Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [4009,2,Mod(1,4009)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(4009, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([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("4009.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 4009 = 19 \cdot 211 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 4009.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: | \(32.0120261703\) |
Analytic rank: | \(0\) |
Dimension: | \(82\) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.18 | ||
Character | \(\chi\) | \(=\) | 4009.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.53574 | −1.08594 | −0.542968 | − | 0.839754i | \(-0.682699\pi\) | ||||
−0.542968 | + | 0.839754i | \(0.682699\pi\) | |||||||
\(3\) | 2.00602 | 1.15817 | 0.579087 | − | 0.815266i | \(-0.303409\pi\) | ||||
0.579087 | + | 0.815266i | \(0.303409\pi\) | |||||||
\(4\) | 0.358512 | 0.179256 | ||||||||
\(5\) | 1.47205 | 0.658321 | 0.329161 | − | 0.944274i | \(-0.393234\pi\) | ||||
0.329161 | + | 0.944274i | \(0.393234\pi\) | |||||||
\(6\) | −3.08073 | −1.25770 | ||||||||
\(7\) | −4.88163 | −1.84508 | −0.922542 | − | 0.385897i | \(-0.873892\pi\) | ||||
−0.922542 | + | 0.385897i | \(0.873892\pi\) | |||||||
\(8\) | 2.52091 | 0.891275 | ||||||||
\(9\) | 1.02410 | 0.341367 | ||||||||
\(10\) | −2.26069 | −0.714894 | ||||||||
\(11\) | 4.27935 | 1.29027 | 0.645136 | − | 0.764067i | \(-0.276801\pi\) | ||||
0.645136 | + | 0.764067i | \(0.276801\pi\) | |||||||
\(12\) | 0.719181 | 0.207610 | ||||||||
\(13\) | −4.21981 | −1.17037 | −0.585183 | − | 0.810901i | \(-0.698977\pi\) | ||||
−0.585183 | + | 0.810901i | \(0.698977\pi\) | |||||||
\(14\) | 7.49694 | 2.00364 | ||||||||
\(15\) | 2.95296 | 0.762451 | ||||||||
\(16\) | −4.58849 | −1.14712 | ||||||||
\(17\) | −3.61352 | −0.876407 | −0.438203 | − | 0.898876i | \(-0.644385\pi\) | ||||
−0.438203 | + | 0.898876i | \(0.644385\pi\) | |||||||
\(18\) | −1.57276 | −0.370703 | ||||||||
\(19\) | 1.00000 | 0.229416 | ||||||||
\(20\) | 0.527748 | 0.118008 | ||||||||
\(21\) | −9.79263 | −2.13693 | ||||||||
\(22\) | −6.57199 | −1.40115 | ||||||||
\(23\) | −3.93404 | −0.820305 | −0.410152 | − | 0.912017i | \(-0.634524\pi\) | ||||
−0.410152 | + | 0.912017i | \(0.634524\pi\) | |||||||
\(24\) | 5.05698 | 1.03225 | ||||||||
\(25\) | −2.83307 | −0.566613 | ||||||||
\(26\) | 6.48056 | 1.27094 | ||||||||
\(27\) | −3.96368 | −0.762811 | ||||||||
\(28\) | −1.75012 | −0.330742 | ||||||||
\(29\) | 0.0888231 | 0.0164940 | 0.00824702 | − | 0.999966i | \(-0.497375\pi\) | ||||
0.00824702 | + | 0.999966i | \(0.497375\pi\) | |||||||
\(30\) | −4.53499 | −0.827972 | ||||||||
\(31\) | 3.73800 | 0.671364 | 0.335682 | − | 0.941975i | \(-0.391033\pi\) | ||||
0.335682 | + | 0.941975i | \(0.391033\pi\) | |||||||
\(32\) | 2.00494 | 0.354427 | ||||||||
\(33\) | 8.58445 | 1.49436 | ||||||||
\(34\) | 5.54944 | 0.951721 | ||||||||
\(35\) | −7.18601 | −1.21466 | ||||||||
\(36\) | 0.367153 | 0.0611922 | ||||||||
\(37\) | 4.88664 | 0.803359 | 0.401679 | − | 0.915780i | \(-0.368427\pi\) | ||||
0.401679 | + | 0.915780i | \(0.368427\pi\) | |||||||
\(38\) | −1.53574 | −0.249131 | ||||||||
\(39\) | −8.46502 | −1.35549 | ||||||||
\(40\) | 3.71090 | 0.586745 | ||||||||
\(41\) | 7.87714 | 1.23020 | 0.615101 | − | 0.788448i | \(-0.289115\pi\) | ||||
0.615101 | + | 0.788448i | \(0.289115\pi\) | |||||||
\(42\) | 15.0390 | 2.32057 | ||||||||
\(43\) | 6.60373 | 1.00706 | 0.503529 | − | 0.863978i | \(-0.332035\pi\) | ||||
0.503529 | + | 0.863978i | \(0.332035\pi\) | |||||||
\(44\) | 1.53420 | 0.231289 | ||||||||
\(45\) | 1.50753 | 0.224729 | ||||||||
\(46\) | 6.04168 | 0.890798 | ||||||||
\(47\) | 2.93809 | 0.428564 | 0.214282 | − | 0.976772i | \(-0.431259\pi\) | ||||
0.214282 | + | 0.976772i | \(0.431259\pi\) | |||||||
\(48\) | −9.20459 | −1.32857 | ||||||||
\(49\) | 16.8303 | 2.40433 | ||||||||
\(50\) | 4.35087 | 0.615305 | ||||||||
\(51\) | −7.24877 | −1.01503 | ||||||||
\(52\) | −1.51285 | −0.209795 | ||||||||
\(53\) | 9.76937 | 1.34193 | 0.670963 | − | 0.741491i | \(-0.265881\pi\) | ||||
0.670963 | + | 0.741491i | \(0.265881\pi\) | |||||||
\(54\) | 6.08721 | 0.828364 | ||||||||
\(55\) | 6.29942 | 0.849414 | ||||||||
\(56\) | −12.3061 | −1.64448 | ||||||||
\(57\) | 2.00602 | 0.265703 | ||||||||
\(58\) | −0.136410 | −0.0179115 | ||||||||
\(59\) | −6.33595 | −0.824871 | −0.412435 | − | 0.910987i | \(-0.635322\pi\) | ||||
−0.412435 | + | 0.910987i | \(0.635322\pi\) | |||||||
\(60\) | 1.05867 | 0.136674 | ||||||||
\(61\) | 9.65676 | 1.23642 | 0.618211 | − | 0.786012i | \(-0.287858\pi\) | ||||
0.618211 | + | 0.786012i | \(0.287858\pi\) | |||||||
\(62\) | −5.74061 | −0.729058 | ||||||||
\(63\) | −4.99929 | −0.629851 | ||||||||
\(64\) | 6.09791 | 0.762239 | ||||||||
\(65\) | −6.21178 | −0.770477 | ||||||||
\(66\) | −13.1835 | −1.62278 | ||||||||
\(67\) | −5.52411 | −0.674878 | −0.337439 | − | 0.941347i | \(-0.609561\pi\) | ||||
−0.337439 | + | 0.941347i | \(0.609561\pi\) | |||||||
\(68\) | −1.29549 | −0.157101 | ||||||||
\(69\) | −7.89175 | −0.950056 | ||||||||
\(70\) | 11.0359 | 1.31904 | ||||||||
\(71\) | 0.430221 | 0.0510579 | 0.0255289 | − | 0.999674i | \(-0.491873\pi\) | ||||
0.0255289 | + | 0.999674i | \(0.491873\pi\) | |||||||
\(72\) | 2.58167 | 0.304252 | ||||||||
\(73\) | 6.78411 | 0.794021 | 0.397010 | − | 0.917814i | \(-0.370048\pi\) | ||||
0.397010 | + | 0.917814i | \(0.370048\pi\) | |||||||
\(74\) | −7.50463 | −0.872396 | ||||||||
\(75\) | −5.68318 | −0.656237 | ||||||||
\(76\) | 0.358512 | 0.0411241 | ||||||||
\(77\) | −20.8902 | −2.38066 | ||||||||
\(78\) | 13.0001 | 1.47197 | ||||||||
\(79\) | 12.2748 | 1.38102 | 0.690511 | − | 0.723322i | \(-0.257386\pi\) | ||||
0.690511 | + | 0.723322i | \(0.257386\pi\) | |||||||
\(80\) | −6.75450 | −0.755176 | ||||||||
\(81\) | −11.0235 | −1.22484 | ||||||||
\(82\) | −12.0973 | −1.33592 | ||||||||
\(83\) | 8.62368 | 0.946572 | 0.473286 | − | 0.880909i | \(-0.343068\pi\) | ||||
0.473286 | + | 0.880909i | \(0.343068\pi\) | |||||||
\(84\) | −3.51078 | −0.383057 | ||||||||
\(85\) | −5.31928 | −0.576957 | ||||||||
\(86\) | −10.1416 | −1.09360 | ||||||||
\(87\) | 0.178181 | 0.0191030 | ||||||||
\(88\) | 10.7878 | 1.14999 | ||||||||
\(89\) | −0.167478 | −0.0177527 | −0.00887634 | − | 0.999961i | \(-0.502825\pi\) | ||||
−0.00887634 | + | 0.999961i | \(0.502825\pi\) | |||||||
\(90\) | −2.31518 | −0.244042 | ||||||||
\(91\) | 20.5996 | 2.15942 | ||||||||
\(92\) | −1.41040 | −0.147045 | ||||||||
\(93\) | 7.49849 | 0.777557 | ||||||||
\(94\) | −4.51215 | −0.465393 | ||||||||
\(95\) | 1.47205 | 0.151029 | ||||||||
\(96\) | 4.02195 | 0.410488 | ||||||||
\(97\) | −14.7752 | −1.50019 | −0.750095 | − | 0.661330i | \(-0.769992\pi\) | ||||
−0.750095 | + | 0.661330i | \(0.769992\pi\) | |||||||
\(98\) | −25.8471 | −2.61095 | ||||||||
\(99\) | 4.38249 | 0.440457 | ||||||||
\(100\) | −1.01569 | −0.101569 | ||||||||
\(101\) | −0.141822 | −0.0141118 | −0.00705592 | − | 0.999975i | \(-0.502246\pi\) | ||||
−0.00705592 | + | 0.999975i | \(0.502246\pi\) | |||||||
\(102\) | 11.1323 | 1.10226 | ||||||||
\(103\) | 9.94263 | 0.979677 | 0.489838 | − | 0.871813i | \(-0.337056\pi\) | ||||
0.489838 | + | 0.871813i | \(0.337056\pi\) | |||||||
