Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [8041,2,Mod(1,8041)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(8041, 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("8041.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 8041 = 11 \cdot 17 \cdot 43 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 8041.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: | \(64.2077082653\) |
Analytic rank: | \(0\) |
Dimension: | \(82\) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.6 | ||
Character | \(\chi\) | \(=\) | 8041.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −2.55417 | −1.80607 | −0.903035 | − | 0.429567i | \(-0.858666\pi\) | ||||
−0.903035 | + | 0.429567i | \(0.858666\pi\) | |||||||
\(3\) | −3.23448 | −1.86743 | −0.933713 | − | 0.358023i | \(-0.883451\pi\) | ||||
−0.933713 | + | 0.358023i | \(0.883451\pi\) | |||||||
\(4\) | 4.52378 | 2.26189 | ||||||||
\(5\) | −3.35627 | −1.50097 | −0.750486 | − | 0.660887i | \(-0.770180\pi\) | ||||
−0.750486 | + | 0.660887i | \(0.770180\pi\) | |||||||
\(6\) | 8.26140 | 3.37270 | ||||||||
\(7\) | 1.37818 | 0.520905 | 0.260452 | − | 0.965487i | \(-0.416128\pi\) | ||||
0.260452 | + | 0.965487i | \(0.416128\pi\) | |||||||
\(8\) | −6.44616 | −2.27906 | ||||||||
\(9\) | 7.46183 | 2.48728 | ||||||||
\(10\) | 8.57249 | 2.71086 | ||||||||
\(11\) | 1.00000 | 0.301511 | ||||||||
\(12\) | −14.6321 | −4.22391 | ||||||||
\(13\) | −5.93482 | −1.64602 | −0.823012 | − | 0.568024i | \(-0.807708\pi\) | ||||
−0.823012 | + | 0.568024i | \(0.807708\pi\) | |||||||
\(14\) | −3.52011 | −0.940790 | ||||||||
\(15\) | 10.8558 | 2.80295 | ||||||||
\(16\) | 7.41702 | 1.85425 | ||||||||
\(17\) | 1.00000 | 0.242536 | ||||||||
\(18\) | −19.0588 | −4.49220 | ||||||||
\(19\) | 0.524776 | 0.120392 | 0.0601960 | − | 0.998187i | \(-0.480827\pi\) | ||||
0.0601960 | + | 0.998187i | \(0.480827\pi\) | |||||||
\(20\) | −15.1830 | −3.39503 | ||||||||
\(21\) | −4.45770 | −0.972750 | ||||||||
\(22\) | −2.55417 | −0.544551 | ||||||||
\(23\) | 5.85725 | 1.22132 | 0.610661 | − | 0.791892i | \(-0.290904\pi\) | ||||
0.610661 | + | 0.791892i | \(0.290904\pi\) | |||||||
\(24\) | 20.8499 | 4.25598 | ||||||||
\(25\) | 6.26457 | 1.25291 | ||||||||
\(26\) | 15.1585 | 2.97283 | ||||||||
\(27\) | −14.4317 | −2.77738 | ||||||||
\(28\) | 6.23460 | 1.17823 | ||||||||
\(29\) | −0.806143 | −0.149697 | −0.0748485 | − | 0.997195i | \(-0.523847\pi\) | ||||
−0.0748485 | + | 0.997195i | \(0.523847\pi\) | |||||||
\(30\) | −27.7275 | −5.06233 | ||||||||
\(31\) | −8.85305 | −1.59005 | −0.795027 | − | 0.606574i | \(-0.792543\pi\) | ||||
−0.795027 | + | 0.606574i | \(0.792543\pi\) | |||||||
\(32\) | −6.05200 | −1.06985 | ||||||||
\(33\) | −3.23448 | −0.563050 | ||||||||
\(34\) | −2.55417 | −0.438036 | ||||||||
\(35\) | −4.62556 | −0.781863 | ||||||||
\(36\) | 33.7557 | 5.62595 | ||||||||
\(37\) | −1.29326 | −0.212610 | −0.106305 | − | 0.994334i | \(-0.533902\pi\) | ||||
−0.106305 | + | 0.994334i | \(0.533902\pi\) | |||||||
\(38\) | −1.34037 | −0.217436 | ||||||||
\(39\) | 19.1960 | 3.07383 | ||||||||
\(40\) | 21.6351 | 3.42080 | ||||||||
\(41\) | 11.2002 | 1.74917 | 0.874587 | − | 0.484870i | \(-0.161133\pi\) | ||||
0.874587 | + | 0.484870i | \(0.161133\pi\) | |||||||
\(42\) | 11.3857 | 1.75686 | ||||||||
\(43\) | 1.00000 | 0.152499 | ||||||||
\(44\) | 4.52378 | 0.681985 | ||||||||
\(45\) | −25.0440 | −3.73333 | ||||||||
\(46\) | −14.9604 | −2.20579 | ||||||||
\(47\) | −9.73357 | −1.41979 | −0.709893 | − | 0.704309i | \(-0.751257\pi\) | ||||
−0.709893 | + | 0.704309i | \(0.751257\pi\) | |||||||
\(48\) | −23.9902 | −3.46268 | ||||||||
\(49\) | −5.10061 | −0.728658 | ||||||||
\(50\) | −16.0008 | −2.26285 | ||||||||
\(51\) | −3.23448 | −0.452917 | ||||||||
\(52\) | −26.8478 | −3.72312 | ||||||||
\(53\) | 5.69213 | 0.781874 | 0.390937 | − | 0.920417i | \(-0.372151\pi\) | ||||
0.390937 | + | 0.920417i | \(0.372151\pi\) | |||||||
\(54\) | 36.8610 | 5.01615 | ||||||||
\(55\) | −3.35627 | −0.452560 | ||||||||
\(56\) | −8.88399 | −1.18717 | ||||||||
\(57\) | −1.69738 | −0.224823 | ||||||||
\(58\) | 2.05903 | 0.270363 | ||||||||
\(59\) | 10.4120 | 1.35553 | 0.677763 | − | 0.735281i | \(-0.262950\pi\) | ||||
0.677763 | + | 0.735281i | \(0.262950\pi\) | |||||||
\(60\) | 49.1092 | 6.33997 | ||||||||
\(61\) | −2.19688 | −0.281282 | −0.140641 | − | 0.990061i | \(-0.544916\pi\) | ||||
−0.140641 | + | 0.990061i | \(0.544916\pi\) | |||||||
\(62\) | 22.6122 | 2.87175 | ||||||||
\(63\) | 10.2838 | 1.29563 | ||||||||
\(64\) | 0.623802 | 0.0779752 | ||||||||
\(65\) | 19.9189 | 2.47063 | ||||||||
\(66\) | 8.26140 | 1.01691 | ||||||||
\(67\) | 2.89361 | 0.353511 | 0.176755 | − | 0.984255i | \(-0.443440\pi\) | ||||
0.176755 | + | 0.984255i | \(0.443440\pi\) | |||||||
\(68\) | 4.52378 | 0.548589 | ||||||||
\(69\) | −18.9451 | −2.28073 | ||||||||
\(70\) | 11.8145 | 1.41210 | ||||||||
\(71\) | 8.86691 | 1.05231 | 0.526154 | − | 0.850389i | \(-0.323633\pi\) | ||||
0.526154 | + | 0.850389i | \(0.323633\pi\) | |||||||
\(72\) | −48.1002 | −5.66866 | ||||||||
\(73\) | −11.0044 | −1.28796 | −0.643981 | − | 0.765041i | \(-0.722719\pi\) | ||||
−0.643981 | + | 0.765041i | \(0.722719\pi\) | |||||||
\(74\) | 3.30320 | 0.383989 | ||||||||
\(75\) | −20.2626 | −2.33972 | ||||||||
\(76\) | 2.37397 | 0.272313 | ||||||||
\(77\) | 1.37818 | 0.157059 | ||||||||
\(78\) | −49.0299 | −5.55155 | ||||||||
\(79\) | 11.8348 | 1.33152 | 0.665758 | − | 0.746167i | \(-0.268108\pi\) | ||||
0.665758 | + | 0.746167i | \(0.268108\pi\) | |||||||
\(80\) | −24.8935 | −2.78318 | ||||||||
\(81\) | 24.2935 | 2.69927 | ||||||||
\(82\) | −28.6071 | −3.15913 | ||||||||
\(83\) | −15.7774 | −1.73179 | −0.865895 | − | 0.500226i | \(-0.833250\pi\) | ||||
−0.865895 | + | 0.500226i | \(0.833250\pi\) | |||||||
\(84\) | −20.1657 | −2.20025 | ||||||||
\(85\) | −3.35627 | −0.364039 | ||||||||
\(86\) | −2.55417 | −0.275423 | ||||||||
\(87\) | 2.60745 | 0.279548 | ||||||||
\(88\) | −6.44616 | −0.687163 | ||||||||
\(89\) | −1.57241 | −0.166675 | −0.0833376 | − | 0.996521i | \(-0.526558\pi\) | ||||
−0.0833376 | + | 0.996521i | \(0.526558\pi\) | |||||||
\(90\) | 63.9665 | 6.74266 | ||||||||
\(91\) | −8.17928 | −0.857421 | ||||||||
\(92\) | 26.4969 | 2.76249 | ||||||||
\(93\) | 28.6350 | 2.96931 | ||||||||
\(94\) | 24.8612 | 2.56423 | ||||||||
\(95\) | −1.76129 | −0.180705 | ||||||||
\(96\) | 19.5751 | 1.99787 | ||||||||
\(97\) | 12.2296 | 1.24173 | 0.620864 | − | 0.783918i | \(-0.286782\pi\) | ||||
0.620864 | + | 0.783918i | \(0.286782\pi\) | |||||||
\(98\) | 13.0278 | 1.31601 | ||||||||
\(99\) | 7.46183 | 0.749943 | ||||||||
\(100\) | 28.3395 | 2.83395 | ||||||||
\(101\) | 13.2908 | 1.32249 | 0.661243 | − | 0.750172i | \(-0.270029\pi\) | ||||
0.661243 | + | 0.750172i | \(0.270029\pi\) | |||||||
\(102\) | 8.26140 | 0.818000 | ||||||||
\(103\) | 14.7617 | 1.45451 | 0.727257 | − | 0.686365i | \(-0.240795\pi\) | ||||
0.727257 | + | 0.686365i | \(0.240795\pi\) | |||||||
\(104\) | 38.2568 | 3.75139 | ||||||||
\(105\) | 14.9613 | 1.46007 | ||||||||
\(106\) | −14.5387 | −1.41212 | ||||||||
\(107\) | 1.55105 | 0.149946 | 0.0749730 | − | 0.997186i | \(-0.476113\pi\) | ||||
