Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [4029,2,Mod(1,4029)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(4029, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("4029.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 4029 = 3 \cdot 17 \cdot 79 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 4029.a (trivial) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | yes |
Analytic conductor: | \(32.1717269744\) |
Analytic rank: | \(0\) |
Dimension: | \(32\) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.8 | ||
Character | \(\chi\) | \(=\) | 4029.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.67650 | −1.18547 | −0.592733 | − | 0.805399i | \(-0.701951\pi\) | ||||
−0.592733 | + | 0.805399i | \(0.701951\pi\) | |||||||
\(3\) | −1.00000 | −0.577350 | ||||||||
\(4\) | 0.810659 | 0.405330 | ||||||||
\(5\) | −3.83953 | −1.71709 | −0.858544 | − | 0.512740i | \(-0.828631\pi\) | ||||
−0.858544 | + | 0.512740i | \(0.828631\pi\) | |||||||
\(6\) | 1.67650 | 0.684429 | ||||||||
\(7\) | −4.72769 | −1.78690 | −0.893450 | − | 0.449162i | \(-0.851722\pi\) | ||||
−0.893450 | + | 0.449162i | \(0.851722\pi\) | |||||||
\(8\) | 1.99393 | 0.704962 | ||||||||
\(9\) | 1.00000 | 0.333333 | ||||||||
\(10\) | 6.43697 | 2.03555 | ||||||||
\(11\) | 6.37239 | 1.92135 | 0.960673 | − | 0.277681i | \(-0.0895657\pi\) | ||||
0.960673 | + | 0.277681i | \(0.0895657\pi\) | |||||||
\(12\) | −0.810659 | −0.234017 | ||||||||
\(13\) | 6.95110 | 1.92789 | 0.963944 | − | 0.266105i | \(-0.0857369\pi\) | ||||
0.963944 | + | 0.266105i | \(0.0857369\pi\) | |||||||
\(14\) | 7.92599 | 2.11831 | ||||||||
\(15\) | 3.83953 | 0.991361 | ||||||||
\(16\) | −4.96415 | −1.24104 | ||||||||
\(17\) | −1.00000 | −0.242536 | ||||||||
\(18\) | −1.67650 | −0.395155 | ||||||||
\(19\) | 6.78856 | 1.55740 | 0.778701 | − | 0.627396i | \(-0.215879\pi\) | ||||
0.778701 | + | 0.627396i | \(0.215879\pi\) | |||||||
\(20\) | −3.11255 | −0.695987 | ||||||||
\(21\) | 4.72769 | 1.03167 | ||||||||
\(22\) | −10.6833 | −2.27769 | ||||||||
\(23\) | 5.35418 | 1.11642 | 0.558212 | − | 0.829699i | \(-0.311488\pi\) | ||||
0.558212 | + | 0.829699i | \(0.311488\pi\) | |||||||
\(24\) | −1.99393 | −0.407010 | ||||||||
\(25\) | 9.74196 | 1.94839 | ||||||||
\(26\) | −11.6535 | −2.28545 | ||||||||
\(27\) | −1.00000 | −0.192450 | ||||||||
\(28\) | −3.83255 | −0.724284 | ||||||||
\(29\) | −3.88066 | −0.720620 | −0.360310 | − | 0.932833i | \(-0.617329\pi\) | ||||
−0.360310 | + | 0.932833i | \(0.617329\pi\) | |||||||
\(30\) | −6.43697 | −1.17523 | ||||||||
\(31\) | −4.37999 | −0.786670 | −0.393335 | − | 0.919395i | \(-0.628679\pi\) | ||||
−0.393335 | + | 0.919395i | \(0.628679\pi\) | |||||||
\(32\) | 4.33454 | 0.766246 | ||||||||
\(33\) | −6.37239 | −1.10929 | ||||||||
\(34\) | 1.67650 | 0.287518 | ||||||||
\(35\) | 18.1521 | 3.06827 | ||||||||
\(36\) | 0.810659 | 0.135110 | ||||||||
\(37\) | −1.41918 | −0.233312 | −0.116656 | − | 0.993172i | \(-0.537217\pi\) | ||||
−0.116656 | + | 0.993172i | \(0.537217\pi\) | |||||||
\(38\) | −11.3810 | −1.84625 | ||||||||
\(39\) | −6.95110 | −1.11307 | ||||||||
\(40\) | −7.65575 | −1.21048 | ||||||||
\(41\) | 6.61973 | 1.03383 | 0.516914 | − | 0.856037i | \(-0.327081\pi\) | ||||
0.516914 | + | 0.856037i | \(0.327081\pi\) | |||||||
\(42\) | −7.92599 | −1.22301 | ||||||||
\(43\) | 11.3206 | 1.72637 | 0.863186 | − | 0.504886i | \(-0.168466\pi\) | ||||
0.863186 | + | 0.504886i | \(0.168466\pi\) | |||||||
\(44\) | 5.16583 | 0.778779 | ||||||||
\(45\) | −3.83953 | −0.572363 | ||||||||
\(46\) | −8.97629 | −1.32348 | ||||||||
\(47\) | 3.03205 | 0.442270 | 0.221135 | − | 0.975243i | \(-0.429024\pi\) | ||||
0.221135 | + | 0.975243i | \(0.429024\pi\) | |||||||
\(48\) | 4.96415 | 0.716513 | ||||||||
\(49\) | 15.3511 | 2.19301 | ||||||||
\(50\) | −16.3324 | −2.30975 | ||||||||
\(51\) | 1.00000 | 0.140028 | ||||||||
\(52\) | 5.63497 | 0.781430 | ||||||||
\(53\) | −3.69509 | −0.507559 | −0.253780 | − | 0.967262i | \(-0.581674\pi\) | ||||
−0.253780 | + | 0.967262i | \(0.581674\pi\) | |||||||
\(54\) | 1.67650 | 0.228143 | ||||||||
\(55\) | −24.4669 | −3.29912 | ||||||||
\(56\) | −9.42670 | −1.25970 | ||||||||
\(57\) | −6.78856 | −0.899166 | ||||||||
\(58\) | 6.50593 | 0.854271 | ||||||||
\(59\) | −0.276229 | −0.0359619 | −0.0179810 | − | 0.999838i | \(-0.505724\pi\) | ||||
−0.0179810 | + | 0.999838i | \(0.505724\pi\) | |||||||
\(60\) | 3.11255 | 0.401828 | ||||||||
\(61\) | 4.92566 | 0.630666 | 0.315333 | − | 0.948981i | \(-0.397884\pi\) | ||||
0.315333 | + | 0.948981i | \(0.397884\pi\) | |||||||
\(62\) | 7.34307 | 0.932571 | ||||||||
\(63\) | −4.72769 | −0.595633 | ||||||||
\(64\) | 2.66143 | 0.332679 | ||||||||
\(65\) | −26.6889 | −3.31035 | ||||||||
\(66\) | 10.6833 | 1.31503 | ||||||||
\(67\) | −4.08227 | −0.498729 | −0.249364 | − | 0.968410i | \(-0.580222\pi\) | ||||
−0.249364 | + | 0.968410i | \(0.580222\pi\) | |||||||
\(68\) | −0.810659 | −0.0983069 | ||||||||
\(69\) | −5.35418 | −0.644567 | ||||||||
\(70\) | −30.4320 | −3.63732 | ||||||||
\(71\) | −10.7630 | −1.27733 | −0.638667 | − | 0.769483i | \(-0.720514\pi\) | ||||
−0.638667 | + | 0.769483i | \(0.720514\pi\) | |||||||
\(72\) | 1.99393 | 0.234987 | ||||||||
\(73\) | 1.10125 | 0.128891 | 0.0644456 | − | 0.997921i | \(-0.479472\pi\) | ||||
0.0644456 | + | 0.997921i | \(0.479472\pi\) | |||||||
\(74\) | 2.37926 | 0.276583 | ||||||||
\(75\) | −9.74196 | −1.12490 | ||||||||
\(76\) | 5.50321 | 0.631261 | ||||||||
\(77\) | −30.1267 | −3.43326 | ||||||||
\(78\) | 11.6535 | 1.31950 | ||||||||
\(79\) | 1.00000 | 0.112509 | ||||||||
\(80\) | 19.0600 | 2.13097 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | −11.0980 | −1.22557 | ||||||||
\(83\) | −3.30768 | −0.363066 | −0.181533 | − | 0.983385i | \(-0.558106\pi\) | ||||
−0.181533 | + | 0.983385i | \(0.558106\pi\) | |||||||
\(84\) | 3.83255 | 0.418165 | ||||||||
\(85\) | 3.83953 | 0.416455 | ||||||||
\(86\) | −18.9790 | −2.04655 | ||||||||
\(87\) | 3.88066 | 0.416050 | ||||||||
\(88\) | 12.7061 | 1.35448 | ||||||||
\(89\) | 9.92560 | 1.05211 | 0.526056 | − | 0.850450i | \(-0.323670\pi\) | ||||
0.526056 | + | 0.850450i | \(0.323670\pi\) | |||||||
\(90\) | 6.43697 | 0.678517 | ||||||||
\(91\) | −32.8627 | −3.44494 | ||||||||
\(92\) | 4.34041 | 0.452519 | ||||||||
\(93\) | 4.37999 | 0.454184 | ||||||||
\(94\) | −5.08324 | −0.524296 | ||||||||
\(95\) | −26.0648 | −2.67420 | ||||||||
\(96\) | −4.33454 | −0.442392 | ||||||||
\(97\) | 10.7466 | 1.09116 | 0.545578 | − | 0.838060i | \(-0.316310\pi\) | ||||
0.545578 | + | 0.838060i | \(0.316310\pi\) | |||||||
\(98\) | −25.7361 | −2.59974 | ||||||||
\(99\) | 6.37239 | 0.640449 | ||||||||
\(100\) | 7.89741 | 0.789741 | ||||||||
\(101\) | −2.96492 | −0.295021 | −0.147510 | − | 0.989061i | \(-0.547126\pi\) | ||||
−0.147510 | + | 0.989061i | \(0.547126\pi\) | |||||||
\(102\) | −1.67650 | −0.165998 | ||||||||
\(103\) | 3.79769 | 0.374197 | 0.187099 | − | 0.982341i | \(-0.440092\pi\) | ||||
0.187099 | + | 0.982341i | \(0.440092\pi\) | |||||||
\(104\) | 13.8600 | 1.35909 | ||||||||
\(105\) | −18.1521 | −1.77146 | ||||||||
\(106\) | 6.19482 | 0.601694 | ||||||||
\(107\) | −4.59844 | −0.444548 | −0.222274 | − | 0.974984i | \(-0.571348\pi\) | ||||