\(104\) | −10.6378 | −1.04312 | ||||||||
\(105\) | −14.4153 | −1.40679 | ||||||||
\(106\) | −15.0033 | −1.45725 | ||||||||
\(107\) | 5.62464 | 0.543754 | 0.271877 | − | 0.962332i | \(-0.412356\pi\) | ||||
0.271877 | + | 0.962332i | \(0.412356\pi\) | |||||||
\(108\) | −1.42103 | −0.136738 | ||||||||
\(109\) | 0.703976 | 0.0674286 | 0.0337143 | − | 0.999432i | \(-0.489266\pi\) | ||||
0.0337143 | + | 0.999432i | \(0.489266\pi\) | |||||||
\(110\) | −9.67430 | −0.922409 | ||||||||
\(111\) | 9.80268 | 0.930429 | ||||||||
\(112\) | 22.3993 | 2.11654 | ||||||||
\(113\) | −6.44914 | −0.606684 | −0.303342 | − | 0.952882i | \(-0.598102\pi\) | ||||
−0.303342 | + | 0.952882i | \(0.598102\pi\) | |||||||
\(114\) | −3.08073 | −0.288537 | ||||||||
\(115\) | −5.79111 | −0.540024 | ||||||||
\(116\) | 0.0318442 | 0.00295666 | ||||||||
\(117\) | −4.32152 | −0.399525 | ||||||||
\(118\) | 9.73040 | 0.895756 | ||||||||
\(119\) | 17.6399 | 1.61704 | ||||||||
\(120\) | 7.44413 | 0.679553 | ||||||||
\(121\) | 7.31284 | 0.664804 | ||||||||
\(122\) | −14.8303 | −1.34267 | ||||||||
\(123\) | 15.8017 | 1.42479 | ||||||||
\(124\) | 1.34012 | 0.120346 | ||||||||
\(125\) | −11.5307 | −1.03133 | ||||||||
\(126\) | 7.67763 | 0.683978 | ||||||||
\(127\) | 18.8137 | 1.66944 | 0.834722 | − | 0.550672i | \(-0.185628\pi\) | ||||
0.834722 | + | 0.550672i | \(0.185628\pi\) | |||||||
\(128\) | −13.3747 | −1.18217 | ||||||||
\(129\) | 13.2472 | 1.16635 | ||||||||
\(130\) | 9.53971 | 0.836688 | ||||||||
\(131\) | 6.03744 | 0.527493 | 0.263747 | − | 0.964592i | \(-0.415042\pi\) | ||||
0.263747 | + | 0.964592i | \(0.415042\pi\) | |||||||
\(132\) | 3.07763 | 0.267873 | ||||||||
\(133\) | −4.88163 | −0.423291 | ||||||||
\(134\) | 8.48362 | 0.732874 | ||||||||
\(135\) | −5.83474 | −0.502175 | ||||||||
\(136\) | −9.10934 | −0.781119 | ||||||||
\(137\) | 11.5872 | 0.989961 | 0.494981 | − | 0.868904i | \(-0.335175\pi\) | ||||
0.494981 | + | 0.868904i | \(0.335175\pi\) | |||||||
\(138\) | 12.1197 | 1.03170 | ||||||||
\(139\) | −9.00976 | −0.764198 | −0.382099 | − | 0.924121i | \(-0.624799\pi\) | ||||
−0.382099 | + | 0.924121i | \(0.624799\pi\) | |||||||
\(140\) | −2.57627 | −0.217735 | ||||||||
\(141\) | 5.89385 | 0.496352 | ||||||||
\(142\) | −0.660710 | −0.0554456 | ||||||||
\(143\) | −18.0581 | −1.51009 | ||||||||
\(144\) | −4.69909 | −0.391591 | ||||||||
\(145\) | 0.130752 | 0.0108584 | ||||||||
\(146\) | −10.4187 | −0.862255 | ||||||||
\(147\) | 33.7619 | 2.78464 | ||||||||
\(148\) | 1.75192 | 0.144007 | ||||||||
\(149\) | 16.0740 | 1.31683 | 0.658417 | − | 0.752653i | \(-0.271226\pi\) | ||||
0.658417 | + | 0.752653i | \(0.271226\pi\) | |||||||
\(150\) | 8.72791 | 0.712631 | ||||||||
\(151\) | 9.21645 | 0.750024 | 0.375012 | − | 0.927020i | \(-0.377639\pi\) | ||||
0.375012 | + | 0.927020i | \(0.377639\pi\) | |||||||
\(152\) | 2.52091 | 0.204473 | ||||||||
\(153\) | −3.70061 | −0.299177 | ||||||||
\(154\) | 32.0820 | 2.58524 | ||||||||
\(155\) | 5.50252 | 0.441973 | ||||||||
\(156\) | −3.03481 | −0.242979 | ||||||||
\(157\) | 1.39311 | 0.111182 | 0.0555911 | − | 0.998454i | \(-0.482296\pi\) | ||||
0.0555911 | + | 0.998454i | \(0.482296\pi\) | |||||||
\(158\) | −18.8510 | −1.49970 | ||||||||
\(159\) | 19.5975 | 1.55418 | ||||||||
\(160\) | 2.95138 | 0.233327 | ||||||||
\(161\) | 19.2045 | 1.51353 | ||||||||
\(162\) | 16.9293 | 1.33009 | ||||||||
\(163\) | −20.5818 | −1.61209 | −0.806045 | − | 0.591854i | \(-0.798396\pi\) | ||||
−0.806045 | + | 0.591854i | \(0.798396\pi\) | |||||||
\(164\) | 2.82405 | 0.220521 | ||||||||
\(165\) | 12.6367 | 0.983769 | ||||||||
\(166\) | −13.2438 | −1.02792 | ||||||||
\(167\) | −15.7123 | −1.21585 | −0.607927 | − | 0.793993i | \(-0.707999\pi\) | ||||
−0.607927 | + | 0.793993i | \(0.707999\pi\) | |||||||
\(168\) | −24.6863 | −1.90459 | ||||||||
\(169\) | 4.80683 | 0.369756 | ||||||||
\(170\) | 8.16906 | 0.626538 | ||||||||
\(171\) | 1.02410 | 0.0783151 | ||||||||
\(172\) | 2.36752 | 0.180521 | ||||||||
\(173\) | −1.07972 | −0.0820899 | −0.0410450 | − | 0.999157i | \(-0.513069\pi\) | ||||
−0.0410450 | + | 0.999157i | \(0.513069\pi\) | |||||||
\(174\) | −0.273640 | −0.0207446 | ||||||||
\(175\) | 13.8300 | 1.04545 | ||||||||
\(176\) | −19.6358 | −1.48010 | ||||||||
\(177\) | −12.7100 | −0.955344 | ||||||||
\(178\) | 0.257204 | 0.0192783 | ||||||||
\(179\) | −11.7559 | −0.878675 | −0.439338 | − | 0.898322i | \(-0.644787\pi\) | ||||
−0.439338 | + | 0.898322i | \(0.644787\pi\) | |||||||
\(180\) | 0.540468 | 0.0402841 | ||||||||
\(181\) | 17.8402 | 1.32605 | 0.663027 | − | 0.748596i | \(-0.269272\pi\) | ||||
0.663027 | + | 0.748596i | \(0.269272\pi\) | |||||||
\(182\) | −31.6357 | −2.34499 | ||||||||
\(183\) | 19.3716 | 1.43199 | ||||||||
\(184\) | −9.91735 | −0.731117 | ||||||||
\(185\) | 7.19338 | 0.528868 | ||||||||
\(186\) | −11.5158 | −0.844377 | ||||||||
\(187\) | −15.4635 | −1.13080 | ||||||||
\(188\) | 1.05334 | 0.0768227 | ||||||||
\(189\) | 19.3492 | 1.40745 | ||||||||
\(190\) | −2.26069 | −0.164008 | ||||||||
\(191\) | 3.14805 | 0.227785 | 0.113893 | − | 0.993493i | \(-0.463668\pi\) | ||||
0.113893 | + | 0.993493i | \(0.463668\pi\) | |||||||
\(192\) | 12.2325 | 0.882805 | ||||||||
\(193\) | 18.7989 | 1.35317 | 0.676586 | − | 0.736364i | \(-0.263459\pi\) | ||||
0.676586 | + | 0.736364i | \(0.263459\pi\) | |||||||
\(194\) | 22.6909 | 1.62911 | ||||||||
\(195\) | −12.4609 | −0.892346 | ||||||||
\(196\) | 6.03388 | 0.430991 | ||||||||
\(197\) | −9.11632 | −0.649511 | −0.324755 | − | 0.945798i | \(-0.605282\pi\) | ||||
−0.324755 | + | 0.945798i | \(0.605282\pi\) | |||||||
\(198\) | −6.73039 | −0.478308 | ||||||||
\(199\) | 10.7486 | 0.761949 | 0.380975 | − | 0.924586i | \(-0.375589\pi\) | ||||
0.380975 | + | 0.924586i | \(0.375589\pi\) | |||||||
\(200\) | −7.14190 | −0.505008 | ||||||||
\(201\) | −11.0815 | −0.781626 | ||||||||
\(202\) | 0.217803 | 0.0153245 | ||||||||
\(203\) | −0.433602 | −0.0304329 | ||||||||
\(204\) | −2.59877 | −0.181950 | ||||||||
\(205\) | 11.5955 | 0.809868 | ||||||||
\(206\) | −15.2693 | −1.06387 | ||||||||
\(207\) | −4.02886 | −0.280025 | ||||||||
\(208\) | 19.3626 | 1.34255 | ||||||||
\(209\) | 4.27935 | 0.296009 | ||||||||
\(210\) | 22.1382 | 1.52768 | ||||||||
\(211\) | −1.00000 | −0.0688428 | ||||||||
\(212\) | 3.50244 | 0.240548 | ||||||||
\(213\) | 0.863031 | 0.0591339 | ||||||||
\(214\) | −8.63800 | −0.590482 | ||||||||
\(215\) | 9.72102 | 0.662968 | ||||||||
\(216\) | −9.99208 | −0.679875 | ||||||||
\(217\) | −18.2475 | −1.23872 | ||||||||
\(218\) | −1.08113 | −0.0732231 | ||||||||
\(219\) | 13.6090 | 0.919614 | ||||||||
\(220\) | 2.25842 | 0.152263 | ||||||||
\(221\) | 15.2484 | 1.02572 | ||||||||
\(222\) | −15.0544 | −1.01039 | ||||||||
\(223\) | 6.27635 | 0.420295 | 0.210148 | − | 0.977670i | \(-0.432606\pi\) | ||||
0.210148 | + | 0.977670i | \(0.432606\pi\) | |||||||
\(224\) | −9.78739 | −0.653947 | ||||||||
\(225\) | −2.90135 | −0.193423 | ||||||||
\(226\) | 9.90423 | 0.658819 | ||||||||
\(227\) | −17.5153 | −1.16253 | −0.581267 | − | 0.813713i | \(-0.697443\pi\) | ||||
−0.581267 | + | 0.813713i | \(0.697443\pi\) | |||||||
\(228\) | 0.719181 | 0.0476289 | ||||||||
\(229\) | 4.54019 | 0.300024 | 0.150012 | − | 0.988684i | \(-0.452069\pi\) | ||||
