Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1183,2,Mod(337,1183)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1183, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 1]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1183.337");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1183 = 7 \cdot 13^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1183.c (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: | \(9.44630255912\) |
Analytic rank: | \(0\) |
Dimension: | \(24\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 337.8 | ||
Character | \(\chi\) | \(=\) | 1183.337 |
Dual form | 1183.2.c.j.337.17 |
$q$-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 \(\left(\mathbb{Z}/1183\mathbb{Z}\right)^\times\).
\(n\) | \(339\) | \(1016\) |
\(\chi(n)\) | \(1\) | \(-1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | − 1.10989i | − 0.784809i | −0.919793 | − | 0.392404i | \(-0.871643\pi\) | ||||
0.919793 | − | 0.392404i | \(-0.128357\pi\) | |||||||
\(3\) | 0.955760 | 0.551808 | 0.275904 | − | 0.961185i | \(-0.411023\pi\) | ||||
0.275904 | + | 0.961185i | \(0.411023\pi\) | |||||||
\(4\) | 0.768150 | 0.384075 | ||||||||
\(5\) | − 3.55862i | − 1.59146i | −0.605650 | − | 0.795731i | \(-0.707087\pi\) | ||||
0.605650 | − | 0.795731i | \(-0.292913\pi\) | |||||||
\(6\) | − 1.06079i | − 0.433064i | ||||||||
\(7\) | − 1.00000i | − 0.377964i | ||||||||
\(8\) | − 3.07233i | − 1.08623i | ||||||||
\(9\) | −2.08652 | −0.695508 | ||||||||
\(10\) | −3.94966 | −1.24899 | ||||||||
\(11\) | 4.00483i | 1.20750i | 0.797173 | + | 0.603751i | \(0.206328\pi\) | ||||
−0.797173 | + | 0.603751i | \(0.793672\pi\) | |||||||
\(12\) | 0.734167 | 0.211936 | ||||||||
\(13\) | 0 | 0 | ||||||||
\(14\) | −1.10989 | −0.296630 | ||||||||
\(15\) | − 3.40118i | − 0.878182i | ||||||||
\(16\) | −1.87364 | −0.468411 | ||||||||
\(17\) | −1.86471 | −0.452258 | −0.226129 | − | 0.974097i | \(-0.572607\pi\) | ||||
−0.226129 | + | 0.974097i | \(0.572607\pi\) | |||||||
\(18\) | 2.31581i | 0.545841i | ||||||||
\(19\) | − 6.34660i | − 1.45601i | −0.685572 | − | 0.728005i | \(-0.740448\pi\) | ||||
0.685572 | − | 0.728005i | \(-0.259552\pi\) | |||||||
\(20\) | − 2.73355i | − 0.611241i | ||||||||
\(21\) | − 0.955760i | − 0.208564i | ||||||||
\(22\) | 4.44491 | 0.947658 | ||||||||
\(23\) | −4.50206 | −0.938744 | −0.469372 | − | 0.883001i | \(-0.655520\pi\) | ||||
−0.469372 | + | 0.883001i | \(0.655520\pi\) | |||||||
\(24\) | − 2.93641i | − 0.599393i | ||||||||
\(25\) | −7.66376 | −1.53275 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −4.86149 | −0.935595 | ||||||||
\(28\) | − 0.768150i | − 0.145167i | ||||||||
\(29\) | 8.63110 | 1.60275 | 0.801377 | − | 0.598159i | \(-0.204101\pi\) | ||||
0.801377 | + | 0.598159i | \(0.204101\pi\) | |||||||
\(30\) | −3.77493 | −0.689205 | ||||||||
\(31\) | − 3.22435i | − 0.579110i | −0.957161 | − | 0.289555i | \(-0.906493\pi\) | ||||
0.957161 | − | 0.289555i | \(-0.0935073\pi\) | |||||||
\(32\) | − 4.06514i | − 0.718621i | ||||||||
\(33\) | 3.82766i | 0.666309i | ||||||||
\(34\) | 2.06962i | 0.354936i | ||||||||
\(35\) | −3.55862 | −0.601516 | ||||||||
\(36\) | −1.60276 | −0.267127 | ||||||||
\(37\) | − 1.83406i | − 0.301517i | −0.988571 | − | 0.150758i | \(-0.951828\pi\) | ||||
0.988571 | − | 0.150758i | \(-0.0481716\pi\) | |||||||
\(38\) | −7.04401 | −1.14269 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | −10.9333 | −1.72870 | ||||||||
\(41\) | 10.3590i | 1.61780i | 0.587947 | + | 0.808899i | \(0.299936\pi\) | ||||
−0.587947 | + | 0.808899i | \(0.700064\pi\) | |||||||
\(42\) | −1.06079 | −0.163683 | ||||||||
\(43\) | 10.3318 | 1.57559 | 0.787793 | − | 0.615941i | \(-0.211224\pi\) | ||||
0.787793 | + | 0.615941i | \(0.211224\pi\) | |||||||
\(44\) | 3.07631i | 0.463771i | ||||||||
\(45\) | 7.42514i | 1.10687i | ||||||||
\(46\) | 4.99678i | 0.736735i | ||||||||
\(47\) | 0.832988i | 0.121504i | 0.998153 | + | 0.0607519i | \(0.0193498\pi\) | ||||
−0.998153 | + | 0.0607519i | \(0.980650\pi\) | |||||||
\(48\) | −1.79075 | −0.258473 | ||||||||
\(49\) | −1.00000 | −0.142857 | ||||||||
\(50\) | 8.50590i | 1.20292i | ||||||||
\(51\) | −1.78221 | −0.249560 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 6.53512 | 0.897667 | 0.448834 | − | 0.893615i | \(-0.351840\pi\) | ||||
0.448834 | + | 0.893615i | \(0.351840\pi\) | |||||||
\(54\) | 5.39571i | 0.734263i | ||||||||
\(55\) | 14.2517 | 1.92169 | ||||||||
\(56\) | −3.07233 | −0.410558 | ||||||||
\(57\) | − 6.06582i | − 0.803438i | ||||||||
\(58\) | − 9.57955i | − 1.25786i | ||||||||
\(59\) | − 5.20780i | − 0.677997i | −0.940787 | − | 0.338999i | \(-0.889912\pi\) | ||||
0.940787 | − | 0.338999i | \(-0.110088\pi\) | |||||||
\(60\) | − 2.61262i | − 0.337288i | ||||||||
\(61\) | −1.83794 | −0.235324 | −0.117662 | − | 0.993054i | \(-0.537540\pi\) | ||||
−0.117662 | + | 0.993054i | \(0.537540\pi\) | |||||||
\(62\) | −3.57866 | −0.454491 | ||||||||
\(63\) | 2.08652i | 0.262877i | ||||||||
\(64\) | −8.25913 | −1.03239 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 4.24827 | 0.522925 | ||||||||
\(67\) | 3.05008i | 0.372626i | 0.982490 | + | 0.186313i | \(0.0596539\pi\) | ||||
−0.982490 | + | 0.186313i | \(0.940346\pi\) | |||||||
\(68\) | −1.43238 | −0.173701 | ||||||||
\(69\) | −4.30289 | −0.518007 | ||||||||
\(70\) | 3.94966i | 0.472075i | ||||||||
\(71\) | 14.4391i | 1.71361i | 0.515640 | + | 0.856805i | \(0.327554\pi\) | ||||
−0.515640 | + | 0.856805i | \(0.672446\pi\) | |||||||
\(72\) | 6.41050i | 0.755484i | ||||||||
\(73\) | − 12.9055i | − 1.51047i | −0.655454 | − | 0.755235i | \(-0.727523\pi\) | ||||
0.655454 | − | 0.755235i | \(-0.272477\pi\) | |||||||
\(74\) | −2.03559 | −0.236633 | ||||||||
\(75\) | −7.32471 | −0.845785 | ||||||||
\(76\) | − 4.87514i | − 0.559217i | ||||||||
\(77\) | 4.00483 | 0.456393 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 0.0931919 | 0.0104849 | 0.00524245 | − | 0.999986i | \(-0.498331\pi\) | ||||
0.00524245 | + | 0.999986i | \(0.498331\pi\) | |||||||
\(80\) | 6.66758i | 0.745458i | ||||||||
\(81\) | 1.61315 | 0.179239 | ||||||||
\(82\) | 11.4973 | 1.26966 | ||||||||
\(83\) | 3.17863i | 0.348900i | 0.984666 | + | 0.174450i | \(0.0558147\pi\) | ||||
−0.984666 | + | 0.174450i | \(0.944185\pi\) | |||||||
\(84\) | − 0.734167i | − 0.0801042i | ||||||||
\(85\) | 6.63578i | 0.719752i | ||||||||
\(86\) | − 11.4671i | − 1.23653i | ||||||||
\(87\) | 8.24926 | 0.884413 | ||||||||
\(88\) | 12.3042 | 1.31163 | ||||||||
\(89\) | − 12.2290i | − 1.29627i | −0.761524 | − | 0.648137i | \(-0.775549\pi\) | ||||
0.761524 | − | 0.648137i | \(-0.224451\pi\) | |||||||
\(90\) | 8.24106 | 0.868684 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | −3.45826 | −0.360548 | ||||||||
\(93\) | − 3.08170i | − 0.319558i | ||||||||
\(94\) | 0.924522 | 0.0953572 | ||||||||
\(95\) | −22.5851 | −2.31718 | ||||||||
\(96\) | − 3.88529i | − 0.396541i | ||||||||
\(97\) | − 13.1916i | − 1.33941i | −0.742628 | − | 0.669704i | \(-0.766421\pi\) | ||||
0.742628 | − | 0.669704i | \(-0.233579\pi\) | |||||||
\(98\) | 1.10989i | 0.112116i | ||||||||
\(99\) | − 8.35617i | − 0.839827i | ||||||||
\(100\) | −5.88692 | −0.588692 | ||||||||
\(101\) | 7.73025 | 0.769188 | 0.384594 | − | 0.923086i | \(-0.374341\pi\) | ||||
0.384594 | + | 0.923086i | \(0.374341\pi\) | |||||||
\(102\) | 1.97806i | 0.195857i | ||||||||
\(103\) | 0.359154 | 0.0353885 | 0.0176943 | − | 0.999843i | \(-0.494367\pi\) | ||||
