Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1680,2,Mod(209,1680)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1680, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 1, 1, 1]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1680.209");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1680 = 2^{4} \cdot 3 \cdot 5 \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1680.k (of order \(2\), degree \(1\), not minimal) |
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: | no |
Analytic conductor: | \(13.4148675396\) |
Analytic rank: | \(0\) |
Dimension: | \(24\) |
Twist minimal: | no (minimal twist has level 840) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 209.20 | ||
Character | \(\chi\) | \(=\) | 1680.209 |
Dual form | 1680.2.k.i.209.19 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/1680\mathbb{Z}\right)^\times\).
\(n\) | \(241\) | \(337\) | \(421\) | \(1121\) | \(1471\) |
\(\chi(n)\) | \(-1\) | \(-1\) | \(1\) | \(-1\) | \(1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | 1.37873 | + | 1.04838i | 0.796009 | + | 0.605285i | ||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −1.84099 | − | 1.26915i | −0.823317 | − | 0.567582i | ||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −2.63201 | + | 0.269297i | −0.994806 | + | 0.101785i | ||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0.801780 | + | 2.89087i | 0.267260 | + | 0.963624i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | − | 3.01442i | − | 0.908881i | −0.890777 | − | 0.454440i | \(-0.849839\pi\) | ||
0.890777 | − | 0.454440i | \(-0.150161\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 4.39041 | 1.21768 | 0.608840 | − | 0.793293i | \(-0.291635\pi\) | ||||
0.608840 | + | 0.793293i | \(0.291635\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −1.20767 | − | 3.67988i | −0.311818 | − | 0.950142i | ||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 2.71017i | 0.657314i | 0.944449 | + | 0.328657i | \(0.106596\pi\) | ||||
−0.944449 | + | 0.328657i | \(0.893404\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 8.23502i | 1.88924i | 0.328163 | + | 0.944621i | \(0.393570\pi\) | ||||
−0.328163 | + | 0.944621i | \(0.606430\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −3.91115 | − | 2.38807i | −0.853484 | − | 0.521120i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −3.81803 | −0.796114 | −0.398057 | − | 0.917361i | \(-0.630315\pi\) | ||||
−0.398057 | + | 0.917361i | \(0.630315\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 1.77850 | + | 4.67300i | 0.355701 | + | 0.934600i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −1.92531 | + | 4.82630i | −0.370526 | + | 0.928822i | ||||
\(28\) | 0 | 0 | ||||||||
\(29\) | − | 1.17337i | − | 0.217889i | −0.994048 | − | 0.108944i | \(-0.965253\pi\) | ||
0.994048 | − | 0.108944i | \(-0.0347471\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | − | 1.73412i | − | 0.311458i | −0.987800 | − | 0.155729i | \(-0.950227\pi\) | ||
0.987800 | − | 0.155729i | \(-0.0497726\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 3.16027 | − | 4.15606i | 0.550132 | − | 0.723477i | ||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 5.18729 | + | 2.84465i | 0.876812 | + | 0.480833i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | − | 4.60838i | − | 0.757613i | −0.925476 | − | 0.378806i | \(-0.876335\pi\) | ||
0.925476 | − | 0.378806i | \(-0.123665\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 6.05318 | + | 4.60284i | 0.969284 | + | 0.737044i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −10.6600 | −1.66482 | −0.832408 | − | 0.554163i | \(-0.813038\pi\) | ||||
−0.832408 | + | 0.554163i | \(0.813038\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 9.18515i | 1.40072i | 0.713789 | + | 0.700361i | \(0.246978\pi\) | ||||
−0.713789 | + | 0.700361i | \(0.753022\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 2.19289 | − | 6.33966i | 0.326896 | − | 0.945060i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 12.0659i | 1.75999i | 0.474980 | + | 0.879997i | \(0.342455\pi\) | ||||
−0.474980 | + | 0.879997i | \(0.657545\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 6.85496 | − | 1.41759i | 0.979280 | − | 0.202512i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −2.84130 | + | 3.73659i | −0.397862 | + | 0.523227i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 7.14027 | 0.980791 | 0.490396 | − | 0.871500i | \(-0.336852\pi\) | ||||
0.490396 | + | 0.871500i | \(0.336852\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −3.82575 | + | 5.54952i | −0.515865 | + | 0.748297i | ||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −8.63346 | + | 11.3538i | −1.14353 | + | 1.50385i | ||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −9.11464 | −1.18663 | −0.593313 | − | 0.804972i | \(-0.702180\pi\) | ||||
−0.593313 | + | 0.804972i | \(0.702180\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 13.5606i | 1.73626i | 0.496340 | + | 0.868128i | \(0.334677\pi\) | ||||
−0.496340 | + | 0.868128i | \(0.665323\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −2.88880 | − | 7.39289i | −0.363954 | − | 0.931417i | ||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −8.08271 | − | 5.57210i | −1.00254 | − | 0.691134i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 0.494447i | 0.0604063i | 0.999544 | + | 0.0302031i | \(0.00961542\pi\) | ||||
−0.999544 | + | 0.0302031i | \(0.990385\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −5.26402 | − | 4.00276i | −0.633714 | − | 0.481876i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 5.15821i | 0.612167i | 0.952005 | + | 0.306084i | \(0.0990187\pi\) | ||||
−0.952005 | + | 0.306084i | \(0.900981\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 4.76038 | 0.557160 | 0.278580 | − | 0.960413i | \(-0.410136\pi\) | ||||
0.278580 | + | 0.960413i | \(0.410136\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −2.44703 | + | 8.30735i | −0.282558 | + | 0.959250i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 0.811774 | + | 7.93398i | 0.0925102 | + | 0.904161i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −12.1064 | −1.36207 | −0.681036 | − | 0.732250i | \(-0.738470\pi\) | ||||
−0.681036 | + | 0.732250i | \(0.738470\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −7.71430 | + | 4.63569i | −0.857144 | + | 0.515077i | ||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 8.16745i | 0.896494i | 0.893910 | + | 0.448247i | \(0.147952\pi\) | ||||
−0.893910 | + | 0.448247i | \(0.852048\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 3.43962 | − | 4.98941i | 0.373080 | − | 0.541177i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 1.23014 | − | 1.61776i | 0.131885 | − | 0.173442i | ||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −2.26858 | −0.240469 | −0.120235 | − | 0.992745i | \(-0.538365\pi\) | ||||
−0.120235 | + | 0.992745i | \(0.538365\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −11.5556 | + | 1.18232i | −1.21136 | + | 0.123941i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 1.81803 | − | 2.39088i | 0.188521 | − | 0.247923i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 10.4515 | − | 15.1606i | 1.07230 | − | 1.55544i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 2.92728 | 0.297220 | 0.148610 | − | 0.988896i | \(-0.452520\pi\) | ||||
0.148610 | + | 0.988896i | \(0.452520\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 8.71430 | − | 2.41690i | 0.875820 | − | 0.242908i | ||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 0.416078 | 0.0414013 | 0.0207007 | − | 0.999786i | \(-0.493410\pi\) | ||||
0.0207007 | + | 0.999786i | \(0.493410\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 10.4552 | 1.03019 | 0.515093 | − | 0.857134i | \(-0.327757\pi\) | ||||
0.515093 | + | 0.857134i | \(0.327757\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 4.16958 | + | 9.36027i | 0.406909 | + | 0.913469i | ||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 5.93315 | 0.573579 | 0.286789 | − | 0.957994i | \(-0.407412\pi\) | ||||