0.150012 | + | 0.988684i | \(0.452069\pi\) | |||||||
\(230\) | 8.89367 | 0.586431 | ||||||||
\(231\) | −41.9061 | −2.75722 | ||||||||
\(232\) | 0.223915 | 0.0147007 | ||||||||
\(233\) | 4.10062 | 0.268641 | 0.134320 | − | 0.990938i | \(-0.457115\pi\) | ||||
0.134320 | + | 0.990938i | \(0.457115\pi\) | |||||||
\(234\) | 6.63675 | 0.433858 | ||||||||
\(235\) | 4.32502 | 0.282133 | ||||||||
\(236\) | −2.27151 | −0.147863 | ||||||||
\(237\) | 24.6234 | 1.59946 | ||||||||
\(238\) | −27.0903 | −1.75600 | ||||||||
\(239\) | 17.4541 | 1.12901 | 0.564507 | − | 0.825429i | \(-0.309066\pi\) | ||||
0.564507 | + | 0.825429i | \(0.309066\pi\) | |||||||
\(240\) | −13.5496 | −0.874625 | ||||||||
\(241\) | −10.3230 | −0.664964 | −0.332482 | − | 0.943110i | \(-0.607886\pi\) | ||||
−0.332482 | + | 0.943110i | \(0.607886\pi\) | |||||||
\(242\) | −11.2307 | −0.721934 | ||||||||
\(243\) | −10.2223 | −0.655762 | ||||||||
\(244\) | 3.46207 | 0.221636 | ||||||||
\(245\) | 24.7751 | 1.58282 | ||||||||
\(246\) | −24.2673 | −1.54723 | ||||||||
\(247\) | −4.21981 | −0.268500 | ||||||||
\(248\) | 9.42314 | 0.598370 | ||||||||
\(249\) | 17.2992 | 1.09629 | ||||||||
\(250\) | 17.7082 | 1.11996 | ||||||||
\(251\) | 20.2847 | 1.28036 | 0.640180 | − | 0.768225i | \(-0.278860\pi\) | ||||
0.640180 | + | 0.768225i | \(0.278860\pi\) | |||||||
\(252\) | −1.79231 | −0.112905 | ||||||||
\(253\) | −16.8351 | −1.05842 | ||||||||
\(254\) | −28.8930 | −1.81291 | ||||||||
\(255\) | −10.6706 | −0.668217 | ||||||||
\(256\) | 8.34433 | 0.521521 | ||||||||
\(257\) | −10.7336 | −0.669542 | −0.334771 | − | 0.942300i | \(-0.608659\pi\) | ||||
−0.334771 | + | 0.942300i | \(0.608659\pi\) | |||||||
\(258\) | −20.3443 | −1.26658 | ||||||||
\(259\) | −23.8548 | −1.48226 | ||||||||
\(260\) | −2.22700 | −0.138113 | ||||||||
\(261\) | 0.0909640 | 0.00563053 | ||||||||
\(262\) | −9.27196 | −0.572824 | ||||||||
\(263\) | 13.5423 | 0.835056 | 0.417528 | − | 0.908664i | \(-0.362897\pi\) | ||||
0.417528 | + | 0.908664i | \(0.362897\pi\) | |||||||
\(264\) | 21.6406 | 1.33189 | ||||||||
\(265\) | 14.3810 | 0.883419 | ||||||||
\(266\) | 7.49694 | 0.459667 | ||||||||
\(267\) | −0.335964 | −0.0205607 | ||||||||
\(268\) | −1.98046 | −0.120976 | ||||||||
\(269\) | 1.73151 | 0.105572 | 0.0527861 | − | 0.998606i | \(-0.483190\pi\) | ||||
0.0527861 | + | 0.998606i | \(0.483190\pi\) | |||||||
\(270\) | 8.96068 | 0.545329 | ||||||||
\(271\) | 6.43808 | 0.391086 | 0.195543 | − | 0.980695i | \(-0.437353\pi\) | ||||
0.195543 | + | 0.980695i | \(0.437353\pi\) | |||||||
\(272\) | 16.5806 | 1.00535 | ||||||||
\(273\) | 41.3231 | 2.50099 | ||||||||
\(274\) | −17.7950 | −1.07503 | ||||||||
\(275\) | −12.1237 | −0.731086 | ||||||||
\(276\) | −2.82929 | −0.170303 | ||||||||
\(277\) | −14.6774 | −0.881881 | −0.440941 | − | 0.897536i | \(-0.645355\pi\) | ||||
−0.440941 | + | 0.897536i | \(0.645355\pi\) | |||||||
\(278\) | 13.8367 | 0.829870 | ||||||||
\(279\) | 3.82809 | 0.229182 | ||||||||
\(280\) | −18.1153 | −1.08259 | ||||||||
\(281\) | −11.2810 | −0.672968 | −0.336484 | − | 0.941689i | \(-0.609238\pi\) | ||||
−0.336484 | + | 0.941689i | \(0.609238\pi\) | |||||||
\(282\) | −9.05146 | −0.539006 | ||||||||
\(283\) | 5.23002 | 0.310893 | 0.155446 | − | 0.987844i | \(-0.450318\pi\) | ||||
0.155446 | + | 0.987844i | \(0.450318\pi\) | |||||||
\(284\) | 0.154240 | 0.00915243 | ||||||||
\(285\) | 2.95296 | 0.174918 | ||||||||
\(286\) | 27.7326 | 1.63986 | ||||||||
\(287\) | −38.4533 | −2.26983 | ||||||||
\(288\) | 2.05326 | 0.120990 | ||||||||
\(289\) | −3.94250 | −0.231911 | ||||||||
\(290\) | −0.200802 | −0.0117915 | ||||||||
\(291\) | −29.6392 | −1.73748 | ||||||||
\(292\) | 2.43219 | 0.142333 | ||||||||
\(293\) | −4.03732 | −0.235862 | −0.117931 | − | 0.993022i | \(-0.537626\pi\) | ||||
−0.117931 | + | 0.993022i | \(0.537626\pi\) | |||||||
\(294\) | −51.8497 | −3.02394 | ||||||||
\(295\) | −9.32684 | −0.543030 | ||||||||
\(296\) | 12.3188 | 0.716014 | ||||||||
\(297\) | −16.9620 | −0.984234 | ||||||||
\(298\) | −24.6856 | −1.43000 | ||||||||
\(299\) | 16.6009 | 0.960056 | ||||||||
\(300\) | −2.03749 | −0.117634 | ||||||||
\(301\) | −32.2370 | −1.85811 | ||||||||
\(302\) | −14.1541 | −0.814478 | ||||||||
\(303\) | −0.284498 | −0.0163440 | ||||||||
\(304\) | −4.58849 | −0.263168 | ||||||||
\(305\) | 14.2152 | 0.813963 | ||||||||
\(306\) | 5.68319 | 0.324887 | ||||||||
\(307\) | −22.0404 | −1.25791 | −0.628955 | − | 0.777442i | \(-0.716517\pi\) | ||||
−0.628955 | + | 0.777442i | \(0.716517\pi\) | |||||||
\(308\) | −7.48939 | −0.426748 | ||||||||
\(309\) | 19.9451 | 1.13464 | ||||||||
\(310\) | −8.45047 | −0.479955 | ||||||||
\(311\) | 12.5735 | 0.712975 | 0.356488 | − | 0.934300i | \(-0.383974\pi\) | ||||
0.356488 | + | 0.934300i | \(0.383974\pi\) | |||||||
\(312\) | −21.3395 | −1.20811 | ||||||||
\(313\) | 17.8786 | 1.01056 | 0.505280 | − | 0.862955i | \(-0.331389\pi\) | ||||
0.505280 | + | 0.862955i | \(0.331389\pi\) | |||||||
\(314\) | −2.13946 | −0.120737 | ||||||||
\(315\) | −7.35921 | −0.414645 | ||||||||
\(316\) | 4.40066 | 0.247557 | ||||||||
\(317\) | −6.17814 | −0.346999 | −0.173499 | − | 0.984834i | \(-0.555507\pi\) | ||||
−0.173499 | + | 0.984834i | \(0.555507\pi\) | |||||||
\(318\) | −30.0968 | −1.68774 | ||||||||
\(319\) | 0.380105 | 0.0212818 | ||||||||
\(320\) | 8.97643 | 0.501798 | ||||||||
\(321\) | 11.2831 | 0.629762 | ||||||||
\(322\) | −29.4933 | −1.64360 | ||||||||
\(323\) | −3.61352 | −0.201061 | ||||||||
\(324\) | −3.95206 | −0.219559 | ||||||||
\(325\) | 11.9550 | 0.663145 | ||||||||
\(326\) | 31.6084 | 1.75063 | ||||||||
\(327\) | 1.41219 | 0.0780941 | ||||||||
\(328\) | 19.8575 | 1.09645 | ||||||||
\(329\) | −14.3427 | −0.790737 | ||||||||
\(330\) | −19.4068 | −1.06831 | ||||||||
\(331\) | −27.4284 | −1.50760 | −0.753801 | − | 0.657103i | \(-0.771782\pi\) | ||||
−0.753801 | + | 0.657103i | \(0.771782\pi\) | |||||||
\(332\) | 3.09169 | 0.169679 | ||||||||
\(333\) | 5.00442 | 0.274241 | ||||||||
\(334\) | 24.1301 | 1.32034 | ||||||||
\(335\) | −8.13177 | −0.444286 | ||||||||
\(336\) | 44.9334 | 2.45132 | ||||||||
\(337\) | 20.3760 | 1.10995 | 0.554977 | − | 0.831866i | \(-0.312727\pi\) | ||||
0.554977 | + | 0.831866i | \(0.312727\pi\) | |||||||
\(338\) | −7.38206 | −0.401531 | ||||||||
\(339\) | −12.9371 | −0.702645 | ||||||||
\(340\) | −1.90703 | −0.103423 | ||||||||
\(341\) | 15.9962 | 0.866243 | ||||||||
\(342\) | −1.57276 | −0.0850451 | ||||||||
\(343\) | −47.9881 | −2.59111 | ||||||||
\(344\) | 16.6474 | 0.897566 | ||||||||
\(345\) | −11.6171 | −0.625442 | ||||||||
\(346\) | 1.65818 | 0.0891444 | ||||||||
\(347\) | −17.2807 | −0.927677 | −0.463838 | − | 0.885920i | \(-0.653528\pi\) | ||||
−0.463838 | + | 0.885920i | \(0.653528\pi\) | |||||||
\(348\) | 0.0638799 | 0.00342432 | ||||||||
\(349\) | −1.14966 | −0.0615402 | −0.0307701 | − | 0.999526i | \(-0.509796\pi\) | ||||
−0.0307701 | + | 0.999526i | \(0.509796\pi\) | |||||||
\(350\) | −21.2393 | −1.13529 | ||||||||
\(351\) | 16.7260 | 0.892768 | ||||||||
\(352\) | 8.57985 | 0.457307 | ||||||||
\(353\) | 34.0723 | 1.81349 | 0.906744 | − | 0.421683i | \(-0.138560\pi\) | ||||
0.906744 | + | 0.421683i | \(0.138560\pi\) | |||||||
