Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [8042,2,Mod(1,8042)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(8042, 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("8042.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 8042 = 2 \cdot 4021 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 8042.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: | \(64.2156933055\) |
Analytic rank: | \(0\) |
Dimension: | \(86\) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.16 | ||
Character | \(\chi\) | \(=\) | 8042.1 |
$q$-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 | ||||||||
\(3\) | −2.10336 | −1.21438 | −0.607188 | − | 0.794558i | \(-0.707703\pi\) | ||||
−0.607188 | + | 0.794558i | \(0.707703\pi\) | |||||||
\(4\) | 1.00000 | 0.500000 | ||||||||
\(5\) | −2.86600 | −1.28172 | −0.640858 | − | 0.767660i | \(-0.721421\pi\) | ||||
−0.640858 | + | 0.767660i | \(0.721421\pi\) | |||||||
\(6\) | 2.10336 | 0.858694 | ||||||||
\(7\) | 3.42965 | 1.29629 | 0.648143 | − | 0.761518i | \(-0.275546\pi\) | ||||
0.648143 | + | 0.761518i | \(0.275546\pi\) | |||||||
\(8\) | −1.00000 | −0.353553 | ||||||||
\(9\) | 1.42413 | 0.474709 | ||||||||
\(10\) | 2.86600 | 0.906309 | ||||||||
\(11\) | −1.51191 | −0.455859 | −0.227930 | − | 0.973678i | \(-0.573196\pi\) | ||||
−0.227930 | + | 0.973678i | \(0.573196\pi\) | |||||||
\(12\) | −2.10336 | −0.607188 | ||||||||
\(13\) | −1.17483 | −0.325839 | −0.162919 | − | 0.986639i | \(-0.552091\pi\) | ||||
−0.162919 | + | 0.986639i | \(0.552091\pi\) | |||||||
\(14\) | −3.42965 | −0.916613 | ||||||||
\(15\) | 6.02824 | 1.55648 | ||||||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | −7.28415 | −1.76667 | −0.883333 | − | 0.468745i | \(-0.844706\pi\) | ||||
−0.883333 | + | 0.468745i | \(0.844706\pi\) | |||||||
\(18\) | −1.42413 | −0.335670 | ||||||||
\(19\) | −3.37924 | −0.775251 | −0.387626 | − | 0.921817i | \(-0.626705\pi\) | ||||
−0.387626 | + | 0.921817i | \(0.626705\pi\) | |||||||
\(20\) | −2.86600 | −0.640858 | ||||||||
\(21\) | −7.21380 | −1.57418 | ||||||||
\(22\) | 1.51191 | 0.322341 | ||||||||
\(23\) | −2.46602 | −0.514200 | −0.257100 | − | 0.966385i | \(-0.582767\pi\) | ||||
−0.257100 | + | 0.966385i | \(0.582767\pi\) | |||||||
\(24\) | 2.10336 | 0.429347 | ||||||||
\(25\) | 3.21397 | 0.642793 | ||||||||
\(26\) | 1.17483 | 0.230403 | ||||||||
\(27\) | 3.31463 | 0.637900 | ||||||||
\(28\) | 3.42965 | 0.648143 | ||||||||
\(29\) | 4.84908 | 0.900451 | 0.450226 | − | 0.892915i | \(-0.351344\pi\) | ||||
0.450226 | + | 0.892915i | \(0.351344\pi\) | |||||||
\(30\) | −6.02824 | −1.10060 | ||||||||
\(31\) | −8.53296 | −1.53257 | −0.766283 | − | 0.642503i | \(-0.777896\pi\) | ||||
−0.766283 | + | 0.642503i | \(0.777896\pi\) | |||||||
\(32\) | −1.00000 | −0.176777 | ||||||||
\(33\) | 3.18010 | 0.553585 | ||||||||
\(34\) | 7.28415 | 1.24922 | ||||||||
\(35\) | −9.82939 | −1.66147 | ||||||||
\(36\) | 1.42413 | 0.237355 | ||||||||
\(37\) | −3.32091 | −0.545954 | −0.272977 | − | 0.962021i | \(-0.588008\pi\) | ||||
−0.272977 | + | 0.962021i | \(0.588008\pi\) | |||||||
\(38\) | 3.37924 | 0.548185 | ||||||||
\(39\) | 2.47109 | 0.395691 | ||||||||
\(40\) | 2.86600 | 0.453155 | ||||||||
\(41\) | −9.68874 | −1.51313 | −0.756563 | − | 0.653921i | \(-0.773123\pi\) | ||||
−0.756563 | + | 0.653921i | \(0.773123\pi\) | |||||||
\(42\) | 7.21380 | 1.11311 | ||||||||
\(43\) | −1.96662 | −0.299907 | −0.149954 | − | 0.988693i | \(-0.547912\pi\) | ||||
−0.149954 | + | 0.988693i | \(0.547912\pi\) | |||||||
\(44\) | −1.51191 | −0.227930 | ||||||||
\(45\) | −4.08155 | −0.608442 | ||||||||
\(46\) | 2.46602 | 0.363595 | ||||||||
\(47\) | −0.645154 | −0.0941054 | −0.0470527 | − | 0.998892i | \(-0.514983\pi\) | ||||
−0.0470527 | + | 0.998892i | \(0.514983\pi\) | |||||||
\(48\) | −2.10336 | −0.303594 | ||||||||
\(49\) | 4.76251 | 0.680359 | ||||||||
\(50\) | −3.21397 | −0.454524 | ||||||||
\(51\) | 15.3212 | 2.14540 | ||||||||
\(52\) | −1.17483 | −0.162919 | ||||||||
\(53\) | −9.65253 | −1.32588 | −0.662938 | − | 0.748674i | \(-0.730691\pi\) | ||||
−0.662938 | + | 0.748674i | \(0.730691\pi\) | |||||||
\(54\) | −3.31463 | −0.451064 | ||||||||
\(55\) | 4.33315 | 0.584282 | ||||||||
\(56\) | −3.42965 | −0.458307 | ||||||||
\(57\) | 7.10777 | 0.941447 | ||||||||
\(58\) | −4.84908 | −0.636715 | ||||||||
\(59\) | −0.822649 | −0.107100 | −0.0535499 | − | 0.998565i | \(-0.517054\pi\) | ||||
−0.0535499 | + | 0.998565i | \(0.517054\pi\) | |||||||
\(60\) | 6.02824 | 0.778242 | ||||||||
\(61\) | 10.3443 | 1.32445 | 0.662223 | − | 0.749307i | \(-0.269613\pi\) | ||||
0.662223 | + | 0.749307i | \(0.269613\pi\) | |||||||
\(62\) | 8.53296 | 1.08369 | ||||||||
\(63\) | 4.88426 | 0.615359 | ||||||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | 3.36706 | 0.417632 | ||||||||
\(66\) | −3.18010 | −0.391443 | ||||||||
\(67\) | −5.13750 | −0.627645 | −0.313823 | − | 0.949482i | \(-0.601610\pi\) | ||||
−0.313823 | + | 0.949482i | \(0.601610\pi\) | |||||||
\(68\) | −7.28415 | −0.883333 | ||||||||
\(69\) | 5.18693 | 0.624433 | ||||||||
\(70\) | 9.82939 | 1.17484 | ||||||||
\(71\) | −10.7203 | −1.27226 | −0.636132 | − | 0.771581i | \(-0.719466\pi\) | ||||
−0.636132 | + | 0.771581i | \(0.719466\pi\) | |||||||
\(72\) | −1.42413 | −0.167835 | ||||||||
\(73\) | 6.12864 | 0.717302 | 0.358651 | − | 0.933472i | \(-0.383237\pi\) | ||||
0.358651 | + | 0.933472i | \(0.383237\pi\) | |||||||
\(74\) | 3.32091 | 0.386048 | ||||||||
\(75\) | −6.76013 | −0.780593 | ||||||||
\(76\) | −3.37924 | −0.387626 | ||||||||
\(77\) | −5.18534 | −0.590924 | ||||||||
\(78\) | −2.47109 | −0.279795 | ||||||||
\(79\) | 15.3907 | 1.73159 | 0.865794 | − | 0.500400i | \(-0.166814\pi\) | ||||
0.865794 | + | 0.500400i | \(0.166814\pi\) | |||||||
\(80\) | −2.86600 | −0.320429 | ||||||||
\(81\) | −11.2442 | −1.24936 | ||||||||
\(82\) | 9.68874 | 1.06994 | ||||||||
\(83\) | −6.42446 | −0.705176 | −0.352588 | − | 0.935779i | \(-0.614698\pi\) | ||||
−0.352588 | + | 0.935779i | \(0.614698\pi\) | |||||||
\(84\) | −7.21380 | −0.787090 | ||||||||
\(85\) | 20.8764 | 2.26436 | ||||||||
\(86\) | 1.96662 | 0.212066 | ||||||||
\(87\) | −10.1994 | −1.09349 | ||||||||
\(88\) | 1.51191 | 0.161171 | ||||||||
\(89\) | −12.7659 | −1.35318 | −0.676591 | − | 0.736359i | \(-0.736544\pi\) | ||||
−0.676591 | + | 0.736359i | \(0.736544\pi\) | |||||||
\(90\) | 4.08155 | 0.430234 | ||||||||
\(91\) | −4.02925 | −0.422380 | ||||||||
\(92\) | −2.46602 | −0.257100 | ||||||||
\(93\) | 17.9479 | 1.86111 | ||||||||
\(94\) | 0.645154 | 0.0665425 | ||||||||
\(95\) | 9.68491 | 0.993651 | ||||||||
\(96\) | 2.10336 | 0.214673 | ||||||||
\(97\) | 3.11750 | 0.316534 | 0.158267 | − | 0.987396i | \(-0.449409\pi\) | ||||
0.158267 | + | 0.987396i | \(0.449409\pi\) | |||||||
\(98\) | −4.76251 | −0.481086 | ||||||||
\(99\) | −2.15316 | −0.216401 | ||||||||
\(100\) | 3.21397 | 0.321397 | ||||||||
\(101\) | −12.3350 | −1.22737 | −0.613687 | − | 0.789549i | \(-0.710314\pi\) | ||||
−0.613687 | + | 0.789549i | \(0.710314\pi\) | |||||||
\(102\) | −15.3212 | −1.51703 | ||||||||
\(103\) | −7.97045 | −0.785352 | −0.392676 | − | 0.919677i | \(-0.628451\pi\) | ||||
−0.392676 | + | 0.919677i | \(0.628451\pi\) | |||||||
\(104\) | 1.17483 | 0.115201 | ||||||||