0.286789 | + | 0.957994i | \(0.407412\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −11.7565 | −1.12607 | −0.563033 | − | 0.826435i | \(-0.690365\pi\) | ||||
−0.563033 | + | 0.826435i | \(0.690365\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 4.83135 | − | 6.35370i | 0.458572 | − | 0.603066i | ||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 14.2543 | 1.34093 | 0.670465 | − | 0.741941i | \(-0.266095\pi\) | ||||
0.670465 | + | 0.741941i | \(0.266095\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 7.02896 | + | 4.84566i | 0.655454 | + | 0.451860i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 3.52014 | + | 12.6921i | 0.325437 | + | 1.17339i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −0.729842 | − | 7.13321i | −0.0669045 | − | 0.653900i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 1.91329 | 0.173936 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −14.6973 | − | 11.1758i | −1.32521 | − | 1.00769i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 2.65654 | − | 10.8601i | 0.237608 | − | 0.971361i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | − | 15.4193i | − | 1.36824i | −0.729371 | − | 0.684119i | \(-0.760187\pi\) | ||
0.729371 | − | 0.684119i | \(-0.239813\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −9.62956 | + | 12.6638i | −0.847836 | + | 1.11499i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −7.07988 | −0.618572 | −0.309286 | − | 0.950969i | \(-0.600090\pi\) | ||||
−0.309286 | + | 0.950969i | \(0.600090\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −2.21767 | − | 21.6746i | −0.192296 | − | 1.87943i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 9.66979 | − | 6.44167i | 0.832243 | − | 0.554411i | ||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 13.6571 | 1.16681 | 0.583403 | − | 0.812183i | \(-0.301721\pi\) | ||||
0.583403 | + | 0.812183i | \(0.301721\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | − | 7.97668i | − | 0.676573i | −0.941043 | − | 0.338286i | \(-0.890153\pi\) | ||
0.941043 | − | 0.338286i | \(-0.109847\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −12.6497 | + | 16.6356i | −1.06530 | + | 1.40097i | ||||
\(142\) | 0 | 0 | ||||||||
\(143\) | − | 13.2345i | − | 1.10673i | ||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −1.48918 | + | 2.16016i | −0.123670 | + | 0.179392i | ||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 10.9373 | + | 5.23217i | 0.902093 | + | 0.431542i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | − | 11.2515i | − | 0.921755i | −0.887464 | − | 0.460878i | \(-0.847535\pi\) | ||
0.887464 | − | 0.460878i | \(-0.152465\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 2.87722 | 0.234145 | 0.117072 | − | 0.993123i | \(-0.462649\pi\) | ||||
0.117072 | + | 0.993123i | \(0.462649\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −7.83477 | + | 2.17296i | −0.633404 | + | 0.175674i | ||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −2.20087 | + | 3.19251i | −0.176778 | + | 0.256428i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −10.7109 | −0.854826 | −0.427413 | − | 0.904056i | \(-0.640575\pi\) | ||||
−0.427413 | + | 0.904056i | \(0.640575\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 9.84448 | + | 7.48574i | 0.780718 | + | 0.593658i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 10.0491 | − | 1.02818i | 0.791979 | − | 0.0810323i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 13.9669i | 1.09397i | 0.837141 | + | 0.546987i | \(0.184225\pi\) | ||||
−0.837141 | + | 0.546987i | \(0.815775\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −11.0927 | + | 3.64041i | −0.863566 | + | 0.283406i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | − | 8.59766i | − | 0.665307i | −0.943049 | − | 0.332653i | \(-0.892056\pi\) | ||
0.943049 | − | 0.332653i | \(-0.107944\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 6.27569 | 0.482745 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −23.8064 | + | 6.60267i | −1.82052 | + | 0.504919i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 8.74412i | 0.664803i | 0.943138 | + | 0.332401i | \(0.107859\pi\) | ||||
−0.943138 | + | 0.332401i | \(0.892141\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −5.93947 | − | 11.8204i | −0.448982 | − | 0.893541i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −12.5666 | − | 9.55565i | −0.944564 | − | 0.718246i | ||||
\(178\) | 0 | 0 | ||||||||
\(179\) | − | 17.0676i | − | 1.27569i | −0.770165 | − | 0.637845i | \(-0.779826\pi\) | ||
0.770165 | − | 0.637845i | \(-0.220174\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | − | 6.65867i | − | 0.494935i | −0.968896 | − | 0.247468i | \(-0.920402\pi\) | ||
0.968896 | − | 0.247468i | \(-0.0795984\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −14.2167 | + | 18.6964i | −1.05093 | + | 1.38208i | ||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −5.84873 | + | 8.48399i | −0.430008 | + | 0.623755i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 8.16959 | 0.597420 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 3.76773 | − | 13.2214i | 0.274062 | − | 0.961712i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 13.1256i | 0.949733i | 0.880058 | + | 0.474866i | \(0.157504\pi\) | ||||
−0.880058 | + | 0.474866i | \(0.842496\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | − | 10.7880i | − | 0.776538i | −0.921546 | − | 0.388269i | \(-0.873073\pi\) | ||
0.921546 | − | 0.388269i | \(-0.126927\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −5.30215 | − | 16.1562i | −0.379695 | − | 1.15697i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −15.1781 | −1.08139 | −0.540696 | − | 0.841218i | \(-0.681839\pi\) | ||||
−0.540696 | + | 0.841218i | \(0.681839\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | − | 19.8125i | − | 1.40447i | −0.711944 | − | 0.702236i | \(-0.752185\pi\) | ||
0.711944 | − | 0.702236i | \(-0.247815\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −0.518370 | + | 0.681707i | −0.0365630 | + | 0.0480839i | ||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 0.315985 | + | 3.08832i | 0.0221778 | + | 0.216757i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 19.6250 | + | 13.5292i | 1.37067 | + | 0.944920i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −3.06122 | − | 11.0374i | −0.212769 | − | 0.767155i | ||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 24.8238 | 1.71710 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −5.58950 | −0.384797 | −0.192399 | − | 0.981317i | \(-0.561627\pi\) | ||||
−0.192399 | + | 0.981317i | \(0.561627\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −5.40779 | + | 7.11177i | −0.370536 | + | 0.487291i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 11.6573 | − | 16.9098i | 0.795025 | − | 1.15324i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 0.466995 | + | 4.56423i | 0.0317017 | + | 0.309840i | ||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 6.56326 | + | 4.99070i | 0.443504 | + | 0.337241i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 11.8988i | 0.800398i | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −2.13609 | −0.143043 | −0.0715216 | − | 0.997439i | \(-0.522785\pi\) | ||||
−0.0715216 | + | 0.997439i | \(0.522785\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −12.0831 | + | 8.88815i | −0.805539 | + | 0.592543i | ||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 3.92566i | 0.260555i | 0.991478 | + | 0.130277i | \(0.0415868\pi\) | ||||
−0.991478 | + | 0.130277i | \(0.958413\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 15.0457i | 0.994251i | 0.867679 | + | 0.497126i | \(0.165611\pi\) | ||||
−0.867679 | + | 0.497126i | \(0.834389\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −7.19864 | + | 11.7898i | −0.473636 | + | 0.775715i | ||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 9.72492 | 0.637101 | 0.318550 | − | 0.947906i | \(-0.396804\pi\) | ||||
