Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [5077,2,Mod(1,5077)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(5077, 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("5077.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 5077 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 5077.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: | \(40.5400491062\) |
Analytic rank: | \(0\) |
Dimension: | \(216\) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.11 | ||
Character | \(\chi\) | \(=\) | 5077.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −2.50572 | −1.77181 | −0.885906 | − | 0.463866i | \(-0.846462\pi\) | ||||
−0.885906 | + | 0.463866i | \(0.846462\pi\) | |||||||
\(3\) | 0.313570 | 0.181040 | 0.0905199 | − | 0.995895i | \(-0.471147\pi\) | ||||
0.0905199 | + | 0.995895i | \(0.471147\pi\) | |||||||
\(4\) | 4.27863 | 2.13931 | ||||||||
\(5\) | 0.450260 | 0.201363 | 0.100681 | − | 0.994919i | \(-0.467898\pi\) | ||||
0.100681 | + | 0.994919i | \(0.467898\pi\) | |||||||
\(6\) | −0.785719 | −0.320768 | ||||||||
\(7\) | −2.26718 | −0.856912 | −0.428456 | − | 0.903563i | \(-0.640942\pi\) | ||||
−0.428456 | + | 0.903563i | \(0.640942\pi\) | |||||||
\(8\) | −5.70960 | −2.01865 | ||||||||
\(9\) | −2.90167 | −0.967225 | ||||||||
\(10\) | −1.12823 | −0.356776 | ||||||||
\(11\) | −2.74396 | −0.827336 | −0.413668 | − | 0.910428i | \(-0.635753\pi\) | ||||
−0.413668 | + | 0.910428i | \(0.635753\pi\) | |||||||
\(12\) | 1.34165 | 0.387301 | ||||||||
\(13\) | −2.41966 | −0.671093 | −0.335546 | − | 0.942024i | \(-0.608921\pi\) | ||||
−0.335546 | + | 0.942024i | \(0.608921\pi\) | |||||||
\(14\) | 5.68090 | 1.51829 | ||||||||
\(15\) | 0.141188 | 0.0364546 | ||||||||
\(16\) | 5.74941 | 1.43735 | ||||||||
\(17\) | −7.94330 | −1.92653 | −0.963267 | − | 0.268547i | \(-0.913457\pi\) | ||||
−0.963267 | + | 0.268547i | \(0.913457\pi\) | |||||||
\(18\) | 7.27078 | 1.71374 | ||||||||
\(19\) | −1.73497 | −0.398030 | −0.199015 | − | 0.979996i | \(-0.563774\pi\) | ||||
−0.199015 | + | 0.979996i | \(0.563774\pi\) | |||||||
\(20\) | 1.92650 | 0.430778 | ||||||||
\(21\) | −0.710918 | −0.155135 | ||||||||
\(22\) | 6.87560 | 1.46588 | ||||||||
\(23\) | −2.77360 | −0.578336 | −0.289168 | − | 0.957278i | \(-0.593379\pi\) | ||||
−0.289168 | + | 0.957278i | \(0.593379\pi\) | |||||||
\(24\) | −1.79036 | −0.365456 | ||||||||
\(25\) | −4.79727 | −0.959453 | ||||||||
\(26\) | 6.06299 | 1.18905 | ||||||||
\(27\) | −1.85059 | −0.356146 | ||||||||
\(28\) | −9.70040 | −1.83320 | ||||||||
\(29\) | −0.443430 | −0.0823428 | −0.0411714 | − | 0.999152i | \(-0.513109\pi\) | ||||
−0.0411714 | + | 0.999152i | \(0.513109\pi\) | |||||||
\(30\) | −0.353778 | −0.0645907 | ||||||||
\(31\) | −5.40312 | −0.970428 | −0.485214 | − | 0.874395i | \(-0.661258\pi\) | ||||
−0.485214 | + | 0.874395i | \(0.661258\pi\) | |||||||
\(32\) | −2.98719 | −0.528066 | ||||||||
\(33\) | −0.860425 | −0.149781 | ||||||||
\(34\) | 19.9037 | 3.41345 | ||||||||
\(35\) | −1.02082 | −0.172550 | ||||||||
\(36\) | −12.4152 | −2.06920 | ||||||||
\(37\) | −6.10114 | −1.00302 | −0.501511 | − | 0.865151i | \(-0.667222\pi\) | ||||
−0.501511 | + | 0.865151i | \(0.667222\pi\) | |||||||
\(38\) | 4.34736 | 0.705234 | ||||||||
\(39\) | −0.758733 | −0.121494 | ||||||||
\(40\) | −2.57081 | −0.406481 | ||||||||
\(41\) | 0.142888 | 0.0223154 | 0.0111577 | − | 0.999938i | \(-0.496448\pi\) | ||||
0.0111577 | + | 0.999938i | \(0.496448\pi\) | |||||||
\(42\) | 1.78136 | 0.274870 | ||||||||
\(43\) | 0.303010 | 0.0462085 | 0.0231043 | − | 0.999733i | \(-0.492645\pi\) | ||||
0.0231043 | + | 0.999733i | \(0.492645\pi\) | |||||||
\(44\) | −11.7404 | −1.76993 | ||||||||
\(45\) | −1.30651 | −0.194763 | ||||||||
\(46\) | 6.94987 | 1.02470 | ||||||||
\(47\) | 5.28366 | 0.770702 | 0.385351 | − | 0.922770i | \(-0.374080\pi\) | ||||
0.385351 | + | 0.922770i | \(0.374080\pi\) | |||||||
\(48\) | 1.80284 | 0.260218 | ||||||||
\(49\) | −1.85992 | −0.265702 | ||||||||
\(50\) | 12.0206 | 1.69997 | ||||||||
\(51\) | −2.49078 | −0.348779 | ||||||||
\(52\) | −10.3528 | −1.43568 | ||||||||
\(53\) | 6.89349 | 0.946894 | 0.473447 | − | 0.880822i | \(-0.343010\pi\) | ||||
0.473447 | + | 0.880822i | \(0.343010\pi\) | |||||||
\(54\) | 4.63705 | 0.631023 | ||||||||
\(55\) | −1.23550 | −0.166595 | ||||||||
\(56\) | 12.9447 | 1.72980 | ||||||||
\(57\) | −0.544036 | −0.0720593 | ||||||||
\(58\) | 1.11111 | 0.145896 | ||||||||
\(59\) | −10.4058 | −1.35472 | −0.677360 | − | 0.735652i | \(-0.736876\pi\) | ||||
−0.677360 | + | 0.735652i | \(0.736876\pi\) | |||||||
\(60\) | 0.604092 | 0.0779879 | ||||||||
\(61\) | −7.98425 | −1.02228 | −0.511139 | − | 0.859498i | \(-0.670776\pi\) | ||||
−0.511139 | + | 0.859498i | \(0.670776\pi\) | |||||||
\(62\) | 13.5387 | 1.71942 | ||||||||
\(63\) | 6.57860 | 0.828826 | ||||||||
\(64\) | −4.01375 | −0.501719 | ||||||||
\(65\) | −1.08948 | −0.135133 | ||||||||
\(66\) | 2.15598 | 0.265383 | ||||||||
\(67\) | 2.58071 | 0.315284 | 0.157642 | − | 0.987496i | \(-0.449611\pi\) | ||||
0.157642 | + | 0.987496i | \(0.449611\pi\) | |||||||
\(68\) | −33.9864 | −4.12146 | ||||||||
\(69\) | −0.869719 | −0.104702 | ||||||||
\(70\) | 2.55789 | 0.305726 | ||||||||
\(71\) | −10.4845 | −1.24428 | −0.622140 | − | 0.782906i | \(-0.713737\pi\) | ||||
−0.622140 | + | 0.782906i | \(0.713737\pi\) | |||||||
\(72\) | 16.5674 | 1.95249 | ||||||||
\(73\) | −1.45158 | −0.169894 | −0.0849472 | − | 0.996385i | \(-0.527072\pi\) | ||||
−0.0849472 | + | 0.996385i | \(0.527072\pi\) | |||||||
\(74\) | 15.2878 | 1.77717 | ||||||||
\(75\) | −1.50428 | −0.173699 | ||||||||
\(76\) | −7.42331 | −0.851512 | ||||||||
\(77\) | 6.22105 | 0.708954 | ||||||||
\(78\) | 1.90117 | 0.215265 | ||||||||
\(79\) | −11.3006 | −1.27142 | −0.635711 | − | 0.771928i | \(-0.719293\pi\) | ||||
−0.635711 | + | 0.771928i | \(0.719293\pi\) | |||||||
\(80\) | 2.58873 | 0.289429 | ||||||||
\(81\) | 8.12473 | 0.902748 | ||||||||
\(82\) | −0.358037 | −0.0395386 | ||||||||
\(83\) | −3.05458 | −0.335283 | −0.167642 | − | 0.985848i | \(-0.553615\pi\) | ||||
−0.167642 | + | 0.985848i | \(0.553615\pi\) | |||||||
\(84\) | −3.04176 | −0.331883 | ||||||||
\(85\) | −3.57655 | −0.387932 | ||||||||
\(86\) | −0.759257 | −0.0818728 | ||||||||
\(87\) | −0.139046 | −0.0149073 | ||||||||
\(88\) | 15.6669 | 1.67010 | ||||||||
\(89\) | 1.92687 | 0.204248 | 0.102124 | − | 0.994772i | \(-0.467436\pi\) | ||||
0.102124 | + | 0.994772i | \(0.467436\pi\) | |||||||
\(90\) | 3.27374 | 0.345083 | ||||||||
\(91\) | 5.48579 | 0.575067 | ||||||||
\(92\) | −11.8672 | −1.23724 | ||||||||
\(93\) | −1.69426 | −0.175686 | ||||||||
\(94\) | −13.2394 | −1.36554 | ||||||||
\(95\) | −0.781190 | −0.0801484 | ||||||||
\(96\) | −0.936694 | −0.0956010 | ||||||||
\(97\) | −14.5873 | −1.48112 | −0.740559 | − | 0.671991i | \(-0.765439\pi\) | ||||
−0.740559 | + | 0.671991i | \(0.765439\pi\) | |||||||
\(98\) | 4.66043 | 0.470774 | ||||||||
\(99\) | 7.96209 | 0.800220 | ||||||||
\(100\) | −20.5257 | −2.05257 | ||||||||
\(101\) | 11.6875 | 1.16295 | 0.581474 | − | 0.813565i | \(-0.302476\pi\) | ||||
0.581474 | + | 0.813565i | \(0.302476\pi\) | |||||||
\(102\) | 6.24120 | 0.617971 | ||||||||
\(103\) | 8.80260 | 0.867346 | 0.433673 | − | 0.901070i | \(-0.357217\pi\) | ||||
