | + | 0.997501i | \(0.477492\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −1.53684 | −0.234366 | −0.117183 | − | 0.993110i | \(-0.537386\pi\) | ||||
−0.117183 | + | 0.993110i | \(0.537386\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −15.5334 | −2.31559 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −0.899086 | −0.131145 | −0.0655726 | − | 0.997848i | \(-0.520887\pi\) | ||||
−0.0655726 | + | 0.997848i | \(0.520887\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −1.30364 | −0.186234 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −4.27338 | −0.598393 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −13.1544 | −1.80689 | −0.903447 | − | 0.428701i | \(-0.858971\pi\) | ||||
−0.903447 | + | 0.428701i | \(0.858971\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 6.41303 | 0.864732 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 7.24061 | 0.959042 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −4.36931 | −0.568836 | −0.284418 | − | 0.958700i | \(-0.591800\pi\) | ||||
−0.284418 | + | 0.958700i | \(0.591800\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −2.15372 | −0.275756 | −0.137878 | − | 0.990449i | \(-0.544028\pi\) | ||||
−0.137878 | + | 0.990449i | \(0.544028\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 16.3712 | 2.06258 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −12.6867 | −1.57359 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 12.5533 | 1.53363 | 0.766814 | − | 0.641869i | \(-0.221841\pi\) | ||||
0.766814 | + | 0.641869i | \(0.221841\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −2.69029 | −0.323873 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −5.16981 | −0.613543 | −0.306772 | − | 0.951783i | \(-0.599249\pi\) | ||||
−0.306772 | + | 0.951783i | \(0.599249\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 10.4687 | 1.22526 | 0.612632 | − | 0.790368i | \(-0.290111\pi\) | ||||
0.612632 | + | 0.790368i | \(0.290111\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −0.402761 | −0.0465068 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −6.75891 | −0.770249 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 5.89045 | 0.662728 | 0.331364 | − | 0.943503i | \(-0.392491\pi\) | ||||
0.331364 | + | 0.943503i | \(0.392491\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 17.4724 | 1.94138 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 9.87590 | 1.08402 | 0.542010 | − | 0.840372i | \(-0.317663\pi\) | ||||
0.542010 | + | 0.840372i | \(0.317663\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −3.08200 | −0.334290 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −5.87085 | −0.629421 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 13.6159 | 1.44328 | 0.721640 | − | 0.692268i | \(-0.243388\pi\) | ||||
0.721640 | + | 0.692268i | \(0.243388\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 13.3709 | 1.40166 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 13.8614 | 1.43736 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 5.22200 | 0.535766 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 4.52615 | 0.459560 | 0.229780 | − | 0.973243i | \(-0.426199\pi\) | ||||
0.229780 | + | 0.973243i | \(0.426199\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −19.4249 | −1.95228 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −5.24580 | −0.521976 | −0.260988 | − | 0.965342i | \(-0.584048\pi\) | ||||
−0.260988 | + | 0.965342i | \(0.584048\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −2.44635 | −0.241046 | −0.120523 | − | 0.992711i | \(-0.538457\pi\) | ||||
−0.120523 | + | 0.992711i | \(0.538457\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 16.9710 | 1.65620 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −17.1122 | −1.65430 | −0.827152 | − | 0.561979i | \(-0.810040\pi\) | ||||
−0.827152 | + | 0.561979i | \(0.810040\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 11.8001 | 1.13024 | 0.565121 | − | 0.825008i | \(-0.308829\pi\) | ||||
0.565121 | + | 0.825008i | \(0.308829\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 3.81149 | 0.361771 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 18.1037 | 1.70305 | 0.851525 | − | 0.524315i | \(-0.175678\pi\) | ||||
0.851525 | + | 0.524315i | \(0.175678\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −1.94026 | −0.180931 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 38.4277 | 3.55264 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 3.24823 | 0.297765 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −2.98035 | −0.270941 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −2.84095 | −0.256160 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 11.0324 | 0.986765 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −0.996277 | −0.0884053 | −0.0442026 | − | 0.999023i | \(-0.514075\pi\) | ||||
−0.0442026 | + | 0.999023i | \(0.514075\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 4.82562 | 0.424872 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −15.6185 | −1.36460 | −0.682298 | − | 0.731075i | \(-0.739019\pi\) | ||||
−0.682298 | + | 0.731075i | \(0.739019\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −5.50364 | −0.477226 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 27.4423 | 2.36186 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −8.29331 | −0.708545 | −0.354273 | − | 0.935142i | \(-0.615271\pi\) | ||||
−0.354273 | + | 0.935142i | \(0.615271\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −12.4062 | −1.05228 | −0.526141 | − | 0.850398i | \(-0.676361\pi\) | ||||
−0.526141 | + | 0.850398i | \(0.676361\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 2.82309 | 0.237747 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −15.8650 | −1.32670 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −4.23412 | −0.351624 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 4.09336 | 0.337614 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −6.14114 | −0.503102 | −0.251551 | − | 0.967844i | \(-0.580941\pi\) | ||||
−0.251551 | + | 0.967844i | \(0.580941\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 0.353629 | 0.0287779 | 0.0143889 | − | 0.999896i | \(-0.495420\pi\) | ||||