\(105\) | 20.6748 | 2.01765 | ||||||||
\(106\) | 9.65253 | 0.937537 | ||||||||
\(107\) | 0.791050 | 0.0764737 | 0.0382369 | − | 0.999269i | \(-0.487826\pi\) | ||||
0.0382369 | + | 0.999269i | \(0.487826\pi\) | |||||||
\(108\) | 3.31463 | 0.318950 | ||||||||
\(109\) | −1.22575 | −0.117406 | −0.0587029 | − | 0.998275i | \(-0.518696\pi\) | ||||
−0.0587029 | + | 0.998275i | \(0.518696\pi\) | |||||||
\(110\) | −4.33315 | −0.413150 | ||||||||
\(111\) | 6.98507 | 0.662994 | ||||||||
\(112\) | 3.42965 | 0.324072 | ||||||||
\(113\) | 12.5726 | 1.18273 | 0.591363 | − | 0.806405i | \(-0.298590\pi\) | ||||
0.591363 | + | 0.806405i | \(0.298590\pi\) | |||||||
\(114\) | −7.10777 | −0.665703 | ||||||||
\(115\) | 7.06761 | 0.659058 | ||||||||
\(116\) | 4.84908 | 0.450226 | ||||||||
\(117\) | −1.67311 | −0.154679 | ||||||||
\(118\) | 0.822649 | 0.0757310 | ||||||||
\(119\) | −24.9821 | −2.29011 | ||||||||
\(120\) | −6.02824 | −0.550300 | ||||||||
\(121\) | −8.71412 | −0.792192 | ||||||||
\(122\) | −10.3443 | −0.936525 | ||||||||
\(123\) | 20.3789 | 1.83750 | ||||||||
\(124\) | −8.53296 | −0.766283 | ||||||||
\(125\) | 5.11877 | 0.457837 | ||||||||
\(126\) | −4.88426 | −0.435125 | ||||||||
\(127\) | 3.10468 | 0.275496 | 0.137748 | − | 0.990467i | \(-0.456014\pi\) | ||||
0.137748 | + | 0.990467i | \(0.456014\pi\) | |||||||
\(128\) | −1.00000 | −0.0883883 | ||||||||
\(129\) | 4.13652 | 0.364200 | ||||||||
\(130\) | −3.36706 | −0.295311 | ||||||||
\(131\) | 0.692149 | 0.0604734 | 0.0302367 | − | 0.999543i | \(-0.490374\pi\) | ||||
0.0302367 | + | 0.999543i | \(0.490374\pi\) | |||||||
\(132\) | 3.18010 | 0.276792 | ||||||||
\(133\) | −11.5896 | −1.00495 | ||||||||
\(134\) | 5.13750 | 0.443812 | ||||||||
\(135\) | −9.49973 | −0.817606 | ||||||||
\(136\) | 7.28415 | 0.624611 | ||||||||
\(137\) | 5.61252 | 0.479510 | 0.239755 | − | 0.970833i | \(-0.422933\pi\) | ||||
0.239755 | + | 0.970833i | \(0.422933\pi\) | |||||||
\(138\) | −5.18693 | −0.441540 | ||||||||
\(139\) | −3.42114 | −0.290177 | −0.145089 | − | 0.989419i | \(-0.546347\pi\) | ||||
−0.145089 | + | 0.989419i | \(0.546347\pi\) | |||||||
\(140\) | −9.82939 | −0.830735 | ||||||||
\(141\) | 1.35699 | 0.114279 | ||||||||
\(142\) | 10.7203 | 0.899626 | ||||||||
\(143\) | 1.77624 | 0.148537 | ||||||||
\(144\) | 1.42413 | 0.118677 | ||||||||
\(145\) | −13.8975 | −1.15412 | ||||||||
\(146\) | −6.12864 | −0.507209 | ||||||||
\(147\) | −10.0173 | −0.826212 | ||||||||
\(148\) | −3.32091 | −0.272977 | ||||||||
\(149\) | 17.9357 | 1.46935 | 0.734677 | − | 0.678417i | \(-0.237334\pi\) | ||||
0.734677 | + | 0.678417i | \(0.237334\pi\) | |||||||
\(150\) | 6.76013 | 0.551963 | ||||||||
\(151\) | −13.4578 | −1.09518 | −0.547591 | − | 0.836746i | \(-0.684455\pi\) | ||||
−0.547591 | + | 0.836746i | \(0.684455\pi\) | |||||||
\(152\) | 3.37924 | 0.274093 | ||||||||
\(153\) | −10.3736 | −0.838653 | ||||||||
\(154\) | 5.18534 | 0.417847 | ||||||||
\(155\) | 24.4555 | 1.96431 | ||||||||
\(156\) | 2.47109 | 0.197845 | ||||||||
\(157\) | 6.87183 | 0.548432 | 0.274216 | − | 0.961668i | \(-0.411582\pi\) | ||||
0.274216 | + | 0.961668i | \(0.411582\pi\) | |||||||
\(158\) | −15.3907 | −1.22442 | ||||||||
\(159\) | 20.3028 | 1.61011 | ||||||||
\(160\) | 2.86600 | 0.226577 | ||||||||
\(161\) | −8.45758 | −0.666551 | ||||||||
\(162\) | 11.2442 | 0.883431 | ||||||||
\(163\) | −24.4552 | −1.91548 | −0.957740 | − | 0.287635i | \(-0.907131\pi\) | ||||
−0.957740 | + | 0.287635i | \(0.907131\pi\) | |||||||
\(164\) | −9.68874 | −0.756563 | ||||||||
\(165\) | −9.11418 | −0.709538 | ||||||||
\(166\) | 6.42446 | 0.498635 | ||||||||
\(167\) | −13.8409 | −1.07104 | −0.535522 | − | 0.844521i | \(-0.679885\pi\) | ||||
−0.535522 | + | 0.844521i | \(0.679885\pi\) | |||||||
\(168\) | 7.21380 | 0.556557 | ||||||||
\(169\) | −11.6198 | −0.893829 | ||||||||
\(170\) | −20.8764 | −1.60115 | ||||||||
\(171\) | −4.81247 | −0.368019 | ||||||||
\(172\) | −1.96662 | −0.149954 | ||||||||
\(173\) | −7.18295 | −0.546110 | −0.273055 | − | 0.961998i | \(-0.588034\pi\) | ||||
−0.273055 | + | 0.961998i | \(0.588034\pi\) | |||||||
\(174\) | 10.1994 | 0.773212 | ||||||||
\(175\) | 11.0228 | 0.833245 | ||||||||
\(176\) | −1.51191 | −0.113965 | ||||||||
\(177\) | 1.73033 | 0.130059 | ||||||||
\(178\) | 12.7659 | 0.956845 | ||||||||
\(179\) | −2.51685 | −0.188118 | −0.0940591 | − | 0.995567i | \(-0.529984\pi\) | ||||
−0.0940591 | + | 0.995567i | \(0.529984\pi\) | |||||||
\(180\) | −4.08155 | −0.304221 | ||||||||
\(181\) | 8.28994 | 0.616186 | 0.308093 | − | 0.951356i | \(-0.400309\pi\) | ||||
0.308093 | + | 0.951356i | \(0.400309\pi\) | |||||||
\(182\) | 4.02925 | 0.298668 | ||||||||
\(183\) | −21.7577 | −1.60838 | ||||||||
\(184\) | 2.46602 | 0.181797 | ||||||||
\(185\) | 9.51773 | 0.699758 | ||||||||
\(186\) | −17.9479 | −1.31600 | ||||||||
\(187\) | 11.0130 | 0.805351 | ||||||||
\(188\) | −0.645154 | −0.0470527 | ||||||||
\(189\) | 11.3680 | 0.826902 | ||||||||
\(190\) | −9.68491 | −0.702617 | ||||||||
\(191\) | −12.2518 | −0.886512 | −0.443256 | − | 0.896395i | \(-0.646177\pi\) | ||||
−0.443256 | + | 0.896395i | \(0.646177\pi\) | |||||||
\(192\) | −2.10336 | −0.151797 | ||||||||
\(193\) | 4.61562 | 0.332239 | 0.166120 | − | 0.986106i | \(-0.446876\pi\) | ||||
0.166120 | + | 0.986106i | \(0.446876\pi\) | |||||||
\(194\) | −3.11750 | −0.223824 | ||||||||
\(195\) | −7.08214 | −0.507163 | ||||||||
\(196\) | 4.76251 | 0.340180 | ||||||||
\(197\) | −12.3012 | −0.876426 | −0.438213 | − | 0.898871i | \(-0.644388\pi\) | ||||
−0.438213 | + | 0.898871i | \(0.644388\pi\) | |||||||
\(198\) | 2.15316 | 0.153018 | ||||||||
\(199\) | −18.0187 | −1.27731 | −0.638655 | − | 0.769493i | \(-0.720509\pi\) | ||||
−0.638655 | + | 0.769493i | \(0.720509\pi\) | |||||||
\(200\) | −3.21397 | −0.227262 | ||||||||
\(201\) | 10.8060 | 0.762197 | ||||||||
\(202\) | 12.3350 | 0.867885 | ||||||||
\(203\) | 16.6307 | 1.16724 | ||||||||
\(204\) | 15.3212 | 1.07270 | ||||||||
\(205\) | 27.7679 | 1.93940 | ||||||||
\(206\) | 7.97045 | 0.555328 | ||||||||
\(207\) | −3.51193 | −0.244096 | ||||||||
\(208\) | −1.17483 | −0.0814596 | ||||||||
\(209\) | 5.10912 | 0.353405 | ||||||||
\(210\) | −20.6748 | −1.42669 | ||||||||
\(211\) | −27.1505 | −1.86911 | −0.934557 | − | 0.355813i | \(-0.884204\pi\) | ||||
−0.934557 | + | 0.355813i | \(0.884204\pi\) | |||||||
\(212\) | −9.65253 | −0.662938 | ||||||||
\(213\) | 22.5486 | 1.54501 | ||||||||
\(214\) | −0.791050 | −0.0540751 | ||||||||
\(215\) | 5.63634 | 0.384396 | ||||||||
\(216\) | −3.31463 | −0.225532 | ||||||||
\(217\) | −29.2651 | −1.98664 | ||||||||
\(218\) | 1.22575 | 0.0830184 | ||||||||
\(219\) | −12.8907 | −0.871075 | ||||||||
\(220\) | 4.33315 | 0.292141 | ||||||||
\(221\) | 8.55762 | 0.575648 | ||||||||
\(222\) | −6.98507 | −0.468807 | ||||||||
\(223\) | −2.51162 | −0.168190 | −0.0840952 | − | 0.996458i | \(-0.526800\pi\) | ||||
−0.0840952 | + | 0.996458i | \(0.526800\pi\) | |||||||
\(224\) | −3.42965 | −0.229153 | ||||||||
\(225\) | 4.57710 | 0.305140 | ||||||||
\(226\) | −12.5726 | −0.836314 | ||||||||
\(227\) | 22.5312 | 1.49545 | 0.747723 | − | 0.664011i | \(-0.231147\pi\) | ||||
0.747723 | + | 0.664011i | \(0.231147\pi\) | |||||||
\(228\) | 7.10777 | 0.470723 | ||||||||