0.318550 | + | 0.947906i | \(0.396804\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 15.3135 | − | 22.2132i | 0.998941 | − | 1.44903i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −16.6914 | − | 12.6921i | −1.08422 | − | 0.824441i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 2.52992i | 0.163647i | 0.996647 | + | 0.0818233i | \(0.0260743\pi\) | ||||
−0.996647 | + | 0.0818233i | \(0.973926\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | − | 9.87223i | − | 0.635926i | −0.948103 | − | 0.317963i | \(-0.897001\pi\) | ||
0.948103 | − | 0.317963i | \(-0.102999\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −15.4959 | − | 1.69620i | −0.994062 | − | 0.108811i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −14.4191 | − | 6.09022i | −0.921200 | − | 0.389090i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 36.1551i | 2.30049i | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −8.56263 | + | 11.2607i | −0.542635 | + | 0.713617i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 17.2182 | 1.08680 | 0.543402 | − | 0.839473i | \(-0.317136\pi\) | ||||
0.543402 | + | 0.839473i | \(0.317136\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 11.5091i | 0.723573i | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 9.97312 | − | 3.27299i | 0.624541 | − | 0.204962i | ||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 6.40758i | 0.399694i | 0.979827 | + | 0.199847i | \(0.0640445\pi\) | ||||
−0.979827 | + | 0.199847i | \(0.935955\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 1.24102 | + | 12.1293i | 0.0771135 | + | 0.753678i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 3.39206 | − | 0.940783i | 0.209963 | − | 0.0582330i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 3.69040 | 0.227560 | 0.113780 | − | 0.993506i | \(-0.463704\pi\) | ||||
0.113780 | + | 0.993506i | \(0.463704\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −13.1452 | − | 9.06209i | −0.807502 | − | 0.556680i | ||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −3.12776 | − | 2.37835i | −0.191416 | − | 0.145553i | ||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 17.4759 | 1.06553 | 0.532763 | − | 0.846264i | \(-0.321154\pi\) | ||||
0.532763 | + | 0.846264i | \(0.321154\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | − | 3.60083i | − | 0.218735i | −0.994001 | − | 0.109367i | \(-0.965118\pi\) | ||
0.994001 | − | 0.109367i | \(-0.0348825\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −17.1716 | − | 10.4846i | −1.03927 | − | 0.634557i | ||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 14.0864 | − | 5.36115i | 0.849440 | − | 0.323290i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 9.39015i | 0.564199i | 0.959385 | + | 0.282100i | \(0.0910309\pi\) | ||||
−0.959385 | + | 0.282100i | \(0.908969\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 5.01313 | − | 1.39039i | 0.300128 | − | 0.0832402i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 2.80219i | 0.167165i | 0.996501 | + | 0.0835824i | \(0.0266362\pi\) | ||||
−0.996501 | + | 0.0835824i | \(0.973364\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 11.8686 | 0.705518 | 0.352759 | − | 0.935714i | \(-0.385244\pi\) | ||||
0.352759 | + | 0.935714i | \(0.385244\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 30.3039 | − | 9.94516i | 1.79505 | − | 0.589100i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 28.0573 | − | 2.87072i | 1.65617 | − | 0.169453i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 9.65496 | 0.567939 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 4.03592 | + | 3.06891i | 0.236590 | + | 0.179903i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 15.5145i | 0.906366i | 0.891418 | + | 0.453183i | \(0.149712\pi\) | ||||
−0.891418 | + | 0.453183i | \(0.850288\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 16.7800 | + | 11.5679i | 0.976968 | + | 0.673507i | ||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 14.5485 | + | 5.80369i | 0.844189 | + | 0.336764i | ||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −16.7627 | −0.969412 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −2.47353 | − | 24.1754i | −0.142572 | − | 1.39345i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0.573658 | + | 0.436210i | 0.0329558 | + | 0.0250596i | ||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 17.2105 | − | 24.9650i | 0.985468 | − | 1.42949i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −4.98662 | −0.284601 | −0.142301 | − | 0.989823i | \(-0.545450\pi\) | ||||
−0.142301 | + | 0.989823i | \(0.545450\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 14.4149 | + | 10.9611i | 0.820037 | + | 0.623556i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 23.2945 | 1.32091 | 0.660455 | − | 0.750865i | \(-0.270363\pi\) | ||||
0.660455 | + | 0.750865i | \(0.270363\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 7.16856 | 0.405191 | 0.202595 | − | 0.979263i | \(-0.435062\pi\) | ||||
0.202595 | + | 0.979263i | \(0.435062\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −4.06445 | + | 17.2766i | −0.229006 | + | 0.973425i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 2.91003 | 0.163444 | 0.0817218 | − | 0.996655i | \(-0.473958\pi\) | ||||
0.0817218 | + | 0.996655i | \(0.473958\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −3.53702 | −0.198035 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 8.18019 | + | 6.22022i | 0.456574 | + | 0.347179i | ||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −22.3183 | −1.24182 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 7.80836 | + | 20.5164i | 0.433130 | + | 1.13804i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −16.2090 | − | 12.3253i | −0.896358 | − | 0.681591i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −3.24932 | − | 31.7576i | −0.179141 | − | 1.75085i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −29.4323 | −1.61775 | −0.808874 | − | 0.587982i | \(-0.799922\pi\) | ||||
−0.808874 | + | 0.587982i | \(0.799922\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 13.3222 | − | 3.69491i | 0.730054 | − | 0.202480i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 0.627528 | − | 0.910273i | 0.0342855 | − | 0.0497335i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 15.8598i | 0.863940i | 0.901888 | + | 0.431970i | \(0.142181\pi\) | ||||
−0.901888 | + | 0.431970i | \(0.857819\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 19.6528 | + | 14.9440i | 1.06739 | + | 0.811645i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −5.22737 | −0.283078 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −17.6606 | + | 5.57712i | −0.953581 | + | 0.301136i | ||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 4.61091 | + | 14.0499i | 0.248243 | + | 0.756421i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 11.0724 | 0.594400 | 0.297200 | − | 0.954815i | \(-0.403947\pi\) | ||||
0.297200 | + | 0.954815i | \(0.403947\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | − | 13.9422i | − | 0.746306i | −0.927770 | − | 0.373153i | \(-0.878277\pi\) | ||
0.927770 | − | 0.373153i | \(-0.121723\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −8.45290 | + | 21.1894i | −0.451182 | + | 1.13101i | ||||
\(352\) | 0 | 0 | ||||||||
\(353\) | − | 31.2855i | − | 1.66516i | −0.553904 | − | 0.832580i | \(-0.686863\pi\) | ||
0.553904 | − | 0.832580i | \(-0.313137\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 6.54656 | − | 9.49623i | 0.347455 | − | 0.504008i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 6.47209 | − | 10.5999i | 0.342539 | − | 0.561006i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 2.58454i | 0.136407i | 0.997671 | + | 0.0682033i | \(0.0217267\pi\) | ||||