0.0143889 | + | 0.999896i | \(0.495420\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 9.33532 | 0.754716 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 9.99699 | 0.802977 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −0.473917 | −0.0378227 | −0.0189113 | − | 0.999821i | \(-0.506020\pi\) | ||||
−0.0189113 | + | 0.999821i | \(0.506020\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 41.3042 | 3.27563 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 2.04491 | 0.161162 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 6.31884 | 0.494930 | 0.247465 | − | 0.968897i | \(-0.420402\pi\) | ||||
0.247465 | + | 0.968897i | \(0.420402\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −20.1366 | −1.56763 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −8.37454 | −0.648042 | −0.324021 | − | 0.946050i | \(-0.605035\pi\) | ||||
−0.324021 | + | 0.946050i | \(0.605035\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 18.3853 | 1.41425 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −15.8173 | −1.20958 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 14.8959 | 1.13251 | 0.566256 | − | 0.824230i | \(-0.308391\pi\) | ||||
0.566256 | + | 0.824230i | \(0.308391\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0.306142 | 0.0231421 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 13.7195 | 1.03122 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −2.89130 | −0.216106 | −0.108053 | − | 0.994145i | \(-0.534462\pi\) | ||||
−0.108053 | + | 0.994145i | \(0.534462\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −10.3437 | −0.768840 | −0.384420 | − | 0.923158i | \(-0.625598\pi\) | ||||
−0.384420 | + | 0.923158i | \(0.625598\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 6.76260 | 0.499906 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 2.74889 | 0.202102 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −3.85412 | −0.281841 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −28.9224 | −2.10380 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 0.103580 | 0.00749476 | 0.00374738 | − | 0.999993i | \(-0.498807\pi\) | ||||
0.00374738 | + | 0.999993i | \(0.498807\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −0.978935 | −0.0704653 | −0.0352326 | − | 0.999379i | \(-0.511217\pi\) | ||||
−0.0352326 | + | 0.999379i | \(0.511217\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 39.8357 | 2.85269 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 5.41931 | 0.386110 | 0.193055 | − | 0.981188i | \(-0.438160\pi\) | ||||
0.193055 | + | 0.981188i | \(0.438160\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −25.7543 | −1.82567 | −0.912836 | − | 0.408326i | \(-0.866113\pi\) | ||||
−0.912836 | + | 0.408326i | \(0.866113\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −39.4168 | −2.78025 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 4.46248 | 0.313205 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −2.04892 | −0.143103 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 5.87702 | 0.408481 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 6.53024 | 0.451706 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 17.0671 | 1.17495 | 0.587475 | − | 0.809242i | \(-0.300122\pi\) | ||||
0.587475 | + | 0.809242i | \(0.300122\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 16.2330 | 1.11227 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 3.48028 | 0.237353 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −10.5362 | −0.715242 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −32.8712 | −2.22123 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 7.62449 | 0.512879 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −0.756263 | −0.0506431 | −0.0253216 | − | 0.999679i | \(-0.508061\pi\) | ||||
−0.0253216 | + | 0.999679i | \(0.508061\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0.879843 | 0.0586562 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −7.41771 | −0.492331 | −0.246165 | − | 0.969228i | \(-0.579171\pi\) | ||||
−0.246165 | + | 0.969228i | \(0.579171\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 18.5585 | 1.22638 | 0.613190 | − | 0.789935i | \(-0.289886\pi\) | ||||
0.613190 | + | 0.789935i | \(0.289886\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 21.2227 | 1.39635 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 26.5430 | 1.73889 | 0.869444 | − | 0.494032i | \(-0.164477\pi\) | ||||
0.869444 | + | 0.494032i | \(0.164477\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 2.03604 | 0.132817 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −18.4958 | −1.20143 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 25.6986 | 1.66230 | 0.831152 | − | 0.556045i | \(-0.187682\pi\) | ||||
0.831152 | + | 0.556045i | \(0.187682\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 1.17731 | 0.0758371 | 0.0379186 | − | 0.999281i | \(-0.487927\pi\) | ||||
0.0379186 | + | 0.999281i | \(0.487927\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −18.5082 | −1.18730 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 2.95217 | 0.188607 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −12.9186 | −0.821989 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −31.0099 | −1.96517 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 1.00000 | 0.0631194 | ||||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −2.42635 | −0.152543 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 9.67736 | 0.606020 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −5.98720 | −0.373471 | −0.186736 | − | 0.982410i | \(-0.559791\pi\) | ||||
−0.186736 | + | 0.982410i | \(0.559791\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −2.89715 | −0.180020 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 12.8250 | 0.793850 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −19.6964 | −1.21453 | −0.607265 | − | 0.794499i | \(-0.707733\pi\) | ||||
−0.607265 | + | 0.794499i | \(0.707733\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 29.7890 | 1.82992 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −42.7533 | −2.61646 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −11.2348 | −0.684997 | −0.342499 | − | 0.939518i | \(-0.611273\pi\) | ||||
−0.342499 | + | 0.939518i | \(0.611273\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 12.9484 | 0.786557 | 0.393279 | − | 0.919419i | \(-0.371341\pi\) | ||||