0.0749730 | + | 0.997186i | \(0.476113\pi\) | |||||||
\(108\) | −65.2858 | −6.28213 | ||||||||
\(109\) | 7.67263 | 0.734904 | 0.367452 | − | 0.930042i | \(-0.380230\pi\) | ||||
0.367452 | + | 0.930042i | \(0.380230\pi\) | |||||||
\(110\) | 8.57249 | 0.817355 | ||||||||
\(111\) | 4.18301 | 0.397034 | ||||||||
\(112\) | 10.2220 | 0.965890 | ||||||||
\(113\) | 7.41517 | 0.697561 | 0.348780 | − | 0.937205i | \(-0.386596\pi\) | ||||
0.348780 | + | 0.937205i | \(0.386596\pi\) | |||||||
\(114\) | 4.33539 | 0.406046 | ||||||||
\(115\) | −19.6585 | −1.83317 | ||||||||
\(116\) | −3.64681 | −0.338598 | ||||||||
\(117\) | −44.2847 | −4.09412 | ||||||||
\(118\) | −26.5940 | −2.44817 | ||||||||
\(119\) | 1.37818 | 0.126338 | ||||||||
\(120\) | −69.9781 | −6.38810 | ||||||||
\(121\) | 1.00000 | 0.0909091 | ||||||||
\(122\) | 5.61120 | 0.508014 | ||||||||
\(123\) | −36.2267 | −3.26645 | ||||||||
\(124\) | −40.0492 | −3.59653 | ||||||||
\(125\) | −4.24425 | −0.379617 | ||||||||
\(126\) | −26.2665 | −2.34001 | ||||||||
\(127\) | 0.552737 | 0.0490474 | 0.0245237 | − | 0.999699i | \(-0.492193\pi\) | ||||
0.0245237 | + | 0.999699i | \(0.492193\pi\) | |||||||
\(128\) | 10.5107 | 0.929025 | ||||||||
\(129\) | −3.23448 | −0.284780 | ||||||||
\(130\) | −50.8762 | −4.46214 | ||||||||
\(131\) | 1.76387 | 0.154110 | 0.0770548 | − | 0.997027i | \(-0.475448\pi\) | ||||
0.0770548 | + | 0.997027i | \(0.475448\pi\) | |||||||
\(132\) | −14.6321 | −1.27356 | ||||||||
\(133\) | 0.723239 | 0.0627127 | ||||||||
\(134\) | −7.39077 | −0.638465 | ||||||||
\(135\) | 48.4367 | 4.16877 | ||||||||
\(136\) | −6.44616 | −0.552754 | ||||||||
\(137\) | 4.44502 | 0.379764 | 0.189882 | − | 0.981807i | \(-0.439189\pi\) | ||||
0.189882 | + | 0.981807i | \(0.439189\pi\) | |||||||
\(138\) | 48.3891 | 4.11915 | ||||||||
\(139\) | −2.58705 | −0.219431 | −0.109715 | − | 0.993963i | \(-0.534994\pi\) | ||||
−0.109715 | + | 0.993963i | \(0.534994\pi\) | |||||||
\(140\) | −20.9250 | −1.76849 | ||||||||
\(141\) | 31.4830 | 2.65135 | ||||||||
\(142\) | −22.6476 | −1.90054 | ||||||||
\(143\) | −5.93482 | −0.496295 | ||||||||
\(144\) | 55.3446 | 4.61205 | ||||||||
\(145\) | 2.70564 | 0.224691 | ||||||||
\(146\) | 28.1070 | 2.32615 | ||||||||
\(147\) | 16.4978 | 1.36072 | ||||||||
\(148\) | −5.85041 | −0.480901 | ||||||||
\(149\) | 0.313474 | 0.0256808 | 0.0128404 | − | 0.999918i | \(-0.495913\pi\) | ||||
0.0128404 | + | 0.999918i | \(0.495913\pi\) | |||||||
\(150\) | 51.7541 | 4.22571 | ||||||||
\(151\) | 5.19538 | 0.422794 | 0.211397 | − | 0.977400i | \(-0.432199\pi\) | ||||
0.211397 | + | 0.977400i | \(0.432199\pi\) | |||||||
\(152\) | −3.38279 | −0.274381 | ||||||||
\(153\) | 7.46183 | 0.603254 | ||||||||
\(154\) | −3.52011 | −0.283659 | ||||||||
\(155\) | 29.7132 | 2.38662 | ||||||||
\(156\) | 86.8387 | 6.95266 | ||||||||
\(157\) | −3.30167 | −0.263502 | −0.131751 | − | 0.991283i | \(-0.542060\pi\) | ||||
−0.131751 | + | 0.991283i | \(0.542060\pi\) | |||||||
\(158\) | −30.2280 | −2.40481 | ||||||||
\(159\) | −18.4111 | −1.46009 | ||||||||
\(160\) | 20.3122 | 1.60582 | ||||||||
\(161\) | 8.07237 | 0.636192 | ||||||||
\(162\) | −62.0496 | −4.87508 | ||||||||
\(163\) | −22.4799 | −1.76076 | −0.880380 | − | 0.474269i | \(-0.842712\pi\) | ||||
−0.880380 | + | 0.474269i | \(0.842712\pi\) | |||||||
\(164\) | 50.6671 | 3.95644 | ||||||||
\(165\) | 10.8558 | 0.845122 | ||||||||
\(166\) | 40.2980 | 3.12773 | ||||||||
\(167\) | 1.31422 | 0.101697 | 0.0508486 | − | 0.998706i | \(-0.483807\pi\) | ||||
0.0508486 | + | 0.998706i | \(0.483807\pi\) | |||||||
\(168\) | 28.7351 | 2.21696 | ||||||||
\(169\) | 22.2221 | 1.70939 | ||||||||
\(170\) | 8.57249 | 0.657480 | ||||||||
\(171\) | 3.91580 | 0.299448 | ||||||||
\(172\) | 4.52378 | 0.344935 | ||||||||
\(173\) | −21.0326 | −1.59908 | −0.799540 | − | 0.600613i | \(-0.794923\pi\) | ||||
−0.799540 | + | 0.600613i | \(0.794923\pi\) | |||||||
\(174\) | −6.65987 | −0.504883 | ||||||||
\(175\) | 8.63373 | 0.652649 | ||||||||
\(176\) | 7.41702 | 0.559079 | ||||||||
\(177\) | −33.6773 | −2.53134 | ||||||||
\(178\) | 4.01620 | 0.301027 | ||||||||
\(179\) | −3.94618 | −0.294952 | −0.147476 | − | 0.989066i | \(-0.547115\pi\) | ||||
−0.147476 | + | 0.989066i | \(0.547115\pi\) | |||||||
\(180\) | −113.293 | −8.44439 | ||||||||
\(181\) | −15.3567 | −1.14145 | −0.570727 | − | 0.821140i | \(-0.693338\pi\) | ||||
−0.570727 | + | 0.821140i | \(0.693338\pi\) | |||||||
\(182\) | 20.8913 | 1.54856 | ||||||||
\(183\) | 7.10575 | 0.525272 | ||||||||
\(184\) | −37.7568 | −2.78347 | ||||||||
\(185\) | 4.34052 | 0.319122 | ||||||||
\(186\) | −73.1385 | −5.36278 | ||||||||
\(187\) | 1.00000 | 0.0731272 | ||||||||
\(188\) | −44.0325 | −3.21140 | ||||||||
\(189\) | −19.8895 | −1.44675 | ||||||||
\(190\) | 4.49864 | 0.326366 | ||||||||
\(191\) | 4.06337 | 0.294015 | 0.147008 | − | 0.989135i | \(-0.453036\pi\) | ||||
0.147008 | + | 0.989135i | \(0.453036\pi\) | |||||||
\(192\) | −2.01767 | −0.145613 | ||||||||
\(193\) | −13.1024 | −0.943133 | −0.471566 | − | 0.881831i | \(-0.656311\pi\) | ||||
−0.471566 | + | 0.881831i | \(0.656311\pi\) | |||||||
\(194\) | −31.2365 | −2.24265 | ||||||||
\(195\) | −64.4272 | −4.61373 | ||||||||
\(196\) | −23.0740 | −1.64814 | ||||||||
\(197\) | 20.1168 | 1.43327 | 0.716633 | − | 0.697451i | \(-0.245682\pi\) | ||||
0.716633 | + | 0.697451i | \(0.245682\pi\) | |||||||
\(198\) | −19.0588 | −1.35445 | ||||||||
\(199\) | −16.5753 | −1.17499 | −0.587496 | − | 0.809227i | \(-0.699886\pi\) | ||||
−0.587496 | + | 0.809227i | \(0.699886\pi\) | |||||||
\(200\) | −40.3824 | −2.85547 | ||||||||
\(201\) | −9.35931 | −0.660155 | ||||||||
\(202\) | −33.9470 | −2.38850 | ||||||||
\(203\) | −1.11101 | −0.0779778 | ||||||||
\(204\) | −14.6321 | −1.02445 | ||||||||
\(205\) | −37.5908 | −2.62546 | ||||||||
\(206\) | −37.7039 | −2.62696 | ||||||||
\(207\) | 43.7058 | 3.03777 | ||||||||
\(208\) | −44.0187 | −3.05215 | ||||||||
\(209\) | 0.524776 | 0.0362995 | ||||||||
\(210\) | −38.2136 | −2.63699 | ||||||||
\(211\) | −0.334550 | −0.0230314 | −0.0115157 | − | 0.999934i | \(-0.503666\pi\) | ||||
−0.0115157 | + | 0.999934i | \(0.503666\pi\) | |||||||
\(212\) | 25.7499 | 1.76851 | ||||||||
\(213\) | −28.6798 | −1.96511 | ||||||||
\(214\) | −3.96165 | −0.270813 | ||||||||
\(215\) | −3.35627 | −0.228896 | ||||||||
\(216\) | 93.0290 | 6.32982 | ||||||||
\(217\) | −12.2011 | −0.828266 | ||||||||
\(218\) | −19.5972 | −1.32729 | ||||||||
\(219\) | 35.5933 | 2.40517 | ||||||||
\(220\) | −15.1830 | −1.02364 | ||||||||
\(221\) | −5.93482 | −0.399219 | ||||||||
\(222\) | −10.6841 | −0.717071 | ||||||||
\(223\) | −5.22511 | −0.349899 | −0.174950 | − | 0.984577i | \(-0.555976\pi\) | ||||
−0.174950 | + | 0.984577i | \(0.555976\pi\) | |||||||
\(224\) | −8.34077 | −0.557291 | ||||||||
\(225\) | 46.7452 | 3.11635 | ||||||||
\(226\) | −18.9396 | −1.25984 | ||||||||
\(227\) | −9.06116 | −0.601410 | −0.300705 | − | 0.953717i | \(-0.597222\pi\) | ||||
−0.300705 | + | 0.953717i | \(0.597222\pi\) | |||||||
\(228\) | −7.67856 | −0.508525 | ||||||||
\(229\) | −2.89718 | −0.191451 | −0.0957257 | − | 0.995408i | \(-0.530517\pi\) | ||||
−0.0957257 | + | 0.995408i | \(0.530517\pi\) | |||||||