−0.997671 | + | 0.0682033i | \(0.978273\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −48.8155 | −2.56924 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 2.63791 | + | 2.00586i | 0.138454 | + | 0.105281i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −8.76381 | − | 6.04164i | −0.458719 | − | 0.316234i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −25.8803 | −1.35094 | −0.675470 | − | 0.737388i | \(-0.736059\pi\) | ||||
−0.675470 | + | 0.737388i | \(0.736059\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −8.54700 | − | 30.8168i | −0.444939 | − | 1.60426i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −18.7933 | + | 1.92285i | −0.975697 | + | 0.0998296i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 5.37044i | 0.278071i | 0.990287 | + | 0.139035i | \(0.0444002\pi\) | ||||
−0.990287 | + | 0.139035i | \(0.955600\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 15.0483 | − | 12.1881i | 0.777088 | − | 0.629392i | ||||
\(376\) | 0 | 0 | ||||||||
\(377\) | − | 5.15157i | − | 0.265319i | ||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 33.6626 | 1.72913 | 0.864565 | − | 0.502521i | \(-0.167594\pi\) | ||||
0.864565 | + | 0.502521i | \(0.167594\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 16.1653 | − | 21.2590i | 0.828174 | − | 1.08913i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | − | 5.70589i | − | 0.291557i | −0.989317 | − | 0.145779i | \(-0.953431\pi\) | ||
0.989317 | − | 0.145779i | \(-0.0465687\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 8.57496 | − | 15.6367i | 0.437020 | − | 0.796918i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −26.5531 | + | 7.36447i | −1.34977 | + | 0.374357i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 30.8578i | 1.56455i | 0.622930 | + | 0.782277i | \(0.285942\pi\) | ||||
−0.622930 | + | 0.782277i | \(0.714058\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | − | 10.3475i | − | 0.523297i | ||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −9.76122 | − | 7.42243i | −0.492388 | − | 0.374412i | ||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 22.2877 | + | 15.3648i | 1.12142 | + | 0.773088i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −22.7345 | −1.14101 | −0.570505 | − | 0.821294i | \(-0.693253\pi\) | ||||
−0.570505 | + | 0.821294i | \(0.693253\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 19.6658 | − | 32.2084i | 0.984522 | − | 1.61244i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 13.7170i | 0.684992i | 0.939519 | + | 0.342496i | \(0.111272\pi\) | ||||
−0.939519 | + | 0.342496i | \(0.888728\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | − | 7.61351i | − | 0.379256i | ||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 20.0854 | + | 1.25635i | 0.998049 | + | 0.0624286i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −13.8916 | −0.688580 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | − | 12.6202i | − | 0.624030i | −0.950077 | − | 0.312015i | \(-0.898996\pi\) | ||
0.950077 | − | 0.312015i | \(-0.101004\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 18.8294 | + | 14.3179i | 0.928788 | + | 0.706250i | ||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 23.9898 | − | 2.45455i | 1.18046 | − | 0.120780i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 10.3657 | − | 15.0362i | 0.508834 | − | 0.738099i | ||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 8.36262 | − | 10.9977i | 0.409519 | − | 0.538558i | ||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −23.6389 | −1.15484 | −0.577418 | − | 0.816449i | \(-0.695940\pi\) | ||||
−0.577418 | + | 0.816449i | \(0.695940\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −8.42017 | −0.410374 | −0.205187 | − | 0.978723i | \(-0.565780\pi\) | ||||
−0.205187 | + | 0.978723i | \(0.565780\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −34.8810 | + | 9.67421i | −1.69597 | + | 0.470376i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −12.6646 | + | 4.82006i | −0.614325 | + | 0.233807i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −3.65183 | − | 35.6916i | −0.176725 | − | 1.72724i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 13.8749 | − | 18.2468i | 0.669885 | − | 0.880964i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | − | 18.5310i | − | 0.892606i | −0.894882 | − | 0.446303i | \(-0.852740\pi\) | ||
0.894882 | − | 0.446303i | \(-0.147260\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 9.12614 | 0.438574 | 0.219287 | − | 0.975660i | \(-0.429627\pi\) | ||||
0.219287 | + | 0.975660i | \(0.429627\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −4.31786 | + | 1.41704i | −0.207025 | + | 0.0679418i | ||||
\(436\) | 0 | 0 | ||||||||
\(437\) | − | 31.4415i | − | 1.50405i | ||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | − | 16.9640i | − | 0.809645i | −0.914395 | − | 0.404823i | \(-0.867333\pi\) | ||
0.914395 | − | 0.404823i | \(-0.132667\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 9.59423 | + | 18.6802i | 0.456868 | + | 0.889534i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 4.34739 | 0.206551 | 0.103275 | − | 0.994653i | \(-0.467068\pi\) | ||||
0.103275 | + | 0.994653i | \(0.467068\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 4.17644 | + | 2.87918i | 0.197982 | + | 0.136486i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 11.7959 | − | 15.5127i | 0.557925 | − | 0.733725i | ||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 15.9781i | 0.754053i | 0.926202 | + | 0.377027i | \(0.123053\pi\) | ||||
−0.926202 | + | 0.377027i | \(0.876947\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 32.1338i | 1.51312i | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 3.96690 | + | 3.01643i | 0.186381 | + | 0.141724i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 22.7743 | + | 12.4892i | 1.06768 | + | 0.585501i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | − | 16.4839i | − | 0.771085i | −0.922690 | − | 0.385542i | \(-0.874014\pi\) | ||
0.922690 | − | 0.385542i | \(-0.125986\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −13.0801 | − | 5.21792i | −0.610527 | − | 0.243552i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −20.8741 | −0.972203 | −0.486102 | − | 0.873902i | \(-0.661581\pi\) | ||||
−0.486102 | + | 0.873902i | \(0.661581\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | − | 9.46270i | − | 0.439769i | −0.975526 | − | 0.219885i | \(-0.929432\pi\) | ||
0.975526 | − | 0.219885i | \(-0.0705681\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −6.38137 | + | 2.09424i | −0.295929 | + | 0.0971182i | ||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 19.1519i | 0.886245i | 0.896461 | + | 0.443122i | \(0.146129\pi\) | ||||
−0.896461 | + | 0.443122i | \(0.853871\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −0.133153 | − | 1.30139i | −0.00614844 | − | 0.0600926i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −14.7675 | − | 11.2292i | −0.680449 | − | 0.517414i | ||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 27.6879 | 1.27309 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −38.4822 | + | 14.6460i | −1.76569 | + | 0.672005i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 5.72492 | + | 20.6416i | 0.262126 | + | 0.945114i | ||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 22.9310 | 1.04774 | 0.523871 | − | 0.851798i | \(-0.324487\pi\) | ||||
0.523871 | + | 0.851798i | \(0.324487\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | − | 20.2327i | − | 0.922530i | ||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 14.9329 | + | 9.11772i | 0.679470 | + | 0.414871i | ||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −5.38909 | − | 3.71516i | −0.244706 | − | 0.168697i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | − | 31.0733i | − | 1.40807i | −0.710167 | − | 0.704033i | \(-0.751381\pi\) | ||
0.710167 | − | 0.704033i | \(-0.248619\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −14.6427 | + | 19.2566i | −0.662166 | + | 0.870812i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 5.50641i | 0.248501i | 0.992251 | + | 0.124250i | \(0.0396526\pi\) | ||||