\(354\) | 19.5194 | 1.03744 | ||||||||
\(355\) | 0.633308 | 0.0336125 | ||||||||
\(356\) | −0.0600430 | −0.00318227 | ||||||||
\(357\) | 35.3859 | 1.87282 | ||||||||
\(358\) | 18.0540 | 0.954185 | ||||||||
\(359\) | 3.91681 | 0.206721 | 0.103361 | − | 0.994644i | \(-0.467040\pi\) | ||||
0.103361 | + | 0.994644i | \(0.467040\pi\) | |||||||
\(360\) | 3.80034 | 0.200296 | ||||||||
\(361\) | 1.00000 | 0.0526316 | ||||||||
\(362\) | −27.3980 | −1.44001 | ||||||||
\(363\) | 14.6697 | 0.769958 | ||||||||
\(364\) | 7.38520 | 0.387089 | ||||||||
\(365\) | 9.98656 | 0.522721 | ||||||||
\(366\) | −29.7499 | −1.55505 | ||||||||
\(367\) | −28.6057 | −1.49320 | −0.746602 | − | 0.665271i | \(-0.768316\pi\) | ||||
−0.746602 | + | 0.665271i | \(0.768316\pi\) | |||||||
\(368\) | 18.0513 | 0.940990 | ||||||||
\(369\) | 8.06700 | 0.419951 | ||||||||
\(370\) | −11.0472 | −0.574317 | ||||||||
\(371\) | −47.6905 | −2.47597 | ||||||||
\(372\) | 2.68830 | 0.139382 | ||||||||
\(373\) | −5.34067 | −0.276530 | −0.138265 | − | 0.990395i | \(-0.544152\pi\) | ||||
−0.138265 | + | 0.990395i | \(0.544152\pi\) | |||||||
\(374\) | 23.7480 | 1.22798 | ||||||||
\(375\) | −23.1307 | −1.19447 | ||||||||
\(376\) | 7.40665 | 0.381969 | ||||||||
\(377\) | −0.374817 | −0.0193041 | ||||||||
\(378\) | −29.7155 | −1.52840 | ||||||||
\(379\) | 15.0287 | 0.771974 | 0.385987 | − | 0.922504i | \(-0.373861\pi\) | ||||
0.385987 | + | 0.922504i | \(0.373861\pi\) | |||||||
\(380\) | 0.527748 | 0.0270729 | ||||||||
\(381\) | 37.7406 | 1.93351 | ||||||||
\(382\) | −4.83460 | −0.247360 | ||||||||
\(383\) | 20.5231 | 1.04868 | 0.524341 | − | 0.851508i | \(-0.324312\pi\) | ||||
0.524341 | + | 0.851508i | \(0.324312\pi\) | |||||||
\(384\) | −26.8299 | −1.36916 | ||||||||
\(385\) | −30.7515 | −1.56724 | ||||||||
\(386\) | −28.8703 | −1.46946 | ||||||||
\(387\) | 6.76289 | 0.343777 | ||||||||
\(388\) | −5.29707 | −0.268918 | ||||||||
\(389\) | −1.21872 | −0.0617913 | −0.0308957 | − | 0.999523i | \(-0.509836\pi\) | ||||
−0.0308957 | + | 0.999523i | \(0.509836\pi\) | |||||||
\(390\) | 19.1368 | 0.969030 | ||||||||
\(391\) | 14.2157 | 0.718920 | ||||||||
\(392\) | 42.4277 | 2.14292 | ||||||||
\(393\) | 12.1112 | 0.610929 | ||||||||
\(394\) | 14.0003 | 0.705327 | ||||||||
\(395\) | 18.0691 | 0.909156 | ||||||||
\(396\) | 1.57118 | 0.0789546 | ||||||||
\(397\) | 7.27388 | 0.365066 | 0.182533 | − | 0.983200i | \(-0.441570\pi\) | ||||
0.182533 | + | 0.983200i | \(0.441570\pi\) | |||||||
\(398\) | −16.5071 | −0.827428 | ||||||||
\(399\) | −9.79263 | −0.490245 | ||||||||
\(400\) | 12.9995 | 0.649975 | ||||||||
\(401\) | −9.46397 | −0.472608 | −0.236304 | − | 0.971679i | \(-0.575936\pi\) | ||||
−0.236304 | + | 0.971679i | \(0.575936\pi\) | |||||||
\(402\) | 17.0183 | 0.848795 | ||||||||
\(403\) | −15.7737 | −0.785742 | ||||||||
\(404\) | −0.0508450 | −0.00252963 | ||||||||
\(405\) | −16.2272 | −0.806335 | ||||||||
\(406\) | 0.665902 | 0.0330482 | ||||||||
\(407\) | 20.9116 | 1.03655 | ||||||||
\(408\) | −18.2735 | −0.904672 | ||||||||
\(409\) | 7.96227 | 0.393709 | 0.196855 | − | 0.980433i | \(-0.436927\pi\) | ||||
0.196855 | + | 0.980433i | \(0.436927\pi\) | |||||||
\(410\) | −17.8078 | −0.879465 | ||||||||
\(411\) | 23.2441 | 1.14655 | ||||||||
\(412\) | 3.56455 | 0.175613 | ||||||||
\(413\) | 30.9298 | 1.52196 | ||||||||
\(414\) | 6.18730 | 0.304089 | ||||||||
\(415\) | 12.6945 | 0.623148 | ||||||||
\(416\) | −8.46048 | −0.414809 | ||||||||
\(417\) | −18.0737 | −0.885074 | ||||||||
\(418\) | −6.57199 | −0.321447 | ||||||||
\(419\) | −14.9554 | −0.730620 | −0.365310 | − | 0.930886i | \(-0.619037\pi\) | ||||
−0.365310 | + | 0.930886i | \(0.619037\pi\) | |||||||
\(420\) | −5.16804 | −0.252175 | ||||||||
\(421\) | 31.6025 | 1.54021 | 0.770105 | − | 0.637917i | \(-0.220204\pi\) | ||||
0.770105 | + | 0.637917i | \(0.220204\pi\) | |||||||
\(422\) | 1.53574 | 0.0747589 | ||||||||
\(423\) | 3.00890 | 0.146298 | ||||||||
\(424\) | 24.6277 | 1.19603 | ||||||||
\(425\) | 10.2373 | 0.496584 | ||||||||
\(426\) | −1.32540 | −0.0642156 | ||||||||
\(427\) | −47.1408 | −2.28130 | ||||||||
\(428\) | 2.01650 | 0.0974712 | ||||||||
\(429\) | −36.2248 | −1.74895 | ||||||||
\(430\) | −14.9290 | −0.719941 | ||||||||
\(431\) | 19.5661 | 0.942465 | 0.471233 | − | 0.882009i | \(-0.343809\pi\) | ||||
0.471233 | + | 0.882009i | \(0.343809\pi\) | |||||||
\(432\) | 18.1873 | 0.875039 | ||||||||
\(433\) | −35.5257 | −1.70726 | −0.853629 | − | 0.520882i | \(-0.825603\pi\) | ||||
−0.853629 | + | 0.520882i | \(0.825603\pi\) | |||||||
\(434\) | 28.0236 | 1.34517 | ||||||||
\(435\) | 0.262291 | 0.0125759 | ||||||||
\(436\) | 0.252384 | 0.0120870 | ||||||||
\(437\) | −3.93404 | −0.188191 | ||||||||
\(438\) | −20.9000 | −0.998642 | ||||||||
\(439\) | 40.1189 | 1.91477 | 0.957386 | − | 0.288813i | \(-0.0932605\pi\) | ||||
0.957386 | + | 0.288813i | \(0.0932605\pi\) | |||||||
\(440\) | 15.8803 | 0.757061 | ||||||||
\(441\) | 17.2360 | 0.820761 | ||||||||
\(442\) | −23.4176 | −1.11386 | ||||||||
\(443\) | −6.01366 | −0.285718 | −0.142859 | − | 0.989743i | \(-0.545629\pi\) | ||||
−0.142859 | + | 0.989743i | \(0.545629\pi\) | |||||||
\(444\) | 3.51438 | 0.166785 | ||||||||
\(445\) | −0.246537 | −0.0116870 | ||||||||
\(446\) | −9.63887 | −0.456414 | ||||||||
\(447\) | 32.2447 | 1.52512 | ||||||||
\(448\) | −29.7677 | −1.40639 | ||||||||
\(449\) | 10.3655 | 0.489180 | 0.244590 | − | 0.969627i | \(-0.421347\pi\) | ||||
0.244590 | + | 0.969627i | \(0.421347\pi\) | |||||||
\(450\) | 4.45573 | 0.210045 | ||||||||
\(451\) | 33.7090 | 1.58730 | ||||||||
\(452\) | −2.31209 | −0.108752 | ||||||||
\(453\) | 18.4884 | 0.868659 | ||||||||
\(454\) | 26.8991 | 1.26244 | ||||||||
\(455\) | 30.3236 | 1.42159 | ||||||||
\(456\) | 5.05698 | 0.236815 | ||||||||
\(457\) | 40.5359 | 1.89619 | 0.948094 | − | 0.317990i | \(-0.103008\pi\) | ||||
0.948094 | + | 0.317990i | \(0.103008\pi\) | |||||||
\(458\) | −6.97258 | −0.325807 | ||||||||
\(459\) | 14.3228 | 0.668533 | ||||||||
\(460\) | −2.07618 | −0.0968025 | ||||||||
\(461\) | 37.0218 | 1.72428 | 0.862139 | − | 0.506672i | \(-0.169124\pi\) | ||||
0.862139 | + | 0.506672i | \(0.169124\pi\) | |||||||
\(462\) | 64.3571 | 2.99416 | ||||||||
\(463\) | 0.909026 | 0.0422460 | 0.0211230 | − | 0.999777i | \(-0.493276\pi\) | ||||
0.0211230 | + | 0.999777i | \(0.493276\pi\) | |||||||
\(464\) | −0.407564 | −0.0189207 | ||||||||
\(465\) | 11.0382 | 0.511882 | ||||||||
\(466\) | −6.29751 | −0.291726 | ||||||||
\(467\) | −13.2011 | −0.610874 | −0.305437 | − | 0.952212i | \(-0.598803\pi\) | ||||
−0.305437 | + | 0.952212i | \(0.598803\pi\) | |||||||
\(468\) | −1.54932 | −0.0716172 | ||||||||
\(469\) | 26.9667 | 1.24521 | ||||||||
\(470\) | −6.64212 | −0.306378 | ||||||||
\(471\) | 2.79460 | 0.128768 | ||||||||
\(472\) | −15.9723 | −0.735187 | ||||||||
\(473\) | 28.2597 | 1.29938 | ||||||||
\(474\) | −37.8153 | −1.73692 | ||||||||
\(475\) | −2.83307 | −0.129990 | ||||||||
\(476\) | 6.32410 | 0.289865 | ||||||||
\(477\) | 10.0048 | 0.458090 | ||||||||
\(478\) | −26.8051 | −1.22604 | ||||||||
\(479\) | 25.8755 | 1.18228 | 0.591142 | − | 0.806568i | \(-0.298677\pi\) | ||||
0.591142 | + | 0.806568i | \(0.298677\pi\) | |||||||
\(480\) | 5.92051 | 0.270233 | ||||||||