0.433673 | + | 0.901070i | \(0.357217\pi\) | |||||||
\(104\) | 13.8153 | 1.35470 | ||||||||
\(105\) | −0.320098 | −0.0312384 | ||||||||
\(106\) | −17.2732 | −1.67772 | ||||||||
\(107\) | 2.22688 | 0.215281 | 0.107640 | − | 0.994190i | \(-0.465670\pi\) | ||||
0.107640 | + | 0.994190i | \(0.465670\pi\) | |||||||
\(108\) | −7.91798 | −0.761908 | ||||||||
\(109\) | 17.0924 | 1.63715 | 0.818577 | − | 0.574397i | \(-0.194763\pi\) | ||||
0.818577 | + | 0.574397i | \(0.194763\pi\) | |||||||
\(110\) | 3.09581 | 0.295174 | ||||||||
\(111\) | −1.91314 | −0.181587 | ||||||||
\(112\) | −13.0349 | −1.23168 | ||||||||
\(113\) | 20.3906 | 1.91819 | 0.959094 | − | 0.283086i | \(-0.0913583\pi\) | ||||
0.959094 | + | 0.283086i | \(0.0913583\pi\) | |||||||
\(114\) | 1.36320 | 0.127675 | ||||||||
\(115\) | −1.24884 | −0.116455 | ||||||||
\(116\) | −1.89727 | −0.176157 | ||||||||
\(117\) | 7.02106 | 0.649097 | ||||||||
\(118\) | 26.0740 | 2.40031 | ||||||||
\(119\) | 18.0089 | 1.65087 | ||||||||
\(120\) | −0.806129 | −0.0735892 | ||||||||
\(121\) | −3.47066 | −0.315515 | ||||||||
\(122\) | 20.0063 | 1.81128 | ||||||||
\(123\) | 0.0448054 | 0.00403997 | ||||||||
\(124\) | −23.1179 | −2.07605 | ||||||||
\(125\) | −4.41132 | −0.394561 | ||||||||
\(126\) | −16.4841 | −1.46852 | ||||||||
\(127\) | 11.4737 | 1.01813 | 0.509064 | − | 0.860729i | \(-0.329992\pi\) | ||||
0.509064 | + | 0.860729i | \(0.329992\pi\) | |||||||
\(128\) | 16.0317 | 1.41702 | ||||||||
\(129\) | 0.0950148 | 0.00836558 | ||||||||
\(130\) | 2.72992 | 0.239430 | ||||||||
\(131\) | −2.77884 | −0.242789 | −0.121394 | − | 0.992604i | \(-0.538737\pi\) | ||||
−0.121394 | + | 0.992604i | \(0.538737\pi\) | |||||||
\(132\) | −3.68144 | −0.320428 | ||||||||
\(133\) | 3.93349 | 0.341077 | ||||||||
\(134\) | −6.46655 | −0.558624 | ||||||||
\(135\) | −0.833247 | −0.0717145 | ||||||||
\(136\) | 45.3531 | 3.88900 | ||||||||
\(137\) | 13.5591 | 1.15843 | 0.579214 | − | 0.815175i | \(-0.303359\pi\) | ||||
0.579214 | + | 0.815175i | \(0.303359\pi\) | |||||||
\(138\) | 2.17927 | 0.185512 | ||||||||
\(139\) | −0.298093 | −0.0252839 | −0.0126419 | − | 0.999920i | \(-0.504024\pi\) | ||||
−0.0126419 | + | 0.999920i | \(0.504024\pi\) | |||||||
\(140\) | −4.36771 | −0.369139 | ||||||||
\(141\) | 1.65680 | 0.139528 | ||||||||
\(142\) | 26.2712 | 2.20463 | ||||||||
\(143\) | 6.63946 | 0.555219 | ||||||||
\(144\) | −16.6829 | −1.39024 | ||||||||
\(145\) | −0.199659 | −0.0165808 | ||||||||
\(146\) | 3.63725 | 0.301021 | ||||||||
\(147\) | −0.583214 | −0.0481027 | ||||||||
\(148\) | −26.1045 | −2.14578 | ||||||||
\(149\) | −10.8572 | −0.889460 | −0.444730 | − | 0.895665i | \(-0.646700\pi\) | ||||
−0.444730 | + | 0.895665i | \(0.646700\pi\) | |||||||
\(150\) | 3.76930 | 0.307762 | ||||||||
\(151\) | 4.99615 | 0.406581 | 0.203290 | − | 0.979119i | \(-0.434836\pi\) | ||||
0.203290 | + | 0.979119i | \(0.434836\pi\) | |||||||
\(152\) | 9.90601 | 0.803484 | ||||||||
\(153\) | 23.0489 | 1.86339 | ||||||||
\(154\) | −15.5882 | −1.25613 | ||||||||
\(155\) | −2.43281 | −0.195408 | ||||||||
\(156\) | −3.24634 | −0.259915 | ||||||||
\(157\) | −10.1695 | −0.811616 | −0.405808 | − | 0.913958i | \(-0.633010\pi\) | ||||
−0.405808 | + | 0.913958i | \(0.633010\pi\) | |||||||
\(158\) | 28.3162 | 2.25272 | ||||||||
\(159\) | 2.16159 | 0.171425 | ||||||||
\(160\) | −1.34502 | −0.106333 | ||||||||
\(161\) | 6.28825 | 0.495583 | ||||||||
\(162\) | −20.3583 | −1.59950 | ||||||||
\(163\) | 0.976437 | 0.0764804 | 0.0382402 | − | 0.999269i | \(-0.487825\pi\) | ||||
0.0382402 | + | 0.999269i | \(0.487825\pi\) | |||||||
\(164\) | 0.611365 | 0.0477396 | ||||||||
\(165\) | −0.387415 | −0.0301602 | ||||||||
\(166\) | 7.65391 | 0.594059 | ||||||||
\(167\) | 7.15683 | 0.553812 | 0.276906 | − | 0.960897i | \(-0.410691\pi\) | ||||
0.276906 | + | 0.960897i | \(0.410691\pi\) | |||||||
\(168\) | 4.05906 | 0.313163 | ||||||||
\(169\) | −7.14525 | −0.549635 | ||||||||
\(170\) | 8.96184 | 0.687342 | ||||||||
\(171\) | 5.03433 | 0.384985 | ||||||||
\(172\) | 1.29647 | 0.0988546 | ||||||||
\(173\) | −12.6323 | −0.960413 | −0.480206 | − | 0.877156i | \(-0.659438\pi\) | ||||
−0.480206 | + | 0.877156i | \(0.659438\pi\) | |||||||
\(174\) | 0.348411 | 0.0264130 | ||||||||
\(175\) | 10.8762 | 0.822167 | ||||||||
\(176\) | −15.7762 | −1.18917 | ||||||||
\(177\) | −3.26295 | −0.245258 | ||||||||
\(178\) | −4.82820 | −0.361889 | ||||||||
\(179\) | −7.05421 | −0.527257 | −0.263628 | − | 0.964624i | \(-0.584919\pi\) | ||||
−0.263628 | + | 0.964624i | \(0.584919\pi\) | |||||||
\(180\) | −5.59007 | −0.416659 | ||||||||
\(181\) | 0.615411 | 0.0457431 | 0.0228716 | − | 0.999738i | \(-0.492719\pi\) | ||||
0.0228716 | + | 0.999738i | \(0.492719\pi\) | |||||||
\(182\) | −13.7459 | −1.01891 | ||||||||
\(183\) | −2.50362 | −0.185073 | ||||||||
\(184\) | 15.8362 | 1.16746 | ||||||||
\(185\) | −2.74710 | −0.201971 | ||||||||
\(186\) | 4.24533 | 0.311283 | ||||||||
\(187\) | 21.7961 | 1.59389 | ||||||||
\(188\) | 22.6068 | 1.64877 | ||||||||
\(189\) | 4.19561 | 0.305186 | ||||||||
\(190\) | 1.95744 | 0.142008 | ||||||||
\(191\) | −17.5576 | −1.27043 | −0.635213 | − | 0.772337i | \(-0.719088\pi\) | ||||
−0.635213 | + | 0.772337i | \(0.719088\pi\) | |||||||
\(192\) | −1.25859 | −0.0908310 | ||||||||
\(193\) | −13.7120 | −0.987014 | −0.493507 | − | 0.869742i | \(-0.664285\pi\) | ||||
−0.493507 | + | 0.869742i | \(0.664285\pi\) | |||||||
\(194\) | 36.5517 | 2.62426 | ||||||||
\(195\) | −0.341627 | −0.0244644 | ||||||||
\(196\) | −7.95789 | −0.568421 | ||||||||
\(197\) | 14.3532 | 1.02262 | 0.511311 | − | 0.859396i | \(-0.329160\pi\) | ||||
0.511311 | + | 0.859396i | \(0.329160\pi\) | |||||||
\(198\) | −19.9508 | −1.41784 | ||||||||
\(199\) | −1.32532 | −0.0939497 | −0.0469749 | − | 0.998896i | \(-0.514958\pi\) | ||||
−0.0469749 | + | 0.998896i | \(0.514958\pi\) | |||||||
\(200\) | 27.3905 | 1.93680 | ||||||||
\(201\) | 0.809235 | 0.0570790 | ||||||||
\(202\) | −29.2855 | −2.06052 | ||||||||
\(203\) | 1.00533 | 0.0705605 | ||||||||
\(204\) | −10.6571 | −0.746148 | ||||||||
\(205\) | 0.0643368 | 0.00449348 | ||||||||
\(206\) | −22.0568 | −1.53677 | ||||||||
\(207\) | 8.04809 | 0.559381 | ||||||||
\(208\) | −13.9116 | −0.964596 | ||||||||
\(209\) | 4.76070 | 0.329305 | ||||||||
\(210\) | 0.802077 | 0.0553486 | ||||||||
\(211\) | −4.74629 | −0.326748 | −0.163374 | − | 0.986564i | \(-0.552238\pi\) | ||||
−0.163374 | + | 0.986564i | \(0.552238\pi\) | |||||||
\(212\) | 29.4947 | 2.02570 | ||||||||
\(213\) | −3.28762 | −0.225264 | ||||||||
\(214\) | −5.57994 | −0.381437 | ||||||||
\(215\) | 0.136433 | 0.00930467 | ||||||||
\(216\) | 10.5661 | 0.718934 | ||||||||
\(217\) | 12.2498 | 0.831572 | ||||||||
\(218\) | −42.8287 | −2.90073 | ||||||||
\(219\) | −0.455171 | −0.0307576 | ||||||||
\(220\) | −5.28624 | −0.356398 | ||||||||
\(221\) | 19.2201 | 1.29288 | ||||||||
\(222\) | 4.79378 | 0.321738 | ||||||||
\(223\) | −8.27587 | −0.554193 | −0.277097 | − | 0.960842i | \(-0.589372\pi\) | ||||
−0.277097 | + | 0.960842i | \(0.589372\pi\) | |||||||
\(224\) | 6.77249 | 0.452506 | ||||||||
\(225\) | 13.9201 | 0.928007 | ||||||||
\(226\) | −51.0932 | −3.39867 | ||||||||
\(227\) | −16.3732 | −1.08673 | −0.543363 | − | 0.839498i | \(-0.682849\pi\) | ||||