0.0176943 | + | 0.999843i | \(0.494367\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −3.40118 | −0.331922 | ||||||||
\(106\) | − 7.25324i | − 0.704497i | ||||||||
\(107\) | −3.99044 | −0.385770 | −0.192885 | − | 0.981221i | \(-0.561784\pi\) | ||||
−0.192885 | + | 0.981221i | \(0.561784\pi\) | |||||||
\(108\) | −3.73436 | −0.359339 | ||||||||
\(109\) | − 9.65395i | − 0.924681i | −0.886702 | − | 0.462341i | \(-0.847010\pi\) | ||||
0.886702 | − | 0.462341i | \(-0.152990\pi\) | |||||||
\(110\) | − 15.8177i | − 1.50816i | ||||||||
\(111\) | − 1.75292i | − 0.166379i | ||||||||
\(112\) | 1.87364i | 0.177043i | ||||||||
\(113\) | 2.08248 | 0.195904 | 0.0979518 | − | 0.995191i | \(-0.468771\pi\) | ||||
0.0979518 | + | 0.995191i | \(0.468771\pi\) | |||||||
\(114\) | −6.73238 | −0.630545 | ||||||||
\(115\) | 16.0211i | 1.49398i | ||||||||
\(116\) | 6.62998 | 0.615578 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | −5.78007 | −0.532098 | ||||||||
\(119\) | 1.86471i | 0.170937i | ||||||||
\(120\) | −10.4496 | −0.953911 | ||||||||
\(121\) | −5.03866 | −0.458060 | ||||||||
\(122\) | 2.03991i | 0.184685i | ||||||||
\(123\) | 9.90068i | 0.892714i | ||||||||
\(124\) | − 2.47678i | − 0.222422i | ||||||||
\(125\) | 9.47929i | 0.847853i | ||||||||
\(126\) | 2.31581 | 0.206308 | ||||||||
\(127\) | −7.18287 | −0.637376 | −0.318688 | − | 0.947860i | \(-0.603242\pi\) | ||||
−0.318688 | + | 0.947860i | \(0.603242\pi\) | |||||||
\(128\) | 1.03643i | 0.0916084i | ||||||||
\(129\) | 9.87472 | 0.869421 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −1.48085 | −0.129383 | −0.0646913 | − | 0.997905i | \(-0.520606\pi\) | ||||
−0.0646913 | + | 0.997905i | \(0.520606\pi\) | |||||||
\(132\) | 2.94022i | 0.255913i | ||||||||
\(133\) | −6.34660 | −0.550320 | ||||||||
\(134\) | 3.38524 | 0.292440 | ||||||||
\(135\) | 17.3002i | 1.48896i | ||||||||
\(136\) | 5.72901i | 0.491258i | ||||||||
\(137\) | 4.43864i | 0.379219i | 0.981860 | + | 0.189609i | \(0.0607222\pi\) | ||||
−0.981860 | + | 0.189609i | \(0.939278\pi\) | |||||||
\(138\) | 4.77572i | 0.406536i | ||||||||
\(139\) | 17.3529 | 1.47186 | 0.735929 | − | 0.677059i | \(-0.236746\pi\) | ||||
0.735929 | + | 0.677059i | \(0.236746\pi\) | |||||||
\(140\) | −2.73355 | −0.231027 | ||||||||
\(141\) | 0.796136i | 0.0670468i | ||||||||
\(142\) | 16.0258 | 1.34486 | ||||||||
\(143\) | 0 | 0 | ||||||||
\(144\) | 3.90940 | 0.325783 | ||||||||
\(145\) | − 30.7148i | − 2.55072i | ||||||||
\(146\) | −14.3236 | −1.18543 | ||||||||
\(147\) | −0.955760 | −0.0788297 | ||||||||
\(148\) | − 1.40883i | − 0.115805i | ||||||||
\(149\) | 23.1381i | 1.89554i | 0.318950 | + | 0.947771i | \(0.396670\pi\) | ||||
−0.318950 | + | 0.947771i | \(0.603330\pi\) | |||||||
\(150\) | 8.12960i | 0.663779i | ||||||||
\(151\) | − 10.8846i | − 0.885778i | −0.896576 | − | 0.442889i | \(-0.853953\pi\) | ||||
0.896576 | − | 0.442889i | \(-0.146047\pi\) | |||||||
\(152\) | −19.4989 | −1.58157 | ||||||||
\(153\) | 3.89076 | 0.314549 | ||||||||
\(154\) | − 4.44491i | − 0.358181i | ||||||||
\(155\) | −11.4742 | −0.921632 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 14.2555 | 1.13771 | 0.568855 | − | 0.822438i | \(-0.307387\pi\) | ||||
0.568855 | + | 0.822438i | \(0.307387\pi\) | |||||||
\(158\) | − 0.103432i | − 0.00822865i | ||||||||
\(159\) | 6.24600 | 0.495340 | ||||||||
\(160\) | −14.4663 | −1.14366 | ||||||||
\(161\) | 4.50206i | 0.354812i | ||||||||
\(162\) | − 1.79041i | − 0.140668i | ||||||||
\(163\) | 2.01430i | 0.157772i | 0.996884 | + | 0.0788861i | \(0.0251364\pi\) | ||||
−0.996884 | + | 0.0788861i | \(0.974864\pi\) | |||||||
\(164\) | 7.95724i | 0.621356i | ||||||||
\(165\) | 13.6212 | 1.06041 | ||||||||
\(166\) | 3.52792 | 0.273820 | ||||||||
\(167\) | 18.8978i | 1.46236i | 0.682187 | + | 0.731178i | \(0.261029\pi\) | ||||
−0.682187 | + | 0.731178i | \(0.738971\pi\) | |||||||
\(168\) | −2.93641 | −0.226549 | ||||||||
\(169\) | 0 | 0 | ||||||||
\(170\) | 7.36497 | 0.564867 | ||||||||
\(171\) | 13.2423i | 1.01267i | ||||||||
\(172\) | 7.93638 | 0.605143 | ||||||||
\(173\) | 12.4146 | 0.943868 | 0.471934 | − | 0.881634i | \(-0.343556\pi\) | ||||
0.471934 | + | 0.881634i | \(0.343556\pi\) | |||||||
\(174\) | − 9.15575i | − 0.694095i | ||||||||
\(175\) | 7.66376i | 0.579325i | ||||||||
\(176\) | − 7.50363i | − 0.565607i | ||||||||
\(177\) | − 4.97740i | − 0.374125i | ||||||||
\(178\) | −13.5728 | −1.01733 | ||||||||
\(179\) | 9.37393 | 0.700641 | 0.350320 | − | 0.936630i | \(-0.386073\pi\) | ||||
0.350320 | + | 0.936630i | \(0.386073\pi\) | |||||||
\(180\) | 5.70362i | 0.425123i | ||||||||
\(181\) | −5.83547 | −0.433747 | −0.216873 | − | 0.976200i | \(-0.569586\pi\) | ||||
−0.216873 | + | 0.976200i | \(0.569586\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −1.75663 | −0.129854 | ||||||||
\(184\) | 13.8318i | 1.01970i | ||||||||
\(185\) | −6.52670 | −0.479852 | ||||||||
\(186\) | −3.42034 | −0.250792 | ||||||||
\(187\) | − 7.46784i | − 0.546102i | ||||||||
\(188\) | 0.639860i | 0.0466666i | ||||||||
\(189\) | 4.86149i | 0.353622i | ||||||||
\(190\) | 25.0669i | 1.81855i | ||||||||
\(191\) | −16.3051 | −1.17980 | −0.589899 | − | 0.807477i | \(-0.700833\pi\) | ||||
−0.589899 | + | 0.807477i | \(0.700833\pi\) | |||||||
\(192\) | −7.89375 | −0.569682 | ||||||||
\(193\) | − 21.2251i | − 1.52782i | −0.645323 | − | 0.763910i | \(-0.723277\pi\) | ||||
0.645323 | − | 0.763910i | \(-0.276723\pi\) | |||||||
\(194\) | −14.6412 | −1.05118 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −0.768150 | −0.0548679 | ||||||||
\(197\) | − 16.0798i | − 1.14564i | −0.819683 | − | 0.572818i | \(-0.805850\pi\) | ||||
0.819683 | − | 0.572818i | \(-0.194150\pi\) | |||||||
\(198\) | −9.27441 | −0.659103 | ||||||||
\(199\) | 15.4383 | 1.09440 | 0.547198 | − | 0.837003i | \(-0.315695\pi\) | ||||
0.547198 | + | 0.837003i | \(0.315695\pi\) | |||||||
\(200\) | 23.5456i | 1.66493i | ||||||||
\(201\) | 2.91514i | 0.205618i | ||||||||
\(202\) | − 8.57970i | − 0.603666i | ||||||||
\(203\) | − 8.63110i | − 0.605784i | ||||||||
\(204\) | −1.36901 | −0.0958497 | ||||||||
\(205\) | 36.8636 | 2.57466 | ||||||||
\(206\) | − 0.398621i | − 0.0277732i | ||||||||
\(207\) | 9.39365 | 0.652904 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 25.4170 | 1.75813 | ||||||||
\(210\) | 3.77493i | 0.260495i | ||||||||
\(211\) | 3.45377 | 0.237767 | 0.118884 | − | 0.992908i | \(-0.462068\pi\) | ||||
0.118884 | + | 0.992908i | \(0.462068\pi\) | |||||||
\(212\) | 5.01995 | 0.344772 | ||||||||
\(213\) | 13.8004i | 0.945584i | ||||||||
\(214\) | 4.42893i | 0.302756i | ||||||||
\(215\) | − 36.7669i | − 2.50748i | ||||||||
\(216\) | 14.9361i | 1.01628i | ||||||||
\(217\) | −3.22435 | −0.218883 | ||||||||
\(218\) | −10.7148 | −0.725698 | ||||||||
\(219\) | − 12.3345i | − 0.833490i | ||||||||
\(220\) | 10.9474 | 0.738075 | ||||||||
\(221\) | 0 | 0 | ||||||||
\(222\) | −1.94554 | −0.130576 | ||||||||
\(223\) | 15.6638i | 1.04893i | 0.851433 | + | 0.524464i | \(0.175734\pi\) | ||||
−0.851433 | + | 0.524464i | \(0.824266\pi\) | |||||||
\(224\) | −4.06514 | −0.271613 | ||||||||
\(225\) | 15.9906 | 1.06604 | ||||||||
\(226\) | − 2.31132i | − 0.153747i | ||||||||
\(227\) | − 8.05474i | − 0.534612i | −0.963612 | − | 0.267306i | \(-0.913867\pi\) | ||||
0.963612 | − | 0.267306i | \(-0.0861335\pi\) | |||||||