−0.222274 | + | 0.974984i | \(0.571348\pi\) | |||||||
\(108\) | −0.810659 | −0.0780057 | ||||||||
\(109\) | 3.43875 | 0.329372 | 0.164686 | − | 0.986346i | \(-0.447339\pi\) | ||||
0.164686 | + | 0.986346i | \(0.447339\pi\) | |||||||
\(110\) | 41.0189 | 3.91100 | ||||||||
\(111\) | 1.41918 | 0.134703 | ||||||||
\(112\) | 23.4690 | 2.21761 | ||||||||
\(113\) | 2.48008 | 0.233306 | 0.116653 | − | 0.993173i | \(-0.462783\pi\) | ||||
0.116653 | + | 0.993173i | \(0.462783\pi\) | |||||||
\(114\) | 11.3810 | 1.06593 | ||||||||
\(115\) | −20.5575 | −1.91700 | ||||||||
\(116\) | −3.14589 | −0.292089 | ||||||||
\(117\) | 6.95110 | 0.642629 | ||||||||
\(118\) | 0.463098 | 0.0426316 | ||||||||
\(119\) | 4.72769 | 0.433387 | ||||||||
\(120\) | 7.65575 | 0.698872 | ||||||||
\(121\) | 29.6073 | 2.69157 | ||||||||
\(122\) | −8.25787 | −0.747633 | ||||||||
\(123\) | −6.61973 | −0.596881 | ||||||||
\(124\) | −3.55068 | −0.318861 | ||||||||
\(125\) | −18.2069 | −1.62847 | ||||||||
\(126\) | 7.92599 | 0.706103 | ||||||||
\(127\) | 0.406380 | 0.0360604 | 0.0180302 | − | 0.999837i | \(-0.494260\pi\) | ||||
0.0180302 | + | 0.999837i | \(0.494260\pi\) | |||||||
\(128\) | −13.1310 | −1.16063 | ||||||||
\(129\) | −11.3206 | −0.996721 | ||||||||
\(130\) | 44.7440 | 3.92431 | ||||||||
\(131\) | 18.2641 | 1.59574 | 0.797869 | − | 0.602831i | \(-0.205961\pi\) | ||||
0.797869 | + | 0.602831i | \(0.205961\pi\) | |||||||
\(132\) | −5.16583 | −0.449628 | ||||||||
\(133\) | −32.0942 | −2.78292 | ||||||||
\(134\) | 6.84394 | 0.591226 | ||||||||
\(135\) | 3.83953 | 0.330454 | ||||||||
\(136\) | −1.99393 | −0.170978 | ||||||||
\(137\) | −21.4296 | −1.83086 | −0.915429 | − | 0.402480i | \(-0.868148\pi\) | ||||
−0.915429 | + | 0.402480i | \(0.868148\pi\) | |||||||
\(138\) | 8.97629 | 0.764112 | ||||||||
\(139\) | −6.87852 | −0.583428 | −0.291714 | − | 0.956506i | \(-0.594226\pi\) | ||||
−0.291714 | + | 0.956506i | \(0.594226\pi\) | |||||||
\(140\) | 14.7152 | 1.24366 | ||||||||
\(141\) | −3.03205 | −0.255345 | ||||||||
\(142\) | 18.0442 | 1.51424 | ||||||||
\(143\) | 44.2951 | 3.70414 | ||||||||
\(144\) | −4.96415 | −0.413679 | ||||||||
\(145\) | 14.8999 | 1.23737 | ||||||||
\(146\) | −1.84624 | −0.152796 | ||||||||
\(147\) | −15.3511 | −1.26614 | ||||||||
\(148\) | −1.15047 | −0.0945682 | ||||||||
\(149\) | 12.5327 | 1.02672 | 0.513361 | − | 0.858173i | \(-0.328400\pi\) | ||||
0.513361 | + | 0.858173i | \(0.328400\pi\) | |||||||
\(150\) | 16.3324 | 1.33354 | ||||||||
\(151\) | 5.31777 | 0.432754 | 0.216377 | − | 0.976310i | \(-0.430576\pi\) | ||||
0.216377 | + | 0.976310i | \(0.430576\pi\) | |||||||
\(152\) | 13.5359 | 1.09791 | ||||||||
\(153\) | −1.00000 | −0.0808452 | ||||||||
\(154\) | 50.5075 | 4.07001 | ||||||||
\(155\) | 16.8171 | 1.35078 | ||||||||
\(156\) | −5.63497 | −0.451159 | ||||||||
\(157\) | 9.23022 | 0.736652 | 0.368326 | − | 0.929697i | \(-0.379931\pi\) | ||||
0.368326 | + | 0.929697i | \(0.379931\pi\) | |||||||
\(158\) | −1.67650 | −0.133375 | ||||||||
\(159\) | 3.69509 | 0.293039 | ||||||||
\(160\) | −16.6426 | −1.31571 | ||||||||
\(161\) | −25.3129 | −1.99494 | ||||||||
\(162\) | −1.67650 | −0.131718 | ||||||||
\(163\) | −2.51559 | −0.197037 | −0.0985183 | − | 0.995135i | \(-0.531410\pi\) | ||||
−0.0985183 | + | 0.995135i | \(0.531410\pi\) | |||||||
\(164\) | 5.36635 | 0.419041 | ||||||||
\(165\) | 24.4669 | 1.90475 | ||||||||
\(166\) | 5.54534 | 0.430402 | ||||||||
\(167\) | −9.03274 | −0.698975 | −0.349487 | − | 0.936941i | \(-0.613644\pi\) | ||||
−0.349487 | + | 0.936941i | \(0.613644\pi\) | |||||||
\(168\) | 9.42670 | 0.727286 | ||||||||
\(169\) | 35.3178 | 2.71675 | ||||||||
\(170\) | −6.43697 | −0.493693 | ||||||||
\(171\) | 6.78856 | 0.519134 | ||||||||
\(172\) | 9.17713 | 0.699750 | ||||||||
\(173\) | −19.7222 | −1.49945 | −0.749725 | − | 0.661750i | \(-0.769814\pi\) | ||||
−0.749725 | + | 0.661750i | \(0.769814\pi\) | |||||||
\(174\) | −6.50593 | −0.493214 | ||||||||
\(175\) | −46.0570 | −3.48158 | ||||||||
\(176\) | −31.6335 | −2.38446 | ||||||||
\(177\) | 0.276229 | 0.0207626 | ||||||||
\(178\) | −16.6403 | −1.24724 | ||||||||
\(179\) | −9.96833 | −0.745068 | −0.372534 | − | 0.928018i | \(-0.621511\pi\) | ||||
−0.372534 | + | 0.928018i | \(0.621511\pi\) | |||||||
\(180\) | −3.11255 | −0.231996 | ||||||||
\(181\) | 17.2092 | 1.27915 | 0.639576 | − | 0.768728i | \(-0.279110\pi\) | ||||
0.639576 | + | 0.768728i | \(0.279110\pi\) | |||||||
\(182\) | 55.0943 | 4.08386 | ||||||||
\(183\) | −4.92566 | −0.364115 | ||||||||
\(184\) | 10.6759 | 0.787035 | ||||||||
\(185\) | 5.44898 | 0.400617 | ||||||||
\(186\) | −7.34307 | −0.538420 | ||||||||
\(187\) | −6.37239 | −0.465995 | ||||||||
\(188\) | 2.45796 | 0.179265 | ||||||||
\(189\) | 4.72769 | 0.343889 | ||||||||
\(190\) | 43.6978 | 3.17017 | ||||||||
\(191\) | −5.04833 | −0.365284 | −0.182642 | − | 0.983179i | \(-0.558465\pi\) | ||||
−0.182642 | + | 0.983179i | \(0.558465\pi\) | |||||||
\(192\) | −2.66143 | −0.192072 | ||||||||
\(193\) | −11.0035 | −0.792049 | −0.396024 | − | 0.918240i | \(-0.629610\pi\) | ||||
−0.396024 | + | 0.918240i | \(0.629610\pi\) | |||||||
\(194\) | −18.0168 | −1.29353 | ||||||||
\(195\) | 26.6889 | 1.91123 | ||||||||
\(196\) | 12.4445 | 0.888893 | ||||||||
\(197\) | 18.2973 | 1.30363 | 0.651813 | − | 0.758380i | \(-0.274009\pi\) | ||||
0.651813 | + | 0.758380i | \(0.274009\pi\) | |||||||
\(198\) | −10.6833 | −0.759230 | ||||||||
\(199\) | 3.98259 | 0.282319 | 0.141159 | − | 0.989987i | \(-0.454917\pi\) | ||||
0.141159 | + | 0.989987i | \(0.454917\pi\) | |||||||
\(200\) | 19.4248 | 1.37354 | ||||||||
\(201\) | 4.08227 | 0.287941 | ||||||||
\(202\) | 4.97070 | 0.349737 | ||||||||
\(203\) | 18.3466 | 1.28768 | ||||||||
\(204\) | 0.810659 | 0.0567575 | ||||||||
\(205\) | −25.4166 | −1.77518 | ||||||||
\(206\) | −6.36683 | −0.443598 | ||||||||
\(207\) | 5.35418 | 0.372141 | ||||||||
\(208\) | −34.5063 | −2.39258 | ||||||||
\(209\) | 43.2593 | 2.99231 | ||||||||
\(210\) | 30.4320 | 2.10001 | ||||||||
\(211\) | 19.0801 | 1.31353 | 0.656766 | − | 0.754095i | \(-0.271924\pi\) | ||||
0.656766 | + | 0.754095i | \(0.271924\pi\) | |||||||
\(212\) | −2.99546 | −0.205729 | ||||||||
\(213\) | 10.7630 | 0.737470 | ||||||||
\(214\) | 7.70929 | 0.526996 | ||||||||
\(215\) | −43.4656 | −2.96433 | ||||||||
\(216\) | −1.99393 | −0.135670 | ||||||||
\(217\) | 20.7073 | 1.40570 | ||||||||
\(218\) | −5.76506 | −0.390459 | ||||||||
\(219\) | −1.10125 | −0.0744154 | ||||||||
\(220\) | −19.8344 | −1.33723 | ||||||||
\(221\) | −6.95110 | −0.467581 | ||||||||
\(222\) | −2.37926 | −0.159685 | ||||||||
\(223\) | 13.1357 | 0.879630 | 0.439815 | − | 0.898088i | \(-0.355044\pi\) | ||||
0.439815 | + | 0.898088i | \(0.355044\pi\) | |||||||
\(224\) | −20.4924 | −1.36921 | ||||||||
\(225\) | 9.74196 | 0.649464 | ||||||||
\(226\) | −4.15785 | −0.276576 | ||||||||
\(227\) | −17.1471 | −1.13810 | −0.569048 | − | 0.822304i | \(-0.692688\pi\) | ||||
−0.569048 | + | 0.822304i | \(0.692688\pi\) | |||||||
\(228\) | −5.50321 | −0.364459 | ||||||||
\(229\) | −11.9431 | −0.789220 | −0.394610 | − | 0.918849i | \(-0.629120\pi\) | ||||
−0.394610 | + | 0.918849i | \(0.629120\pi\) | |||||||
