Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [8007,2,Mod(1,8007)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(8007, 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("8007.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 8007 = 3 \cdot 17 \cdot 157 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 8007.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: | \(63.9362168984\) |
Analytic rank: | \(1\) |
Dimension: | \(40\) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.6 | ||
Character | \(\chi\) | \(=\) | 8007.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −2.17139 | −1.53541 | −0.767703 | − | 0.640806i | \(-0.778600\pi\) | ||||
−0.767703 | + | 0.640806i | \(0.778600\pi\) | |||||||
\(3\) | 1.00000 | 0.577350 | ||||||||
\(4\) | 2.71494 | 1.35747 | ||||||||
\(5\) | −0.590074 | −0.263889 | −0.131945 | − | 0.991257i | \(-0.542122\pi\) | ||||
−0.131945 | + | 0.991257i | \(0.542122\pi\) | |||||||
\(6\) | −2.17139 | −0.886467 | ||||||||
\(7\) | −3.96431 | −1.49837 | −0.749184 | − | 0.662362i | \(-0.769554\pi\) | ||||
−0.749184 | + | 0.662362i | \(0.769554\pi\) | |||||||
\(8\) | −1.55242 | −0.548864 | ||||||||
\(9\) | 1.00000 | 0.333333 | ||||||||
\(10\) | 1.28128 | 0.405177 | ||||||||
\(11\) | 6.46148 | 1.94821 | 0.974104 | − | 0.226100i | \(-0.0725976\pi\) | ||||
0.974104 | + | 0.226100i | \(0.0725976\pi\) | |||||||
\(12\) | 2.71494 | 0.783737 | ||||||||
\(13\) | −1.30782 | −0.362723 | −0.181362 | − | 0.983416i | \(-0.558050\pi\) | ||||
−0.181362 | + | 0.983416i | \(0.558050\pi\) | |||||||
\(14\) | 8.60807 | 2.30060 | ||||||||
\(15\) | −0.590074 | −0.152356 | ||||||||
\(16\) | −2.05897 | −0.514743 | ||||||||
\(17\) | 1.00000 | 0.242536 | ||||||||
\(18\) | −2.17139 | −0.511802 | ||||||||
\(19\) | −5.13813 | −1.17877 | −0.589384 | − | 0.807853i | \(-0.700630\pi\) | ||||
−0.589384 | + | 0.807853i | \(0.700630\pi\) | |||||||
\(20\) | −1.60202 | −0.358222 | ||||||||
\(21\) | −3.96431 | −0.865083 | ||||||||
\(22\) | −14.0304 | −2.99129 | ||||||||
\(23\) | 1.75448 | 0.365833 | 0.182917 | − | 0.983128i | \(-0.441446\pi\) | ||||
0.182917 | + | 0.983128i | \(0.441446\pi\) | |||||||
\(24\) | −1.55242 | −0.316887 | ||||||||
\(25\) | −4.65181 | −0.930363 | ||||||||
\(26\) | 2.83978 | 0.556928 | ||||||||
\(27\) | 1.00000 | 0.192450 | ||||||||
\(28\) | −10.7629 | −2.03399 | ||||||||
\(29\) | −7.00535 | −1.30086 | −0.650431 | − | 0.759566i | \(-0.725412\pi\) | ||||
−0.650431 | + | 0.759566i | \(0.725412\pi\) | |||||||
\(30\) | 1.28128 | 0.233929 | ||||||||
\(31\) | 4.10645 | 0.737541 | 0.368770 | − | 0.929520i | \(-0.379779\pi\) | ||||
0.368770 | + | 0.929520i | \(0.379779\pi\) | |||||||
\(32\) | 7.57567 | 1.33920 | ||||||||
\(33\) | 6.46148 | 1.12480 | ||||||||
\(34\) | −2.17139 | −0.372391 | ||||||||
\(35\) | 2.33924 | 0.395403 | ||||||||
\(36\) | 2.71494 | 0.452491 | ||||||||
\(37\) | −0.396977 | −0.0652626 | −0.0326313 | − | 0.999467i | \(-0.510389\pi\) | ||||
−0.0326313 | + | 0.999467i | \(0.510389\pi\) | |||||||
\(38\) | 11.1569 | 1.80989 | ||||||||
\(39\) | −1.30782 | −0.209418 | ||||||||
\(40\) | 0.916044 | 0.144839 | ||||||||
\(41\) | 11.0650 | 1.72806 | 0.864028 | − | 0.503444i | \(-0.167934\pi\) | ||||
0.864028 | + | 0.503444i | \(0.167934\pi\) | |||||||
\(42\) | 8.60807 | 1.32825 | ||||||||
\(43\) | 1.45777 | 0.222307 | 0.111154 | − | 0.993803i | \(-0.464545\pi\) | ||||
0.111154 | + | 0.993803i | \(0.464545\pi\) | |||||||
\(44\) | 17.5425 | 2.64464 | ||||||||
\(45\) | −0.590074 | −0.0879631 | ||||||||
\(46\) | −3.80965 | −0.561703 | ||||||||
\(47\) | −1.88063 | −0.274318 | −0.137159 | − | 0.990549i | \(-0.543797\pi\) | ||||
−0.137159 | + | 0.990549i | \(0.543797\pi\) | |||||||
\(48\) | −2.05897 | −0.297187 | ||||||||
\(49\) | 8.71575 | 1.24511 | ||||||||
\(50\) | 10.1009 | 1.42848 | ||||||||
\(51\) | 1.00000 | 0.140028 | ||||||||
\(52\) | −3.55065 | −0.492387 | ||||||||
\(53\) | 6.90904 | 0.949030 | 0.474515 | − | 0.880248i | \(-0.342624\pi\) | ||||
0.474515 | + | 0.880248i | \(0.342624\pi\) | |||||||
\(54\) | −2.17139 | −0.295489 | ||||||||
\(55\) | −3.81275 | −0.514111 | ||||||||
\(56\) | 6.15428 | 0.822400 | ||||||||
\(57\) | −5.13813 | −0.680562 | ||||||||
\(58\) | 15.2114 | 1.99735 | ||||||||
\(59\) | −13.0653 | −1.70095 | −0.850475 | − | 0.526015i | \(-0.823686\pi\) | ||||
−0.850475 | + | 0.526015i | \(0.823686\pi\) | |||||||
\(60\) | −1.60202 | −0.206820 | ||||||||
\(61\) | 12.5260 | 1.60379 | 0.801893 | − | 0.597468i | \(-0.203827\pi\) | ||||
0.801893 | + | 0.597468i | \(0.203827\pi\) | |||||||
\(62\) | −8.91672 | −1.13242 | ||||||||
\(63\) | −3.96431 | −0.499456 | ||||||||
\(64\) | −12.3318 | −1.54148 | ||||||||
\(65\) | 0.771709 | 0.0957188 | ||||||||
\(66\) | −14.0304 | −1.72702 | ||||||||
\(67\) | −1.01183 | −0.123615 | −0.0618076 | − | 0.998088i | \(-0.519687\pi\) | ||||
−0.0618076 | + | 0.998088i | \(0.519687\pi\) | |||||||
\(68\) | 2.71494 | 0.329235 | ||||||||
\(69\) | 1.75448 | 0.211214 | ||||||||
\(70\) | −5.07940 | −0.607104 | ||||||||
\(71\) | 0.00821806 | 0.000975305 0 | 0.000487652 | − | 1.00000i | \(-0.499845\pi\) | ||||
0.000487652 | 1.00000i | \(0.499845\pi\) | ||||||||
\(72\) | −1.55242 | −0.182955 | ||||||||
\(73\) | −5.75478 | −0.673546 | −0.336773 | − | 0.941586i | \(-0.609335\pi\) | ||||
−0.336773 | + | 0.941586i | \(0.609335\pi\) | |||||||
\(74\) | 0.861993 | 0.100205 | ||||||||
\(75\) | −4.65181 | −0.537145 | ||||||||
\(76\) | −13.9497 | −1.60014 | ||||||||
\(77\) | −25.6153 | −2.91913 | ||||||||
\(78\) | 2.83978 | 0.321542 | ||||||||
\(79\) | 6.74411 | 0.758772 | 0.379386 | − | 0.925239i | \(-0.376135\pi\) | ||||
0.379386 | + | 0.925239i | \(0.376135\pi\) | |||||||
\(80\) | 1.21495 | 0.135835 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | −24.0264 | −2.65327 | ||||||||
\(83\) | 6.24798 | 0.685805 | 0.342902 | − | 0.939371i | \(-0.388590\pi\) | ||||
0.342902 | + | 0.939371i | \(0.388590\pi\) | |||||||
\(84\) | −10.7629 | −1.17433 | ||||||||
\(85\) | −0.590074 | −0.0640025 | ||||||||
\(86\) | −3.16538 | −0.341332 | ||||||||
\(87\) | −7.00535 | −0.751053 | ||||||||
\(88\) | −10.0309 | −1.06930 | ||||||||
\(89\) | −6.85979 | −0.727136 | −0.363568 | − | 0.931568i | \(-0.618442\pi\) | ||||
−0.363568 | + | 0.931568i | \(0.618442\pi\) | |||||||
\(90\) | 1.28128 | 0.135059 | ||||||||
\(91\) | 5.18459 | 0.543493 | ||||||||
\(92\) | 4.76330 | 0.496608 | ||||||||
\(93\) | 4.10645 | 0.425819 | ||||||||
\(94\) | 4.08358 | 0.421189 | ||||||||
\(95\) | 3.03188 | 0.311064 | ||||||||
\(96\) | 7.57567 | 0.773189 | ||||||||
\(97\) | −2.37523 | −0.241168 | −0.120584 | − | 0.992703i | \(-0.538477\pi\) | ||||
−0.120584 | + | 0.992703i | \(0.538477\pi\) | |||||||
\(98\) | −18.9253 | −1.91174 | ||||||||
\(99\) | 6.46148 | 0.649403 | ||||||||
\(100\) | −12.6294 | −1.26294 | ||||||||
\(101\) | −3.63503 | −0.361699 | −0.180850 | − | 0.983511i | \(-0.557885\pi\) | ||||
−0.180850 | + | 0.983511i | \(0.557885\pi\) | |||||||
\(102\) | −2.17139 | −0.215000 | ||||||||
\(103\) | −12.4551 | −1.22724 | −0.613618 | − | 0.789603i | \(-0.710287\pi\) | ||||
−0.613618 | + | 0.789603i | \(0.710287\pi\) | |||||||
\(104\) | 2.03028 | 0.199086 | ||||||||
\(105\) | 2.33924 | 0.228286 | ||||||||
\(106\) | −15.0022 | −1.45715 | ||||||||
