Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [8026,2,Mod(1,8026)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(8026, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("8026.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 8026 = 2 \cdot 4013 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 8026.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: | \(64.0879326623\) |
Analytic rank: | \(0\) |
Dimension: | \(96\) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.16 | ||
Character | \(\chi\) | \(=\) | 8026.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 1.00000 | 0.707107 | ||||||||
\(3\) | −2.39250 | −1.38131 | −0.690656 | − | 0.723184i | \(-0.742678\pi\) | ||||
−0.690656 | + | 0.723184i | \(0.742678\pi\) | |||||||
\(4\) | 1.00000 | 0.500000 | ||||||||
\(5\) | 1.27700 | 0.571091 | 0.285546 | − | 0.958365i | \(-0.407825\pi\) | ||||
0.285546 | + | 0.958365i | \(0.407825\pi\) | |||||||
\(6\) | −2.39250 | −0.976734 | ||||||||
\(7\) | 3.72505 | 1.40794 | 0.703969 | − | 0.710231i | \(-0.251409\pi\) | ||||
0.703969 | + | 0.710231i | \(0.251409\pi\) | |||||||
\(8\) | 1.00000 | 0.353553 | ||||||||
\(9\) | 2.72406 | 0.908020 | ||||||||
\(10\) | 1.27700 | 0.403822 | ||||||||
\(11\) | 5.70892 | 1.72130 | 0.860652 | − | 0.509194i | \(-0.170056\pi\) | ||||
0.860652 | + | 0.509194i | \(0.170056\pi\) | |||||||
\(12\) | −2.39250 | −0.690656 | ||||||||
\(13\) | 2.09104 | 0.579951 | 0.289975 | − | 0.957034i | \(-0.406353\pi\) | ||||
0.289975 | + | 0.957034i | \(0.406353\pi\) | |||||||
\(14\) | 3.72505 | 0.995563 | ||||||||
\(15\) | −3.05522 | −0.788855 | ||||||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | −3.61846 | −0.877605 | −0.438803 | − | 0.898584i | \(-0.644597\pi\) | ||||
−0.438803 | + | 0.898584i | \(0.644597\pi\) | |||||||
\(18\) | 2.72406 | 0.642067 | ||||||||
\(19\) | 7.92384 | 1.81785 | 0.908927 | − | 0.416956i | \(-0.136903\pi\) | ||||
0.908927 | + | 0.416956i | \(0.136903\pi\) | |||||||
\(20\) | 1.27700 | 0.285546 | ||||||||
\(21\) | −8.91220 | −1.94480 | ||||||||
\(22\) | 5.70892 | 1.21715 | ||||||||
\(23\) | 0.657930 | 0.137188 | 0.0685940 | − | 0.997645i | \(-0.478149\pi\) | ||||
0.0685940 | + | 0.997645i | \(0.478149\pi\) | |||||||
\(24\) | −2.39250 | −0.488367 | ||||||||
\(25\) | −3.36927 | −0.673855 | ||||||||
\(26\) | 2.09104 | 0.410087 | ||||||||
\(27\) | 0.660186 | 0.127053 | ||||||||
\(28\) | 3.72505 | 0.703969 | ||||||||
\(29\) | 8.28737 | 1.53893 | 0.769463 | − | 0.638692i | \(-0.220524\pi\) | ||||
0.769463 | + | 0.638692i | \(0.220524\pi\) | |||||||
\(30\) | −3.05522 | −0.557804 | ||||||||
\(31\) | 0.384931 | 0.0691356 | 0.0345678 | − | 0.999402i | \(-0.488995\pi\) | ||||
0.0345678 | + | 0.999402i | \(0.488995\pi\) | |||||||
\(32\) | 1.00000 | 0.176777 | ||||||||
\(33\) | −13.6586 | −2.37766 | ||||||||
\(34\) | −3.61846 | −0.620561 | ||||||||
\(35\) | 4.75689 | 0.804061 | ||||||||
\(36\) | 2.72406 | 0.454010 | ||||||||
\(37\) | 4.42642 | 0.727698 | 0.363849 | − | 0.931458i | \(-0.381462\pi\) | ||||
0.363849 | + | 0.931458i | \(0.381462\pi\) | |||||||
\(38\) | 7.92384 | 1.28542 | ||||||||
\(39\) | −5.00282 | −0.801093 | ||||||||
\(40\) | 1.27700 | 0.201911 | ||||||||
\(41\) | −0.620273 | −0.0968703 | −0.0484352 | − | 0.998826i | \(-0.515423\pi\) | ||||
−0.0484352 | + | 0.998826i | \(0.515423\pi\) | |||||||
\(42\) | −8.91220 | −1.37518 | ||||||||
\(43\) | 1.59179 | 0.242746 | 0.121373 | − | 0.992607i | \(-0.461270\pi\) | ||||
0.121373 | + | 0.992607i | \(0.461270\pi\) | |||||||
\(44\) | 5.70892 | 0.860652 | ||||||||
\(45\) | 3.47862 | 0.518562 | ||||||||
\(46\) | 0.657930 | 0.0970065 | ||||||||
\(47\) | 9.63330 | 1.40516 | 0.702581 | − | 0.711604i | \(-0.252031\pi\) | ||||
0.702581 | + | 0.711604i | \(0.252031\pi\) | |||||||
\(48\) | −2.39250 | −0.345328 | ||||||||
\(49\) | 6.87603 | 0.982290 | ||||||||
\(50\) | −3.36927 | −0.476487 | ||||||||
\(51\) | 8.65717 | 1.21225 | ||||||||
\(52\) | 2.09104 | 0.289975 | ||||||||
\(53\) | −6.79811 | −0.933792 | −0.466896 | − | 0.884312i | \(-0.654628\pi\) | ||||
−0.466896 | + | 0.884312i | \(0.654628\pi\) | |||||||
\(54\) | 0.660186 | 0.0898399 | ||||||||
\(55\) | 7.29028 | 0.983021 | ||||||||
\(56\) | 3.72505 | 0.497781 | ||||||||
\(57\) | −18.9578 | −2.51102 | ||||||||
\(58\) | 8.28737 | 1.08818 | ||||||||
\(59\) | −8.52656 | −1.11006 | −0.555032 | − | 0.831829i | \(-0.687294\pi\) | ||||
−0.555032 | + | 0.831829i | \(0.687294\pi\) | |||||||
\(60\) | −3.05522 | −0.394427 | ||||||||
\(61\) | 10.1503 | 1.29961 | 0.649805 | − | 0.760101i | \(-0.274851\pi\) | ||||
0.649805 | + | 0.760101i | \(0.274851\pi\) | |||||||
\(62\) | 0.384931 | 0.0488863 | ||||||||
\(63\) | 10.1473 | 1.27844 | ||||||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | 2.67026 | 0.331205 | ||||||||
\(66\) | −13.6586 | −1.68126 | ||||||||
\(67\) | 2.40652 | 0.294003 | 0.147002 | − | 0.989136i | \(-0.453038\pi\) | ||||
0.147002 | + | 0.989136i | \(0.453038\pi\) | |||||||
\(68\) | −3.61846 | −0.438803 | ||||||||
\(69\) | −1.57410 | −0.189499 | ||||||||
\(70\) | 4.75689 | 0.568557 | ||||||||
\(71\) | −1.48175 | −0.175851 | −0.0879255 | − | 0.996127i | \(-0.528024\pi\) | ||||
−0.0879255 | + | 0.996127i | \(0.528024\pi\) | |||||||
\(72\) | 2.72406 | 0.321034 | ||||||||
\(73\) | −8.09022 | −0.946889 | −0.473444 | − | 0.880824i | \(-0.656989\pi\) | ||||
−0.473444 | + | 0.880824i | \(0.656989\pi\) | |||||||
\(74\) | 4.42642 | 0.514561 | ||||||||
\(75\) | 8.06099 | 0.930803 | ||||||||
\(76\) | 7.92384 | 0.908927 | ||||||||
\(77\) | 21.2660 | 2.42349 | ||||||||
\(78\) | −5.00282 | −0.566458 | ||||||||
\(79\) | −3.47393 | −0.390848 | −0.195424 | − | 0.980719i | \(-0.562608\pi\) | ||||
−0.195424 | + | 0.980719i | \(0.562608\pi\) | |||||||
\(80\) | 1.27700 | 0.142773 | ||||||||
\(81\) | −9.75168 | −1.08352 | ||||||||
\(82\) | −0.620273 | −0.0684977 | ||||||||
\(83\) | −2.31114 | −0.253680 | −0.126840 | − | 0.991923i | \(-0.540484\pi\) | ||||
−0.126840 | + | 0.991923i | \(0.540484\pi\) | |||||||
\(84\) | −8.91220 | −0.972400 | ||||||||
\(85\) | −4.62077 | −0.501193 | ||||||||
\(86\) | 1.59179 | 0.171647 | ||||||||
\(87\) | −19.8275 | −2.12573 | ||||||||
\(88\) | 5.70892 | 0.608573 | ||||||||
\(89\) | 2.26902 | 0.240516 | 0.120258 | − | 0.992743i | \(-0.461628\pi\) | ||||
0.120258 | + | 0.992743i | \(0.461628\pi\) | |||||||
\(90\) | 3.47862 | 0.366679 | ||||||||
\(91\) | 7.78925 | 0.816535 | ||||||||
\(92\) | 0.657930 | 0.0685940 | ||||||||
\(93\) | −0.920947 | −0.0954978 | ||||||||
\(94\) | 9.63330 | 0.993599 | ||||||||
\(95\) | 10.1187 | 1.03816 | ||||||||
\(96\) | −2.39250 | −0.244184 | ||||||||
\(97\) | −15.1111 | −1.53430 | −0.767148 | − | 0.641470i | \(-0.778325\pi\) | ||||
−0.767148 | + | 0.641470i | \(0.778325\pi\) | |||||||
\(98\) | 6.87603 | 0.694584 | ||||||||
\(99\) | 15.5514 | 1.56298 | ||||||||
\(100\) | −3.36927 | −0.336927 | ||||||||
\(101\) | 2.50820 | 0.249575 | 0.124787 | − | 0.992183i | \(-0.460175\pi\) | ||||
0.124787 | + | 0.992183i | \(0.460175\pi\) | |||||||
\(102\) | 8.65717 | 0.857187 | ||||||||
\(103\) | −10.5767 | −1.04216 | −0.521079 | − | 0.853508i | \(-0.674470\pi\) | ||||
−0.521079 | + | 0.853508i | \(0.674470\pi\) | |||||||
\(104\) | 2.09104 | 0.205044 | ||||||||