−0.543363 | + | 0.839498i | \(0.682849\pi\) | |||||||
\(228\) | −2.32773 | −0.154158 | ||||||||
\(229\) | 11.2075 | 0.740616 | 0.370308 | − | 0.928909i | \(-0.379252\pi\) | ||||
0.370308 | + | 0.928909i | \(0.379252\pi\) | |||||||
\(230\) | 3.12925 | 0.206337 | ||||||||
\(231\) | 1.95073 | 0.128349 | ||||||||
\(232\) | 2.53181 | 0.166221 | ||||||||
\(233\) | −16.1590 | −1.05861 | −0.529307 | − | 0.848431i | \(-0.677548\pi\) | ||||
−0.529307 | + | 0.848431i | \(0.677548\pi\) | |||||||
\(234\) | −17.5928 | −1.15008 | ||||||||
\(235\) | 2.37903 | 0.155190 | ||||||||
\(236\) | −44.5226 | −2.89817 | ||||||||
\(237\) | −3.54354 | −0.230178 | ||||||||
\(238\) | −45.1251 | −2.92503 | ||||||||
\(239\) | −5.16096 | −0.333835 | −0.166917 | − | 0.985971i | \(-0.553381\pi\) | ||||
−0.166917 | + | 0.985971i | \(0.553381\pi\) | |||||||
\(240\) | 0.811749 | 0.0523981 | ||||||||
\(241\) | −13.7237 | −0.884024 | −0.442012 | − | 0.897009i | \(-0.645735\pi\) | ||||
−0.442012 | + | 0.897009i | \(0.645735\pi\) | |||||||
\(242\) | 8.69651 | 0.559033 | ||||||||
\(243\) | 8.09944 | 0.519579 | ||||||||
\(244\) | −34.1616 | −2.18698 | ||||||||
\(245\) | −0.837447 | −0.0535025 | ||||||||
\(246\) | −0.112270 | −0.00715806 | ||||||||
\(247\) | 4.19804 | 0.267115 | ||||||||
\(248\) | 30.8497 | 1.95896 | ||||||||
\(249\) | −0.957824 | −0.0606996 | ||||||||
\(250\) | 11.0535 | 0.699087 | ||||||||
\(251\) | 7.40750 | 0.467557 | 0.233779 | − | 0.972290i | \(-0.424891\pi\) | ||||
0.233779 | + | 0.972290i | \(0.424891\pi\) | |||||||
\(252\) | 28.1474 | 1.77312 | ||||||||
\(253\) | 7.61067 | 0.478479 | ||||||||
\(254\) | −28.7499 | −1.80393 | ||||||||
\(255\) | −1.12150 | −0.0702311 | ||||||||
\(256\) | −32.1435 | −2.00897 | ||||||||
\(257\) | 28.2807 | 1.76410 | 0.882049 | − | 0.471157i | \(-0.156163\pi\) | ||||
0.882049 | + | 0.471157i | \(0.156163\pi\) | |||||||
\(258\) | −0.238080 | −0.0148222 | ||||||||
\(259\) | 13.8324 | 0.859501 | ||||||||
\(260\) | −4.66147 | −0.289092 | ||||||||
\(261\) | 1.28669 | 0.0796440 | ||||||||
\(262\) | 6.96300 | 0.430176 | ||||||||
\(263\) | −20.4513 | −1.26108 | −0.630539 | − | 0.776157i | \(-0.717166\pi\) | ||||
−0.630539 | + | 0.776157i | \(0.717166\pi\) | |||||||
\(264\) | 4.91269 | 0.302355 | ||||||||
\(265\) | 3.10387 | 0.190669 | ||||||||
\(266\) | −9.85622 | −0.604324 | ||||||||
\(267\) | 0.604210 | 0.0369770 | ||||||||
\(268\) | 11.0419 | 0.674493 | ||||||||
\(269\) | 13.4126 | 0.817780 | 0.408890 | − | 0.912584i | \(-0.365916\pi\) | ||||
0.408890 | + | 0.912584i | \(0.365916\pi\) | |||||||
\(270\) | 2.08788 | 0.127064 | ||||||||
\(271\) | −10.8581 | −0.659585 | −0.329793 | − | 0.944053i | \(-0.606979\pi\) | ||||
−0.329793 | + | 0.944053i | \(0.606979\pi\) | |||||||
\(272\) | −45.6693 | −2.76911 | ||||||||
\(273\) | 1.72018 | 0.104110 | ||||||||
\(274\) | −33.9752 | −2.05252 | ||||||||
\(275\) | 13.1635 | 0.793790 | ||||||||
\(276\) | −3.72121 | −0.223990 | ||||||||
\(277\) | 4.47678 | 0.268983 | 0.134492 | − | 0.990915i | \(-0.457060\pi\) | ||||
0.134492 | + | 0.990915i | \(0.457060\pi\) | |||||||
\(278\) | 0.746937 | 0.0447983 | ||||||||
\(279\) | 15.6781 | 0.938622 | ||||||||
\(280\) | 5.82848 | 0.348318 | ||||||||
\(281\) | −25.0148 | −1.49226 | −0.746130 | − | 0.665800i | \(-0.768090\pi\) | ||||
−0.746130 | + | 0.665800i | \(0.768090\pi\) | |||||||
\(282\) | −4.15147 | −0.247217 | ||||||||
\(283\) | −11.0347 | −0.655946 | −0.327973 | − | 0.944687i | \(-0.606365\pi\) | ||||
−0.327973 | + | 0.944687i | \(0.606365\pi\) | |||||||
\(284\) | −44.8593 | −2.66191 | ||||||||
\(285\) | −0.244958 | −0.0145100 | ||||||||
\(286\) | −16.6366 | −0.983744 | ||||||||
\(287\) | −0.323952 | −0.0191223 | ||||||||
\(288\) | 8.66786 | 0.510759 | ||||||||
\(289\) | 46.0960 | 2.71153 | ||||||||
\(290\) | 0.500289 | 0.0293780 | ||||||||
\(291\) | −4.57415 | −0.268141 | ||||||||
\(292\) | −6.21076 | −0.363457 | ||||||||
\(293\) | 7.78307 | 0.454692 | 0.227346 | − | 0.973814i | \(-0.426995\pi\) | ||||
0.227346 | + | 0.973814i | \(0.426995\pi\) | |||||||
\(294\) | 1.46137 | 0.0852289 | ||||||||
\(295\) | −4.68532 | −0.272790 | ||||||||
\(296\) | 34.8351 | 2.02475 | ||||||||
\(297\) | 5.07795 | 0.294652 | ||||||||
\(298\) | 27.2052 | 1.57595 | ||||||||
\(299\) | 6.71118 | 0.388117 | ||||||||
\(300\) | −6.43625 | −0.371597 | ||||||||
\(301\) | −0.686976 | −0.0395966 | ||||||||
\(302\) | −12.5189 | −0.720384 | ||||||||
\(303\) | 3.66484 | 0.210540 | ||||||||
\(304\) | −9.97507 | −0.572110 | ||||||||
\(305\) | −3.59499 | −0.205849 | ||||||||
\(306\) | −57.7540 | −3.30158 | ||||||||
\(307\) | −25.9073 | −1.47861 | −0.739304 | − | 0.673372i | \(-0.764845\pi\) | ||||
−0.739304 | + | 0.673372i | \(0.764845\pi\) | |||||||
\(308\) | 26.6176 | 1.51668 | ||||||||
\(309\) | 2.76023 | 0.157024 | ||||||||
\(310\) | 6.09594 | 0.346226 | ||||||||
\(311\) | −16.6273 | −0.942846 | −0.471423 | − | 0.881907i | \(-0.656260\pi\) | ||||
−0.471423 | + | 0.881907i | \(0.656260\pi\) | |||||||
\(312\) | 4.33206 | 0.245255 | ||||||||
\(313\) | −12.3582 | −0.698524 | −0.349262 | − | 0.937025i | \(-0.613568\pi\) | ||||
−0.349262 | + | 0.937025i | \(0.613568\pi\) | |||||||
\(314\) | 25.4820 | 1.43803 | ||||||||
\(315\) | 2.96209 | 0.166895 | ||||||||
\(316\) | −48.3512 | −2.71997 | ||||||||
\(317\) | −2.83807 | −0.159402 | −0.0797009 | − | 0.996819i | \(-0.525397\pi\) | ||||
−0.0797009 | + | 0.996819i | \(0.525397\pi\) | |||||||
\(318\) | −5.41634 | −0.303733 | ||||||||
\(319\) | 1.21675 | 0.0681252 | ||||||||
\(320\) | −1.80723 | −0.101027 | ||||||||
\(321\) | 0.698284 | 0.0389744 | ||||||||
\(322\) | −15.7566 | −0.878080 | ||||||||
\(323\) | 13.7814 | 0.766819 | ||||||||
\(324\) | 34.7627 | 1.93126 | ||||||||
\(325\) | 11.6077 | 0.643882 | ||||||||
\(326\) | −2.44668 | −0.135509 | ||||||||
\(327\) | 5.35966 | 0.296390 | ||||||||
\(328\) | −0.815834 | −0.0450469 | ||||||||
\(329\) | −11.9790 | −0.660423 | ||||||||
\(330\) | 0.970754 | 0.0534382 | ||||||||
\(331\) | −14.7257 | −0.809396 | −0.404698 | − | 0.914450i | \(-0.632623\pi\) | ||||
−0.404698 | + | 0.914450i | \(0.632623\pi\) | |||||||
\(332\) | −13.0694 | −0.717277 | ||||||||
\(333\) | 17.7035 | 0.970147 | ||||||||
\(334\) | −17.9330 | −0.981250 | ||||||||
\(335\) | 1.16199 | 0.0634865 | ||||||||
\(336\) | −4.08736 | −0.222984 | ||||||||
\(337\) | −31.7608 | −1.73012 | −0.865060 | − | 0.501669i | \(-0.832720\pi\) | ||||
−0.865060 | + | 0.501669i | \(0.832720\pi\) | |||||||
\(338\) | 17.9040 | 0.973849 | ||||||||
\(339\) | 6.39389 | 0.347268 | ||||||||
\(340\) | −15.3027 | −0.829908 | ||||||||
\(341\) | 14.8260 | 0.802871 | ||||||||
\(342\) | −12.6146 | −0.682120 | ||||||||
\(343\) | 20.0870 | 1.08460 | ||||||||
\(344\) | −1.73007 | −0.0932789 | ||||||||
\(345\) | −0.391600 | −0.0210830 | ||||||||
\(346\) | 31.6529 | 1.70167 | ||||||||
\(347\) | −15.6529 | −0.840292 | −0.420146 | − | 0.907457i | \(-0.638021\pi\) | ||||
−0.420146 | + | 0.907457i | \(0.638021\pi\) | |||||||
\(348\) | −0.594927 | −0.0318914 | ||||||||
\(349\) | −13.1459 | −0.703685 | −0.351842 | − | 0.936059i | \(-0.614445\pi\) | ||||
−0.351842 | + | 0.936059i | \(0.614445\pi\) | |||||||
\(350\) | −27.2528 | −1.45672 | ||||||||
\(351\) | 4.47779 | 0.239007 | ||||||||
\(352\) | 8.19675 | 0.436888 | ||||||||