\(107\) | −17.8878 | −1.72928 | −0.864640 | − | 0.502391i | \(-0.832454\pi\) | ||||
−0.864640 | + | 0.502391i | \(0.832454\pi\) | |||||||
\(108\) | 2.71494 | 0.261246 | ||||||||
\(109\) | −12.0238 | −1.15167 | −0.575836 | − | 0.817565i | \(-0.695323\pi\) | ||||
−0.575836 | + | 0.817565i | \(0.695323\pi\) | |||||||
\(110\) | 8.27897 | 0.789369 | ||||||||
\(111\) | −0.396977 | −0.0376794 | ||||||||
\(112\) | 8.16240 | 0.771274 | ||||||||
\(113\) | −18.7696 | −1.76570 | −0.882850 | − | 0.469656i | \(-0.844378\pi\) | ||||
−0.882850 | + | 0.469656i | \(0.844378\pi\) | |||||||
\(114\) | 11.1569 | 1.04494 | ||||||||
\(115\) | −1.03527 | −0.0965395 | ||||||||
\(116\) | −19.0191 | −1.76588 | ||||||||
\(117\) | −1.30782 | −0.120908 | ||||||||
\(118\) | 28.3698 | 2.61165 | ||||||||
\(119\) | −3.96431 | −0.363408 | ||||||||
\(120\) | 0.916044 | 0.0836230 | ||||||||
\(121\) | 30.7507 | 2.79552 | ||||||||
\(122\) | −27.1988 | −2.46246 | ||||||||
\(123\) | 11.0650 | 0.997693 | ||||||||
\(124\) | 11.1488 | 1.00119 | ||||||||
\(125\) | 5.69528 | 0.509402 | ||||||||
\(126\) | 8.60807 | 0.766868 | ||||||||
\(127\) | 5.56136 | 0.493491 | 0.246745 | − | 0.969080i | \(-0.420639\pi\) | ||||
0.246745 | + | 0.969080i | \(0.420639\pi\) | |||||||
\(128\) | 11.6259 | 1.02759 | ||||||||
\(129\) | 1.45777 | 0.128349 | ||||||||
\(130\) | −1.67568 | −0.146967 | ||||||||
\(131\) | −18.3981 | −1.60745 | −0.803723 | − | 0.595004i | \(-0.797150\pi\) | ||||
−0.803723 | + | 0.595004i | \(0.797150\pi\) | |||||||
\(132\) | 17.5425 | 1.52688 | ||||||||
\(133\) | 20.3692 | 1.76623 | ||||||||
\(134\) | 2.19709 | 0.189800 | ||||||||
\(135\) | −0.590074 | −0.0507855 | ||||||||
\(136\) | −1.55242 | −0.133119 | ||||||||
\(137\) | 11.2302 | 0.959459 | 0.479729 | − | 0.877416i | \(-0.340735\pi\) | ||||
0.479729 | + | 0.877416i | \(0.340735\pi\) | |||||||
\(138\) | −3.80965 | −0.324299 | ||||||||
\(139\) | 17.9824 | 1.52525 | 0.762624 | − | 0.646842i | \(-0.223911\pi\) | ||||
0.762624 | + | 0.646842i | \(0.223911\pi\) | |||||||
\(140\) | 6.35089 | 0.536748 | ||||||||
\(141\) | −1.88063 | −0.158377 | ||||||||
\(142\) | −0.0178446 | −0.00149749 | ||||||||
\(143\) | −8.45043 | −0.706661 | ||||||||
\(144\) | −2.05897 | −0.171581 | ||||||||
\(145\) | 4.13368 | 0.343283 | ||||||||
\(146\) | 12.4959 | 1.03417 | ||||||||
\(147\) | 8.71575 | 0.718863 | ||||||||
\(148\) | −1.07777 | −0.0885922 | ||||||||
\(149\) | −8.05893 | −0.660213 | −0.330106 | − | 0.943944i | \(-0.607085\pi\) | ||||
−0.330106 | + | 0.943944i | \(0.607085\pi\) | |||||||
\(150\) | 10.1009 | 0.824736 | ||||||||
\(151\) | 20.1868 | 1.64278 | 0.821389 | − | 0.570369i | \(-0.193200\pi\) | ||||
0.821389 | + | 0.570369i | \(0.193200\pi\) | |||||||
\(152\) | 7.97655 | 0.646984 | ||||||||
\(153\) | 1.00000 | 0.0808452 | ||||||||
\(154\) | 55.6208 | 4.48205 | ||||||||
\(155\) | −2.42311 | −0.194629 | ||||||||
\(156\) | −3.55065 | −0.284280 | ||||||||
\(157\) | −1.00000 | −0.0798087 | ||||||||
\(158\) | −14.6441 | −1.16502 | ||||||||
\(159\) | 6.90904 | 0.547923 | ||||||||
\(160\) | −4.47021 | −0.353401 | ||||||||
\(161\) | −6.95528 | −0.548153 | ||||||||
\(162\) | −2.17139 | −0.170601 | ||||||||
\(163\) | −12.1468 | −0.951412 | −0.475706 | − | 0.879604i | \(-0.657807\pi\) | ||||
−0.475706 | + | 0.879604i | \(0.657807\pi\) | |||||||
\(164\) | 30.0407 | 2.34579 | ||||||||
\(165\) | −3.81275 | −0.296822 | ||||||||
\(166\) | −13.5668 | −1.05299 | ||||||||
\(167\) | 17.6646 | 1.36693 | 0.683463 | − | 0.729985i | \(-0.260473\pi\) | ||||
0.683463 | + | 0.729985i | \(0.260473\pi\) | |||||||
\(168\) | 6.15428 | 0.474813 | ||||||||
\(169\) | −11.2896 | −0.868432 | ||||||||
\(170\) | 1.28128 | 0.0982699 | ||||||||
\(171\) | −5.13813 | −0.392923 | ||||||||
\(172\) | 3.95775 | 0.301776 | ||||||||
\(173\) | 12.3749 | 0.940849 | 0.470424 | − | 0.882440i | \(-0.344101\pi\) | ||||
0.470424 | + | 0.882440i | \(0.344101\pi\) | |||||||
\(174\) | 15.2114 | 1.15317 | ||||||||
\(175\) | 18.4412 | 1.39403 | ||||||||
\(176\) | −13.3040 | −1.00283 | ||||||||
\(177\) | −13.0653 | −0.982044 | ||||||||
\(178\) | 14.8953 | 1.11645 | ||||||||
\(179\) | 15.3261 | 1.14553 | 0.572763 | − | 0.819721i | \(-0.305872\pi\) | ||||
0.572763 | + | 0.819721i | \(0.305872\pi\) | |||||||
\(180\) | −1.60202 | −0.119407 | ||||||||
\(181\) | −20.4932 | −1.52325 | −0.761624 | − | 0.648019i | \(-0.775598\pi\) | ||||
−0.761624 | + | 0.648019i | \(0.775598\pi\) | |||||||
\(182\) | −11.2578 | −0.834483 | ||||||||
\(183\) | 12.5260 | 0.925946 | ||||||||
\(184\) | −2.72368 | −0.200793 | ||||||||
\(185\) | 0.234246 | 0.0172221 | ||||||||
\(186\) | −8.91672 | −0.653806 | ||||||||
\(187\) | 6.46148 | 0.472510 | ||||||||
\(188\) | −5.10580 | −0.372378 | ||||||||
\(189\) | −3.96431 | −0.288361 | ||||||||
\(190\) | −6.58340 | −0.477610 | ||||||||
\(191\) | 22.7471 | 1.64593 | 0.822963 | − | 0.568096i | \(-0.192320\pi\) | ||||
0.822963 | + | 0.568096i | \(0.192320\pi\) | |||||||
\(192\) | −12.3318 | −0.889972 | ||||||||
\(193\) | −23.1999 | −1.66996 | −0.834982 | − | 0.550278i | \(-0.814522\pi\) | ||||
−0.834982 | + | 0.550278i | \(0.814522\pi\) | |||||||
\(194\) | 5.15755 | 0.370291 | ||||||||
\(195\) | 0.771709 | 0.0552633 | ||||||||
\(196\) | 23.6628 | 1.69020 | ||||||||
\(197\) | 5.11502 | 0.364430 | 0.182215 | − | 0.983259i | \(-0.441673\pi\) | ||||
0.182215 | + | 0.983259i | \(0.441673\pi\) | |||||||
\(198\) | −14.0304 | −0.997097 | ||||||||
\(199\) | 7.90668 | 0.560490 | 0.280245 | − | 0.959929i | \(-0.409584\pi\) | ||||
0.280245 | + | 0.959929i | \(0.409584\pi\) | |||||||
\(200\) | 7.22157 | 0.510642 | ||||||||
\(201\) | −1.01183 | −0.0713693 | ||||||||
\(202\) | 7.89308 | 0.555355 | ||||||||
\(203\) | 27.7714 | 1.94917 | ||||||||
\(204\) | 2.71494 | 0.190084 | ||||||||
\(205\) | −6.52914 | −0.456015 | ||||||||
\(206\) | 27.0449 | 1.88431 | ||||||||
\(207\) | 1.75448 | 0.121944 | ||||||||
\(208\) | 2.69276 | 0.186709 | ||||||||
\(209\) | −33.1999 | −2.29649 | ||||||||
\(210\) | −5.07940 | −0.350512 | ||||||||
\(211\) | 4.43118 | 0.305055 | 0.152528 | − | 0.988299i | \(-0.451259\pi\) | ||||
0.152528 | + | 0.988299i | \(0.451259\pi\) | |||||||
\(212\) | 18.7577 | 1.28828 | ||||||||
\(213\) | 0.00821806 | 0.000563092 0 | ||||||||
\(214\) | 38.8415 | 2.65515 | ||||||||
\(215\) | −0.860191 | −0.0586645 | ||||||||
\(216\) | −1.55242 | −0.105629 | ||||||||
\(217\) | −16.2793 | −1.10511 | ||||||||
\(218\) | 26.1084 | 1.76828 | ||||||||
\(219\) | −5.75478 | −0.388872 | ||||||||
\(220\) | −10.3514 | −0.697891 | ||||||||
\(221\) | −1.30782 | −0.0879733 | ||||||||
\(222\) | 0.861993 | 0.0578532 | ||||||||
\(223\) | −9.21719 | −0.617229 | −0.308614 | − | 0.951187i | \(-0.599865\pi\) | ||||
−0.308614 | + | 0.951187i | \(0.599865\pi\) | |||||||
\(224\) | −30.0323 | −2.00662 | ||||||||
\(225\) | −4.65181 | −0.310121 | ||||||||
\(226\) | 40.7562 | 2.71107 | ||||||||
\(227\) | −6.97144 | −0.462711 | −0.231355 | − | 0.972869i | \(-0.574316\pi\) | ||||
−0.231355 | + | 0.972869i | \(0.574316\pi\) | |||||||
\(228\) | −13.9497 | −0.923844 | ||||||||
\(229\) | 22.8134 | 1.50755 | 0.753777 | − | 0.657131i | \(-0.228230\pi\) | ||||
0.753777 | + | 0.657131i | \(0.228230\pi\) | |||||||
\(230\) | 2.24798 | 0.148227 | ||||||||