\(105\) | −11.3809 | −1.11066 | ||||||||
\(106\) | −6.79811 | −0.660290 | ||||||||
\(107\) | 16.3661 | 1.58217 | 0.791087 | − | 0.611704i | \(-0.209516\pi\) | ||||
0.791087 | + | 0.611704i | \(0.209516\pi\) | |||||||
\(108\) | 0.660186 | 0.0635264 | ||||||||
\(109\) | −17.1222 | −1.64001 | −0.820004 | − | 0.572358i | \(-0.806029\pi\) | ||||
−0.820004 | + | 0.572358i | \(0.806029\pi\) | |||||||
\(110\) | 7.29028 | 0.695101 | ||||||||
\(111\) | −10.5902 | −1.00518 | ||||||||
\(112\) | 3.72505 | 0.351985 | ||||||||
\(113\) | −10.5780 | −0.995097 | −0.497548 | − | 0.867436i | \(-0.665766\pi\) | ||||
−0.497548 | + | 0.867436i | \(0.665766\pi\) | |||||||
\(114\) | −18.9578 | −1.77556 | ||||||||
\(115\) | 0.840176 | 0.0783468 | ||||||||
\(116\) | 8.28737 | 0.769463 | ||||||||
\(117\) | 5.69613 | 0.526607 | ||||||||
\(118\) | −8.52656 | −0.784933 | ||||||||
\(119\) | −13.4790 | −1.23561 | ||||||||
\(120\) | −3.05522 | −0.278902 | ||||||||
\(121\) | 21.5918 | 1.96289 | ||||||||
\(122\) | 10.1503 | 0.918963 | ||||||||
\(123\) | 1.48400 | 0.133808 | ||||||||
\(124\) | 0.384931 | 0.0345678 | ||||||||
\(125\) | −10.6876 | −0.955924 | ||||||||
\(126\) | 10.1473 | 0.903991 | ||||||||
\(127\) | −6.67493 | −0.592304 | −0.296152 | − | 0.955141i | \(-0.595703\pi\) | ||||
−0.296152 | + | 0.955141i | \(0.595703\pi\) | |||||||
\(128\) | 1.00000 | 0.0883883 | ||||||||
\(129\) | −3.80836 | −0.335308 | ||||||||
\(130\) | 2.67026 | 0.234197 | ||||||||
\(131\) | 8.89195 | 0.776893 | 0.388447 | − | 0.921471i | \(-0.373012\pi\) | ||||
0.388447 | + | 0.921471i | \(0.373012\pi\) | |||||||
\(132\) | −13.6586 | −1.18883 | ||||||||
\(133\) | 29.5167 | 2.55943 | ||||||||
\(134\) | 2.40652 | 0.207892 | ||||||||
\(135\) | 0.843056 | 0.0725587 | ||||||||
\(136\) | −3.61846 | −0.310280 | ||||||||
\(137\) | −21.1507 | −1.80702 | −0.903511 | − | 0.428564i | \(-0.859020\pi\) | ||||
−0.903511 | + | 0.428564i | \(0.859020\pi\) | |||||||
\(138\) | −1.57410 | −0.133996 | ||||||||
\(139\) | −8.47259 | −0.718635 | −0.359318 | − | 0.933215i | \(-0.616991\pi\) | ||||
−0.359318 | + | 0.933215i | \(0.616991\pi\) | |||||||
\(140\) | 4.75689 | 0.402031 | ||||||||
\(141\) | −23.0477 | −1.94096 | ||||||||
\(142\) | −1.48175 | −0.124346 | ||||||||
\(143\) | 11.9376 | 0.998272 | ||||||||
\(144\) | 2.72406 | 0.227005 | ||||||||
\(145\) | 10.5830 | 0.878867 | ||||||||
\(146\) | −8.09022 | −0.669551 | ||||||||
\(147\) | −16.4509 | −1.35685 | ||||||||
\(148\) | 4.42642 | 0.363849 | ||||||||
\(149\) | −12.1670 | −0.996758 | −0.498379 | − | 0.866959i | \(-0.666071\pi\) | ||||
−0.498379 | + | 0.866959i | \(0.666071\pi\) | |||||||
\(150\) | 8.06099 | 0.658177 | ||||||||
\(151\) | −16.4280 | −1.33689 | −0.668447 | − | 0.743760i | \(-0.733040\pi\) | ||||
−0.668447 | + | 0.743760i | \(0.733040\pi\) | |||||||
\(152\) | 7.92384 | 0.642708 | ||||||||
\(153\) | −9.85690 | −0.796883 | ||||||||
\(154\) | 21.2660 | 1.71367 | ||||||||
\(155\) | 0.491556 | 0.0394827 | ||||||||
\(156\) | −5.00282 | −0.400546 | ||||||||
\(157\) | 9.78684 | 0.781075 | 0.390537 | − | 0.920587i | \(-0.372289\pi\) | ||||
0.390537 | + | 0.920587i | \(0.372289\pi\) | |||||||
\(158\) | −3.47393 | −0.276371 | ||||||||
\(159\) | 16.2645 | 1.28986 | ||||||||
\(160\) | 1.27700 | 0.100956 | ||||||||
\(161\) | 2.45083 | 0.193152 | ||||||||
\(162\) | −9.75168 | −0.766164 | ||||||||
\(163\) | 2.86243 | 0.224203 | 0.112101 | − | 0.993697i | \(-0.464242\pi\) | ||||
0.112101 | + | 0.993697i | \(0.464242\pi\) | |||||||
\(164\) | −0.620273 | −0.0484352 | ||||||||
\(165\) | −17.4420 | −1.35786 | ||||||||
\(166\) | −2.31114 | −0.179379 | ||||||||
\(167\) | −15.4030 | −1.19192 | −0.595960 | − | 0.803014i | \(-0.703228\pi\) | ||||
−0.595960 | + | 0.803014i | \(0.703228\pi\) | |||||||
\(168\) | −8.91220 | −0.687591 | ||||||||
\(169\) | −8.62754 | −0.663657 | ||||||||
\(170\) | −4.62077 | −0.354397 | ||||||||
\(171\) | 21.5850 | 1.65065 | ||||||||
\(172\) | 1.59179 | 0.121373 | ||||||||
\(173\) | 5.62302 | 0.427510 | 0.213755 | − | 0.976887i | \(-0.431431\pi\) | ||||
0.213755 | + | 0.976887i | \(0.431431\pi\) | |||||||
\(174\) | −19.8275 | −1.50312 | ||||||||
\(175\) | −12.5507 | −0.948746 | ||||||||
\(176\) | 5.70892 | 0.430326 | ||||||||
\(177\) | 20.3998 | 1.53334 | ||||||||
\(178\) | 2.26902 | 0.170070 | ||||||||
\(179\) | −7.93544 | −0.593123 | −0.296561 | − | 0.955014i | \(-0.595840\pi\) | ||||
−0.296561 | + | 0.955014i | \(0.595840\pi\) | |||||||
\(180\) | 3.47862 | 0.259281 | ||||||||
\(181\) | 19.5495 | 1.45311 | 0.726553 | − | 0.687111i | \(-0.241121\pi\) | ||||
0.726553 | + | 0.687111i | \(0.241121\pi\) | |||||||
\(182\) | 7.78925 | 0.577378 | ||||||||
\(183\) | −24.2845 | −1.79517 | ||||||||
\(184\) | 0.657930 | 0.0485033 | ||||||||
\(185\) | 5.65253 | 0.415582 | ||||||||
\(186\) | −0.920947 | −0.0675271 | ||||||||
\(187\) | −20.6575 | −1.51062 | ||||||||
\(188\) | 9.63330 | 0.702581 | ||||||||
\(189\) | 2.45923 | 0.178882 | ||||||||
\(190\) | 10.1187 | 0.734090 | ||||||||
\(191\) | 5.06025 | 0.366147 | 0.183073 | − | 0.983099i | \(-0.441395\pi\) | ||||
0.183073 | + | 0.983099i | \(0.441395\pi\) | |||||||
\(192\) | −2.39250 | −0.172664 | ||||||||
\(193\) | −20.6196 | −1.48423 | −0.742115 | − | 0.670273i | \(-0.766177\pi\) | ||||
−0.742115 | + | 0.670273i | \(0.766177\pi\) | |||||||
\(194\) | −15.1111 | −1.08491 | ||||||||
\(195\) | −6.38860 | −0.457497 | ||||||||
\(196\) | 6.87603 | 0.491145 | ||||||||
\(197\) | 6.16126 | 0.438971 | 0.219486 | − | 0.975616i | \(-0.429562\pi\) | ||||
0.219486 | + | 0.975616i | \(0.429562\pi\) | |||||||
\(198\) | 15.5514 | 1.10519 | ||||||||
\(199\) | −20.5246 | −1.45495 | −0.727477 | − | 0.686132i | \(-0.759307\pi\) | ||||
−0.727477 | + | 0.686132i | \(0.759307\pi\) | |||||||
\(200\) | −3.36927 | −0.238244 | ||||||||
\(201\) | −5.75760 | −0.406110 | ||||||||
\(202\) | 2.50820 | 0.176476 | ||||||||
\(203\) | 30.8709 | 2.16671 | ||||||||
\(204\) | 8.65717 | 0.606123 | ||||||||
\(205\) | −0.792088 | −0.0553218 | ||||||||
\(206\) | −10.5767 | −0.736917 | ||||||||
\(207\) | 1.79224 | 0.124569 | ||||||||
\(208\) | 2.09104 | 0.144988 | ||||||||
\(209\) | 45.2366 | 3.12908 | ||||||||
\(210\) | −11.3809 | −0.785354 | ||||||||
\(211\) | −2.32561 | −0.160102 | −0.0800509 | − | 0.996791i | \(-0.525508\pi\) | ||||
−0.0800509 | + | 0.996791i | \(0.525508\pi\) | |||||||
\(212\) | −6.79811 | −0.466896 | ||||||||
\(213\) | 3.54508 | 0.242905 | ||||||||
\(214\) | 16.3661 | 1.11877 | ||||||||
\(215\) | 2.03272 | 0.138630 | ||||||||
\(216\) | 0.660186 | 0.0449199 | ||||||||
\(217\) | 1.43389 | 0.0973387 | ||||||||
\(218\) | −17.1222 | −1.15966 | ||||||||
\(219\) | 19.3559 | 1.30795 | ||||||||
\(220\) | 7.29028 | 0.491511 | ||||||||
\(221\) | −7.56635 | −0.508968 | ||||||||
\(222\) | −10.5902 | −0.710768 | ||||||||
\(223\) | 4.23177 | 0.283380 | 0.141690 | − | 0.989911i | \(-0.454746\pi\) | ||||
0.141690 | + | 0.989911i | \(0.454746\pi\) | |||||||
\(224\) | 3.72505 | 0.248891 | ||||||||
\(225\) | −9.17811 | −0.611874 | ||||||||
\(226\) | −10.5780 | −0.703640 | ||||||||
\(227\) | −5.60126 | −0.371768 | −0.185884 | − | 0.982572i | \(-0.559515\pi\) | ||||
−0.185884 | + | 0.982572i | \(0.559515\pi\) | |||||||
\(228\) | −18.9578 | −1.25551 | ||||||||