\(353\) | 28.0385 | 1.49234 | 0.746168 | − | 0.665757i | \(-0.231891\pi\) | ||||
0.746168 | + | 0.665757i | \(0.231891\pi\) | |||||||
\(354\) | 8.17603 | 0.434551 | ||||||||
\(355\) | −4.72075 | −0.250552 | ||||||||
\(356\) | 8.24438 | 0.436951 | ||||||||
\(357\) | 5.64704 | 0.298873 | ||||||||
\(358\) | 17.6759 | 0.934199 | ||||||||
\(359\) | 4.10661 | 0.216739 | 0.108369 | − | 0.994111i | \(-0.465437\pi\) | ||||
0.108369 | + | 0.994111i | \(0.465437\pi\) | |||||||
\(360\) | 7.45965 | 0.393158 | ||||||||
\(361\) | −15.9899 | −0.841572 | ||||||||
\(362\) | −1.54205 | −0.0810481 | ||||||||
\(363\) | −1.08830 | −0.0571207 | ||||||||
\(364\) | 23.4717 | 1.23025 | ||||||||
\(365\) | −0.653588 | −0.0342104 | ||||||||
\(366\) | 6.27337 | 0.327915 | ||||||||
\(367\) | 23.1623 | 1.20906 | 0.604532 | − | 0.796581i | \(-0.293360\pi\) | ||||
0.604532 | + | 0.796581i | \(0.293360\pi\) | |||||||
\(368\) | −15.9466 | −0.831273 | ||||||||
\(369\) | −0.414614 | −0.0215840 | ||||||||
\(370\) | 6.88347 | 0.357855 | ||||||||
\(371\) | −15.6288 | −0.811404 | ||||||||
\(372\) | −7.24909 | −0.375848 | ||||||||
\(373\) | −33.7730 | −1.74870 | −0.874350 | − | 0.485295i | \(-0.838712\pi\) | ||||
−0.874350 | + | 0.485295i | \(0.838712\pi\) | |||||||
\(374\) | −54.6150 | −2.82407 | ||||||||
\(375\) | −1.38326 | −0.0714312 | ||||||||
\(376\) | −30.1676 | −1.55578 | ||||||||
\(377\) | 1.07295 | 0.0552596 | ||||||||
\(378\) | −10.5130 | −0.540731 | ||||||||
\(379\) | −31.0955 | −1.59727 | −0.798634 | − | 0.601816i | \(-0.794444\pi\) | ||||
−0.798634 | + | 0.601816i | \(0.794444\pi\) | |||||||
\(380\) | −3.34242 | −0.171463 | ||||||||
\(381\) | 3.59782 | 0.184322 | ||||||||
\(382\) | 43.9945 | 2.25096 | ||||||||
\(383\) | 29.9493 | 1.53034 | 0.765170 | − | 0.643828i | \(-0.222655\pi\) | ||||
0.765170 | + | 0.643828i | \(0.222655\pi\) | |||||||
\(384\) | 5.02707 | 0.256536 | ||||||||
\(385\) | 2.80109 | 0.142757 | ||||||||
\(386\) | 34.3585 | 1.74880 | ||||||||
\(387\) | −0.879235 | −0.0446940 | ||||||||
\(388\) | −62.4137 | −3.16858 | ||||||||
\(389\) | −33.3230 | −1.68954 | −0.844771 | − | 0.535128i | \(-0.820264\pi\) | ||||
−0.844771 | + | 0.535128i | \(0.820264\pi\) | |||||||
\(390\) | 0.856022 | 0.0433464 | ||||||||
\(391\) | 22.0316 | 1.11418 | ||||||||
\(392\) | 10.6194 | 0.536360 | ||||||||
\(393\) | −0.871362 | −0.0439544 | ||||||||
\(394\) | −35.9650 | −1.81189 | ||||||||
\(395\) | −5.08823 | −0.256017 | ||||||||
\(396\) | 34.0668 | 1.71192 | ||||||||
\(397\) | 6.52875 | 0.327668 | 0.163834 | − | 0.986488i | \(-0.447614\pi\) | ||||
0.163834 | + | 0.986488i | \(0.447614\pi\) | |||||||
\(398\) | 3.32089 | 0.166461 | ||||||||
\(399\) | 1.23342 | 0.0617485 | ||||||||
\(400\) | −27.5814 | −1.37907 | ||||||||
\(401\) | −30.5305 | −1.52462 | −0.762309 | − | 0.647213i | \(-0.775934\pi\) | ||||
−0.762309 | + | 0.647213i | \(0.775934\pi\) | |||||||
\(402\) | −2.02772 | −0.101133 | ||||||||
\(403\) | 13.0737 | 0.651247 | ||||||||
\(404\) | 50.0064 | 2.48791 | ||||||||
\(405\) | 3.65825 | 0.181780 | ||||||||
\(406\) | −2.51908 | −0.125020 | ||||||||
\(407\) | 16.7413 | 0.829836 | ||||||||
\(408\) | 14.2214 | 0.704063 | ||||||||
\(409\) | 6.27097 | 0.310080 | 0.155040 | − | 0.987908i | \(-0.450449\pi\) | ||||
0.155040 | + | 0.987908i | \(0.450449\pi\) | |||||||
\(410\) | −0.161210 | −0.00796159 | ||||||||
\(411\) | 4.25172 | 0.209722 | ||||||||
\(412\) | 37.6631 | 1.85553 | ||||||||
\(413\) | 23.5918 | 1.16088 | ||||||||
\(414\) | −20.1663 | −0.991118 | ||||||||
\(415\) | −1.37536 | −0.0675135 | ||||||||
\(416\) | 7.22799 | 0.354381 | ||||||||
\(417\) | −0.0934730 | −0.00457739 | ||||||||
\(418\) | −11.9290 | −0.583466 | ||||||||
\(419\) | 28.7723 | 1.40562 | 0.702810 | − | 0.711378i | \(-0.251929\pi\) | ||||
0.702810 | + | 0.711378i | \(0.251929\pi\) | |||||||
\(420\) | −1.36958 | −0.0668288 | ||||||||
\(421\) | −4.48112 | −0.218396 | −0.109198 | − | 0.994020i | \(-0.534828\pi\) | ||||
−0.109198 | + | 0.994020i | \(0.534828\pi\) | |||||||
\(422\) | 11.8929 | 0.578936 | ||||||||
\(423\) | −15.3315 | −0.745442 | ||||||||
\(424\) | −39.3591 | −1.91145 | ||||||||
\(425\) | 38.1061 | 1.84842 | ||||||||
\(426\) | 8.23786 | 0.399126 | ||||||||
\(427\) | 18.1017 | 0.876003 | ||||||||
\(428\) | 9.52801 | 0.460554 | ||||||||
\(429\) | 2.08193 | 0.100517 | ||||||||
\(430\) | −0.341864 | −0.0164861 | ||||||||
\(431\) | −9.12226 | −0.439404 | −0.219702 | − | 0.975567i | \(-0.570509\pi\) | ||||
−0.219702 | + | 0.975567i | \(0.570509\pi\) | |||||||
\(432\) | −10.6398 | −0.511907 | ||||||||
\(433\) | −11.2021 | −0.538340 | −0.269170 | − | 0.963093i | \(-0.586749\pi\) | ||||
−0.269170 | + | 0.963093i | \(0.586749\pi\) | |||||||
\(434\) | −30.6946 | −1.47339 | ||||||||
\(435\) | −0.0626070 | −0.00300178 | ||||||||
\(436\) | 73.1320 | 3.50239 | ||||||||
\(437\) | 4.81213 | 0.230195 | ||||||||
\(438\) | 1.14053 | 0.0544967 | ||||||||
\(439\) | −16.1141 | −0.769085 | −0.384542 | − | 0.923107i | \(-0.625641\pi\) | ||||
−0.384542 | + | 0.923107i | \(0.625641\pi\) | |||||||
\(440\) | 7.05421 | 0.336296 | ||||||||
\(441\) | 5.39687 | 0.256994 | ||||||||
\(442\) | −48.1601 | −2.29074 | ||||||||
\(443\) | 18.2568 | 0.867407 | 0.433704 | − | 0.901056i | \(-0.357206\pi\) | ||||
0.433704 | + | 0.901056i | \(0.357206\pi\) | |||||||
\(444\) | −8.18560 | −0.388471 | ||||||||
\(445\) | 0.867595 | 0.0411280 | ||||||||
\(446\) | 20.7370 | 0.981926 | ||||||||
\(447\) | −3.40451 | −0.161028 | ||||||||
\(448\) | 9.09987 | 0.429929 | ||||||||
\(449\) | 31.7958 | 1.50054 | 0.750269 | − | 0.661133i | \(-0.229924\pi\) | ||||
0.750269 | + | 0.661133i | \(0.229924\pi\) | |||||||
\(450\) | −34.8799 | −1.64425 | ||||||||
\(451\) | −0.392079 | −0.0184623 | ||||||||
\(452\) | 87.2439 | 4.10361 | ||||||||
\(453\) | 1.56664 | 0.0736073 | ||||||||
\(454\) | 41.0266 | 1.92547 | ||||||||
\(455\) | 2.47003 | 0.115797 | ||||||||
\(456\) | 3.10623 | 0.145463 | ||||||||
\(457\) | −34.1179 | −1.59597 | −0.797984 | − | 0.602678i | \(-0.794100\pi\) | ||||
−0.797984 | + | 0.602678i | \(0.794100\pi\) | |||||||
\(458\) | −28.0830 | −1.31223 | ||||||||
\(459\) | 14.6998 | 0.686127 | ||||||||
\(460\) | −5.34334 | −0.249135 | ||||||||
\(461\) | −12.8224 | −0.597200 | −0.298600 | − | 0.954378i | \(-0.596520\pi\) | ||||
−0.298600 | + | 0.954378i | \(0.596520\pi\) | |||||||
\(462\) | −4.88799 | −0.227410 | ||||||||
\(463\) | 22.8633 | 1.06255 | 0.531273 | − | 0.847201i | \(-0.321714\pi\) | ||||
0.531273 | + | 0.847201i | \(0.321714\pi\) | |||||||
\(464\) | −2.54946 | −0.118356 | ||||||||
\(465\) | −0.762856 | −0.0353766 | ||||||||
\(466\) | 40.4900 | 1.87566 | ||||||||
\(467\) | −20.0188 | −0.926360 | −0.463180 | − | 0.886264i | \(-0.653292\pi\) | ||||
−0.463180 | + | 0.886264i | \(0.653292\pi\) | |||||||
\(468\) | 30.0405 | 1.38862 | ||||||||
\(469\) | −5.85093 | −0.270171 | ||||||||
\(470\) | −5.96117 | −0.274968 | ||||||||
\(471\) | −3.18886 | −0.146935 | ||||||||
\(472\) | 59.4130 | 2.73471 | ||||||||
\(473\) | −0.831448 | −0.0382300 | ||||||||
\(474\) | 8.87912 | 0.407832 | ||||||||
\(475\) | 8.32313 | 0.381891 | ||||||||
\(476\) | 77.0532 | 3.53173 | ||||||||
\(477\) | −20.0027 | −0.915859 | ||||||||
\(478\) | 12.9319 | 0.591492 | ||||||||
\(479\) | 18.2110 | 0.832080 | 0.416040 | − | 0.909346i | \(-0.363418\pi\) | ||||