\(229\) | −18.3882 | −1.21512 | −0.607562 | − | 0.794273i | \(-0.707852\pi\) | ||||
−0.607562 | + | 0.794273i | \(0.707852\pi\) | |||||||
\(230\) | −7.06761 | −0.466025 | ||||||||
\(231\) | 10.9066 | 0.717604 | ||||||||
\(232\) | −4.84908 | −0.318358 | ||||||||
\(233\) | −8.43449 | −0.552561 | −0.276281 | − | 0.961077i | \(-0.589102\pi\) | ||||
−0.276281 | + | 0.961077i | \(0.589102\pi\) | |||||||
\(234\) | 1.67311 | 0.109374 | ||||||||
\(235\) | 1.84901 | 0.120616 | ||||||||
\(236\) | −0.822649 | −0.0535499 | ||||||||
\(237\) | −32.3722 | −2.10280 | ||||||||
\(238\) | 24.9821 | 1.61935 | ||||||||
\(239\) | 19.8057 | 1.28112 | 0.640561 | − | 0.767907i | \(-0.278702\pi\) | ||||
0.640561 | + | 0.767907i | \(0.278702\pi\) | |||||||
\(240\) | 6.02824 | 0.389121 | ||||||||
\(241\) | −28.3492 | −1.82613 | −0.913066 | − | 0.407811i | \(-0.866292\pi\) | ||||
−0.913066 | + | 0.407811i | \(0.866292\pi\) | |||||||
\(242\) | 8.71412 | 0.560165 | ||||||||
\(243\) | 13.7068 | 0.879293 | ||||||||
\(244\) | 10.3443 | 0.662223 | ||||||||
\(245\) | −13.6494 | −0.872026 | ||||||||
\(246\) | −20.3789 | −1.29931 | ||||||||
\(247\) | 3.97003 | 0.252607 | ||||||||
\(248\) | 8.53296 | 0.541844 | ||||||||
\(249\) | 13.5130 | 0.856349 | ||||||||
\(250\) | −5.11877 | −0.323740 | ||||||||
\(251\) | −21.0654 | −1.32964 | −0.664818 | − | 0.747006i | \(-0.731491\pi\) | ||||
−0.664818 | + | 0.747006i | \(0.731491\pi\) | |||||||
\(252\) | 4.88426 | 0.307680 | ||||||||
\(253\) | 3.72841 | 0.234403 | ||||||||
\(254\) | −3.10468 | −0.194805 | ||||||||
\(255\) | −43.9106 | −2.74979 | ||||||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | −6.93510 | −0.432600 | −0.216300 | − | 0.976327i | \(-0.569399\pi\) | ||||
−0.216300 | + | 0.976327i | \(0.569399\pi\) | |||||||
\(258\) | −4.13652 | −0.257528 | ||||||||
\(259\) | −11.3896 | −0.707713 | ||||||||
\(260\) | 3.36706 | 0.208816 | ||||||||
\(261\) | 6.90571 | 0.427453 | ||||||||
\(262\) | −0.692149 | −0.0427611 | ||||||||
\(263\) | −30.6371 | −1.88916 | −0.944581 | − | 0.328278i | \(-0.893532\pi\) | ||||
−0.944581 | + | 0.328278i | \(0.893532\pi\) | |||||||
\(264\) | −3.18010 | −0.195722 | ||||||||
\(265\) | 27.6642 | 1.69940 | ||||||||
\(266\) | 11.5896 | 0.710605 | ||||||||
\(267\) | 26.8513 | 1.64327 | ||||||||
\(268\) | −5.13750 | −0.313823 | ||||||||
\(269\) | −5.70907 | −0.348088 | −0.174044 | − | 0.984738i | \(-0.555684\pi\) | ||||
−0.174044 | + | 0.984738i | \(0.555684\pi\) | |||||||
\(270\) | 9.49973 | 0.578135 | ||||||||
\(271\) | 31.4036 | 1.90763 | 0.953817 | − | 0.300388i | \(-0.0971161\pi\) | ||||
0.953817 | + | 0.300388i | \(0.0971161\pi\) | |||||||
\(272\) | −7.28415 | −0.441667 | ||||||||
\(273\) | 8.47497 | 0.512928 | ||||||||
\(274\) | −5.61252 | −0.339065 | ||||||||
\(275\) | −4.85924 | −0.293023 | ||||||||
\(276\) | 5.18693 | 0.312216 | ||||||||
\(277\) | 4.12553 | 0.247879 | 0.123940 | − | 0.992290i | \(-0.460447\pi\) | ||||
0.123940 | + | 0.992290i | \(0.460447\pi\) | |||||||
\(278\) | 3.42114 | 0.205186 | ||||||||
\(279\) | −12.1520 | −0.727523 | ||||||||
\(280\) | 9.82939 | 0.587418 | ||||||||
\(281\) | −23.9809 | −1.43058 | −0.715290 | − | 0.698828i | \(-0.753705\pi\) | ||||
−0.715290 | + | 0.698828i | \(0.753705\pi\) | |||||||
\(282\) | −1.35699 | −0.0808077 | ||||||||
\(283\) | −14.1399 | −0.840531 | −0.420265 | − | 0.907401i | \(-0.638063\pi\) | ||||
−0.420265 | + | 0.907401i | \(0.638063\pi\) | |||||||
\(284\) | −10.7203 | −0.636132 | ||||||||
\(285\) | −20.3709 | −1.20667 | ||||||||
\(286\) | −1.77624 | −0.105031 | ||||||||
\(287\) | −33.2290 | −1.96145 | ||||||||
\(288\) | −1.42413 | −0.0839176 | ||||||||
\(289\) | 36.0589 | 2.12111 | ||||||||
\(290\) | 13.8975 | 0.816087 | ||||||||
\(291\) | −6.55723 | −0.384392 | ||||||||
\(292\) | 6.12864 | 0.358651 | ||||||||
\(293\) | 8.61165 | 0.503098 | 0.251549 | − | 0.967845i | \(-0.419060\pi\) | ||||
0.251549 | + | 0.967845i | \(0.419060\pi\) | |||||||
\(294\) | 10.0173 | 0.584220 | ||||||||
\(295\) | 2.35771 | 0.137271 | ||||||||
\(296\) | 3.32091 | 0.193024 | ||||||||
\(297\) | −5.01143 | −0.290793 | ||||||||
\(298\) | −17.9357 | −1.03899 | ||||||||
\(299\) | 2.89715 | 0.167546 | ||||||||
\(300\) | −6.76013 | −0.390297 | ||||||||
\(301\) | −6.74483 | −0.388766 | ||||||||
\(302\) | 13.4578 | 0.774411 | ||||||||
\(303\) | 25.9449 | 1.49049 | ||||||||
\(304\) | −3.37924 | −0.193813 | ||||||||
\(305\) | −29.6466 | −1.69756 | ||||||||
\(306\) | 10.3736 | 0.593017 | ||||||||
\(307\) | −10.2691 | −0.586091 | −0.293045 | − | 0.956099i | \(-0.594669\pi\) | ||||
−0.293045 | + | 0.956099i | \(0.594669\pi\) | |||||||
\(308\) | −5.18534 | −0.295462 | ||||||||
\(309\) | 16.7647 | 0.953713 | ||||||||
\(310\) | −24.4555 | −1.38898 | ||||||||
\(311\) | −3.65819 | −0.207437 | −0.103719 | − | 0.994607i | \(-0.533074\pi\) | ||||
−0.103719 | + | 0.994607i | \(0.533074\pi\) | |||||||
\(312\) | −2.47109 | −0.139898 | ||||||||
\(313\) | −13.5030 | −0.763235 | −0.381617 | − | 0.924320i | \(-0.624633\pi\) | ||||
−0.381617 | + | 0.924320i | \(0.624633\pi\) | |||||||
\(314\) | −6.87183 | −0.387800 | ||||||||
\(315\) | −13.9983 | −0.788715 | ||||||||
\(316\) | 15.3907 | 0.865794 | ||||||||
\(317\) | 0.0257917 | 0.00144860 | 0.000724302 | − | 1.00000i | \(-0.499769\pi\) | ||||
0.000724302 | 1.00000i | \(0.499769\pi\) | ||||||||
\(318\) | −20.3028 | −1.13852 | ||||||||
\(319\) | −7.33139 | −0.410479 | ||||||||
\(320\) | −2.86600 | −0.160214 | ||||||||
\(321\) | −1.66386 | −0.0928679 | ||||||||
\(322\) | 8.45758 | 0.471323 | ||||||||
\(323\) | 24.6149 | 1.36961 | ||||||||
\(324\) | −11.2442 | −0.624680 | ||||||||
\(325\) | −3.77586 | −0.209447 | ||||||||
\(326\) | 24.4552 | 1.35445 | ||||||||
\(327\) | 2.57820 | 0.142575 | ||||||||
\(328\) | 9.68874 | 0.534971 | ||||||||
\(329\) | −2.21265 | −0.121988 | ||||||||
\(330\) | 9.11418 | 0.501719 | ||||||||
\(331\) | 14.0491 | 0.772210 | 0.386105 | − | 0.922455i | \(-0.373820\pi\) | ||||
0.386105 | + | 0.922455i | \(0.373820\pi\) | |||||||
\(332\) | −6.42446 | −0.352588 | ||||||||
\(333\) | −4.72940 | −0.259170 | ||||||||
\(334\) | 13.8409 | 0.757343 | ||||||||
\(335\) | 14.7241 | 0.804462 | ||||||||
\(336\) | −7.21380 | −0.393545 | ||||||||
\(337\) | 24.2966 | 1.32352 | 0.661761 | − | 0.749715i | \(-0.269809\pi\) | ||||
0.661761 | + | 0.749715i | \(0.269809\pi\) | |||||||
\(338\) | 11.6198 | 0.632033 | ||||||||
\(339\) | −26.4446 | −1.43628 | ||||||||
\(340\) | 20.8764 | 1.13218 | ||||||||
\(341\) | 12.9011 | 0.698634 | ||||||||
\(342\) | 4.81247 | 0.260229 | ||||||||
\(343\) | −7.67380 | −0.414346 | ||||||||
\(344\) | 1.96662 | 0.106033 | ||||||||
\(345\) | −14.8657 | −0.800345 | ||||||||
\(346\) | 7.18295 | 0.386158 | ||||||||
\(347\) | 0.948564 | 0.0509216 | 0.0254608 | − | 0.999676i | \(-0.491895\pi\) | ||||
0.0254608 | + | 0.999676i | \(0.491895\pi\) | |||||||
\(348\) | −10.1994 | −0.546743 | ||||||||
\(349\) | −10.6983 | −0.572665 | −0.286333 | − | 0.958130i | \(-0.592436\pi\) | ||||
−0.286333 | + | 0.958130i | \(0.592436\pi\) | |||||||
\(350\) | −11.0228 | −0.589193 | ||||||||
\(351\) | −3.89412 | −0.207853 | ||||||||
\(352\) | 1.51191 | 0.0805853 | ||||||||
\(353\) | −10.1166 | −0.538453 | −0.269227 | − | 0.963077i | \(-0.586768\pi\) | ||||