\(481\) | −20.6207 | −0.940224 | ||||||||
\(482\) | 15.8535 | 0.722108 | ||||||||
\(483\) | 38.5246 | 1.75293 | ||||||||
\(484\) | 2.62174 | 0.119170 | ||||||||
\(485\) | −21.7498 | −0.987607 | ||||||||
\(486\) | 15.6989 | 0.712115 | ||||||||
\(487\) | −7.16353 | −0.324610 | −0.162305 | − | 0.986741i | \(-0.551893\pi\) | ||||
−0.162305 | + | 0.986741i | \(0.551893\pi\) | |||||||
\(488\) | 24.3438 | 1.10199 | ||||||||
\(489\) | −41.2874 | −1.86708 | ||||||||
\(490\) | −38.0482 | −1.71884 | ||||||||
\(491\) | −41.4786 | −1.87190 | −0.935951 | − | 0.352129i | \(-0.885458\pi\) | ||||
−0.935951 | + | 0.352129i | \(0.885458\pi\) | |||||||
\(492\) | 5.66509 | 0.255402 | ||||||||
\(493\) | −0.320964 | −0.0144555 | ||||||||
\(494\) | 6.48056 | 0.291574 | ||||||||
\(495\) | 6.45125 | 0.289962 | ||||||||
\(496\) | −17.1518 | −0.770138 | ||||||||
\(497\) | −2.10018 | −0.0942061 | ||||||||
\(498\) | −26.5672 | −1.19051 | ||||||||
\(499\) | 26.8722 | 1.20296 | 0.601482 | − | 0.798886i | \(-0.294577\pi\) | ||||
0.601482 | + | 0.798886i | \(0.294577\pi\) | |||||||
\(500\) | −4.13388 | −0.184873 | ||||||||
\(501\) | −31.5192 | −1.40817 | ||||||||
\(502\) | −31.1521 | −1.39039 | ||||||||
\(503\) | 35.1047 | 1.56524 | 0.782620 | − | 0.622500i | \(-0.213883\pi\) | ||||
0.782620 | + | 0.622500i | \(0.213883\pi\) | |||||||
\(504\) | −12.6027 | −0.561371 | ||||||||
\(505\) | −0.208769 | −0.00929012 | ||||||||
\(506\) | 25.8545 | 1.14937 | ||||||||
\(507\) | 9.64258 | 0.428242 | ||||||||
\(508\) | 6.74493 | 0.299258 | ||||||||
\(509\) | −42.2821 | −1.87412 | −0.937062 | − | 0.349164i | \(-0.886466\pi\) | ||||
−0.937062 | + | 0.349164i | \(0.886466\pi\) | |||||||
\(510\) | 16.3873 | 0.725640 | ||||||||
\(511\) | −33.1176 | −1.46503 | ||||||||
\(512\) | 13.9347 | 0.615831 | ||||||||
\(513\) | −3.96368 | −0.175001 | ||||||||
\(514\) | 16.4840 | 0.727080 | ||||||||
\(515\) | 14.6361 | 0.644942 | ||||||||
\(516\) | 4.74927 | 0.209075 | ||||||||
\(517\) | 12.5731 | 0.552965 | ||||||||
\(518\) | 36.6349 | 1.60964 | ||||||||
\(519\) | −2.16595 | −0.0950744 | ||||||||
\(520\) | −15.6593 | −0.686707 | ||||||||
\(521\) | 25.9128 | 1.13526 | 0.567630 | − | 0.823284i | \(-0.307860\pi\) | ||||
0.567630 | + | 0.823284i | \(0.307860\pi\) | |||||||
\(522\) | −0.139697 | −0.00611439 | ||||||||
\(523\) | 23.4648 | 1.02604 | 0.513021 | − | 0.858376i | \(-0.328526\pi\) | ||||
0.513021 | + | 0.858376i | \(0.328526\pi\) | |||||||
\(524\) | 2.16449 | 0.0945563 | ||||||||
\(525\) | 27.7432 | 1.21081 | ||||||||
\(526\) | −20.7976 | −0.906816 | ||||||||
\(527\) | −13.5073 | −0.588388 | ||||||||
\(528\) | −39.3897 | −1.71422 | ||||||||
\(529\) | −7.52331 | −0.327100 | ||||||||
\(530\) | −22.0856 | −0.959336 | ||||||||
\(531\) | −6.48866 | −0.281584 | ||||||||
\(532\) | −1.75012 | −0.0758775 | ||||||||
\(533\) | −33.2401 | −1.43979 | ||||||||
\(534\) | 0.515956 | 0.0223276 | ||||||||
\(535\) | 8.27975 | 0.357965 | ||||||||
\(536\) | −13.9258 | −0.601502 | ||||||||
\(537\) | −23.5825 | −1.01766 | ||||||||
\(538\) | −2.65916 | −0.114645 | ||||||||
\(539\) | 72.0229 | 3.10225 | ||||||||
\(540\) | −2.09183 | −0.0900178 | ||||||||
\(541\) | −43.2915 | −1.86125 | −0.930625 | − | 0.365975i | \(-0.880735\pi\) | ||||
−0.930625 | + | 0.365975i | \(0.880735\pi\) | |||||||
\(542\) | −9.88725 | −0.424694 | ||||||||
\(543\) | 35.7878 | 1.53580 | ||||||||
\(544\) | −7.24489 | −0.310622 | ||||||||
\(545\) | 1.03629 | 0.0443897 | ||||||||
\(546\) | −63.4617 | −2.71591 | ||||||||
\(547\) | 19.5022 | 0.833852 | 0.416926 | − | 0.908940i | \(-0.363107\pi\) | ||||
0.416926 | + | 0.908940i | \(0.363107\pi\) | |||||||
\(548\) | 4.15415 | 0.177457 | ||||||||
\(549\) | 9.88951 | 0.422074 | ||||||||
\(550\) | 18.6189 | 0.793912 | ||||||||
\(551\) | 0.0888231 | 0.00378399 | ||||||||
\(552\) | −19.8944 | −0.846761 | ||||||||
\(553\) | −59.9210 | −2.54810 | ||||||||
\(554\) | 22.5408 | 0.957666 | ||||||||
\(555\) | 14.4300 | 0.612521 | ||||||||
\(556\) | −3.23011 | −0.136987 | ||||||||
\(557\) | 32.0467 | 1.35786 | 0.678931 | − | 0.734202i | \(-0.262444\pi\) | ||||
0.678931 | + | 0.734202i | \(0.262444\pi\) | |||||||
\(558\) | −5.87897 | −0.248877 | ||||||||
\(559\) | −27.8665 | −1.17863 | ||||||||
\(560\) | 32.9730 | 1.39336 | ||||||||
\(561\) | −31.0200 | −1.30967 | ||||||||
\(562\) | 17.3247 | 0.730800 | ||||||||
\(563\) | −36.5044 | −1.53848 | −0.769239 | − | 0.638961i | \(-0.779364\pi\) | ||||
−0.769239 | + | 0.638961i | \(0.779364\pi\) | |||||||
\(564\) | 2.11302 | 0.0889741 | ||||||||
\(565\) | −9.49346 | −0.399393 | ||||||||
\(566\) | −8.03198 | −0.337609 | ||||||||
\(567\) | 53.8128 | 2.25992 | ||||||||
\(568\) | 1.08455 | 0.0455066 | ||||||||
\(569\) | −1.08710 | −0.0455735 | −0.0227868 | − | 0.999740i | \(-0.507254\pi\) | ||||
−0.0227868 | + | 0.999740i | \(0.507254\pi\) | |||||||
\(570\) | −4.53499 | −0.189950 | ||||||||
\(571\) | 31.7497 | 1.32868 | 0.664342 | − | 0.747429i | \(-0.268712\pi\) | ||||
0.664342 | + | 0.747429i | \(0.268712\pi\) | |||||||
\(572\) | −6.47403 | −0.270693 | ||||||||
\(573\) | 6.31505 | 0.263815 | ||||||||
\(574\) | 59.0544 | 2.46489 | ||||||||
\(575\) | 11.1454 | 0.464795 | ||||||||
\(576\) | 6.24488 | 0.260203 | ||||||||
\(577\) | −4.11240 | −0.171202 | −0.0856008 | − | 0.996330i | \(-0.527281\pi\) | ||||
−0.0856008 | + | 0.996330i | \(0.527281\pi\) | |||||||
\(578\) | 6.05467 | 0.251841 | ||||||||
\(579\) | 37.7108 | 1.56721 | ||||||||
\(580\) | 0.0468762 | 0.00194643 | ||||||||
\(581\) | −42.0976 | −1.74650 | ||||||||
\(582\) | 45.5183 | 1.88679 | ||||||||
\(583\) | 41.8066 | 1.73145 | ||||||||
\(584\) | 17.1021 | 0.707691 | ||||||||
\(585\) | −6.36150 | −0.263016 | ||||||||
\(586\) | 6.20029 | 0.256131 | ||||||||
\(587\) | 27.0772 | 1.11760 | 0.558798 | − | 0.829304i | \(-0.311263\pi\) | ||||
0.558798 | + | 0.829304i | \(0.311263\pi\) | |||||||
\(588\) | 12.1041 | 0.499163 | ||||||||
\(589\) | 3.73800 | 0.154022 | ||||||||
\(590\) | 14.3236 | 0.589695 | ||||||||
\(591\) | −18.2875 | −0.752247 | ||||||||
\(592\) | −22.4223 | −0.921552 | ||||||||
\(593\) | −41.4809 | −1.70342 | −0.851708 | − | 0.524016i | \(-0.824433\pi\) | ||||
−0.851708 | + | 0.524016i | \(0.824433\pi\) | |||||||
\(594\) | 26.0493 | 1.06882 | ||||||||
\(595\) | 25.9668 | 1.06453 | ||||||||
\(596\) | 5.76273 | 0.236050 | ||||||||
\(597\) | 21.5619 | 0.882470 | ||||||||
\(598\) | −25.4948 | −1.04256 | ||||||||
\(599\) | −46.1464 | −1.88549 | −0.942745 | − | 0.333514i | \(-0.891765\pi\) | ||||
−0.942745 | + | 0.333514i | \(0.891765\pi\) | |||||||
\(600\) | −14.3268 | −0.584888 | ||||||||
\(601\) | 15.4986 | 0.632201 | 0.316100 | − | 0.948726i | \(-0.397626\pi\) | ||||
0.316100 | + | 0.948726i | \(0.397626\pi\) | |||||||
\(602\) | 49.5077 | 2.01779 | ||||||||
\(603\) | −5.65725 | −0.230381 | ||||||||
\(604\) | 3.30421 | 0.134446 | ||||||||
\(605\) | 10.7649 | 0.437654 | ||||||||
\(606\) | 0.436916 | 0.0177485 | ||||||||
\(607\) | −36.0731 | −1.46416 | −0.732080 | − | 0.681219i | \(-0.761450\pi\) | ||||
−0.732080 | + | 0.681219i | \(0.761450\pi\) | |||||||
\(608\) | 2.00494 | 0.0813111 | ||||||||
\(609\) | −0.869813 | −0.0352466 | ||||||||
\(610\) | −21.8310 | −0.883911 | ||||||||
\(611\) | −12.3982 | −0.501577 | ||||||||