\(231\) | −25.6153 | −1.68536 | ||||||||
\(232\) | 10.8753 | 0.713996 | ||||||||
\(233\) | 19.2038 | 1.25809 | 0.629043 | − | 0.777371i | \(-0.283447\pi\) | ||||
0.629043 | + | 0.777371i | \(0.283447\pi\) | |||||||
\(234\) | 2.83978 | 0.185643 | ||||||||
\(235\) | 1.10971 | 0.0723895 | ||||||||
\(236\) | −35.4714 | −2.30899 | ||||||||
\(237\) | 6.74411 | 0.438077 | ||||||||
\(238\) | 8.60807 | 0.557978 | ||||||||
\(239\) | −16.3090 | −1.05494 | −0.527472 | − | 0.849573i | \(-0.676860\pi\) | ||||
−0.527472 | + | 0.849573i | \(0.676860\pi\) | |||||||
\(240\) | 1.21495 | 0.0784244 | ||||||||
\(241\) | −22.3956 | −1.44263 | −0.721315 | − | 0.692607i | \(-0.756462\pi\) | ||||
−0.721315 | + | 0.692607i | \(0.756462\pi\) | |||||||
\(242\) | −66.7717 | −4.29225 | ||||||||
\(243\) | 1.00000 | 0.0641500 | ||||||||
\(244\) | 34.0073 | 2.17709 | ||||||||
\(245\) | −5.14294 | −0.328570 | ||||||||
\(246\) | −24.0264 | −1.53186 | ||||||||
\(247\) | 6.71974 | 0.427567 | ||||||||
\(248\) | −6.37495 | −0.404810 | ||||||||
\(249\) | 6.24798 | 0.395949 | ||||||||
\(250\) | −12.3667 | −0.782139 | ||||||||
\(251\) | −17.3712 | −1.09646 | −0.548230 | − | 0.836327i | \(-0.684698\pi\) | ||||
−0.548230 | + | 0.836327i | \(0.684698\pi\) | |||||||
\(252\) | −10.7629 | −0.677997 | ||||||||
\(253\) | 11.3365 | 0.712720 | ||||||||
\(254\) | −12.0759 | −0.757709 | ||||||||
\(255\) | −0.590074 | −0.0369519 | ||||||||
\(256\) | −0.580666 | −0.0362916 | ||||||||
\(257\) | −0.703605 | −0.0438897 | −0.0219448 | − | 0.999759i | \(-0.506986\pi\) | ||||
−0.0219448 | + | 0.999759i | \(0.506986\pi\) | |||||||
\(258\) | −3.16538 | −0.197068 | ||||||||
\(259\) | 1.57374 | 0.0977875 | ||||||||
\(260\) | 2.09515 | 0.129935 | ||||||||
\(261\) | −7.00535 | −0.433621 | ||||||||
\(262\) | 39.9494 | 2.46808 | ||||||||
\(263\) | −19.8442 | −1.22364 | −0.611822 | − | 0.790995i | \(-0.709563\pi\) | ||||
−0.611822 | + | 0.790995i | \(0.709563\pi\) | |||||||
\(264\) | −10.0309 | −0.617361 | ||||||||
\(265\) | −4.07685 | −0.250439 | ||||||||
\(266\) | −44.2294 | −2.71188 | ||||||||
\(267\) | −6.85979 | −0.419812 | ||||||||
\(268\) | −2.74707 | −0.167804 | ||||||||
\(269\) | 28.1218 | 1.71462 | 0.857310 | − | 0.514801i | \(-0.172134\pi\) | ||||
0.857310 | + | 0.514801i | \(0.172134\pi\) | |||||||
\(270\) | 1.28128 | 0.0779764 | ||||||||
\(271\) | 19.7193 | 1.19786 | 0.598930 | − | 0.800801i | \(-0.295593\pi\) | ||||
0.598930 | + | 0.800801i | \(0.295593\pi\) | |||||||
\(272\) | −2.05897 | −0.124843 | ||||||||
\(273\) | 5.18459 | 0.313786 | ||||||||
\(274\) | −24.3851 | −1.47316 | ||||||||
\(275\) | −30.0576 | −1.81254 | ||||||||
\(276\) | 4.76330 | 0.286717 | ||||||||
\(277\) | −9.07317 | −0.545154 | −0.272577 | − | 0.962134i | \(-0.587876\pi\) | ||||
−0.272577 | + | 0.962134i | \(0.587876\pi\) | |||||||
\(278\) | −39.0469 | −2.34188 | ||||||||
\(279\) | 4.10645 | 0.245847 | ||||||||
\(280\) | −3.63148 | −0.217022 | ||||||||
\(281\) | −4.79242 | −0.285892 | −0.142946 | − | 0.989730i | \(-0.545658\pi\) | ||||
−0.142946 | + | 0.989730i | \(0.545658\pi\) | |||||||
\(282\) | 4.08358 | 0.243174 | ||||||||
\(283\) | −18.8554 | −1.12084 | −0.560419 | − | 0.828209i | \(-0.689360\pi\) | ||||
−0.560419 | + | 0.828209i | \(0.689360\pi\) | |||||||
\(284\) | 0.0223116 | 0.00132395 | ||||||||
\(285\) | 3.03188 | 0.179593 | ||||||||
\(286\) | 18.3492 | 1.08501 | ||||||||
\(287\) | −43.8649 | −2.58926 | ||||||||
\(288\) | 7.57567 | 0.446401 | ||||||||
\(289\) | 1.00000 | 0.0588235 | ||||||||
\(290\) | −8.97583 | −0.527079 | ||||||||
\(291\) | −2.37523 | −0.139238 | ||||||||
\(292\) | −15.6239 | −0.914319 | ||||||||
\(293\) | 3.03961 | 0.177576 | 0.0887880 | − | 0.996051i | \(-0.471701\pi\) | ||||
0.0887880 | + | 0.996051i | \(0.471701\pi\) | |||||||
\(294\) | −18.9253 | −1.10375 | ||||||||
\(295\) | 7.70947 | 0.448862 | ||||||||
\(296\) | 0.616276 | 0.0358203 | ||||||||
\(297\) | 6.46148 | 0.374933 | ||||||||
\(298\) | 17.4991 | 1.01369 | ||||||||
\(299\) | −2.29453 | −0.132696 | ||||||||
\(300\) | −12.6294 | −0.729159 | ||||||||
\(301\) | −5.77904 | −0.333098 | ||||||||
\(302\) | −43.8334 | −2.52233 | ||||||||
\(303\) | −3.63503 | −0.208827 | ||||||||
\(304\) | 10.5793 | 0.606762 | ||||||||
\(305\) | −7.39125 | −0.423222 | ||||||||
\(306\) | −2.17139 | −0.124130 | ||||||||
\(307\) | −11.3180 | −0.645950 | −0.322975 | − | 0.946407i | \(-0.604683\pi\) | ||||
−0.322975 | + | 0.946407i | \(0.604683\pi\) | |||||||
\(308\) | −69.5440 | −3.96264 | ||||||||
\(309\) | −12.4551 | −0.708545 | ||||||||
\(310\) | 5.26153 | 0.298835 | ||||||||
\(311\) | −25.1335 | −1.42519 | −0.712595 | − | 0.701576i | \(-0.752480\pi\) | ||||
−0.712595 | + | 0.701576i | \(0.752480\pi\) | |||||||
\(312\) | 2.03028 | 0.114942 | ||||||||
\(313\) | −26.9076 | −1.52090 | −0.760452 | − | 0.649394i | \(-0.775023\pi\) | ||||
−0.760452 | + | 0.649394i | \(0.775023\pi\) | |||||||
\(314\) | 2.17139 | 0.122539 | ||||||||
\(315\) | 2.33924 | 0.131801 | ||||||||
\(316\) | 18.3099 | 1.03001 | ||||||||
\(317\) | 25.6434 | 1.44028 | 0.720139 | − | 0.693830i | \(-0.244078\pi\) | ||||
0.720139 | + | 0.693830i | \(0.244078\pi\) | |||||||
\(318\) | −15.0022 | −0.841284 | ||||||||
\(319\) | −45.2649 | −2.53435 | ||||||||
\(320\) | 7.27669 | 0.406779 | ||||||||
\(321\) | −17.8878 | −0.998401 | ||||||||
\(322\) | 15.1026 | 0.841637 | ||||||||
\(323\) | −5.13813 | −0.285893 | ||||||||
\(324\) | 2.71494 | 0.150830 | ||||||||
\(325\) | 6.08372 | 0.337464 | ||||||||
\(326\) | 26.3755 | 1.46080 | ||||||||
\(327\) | −12.0238 | −0.664918 | ||||||||
\(328\) | −17.1775 | −0.948467 | ||||||||
\(329\) | 7.45539 | 0.411029 | ||||||||
\(330\) | 8.27897 | 0.455742 | ||||||||
\(331\) | 17.0344 | 0.936294 | 0.468147 | − | 0.883651i | \(-0.344922\pi\) | ||||
0.468147 | + | 0.883651i | \(0.344922\pi\) | |||||||
\(332\) | 16.9629 | 0.930960 | ||||||||
\(333\) | −0.396977 | −0.0217542 | ||||||||
\(334\) | −38.3567 | −2.09879 | ||||||||
\(335\) | 0.597057 | 0.0326207 | ||||||||
\(336\) | 8.16240 | 0.445295 | ||||||||
\(337\) | 25.7017 | 1.40006 | 0.700030 | − | 0.714114i | \(-0.253170\pi\) | ||||
0.700030 | + | 0.714114i | \(0.253170\pi\) | |||||||
\(338\) | 24.5142 | 1.33340 | ||||||||
\(339\) | −18.7696 | −1.01943 | ||||||||
\(340\) | −1.60202 | −0.0868816 | ||||||||
\(341\) | 26.5338 | 1.43688 | ||||||||
\(342\) | 11.1569 | 0.603296 | ||||||||
\(343\) | −6.80175 | −0.367260 | ||||||||
\(344\) | −2.26307 | −0.122016 | ||||||||
\(345\) | −1.03527 | −0.0557371 | ||||||||
\(346\) | −26.8708 | −1.44458 | ||||||||
\(347\) | −4.01523 | −0.215549 | −0.107774 | − | 0.994175i | \(-0.534372\pi\) | ||||
−0.107774 | + | 0.994175i | \(0.534372\pi\) | |||||||
\(348\) | −19.0191 | −1.01953 | ||||||||
\(349\) | 14.1995 | 0.760084 | 0.380042 | − | 0.924969i | \(-0.375909\pi\) | ||||
0.380042 | + | 0.924969i | \(0.375909\pi\) | |||||||
\(350\) | −40.0431 | −2.14039 | ||||||||
\(351\) | −1.30782 | −0.0698061 | ||||||||
\(352\) | 48.9500 | 2.60905 | ||||||||
\(353\) | −11.6289 | −0.618945 | −0.309473 | − | 0.950908i | \(-0.600152\pi\) | ||||
−0.309473 | + | 0.950908i | \(0.600152\pi\) | |||||||
\(354\) | 28.3698 | 1.50784 | ||||||||
\(355\) | −0.00484927 | −0.000257372 0 | ||||||||
\(356\) | −18.6239 | −0.987067 | ||||||||