\(230\) | 34.4647 | 2.27253 | ||||||||
\(231\) | 30.1267 | 1.98219 | ||||||||
\(232\) | −7.73777 | −0.508010 | ||||||||
\(233\) | −1.82958 | −0.119860 | −0.0599299 | − | 0.998203i | \(-0.519088\pi\) | ||||
−0.0599299 | + | 0.998203i | \(0.519088\pi\) | |||||||
\(234\) | −11.6535 | −0.761815 | ||||||||
\(235\) | −11.6416 | −0.759417 | ||||||||
\(236\) | −0.223927 | −0.0145764 | ||||||||
\(237\) | −1.00000 | −0.0649570 | ||||||||
\(238\) | −7.92599 | −0.513766 | ||||||||
\(239\) | 17.2064 | 1.11299 | 0.556495 | − | 0.830851i | \(-0.312146\pi\) | ||||
0.556495 | + | 0.830851i | \(0.312146\pi\) | |||||||
\(240\) | −19.0600 | −1.23032 | ||||||||
\(241\) | −6.89593 | −0.444206 | −0.222103 | − | 0.975023i | \(-0.571292\pi\) | ||||
−0.222103 | + | 0.975023i | \(0.571292\pi\) | |||||||
\(242\) | −49.6367 | −3.19077 | ||||||||
\(243\) | −1.00000 | −0.0641500 | ||||||||
\(244\) | 3.99303 | 0.255628 | ||||||||
\(245\) | −58.9409 | −3.76560 | ||||||||
\(246\) | 11.0980 | 0.707582 | ||||||||
\(247\) | 47.1879 | 3.00250 | ||||||||
\(248\) | −8.73341 | −0.554572 | ||||||||
\(249\) | 3.30768 | 0.209616 | ||||||||
\(250\) | 30.5239 | 1.93050 | ||||||||
\(251\) | −29.6853 | −1.87372 | −0.936860 | − | 0.349705i | \(-0.886282\pi\) | ||||
−0.936860 | + | 0.349705i | \(0.886282\pi\) | |||||||
\(252\) | −3.83255 | −0.241428 | ||||||||
\(253\) | 34.1189 | 2.14504 | ||||||||
\(254\) | −0.681298 | −0.0427484 | ||||||||
\(255\) | −3.83953 | −0.240440 | ||||||||
\(256\) | 16.6913 | 1.04320 | ||||||||
\(257\) | −3.05355 | −0.190475 | −0.0952375 | − | 0.995455i | \(-0.530361\pi\) | ||||
−0.0952375 | + | 0.995455i | \(0.530361\pi\) | |||||||
\(258\) | 18.9790 | 1.18158 | ||||||||
\(259\) | 6.70945 | 0.416905 | ||||||||
\(260\) | −21.6356 | −1.34178 | ||||||||
\(261\) | −3.88066 | −0.240207 | ||||||||
\(262\) | −30.6197 | −1.89169 | ||||||||
\(263\) | −5.81981 | −0.358865 | −0.179432 | − | 0.983770i | \(-0.557426\pi\) | ||||
−0.179432 | + | 0.983770i | \(0.557426\pi\) | |||||||
\(264\) | −12.7061 | −0.782007 | ||||||||
\(265\) | 14.1874 | 0.871524 | ||||||||
\(266\) | 53.8060 | 3.29906 | ||||||||
\(267\) | −9.92560 | −0.607437 | ||||||||
\(268\) | −3.30933 | −0.202150 | ||||||||
\(269\) | −2.35629 | −0.143666 | −0.0718328 | − | 0.997417i | \(-0.522885\pi\) | ||||
−0.0718328 | + | 0.997417i | \(0.522885\pi\) | |||||||
\(270\) | −6.43697 | −0.391742 | ||||||||
\(271\) | 29.5281 | 1.79370 | 0.896852 | − | 0.442330i | \(-0.145848\pi\) | ||||
0.896852 | + | 0.442330i | \(0.145848\pi\) | |||||||
\(272\) | 4.96415 | 0.300996 | ||||||||
\(273\) | 32.8627 | 1.98894 | ||||||||
\(274\) | 35.9268 | 2.17042 | ||||||||
\(275\) | 62.0795 | 3.74354 | ||||||||
\(276\) | −4.34041 | −0.261262 | ||||||||
\(277\) | −14.5426 | −0.873781 | −0.436890 | − | 0.899515i | \(-0.643920\pi\) | ||||
−0.436890 | + | 0.899515i | \(0.643920\pi\) | |||||||
\(278\) | 11.5318 | 0.691634 | ||||||||
\(279\) | −4.37999 | −0.262223 | ||||||||
\(280\) | 36.1941 | 2.16301 | ||||||||
\(281\) | −16.1433 | −0.963031 | −0.481515 | − | 0.876438i | \(-0.659913\pi\) | ||||
−0.481515 | + | 0.876438i | \(0.659913\pi\) | |||||||
\(282\) | 5.08324 | 0.302703 | ||||||||
\(283\) | −9.45035 | −0.561765 | −0.280882 | − | 0.959742i | \(-0.590627\pi\) | ||||
−0.280882 | + | 0.959742i | \(0.590627\pi\) | |||||||
\(284\) | −8.72514 | −0.517742 | ||||||||
\(285\) | 26.0648 | 1.54395 | ||||||||
\(286\) | −74.2608 | −4.39113 | ||||||||
\(287\) | −31.2961 | −1.84735 | ||||||||
\(288\) | 4.33454 | 0.255415 | ||||||||
\(289\) | 1.00000 | 0.0588235 | ||||||||
\(290\) | −24.9797 | −1.46686 | ||||||||
\(291\) | −10.7466 | −0.629979 | ||||||||
\(292\) | 0.892736 | 0.0522434 | ||||||||
\(293\) | 5.12156 | 0.299204 | 0.149602 | − | 0.988746i | \(-0.452201\pi\) | ||||
0.149602 | + | 0.988746i | \(0.452201\pi\) | |||||||
\(294\) | 25.7361 | 1.50096 | ||||||||
\(295\) | 1.06059 | 0.0617498 | ||||||||
\(296\) | −2.82975 | −0.164476 | ||||||||
\(297\) | −6.37239 | −0.369763 | ||||||||
\(298\) | −21.0112 | −1.21714 | ||||||||
\(299\) | 37.2174 | 2.15234 | ||||||||
\(300\) | −7.89741 | −0.455957 | ||||||||
\(301\) | −53.5202 | −3.08485 | ||||||||
\(302\) | −8.91526 | −0.513016 | ||||||||
\(303\) | 2.96492 | 0.170330 | ||||||||
\(304\) | −33.6994 | −1.93279 | ||||||||
\(305\) | −18.9122 | −1.08291 | ||||||||
\(306\) | 1.67650 | 0.0958392 | ||||||||
\(307\) | −13.2993 | −0.759028 | −0.379514 | − | 0.925186i | \(-0.623909\pi\) | ||||
−0.379514 | + | 0.925186i | \(0.623909\pi\) | |||||||
\(308\) | −24.4225 | −1.39160 | ||||||||
\(309\) | −3.79769 | −0.216043 | ||||||||
\(310\) | −28.1939 | −1.60131 | ||||||||
\(311\) | 7.15879 | 0.405938 | 0.202969 | − | 0.979185i | \(-0.434941\pi\) | ||||
0.202969 | + | 0.979185i | \(0.434941\pi\) | |||||||
\(312\) | −13.8600 | −0.784669 | ||||||||
\(313\) | −6.89071 | −0.389486 | −0.194743 | − | 0.980854i | \(-0.562387\pi\) | ||||
−0.194743 | + | 0.980854i | \(0.562387\pi\) | |||||||
\(314\) | −15.4745 | −0.873275 | ||||||||
\(315\) | 18.1521 | 1.02276 | ||||||||
\(316\) | 0.810659 | 0.0456031 | ||||||||
\(317\) | −21.4196 | −1.20304 | −0.601522 | − | 0.798856i | \(-0.705439\pi\) | ||||
−0.601522 | + | 0.798856i | \(0.705439\pi\) | |||||||
\(318\) | −6.19482 | −0.347388 | ||||||||
\(319\) | −24.7291 | −1.38456 | ||||||||
\(320\) | −10.2186 | −0.571239 | ||||||||
\(321\) | 4.59844 | 0.256660 | ||||||||
\(322\) | 42.4371 | 2.36493 | ||||||||
\(323\) | −6.78856 | −0.377725 | ||||||||
\(324\) | 0.810659 | 0.0450366 | ||||||||
\(325\) | 67.7173 | 3.75628 | ||||||||
\(326\) | 4.21740 | 0.233580 | ||||||||
\(327\) | −3.43875 | −0.190163 | ||||||||
\(328\) | 13.1993 | 0.728809 | ||||||||
\(329\) | −14.3346 | −0.790293 | ||||||||
\(330\) | −41.0189 | −2.25802 | ||||||||
\(331\) | 20.0992 | 1.10475 | 0.552375 | − | 0.833596i | \(-0.313722\pi\) | ||||
0.552375 | + | 0.833596i | \(0.313722\pi\) | |||||||
\(332\) | −2.68141 | −0.147161 | ||||||||
\(333\) | −1.41918 | −0.0777706 | ||||||||
\(334\) | 15.1434 | 0.828611 | ||||||||
\(335\) | 15.6740 | 0.856362 | ||||||||
\(336\) | −23.4690 | −1.28034 | ||||||||
\(337\) | 22.7664 | 1.24016 | 0.620082 | − | 0.784537i | \(-0.287099\pi\) | ||||
0.620082 | + | 0.784537i | \(0.287099\pi\) | |||||||
\(338\) | −59.2103 | −3.22062 | ||||||||
\(339\) | −2.48008 | −0.134699 | ||||||||
\(340\) | 3.11255 | 0.168802 | ||||||||
\(341\) | −27.9110 | −1.51147 | ||||||||
\(342\) | −11.3810 | −0.615416 | ||||||||
\(343\) | −39.4814 | −2.13179 | ||||||||
\(344\) | 22.5725 | 1.21703 | ||||||||
\(345\) | 20.5575 | 1.10678 | ||||||||
\(346\) | 33.0643 | 1.77755 | ||||||||
\(347\) | −17.6912 | −0.949712 | −0.474856 | − | 0.880063i | \(-0.657500\pi\) | ||||
−0.474856 | + | 0.880063i | \(0.657500\pi\) | |||||||
\(348\) | 3.14589 | 0.168638 | ||||||||
\(349\) | 5.42603 | 0.290449 | 0.145224 | − | 0.989399i | \(-0.453610\pi\) | ||||
0.145224 | + | 0.989399i | \(0.453610\pi\) | |||||||
\(350\) | 77.2147 | 4.12730 | ||||||||
\(351\) | −6.95110 | −0.371022 | ||||||||
\(352\) | 27.6214 | 1.47222 | ||||||||
\(353\) | 0.406109 | 0.0216150 | 0.0108075 | − | 0.999942i | \(-0.496560\pi\) | ||||
0.0108075 | + | 0.999942i | \(0.496560\pi\) | |||||||
\(354\) | −0.463098 | −0.0246134 | ||||||||