−0.269227 | + | 0.963077i | \(0.586768\pi\) | |||||||
\(354\) | −1.73033 | −0.0919659 | ||||||||
\(355\) | 30.7243 | 1.63068 | ||||||||
\(356\) | −12.7659 | −0.676591 | ||||||||
\(357\) | 52.5464 | 2.78105 | ||||||||
\(358\) | 2.51685 | 0.133020 | ||||||||
\(359\) | 0.328326 | 0.0173284 | 0.00866420 | − | 0.999962i | \(-0.497242\pi\) | ||||
0.00866420 | + | 0.999962i | \(0.497242\pi\) | |||||||
\(360\) | 4.08155 | 0.215117 | ||||||||
\(361\) | −7.58073 | −0.398986 | ||||||||
\(362\) | −8.28994 | −0.435710 | ||||||||
\(363\) | 18.3289 | 0.962019 | ||||||||
\(364\) | −4.02925 | −0.211190 | ||||||||
\(365\) | −17.5647 | −0.919377 | ||||||||
\(366\) | 21.7577 | 1.13729 | ||||||||
\(367\) | 15.4184 | 0.804835 | 0.402417 | − | 0.915456i | \(-0.368170\pi\) | ||||
0.402417 | + | 0.915456i | \(0.368170\pi\) | |||||||
\(368\) | −2.46602 | −0.128550 | ||||||||
\(369\) | −13.7980 | −0.718295 | ||||||||
\(370\) | −9.51773 | −0.494803 | ||||||||
\(371\) | −33.1048 | −1.71872 | ||||||||
\(372\) | 17.9479 | 0.930555 | ||||||||
\(373\) | 26.7105 | 1.38302 | 0.691509 | − | 0.722368i | \(-0.256946\pi\) | ||||
0.691509 | + | 0.722368i | \(0.256946\pi\) | |||||||
\(374\) | −11.0130 | −0.569469 | ||||||||
\(375\) | −10.7666 | −0.555986 | ||||||||
\(376\) | 0.645154 | 0.0332713 | ||||||||
\(377\) | −5.69683 | −0.293402 | ||||||||
\(378\) | −11.3680 | −0.584708 | ||||||||
\(379\) | 30.8165 | 1.58294 | 0.791469 | − | 0.611209i | \(-0.209317\pi\) | ||||
0.791469 | + | 0.611209i | \(0.209317\pi\) | |||||||
\(380\) | 9.68491 | 0.496826 | ||||||||
\(381\) | −6.53027 | −0.334556 | ||||||||
\(382\) | 12.2518 | 0.626858 | ||||||||
\(383\) | 36.1044 | 1.84485 | 0.922425 | − | 0.386177i | \(-0.126205\pi\) | ||||
0.922425 | + | 0.386177i | \(0.126205\pi\) | |||||||
\(384\) | 2.10336 | 0.107337 | ||||||||
\(385\) | 14.8612 | 0.757397 | ||||||||
\(386\) | −4.61562 | −0.234929 | ||||||||
\(387\) | −2.80072 | −0.142369 | ||||||||
\(388\) | 3.11750 | 0.158267 | ||||||||
\(389\) | 30.8209 | 1.56268 | 0.781342 | − | 0.624103i | \(-0.214536\pi\) | ||||
0.781342 | + | 0.624103i | \(0.214536\pi\) | |||||||
\(390\) | 7.08214 | 0.358618 | ||||||||
\(391\) | 17.9629 | 0.908421 | ||||||||
\(392\) | −4.76251 | −0.240543 | ||||||||
\(393\) | −1.45584 | −0.0734374 | ||||||||
\(394\) | 12.3012 | 0.619727 | ||||||||
\(395\) | −44.1098 | −2.21940 | ||||||||
\(396\) | −2.15316 | −0.108200 | ||||||||
\(397\) | 14.9668 | 0.751161 | 0.375581 | − | 0.926790i | \(-0.377443\pi\) | ||||
0.375581 | + | 0.926790i | \(0.377443\pi\) | |||||||
\(398\) | 18.0187 | 0.903195 | ||||||||
\(399\) | 24.3772 | 1.22038 | ||||||||
\(400\) | 3.21397 | 0.160698 | ||||||||
\(401\) | −4.58532 | −0.228980 | −0.114490 | − | 0.993424i | \(-0.536523\pi\) | ||||
−0.114490 | + | 0.993424i | \(0.536523\pi\) | |||||||
\(402\) | −10.8060 | −0.538955 | ||||||||
\(403\) | 10.0248 | 0.499369 | ||||||||
\(404\) | −12.3350 | −0.613687 | ||||||||
\(405\) | 32.2260 | 1.60132 | ||||||||
\(406\) | −16.6307 | −0.825365 | ||||||||
\(407\) | 5.02093 | 0.248878 | ||||||||
\(408\) | −15.3212 | −0.758513 | ||||||||
\(409\) | 17.5640 | 0.868482 | 0.434241 | − | 0.900797i | \(-0.357017\pi\) | ||||
0.434241 | + | 0.900797i | \(0.357017\pi\) | |||||||
\(410\) | −27.7679 | −1.37136 | ||||||||
\(411\) | −11.8052 | −0.582305 | ||||||||
\(412\) | −7.97045 | −0.392676 | ||||||||
\(413\) | −2.82140 | −0.138832 | ||||||||
\(414\) | 3.51193 | 0.172602 | ||||||||
\(415\) | 18.4125 | 0.903835 | ||||||||
\(416\) | 1.17483 | 0.0576007 | ||||||||
\(417\) | 7.19589 | 0.352384 | ||||||||
\(418\) | −5.10912 | −0.249895 | ||||||||
\(419\) | 35.6335 | 1.74081 | 0.870405 | − | 0.492336i | \(-0.163857\pi\) | ||||
0.870405 | + | 0.492336i | \(0.163857\pi\) | |||||||
\(420\) | 20.6748 | 1.00882 | ||||||||
\(421\) | 37.4786 | 1.82660 | 0.913298 | − | 0.407291i | \(-0.133527\pi\) | ||||
0.913298 | + | 0.407291i | \(0.133527\pi\) | |||||||
\(422\) | 27.1505 | 1.32166 | ||||||||
\(423\) | −0.918782 | −0.0446727 | ||||||||
\(424\) | 9.65253 | 0.468768 | ||||||||
\(425\) | −23.4110 | −1.13560 | ||||||||
\(426\) | −22.5486 | −1.09248 | ||||||||
\(427\) | 35.4772 | 1.71686 | ||||||||
\(428\) | 0.791050 | 0.0382369 | ||||||||
\(429\) | −3.73607 | −0.180379 | ||||||||
\(430\) | −5.63634 | −0.271809 | ||||||||
\(431\) | 31.3578 | 1.51045 | 0.755226 | − | 0.655464i | \(-0.227527\pi\) | ||||
0.755226 | + | 0.655464i | \(0.227527\pi\) | |||||||
\(432\) | 3.31463 | 0.159475 | ||||||||
\(433\) | 21.2769 | 1.02250 | 0.511250 | − | 0.859432i | \(-0.329182\pi\) | ||||
0.511250 | + | 0.859432i | \(0.329182\pi\) | |||||||
\(434\) | 29.2651 | 1.40477 | ||||||||
\(435\) | 29.2314 | 1.40154 | ||||||||
\(436\) | −1.22575 | −0.0587029 | ||||||||
\(437\) | 8.33327 | 0.398634 | ||||||||
\(438\) | 12.8907 | 0.615943 | ||||||||
\(439\) | −2.41774 | −0.115393 | −0.0576963 | − | 0.998334i | \(-0.518376\pi\) | ||||
−0.0576963 | + | 0.998334i | \(0.518376\pi\) | |||||||
\(440\) | −4.33315 | −0.206575 | ||||||||
\(441\) | 6.78243 | 0.322973 | ||||||||
\(442\) | −8.55762 | −0.407045 | ||||||||
\(443\) | 29.6406 | 1.40827 | 0.704133 | − | 0.710068i | \(-0.251336\pi\) | ||||
0.704133 | + | 0.710068i | \(0.251336\pi\) | |||||||
\(444\) | 6.98507 | 0.331497 | ||||||||
\(445\) | 36.5871 | 1.73439 | ||||||||
\(446\) | 2.51162 | 0.118929 | ||||||||
\(447\) | −37.7254 | −1.78435 | ||||||||
\(448\) | 3.42965 | 0.162036 | ||||||||
\(449\) | −17.6851 | −0.834611 | −0.417305 | − | 0.908766i | \(-0.637025\pi\) | ||||
−0.417305 | + | 0.908766i | \(0.637025\pi\) | |||||||
\(450\) | −4.57710 | −0.215767 | ||||||||
\(451\) | 14.6485 | 0.689773 | ||||||||
\(452\) | 12.5726 | 0.591363 | ||||||||
\(453\) | 28.3067 | 1.32996 | ||||||||
\(454\) | −22.5312 | −1.05744 | ||||||||
\(455\) | 11.5478 | 0.541371 | ||||||||
\(456\) | −7.10777 | −0.332852 | ||||||||
\(457\) | 0.459735 | 0.0215055 | 0.0107527 | − | 0.999942i | \(-0.496577\pi\) | ||||
0.0107527 | + | 0.999942i | \(0.496577\pi\) | |||||||
\(458\) | 18.3882 | 0.859222 | ||||||||
\(459\) | −24.1443 | −1.12696 | ||||||||
\(460\) | 7.06761 | 0.329529 | ||||||||
\(461\) | 7.88790 | 0.367376 | 0.183688 | − | 0.982985i | \(-0.441196\pi\) | ||||
0.183688 | + | 0.982985i | \(0.441196\pi\) | |||||||
\(462\) | −10.9066 | −0.507423 | ||||||||
\(463\) | −37.5488 | −1.74504 | −0.872521 | − | 0.488576i | \(-0.837517\pi\) | ||||
−0.872521 | + | 0.488576i | \(0.837517\pi\) | |||||||
\(464\) | 4.84908 | 0.225113 | ||||||||
\(465\) | −51.4387 | −2.38541 | ||||||||
\(466\) | 8.43449 | 0.390720 | ||||||||
\(467\) | −41.4338 | −1.91733 | −0.958664 | − | 0.284542i | \(-0.908158\pi\) | ||||
−0.958664 | + | 0.284542i | \(0.908158\pi\) | |||||||
\(468\) | −1.67311 | −0.0773393 | ||||||||
\(469\) | −17.6198 | −0.813608 | ||||||||
\(470\) | −1.84901 | −0.0852886 | ||||||||
\(471\) | −14.4539 | −0.666003 | ||||||||
\(472\) | 0.822649 | 0.0378655 | ||||||||
\(473\) | 2.97336 | 0.136715 | ||||||||
\(474\) | 32.3722 | 1.48690 | ||||||||
\(475\) | −10.8608 | −0.498326 | ||||||||
\(476\) | −24.9821 | −1.14505 | ||||||||
\(477\) | −13.7464 | −0.629406 | ||||||||
\(478\) | −19.8057 | −0.905890 | ||||||||
\(479\) | −27.2202 | −1.24372 | −0.621860 | − | 0.783128i | \(-0.713623\pi\) | ||||