−0.992251 | + | 0.124250i | \(0.960347\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 3.18003 | 0.143221 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −19.1104 | − | 6.61028i | −0.858947 | − | 0.297110i | ||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −1.38909 | − | 13.5765i | −0.0623093 | − | 0.608988i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 22.6482 | 1.01387 | 0.506937 | − | 0.861983i | \(-0.330778\pi\) | ||||
0.506937 | + | 0.861983i | \(0.330778\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 9.01365 | − | 11.8538i | 0.402700 | − | 0.529590i | ||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 3.10345i | 0.138376i | 0.997604 | + | 0.0691881i | \(0.0220409\pi\) | ||||
−0.997604 | + | 0.0691881i | \(0.977959\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −0.765997 | − | 0.528067i | −0.0340864 | − | 0.0234987i | ||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 8.65246 | + | 6.57933i | 0.384269 | + | 0.292198i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 22.9387 | 1.01674 | 0.508371 | − | 0.861138i | \(-0.330248\pi\) | ||||
0.508371 | + | 0.861138i | \(0.330248\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −12.5294 | + | 1.28196i | −0.554266 | + | 0.0567104i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −39.7447 | − | 15.8550i | −1.75477 | − | 0.700014i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −19.2480 | − | 13.2693i | −0.848170 | − | 0.584715i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 36.3717 | 1.59962 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −9.16719 | + | 12.0558i | −0.402395 | + | 0.529189i | ||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 17.6343 | 0.772572 | 0.386286 | − | 0.922379i | \(-0.373758\pi\) | ||||
0.386286 | + | 0.922379i | \(0.373758\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 31.8408 | 1.39230 | 0.696151 | − | 0.717895i | \(-0.254894\pi\) | ||||
0.696151 | + | 0.717895i | \(0.254894\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 4.20345 | − | 22.5240i | 0.183454 | − | 0.983028i | ||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 4.69978 | 0.204725 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −8.42266 | −0.366203 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −7.30794 | − | 26.3493i | −0.317138 | − | 1.14346i | ||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −46.8019 | −2.02721 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −10.9229 | − | 7.53007i | −0.472237 | − | 0.325553i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 17.8934 | − | 23.5315i | 0.772156 | − | 1.01546i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −4.27320 | − | 20.6637i | −0.184060 | − | 0.890049i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −29.4219 | −1.26494 | −0.632472 | − | 0.774583i | \(-0.717960\pi\) | ||||
−0.632472 | + | 0.774583i | \(0.717960\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 6.98085 | − | 9.18050i | 0.299577 | − | 0.393973i | ||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 21.6436 | + | 14.9207i | 0.927108 | + | 0.639135i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 20.7168i | 0.885784i | 0.896575 | + | 0.442892i | \(0.146048\pi\) | ||||
−0.896575 | + | 0.442892i | \(0.853952\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −39.2020 | + | 10.8726i | −1.67310 | + | 0.464032i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 9.66270 | 0.411645 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 31.8641 | − | 3.26021i | 1.35500 | − | 0.138638i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −16.9583 | + | 5.56539i | −0.719840 | + | 0.236238i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −8.76381 | −0.371335 | −0.185667 | − | 0.982613i | \(-0.559445\pi\) | ||||
−0.185667 | + | 0.982613i | \(0.559445\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 40.3265i | 1.70563i | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 11.2636 | + | 8.56487i | 0.475551 | + | 0.361609i | ||||
\(562\) | 0 | 0 | ||||||||
\(563\) | − | 1.85064i | − | 0.0779952i | −0.999239 | − | 0.0389976i | \(-0.987584\pi\) | ||
0.999239 | − | 0.0389976i | \(-0.0124165\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −26.2420 | − | 18.0909i | −1.10401 | − | 0.761088i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 19.0557 | − | 14.2786i | 0.800266 | − | 0.599646i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | − | 11.8626i | − | 0.497307i | −0.968593 | − | 0.248653i | \(-0.920012\pi\) | ||
0.968593 | − | 0.248653i | \(-0.0799880\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −29.9166 | −1.25197 | −0.625985 | − | 0.779835i | \(-0.715303\pi\) | ||||
−0.625985 | + | 0.779835i | \(0.715303\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −13.7606 | + | 18.0966i | −0.574859 | + | 0.755996i | ||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −6.79038 | − | 17.8416i | −0.283178 | − | 0.744048i | ||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −30.5778 | −1.27297 | −0.636486 | − | 0.771288i | \(-0.719613\pi\) | ||||
−0.636486 | + | 0.771288i | \(0.719613\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 11.3100 | − | 14.8737i | 0.470027 | − | 0.618131i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −2.19947 | − | 21.4968i | −0.0912495 | − | 0.891838i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | − | 21.5237i | − | 0.891422i | ||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 9.62767 | − | 27.8337i | 0.398055 | − | 1.15078i | ||||
\(586\) | 0 | 0 | ||||||||
\(587\) | − | 39.6667i | − | 1.63722i | −0.574351 | − | 0.818609i | \(-0.694745\pi\) | ||
0.574351 | − | 0.818609i | \(-0.305255\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 14.2805 | 0.588419 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −20.9264 | − | 15.9124i | −0.860797 | − | 0.654550i | ||||
\(592\) | 0 | 0 | ||||||||
\(593\) | − | 23.8526i | − | 0.979509i | −0.871860 | − | 0.489755i | \(-0.837086\pi\) | ||
0.871860 | − | 0.489755i | \(-0.162914\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −7.70949 | + | 14.0585i | −0.316058 | + | 0.576341i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 20.7711 | − | 27.3161i | 0.850106 | − | 1.11797i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 37.7489i | 1.54238i | 0.636605 | + | 0.771190i | \(0.280338\pi\) | ||||
−0.636605 | + | 0.771190i | \(0.719662\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 43.9087i | 1.79107i | 0.444986 | + | 0.895537i | \(0.353209\pi\) | ||||
−0.444986 | + | 0.895537i | \(0.646791\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −1.42938 | + | 0.396438i | −0.0582090 | + | 0.0161442i | ||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −3.52235 | − | 2.42826i | −0.143204 | − | 0.0987227i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −4.62053 | −0.187542 | −0.0937709 | − | 0.995594i | \(-0.529892\pi\) | ||||
−0.0937709 | + | 0.995594i | \(0.529892\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −2.80209 | + | 4.58922i | −0.113546 | + | 0.185965i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 52.9743i | 2.14311i | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 28.2008i | 1.13902i | 0.821985 | + | 0.569510i | \(0.192867\pi\) | ||||
−0.821985 | + | 0.569510i | \(0.807133\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 12.8738 | + | 39.2277i | 0.519120 | + | 1.58181i | ||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 7.84004 | 0.315628 | 0.157814 | − | 0.987469i | \(-0.449555\pi\) | ||||
0.157814 | + | 0.987469i | \(0.449555\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 9.24487i | 0.371583i | 0.982589 | + | 0.185791i | \(0.0594849\pi\) | ||||
−0.982589 | + | 0.185791i | \(0.940515\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 7.35089 | − | 18.4270i | 0.294981 | − | 0.739448i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 5.97094 | − | 0.610923i | 0.239220 | − | 0.0244761i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −18.6738 | + | 16.6219i | −0.746954 | + | 0.664876i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 34.2252 | + | 26.0249i | 1.36682 | + | 1.03933i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 12.4895 | 0.497989 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 34.6577 | 1.37970 | 0.689851 | − | 0.723951i | \(-0.257676\pi\) | ||||