0.416040 | + | 0.909346i | \(0.363418\pi\) | |||||||
\(480\) | −0.421756 | −0.0192505 | ||||||||
\(481\) | 14.7627 | 0.673121 | ||||||||
\(482\) | 34.3879 | 1.56632 | ||||||||
\(483\) | 1.97181 | 0.0897203 | ||||||||
\(484\) | −14.8497 | −0.674986 | ||||||||
\(485\) | −6.56809 | −0.298242 | ||||||||
\(486\) | −20.2949 | −0.920596 | ||||||||
\(487\) | 13.9922 | 0.634048 | 0.317024 | − | 0.948418i | \(-0.397316\pi\) | ||||
0.317024 | + | 0.948418i | \(0.397316\pi\) | |||||||
\(488\) | 45.5869 | 2.06362 | ||||||||
\(489\) | 0.306181 | 0.0138460 | ||||||||
\(490\) | 2.09841 | 0.0947963 | ||||||||
\(491\) | 15.2007 | 0.685997 | 0.342999 | − | 0.939336i | \(-0.388557\pi\) | ||||
0.342999 | + | 0.939336i | \(0.388557\pi\) | |||||||
\(492\) | 0.191706 | 0.00864276 | ||||||||
\(493\) | 3.52229 | 0.158636 | ||||||||
\(494\) | −10.5191 | −0.473278 | ||||||||
\(495\) | 3.58501 | 0.161134 | ||||||||
\(496\) | −31.0647 | −1.39485 | ||||||||
\(497\) | 23.7702 | 1.06624 | ||||||||
\(498\) | 2.40004 | 0.107548 | ||||||||
\(499\) | 4.38295 | 0.196208 | 0.0981040 | − | 0.995176i | \(-0.468722\pi\) | ||||
0.0981040 | + | 0.995176i | \(0.468722\pi\) | |||||||
\(500\) | −18.8744 | −0.844089 | ||||||||
\(501\) | 2.24417 | 0.100262 | ||||||||
\(502\) | −18.5611 | −0.828423 | ||||||||
\(503\) | 14.7282 | 0.656699 | 0.328350 | − | 0.944556i | \(-0.393508\pi\) | ||||
0.328350 | + | 0.944556i | \(0.393508\pi\) | |||||||
\(504\) | −37.5612 | −1.67311 | ||||||||
\(505\) | 5.26241 | 0.234174 | ||||||||
\(506\) | −19.0702 | −0.847774 | ||||||||
\(507\) | −2.24054 | −0.0995057 | ||||||||
\(508\) | 49.0918 | 2.17810 | ||||||||
\(509\) | −3.67043 | −0.162689 | −0.0813444 | − | 0.996686i | \(-0.525921\pi\) | ||||
−0.0813444 | + | 0.996686i | \(0.525921\pi\) | |||||||
\(510\) | 2.81016 | 0.124436 | ||||||||
\(511\) | 3.29098 | 0.145584 | ||||||||
\(512\) | 48.4791 | 2.14249 | ||||||||
\(513\) | 3.21072 | 0.141757 | ||||||||
\(514\) | −70.8634 | −3.12565 | ||||||||
\(515\) | 3.96346 | 0.174651 | ||||||||
\(516\) | 0.406533 | 0.0178966 | ||||||||
\(517\) | −14.4982 | −0.637629 | ||||||||
\(518\) | −34.6600 | −1.52287 | ||||||||
\(519\) | −3.96110 | −0.173873 | ||||||||
\(520\) | 6.22048 | 0.272786 | ||||||||
\(521\) | −13.1276 | −0.575129 | −0.287565 | − | 0.957761i | \(-0.592846\pi\) | ||||
−0.287565 | + | 0.957761i | \(0.592846\pi\) | |||||||
\(522\) | −3.22408 | −0.141114 | ||||||||
\(523\) | 3.89184 | 0.170178 | 0.0850892 | − | 0.996373i | \(-0.472882\pi\) | ||||
0.0850892 | + | 0.996373i | \(0.472882\pi\) | |||||||
\(524\) | −11.8896 | −0.519402 | ||||||||
\(525\) | 3.41046 | 0.148845 | ||||||||
\(526\) | 51.2451 | 2.23439 | ||||||||
\(527\) | 42.9186 | 1.86956 | ||||||||
\(528\) | −4.94693 | −0.215288 | ||||||||
\(529\) | −15.3071 | −0.665527 | ||||||||
\(530\) | −7.77742 | −0.337829 | ||||||||
\(531\) | 30.1943 | 1.31032 | ||||||||
\(532\) | 16.8299 | 0.729671 | ||||||||
\(533\) | −0.345740 | −0.0149757 | ||||||||
\(534\) | −1.51398 | −0.0655163 | ||||||||
\(535\) | 1.00268 | 0.0433495 | ||||||||
\(536\) | −14.7349 | −0.636449 | ||||||||
\(537\) | −2.21199 | −0.0954544 | ||||||||
\(538\) | −33.6082 | −1.44895 | ||||||||
\(539\) | 5.10354 | 0.219825 | ||||||||
\(540\) | −3.56515 | −0.153420 | ||||||||
\(541\) | −7.52504 | −0.323527 | −0.161763 | − | 0.986830i | \(-0.551718\pi\) | ||||
−0.161763 | + | 0.986830i | \(0.551718\pi\) | |||||||
\(542\) | 27.2074 | 1.16866 | ||||||||
\(543\) | 0.192974 | 0.00828132 | ||||||||
\(544\) | 23.7282 | 1.01734 | ||||||||
\(545\) | 7.69602 | 0.329661 | ||||||||
\(546\) | −4.31029 | −0.184463 | ||||||||
\(547\) | 23.3623 | 0.998899 | 0.499449 | − | 0.866343i | \(-0.333536\pi\) | ||||
0.499449 | + | 0.866343i | \(0.333536\pi\) | |||||||
\(548\) | 58.0142 | 2.47824 | ||||||||
\(549\) | 23.1677 | 0.988773 | ||||||||
\(550\) | −32.9841 | −1.40645 | ||||||||
\(551\) | 0.769339 | 0.0327749 | ||||||||
\(552\) | 4.96575 | 0.211356 | ||||||||
\(553\) | 25.6205 | 1.08950 | ||||||||
\(554\) | −11.2175 | −0.476588 | ||||||||
\(555\) | −0.861409 | −0.0365648 | ||||||||
\(556\) | −1.27543 | −0.0540902 | ||||||||
\(557\) | −14.0713 | −0.596219 | −0.298109 | − | 0.954532i | \(-0.596356\pi\) | ||||
−0.298109 | + | 0.954532i | \(0.596356\pi\) | |||||||
\(558\) | −39.2849 | −1.66306 | ||||||||
\(559\) | −0.733180 | −0.0310102 | ||||||||
\(560\) | −5.86911 | −0.248015 | ||||||||
\(561\) | 6.83461 | 0.288558 | ||||||||
\(562\) | 62.6802 | 2.64400 | ||||||||
\(563\) | −6.33521 | −0.266997 | −0.133499 | − | 0.991049i | \(-0.542621\pi\) | ||||
−0.133499 | + | 0.991049i | \(0.542621\pi\) | |||||||
\(564\) | 7.08883 | 0.298493 | ||||||||
\(565\) | 9.18109 | 0.386251 | ||||||||
\(566\) | 27.6499 | 1.16221 | ||||||||
\(567\) | −18.4202 | −0.773575 | ||||||||
\(568\) | 59.8623 | 2.51177 | ||||||||
\(569\) | 30.8370 | 1.29275 | 0.646377 | − | 0.763018i | \(-0.276283\pi\) | ||||
0.646377 | + | 0.763018i | \(0.276283\pi\) | |||||||
\(570\) | 0.613796 | 0.0257091 | ||||||||
\(571\) | −0.782704 | −0.0327551 | −0.0163776 | − | 0.999866i | \(-0.505213\pi\) | ||||
−0.0163776 | + | 0.999866i | \(0.505213\pi\) | |||||||
\(572\) | 28.4078 | 1.18779 | ||||||||
\(573\) | −5.50555 | −0.229998 | ||||||||
\(574\) | 0.811733 | 0.0338811 | ||||||||
\(575\) | 13.3057 | 0.554887 | ||||||||
\(576\) | 11.6466 | 0.485275 | ||||||||
\(577\) | 11.1486 | 0.464121 | 0.232061 | − | 0.972701i | \(-0.425453\pi\) | ||||
0.232061 | + | 0.972701i | \(0.425453\pi\) | |||||||
\(578\) | −115.504 | −4.80432 | ||||||||
\(579\) | −4.29968 | −0.178689 | ||||||||
\(580\) | −0.854266 | −0.0354715 | ||||||||
\(581\) | 6.92526 | 0.287308 | ||||||||
\(582\) | 11.4615 | 0.475096 | ||||||||
\(583\) | −18.9155 | −0.783400 | ||||||||
\(584\) | 8.28794 | 0.342957 | ||||||||
\(585\) | 3.16131 | 0.130704 | ||||||||
\(586\) | −19.5022 | −0.805628 | ||||||||
\(587\) | −32.2431 | −1.33081 | −0.665407 | − | 0.746480i | \(-0.731742\pi\) | ||||
−0.665407 | + | 0.746480i | \(0.731742\pi\) | |||||||
\(588\) | −2.49536 | −0.102907 | ||||||||
\(589\) | 9.37426 | 0.386260 | ||||||||
\(590\) | 11.7401 | 0.483332 | ||||||||
\(591\) | 4.50073 | 0.185135 | ||||||||
\(592\) | −35.0780 | −1.44170 | ||||||||
\(593\) | −31.1141 | −1.27770 | −0.638851 | − | 0.769331i | \(-0.720590\pi\) | ||||
−0.638851 | + | 0.769331i | \(0.720590\pi\) | |||||||
\(594\) | −12.7239 | −0.522068 | ||||||||
\(595\) | 8.10868 | 0.332423 | ||||||||
\(596\) | −46.4541 | −1.90283 | ||||||||
\(597\) | −0.415582 | −0.0170086 | ||||||||
\(598\) | −16.8163 | −0.687671 | ||||||||
\(599\) | 2.06383 | 0.0843259 | 0.0421629 | − | 0.999111i | \(-0.486575\pi\) | ||||
0.0421629 | + | 0.999111i | \(0.486575\pi\) | |||||||
\(600\) | 8.58884 | 0.350638 | ||||||||
\(601\) | −24.4708 | −0.998184 | −0.499092 | − | 0.866549i | \(-0.666333\pi\) | ||||
−0.499092 | + | 0.866549i | \(0.666333\pi\) | |||||||
\(602\) | 1.72137 | 0.0701578 | ||||||||
\(603\) | −7.48839 | −0.304951 | ||||||||
\(604\) | 21.3767 | 0.869804 | ||||||||
\(605\) | −1.56270 | −0.0635329 | ||||||||
\(606\) | −9.18307 | −0.373037 | ||||||||
\(607\) | −17.6775 | −0.717506 | −0.358753 | − | 0.933433i | \(-0.616798\pi\) | ||||
−0.358753 | + | 0.933433i | \(0.616798\pi\) | |||||||
\(608\) | 5.18270 | 0.210186 | ||||||||