0.393279 | + | 0.919419i | \(0.371341\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −41.9842 | −2.54100 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −0.363246 | −0.0219046 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 21.7827 | 1.30879 | 0.654396 | − | 0.756152i | \(-0.272923\pi\) | ||||
0.654396 | + | 0.756152i | \(0.272923\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −30.2807 | −1.81286 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −23.4725 | −1.40025 | −0.700127 | − | 0.714019i | \(-0.746873\pi\) | ||||
−0.700127 | + | 0.714019i | \(0.746873\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 10.1297 | 0.602148 | 0.301074 | − | 0.953601i | \(-0.402655\pi\) | ||||
0.301074 | + | 0.953601i | \(0.402655\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −16.3969 | −0.971266 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 2.15943 | 0.127467 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −15.1478 | −0.891045 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −14.2119 | −0.833116 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 6.40062 | 0.373928 | 0.186964 | − | 0.982367i | \(-0.440135\pi\) | ||||
0.186964 | + | 0.982367i | \(0.440135\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 9.89461 | 0.576086 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 34.3173 | 1.99129 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 4.79997 | 0.277589 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −3.66799 | −0.211419 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 16.4716 | 0.946268 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 4.87725 | 0.279271 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 1.10123 | 0.0628504 | 0.0314252 | − | 0.999506i | \(-0.489995\pi\) | ||||
0.0314252 | + | 0.999506i | \(0.489995\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 7.68142 | 0.436981 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 12.0589 | 0.683798 | 0.341899 | − | 0.939737i | \(-0.388930\pi\) | ||||
0.341899 | + | 0.939737i | \(0.388930\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 2.16495 | 0.122370 | 0.0611851 | − | 0.998126i | \(-0.480512\pi\) | ||||
0.0611851 | + | 0.998126i | \(0.480512\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −37.0737 | −2.08887 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −21.6775 | −1.21753 | −0.608764 | − | 0.793351i | \(-0.708334\pi\) | ||||
−0.608764 | + | 0.793351i | \(0.708334\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −5.29487 | −0.296456 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 53.7317 | 2.99901 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −3.13833 | −0.174622 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 0.718599 | 0.0398607 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −37.0517 | −2.04897 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −2.14585 | −0.118305 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −15.0529 | −0.827381 | −0.413691 | − | 0.910417i | \(-0.635761\pi\) | ||||
−0.413691 | + | 0.910417i | \(0.635761\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −8.32632 | −0.456279 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −28.4278 | −1.55318 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −3.16475 | −0.172395 | −0.0861975 | − | 0.996278i | \(-0.527472\pi\) | ||||
−0.0861975 | + | 0.996278i | \(0.527472\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −56.8447 | −3.08738 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 12.5015 | 0.676993 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −19.8183 | −1.07009 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 6.09234 | 0.328001 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −13.2042 | −0.708839 | −0.354419 | − | 0.935087i | \(-0.615321\pi\) | ||||
−0.354419 | + | 0.935087i | \(0.615321\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 10.6989 | 0.572700 | 0.286350 | − | 0.958125i | \(-0.407558\pi\) | ||||
0.286350 | + | 0.958125i | \(0.407558\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −67.8888 | −3.62364 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −23.9918 | −1.27696 | −0.638478 | − | 0.769640i | \(-0.720436\pi\) | ||||
−0.638478 | + | 0.769640i | \(0.720436\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 11.7074 | 0.621364 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −10.1993 | −0.539804 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −26.1374 | −1.37948 | −0.689741 | − | 0.724056i | \(-0.742276\pi\) | ||||
−0.689741 | + | 0.724056i | \(0.742276\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −13.6826 | −0.720135 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 9.35817 | 0.491177 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −23.7070 | −1.24088 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 14.1155 | 0.736825 | 0.368412 | − | 0.929662i | \(-0.379901\pi\) | ||||
0.368412 | + | 0.929662i | \(0.379901\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 6.20615 | 0.323079 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −31.3956 | −1.62998 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −35.3420 | −1.82994 | −0.914968 | − | 0.403525i | \(-0.867785\pi\) | ||||
−0.914968 | + | 0.403525i | \(0.867785\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −34.6412 | −1.78886 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 10.4747 | 0.539473 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 34.1121 | 1.75222 | 0.876111 | − | 0.482110i | \(-0.160129\pi\) | ||||
0.876111 | + | 0.482110i | \(0.160129\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 3.12827 | 0.160266 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −29.8940 | −1.52751 | −0.763757 | − | 0.645504i | \(-0.776647\pi\) | ||||
−0.763757 | + | 0.645504i | \(0.776647\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 15.3060 | 0.780067 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −10.5417 | −0.535865 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −2.32922 | −0.118096 | −0.0590480 | − | 0.998255i | \(-0.518807\pi\) | ||||