\(229\) | −17.9761 | −1.18790 | −0.593948 | − | 0.804504i | \(-0.702431\pi\) | ||||
−0.593948 | + | 0.804504i | \(0.702431\pi\) | |||||||
\(230\) | 0.840176 | 0.0553996 | ||||||||
\(231\) | −50.8790 | −3.34759 | ||||||||
\(232\) | 8.28737 | 0.544092 | ||||||||
\(233\) | −18.3706 | −1.20350 | −0.601750 | − | 0.798684i | \(-0.705530\pi\) | ||||
−0.601750 | + | 0.798684i | \(0.705530\pi\) | |||||||
\(234\) | 5.69613 | 0.372368 | ||||||||
\(235\) | 12.3017 | 0.802475 | ||||||||
\(236\) | −8.52656 | −0.555032 | ||||||||
\(237\) | 8.31138 | 0.539882 | ||||||||
\(238\) | −13.4790 | −0.873711 | ||||||||
\(239\) | 8.96537 | 0.579922 | 0.289961 | − | 0.957039i | \(-0.406358\pi\) | ||||
0.289961 | + | 0.957039i | \(0.406358\pi\) | |||||||
\(240\) | −3.05522 | −0.197214 | ||||||||
\(241\) | 9.57416 | 0.616726 | 0.308363 | − | 0.951269i | \(-0.400219\pi\) | ||||
0.308363 | + | 0.951269i | \(0.400219\pi\) | |||||||
\(242\) | 21.5918 | 1.38797 | ||||||||
\(243\) | 21.3503 | 1.36962 | ||||||||
\(244\) | 10.1503 | 0.649805 | ||||||||
\(245\) | 8.78068 | 0.560977 | ||||||||
\(246\) | 1.48400 | 0.0946166 | ||||||||
\(247\) | 16.5691 | 1.05427 | ||||||||
\(248\) | 0.384931 | 0.0244431 | ||||||||
\(249\) | 5.52940 | 0.350411 | ||||||||
\(250\) | −10.6876 | −0.675940 | ||||||||
\(251\) | 1.64720 | 0.103970 | 0.0519851 | − | 0.998648i | \(-0.483445\pi\) | ||||
0.0519851 | + | 0.998648i | \(0.483445\pi\) | |||||||
\(252\) | 10.1473 | 0.639218 | ||||||||
\(253\) | 3.75607 | 0.236142 | ||||||||
\(254\) | −6.67493 | −0.418822 | ||||||||
\(255\) | 11.0552 | 0.692303 | ||||||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | 19.2633 | 1.20161 | 0.600805 | − | 0.799395i | \(-0.294847\pi\) | ||||
0.600805 | + | 0.799395i | \(0.294847\pi\) | |||||||
\(258\) | −3.80836 | −0.237098 | ||||||||
\(259\) | 16.4886 | 1.02455 | ||||||||
\(260\) | 2.67026 | 0.165602 | ||||||||
\(261\) | 22.5753 | 1.39738 | ||||||||
\(262\) | 8.89195 | 0.549347 | ||||||||
\(263\) | −14.9341 | −0.920877 | −0.460438 | − | 0.887692i | \(-0.652308\pi\) | ||||
−0.460438 | + | 0.887692i | \(0.652308\pi\) | |||||||
\(264\) | −13.6586 | −0.840628 | ||||||||
\(265\) | −8.68117 | −0.533280 | ||||||||
\(266\) | 29.5167 | 1.80979 | ||||||||
\(267\) | −5.42864 | −0.332227 | ||||||||
\(268\) | 2.40652 | 0.147002 | ||||||||
\(269\) | 17.9977 | 1.09734 | 0.548669 | − | 0.836039i | \(-0.315135\pi\) | ||||
0.548669 | + | 0.836039i | \(0.315135\pi\) | |||||||
\(270\) | 0.843056 | 0.0513068 | ||||||||
\(271\) | 5.18649 | 0.315057 | 0.157528 | − | 0.987514i | \(-0.449647\pi\) | ||||
0.157528 | + | 0.987514i | \(0.449647\pi\) | |||||||
\(272\) | −3.61846 | −0.219401 | ||||||||
\(273\) | −18.6358 | −1.12789 | ||||||||
\(274\) | −21.1507 | −1.27776 | ||||||||
\(275\) | −19.2349 | −1.15991 | ||||||||
\(276\) | −1.57410 | −0.0947496 | ||||||||
\(277\) | 14.5674 | 0.875271 | 0.437636 | − | 0.899152i | \(-0.355816\pi\) | ||||
0.437636 | + | 0.899152i | \(0.355816\pi\) | |||||||
\(278\) | −8.47259 | −0.508152 | ||||||||
\(279\) | 1.04857 | 0.0627765 | ||||||||
\(280\) | 4.75689 | 0.284279 | ||||||||
\(281\) | 0.0182862 | 0.00109086 | 0.000545431 | − | 1.00000i | \(-0.499826\pi\) | ||||
0.000545431 | 1.00000i | \(0.499826\pi\) | ||||||||
\(282\) | −23.0477 | −1.37247 | ||||||||
\(283\) | 17.0100 | 1.01114 | 0.505569 | − | 0.862786i | \(-0.331283\pi\) | ||||
0.505569 | + | 0.862786i | \(0.331283\pi\) | |||||||
\(284\) | −1.48175 | −0.0879255 | ||||||||
\(285\) | −24.2091 | −1.43402 | ||||||||
\(286\) | 11.9376 | 0.705885 | ||||||||
\(287\) | −2.31055 | −0.136387 | ||||||||
\(288\) | 2.72406 | 0.160517 | ||||||||
\(289\) | −3.90676 | −0.229809 | ||||||||
\(290\) | 10.5830 | 0.621453 | ||||||||
\(291\) | 36.1532 | 2.11934 | ||||||||
\(292\) | −8.09022 | −0.473444 | ||||||||
\(293\) | −22.2830 | −1.30178 | −0.650892 | − | 0.759170i | \(-0.725605\pi\) | ||||
−0.650892 | + | 0.759170i | \(0.725605\pi\) | |||||||
\(294\) | −16.4509 | −0.959436 | ||||||||
\(295\) | −10.8884 | −0.633947 | ||||||||
\(296\) | 4.42642 | 0.257280 | ||||||||
\(297\) | 3.76895 | 0.218696 | ||||||||
\(298\) | −12.1670 | −0.704815 | ||||||||
\(299\) | 1.37576 | 0.0795623 | ||||||||
\(300\) | 8.06099 | 0.465402 | ||||||||
\(301\) | 5.92951 | 0.341771 | ||||||||
\(302\) | −16.4280 | −0.945326 | ||||||||
\(303\) | −6.00086 | −0.344741 | ||||||||
\(304\) | 7.92384 | 0.454463 | ||||||||
\(305\) | 12.9619 | 0.742196 | ||||||||
\(306\) | −9.85690 | −0.563481 | ||||||||
\(307\) | −22.0570 | −1.25886 | −0.629429 | − | 0.777058i | \(-0.716711\pi\) | ||||
−0.629429 | + | 0.777058i | \(0.716711\pi\) | |||||||
\(308\) | 21.2660 | 1.21174 | ||||||||
\(309\) | 25.3049 | 1.43954 | ||||||||
\(310\) | 0.491556 | 0.0279185 | ||||||||
\(311\) | 25.3530 | 1.43764 | 0.718819 | − | 0.695197i | \(-0.244683\pi\) | ||||
0.718819 | + | 0.695197i | \(0.244683\pi\) | |||||||
\(312\) | −5.00282 | −0.283229 | ||||||||
\(313\) | 19.1017 | 1.07969 | 0.539846 | − | 0.841764i | \(-0.318482\pi\) | ||||
0.539846 | + | 0.841764i | \(0.318482\pi\) | |||||||
\(314\) | 9.78684 | 0.552303 | ||||||||
\(315\) | 12.9581 | 0.730104 | ||||||||
\(316\) | −3.47393 | −0.195424 | ||||||||
\(317\) | 9.43398 | 0.529865 | 0.264932 | − | 0.964267i | \(-0.414650\pi\) | ||||
0.264932 | + | 0.964267i | \(0.414650\pi\) | |||||||
\(318\) | 16.2645 | 0.912066 | ||||||||
\(319\) | 47.3119 | 2.64896 | ||||||||
\(320\) | 1.27700 | 0.0713864 | ||||||||
\(321\) | −39.1560 | −2.18547 | ||||||||
\(322\) | 2.45083 | 0.136579 | ||||||||
\(323\) | −28.6721 | −1.59536 | ||||||||
\(324\) | −9.75168 | −0.541760 | ||||||||
\(325\) | −7.04530 | −0.390803 | ||||||||
\(326\) | 2.86243 | 0.158535 | ||||||||
\(327\) | 40.9648 | 2.26536 | ||||||||
\(328\) | −0.620273 | −0.0342488 | ||||||||
\(329\) | 35.8846 | 1.97838 | ||||||||
\(330\) | −17.4420 | −0.960151 | ||||||||
\(331\) | −9.74999 | −0.535908 | −0.267954 | − | 0.963432i | \(-0.586348\pi\) | ||||
−0.267954 | + | 0.963432i | \(0.586348\pi\) | |||||||
\(332\) | −2.31114 | −0.126840 | ||||||||
\(333\) | 12.0578 | 0.660765 | ||||||||
\(334\) | −15.4030 | −0.842815 | ||||||||
\(335\) | 3.07312 | 0.167903 | ||||||||
\(336\) | −8.91220 | −0.486200 | ||||||||
\(337\) | −13.3092 | −0.724999 | −0.362500 | − | 0.931984i | \(-0.618077\pi\) | ||||
−0.362500 | + | 0.931984i | \(0.618077\pi\) | |||||||
\(338\) | −8.62754 | −0.469276 | ||||||||
\(339\) | 25.3079 | 1.37454 | ||||||||
\(340\) | −4.62077 | −0.250596 | ||||||||
\(341\) | 2.19754 | 0.119003 | ||||||||
\(342\) | 21.5850 | 1.16718 | ||||||||
\(343\) | −0.461796 | −0.0249346 | ||||||||
\(344\) | 1.59179 | 0.0858237 | ||||||||
\(345\) | −2.01012 | −0.108221 | ||||||||
\(346\) | 5.62302 | 0.302295 | ||||||||
\(347\) | 2.08092 | 0.111710 | 0.0558549 | − | 0.998439i | \(-0.482212\pi\) | ||||
0.0558549 | + | 0.998439i | \(0.482212\pi\) | |||||||
\(348\) | −19.8275 | −1.06287 | ||||||||
\(349\) | −30.4313 | −1.62895 | −0.814474 | − | 0.580200i | \(-0.802974\pi\) | ||||
−0.814474 | + | 0.580200i | \(0.802974\pi\) | |||||||
\(350\) | −12.5507 | −0.670865 | ||||||||
\(351\) | 1.38048 | 0.0736844 | ||||||||
\(352\) | 5.70892 | 0.304286 | ||||||||
\(353\) | 13.6586 | 0.726976 | 0.363488 | − | 0.931599i | \(-0.381586\pi\) | ||||
0.363488 | + | 0.931599i | \(0.381586\pi\) | |||||||