\(609\) | 0.315242 | 0.0127743 | ||||||||
\(610\) | 9.00804 | 0.364725 | ||||||||
\(611\) | −12.7847 | −0.517212 | ||||||||
\(612\) | 98.6175 | 3.98638 | ||||||||
\(613\) | −4.51992 | −0.182558 | −0.0912790 | − | 0.995825i | \(-0.529096\pi\) | ||||
−0.0912790 | + | 0.995825i | \(0.529096\pi\) | |||||||
\(614\) | 64.9164 | 2.61981 | ||||||||
\(615\) | 0.0201741 | 0.000813498 0 | ||||||||
\(616\) | −35.5197 | −1.43113 | ||||||||
\(617\) | 17.7745 | 0.715573 | 0.357786 | − | 0.933803i | \(-0.383532\pi\) | ||||
0.357786 | + | 0.933803i | \(0.383532\pi\) | |||||||
\(618\) | −6.91637 | −0.278217 | ||||||||
\(619\) | −26.0447 | −1.04682 | −0.523412 | − | 0.852079i | \(-0.675341\pi\) | ||||
−0.523412 | + | 0.852079i | \(0.675341\pi\) | |||||||
\(620\) | −10.4091 | −0.418039 | ||||||||
\(621\) | 5.13280 | 0.205972 | ||||||||
\(622\) | 41.6633 | 1.67055 | ||||||||
\(623\) | −4.36856 | −0.175023 | ||||||||
\(624\) | −4.36226 | −0.174630 | ||||||||
\(625\) | 22.0001 | 0.880003 | ||||||||
\(626\) | 30.9661 | 1.23765 | ||||||||
\(627\) | 1.49281 | 0.0596173 | ||||||||
\(628\) | −43.5116 | −1.73630 | ||||||||
\(629\) | 48.4632 | 1.93235 | ||||||||
\(630\) | −7.42215 | −0.295706 | ||||||||
\(631\) | 49.1776 | 1.95773 | 0.978864 | − | 0.204513i | \(-0.0655611\pi\) | ||||
0.978864 | + | 0.204513i | \(0.0655611\pi\) | |||||||
\(632\) | 64.5222 | 2.56655 | ||||||||
\(633\) | −1.48829 | −0.0591544 | ||||||||
\(634\) | 7.11140 | 0.282430 | ||||||||
\(635\) | 5.16616 | 0.205013 | ||||||||
\(636\) | 9.24865 | 0.366733 | ||||||||
\(637\) | 4.50036 | 0.178311 | ||||||||
\(638\) | −3.04885 | −0.120705 | ||||||||
\(639\) | 30.4226 | 1.20350 | ||||||||
\(640\) | 7.21845 | 0.285334 | ||||||||
\(641\) | −19.9382 | −0.787512 | −0.393756 | − | 0.919215i | \(-0.628825\pi\) | ||||
−0.393756 | + | 0.919215i | \(0.628825\pi\) | |||||||
\(642\) | −1.74970 | −0.0690553 | ||||||||
\(643\) | 23.4457 | 0.924608 | 0.462304 | − | 0.886722i | \(-0.347023\pi\) | ||||
0.462304 | + | 0.886722i | \(0.347023\pi\) | |||||||
\(644\) | 26.9051 | 1.06021 | ||||||||
\(645\) | 0.0427814 | 0.00168452 | ||||||||
\(646\) | −34.5324 | −1.35866 | ||||||||
\(647\) | 22.6253 | 0.889493 | 0.444746 | − | 0.895657i | \(-0.353294\pi\) | ||||
0.444746 | + | 0.895657i | \(0.353294\pi\) | |||||||
\(648\) | −46.3890 | −1.82233 | ||||||||
\(649\) | 28.5531 | 1.12081 | ||||||||
\(650\) | −29.0858 | −1.14084 | ||||||||
\(651\) | 3.84117 | 0.150548 | ||||||||
\(652\) | 4.17781 | 0.163616 | ||||||||
\(653\) | 32.3837 | 1.26727 | 0.633635 | − | 0.773632i | \(-0.281562\pi\) | ||||
0.633635 | + | 0.773632i | \(0.281562\pi\) | |||||||
\(654\) | −13.4298 | −0.525147 | ||||||||
\(655\) | −1.25120 | −0.0488886 | ||||||||
\(656\) | 0.821521 | 0.0320750 | ||||||||
\(657\) | 4.21201 | 0.164326 | ||||||||
\(658\) | 30.0160 | 1.17015 | ||||||||
\(659\) | −40.7978 | −1.58926 | −0.794628 | − | 0.607097i | \(-0.792334\pi\) | ||||
−0.794628 | + | 0.607097i | \(0.792334\pi\) | |||||||
\(660\) | −1.65761 | −0.0645222 | ||||||||
\(661\) | 22.9972 | 0.894489 | 0.447244 | − | 0.894412i | \(-0.352405\pi\) | ||||
0.447244 | + | 0.894412i | \(0.352405\pi\) | |||||||
\(662\) | 36.8984 | 1.43410 | ||||||||
\(663\) | 6.02684 | 0.234063 | ||||||||
\(664\) | 17.4404 | 0.676820 | ||||||||
\(665\) | 1.77109 | 0.0686801 | ||||||||
\(666\) | −44.3601 | −1.71892 | ||||||||
\(667\) | 1.22990 | 0.0476218 | ||||||||
\(668\) | 30.6214 | 1.18478 | ||||||||
\(669\) | −2.59507 | −0.100331 | ||||||||
\(670\) | −2.91163 | −0.112486 | ||||||||
\(671\) | 21.9085 | 0.845768 | ||||||||
\(672\) | 2.12365 | 0.0819216 | ||||||||
\(673\) | 2.94046 | 0.113346 | 0.0566731 | − | 0.998393i | \(-0.481951\pi\) | ||||
0.0566731 | + | 0.998393i | \(0.481951\pi\) | |||||||
\(674\) | 79.5836 | 3.06545 | ||||||||
\(675\) | 8.87776 | 0.341705 | ||||||||
\(676\) | −30.5719 | −1.17584 | ||||||||
\(677\) | −35.4035 | −1.36067 | −0.680333 | − | 0.732903i | \(-0.738165\pi\) | ||||
−0.680333 | + | 0.732903i | \(0.738165\pi\) | |||||||
\(678\) | −16.0213 | −0.615294 | ||||||||
\(679\) | 33.0720 | 1.26919 | ||||||||
\(680\) | 20.4207 | 0.783098 | ||||||||
\(681\) | −5.13413 | −0.196740 | ||||||||
\(682\) | −37.1497 | −1.42253 | ||||||||
\(683\) | 25.6966 | 0.983254 | 0.491627 | − | 0.870806i | \(-0.336402\pi\) | ||||
0.491627 | + | 0.870806i | \(0.336402\pi\) | |||||||
\(684\) | 21.5400 | 0.823603 | ||||||||
\(685\) | 6.10511 | 0.233264 | ||||||||
\(686\) | −50.3323 | −1.92170 | ||||||||
\(687\) | 3.51435 | 0.134081 | ||||||||
\(688\) | 1.74213 | 0.0664179 | ||||||||
\(689\) | −16.6799 | −0.635454 | ||||||||
\(690\) | 0.981240 | 0.0373552 | ||||||||
\(691\) | 46.1735 | 1.75652 | 0.878261 | − | 0.478182i | \(-0.158704\pi\) | ||||
0.878261 | + | 0.478182i | \(0.158704\pi\) | |||||||
\(692\) | −54.0487 | −2.05463 | ||||||||
\(693\) | −18.0514 | −0.685718 | ||||||||
\(694\) | 39.2218 | 1.48884 | ||||||||
\(695\) | −0.134219 | −0.00509123 | ||||||||
\(696\) | 0.793899 | 0.0300927 | ||||||||
\(697\) | −1.13500 | −0.0429913 | ||||||||
\(698\) | 32.9400 | 1.24680 | ||||||||
\(699\) | −5.06699 | −0.191651 | ||||||||
\(700\) | 46.5354 | 1.75887 | ||||||||
\(701\) | 7.75805 | 0.293017 | 0.146509 | − | 0.989209i | \(-0.453196\pi\) | ||||
0.146509 | + | 0.989209i | \(0.453196\pi\) | |||||||
\(702\) | −11.2201 | −0.423475 | ||||||||
\(703\) | 10.5853 | 0.399233 | ||||||||
\(704\) | 11.0136 | 0.415090 | ||||||||
\(705\) | 0.745991 | 0.0280956 | ||||||||
\(706\) | −70.2565 | −2.64414 | ||||||||
\(707\) | −26.4976 | −0.996543 | ||||||||
\(708\) | −13.9609 | −0.524685 | ||||||||
\(709\) | 12.5360 | 0.470800 | 0.235400 | − | 0.971899i | \(-0.424360\pi\) | ||||
0.235400 | + | 0.971899i | \(0.424360\pi\) | |||||||
\(710\) | 11.8289 | 0.443930 | ||||||||
\(711\) | 32.7908 | 1.22975 | ||||||||
\(712\) | −11.0017 | −0.412306 | ||||||||
\(713\) | 14.9861 | 0.561234 | ||||||||
\(714\) | −14.1499 | −0.529546 | ||||||||
\(715\) | 2.98948 | 0.111800 | ||||||||
\(716\) | −30.1824 | −1.12797 | ||||||||
\(717\) | −1.61832 | −0.0604374 | ||||||||
\(718\) | −10.2900 | −0.384020 | ||||||||
\(719\) | −31.2742 | −1.16633 | −0.583165 | − | 0.812354i | \(-0.698186\pi\) | ||||
−0.583165 | + | 0.812354i | \(0.698186\pi\) | |||||||
\(720\) | −7.51165 | −0.279943 | ||||||||
\(721\) | −19.9570 | −0.743239 | ||||||||
\(722\) | 40.0661 | 1.49111 | ||||||||
\(723\) | −4.30336 | −0.160044 | ||||||||
\(724\) | 2.63311 | 0.0978589 | ||||||||
\(725\) | 2.12725 | 0.0790041 | ||||||||
\(726\) | 2.72696 | 0.101207 | ||||||||
\(727\) | 19.7903 | 0.733982 | 0.366991 | − | 0.930224i | \(-0.380388\pi\) | ||||
0.366991 | + | 0.930224i | \(0.380388\pi\) | |||||||
\(728\) | −31.3217 | −1.16086 | ||||||||
\(729\) | −21.8345 | −0.808684 | ||||||||
\(730\) | 1.63771 | 0.0606143 | ||||||||
\(731\) | −2.40690 | −0.0890223 | ||||||||
\(732\) | −10.7121 | −0.395930 | ||||||||
\(733\) | −38.5548 | −1.42406 | −0.712028 | − | 0.702151i | \(-0.752223\pi\) | ||||
−0.712028 | + | 0.702151i | \(0.752223\pi\) | |||||||
\(734\) | −58.0383 | −2.14223 | ||||||||
\(735\) | −0.262598 | −0.00968608 | ||||||||
\(736\) | 8.28529 | 0.305400 | ||||||||
\(737\) | −7.08139 | −0.260846 | ||||||||
\(738\) | 1.03891 | 0.0382427 | ||||||||
\(739\) | −6.00577 | −0.220926 | −0.110463 | − | 0.993880i | \(-0.535233\pi\) | ||||