\(355\) | 41.3249 | 2.19330 | ||||||||
\(356\) | 8.04628 | 0.426452 | ||||||||
\(357\) | −4.72769 | −0.250216 | ||||||||
\(358\) | 16.7119 | 0.883253 | ||||||||
\(359\) | −36.9440 | −1.94983 | −0.974915 | − | 0.222576i | \(-0.928554\pi\) | ||||
−0.974915 | + | 0.222576i | \(0.928554\pi\) | |||||||
\(360\) | −7.65575 | −0.403494 | ||||||||
\(361\) | 27.0845 | 1.42550 | ||||||||
\(362\) | −28.8513 | −1.51639 | ||||||||
\(363\) | −29.6073 | −1.55398 | ||||||||
\(364\) | −26.6404 | −1.39634 | ||||||||
\(365\) | −4.22827 | −0.221318 | ||||||||
\(366\) | 8.25787 | 0.431646 | ||||||||
\(367\) | −11.3105 | −0.590406 | −0.295203 | − | 0.955435i | \(-0.595387\pi\) | ||||
−0.295203 | + | 0.955435i | \(0.595387\pi\) | |||||||
\(368\) | −26.5789 | −1.38552 | ||||||||
\(369\) | 6.61973 | 0.344610 | ||||||||
\(370\) | −9.13523 | −0.474918 | ||||||||
\(371\) | 17.4692 | 0.906957 | ||||||||
\(372\) | 3.55068 | 0.184094 | ||||||||
\(373\) | −31.0020 | −1.60523 | −0.802613 | − | 0.596501i | \(-0.796557\pi\) | ||||
−0.802613 | + | 0.596501i | \(0.796557\pi\) | |||||||
\(374\) | 10.6833 | 0.552421 | ||||||||
\(375\) | 18.2069 | 0.940199 | ||||||||
\(376\) | 6.04571 | 0.311784 | ||||||||
\(377\) | −26.9748 | −1.38928 | ||||||||
\(378\) | −7.92599 | −0.407669 | ||||||||
\(379\) | 37.7767 | 1.94046 | 0.970230 | − | 0.242187i | \(-0.0778648\pi\) | ||||
0.970230 | + | 0.242187i | \(0.0778648\pi\) | |||||||
\(380\) | −21.1297 | −1.08393 | ||||||||
\(381\) | −0.406380 | −0.0208195 | ||||||||
\(382\) | 8.46353 | 0.433032 | ||||||||
\(383\) | 31.6180 | 1.61560 | 0.807802 | − | 0.589454i | \(-0.200657\pi\) | ||||
0.807802 | + | 0.589454i | \(0.200657\pi\) | |||||||
\(384\) | 13.1310 | 0.670087 | ||||||||
\(385\) | 115.672 | 5.89520 | ||||||||
\(386\) | 18.4474 | 0.938947 | ||||||||
\(387\) | 11.3206 | 0.575457 | ||||||||
\(388\) | 8.71186 | 0.442278 | ||||||||
\(389\) | −3.85735 | −0.195576 | −0.0977878 | − | 0.995207i | \(-0.531177\pi\) | ||||
−0.0977878 | + | 0.995207i | \(0.531177\pi\) | |||||||
\(390\) | −44.7440 | −2.26570 | ||||||||
\(391\) | −5.35418 | −0.270772 | ||||||||
\(392\) | 30.6090 | 1.54599 | ||||||||
\(393\) | −18.2641 | −0.921300 | ||||||||
\(394\) | −30.6754 | −1.54540 | ||||||||
\(395\) | −3.83953 | −0.193188 | ||||||||
\(396\) | 5.16583 | 0.259593 | ||||||||
\(397\) | −32.8523 | −1.64881 | −0.824404 | − | 0.566002i | \(-0.808490\pi\) | ||||
−0.824404 | + | 0.566002i | \(0.808490\pi\) | |||||||
\(398\) | −6.67683 | −0.334679 | ||||||||
\(399\) | 32.0942 | 1.60672 | ||||||||
\(400\) | −48.3606 | −2.41803 | ||||||||
\(401\) | 19.8461 | 0.991066 | 0.495533 | − | 0.868589i | \(-0.334973\pi\) | ||||
0.495533 | + | 0.868589i | \(0.334973\pi\) | |||||||
\(402\) | −6.84394 | −0.341345 | ||||||||
\(403\) | −30.4458 | −1.51661 | ||||||||
\(404\) | −2.40354 | −0.119581 | ||||||||
\(405\) | −3.83953 | −0.190788 | ||||||||
\(406\) | −30.7581 | −1.52650 | ||||||||
\(407\) | −9.04357 | −0.448273 | ||||||||
\(408\) | 1.99393 | 0.0987144 | ||||||||
\(409\) | 15.7146 | 0.777036 | 0.388518 | − | 0.921441i | \(-0.372987\pi\) | ||||
0.388518 | + | 0.921441i | \(0.372987\pi\) | |||||||
\(410\) | 42.6110 | 2.10441 | ||||||||
\(411\) | 21.4296 | 1.05705 | ||||||||
\(412\) | 3.07863 | 0.151673 | ||||||||
\(413\) | 1.30592 | 0.0642603 | ||||||||
\(414\) | −8.97629 | −0.441161 | ||||||||
\(415\) | 12.6999 | 0.623416 | ||||||||
\(416\) | 30.1298 | 1.47724 | ||||||||
\(417\) | 6.87852 | 0.336842 | ||||||||
\(418\) | −72.5243 | −3.54728 | ||||||||
\(419\) | 2.73740 | 0.133731 | 0.0668655 | − | 0.997762i | \(-0.478700\pi\) | ||||
0.0668655 | + | 0.997762i | \(0.478700\pi\) | |||||||
\(420\) | −14.7152 | −0.718027 | ||||||||
\(421\) | −27.3254 | −1.33176 | −0.665879 | − | 0.746060i | \(-0.731943\pi\) | ||||
−0.665879 | + | 0.746060i | \(0.731943\pi\) | |||||||
\(422\) | −31.9879 | −1.55715 | ||||||||
\(423\) | 3.03205 | 0.147423 | ||||||||
\(424\) | −7.36775 | −0.357810 | ||||||||
\(425\) | −9.74196 | −0.472554 | ||||||||
\(426\) | −18.0442 | −0.874245 | ||||||||
\(427\) | −23.2870 | −1.12694 | ||||||||
\(428\) | −3.72777 | −0.180188 | ||||||||
\(429\) | −44.2951 | −2.13859 | ||||||||
\(430\) | 72.8702 | 3.51412 | ||||||||
\(431\) | −11.5588 | −0.556770 | −0.278385 | − | 0.960470i | \(-0.589799\pi\) | ||||
−0.278385 | + | 0.960470i | \(0.589799\pi\) | |||||||
\(432\) | 4.96415 | 0.238838 | ||||||||
\(433\) | −18.3469 | −0.881695 | −0.440848 | − | 0.897582i | \(-0.645322\pi\) | ||||
−0.440848 | + | 0.897582i | \(0.645322\pi\) | |||||||
\(434\) | −34.7158 | −1.66641 | ||||||||
\(435\) | −14.8999 | −0.714395 | ||||||||
\(436\) | 2.78765 | 0.133504 | ||||||||
\(437\) | 36.3471 | 1.73872 | ||||||||
\(438\) | 1.84624 | 0.0882169 | ||||||||
\(439\) | 0.900201 | 0.0429643 | 0.0214821 | − | 0.999769i | \(-0.493161\pi\) | ||||
0.0214821 | + | 0.999769i | \(0.493161\pi\) | |||||||
\(440\) | −48.7854 | −2.32575 | ||||||||
\(441\) | 15.3511 | 0.731004 | ||||||||
\(442\) | 11.6535 | 0.554302 | ||||||||
\(443\) | −0.0573528 | −0.00272491 | −0.00136246 | − | 0.999999i | \(-0.500434\pi\) | ||||
−0.00136246 | + | 0.999999i | \(0.500434\pi\) | |||||||
\(444\) | 1.15047 | 0.0545990 | ||||||||
\(445\) | −38.1096 | −1.80657 | ||||||||
\(446\) | −22.0220 | −1.04277 | ||||||||
\(447\) | −12.5327 | −0.592778 | ||||||||
\(448\) | −12.5824 | −0.594463 | ||||||||
\(449\) | 33.9099 | 1.60030 | 0.800152 | − | 0.599797i | \(-0.204752\pi\) | ||||
0.800152 | + | 0.599797i | \(0.204752\pi\) | |||||||
\(450\) | −16.3324 | −0.769918 | ||||||||
\(451\) | 42.1835 | 1.98634 | ||||||||
\(452\) | 2.01050 | 0.0945658 | ||||||||
\(453\) | −5.31777 | −0.249851 | ||||||||
\(454\) | 28.7472 | 1.34917 | ||||||||
\(455\) | 126.177 | 5.91527 | ||||||||
\(456\) | −13.5359 | −0.633878 | ||||||||
\(457\) | −40.9848 | −1.91719 | −0.958594 | − | 0.284777i | \(-0.908081\pi\) | ||||
−0.958594 | + | 0.284777i | \(0.908081\pi\) | |||||||
\(458\) | 20.0226 | 0.935594 | ||||||||
\(459\) | 1.00000 | 0.0466760 | ||||||||
\(460\) | −16.6651 | −0.777016 | ||||||||
\(461\) | −19.8599 | −0.924967 | −0.462484 | − | 0.886628i | \(-0.653042\pi\) | ||||
−0.462484 | + | 0.886628i | \(0.653042\pi\) | |||||||
\(462\) | −50.5075 | −2.34982 | ||||||||
\(463\) | −14.5222 | −0.674902 | −0.337451 | − | 0.941343i | \(-0.609565\pi\) | ||||
−0.337451 | + | 0.941343i | \(0.609565\pi\) | |||||||
\(464\) | 19.2642 | 0.894317 | ||||||||
\(465\) | −16.8171 | −0.779874 | ||||||||
\(466\) | 3.06730 | 0.142090 | ||||||||
\(467\) | 32.6267 | 1.50978 | 0.754891 | − | 0.655850i | \(-0.227690\pi\) | ||||
0.754891 | + | 0.655850i | \(0.227690\pi\) | |||||||
\(468\) | 5.63497 | 0.260477 | ||||||||
\(469\) | 19.2997 | 0.891179 | ||||||||
\(470\) | 19.5172 | 0.900263 | ||||||||
\(471\) | −9.23022 | −0.425306 | ||||||||
\(472\) | −0.550781 | −0.0253518 | ||||||||
\(473\) | 72.1391 | 3.31696 | ||||||||
\(474\) | 1.67650 | 0.0770043 | ||||||||
\(475\) | 66.1338 | 3.03443 | ||||||||
\(476\) | 3.83255 | 0.175665 | ||||||||
\(477\) | −3.69509 | −0.169186 | ||||||||
\(478\) | −28.8466 | −1.31941 | ||||||||
\(479\) | 32.7846 | 1.49797 | 0.748984 | − | 0.662589i | \(-0.230542\pi\) | ||||
0.748984 | + | 0.662589i | \(0.230542\pi\) | |||||||
\(480\) | 16.6426 | 0.759627 | ||||||||