\(357\) | −3.96431 | −0.209813 | ||||||||
\(358\) | −33.2789 | −1.75885 | ||||||||
\(359\) | −11.0007 | −0.580594 | −0.290297 | − | 0.956937i | \(-0.593754\pi\) | ||||
−0.290297 | + | 0.956937i | \(0.593754\pi\) | |||||||
\(360\) | 0.916044 | 0.0482797 | ||||||||
\(361\) | 7.40042 | 0.389496 | ||||||||
\(362\) | 44.4988 | 2.33880 | ||||||||
\(363\) | 30.7507 | 1.61399 | ||||||||
\(364\) | 14.0759 | 0.737776 | ||||||||
\(365\) | 3.39574 | 0.177741 | ||||||||
\(366\) | −27.1988 | −1.42170 | ||||||||
\(367\) | −18.3620 | −0.958490 | −0.479245 | − | 0.877681i | \(-0.659090\pi\) | ||||
−0.479245 | + | 0.877681i | \(0.659090\pi\) | |||||||
\(368\) | −3.61241 | −0.188310 | ||||||||
\(369\) | 11.0650 | 0.576018 | ||||||||
\(370\) | −0.508640 | −0.0264429 | ||||||||
\(371\) | −27.3896 | −1.42200 | ||||||||
\(372\) | 11.1488 | 0.578038 | ||||||||
\(373\) | 2.85462 | 0.147807 | 0.0739033 | − | 0.997265i | \(-0.476454\pi\) | ||||
0.0739033 | + | 0.997265i | \(0.476454\pi\) | |||||||
\(374\) | −14.0304 | −0.725494 | ||||||||
\(375\) | 5.69528 | 0.294103 | ||||||||
\(376\) | 2.91953 | 0.150563 | ||||||||
\(377\) | 9.16173 | 0.471853 | ||||||||
\(378\) | 8.60807 | 0.442751 | ||||||||
\(379\) | −17.7492 | −0.911714 | −0.455857 | − | 0.890053i | \(-0.650667\pi\) | ||||
−0.455857 | + | 0.890053i | \(0.650667\pi\) | |||||||
\(380\) | 8.23138 | 0.422261 | ||||||||
\(381\) | 5.56136 | 0.284917 | ||||||||
\(382\) | −49.3930 | −2.52716 | ||||||||
\(383\) | 3.55062 | 0.181428 | 0.0907142 | − | 0.995877i | \(-0.471085\pi\) | ||||
0.0907142 | + | 0.995877i | \(0.471085\pi\) | |||||||
\(384\) | 11.6259 | 0.593280 | ||||||||
\(385\) | 15.1149 | 0.770328 | ||||||||
\(386\) | 50.3760 | 2.56407 | ||||||||
\(387\) | 1.45777 | 0.0741025 | ||||||||
\(388\) | −6.44861 | −0.327379 | ||||||||
\(389\) | −25.7063 | −1.30336 | −0.651680 | − | 0.758494i | \(-0.725936\pi\) | ||||
−0.651680 | + | 0.758494i | \(0.725936\pi\) | |||||||
\(390\) | −1.67568 | −0.0848515 | ||||||||
\(391\) | 1.75448 | 0.0887276 | ||||||||
\(392\) | −13.5305 | −0.683394 | ||||||||
\(393\) | −18.3981 | −0.928059 | ||||||||
\(394\) | −11.1067 | −0.559548 | ||||||||
\(395\) | −3.97953 | −0.200232 | ||||||||
\(396\) | 17.5425 | 0.881546 | ||||||||
\(397\) | −4.53480 | −0.227595 | −0.113798 | − | 0.993504i | \(-0.536302\pi\) | ||||
−0.113798 | + | 0.993504i | \(0.536302\pi\) | |||||||
\(398\) | −17.1685 | −0.860579 | ||||||||
\(399\) | 20.3692 | 1.01973 | ||||||||
\(400\) | 9.57794 | 0.478897 | ||||||||
\(401\) | −29.4181 | −1.46907 | −0.734534 | − | 0.678572i | \(-0.762599\pi\) | ||||
−0.734534 | + | 0.678572i | \(0.762599\pi\) | |||||||
\(402\) | 2.19709 | 0.109581 | ||||||||
\(403\) | −5.37049 | −0.267523 | ||||||||
\(404\) | −9.86890 | −0.490996 | ||||||||
\(405\) | −0.590074 | −0.0293210 | ||||||||
\(406\) | −60.3026 | −2.99277 | ||||||||
\(407\) | −2.56506 | −0.127145 | ||||||||
\(408\) | −1.55242 | −0.0768563 | ||||||||
\(409\) | −29.9625 | −1.48155 | −0.740775 | − | 0.671753i | \(-0.765542\pi\) | ||||
−0.740775 | + | 0.671753i | \(0.765542\pi\) | |||||||
\(410\) | 14.1773 | 0.700168 | ||||||||
\(411\) | 11.2302 | 0.553944 | ||||||||
\(412\) | −33.8148 | −1.66594 | ||||||||
\(413\) | 51.7947 | 2.54865 | ||||||||
\(414\) | −3.80965 | −0.187234 | ||||||||
\(415\) | −3.68677 | −0.180976 | ||||||||
\(416\) | −9.90760 | −0.485760 | ||||||||
\(417\) | 17.9824 | 0.880603 | ||||||||
\(418\) | 72.0900 | 3.52604 | ||||||||
\(419\) | −4.24270 | −0.207269 | −0.103635 | − | 0.994615i | \(-0.533047\pi\) | ||||
−0.103635 | + | 0.994615i | \(0.533047\pi\) | |||||||
\(420\) | 6.35089 | 0.309892 | ||||||||
\(421\) | 19.8952 | 0.969633 | 0.484817 | − | 0.874616i | \(-0.338886\pi\) | ||||
0.484817 | + | 0.874616i | \(0.338886\pi\) | |||||||
\(422\) | −9.62183 | −0.468383 | ||||||||
\(423\) | −1.88063 | −0.0914392 | ||||||||
\(424\) | −10.7257 | −0.520888 | ||||||||
\(425\) | −4.65181 | −0.225646 | ||||||||
\(426\) | −0.0178446 | −0.000864576 0 | ||||||||
\(427\) | −49.6568 | −2.40306 | ||||||||
\(428\) | −48.5644 | −2.34745 | ||||||||
\(429\) | −8.45043 | −0.407991 | ||||||||
\(430\) | 1.86781 | 0.0900738 | ||||||||
\(431\) | −7.25128 | −0.349282 | −0.174641 | − | 0.984632i | \(-0.555876\pi\) | ||||
−0.174641 | + | 0.984632i | \(0.555876\pi\) | |||||||
\(432\) | −2.05897 | −0.0990623 | ||||||||
\(433\) | 8.71383 | 0.418760 | 0.209380 | − | 0.977834i | \(-0.432855\pi\) | ||||
0.209380 | + | 0.977834i | \(0.432855\pi\) | |||||||
\(434\) | 35.3486 | 1.69679 | ||||||||
\(435\) | 4.13368 | 0.198195 | ||||||||
\(436\) | −32.6439 | −1.56336 | ||||||||
\(437\) | −9.01473 | −0.431233 | ||||||||
\(438\) | 12.4959 | 0.597076 | ||||||||
\(439\) | 41.0432 | 1.95889 | 0.979443 | − | 0.201723i | \(-0.0646541\pi\) | ||||
0.979443 | + | 0.201723i | \(0.0646541\pi\) | |||||||
\(440\) | 5.91899 | 0.282177 | ||||||||
\(441\) | 8.71575 | 0.415036 | ||||||||
\(442\) | 2.83978 | 0.135075 | ||||||||
\(443\) | −14.9508 | −0.710333 | −0.355167 | − | 0.934803i | \(-0.615576\pi\) | ||||
−0.355167 | + | 0.934803i | \(0.615576\pi\) | |||||||
\(444\) | −1.07777 | −0.0511487 | ||||||||
\(445\) | 4.04778 | 0.191883 | ||||||||
\(446\) | 20.0141 | 0.947697 | ||||||||
\(447\) | −8.05893 | −0.381174 | ||||||||
\(448\) | 48.8871 | 2.30970 | ||||||||
\(449\) | 22.7039 | 1.07147 | 0.535733 | − | 0.844388i | \(-0.320035\pi\) | ||||
0.535733 | + | 0.844388i | \(0.320035\pi\) | |||||||
\(450\) | 10.1009 | 0.476161 | ||||||||
\(451\) | 71.4959 | 3.36661 | ||||||||
\(452\) | −50.9585 | −2.39689 | ||||||||
\(453\) | 20.1868 | 0.948458 | ||||||||
\(454\) | 15.1377 | 0.710449 | ||||||||
\(455\) | −3.05929 | −0.143422 | ||||||||
\(456\) | 7.97655 | 0.373536 | ||||||||
\(457\) | −28.4765 | −1.33207 | −0.666037 | − | 0.745919i | \(-0.732011\pi\) | ||||
−0.666037 | + | 0.745919i | \(0.732011\pi\) | |||||||
\(458\) | −49.5369 | −2.31471 | ||||||||
\(459\) | 1.00000 | 0.0466760 | ||||||||
\(460\) | −2.81070 | −0.131050 | ||||||||
\(461\) | 16.7453 | 0.779908 | 0.389954 | − | 0.920834i | \(-0.372491\pi\) | ||||
0.389954 | + | 0.920834i | \(0.372491\pi\) | |||||||
\(462\) | 55.6208 | 2.58772 | ||||||||
\(463\) | −10.4543 | −0.485854 | −0.242927 | − | 0.970045i | \(-0.578107\pi\) | ||||
−0.242927 | + | 0.970045i | \(0.578107\pi\) | |||||||
\(464\) | 14.4238 | 0.669609 | ||||||||
\(465\) | −2.42311 | −0.112369 | ||||||||
\(466\) | −41.6991 | −1.93167 | ||||||||
\(467\) | −10.8089 | −0.500179 | −0.250089 | − | 0.968223i | \(-0.580460\pi\) | ||||
−0.250089 | + | 0.968223i | \(0.580460\pi\) | |||||||
\(468\) | −3.55065 | −0.164129 | ||||||||
\(469\) | 4.01122 | 0.185221 | ||||||||
\(470\) | −2.40961 | −0.111147 | ||||||||
\(471\) | −1.00000 | −0.0460776 | ||||||||
\(472\) | 20.2828 | 0.933590 | ||||||||
\(473\) | 9.41932 | 0.433101 | ||||||||
\(474\) | −14.6441 | −0.672626 | ||||||||
\(475\) | 23.9016 | 1.09668 | ||||||||
\(476\) | −10.7629 | −0.493315 | ||||||||
\(477\) | 6.90904 | 0.316343 | ||||||||
\(478\) | 35.4133 | 1.61977 | ||||||||
\(479\) | −22.2267 | −1.01556 | −0.507782 | − | 0.861486i | \(-0.669534\pi\) | ||||
−0.507782 | + | 0.861486i | \(0.669534\pi\) | |||||||
\(480\) | −4.47021 | −0.204036 | ||||||||
\(481\) | 0.519174 | 0.0236723 | ||||||||