\(230\) | 50.2112 | 3.31083 | ||||||||
\(231\) | −4.45770 | −0.293295 | ||||||||
\(232\) | 5.19652 | 0.341169 | ||||||||
\(233\) | −24.5253 | −1.60671 | −0.803354 | − | 0.595502i | \(-0.796953\pi\) | ||||
−0.803354 | + | 0.595502i | \(0.796953\pi\) | |||||||
\(234\) | 113.111 | 7.39427 | ||||||||
\(235\) | 32.6685 | 2.13106 | ||||||||
\(236\) | 47.1015 | 3.06605 | ||||||||
\(237\) | −38.2793 | −2.48651 | ||||||||
\(238\) | −3.52011 | −0.228175 | ||||||||
\(239\) | −8.04199 | −0.520193 | −0.260096 | − | 0.965583i | \(-0.583754\pi\) | ||||
−0.260096 | + | 0.965583i | \(0.583754\pi\) | |||||||
\(240\) | 80.5176 | 5.19739 | ||||||||
\(241\) | −17.3835 | −1.11977 | −0.559885 | − | 0.828570i | \(-0.689155\pi\) | ||||
−0.559885 | + | 0.828570i | \(0.689155\pi\) | |||||||
\(242\) | −2.55417 | −0.164188 | ||||||||
\(243\) | −35.2815 | −2.26331 | ||||||||
\(244\) | −9.93819 | −0.636228 | ||||||||
\(245\) | 17.1190 | 1.09370 | ||||||||
\(246\) | 92.5291 | 5.89944 | ||||||||
\(247\) | −3.11446 | −0.198168 | ||||||||
\(248\) | 57.0681 | 3.62383 | ||||||||
\(249\) | 51.0315 | 3.23399 | ||||||||
\(250\) | 10.8405 | 0.685615 | ||||||||
\(251\) | −23.3782 | −1.47562 | −0.737810 | − | 0.675009i | \(-0.764140\pi\) | ||||
−0.737810 | + | 0.675009i | \(0.764140\pi\) | |||||||
\(252\) | 46.5216 | 2.93058 | ||||||||
\(253\) | 5.85725 | 0.368242 | ||||||||
\(254\) | −1.41178 | −0.0885831 | ||||||||
\(255\) | 10.8558 | 0.679816 | ||||||||
\(256\) | −28.0937 | −1.75586 | ||||||||
\(257\) | 9.17874 | 0.572554 | 0.286277 | − | 0.958147i | \(-0.407582\pi\) | ||||
0.286277 | + | 0.958147i | \(0.407582\pi\) | |||||||
\(258\) | 8.26140 | 0.514332 | ||||||||
\(259\) | −1.78235 | −0.110750 | ||||||||
\(260\) | 90.1087 | 5.58830 | ||||||||
\(261\) | −6.01530 | −0.372338 | ||||||||
\(262\) | −4.50521 | −0.278333 | ||||||||
\(263\) | −25.7970 | −1.59071 | −0.795355 | − | 0.606143i | \(-0.792716\pi\) | ||||
−0.795355 | + | 0.606143i | \(0.792716\pi\) | |||||||
\(264\) | 20.8499 | 1.28323 | ||||||||
\(265\) | −19.1044 | −1.17357 | ||||||||
\(266\) | −1.84727 | −0.113264 | ||||||||
\(267\) | 5.08592 | 0.311254 | ||||||||
\(268\) | 13.0901 | 0.799602 | ||||||||
\(269\) | 8.71268 | 0.531222 | 0.265611 | − | 0.964080i | \(-0.414426\pi\) | ||||
0.265611 | + | 0.964080i | \(0.414426\pi\) | |||||||
\(270\) | −123.716 | −7.52909 | ||||||||
\(271\) | 31.9214 | 1.93909 | 0.969543 | − | 0.244923i | \(-0.0787626\pi\) | ||||
0.969543 | + | 0.244923i | \(0.0787626\pi\) | |||||||
\(272\) | 7.41702 | 0.449723 | ||||||||
\(273\) | 26.4557 | 1.60117 | ||||||||
\(274\) | −11.3533 | −0.685880 | ||||||||
\(275\) | 6.26457 | 0.377768 | ||||||||
\(276\) | −85.7036 | −5.15875 | ||||||||
\(277\) | −22.4204 | −1.34711 | −0.673557 | − | 0.739135i | \(-0.735234\pi\) | ||||
−0.673557 | + | 0.739135i | \(0.735234\pi\) | |||||||
\(278\) | 6.60776 | 0.396307 | ||||||||
\(279\) | −66.0600 | −3.95491 | ||||||||
\(280\) | 29.8171 | 1.78191 | ||||||||
\(281\) | −6.59654 | −0.393516 | −0.196758 | − | 0.980452i | \(-0.563041\pi\) | ||||
−0.196758 | + | 0.980452i | \(0.563041\pi\) | |||||||
\(282\) | −80.4129 | −4.78852 | ||||||||
\(283\) | 1.26338 | 0.0750999 | 0.0375500 | − | 0.999295i | \(-0.488045\pi\) | ||||
0.0375500 | + | 0.999295i | \(0.488045\pi\) | |||||||
\(284\) | 40.1119 | 2.38021 | ||||||||
\(285\) | 5.69686 | 0.337453 | ||||||||
\(286\) | 15.1585 | 0.896343 | ||||||||
\(287\) | 15.4359 | 0.911152 | ||||||||
\(288\) | −45.1590 | −2.66102 | ||||||||
\(289\) | 1.00000 | 0.0588235 | ||||||||
\(290\) | −6.91065 | −0.405807 | ||||||||
\(291\) | −39.5564 | −2.31884 | ||||||||
\(292\) | −49.7813 | −2.91323 | ||||||||
\(293\) | 31.0522 | 1.81409 | 0.907043 | − | 0.421037i | \(-0.138334\pi\) | ||||
0.907043 | + | 0.421037i | \(0.138334\pi\) | |||||||
\(294\) | −42.1382 | −2.45755 | ||||||||
\(295\) | −34.9455 | −2.03460 | ||||||||
\(296\) | 8.33654 | 0.484552 | ||||||||
\(297\) | −14.4317 | −0.837412 | ||||||||
\(298\) | −0.800665 | −0.0463813 | ||||||||
\(299\) | −34.7617 | −2.01032 | ||||||||
\(300\) | −91.6636 | −5.29220 | ||||||||
\(301\) | 1.37818 | 0.0794372 | ||||||||
\(302\) | −13.2699 | −0.763596 | ||||||||
\(303\) | −42.9888 | −2.46964 | ||||||||
\(304\) | 3.89228 | 0.223237 | ||||||||
\(305\) | 7.37333 | 0.422195 | ||||||||
\(306\) | −19.0588 | −1.08952 | ||||||||
\(307\) | 20.5178 | 1.17101 | 0.585506 | − | 0.810668i | \(-0.300896\pi\) | ||||
0.585506 | + | 0.810668i | \(0.300896\pi\) | |||||||
\(308\) | 6.23460 | 0.355249 | ||||||||
\(309\) | −47.7464 | −2.71620 | ||||||||
\(310\) | −75.8926 | −4.31041 | ||||||||
\(311\) | −14.8101 | −0.839806 | −0.419903 | − | 0.907569i | \(-0.637936\pi\) | ||||
−0.419903 | + | 0.907569i | \(0.637936\pi\) | |||||||
\(312\) | −123.741 | −7.00544 | ||||||||
\(313\) | 32.8935 | 1.85925 | 0.929626 | − | 0.368505i | \(-0.120130\pi\) | ||||
0.929626 | + | 0.368505i | \(0.120130\pi\) | |||||||
\(314\) | 8.43303 | 0.475903 | ||||||||
\(315\) | −34.5152 | −1.94471 | ||||||||
\(316\) | 53.5379 | 3.01174 | ||||||||
\(317\) | 7.02870 | 0.394771 | 0.197386 | − | 0.980326i | \(-0.436755\pi\) | ||||
0.197386 | + | 0.980326i | \(0.436755\pi\) | |||||||
\(318\) | 47.0250 | 2.63703 | ||||||||
\(319\) | −0.806143 | −0.0451353 | ||||||||
\(320\) | −2.09365 | −0.117039 | ||||||||
\(321\) | −5.01684 | −0.280013 | ||||||||
\(322\) | −20.6182 | −1.14901 | ||||||||
\(323\) | 0.524776 | 0.0291993 | ||||||||
\(324\) | 109.898 | 6.10546 | ||||||||
\(325\) | −37.1791 | −2.06233 | ||||||||
\(326\) | 57.4174 | 3.18006 | ||||||||
\(327\) | −24.8169 | −1.37238 | ||||||||
\(328\) | −72.1981 | −3.98647 | ||||||||
\(329\) | −13.4146 | −0.739574 | ||||||||
\(330\) | −27.7275 | −1.52635 | ||||||||
\(331\) | 12.0888 | 0.664463 | 0.332231 | − | 0.943198i | \(-0.392199\pi\) | ||||
0.332231 | + | 0.943198i | \(0.392199\pi\) | |||||||
\(332\) | −71.3733 | −3.91712 | ||||||||
\(333\) | −9.65007 | −0.528821 | ||||||||
\(334\) | −3.35673 | −0.183672 | ||||||||
\(335\) | −9.71175 | −0.530610 | ||||||||
\(336\) | −33.0629 | −1.80373 | ||||||||
\(337\) | −13.8127 | −0.752424 | −0.376212 | − | 0.926534i | \(-0.622774\pi\) | ||||
−0.376212 | + | 0.926534i | \(0.622774\pi\) | |||||||
\(338\) | −56.7591 | −3.08729 | ||||||||
\(339\) | −23.9842 | −1.30264 | ||||||||
\(340\) | −15.1830 | −0.823416 | ||||||||
\(341\) | −8.85305 | −0.479419 | ||||||||
\(342\) | −10.0016 | −0.540825 | ||||||||
\(343\) | −16.6769 | −0.900466 | ||||||||
\(344\) | −6.44616 | −0.347554 | ||||||||
\(345\) | 63.5850 | 3.42330 | ||||||||
\(346\) | 53.7209 | 2.88805 | ||||||||
\(347\) | −8.94658 | −0.480277 | −0.240139 | − | 0.970739i | \(-0.577193\pi\) | ||||
−0.240139 | + | 0.970739i | \(0.577193\pi\) | |||||||
\(348\) | 11.7955 | 0.632307 | ||||||||
\(349\) | 8.83961 | 0.473174 | 0.236587 | − | 0.971610i | \(-0.423971\pi\) | ||||
0.236587 | + | 0.971610i | \(0.423971\pi\) | |||||||
\(350\) | −22.0520 | −1.17873 | ||||||||
\(351\) | 85.6496 | 4.57164 | ||||||||
\(352\) | −6.05200 | −0.322573 | ||||||||
\(353\) | −11.6584 | −0.620513 | −0.310257 | − | 0.950653i | \(-0.600415\pi\) | ||||
−0.310257 | + | 0.950653i | \(0.600415\pi\) | |||||||
\(354\) | 86.0176 | 4.57178 | ||||||||