−0.110463 | + | 0.993880i | \(0.535233\pi\) | |||||||
\(740\) | −11.7538 | −0.432080 | ||||||||
\(741\) | 1.31638 | 0.0483585 | ||||||||
\(742\) | 39.1613 | 1.43766 | ||||||||
\(743\) | 22.9137 | 0.840622 | 0.420311 | − | 0.907380i | \(-0.361921\pi\) | ||||
0.420311 | + | 0.907380i | \(0.361921\pi\) | |||||||
\(744\) | 9.67353 | 0.354649 | ||||||||
\(745\) | −4.88859 | −0.179104 | ||||||||
\(746\) | 84.6257 | 3.09837 | ||||||||
\(747\) | 8.86339 | 0.324294 | ||||||||
\(748\) | 93.2575 | 3.40983 | ||||||||
\(749\) | −5.04873 | −0.184477 | ||||||||
\(750\) | 3.46606 | 0.126563 | ||||||||
\(751\) | −31.4220 | −1.14661 | −0.573303 | − | 0.819343i | \(-0.694338\pi\) | ||||
−0.573303 | + | 0.819343i | \(0.694338\pi\) | |||||||
\(752\) | 30.3779 | 1.10777 | ||||||||
\(753\) | 2.32277 | 0.0846465 | ||||||||
\(754\) | −2.68851 | −0.0979097 | ||||||||
\(755\) | 2.24957 | 0.0818701 | ||||||||
\(756\) | 17.9515 | 0.652888 | ||||||||
\(757\) | −30.1880 | −1.09720 | −0.548601 | − | 0.836084i | \(-0.684839\pi\) | ||||
−0.548601 | + | 0.836084i | \(0.684839\pi\) | |||||||
\(758\) | 77.9166 | 2.83006 | ||||||||
\(759\) | 2.38648 | 0.0866236 | ||||||||
\(760\) | 4.46029 | 0.161792 | ||||||||
\(761\) | 9.31657 | 0.337725 | 0.168863 | − | 0.985640i | \(-0.445991\pi\) | ||||
0.168863 | + | 0.985640i | \(0.445991\pi\) | |||||||
\(762\) | −9.01512 | −0.326583 | ||||||||
\(763\) | −38.7514 | −1.40290 | ||||||||
\(764\) | −75.1226 | −2.71784 | ||||||||
\(765\) | 10.3780 | 0.375217 | ||||||||
\(766\) | −75.0447 | −2.71147 | ||||||||
\(767\) | 25.1785 | 0.909143 | ||||||||
\(768\) | −10.0792 | −0.363703 | ||||||||
\(769\) | −10.3196 | −0.372133 | −0.186066 | − | 0.982537i | \(-0.559574\pi\) | ||||
−0.186066 | + | 0.982537i | \(0.559574\pi\) | |||||||
\(770\) | −7.01875 | −0.252938 | ||||||||
\(771\) | 8.86797 | 0.319372 | ||||||||
\(772\) | −58.6687 | −2.11153 | ||||||||
\(773\) | −27.4937 | −0.988881 | −0.494441 | − | 0.869211i | \(-0.664627\pi\) | ||||
−0.494441 | + | 0.869211i | \(0.664627\pi\) | |||||||
\(774\) | 2.20312 | 0.0791894 | ||||||||
\(775\) | 25.9202 | 0.931081 | ||||||||
\(776\) | 83.2878 | 2.98986 | ||||||||
\(777\) | 4.33741 | 0.155604 | ||||||||
\(778\) | 83.4981 | 2.99355 | ||||||||
\(779\) | −0.247907 | −0.00888218 | ||||||||
\(780\) | −1.46170 | −0.0523371 | ||||||||
\(781\) | 28.7691 | 1.02944 | ||||||||
\(782\) | −55.2049 | −1.97412 | ||||||||
\(783\) | 0.820605 | 0.0293260 | ||||||||
\(784\) | −10.6934 | −0.381908 | ||||||||
\(785\) | −4.57893 | −0.163429 | ||||||||
\(786\) | 2.18339 | 0.0778789 | ||||||||
\(787\) | −39.1479 | −1.39547 | −0.697736 | − | 0.716355i | \(-0.745809\pi\) | ||||
−0.697736 | + | 0.716355i | \(0.745809\pi\) | |||||||
\(788\) | 61.4119 | 2.18771 | ||||||||
\(789\) | −6.41290 | −0.228305 | ||||||||
\(790\) | 12.7497 | 0.453613 | ||||||||
\(791\) | −46.2291 | −1.64372 | ||||||||
\(792\) | −45.4604 | −1.61536 | ||||||||
\(793\) | 19.3192 | 0.686044 | ||||||||
\(794\) | −16.3592 | −0.580566 | ||||||||
\(795\) | 0.973280 | 0.0345187 | ||||||||
\(796\) | −5.67057 | −0.200988 | ||||||||
\(797\) | 9.64106 | 0.341504 | 0.170752 | − | 0.985314i | \(-0.445380\pi\) | ||||
0.170752 | + | 0.985314i | \(0.445380\pi\) | |||||||
\(798\) | −3.09062 | −0.109407 | ||||||||
\(799\) | −41.9697 | −1.48478 | ||||||||
\(800\) | 14.3304 | 0.506655 | ||||||||
\(801\) | −5.59116 | −0.197554 | ||||||||
\(802\) | 76.5007 | 2.70133 | ||||||||
\(803\) | 3.98308 | 0.140560 | ||||||||
\(804\) | 3.46242 | 0.122110 | ||||||||
\(805\) | 2.83135 | 0.0997919 | ||||||||
\(806\) | −32.7590 | −1.15389 | ||||||||
\(807\) | 4.20579 | 0.148051 | ||||||||
\(808\) | −66.7309 | −2.34758 | ||||||||
\(809\) | 52.6848 | 1.85230 | 0.926149 | − | 0.377158i | \(-0.123098\pi\) | ||||
0.926149 | + | 0.377158i | \(0.123098\pi\) | |||||||
\(810\) | −9.16654 | −0.322079 | ||||||||
\(811\) | 12.1832 | 0.427809 | 0.213905 | − | 0.976855i | \(-0.431382\pi\) | ||||
0.213905 | + | 0.976855i | \(0.431382\pi\) | |||||||
\(812\) | 4.30144 | 0.150951 | ||||||||
\(813\) | −3.40479 | −0.119411 | ||||||||
\(814\) | −41.9490 | −1.47031 | ||||||||
\(815\) | 0.439651 | 0.0154003 | ||||||||
\(816\) | −14.3205 | −0.501318 | ||||||||
\(817\) | −0.525714 | −0.0183924 | ||||||||
\(818\) | −15.7133 | −0.549402 | ||||||||
\(819\) | −15.9180 | −0.556219 | ||||||||
\(820\) | 0.275273 | 0.00961296 | ||||||||
\(821\) | −21.9469 | −0.765951 | −0.382975 | − | 0.923759i | \(-0.625101\pi\) | ||||
−0.382975 | + | 0.923759i | \(0.625101\pi\) | |||||||
\(822\) | −10.6536 | −0.371587 | ||||||||
\(823\) | −41.9032 | −1.46065 | −0.730327 | − | 0.683098i | \(-0.760632\pi\) | ||||
−0.730327 | + | 0.683098i | \(0.760632\pi\) | |||||||
\(824\) | −50.2594 | −1.75087 | ||||||||
\(825\) | 4.12769 | 0.143708 | ||||||||
\(826\) | −59.1144 | −2.05685 | ||||||||
\(827\) | −7.21165 | −0.250774 | −0.125387 | − | 0.992108i | \(-0.540017\pi\) | ||||
−0.125387 | + | 0.992108i | \(0.540017\pi\) | |||||||
\(828\) | 34.4348 | 1.19669 | ||||||||
\(829\) | 50.0425 | 1.73805 | 0.869024 | − | 0.494770i | \(-0.164748\pi\) | ||||
0.869024 | + | 0.494770i | \(0.164748\pi\) | |||||||
\(830\) | 3.44625 | 0.119621 | ||||||||
\(831\) | 1.40378 | 0.0486967 | ||||||||
\(832\) | 9.71190 | 0.336700 | ||||||||
\(833\) | 14.7739 | 0.511884 | ||||||||
\(834\) | 0.234217 | 0.00811027 | ||||||||
\(835\) | 3.22244 | 0.111517 | ||||||||
\(836\) | 20.3693 | 0.704487 | ||||||||
\(837\) | 9.99894 | 0.345614 | ||||||||
\(838\) | −72.0953 | −2.49049 | ||||||||
\(839\) | 15.1486 | 0.522989 | 0.261495 | − | 0.965205i | \(-0.415785\pi\) | ||||
0.261495 | + | 0.965205i | \(0.415785\pi\) | |||||||
\(840\) | 1.82764 | 0.0630594 | ||||||||
\(841\) | −28.8034 | −0.993220 | ||||||||
\(842\) | 11.2284 | 0.386957 | ||||||||
\(843\) | −7.84391 | −0.270159 | ||||||||
\(844\) | −20.3076 | −0.699017 | ||||||||
\(845\) | −3.21722 | −0.110676 | ||||||||
\(846\) | 38.4164 | 1.32078 | ||||||||
\(847\) | 7.86860 | 0.270368 | ||||||||
\(848\) | 39.6335 | 1.36102 | ||||||||
\(849\) | −3.46016 | −0.118752 | ||||||||
\(850\) | −95.4832 | −3.27505 | ||||||||
\(851\) | 16.9222 | 0.580084 | ||||||||
\(852\) | −14.0665 | −0.481911 | ||||||||
\(853\) | −37.8000 | −1.29425 | −0.647124 | − | 0.762385i | \(-0.724028\pi\) | ||||
−0.647124 | + | 0.762385i | \(0.724028\pi\) | |||||||
\(854\) | −45.3578 | −1.55211 | ||||||||
\(855\) | 2.26676 | 0.0775215 | ||||||||
\(856\) | −12.7146 | −0.434577 | ||||||||
\(857\) | −22.4546 | −0.767033 | −0.383517 | − | 0.923534i | \(-0.625287\pi\) | ||||
−0.383517 | + | 0.923534i | \(0.625287\pi\) | |||||||
\(858\) | −5.21674 | −0.178097 | ||||||||
\(859\) | 24.8383 | 0.847471 | 0.423736 | − | 0.905786i | \(-0.360719\pi\) | ||||
0.423736 | + | 0.905786i | \(0.360719\pi\) | |||||||
\(860\) | 0.583747 | 0.0199056 | ||||||||
\(861\) | −0.101582 | −0.00346189 | ||||||||
\(862\) | 22.8578 | 0.778541 | ||||||||
\(863\) | 22.1548 | 0.754158 | 0.377079 | − | 0.926181i | \(-0.376929\pi\) | ||||
0.377079 | + | 0.926181i | \(0.376929\pi\) | |||||||
\(864\) | 5.52806 | 0.188069 | ||||||||
\(865\) | −5.68781 | −0.193391 | ||||||||
\(866\) | 28.0694 | 0.953837 | ||||||||
\(867\) | 14.4543 | 0.490895 | ||||||||
\(868\) | 52.4124 | 1.77899 | ||||||||
\(869\) | 31.0085 | 1.05189 | ||||||||
\(870\) | 0.156876 | 0.00531858 | ||||||||