\(482\) | 48.6297 | 2.21502 | ||||||||
\(483\) | −6.95528 | −0.316476 | ||||||||
\(484\) | 83.4863 | 3.79483 | ||||||||
\(485\) | 1.40156 | 0.0636416 | ||||||||
\(486\) | −2.17139 | −0.0984963 | ||||||||
\(487\) | −22.3139 | −1.01114 | −0.505570 | − | 0.862785i | \(-0.668718\pi\) | ||||
−0.505570 | + | 0.862785i | \(0.668718\pi\) | |||||||
\(488\) | −19.4456 | −0.880260 | ||||||||
\(489\) | −12.1468 | −0.549298 | ||||||||
\(490\) | 11.1673 | 0.504489 | ||||||||
\(491\) | 9.47979 | 0.427817 | 0.213909 | − | 0.976854i | \(-0.431381\pi\) | ||||
0.213909 | + | 0.976854i | \(0.431381\pi\) | |||||||
\(492\) | 30.0407 | 1.35434 | ||||||||
\(493\) | −7.00535 | −0.315505 | ||||||||
\(494\) | −14.5912 | −0.656489 | ||||||||
\(495\) | −3.81275 | −0.171370 | ||||||||
\(496\) | −8.45507 | −0.379644 | ||||||||
\(497\) | −0.0325789 | −0.00146137 | ||||||||
\(498\) | −13.5668 | −0.607943 | ||||||||
\(499\) | −38.1518 | −1.70791 | −0.853956 | − | 0.520346i | \(-0.825803\pi\) | ||||
−0.853956 | + | 0.520346i | \(0.825803\pi\) | |||||||
\(500\) | 15.4624 | 0.691498 | ||||||||
\(501\) | 17.6646 | 0.789195 | ||||||||
\(502\) | 37.7197 | 1.68351 | ||||||||
\(503\) | −15.0084 | −0.669191 | −0.334595 | − | 0.942362i | \(-0.608600\pi\) | ||||
−0.334595 | + | 0.942362i | \(0.608600\pi\) | |||||||
\(504\) | 6.15428 | 0.274133 | ||||||||
\(505\) | 2.14494 | 0.0954485 | ||||||||
\(506\) | −24.6160 | −1.09431 | ||||||||
\(507\) | −11.2896 | −0.501389 | ||||||||
\(508\) | 15.0988 | 0.669900 | ||||||||
\(509\) | 5.38947 | 0.238884 | 0.119442 | − | 0.992841i | \(-0.461889\pi\) | ||||
0.119442 | + | 0.992841i | \(0.461889\pi\) | |||||||
\(510\) | 1.28128 | 0.0567361 | ||||||||
\(511\) | 22.8137 | 1.00922 | ||||||||
\(512\) | −21.9909 | −0.971868 | ||||||||
\(513\) | −5.13813 | −0.226854 | ||||||||
\(514\) | 1.52780 | 0.0673884 | ||||||||
\(515\) | 7.34942 | 0.323854 | ||||||||
\(516\) | 3.95775 | 0.174230 | ||||||||
\(517\) | −12.1516 | −0.534428 | ||||||||
\(518\) | −3.41721 | −0.150143 | ||||||||
\(519\) | 12.3749 | 0.543199 | ||||||||
\(520\) | −1.19802 | −0.0525366 | ||||||||
\(521\) | 4.06694 | 0.178176 | 0.0890879 | − | 0.996024i | \(-0.471605\pi\) | ||||
0.0890879 | + | 0.996024i | \(0.471605\pi\) | |||||||
\(522\) | 15.2114 | 0.665784 | ||||||||
\(523\) | 17.1843 | 0.751416 | 0.375708 | − | 0.926738i | \(-0.377400\pi\) | ||||
0.375708 | + | 0.926738i | \(0.377400\pi\) | |||||||
\(524\) | −49.9497 | −2.18206 | ||||||||
\(525\) | 18.4412 | 0.804841 | ||||||||
\(526\) | 43.0895 | 1.87879 | ||||||||
\(527\) | 4.10645 | 0.178880 | ||||||||
\(528\) | −13.3040 | −0.578982 | ||||||||
\(529\) | −19.9218 | −0.866166 | ||||||||
\(530\) | 8.85243 | 0.384525 | ||||||||
\(531\) | −13.0653 | −0.566984 | ||||||||
\(532\) | 55.3011 | 2.39761 | ||||||||
\(533\) | −14.4709 | −0.626806 | ||||||||
\(534\) | 14.8953 | 0.644582 | ||||||||
\(535\) | 10.5551 | 0.456338 | ||||||||
\(536\) | 1.57079 | 0.0678480 | ||||||||
\(537\) | 15.3261 | 0.661370 | ||||||||
\(538\) | −61.0636 | −2.63264 | ||||||||
\(539\) | 56.3166 | 2.42573 | ||||||||
\(540\) | −1.60202 | −0.0689399 | ||||||||
\(541\) | 33.2155 | 1.42805 | 0.714023 | − | 0.700123i | \(-0.246871\pi\) | ||||
0.714023 | + | 0.700123i | \(0.246871\pi\) | |||||||
\(542\) | −42.8183 | −1.83920 | ||||||||
\(543\) | −20.4932 | −0.879448 | ||||||||
\(544\) | 7.57567 | 0.324804 | ||||||||
\(545\) | 7.09494 | 0.303914 | ||||||||
\(546\) | −11.2578 | −0.481789 | ||||||||
\(547\) | −14.0982 | −0.602795 | −0.301397 | − | 0.953499i | \(-0.597453\pi\) | ||||
−0.301397 | + | 0.953499i | \(0.597453\pi\) | |||||||
\(548\) | 30.4893 | 1.30244 | ||||||||
\(549\) | 12.5260 | 0.534595 | ||||||||
\(550\) | 65.2668 | 2.78298 | ||||||||
\(551\) | 35.9944 | 1.53341 | ||||||||
\(552\) | −2.72368 | −0.115928 | ||||||||
\(553\) | −26.7357 | −1.13692 | ||||||||
\(554\) | 19.7014 | 0.837032 | ||||||||
\(555\) | 0.234246 | 0.00994319 | ||||||||
\(556\) | 48.8212 | 2.07048 | ||||||||
\(557\) | −24.0407 | −1.01864 | −0.509318 | − | 0.860578i | \(-0.670102\pi\) | ||||
−0.509318 | + | 0.860578i | \(0.670102\pi\) | |||||||
\(558\) | −8.91672 | −0.377475 | ||||||||
\(559\) | −1.90649 | −0.0806361 | ||||||||
\(560\) | −4.81642 | −0.203531 | ||||||||
\(561\) | 6.46148 | 0.272804 | ||||||||
\(562\) | 10.4062 | 0.438960 | ||||||||
\(563\) | 12.1261 | 0.511055 | 0.255527 | − | 0.966802i | \(-0.417751\pi\) | ||||
0.255527 | + | 0.966802i | \(0.417751\pi\) | |||||||
\(564\) | −5.10580 | −0.214993 | ||||||||
\(565\) | 11.0755 | 0.465949 | ||||||||
\(566\) | 40.9425 | 1.72094 | ||||||||
\(567\) | −3.96431 | −0.166485 | ||||||||
\(568\) | −0.0127579 | −0.000535310 0 | ||||||||
\(569\) | −31.5818 | −1.32398 | −0.661988 | − | 0.749514i | \(-0.730287\pi\) | ||||
−0.661988 | + | 0.749514i | \(0.730287\pi\) | |||||||
\(570\) | −6.58340 | −0.275748 | ||||||||
\(571\) | −33.7049 | −1.41051 | −0.705254 | − | 0.708955i | \(-0.749167\pi\) | ||||
−0.705254 | + | 0.708955i | \(0.749167\pi\) | |||||||
\(572\) | −22.9424 | −0.959272 | ||||||||
\(573\) | 22.7471 | 0.950275 | ||||||||
\(574\) | 95.2479 | 3.97557 | ||||||||
\(575\) | −8.16149 | −0.340358 | ||||||||
\(576\) | −12.3318 | −0.513826 | ||||||||
\(577\) | −0.903216 | −0.0376014 | −0.0188007 | − | 0.999823i | \(-0.505985\pi\) | ||||
−0.0188007 | + | 0.999823i | \(0.505985\pi\) | |||||||
\(578\) | −2.17139 | −0.0903180 | ||||||||
\(579\) | −23.1999 | −0.964154 | ||||||||
\(580\) | 11.2227 | 0.465997 | ||||||||
\(581\) | −24.7689 | −1.02759 | ||||||||
\(582\) | 5.15755 | 0.213787 | ||||||||
\(583\) | 44.6426 | 1.84891 | ||||||||
\(584\) | 8.93384 | 0.369685 | ||||||||
\(585\) | 0.771709 | 0.0319063 | ||||||||
\(586\) | −6.60019 | −0.272651 | ||||||||
\(587\) | 20.2005 | 0.833764 | 0.416882 | − | 0.908961i | \(-0.363123\pi\) | ||||
0.416882 | + | 0.908961i | \(0.363123\pi\) | |||||||
\(588\) | 23.6628 | 0.975836 | ||||||||
\(589\) | −21.0995 | −0.869390 | ||||||||
\(590\) | −16.7403 | −0.689186 | ||||||||
\(591\) | 5.11502 | 0.210404 | ||||||||
\(592\) | 0.817364 | 0.0335935 | ||||||||
\(593\) | 19.1038 | 0.784497 | 0.392249 | − | 0.919859i | \(-0.371697\pi\) | ||||
0.392249 | + | 0.919859i | \(0.371697\pi\) | |||||||
\(594\) | −14.0304 | −0.575674 | ||||||||
\(595\) | 2.33924 | 0.0958993 | ||||||||
\(596\) | −21.8795 | −0.896220 | ||||||||
\(597\) | 7.90668 | 0.323599 | ||||||||
\(598\) | 4.98233 | 0.203743 | ||||||||
\(599\) | 6.40189 | 0.261574 | 0.130787 | − | 0.991410i | \(-0.458250\pi\) | ||||
0.130787 | + | 0.991410i | \(0.458250\pi\) | |||||||
\(600\) | 7.22157 | 0.294820 | ||||||||
\(601\) | −0.733997 | −0.0299404 | −0.0149702 | − | 0.999888i | \(-0.504765\pi\) | ||||
−0.0149702 | + | 0.999888i | \(0.504765\pi\) | |||||||
\(602\) | 12.5486 | 0.511441 | ||||||||
\(603\) | −1.01183 | −0.0412051 | ||||||||
\(604\) | 54.8060 | 2.23002 | ||||||||
\(605\) | −18.1452 | −0.737706 | ||||||||
\(606\) | 7.89308 | 0.320634 | ||||||||
\(607\) | −28.7646 | −1.16752 | −0.583760 | − | 0.811926i | \(-0.698419\pi\) | ||||
−0.583760 | + | 0.811926i | \(0.698419\pi\) | |||||||
\(608\) | −38.9248 | −1.57861 | ||||||||
\(609\) | 27.7714 | 1.12535 | ||||||||
\(610\) | 16.0493 | 0.649817 | ||||||||
\(611\) | 2.45952 | 0.0995014 | ||||||||
\(612\) | 2.71494 | 0.109745 | ||||||||