\(228\) | − 4.65947i | − 0.308581i | ||||||||
\(229\) | 19.9670i | 1.31946i | 0.751503 | + | 0.659730i | \(0.229329\pi\) | ||||
−0.751503 | + | 0.659730i | \(0.770671\pi\) | |||||||
\(230\) | 17.7816 | 1.17248 | ||||||||
\(231\) | 3.82766 | 0.251841 | ||||||||
\(232\) | − 26.5176i | − 1.74097i | ||||||||
\(233\) | −12.1790 | −0.797871 | −0.398935 | − | 0.916979i | \(-0.630620\pi\) | ||||
−0.398935 | + | 0.916979i | \(0.630620\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 2.96428 | 0.193369 | ||||||||
\(236\) | − 4.00037i | − 0.260402i | ||||||||
\(237\) | 0.0890691 | 0.00578566 | ||||||||
\(238\) | 2.06962 | 0.134153 | ||||||||
\(239\) | 15.5704i | 1.00717i | 0.863946 | + | 0.503584i | \(0.167986\pi\) | ||||
−0.863946 | + | 0.503584i | \(0.832014\pi\) | |||||||
\(240\) | 6.37261i | 0.411350i | ||||||||
\(241\) | − 1.30581i | − 0.0841148i | −0.999115 | − | 0.0420574i | \(-0.986609\pi\) | ||||
0.999115 | − | 0.0420574i | \(-0.0133912\pi\) | |||||||
\(242\) | 5.59235i | 0.359490i | ||||||||
\(243\) | 16.1263 | 1.03450 | ||||||||
\(244\) | −1.41182 | −0.0903822 | ||||||||
\(245\) | 3.55862i | 0.227352i | ||||||||
\(246\) | 10.9886 | 0.700610 | ||||||||
\(247\) | 0 | 0 | ||||||||
\(248\) | −9.90628 | −0.629049 | ||||||||
\(249\) | 3.03801i | 0.192526i | ||||||||
\(250\) | 10.5209 | 0.665402 | ||||||||
\(251\) | 20.2852 | 1.28039 | 0.640196 | − | 0.768212i | \(-0.278853\pi\) | ||||
0.640196 | + | 0.768212i | \(0.278853\pi\) | |||||||
\(252\) | 1.60276i | 0.100965i | ||||||||
\(253\) | − 18.0300i | − 1.13353i | ||||||||
\(254\) | 7.97217i | 0.500219i | ||||||||
\(255\) | 6.34221i | 0.397165i | ||||||||
\(256\) | −15.3679 | −0.960496 | ||||||||
\(257\) | −17.3450 | −1.08195 | −0.540977 | − | 0.841038i | \(-0.681945\pi\) | ||||
−0.540977 | + | 0.841038i | \(0.681945\pi\) | |||||||
\(258\) | − 10.9598i | − 0.682329i | ||||||||
\(259\) | −1.83406 | −0.113963 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −18.0090 | −1.11473 | ||||||||
\(262\) | 1.64358i | 0.101541i | ||||||||
\(263\) | −10.8891 | −0.671448 | −0.335724 | − | 0.941960i | \(-0.608981\pi\) | ||||
−0.335724 | + | 0.941960i | \(0.608981\pi\) | |||||||
\(264\) | 11.7598 | 0.723768 | ||||||||
\(265\) | − 23.2560i | − 1.42860i | ||||||||
\(266\) | 7.04401i | 0.431896i | ||||||||
\(267\) | − 11.6880i | − 0.715294i | ||||||||
\(268\) | 2.34292i | 0.143117i | ||||||||
\(269\) | 8.99414 | 0.548382 | 0.274191 | − | 0.961675i | \(-0.411590\pi\) | ||||
0.274191 | + | 0.961675i | \(0.411590\pi\) | |||||||
\(270\) | 19.2013 | 1.16855 | ||||||||
\(271\) | − 4.94282i | − 0.300255i | −0.988667 | − | 0.150127i | \(-0.952032\pi\) | ||||
0.988667 | − | 0.150127i | \(-0.0479684\pi\) | |||||||
\(272\) | 3.49380 | 0.211843 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 4.92639 | 0.297614 | ||||||||
\(275\) | − 30.6920i | − 1.85080i | ||||||||
\(276\) | −3.30526 | −0.198954 | ||||||||
\(277\) | −19.4610 | −1.16930 | −0.584650 | − | 0.811286i | \(-0.698768\pi\) | ||||
−0.584650 | + | 0.811286i | \(0.698768\pi\) | |||||||
\(278\) | − 19.2598i | − 1.15513i | ||||||||
\(279\) | 6.72768i | 0.402776i | ||||||||
\(280\) | 10.9333i | 0.653387i | ||||||||
\(281\) | 20.1468i | 1.20185i | 0.799304 | + | 0.600927i | \(0.205202\pi\) | ||||
−0.799304 | + | 0.600927i | \(0.794798\pi\) | |||||||
\(282\) | 0.883621 | 0.0526189 | ||||||||
\(283\) | 22.8282 | 1.35699 | 0.678496 | − | 0.734604i | \(-0.262632\pi\) | ||||
0.678496 | + | 0.734604i | \(0.262632\pi\) | |||||||
\(284\) | 11.0914i | 0.658155i | ||||||||
\(285\) | −21.5859 | −1.27864 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 10.3590 | 0.611470 | ||||||||
\(288\) | 8.48200i | 0.499807i | ||||||||
\(289\) | −13.5229 | −0.795463 | ||||||||
\(290\) | −34.0899 | −2.00183 | ||||||||
\(291\) | − 12.6080i | − 0.739096i | ||||||||
\(292\) | − 9.91334i | − 0.580134i | ||||||||
\(293\) | − 26.5717i | − 1.55233i | −0.630528 | − | 0.776166i | \(-0.717162\pi\) | ||||
0.630528 | − | 0.776166i | \(-0.282838\pi\) | |||||||
\(294\) | 1.06079i | 0.0618663i | ||||||||
\(295\) | −18.5326 | −1.07901 | ||||||||
\(296\) | −5.63483 | −0.327518 | ||||||||
\(297\) | − 19.4695i | − 1.12973i | ||||||||
\(298\) | 25.6806 | 1.48764 | ||||||||
\(299\) | 0 | 0 | ||||||||
\(300\) | −5.62648 | −0.324845 | ||||||||
\(301\) | − 10.3318i | − 0.595515i | ||||||||
\(302\) | −12.0807 | −0.695167 | ||||||||
\(303\) | 7.38826 | 0.424444 | ||||||||
\(304\) | 11.8913i | 0.682011i | ||||||||
\(305\) | 6.54053i | 0.374510i | ||||||||
\(306\) | − 4.31830i | − 0.246861i | ||||||||
\(307\) | 7.16833i | 0.409118i | 0.978854 | + | 0.204559i | \(0.0655761\pi\) | ||||
−0.978854 | + | 0.204559i | \(0.934424\pi\) | |||||||
\(308\) | 3.07631 | 0.175289 | ||||||||
\(309\) | 0.343265 | 0.0195277 | ||||||||
\(310\) | 12.7351i | 0.723305i | ||||||||
\(311\) | 13.6640 | 0.774817 | 0.387408 | − | 0.921908i | \(-0.373370\pi\) | ||||
0.387408 | + | 0.921908i | \(0.373370\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 10.5821 | 0.598137 | 0.299068 | − | 0.954232i | \(-0.403324\pi\) | ||||
0.299068 | + | 0.954232i | \(0.403324\pi\) | |||||||
\(314\) | − 15.8219i | − 0.892884i | ||||||||
\(315\) | 7.42514 | 0.418359 | ||||||||
\(316\) | 0.0715854 | 0.00402699 | ||||||||
\(317\) | − 3.65041i | − 0.205027i | −0.994732 | − | 0.102514i | \(-0.967311\pi\) | ||||
0.994732 | − | 0.102514i | \(-0.0326886\pi\) | |||||||
\(318\) | − 6.93236i | − 0.388747i | ||||||||
\(319\) | 34.5661i | 1.93533i | ||||||||
\(320\) | 29.3911i | 1.64301i | ||||||||
\(321\) | −3.81390 | −0.212871 | ||||||||
\(322\) | 4.99678 | 0.278459 | ||||||||
\(323\) | 11.8346i | 0.658492i | ||||||||
\(324\) | 1.23914 | 0.0688411 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 2.23565 | 0.123821 | ||||||||
\(327\) | − 9.22686i | − 0.510247i | ||||||||
\(328\) | 31.8262 | 1.75731 | ||||||||
\(329\) | 0.832988 | 0.0459241 | ||||||||
\(330\) | − 15.1180i | − 0.832216i | ||||||||
\(331\) | 21.7576i | 1.19590i | 0.801532 | + | 0.597952i | \(0.204019\pi\) | ||||
−0.801532 | + | 0.597952i | \(0.795981\pi\) | |||||||
\(332\) | 2.44167i | 0.134004i | ||||||||
\(333\) | 3.82680i | 0.209707i | ||||||||
\(334\) | 20.9744 | 1.14767 | ||||||||
\(335\) | 10.8541 | 0.593021 | ||||||||
\(336\) | 1.79075i | 0.0976936i | ||||||||
\(337\) | 17.8877 | 0.974405 | 0.487202 | − | 0.873289i | \(-0.338017\pi\) | ||||
0.487202 | + | 0.873289i | \(0.338017\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 1.99036 | 0.108101 | ||||||||
\(340\) | 5.09728i | 0.276439i | ||||||||
\(341\) | 12.9130 | 0.699276 | ||||||||
\(342\) | 14.6975 | 0.794749 | ||||||||
\(343\) | 1.00000i | 0.0539949i | ||||||||
\(344\) | − 31.7428i | − 1.71145i | ||||||||
\(345\) | 15.3123i | 0.824388i | ||||||||
\(346\) | − 13.7789i | − 0.740756i | ||||||||
\(347\) | 11.2388 | 0.603331 | 0.301666 | − | 0.953414i | \(-0.402457\pi\) | ||||
0.301666 | + | 0.953414i | \(0.402457\pi\) | |||||||
\(348\) | 6.33667 | 0.339681 | ||||||||
\(349\) | 24.4183i | 1.30708i | 0.756891 | + | 0.653542i | \(0.226718\pi\) | ||||
−0.756891 | + | 0.653542i | \(0.773282\pi\) | |||||||
\(350\) | 8.50590 | 0.454660 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 16.2802 | 0.867736 | ||||||||
\(353\) | − 15.9072i | − 0.846655i | −0.905977 | − | 0.423327i | \(-0.860862\pi\) | ||||
0.905977 | − | 0.423327i | \(-0.139138\pi\) | |||||||
\(354\) | −5.52436 | −0.293616 | ||||||||
\(355\) | 51.3834 | 2.72715 | ||||||||