\(355\) | −29.7598 | −1.57948 | ||||||||
\(356\) | −7.11324 | −0.377001 | ||||||||
\(357\) | −4.45770 | −0.235927 | ||||||||
\(358\) | 10.0792 | 0.532703 | ||||||||
\(359\) | 7.79998 | 0.411667 | 0.205834 | − | 0.978587i | \(-0.434009\pi\) | ||||
0.205834 | + | 0.978587i | \(0.434009\pi\) | |||||||
\(360\) | 161.437 | 8.50849 | ||||||||
\(361\) | −18.7246 | −0.985506 | ||||||||
\(362\) | 39.2236 | 2.06154 | ||||||||
\(363\) | −3.23448 | −0.169766 | ||||||||
\(364\) | −37.0013 | −1.93939 | ||||||||
\(365\) | 36.9336 | 1.93319 | ||||||||
\(366\) | −18.1493 | −0.948679 | ||||||||
\(367\) | −18.7115 | −0.976731 | −0.488366 | − | 0.872639i | \(-0.662407\pi\) | ||||
−0.488366 | + | 0.872639i | \(0.662407\pi\) | |||||||
\(368\) | 43.4433 | 2.26464 | ||||||||
\(369\) | 83.5738 | 4.35068 | ||||||||
\(370\) | −11.0864 | −0.576356 | ||||||||
\(371\) | 7.84481 | 0.407282 | ||||||||
\(372\) | 129.538 | 6.71624 | ||||||||
\(373\) | −15.9039 | −0.823475 | −0.411738 | − | 0.911302i | \(-0.635078\pi\) | ||||
−0.411738 | + | 0.911302i | \(0.635078\pi\) | |||||||
\(374\) | −2.55417 | −0.132073 | ||||||||
\(375\) | 13.7279 | 0.708907 | ||||||||
\(376\) | 62.7441 | 3.23578 | ||||||||
\(377\) | 4.78432 | 0.246405 | ||||||||
\(378\) | 50.8012 | 2.61293 | ||||||||
\(379\) | 11.1411 | 0.572278 | 0.286139 | − | 0.958188i | \(-0.407628\pi\) | ||||
0.286139 | + | 0.958188i | \(0.407628\pi\) | |||||||
\(380\) | −7.96770 | −0.408735 | ||||||||
\(381\) | −1.78781 | −0.0915925 | ||||||||
\(382\) | −10.3785 | −0.531012 | ||||||||
\(383\) | −3.19351 | −0.163181 | −0.0815905 | − | 0.996666i | \(-0.526000\pi\) | ||||
−0.0815905 | + | 0.996666i | \(0.526000\pi\) | |||||||
\(384\) | −33.9966 | −1.73488 | ||||||||
\(385\) | −4.62556 | −0.235740 | ||||||||
\(386\) | 33.4658 | 1.70336 | ||||||||
\(387\) | 7.46183 | 0.379306 | ||||||||
\(388\) | 55.3240 | 2.80865 | ||||||||
\(389\) | 1.08134 | 0.0548260 | 0.0274130 | − | 0.999624i | \(-0.491273\pi\) | ||||
0.0274130 | + | 0.999624i | \(0.491273\pi\) | |||||||
\(390\) | 164.558 | 8.33271 | ||||||||
\(391\) | 5.85725 | 0.296214 | ||||||||
\(392\) | 32.8793 | 1.66066 | ||||||||
\(393\) | −5.70518 | −0.287788 | ||||||||
\(394\) | −51.3818 | −2.58858 | ||||||||
\(395\) | −39.7208 | −1.99857 | ||||||||
\(396\) | 33.7557 | 1.69629 | ||||||||
\(397\) | −31.7452 | −1.59325 | −0.796624 | − | 0.604475i | \(-0.793383\pi\) | ||||
−0.796624 | + | 0.604475i | \(0.793383\pi\) | |||||||
\(398\) | 42.3361 | 2.12212 | ||||||||
\(399\) | −2.33930 | −0.117111 | ||||||||
\(400\) | 46.4644 | 2.32322 | ||||||||
\(401\) | −27.3622 | −1.36640 | −0.683201 | − | 0.730231i | \(-0.739413\pi\) | ||||
−0.683201 | + | 0.730231i | \(0.739413\pi\) | |||||||
\(402\) | 23.9053 | 1.19229 | ||||||||
\(403\) | 52.5413 | 2.61727 | ||||||||
\(404\) | 60.1247 | 2.99132 | ||||||||
\(405\) | −81.5355 | −4.05153 | ||||||||
\(406\) | 2.83772 | 0.140833 | ||||||||
\(407\) | −1.29326 | −0.0641044 | ||||||||
\(408\) | 20.8499 | 1.03223 | ||||||||
\(409\) | 10.0088 | 0.494903 | 0.247451 | − | 0.968900i | \(-0.420407\pi\) | ||||
0.247451 | + | 0.968900i | \(0.420407\pi\) | |||||||
\(410\) | 96.0134 | 4.74176 | ||||||||
\(411\) | −14.3773 | −0.709181 | ||||||||
\(412\) | 66.7787 | 3.28995 | ||||||||
\(413\) | 14.3496 | 0.706100 | ||||||||
\(414\) | −111.632 | −5.48642 | ||||||||
\(415\) | 52.9531 | 2.59937 | ||||||||
\(416\) | 35.9176 | 1.76100 | ||||||||
\(417\) | 8.36775 | 0.409771 | ||||||||
\(418\) | −1.34037 | −0.0655595 | ||||||||
\(419\) | −30.7938 | −1.50438 | −0.752188 | − | 0.658948i | \(-0.771002\pi\) | ||||
−0.752188 | + | 0.658948i | \(0.771002\pi\) | |||||||
\(420\) | 67.6815 | 3.30252 | ||||||||
\(421\) | −20.8669 | −1.01699 | −0.508495 | − | 0.861065i | \(-0.669798\pi\) | ||||
−0.508495 | + | 0.861065i | \(0.669798\pi\) | |||||||
\(422\) | 0.854497 | 0.0415963 | ||||||||
\(423\) | −72.6303 | −3.53140 | ||||||||
\(424\) | −36.6924 | −1.78194 | ||||||||
\(425\) | 6.26457 | 0.303876 | ||||||||
\(426\) | 73.2530 | 3.54912 | ||||||||
\(427\) | −3.02770 | −0.146521 | ||||||||
\(428\) | 7.01662 | 0.339161 | ||||||||
\(429\) | 19.1960 | 0.926794 | ||||||||
\(430\) | 8.57249 | 0.413402 | ||||||||
\(431\) | 5.79030 | 0.278909 | 0.139455 | − | 0.990228i | \(-0.455465\pi\) | ||||
0.139455 | + | 0.990228i | \(0.455465\pi\) | |||||||
\(432\) | −107.040 | −5.14997 | ||||||||
\(433\) | −23.5918 | −1.13375 | −0.566875 | − | 0.823804i | \(-0.691848\pi\) | ||||
−0.566875 | + | 0.823804i | \(0.691848\pi\) | |||||||
\(434\) | 31.1637 | 1.49591 | ||||||||
\(435\) | −8.75131 | −0.419593 | ||||||||
\(436\) | 34.7093 | 1.66227 | ||||||||
\(437\) | 3.07375 | 0.147037 | ||||||||
\(438\) | −90.9114 | −4.34391 | ||||||||
\(439\) | −16.9166 | −0.807388 | −0.403694 | − | 0.914894i | \(-0.632274\pi\) | ||||
−0.403694 | + | 0.914894i | \(0.632274\pi\) | |||||||
\(440\) | 21.6351 | 1.03141 | ||||||||
\(441\) | −38.0599 | −1.81238 | ||||||||
\(442\) | 15.1585 | 0.721018 | ||||||||
\(443\) | 6.90701 | 0.328162 | 0.164081 | − | 0.986447i | \(-0.447534\pi\) | ||||
0.164081 | + | 0.986447i | \(0.447534\pi\) | |||||||
\(444\) | 18.9230 | 0.898046 | ||||||||
\(445\) | 5.27744 | 0.250175 | ||||||||
\(446\) | 13.3458 | 0.631942 | ||||||||
\(447\) | −1.01392 | −0.0479569 | ||||||||
\(448\) | 0.859714 | 0.0406176 | ||||||||
\(449\) | 34.7352 | 1.63926 | 0.819628 | − | 0.572897i | \(-0.194180\pi\) | ||||
0.819628 | + | 0.572897i | \(0.194180\pi\) | |||||||
\(450\) | −119.395 | −5.62834 | ||||||||
\(451\) | 11.2002 | 0.527396 | ||||||||
\(452\) | 33.5446 | 1.57781 | ||||||||
\(453\) | −16.8043 | −0.789537 | ||||||||
\(454\) | 23.1437 | 1.08619 | ||||||||
\(455\) | 27.4519 | 1.28696 | ||||||||
\(456\) | 10.9416 | 0.512385 | ||||||||
\(457\) | 32.3147 | 1.51162 | 0.755809 | − | 0.654793i | \(-0.227244\pi\) | ||||
0.755809 | + | 0.654793i | \(0.227244\pi\) | |||||||
\(458\) | 7.39990 | 0.345775 | ||||||||
\(459\) | −14.4317 | −0.673614 | ||||||||
\(460\) | −88.9309 | −4.14642 | ||||||||
\(461\) | 10.8304 | 0.504422 | 0.252211 | − | 0.967672i | \(-0.418842\pi\) | ||||
0.252211 | + | 0.967672i | \(0.418842\pi\) | |||||||
\(462\) | 11.3857 | 0.529712 | ||||||||
\(463\) | 24.5364 | 1.14030 | 0.570152 | − | 0.821539i | \(-0.306884\pi\) | ||||
0.570152 | + | 0.821539i | \(0.306884\pi\) | |||||||
\(464\) | −5.97918 | −0.277576 | ||||||||
\(465\) | −96.1068 | −4.45684 | ||||||||
\(466\) | 62.6419 | 2.90183 | ||||||||
\(467\) | −26.1616 | −1.21062 | −0.605308 | − | 0.795991i | \(-0.706950\pi\) | ||||
−0.605308 | + | 0.795991i | \(0.706950\pi\) | |||||||
\(468\) | −200.334 | −9.26045 | ||||||||
\(469\) | 3.98793 | 0.184145 | ||||||||
\(470\) | −83.4409 | −3.84884 | ||||||||
\(471\) | 10.6792 | 0.492071 | ||||||||
\(472\) | −67.1173 | −3.08933 | ||||||||
\(473\) | 1.00000 | 0.0459800 | ||||||||
\(474\) | 97.7718 | 4.49081 | ||||||||
\(475\) | 3.28750 | 0.150841 | ||||||||
\(476\) | 6.23460 | 0.285762 | ||||||||
\(477\) | 42.4737 | 1.94474 | ||||||||
\(478\) | 20.5406 | 0.939505 | ||||||||
\(479\) | 18.2621 | 0.834415 | 0.417208 | − | 0.908811i | \(-0.363009\pi\) | ||||
0.417208 | + | 0.908811i | \(0.363009\pi\) | |||||||
\(480\) | −65.6993 | −2.99875 | ||||||||
\(481\) | 7.67525 | 0.349961 | ||||||||