\(612\) | −1.32671 | −0.0536292 | ||||||||
\(613\) | −6.57977 | −0.265754 | −0.132877 | − | 0.991133i | \(-0.542422\pi\) | ||||
−0.132877 | + | 0.991133i | \(0.542422\pi\) | |||||||
\(614\) | 33.8484 | 1.36601 | ||||||||
\(615\) | 23.2609 | 0.937969 | ||||||||
\(616\) | −52.6623 | −2.12182 | ||||||||
\(617\) | 7.90342 | 0.318180 | 0.159090 | − | 0.987264i | \(-0.449144\pi\) | ||||
0.159090 | + | 0.987264i | \(0.449144\pi\) | |||||||
\(618\) | −30.6306 | −1.23214 | ||||||||
\(619\) | −18.7316 | −0.752886 | −0.376443 | − | 0.926440i | \(-0.622853\pi\) | ||||
−0.376443 | + | 0.926440i | \(0.622853\pi\) | |||||||
\(620\) | 1.97272 | 0.0792264 | ||||||||
\(621\) | 15.5933 | 0.625738 | ||||||||
\(622\) | −19.3096 | −0.774245 | ||||||||
\(623\) | 0.817568 | 0.0327552 | ||||||||
\(624\) | 38.8417 | 1.55491 | ||||||||
\(625\) | −2.80840 | −0.112336 | ||||||||
\(626\) | −27.4570 | −1.09740 | ||||||||
\(627\) | 8.58445 | 0.342830 | ||||||||
\(628\) | 0.499446 | 0.0199301 | ||||||||
\(629\) | −17.6580 | −0.704069 | ||||||||
\(630\) | 11.3019 | 0.450277 | ||||||||
\(631\) | −30.7281 | −1.22327 | −0.611634 | − | 0.791141i | \(-0.709487\pi\) | ||||
−0.611634 | + | 0.791141i | \(0.709487\pi\) | |||||||
\(632\) | 30.9436 | 1.23087 | ||||||||
\(633\) | −2.00602 | −0.0797320 | ||||||||
\(634\) | 9.48804 | 0.376818 | ||||||||
\(635\) | 27.6947 | 1.09903 | ||||||||
\(636\) | 7.02595 | 0.278597 | ||||||||
\(637\) | −71.0209 | −2.81395 | ||||||||
\(638\) | −0.583745 | −0.0231107 | ||||||||
\(639\) | 0.440591 | 0.0174295 | ||||||||
\(640\) | −19.6883 | −0.778247 | ||||||||
\(641\) | 25.7140 | 1.01564 | 0.507820 | − | 0.861463i | \(-0.330451\pi\) | ||||
0.507820 | + | 0.861463i | \(0.330451\pi\) | |||||||
\(642\) | −17.3280 | −0.683881 | ||||||||
\(643\) | 9.38776 | 0.370217 | 0.185109 | − | 0.982718i | \(-0.440736\pi\) | ||||
0.185109 | + | 0.982718i | \(0.440736\pi\) | |||||||
\(644\) | 6.88506 | 0.271309 | ||||||||
\(645\) | 19.5005 | 0.767833 | ||||||||
\(646\) | 5.54944 | 0.218340 | ||||||||
\(647\) | 31.4018 | 1.23453 | 0.617267 | − | 0.786754i | \(-0.288240\pi\) | ||||
0.617267 | + | 0.786754i | \(0.288240\pi\) | |||||||
\(648\) | −27.7893 | −1.09167 | ||||||||
\(649\) | −27.1138 | −1.06431 | ||||||||
\(650\) | −18.3598 | −0.720132 | ||||||||
\(651\) | −36.6048 | −1.43466 | ||||||||
\(652\) | −7.37882 | −0.288977 | ||||||||
\(653\) | −43.1364 | −1.68806 | −0.844028 | − | 0.536299i | \(-0.819822\pi\) | ||||
−0.844028 | + | 0.536299i | \(0.819822\pi\) | |||||||
\(654\) | −2.16876 | −0.0848052 | ||||||||
\(655\) | 8.88741 | 0.347260 | ||||||||
\(656\) | −36.1442 | −1.41119 | ||||||||
\(657\) | 6.94763 | 0.271053 | ||||||||
\(658\) | 22.0267 | 0.858689 | ||||||||
\(659\) | 21.8339 | 0.850528 | 0.425264 | − | 0.905069i | \(-0.360181\pi\) | ||||
0.425264 | + | 0.905069i | \(0.360181\pi\) | |||||||
\(660\) | 4.53042 | 0.176347 | ||||||||
\(661\) | 3.60798 | 0.140334 | 0.0701670 | − | 0.997535i | \(-0.477647\pi\) | ||||
0.0701670 | + | 0.997535i | \(0.477647\pi\) | |||||||
\(662\) | 42.1230 | 1.63716 | ||||||||
\(663\) | 30.5885 | 1.18796 | ||||||||
\(664\) | 21.7395 | 0.843656 | ||||||||
\(665\) | −7.18601 | −0.278662 | ||||||||
\(666\) | −7.68551 | −0.297808 | ||||||||
\(667\) | −0.349434 | −0.0135301 | ||||||||
\(668\) | −5.63305 | −0.217949 | ||||||||
\(669\) | 12.5905 | 0.486775 | ||||||||
\(670\) | 12.4883 | 0.482466 | ||||||||
\(671\) | 41.3247 | 1.59532 | ||||||||
\(672\) | −19.6337 | −0.757385 | ||||||||
\(673\) | 2.91281 | 0.112280 | 0.0561402 | − | 0.998423i | \(-0.482121\pi\) | ||||
0.0561402 | + | 0.998423i | \(0.482121\pi\) | |||||||
\(674\) | −31.2924 | −1.20534 | ||||||||
\(675\) | 11.2294 | 0.432219 | ||||||||
\(676\) | 1.72331 | 0.0662810 | ||||||||
\(677\) | 12.9879 | 0.499164 | 0.249582 | − | 0.968354i | \(-0.419707\pi\) | ||||
0.249582 | + | 0.968354i | \(0.419707\pi\) | |||||||
\(678\) | 19.8680 | 0.763027 | ||||||||
\(679\) | 72.1269 | 2.76798 | ||||||||
\(680\) | −13.4094 | −0.514227 | ||||||||
\(681\) | −35.1361 | −1.34642 | ||||||||
\(682\) | −24.5661 | −0.940684 | ||||||||
\(683\) | 6.10046 | 0.233427 | 0.116714 | − | 0.993166i | \(-0.462764\pi\) | ||||
0.116714 | + | 0.993166i | \(0.462764\pi\) | |||||||
\(684\) | 0.367153 | 0.0140384 | ||||||||
\(685\) | 17.0569 | 0.651712 | ||||||||
\(686\) | 73.6974 | 2.81378 | ||||||||
\(687\) | 9.10770 | 0.347480 | ||||||||
\(688\) | −30.3012 | −1.15522 | ||||||||
\(689\) | −41.2249 | −1.57055 | ||||||||
\(690\) | 17.8408 | 0.679189 | ||||||||
\(691\) | −36.3770 | −1.38385 | −0.691923 | − | 0.721972i | \(-0.743236\pi\) | ||||
−0.691923 | + | 0.721972i | \(0.743236\pi\) | |||||||
\(692\) | −0.387094 | −0.0147151 | ||||||||
\(693\) | −21.3937 | −0.812680 | ||||||||
\(694\) | 26.5387 | 1.00740 | ||||||||
\(695\) | −13.2628 | −0.503088 | ||||||||
\(696\) | 0.449177 | 0.0170260 | ||||||||
\(697\) | −28.4642 | −1.07816 | ||||||||
\(698\) | 1.76559 | 0.0668286 | ||||||||
\(699\) | 8.22591 | 0.311133 | ||||||||
\(700\) | 4.95822 | 0.187403 | ||||||||
\(701\) | −0.751456 | −0.0283821 | −0.0141911 | − | 0.999899i | \(-0.504517\pi\) | ||||
−0.0141911 | + | 0.999899i | \(0.504517\pi\) | |||||||
\(702\) | −25.6869 | −0.969489 | ||||||||
\(703\) | 4.88664 | 0.184303 | ||||||||
\(704\) | 26.0951 | 0.983496 | ||||||||
\(705\) | 8.67605 | 0.326759 | ||||||||
\(706\) | −52.3264 | −1.96933 | ||||||||
\(707\) | 0.692324 | 0.0260375 | ||||||||
\(708\) | −4.55670 | −0.171251 | ||||||||
\(709\) | −23.0597 | −0.866024 | −0.433012 | − | 0.901388i | \(-0.642549\pi\) | ||||
−0.433012 | + | 0.901388i | \(0.642549\pi\) | |||||||
\(710\) | −0.972599 | −0.0365010 | ||||||||
\(711\) | 12.5706 | 0.471436 | ||||||||
\(712\) | −0.422197 | −0.0158225 | ||||||||
\(713\) | −14.7054 | −0.550723 | ||||||||
\(714\) | −54.3436 | −2.03376 | ||||||||
\(715\) | −26.5824 | −0.994125 | ||||||||
\(716\) | −4.21462 | −0.157508 | ||||||||
\(717\) | 35.0133 | 1.30759 | ||||||||
\(718\) | −6.01521 | −0.224486 | ||||||||
\(719\) | −8.79812 | −0.328115 | −0.164057 | − | 0.986451i | \(-0.552458\pi\) | ||||
−0.164057 | + | 0.986451i | \(0.552458\pi\) | |||||||
\(720\) | −6.91729 | −0.257792 | ||||||||
\(721\) | −48.5363 | −1.80759 | ||||||||
\(722\) | −1.53574 | −0.0571545 | ||||||||
\(723\) | −20.7082 | −0.770144 | ||||||||
\(724\) | 6.39593 | 0.237703 | ||||||||
\(725\) | −0.251642 | −0.00934574 | ||||||||
\(726\) | −22.5289 | −0.836125 | ||||||||
\(727\) | 16.8871 | 0.626310 | 0.313155 | − | 0.949702i | \(-0.398614\pi\) | ||||
0.313155 | + | 0.949702i | \(0.398614\pi\) | |||||||
\(728\) | 51.9296 | 1.92464 | ||||||||
\(729\) | 12.5644 | 0.465349 | ||||||||
\(730\) | −15.3368 | −0.567641 | ||||||||
\(731\) | −23.8627 | −0.882593 | ||||||||
\(732\) | 6.94496 | 0.256693 | ||||||||
\(733\) | 11.2004 | 0.413695 | 0.206848 | − | 0.978373i | \(-0.433680\pi\) | ||||
0.206848 | + | 0.978373i | \(0.433680\pi\) | |||||||
\(734\) | 43.9310 | 1.62152 | ||||||||
\(735\) | 49.6993 | 1.83319 | ||||||||
\(736\) | −7.88752 | −0.290738 | ||||||||
\(737\) | −23.6396 | −0.870776 | ||||||||
\(738\) | −12.3888 | −0.456040 | ||||||||
\(739\) | 45.6500 | 1.67926 | 0.839632 | − | 0.543156i | \(-0.182771\pi\) | ||||
0.839632 | + | 0.543156i | \(0.182771\pi\) | |||||||
\(740\) | 2.57891 | 0.0948028 | ||||||||