\(481\) | −9.86487 | −0.449799 | ||||||||
\(482\) | 11.5610 | 0.526591 | ||||||||
\(483\) | 25.3129 | 1.15178 | ||||||||
\(484\) | 24.0014 | 1.09097 | ||||||||
\(485\) | −41.2620 | −1.87361 | ||||||||
\(486\) | 1.67650 | 0.0760477 | ||||||||
\(487\) | 23.7069 | 1.07426 | 0.537130 | − | 0.843499i | \(-0.319508\pi\) | ||||
0.537130 | + | 0.843499i | \(0.319508\pi\) | |||||||
\(488\) | 9.82143 | 0.444595 | ||||||||
\(489\) | 2.51559 | 0.113759 | ||||||||
\(490\) | 98.8145 | 4.46399 | ||||||||
\(491\) | 9.44727 | 0.426349 | 0.213175 | − | 0.977014i | \(-0.431620\pi\) | ||||
0.213175 | + | 0.977014i | \(0.431620\pi\) | |||||||
\(492\) | −5.36635 | −0.241934 | ||||||||
\(493\) | 3.88066 | 0.174776 | ||||||||
\(494\) | −79.1106 | −3.55936 | ||||||||
\(495\) | −24.4669 | −1.09971 | ||||||||
\(496\) | 21.7429 | 0.976287 | ||||||||
\(497\) | 50.8842 | 2.28247 | ||||||||
\(498\) | −5.54534 | −0.248493 | ||||||||
\(499\) | 6.44483 | 0.288510 | 0.144255 | − | 0.989541i | \(-0.453921\pi\) | ||||
0.144255 | + | 0.989541i | \(0.453921\pi\) | |||||||
\(500\) | −14.7596 | −0.660068 | ||||||||
\(501\) | 9.03274 | 0.403553 | ||||||||
\(502\) | 49.7675 | 2.22123 | ||||||||
\(503\) | 2.88139 | 0.128475 | 0.0642373 | − | 0.997935i | \(-0.479539\pi\) | ||||
0.0642373 | + | 0.997935i | \(0.479539\pi\) | |||||||
\(504\) | −9.42670 | −0.419899 | ||||||||
\(505\) | 11.3839 | 0.506577 | ||||||||
\(506\) | −57.2004 | −2.54287 | ||||||||
\(507\) | −35.3178 | −1.56852 | ||||||||
\(508\) | 0.329436 | 0.0146164 | ||||||||
\(509\) | 6.19045 | 0.274387 | 0.137193 | − | 0.990544i | \(-0.456192\pi\) | ||||
0.137193 | + | 0.990544i | \(0.456192\pi\) | |||||||
\(510\) | 6.43697 | 0.285034 | ||||||||
\(511\) | −5.20636 | −0.230316 | ||||||||
\(512\) | −1.72097 | −0.0760567 | ||||||||
\(513\) | −6.78856 | −0.299722 | ||||||||
\(514\) | 5.11928 | 0.225802 | ||||||||
\(515\) | −14.5813 | −0.642530 | ||||||||
\(516\) | −9.17713 | −0.404001 | ||||||||
\(517\) | 19.3214 | 0.849755 | ||||||||
\(518\) | −11.2484 | −0.494227 | ||||||||
\(519\) | 19.7222 | 0.865708 | ||||||||
\(520\) | −53.2159 | −2.33367 | ||||||||
\(521\) | 29.6116 | 1.29731 | 0.648655 | − | 0.761083i | \(-0.275332\pi\) | ||||
0.648655 | + | 0.761083i | \(0.275332\pi\) | |||||||
\(522\) | 6.50593 | 0.284757 | ||||||||
\(523\) | −18.8165 | −0.822787 | −0.411393 | − | 0.911458i | \(-0.634958\pi\) | ||||
−0.411393 | + | 0.911458i | \(0.634958\pi\) | |||||||
\(524\) | 14.8059 | 0.646800 | ||||||||
\(525\) | 46.0570 | 2.01009 | ||||||||
\(526\) | 9.75692 | 0.425422 | ||||||||
\(527\) | 4.37999 | 0.190795 | ||||||||
\(528\) | 31.6335 | 1.37667 | ||||||||
\(529\) | 5.66721 | 0.246400 | ||||||||
\(530\) | −23.7852 | −1.03316 | ||||||||
\(531\) | −0.276229 | −0.0119873 | ||||||||
\(532\) | −26.0175 | −1.12800 | ||||||||
\(533\) | 46.0144 | 1.99311 | ||||||||
\(534\) | 16.6403 | 0.720096 | ||||||||
\(535\) | 17.6558 | 0.763328 | ||||||||
\(536\) | −8.13977 | −0.351585 | ||||||||
\(537\) | 9.96833 | 0.430165 | ||||||||
\(538\) | 3.95033 | 0.170311 | ||||||||
\(539\) | 97.8231 | 4.21354 | ||||||||
\(540\) | 3.11255 | 0.133943 | ||||||||
\(541\) | −11.9511 | −0.513819 | −0.256910 | − | 0.966435i | \(-0.582704\pi\) | ||||
−0.256910 | + | 0.966435i | \(0.582704\pi\) | |||||||
\(542\) | −49.5039 | −2.12638 | ||||||||
\(543\) | −17.2092 | −0.738518 | ||||||||
\(544\) | −4.33454 | −0.185842 | ||||||||
\(545\) | −13.2032 | −0.565561 | ||||||||
\(546\) | −55.0943 | −2.35782 | ||||||||
\(547\) | 2.57315 | 0.110020 | 0.0550100 | − | 0.998486i | \(-0.482481\pi\) | ||||
0.0550100 | + | 0.998486i | \(0.482481\pi\) | |||||||
\(548\) | −17.3721 | −0.742101 | ||||||||
\(549\) | 4.92566 | 0.210222 | ||||||||
\(550\) | −104.076 | −4.43784 | ||||||||
\(551\) | −26.3441 | −1.12230 | ||||||||
\(552\) | −10.6759 | −0.454395 | ||||||||
\(553\) | −4.72769 | −0.201042 | ||||||||
\(554\) | 24.3807 | 1.03584 | ||||||||
\(555\) | −5.44898 | −0.231296 | ||||||||
\(556\) | −5.57613 | −0.236481 | ||||||||
\(557\) | 27.6812 | 1.17289 | 0.586446 | − | 0.809988i | \(-0.300527\pi\) | ||||
0.586446 | + | 0.809988i | \(0.300527\pi\) | |||||||
\(558\) | 7.34307 | 0.310857 | ||||||||
\(559\) | 78.6904 | 3.32825 | ||||||||
\(560\) | −90.1098 | −3.80783 | ||||||||
\(561\) | 6.37239 | 0.269042 | ||||||||
\(562\) | 27.0643 | 1.14164 | ||||||||
\(563\) | 25.1911 | 1.06168 | 0.530840 | − | 0.847472i | \(-0.321877\pi\) | ||||
0.530840 | + | 0.847472i | \(0.321877\pi\) | |||||||
\(564\) | −2.45796 | −0.103499 | ||||||||
\(565\) | −9.52232 | −0.400607 | ||||||||
\(566\) | 15.8435 | 0.665953 | ||||||||
\(567\) | −4.72769 | −0.198544 | ||||||||
\(568\) | −21.4607 | −0.900472 | ||||||||
\(569\) | 14.4312 | 0.604986 | 0.302493 | − | 0.953152i | \(-0.402181\pi\) | ||||
0.302493 | + | 0.953152i | \(0.402181\pi\) | |||||||
\(570\) | −43.6978 | −1.83030 | ||||||||
\(571\) | 23.9711 | 1.00316 | 0.501581 | − | 0.865111i | \(-0.332752\pi\) | ||||
0.501581 | + | 0.865111i | \(0.332752\pi\) | |||||||
\(572\) | 35.9082 | 1.50140 | ||||||||
\(573\) | 5.04833 | 0.210897 | ||||||||
\(574\) | 52.4679 | 2.18997 | ||||||||
\(575\) | 52.1602 | 2.17523 | ||||||||
\(576\) | 2.66143 | 0.110893 | ||||||||
\(577\) | −3.12979 | −0.130295 | −0.0651475 | − | 0.997876i | \(-0.520752\pi\) | ||||
−0.0651475 | + | 0.997876i | \(0.520752\pi\) | |||||||
\(578\) | −1.67650 | −0.0697333 | ||||||||
\(579\) | 11.0035 | 0.457290 | ||||||||
\(580\) | 12.0787 | 0.501542 | ||||||||
\(581\) | 15.6377 | 0.648762 | ||||||||
\(582\) | 18.0168 | 0.746819 | ||||||||
\(583\) | −23.5465 | −0.975197 | ||||||||
\(584\) | 2.19581 | 0.0908633 | ||||||||
\(585\) | −26.6889 | −1.10345 | ||||||||
\(586\) | −8.58630 | −0.354697 | ||||||||
\(587\) | −13.5379 | −0.558768 | −0.279384 | − | 0.960180i | \(-0.590130\pi\) | ||||
−0.279384 | + | 0.960180i | \(0.590130\pi\) | |||||||
\(588\) | −12.4445 | −0.513203 | ||||||||
\(589\) | −29.7338 | −1.22516 | ||||||||
\(590\) | −1.77808 | −0.0732022 | ||||||||
\(591\) | −18.2973 | −0.752649 | ||||||||
\(592\) | 7.04503 | 0.289549 | ||||||||
\(593\) | 9.33997 | 0.383546 | 0.191773 | − | 0.981439i | \(-0.438576\pi\) | ||||
0.191773 | + | 0.981439i | \(0.438576\pi\) | |||||||
\(594\) | 10.6833 | 0.438342 | ||||||||
\(595\) | −18.1521 | −0.744164 | ||||||||
\(596\) | 10.1598 | 0.416161 | ||||||||
\(597\) | −3.98259 | −0.162997 | ||||||||
\(598\) | −62.3951 | −2.55152 | ||||||||
\(599\) | 24.2391 | 0.990382 | 0.495191 | − | 0.868784i | \(-0.335098\pi\) | ||||
0.495191 | + | 0.868784i | \(0.335098\pi\) | |||||||
\(600\) | −19.4248 | −0.793014 | ||||||||
\(601\) | −18.4338 | −0.751932 | −0.375966 | − | 0.926634i | \(-0.622689\pi\) | ||||
−0.375966 | + | 0.926634i | \(0.622689\pi\) | |||||||
\(602\) | 89.7267 | 3.65699 | ||||||||
\(603\) | −4.08227 | −0.166243 | ||||||||
\(604\) | 4.31090 | 0.175408 | ||||||||
\(605\) | −113.678 | −4.62167 | ||||||||
\(606\) | −4.97070 | −0.201921 | ||||||||
\(607\) | 29.5438 | 1.19914 | 0.599572 | − | 0.800321i | \(-0.295338\pi\) | ||||
0.599572 | + | 0.800321i | \(0.295338\pi\) | |||||||
\(608\) | 29.4253 | 1.19335 | ||||||||
\(609\) | −18.3466 | −0.743440 | ||||||||
\(610\) | 31.7063 | 1.28375 | ||||||||
\(611\) | 21.0761 | 0.852648 | ||||||||