\(482\) | 44.4004 | 2.02238 | ||||||||
\(483\) | −26.1099 | −1.18804 | ||||||||
\(484\) | 4.52378 | 0.205626 | ||||||||
\(485\) | −41.0459 | −1.86380 | ||||||||
\(486\) | 90.1150 | 4.08770 | ||||||||
\(487\) | 21.4633 | 0.972597 | 0.486298 | − | 0.873793i | \(-0.338347\pi\) | ||||
0.486298 | + | 0.873793i | \(0.338347\pi\) | |||||||
\(488\) | 14.1614 | 0.641058 | ||||||||
\(489\) | 72.7106 | 3.28809 | ||||||||
\(490\) | −43.7249 | −1.97529 | ||||||||
\(491\) | −32.7277 | −1.47698 | −0.738490 | − | 0.674264i | \(-0.764461\pi\) | ||||
−0.738490 | + | 0.674264i | \(0.764461\pi\) | |||||||
\(492\) | −163.882 | −7.38835 | ||||||||
\(493\) | −0.806143 | −0.0363068 | ||||||||
\(494\) | 7.95485 | 0.357905 | ||||||||
\(495\) | −25.0440 | −1.12564 | ||||||||
\(496\) | −65.6632 | −2.94836 | ||||||||
\(497\) | 12.2202 | 0.548152 | ||||||||
\(498\) | −130.343 | −5.84081 | ||||||||
\(499\) | −35.9455 | −1.60914 | −0.804571 | − | 0.593857i | \(-0.797605\pi\) | ||||
−0.804571 | + | 0.593857i | \(0.797605\pi\) | |||||||
\(500\) | −19.2000 | −0.858652 | ||||||||
\(501\) | −4.25080 | −0.189912 | ||||||||
\(502\) | 59.7119 | 2.66507 | ||||||||
\(503\) | 21.9715 | 0.979662 | 0.489831 | − | 0.871818i | \(-0.337059\pi\) | ||||
0.489831 | + | 0.871818i | \(0.337059\pi\) | |||||||
\(504\) | −66.2909 | −2.95283 | ||||||||
\(505\) | −44.6076 | −1.98501 | ||||||||
\(506\) | −14.9604 | −0.665071 | ||||||||
\(507\) | −71.8770 | −3.19217 | ||||||||
\(508\) | 2.50046 | 0.110940 | ||||||||
\(509\) | 20.5308 | 0.910010 | 0.455005 | − | 0.890489i | \(-0.349637\pi\) | ||||
0.455005 | + | 0.890489i | \(0.349637\pi\) | |||||||
\(510\) | −27.7275 | −1.22779 | ||||||||
\(511\) | −15.1660 | −0.670906 | ||||||||
\(512\) | 50.7347 | 2.24218 | ||||||||
\(513\) | −7.57341 | −0.334374 | ||||||||
\(514\) | −23.4441 | −1.03407 | ||||||||
\(515\) | −49.5443 | −2.18318 | ||||||||
\(516\) | −14.6321 | −0.644140 | ||||||||
\(517\) | −9.73357 | −0.428082 | ||||||||
\(518\) | 4.55241 | 0.200022 | ||||||||
\(519\) | 68.0295 | 2.98616 | ||||||||
\(520\) | −128.400 | −5.63073 | ||||||||
\(521\) | 26.5945 | 1.16512 | 0.582562 | − | 0.812786i | \(-0.302050\pi\) | ||||
0.582562 | + | 0.812786i | \(0.302050\pi\) | |||||||
\(522\) | 15.3641 | 0.672469 | ||||||||
\(523\) | −9.86949 | −0.431563 | −0.215781 | − | 0.976442i | \(-0.569230\pi\) | ||||
−0.215781 | + | 0.976442i | \(0.569230\pi\) | |||||||
\(524\) | 7.97934 | 0.348579 | ||||||||
\(525\) | −27.9256 | −1.21877 | ||||||||
\(526\) | 65.8899 | 2.87294 | ||||||||
\(527\) | −8.85305 | −0.385645 | ||||||||
\(528\) | −23.9902 | −1.04404 | ||||||||
\(529\) | 11.3074 | 0.491625 | ||||||||
\(530\) | 48.7957 | 2.11955 | ||||||||
\(531\) | 77.6925 | 3.37157 | ||||||||
\(532\) | 3.27177 | 0.141849 | ||||||||
\(533\) | −66.4710 | −2.87918 | ||||||||
\(534\) | −12.9903 | −0.562146 | ||||||||
\(535\) | −5.20576 | −0.225065 | ||||||||
\(536\) | −18.6527 | −0.805673 | ||||||||
\(537\) | 12.7638 | 0.550800 | ||||||||
\(538\) | −22.2537 | −0.959423 | ||||||||
\(539\) | −5.10061 | −0.219699 | ||||||||
\(540\) | 219.117 | 9.42929 | ||||||||
\(541\) | 0.336012 | 0.0144463 | 0.00722315 | − | 0.999974i | \(-0.497701\pi\) | ||||
0.00722315 | + | 0.999974i | \(0.497701\pi\) | |||||||
\(542\) | −81.5326 | −3.50212 | ||||||||
\(543\) | 49.6708 | 2.13158 | ||||||||
\(544\) | −6.05200 | −0.259478 | ||||||||
\(545\) | −25.7514 | −1.10307 | ||||||||
\(546\) | −67.5723 | −2.89183 | ||||||||
\(547\) | −21.9888 | −0.940172 | −0.470086 | − | 0.882621i | \(-0.655777\pi\) | ||||
−0.470086 | + | 0.882621i | \(0.655777\pi\) | |||||||
\(548\) | 20.1083 | 0.858984 | ||||||||
\(549\) | −16.3927 | −0.699625 | ||||||||
\(550\) | −16.0008 | −0.682275 | ||||||||
\(551\) | −0.423045 | −0.0180223 | ||||||||
\(552\) | 122.123 | 5.19791 | ||||||||
\(553\) | 16.3105 | 0.693593 | ||||||||
\(554\) | 57.2656 | 2.43298 | ||||||||
\(555\) | −14.0393 | −0.595936 | ||||||||
\(556\) | −11.7032 | −0.496328 | ||||||||
\(557\) | 5.51343 | 0.233611 | 0.116806 | − | 0.993155i | \(-0.462735\pi\) | ||||
0.116806 | + | 0.993155i | \(0.462735\pi\) | |||||||
\(558\) | 168.728 | 7.14284 | ||||||||
\(559\) | −5.93482 | −0.251016 | ||||||||
\(560\) | −34.3079 | −1.44977 | ||||||||
\(561\) | −3.23448 | −0.136560 | ||||||||
\(562\) | 16.8487 | 0.710718 | ||||||||
\(563\) | 10.9402 | 0.461075 | 0.230537 | − | 0.973063i | \(-0.425952\pi\) | ||||
0.230537 | + | 0.973063i | \(0.425952\pi\) | |||||||
\(564\) | 142.422 | 5.99705 | ||||||||
\(565\) | −24.8873 | −1.04702 | ||||||||
\(566\) | −3.22688 | −0.135636 | ||||||||
\(567\) | 33.4809 | 1.40606 | ||||||||
\(568\) | −57.1575 | −2.39827 | ||||||||
\(569\) | −46.1074 | −1.93292 | −0.966462 | − | 0.256809i | \(-0.917329\pi\) | ||||
−0.966462 | + | 0.256809i | \(0.917329\pi\) | |||||||
\(570\) | −14.5507 | −0.609464 | ||||||||
\(571\) | −10.8126 | −0.452493 | −0.226247 | − | 0.974070i | \(-0.572646\pi\) | ||||
−0.226247 | + | 0.974070i | \(0.572646\pi\) | |||||||
\(572\) | −26.8478 | −1.12256 | ||||||||
\(573\) | −13.1429 | −0.549052 | ||||||||
\(574\) | −39.4259 | −1.64560 | ||||||||
\(575\) | 36.6932 | 1.53021 | ||||||||
\(576\) | 4.65471 | 0.193946 | ||||||||
\(577\) | 28.4683 | 1.18515 | 0.592575 | − | 0.805515i | \(-0.298111\pi\) | ||||
0.592575 | + | 0.805515i | \(0.298111\pi\) | |||||||
\(578\) | −2.55417 | −0.106239 | ||||||||
\(579\) | 42.3795 | 1.76123 | ||||||||
\(580\) | 12.2397 | 0.508226 | ||||||||
\(581\) | −21.7441 | −0.902097 | ||||||||
\(582\) | 101.034 | 4.18798 | ||||||||
\(583\) | 5.69213 | 0.235744 | ||||||||
\(584\) | 70.9358 | 2.93535 | ||||||||
\(585\) | 148.631 | 6.14515 | ||||||||
\(586\) | −79.3125 | −3.27637 | ||||||||
\(587\) | 48.2610 | 1.99194 | 0.995971 | − | 0.0896706i | \(-0.0285814\pi\) | ||||
0.995971 | + | 0.0896706i | \(0.0285814\pi\) | |||||||
\(588\) | 74.6324 | 3.07779 | ||||||||
\(589\) | −4.64587 | −0.191430 | ||||||||
\(590\) | 89.2567 | 3.67464 | ||||||||
\(591\) | −65.0674 | −2.67652 | ||||||||
\(592\) | −9.59211 | −0.394233 | ||||||||
\(593\) | 37.0365 | 1.52091 | 0.760454 | − | 0.649392i | \(-0.224977\pi\) | ||||
0.760454 | + | 0.649392i | \(0.224977\pi\) | |||||||
\(594\) | 36.8610 | 1.51242 | ||||||||
\(595\) | −4.62556 | −0.189630 | ||||||||
\(596\) | 1.41809 | 0.0580871 | ||||||||
\(597\) | 53.6124 | 2.19421 | ||||||||
\(598\) | 88.7874 | 3.63079 | ||||||||
\(599\) | 23.3037 | 0.952165 | 0.476082 | − | 0.879401i | \(-0.342056\pi\) | ||||
0.476082 | + | 0.879401i | \(0.342056\pi\) | |||||||
\(600\) | 130.616 | 5.33237 | ||||||||
\(601\) | 36.3416 | 1.48240 | 0.741202 | − | 0.671282i | \(-0.234256\pi\) | ||||
0.741202 | + | 0.671282i | \(0.234256\pi\) | |||||||
\(602\) | −3.52011 | −0.143469 | ||||||||
\(603\) | 21.5916 | 0.879280 | ||||||||
\(604\) | 23.5028 | 0.956314 | ||||||||
\(605\) | −3.35627 | −0.136452 | ||||||||
\(606\) | 109.801 | 4.46035 | ||||||||
\(607\) | −44.7723 | −1.81725 | −0.908627 | − | 0.417609i | \(-0.862868\pi\) | ||||
−0.908627 | + | 0.417609i | \(0.862868\pi\) | |||||||
\(608\) | −3.17595 | −0.128802 | ||||||||
\(609\) | 3.59355 | 0.145618 | ||||||||
\(610\) | −18.8327 | −0.762515 | ||||||||
\(611\) | 57.7670 | 2.33700 | ||||||||