\(741\) | −8.46502 | −0.310970 | ||||||||
\(742\) | 73.2404 | 2.68874 | ||||||||
\(743\) | −3.23921 | −0.118835 | −0.0594176 | − | 0.998233i | \(-0.518924\pi\) | ||||
−0.0594176 | + | 0.998233i | \(0.518924\pi\) | |||||||
\(744\) | 18.9030 | 0.693017 | ||||||||
\(745\) | 23.6618 | 0.866900 | ||||||||
\(746\) | 8.20191 | 0.300293 | ||||||||
\(747\) | 8.83153 | 0.323129 | ||||||||
\(748\) | −5.54385 | −0.202703 | ||||||||
\(749\) | −27.4574 | −1.00327 | ||||||||
\(750\) | 35.5229 | 1.29711 | ||||||||
\(751\) | −18.0882 | −0.660050 | −0.330025 | − | 0.943972i | \(-0.607057\pi\) | ||||
−0.330025 | + | 0.943972i | \(0.607057\pi\) | |||||||
\(752\) | −13.4814 | −0.491616 | ||||||||
\(753\) | 40.6915 | 1.48288 | ||||||||
\(754\) | 0.575623 | 0.0209630 | ||||||||
\(755\) | 13.5671 | 0.493757 | ||||||||
\(756\) | 6.93694 | 0.252294 | ||||||||
\(757\) | 33.3156 | 1.21088 | 0.605438 | − | 0.795892i | \(-0.292998\pi\) | ||||
0.605438 | + | 0.795892i | \(0.292998\pi\) | |||||||
\(758\) | −23.0803 | −0.838314 | ||||||||
\(759\) | −33.7716 | −1.22583 | ||||||||
\(760\) | 3.71090 | 0.134609 | ||||||||
\(761\) | 19.4472 | 0.704961 | 0.352480 | − | 0.935819i | \(-0.385338\pi\) | ||||
0.352480 | + | 0.935819i | \(0.385338\pi\) | |||||||
\(762\) | −57.9599 | −2.09966 | ||||||||
\(763\) | −3.43655 | −0.124411 | ||||||||
\(764\) | 1.12861 | 0.0408318 | ||||||||
\(765\) | −5.44749 | −0.196954 | ||||||||
\(766\) | −31.5183 | −1.13880 | ||||||||
\(767\) | 26.7365 | 0.965400 | ||||||||
\(768\) | 16.7389 | 0.604012 | ||||||||
\(769\) | −44.4046 | −1.60127 | −0.800636 | − | 0.599151i | \(-0.795505\pi\) | ||||
−0.800636 | + | 0.599151i | \(0.795505\pi\) | |||||||
\(770\) | 47.2264 | 1.70192 | ||||||||
\(771\) | −21.5317 | −0.775446 | ||||||||
\(772\) | 6.73962 | 0.242564 | ||||||||
\(773\) | −38.9430 | −1.40068 | −0.700340 | − | 0.713809i | \(-0.746968\pi\) | ||||
−0.700340 | + | 0.713809i | \(0.746968\pi\) | |||||||
\(774\) | −10.3861 | −0.373320 | ||||||||
\(775\) | −10.5900 | −0.380404 | ||||||||
\(776\) | −37.2468 | −1.33708 | ||||||||
\(777\) | −47.8531 | −1.71672 | ||||||||
\(778\) | 1.87164 | 0.0671014 | ||||||||
\(779\) | 7.87714 | 0.282228 | ||||||||
\(780\) | −4.46739 | −0.159958 | ||||||||
\(781\) | 1.84107 | 0.0658786 | ||||||||
\(782\) | −21.8317 | −0.780701 | ||||||||
\(783\) | −0.352067 | −0.0125818 | ||||||||
\(784\) | −77.2259 | −2.75807 | ||||||||
\(785\) | 2.05073 | 0.0731936 | ||||||||
\(786\) | −18.5997 | −0.663430 | ||||||||
\(787\) | 22.9207 | 0.817034 | 0.408517 | − | 0.912751i | \(-0.366046\pi\) | ||||
0.408517 | + | 0.912751i | \(0.366046\pi\) | |||||||
\(788\) | −3.26831 | −0.116429 | ||||||||
\(789\) | 27.1661 | 0.967140 | ||||||||
\(790\) | −27.7496 | −0.987285 | ||||||||
\(791\) | 31.4823 | 1.11938 | ||||||||
\(792\) | 11.0479 | 0.392568 | ||||||||
\(793\) | −40.7497 | −1.44707 | ||||||||
\(794\) | −11.1708 | −0.396438 | ||||||||
\(795\) | 28.8486 | 1.02315 | ||||||||
\(796\) | 3.85351 | 0.136584 | ||||||||
\(797\) | −19.0593 | −0.675117 | −0.337558 | − | 0.941305i | \(-0.609601\pi\) | ||||
−0.337558 | + | 0.941305i | \(0.609601\pi\) | |||||||
\(798\) | 15.0390 | 0.532374 | ||||||||
\(799\) | −10.6168 | −0.375597 | ||||||||
\(800\) | −5.68013 | −0.200823 | ||||||||
\(801\) | −0.171515 | −0.00606018 | ||||||||
\(802\) | 14.5342 | 0.513222 | ||||||||
\(803\) | 29.0316 | 1.02450 | ||||||||
\(804\) | −3.97284 | −0.140111 | ||||||||
\(805\) | 28.2701 | 0.996389 | ||||||||
\(806\) | 24.2243 | 0.853265 | ||||||||
\(807\) | 3.47344 | 0.122271 | ||||||||
\(808\) | −0.357520 | −0.0125775 | ||||||||
\(809\) | 14.0874 | 0.495285 | 0.247643 | − | 0.968851i | \(-0.420344\pi\) | ||||
0.247643 | + | 0.968851i | \(0.420344\pi\) | |||||||
\(810\) | 24.9208 | 0.875628 | ||||||||
\(811\) | −23.5328 | −0.826347 | −0.413174 | − | 0.910652i | \(-0.635580\pi\) | ||||
−0.413174 | + | 0.910652i | \(0.635580\pi\) | |||||||
\(812\) | −0.155451 | −0.00545528 | ||||||||
\(813\) | 12.9149 | 0.452945 | ||||||||
\(814\) | −32.1150 | −1.12563 | ||||||||
\(815\) | −30.2974 | −1.06127 | ||||||||
\(816\) | 33.2610 | 1.16437 | ||||||||
\(817\) | 6.60373 | 0.231035 | ||||||||
\(818\) | −12.2280 | −0.427543 | ||||||||
\(819\) | 21.0961 | 0.737157 | ||||||||
\(820\) | 4.15714 | 0.145174 | ||||||||
\(821\) | −2.09164 | −0.0729986 | −0.0364993 | − | 0.999334i | \(-0.511621\pi\) | ||||
−0.0364993 | + | 0.999334i | \(0.511621\pi\) | |||||||
\(822\) | −35.6970 | −1.24508 | ||||||||
\(823\) | −3.65827 | −0.127519 | −0.0637596 | − | 0.997965i | \(-0.520309\pi\) | ||||
−0.0637596 | + | 0.997965i | \(0.520309\pi\) | |||||||
\(824\) | 25.0645 | 0.873162 | ||||||||
\(825\) | −24.3203 | −0.846724 | ||||||||
\(826\) | −47.5003 | −1.65275 | ||||||||
\(827\) | −21.3459 | −0.742270 | −0.371135 | − | 0.928579i | \(-0.621031\pi\) | ||||
−0.371135 | + | 0.928579i | \(0.621031\pi\) | |||||||
\(828\) | −1.44440 | −0.0501962 | ||||||||
\(829\) | 56.8573 | 1.97473 | 0.987367 | − | 0.158448i | \(-0.0506490\pi\) | ||||
0.987367 | + | 0.158448i | \(0.0506490\pi\) | |||||||
\(830\) | −19.4955 | −0.676699 | ||||||||
\(831\) | −29.4432 | −1.02137 | ||||||||
\(832\) | −25.7320 | −0.892098 | ||||||||
\(833\) | −60.8167 | −2.10717 | ||||||||
\(834\) | 27.7566 | 0.961133 | ||||||||
\(835\) | −23.1293 | −0.800423 | ||||||||
\(836\) | 1.53420 | 0.0530614 | ||||||||
\(837\) | −14.8162 | −0.512124 | ||||||||
\(838\) | 22.9677 | 0.793406 | ||||||||
\(839\) | 36.2399 | 1.25114 | 0.625570 | − | 0.780168i | \(-0.284866\pi\) | ||||
0.625570 | + | 0.780168i | \(0.284866\pi\) | |||||||
\(840\) | −36.3395 | −1.25383 | ||||||||
\(841\) | −28.9921 | −0.999728 | ||||||||
\(842\) | −48.5333 | −1.67257 | ||||||||
\(843\) | −22.6299 | −0.779414 | ||||||||
\(844\) | −0.358512 | −0.0123405 | ||||||||
\(845\) | 7.07590 | 0.243418 | ||||||||
\(846\) | −4.62091 | −0.158870 | ||||||||
\(847\) | −35.6986 | −1.22662 | ||||||||
\(848\) | −44.8267 | −1.53936 | ||||||||
\(849\) | 10.4915 | 0.360068 | ||||||||
\(850\) | −15.7219 | −0.539258 | ||||||||
\(851\) | −19.2243 | −0.658999 | ||||||||
\(852\) | 0.309407 | 0.0106001 | ||||||||
\(853\) | −8.85313 | −0.303126 | −0.151563 | − | 0.988448i | \(-0.548431\pi\) | ||||
−0.151563 | + | 0.988448i | \(0.548431\pi\) | |||||||
\(854\) | 72.3962 | 2.47735 | ||||||||
\(855\) | 1.50753 | 0.0515565 | ||||||||
\(856\) | 14.1792 | 0.484634 | ||||||||
\(857\) | −22.4249 | −0.766020 | −0.383010 | − | 0.923744i | \(-0.625112\pi\) | ||||
−0.383010 | + | 0.923744i | \(0.625112\pi\) | |||||||
\(858\) | 55.6320 | 1.89925 | ||||||||
\(859\) | 15.7193 | 0.536336 | 0.268168 | − | 0.963372i | \(-0.413582\pi\) | ||||
0.268168 | + | 0.963372i | \(0.413582\pi\) | |||||||
\(860\) | 3.48510 | 0.118841 | ||||||||
\(861\) | −77.1379 | −2.62885 | ||||||||
\(862\) | −30.0485 | −1.02346 | ||||||||
\(863\) | 54.4747 | 1.85434 | 0.927170 | − | 0.374640i | \(-0.122234\pi\) | ||||
0.927170 | + | 0.374640i | \(0.122234\pi\) | |||||||
\(864\) | −7.94695 | −0.270361 | ||||||||
\(865\) | −1.58941 | −0.0540415 | ||||||||
\(866\) | 54.5584 | 1.85397 | ||||||||
\(867\) | −7.90871 | −0.268594 | ||||||||
\(868\) | −6.54196 | −0.222049 | ||||||||
\(869\) | 52.5281 | 1.78190 | ||||||||
\(870\) | −0.402812 | −0.0136566 | ||||||||