−0.0590480 | + | 0.998255i | \(0.518807\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 1.16607 | 0.0589705 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 49.0414 | 2.47381 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −13.3393 | −0.671175 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 18.3689 | 0.921907 | 0.460953 | − | 0.887424i | \(-0.347508\pi\) | ||||
0.460953 | + | 0.887424i | \(0.347508\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 17.2812 | 0.865142 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −38.3880 | −1.91701 | −0.958503 | − | 0.285082i | \(-0.907979\pi\) | ||||
−0.958503 | + | 0.285082i | \(0.907979\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −24.7313 | −1.23195 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −39.5674 | −1.96612 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 3.43755 | 0.170393 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −7.56170 | −0.373902 | −0.186951 | − | 0.982369i | \(-0.559861\pi\) | ||||
−0.186951 | + | 0.982369i | \(0.559861\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 26.0406 | 1.28449 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −10.4283 | −0.513142 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −22.3646 | −1.09784 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 38.9550 | 1.90763 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −0.448297 | −0.0219007 | −0.0109504 | − | 0.999940i | \(-0.503486\pi\) | ||||
−0.0109504 | + | 0.999940i | \(0.503486\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −16.0003 | −0.779806 | −0.389903 | − | 0.920856i | \(-0.627492\pi\) | ||||
−0.389903 | + | 0.920856i | \(0.627492\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −6.16713 | −0.299856 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 0.174571 | 0.00846792 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −5.14030 | −0.248757 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 49.8155 | 2.40511 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 14.9477 | 0.720006 | 0.360003 | − | 0.932951i | \(-0.382776\pi\) | ||||
0.360003 | + | 0.932951i | \(0.382776\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −11.0750 | −0.532231 | −0.266116 | − | 0.963941i | \(-0.585740\pi\) | ||||
−0.266116 | + | 0.963941i | \(0.585740\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 13.2949 | 0.637444 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −1.97573 | −0.0945118 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −0.213196 | −0.0101753 | −0.00508765 | − | 0.999987i | \(-0.501619\pi\) | ||||
−0.00508765 | + | 0.999987i | \(0.501619\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −8.94206 | −0.425812 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −10.3439 | −0.491455 | −0.245727 | − | 0.969339i | \(-0.579027\pi\) | ||||
−0.245727 | + | 0.969339i | \(0.579027\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −30.8341 | −1.46168 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 19.2829 | 0.912051 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 7.79773 | 0.367998 | 0.183999 | − | 0.982926i | \(-0.441096\pi\) | ||||
0.183999 | + | 0.982926i | \(0.441096\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −2.56223 | −0.120651 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −1.11038 | −0.0521701 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −30.2794 | −1.41952 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 17.3806 | 0.813030 | 0.406515 | − | 0.913644i | \(-0.366744\pi\) | ||||
0.406515 | + | 0.913644i | \(0.366744\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −16.4924 | −0.769798 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 1.34676 | 0.0627249 | 0.0313625 | − | 0.999508i | \(-0.490015\pi\) | ||||
0.0313625 | + | 0.999508i | \(0.490015\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 3.66132 | 0.170156 | 0.0850781 | − | 0.996374i | \(-0.472886\pi\) | ||||
0.0850781 | + | 0.996374i | \(0.472886\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −31.3901 | −1.45568 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −23.1204 | −1.06988 | −0.534942 | − | 0.844889i | \(-0.679667\pi\) | ||||
−0.534942 | + | 0.844889i | \(0.679667\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 29.9610 | 1.38347 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 1.48808 | 0.0685670 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 4.35218 | 0.200114 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −0.295784 | −0.0135715 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −90.2302 | −4.13136 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −19.0089 | −0.868540 | −0.434270 | − | 0.900783i | \(-0.642994\pi\) | ||||
−0.434270 | + | 0.900783i | \(0.642994\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −6.80040 | −0.310071 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −6.42093 | −0.292162 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −10.2498 | −0.465418 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −29.7339 | −1.34737 | −0.673686 | − | 0.739017i | \(-0.735290\pi\) | ||||
−0.673686 | + | 0.739017i | \(0.735290\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −19.8409 | −0.897236 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −7.90998 | −0.356973 | −0.178486 | − | 0.983942i | \(-0.557120\pi\) | ||||
−0.178486 | + | 0.983942i | \(0.557120\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 2.54463 | 0.114604 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 43.9891 | 1.97716 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −12.3388 | −0.553471 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 15.8519 | 0.709628 | 0.354814 | − | 0.934937i | \(-0.384544\pi\) | ||||
0.354814 | + | 0.934937i | \(0.384544\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 26.2957 | 1.17481 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 22.6578 | 1.01026 | 0.505132 | − | 0.863042i | \(-0.331444\pi\) | ||||
0.505132 | + | 0.863042i | \(0.331444\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 11.8795 | 0.528629 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −57.7290 | −2.56383 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −10.8726 | −0.481919 | −0.240959 | − | 0.970535i | \(-0.577462\pi\) | ||||