−0.621860 | + | 0.783128i | \(0.713623\pi\) | |||||||
\(480\) | −6.02824 | −0.275150 | ||||||||
\(481\) | 3.90150 | 0.177893 | ||||||||
\(482\) | 28.3492 | 1.29127 | ||||||||
\(483\) | 17.7894 | 0.809444 | ||||||||
\(484\) | −8.71412 | −0.396096 | ||||||||
\(485\) | −8.93477 | −0.405707 | ||||||||
\(486\) | −13.7068 | −0.621754 | ||||||||
\(487\) | 7.85504 | 0.355946 | 0.177973 | − | 0.984035i | \(-0.443046\pi\) | ||||
0.177973 | + | 0.984035i | \(0.443046\pi\) | |||||||
\(488\) | −10.3443 | −0.468262 | ||||||||
\(489\) | 51.4381 | 2.32611 | ||||||||
\(490\) | 13.6494 | 0.616616 | ||||||||
\(491\) | 28.6606 | 1.29343 | 0.646717 | − | 0.762730i | \(-0.276141\pi\) | ||||
0.646717 | + | 0.762730i | \(0.276141\pi\) | |||||||
\(492\) | 20.3789 | 0.918752 | ||||||||
\(493\) | −35.3214 | −1.59080 | ||||||||
\(494\) | −3.97003 | −0.178620 | ||||||||
\(495\) | 6.17096 | 0.277364 | ||||||||
\(496\) | −8.53296 | −0.383141 | ||||||||
\(497\) | −36.7668 | −1.64922 | ||||||||
\(498\) | −13.5130 | −0.605530 | ||||||||
\(499\) | 35.3208 | 1.58118 | 0.790589 | − | 0.612347i | \(-0.209775\pi\) | ||||
0.790589 | + | 0.612347i | \(0.209775\pi\) | |||||||
\(500\) | 5.11877 | 0.228918 | ||||||||
\(501\) | 29.1125 | 1.30065 | ||||||||
\(502\) | 21.0654 | 0.940194 | ||||||||
\(503\) | −23.4898 | −1.04736 | −0.523679 | − | 0.851915i | \(-0.675441\pi\) | ||||
−0.523679 | + | 0.851915i | \(0.675441\pi\) | |||||||
\(504\) | −4.88426 | −0.217562 | ||||||||
\(505\) | 35.3520 | 1.57314 | ||||||||
\(506\) | −3.72841 | −0.165748 | ||||||||
\(507\) | 24.4406 | 1.08544 | ||||||||
\(508\) | 3.10468 | 0.137748 | ||||||||
\(509\) | 13.6674 | 0.605797 | 0.302898 | − | 0.953023i | \(-0.402046\pi\) | ||||
0.302898 | + | 0.953023i | \(0.402046\pi\) | |||||||
\(510\) | 43.9106 | 1.94439 | ||||||||
\(511\) | 21.0191 | 0.929830 | ||||||||
\(512\) | −1.00000 | −0.0441942 | ||||||||
\(513\) | −11.2009 | −0.494533 | ||||||||
\(514\) | 6.93510 | 0.305894 | ||||||||
\(515\) | 22.8433 | 1.00660 | ||||||||
\(516\) | 4.13652 | 0.182100 | ||||||||
\(517\) | 0.975417 | 0.0428988 | ||||||||
\(518\) | 11.3896 | 0.500429 | ||||||||
\(519\) | 15.1083 | 0.663183 | ||||||||
\(520\) | −3.36706 | −0.147655 | ||||||||
\(521\) | −20.5598 | −0.900740 | −0.450370 | − | 0.892842i | \(-0.648708\pi\) | ||||
−0.450370 | + | 0.892842i | \(0.648708\pi\) | |||||||
\(522\) | −6.90571 | −0.302255 | ||||||||
\(523\) | 23.1195 | 1.01094 | 0.505472 | − | 0.862843i | \(-0.331318\pi\) | ||||
0.505472 | + | 0.862843i | \(0.331318\pi\) | |||||||
\(524\) | 0.692149 | 0.0302367 | ||||||||
\(525\) | −23.1849 | −1.01187 | ||||||||
\(526\) | 30.6371 | 1.33584 | ||||||||
\(527\) | 62.1554 | 2.70753 | ||||||||
\(528\) | 3.18010 | 0.138396 | ||||||||
\(529\) | −16.9188 | −0.735598 | ||||||||
\(530\) | −27.6642 | −1.20165 | ||||||||
\(531\) | −1.17156 | −0.0508413 | ||||||||
\(532\) | −11.5896 | −0.502474 | ||||||||
\(533\) | 11.3826 | 0.493035 | ||||||||
\(534\) | −26.8513 | −1.16197 | ||||||||
\(535\) | −2.26715 | −0.0980175 | ||||||||
\(536\) | 5.13750 | 0.221906 | ||||||||
\(537\) | 5.29384 | 0.228446 | ||||||||
\(538\) | 5.70907 | 0.246136 | ||||||||
\(539\) | −7.20051 | −0.310148 | ||||||||
\(540\) | −9.49973 | −0.408803 | ||||||||
\(541\) | −28.1794 | −1.21153 | −0.605764 | − | 0.795644i | \(-0.707133\pi\) | ||||
−0.605764 | + | 0.795644i | \(0.707133\pi\) | |||||||
\(542\) | −31.4036 | −1.34890 | ||||||||
\(543\) | −17.4367 | −0.748282 | ||||||||
\(544\) | 7.28415 | 0.312305 | ||||||||
\(545\) | 3.51301 | 0.150481 | ||||||||
\(546\) | −8.47497 | −0.362695 | ||||||||
\(547\) | 39.8372 | 1.70332 | 0.851658 | − | 0.524097i | \(-0.175597\pi\) | ||||
0.851658 | + | 0.524097i | \(0.175597\pi\) | |||||||
\(548\) | 5.61252 | 0.239755 | ||||||||
\(549\) | 14.7315 | 0.628727 | ||||||||
\(550\) | 4.85924 | 0.207199 | ||||||||
\(551\) | −16.3862 | −0.698076 | ||||||||
\(552\) | −5.18693 | −0.220770 | ||||||||
\(553\) | 52.7847 | 2.24464 | ||||||||
\(554\) | −4.12553 | −0.175277 | ||||||||
\(555\) | −20.0192 | −0.849769 | ||||||||
\(556\) | −3.42114 | −0.145089 | ||||||||
\(557\) | 27.5288 | 1.16643 | 0.583216 | − | 0.812317i | \(-0.301794\pi\) | ||||
0.583216 | + | 0.812317i | \(0.301794\pi\) | |||||||
\(558\) | 12.1520 | 0.514437 | ||||||||
\(559\) | 2.31044 | 0.0977213 | ||||||||
\(560\) | −9.82939 | −0.415368 | ||||||||
\(561\) | −23.1643 | −0.977999 | ||||||||
\(562\) | 23.9809 | 1.01157 | ||||||||
\(563\) | −23.5606 | −0.992962 | −0.496481 | − | 0.868047i | \(-0.665375\pi\) | ||||
−0.496481 | + | 0.868047i | \(0.665375\pi\) | |||||||
\(564\) | 1.35699 | 0.0571397 | ||||||||
\(565\) | −36.0330 | −1.51592 | ||||||||
\(566\) | 14.1399 | 0.594345 | ||||||||
\(567\) | −38.5638 | −1.61953 | ||||||||
\(568\) | 10.7203 | 0.449813 | ||||||||
\(569\) | −41.1421 | −1.72476 | −0.862382 | − | 0.506257i | \(-0.831029\pi\) | ||||
−0.862382 | + | 0.506257i | \(0.831029\pi\) | |||||||
\(570\) | 20.3709 | 0.853242 | ||||||||
\(571\) | −8.88139 | −0.371675 | −0.185837 | − | 0.982581i | \(-0.559500\pi\) | ||||
−0.185837 | + | 0.982581i | \(0.559500\pi\) | |||||||
\(572\) | 1.77624 | 0.0742683 | ||||||||
\(573\) | 25.7700 | 1.07656 | ||||||||
\(574\) | 33.2290 | 1.38695 | ||||||||
\(575\) | −7.92570 | −0.330525 | ||||||||
\(576\) | 1.42413 | 0.0593387 | ||||||||
\(577\) | 23.0948 | 0.961450 | 0.480725 | − | 0.876871i | \(-0.340373\pi\) | ||||
0.480725 | + | 0.876871i | \(0.340373\pi\) | |||||||
\(578\) | −36.0589 | −1.49985 | ||||||||
\(579\) | −9.70831 | −0.403463 | ||||||||
\(580\) | −13.8975 | −0.577061 | ||||||||
\(581\) | −22.0337 | −0.914110 | ||||||||
\(582\) | 6.55723 | 0.271806 | ||||||||
\(583\) | 14.5938 | 0.604413 | ||||||||
\(584\) | −6.12864 | −0.253605 | ||||||||
\(585\) | 4.79512 | 0.198254 | ||||||||
\(586\) | −8.61165 | −0.355744 | ||||||||
\(587\) | −3.56091 | −0.146974 | −0.0734872 | − | 0.997296i | \(-0.523413\pi\) | ||||
−0.0734872 | + | 0.997296i | \(0.523413\pi\) | |||||||
\(588\) | −10.0173 | −0.413106 | ||||||||
\(589\) | 28.8349 | 1.18812 | ||||||||
\(590\) | −2.35771 | −0.0970655 | ||||||||
\(591\) | 25.8739 | 1.06431 | ||||||||
\(592\) | −3.32091 | −0.136489 | ||||||||
\(593\) | −9.58874 | −0.393762 | −0.196881 | − | 0.980427i | \(-0.563081\pi\) | ||||
−0.196881 | + | 0.980427i | \(0.563081\pi\) | |||||||
\(594\) | 5.01143 | 0.205622 | ||||||||
\(595\) | 71.5988 | 2.93526 | ||||||||
\(596\) | 17.9357 | 0.734677 | ||||||||
\(597\) | 37.8998 | 1.55114 | ||||||||
\(598\) | −2.89715 | −0.118473 | ||||||||
\(599\) | 26.7794 | 1.09418 | 0.547088 | − | 0.837075i | \(-0.315736\pi\) | ||||
0.547088 | + | 0.837075i | \(0.315736\pi\) | |||||||
\(600\) | 6.76013 | 0.275981 | ||||||||
\(601\) | 21.0157 | 0.857249 | 0.428624 | − | 0.903483i | \(-0.358998\pi\) | ||||
0.428624 | + | 0.903483i | \(0.358998\pi\) | |||||||
\(602\) | 6.74483 | 0.274899 | ||||||||
\(603\) | −7.31645 | −0.297949 | ||||||||
\(604\) | −13.4578 | −0.547591 | ||||||||
\(605\) | 24.9747 | 1.01536 | ||||||||
\(606\) | −25.9449 | −1.05394 | ||||||||
\(607\) | −32.5724 | −1.32207 | −0.661037 | − | 0.750353i | \(-0.729883\pi\) | ||||
−0.661037 | + | 0.750353i | \(0.729883\pi\) | |||||||
\(608\) | 3.37924 | 0.137046 | ||||||||
\(609\) | −34.9803 | −1.41747 | ||||||||
\(610\) | 29.6466 | 1.20036 | ||||||||