\(612\) | 33.7557 | 1.36449 | ||||||||
\(613\) | 22.4024 | 0.904823 | 0.452411 | − | 0.891809i | \(-0.350564\pi\) | ||||
0.452411 | + | 0.891809i | \(0.350564\pi\) | |||||||
\(614\) | −52.4059 | −2.11493 | ||||||||
\(615\) | 121.587 | 4.90285 | ||||||||
\(616\) | −8.88399 | −0.357946 | ||||||||
\(617\) | −24.7601 | −0.996805 | −0.498403 | − | 0.866946i | \(-0.666080\pi\) | ||||
−0.498403 | + | 0.866946i | \(0.666080\pi\) | |||||||
\(618\) | 121.952 | 4.90564 | ||||||||
\(619\) | 5.72666 | 0.230174 | 0.115087 | − | 0.993355i | \(-0.463285\pi\) | ||||
0.115087 | + | 0.993355i | \(0.463285\pi\) | |||||||
\(620\) | 134.416 | 5.39828 | ||||||||
\(621\) | −84.5300 | −3.39207 | ||||||||
\(622\) | 37.8276 | 1.51675 | ||||||||
\(623\) | −2.16707 | −0.0868219 | ||||||||
\(624\) | 142.377 | 5.69966 | ||||||||
\(625\) | −17.0780 | −0.683120 | ||||||||
\(626\) | −84.0156 | −3.35794 | ||||||||
\(627\) | −1.69738 | −0.0677867 | ||||||||
\(628\) | −14.9360 | −0.596013 | ||||||||
\(629\) | −1.29326 | −0.0515655 | ||||||||
\(630\) | 88.1576 | 3.51228 | ||||||||
\(631\) | −17.6119 | −0.701118 | −0.350559 | − | 0.936541i | \(-0.614008\pi\) | ||||
−0.350559 | + | 0.936541i | \(0.614008\pi\) | |||||||
\(632\) | −76.2889 | −3.03461 | ||||||||
\(633\) | 1.08209 | 0.0430094 | ||||||||
\(634\) | −17.9525 | −0.712984 | ||||||||
\(635\) | −1.85514 | −0.0736188 | ||||||||
\(636\) | −83.2876 | −3.30257 | ||||||||
\(637\) | 30.2712 | 1.19939 | ||||||||
\(638\) | 2.05903 | 0.0815176 | ||||||||
\(639\) | 66.1634 | 2.61738 | ||||||||
\(640\) | −35.2768 | −1.39444 | ||||||||
\(641\) | −5.36006 | −0.211710 | −0.105855 | − | 0.994382i | \(-0.533758\pi\) | ||||
−0.105855 | + | 0.994382i | \(0.533758\pi\) | |||||||
\(642\) | 12.8139 | 0.505723 | ||||||||
\(643\) | −23.4496 | −0.924760 | −0.462380 | − | 0.886682i | \(-0.653004\pi\) | ||||
−0.462380 | + | 0.886682i | \(0.653004\pi\) | |||||||
\(644\) | 36.5176 | 1.43900 | ||||||||
\(645\) | 10.8558 | 0.427446 | ||||||||
\(646\) | −1.34037 | −0.0527361 | ||||||||
\(647\) | 21.7715 | 0.855926 | 0.427963 | − | 0.903796i | \(-0.359231\pi\) | ||||
0.427963 | + | 0.903796i | \(0.359231\pi\) | |||||||
\(648\) | −156.600 | −6.15181 | ||||||||
\(649\) | 10.4120 | 0.408706 | ||||||||
\(650\) | 94.9618 | 3.72471 | ||||||||
\(651\) | 39.4642 | 1.54673 | ||||||||
\(652\) | −101.694 | −3.98264 | ||||||||
\(653\) | 7.20019 | 0.281765 | 0.140883 | − | 0.990026i | \(-0.455006\pi\) | ||||
0.140883 | + | 0.990026i | \(0.455006\pi\) | |||||||
\(654\) | 63.3866 | 2.47861 | ||||||||
\(655\) | −5.92001 | −0.231314 | ||||||||
\(656\) | 83.0719 | 3.24341 | ||||||||
\(657\) | −82.1127 | −3.20352 | ||||||||
\(658\) | 34.2633 | 1.33572 | ||||||||
\(659\) | 7.27702 | 0.283472 | 0.141736 | − | 0.989904i | \(-0.454732\pi\) | ||||
0.141736 | + | 0.989904i | \(0.454732\pi\) | |||||||
\(660\) | 49.1092 | 1.91157 | ||||||||
\(661\) | −8.85333 | −0.344355 | −0.172177 | − | 0.985066i | \(-0.555080\pi\) | ||||
−0.172177 | + | 0.985066i | \(0.555080\pi\) | |||||||
\(662\) | −30.8769 | −1.20007 | ||||||||
\(663\) | 19.1960 | 0.745513 | ||||||||
\(664\) | 101.703 | 3.94686 | ||||||||
\(665\) | −2.42739 | −0.0941300 | ||||||||
\(666\) | 24.6479 | 0.955087 | ||||||||
\(667\) | −4.72178 | −0.182828 | ||||||||
\(668\) | 5.94523 | 0.230028 | ||||||||
\(669\) | 16.9005 | 0.653411 | ||||||||
\(670\) | 24.8054 | 0.958318 | ||||||||
\(671\) | −2.19688 | −0.0848096 | ||||||||
\(672\) | 26.9780 | 1.04070 | ||||||||
\(673\) | −40.1144 | −1.54630 | −0.773148 | − | 0.634225i | \(-0.781319\pi\) | ||||
−0.773148 | + | 0.634225i | \(0.781319\pi\) | |||||||
\(674\) | 35.2799 | 1.35893 | ||||||||
\(675\) | −90.4084 | −3.47982 | ||||||||
\(676\) | 100.528 | 3.86646 | ||||||||
\(677\) | −38.9840 | −1.49828 | −0.749139 | − | 0.662413i | \(-0.769532\pi\) | ||||
−0.749139 | + | 0.662413i | \(0.769532\pi\) | |||||||
\(678\) | 61.2597 | 2.35266 | ||||||||
\(679\) | 16.8546 | 0.646822 | ||||||||
\(680\) | 21.6351 | 0.829667 | ||||||||
\(681\) | 29.3081 | 1.12309 | ||||||||
\(682\) | 22.6122 | 0.865865 | ||||||||
\(683\) | −25.9123 | −0.991506 | −0.495753 | − | 0.868464i | \(-0.665108\pi\) | ||||
−0.495753 | + | 0.868464i | \(0.665108\pi\) | |||||||
\(684\) | 17.7142 | 0.677319 | ||||||||
\(685\) | −14.9187 | −0.570015 | ||||||||
\(686\) | 42.5955 | 1.62630 | ||||||||
\(687\) | 9.37087 | 0.357521 | ||||||||
\(688\) | 7.41702 | 0.282771 | ||||||||
\(689\) | −33.7818 | −1.28698 | ||||||||
\(690\) | −162.407 | −6.18273 | ||||||||
\(691\) | 10.3583 | 0.394049 | 0.197025 | − | 0.980399i | \(-0.436872\pi\) | ||||
0.197025 | + | 0.980399i | \(0.436872\pi\) | |||||||
\(692\) | −95.1469 | −3.61694 | ||||||||
\(693\) | 10.2838 | 0.390649 | ||||||||
\(694\) | 22.8511 | 0.867415 | ||||||||
\(695\) | 8.68285 | 0.329359 | ||||||||
\(696\) | −16.8080 | −0.637107 | ||||||||
\(697\) | 11.2002 | 0.424237 | ||||||||
\(698\) | −22.5779 | −0.854585 | ||||||||
\(699\) | 79.3266 | 3.00041 | ||||||||
\(700\) | 39.0571 | 1.47622 | ||||||||
\(701\) | −13.2522 | −0.500529 | −0.250265 | − | 0.968178i | \(-0.580518\pi\) | ||||
−0.250265 | + | 0.968178i | \(0.580518\pi\) | |||||||
\(702\) | −218.763 | −8.25670 | ||||||||
\(703\) | −0.678671 | −0.0255966 | ||||||||
\(704\) | 0.623802 | 0.0235104 | ||||||||
\(705\) | −105.666 | −3.97959 | ||||||||
\(706\) | 29.7775 | 1.12069 | ||||||||
\(707\) | 18.3172 | 0.688889 | ||||||||
\(708\) | −152.349 | −5.72562 | ||||||||
\(709\) | 1.18051 | 0.0443348 | 0.0221674 | − | 0.999754i | \(-0.492943\pi\) | ||||
0.0221674 | + | 0.999754i | \(0.492943\pi\) | |||||||
\(710\) | 76.0115 | 2.85266 | ||||||||
\(711\) | 88.3092 | 3.31185 | ||||||||
\(712\) | 10.1360 | 0.379863 | ||||||||
\(713\) | −51.8545 | −1.94197 | ||||||||
\(714\) | 11.3857 | 0.426100 | ||||||||
\(715\) | 19.9189 | 0.744924 | ||||||||
\(716\) | −17.8517 | −0.667148 | ||||||||
\(717\) | 26.0116 | 0.971422 | ||||||||
\(718\) | −19.9225 | −0.743500 | ||||||||
\(719\) | 26.7223 | 0.996572 | 0.498286 | − | 0.867013i | \(-0.333963\pi\) | ||||
0.498286 | + | 0.867013i | \(0.333963\pi\) | |||||||
\(720\) | −185.752 | −6.92255 | ||||||||
\(721\) | 20.3444 | 0.757663 | ||||||||
\(722\) | 47.8258 | 1.77989 | ||||||||
\(723\) | 56.2266 | 2.09109 | ||||||||
\(724\) | −69.4702 | −2.58184 | ||||||||
\(725\) | −5.05014 | −0.187557 | ||||||||
\(726\) | 8.26140 | 0.306609 | ||||||||
\(727\) | 22.8693 | 0.848175 | 0.424088 | − | 0.905621i | \(-0.360595\pi\) | ||||
0.424088 | + | 0.905621i | \(0.360595\pi\) | |||||||
\(728\) | 52.7249 | 1.95412 | ||||||||
\(729\) | 41.2369 | 1.52729 | ||||||||
\(730\) | −94.3348 | −3.49149 | ||||||||
\(731\) | 1.00000 | 0.0369863 | ||||||||
\(732\) | 32.1449 | 1.18811 | ||||||||
\(733\) | −4.91443 | −0.181518 | −0.0907592 | − | 0.995873i | \(-0.528929\pi\) | ||||
−0.0907592 | + | 0.995873i | \(0.528929\pi\) | |||||||
\(734\) | 47.7923 | 1.76404 | ||||||||
\(735\) | −55.3711 | −2.04239 | ||||||||
\(736\) | −35.4481 | −1.30663 | ||||||||
\(737\) | 2.89361 | 0.106588 | ||||||||
\(738\) | −213.462 | −7.85763 | ||||||||
\(739\) | 5.04742 | 0.185672 | 0.0928362 | − | 0.995681i | \(-0.470407\pi\) | ||||
0.0928362 | + | 0.995681i | \(0.470407\pi\) | |||||||
\(740\) | 19.6356 | 0.721818 | ||||||||