\(613\) | −25.7709 | −1.04087 | −0.520437 | − | 0.853900i | \(-0.674231\pi\) | ||||
−0.520437 | + | 0.853900i | \(0.674231\pi\) | |||||||
\(614\) | 24.5757 | 0.991796 | ||||||||
\(615\) | −6.52914 | −0.263280 | ||||||||
\(616\) | 39.7657 | 1.60221 | ||||||||
\(617\) | −47.5476 | −1.91419 | −0.957097 | − | 0.289768i | \(-0.906422\pi\) | ||||
−0.957097 | + | 0.289768i | \(0.906422\pi\) | |||||||
\(618\) | 27.0449 | 1.08790 | ||||||||
\(619\) | −39.3330 | −1.58093 | −0.790464 | − | 0.612509i | \(-0.790160\pi\) | ||||
−0.790464 | + | 0.612509i | \(0.790160\pi\) | |||||||
\(620\) | −6.57861 | −0.264203 | ||||||||
\(621\) | 1.75448 | 0.0704047 | ||||||||
\(622\) | 54.5747 | 2.18825 | ||||||||
\(623\) | 27.1943 | 1.08952 | ||||||||
\(624\) | 2.69276 | 0.107797 | ||||||||
\(625\) | 19.8984 | 0.795937 | ||||||||
\(626\) | 58.4268 | 2.33521 | ||||||||
\(627\) | −33.1999 | −1.32588 | ||||||||
\(628\) | −2.71494 | −0.108338 | ||||||||
\(629\) | −0.396977 | −0.0158285 | ||||||||
\(630\) | −5.07940 | −0.202368 | ||||||||
\(631\) | 30.7981 | 1.22605 | 0.613026 | − | 0.790063i | \(-0.289952\pi\) | ||||
0.613026 | + | 0.790063i | \(0.289952\pi\) | |||||||
\(632\) | −10.4697 | −0.416462 | ||||||||
\(633\) | 4.43118 | 0.176124 | ||||||||
\(634\) | −55.6819 | −2.21141 | ||||||||
\(635\) | −3.28162 | −0.130227 | ||||||||
\(636\) | 18.7577 | 0.743789 | ||||||||
\(637\) | −11.3986 | −0.451629 | ||||||||
\(638\) | 98.2879 | 3.89125 | ||||||||
\(639\) | 0.00821806 | 0.000325102 0 | ||||||||
\(640\) | −6.86012 | −0.271170 | ||||||||
\(641\) | −20.1378 | −0.795394 | −0.397697 | − | 0.917517i | \(-0.630190\pi\) | ||||
−0.397697 | + | 0.917517i | \(0.630190\pi\) | |||||||
\(642\) | 38.8415 | 1.53295 | ||||||||
\(643\) | −17.7986 | −0.701909 | −0.350955 | − | 0.936392i | \(-0.614143\pi\) | ||||
−0.350955 | + | 0.936392i | \(0.614143\pi\) | |||||||
\(644\) | −18.8832 | −0.744102 | ||||||||
\(645\) | −0.860191 | −0.0338700 | ||||||||
\(646\) | 11.1569 | 0.438962 | ||||||||
\(647\) | −37.2669 | −1.46511 | −0.732556 | − | 0.680707i | \(-0.761673\pi\) | ||||
−0.732556 | + | 0.680707i | \(0.761673\pi\) | |||||||
\(648\) | −1.55242 | −0.0609849 | ||||||||
\(649\) | −84.4208 | −3.31381 | ||||||||
\(650\) | −13.2101 | −0.518145 | ||||||||
\(651\) | −16.2793 | −0.638034 | ||||||||
\(652\) | −32.9779 | −1.29151 | ||||||||
\(653\) | −25.1114 | −0.982685 | −0.491342 | − | 0.870967i | \(-0.663494\pi\) | ||||
−0.491342 | + | 0.870967i | \(0.663494\pi\) | |||||||
\(654\) | 26.1084 | 1.02092 | ||||||||
\(655\) | 10.8562 | 0.424187 | ||||||||
\(656\) | −22.7824 | −0.889504 | ||||||||
\(657\) | −5.75478 | −0.224515 | ||||||||
\(658\) | −16.1886 | −0.631096 | ||||||||
\(659\) | −7.86567 | −0.306403 | −0.153202 | − | 0.988195i | \(-0.548958\pi\) | ||||
−0.153202 | + | 0.988195i | \(0.548958\pi\) | |||||||
\(660\) | −10.3514 | −0.402928 | ||||||||
\(661\) | 24.5015 | 0.952998 | 0.476499 | − | 0.879175i | \(-0.341906\pi\) | ||||
0.476499 | + | 0.879175i | \(0.341906\pi\) | |||||||
\(662\) | −36.9883 | −1.43759 | ||||||||
\(663\) | −1.30782 | −0.0507914 | ||||||||
\(664\) | −9.69949 | −0.376413 | ||||||||
\(665\) | −12.0193 | −0.466089 | ||||||||
\(666\) | 0.861993 | 0.0334015 | ||||||||
\(667\) | −12.2907 | −0.475899 | ||||||||
\(668\) | 47.9583 | 1.85556 | ||||||||
\(669\) | −9.21719 | −0.356357 | ||||||||
\(670\) | −1.29645 | −0.0500861 | ||||||||
\(671\) | 80.9362 | 3.12451 | ||||||||
\(672\) | −30.0323 | −1.15852 | ||||||||
\(673\) | −28.9826 | −1.11720 | −0.558598 | − | 0.829438i | \(-0.688661\pi\) | ||||
−0.558598 | + | 0.829438i | \(0.688661\pi\) | |||||||
\(674\) | −55.8084 | −2.14966 | ||||||||
\(675\) | −4.65181 | −0.179048 | ||||||||
\(676\) | −30.6507 | −1.17887 | ||||||||
\(677\) | −2.02366 | −0.0777754 | −0.0388877 | − | 0.999244i | \(-0.512381\pi\) | ||||
−0.0388877 | + | 0.999244i | \(0.512381\pi\) | |||||||
\(678\) | 40.7562 | 1.56523 | ||||||||
\(679\) | 9.41614 | 0.361358 | ||||||||
\(680\) | 0.916044 | 0.0351287 | ||||||||
\(681\) | −6.97144 | −0.267146 | ||||||||
\(682\) | −57.6152 | −2.20620 | ||||||||
\(683\) | −33.8448 | −1.29504 | −0.647518 | − | 0.762051i | \(-0.724193\pi\) | ||||
−0.647518 | + | 0.762051i | \(0.724193\pi\) | |||||||
\(684\) | −13.9497 | −0.533382 | ||||||||
\(685\) | −6.62664 | −0.253191 | ||||||||
\(686\) | 14.7693 | 0.563893 | ||||||||
\(687\) | 22.8134 | 0.870386 | ||||||||
\(688\) | −3.00150 | −0.114431 | ||||||||
\(689\) | −9.03576 | −0.344235 | ||||||||
\(690\) | 2.24798 | 0.0855791 | ||||||||
\(691\) | 45.7095 | 1.73887 | 0.869435 | − | 0.494047i | \(-0.164483\pi\) | ||||
0.869435 | + | 0.494047i | \(0.164483\pi\) | |||||||
\(692\) | 33.5972 | 1.27718 | ||||||||
\(693\) | −25.6153 | −0.973044 | ||||||||
\(694\) | 8.71863 | 0.330955 | ||||||||
\(695\) | −10.6110 | −0.402497 | ||||||||
\(696\) | 10.8753 | 0.412226 | ||||||||
\(697\) | 11.0650 | 0.419115 | ||||||||
\(698\) | −30.8328 | −1.16704 | ||||||||
\(699\) | 19.2038 | 0.726356 | ||||||||
\(700\) | 50.0669 | 1.89235 | ||||||||
\(701\) | 11.9106 | 0.449856 | 0.224928 | − | 0.974375i | \(-0.427785\pi\) | ||||
0.224928 | + | 0.974375i | \(0.427785\pi\) | |||||||
\(702\) | 2.83978 | 0.107181 | ||||||||
\(703\) | 2.03972 | 0.0769296 | ||||||||
\(704\) | −79.6817 | −3.00312 | ||||||||
\(705\) | 1.10971 | 0.0417941 | ||||||||
\(706\) | 25.2509 | 0.950332 | ||||||||
\(707\) | 14.4104 | 0.541958 | ||||||||
\(708\) | −35.4714 | −1.33310 | ||||||||
\(709\) | −2.40322 | −0.0902548 | −0.0451274 | − | 0.998981i | \(-0.514369\pi\) | ||||
−0.0451274 | + | 0.998981i | \(0.514369\pi\) | |||||||
\(710\) | 0.0105297 | 0.000395171 0 | ||||||||
\(711\) | 6.74411 | 0.252924 | ||||||||
\(712\) | 10.6493 | 0.399099 | ||||||||
\(713\) | 7.20467 | 0.269817 | ||||||||
\(714\) | 8.60807 | 0.322149 | ||||||||
\(715\) | 4.98638 | 0.186480 | ||||||||
\(716\) | 41.6095 | 1.55502 | ||||||||
\(717\) | −16.3090 | −0.609072 | ||||||||
\(718\) | 23.8868 | 0.891448 | ||||||||
\(719\) | 2.92059 | 0.108920 | 0.0544598 | − | 0.998516i | \(-0.482656\pi\) | ||||
0.0544598 | + | 0.998516i | \(0.482656\pi\) | |||||||
\(720\) | 1.21495 | 0.0452783 | ||||||||
\(721\) | 49.3758 | 1.83885 | ||||||||
\(722\) | −16.0692 | −0.598034 | ||||||||
\(723\) | −22.3956 | −0.832903 | ||||||||
\(724\) | −55.6379 | −2.06777 | ||||||||
\(725\) | 32.5876 | 1.21027 | ||||||||
\(726\) | −66.7717 | −2.47813 | ||||||||
\(727\) | 18.5096 | 0.686482 | 0.343241 | − | 0.939247i | \(-0.388475\pi\) | ||||
0.343241 | + | 0.939247i | \(0.388475\pi\) | |||||||
\(728\) | −8.04867 | −0.298304 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | −7.37349 | −0.272905 | ||||||||
\(731\) | 1.45777 | 0.0539175 | ||||||||
\(732\) | 34.0073 | 1.25695 | ||||||||
\(733\) | −12.4054 | −0.458203 | −0.229102 | − | 0.973403i | \(-0.573579\pi\) | ||||
−0.229102 | + | 0.973403i | \(0.573579\pi\) | |||||||
\(734\) | 39.8712 | 1.47167 | ||||||||
\(735\) | −5.14294 | −0.189700 | ||||||||
\(736\) | 13.2913 | 0.489925 | ||||||||
\(737\) | −6.53794 | −0.240828 | ||||||||
\(738\) | −24.0264 | −0.884422 | ||||||||
\(739\) | −9.77302 | −0.359506 | −0.179753 | − | 0.983712i | \(-0.557530\pi\) | ||||
−0.179753 | + | 0.983712i | \(0.557530\pi\) | |||||||
\(740\) | 0.635964 | 0.0233785 | ||||||||