−0.240959 | + | 0.970535i | \(0.577462\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 24.9856 | 1.10530 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 27.9439 | 1.23375 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 5.53992 | 0.244118 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 2.54612 | 0.111978 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −46.7724 | −2.05308 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 2.93700 | 0.128672 | 0.0643362 | − | 0.997928i | \(-0.479507\pi\) | ||||
0.0643362 | + | 0.997928i | \(0.479507\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 16.7036 | 0.730397 | 0.365198 | − | 0.930930i | \(-0.381001\pi\) | ||||
0.365198 | + | 0.930930i | \(0.381001\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | −0.961271 | −0.0419533 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −6.00802 | −0.261714 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −22.2659 | −0.968083 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −29.9706 | −1.30061 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 5.06878 | 0.219553 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 38.7518 | 1.67539 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 9.07855 | 0.391768 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 3.69176 | 0.159015 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 34.6446 | 1.48949 | 0.744745 | − | 0.667350i | \(-0.232571\pi\) | ||||
0.744745 | + | 0.667350i | \(0.232571\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 32.4787 | 1.39379 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −26.7221 | −1.14465 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 41.8744 | 1.79042 | 0.895210 | − | 0.445644i | \(-0.147025\pi\) | ||||
0.895210 | + | 0.445644i | \(0.147025\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −14.7731 | −0.630500 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −4.31150 | −0.183676 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 14.0588 | 0.597840 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −8.63139 | −0.366382 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −11.1774 | −0.473604 | −0.236802 | − | 0.971558i | \(-0.576099\pi\) | ||||
−0.236802 | + | 0.971558i | \(0.576099\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −8.60978 | −0.364155 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 12.1018 | 0.510937 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 32.5168 | 1.37042 | 0.685210 | − | 0.728346i | \(-0.259711\pi\) | ||||
0.685210 | + | 0.728346i | \(0.259711\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −40.9970 | −1.72476 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 41.7015 | 1.75130 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −28.9106 | −1.21200 | −0.605999 | − | 0.795466i | \(-0.707226\pi\) | ||||
−0.605999 | + | 0.795466i | \(0.707226\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 15.0723 | 0.630755 | 0.315378 | − | 0.948966i | \(-0.397869\pi\) | ||||
0.315378 | + | 0.948966i | \(0.397869\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −0.325236 | −0.0135869 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 0.109900 | 0.00458316 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −12.8922 | −0.536709 | −0.268355 | − | 0.963320i | \(-0.586480\pi\) | ||||
−0.268355 | + | 0.963320i | \(0.586480\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 3.07381 | 0.127743 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 23.5709 | 0.977884 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 37.2519 | 1.54281 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −87.0222 | −3.59792 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −9.44592 | −0.389875 | −0.194937 | − | 0.980816i | \(-0.562450\pi\) | ||||
−0.194937 | + | 0.980816i | \(0.562450\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 10.1797 | 0.419447 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −17.0164 | −0.699962 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −33.3718 | −1.37041 | −0.685207 | − | 0.728349i | \(-0.740288\pi\) | ||||
−0.685207 | + | 0.728349i | \(0.740288\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −7.35584 | −0.301560 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 80.8673 | 3.30968 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −28.2779 | −1.15540 | −0.577702 | − | 0.816248i | \(-0.696051\pi\) | ||||
−0.577702 | + | 0.816248i | \(0.696051\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 6.30320 | 0.257113 | 0.128556 | − | 0.991702i | \(-0.458966\pi\) | ||||
0.128556 | + | 0.991702i | \(0.458966\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 86.1071 | 3.50655 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 6.74921 | 0.274394 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −25.8813 | −1.05049 | −0.525245 | − | 0.850951i | \(-0.676026\pi\) | ||||
−0.525245 | + | 0.850951i | \(0.676026\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −14.0120 | −0.567795 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −5.03691 | −0.203772 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 0.402225 | 0.0162457 | 0.00812285 | − | 0.999967i | \(-0.497414\pi\) | ||||
0.00812285 | + | 0.999967i | \(0.497414\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 6.43353 | 0.259425 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −15.8402 | −0.637703 | −0.318851 | − | 0.947805i | \(-0.603297\pi\) | ||||
−0.318851 | + | 0.947805i | \(0.603297\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 43.6388 | 1.75399 | 0.876995 | − | 0.480499i | \(-0.159545\pi\) | ||||
0.876995 | + | 0.480499i | \(0.159545\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −10.3827 | −0.416644 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 32.4971 | 1.30197 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −25.6249 | −1.02500 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −20.5047 | −0.818878 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −1.65203 | −0.0658709 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −15.4687 | −0.615798 | −0.307899 | − | 0.951419i | \(-0.599626\pi\) | ||||