\(354\) | 20.3998 | 1.08424 | ||||||||
\(355\) | −1.89219 | −0.100427 | ||||||||
\(356\) | 2.26902 | 0.120258 | ||||||||
\(357\) | 32.2484 | 1.70677 | ||||||||
\(358\) | −7.93544 | −0.419401 | ||||||||
\(359\) | 4.39473 | 0.231945 | 0.115973 | − | 0.993252i | \(-0.463002\pi\) | ||||
0.115973 | + | 0.993252i | \(0.463002\pi\) | |||||||
\(360\) | 3.47862 | 0.183339 | ||||||||
\(361\) | 43.7872 | 2.30459 | ||||||||
\(362\) | 19.5495 | 1.02750 | ||||||||
\(363\) | −51.6583 | −2.71136 | ||||||||
\(364\) | 7.78925 | 0.408268 | ||||||||
\(365\) | −10.3312 | −0.540760 | ||||||||
\(366\) | −24.2845 | −1.26937 | ||||||||
\(367\) | −23.7517 | −1.23983 | −0.619914 | − | 0.784669i | \(-0.712833\pi\) | ||||
−0.619914 | + | 0.784669i | \(0.712833\pi\) | |||||||
\(368\) | 0.657930 | 0.0342970 | ||||||||
\(369\) | −1.68966 | −0.0879602 | ||||||||
\(370\) | 5.65253 | 0.293861 | ||||||||
\(371\) | −25.3233 | −1.31472 | ||||||||
\(372\) | −0.920947 | −0.0477489 | ||||||||
\(373\) | −18.5517 | −0.960568 | −0.480284 | − | 0.877113i | \(-0.659466\pi\) | ||||
−0.480284 | + | 0.877113i | \(0.659466\pi\) | |||||||
\(374\) | −20.6575 | −1.06817 | ||||||||
\(375\) | 25.5700 | 1.32043 | ||||||||
\(376\) | 9.63330 | 0.496799 | ||||||||
\(377\) | 17.3292 | 0.892501 | ||||||||
\(378\) | 2.45923 | 0.126489 | ||||||||
\(379\) | 23.5187 | 1.20807 | 0.604037 | − | 0.796956i | \(-0.293558\pi\) | ||||
0.604037 | + | 0.796956i | \(0.293558\pi\) | |||||||
\(380\) | 10.1187 | 0.519080 | ||||||||
\(381\) | 15.9698 | 0.818156 | ||||||||
\(382\) | 5.06025 | 0.258905 | ||||||||
\(383\) | −23.6221 | −1.20703 | −0.603515 | − | 0.797351i | \(-0.706234\pi\) | ||||
−0.603515 | + | 0.797351i | \(0.706234\pi\) | |||||||
\(384\) | −2.39250 | −0.122092 | ||||||||
\(385\) | 27.1567 | 1.38403 | ||||||||
\(386\) | −20.6196 | −1.04951 | ||||||||
\(387\) | 4.33614 | 0.220418 | ||||||||
\(388\) | −15.1111 | −0.767148 | ||||||||
\(389\) | −11.6802 | −0.592208 | −0.296104 | − | 0.955156i | \(-0.595687\pi\) | ||||
−0.296104 | + | 0.955156i | \(0.595687\pi\) | |||||||
\(390\) | −6.38860 | −0.323499 | ||||||||
\(391\) | −2.38069 | −0.120397 | ||||||||
\(392\) | 6.87603 | 0.347292 | ||||||||
\(393\) | −21.2740 | −1.07313 | ||||||||
\(394\) | 6.16126 | 0.310400 | ||||||||
\(395\) | −4.43621 | −0.223210 | ||||||||
\(396\) | 15.5514 | 0.781489 | ||||||||
\(397\) | 15.7564 | 0.790791 | 0.395395 | − | 0.918511i | \(-0.370608\pi\) | ||||
0.395395 | + | 0.918511i | \(0.370608\pi\) | |||||||
\(398\) | −20.5246 | −1.02881 | ||||||||
\(399\) | −70.6188 | −3.53536 | ||||||||
\(400\) | −3.36927 | −0.168464 | ||||||||
\(401\) | −7.26663 | −0.362878 | −0.181439 | − | 0.983402i | \(-0.558075\pi\) | ||||
−0.181439 | + | 0.983402i | \(0.558075\pi\) | |||||||
\(402\) | −5.75760 | −0.287163 | ||||||||
\(403\) | 0.804907 | 0.0400953 | ||||||||
\(404\) | 2.50820 | 0.124787 | ||||||||
\(405\) | −12.4529 | −0.618788 | ||||||||
\(406\) | 30.8709 | 1.53210 | ||||||||
\(407\) | 25.2701 | 1.25259 | ||||||||
\(408\) | 8.65717 | 0.428594 | ||||||||
\(409\) | 27.3993 | 1.35481 | 0.677403 | − | 0.735612i | \(-0.263105\pi\) | ||||
0.677403 | + | 0.735612i | \(0.263105\pi\) | |||||||
\(410\) | −0.792088 | −0.0391184 | ||||||||
\(411\) | 50.6030 | 2.49606 | ||||||||
\(412\) | −10.5767 | −0.521079 | ||||||||
\(413\) | −31.7619 | −1.56290 | ||||||||
\(414\) | 1.79224 | 0.0880839 | ||||||||
\(415\) | −2.95132 | −0.144875 | ||||||||
\(416\) | 2.09104 | 0.102522 | ||||||||
\(417\) | 20.2707 | 0.992659 | ||||||||
\(418\) | 45.2366 | 2.21259 | ||||||||
\(419\) | 6.53541 | 0.319276 | 0.159638 | − | 0.987176i | \(-0.448967\pi\) | ||||
0.159638 | + | 0.987176i | \(0.448967\pi\) | |||||||
\(420\) | −11.3809 | −0.555329 | ||||||||
\(421\) | 29.6671 | 1.44589 | 0.722944 | − | 0.690906i | \(-0.242788\pi\) | ||||
0.722944 | + | 0.690906i | \(0.242788\pi\) | |||||||
\(422\) | −2.32561 | −0.113209 | ||||||||
\(423\) | 26.2417 | 1.27591 | ||||||||
\(424\) | −6.79811 | −0.330145 | ||||||||
\(425\) | 12.1916 | 0.591378 | ||||||||
\(426\) | 3.54508 | 0.171760 | ||||||||
\(427\) | 37.8103 | 1.82977 | ||||||||
\(428\) | 16.3661 | 0.791087 | ||||||||
\(429\) | −28.5607 | −1.37892 | ||||||||
\(430\) | 2.03272 | 0.0980263 | ||||||||
\(431\) | 8.52420 | 0.410596 | 0.205298 | − | 0.978699i | \(-0.434184\pi\) | ||||
0.205298 | + | 0.978699i | \(0.434184\pi\) | |||||||
\(432\) | 0.660186 | 0.0317632 | ||||||||
\(433\) | 4.29661 | 0.206482 | 0.103241 | − | 0.994656i | \(-0.467079\pi\) | ||||
0.103241 | + | 0.994656i | \(0.467079\pi\) | |||||||
\(434\) | 1.43389 | 0.0688288 | ||||||||
\(435\) | −25.3197 | −1.21399 | ||||||||
\(436\) | −17.1222 | −0.820004 | ||||||||
\(437\) | 5.21333 | 0.249388 | ||||||||
\(438\) | 19.3559 | 0.924859 | ||||||||
\(439\) | −1.49737 | −0.0714658 | −0.0357329 | − | 0.999361i | \(-0.511377\pi\) | ||||
−0.0357329 | + | 0.999361i | \(0.511377\pi\) | |||||||
\(440\) | 7.29028 | 0.347551 | ||||||||
\(441\) | 18.7307 | 0.891939 | ||||||||
\(442\) | −7.56635 | −0.359895 | ||||||||
\(443\) | 21.0002 | 0.997750 | 0.498875 | − | 0.866674i | \(-0.333747\pi\) | ||||
0.498875 | + | 0.866674i | \(0.333747\pi\) | |||||||
\(444\) | −10.5902 | −0.502589 | ||||||||
\(445\) | 2.89754 | 0.137357 | ||||||||
\(446\) | 4.23177 | 0.200380 | ||||||||
\(447\) | 29.1095 | 1.37683 | ||||||||
\(448\) | 3.72505 | 0.175992 | ||||||||
\(449\) | 36.5879 | 1.72669 | 0.863346 | − | 0.504613i | \(-0.168365\pi\) | ||||
0.863346 | + | 0.504613i | \(0.168365\pi\) | |||||||
\(450\) | −9.17811 | −0.432660 | ||||||||
\(451\) | −3.54109 | −0.166743 | ||||||||
\(452\) | −10.5780 | −0.497548 | ||||||||
\(453\) | 39.3040 | 1.84667 | ||||||||
\(454\) | −5.60126 | −0.262880 | ||||||||
\(455\) | 9.94686 | 0.466316 | ||||||||
\(456\) | −18.9578 | −0.887780 | ||||||||
\(457\) | −10.7943 | −0.504935 | −0.252468 | − | 0.967605i | \(-0.581242\pi\) | ||||
−0.252468 | + | 0.967605i | \(0.581242\pi\) | |||||||
\(458\) | −17.9761 | −0.839969 | ||||||||
\(459\) | −2.38885 | −0.111502 | ||||||||
\(460\) | 0.840176 | 0.0391734 | ||||||||
\(461\) | 33.6511 | 1.56729 | 0.783643 | − | 0.621211i | \(-0.213359\pi\) | ||||
0.783643 | + | 0.621211i | \(0.213359\pi\) | |||||||
\(462\) | −50.8790 | −2.36711 | ||||||||
\(463\) | 1.48531 | 0.0690281 | 0.0345140 | − | 0.999404i | \(-0.489012\pi\) | ||||
0.0345140 | + | 0.999404i | \(0.489012\pi\) | |||||||
\(464\) | 8.28737 | 0.384731 | ||||||||
\(465\) | −1.17605 | −0.0545380 | ||||||||
\(466\) | −18.3706 | −0.851004 | ||||||||
\(467\) | 16.9757 | 0.785544 | 0.392772 | − | 0.919636i | \(-0.371516\pi\) | ||||
0.392772 | + | 0.919636i | \(0.371516\pi\) | |||||||
\(468\) | 5.69613 | 0.263304 | ||||||||
\(469\) | 8.96441 | 0.413938 | ||||||||
\(470\) | 12.3017 | 0.567436 | ||||||||
\(471\) | −23.4150 | −1.07891 | ||||||||
\(472\) | −8.52656 | −0.392467 | ||||||||
\(473\) | 9.08741 | 0.417840 | ||||||||
\(474\) | 8.31138 | 0.381755 | ||||||||
\(475\) | −26.6976 | −1.22497 | ||||||||
\(476\) | −13.4790 | −0.617807 | ||||||||
\(477\) | −18.5185 | −0.847902 | ||||||||
\(478\) | 8.96537 | 0.410066 | ||||||||
\(479\) | 3.03191 | 0.138532 | 0.0692658 | − | 0.997598i | \(-0.477934\pi\) | ||||
0.0692658 | + | 0.997598i | \(0.477934\pi\) | |||||||
\(480\) | −3.05522 | −0.139451 | ||||||||