\(356\) | − 9.39372i | − 0.497866i | ||||||||
\(357\) | 1.78221i | 0.0943247i | ||||||||
\(358\) | − 10.4040i | − 0.549869i | ||||||||
\(359\) | − 12.4456i | − 0.656853i | −0.944529 | − | 0.328427i | \(-0.893482\pi\) | ||||
0.944529 | − | 0.328427i | \(-0.106518\pi\) | |||||||
\(360\) | 22.8125 | 1.20232 | ||||||||
\(361\) | −21.2793 | −1.11996 | ||||||||
\(362\) | 6.47671i | 0.340408i | ||||||||
\(363\) | −4.81575 | −0.252761 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −45.9256 | −2.40386 | ||||||||
\(366\) | 1.94966i | 0.101910i | ||||||||
\(367\) | −18.2038 | −0.950231 | −0.475115 | − | 0.879923i | \(-0.657594\pi\) | ||||
−0.475115 | + | 0.879923i | \(0.657594\pi\) | |||||||
\(368\) | 8.43525 | 0.439718 | ||||||||
\(369\) | − 21.6142i | − 1.12519i | ||||||||
\(370\) | 7.24390i | 0.376592i | ||||||||
\(371\) | − 6.53512i | − 0.339286i | ||||||||
\(372\) | − 2.36721i | − 0.122734i | ||||||||
\(373\) | 32.6828 | 1.69225 | 0.846126 | − | 0.532983i | \(-0.178929\pi\) | ||||
0.846126 | + | 0.532983i | \(0.178929\pi\) | |||||||
\(374\) | −8.28846 | −0.428586 | ||||||||
\(375\) | 9.05992i | 0.467852i | ||||||||
\(376\) | 2.55922 | 0.131982 | ||||||||
\(377\) | 0 | 0 | ||||||||
\(378\) | 5.39571 | 0.277525 | ||||||||
\(379\) | 8.81792i | 0.452946i | 0.974017 | + | 0.226473i | \(0.0727195\pi\) | ||||
−0.974017 | + | 0.226473i | \(0.927280\pi\) | |||||||
\(380\) | −17.3488 | −0.889973 | ||||||||
\(381\) | −6.86510 | −0.351710 | ||||||||
\(382\) | 18.0969i | 0.925916i | ||||||||
\(383\) | − 2.54364i | − 0.129974i | −0.997886 | − | 0.0649870i | \(-0.979299\pi\) | ||||
0.997886 | − | 0.0649870i | \(-0.0207006\pi\) | |||||||
\(384\) | 0.990579i | 0.0505502i | ||||||||
\(385\) | − 14.2517i | − 0.726332i | ||||||||
\(386\) | −23.5575 | −1.19905 | ||||||||
\(387\) | −21.5575 | −1.09583 | ||||||||
\(388\) | − 10.1332i | − 0.514433i | ||||||||
\(389\) | 0.516707 | 0.0261981 | 0.0130990 | − | 0.999914i | \(-0.495830\pi\) | ||||
0.0130990 | + | 0.999914i | \(0.495830\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 8.39502 | 0.424555 | ||||||||
\(392\) | 3.07233i | 0.155176i | ||||||||
\(393\) | −1.41534 | −0.0713944 | ||||||||
\(394\) | −17.8467 | −0.899104 | ||||||||
\(395\) | − 0.331634i | − 0.0166863i | ||||||||
\(396\) | − 6.41880i | − 0.322557i | ||||||||
\(397\) | 25.8956i | 1.29967i | 0.760077 | + | 0.649833i | \(0.225161\pi\) | ||||
−0.760077 | + | 0.649833i | \(0.774839\pi\) | |||||||
\(398\) | − 17.1348i | − 0.858891i | ||||||||
\(399\) | −6.06582 | −0.303671 | ||||||||
\(400\) | 14.3591 | 0.717957 | ||||||||
\(401\) | 10.2493i | 0.511828i | 0.966700 | + | 0.255914i | \(0.0823764\pi\) | ||||
−0.966700 | + | 0.255914i | \(0.917624\pi\) | |||||||
\(402\) | 3.23548 | 0.161371 | ||||||||
\(403\) | 0 | 0 | ||||||||
\(404\) | 5.93799 | 0.295426 | ||||||||
\(405\) | − 5.74057i | − 0.285251i | ||||||||
\(406\) | −9.57955 | −0.475425 | ||||||||
\(407\) | 7.34508 | 0.364082 | ||||||||
\(408\) | 5.47556i | 0.271080i | ||||||||
\(409\) | 20.5100i | 1.01416i | 0.861900 | + | 0.507078i | \(0.169274\pi\) | ||||
−0.861900 | + | 0.507078i | \(0.830726\pi\) | |||||||
\(410\) | − 40.9144i | − 2.02062i | ||||||||
\(411\) | 4.24228i | 0.209256i | ||||||||
\(412\) | 0.275884 | 0.0135918 | ||||||||
\(413\) | −5.20780 | −0.256259 | ||||||||
\(414\) | − 10.4259i | − 0.512405i | ||||||||
\(415\) | 11.3115 | 0.555261 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 16.5852 | 0.812183 | ||||||||
\(418\) | − 28.2101i | − 1.37980i | ||||||||
\(419\) | 15.2380 | 0.744426 | 0.372213 | − | 0.928147i | \(-0.378599\pi\) | ||||
0.372213 | + | 0.928147i | \(0.378599\pi\) | |||||||
\(420\) | −2.61262 | −0.127483 | ||||||||
\(421\) | − 26.3846i | − 1.28590i | −0.765906 | − | 0.642952i | \(-0.777709\pi\) | ||||
0.765906 | − | 0.642952i | \(-0.222291\pi\) | |||||||
\(422\) | − 3.83329i | − 0.186602i | ||||||||
\(423\) | − 1.73805i | − 0.0845068i | ||||||||
\(424\) | − 20.0781i | − 0.975077i | ||||||||
\(425\) | 14.2907 | 0.693199 | ||||||||
\(426\) | 15.3168 | 0.742103 | ||||||||
\(427\) | 1.83794i | 0.0889442i | ||||||||
\(428\) | −3.06526 | −0.148165 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | −40.8071 | −1.96790 | ||||||||
\(431\) | 37.9100i | 1.82606i | 0.407889 | + | 0.913031i | \(0.366265\pi\) | ||||
−0.407889 | + | 0.913031i | \(0.633735\pi\) | |||||||
\(432\) | 9.10871 | 0.438243 | ||||||||
\(433\) | −8.51058 | −0.408993 | −0.204496 | − | 0.978867i | \(-0.565556\pi\) | ||||
−0.204496 | + | 0.978867i | \(0.565556\pi\) | |||||||
\(434\) | 3.57866i | 0.171781i | ||||||||
\(435\) | − 29.3559i | − 1.40751i | ||||||||
\(436\) | − 7.41569i | − 0.355147i | ||||||||
\(437\) | 28.5728i | 1.36682i | ||||||||
\(438\) | −13.6899 | −0.654130 | ||||||||
\(439\) | −18.6101 | −0.888213 | −0.444107 | − | 0.895974i | \(-0.646479\pi\) | ||||
−0.444107 | + | 0.895974i | \(0.646479\pi\) | |||||||
\(440\) | − 43.7859i | − 2.08741i | ||||||||
\(441\) | 2.08652 | 0.0993582 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 26.8582 | 1.27607 | 0.638035 | − | 0.770007i | \(-0.279747\pi\) | ||||
0.638035 | + | 0.770007i | \(0.279747\pi\) | |||||||
\(444\) | − 1.34650i | − 0.0639022i | ||||||||
\(445\) | −43.5184 | −2.06297 | ||||||||
\(446\) | 17.3851 | 0.823208 | ||||||||
\(447\) | 22.1144i | 1.04598i | ||||||||
\(448\) | 8.25913i | 0.390207i | ||||||||
\(449\) | − 15.5278i | − 0.732804i | −0.930457 | − | 0.366402i | \(-0.880589\pi\) | ||||
0.930457 | − | 0.366402i | \(-0.119411\pi\) | |||||||
\(450\) | − 17.7478i | − 0.836638i | ||||||||
\(451\) | −41.4859 | −1.95349 | ||||||||
\(452\) | 1.59966 | 0.0752418 | ||||||||
\(453\) | − 10.4031i | − 0.488780i | ||||||||
\(454\) | −8.93986 | −0.419568 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | −18.6362 | −0.872722 | ||||||||
\(457\) | 33.5563i | 1.56970i | 0.619688 | + | 0.784848i | \(0.287259\pi\) | ||||
−0.619688 | + | 0.784848i | \(0.712741\pi\) | |||||||
\(458\) | 22.1612 | 1.03552 | ||||||||
\(459\) | 9.06527 | 0.423130 | ||||||||
\(460\) | 12.3066i | 0.573799i | ||||||||
\(461\) | − 4.34899i | − 0.202553i | −0.994858 | − | 0.101276i | \(-0.967707\pi\) | ||||
0.994858 | − | 0.101276i | \(-0.0322926\pi\) | |||||||
\(462\) | − 4.24827i | − 0.197647i | ||||||||
\(463\) | − 23.2754i | − 1.08170i | −0.841119 | − | 0.540850i | \(-0.818103\pi\) | ||||
0.841119 | − | 0.540850i | \(-0.181897\pi\) | |||||||
\(464\) | −16.1716 | −0.750748 | ||||||||
\(465\) | −10.9666 | −0.508564 | ||||||||
\(466\) | 13.5173i | 0.626176i | ||||||||
\(467\) | −12.2510 | −0.566909 | −0.283454 | − | 0.958986i | \(-0.591480\pi\) | ||||
−0.283454 | + | 0.958986i | \(0.591480\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 3.05008 | 0.140840 | ||||||||
\(470\) | − 3.29002i | − 0.151757i | ||||||||
\(471\) | 13.6248 | 0.627797 | ||||||||
\(472\) | −16.0001 | −0.736464 | ||||||||
\(473\) | 41.3771i | 1.90252i | ||||||||
\(474\) | − 0.0988566i | − 0.00454063i | ||||||||
\(475\) | 48.6388i | 2.23170i | ||||||||
\(476\) | 1.43238i | 0.0656529i | ||||||||
\(477\) | −13.6357 | −0.624334 | ||||||||
\(478\) | 17.2814 | 0.790434 | ||||||||
\(479\) | 0.683706i | 0.0312393i | 0.999878 | + | 0.0156197i | \(0.00497209\pi\) | ||||
−0.999878 | + | 0.0156197i | \(0.995028\pi\) | |||||||
\(480\) | −13.8263 | −0.631080 | ||||||||
\(481\) | 0 | 0 | ||||||||
\(482\) | −1.44930 | −0.0660140 | ||||||||
\(483\) | 4.30289i | 0.195788i | ||||||||