0.689851 | + | 0.723951i | \(0.257676\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −7.70640 | − | 5.85995i | −0.306302 | − | 0.232912i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −19.5694 | + | 28.3867i | −0.776587 | + | 1.12649i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 30.0961 | − | 6.22378i | 1.19245 | − | 0.246595i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −14.9117 | + | 4.13575i | −0.589899 | + | 0.163608i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | − | 23.1085i | − | 0.912732i | −0.889792 | − | 0.456366i | \(-0.849151\pi\) | ||
0.889792 | − | 0.456366i | \(-0.150849\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −6.11558 | −0.241175 | −0.120588 | − | 0.992703i | \(-0.538478\pi\) | ||||
−0.120588 | + | 0.992703i | \(0.538478\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 33.8003 | − | 11.0926i | 1.33088 | − | 0.436771i | ||||
\(646\) | 0 | 0 | ||||||||
\(647\) | − | 22.7956i | − | 0.896188i | −0.893987 | − | 0.448094i | \(-0.852103\pi\) | ||
0.893987 | − | 0.448094i | \(-0.147897\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 27.4753i | 1.07850i | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −4.14121 | + | 6.78242i | −0.162307 | + | 0.265824i | ||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −17.0044 | −0.665432 | −0.332716 | − | 0.943027i | \(-0.607965\pi\) | ||||
−0.332716 | + | 0.943027i | \(0.607965\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 13.0340 | + | 8.98544i | 0.509280 | + | 0.351090i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 3.81678 | + | 13.7616i | 0.148907 | + | 0.536893i | ||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 13.4782i | 0.525038i | 0.964927 | + | 0.262519i | \(0.0845532\pi\) | ||||
−0.964927 | + | 0.262519i | \(0.915447\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 29.4321i | 1.14478i | 0.819983 | + | 0.572388i | \(0.193983\pi\) | ||||
−0.819983 | + | 0.572388i | \(0.806017\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −12.4745 | + | 16.4052i | −0.484469 | + | 0.637124i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −23.4257 | + | 42.7174i | −0.908411 | + | 1.65651i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 4.47995i | 0.173464i | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −2.94509 | − | 2.23944i | −0.113864 | − | 0.0865819i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 40.8773 | 1.57805 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 4.23323i | 0.163179i | 0.996666 | + | 0.0815895i | \(0.0259996\pi\) | ||||
−0.996666 | + | 0.0815895i | \(0.974000\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −25.9775 | − | 0.413376i | −0.999873 | − | 0.0159108i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 18.8318i | 0.723764i | 0.932224 | + | 0.361882i | \(0.117866\pi\) | ||||
−0.932224 | + | 0.361882i | \(0.882134\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −7.70462 | + | 0.788307i | −0.295676 | + | 0.0302525i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −4.11560 | + | 5.41241i | −0.157710 | + | 0.207404i | ||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 44.2515 | 1.69324 | 0.846618 | − | 0.532202i | \(-0.178635\pi\) | ||||
0.846618 | + | 0.532202i | \(0.178635\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −25.1426 | − | 17.3330i | −0.960651 | − | 0.662259i | ||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −15.7737 | + | 20.7440i | −0.601805 | + | 0.791433i | ||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 31.3487 | 1.19429 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | − | 50.4812i | − | 1.92039i | −0.279322 | − | 0.960197i | \(-0.590110\pi\) | ||
0.279322 | − | 0.960197i | \(-0.409890\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −22.2853 | + | 8.70804i | −0.846547 | + | 0.330791i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −10.1236 | + | 14.6850i | −0.384011 | + | 0.557034i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | − | 28.8905i | − | 1.09431i | ||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 13.4080 | + | 10.1955i | 0.507138 | + | 0.385628i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 44.6207i | 1.68530i | 0.538462 | + | 0.842650i | \(0.319006\pi\) | ||||
−0.538462 | + | 0.842650i | \(0.680994\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 37.9501 | 1.43131 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 44.4011 | − | 14.5716i | 1.67224 | − | 0.548798i | ||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −1.09512 | + | 0.112049i | −0.0411863 | + | 0.00421403i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −0.166857 | −0.00626645 | −0.00313323 | − | 0.999995i | \(-0.500997\pi\) | ||||
−0.00313323 | + | 0.999995i | \(0.500997\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −9.70664 | − | 34.9979i | −0.364027 | − | 1.31253i | ||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 6.62093i | 0.247956i | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −16.7966 | + | 24.3646i | −0.628158 | + | 0.911186i | ||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −2.65232 | + | 3.48806i | −0.0990528 | + | 0.130264i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −32.9774 | −1.22985 | −0.614925 | − | 0.788586i | \(-0.710814\pi\) | ||||
−0.614925 | + | 0.788586i | \(0.710814\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −27.5183 | + | 2.81557i | −1.02484 | + | 0.104857i | ||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 10.3499 | − | 13.6111i | 0.384916 | − | 0.506203i | ||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 5.48315 | − | 2.08684i | 0.203639 | − | 0.0775033i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 35.8146 | 1.32829 | 0.664144 | − | 0.747604i | \(-0.268796\pi\) | ||||
0.664144 | + | 0.747604i | \(0.268796\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −19.5864 | − | 18.5843i | −0.725421 | − | 0.688306i | ||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −24.8933 | −0.920713 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −14.7825 | −0.546003 | −0.273002 | − | 0.962014i | \(-0.588016\pi\) | ||||
−0.273002 | + | 0.962014i | \(0.588016\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | −13.4951 | − | 23.5135i | −0.497773 | − | 0.867307i | ||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 1.49047 | 0.0549021 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 44.5145 | 1.63749 | 0.818746 | − | 0.574156i | \(-0.194670\pi\) | ||||
0.818746 | + | 0.574156i | \(0.194670\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −37.9044 | + | 49.8480i | −1.39245 | + | 1.83121i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 9.42880 | 0.345909 | 0.172955 | − | 0.984930i | \(-0.444669\pi\) | ||||
0.172955 | + | 0.984930i | \(0.444669\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −14.2798 | + | 20.7138i | −0.523172 | + | 0.758897i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −23.6111 | + | 6.54850i | −0.863884 | + | 0.239597i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −15.6161 | + | 1.59778i | −0.570600 | + | 0.0583816i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 23.8428 | 0.870037 | 0.435019 | − | 0.900421i | \(-0.356742\pi\) | ||||
0.435019 | + | 0.900421i | \(0.356742\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 23.7392 | + | 18.0513i | 0.865105 | + | 0.657826i | ||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −5.29694 | − | 3.65163i | −0.192775 | − | 0.132896i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 35.2632i | 1.28166i | 0.767682 | + | 0.640831i | \(0.221410\pi\) | ||||