\(611\) | 0.757945 | 0.0306632 | ||||||||
\(612\) | −10.3736 | −0.419327 | ||||||||
\(613\) | 7.23880 | 0.292372 | 0.146186 | − | 0.989257i | \(-0.453300\pi\) | ||||
0.146186 | + | 0.989257i | \(0.453300\pi\) | |||||||
\(614\) | 10.2691 | 0.414429 | ||||||||
\(615\) | −58.4060 | −2.35516 | ||||||||
\(616\) | 5.18534 | 0.208923 | ||||||||
\(617\) | 14.0526 | 0.565737 | 0.282868 | − | 0.959159i | \(-0.408714\pi\) | ||||
0.282868 | + | 0.959159i | \(0.408714\pi\) | |||||||
\(618\) | −16.7647 | −0.674377 | ||||||||
\(619\) | −2.24759 | −0.0903381 | −0.0451691 | − | 0.998979i | \(-0.514383\pi\) | ||||
−0.0451691 | + | 0.998979i | \(0.514383\pi\) | |||||||
\(620\) | 24.4555 | 0.982156 | ||||||||
\(621\) | −8.17393 | −0.328009 | ||||||||
\(622\) | 3.65819 | 0.146680 | ||||||||
\(623\) | −43.7826 | −1.75411 | ||||||||
\(624\) | 2.47109 | 0.0989226 | ||||||||
\(625\) | −30.7403 | −1.22961 | ||||||||
\(626\) | 13.5030 | 0.539689 | ||||||||
\(627\) | −10.7463 | −0.429167 | ||||||||
\(628\) | 6.87183 | 0.274216 | ||||||||
\(629\) | 24.1900 | 0.964519 | ||||||||
\(630\) | 13.9983 | 0.557706 | ||||||||
\(631\) | 9.18148 | 0.365509 | 0.182754 | − | 0.983159i | \(-0.441499\pi\) | ||||
0.182754 | + | 0.983159i | \(0.441499\pi\) | |||||||
\(632\) | −15.3907 | −0.612209 | ||||||||
\(633\) | 57.1072 | 2.26981 | ||||||||
\(634\) | −0.0257917 | −0.00102432 | ||||||||
\(635\) | −8.89803 | −0.353108 | ||||||||
\(636\) | 20.3028 | 0.805057 | ||||||||
\(637\) | −5.59513 | −0.221687 | ||||||||
\(638\) | 7.33139 | 0.290252 | ||||||||
\(639\) | −15.2671 | −0.603955 | ||||||||
\(640\) | 2.86600 | 0.113289 | ||||||||
\(641\) | −4.87165 | −0.192419 | −0.0962093 | − | 0.995361i | \(-0.530672\pi\) | ||||
−0.0962093 | + | 0.995361i | \(0.530672\pi\) | |||||||
\(642\) | 1.66386 | 0.0656675 | ||||||||
\(643\) | 11.1134 | 0.438269 | 0.219134 | − | 0.975695i | \(-0.429677\pi\) | ||||
0.219134 | + | 0.975695i | \(0.429677\pi\) | |||||||
\(644\) | −8.45758 | −0.333275 | ||||||||
\(645\) | −11.8553 | −0.466801 | ||||||||
\(646\) | −24.6149 | −0.968461 | ||||||||
\(647\) | −4.83049 | −0.189906 | −0.0949530 | − | 0.995482i | \(-0.530270\pi\) | ||||
−0.0949530 | + | 0.995482i | \(0.530270\pi\) | |||||||
\(648\) | 11.2442 | 0.441716 | ||||||||
\(649\) | 1.24377 | 0.0488224 | ||||||||
\(650\) | 3.77586 | 0.148101 | ||||||||
\(651\) | 61.5551 | 2.41253 | ||||||||
\(652\) | −24.4552 | −0.957740 | ||||||||
\(653\) | −1.00841 | −0.0394620 | −0.0197310 | − | 0.999805i | \(-0.506281\pi\) | ||||
−0.0197310 | + | 0.999805i | \(0.506281\pi\) | |||||||
\(654\) | −2.57820 | −0.100816 | ||||||||
\(655\) | −1.98370 | −0.0775096 | ||||||||
\(656\) | −9.68874 | −0.378282 | ||||||||
\(657\) | 8.72796 | 0.340510 | ||||||||
\(658\) | 2.21265 | 0.0862582 | ||||||||
\(659\) | −40.6090 | −1.58190 | −0.790951 | − | 0.611879i | \(-0.790414\pi\) | ||||
−0.790951 | + | 0.611879i | \(0.790414\pi\) | |||||||
\(660\) | −9.11418 | −0.354769 | ||||||||
\(661\) | −33.6944 | −1.31056 | −0.655280 | − | 0.755386i | \(-0.727449\pi\) | ||||
−0.655280 | + | 0.755386i | \(0.727449\pi\) | |||||||
\(662\) | −14.0491 | −0.546035 | ||||||||
\(663\) | −17.9998 | −0.699053 | ||||||||
\(664\) | 6.42446 | 0.249317 | ||||||||
\(665\) | 33.2159 | 1.28806 | ||||||||
\(666\) | 4.72940 | 0.183261 | ||||||||
\(667\) | −11.9579 | −0.463012 | ||||||||
\(668\) | −13.8409 | −0.535522 | ||||||||
\(669\) | 5.28284 | 0.204246 | ||||||||
\(670\) | −14.7241 | −0.568841 | ||||||||
\(671\) | −15.6396 | −0.603761 | ||||||||
\(672\) | 7.21380 | 0.278278 | ||||||||
\(673\) | 18.7103 | 0.721231 | 0.360615 | − | 0.932715i | \(-0.382567\pi\) | ||||
0.360615 | + | 0.932715i | \(0.382567\pi\) | |||||||
\(674\) | −24.2966 | −0.935871 | ||||||||
\(675\) | 10.6531 | 0.410038 | ||||||||
\(676\) | −11.6198 | −0.446915 | ||||||||
\(677\) | −35.0072 | −1.34544 | −0.672719 | − | 0.739898i | \(-0.734874\pi\) | ||||
−0.672719 | + | 0.739898i | \(0.734874\pi\) | |||||||
\(678\) | 26.4446 | 1.01560 | ||||||||
\(679\) | 10.6919 | 0.410319 | ||||||||
\(680\) | −20.8764 | −0.800573 | ||||||||
\(681\) | −47.3912 | −1.81603 | ||||||||
\(682\) | −12.9011 | −0.494009 | ||||||||
\(683\) | 31.3377 | 1.19911 | 0.599553 | − | 0.800335i | \(-0.295345\pi\) | ||||
0.599553 | + | 0.800335i | \(0.295345\pi\) | |||||||
\(684\) | −4.81247 | −0.184010 | ||||||||
\(685\) | −16.0855 | −0.614595 | ||||||||
\(686\) | 7.67380 | 0.292987 | ||||||||
\(687\) | 38.6769 | 1.47562 | ||||||||
\(688\) | −1.96662 | −0.0749768 | ||||||||
\(689\) | 11.3401 | 0.432022 | ||||||||
\(690\) | 14.8657 | 0.565929 | ||||||||
\(691\) | −12.4762 | −0.474618 | −0.237309 | − | 0.971434i | \(-0.576265\pi\) | ||||
−0.237309 | + | 0.971434i | \(0.576265\pi\) | |||||||
\(692\) | −7.18295 | −0.273055 | ||||||||
\(693\) | −7.38459 | −0.280517 | ||||||||
\(694\) | −0.948564 | −0.0360070 | ||||||||
\(695\) | 9.80500 | 0.371925 | ||||||||
\(696\) | 10.1994 | 0.386606 | ||||||||
\(697\) | 70.5742 | 2.67319 | ||||||||
\(698\) | 10.6983 | 0.404935 | ||||||||
\(699\) | 17.7408 | 0.671017 | ||||||||
\(700\) | 11.0228 | 0.416622 | ||||||||
\(701\) | 22.1317 | 0.835905 | 0.417952 | − | 0.908469i | \(-0.362748\pi\) | ||||
0.417952 | + | 0.908469i | \(0.362748\pi\) | |||||||
\(702\) | 3.89412 | 0.146974 | ||||||||
\(703\) | 11.2222 | 0.423252 | ||||||||
\(704\) | −1.51191 | −0.0569824 | ||||||||
\(705\) | −3.88914 | −0.146474 | ||||||||
\(706\) | 10.1166 | 0.380744 | ||||||||
\(707\) | −42.3046 | −1.59103 | ||||||||
\(708\) | 1.73033 | 0.0650297 | ||||||||
\(709\) | 35.7153 | 1.34132 | 0.670658 | − | 0.741767i | \(-0.266012\pi\) | ||||
0.670658 | + | 0.741767i | \(0.266012\pi\) | |||||||
\(710\) | −30.7243 | −1.15306 | ||||||||
\(711\) | 21.9183 | 0.822002 | ||||||||
\(712\) | 12.7659 | 0.478422 | ||||||||
\(713\) | 21.0424 | 0.788046 | ||||||||
\(714\) | −52.5464 | −1.96650 | ||||||||
\(715\) | −5.09070 | −0.190381 | ||||||||
\(716\) | −2.51685 | −0.0940591 | ||||||||
\(717\) | −41.6585 | −1.55576 | ||||||||
\(718\) | −0.328326 | −0.0122530 | ||||||||
\(719\) | 28.8487 | 1.07587 | 0.537937 | − | 0.842985i | \(-0.319204\pi\) | ||||
0.537937 | + | 0.842985i | \(0.319204\pi\) | |||||||
\(720\) | −4.08155 | −0.152111 | ||||||||
\(721\) | −27.3359 | −1.01804 | ||||||||
\(722\) | 7.58073 | 0.282125 | ||||||||
\(723\) | 59.6286 | 2.21761 | ||||||||
\(724\) | 8.28994 | 0.308093 | ||||||||
\(725\) | 15.5848 | 0.578804 | ||||||||
\(726\) | −18.3289 | −0.680251 | ||||||||
\(727\) | −30.3028 | −1.12387 | −0.561935 | − | 0.827182i | \(-0.689943\pi\) | ||||
−0.561935 | + | 0.827182i | \(0.689943\pi\) | |||||||
\(728\) | 4.02925 | 0.149334 | ||||||||
\(729\) | 4.90233 | 0.181568 | ||||||||
\(730\) | 17.5647 | 0.650098 | ||||||||
\(731\) | 14.3252 | 0.529836 | ||||||||
\(732\) | −21.7577 | −0.804188 | ||||||||
\(733\) | 22.3506 | 0.825538 | 0.412769 | − | 0.910836i | \(-0.364562\pi\) | ||||
0.412769 | + | 0.910836i | \(0.364562\pi\) | |||||||
\(734\) | −15.4184 | −0.569104 | ||||||||
\(735\) | 28.7096 | 1.05897 | ||||||||
\(736\) | 2.46602 | 0.0908986 | ||||||||
\(737\) | 7.76745 | 0.286118 | ||||||||
\(738\) | 13.7980 | 0.507912 | ||||||||
\(739\) | −40.2470 | −1.48051 | −0.740255 | − | 0.672327i | \(-0.765295\pi\) | ||||
−0.740255 | + | 0.672327i | \(0.765295\pi\) | |||||||