\(484\) | −3.87045 | −0.175930 | ||||||||
\(485\) | −46.9440 | −2.13162 | ||||||||
\(486\) | − 17.8983i | − 0.811885i | ||||||||
\(487\) | − 2.18545i | − 0.0990323i | −0.998773 | − | 0.0495162i | \(-0.984232\pi\) | ||||
0.998773 | − | 0.0495162i | \(-0.0157679\pi\) | |||||||
\(488\) | 5.64677i | 0.255617i | ||||||||
\(489\) | 1.92519i | 0.0870601i | ||||||||
\(490\) | 3.94966 | 0.178428 | ||||||||
\(491\) | −8.81707 | −0.397909 | −0.198954 | − | 0.980009i | \(-0.563755\pi\) | ||||
−0.198954 | + | 0.980009i | \(0.563755\pi\) | |||||||
\(492\) | 7.60521i | 0.342870i | ||||||||
\(493\) | −16.0945 | −0.724859 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −29.7364 | −1.33655 | ||||||||
\(496\) | 6.04128i | 0.271262i | ||||||||
\(497\) | 14.4391 | 0.647684 | ||||||||
\(498\) | 3.37185 | 0.151096 | ||||||||
\(499\) | 16.3801i | 0.733275i | 0.930364 | + | 0.366637i | \(0.119491\pi\) | ||||
−0.930364 | + | 0.366637i | \(0.880509\pi\) | |||||||
\(500\) | 7.28152i | 0.325639i | ||||||||
\(501\) | 18.0618i | 0.806940i | ||||||||
\(502\) | − 22.5143i | − 1.00486i | ||||||||
\(503\) | −11.5765 | −0.516168 | −0.258084 | − | 0.966122i | \(-0.583091\pi\) | ||||
−0.258084 | + | 0.966122i | \(0.583091\pi\) | |||||||
\(504\) | 6.41050 | 0.285546 | ||||||||
\(505\) | − 27.5090i | − 1.22413i | ||||||||
\(506\) | −20.0112 | −0.889608 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | −5.51752 | −0.244800 | ||||||||
\(509\) | 13.3984i | 0.593874i | 0.954897 | + | 0.296937i | \(0.0959651\pi\) | ||||
−0.954897 | + | 0.296937i | \(0.904035\pi\) | |||||||
\(510\) | 7.03914 | 0.311698 | ||||||||
\(511\) | −12.9055 | −0.570904 | ||||||||
\(512\) | 19.1295i | 0.845414i | ||||||||
\(513\) | 30.8540i | 1.36224i | ||||||||
\(514\) | 19.2510i | 0.849127i | ||||||||
\(515\) | − 1.27809i | − 0.0563195i | ||||||||
\(516\) | 7.58527 | 0.333923 | ||||||||
\(517\) | −3.33597 | −0.146716 | ||||||||
\(518\) | 2.03559i | 0.0894389i | ||||||||
\(519\) | 11.8654 | 0.520834 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 38.0891 | 1.66871 | 0.834356 | − | 0.551226i | \(-0.185840\pi\) | ||||
0.834356 | + | 0.551226i | \(0.185840\pi\) | |||||||
\(522\) | 19.9879i | 0.874848i | ||||||||
\(523\) | 1.91936 | 0.0839276 | 0.0419638 | − | 0.999119i | \(-0.486639\pi\) | ||||
0.0419638 | + | 0.999119i | \(0.486639\pi\) | |||||||
\(524\) | −1.13752 | −0.0496927 | ||||||||
\(525\) | 7.32471i | 0.319677i | ||||||||
\(526\) | 12.0856i | 0.526959i | ||||||||
\(527\) | 6.01247i | 0.261907i | ||||||||
\(528\) | − 7.17166i | − 0.312107i | ||||||||
\(529\) | −2.73147 | −0.118760 | ||||||||
\(530\) | −25.8115 | −1.12118 | ||||||||
\(531\) | 10.8662i | 0.471552i | ||||||||
\(532\) | −4.87514 | −0.211364 | ||||||||
\(533\) | 0 | 0 | ||||||||
\(534\) | −12.9724 | −0.561369 | ||||||||
\(535\) | 14.2004i | 0.613938i | ||||||||
\(536\) | 9.37086 | 0.404760 | ||||||||
\(537\) | 8.95923 | 0.386619 | ||||||||
\(538\) | − 9.98248i | − 0.430375i | ||||||||
\(539\) | − 4.00483i | − 0.172500i | ||||||||
\(540\) | 13.2892i | 0.571874i | ||||||||
\(541\) | 7.49222i | 0.322116i | 0.986945 | + | 0.161058i | \(0.0514905\pi\) | ||||
−0.986945 | + | 0.161058i | \(0.948509\pi\) | |||||||
\(542\) | −5.48597 | −0.235642 | ||||||||
\(543\) | −5.57731 | −0.239345 | ||||||||
\(544\) | 7.58029i | 0.325002i | ||||||||
\(545\) | −34.3547 | −1.47159 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 14.7156 | 0.629192 | 0.314596 | − | 0.949226i | \(-0.398131\pi\) | ||||
0.314596 | + | 0.949226i | \(0.398131\pi\) | |||||||
\(548\) | 3.40955i | 0.145649i | ||||||||
\(549\) | 3.83491 | 0.163670 | ||||||||
\(550\) | −34.0647 | −1.45252 | ||||||||
\(551\) | − 54.7781i | − 2.33363i | ||||||||
\(552\) | 13.2199i | 0.562677i | ||||||||
\(553\) | − 0.0931919i | − 0.00396292i | ||||||||
\(554\) | 21.5995i | 0.917677i | ||||||||
\(555\) | −6.23796 | −0.264787 | ||||||||
\(556\) | 13.3297 | 0.565304 | ||||||||
\(557\) | 5.45353i | 0.231073i | 0.993303 | + | 0.115537i | \(0.0368588\pi\) | ||||
−0.993303 | + | 0.115537i | \(0.963141\pi\) | |||||||
\(558\) | 7.46696 | 0.316102 | ||||||||
\(559\) | 0 | 0 | ||||||||
\(560\) | 6.66758 | 0.281757 | ||||||||
\(561\) | − 7.13746i | − 0.301344i | ||||||||
\(562\) | 22.3606 | 0.943226 | ||||||||
\(563\) | −36.8364 | −1.55247 | −0.776235 | − | 0.630444i | \(-0.782873\pi\) | ||||
−0.776235 | + | 0.630444i | \(0.782873\pi\) | |||||||
\(564\) | 0.611552i | 0.0257510i | ||||||||
\(565\) | − 7.41077i | − 0.311773i | ||||||||
\(566\) | − 25.3367i | − 1.06498i | ||||||||
\(567\) | − 1.61315i | − 0.0677458i | ||||||||
\(568\) | 44.3619 | 1.86138 | ||||||||
\(569\) | −15.0251 | −0.629885 | −0.314942 | − | 0.949111i | \(-0.601985\pi\) | ||||
−0.314942 | + | 0.949111i | \(0.601985\pi\) | |||||||
\(570\) | 23.9580i | 1.00349i | ||||||||
\(571\) | −33.2518 | −1.39155 | −0.695773 | − | 0.718262i | \(-0.744938\pi\) | ||||
−0.695773 | + | 0.718262i | \(0.744938\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −15.5838 | −0.651023 | ||||||||
\(574\) | − 11.4973i | − 0.479887i | ||||||||
\(575\) | 34.5027 | 1.43886 | ||||||||
\(576\) | 17.2329 | 0.718036 | ||||||||
\(577\) | 34.7983i | 1.44867i | 0.689448 | + | 0.724335i | \(0.257853\pi\) | ||||
−0.689448 | + | 0.724335i | \(0.742147\pi\) | |||||||
\(578\) | 15.0089i | 0.624286i | ||||||||
\(579\) | − 20.2861i | − 0.843063i | ||||||||
\(580\) | − 23.5936i | − 0.979670i | ||||||||
\(581\) | 3.17863 | 0.131872 | ||||||||
\(582\) | −13.9935 | −0.580049 | ||||||||
\(583\) | 26.1720i | 1.08393i | ||||||||
\(584\) | −39.6499 | −1.64072 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −29.4915 | −1.21828 | ||||||||
\(587\) | − 19.7267i | − 0.814210i | −0.913381 | − | 0.407105i | \(-0.866538\pi\) | ||||
0.913381 | − | 0.407105i | \(-0.133462\pi\) | |||||||
\(588\) | −0.734167 | −0.0302766 | ||||||||
\(589\) | −20.4636 | −0.843190 | ||||||||
\(590\) | 20.5690i | 0.846814i | ||||||||
\(591\) | − 15.3684i | − 0.632171i | ||||||||
\(592\) | 3.43637i | 0.141234i | ||||||||
\(593\) | − 7.56122i | − 0.310502i | −0.987875 | − | 0.155251i | \(-0.950381\pi\) | ||||
0.987875 | − | 0.155251i | \(-0.0496186\pi\) | |||||||
\(594\) | −21.6089 | −0.886624 | ||||||||
\(595\) | 6.63578 | 0.272041 | ||||||||
\(596\) | 17.7735i | 0.728031i | ||||||||
\(597\) | 14.7554 | 0.603896 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 3.48332 | 0.142325 | 0.0711623 | − | 0.997465i | \(-0.477329\pi\) | ||||
0.0711623 | + | 0.997465i | \(0.477329\pi\) | |||||||
\(600\) | 22.5040i | 0.918720i | ||||||||
\(601\) | −43.3614 | −1.76875 | −0.884374 | − | 0.466778i | \(-0.845415\pi\) | ||||
−0.884374 | + | 0.466778i | \(0.845415\pi\) | |||||||
\(602\) | −11.4671 | −0.467366 | ||||||||
\(603\) | − 6.36406i | − 0.259165i | ||||||||
\(604\) | − 8.36103i | − 0.340206i | ||||||||
\(605\) | 17.9307i | 0.728985i | ||||||||
\(606\) | − 8.20013i | − 0.333108i | ||||||||
\(607\) | −24.5108 | −0.994864 | −0.497432 | − | 0.867503i | \(-0.665724\pi\) | ||||
−0.497432 | + | 0.867503i | \(0.665724\pi\) | |||||||
\(608\) | −25.7998 | −1.04632 | ||||||||
\(609\) | − 8.24926i | − 0.334277i | ||||||||
\(610\) | 7.25925 | 0.293918 | ||||||||
\(611\) | 0 | 0 | ||||||||
\(612\) | 2.98869 | 0.120810 | ||||||||
\(613\) | − 0.842003i | − 0.0340082i | −0.999855 | − | 0.0170041i | \(-0.994587\pi\) | ||||
0.999855 | − | 0.0170041i | \(-0.00541283\pi\) | |||||||