\(741\) | 6.71974 | 0.246856 | ||||||||
\(742\) | 59.4735 | 2.18334 | ||||||||
\(743\) | −19.4224 | −0.712538 | −0.356269 | − | 0.934383i | \(-0.615951\pi\) | ||||
−0.356269 | + | 0.934383i | \(0.615951\pi\) | |||||||
\(744\) | −6.37495 | −0.233717 | ||||||||
\(745\) | 4.75536 | 0.174223 | ||||||||
\(746\) | −6.19850 | −0.226943 | ||||||||
\(747\) | 6.24798 | 0.228602 | ||||||||
\(748\) | 17.5425 | 0.641419 | ||||||||
\(749\) | 70.9128 | 2.59110 | ||||||||
\(750\) | −12.3667 | −0.451568 | ||||||||
\(751\) | −5.91752 | −0.215933 | −0.107967 | − | 0.994155i | \(-0.534434\pi\) | ||||
−0.107967 | + | 0.994155i | \(0.534434\pi\) | |||||||
\(752\) | 3.87216 | 0.141203 | ||||||||
\(753\) | −17.3712 | −0.633042 | ||||||||
\(754\) | −19.8937 | −0.724486 | ||||||||
\(755\) | −11.9117 | −0.433511 | ||||||||
\(756\) | −10.7629 | −0.391442 | ||||||||
\(757\) | −39.9597 | −1.45236 | −0.726180 | − | 0.687505i | \(-0.758706\pi\) | ||||
−0.726180 | + | 0.687505i | \(0.758706\pi\) | |||||||
\(758\) | 38.5404 | 1.39985 | ||||||||
\(759\) | 11.3365 | 0.411489 | ||||||||
\(760\) | −4.70676 | −0.170732 | ||||||||
\(761\) | −6.65333 | −0.241183 | −0.120591 | − | 0.992702i | \(-0.538479\pi\) | ||||
−0.120591 | + | 0.992702i | \(0.538479\pi\) | |||||||
\(762\) | −12.0759 | −0.437463 | ||||||||
\(763\) | 47.6661 | 1.72563 | ||||||||
\(764\) | 61.7572 | 2.23430 | ||||||||
\(765\) | −0.590074 | −0.0213342 | ||||||||
\(766\) | −7.70979 | −0.278566 | ||||||||
\(767\) | 17.0870 | 0.616975 | ||||||||
\(768\) | −0.580666 | −0.0209530 | ||||||||
\(769\) | −18.8416 | −0.679447 | −0.339723 | − | 0.940525i | \(-0.610333\pi\) | ||||
−0.339723 | + | 0.940525i | \(0.610333\pi\) | |||||||
\(770\) | −32.8204 | −1.18277 | ||||||||
\(771\) | −0.703605 | −0.0253397 | ||||||||
\(772\) | −62.9863 | −2.26693 | ||||||||
\(773\) | −43.0504 | −1.54841 | −0.774207 | − | 0.632933i | \(-0.781851\pi\) | ||||
−0.774207 | + | 0.632933i | \(0.781851\pi\) | |||||||
\(774\) | −3.16538 | −0.113777 | ||||||||
\(775\) | −19.1025 | −0.686180 | ||||||||
\(776\) | 3.68736 | 0.132368 | ||||||||
\(777\) | 1.57374 | 0.0564576 | ||||||||
\(778\) | 55.8184 | 2.00119 | ||||||||
\(779\) | −56.8532 | −2.03698 | ||||||||
\(780\) | 2.09515 | 0.0750183 | ||||||||
\(781\) | 0.0531008 | 0.00190010 | ||||||||
\(782\) | −3.80965 | −0.136233 | ||||||||
\(783\) | −7.00535 | −0.250351 | ||||||||
\(784\) | −17.9455 | −0.640909 | ||||||||
\(785\) | 0.590074 | 0.0210606 | ||||||||
\(786\) | 39.9494 | 1.42495 | ||||||||
\(787\) | −19.1056 | −0.681040 | −0.340520 | − | 0.940237i | \(-0.610603\pi\) | ||||
−0.340520 | + | 0.940237i | \(0.610603\pi\) | |||||||
\(788\) | 13.8870 | 0.494704 | ||||||||
\(789\) | −19.8442 | −0.706471 | ||||||||
\(790\) | 8.64111 | 0.307437 | ||||||||
\(791\) | 74.4087 | 2.64567 | ||||||||
\(792\) | −10.0309 | −0.356434 | ||||||||
\(793\) | −16.3817 | −0.581730 | ||||||||
\(794\) | 9.84683 | 0.349451 | ||||||||
\(795\) | −4.07685 | −0.144591 | ||||||||
\(796\) | 21.4662 | 0.760849 | ||||||||
\(797\) | −33.1974 | −1.17591 | −0.587957 | − | 0.808892i | \(-0.700067\pi\) | ||||
−0.587957 | + | 0.808892i | \(0.700067\pi\) | |||||||
\(798\) | −44.2294 | −1.56570 | ||||||||
\(799\) | −1.88063 | −0.0665318 | ||||||||
\(800\) | −35.2406 | −1.24594 | ||||||||
\(801\) | −6.85979 | −0.242379 | ||||||||
\(802\) | 63.8781 | 2.25562 | ||||||||
\(803\) | −37.1843 | −1.31221 | ||||||||
\(804\) | −2.74707 | −0.0968818 | ||||||||
\(805\) | 4.10413 | 0.144652 | ||||||||
\(806\) | 11.6614 | 0.410757 | ||||||||
\(807\) | 28.1218 | 0.989936 | ||||||||
\(808\) | 5.64310 | 0.198524 | ||||||||
\(809\) | −12.4805 | −0.438791 | −0.219395 | − | 0.975636i | \(-0.570408\pi\) | ||||
−0.219395 | + | 0.975636i | \(0.570408\pi\) | |||||||
\(810\) | 1.28128 | 0.0450197 | ||||||||
\(811\) | −34.5539 | −1.21335 | −0.606676 | − | 0.794949i | \(-0.707497\pi\) | ||||
−0.606676 | + | 0.794949i | \(0.707497\pi\) | |||||||
\(812\) | 75.3977 | 2.64594 | ||||||||
\(813\) | 19.7193 | 0.691585 | ||||||||
\(814\) | 5.56975 | 0.195220 | ||||||||
\(815\) | 7.16752 | 0.251067 | ||||||||
\(816\) | −2.05897 | −0.0720784 | ||||||||
\(817\) | −7.49020 | −0.262049 | ||||||||
\(818\) | 65.0604 | 2.27478 | ||||||||
\(819\) | 5.18459 | 0.181164 | ||||||||
\(820\) | −17.7263 | −0.619028 | ||||||||
\(821\) | −9.99497 | −0.348827 | −0.174413 | − | 0.984673i | \(-0.555803\pi\) | ||||
−0.174413 | + | 0.984673i | \(0.555803\pi\) | |||||||
\(822\) | −24.3851 | −0.850529 | ||||||||
\(823\) | −30.7052 | −1.07032 | −0.535159 | − | 0.844752i | \(-0.679748\pi\) | ||||
−0.535159 | + | 0.844752i | \(0.679748\pi\) | |||||||
\(824\) | 19.3355 | 0.673586 | ||||||||
\(825\) | −30.0576 | −1.04647 | ||||||||
\(826\) | −112.467 | −3.91321 | ||||||||
\(827\) | 34.8385 | 1.21145 | 0.605726 | − | 0.795673i | \(-0.292883\pi\) | ||||
0.605726 | + | 0.795673i | \(0.292883\pi\) | |||||||
\(828\) | 4.76330 | 0.165536 | ||||||||
\(829\) | −35.7546 | −1.24181 | −0.620904 | − | 0.783887i | \(-0.713234\pi\) | ||||
−0.620904 | + | 0.783887i | \(0.713234\pi\) | |||||||
\(830\) | 8.00542 | 0.277872 | ||||||||
\(831\) | −9.07317 | −0.314745 | ||||||||
\(832\) | 16.1278 | 0.559130 | ||||||||
\(833\) | 8.71575 | 0.301983 | ||||||||
\(834\) | −39.0469 | −1.35208 | ||||||||
\(835\) | −10.4234 | −0.360717 | ||||||||
\(836\) | −90.1359 | −3.11742 | ||||||||
\(837\) | 4.10645 | 0.141940 | ||||||||
\(838\) | 9.21255 | 0.318242 | ||||||||
\(839\) | 23.6459 | 0.816346 | 0.408173 | − | 0.912905i | \(-0.366166\pi\) | ||||
0.408173 | + | 0.912905i | \(0.366166\pi\) | |||||||
\(840\) | −3.63148 | −0.125298 | ||||||||
\(841\) | 20.0750 | 0.692241 | ||||||||
\(842\) | −43.2003 | −1.48878 | ||||||||
\(843\) | −4.79242 | −0.165060 | ||||||||
\(844\) | 12.0304 | 0.414103 | ||||||||
\(845\) | 6.66171 | 0.229170 | ||||||||
\(846\) | 4.08358 | 0.140396 | ||||||||
\(847\) | −121.905 | −4.18871 | ||||||||
\(848\) | −14.2255 | −0.488506 | ||||||||
\(849\) | −18.8554 | −0.647116 | ||||||||
\(850\) | 10.1009 | 0.346458 | ||||||||
\(851\) | −0.696487 | −0.0238753 | ||||||||
\(852\) | 0.0223116 | 0.000764382 0 | ||||||||
\(853\) | −12.8822 | −0.441077 | −0.220538 | − | 0.975378i | \(-0.570781\pi\) | ||||
−0.220538 | + | 0.975378i | \(0.570781\pi\) | |||||||
\(854\) | 107.824 | 3.68967 | ||||||||
\(855\) | 3.03188 | 0.103688 | ||||||||
\(856\) | 27.7694 | 0.949140 | ||||||||
\(857\) | 32.1545 | 1.09838 | 0.549188 | − | 0.835699i | \(-0.314937\pi\) | ||||
0.549188 | + | 0.835699i | \(0.314937\pi\) | |||||||
\(858\) | 18.3492 | 0.626431 | ||||||||
\(859\) | 8.60864 | 0.293723 | 0.146861 | − | 0.989157i | \(-0.453083\pi\) | ||||
0.146861 | + | 0.989157i | \(0.453083\pi\) | |||||||
\(860\) | −2.33537 | −0.0796354 | ||||||||
\(861\) | −43.8649 | −1.49491 | ||||||||
\(862\) | 15.7454 | 0.536289 | ||||||||
\(863\) | −55.2073 | −1.87928 | −0.939639 | − | 0.342167i | \(-0.888839\pi\) | ||||
−0.939639 | + | 0.342167i | \(0.888839\pi\) | |||||||
\(864\) | 7.57567 | 0.257730 | ||||||||
\(865\) | −7.30213 | −0.248280 | ||||||||
\(866\) | −18.9211 | −0.642967 | ||||||||
\(867\) | 1.00000 | 0.0339618 | ||||||||
\(868\) | −44.1972 | −1.50015 | ||||||||
\(869\) | 43.5769 | 1.47825 | ||||||||
\(870\) | −8.97583 | −0.304309 | ||||||||
\(871\) | 1.32330 | 0.0448381 | ||||||||