−0.307899 | + | 0.951419i | \(0.599626\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −53.5901 | −2.13001 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 2.25614 | 0.0895321 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −7.30330 | −0.289367 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −35.4614 | −1.40283 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −8.69808 | −0.343554 | −0.171777 | − | 0.985136i | \(-0.554951\pi\) | ||||
−0.171777 | + | 0.985136i | \(0.554951\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −11.8322 | −0.466618 | −0.233309 | − | 0.972403i | \(-0.574955\pi\) | ||||
−0.233309 | + | 0.972403i | \(0.574955\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −10.9279 | −0.430287 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −8.08234 | −0.317750 | −0.158875 | − | 0.987299i | \(-0.550787\pi\) | ||||
−0.158875 | + | 0.987299i | \(0.550787\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 12.3735 | 0.485701 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 33.0831 | 1.29663 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −19.6037 | −0.767154 | −0.383577 | − | 0.923509i | \(-0.625308\pi\) | ||||
−0.383577 | + | 0.923509i | \(0.625308\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 35.3692 | 1.38199 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 71.8080 | 2.80150 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −23.1836 | −0.903105 | −0.451552 | − | 0.892245i | \(-0.649130\pi\) | ||||
−0.451552 | + | 0.892245i | \(0.649130\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 19.7025 | 0.766339 | 0.383169 | − | 0.923678i | \(-0.374833\pi\) | ||||
0.383169 | + | 0.923678i | \(0.374833\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −23.9406 | −0.929774 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 12.4634 | 0.483309 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 1.60196 | 0.0620283 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 2.37463 | 0.0918086 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 6.09912 | 0.235454 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −48.8593 | −1.88339 | −0.941695 | − | 0.336469i | \(-0.890767\pi\) | ||||
−0.941695 | + | 0.336469i | \(0.890767\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −1.55439 | −0.0598283 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −41.5110 | −1.59540 | −0.797699 | − | 0.603056i | \(-0.793950\pi\) | ||||
−0.797699 | + | 0.603056i | \(0.793950\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 10.8026 | 0.414565 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 23.2913 | 0.892524 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −29.7708 | −1.13915 | −0.569574 | − | 0.821940i | \(-0.692892\pi\) | ||||
−0.569574 | + | 0.821940i | \(0.692892\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 18.7808 | 0.717576 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −58.2729 | −2.22325 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −73.6942 | −2.80753 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 2.22104 | 0.0844924 | 0.0422462 | − | 0.999107i | \(-0.486549\pi\) | ||||
0.0422462 | + | 0.999107i | \(0.486549\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −46.3616 | −1.76113 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 28.0947 | 1.06569 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 1.23137 | 0.0466414 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −83.3438 | −3.15235 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −29.8962 | −1.12916 | −0.564582 | − | 0.825377i | \(-0.690963\pi\) | ||||
−0.564582 | + | 0.825377i | \(0.690963\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 2.79913 | 0.105571 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −6.39309 | −0.240778 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −12.5202 | −0.470870 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 0.489981 | 0.0184016 | 0.00920081 | − | 0.999958i | \(-0.497071\pi\) | ||||
0.00920081 | + | 0.999958i | \(0.497071\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 40.4046 | 1.51529 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −3.78233 | −0.141649 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 35.9274 | 1.34361 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −80.6925 | −3.01352 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −6.84580 | −0.255305 | −0.127653 | − | 0.991819i | \(-0.540744\pi\) | ||||
−0.127653 | + | 0.991819i | \(0.540744\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −5.83871 | −0.217445 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −3.69670 | −0.137482 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 0.239828 | 0.00890700 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −37.0644 | −1.37464 | −0.687322 | − | 0.726353i | \(-0.741214\pi\) | ||||
−0.687322 | + | 0.726353i | \(0.741214\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 5.69779 | 0.211029 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −2.09159 | −0.0773603 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −38.8813 | −1.43611 | −0.718057 | − | 0.695985i | \(-0.754968\pi\) | ||||
−0.718057 | + | 0.695985i | \(0.754968\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | −9.26969 | −0.341918 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −35.5496 | −1.30949 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 1.53607 | 0.0565051 | 0.0282525 | − | 0.999601i | \(-0.491006\pi\) | ||||
0.0282525 | + | 0.999601i | \(0.491006\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 40.5637 | 1.49015 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −15.8411 | −0.581155 | −0.290578 | − | 0.956851i | \(-0.593847\pi\) | ||||
−0.290578 | + | 0.956851i | \(0.593847\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 13.9070 | 0.509514 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 67.7420 | 2.47855 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −40.8419 | −1.49233 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 50.0654 | 1.82691 | 0.913456 | − | 0.406937i | \(-0.133403\pi\) | ||||
0.913456 | + | 0.406937i | \(0.133403\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −3.13996 | −0.114426 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −0.800816 | −0.0291447 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −33.3030 | −1.21042 | −0.605210 | − | 0.796066i | \(-0.706911\pi\) | ||||