\(614\) | 7.95604 | 0.321080 | ||||||||
\(615\) | 35.2327 | 1.42072 | ||||||||
\(616\) | − 12.3042i | − 0.495749i | ||||||||
\(617\) | 11.6951i | 0.470828i | 0.971895 | + | 0.235414i | \(0.0756446\pi\) | ||||
−0.971895 | + | 0.235414i | \(0.924355\pi\) | |||||||
\(618\) | − 0.380986i | − 0.0153255i | ||||||||
\(619\) | − 30.4915i | − 1.22556i | −0.790254 | − | 0.612779i | \(-0.790052\pi\) | ||||
0.790254 | − | 0.612779i | \(-0.209948\pi\) | |||||||
\(620\) | −8.81393 | −0.353976 | ||||||||
\(621\) | 21.8867 | 0.878284 | ||||||||
\(622\) | − 15.1655i | − 0.608083i | ||||||||
\(623\) | −12.2290 | −0.489945 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −4.58563 | −0.183425 | ||||||||
\(626\) | − 11.7450i | − 0.469423i | ||||||||
\(627\) | 24.2926 | 0.970153 | ||||||||
\(628\) | 10.9503 | 0.436966 | ||||||||
\(629\) | 3.41998i | 0.136363i | ||||||||
\(630\) | − 8.24106i | − 0.328332i | ||||||||
\(631\) | 19.0797i | 0.759552i | 0.925078 | + | 0.379776i | \(0.123999\pi\) | ||||
−0.925078 | + | 0.379776i | \(0.876001\pi\) | |||||||
\(632\) | − 0.286317i | − 0.0113891i | ||||||||
\(633\) | 3.30097 | 0.131202 | ||||||||
\(634\) | −4.05154 | −0.160907 | ||||||||
\(635\) | 25.5611i | 1.01436i | ||||||||
\(636\) | 4.79787 | 0.190248 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | 38.3644 | 1.51886 | ||||||||
\(639\) | − 30.1276i | − 1.19183i | ||||||||
\(640\) | 3.68826 | 0.145791 | ||||||||
\(641\) | −26.9166 | −1.06314 | −0.531571 | − | 0.847014i | \(-0.678398\pi\) | ||||
−0.531571 | + | 0.847014i | \(0.678398\pi\) | |||||||
\(642\) | 4.23300i | 0.167063i | ||||||||
\(643\) | − 50.6462i | − 1.99729i | −0.0520237 | − | 0.998646i | \(-0.516567\pi\) | ||||
0.0520237 | − | 0.998646i | \(-0.483433\pi\) | |||||||
\(644\) | 3.45826i | 0.136274i | ||||||||
\(645\) | − 35.1404i | − 1.38365i | ||||||||
\(646\) | 13.1350 | 0.516790 | ||||||||
\(647\) | 38.2321 | 1.50306 | 0.751530 | − | 0.659699i | \(-0.229316\pi\) | ||||
0.751530 | + | 0.659699i | \(0.229316\pi\) | |||||||
\(648\) | − 4.95613i | − 0.194695i | ||||||||
\(649\) | 20.8563 | 0.818683 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −3.08170 | −0.120781 | ||||||||
\(652\) | 1.54729i | 0.0605964i | ||||||||
\(653\) | −10.3427 | −0.404742 | −0.202371 | − | 0.979309i | \(-0.564865\pi\) | ||||
−0.202371 | + | 0.979309i | \(0.564865\pi\) | |||||||
\(654\) | −10.2408 | −0.400446 | ||||||||
\(655\) | 5.26979i | 0.205908i | ||||||||
\(656\) | − 19.4090i | − 0.757795i | ||||||||
\(657\) | 26.9275i | 1.05054i | ||||||||
\(658\) | − 0.924522i | − 0.0360416i | ||||||||
\(659\) | 12.8844 | 0.501904 | 0.250952 | − | 0.968000i | \(-0.419256\pi\) | ||||
0.250952 | + | 0.968000i | \(0.419256\pi\) | |||||||
\(660\) | 10.4631 | 0.407276 | ||||||||
\(661\) | 19.1895i | 0.746385i | 0.927754 | + | 0.373192i | \(0.121737\pi\) | ||||
−0.927754 | + | 0.373192i | \(0.878263\pi\) | |||||||
\(662\) | 24.1484 | 0.938555 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 9.76582 | 0.378987 | ||||||||
\(665\) | 22.5851i | 0.875813i | ||||||||
\(666\) | 4.24731 | 0.164580 | ||||||||
\(667\) | −38.8577 | −1.50458 | ||||||||
\(668\) | 14.5163i | 0.561654i | ||||||||
\(669\) | 14.9709i | 0.578807i | ||||||||
\(670\) | − 12.0468i | − 0.465408i | ||||||||
\(671\) | − 7.36064i | − 0.284154i | ||||||||
\(672\) | −3.88529 | −0.149878 | ||||||||
\(673\) | −11.1856 | −0.431172 | −0.215586 | − | 0.976485i | \(-0.569166\pi\) | ||||
−0.215586 | + | 0.976485i | \(0.569166\pi\) | |||||||
\(674\) | − 19.8533i | − 0.764721i | ||||||||
\(675\) | 37.2573 | 1.43403 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −16.4527 | −0.632330 | −0.316165 | − | 0.948704i | \(-0.602395\pi\) | ||||
−0.316165 | + | 0.948704i | \(0.602395\pi\) | |||||||
\(678\) | − 2.20907i | − 0.0848388i | ||||||||
\(679\) | −13.1916 | −0.506248 | ||||||||
\(680\) | 20.3873 | 0.781819 | ||||||||
\(681\) | − 7.69840i | − 0.295003i | ||||||||
\(682\) | − 14.3319i | − 0.548798i | ||||||||
\(683\) | − 13.5271i | − 0.517600i | −0.965931 | − | 0.258800i | \(-0.916673\pi\) | ||||
0.965931 | − | 0.258800i | \(-0.0833271\pi\) | |||||||
\(684\) | 10.1721i | 0.388940i | ||||||||
\(685\) | 15.7954 | 0.603512 | ||||||||
\(686\) | 1.10989 | 0.0423757 | ||||||||
\(687\) | 19.0837i | 0.728089i | ||||||||
\(688\) | −19.3581 | −0.738021 | ||||||||
\(689\) | 0 | 0 | ||||||||
\(690\) | 16.9950 | 0.646987 | ||||||||
\(691\) | 20.5171i | 0.780507i | 0.920707 | + | 0.390254i | \(0.127613\pi\) | ||||
−0.920707 | + | 0.390254i | \(0.872387\pi\) | |||||||
\(692\) | 9.53632 | 0.362516 | ||||||||
\(693\) | −8.35617 | −0.317425 | ||||||||
\(694\) | − 12.4738i | − 0.473500i | ||||||||
\(695\) | − 61.7525i | − 2.34241i | ||||||||
\(696\) | − 25.3445i | − 0.960680i | ||||||||
\(697\) | − 19.3164i | − 0.731662i | ||||||||
\(698\) | 27.1016 | 1.02581 | ||||||||
\(699\) | −11.6402 | −0.440272 | ||||||||
\(700\) | 5.88692i | 0.222505i | ||||||||
\(701\) | −46.6380 | −1.76149 | −0.880747 | − | 0.473587i | \(-0.842959\pi\) | ||||
−0.880747 | + | 0.473587i | \(0.842959\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −11.6400 | −0.439011 | ||||||||
\(704\) | − 33.0764i | − 1.24661i | ||||||||
\(705\) | 2.83314 | 0.106702 | ||||||||
\(706\) | −17.6552 | −0.664462 | ||||||||
\(707\) | − 7.73025i | − 0.290726i | ||||||||
\(708\) | − 3.82339i | − 0.143692i | ||||||||
\(709\) | − 42.2314i | − 1.58603i | −0.609199 | − | 0.793017i | \(-0.708509\pi\) | ||||
0.609199 | − | 0.793017i | \(-0.291491\pi\) | |||||||
\(710\) | − 57.0297i | − 2.14029i | ||||||||
\(711\) | −0.194447 | −0.00729233 | ||||||||
\(712\) | −37.5716 | −1.40806 | ||||||||
\(713\) | 14.5162i | 0.543636i | ||||||||
\(714\) | 1.97806 | 0.0740269 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 7.20059 | 0.269099 | ||||||||
\(717\) | 14.8816i | 0.555764i | ||||||||
\(718\) | −13.8132 | −0.515504 | ||||||||
\(719\) | −37.9404 | −1.41494 | −0.707469 | − | 0.706744i | \(-0.750163\pi\) | ||||
−0.707469 | + | 0.706744i | \(0.750163\pi\) | |||||||
\(720\) | − 13.9121i | − 0.518472i | ||||||||
\(721\) | − 0.359154i | − 0.0133756i | ||||||||
\(722\) | 23.6176i | 0.878957i | ||||||||
\(723\) | − 1.24804i | − 0.0464152i | ||||||||
\(724\) | −4.48252 | −0.166591 | ||||||||
\(725\) | −66.1466 | −2.45662 | ||||||||
\(726\) | 5.34494i | 0.198369i | ||||||||
\(727\) | 16.5215 | 0.612748 | 0.306374 | − | 0.951911i | \(-0.400884\pi\) | ||||
0.306374 | + | 0.951911i | \(0.400884\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 10.5734 | 0.391607 | ||||||||
\(730\) | 50.9722i | 1.88657i | ||||||||
\(731\) | −19.2658 | −0.712571 | ||||||||
\(732\) | −1.34936 | −0.0498737 | ||||||||
\(733\) | 17.6511i | 0.651957i | 0.945377 | + | 0.325978i | \(0.105694\pi\) | ||||
−0.945377 | + | 0.325978i | \(0.894306\pi\) | |||||||
\(734\) | 20.2042i | 0.745750i | ||||||||
\(735\) | 3.40118i | 0.125455i | ||||||||
\(736\) | 18.3015i | 0.674601i | ||||||||
\(737\) | −12.2150 | −0.449947 | ||||||||
\(738\) | −23.9893 | −0.883060 | ||||||||
\(739\) | 0.370373i | 0.0136244i | 0.999977 | + | 0.00681220i | \(0.00216841\pi\) | ||||
−0.999977 | + | 0.00681220i | \(0.997832\pi\) | |||||||
\(740\) | −5.01349 | −0.184299 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | −7.25324 | −0.266275 | ||||||||
\(743\) | 17.5579i | 0.644137i | 0.946716 | + | 0.322068i | \(0.104378\pi\) | ||||
−0.946716 | + | 0.322068i | \(0.895622\pi\) | |||||||