\(612\) | −0.810659 | −0.0327690 | ||||||||
\(613\) | −12.4238 | −0.501794 | −0.250897 | − | 0.968014i | \(-0.580726\pi\) | ||||
−0.250897 | + | 0.968014i | \(0.580726\pi\) | |||||||
\(614\) | 22.2962 | 0.899802 | ||||||||
\(615\) | 25.4166 | 1.02490 | ||||||||
\(616\) | −60.0706 | −2.42031 | ||||||||
\(617\) | −20.7760 | −0.836409 | −0.418205 | − | 0.908353i | \(-0.637341\pi\) | ||||
−0.418205 | + | 0.908353i | \(0.637341\pi\) | |||||||
\(618\) | 6.36683 | 0.256112 | ||||||||
\(619\) | −7.95561 | −0.319763 | −0.159882 | − | 0.987136i | \(-0.551111\pi\) | ||||
−0.159882 | + | 0.987136i | \(0.551111\pi\) | |||||||
\(620\) | 13.6329 | 0.547512 | ||||||||
\(621\) | −5.35418 | −0.214856 | ||||||||
\(622\) | −12.0017 | −0.481226 | ||||||||
\(623\) | −46.9252 | −1.88002 | ||||||||
\(624\) | 34.5063 | 1.38136 | ||||||||
\(625\) | 21.1960 | 0.847840 | ||||||||
\(626\) | 11.5523 | 0.461722 | ||||||||
\(627\) | −43.2593 | −1.72761 | ||||||||
\(628\) | 7.48256 | 0.298587 | ||||||||
\(629\) | 1.41918 | 0.0565865 | ||||||||
\(630\) | −30.4320 | −1.21244 | ||||||||
\(631\) | 7.35370 | 0.292746 | 0.146373 | − | 0.989229i | \(-0.453240\pi\) | ||||
0.146373 | + | 0.989229i | \(0.453240\pi\) | |||||||
\(632\) | 1.99393 | 0.0793144 | ||||||||
\(633\) | −19.0801 | −0.758368 | ||||||||
\(634\) | 35.9100 | 1.42617 | ||||||||
\(635\) | −1.56031 | −0.0619189 | ||||||||
\(636\) | 2.99546 | 0.118778 | ||||||||
\(637\) | 106.707 | 4.22788 | ||||||||
\(638\) | 41.4583 | 1.64135 | ||||||||
\(639\) | −10.7630 | −0.425778 | ||||||||
\(640\) | 50.4167 | 1.99290 | ||||||||
\(641\) | −23.9838 | −0.947302 | −0.473651 | − | 0.880713i | \(-0.657064\pi\) | ||||
−0.473651 | + | 0.880713i | \(0.657064\pi\) | |||||||
\(642\) | −7.70929 | −0.304262 | ||||||||
\(643\) | 39.8466 | 1.57140 | 0.785698 | − | 0.618610i | \(-0.212304\pi\) | ||||
0.785698 | + | 0.618610i | \(0.212304\pi\) | |||||||
\(644\) | −20.5201 | −0.808607 | ||||||||
\(645\) | 43.4656 | 1.71146 | ||||||||
\(646\) | 11.3810 | 0.447781 | ||||||||
\(647\) | −23.7285 | −0.932863 | −0.466432 | − | 0.884557i | \(-0.654461\pi\) | ||||
−0.466432 | + | 0.884557i | \(0.654461\pi\) | |||||||
\(648\) | 1.99393 | 0.0783291 | ||||||||
\(649\) | −1.76024 | −0.0690953 | ||||||||
\(650\) | −113.528 | −4.45294 | ||||||||
\(651\) | −20.7073 | −0.811582 | ||||||||
\(652\) | −2.03929 | −0.0798648 | ||||||||
\(653\) | 18.3307 | 0.717337 | 0.358669 | − | 0.933465i | \(-0.383231\pi\) | ||||
0.358669 | + | 0.933465i | \(0.383231\pi\) | |||||||
\(654\) | 5.76506 | 0.225432 | ||||||||
\(655\) | −70.1253 | −2.74002 | ||||||||
\(656\) | −32.8614 | −1.28302 | ||||||||
\(657\) | 1.10125 | 0.0429637 | ||||||||
\(658\) | 24.0320 | 0.936865 | ||||||||
\(659\) | 1.28907 | 0.0502151 | 0.0251075 | − | 0.999685i | \(-0.492007\pi\) | ||||
0.0251075 | + | 0.999685i | \(0.492007\pi\) | |||||||
\(660\) | 19.8344 | 0.772051 | ||||||||
\(661\) | 9.08212 | 0.353254 | 0.176627 | − | 0.984278i | \(-0.443481\pi\) | ||||
0.176627 | + | 0.984278i | \(0.443481\pi\) | |||||||
\(662\) | −33.6963 | −1.30964 | ||||||||
\(663\) | 6.95110 | 0.269958 | ||||||||
\(664\) | −6.59530 | −0.255947 | ||||||||
\(665\) | 123.227 | 4.77852 | ||||||||
\(666\) | 2.37926 | 0.0921944 | ||||||||
\(667\) | −20.7777 | −0.804517 | ||||||||
\(668\) | −7.32248 | −0.283315 | ||||||||
\(669\) | −13.1357 | −0.507855 | ||||||||
\(670\) | −26.2775 | −1.01519 | ||||||||
\(671\) | 31.3882 | 1.21173 | ||||||||
\(672\) | 20.4924 | 0.790511 | ||||||||
\(673\) | 2.47132 | 0.0952624 | 0.0476312 | − | 0.998865i | \(-0.484833\pi\) | ||||
0.0476312 | + | 0.998865i | \(0.484833\pi\) | |||||||
\(674\) | −38.1679 | −1.47017 | ||||||||
\(675\) | −9.74196 | −0.374968 | ||||||||
\(676\) | 28.6307 | 1.10118 | ||||||||
\(677\) | 0.0788017 | 0.00302860 | 0.00151430 | − | 0.999999i | \(-0.499518\pi\) | ||||
0.00151430 | + | 0.999999i | \(0.499518\pi\) | |||||||
\(678\) | 4.15785 | 0.159681 | ||||||||
\(679\) | −50.8068 | −1.94979 | ||||||||
\(680\) | 7.65575 | 0.293585 | ||||||||
\(681\) | 17.1471 | 0.657080 | ||||||||
\(682\) | 46.7929 | 1.79179 | ||||||||
\(683\) | −49.1204 | −1.87954 | −0.939770 | − | 0.341806i | \(-0.888961\pi\) | ||||
−0.939770 | + | 0.341806i | \(0.888961\pi\) | |||||||
\(684\) | 5.50321 | 0.210420 | ||||||||
\(685\) | 82.2797 | 3.14374 | ||||||||
\(686\) | 66.1906 | 2.52717 | ||||||||
\(687\) | 11.9431 | 0.455656 | ||||||||
\(688\) | −56.1970 | −2.14249 | ||||||||
\(689\) | −25.6849 | −0.978517 | ||||||||
\(690\) | −34.4647 | −1.31205 | ||||||||
\(691\) | −1.60298 | −0.0609802 | −0.0304901 | − | 0.999535i | \(-0.509707\pi\) | ||||
−0.0304901 | + | 0.999535i | \(0.509707\pi\) | |||||||
\(692\) | −15.9880 | −0.607771 | ||||||||
\(693\) | −30.1267 | −1.14442 | ||||||||
\(694\) | 29.6593 | 1.12585 | ||||||||
\(695\) | 26.4102 | 1.00180 | ||||||||
\(696\) | 7.73777 | 0.293299 | ||||||||
\(697\) | −6.61973 | −0.250740 | ||||||||
\(698\) | −9.09675 | −0.344317 | ||||||||
\(699\) | 1.82958 | 0.0692011 | ||||||||
\(700\) | −37.3365 | −1.41119 | ||||||||
\(701\) | −30.6068 | −1.15600 | −0.578001 | − | 0.816036i | \(-0.696167\pi\) | ||||
−0.578001 | + | 0.816036i | \(0.696167\pi\) | |||||||
\(702\) | 11.6535 | 0.439834 | ||||||||
\(703\) | −9.63419 | −0.363360 | ||||||||
\(704\) | 16.9597 | 0.639191 | ||||||||
\(705\) | 11.6416 | 0.438450 | ||||||||
\(706\) | −0.680843 | −0.0256239 | ||||||||
\(707\) | 14.0172 | 0.527173 | ||||||||
\(708\) | 0.223927 | 0.00841570 | ||||||||
\(709\) | −21.8444 | −0.820385 | −0.410193 | − | 0.911999i | \(-0.634538\pi\) | ||||
−0.410193 | + | 0.911999i | \(0.634538\pi\) | |||||||
\(710\) | −69.2812 | −2.60008 | ||||||||
\(711\) | 1.00000 | 0.0375029 | ||||||||
\(712\) | 19.7910 | 0.741698 | ||||||||
\(713\) | −23.4513 | −0.878256 | ||||||||
\(714\) | 7.92599 | 0.296623 | ||||||||
\(715\) | −170.072 | −6.36034 | ||||||||
\(716\) | −8.08092 | −0.301998 | ||||||||
\(717\) | −17.2064 | −0.642585 | ||||||||
\(718\) | 61.9367 | 2.31146 | ||||||||
\(719\) | −29.7035 | −1.10775 | −0.553877 | − | 0.832598i | \(-0.686852\pi\) | ||||
−0.553877 | + | 0.832598i | \(0.686852\pi\) | |||||||
\(720\) | 19.0600 | 0.710324 | ||||||||
\(721\) | −17.9543 | −0.668653 | ||||||||
\(722\) | −45.4072 | −1.68988 | ||||||||
\(723\) | 6.89593 | 0.256462 | ||||||||
\(724\) | 13.9508 | 0.518478 | ||||||||
\(725\) | −37.8052 | −1.40405 | ||||||||
\(726\) | 49.6367 | 1.84219 | ||||||||
\(727\) | −5.55713 | −0.206103 | −0.103051 | − | 0.994676i | \(-0.532861\pi\) | ||||
−0.103051 | + | 0.994676i | \(0.532861\pi\) | |||||||
\(728\) | −65.5259 | −2.42855 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | 7.08870 | 0.262364 | ||||||||
\(731\) | −11.3206 | −0.418707 | ||||||||
\(732\) | −3.99303 | −0.147587 | ||||||||
\(733\) | −12.8972 | −0.476368 | −0.238184 | − | 0.971220i | \(-0.576552\pi\) | ||||
−0.238184 | + | 0.971220i | \(0.576552\pi\) | |||||||
\(734\) | 18.9622 | 0.699906 | ||||||||
\(735\) | 58.9409 | 2.17407 | ||||||||
\(736\) | 23.2079 | 0.855455 | ||||||||
\(737\) | −26.0138 | −0.958231 | ||||||||
\(738\) | −11.0980 | −0.408523 | ||||||||
\(739\) | −18.9291 | −0.696319 | −0.348159 | − | 0.937435i | \(-0.613193\pi\) | ||||
−0.348159 | + | 0.937435i | \(0.613193\pi\) | |||||||