\(740\) | 9.51773 | 0.349879 | ||||||||
\(741\) | −8.35040 | −0.306760 | ||||||||
\(742\) | 33.1048 | 1.21532 | ||||||||
\(743\) | −12.5623 | −0.460867 | −0.230433 | − | 0.973088i | \(-0.574014\pi\) | ||||
−0.230433 | + | 0.973088i | \(0.574014\pi\) | |||||||
\(744\) | −17.9479 | −0.658002 | ||||||||
\(745\) | −51.4039 | −1.88329 | ||||||||
\(746\) | −26.7105 | −0.977941 | ||||||||
\(747\) | −9.14925 | −0.334754 | ||||||||
\(748\) | 11.0130 | 0.402676 | ||||||||
\(749\) | 2.71303 | 0.0991319 | ||||||||
\(750\) | 10.7666 | 0.393142 | ||||||||
\(751\) | 7.38580 | 0.269512 | 0.134756 | − | 0.990879i | \(-0.456975\pi\) | ||||
0.134756 | + | 0.990879i | \(0.456975\pi\) | |||||||
\(752\) | −0.645154 | −0.0235263 | ||||||||
\(753\) | 44.3081 | 1.61468 | ||||||||
\(754\) | 5.69683 | 0.207466 | ||||||||
\(755\) | 38.5702 | 1.40371 | ||||||||
\(756\) | 11.3680 | 0.413451 | ||||||||
\(757\) | −24.3461 | −0.884874 | −0.442437 | − | 0.896799i | \(-0.645886\pi\) | ||||
−0.442437 | + | 0.896799i | \(0.645886\pi\) | |||||||
\(758\) | −30.8165 | −1.11931 | ||||||||
\(759\) | −7.84219 | −0.284653 | ||||||||
\(760\) | −9.68491 | −0.351309 | ||||||||
\(761\) | −10.2975 | −0.373285 | −0.186643 | − | 0.982428i | \(-0.559761\pi\) | ||||
−0.186643 | + | 0.982428i | \(0.559761\pi\) | |||||||
\(762\) | 6.53027 | 0.236567 | ||||||||
\(763\) | −4.20390 | −0.152191 | ||||||||
\(764\) | −12.2518 | −0.443256 | ||||||||
\(765\) | 29.7307 | 1.07491 | ||||||||
\(766\) | −36.1044 | −1.30451 | ||||||||
\(767\) | 0.966471 | 0.0348972 | ||||||||
\(768\) | −2.10336 | −0.0758985 | ||||||||
\(769\) | −30.8671 | −1.11310 | −0.556548 | − | 0.830815i | \(-0.687875\pi\) | ||||
−0.556548 | + | 0.830815i | \(0.687875\pi\) | |||||||
\(770\) | −14.8612 | −0.535560 | ||||||||
\(771\) | 14.5870 | 0.525339 | ||||||||
\(772\) | 4.61562 | 0.166120 | ||||||||
\(773\) | −9.07233 | −0.326309 | −0.163154 | − | 0.986601i | \(-0.552167\pi\) | ||||
−0.163154 | + | 0.986601i | \(0.552167\pi\) | |||||||
\(774\) | 2.80072 | 0.100670 | ||||||||
\(775\) | −27.4247 | −0.985123 | ||||||||
\(776\) | −3.11750 | −0.111912 | ||||||||
\(777\) | 23.9564 | 0.859430 | ||||||||
\(778\) | −30.8209 | −1.10498 | ||||||||
\(779\) | 32.7406 | 1.17305 | ||||||||
\(780\) | −7.08214 | −0.253581 | ||||||||
\(781\) | 16.2081 | 0.579973 | ||||||||
\(782\) | −17.9629 | −0.642350 | ||||||||
\(783\) | 16.0729 | 0.574398 | ||||||||
\(784\) | 4.76251 | 0.170090 | ||||||||
\(785\) | −19.6947 | −0.702933 | ||||||||
\(786\) | 1.45584 | 0.0519281 | ||||||||
\(787\) | 8.12236 | 0.289531 | 0.144765 | − | 0.989466i | \(-0.453757\pi\) | ||||
0.144765 | + | 0.989466i | \(0.453757\pi\) | |||||||
\(788\) | −12.3012 | −0.438213 | ||||||||
\(789\) | 64.4408 | 2.29415 | ||||||||
\(790\) | 44.1098 | 1.56936 | ||||||||
\(791\) | 43.1195 | 1.53315 | ||||||||
\(792\) | 2.15316 | 0.0765092 | ||||||||
\(793\) | −12.1527 | −0.431556 | ||||||||
\(794\) | −14.9668 | −0.531151 | ||||||||
\(795\) | −58.1877 | −2.06371 | ||||||||
\(796\) | −18.0187 | −0.638655 | ||||||||
\(797\) | −17.1401 | −0.607132 | −0.303566 | − | 0.952810i | \(-0.598177\pi\) | ||||
−0.303566 | + | 0.952810i | \(0.598177\pi\) | |||||||
\(798\) | −24.3772 | −0.862942 | ||||||||
\(799\) | 4.69940 | 0.166253 | ||||||||
\(800\) | −3.21397 | −0.113631 | ||||||||
\(801\) | −18.1803 | −0.642369 | ||||||||
\(802\) | 4.58532 | 0.161913 | ||||||||
\(803\) | −9.26597 | −0.326989 | ||||||||
\(804\) | 10.8060 | 0.381099 | ||||||||
\(805\) | 24.2395 | 0.854328 | ||||||||
\(806\) | −10.0248 | −0.353107 | ||||||||
\(807\) | 12.0082 | 0.422710 | ||||||||
\(808\) | 12.3350 | 0.433943 | ||||||||
\(809\) | 26.6469 | 0.936854 | 0.468427 | − | 0.883502i | \(-0.344821\pi\) | ||||
0.468427 | + | 0.883502i | \(0.344821\pi\) | |||||||
\(810\) | −32.2260 | −1.13231 | ||||||||
\(811\) | −8.06325 | −0.283139 | −0.141570 | − | 0.989928i | \(-0.545215\pi\) | ||||
−0.141570 | + | 0.989928i | \(0.545215\pi\) | |||||||
\(812\) | 16.6307 | 0.583621 | ||||||||
\(813\) | −66.0532 | −2.31659 | ||||||||
\(814\) | −5.02093 | −0.175984 | ||||||||
\(815\) | 70.0887 | 2.45510 | ||||||||
\(816\) | 15.3212 | 0.536349 | ||||||||
\(817\) | 6.64569 | 0.232503 | ||||||||
\(818\) | −17.5640 | −0.614110 | ||||||||
\(819\) | −5.73817 | −0.200508 | ||||||||
\(820\) | 27.7679 | 0.969698 | ||||||||
\(821\) | 29.0669 | 1.01444 | 0.507221 | − | 0.861816i | \(-0.330673\pi\) | ||||
0.507221 | + | 0.861816i | \(0.330673\pi\) | |||||||
\(822\) | 11.8052 | 0.411752 | ||||||||
\(823\) | 33.1970 | 1.15718 | 0.578588 | − | 0.815620i | \(-0.303604\pi\) | ||||
0.578588 | + | 0.815620i | \(0.303604\pi\) | |||||||
\(824\) | 7.97045 | 0.277664 | ||||||||
\(825\) | 10.2207 | 0.355841 | ||||||||
\(826\) | 2.82140 | 0.0981691 | ||||||||
\(827\) | 50.0174 | 1.73928 | 0.869638 | − | 0.493689i | \(-0.164352\pi\) | ||||
0.869638 | + | 0.493689i | \(0.164352\pi\) | |||||||
\(828\) | −3.51193 | −0.122048 | ||||||||
\(829\) | −45.3776 | −1.57603 | −0.788015 | − | 0.615655i | \(-0.788891\pi\) | ||||
−0.788015 | + | 0.615655i | \(0.788891\pi\) | |||||||
\(830\) | −18.4125 | −0.639108 | ||||||||
\(831\) | −8.67749 | −0.301019 | ||||||||
\(832\) | −1.17483 | −0.0407298 | ||||||||
\(833\) | −34.6909 | −1.20197 | ||||||||
\(834\) | −7.19589 | −0.249173 | ||||||||
\(835\) | 39.6682 | 1.37277 | ||||||||
\(836\) | 5.10912 | 0.176703 | ||||||||
\(837\) | −28.2836 | −0.977624 | ||||||||
\(838\) | −35.6335 | −1.23094 | ||||||||
\(839\) | 1.03059 | 0.0355799 | 0.0177900 | − | 0.999842i | \(-0.494337\pi\) | ||||
0.0177900 | + | 0.999842i | \(0.494337\pi\) | |||||||
\(840\) | −20.6748 | −0.713347 | ||||||||
\(841\) | −5.48644 | −0.189188 | ||||||||
\(842\) | −37.4786 | −1.29160 | ||||||||
\(843\) | 50.4405 | 1.73726 | ||||||||
\(844\) | −27.1505 | −0.934557 | ||||||||
\(845\) | 33.3023 | 1.14563 | ||||||||
\(846\) | 0.918782 | 0.0315884 | ||||||||
\(847\) | −29.8864 | −1.02691 | ||||||||
\(848\) | −9.65253 | −0.331469 | ||||||||
\(849\) | 29.7414 | 1.02072 | ||||||||
\(850\) | 23.4110 | 0.802992 | ||||||||
\(851\) | 8.18942 | 0.280730 | ||||||||
\(852\) | 22.5486 | 0.772503 | ||||||||
\(853\) | 13.8081 | 0.472781 | 0.236390 | − | 0.971658i | \(-0.424036\pi\) | ||||
0.236390 | + | 0.971658i | \(0.424036\pi\) | |||||||
\(854\) | −35.4772 | −1.21400 | ||||||||
\(855\) | 13.7926 | 0.471696 | ||||||||
\(856\) | −0.791050 | −0.0270375 | ||||||||
\(857\) | 51.1022 | 1.74562 | 0.872809 | − | 0.488062i | \(-0.162296\pi\) | ||||
0.872809 | + | 0.488062i | \(0.162296\pi\) | |||||||
\(858\) | 3.73607 | 0.127547 | ||||||||
\(859\) | −8.73015 | −0.297869 | −0.148934 | − | 0.988847i | \(-0.547584\pi\) | ||||
−0.148934 | + | 0.988847i | \(0.547584\pi\) | |||||||
\(860\) | 5.63634 | 0.192198 | ||||||||
\(861\) | 69.8926 | 2.38193 | ||||||||
\(862\) | −31.3578 | −1.06805 | ||||||||
\(863\) | 23.4756 | 0.799118 | 0.399559 | − | 0.916707i | \(-0.369163\pi\) | ||||
0.399559 | + | 0.916707i | \(0.369163\pi\) | |||||||
\(864\) | −3.31463 | −0.112766 | ||||||||
\(865\) | 20.5864 | 0.699957 | ||||||||
\(866\) | −21.2769 | −0.723017 | ||||||||
\(867\) | −75.8449 | −2.57583 | ||||||||
\(868\) | −29.2651 | −0.993322 | ||||||||
\(869\) | −23.2694 | −0.789361 | ||||||||
\(870\) | −29.2314 | −0.991037 | ||||||||