\(741\) | 10.0736 | 0.370064 | ||||||||
\(742\) | −20.0370 | −0.735580 | ||||||||
\(743\) | 17.9495 | 0.658504 | 0.329252 | − | 0.944242i | \(-0.393203\pi\) | ||||
0.329252 | + | 0.944242i | \(0.393203\pi\) | |||||||
\(744\) | −184.585 | −6.76723 | ||||||||
\(745\) | −1.05210 | −0.0385461 | ||||||||
\(746\) | 40.6214 | 1.48725 | ||||||||
\(747\) | −117.728 | −4.30744 | ||||||||
\(748\) | 4.52378 | 0.165406 | ||||||||
\(749\) | 2.13764 | 0.0781075 | ||||||||
\(750\) | −35.0634 | −1.28034 | ||||||||
\(751\) | 17.7075 | 0.646156 | 0.323078 | − | 0.946372i | \(-0.395282\pi\) | ||||
0.323078 | + | 0.946372i | \(0.395282\pi\) | |||||||
\(752\) | −72.1941 | −2.63265 | ||||||||
\(753\) | 75.6162 | 2.75561 | ||||||||
\(754\) | −12.2200 | −0.445024 | ||||||||
\(755\) | −17.4371 | −0.634602 | ||||||||
\(756\) | −89.9758 | −3.27239 | ||||||||
\(757\) | 32.9132 | 1.19625 | 0.598126 | − | 0.801402i | \(-0.295912\pi\) | ||||
0.598126 | + | 0.801402i | \(0.295912\pi\) | |||||||
\(758\) | −28.4561 | −1.03357 | ||||||||
\(759\) | −18.9451 | −0.687665 | ||||||||
\(760\) | 11.3536 | 0.411837 | ||||||||
\(761\) | −23.0245 | −0.834636 | −0.417318 | − | 0.908760i | \(-0.637030\pi\) | ||||
−0.417318 | + | 0.908760i | \(0.637030\pi\) | |||||||
\(762\) | 4.56638 | 0.165422 | ||||||||
\(763\) | 10.5743 | 0.382815 | ||||||||
\(764\) | 18.3818 | 0.665030 | ||||||||
\(765\) | −25.0440 | −0.905466 | ||||||||
\(766\) | 8.15677 | 0.294716 | ||||||||
\(767\) | −61.7933 | −2.23123 | ||||||||
\(768\) | 90.8685 | 3.27894 | ||||||||
\(769\) | −13.7130 | −0.494503 | −0.247251 | − | 0.968951i | \(-0.579527\pi\) | ||||
−0.247251 | + | 0.968951i | \(0.579527\pi\) | |||||||
\(770\) | 11.8145 | 0.425764 | ||||||||
\(771\) | −29.6884 | −1.06920 | ||||||||
\(772\) | −59.2725 | −2.13326 | ||||||||
\(773\) | 2.20396 | 0.0792708 | 0.0396354 | − | 0.999214i | \(-0.487380\pi\) | ||||
0.0396354 | + | 0.999214i | \(0.487380\pi\) | |||||||
\(774\) | −19.0588 | −0.685054 | ||||||||
\(775\) | −55.4605 | −1.99220 | ||||||||
\(776\) | −78.8340 | −2.82998 | ||||||||
\(777\) | 5.76496 | 0.206817 | ||||||||
\(778\) | −2.76192 | −0.0990196 | ||||||||
\(779\) | 5.87759 | 0.210586 | ||||||||
\(780\) | −291.454 | −10.4357 | ||||||||
\(781\) | 8.86691 | 0.317283 | ||||||||
\(782\) | −14.9604 | −0.534983 | ||||||||
\(783\) | 11.6340 | 0.415766 | ||||||||
\(784\) | −37.8313 | −1.35112 | ||||||||
\(785\) | 11.0813 | 0.395509 | ||||||||
\(786\) | 14.5720 | 0.519766 | ||||||||
\(787\) | 17.9522 | 0.639927 | 0.319964 | − | 0.947430i | \(-0.396329\pi\) | ||||
0.319964 | + | 0.947430i | \(0.396329\pi\) | |||||||
\(788\) | 91.0042 | 3.24189 | ||||||||
\(789\) | 83.4398 | 2.97053 | ||||||||
\(790\) | 101.454 | 3.60955 | ||||||||
\(791\) | 10.2195 | 0.363363 | ||||||||
\(792\) | −48.1002 | −1.70916 | ||||||||
\(793\) | 13.0381 | 0.462996 | ||||||||
\(794\) | 81.0827 | 2.87752 | ||||||||
\(795\) | 61.7926 | 2.19156 | ||||||||
\(796\) | −74.9830 | −2.65770 | ||||||||
\(797\) | −38.7993 | −1.37434 | −0.687170 | − | 0.726497i | \(-0.741147\pi\) | ||||
−0.687170 | + | 0.726497i | \(0.741147\pi\) | |||||||
\(798\) | 5.97496 | 0.211511 | ||||||||
\(799\) | −9.73357 | −0.344349 | ||||||||
\(800\) | −37.9132 | −1.34043 | ||||||||
\(801\) | −11.7331 | −0.414568 | ||||||||
\(802\) | 69.8876 | 2.46782 | ||||||||
\(803\) | −11.0044 | −0.388335 | ||||||||
\(804\) | −42.3395 | −1.49320 | ||||||||
\(805\) | −27.0931 | −0.954905 | ||||||||
\(806\) | −134.199 | −4.72697 | ||||||||
\(807\) | −28.1810 | −0.992017 | ||||||||
\(808\) | −85.6747 | −3.01402 | ||||||||
\(809\) | 44.1907 | 1.55366 | 0.776831 | − | 0.629709i | \(-0.216826\pi\) | ||||
0.776831 | + | 0.629709i | \(0.216826\pi\) | |||||||
\(810\) | 208.255 | 7.31735 | ||||||||
\(811\) | 48.8606 | 1.71573 | 0.857864 | − | 0.513877i | \(-0.171791\pi\) | ||||
0.857864 | + | 0.513877i | \(0.171791\pi\) | |||||||
\(812\) | −5.02598 | −0.176377 | ||||||||
\(813\) | −103.249 | −3.62110 | ||||||||
\(814\) | 3.30320 | 0.115777 | ||||||||
\(815\) | 75.4486 | 2.64285 | ||||||||
\(816\) | −23.9902 | −0.839824 | ||||||||
\(817\) | 0.524776 | 0.0183596 | ||||||||
\(818\) | −25.5641 | −0.893829 | ||||||||
\(819\) | −61.0324 | −2.13265 | ||||||||
\(820\) | −170.053 | −5.93850 | ||||||||
\(821\) | −38.4371 | −1.34147 | −0.670733 | − | 0.741699i | \(-0.734020\pi\) | ||||
−0.670733 | + | 0.741699i | \(0.734020\pi\) | |||||||
\(822\) | 36.7221 | 1.28083 | ||||||||
\(823\) | 28.2441 | 0.984527 | 0.492263 | − | 0.870446i | \(-0.336170\pi\) | ||||
0.492263 | + | 0.870446i | \(0.336170\pi\) | |||||||
\(824\) | −95.1563 | −3.31493 | ||||||||
\(825\) | −20.2626 | −0.705453 | ||||||||
\(826\) | −36.6514 | −1.27527 | ||||||||
\(827\) | −18.6964 | −0.650137 | −0.325069 | − | 0.945690i | \(-0.605387\pi\) | ||||
−0.325069 | + | 0.945690i | \(0.605387\pi\) | |||||||
\(828\) | 197.716 | 6.87109 | ||||||||
\(829\) | 17.8475 | 0.619870 | 0.309935 | − | 0.950758i | \(-0.399693\pi\) | ||||
0.309935 | + | 0.950758i | \(0.399693\pi\) | |||||||
\(830\) | −135.251 | −4.69464 | ||||||||
\(831\) | 72.5184 | 2.51563 | ||||||||
\(832\) | −3.70215 | −0.128349 | ||||||||
\(833\) | −5.10061 | −0.176726 | ||||||||
\(834\) | −21.3727 | −0.740074 | ||||||||
\(835\) | −4.41087 | −0.152645 | ||||||||
\(836\) | 2.37397 | 0.0821056 | ||||||||
\(837\) | 127.764 | 4.41619 | ||||||||
\(838\) | 78.6526 | 2.71701 | ||||||||
\(839\) | 49.5585 | 1.71095 | 0.855474 | − | 0.517845i | \(-0.173266\pi\) | ||||
0.855474 | + | 0.517845i | \(0.173266\pi\) | |||||||
\(840\) | −96.4427 | −3.32759 | ||||||||
\(841\) | −28.3501 | −0.977591 | ||||||||
\(842\) | 53.2976 | 1.83676 | ||||||||
\(843\) | 21.3363 | 0.734863 | ||||||||
\(844\) | −1.51343 | −0.0520944 | ||||||||
\(845\) | −74.5836 | −2.56575 | ||||||||
\(846\) | 185.510 | 6.37797 | ||||||||
\(847\) | 1.37818 | 0.0473550 | ||||||||
\(848\) | 42.2187 | 1.44979 | ||||||||
\(849\) | −4.08636 | −0.140244 | ||||||||
\(850\) | −16.0008 | −0.548822 | ||||||||
\(851\) | −7.57493 | −0.259665 | ||||||||
\(852\) | −129.741 | −4.44486 | ||||||||
\(853\) | 18.4565 | 0.631939 | 0.315970 | − | 0.948769i | \(-0.397670\pi\) | ||||
0.315970 | + | 0.948769i | \(0.397670\pi\) | |||||||
\(854\) | 7.73327 | 0.264627 | ||||||||
\(855\) | −13.1425 | −0.449463 | ||||||||
\(856\) | −9.99833 | −0.341736 | ||||||||
\(857\) | −43.3772 | −1.48174 | −0.740869 | − | 0.671650i | \(-0.765586\pi\) | ||||
−0.740869 | + | 0.671650i | \(0.765586\pi\) | |||||||
\(858\) | −49.0299 | −1.67385 | ||||||||
\(859\) | 26.9066 | 0.918041 | 0.459020 | − | 0.888426i | \(-0.348201\pi\) | ||||
0.459020 | + | 0.888426i | \(0.348201\pi\) | |||||||
\(860\) | −15.1830 | −0.517737 | ||||||||
\(861\) | −49.9270 | −1.70151 | ||||||||
\(862\) | −14.7894 | −0.503729 | ||||||||
\(863\) | 26.1250 | 0.889306 | 0.444653 | − | 0.895703i | \(-0.353327\pi\) | ||||
0.444653 | + | 0.895703i | \(0.353327\pi\) | |||||||
\(864\) | 87.3407 | 2.97139 | ||||||||
\(865\) | 70.5912 | 2.40017 | ||||||||
\(866\) | 60.2575 | 2.04763 | ||||||||
\(867\) | −3.23448 | −0.109849 | ||||||||
\(868\) | −55.1952 | −1.87345 | ||||||||
\(869\) | 11.8348 | 0.401467 | ||||||||
\(870\) | 22.3523 | 0.757815 | ||||||||
\(871\) | −17.1731 | −0.581887 | ||||||||