\(740\) | 4.41727 | 0.162382 | ||||||||
\(741\) | −47.1879 | −1.73349 | ||||||||
\(742\) | −29.2872 | −1.07517 | ||||||||
\(743\) | 21.2235 | 0.778616 | 0.389308 | − | 0.921108i | \(-0.372714\pi\) | ||||
0.389308 | + | 0.921108i | \(0.372714\pi\) | |||||||
\(744\) | 8.73341 | 0.320182 | ||||||||
\(745\) | −48.1198 | −1.76297 | ||||||||
\(746\) | 51.9750 | 1.90294 | ||||||||
\(747\) | −3.30768 | −0.121022 | ||||||||
\(748\) | −5.16583 | −0.188882 | ||||||||
\(749\) | 21.7400 | 0.794363 | ||||||||
\(750\) | −30.5239 | −1.11457 | ||||||||
\(751\) | 13.0781 | 0.477227 | 0.238613 | − | 0.971115i | \(-0.423307\pi\) | ||||
0.238613 | + | 0.971115i | \(0.423307\pi\) | |||||||
\(752\) | −15.0516 | −0.548874 | ||||||||
\(753\) | 29.6853 | 1.08179 | ||||||||
\(754\) | 45.2234 | 1.64694 | ||||||||
\(755\) | −20.4177 | −0.743077 | ||||||||
\(756\) | 3.83255 | 0.139388 | ||||||||
\(757\) | 22.0581 | 0.801715 | 0.400857 | − | 0.916140i | \(-0.368712\pi\) | ||||
0.400857 | + | 0.916140i | \(0.368712\pi\) | |||||||
\(758\) | −63.3327 | −2.30035 | ||||||||
\(759\) | −34.1189 | −1.23844 | ||||||||
\(760\) | −51.9715 | −1.88521 | ||||||||
\(761\) | 14.2847 | 0.517820 | 0.258910 | − | 0.965901i | \(-0.416637\pi\) | ||||
0.258910 | + | 0.965901i | \(0.416637\pi\) | |||||||
\(762\) | 0.681298 | 0.0246808 | ||||||||
\(763\) | −16.2573 | −0.588555 | ||||||||
\(764\) | −4.09247 | −0.148061 | ||||||||
\(765\) | 3.83953 | 0.138818 | ||||||||
\(766\) | −53.0076 | −1.91524 | ||||||||
\(767\) | −1.92009 | −0.0693305 | ||||||||
\(768\) | −16.6913 | −0.602294 | ||||||||
\(769\) | 32.7936 | 1.18257 | 0.591284 | − | 0.806464i | \(-0.298621\pi\) | ||||
0.591284 | + | 0.806464i | \(0.298621\pi\) | |||||||
\(770\) | −193.925 | −6.98856 | ||||||||
\(771\) | 3.05355 | 0.109971 | ||||||||
\(772\) | −8.92008 | −0.321041 | ||||||||
\(773\) | −20.6646 | −0.743252 | −0.371626 | − | 0.928382i | \(-0.621200\pi\) | ||||
−0.371626 | + | 0.928382i | \(0.621200\pi\) | |||||||
\(774\) | −18.9790 | −0.682185 | ||||||||
\(775\) | −42.6697 | −1.53274 | ||||||||
\(776\) | 21.4281 | 0.769223 | ||||||||
\(777\) | −6.70945 | −0.240700 | ||||||||
\(778\) | 6.46686 | 0.231848 | ||||||||
\(779\) | 44.9384 | 1.61009 | ||||||||
\(780\) | 21.6356 | 0.774680 | ||||||||
\(781\) | −68.5861 | −2.45420 | ||||||||
\(782\) | 8.97629 | 0.320991 | ||||||||
\(783\) | 3.88066 | 0.138683 | ||||||||
\(784\) | −76.2051 | −2.72161 | ||||||||
\(785\) | −35.4397 | −1.26490 | ||||||||
\(786\) | 30.6197 | 1.09217 | ||||||||
\(787\) | 21.9481 | 0.782365 | 0.391183 | − | 0.920313i | \(-0.372066\pi\) | ||||
0.391183 | + | 0.920313i | \(0.372066\pi\) | |||||||
\(788\) | 14.8328 | 0.528398 | ||||||||
\(789\) | 5.81981 | 0.207191 | ||||||||
\(790\) | 6.43697 | 0.229017 | ||||||||
\(791\) | −11.7250 | −0.416894 | ||||||||
\(792\) | 12.7061 | 0.451492 | ||||||||
\(793\) | 34.2387 | 1.21585 | ||||||||
\(794\) | 55.0769 | 1.95461 | ||||||||
\(795\) | −14.1874 | −0.503174 | ||||||||
\(796\) | 3.22853 | 0.114432 | ||||||||
\(797\) | 51.0625 | 1.80873 | 0.904364 | − | 0.426762i | \(-0.140346\pi\) | ||||
0.904364 | + | 0.426762i | \(0.140346\pi\) | |||||||
\(798\) | −53.8060 | −1.90471 | ||||||||
\(799\) | −3.03205 | −0.107266 | ||||||||
\(800\) | 42.2270 | 1.49295 | ||||||||
\(801\) | 9.92560 | 0.350704 | ||||||||
\(802\) | −33.2720 | −1.17488 | ||||||||
\(803\) | 7.01757 | 0.247645 | ||||||||
\(804\) | 3.30933 | 0.116711 | ||||||||
\(805\) | 97.1896 | 3.42548 | ||||||||
\(806\) | 51.0424 | 1.79789 | ||||||||
\(807\) | 2.35629 | 0.0829454 | ||||||||
\(808\) | −5.91186 | −0.207978 | ||||||||
\(809\) | −37.7956 | −1.32882 | −0.664412 | − | 0.747367i | \(-0.731318\pi\) | ||||
−0.664412 | + | 0.747367i | \(0.731318\pi\) | |||||||
\(810\) | 6.43697 | 0.226172 | ||||||||
\(811\) | −15.2981 | −0.537190 | −0.268595 | − | 0.963253i | \(-0.586559\pi\) | ||||
−0.268595 | + | 0.963253i | \(0.586559\pi\) | |||||||
\(812\) | 14.8728 | 0.521934 | ||||||||
\(813\) | −29.5281 | −1.03560 | ||||||||
\(814\) | 15.1616 | 0.531413 | ||||||||
\(815\) | 9.65869 | 0.338329 | ||||||||
\(816\) | −4.96415 | −0.173780 | ||||||||
\(817\) | 76.8504 | 2.68865 | ||||||||
\(818\) | −26.3455 | −0.921150 | ||||||||
\(819\) | −32.8627 | −1.14831 | ||||||||
\(820\) | −20.6042 | −0.719531 | ||||||||
\(821\) | −10.4100 | −0.363312 | −0.181656 | − | 0.983362i | \(-0.558146\pi\) | ||||
−0.181656 | + | 0.983362i | \(0.558146\pi\) | |||||||
\(822\) | −35.9268 | −1.25309 | ||||||||
\(823\) | 22.1248 | 0.771223 | 0.385612 | − | 0.922661i | \(-0.373990\pi\) | ||||
0.385612 | + | 0.922661i | \(0.373990\pi\) | |||||||
\(824\) | 7.57233 | 0.263795 | ||||||||
\(825\) | −62.0795 | −2.16133 | ||||||||
\(826\) | −2.18938 | −0.0761784 | ||||||||
\(827\) | −22.8024 | −0.792918 | −0.396459 | − | 0.918052i | \(-0.629761\pi\) | ||||
−0.396459 | + | 0.918052i | \(0.629761\pi\) | |||||||
\(828\) | 4.34041 | 0.150840 | ||||||||
\(829\) | −46.4492 | −1.61325 | −0.806624 | − | 0.591065i | \(-0.798708\pi\) | ||||
−0.806624 | + | 0.591065i | \(0.798708\pi\) | |||||||
\(830\) | −21.2915 | −0.739038 | ||||||||
\(831\) | 14.5426 | 0.504478 | ||||||||
\(832\) | 18.4999 | 0.641367 | ||||||||
\(833\) | −15.3511 | −0.531884 | ||||||||
\(834\) | −11.5318 | −0.399315 | ||||||||
\(835\) | 34.6815 | 1.20020 | ||||||||
\(836\) | 35.0686 | 1.21287 | ||||||||
\(837\) | 4.37999 | 0.151395 | ||||||||
\(838\) | −4.58926 | −0.158533 | ||||||||
\(839\) | 23.1115 | 0.797898 | 0.398949 | − | 0.916973i | \(-0.369375\pi\) | ||||
0.398949 | + | 0.916973i | \(0.369375\pi\) | |||||||
\(840\) | −36.1941 | −1.24881 | ||||||||
\(841\) | −13.9405 | −0.480706 | ||||||||
\(842\) | 45.8111 | 1.57875 | ||||||||
\(843\) | 16.1433 | 0.556006 | ||||||||
\(844\) | 15.4675 | 0.532413 | ||||||||
\(845\) | −135.603 | −4.66490 | ||||||||
\(846\) | −5.08324 | −0.174765 | ||||||||
\(847\) | −139.974 | −4.80957 | ||||||||
\(848\) | 18.3430 | 0.629900 | ||||||||
\(849\) | 9.45035 | 0.324335 | ||||||||
\(850\) | 16.3324 | 0.560197 | ||||||||
\(851\) | −7.59855 | −0.260475 | ||||||||
\(852\) | 8.72514 | 0.298918 | ||||||||
\(853\) | 42.8850 | 1.46835 | 0.734177 | − | 0.678958i | \(-0.237568\pi\) | ||||
0.734177 | + | 0.678958i | \(0.237568\pi\) | |||||||
\(854\) | 39.0407 | 1.33595 | ||||||||
\(855\) | −26.0648 | −0.891399 | ||||||||
\(856\) | −9.16898 | −0.313389 | ||||||||
\(857\) | 51.2242 | 1.74979 | 0.874893 | − | 0.484316i | \(-0.160932\pi\) | ||||
0.874893 | + | 0.484316i | \(0.160932\pi\) | |||||||
\(858\) | 74.2608 | 2.53522 | ||||||||
\(859\) | −5.55864 | −0.189658 | −0.0948291 | − | 0.995494i | \(-0.530230\pi\) | ||||
−0.0948291 | + | 0.995494i | \(0.530230\pi\) | |||||||
\(860\) | −35.2358 | −1.20153 | ||||||||
\(861\) | 31.2961 | 1.06657 | ||||||||
\(862\) | 19.3784 | 0.660032 | ||||||||
\(863\) | 33.4681 | 1.13927 | 0.569633 | − | 0.821899i | \(-0.307085\pi\) | ||||
0.569633 | + | 0.821899i | \(0.307085\pi\) | |||||||
\(864\) | −4.33454 | −0.147464 | ||||||||
\(865\) | 75.7238 | 2.57469 | ||||||||
\(866\) | 30.7586 | 1.04522 | ||||||||
\(867\) | −1.00000 | −0.0339618 | ||||||||
\(868\) | 16.7865 | 0.569772 | ||||||||
\(869\) | 6.37239 | 0.216168 | ||||||||
\(870\) | 24.9797 | 0.846891 | ||||||||
\(871\) | −28.3763 | −0.961493 | ||||||||