\(744\) | −9.46802 | −0.347115 | ||||||||
\(745\) | 82.3395 | 3.01668 | ||||||||
\(746\) | − 36.2742i | − 1.32809i | ||||||||
\(747\) | − 6.63229i | − 0.242663i | ||||||||
\(748\) | − 5.73642i | − 0.209744i | ||||||||
\(749\) | 3.99044i | 0.145807i | ||||||||
\(750\) | 10.0555 | 0.367175 | ||||||||
\(751\) | 15.0706 | 0.549933 | 0.274967 | − | 0.961454i | \(-0.411333\pi\) | ||||
0.274967 | + | 0.961454i | \(0.411333\pi\) | |||||||
\(752\) | − 1.56072i | − 0.0569137i | ||||||||
\(753\) | 19.3878 | 0.706530 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −38.7342 | −1.40968 | ||||||||
\(756\) | 3.73436i | 0.135817i | ||||||||
\(757\) | 39.8030 | 1.44666 | 0.723332 | − | 0.690500i | \(-0.242609\pi\) | ||||
0.723332 | + | 0.690500i | \(0.242609\pi\) | |||||||
\(758\) | 9.78689 | 0.355476 | ||||||||
\(759\) | − 17.2323i | − 0.625494i | ||||||||
\(760\) | 69.3890i | 2.51700i | ||||||||
\(761\) | − 20.7066i | − 0.750613i | −0.926901 | − | 0.375306i | \(-0.877538\pi\) | ||||
0.926901 | − | 0.375306i | \(-0.122462\pi\) | |||||||
\(762\) | 7.61948i | 0.276025i | ||||||||
\(763\) | −9.65395 | −0.349497 | ||||||||
\(764\) | −12.5248 | −0.453131 | ||||||||
\(765\) | − 13.8457i | − 0.500593i | ||||||||
\(766\) | −2.82315 | −0.102005 | ||||||||
\(767\) | 0 | 0 | ||||||||
\(768\) | −14.6881 | −0.530010 | ||||||||
\(769\) | − 13.2638i | − 0.478306i | −0.970982 | − | 0.239153i | \(-0.923130\pi\) | ||||
0.970982 | − | 0.239153i | \(-0.0768698\pi\) | |||||||
\(770\) | −15.8177 | −0.570031 | ||||||||
\(771\) | −16.5777 | −0.597031 | ||||||||
\(772\) | − 16.3041i | − 0.586798i | ||||||||
\(773\) | − 11.6627i | − 0.419478i | −0.977757 | − | 0.209739i | \(-0.932739\pi\) | ||||
0.977757 | − | 0.209739i | \(-0.0672614\pi\) | |||||||
\(774\) | 23.9264i | 0.860018i | ||||||||
\(775\) | 24.7106i | 0.887632i | ||||||||
\(776\) | −40.5291 | −1.45491 | ||||||||
\(777\) | −1.75292 | −0.0628855 | ||||||||
\(778\) | − 0.573486i | − 0.0205605i | ||||||||
\(779\) | 65.7442 | 2.35553 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −57.8263 | −2.06919 | ||||||||
\(782\) | − 9.31753i | − 0.333194i | ||||||||
\(783\) | −41.9600 | −1.49953 | ||||||||
\(784\) | 1.87364 | 0.0669159 | ||||||||
\(785\) | − 50.7297i | − 1.81062i | ||||||||
\(786\) | 1.57087i | 0.0560310i | ||||||||
\(787\) | 5.00642i | 0.178460i | 0.996011 | + | 0.0892298i | \(0.0284405\pi\) | ||||
−0.996011 | + | 0.0892298i | \(0.971559\pi\) | |||||||
\(788\) | − 12.3517i | − 0.440010i | ||||||||
\(789\) | −10.4073 | −0.370511 | ||||||||
\(790\) | −0.368077 | −0.0130956 | ||||||||
\(791\) | − 2.08248i | − 0.0740446i | ||||||||
\(792\) | −25.6730 | −0.912249 | ||||||||
\(793\) | 0 | 0 | ||||||||
\(794\) | 28.7412 | 1.01999 | ||||||||
\(795\) | − 22.2271i | − 0.788315i | ||||||||
\(796\) | 11.8590 | 0.420330 | ||||||||
\(797\) | −9.95893 | −0.352763 | −0.176382 | − | 0.984322i | \(-0.556439\pi\) | ||||
−0.176382 | + | 0.984322i | \(0.556439\pi\) | |||||||
\(798\) | 6.73238i | 0.238324i | ||||||||
\(799\) | − 1.55328i | − 0.0549511i | ||||||||
\(800\) | 31.1542i | 1.10147i | ||||||||
\(801\) | 25.5161i | 0.901568i | ||||||||
\(802\) | 11.3756 | 0.401687 | ||||||||
\(803\) | 51.6842 | 1.82389 | ||||||||
\(804\) | 2.23927i | 0.0789729i | ||||||||
\(805\) | 16.0211 | 0.564670 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 8.59623 | 0.302602 | ||||||||
\(808\) | − 23.7499i | − 0.835519i | ||||||||
\(809\) | 12.0200 | 0.422601 | 0.211300 | − | 0.977421i | \(-0.432230\pi\) | ||||
0.211300 | + | 0.977421i | \(0.432230\pi\) | |||||||
\(810\) | −6.37139 | −0.223868 | ||||||||
\(811\) | 2.91856i | 0.102484i | 0.998686 | + | 0.0512422i | \(0.0163180\pi\) | ||||
−0.998686 | + | 0.0512422i | \(0.983682\pi\) | |||||||
\(812\) | − 6.62998i | − 0.232667i | ||||||||
\(813\) | − 4.72414i | − 0.165683i | ||||||||
\(814\) | − 8.15221i | − 0.285735i | ||||||||
\(815\) | 7.16813 | 0.251089 | ||||||||
\(816\) | 3.33923 | 0.116897 | ||||||||
\(817\) | − 65.5718i | − 2.29407i | ||||||||
\(818\) | 22.7638 | 0.795919 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 28.3168 | 0.988865 | ||||||||
\(821\) | 12.9996i | 0.453689i | 0.973931 | + | 0.226844i | \(0.0728409\pi\) | ||||
−0.973931 | + | 0.226844i | \(0.927159\pi\) | |||||||
\(822\) | 4.70845 | 0.164226 | ||||||||
\(823\) | 39.6283 | 1.38136 | 0.690678 | − | 0.723163i | \(-0.257312\pi\) | ||||
0.690678 | + | 0.723163i | \(0.257312\pi\) | |||||||
\(824\) | − 1.10344i | − 0.0384402i | ||||||||
\(825\) | − 29.3342i | − 1.02129i | ||||||||
\(826\) | 5.78007i | 0.201114i | ||||||||
\(827\) | 31.5319i | 1.09647i | 0.836323 | + | 0.548237i | \(0.184701\pi\) | ||||
−0.836323 | + | 0.548237i | \(0.815299\pi\) | |||||||
\(828\) | 7.21574 | 0.250764 | ||||||||
\(829\) | −36.2352 | −1.25850 | −0.629251 | − | 0.777202i | \(-0.716638\pi\) | ||||
−0.629251 | + | 0.777202i | \(0.716638\pi\) | |||||||
\(830\) | − 12.5545i | − 0.435774i | ||||||||
\(831\) | −18.6001 | −0.645229 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 1.86471 | 0.0646083 | ||||||||
\(834\) | − 18.4078i | − 0.637408i | ||||||||
\(835\) | 67.2500 | 2.32728 | ||||||||
\(836\) | 19.5241 | 0.675256 | ||||||||
\(837\) | 15.6752i | 0.541813i | ||||||||
\(838\) | − 16.9125i | − 0.584232i | ||||||||
\(839\) | 12.0623i | 0.416438i | 0.978082 | + | 0.208219i | \(0.0667667\pi\) | ||||
−0.978082 | + | 0.208219i | \(0.933233\pi\) | |||||||
\(840\) | 10.4496i | 0.360545i | ||||||||
\(841\) | 45.4959 | 1.56882 | ||||||||
\(842\) | −29.2839 | −1.00919 | ||||||||
\(843\) | 19.2555i | 0.663193i | ||||||||
\(844\) | 2.65301 | 0.0913204 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | −1.92904 | −0.0663217 | ||||||||
\(847\) | 5.03866i | 0.173130i | ||||||||
\(848\) | −12.2445 | −0.420477 | ||||||||
\(849\) | 21.8182 | 0.748800 | ||||||||
\(850\) | − 15.8610i | − 0.544029i | ||||||||
\(851\) | 8.25702i | 0.283047i | ||||||||
\(852\) | 10.6007i | 0.363176i | ||||||||
\(853\) | 11.7255i | 0.401475i | 0.979645 | + | 0.200738i | \(0.0643339\pi\) | ||||
−0.979645 | + | 0.200738i | \(0.935666\pi\) | |||||||
\(854\) | 2.03991 | 0.0698042 | ||||||||
\(855\) | 47.1244 | 1.61162 | ||||||||
\(856\) | 12.2600i | 0.419037i | ||||||||
\(857\) | −28.0128 | −0.956900 | −0.478450 | − | 0.878115i | \(-0.658801\pi\) | ||||
−0.478450 | + | 0.878115i | \(0.658801\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 5.70001 | 0.194482 | 0.0972408 | − | 0.995261i | \(-0.468998\pi\) | ||||
0.0972408 | + | 0.995261i | \(0.468998\pi\) | |||||||
\(860\) | − 28.2425i | − 0.963063i | ||||||||
\(861\) | 9.90068 | 0.337414 | ||||||||
\(862\) | 42.0759 | 1.43311 | ||||||||
\(863\) | 41.0325i | 1.39676i | 0.715726 | + | 0.698381i | \(0.246096\pi\) | ||||
−0.715726 | + | 0.698381i | \(0.753904\pi\) | |||||||
\(864\) | 19.7626i | 0.672339i | ||||||||
\(865\) | − 44.1790i | − 1.50213i | ||||||||
\(866\) | 9.44579i | 0.320981i | ||||||||
\(867\) | −12.9246 | −0.438943 | ||||||||
\(868\) | −2.47678 | −0.0840676 | ||||||||
\(869\) | 0.373218i | 0.0126605i | ||||||||
\(870\) | −32.5818 | −1.10463 | ||||||||
\(871\) | 0 | 0 | ||||||||
\(872\) | −29.6602 | −1.00442 | ||||||||
\(873\) | 27.5246i | 0.931568i | ||||||||
\(874\) | 31.7125 | 1.07269 | ||||||||
\(875\) | 9.47929 | 0.320458 | ||||||||
\(876\) | − 9.47477i | − 0.320123i | ||||||||
\(877\) | 10.7401i | 0.362668i | 0.983422 | + | 0.181334i | \(0.0580415\pi\) | ||||
−0.983422 | + | 0.181334i | \(0.941958\pi\) | |||||||