\(871\) | −6.24445 | −0.211585 | ||||||||
\(872\) | −97.5908 | −3.30484 | ||||||||
\(873\) | 42.3277 | 1.43257 | ||||||||
\(874\) | −12.0578 | −0.407863 | ||||||||
\(875\) | 10.0012 | 0.338104 | ||||||||
\(876\) | −1.94751 | −0.0658003 | ||||||||
\(877\) | −34.5612 | −1.16705 | −0.583525 | − | 0.812095i | \(-0.698327\pi\) | ||||
−0.583525 | + | 0.812095i | \(0.698327\pi\) | |||||||
\(878\) | 40.3775 | 1.36267 | ||||||||
\(879\) | 2.44054 | 0.0823173 | ||||||||
\(880\) | −7.10338 | −0.239455 | ||||||||
\(881\) | −18.1847 | −0.612659 | −0.306330 | − | 0.951925i | \(-0.599101\pi\) | ||||
−0.306330 | + | 0.951925i | \(0.599101\pi\) | |||||||
\(882\) | −13.5230 | −0.455344 | ||||||||
\(883\) | −1.51004 | −0.0508169 | −0.0254084 | − | 0.999677i | \(-0.508089\pi\) | ||||
−0.0254084 | + | 0.999677i | \(0.508089\pi\) | |||||||
\(884\) | 82.2356 | 2.76588 | ||||||||
\(885\) | −1.46918 | −0.0493858 | ||||||||
\(886\) | −45.7464 | −1.53688 | ||||||||
\(887\) | 11.8609 | 0.398251 | 0.199125 | − | 0.979974i | \(-0.436190\pi\) | ||||
0.199125 | + | 0.979974i | \(0.436190\pi\) | |||||||
\(888\) | 10.9232 | 0.366560 | ||||||||
\(889\) | −26.0129 | −0.872446 | ||||||||
\(890\) | −2.17395 | −0.0728710 | ||||||||
\(891\) | −22.2940 | −0.746876 | ||||||||
\(892\) | −35.4094 | −1.18559 | ||||||||
\(893\) | −9.16702 | −0.306763 | ||||||||
\(894\) | 8.53074 | 0.285311 | ||||||||
\(895\) | −3.17623 | −0.106170 | ||||||||
\(896\) | −36.3467 | −1.21426 | ||||||||
\(897\) | 2.10442 | 0.0702647 | ||||||||
\(898\) | −79.6714 | −2.65867 | ||||||||
\(899\) | 2.39590 | 0.0799078 | ||||||||
\(900\) | 59.5589 | 1.98530 | ||||||||
\(901\) | −54.7571 | −1.82422 | ||||||||
\(902\) | 0.982441 | 0.0327117 | ||||||||
\(903\) | −0.215415 | −0.00716857 | ||||||||
\(904\) | −116.422 | −3.87215 | ||||||||
\(905\) | 0.277095 | 0.00921095 | ||||||||
\(906\) | −3.92556 | −0.130418 | ||||||||
\(907\) | 5.84159 | 0.193967 | 0.0969835 | − | 0.995286i | \(-0.469081\pi\) | ||||
0.0969835 | + | 0.995286i | \(0.469081\pi\) | |||||||
\(908\) | −70.0547 | −2.32485 | ||||||||
\(909\) | −33.9132 | −1.12483 | ||||||||
\(910\) | −6.18921 | −0.205170 | ||||||||
\(911\) | 49.9718 | 1.65564 | 0.827820 | − | 0.560993i | \(-0.189581\pi\) | ||||
0.827820 | + | 0.560993i | \(0.189581\pi\) | |||||||
\(912\) | −3.12788 | −0.103575 | ||||||||
\(913\) | 8.38165 | 0.277392 | ||||||||
\(914\) | 85.4899 | 2.82776 | ||||||||
\(915\) | −1.12728 | −0.0372668 | ||||||||
\(916\) | 47.9529 | 1.58441 | ||||||||
\(917\) | 6.30013 | 0.208049 | ||||||||
\(918\) | −36.8335 | −1.21569 | ||||||||
\(919\) | −59.6154 | −1.96653 | −0.983265 | − | 0.182180i | \(-0.941685\pi\) | ||||
−0.983265 | + | 0.182180i | \(0.941685\pi\) | |||||||
\(920\) | 7.13041 | 0.235083 | ||||||||
\(921\) | −8.12375 | −0.267687 | ||||||||
\(922\) | 32.1294 | 1.05813 | ||||||||
\(923\) | 25.3689 | 0.835028 | ||||||||
\(924\) | 8.34647 | 0.274579 | ||||||||
\(925\) | 29.2688 | 0.962352 | ||||||||
\(926\) | −57.2889 | −1.88263 | ||||||||
\(927\) | −25.5423 | −0.838918 | ||||||||
\(928\) | 1.32461 | 0.0434824 | ||||||||
\(929\) | 29.6554 | 0.972961 | 0.486481 | − | 0.873691i | \(-0.338280\pi\) | ||||
0.486481 | + | 0.873691i | \(0.338280\pi\) | |||||||
\(930\) | 1.91150 | 0.0626807 | ||||||||
\(931\) | 3.22690 | 0.105758 | ||||||||
\(932\) | −69.1385 | −2.26471 | ||||||||
\(933\) | −5.21382 | −0.170693 | ||||||||
\(934\) | 50.1615 | 1.64133 | ||||||||
\(935\) | 9.81393 | 0.320950 | ||||||||
\(936\) | −40.0875 | −1.31030 | ||||||||
\(937\) | 40.4045 | 1.31996 | 0.659978 | − | 0.751285i | \(-0.270566\pi\) | ||||
0.659978 | + | 0.751285i | \(0.270566\pi\) | |||||||
\(938\) | 14.6608 | 0.478692 | ||||||||
\(939\) | −3.87515 | −0.126461 | ||||||||
\(940\) | 10.1790 | 0.332001 | ||||||||
\(941\) | −15.8654 | −0.517196 | −0.258598 | − | 0.965985i | \(-0.583260\pi\) | ||||
−0.258598 | + | 0.965985i | \(0.583260\pi\) | |||||||
\(942\) | 7.99038 | 0.260341 | ||||||||
\(943\) | −0.396315 | −0.0129058 | ||||||||
\(944\) | −59.8272 | −1.94721 | ||||||||
\(945\) | 1.88912 | 0.0614530 | ||||||||
\(946\) | 2.08337 | 0.0677363 | ||||||||
\(947\) | 35.6003 | 1.15685 | 0.578427 | − | 0.815734i | \(-0.303667\pi\) | ||||
0.578427 | + | 0.815734i | \(0.303667\pi\) | |||||||
\(948\) | −15.1615 | −0.492423 | ||||||||
\(949\) | 3.51232 | 0.114015 | ||||||||
\(950\) | −20.8554 | −0.676639 | ||||||||
\(951\) | −0.889933 | −0.0288581 | ||||||||
\(952\) | −102.823 | −3.33253 | ||||||||
\(953\) | −26.6967 | −0.864792 | −0.432396 | − | 0.901684i | \(-0.642332\pi\) | ||||
−0.432396 | + | 0.901684i | \(0.642332\pi\) | |||||||
\(954\) | 50.1211 | 1.62273 | ||||||||
\(955\) | −7.90551 | −0.255816 | ||||||||
\(956\) | −22.0818 | −0.714178 | ||||||||
\(957\) | 0.381538 | 0.0123334 | ||||||||
\(958\) | −45.6316 | −1.47429 | ||||||||
\(959\) | −30.7408 | −0.992671 | ||||||||
\(960\) | −0.566694 | −0.0182900 | ||||||||
\(961\) | −1.80633 | −0.0582687 | ||||||||
\(962\) | −36.9911 | −1.19264 | ||||||||
\(963\) | −6.46169 | −0.208225 | ||||||||
\(964\) | −58.7188 | −1.89121 | ||||||||
\(965\) | −6.17399 | −0.198748 | ||||||||
\(966\) | −4.94079 | −0.158967 | ||||||||
\(967\) | 43.2358 | 1.39037 | 0.695185 | − | 0.718831i | \(-0.255322\pi\) | ||||
0.695185 | + | 0.718831i | \(0.255322\pi\) | |||||||
\(968\) | 19.8161 | 0.636914 | ||||||||
\(969\) | 4.32144 | 0.138825 | ||||||||
\(970\) | 16.4578 | 0.528428 | ||||||||
\(971\) | −35.7737 | −1.14803 | −0.574017 | − | 0.818844i | \(-0.694616\pi\) | ||||
−0.574017 | + | 0.818844i | \(0.694616\pi\) | |||||||
\(972\) | 34.6545 | 1.11154 | ||||||||
\(973\) | 0.675829 | 0.0216661 | ||||||||
\(974\) | −35.0606 | −1.12341 | ||||||||
\(975\) | 3.63984 | 0.116568 | ||||||||
\(976\) | −45.9047 | −1.46937 | ||||||||
\(977\) | −25.7365 | −0.823385 | −0.411693 | − | 0.911323i | \(-0.635062\pi\) | ||||
−0.411693 | + | 0.911323i | \(0.635062\pi\) | |||||||
\(978\) | −0.767204 | −0.0245325 | ||||||||
\(979\) | −5.28727 | −0.168982 | ||||||||
\(980\) | −3.58312 | −0.114459 | ||||||||
\(981\) | −49.5965 | −1.58350 | ||||||||
\(982\) | −38.0886 | −1.21546 | ||||||||
\(983\) | 11.4551 | 0.365361 | 0.182681 | − | 0.983172i | \(-0.441523\pi\) | ||||
0.182681 | + | 0.983172i | \(0.441523\pi\) | |||||||
\(984\) | −0.255821 | −0.00815528 | ||||||||
\(985\) | 6.46267 | 0.205918 | ||||||||
\(986\) | −8.82588 | −0.281073 | ||||||||
\(987\) | −3.75625 | −0.119563 | ||||||||
\(988\) | 17.9619 | 0.571443 | ||||||||
\(989\) | −0.840429 | −0.0267241 | ||||||||
\(990\) | −8.98304 | −0.285500 | ||||||||
\(991\) | −26.7326 | −0.849188 | −0.424594 | − | 0.905384i | \(-0.639583\pi\) | ||||
−0.424594 | + | 0.905384i | \(0.639583\pi\) | |||||||
\(992\) | 16.1402 | 0.512450 | ||||||||
\(993\) | −4.61753 | −0.146533 | ||||||||
\(994\) | −59.5614 | −1.88917 | ||||||||
\(995\) | −0.596741 | −0.0189180 | ||||||||
\(996\) | −4.09817 | −0.129856 | ||||||||
\(997\) | 36.2075 | 1.14670 | 0.573351 | − | 0.819310i | \(-0.305643\pi\) | ||||
0.573351 | + | 0.819310i | \(0.305643\pi\) | |||||||
\(998\) | −10.9825 | −0.347644 | ||||||||
\(999\) | 11.2907 | 0.357222 |
(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 | 5077.2.a.c.1.11 | ✓ | 216 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
5077.2.a.c.1.11 | ✓ | 216 | 1.1 | even | 1 | trivial |