−0.605210 | + | 0.796066i | \(0.706911\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 7.61863 | 0.276539 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 32.7116 | 1.18580 | 0.592898 | − | 0.805278i | \(-0.297984\pi\) | ||||
0.592898 | + | 0.805278i | \(0.297984\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 28.1633 | 1.01958 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −21.1405 | −0.764336 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −24.4780 | −0.883850 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −5.39161 | −0.194426 | −0.0972132 | − | 0.995264i | \(-0.530993\pi\) | ||||
−0.0972132 | + | 0.995264i | \(0.530993\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 18.7996 | 0.677049 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 49.7123 | 1.78803 | 0.894013 | − | 0.448041i | \(-0.147878\pi\) | ||||
0.894013 | + | 0.448041i | \(0.147878\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −0.566249 | −0.0203402 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 9.09691 | 0.326350 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −2.08637 | −0.0747520 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 14.6404 | 0.523874 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −22.6575 | −0.809714 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 1.07322 | 0.0383047 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 2.23424 | 0.0796420 | 0.0398210 | − | 0.999207i | \(-0.487321\pi\) | ||||
0.0398210 | + | 0.999207i | \(0.487321\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 61.8458 | 2.20177 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 43.2081 | 1.53630 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −12.0657 | −0.428466 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −93.5361 | −3.31739 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 40.6850 | 1.44113 | 0.720567 | − | 0.693385i | \(-0.243881\pi\) | ||||
0.720567 | + | 0.693385i | \(0.243881\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −1.22363 | −0.0432888 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 93.3958 | 3.29998 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −29.6462 | −1.04619 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −4.63084 | −0.163216 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 35.2768 | 1.24180 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −41.7414 | −1.46755 | −0.733775 | − | 0.679392i | \(-0.762243\pi\) | ||||
−0.733775 | + | 0.679392i | \(0.762243\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 9.29843 | 0.326512 | 0.163256 | − | 0.986584i | \(-0.447800\pi\) | ||||
0.163256 | + | 0.986584i | \(0.447800\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −40.6573 | −1.42591 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −14.3095 | −0.501238 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 3.54389 | 0.123985 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 91.7157 | 3.20480 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 39.0610 | 1.36324 | 0.681619 | − | 0.731707i | \(-0.261276\pi\) | ||||
0.681619 | + | 0.731707i | \(0.261276\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −13.1337 | −0.457813 | −0.228907 | − | 0.973448i | \(-0.573515\pi\) | ||||
−0.228907 | + | 0.973448i | \(0.573515\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 1.14058 | 0.0397098 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −29.1382 | −1.01323 | −0.506617 | − | 0.862171i | \(-0.669104\pi\) | ||||
−0.506617 | + | 0.862171i | \(0.669104\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −30.7340 | −1.06744 | −0.533718 | − | 0.845663i | \(-0.679206\pi\) | ||||
−0.533718 | + | 0.845663i | \(0.679206\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −68.3966 | −2.37265 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −1.77421 | −0.0614726 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 18.9647 | 0.656301 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 53.4957 | 1.84908 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 10.2263 | 0.353049 | 0.176525 | − | 0.984296i | \(-0.443514\pi\) | ||||
0.176525 | + | 0.984296i | \(0.443514\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −25.5041 | −0.879453 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 73.7027 | 2.53846 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −41.6347 | −1.43228 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −7.11322 | −0.244413 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −31.8068 | −1.09161 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −1.04003 | −0.0356518 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 31.1549 | 1.06672 | 0.533361 | − | 0.845888i | \(-0.320929\pi\) | ||||
0.533361 | + | 0.845888i | \(0.320929\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 35.8194 | 1.22500 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 6.13967 | 0.209727 | 0.104864 | − | 0.994487i | \(-0.466559\pi\) | ||||
0.104864 | + | 0.994487i | \(0.466559\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −25.7512 | −0.878621 | −0.439310 | − | 0.898335i | \(-0.644777\pi\) | ||||
−0.439310 | + | 0.898335i | \(0.644777\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −6.78052 | −0.231079 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 48.3413 | 1.64556 | 0.822778 | − | 0.568363i | \(-0.192423\pi\) | ||||
0.822778 | + | 0.568363i | \(0.192423\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −33.7327 | −1.14695 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 47.5633 | 1.61534 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −16.6812 | −0.565870 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 70.3267 | 2.38293 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 31.0463 | 1.05076 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 26.3310 | 0.890151 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 25.9748 | 0.877107 | 0.438554 | − | 0.898705i | \(-0.355491\pi\) | ||||
0.438554 | + | 0.898705i | \(0.355491\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −20.0977 | −0.677878 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −13.7848 | −0.464422 | −0.232211 | − | 0.972665i | \(-0.574596\pi\) | ||||