\(481\) | 9.25583 | 0.422029 | ||||||||
\(482\) | 9.57416 | 0.436091 | ||||||||
\(483\) | −5.86360 | −0.266803 | ||||||||
\(484\) | 21.5918 | 0.981443 | ||||||||
\(485\) | −19.2968 | −0.876223 | ||||||||
\(486\) | 21.3503 | 0.968471 | ||||||||
\(487\) | −32.7655 | −1.48475 | −0.742374 | − | 0.669986i | \(-0.766300\pi\) | ||||
−0.742374 | + | 0.669986i | \(0.766300\pi\) | |||||||
\(488\) | 10.1503 | 0.459481 | ||||||||
\(489\) | −6.84837 | −0.309694 | ||||||||
\(490\) | 8.78068 | 0.396671 | ||||||||
\(491\) | −18.7709 | −0.847119 | −0.423559 | − | 0.905868i | \(-0.639219\pi\) | ||||
−0.423559 | + | 0.905868i | \(0.639219\pi\) | |||||||
\(492\) | 1.48400 | 0.0669040 | ||||||||
\(493\) | −29.9875 | −1.35057 | ||||||||
\(494\) | 16.5691 | 0.745479 | ||||||||
\(495\) | 19.8592 | 0.892603 | ||||||||
\(496\) | 0.384931 | 0.0172839 | ||||||||
\(497\) | −5.51959 | −0.247587 | ||||||||
\(498\) | 5.52940 | 0.247778 | ||||||||
\(499\) | 1.31359 | 0.0588046 | 0.0294023 | − | 0.999568i | \(-0.490640\pi\) | ||||
0.0294023 | + | 0.999568i | \(0.490640\pi\) | |||||||
\(500\) | −10.6876 | −0.477962 | ||||||||
\(501\) | 36.8517 | 1.64641 | ||||||||
\(502\) | 1.64720 | 0.0735180 | ||||||||
\(503\) | −6.95995 | −0.310329 | −0.155164 | − | 0.987889i | \(-0.549591\pi\) | ||||
−0.155164 | + | 0.987889i | \(0.549591\pi\) | |||||||
\(504\) | 10.1473 | 0.451995 | ||||||||
\(505\) | 3.20296 | 0.142530 | ||||||||
\(506\) | 3.75607 | 0.166978 | ||||||||
\(507\) | 20.6414 | 0.916717 | ||||||||
\(508\) | −6.67493 | −0.296152 | ||||||||
\(509\) | −26.9033 | −1.19247 | −0.596234 | − | 0.802810i | \(-0.703337\pi\) | ||||
−0.596234 | + | 0.802810i | \(0.703337\pi\) | |||||||
\(510\) | 11.0552 | 0.489532 | ||||||||
\(511\) | −30.1365 | −1.33316 | ||||||||
\(512\) | 1.00000 | 0.0441942 | ||||||||
\(513\) | 5.23120 | 0.230963 | ||||||||
\(514\) | 19.2633 | 0.849667 | ||||||||
\(515\) | −13.5065 | −0.595167 | ||||||||
\(516\) | −3.80836 | −0.167654 | ||||||||
\(517\) | 54.9957 | 2.41871 | ||||||||
\(518\) | 16.4886 | 0.724469 | ||||||||
\(519\) | −13.4531 | −0.590524 | ||||||||
\(520\) | 2.67026 | 0.117099 | ||||||||
\(521\) | −8.43800 | −0.369676 | −0.184838 | − | 0.982769i | \(-0.559176\pi\) | ||||
−0.184838 | + | 0.982769i | \(0.559176\pi\) | |||||||
\(522\) | 22.5753 | 0.988093 | ||||||||
\(523\) | 12.3508 | 0.540063 | 0.270032 | − | 0.962851i | \(-0.412966\pi\) | ||||
0.270032 | + | 0.962851i | \(0.412966\pi\) | |||||||
\(524\) | 8.89195 | 0.388447 | ||||||||
\(525\) | 30.0276 | 1.31051 | ||||||||
\(526\) | −14.9341 | −0.651158 | ||||||||
\(527\) | −1.39286 | −0.0606738 | ||||||||
\(528\) | −13.6586 | −0.594414 | ||||||||
\(529\) | −22.5671 | −0.981179 | ||||||||
\(530\) | −8.68117 | −0.377086 | ||||||||
\(531\) | −23.2269 | −1.00796 | ||||||||
\(532\) | 29.5167 | 1.27971 | ||||||||
\(533\) | −1.29702 | −0.0561800 | ||||||||
\(534\) | −5.42864 | −0.234920 | ||||||||
\(535\) | 20.8995 | 0.903565 | ||||||||
\(536\) | 2.40652 | 0.103946 | ||||||||
\(537\) | 18.9856 | 0.819287 | ||||||||
\(538\) | 17.9977 | 0.775936 | ||||||||
\(539\) | 39.2547 | 1.69082 | ||||||||
\(540\) | 0.843056 | 0.0362794 | ||||||||
\(541\) | 37.0156 | 1.59143 | 0.795713 | − | 0.605674i | \(-0.207097\pi\) | ||||
0.795713 | + | 0.605674i | \(0.207097\pi\) | |||||||
\(542\) | 5.18649 | 0.222779 | ||||||||
\(543\) | −46.7723 | −2.00719 | ||||||||
\(544\) | −3.61846 | −0.155140 | ||||||||
\(545\) | −21.8650 | −0.936594 | ||||||||
\(546\) | −18.6358 | −0.797538 | ||||||||
\(547\) | −21.6608 | −0.926151 | −0.463076 | − | 0.886319i | \(-0.653254\pi\) | ||||
−0.463076 | + | 0.886319i | \(0.653254\pi\) | |||||||
\(548\) | −21.1507 | −0.903511 | ||||||||
\(549\) | 27.6500 | 1.18007 | ||||||||
\(550\) | −19.2349 | −0.820179 | ||||||||
\(551\) | 65.6678 | 2.79754 | ||||||||
\(552\) | −1.57410 | −0.0669981 | ||||||||
\(553\) | −12.9406 | −0.550290 | ||||||||
\(554\) | 14.5674 | 0.618910 | ||||||||
\(555\) | −13.5237 | −0.574048 | ||||||||
\(556\) | −8.47259 | −0.359318 | ||||||||
\(557\) | 22.4267 | 0.950250 | 0.475125 | − | 0.879918i | \(-0.342403\pi\) | ||||
0.475125 | + | 0.879918i | \(0.342403\pi\) | |||||||
\(558\) | 1.04857 | 0.0443897 | ||||||||
\(559\) | 3.32851 | 0.140781 | ||||||||
\(560\) | 4.75689 | 0.201015 | ||||||||
\(561\) | 49.4231 | 2.08664 | ||||||||
\(562\) | 0.0182862 | 0.000771356 0 | ||||||||
\(563\) | −22.6831 | −0.955980 | −0.477990 | − | 0.878365i | \(-0.658634\pi\) | ||||
−0.477990 | + | 0.878365i | \(0.658634\pi\) | |||||||
\(564\) | −23.0477 | −0.970482 | ||||||||
\(565\) | −13.5081 | −0.568291 | ||||||||
\(566\) | 17.0100 | 0.714982 | ||||||||
\(567\) | −36.3255 | −1.52553 | ||||||||
\(568\) | −1.48175 | −0.0621728 | ||||||||
\(569\) | 33.4083 | 1.40055 | 0.700275 | − | 0.713873i | \(-0.253061\pi\) | ||||
0.700275 | + | 0.713873i | \(0.253061\pi\) | |||||||
\(570\) | −24.2091 | −1.01401 | ||||||||
\(571\) | 5.78608 | 0.242140 | 0.121070 | − | 0.992644i | \(-0.461367\pi\) | ||||
0.121070 | + | 0.992644i | \(0.461367\pi\) | |||||||
\(572\) | 11.9376 | 0.499136 | ||||||||
\(573\) | −12.1067 | −0.505763 | ||||||||
\(574\) | −2.31055 | −0.0964405 | ||||||||
\(575\) | −2.21675 | −0.0924448 | ||||||||
\(576\) | 2.72406 | 0.113503 | ||||||||
\(577\) | 5.34747 | 0.222618 | 0.111309 | − | 0.993786i | \(-0.464496\pi\) | ||||
0.111309 | + | 0.993786i | \(0.464496\pi\) | |||||||
\(578\) | −3.90676 | −0.162500 | ||||||||
\(579\) | 49.3323 | 2.05018 | ||||||||
\(580\) | 10.5830 | 0.439433 | ||||||||
\(581\) | −8.60911 | −0.357166 | ||||||||
\(582\) | 36.1532 | 1.49860 | ||||||||
\(583\) | −38.8098 | −1.60734 | ||||||||
\(584\) | −8.09022 | −0.334776 | ||||||||
\(585\) | 7.27395 | 0.300741 | ||||||||
\(586\) | −22.2830 | −0.920501 | ||||||||
\(587\) | 14.3606 | 0.592726 | 0.296363 | − | 0.955075i | \(-0.404226\pi\) | ||||
0.296363 | + | 0.955075i | \(0.404226\pi\) | |||||||
\(588\) | −16.4509 | −0.678424 | ||||||||
\(589\) | 3.05013 | 0.125678 | ||||||||
\(590\) | −10.8884 | −0.448268 | ||||||||
\(591\) | −14.7408 | −0.606356 | ||||||||
\(592\) | 4.42642 | 0.181925 | ||||||||
\(593\) | 38.5904 | 1.58472 | 0.792358 | − | 0.610056i | \(-0.208853\pi\) | ||||
0.792358 | + | 0.610056i | \(0.208853\pi\) | |||||||
\(594\) | 3.76895 | 0.154642 | ||||||||
\(595\) | −17.2126 | −0.705648 | ||||||||
\(596\) | −12.1670 | −0.498379 | ||||||||
\(597\) | 49.1052 | 2.00974 | ||||||||
\(598\) | 1.37576 | 0.0562590 | ||||||||
\(599\) | 0.427755 | 0.0174776 | 0.00873880 | − | 0.999962i | \(-0.497218\pi\) | ||||
0.00873880 | + | 0.999962i | \(0.497218\pi\) | |||||||
\(600\) | 8.06099 | 0.329089 | ||||||||
\(601\) | 34.6955 | 1.41526 | 0.707630 | − | 0.706583i | \(-0.249764\pi\) | ||||
0.707630 | + | 0.706583i | \(0.249764\pi\) | |||||||
\(602\) | 5.92951 | 0.241669 | ||||||||
\(603\) | 6.55550 | 0.266961 | ||||||||
\(604\) | −16.4280 | −0.668447 | ||||||||
\(605\) | 27.5726 | 1.12099 | ||||||||
\(606\) | −6.00086 | −0.243768 | ||||||||
\(607\) | 6.04932 | 0.245534 | 0.122767 | − | 0.992435i | \(-0.460823\pi\) | ||||
0.122767 | + | 0.992435i | \(0.460823\pi\) | |||||||
\(608\) | 7.92384 | 0.321354 | ||||||||
\(609\) | −73.8586 | −2.99290 | ||||||||
\(610\) | 12.9619 | 0.524812 | ||||||||
\(611\) | 20.1436 | 0.814925 | ||||||||