−0.767682 | + | 0.640831i | \(0.778590\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −12.0660 | + | 15.8680i | −0.437968 | + | 0.575970i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −52.0087 | −1.88531 | −0.942657 | − | 0.333764i | \(-0.891681\pi\) | ||||
−0.942657 | + | 0.333764i | \(0.891681\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 30.9431 | − | 3.16598i | 1.12022 | − | 0.114616i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 17.1816 | + | 5.94311i | 0.621201 | + | 0.214873i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −40.0170 | −1.44493 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | − | 28.0310i | − | 1.01082i | −0.862879 | − | 0.505411i | \(-0.831341\pi\) | ||
0.862879 | − | 0.505411i | \(-0.168659\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −6.71761 | + | 8.83431i | −0.241929 | + | 0.318160i | ||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 46.6884i | 1.67927i | 0.543155 | + | 0.839633i | \(0.317230\pi\) | ||||
−0.543155 | + | 0.839633i | \(0.682770\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 8.10356 | − | 3.08415i | 0.291088 | − | 0.110786i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −11.0051 | + | 18.0241i | −0.394807 | + | 0.646610i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | − | 87.7855i | − | 3.14524i | ||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 15.5490 | 0.556387 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 5.66303 | + | 2.25910i | 0.202380 | + | 0.0807336i | ||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 19.7188 | + | 13.5938i | 0.703793 | + | 0.485184i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 16.1183 | 0.574554 | 0.287277 | − | 0.957847i | \(-0.407250\pi\) | ||||
0.287277 | + | 0.957847i | \(0.407250\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 5.08806 | + | 3.86896i | 0.181140 | + | 0.137739i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −37.5174 | + | 3.83864i | −1.33397 | + | 0.136486i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 59.5366i | 2.11421i | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −8.62307 | − | 26.2753i | −0.305829 | − | 0.931891i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | − | 35.4492i | − | 1.25567i | −0.778345 | − | 0.627837i | \(-0.783940\pi\) | ||
0.778345 | − | 0.627837i | \(-0.216060\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −32.7007 | −1.15687 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −1.81891 | − | 6.55819i | −0.0642679 | − | 0.231722i | ||||
\(802\) | 0 | 0 | ||||||||
\(803\) | − | 14.3498i | − | 0.506392i | ||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −19.8052 | − | 10.8609i | −0.698042 | − | 0.382798i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 24.0946 | + | 18.3215i | 0.848168 | + | 0.644947i | ||||
\(808\) | 0 | 0 | ||||||||
\(809\) | − | 31.8061i | − | 1.11824i | −0.829086 | − | 0.559121i | \(-0.811139\pi\) | ||
0.829086 | − | 0.559121i | \(-0.188861\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | − | 40.0124i | − | 1.40503i | −0.711671 | − | 0.702513i | \(-0.752061\pi\) | ||
0.711671 | − | 0.702513i | \(-0.247939\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 3.77505 | − | 4.96456i | 0.132397 | − | 0.174115i | ||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 17.7261 | − | 25.7130i | 0.620920 | − | 0.900686i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −75.6398 | −2.64630 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −12.6830 | − | 32.4578i | −0.443180 | − | 1.13417i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 46.2101i | 1.61274i | 0.591409 | + | 0.806371i | \(0.298572\pi\) | ||||
−0.591409 | + | 0.806371i | \(0.701428\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 12.6943i | 0.442494i | 0.975218 | + | 0.221247i | \(0.0710128\pi\) | ||||
−0.975218 | + | 0.221247i | \(0.928987\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 25.0418 | + | 7.37636i | 0.871844 | + | 0.256812i | ||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −14.8569 | −0.516626 | −0.258313 | − | 0.966061i | \(-0.583167\pi\) | ||||
−0.258313 | + | 0.966061i | \(0.583167\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | − | 5.46791i | − | 0.189908i | −0.995482 | − | 0.0949542i | \(-0.969730\pi\) | ||
0.995482 | − | 0.0949542i | \(-0.0302705\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −9.84448 | + | 12.9465i | −0.341501 | + | 0.449108i | ||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 3.84191 | + | 18.5781i | 0.133114 | + | 0.643694i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −10.9117 | + | 15.8282i | −0.377616 | + | 0.547758i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 8.36940 | + | 3.33873i | 0.289289 | + | 0.115403i | ||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −47.5202 | −1.64058 | −0.820290 | − | 0.571948i | \(-0.806188\pi\) | ||||
−0.820290 | + | 0.571948i | \(0.806188\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 27.6232 | 0.952524 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −2.93777 | + | 3.86346i | −0.101182 | + | 0.133065i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −11.5535 | − | 7.96480i | −0.397452 | − | 0.273998i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −5.03580 | + | 0.515244i | −0.173032 | + | 0.0177040i | ||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 16.3636 | + | 12.4429i | 0.561598 | + | 0.427039i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 17.5949i | 0.603146i | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 31.8095 | 1.08914 | 0.544569 | − | 0.838716i | \(-0.316693\pi\) | ||||
0.544569 | + | 0.838716i | \(0.316693\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 52.2072 | + | 18.0585i | 1.78545 | + | 0.617587i | ||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 47.8666i | 1.63509i | 0.575864 | + | 0.817545i | \(0.304666\pi\) | ||||
−0.575864 | + | 0.817545i | \(0.695334\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | − | 3.56261i | − | 0.121555i | −0.998151 | − | 0.0607774i | \(-0.980642\pi\) | ||
0.998151 | − | 0.0607774i | \(-0.0193580\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 41.6930 | + | 25.4569i | 1.42089 | + | 0.867569i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −22.3349 | −0.760288 | −0.380144 | − | 0.924927i | \(-0.624126\pi\) | ||||
−0.380144 | + | 0.924927i | \(0.624126\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 11.0976 | − | 16.0978i | 0.377330 | − | 0.547343i | ||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 13.3116 | + | 10.1221i | 0.452084 | + | 0.343765i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 36.4936i | 1.23796i | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 2.17082i | 0.0735555i | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 2.34703 | + | 8.46239i | 0.0794350 | + | 0.286408i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −4.06742 | + | 29.2994i | −0.137504 | + | 0.990501i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | − | 18.6566i | − | 0.629989i | −0.949094 | − | 0.314994i | \(-0.897997\pi\) | ||
0.949094 | − | 0.314994i | \(-0.102003\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −16.2651 | + | 21.3903i | −0.548610 | + | 0.721475i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −26.8648 | −0.905097 | −0.452549 | − | 0.891740i | \(-0.649485\pi\) | ||||
−0.452549 | + | 0.891740i | \(0.649485\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | − | 12.0169i | − | 0.404400i | −0.979344 | − | 0.202200i | \(-0.935191\pi\) | ||
0.979344 | − | 0.202200i | \(-0.0648092\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 11.0075 | + | 33.5408i | 0.370011 | + | 1.12746i | ||||
\(886\) | 0 | 0 | ||||||||
\(887\) | − | 13.9283i | − | 0.467666i | −0.972277 | − | 0.233833i | \(-0.924873\pi\) | ||