−0.232211 | + | 0.972665i | \(0.574596\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −14.3520 | −0.482983 | −0.241492 | − | 0.970403i | \(-0.577637\pi\) | ||||
−0.241492 | + | 0.970403i | \(0.577637\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −31.0686 | −1.04436 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 51.2285 | 1.72008 | 0.860042 | − | 0.510224i | \(-0.170437\pi\) | ||||
0.860042 | + | 0.510224i | \(0.170437\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −2.37782 | −0.0797495 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −49.4801 | −1.65764 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 2.07326 | 0.0693789 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 6.54754 | 0.218860 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −15.0717 | −0.503229 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −8.25393 | −0.275284 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −17.9027 | −0.596425 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 11.5173 | 0.383273 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 23.4240 | 0.778639 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −37.0873 | −1.23146 | −0.615732 | − | 0.787956i | \(-0.711140\pi\) | ||||
−0.615732 | + | 0.787956i | \(0.711140\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −35.9827 | −1.19347 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 56.9130 | 1.88561 | 0.942807 | − | 0.333340i | \(-0.108176\pi\) | ||||
0.942807 | + | 0.333340i | \(0.108176\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −27.9675 | −0.925590 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −15.3144 | −0.506277 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −37.2768 | −1.23099 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 54.1891 | 1.78753 | 0.893766 | − | 0.448533i | \(-0.148053\pi\) | ||||
0.893766 | + | 0.448533i | \(0.148053\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −3.45781 | −0.113939 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −28.9626 | −0.953315 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −0.155702 | −0.00511946 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −16.7803 | −0.551137 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 39.9664 | 1.31125 | 0.655627 | − | 0.755085i | \(-0.272404\pi\) | ||||
0.655627 | + | 0.755085i | \(0.272404\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 3.00613 | 0.0985219 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −37.8645 | −1.23963 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 8.72792 | 0.285434 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 28.7969 | 0.940752 | 0.470376 | − | 0.882466i | \(-0.344118\pi\) | ||||
0.470376 | + | 0.882466i | \(0.344118\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −6.79785 | −0.221839 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 6.77139 | 0.220741 | 0.110371 | − | 0.993891i | \(-0.464796\pi\) | ||||
0.110371 | + | 0.993891i | \(0.464796\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 0.775204 | 0.0252441 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 65.4967 | 2.13061 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 33.7660 | 1.09725 | 0.548624 | − | 0.836069i | \(-0.315152\pi\) | ||||
0.548624 | + | 0.836069i | \(0.315152\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 58.6482 | 1.90380 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 68.0663 | 2.20720 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −40.2508 | −1.30385 | −0.651925 | − | 0.758283i | \(-0.726038\pi\) | ||||
−0.651925 | + | 0.758283i | \(0.726038\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −0.234563 | −0.00759028 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 16.6256 | 0.537431 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −19.7937 | −0.639171 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −11.5120 | −0.371354 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −117.379 | −3.78247 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 2.21686 | 0.0713634 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −20.9363 | −0.673265 | −0.336633 | − | 0.941636i | \(-0.609288\pi\) | ||||
−0.336633 | + | 0.941636i | \(0.609288\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 9.85423 | 0.316564 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −14.1992 | −0.455674 | −0.227837 | − | 0.973699i | \(-0.573165\pi\) | ||||
−0.227837 | + | 0.973699i | \(0.573165\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −29.6100 | −0.949252 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −2.25637 | −0.0722616 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −56.3368 | −1.80238 | −0.901188 | − | 0.433429i | \(-0.857303\pi\) | ||||
−0.901188 | + | 0.433429i | \(0.857303\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −38.5588 | −1.23234 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 80.9406 | 2.58424 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 42.2487 | 1.34753 | 0.673763 | − | 0.738948i | \(-0.264677\pi\) | ||||
0.673763 | + | 0.738948i | \(0.264677\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −12.2724 | −0.391031 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 6.73789 | 0.214469 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −1.31675 | −0.0418703 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −6.08450 | −0.193280 | −0.0966402 | − | 0.995319i | \(-0.530810\pi\) | ||||
−0.0966402 | + | 0.995319i | \(0.530810\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 47.2654 | 1.49992 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 58.3223 | 1.84894 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −44.5460 | −1.41079 | −0.705393 | − | 0.708816i | \(-0.749230\pi\) | ||||
−0.705393 | + | 0.708816i | \(0.749230\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 14.7098 | 0.465398 |
(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 | 8032.2.a.g.1.2 | ✓ | 30 | |
4.3 | odd | 2 | 8032.2.a.j.1.29 | yes | 30 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
8032.2.a.g.1.2 | ✓ | 30 | 1.1 | even | 1 | trivial | |
8032.2.a.j.1.29 | yes | 30 | 4.3 | odd | 2 |