\(871\) | 23.3107 | 0.789854 | ||||||||
\(872\) | 1.77466 | 0.0600975 | ||||||||
\(873\) | −15.1313 | −0.512116 | ||||||||
\(874\) | 6.04168 | 0.204363 | ||||||||
\(875\) | 56.2885 | 1.90290 | ||||||||
\(876\) | 4.87901 | 0.164846 | ||||||||
\(877\) | 8.14358 | 0.274989 | 0.137495 | − | 0.990503i | \(-0.456095\pi\) | ||||
0.137495 | + | 0.990503i | \(0.456095\pi\) | |||||||
\(878\) | −61.6124 | −2.07932 | ||||||||
\(879\) | −8.09892 | −0.273170 | ||||||||
\(880\) | −28.9049 | −0.974382 | ||||||||
\(881\) | 39.3891 | 1.32705 | 0.663526 | − | 0.748153i | \(-0.269059\pi\) | ||||
0.663526 | + | 0.748153i | \(0.269059\pi\) | |||||||
\(882\) | −26.4701 | −0.891294 | ||||||||
\(883\) | −10.8737 | −0.365930 | −0.182965 | − | 0.983119i | \(-0.558570\pi\) | ||||
−0.182965 | + | 0.983119i | \(0.558570\pi\) | |||||||
\(884\) | 5.46672 | 0.183866 | ||||||||
\(885\) | −18.7098 | −0.628923 | ||||||||
\(886\) | 9.23545 | 0.310271 | ||||||||
\(887\) | −1.51350 | −0.0508185 | −0.0254092 | − | 0.999677i | \(-0.508089\pi\) | ||||
−0.0254092 | + | 0.999677i | \(0.508089\pi\) | |||||||
\(888\) | 24.7116 | 0.829269 | ||||||||
\(889\) | −91.8415 | −3.08026 | ||||||||
\(890\) | 0.378617 | 0.0126913 | ||||||||
\(891\) | −47.1735 | −1.58037 | ||||||||
\(892\) | 2.25015 | 0.0753405 | ||||||||
\(893\) | 2.93809 | 0.0983194 | ||||||||
\(894\) | −49.5197 | −1.65619 | ||||||||
\(895\) | −17.3052 | −0.578451 | ||||||||
\(896\) | 65.2904 | 2.18120 | ||||||||
\(897\) | 33.3017 | 1.11191 | ||||||||
\(898\) | −15.9188 | −0.531218 | ||||||||
\(899\) | 0.332021 | 0.0110735 | ||||||||
\(900\) | −1.04017 | −0.0346723 | ||||||||
\(901\) | −35.3018 | −1.17607 | ||||||||
\(902\) | −51.7685 | −1.72370 | ||||||||
\(903\) | −64.6679 | −2.15201 | ||||||||
\(904\) | −16.2577 | −0.540722 | ||||||||
\(905\) | 26.2617 | 0.872969 | ||||||||
\(906\) | −28.3934 | −0.943307 | ||||||||
\(907\) | 29.1807 | 0.968930 | 0.484465 | − | 0.874811i | \(-0.339014\pi\) | ||||
0.484465 | + | 0.874811i | \(0.339014\pi\) | |||||||
\(908\) | −6.27946 | −0.208391 | ||||||||
\(909\) | −0.145240 | −0.00481732 | ||||||||
\(910\) | −46.5694 | −1.54376 | ||||||||
\(911\) | 17.8183 | 0.590348 | 0.295174 | − | 0.955444i | \(-0.404622\pi\) | ||||
0.295174 | + | 0.955444i | \(0.404622\pi\) | |||||||
\(912\) | −9.20459 | −0.304795 | ||||||||
\(913\) | 36.9037 | 1.22134 | ||||||||
\(914\) | −62.2528 | −2.05914 | ||||||||
\(915\) | 28.5160 | 0.942711 | ||||||||
\(916\) | 1.62771 | 0.0537812 | ||||||||
\(917\) | −29.4725 | −0.973269 | ||||||||
\(918\) | −21.9962 | −0.725984 | ||||||||
\(919\) | 4.07301 | 0.134356 | 0.0671780 | − | 0.997741i | \(-0.478600\pi\) | ||||
0.0671780 | + | 0.997741i | \(0.478600\pi\) | |||||||
\(920\) | −14.5988 | −0.481310 | ||||||||
\(921\) | −44.2133 | −1.45688 | ||||||||
\(922\) | −56.8561 | −1.87245 | ||||||||
\(923\) | −1.81545 | −0.0597564 | ||||||||
\(924\) | −15.0238 | −0.494248 | ||||||||
\(925\) | −13.8442 | −0.455194 | ||||||||
\(926\) | −1.39603 | −0.0458765 | ||||||||
\(927\) | 10.1823 | 0.334430 | ||||||||
\(928\) | 0.178085 | 0.00584593 | ||||||||
\(929\) | 3.81445 | 0.125148 | 0.0625739 | − | 0.998040i | \(-0.480069\pi\) | ||||
0.0625739 | + | 0.998040i | \(0.480069\pi\) | |||||||
\(930\) | −16.9518 | −0.555871 | ||||||||
\(931\) | 16.8303 | 0.551592 | ||||||||
\(932\) | 1.47012 | 0.0481554 | ||||||||
\(933\) | 25.2226 | 0.825749 | ||||||||
\(934\) | 20.2735 | 0.663370 | ||||||||
\(935\) | −22.7631 | −0.744432 | ||||||||
\(936\) | −10.8942 | −0.356086 | ||||||||
\(937\) | 47.4794 | 1.55108 | 0.775542 | − | 0.631296i | \(-0.217477\pi\) | ||||
0.775542 | + | 0.631296i | \(0.217477\pi\) | |||||||
\(938\) | −41.4139 | −1.35221 | ||||||||
\(939\) | 35.8649 | 1.17041 | ||||||||
\(940\) | 1.55057 | 0.0505740 | ||||||||
\(941\) | 58.4872 | 1.90663 | 0.953314 | − | 0.301980i | \(-0.0976475\pi\) | ||||
0.953314 | + | 0.301980i | \(0.0976475\pi\) | |||||||
\(942\) | −4.29179 | −0.139834 | ||||||||
\(943\) | −30.9890 | −1.00914 | ||||||||
\(944\) | 29.0725 | 0.946228 | ||||||||
\(945\) | 28.4831 | 0.926554 | ||||||||
\(946\) | −43.3996 | −1.41104 | ||||||||
\(947\) | 21.7542 | 0.706918 | 0.353459 | − | 0.935450i | \(-0.385005\pi\) | ||||
0.353459 | + | 0.935450i | \(0.385005\pi\) | |||||||
\(948\) | 8.82780 | 0.286714 | ||||||||
\(949\) | −28.6277 | −0.929294 | ||||||||
\(950\) | 4.35087 | 0.141161 | ||||||||
\(951\) | −12.3934 | −0.401885 | ||||||||
\(952\) | 44.4684 | 1.44123 | ||||||||
\(953\) | −10.3628 | −0.335684 | −0.167842 | − | 0.985814i | \(-0.553680\pi\) | ||||
−0.167842 | + | 0.985814i | \(0.553680\pi\) | |||||||
\(954\) | −15.3649 | −0.497456 | ||||||||
\(955\) | 4.63409 | 0.149956 | ||||||||
\(956\) | 6.25751 | 0.202382 | ||||||||
\(957\) | 0.762498 | 0.0246480 | ||||||||
\(958\) | −39.7382 | −1.28388 | ||||||||
\(959\) | −56.5644 | −1.82656 | ||||||||
\(960\) | 18.0069 | 0.581169 | ||||||||
\(961\) | −17.0274 | −0.549270 | ||||||||
\(962\) | 31.6682 | 1.02102 | ||||||||
\(963\) | 5.76020 | 0.185620 | ||||||||
\(964\) | −3.70093 | −0.119199 | ||||||||
\(965\) | 27.6729 | 0.890822 | ||||||||
\(966\) | −59.1640 | −1.90357 | ||||||||
\(967\) | 12.5957 | 0.405050 | 0.202525 | − | 0.979277i | \(-0.435085\pi\) | ||||
0.202525 | + | 0.979277i | \(0.435085\pi\) | |||||||
\(968\) | 18.4350 | 0.592523 | ||||||||
\(969\) | −7.24877 | −0.232864 | ||||||||
\(970\) | 33.4021 | 1.07248 | ||||||||
\(971\) | −50.9772 | −1.63594 | −0.817968 | − | 0.575263i | \(-0.804900\pi\) | ||||
−0.817968 | + | 0.575263i | \(0.804900\pi\) | |||||||
\(972\) | −3.66482 | −0.117549 | ||||||||
\(973\) | 43.9823 | 1.41001 | ||||||||
\(974\) | 11.0013 | 0.352506 | ||||||||
\(975\) | 23.9820 | 0.768037 | ||||||||
\(976\) | −44.3100 | −1.41833 | ||||||||
\(977\) | −46.6367 | −1.49204 | −0.746021 | − | 0.665923i | \(-0.768038\pi\) | ||||
−0.746021 | + | 0.665923i | \(0.768038\pi\) | |||||||
\(978\) | 63.4069 | 2.02753 | ||||||||
\(979\) | −0.716699 | −0.0229058 | ||||||||
\(980\) | 8.88217 | 0.283731 | ||||||||
\(981\) | 0.720943 | 0.0230179 | ||||||||
\(982\) | 63.7005 | 2.03277 | ||||||||
\(983\) | −35.2102 | −1.12303 | −0.561515 | − | 0.827466i | \(-0.689781\pi\) | ||||
−0.561515 | + | 0.827466i | \(0.689781\pi\) | |||||||
\(984\) | 39.8345 | 1.26988 | ||||||||
\(985\) | −13.4197 | −0.427587 | ||||||||
\(986\) | 0.492919 | 0.0156977 | ||||||||
\(987\) | −28.7716 | −0.915811 | ||||||||
\(988\) | −1.51285 | −0.0481303 | ||||||||
\(989\) | −25.9793 | −0.826095 | ||||||||
\(990\) | −9.90748 | −0.314880 | ||||||||
\(991\) | 16.2722 | 0.516905 | 0.258452 | − | 0.966024i | \(-0.416788\pi\) | ||||
0.258452 | + | 0.966024i | \(0.416788\pi\) | |||||||
\(992\) | 7.49447 | 0.237950 | ||||||||
\(993\) | −55.0218 | −1.74607 | ||||||||
\(994\) | 3.22534 | 0.102302 | ||||||||
\(995\) | 15.8225 | 0.501607 | ||||||||
\(996\) | 6.20199 | 0.196517 | ||||||||
\(997\) | 8.50252 | 0.269277 | 0.134639 | − | 0.990895i | \(-0.457013\pi\) | ||||
0.134639 | + | 0.990895i | \(0.457013\pi\) | |||||||
\(998\) | −41.2688 | −1.30634 | ||||||||
\(999\) | −19.3691 | −0.612811 |
(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 | 4009.2.a.e.1.18 | ✓ | 82 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
4009.2.a.e.1.18 | ✓ | 82 | 1.1 | even | 1 | trivial |