\(612\) | −9.85690 | −0.398442 | ||||||||
\(613\) | −28.2688 | −1.14177 | −0.570883 | − | 0.821031i | \(-0.693399\pi\) | ||||
−0.570883 | + | 0.821031i | \(0.693399\pi\) | |||||||
\(614\) | −22.0570 | −0.890147 | ||||||||
\(615\) | 1.89507 | 0.0764166 | ||||||||
\(616\) | 21.2660 | 0.856833 | ||||||||
\(617\) | −14.9187 | −0.600603 | −0.300302 | − | 0.953844i | \(-0.597087\pi\) | ||||
−0.300302 | + | 0.953844i | \(0.597087\pi\) | |||||||
\(618\) | 25.3049 | 1.01791 | ||||||||
\(619\) | −32.9734 | −1.32531 | −0.662656 | − | 0.748924i | \(-0.730571\pi\) | ||||
−0.662656 | + | 0.748924i | \(0.730571\pi\) | |||||||
\(620\) | 0.491556 | 0.0197414 | ||||||||
\(621\) | 0.434356 | 0.0174301 | ||||||||
\(622\) | 25.3530 | 1.01656 | ||||||||
\(623\) | 8.45223 | 0.338632 | ||||||||
\(624\) | −5.00282 | −0.200273 | ||||||||
\(625\) | 3.19838 | 0.127935 | ||||||||
\(626\) | 19.1017 | 0.763457 | ||||||||
\(627\) | −108.228 | −4.32223 | ||||||||
\(628\) | 9.78684 | 0.390537 | ||||||||
\(629\) | −16.0168 | −0.638632 | ||||||||
\(630\) | 12.9581 | 0.516261 | ||||||||
\(631\) | 0.432113 | 0.0172022 | 0.00860108 | − | 0.999963i | \(-0.497262\pi\) | ||||
0.00860108 | + | 0.999963i | \(0.497262\pi\) | |||||||
\(632\) | −3.47393 | −0.138186 | ||||||||
\(633\) | 5.56403 | 0.221150 | ||||||||
\(634\) | 9.43398 | 0.374671 | ||||||||
\(635\) | −8.52387 | −0.338260 | ||||||||
\(636\) | 16.2645 | 0.644928 | ||||||||
\(637\) | 14.3781 | 0.569680 | ||||||||
\(638\) | 47.3119 | 1.87310 | ||||||||
\(639\) | −4.03637 | −0.159676 | ||||||||
\(640\) | 1.27700 | 0.0504778 | ||||||||
\(641\) | 6.88156 | 0.271805 | 0.135903 | − | 0.990722i | \(-0.456607\pi\) | ||||
0.135903 | + | 0.990722i | \(0.456607\pi\) | |||||||
\(642\) | −39.1560 | −1.54536 | ||||||||
\(643\) | −20.8519 | −0.822318 | −0.411159 | − | 0.911564i | \(-0.634876\pi\) | ||||
−0.411159 | + | 0.911564i | \(0.634876\pi\) | |||||||
\(644\) | 2.45083 | 0.0965761 | ||||||||
\(645\) | −4.86328 | −0.191491 | ||||||||
\(646\) | −28.6721 | −1.12809 | ||||||||
\(647\) | −46.4209 | −1.82500 | −0.912498 | − | 0.409082i | \(-0.865849\pi\) | ||||
−0.912498 | + | 0.409082i | \(0.865849\pi\) | |||||||
\(648\) | −9.75168 | −0.383082 | ||||||||
\(649\) | −48.6774 | −1.91076 | ||||||||
\(650\) | −7.04530 | −0.276339 | ||||||||
\(651\) | −3.43058 | −0.134455 | ||||||||
\(652\) | 2.86243 | 0.112101 | ||||||||
\(653\) | −29.8425 | −1.16783 | −0.583913 | − | 0.811816i | \(-0.698479\pi\) | ||||
−0.583913 | + | 0.811816i | \(0.698479\pi\) | |||||||
\(654\) | 40.9648 | 1.60185 | ||||||||
\(655\) | 11.3550 | 0.443677 | ||||||||
\(656\) | −0.620273 | −0.0242176 | ||||||||
\(657\) | −22.0382 | −0.859794 | ||||||||
\(658\) | 35.8846 | 1.39893 | ||||||||
\(659\) | −36.2363 | −1.41157 | −0.705784 | − | 0.708427i | \(-0.749405\pi\) | ||||
−0.705784 | + | 0.708427i | \(0.749405\pi\) | |||||||
\(660\) | −17.4420 | −0.678929 | ||||||||
\(661\) | −35.5809 | −1.38394 | −0.691968 | − | 0.721928i | \(-0.743256\pi\) | ||||
−0.691968 | + | 0.721928i | \(0.743256\pi\) | |||||||
\(662\) | −9.74999 | −0.378944 | ||||||||
\(663\) | 18.1025 | 0.703043 | ||||||||
\(664\) | −2.31114 | −0.0896895 | ||||||||
\(665\) | 37.6928 | 1.46167 | ||||||||
\(666\) | 12.0578 | 0.467231 | ||||||||
\(667\) | 5.45251 | 0.211122 | ||||||||
\(668\) | −15.4030 | −0.595960 | ||||||||
\(669\) | −10.1245 | −0.391436 | ||||||||
\(670\) | 3.07312 | 0.118725 | ||||||||
\(671\) | 57.9471 | 2.23702 | ||||||||
\(672\) | −8.91220 | −0.343795 | ||||||||
\(673\) | 7.45739 | 0.287461 | 0.143731 | − | 0.989617i | \(-0.454090\pi\) | ||||
0.143731 | + | 0.989617i | \(0.454090\pi\) | |||||||
\(674\) | −13.3092 | −0.512652 | ||||||||
\(675\) | −2.22435 | −0.0856151 | ||||||||
\(676\) | −8.62754 | −0.331828 | ||||||||
\(677\) | −11.1966 | −0.430321 | −0.215160 | − | 0.976579i | \(-0.569027\pi\) | ||||
−0.215160 | + | 0.976579i | \(0.569027\pi\) | |||||||
\(678\) | 25.3079 | 0.971945 | ||||||||
\(679\) | −56.2895 | −2.16019 | ||||||||
\(680\) | −4.62077 | −0.177198 | ||||||||
\(681\) | 13.4010 | 0.513528 | ||||||||
\(682\) | 2.19754 | 0.0841481 | ||||||||
\(683\) | 3.80792 | 0.145706 | 0.0728530 | − | 0.997343i | \(-0.476790\pi\) | ||||
0.0728530 | + | 0.997343i | \(0.476790\pi\) | |||||||
\(684\) | 21.5850 | 0.825324 | ||||||||
\(685\) | −27.0094 | −1.03197 | ||||||||
\(686\) | −0.461796 | −0.0176314 | ||||||||
\(687\) | 43.0079 | 1.64085 | ||||||||
\(688\) | 1.59179 | 0.0606865 | ||||||||
\(689\) | −14.2151 | −0.541553 | ||||||||
\(690\) | −2.01012 | −0.0765240 | ||||||||
\(691\) | 44.0358 | 1.67520 | 0.837600 | − | 0.546284i | \(-0.183958\pi\) | ||||
0.837600 | + | 0.546284i | \(0.183958\pi\) | |||||||
\(692\) | 5.62302 | 0.213755 | ||||||||
\(693\) | 57.9300 | 2.20058 | ||||||||
\(694\) | 2.08092 | 0.0789908 | ||||||||
\(695\) | −10.8195 | −0.410406 | ||||||||
\(696\) | −19.8275 | −0.751561 | ||||||||
\(697\) | 2.24443 | 0.0850139 | ||||||||
\(698\) | −30.4313 | −1.15184 | ||||||||
\(699\) | 43.9518 | 1.66241 | ||||||||
\(700\) | −12.5507 | −0.474373 | ||||||||
\(701\) | 18.8788 | 0.713041 | 0.356521 | − | 0.934287i | \(-0.383963\pi\) | ||||
0.356521 | + | 0.934287i | \(0.383963\pi\) | |||||||
\(702\) | 1.38048 | 0.0521027 | ||||||||
\(703\) | 35.0742 | 1.32285 | ||||||||
\(704\) | 5.70892 | 0.215163 | ||||||||
\(705\) | −29.4319 | −1.10847 | ||||||||
\(706\) | 13.6586 | 0.514049 | ||||||||
\(707\) | 9.34317 | 0.351386 | ||||||||
\(708\) | 20.3998 | 0.766671 | ||||||||
\(709\) | −24.1516 | −0.907032 | −0.453516 | − | 0.891248i | \(-0.649831\pi\) | ||||
−0.453516 | + | 0.891248i | \(0.649831\pi\) | |||||||
\(710\) | −1.89219 | −0.0710126 | ||||||||
\(711\) | −9.46320 | −0.354898 | ||||||||
\(712\) | 2.26902 | 0.0850352 | ||||||||
\(713\) | 0.253258 | 0.00948457 | ||||||||
\(714\) | 32.2484 | 1.20687 | ||||||||
\(715\) | 15.2443 | 0.570104 | ||||||||
\(716\) | −7.93544 | −0.296561 | ||||||||
\(717\) | −21.4497 | −0.801052 | ||||||||
\(718\) | 4.39473 | 0.164010 | ||||||||
\(719\) | 21.1140 | 0.787421 | 0.393711 | − | 0.919234i | \(-0.371191\pi\) | ||||
0.393711 | + | 0.919234i | \(0.371191\pi\) | |||||||
\(720\) | 3.47862 | 0.129641 | ||||||||
\(721\) | −39.3990 | −1.46729 | ||||||||
\(722\) | 43.7872 | 1.62959 | ||||||||
\(723\) | −22.9062 | −0.851890 | ||||||||
\(724\) | 19.5495 | 0.726553 | ||||||||
\(725\) | −27.9224 | −1.03701 | ||||||||
\(726\) | −51.6583 | −1.91722 | ||||||||
\(727\) | 24.2416 | 0.899070 | 0.449535 | − | 0.893263i | \(-0.351590\pi\) | ||||
0.449535 | + | 0.893263i | \(0.351590\pi\) | |||||||
\(728\) | 7.78925 | 0.288689 | ||||||||
\(729\) | −21.8257 | −0.808358 | ||||||||
\(730\) | −10.3312 | −0.382375 | ||||||||
\(731\) | −5.75983 | −0.213035 | ||||||||
\(732\) | −24.2845 | −0.897583 | ||||||||
\(733\) | 13.2137 | 0.488060 | 0.244030 | − | 0.969768i | \(-0.421530\pi\) | ||||
0.244030 | + | 0.969768i | \(0.421530\pi\) | |||||||
\(734\) | −23.7517 | −0.876691 | ||||||||
\(735\) | −21.0078 | −0.774884 | ||||||||
\(736\) | 0.657930 | 0.0242516 | ||||||||
\(737\) | 13.7386 | 0.506069 | ||||||||
\(738\) | −1.68966 | −0.0621973 | ||||||||
\(739\) | −6.91317 | −0.254305 | −0.127152 | − | 0.991883i | \(-0.540584\pi\) | ||||
−0.127152 | + | 0.991883i | \(0.540584\pi\) | |||||||