\(872\) | 18.6660 | 0.632111 | ||||||||
\(873\) | −2.37523 | −0.0803893 | ||||||||
\(874\) | 19.5745 | 0.662118 | ||||||||
\(875\) | −22.5779 | −0.763271 | ||||||||
\(876\) | −15.6239 | −0.527882 | ||||||||
\(877\) | 24.3253 | 0.821407 | 0.410704 | − | 0.911769i | \(-0.365283\pi\) | ||||
0.410704 | + | 0.911769i | \(0.365283\pi\) | |||||||
\(878\) | −89.1209 | −3.00768 | ||||||||
\(879\) | 3.03961 | 0.102524 | ||||||||
\(880\) | 7.85034 | 0.264635 | ||||||||
\(881\) | −3.96475 | −0.133576 | −0.0667879 | − | 0.997767i | \(-0.521275\pi\) | ||||
−0.0667879 | + | 0.997767i | \(0.521275\pi\) | |||||||
\(882\) | −18.9253 | −0.637248 | ||||||||
\(883\) | −39.8834 | −1.34218 | −0.671092 | − | 0.741374i | \(-0.734175\pi\) | ||||
−0.671092 | + | 0.741374i | \(0.734175\pi\) | |||||||
\(884\) | −3.55065 | −0.119421 | ||||||||
\(885\) | 7.70947 | 0.259151 | ||||||||
\(886\) | 32.4640 | 1.09065 | ||||||||
\(887\) | −4.71937 | −0.158461 | −0.0792305 | − | 0.996856i | \(-0.525246\pi\) | ||||
−0.0792305 | + | 0.996856i | \(0.525246\pi\) | |||||||
\(888\) | 0.616276 | 0.0206809 | ||||||||
\(889\) | −22.0470 | −0.739431 | ||||||||
\(890\) | −8.78933 | −0.294619 | ||||||||
\(891\) | 6.46148 | 0.216468 | ||||||||
\(892\) | −25.0242 | −0.837871 | ||||||||
\(893\) | 9.66291 | 0.323357 | ||||||||
\(894\) | 17.4991 | 0.585257 | ||||||||
\(895\) | −9.04353 | −0.302292 | ||||||||
\(896\) | −46.0885 | −1.53971 | ||||||||
\(897\) | −2.29453 | −0.0766122 | ||||||||
\(898\) | −49.2992 | −1.64513 | ||||||||
\(899\) | −28.7672 | −0.959439 | ||||||||
\(900\) | −12.6294 | −0.420980 | ||||||||
\(901\) | 6.90904 | 0.230174 | ||||||||
\(902\) | −155.246 | −5.16912 | ||||||||
\(903\) | −5.77904 | −0.192314 | ||||||||
\(904\) | 29.1384 | 0.969129 | ||||||||
\(905\) | 12.0925 | 0.401969 | ||||||||
\(906\) | −43.8334 | −1.45627 | ||||||||
\(907\) | 4.01359 | 0.133269 | 0.0666346 | − | 0.997777i | \(-0.478774\pi\) | ||||
0.0666346 | + | 0.997777i | \(0.478774\pi\) | |||||||
\(908\) | −18.9271 | −0.628116 | ||||||||
\(909\) | −3.63503 | −0.120566 | ||||||||
\(910\) | 6.64293 | 0.220211 | ||||||||
\(911\) | −51.2421 | −1.69773 | −0.848863 | − | 0.528613i | \(-0.822712\pi\) | ||||
−0.848863 | + | 0.528613i | \(0.822712\pi\) | |||||||
\(912\) | 10.5793 | 0.350314 | ||||||||
\(913\) | 40.3711 | 1.33609 | ||||||||
\(914\) | 61.8336 | 2.04527 | ||||||||
\(915\) | −7.39125 | −0.244347 | ||||||||
\(916\) | 61.9371 | 2.04646 | ||||||||
\(917\) | 72.9356 | 2.40854 | ||||||||
\(918\) | −2.17139 | −0.0716666 | ||||||||
\(919\) | 45.9274 | 1.51501 | 0.757503 | − | 0.652831i | \(-0.226419\pi\) | ||||
0.757503 | + | 0.652831i | \(0.226419\pi\) | |||||||
\(920\) | 1.60718 | 0.0529870 | ||||||||
\(921\) | −11.3180 | −0.372939 | ||||||||
\(922\) | −36.3607 | −1.19748 | ||||||||
\(923\) | −0.0107477 | −0.000353766 0 | ||||||||
\(924\) | −69.5440 | −2.28783 | ||||||||
\(925\) | 1.84666 | 0.0607179 | ||||||||
\(926\) | 22.7004 | 0.745983 | ||||||||
\(927\) | −12.4551 | −0.409079 | ||||||||
\(928\) | −53.0703 | −1.74212 | ||||||||
\(929\) | −30.0403 | −0.985591 | −0.492796 | − | 0.870145i | \(-0.664025\pi\) | ||||
−0.492796 | + | 0.870145i | \(0.664025\pi\) | |||||||
\(930\) | 5.26153 | 0.172532 | ||||||||
\(931\) | −44.7827 | −1.46769 | ||||||||
\(932\) | 52.1373 | 1.70782 | ||||||||
\(933\) | −25.1335 | −0.822834 | ||||||||
\(934\) | 23.4705 | 0.767977 | ||||||||
\(935\) | −3.81275 | −0.124690 | ||||||||
\(936\) | 2.03028 | 0.0663619 | ||||||||
\(937\) | −8.63411 | −0.282064 | −0.141032 | − | 0.990005i | \(-0.545042\pi\) | ||||
−0.141032 | + | 0.990005i | \(0.545042\pi\) | |||||||
\(938\) | −8.70994 | −0.284390 | ||||||||
\(939\) | −26.9076 | −0.878095 | ||||||||
\(940\) | 3.01280 | 0.0982666 | ||||||||
\(941\) | 48.5566 | 1.58290 | 0.791449 | − | 0.611235i | \(-0.209327\pi\) | ||||
0.791449 | + | 0.611235i | \(0.209327\pi\) | |||||||
\(942\) | 2.17139 | 0.0707478 | ||||||||
\(943\) | 19.4132 | 0.632180 | ||||||||
\(944\) | 26.9010 | 0.875552 | ||||||||
\(945\) | 2.33924 | 0.0760954 | ||||||||
\(946\) | −20.4530 | −0.664986 | ||||||||
\(947\) | 1.29426 | 0.0420578 | 0.0210289 | − | 0.999779i | \(-0.493306\pi\) | ||||
0.0210289 | + | 0.999779i | \(0.493306\pi\) | |||||||
\(948\) | 18.3099 | 0.594677 | ||||||||
\(949\) | 7.52620 | 0.244311 | ||||||||
\(950\) | −51.8998 | −1.68385 | ||||||||
\(951\) | 25.6434 | 0.831545 | ||||||||
\(952\) | 6.15428 | 0.199461 | ||||||||
\(953\) | −4.92796 | −0.159632 | −0.0798162 | − | 0.996810i | \(-0.525433\pi\) | ||||
−0.0798162 | + | 0.996810i | \(0.525433\pi\) | |||||||
\(954\) | −15.0022 | −0.485715 | ||||||||
\(955\) | −13.4225 | −0.434342 | ||||||||
\(956\) | −44.2781 | −1.43206 | ||||||||
\(957\) | −45.2649 | −1.46321 | ||||||||
\(958\) | 48.2629 | 1.55930 | ||||||||
\(959\) | −44.5199 | −1.43762 | ||||||||
\(960\) | 7.27669 | 0.234854 | ||||||||
\(961\) | −14.1370 | −0.456033 | ||||||||
\(962\) | −1.12733 | −0.0363466 | ||||||||
\(963\) | −17.8878 | −0.576427 | ||||||||
\(964\) | −60.8029 | −1.95833 | ||||||||
\(965\) | 13.6896 | 0.440685 | ||||||||
\(966\) | 15.1026 | 0.485920 | ||||||||
\(967\) | 35.8044 | 1.15139 | 0.575696 | − | 0.817664i | \(-0.304731\pi\) | ||||
0.575696 | + | 0.817664i | \(0.304731\pi\) | |||||||
\(968\) | −47.7380 | −1.53436 | ||||||||
\(969\) | −5.13813 | −0.165061 | ||||||||
\(970\) | −3.04334 | −0.0977157 | ||||||||
\(971\) | 4.09774 | 0.131503 | 0.0657513 | − | 0.997836i | \(-0.479056\pi\) | ||||
0.0657513 | + | 0.997836i | \(0.479056\pi\) | |||||||
\(972\) | 2.71494 | 0.0870818 | ||||||||
\(973\) | −71.2878 | −2.28538 | ||||||||
\(974\) | 48.4523 | 1.55251 | ||||||||
\(975\) | 6.08372 | 0.194835 | ||||||||
\(976\) | −25.7906 | −0.825537 | ||||||||
\(977\) | −17.0903 | −0.546767 | −0.273383 | − | 0.961905i | \(-0.588143\pi\) | ||||
−0.273383 | + | 0.961905i | \(0.588143\pi\) | |||||||
\(978\) | 26.3755 | 0.843395 | ||||||||
\(979\) | −44.3244 | −1.41661 | ||||||||
\(980\) | −13.9628 | −0.446025 | ||||||||
\(981\) | −12.0238 | −0.383890 | ||||||||
\(982\) | −20.5843 | −0.656873 | ||||||||
\(983\) | −43.3420 | −1.38240 | −0.691198 | − | 0.722665i | \(-0.742917\pi\) | ||||
−0.691198 | + | 0.722665i | \(0.742917\pi\) | |||||||
\(984\) | −17.1775 | −0.547598 | ||||||||
\(985\) | −3.01824 | −0.0961692 | ||||||||
\(986\) | 15.2114 | 0.484429 | ||||||||
\(987\) | 7.45539 | 0.237308 | ||||||||
\(988\) | 18.2437 | 0.580410 | ||||||||
\(989\) | 2.55762 | 0.0813274 | ||||||||
\(990\) | 8.27897 | 0.263123 | ||||||||
\(991\) | −35.2139 | −1.11861 | −0.559303 | − | 0.828964i | \(-0.688931\pi\) | ||||
−0.559303 | + | 0.828964i | \(0.688931\pi\) | |||||||
\(992\) | 31.1092 | 0.987717 | ||||||||
\(993\) | 17.0344 | 0.540569 | ||||||||
\(994\) | 0.0707417 | 0.00224379 | ||||||||
\(995\) | −4.66553 | −0.147907 | ||||||||
\(996\) | 16.9629 | 0.537490 | ||||||||
\(997\) | −33.7019 | −1.06735 | −0.533676 | − | 0.845689i | \(-0.679190\pi\) | ||||
−0.533676 | + | 0.845689i | \(0.679190\pi\) | |||||||
\(998\) | 82.8426 | 2.62234 | ||||||||
\(999\) | −0.396977 | −0.0125598 |
(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 | 8007.2.a.d.1.6 | ✓ | 40 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
8007.2.a.d.1.6 | ✓ | 40 | 1.1 | even | 1 | trivial |