\(871\) | 6.03567 | 0.204511 | ||||||||
\(872\) | 1.22575 | 0.0415092 | ||||||||
\(873\) | 4.43972 | 0.150262 | ||||||||
\(874\) | −8.33327 | −0.281877 | ||||||||
\(875\) | 17.5556 | 0.593488 | ||||||||
\(876\) | −12.8907 | −0.435538 | ||||||||
\(877\) | 18.8682 | 0.637133 | 0.318567 | − | 0.947900i | \(-0.396799\pi\) | ||||
0.318567 | + | 0.947900i | \(0.396799\pi\) | |||||||
\(878\) | 2.41774 | 0.0815949 | ||||||||
\(879\) | −18.1134 | −0.610950 | ||||||||
\(880\) | 4.33315 | 0.146070 | ||||||||
\(881\) | −28.8640 | −0.972452 | −0.486226 | − | 0.873833i | \(-0.661627\pi\) | ||||
−0.486226 | + | 0.873833i | \(0.661627\pi\) | |||||||
\(882\) | −6.78243 | −0.228376 | ||||||||
\(883\) | −43.3633 | −1.45929 | −0.729645 | − | 0.683826i | \(-0.760315\pi\) | ||||
−0.729645 | + | 0.683826i | \(0.760315\pi\) | |||||||
\(884\) | 8.55762 | 0.287824 | ||||||||
\(885\) | −4.95912 | −0.166699 | ||||||||
\(886\) | −29.6406 | −0.995794 | ||||||||
\(887\) | 12.0826 | 0.405695 | 0.202848 | − | 0.979210i | \(-0.434980\pi\) | ||||
0.202848 | + | 0.979210i | \(0.434980\pi\) | |||||||
\(888\) | −6.98507 | −0.234404 | ||||||||
\(889\) | 10.6480 | 0.357122 | ||||||||
\(890\) | −36.5871 | −1.22640 | ||||||||
\(891\) | 17.0003 | 0.569532 | ||||||||
\(892\) | −2.51162 | −0.0840952 | ||||||||
\(893\) | 2.18013 | 0.0729553 | ||||||||
\(894\) | 37.7254 | 1.26172 | ||||||||
\(895\) | 7.21330 | 0.241114 | ||||||||
\(896\) | −3.42965 | −0.114577 | ||||||||
\(897\) | −6.09374 | −0.203464 | ||||||||
\(898\) | 17.6851 | 0.590159 | ||||||||
\(899\) | −41.3770 | −1.38000 | ||||||||
\(900\) | 4.57710 | 0.152570 | ||||||||
\(901\) | 70.3105 | 2.34238 | ||||||||
\(902\) | −14.6485 | −0.487743 | ||||||||
\(903\) | 14.1868 | 0.472108 | ||||||||
\(904\) | −12.5726 | −0.418157 | ||||||||
\(905\) | −23.7590 | −0.789775 | ||||||||
\(906\) | −28.3067 | −0.940426 | ||||||||
\(907\) | −18.5127 | −0.614703 | −0.307351 | − | 0.951596i | \(-0.599443\pi\) | ||||
−0.307351 | + | 0.951596i | \(0.599443\pi\) | |||||||
\(908\) | 22.5312 | 0.747723 | ||||||||
\(909\) | −17.5666 | −0.582646 | ||||||||
\(910\) | −11.5478 | −0.382807 | ||||||||
\(911\) | 20.7011 | 0.685857 | 0.342929 | − | 0.939361i | \(-0.388581\pi\) | ||||
0.342929 | + | 0.939361i | \(0.388581\pi\) | |||||||
\(912\) | 7.10777 | 0.235362 | ||||||||
\(913\) | 9.71323 | 0.321461 | ||||||||
\(914\) | −0.459735 | −0.0152067 | ||||||||
\(915\) | 62.3576 | 2.06148 | ||||||||
\(916\) | −18.3882 | −0.607562 | ||||||||
\(917\) | 2.37383 | 0.0783908 | ||||||||
\(918\) | 24.1443 | 0.796879 | ||||||||
\(919\) | −18.9549 | −0.625265 | −0.312633 | − | 0.949874i | \(-0.601211\pi\) | ||||
−0.312633 | + | 0.949874i | \(0.601211\pi\) | |||||||
\(920\) | −7.06761 | −0.233012 | ||||||||
\(921\) | 21.5997 | 0.711734 | ||||||||
\(922\) | −7.88790 | −0.259774 | ||||||||
\(923\) | 12.5945 | 0.414552 | ||||||||
\(924\) | 10.9066 | 0.358802 | ||||||||
\(925\) | −10.6733 | −0.350936 | ||||||||
\(926\) | 37.5488 | 1.23393 | ||||||||
\(927\) | −11.3509 | −0.372814 | ||||||||
\(928\) | −4.84908 | −0.159179 | ||||||||
\(929\) | −16.5427 | −0.542749 | −0.271375 | − | 0.962474i | \(-0.587478\pi\) | ||||
−0.271375 | + | 0.962474i | \(0.587478\pi\) | |||||||
\(930\) | 51.4387 | 1.68674 | ||||||||
\(931\) | −16.0937 | −0.527449 | ||||||||
\(932\) | −8.43449 | −0.276281 | ||||||||
\(933\) | 7.69450 | 0.251907 | ||||||||
\(934\) | 41.4338 | 1.35576 | ||||||||
\(935\) | −31.5633 | −1.03223 | ||||||||
\(936\) | 1.67311 | 0.0546872 | ||||||||
\(937\) | −18.9277 | −0.618340 | −0.309170 | − | 0.951007i | \(-0.600051\pi\) | ||||
−0.309170 | + | 0.951007i | \(0.600051\pi\) | |||||||
\(938\) | 17.6198 | 0.575308 | ||||||||
\(939\) | 28.4017 | 0.926854 | ||||||||
\(940\) | 1.84901 | 0.0603081 | ||||||||
\(941\) | 33.7968 | 1.10175 | 0.550873 | − | 0.834589i | \(-0.314295\pi\) | ||||
0.550873 | + | 0.834589i | \(0.314295\pi\) | |||||||
\(942\) | 14.4539 | 0.470935 | ||||||||
\(943\) | 23.8926 | 0.778050 | ||||||||
\(944\) | −0.822649 | −0.0267749 | ||||||||
\(945\) | −32.5808 | −1.05985 | ||||||||
\(946\) | −2.97336 | −0.0966724 | ||||||||
\(947\) | 45.4634 | 1.47736 | 0.738681 | − | 0.674055i | \(-0.235449\pi\) | ||||
0.738681 | + | 0.674055i | \(0.235449\pi\) | |||||||
\(948\) | −32.3722 | −1.05140 | ||||||||
\(949\) | −7.20009 | −0.233725 | ||||||||
\(950\) | 10.8608 | 0.352370 | ||||||||
\(951\) | −0.0542492 | −0.00175915 | ||||||||
\(952\) | 24.9821 | 0.809675 | ||||||||
\(953\) | −44.7905 | −1.45091 | −0.725453 | − | 0.688271i | \(-0.758370\pi\) | ||||
−0.725453 | + | 0.688271i | \(0.758370\pi\) | |||||||
\(954\) | 13.7464 | 0.445057 | ||||||||
\(955\) | 35.1138 | 1.13626 | ||||||||
\(956\) | 19.8057 | 0.640561 | ||||||||
\(957\) | 15.4206 | 0.498476 | ||||||||
\(958\) | 27.2202 | 0.879443 | ||||||||
\(959\) | 19.2490 | 0.621582 | ||||||||
\(960\) | 6.02824 | 0.194561 | ||||||||
\(961\) | 41.8115 | 1.34876 | ||||||||
\(962\) | −3.90150 | −0.125789 | ||||||||
\(963\) | 1.12656 | 0.0363028 | ||||||||
\(964\) | −28.3492 | −0.913066 | ||||||||
\(965\) | −13.2284 | −0.425836 | ||||||||
\(966\) | −17.7894 | −0.572363 | ||||||||
\(967\) | 60.4996 | 1.94554 | 0.972768 | − | 0.231782i | \(-0.0744556\pi\) | ||||
0.972768 | + | 0.231782i | \(0.0744556\pi\) | |||||||
\(968\) | 8.71412 | 0.280082 | ||||||||
\(969\) | −51.7741 | −1.66322 | ||||||||
\(970\) | 8.93477 | 0.286878 | ||||||||
\(971\) | −11.0649 | −0.355091 | −0.177545 | − | 0.984113i | \(-0.556816\pi\) | ||||
−0.177545 | + | 0.984113i | \(0.556816\pi\) | |||||||
\(972\) | 13.7068 | 0.439647 | ||||||||
\(973\) | −11.7333 | −0.376153 | ||||||||
\(974\) | −7.85504 | −0.251692 | ||||||||
\(975\) | 7.94199 | 0.254347 | ||||||||
\(976\) | 10.3443 | 0.331111 | ||||||||
\(977\) | −36.3948 | −1.16437 | −0.582186 | − | 0.813056i | \(-0.697802\pi\) | ||||
−0.582186 | + | 0.813056i | \(0.697802\pi\) | |||||||
\(978\) | −51.4381 | −1.64481 | ||||||||
\(979\) | 19.3009 | 0.616861 | ||||||||
\(980\) | −13.6494 | −0.436013 | ||||||||
\(981\) | −1.74563 | −0.0557336 | ||||||||
\(982\) | −28.6606 | −0.914596 | ||||||||
\(983\) | 32.5565 | 1.03839 | 0.519196 | − | 0.854655i | \(-0.326231\pi\) | ||||
0.519196 | + | 0.854655i | \(0.326231\pi\) | |||||||
\(984\) | −20.3789 | −0.649656 | ||||||||
\(985\) | 35.2553 | 1.12333 | ||||||||
\(986\) | 35.3214 | 1.12486 | ||||||||
\(987\) | 4.65401 | 0.148139 | ||||||||
\(988\) | 3.97003 | 0.126303 | ||||||||
\(989\) | 4.84973 | 0.154212 | ||||||||
\(990\) | −6.17096 | −0.196126 | ||||||||
\(991\) | 17.7721 | 0.564550 | 0.282275 | − | 0.959334i | \(-0.408911\pi\) | ||||
0.282275 | + | 0.959334i | \(0.408911\pi\) | |||||||
\(992\) | 8.53296 | 0.270922 | ||||||||
\(993\) | −29.5504 | −0.937754 | ||||||||
\(994\) | 36.7668 | 1.16617 | ||||||||
\(995\) | 51.6416 | 1.63715 | ||||||||
\(996\) | 13.5130 | 0.428174 | ||||||||
\(997\) | −24.1251 | −0.764049 | −0.382024 | − | 0.924152i | \(-0.624773\pi\) | ||||
−0.382024 | + | 0.924152i | \(0.624773\pi\) | |||||||
\(998\) | −35.3208 | −1.11806 | ||||||||
\(999\) | −11.0076 | −0.348264 |
(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 | 8042.2.a.c.1.16 | ✓ | 86 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
8042.2.a.c.1.16 | ✓ | 86 | 1.1 | even | 1 | trivial |