\(872\) | 6.85663 | 0.232195 | ||||||||
\(873\) | 10.7466 | 0.363719 | ||||||||
\(874\) | −60.9360 | −2.06119 | ||||||||
\(875\) | 86.0765 | 2.90992 | ||||||||
\(876\) | −0.892736 | −0.0301628 | ||||||||
\(877\) | −54.2213 | −1.83092 | −0.915462 | − | 0.402404i | \(-0.868175\pi\) | ||||
−0.915462 | + | 0.402404i | \(0.868175\pi\) | |||||||
\(878\) | −1.50919 | −0.0509327 | ||||||||
\(879\) | −5.12156 | −0.172746 | ||||||||
\(880\) | 121.458 | 4.09433 | ||||||||
\(881\) | 41.8045 | 1.40843 | 0.704215 | − | 0.709987i | \(-0.251299\pi\) | ||||
0.704215 | + | 0.709987i | \(0.251299\pi\) | |||||||
\(882\) | −25.7361 | −0.866581 | ||||||||
\(883\) | −7.63546 | −0.256954 | −0.128477 | − | 0.991713i | \(-0.541009\pi\) | ||||
−0.128477 | + | 0.991713i | \(0.541009\pi\) | |||||||
\(884\) | −5.63497 | −0.189525 | ||||||||
\(885\) | −1.06059 | −0.0356512 | ||||||||
\(886\) | 0.0961520 | 0.00323029 | ||||||||
\(887\) | −26.9704 | −0.905579 | −0.452789 | − | 0.891617i | \(-0.649571\pi\) | ||||
−0.452789 | + | 0.891617i | \(0.649571\pi\) | |||||||
\(888\) | 2.82975 | 0.0949602 | ||||||||
\(889\) | −1.92124 | −0.0644364 | ||||||||
\(890\) | 63.8908 | 2.14162 | ||||||||
\(891\) | 6.37239 | 0.213483 | ||||||||
\(892\) | 10.6486 | 0.356540 | ||||||||
\(893\) | 20.5833 | 0.688792 | ||||||||
\(894\) | 21.0112 | 0.702719 | ||||||||
\(895\) | 38.2737 | 1.27935 | ||||||||
\(896\) | 62.0792 | 2.07392 | ||||||||
\(897\) | −37.2174 | −1.24265 | ||||||||
\(898\) | −56.8499 | −1.89711 | ||||||||
\(899\) | 16.9973 | 0.566890 | ||||||||
\(900\) | 7.89741 | 0.263247 | ||||||||
\(901\) | 3.69509 | 0.123101 | ||||||||
\(902\) | −70.7207 | −2.35474 | ||||||||
\(903\) | 53.5202 | 1.78104 | ||||||||
\(904\) | 4.94510 | 0.164472 | ||||||||
\(905\) | −66.0752 | −2.19642 | ||||||||
\(906\) | 8.91526 | 0.296190 | ||||||||
\(907\) | 41.1282 | 1.36564 | 0.682820 | − | 0.730587i | \(-0.260753\pi\) | ||||
0.682820 | + | 0.730587i | \(0.260753\pi\) | |||||||
\(908\) | −13.9005 | −0.461304 | ||||||||
\(909\) | −2.96492 | −0.0983403 | ||||||||
\(910\) | −211.536 | −7.01235 | ||||||||
\(911\) | −0.439674 | −0.0145670 | −0.00728352 | − | 0.999973i | \(-0.502318\pi\) | ||||
−0.00728352 | + | 0.999973i | \(0.502318\pi\) | |||||||
\(912\) | 33.6994 | 1.11590 | ||||||||
\(913\) | −21.0778 | −0.697575 | ||||||||
\(914\) | 68.7111 | 2.27276 | ||||||||
\(915\) | 18.9122 | 0.625218 | ||||||||
\(916\) | −9.68176 | −0.319894 | ||||||||
\(917\) | −86.3469 | −2.85142 | ||||||||
\(918\) | −1.67650 | −0.0553328 | ||||||||
\(919\) | −18.0160 | −0.594294 | −0.297147 | − | 0.954832i | \(-0.596035\pi\) | ||||
−0.297147 | + | 0.954832i | \(0.596035\pi\) | |||||||
\(920\) | −40.9903 | −1.35141 | ||||||||
\(921\) | 13.2993 | 0.438225 | ||||||||
\(922\) | 33.2952 | 1.09652 | ||||||||
\(923\) | −74.8148 | −2.46256 | ||||||||
\(924\) | 24.4225 | 0.803441 | ||||||||
\(925\) | −13.8256 | −0.454583 | ||||||||
\(926\) | 24.3464 | 0.800074 | ||||||||
\(927\) | 3.79769 | 0.124732 | ||||||||
\(928\) | −16.8209 | −0.552173 | ||||||||
\(929\) | −5.01967 | −0.164690 | −0.0823450 | − | 0.996604i | \(-0.526241\pi\) | ||||
−0.0823450 | + | 0.996604i | \(0.526241\pi\) | |||||||
\(930\) | 28.1939 | 0.924514 | ||||||||
\(931\) | 104.212 | 3.41540 | ||||||||
\(932\) | −1.48317 | −0.0485827 | ||||||||
\(933\) | −7.15879 | −0.234368 | ||||||||
\(934\) | −54.6987 | −1.78980 | ||||||||
\(935\) | 24.4669 | 0.800155 | ||||||||
\(936\) | 13.8600 | 0.453029 | ||||||||
\(937\) | −10.0905 | −0.329643 | −0.164821 | − | 0.986323i | \(-0.552705\pi\) | ||||
−0.164821 | + | 0.986323i | \(0.552705\pi\) | |||||||
\(938\) | −32.3560 | −1.05646 | ||||||||
\(939\) | 6.89071 | 0.224870 | ||||||||
\(940\) | −9.43741 | −0.307814 | ||||||||
\(941\) | 10.1696 | 0.331521 | 0.165760 | − | 0.986166i | \(-0.446992\pi\) | ||||
0.165760 | + | 0.986166i | \(0.446992\pi\) | |||||||
\(942\) | 15.4745 | 0.504186 | ||||||||
\(943\) | 35.4432 | 1.15419 | ||||||||
\(944\) | 1.37124 | 0.0446301 | ||||||||
\(945\) | −18.1521 | −0.590488 | ||||||||
\(946\) | −120.941 | −3.93214 | ||||||||
\(947\) | 52.9560 | 1.72084 | 0.860420 | − | 0.509585i | \(-0.170201\pi\) | ||||
0.860420 | + | 0.509585i | \(0.170201\pi\) | |||||||
\(948\) | −0.810659 | −0.0263290 | ||||||||
\(949\) | 7.65488 | 0.248488 | ||||||||
\(950\) | −110.874 | −3.59721 | ||||||||
\(951\) | 21.4196 | 0.694578 | ||||||||
\(952\) | 9.42670 | 0.305521 | ||||||||
\(953\) | −7.79405 | −0.252474 | −0.126237 | − | 0.992000i | \(-0.540290\pi\) | ||||
−0.126237 | + | 0.992000i | \(0.540290\pi\) | |||||||
\(954\) | 6.19482 | 0.200565 | ||||||||
\(955\) | 19.3832 | 0.627225 | ||||||||
\(956\) | 13.9485 | 0.451128 | ||||||||
\(957\) | 24.7291 | 0.799377 | ||||||||
\(958\) | −54.9635 | −1.77579 | ||||||||
\(959\) | 101.313 | 3.27156 | ||||||||
\(960\) | 10.2186 | 0.329805 | ||||||||
\(961\) | −11.8157 | −0.381150 | ||||||||
\(962\) | 16.5385 | 0.533222 | ||||||||
\(963\) | −4.59844 | −0.148183 | ||||||||
\(964\) | −5.59025 | −0.180050 | ||||||||
\(965\) | 42.2482 | 1.36002 | ||||||||
\(966\) | −42.4371 | −1.36539 | ||||||||
\(967\) | −1.56378 | −0.0502878 | −0.0251439 | − | 0.999684i | \(-0.508004\pi\) | ||||
−0.0251439 | + | 0.999684i | \(0.508004\pi\) | |||||||
\(968\) | 59.0350 | 1.89746 | ||||||||
\(969\) | 6.78856 | 0.218080 | ||||||||
\(970\) | 69.1758 | 2.22110 | ||||||||
\(971\) | 32.3287 | 1.03748 | 0.518738 | − | 0.854933i | \(-0.326402\pi\) | ||||
0.518738 | + | 0.854933i | \(0.326402\pi\) | |||||||
\(972\) | −0.810659 | −0.0260019 | ||||||||
\(973\) | 32.5195 | 1.04253 | ||||||||
\(974\) | −39.7446 | −1.27350 | ||||||||
\(975\) | −67.7173 | −2.16869 | ||||||||
\(976\) | −24.4517 | −0.782680 | ||||||||
\(977\) | −39.9335 | −1.27758 | −0.638792 | − | 0.769379i | \(-0.720566\pi\) | ||||
−0.638792 | + | 0.769379i | \(0.720566\pi\) | |||||||
\(978\) | −4.21740 | −0.134858 | ||||||||
\(979\) | 63.2498 | 2.02147 | ||||||||
\(980\) | −47.7810 | −1.52631 | ||||||||
\(981\) | 3.43875 | 0.109791 | ||||||||
\(982\) | −15.8384 | −0.505423 | ||||||||
\(983\) | −30.7327 | −0.980221 | −0.490110 | − | 0.871660i | \(-0.663044\pi\) | ||||
−0.490110 | + | 0.871660i | \(0.663044\pi\) | |||||||
\(984\) | −13.1993 | −0.420778 | ||||||||
\(985\) | −70.2528 | −2.23844 | ||||||||
\(986\) | −6.50593 | −0.207191 | ||||||||
\(987\) | 14.3346 | 0.456276 | ||||||||
\(988\) | 38.2533 | 1.21700 | ||||||||
\(989\) | 60.6124 | 1.92736 | ||||||||
\(990\) | 41.0189 | 1.30367 | ||||||||
\(991\) | −21.5490 | −0.684528 | −0.342264 | − | 0.939604i | \(-0.611194\pi\) | ||||
−0.342264 | + | 0.939604i | \(0.611194\pi\) | |||||||
\(992\) | −18.9853 | −0.602783 | ||||||||
\(993\) | −20.0992 | −0.637828 | ||||||||
\(994\) | −85.3075 | −2.70579 | ||||||||
\(995\) | −15.2913 | −0.484766 | ||||||||
\(996\) | 2.68141 | 0.0849636 | ||||||||
\(997\) | 0.774472 | 0.0245278 | 0.0122639 | − | 0.999925i | \(-0.496096\pi\) | ||||
0.0122639 | + | 0.999925i | \(0.496096\pi\) | |||||||
\(998\) | −10.8048 | −0.342019 | ||||||||
\(999\) | 1.41918 | 0.0449009 |
(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 | 4029.2.a.l.1.8 | ✓ | 32 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
4029.2.a.l.1.8 | ✓ | 32 | 1.1 | even | 1 | trivial |