\(878\) | 20.6551i | 0.697077i | ||||||||
\(879\) | − 25.3961i | − 0.856590i | ||||||||
\(880\) | −26.7025 | −0.900142 | ||||||||
\(881\) | −37.5517 | −1.26515 | −0.632574 | − | 0.774500i | \(-0.718002\pi\) | ||||
−0.632574 | + | 0.774500i | \(0.718002\pi\) | |||||||
\(882\) | − 2.31581i | − 0.0779772i | ||||||||
\(883\) | −47.1134 | −1.58549 | −0.792745 | − | 0.609553i | \(-0.791349\pi\) | ||||
−0.792745 | + | 0.609553i | \(0.791349\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −17.7127 | −0.595405 | ||||||||
\(886\) | − 29.8095i | − 1.00147i | ||||||||
\(887\) | 5.06090 | 0.169928 | 0.0849642 | − | 0.996384i | \(-0.472922\pi\) | ||||
0.0849642 | + | 0.996384i | \(0.472922\pi\) | |||||||
\(888\) | −5.38555 | −0.180727 | ||||||||
\(889\) | 7.18287i | 0.240906i | ||||||||
\(890\) | 48.3005i | 1.61904i | ||||||||
\(891\) | 6.46038i | 0.216431i | ||||||||
\(892\) | 12.0322i | 0.402867i | ||||||||
\(893\) | 5.28664 | 0.176911 | ||||||||
\(894\) | 24.5445 | 0.820891 | ||||||||
\(895\) | − 33.3582i | − 1.11504i | ||||||||
\(896\) | 1.03643 | 0.0346247 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | −17.2342 | −0.575111 | ||||||||
\(899\) | − 27.8297i | − 0.928171i | ||||||||
\(900\) | 12.2832 | 0.409440 | ||||||||
\(901\) | −12.1861 | −0.405977 | ||||||||
\(902\) | 46.0447i | 1.53312i | ||||||||
\(903\) | − 9.87472i | − 0.328610i | ||||||||
\(904\) | − 6.39809i | − 0.212797i | ||||||||
\(905\) | 20.7662i | 0.690292i | ||||||||
\(906\) | −11.5463 | −0.383599 | ||||||||
\(907\) | 48.6215 | 1.61445 | 0.807226 | − | 0.590243i | \(-0.200968\pi\) | ||||
0.807226 | + | 0.590243i | \(0.200968\pi\) | |||||||
\(908\) | − 6.18726i | − 0.205331i | ||||||||
\(909\) | −16.1293 | −0.534976 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 1.76756 | 0.0585620 | 0.0292810 | − | 0.999571i | \(-0.490678\pi\) | ||||
0.0292810 | + | 0.999571i | \(0.490678\pi\) | |||||||
\(912\) | 11.3652i | 0.376339i | ||||||||
\(913\) | −12.7299 | −0.421297 | ||||||||
\(914\) | 37.2437 | 1.23191 | ||||||||
\(915\) | 6.25118i | 0.206658i | ||||||||
\(916\) | 15.3377i | 0.506772i | ||||||||
\(917\) | 1.48085i | 0.0489021i | ||||||||
\(918\) | − 10.0614i | − 0.332076i | ||||||||
\(919\) | 27.4163 | 0.904380 | 0.452190 | − | 0.891922i | \(-0.350643\pi\) | ||||
0.452190 | + | 0.891922i | \(0.350643\pi\) | |||||||
\(920\) | 49.2222 | 1.62281 | ||||||||
\(921\) | 6.85120i | 0.225755i | ||||||||
\(922\) | −4.82689 | −0.158965 | ||||||||
\(923\) | 0 | 0 | ||||||||
\(924\) | 2.94022 | 0.0967260 | ||||||||
\(925\) | 14.0557i | 0.462150i | ||||||||
\(926\) | −25.8331 | −0.848928 | ||||||||
\(927\) | −0.749383 | −0.0246130 | ||||||||
\(928\) | − 35.0866i | − 1.15177i | ||||||||
\(929\) | − 31.0105i | − 1.01742i | −0.860938 | − | 0.508710i | \(-0.830122\pi\) | ||||
0.860938 | − | 0.508710i | \(-0.169878\pi\) | |||||||
\(930\) | 12.1717i | 0.399125i | ||||||||
\(931\) | 6.34660i | 0.208001i | ||||||||
\(932\) | −9.35528 | −0.306442 | ||||||||
\(933\) | 13.0595 | 0.427550 | ||||||||
\(934\) | 13.5972i | 0.444915i | ||||||||
\(935\) | −26.5752 | −0.869101 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −13.5463 | −0.442537 | −0.221269 | − | 0.975213i | \(-0.571020\pi\) | ||||
−0.221269 | + | 0.975213i | \(0.571020\pi\) | |||||||
\(938\) | − 3.38524i | − 0.110532i | ||||||||
\(939\) | 10.1140 | 0.330057 | ||||||||
\(940\) | 2.27702 | 0.0742681 | ||||||||
\(941\) | − 27.1579i | − 0.885321i | −0.896689 | − | 0.442661i | \(-0.854035\pi\) | ||||
0.896689 | − | 0.442661i | \(-0.145965\pi\) | |||||||
\(942\) | − 15.1220i | − 0.492701i | ||||||||
\(943\) | − 46.6367i | − 1.51870i | ||||||||
\(944\) | 9.75756i | 0.317581i | ||||||||
\(945\) | 17.3002 | 0.562775 | ||||||||
\(946\) | 45.9239 | 1.49312 | ||||||||
\(947\) | − 30.1736i | − 0.980511i | −0.871579 | − | 0.490256i | \(-0.836903\pi\) | ||||
0.871579 | − | 0.490256i | \(-0.163097\pi\) | |||||||
\(948\) | 0.0684184 | 0.00222213 | ||||||||
\(949\) | 0 | 0 | ||||||||
\(950\) | 53.9835 | 1.75146 | ||||||||
\(951\) | − 3.48892i | − 0.113136i | ||||||||
\(952\) | 5.72901 | 0.185678 | ||||||||
\(953\) | −13.0194 | −0.421738 | −0.210869 | − | 0.977514i | \(-0.567629\pi\) | ||||
−0.210869 | + | 0.977514i | \(0.567629\pi\) | |||||||
\(954\) | 15.1341i | 0.489983i | ||||||||
\(955\) | 58.0237i | 1.87760i | ||||||||
\(956\) | 11.9604i | 0.386828i | ||||||||
\(957\) | 33.0369i | 1.06793i | ||||||||
\(958\) | 0.758836 | 0.0245169 | ||||||||
\(959\) | 4.43864 | 0.143331 | ||||||||
\(960\) | 28.0908i | 0.906627i | ||||||||
\(961\) | 20.6036 | 0.664632 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 8.32614 | 0.268306 | ||||||||
\(964\) | − 1.00306i | − 0.0323064i | ||||||||
\(965\) | −75.5322 | −2.43147 | ||||||||
\(966\) | 4.77572 | 0.153656 | ||||||||
\(967\) | 49.5415i | 1.59315i | 0.604542 | + | 0.796573i | \(0.293356\pi\) | ||||
−0.604542 | + | 0.796573i | \(0.706644\pi\) | |||||||
\(968\) | 15.4805i | 0.497561i | ||||||||
\(969\) | 11.3110i | 0.363361i | ||||||||
\(970\) | 52.1025i | 1.67291i | ||||||||
\(971\) | −34.3718 | −1.10304 | −0.551522 | − | 0.834160i | \(-0.685953\pi\) | ||||
−0.551522 | + | 0.834160i | \(0.685953\pi\) | |||||||
\(972\) | 12.3874 | 0.397326 | ||||||||
\(973\) | − 17.3529i | − 0.556310i | ||||||||
\(974\) | −2.42561 | −0.0777214 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 3.44365 | 0.110228 | ||||||||
\(977\) | 10.8964i | 0.348607i | 0.984692 | + | 0.174303i | \(0.0557674\pi\) | ||||
−0.984692 | + | 0.174303i | \(0.944233\pi\) | |||||||
\(978\) | 2.13674 | 0.0683255 | ||||||||
\(979\) | 48.9751 | 1.56525 | ||||||||
\(980\) | 2.73355i | 0.0873202i | ||||||||
\(981\) | 20.1432i | 0.643123i | ||||||||
\(982\) | 9.78595i | 0.312282i | ||||||||
\(983\) | 17.8803i | 0.570293i | 0.958484 | + | 0.285146i | \(0.0920422\pi\) | ||||
−0.958484 | + | 0.285146i | \(0.907958\pi\) | |||||||
\(984\) | 30.4182 | 0.969697 | ||||||||
\(985\) | −57.2217 | −1.82323 | ||||||||
\(986\) | 17.8631i | 0.568876i | ||||||||
\(987\) | 0.796136 | 0.0253413 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −46.5144 | −1.47907 | ||||||||
\(990\) | 33.0041i | 1.04894i | ||||||||
\(991\) | −43.2925 | −1.37523 | −0.687616 | − | 0.726074i | \(-0.741343\pi\) | ||||
−0.687616 | + | 0.726074i | \(0.741343\pi\) | |||||||
\(992\) | −13.1074 | −0.416161 | ||||||||
\(993\) | 20.7950i | 0.659909i | ||||||||
\(994\) | − 16.0258i | − 0.508308i | ||||||||
\(995\) | − 54.9392i | − 1.74169i | ||||||||
\(996\) | 2.33365i | 0.0739444i | ||||||||
\(997\) | 25.7004 | 0.813940 | 0.406970 | − | 0.913442i | \(-0.366585\pi\) | ||||
0.406970 | + | 0.913442i | \(0.366585\pi\) | |||||||
\(998\) | 18.1801 | 0.575480 | ||||||||
\(999\) | 8.91625i | 0.282098i |
(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 | 1183.2.c.j.337.8 | 24 | ||
13.5 | odd | 4 | 1183.2.a.r.1.4 | yes | 12 | ||
13.8 | odd | 4 | 1183.2.a.q.1.9 | ✓ | 12 | ||
13.12 | even | 2 | inner | 1183.2.c.j.337.17 | 24 | ||
91.34 | even | 4 | 8281.2.a.cn.1.9 | 12 | |||
91.83 | even | 4 | 8281.2.a.cq.1.4 | 12 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1183.2.a.q.1.9 | ✓ | 12 | 13.8 | odd | 4 | ||
1183.2.a.r.1.4 | yes | 12 | 13.5 | odd | 4 | ||
1183.2.c.j.337.8 | 24 | 1.1 | even | 1 | trivial | ||
1183.2.c.j.337.17 | 24 | 13.12 | even | 2 | inner | ||
8281.2.a.cn.1.9 | 12 | 91.34 | even | 4 | |||
8281.2.a.cq.1.4 | 12 | 91.83 | even | 4 |