\(740\) | 5.65253 | 0.207791 | ||||||||
\(741\) | −39.6416 | −1.45627 | ||||||||
\(742\) | −25.3233 | −0.929648 | ||||||||
\(743\) | −36.0162 | −1.32131 | −0.660654 | − | 0.750691i | \(-0.729721\pi\) | ||||
−0.660654 | + | 0.750691i | \(0.729721\pi\) | |||||||
\(744\) | −0.920947 | −0.0337636 | ||||||||
\(745\) | −15.5372 | −0.569240 | ||||||||
\(746\) | −18.5517 | −0.679224 | ||||||||
\(747\) | −6.29568 | −0.230347 | ||||||||
\(748\) | −20.6575 | −0.755312 | ||||||||
\(749\) | 60.9647 | 2.22760 | ||||||||
\(750\) | 25.5700 | 0.933684 | ||||||||
\(751\) | 21.0416 | 0.767818 | 0.383909 | − | 0.923371i | \(-0.374578\pi\) | ||||
0.383909 | + | 0.923371i | \(0.374578\pi\) | |||||||
\(752\) | 9.63330 | 0.351290 | ||||||||
\(753\) | −3.94092 | −0.143615 | ||||||||
\(754\) | 17.3292 | 0.631094 | ||||||||
\(755\) | −20.9786 | −0.763488 | ||||||||
\(756\) | 2.45923 | 0.0894412 | ||||||||
\(757\) | 21.8946 | 0.795773 | 0.397887 | − | 0.917435i | \(-0.369744\pi\) | ||||
0.397887 | + | 0.917435i | \(0.369744\pi\) | |||||||
\(758\) | 23.5187 | 0.854237 | ||||||||
\(759\) | −8.98640 | −0.326186 | ||||||||
\(760\) | 10.1187 | 0.367045 | ||||||||
\(761\) | −28.7209 | −1.04113 | −0.520565 | − | 0.853822i | \(-0.674279\pi\) | ||||
−0.520565 | + | 0.853822i | \(0.674279\pi\) | |||||||
\(762\) | 15.9698 | 0.578524 | ||||||||
\(763\) | −63.7810 | −2.30903 | ||||||||
\(764\) | 5.06025 | 0.183073 | ||||||||
\(765\) | −12.5872 | −0.455093 | ||||||||
\(766\) | −23.6221 | −0.853500 | ||||||||
\(767\) | −17.8294 | −0.643782 | ||||||||
\(768\) | −2.39250 | −0.0863319 | ||||||||
\(769\) | −19.2592 | −0.694505 | −0.347253 | − | 0.937772i | \(-0.612885\pi\) | ||||
−0.347253 | + | 0.937772i | \(0.612885\pi\) | |||||||
\(770\) | 27.1567 | 0.978659 | ||||||||
\(771\) | −46.0874 | −1.65980 | ||||||||
\(772\) | −20.6196 | −0.742115 | ||||||||
\(773\) | 46.9897 | 1.69010 | 0.845051 | − | 0.534686i | \(-0.179570\pi\) | ||||
0.845051 | + | 0.534686i | \(0.179570\pi\) | |||||||
\(774\) | 4.33614 | 0.155859 | ||||||||
\(775\) | −1.29694 | −0.0465874 | ||||||||
\(776\) | −15.1111 | −0.542455 | ||||||||
\(777\) | −39.4491 | −1.41523 | ||||||||
\(778\) | −11.6802 | −0.418754 | ||||||||
\(779\) | −4.91494 | −0.176096 | ||||||||
\(780\) | −6.38860 | −0.228748 | ||||||||
\(781\) | −8.45918 | −0.302693 | ||||||||
\(782\) | −2.38069 | −0.0851334 | ||||||||
\(783\) | 5.47120 | 0.195525 | ||||||||
\(784\) | 6.87603 | 0.245572 | ||||||||
\(785\) | 12.4978 | 0.446065 | ||||||||
\(786\) | −21.2740 | −0.758818 | ||||||||
\(787\) | −9.38623 | −0.334583 | −0.167291 | − | 0.985907i | \(-0.553502\pi\) | ||||
−0.167291 | + | 0.985907i | \(0.553502\pi\) | |||||||
\(788\) | 6.16126 | 0.219486 | ||||||||
\(789\) | 35.7299 | 1.27202 | ||||||||
\(790\) | −4.43621 | −0.157833 | ||||||||
\(791\) | −39.4037 | −1.40103 | ||||||||
\(792\) | 15.5514 | 0.552596 | ||||||||
\(793\) | 21.2247 | 0.753710 | ||||||||
\(794\) | 15.7564 | 0.559174 | ||||||||
\(795\) | 20.7697 | 0.736626 | ||||||||
\(796\) | −20.5246 | −0.727477 | ||||||||
\(797\) | 16.1279 | 0.571278 | 0.285639 | − | 0.958337i | \(-0.407794\pi\) | ||||
0.285639 | + | 0.958337i | \(0.407794\pi\) | |||||||
\(798\) | −70.6188 | −2.49988 | ||||||||
\(799\) | −34.8577 | −1.23318 | ||||||||
\(800\) | −3.36927 | −0.119122 | ||||||||
\(801\) | 6.18096 | 0.218393 | ||||||||
\(802\) | −7.26663 | −0.256594 | ||||||||
\(803\) | −46.1864 | −1.62988 | ||||||||
\(804\) | −5.75760 | −0.203055 | ||||||||
\(805\) | 3.12970 | 0.110307 | ||||||||
\(806\) | 0.804907 | 0.0283516 | ||||||||
\(807\) | −43.0595 | −1.51577 | ||||||||
\(808\) | 2.50820 | 0.0882381 | ||||||||
\(809\) | 4.25675 | 0.149659 | 0.0748297 | − | 0.997196i | \(-0.476159\pi\) | ||||
0.0748297 | + | 0.997196i | \(0.476159\pi\) | |||||||
\(810\) | −12.4529 | −0.437550 | ||||||||
\(811\) | −5.59211 | −0.196366 | −0.0981828 | − | 0.995168i | \(-0.531303\pi\) | ||||
−0.0981828 | + | 0.995168i | \(0.531303\pi\) | |||||||
\(812\) | 30.8709 | 1.08336 | ||||||||
\(813\) | −12.4087 | −0.435191 | ||||||||
\(814\) | 25.2701 | 0.885715 | ||||||||
\(815\) | 3.65532 | 0.128040 | ||||||||
\(816\) | 8.65717 | 0.303061 | ||||||||
\(817\) | 12.6131 | 0.441277 | ||||||||
\(818\) | 27.3993 | 0.957993 | ||||||||
\(819\) | 21.2184 | 0.741430 | ||||||||
\(820\) | −0.792088 | −0.0276609 | ||||||||
\(821\) | 37.8931 | 1.32248 | 0.661239 | − | 0.750176i | \(-0.270031\pi\) | ||||
0.661239 | + | 0.750176i | \(0.270031\pi\) | |||||||
\(822\) | 50.6030 | 1.76498 | ||||||||
\(823\) | −15.3567 | −0.535302 | −0.267651 | − | 0.963516i | \(-0.586247\pi\) | ||||
−0.267651 | + | 0.963516i | \(0.586247\pi\) | |||||||
\(824\) | −10.5767 | −0.368459 | ||||||||
\(825\) | 46.0195 | 1.60219 | ||||||||
\(826\) | −31.7619 | −1.10514 | ||||||||
\(827\) | 18.9343 | 0.658411 | 0.329206 | − | 0.944258i | \(-0.393219\pi\) | ||||
0.329206 | + | 0.944258i | \(0.393219\pi\) | |||||||
\(828\) | 1.79224 | 0.0622847 | ||||||||
\(829\) | 12.2030 | 0.423829 | 0.211914 | − | 0.977288i | \(-0.432030\pi\) | ||||
0.211914 | + | 0.977288i | \(0.432030\pi\) | |||||||
\(830\) | −2.95132 | −0.102442 | ||||||||
\(831\) | −34.8526 | −1.20902 | ||||||||
\(832\) | 2.09104 | 0.0724939 | ||||||||
\(833\) | −24.8806 | −0.862063 | ||||||||
\(834\) | 20.2707 | 0.701916 | ||||||||
\(835\) | −19.6696 | −0.680695 | ||||||||
\(836\) | 45.2366 | 1.56454 | ||||||||
\(837\) | 0.254126 | 0.00878387 | ||||||||
\(838\) | 6.53541 | 0.225762 | ||||||||
\(839\) | 36.3343 | 1.25440 | 0.627199 | − | 0.778859i | \(-0.284201\pi\) | ||||
0.627199 | + | 0.778859i | \(0.284201\pi\) | |||||||
\(840\) | −11.3809 | −0.392677 | ||||||||
\(841\) | 39.6804 | 1.36829 | ||||||||
\(842\) | 29.6671 | 1.02240 | ||||||||
\(843\) | −0.0437497 | −0.00150682 | ||||||||
\(844\) | −2.32561 | −0.0800509 | ||||||||
\(845\) | −11.0174 | −0.379009 | ||||||||
\(846\) | 26.2417 | 0.902208 | ||||||||
\(847\) | 80.4304 | 2.76362 | ||||||||
\(848\) | −6.79811 | −0.233448 | ||||||||
\(849\) | −40.6964 | −1.39670 | ||||||||
\(850\) | 12.1916 | 0.418168 | ||||||||
\(851\) | 2.91227 | 0.0998315 | ||||||||
\(852\) | 3.54508 | 0.121453 | ||||||||
\(853\) | 41.1142 | 1.40772 | 0.703862 | − | 0.710337i | \(-0.251457\pi\) | ||||
0.703862 | + | 0.710337i | \(0.251457\pi\) | |||||||
\(854\) | 37.8103 | 1.29384 | ||||||||
\(855\) | 27.5640 | 0.942670 | ||||||||
\(856\) | 16.3661 | 0.559383 | ||||||||
\(857\) | 11.9937 | 0.409696 | 0.204848 | − | 0.978794i | \(-0.434330\pi\) | ||||
0.204848 | + | 0.978794i | \(0.434330\pi\) | |||||||
\(858\) | −28.5607 | −0.975046 | ||||||||
\(859\) | −33.7761 | −1.15242 | −0.576212 | − | 0.817300i | \(-0.695470\pi\) | ||||
−0.576212 | + | 0.817300i | \(0.695470\pi\) | |||||||
\(860\) | 2.03272 | 0.0693150 | ||||||||
\(861\) | 5.52799 | 0.188393 | ||||||||
\(862\) | 8.52420 | 0.290335 | ||||||||
\(863\) | −4.56010 | −0.155228 | −0.0776138 | − | 0.996984i | \(-0.524730\pi\) | ||||
−0.0776138 | + | 0.996984i | \(0.524730\pi\) | |||||||
\(864\) | 0.660186 | 0.0224600 | ||||||||
\(865\) | 7.18059 | 0.244147 | ||||||||
\(866\) | 4.29661 | 0.146005 | ||||||||
\(867\) | 9.34692 | 0.317438 | ||||||||
\(868\) | 1.43389 | 0.0486693 | ||||||||
\(869\) | −19.8324 | −0.672768 | ||||||||
\(870\) | −25.3197 | −0.858419 | ||||||||