\(872\) | −49.4590 | −1.67489 | ||||||||
\(873\) | 91.2553 | 3.08852 | ||||||||
\(874\) | −7.85087 | −0.265560 | ||||||||
\(875\) | −5.84935 | −0.197744 | ||||||||
\(876\) | 161.016 | 5.44024 | ||||||||
\(877\) | 4.20254 | 0.141910 | 0.0709548 | − | 0.997480i | \(-0.477395\pi\) | ||||
0.0709548 | + | 0.997480i | \(0.477395\pi\) | |||||||
\(878\) | 43.2080 | 1.45820 | ||||||||
\(879\) | −100.437 | −3.38767 | ||||||||
\(880\) | −24.8935 | −0.839161 | ||||||||
\(881\) | −38.0143 | −1.28073 | −0.640367 | − | 0.768069i | \(-0.721218\pi\) | ||||
−0.640367 | + | 0.768069i | \(0.721218\pi\) | |||||||
\(882\) | 97.2114 | 3.27328 | ||||||||
\(883\) | −11.5452 | −0.388528 | −0.194264 | − | 0.980949i | \(-0.562232\pi\) | ||||
−0.194264 | + | 0.980949i | \(0.562232\pi\) | |||||||
\(884\) | −26.8478 | −0.902990 | ||||||||
\(885\) | 113.030 | 3.79947 | ||||||||
\(886\) | −17.6417 | −0.592684 | ||||||||
\(887\) | 16.4918 | 0.553741 | 0.276871 | − | 0.960907i | \(-0.410703\pi\) | ||||
0.276871 | + | 0.960907i | \(0.410703\pi\) | |||||||
\(888\) | −26.9643 | −0.904864 | ||||||||
\(889\) | 0.761773 | 0.0255490 | ||||||||
\(890\) | −13.4795 | −0.451833 | ||||||||
\(891\) | 24.2935 | 0.813862 | ||||||||
\(892\) | −23.6372 | −0.791433 | ||||||||
\(893\) | −5.10795 | −0.170931 | ||||||||
\(894\) | 2.58973 | 0.0866136 | ||||||||
\(895\) | 13.2445 | 0.442714 | ||||||||
\(896\) | 14.4857 | 0.483933 | ||||||||
\(897\) | 112.436 | 3.75413 | ||||||||
\(898\) | −88.7196 | −2.96061 | ||||||||
\(899\) | 7.13682 | 0.238026 | ||||||||
\(900\) | 211.465 | 7.04883 | ||||||||
\(901\) | 5.69213 | 0.189632 | ||||||||
\(902\) | −28.6071 | −0.952513 | ||||||||
\(903\) | −4.45770 | −0.148343 | ||||||||
\(904\) | −47.7994 | −1.58978 | ||||||||
\(905\) | 51.5412 | 1.71329 | ||||||||
\(906\) | 42.9211 | 1.42596 | ||||||||
\(907\) | 16.3851 | 0.544059 | 0.272029 | − | 0.962289i | \(-0.412305\pi\) | ||||
0.272029 | + | 0.962289i | \(0.412305\pi\) | |||||||
\(908\) | −40.9907 | −1.36032 | ||||||||
\(909\) | 99.1738 | 3.28939 | ||||||||
\(910\) | −70.1168 | −2.32435 | ||||||||
\(911\) | −52.2144 | −1.72994 | −0.864970 | − | 0.501824i | \(-0.832662\pi\) | ||||
−0.864970 | + | 0.501824i | \(0.832662\pi\) | |||||||
\(912\) | −12.5895 | −0.416879 | ||||||||
\(913\) | −15.7774 | −0.522154 | ||||||||
\(914\) | −82.5372 | −2.73009 | ||||||||
\(915\) | −23.8488 | −0.788419 | ||||||||
\(916\) | −13.1062 | −0.433042 | ||||||||
\(917\) | 2.43093 | 0.0802764 | ||||||||
\(918\) | 36.8610 | 1.21659 | ||||||||
\(919\) | 29.8832 | 0.985757 | 0.492879 | − | 0.870098i | \(-0.335945\pi\) | ||||
0.492879 | + | 0.870098i | \(0.335945\pi\) | |||||||
\(920\) | 126.722 | 4.17790 | ||||||||
\(921\) | −66.3643 | −2.18678 | ||||||||
\(922\) | −27.6627 | −0.911022 | ||||||||
\(923\) | −52.6235 | −1.73212 | ||||||||
\(924\) | −20.1657 | −0.663402 | ||||||||
\(925\) | −8.10170 | −0.266382 | ||||||||
\(926\) | −62.6701 | −2.05947 | ||||||||
\(927\) | 110.149 | 3.61778 | ||||||||
\(928\) | 4.87878 | 0.160154 | ||||||||
\(929\) | −47.7925 | −1.56802 | −0.784011 | − | 0.620747i | \(-0.786829\pi\) | ||||
−0.784011 | + | 0.620747i | \(0.786829\pi\) | |||||||
\(930\) | 245.473 | 8.04937 | ||||||||
\(931\) | −2.67668 | −0.0877246 | ||||||||
\(932\) | −110.947 | −3.63420 | ||||||||
\(933\) | 47.9030 | 1.56827 | ||||||||
\(934\) | 66.8212 | 2.18646 | ||||||||
\(935\) | −3.35627 | −0.109762 | ||||||||
\(936\) | 285.466 | 9.33075 | ||||||||
\(937\) | −19.2335 | −0.628332 | −0.314166 | − | 0.949368i | \(-0.601725\pi\) | ||||
−0.314166 | + | 0.949368i | \(0.601725\pi\) | |||||||
\(938\) | −10.1858 | −0.332580 | ||||||||
\(939\) | −106.393 | −3.47201 | ||||||||
\(940\) | 147.785 | 4.82022 | ||||||||
\(941\) | −49.3214 | −1.60783 | −0.803916 | − | 0.594743i | \(-0.797254\pi\) | ||||
−0.803916 | + | 0.594743i | \(0.797254\pi\) | |||||||
\(942\) | −27.2764 | −0.888714 | ||||||||
\(943\) | 65.6022 | 2.13630 | ||||||||
\(944\) | 77.2259 | 2.51349 | ||||||||
\(945\) | 66.7547 | 2.17153 | ||||||||
\(946\) | −2.55417 | −0.0830432 | ||||||||
\(947\) | 30.1197 | 0.978759 | 0.489379 | − | 0.872071i | \(-0.337223\pi\) | ||||
0.489379 | + | 0.872071i | \(0.337223\pi\) | |||||||
\(948\) | −173.167 | −5.62421 | ||||||||
\(949\) | 65.3089 | 2.12002 | ||||||||
\(950\) | −8.39683 | −0.272429 | ||||||||
\(951\) | −22.7342 | −0.737206 | ||||||||
\(952\) | −8.88399 | −0.287932 | ||||||||
\(953\) | −32.0301 | −1.03756 | −0.518778 | − | 0.854909i | \(-0.673613\pi\) | ||||
−0.518778 | + | 0.854909i | \(0.673613\pi\) | |||||||
\(954\) | −108.485 | −3.51234 | ||||||||
\(955\) | −13.6378 | −0.441308 | ||||||||
\(956\) | −36.3802 | −1.17662 | ||||||||
\(957\) | 2.60745 | 0.0842869 | ||||||||
\(958\) | −46.6444 | −1.50701 | ||||||||
\(959\) | 6.12606 | 0.197821 | ||||||||
\(960\) | 6.77186 | 0.218561 | ||||||||
\(961\) | 47.3764 | 1.52827 | ||||||||
\(962\) | −19.6039 | −0.632055 | ||||||||
\(963\) | 11.5737 | 0.372957 | ||||||||
\(964\) | −78.6392 | −2.53280 | ||||||||
\(965\) | 43.9753 | 1.41562 | ||||||||
\(966\) | 66.6890 | 2.14568 | ||||||||
\(967\) | −46.4739 | −1.49450 | −0.747250 | − | 0.664543i | \(-0.768626\pi\) | ||||
−0.747250 | + | 0.664543i | \(0.768626\pi\) | |||||||
\(968\) | −6.44616 | −0.207187 | ||||||||
\(969\) | −1.69738 | −0.0545276 | ||||||||
\(970\) | 104.838 | 3.36615 | ||||||||
\(971\) | −21.2545 | −0.682090 | −0.341045 | − | 0.940047i | \(-0.610781\pi\) | ||||
−0.341045 | + | 0.940047i | \(0.610781\pi\) | |||||||
\(972\) | −159.606 | −5.11936 | ||||||||
\(973\) | −3.56543 | −0.114302 | ||||||||
\(974\) | −54.8210 | −1.75658 | ||||||||
\(975\) | 120.255 | 3.85124 | ||||||||
\(976\) | −16.2943 | −0.521568 | ||||||||
\(977\) | 33.8197 | 1.08199 | 0.540994 | − | 0.841027i | \(-0.318048\pi\) | ||||
0.540994 | + | 0.841027i | \(0.318048\pi\) | |||||||
\(978\) | −185.715 | −5.93852 | ||||||||
\(979\) | −1.57241 | −0.0502545 | ||||||||
\(980\) | 77.4427 | 2.47382 | ||||||||
\(981\) | 57.2519 | 1.82791 | ||||||||
\(982\) | 83.5921 | 2.66753 | ||||||||
\(983\) | 17.4845 | 0.557668 | 0.278834 | − | 0.960339i | \(-0.410052\pi\) | ||||
0.278834 | + | 0.960339i | \(0.410052\pi\) | |||||||
\(984\) | 233.523 | 7.44444 | ||||||||
\(985\) | −67.5176 | −2.15129 | ||||||||
\(986\) | 2.05903 | 0.0655727 | ||||||||
\(987\) | 43.3894 | 1.38110 | ||||||||
\(988\) | −14.0891 | −0.448234 | ||||||||
\(989\) | 5.85725 | 0.186250 | ||||||||
\(990\) | 63.9665 | 2.03299 | ||||||||
\(991\) | −19.4549 | −0.618005 | −0.309003 | − | 0.951061i | \(-0.599995\pi\) | ||||
−0.309003 | + | 0.951061i | \(0.599995\pi\) | |||||||
\(992\) | 53.5787 | 1.70112 | ||||||||
\(993\) | −39.1011 | −1.24083 | ||||||||
\(994\) | −31.2125 | −0.990001 | ||||||||
\(995\) | 55.6312 | 1.76363 | ||||||||
\(996\) | 230.855 | 7.31493 | ||||||||
\(997\) | 4.47879 | 0.141845 | 0.0709224 | − | 0.997482i | \(-0.477406\pi\) | ||||
0.0709224 | + | 0.997482i | \(0.477406\pi\) | |||||||
\(998\) | 91.8109 | 2.90622 | ||||||||
\(999\) | 18.6639 | 0.590499 |
(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 | 8041.2.a.j.1.6 | ✓ | 82 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
8041.2.a.j.1.6 | ✓ | 82 | 1.1 | even | 1 | trivial |