0.972277 | − | 0.233833i | \(-0.0751268\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 4.15236 | + | 40.5836i | 0.139266 | + | 1.36113i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 13.9739 | + | 23.2541i | 0.468143 | + | 0.779042i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −99.3629 | −3.32505 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −21.6613 | + | 31.4213i | −0.724059 | + | 1.05030i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −23.1112 | − | 17.5738i | −0.771661 | − | 0.586771i | ||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −2.03477 | −0.0678632 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 19.3514i | 0.644687i | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 21.9348 | − | 35.9245i | 0.729944 | − | 1.19549i | ||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −8.45087 | + | 12.2586i | −0.280916 | + | 0.407488i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 23.7097i | 0.787269i | 0.919267 | + | 0.393634i | \(0.128782\pi\) | ||||
−0.919267 | + | 0.393634i | \(0.871218\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0.333603 | + | 1.20283i | 0.0110649 | + | 0.0398953i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 0.247204i | 0.00819025i | 0.999992 | + | 0.00409512i | \(0.00130352\pi\) | ||||
−0.999992 | + | 0.00409512i | \(0.998696\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 24.6201 | 0.814807 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 49.9014 | − | 16.3767i | 1.64969 | − | 0.541397i | ||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 18.6343 | − | 1.90659i | 0.615359 | − | 0.0629612i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 14.4956 | 0.478165 | 0.239083 | − | 0.970999i | \(-0.423153\pi\) | ||||
0.239083 | + | 0.970999i | \(0.423153\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −6.87519 | − | 5.22790i | −0.226545 | − | 0.172265i | ||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 22.6467i | 0.745424i | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 21.5349 | − | 8.19602i | 0.708065 | − | 0.269483i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 8.38281 | + | 30.2248i | 0.275328 | + | 0.992713i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 3.97297 | 0.130349 | 0.0651745 | − | 0.997874i | \(-0.479240\pi\) | ||||
0.0651745 | + | 0.997874i | \(0.479240\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 11.6738 | + | 56.4507i | 0.382595 | + | 1.85010i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 32.1168 | + | 24.4216i | 1.05146 | + | 0.799527i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −15.0402 | − | 10.3685i | −0.491866 | − | 0.339085i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 32.7664 | 1.07043 | 0.535216 | − | 0.844715i | \(-0.320230\pi\) | ||||
0.535216 | + | 0.844715i | \(0.320230\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 9.88349 | + | 7.51540i | 0.322535 | + | 0.245256i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 34.4787 | 1.12397 | 0.561987 | − | 0.827146i | \(-0.310037\pi\) | ||||
0.561987 | + | 0.827146i | \(0.310037\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 40.7003 | 1.32538 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | −23.7163 | + | 19.5586i | −0.771490 | + | 0.636241i | ||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −43.1115 | −1.40093 | −0.700467 | − | 0.713684i | \(-0.747025\pi\) | ||||
−0.700467 | + | 0.713684i | \(0.747025\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 20.9000 | 0.678443 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 4.01214 | + | 3.05083i | 0.130103 | + | 0.0989300i | ||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −53.6918 | −1.73925 | −0.869624 | − | 0.493714i | \(-0.835639\pi\) | ||||
−0.869624 | + | 0.493714i | \(0.835639\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 16.6584 | − | 24.1641i | 0.539052 | − | 0.781931i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −4.87659 | − | 3.70816i | −0.157638 | − | 0.119868i | ||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −35.9457 | + | 3.67782i | −1.16075 | + | 0.118763i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 27.9928 | 0.902994 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 4.75708 | + | 17.1520i | 0.153295 | + | 0.552715i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −13.6916 | + | 19.8606i | −0.440749 | + | 0.639337i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | − | 1.49312i | − | 0.0480155i | −0.999712 | − | 0.0240077i | \(-0.992357\pi\) | ||
0.999712 | − | 0.0240077i | \(-0.00764263\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −30.7709 | − | 23.3982i | −0.988503 | − | 0.751658i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 3.95684 | 0.126981 | 0.0634905 | − | 0.997982i | \(-0.479777\pi\) | ||||
0.0634905 | + | 0.997982i | \(0.479777\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 2.14810 | + | 20.9947i | 0.0688648 | + | 0.673059i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −10.7434 | + | 36.4727i | −0.344066 | + | 1.16806i | ||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 47.6921 | 1.52580 | 0.762902 | − | 0.646514i | \(-0.223774\pi\) | ||||
0.762902 | + | 0.646514i | \(0.223774\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 6.83846i | 0.218558i | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −9.42610 | − | 33.9865i | −0.300952 | − | 1.08510i | ||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 13.0582i | 0.416491i | 0.978077 | + | 0.208245i | \(0.0667752\pi\) | ||||
−0.978077 | + | 0.208245i | \(0.933225\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 27.9427 | + | 19.2633i | 0.890328 | + | 0.613779i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 28.8142 | − | 47.1916i | 0.917168 | − | 1.50213i | ||||
\(988\) | 0 | 0 | ||||||||
\(989\) | − | 35.0691i | − | 1.11513i | ||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −12.6624 | −0.402236 | −0.201118 | − | 0.979567i | \(-0.564457\pi\) | ||||
−0.201118 | + | 0.979567i | \(0.564457\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −40.5792 | − | 30.8564i | −1.28774 | − | 0.979198i | ||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −25.1451 | + | 36.4747i | −0.797153 | + | 1.15633i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 22.6851 | 0.718444 | 0.359222 | − | 0.933252i | \(-0.383042\pi\) | ||||
0.359222 | + | 0.933252i | \(0.383042\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 22.2414 | + | 8.87256i | 0.703687 | + | 0.280715i |
(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 | 1680.2.k.i.209.20 | 24 | ||
3.2 | odd | 2 | 1680.2.k.h.209.19 | 24 | |||
4.3 | odd | 2 | 840.2.k.a.209.5 | ✓ | 24 | ||
5.4 | even | 2 | 1680.2.k.h.209.5 | 24 | |||
7.6 | odd | 2 | inner | 1680.2.k.i.209.5 | 24 | ||
12.11 | even | 2 | 840.2.k.b.209.6 | yes | 24 | ||
15.14 | odd | 2 | inner | 1680.2.k.i.209.6 | 24 | ||
20.19 | odd | 2 | 840.2.k.b.209.20 | yes | 24 | ||
21.20 | even | 2 | 1680.2.k.h.209.6 | 24 | |||
28.27 | even | 2 | 840.2.k.a.209.20 | yes | 24 | ||
35.34 | odd | 2 | 1680.2.k.h.209.20 | 24 | |||
60.59 | even | 2 | 840.2.k.a.209.19 | yes | 24 | ||
84.83 | odd | 2 | 840.2.k.b.209.19 | yes | 24 | ||
105.104 | even | 2 | inner | 1680.2.k.i.209.19 | 24 | ||
140.139 | even | 2 | 840.2.k.b.209.5 | yes | 24 | ||
420.419 | odd | 2 | 840.2.k.a.209.6 | yes | 24 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
840.2.k.a.209.5 | ✓ | 24 | 4.3 | odd | 2 | ||
840.2.k.a.209.6 | yes | 24 | 420.419 | odd | 2 | ||
840.2.k.a.209.19 | yes | 24 | 60.59 | even | 2 | ||
840.2.k.a.209.20 | yes | 24 | 28.27 | even | 2 | ||
840.2.k.b.209.5 | yes | 24 | 140.139 | even | 2 | ||
840.2.k.b.209.6 | yes | 24 | 12.11 | even | 2 | ||
840.2.k.b.209.19 | yes | 24 | 84.83 | odd | 2 | ||
840.2.k.b.209.20 | yes | 24 | 20.19 | odd | 2 | ||
1680.2.k.h.209.5 | 24 | 5.4 | even | 2 | |||
1680.2.k.h.209.6 | 24 | 21.20 | even | 2 | |||
1680.2.k.h.209.19 | 24 | 3.2 | odd | 2 | |||
1680.2.k.h.209.20 | 24 | 35.34 | odd | 2 | |||
1680.2.k.i.209.5 | 24 | 7.6 | odd | 2 | inner | ||
1680.2.k.i.209.6 | 24 | 15.14 | odd | 2 | inner | ||
1680.2.k.i.209.19 | 24 | 105.104 | even | 2 | inner | ||
1680.2.k.i.209.20 | 24 | 1.1 | even | 1 | trivial |