\(871\) | 5.03213 | 0.170507 | ||||||||
\(872\) | −17.1222 | −0.579830 | ||||||||
\(873\) | −41.1634 | −1.39317 | ||||||||
\(874\) | 5.21333 | 0.176344 | ||||||||
\(875\) | −39.8117 | −1.34588 | ||||||||
\(876\) | 19.3559 | 0.653974 | ||||||||
\(877\) | −37.1933 | −1.25593 | −0.627964 | − | 0.778242i | \(-0.716111\pi\) | ||||
−0.627964 | + | 0.778242i | \(0.716111\pi\) | |||||||
\(878\) | −1.49737 | −0.0505339 | ||||||||
\(879\) | 53.3120 | 1.79817 | ||||||||
\(880\) | 7.29028 | 0.245755 | ||||||||
\(881\) | 9.43038 | 0.317718 | 0.158859 | − | 0.987301i | \(-0.449219\pi\) | ||||
0.158859 | + | 0.987301i | \(0.449219\pi\) | |||||||
\(882\) | 18.7307 | 0.630696 | ||||||||
\(883\) | −39.1804 | −1.31853 | −0.659263 | − | 0.751913i | \(-0.729132\pi\) | ||||
−0.659263 | + | 0.751913i | \(0.729132\pi\) | |||||||
\(884\) | −7.56635 | −0.254484 | ||||||||
\(885\) | 26.0505 | 0.875678 | ||||||||
\(886\) | 21.0002 | 0.705516 | ||||||||
\(887\) | 18.0403 | 0.605733 | 0.302867 | − | 0.953033i | \(-0.402056\pi\) | ||||
0.302867 | + | 0.953033i | \(0.402056\pi\) | |||||||
\(888\) | −10.5902 | −0.355384 | ||||||||
\(889\) | −24.8645 | −0.833927 | ||||||||
\(890\) | 2.89754 | 0.0971257 | ||||||||
\(891\) | −55.6715 | −1.86507 | ||||||||
\(892\) | 4.23177 | 0.141690 | ||||||||
\(893\) | 76.3327 | 2.55438 | ||||||||
\(894\) | 29.1095 | 0.973568 | ||||||||
\(895\) | −10.1335 | −0.338727 | ||||||||
\(896\) | 3.72505 | 0.124445 | ||||||||
\(897\) | −3.29151 | −0.109900 | ||||||||
\(898\) | 36.5879 | 1.22095 | ||||||||
\(899\) | 3.19006 | 0.106395 | ||||||||
\(900\) | −9.17811 | −0.305937 | ||||||||
\(901\) | 24.5987 | 0.819500 | ||||||||
\(902\) | −3.54109 | −0.117905 | ||||||||
\(903\) | −14.1864 | −0.472093 | ||||||||
\(904\) | −10.5780 | −0.351820 | ||||||||
\(905\) | 24.9647 | 0.829856 | ||||||||
\(906\) | 39.3040 | 1.30579 | ||||||||
\(907\) | −17.0336 | −0.565590 | −0.282795 | − | 0.959180i | \(-0.591262\pi\) | ||||
−0.282795 | + | 0.959180i | \(0.591262\pi\) | |||||||
\(908\) | −5.60126 | −0.185884 | ||||||||
\(909\) | 6.83248 | 0.226619 | ||||||||
\(910\) | 9.94686 | 0.329735 | ||||||||
\(911\) | −39.6628 | −1.31409 | −0.657044 | − | 0.753852i | \(-0.728193\pi\) | ||||
−0.657044 | + | 0.753852i | \(0.728193\pi\) | |||||||
\(912\) | −18.9578 | −0.627755 | ||||||||
\(913\) | −13.1941 | −0.436661 | ||||||||
\(914\) | −10.7943 | −0.357043 | ||||||||
\(915\) | −31.0113 | −1.02520 | ||||||||
\(916\) | −17.9761 | −0.593948 | ||||||||
\(917\) | 33.1230 | 1.09382 | ||||||||
\(918\) | −2.38885 | −0.0788439 | ||||||||
\(919\) | 17.3224 | 0.571414 | 0.285707 | − | 0.958317i | \(-0.407772\pi\) | ||||
0.285707 | + | 0.958317i | \(0.407772\pi\) | |||||||
\(920\) | 0.840176 | 0.0276998 | ||||||||
\(921\) | 52.7713 | 1.73887 | ||||||||
\(922\) | 33.6511 | 1.10824 | ||||||||
\(923\) | −3.09840 | −0.101985 | ||||||||
\(924\) | −50.8790 | −1.67380 | ||||||||
\(925\) | −14.9138 | −0.490363 | ||||||||
\(926\) | 1.48531 | 0.0488102 | ||||||||
\(927\) | −28.8117 | −0.946301 | ||||||||
\(928\) | 8.28737 | 0.272046 | ||||||||
\(929\) | −48.9154 | −1.60486 | −0.802431 | − | 0.596745i | \(-0.796460\pi\) | ||||
−0.802431 | + | 0.596745i | \(0.796460\pi\) | |||||||
\(930\) | −1.17605 | −0.0385642 | ||||||||
\(931\) | 54.4846 | 1.78566 | ||||||||
\(932\) | −18.3706 | −0.601750 | ||||||||
\(933\) | −60.6571 | −1.98583 | ||||||||
\(934\) | 16.9757 | 0.555463 | ||||||||
\(935\) | −26.3796 | −0.862705 | ||||||||
\(936\) | 5.69613 | 0.186184 | ||||||||
\(937\) | −42.8775 | −1.40075 | −0.700374 | − | 0.713776i | \(-0.746983\pi\) | ||||
−0.700374 | + | 0.713776i | \(0.746983\pi\) | |||||||
\(938\) | 8.96441 | 0.292698 | ||||||||
\(939\) | −45.7008 | −1.49139 | ||||||||
\(940\) | 12.3017 | 0.401238 | ||||||||
\(941\) | −10.5642 | −0.344385 | −0.172192 | − | 0.985063i | \(-0.555085\pi\) | ||||
−0.172192 | + | 0.985063i | \(0.555085\pi\) | |||||||
\(942\) | −23.4150 | −0.762903 | ||||||||
\(943\) | −0.408096 | −0.0132894 | ||||||||
\(944\) | −8.52656 | −0.277516 | ||||||||
\(945\) | 3.14043 | 0.102158 | ||||||||
\(946\) | 9.08741 | 0.295457 | ||||||||
\(947\) | −8.17742 | −0.265730 | −0.132865 | − | 0.991134i | \(-0.542418\pi\) | ||||
−0.132865 | + | 0.991134i | \(0.542418\pi\) | |||||||
\(948\) | 8.31138 | 0.269941 | ||||||||
\(949\) | −16.9170 | −0.549149 | ||||||||
\(950\) | −26.6976 | −0.866184 | ||||||||
\(951\) | −22.5708 | −0.731908 | ||||||||
\(952\) | −13.4790 | −0.436855 | ||||||||
\(953\) | −37.1200 | −1.20243 | −0.601217 | − | 0.799086i | \(-0.705317\pi\) | ||||
−0.601217 | + | 0.799086i | \(0.705317\pi\) | |||||||
\(954\) | −18.5185 | −0.599557 | ||||||||
\(955\) | 6.46193 | 0.209103 | ||||||||
\(956\) | 8.96537 | 0.289961 | ||||||||
\(957\) | −113.194 | −3.65903 | ||||||||
\(958\) | 3.03191 | 0.0979566 | ||||||||
\(959\) | −78.7874 | −2.54418 | ||||||||
\(960\) | −3.05522 | −0.0986068 | ||||||||
\(961\) | −30.8518 | −0.995220 | ||||||||
\(962\) | 9.25583 | 0.298420 | ||||||||
\(963\) | 44.5823 | 1.43665 | ||||||||
\(964\) | 9.57416 | 0.308363 | ||||||||
\(965\) | −26.3312 | −0.847630 | ||||||||
\(966\) | −5.86360 | −0.188658 | ||||||||
\(967\) | 50.4070 | 1.62098 | 0.810490 | − | 0.585752i | \(-0.199201\pi\) | ||||
0.810490 | + | 0.585752i | \(0.199201\pi\) | |||||||
\(968\) | 21.5918 | 0.693985 | ||||||||
\(969\) | 68.5980 | 2.20368 | ||||||||
\(970\) | −19.2968 | −0.619583 | ||||||||
\(971\) | −15.5488 | −0.498984 | −0.249492 | − | 0.968377i | \(-0.580264\pi\) | ||||
−0.249492 | + | 0.968377i | \(0.580264\pi\) | |||||||
\(972\) | 21.3503 | 0.684812 | ||||||||
\(973\) | −31.5608 | −1.01179 | ||||||||
\(974\) | −32.7655 | −1.04988 | ||||||||
\(975\) | 16.8559 | 0.539820 | ||||||||
\(976\) | 10.1503 | 0.324902 | ||||||||
\(977\) | 6.85145 | 0.219197 | 0.109599 | − | 0.993976i | \(-0.465043\pi\) | ||||
0.109599 | + | 0.993976i | \(0.465043\pi\) | |||||||
\(978\) | −6.84837 | −0.218987 | ||||||||
\(979\) | 12.9537 | 0.414001 | ||||||||
\(980\) | 8.78068 | 0.280489 | ||||||||
\(981\) | −46.6418 | −1.48916 | ||||||||
\(982\) | −18.7709 | −0.599003 | ||||||||
\(983\) | 19.0532 | 0.607704 | 0.303852 | − | 0.952719i | \(-0.401727\pi\) | ||||
0.303852 | + | 0.952719i | \(0.401727\pi\) | |||||||
\(984\) | 1.48400 | 0.0473083 | ||||||||
\(985\) | 7.86792 | 0.250693 | ||||||||
\(986\) | −29.9875 | −0.954996 | ||||||||
\(987\) | −85.8538 | −2.73276 | ||||||||
\(988\) | 16.5691 | 0.527133 | ||||||||
\(989\) | 1.04729 | 0.0333018 | ||||||||
\(990\) | 19.8592 | 0.631166 | ||||||||
\(991\) | −22.0558 | −0.700624 | −0.350312 | − | 0.936633i | \(-0.613924\pi\) | ||||
−0.350312 | + | 0.936633i | \(0.613924\pi\) | |||||||
\(992\) | 0.384931 | 0.0122216 | ||||||||
\(993\) | 23.3269 | 0.740256 | ||||||||
\(994\) | −5.51959 | −0.175071 | ||||||||
\(995\) | −26.2099 | −0.830911 | ||||||||
\(996\) | 5.52940 | 0.175206 | ||||||||
\(997\) | 22.0136 | 0.697179 | 0.348589 | − | 0.937276i | \(-0.386661\pi\) | ||||
0.348589 | + | 0.937276i | \(0.386661\pi\) | |||||||
\(998\) | 1.31359 | 0.0415811 | ||||||||
\(999\) | 2.92226 | 0.0924561 |
(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 | 8026.2.a.d.1.16 | ✓ | 96 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
8026.2.a.d.1.16 | ✓ | 96 | 1.1 | even | 1 | trivial |