Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1344,2,Mod(31,1344)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1344, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([3, 3, 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("1344.31");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1344 = 2^{6} \cdot 3 \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1344.bb (of order \(6\), degree \(2\), 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: | \(10.7318940317\) |
Analytic rank: | \(0\) |
Dimension: | \(12\) |
Relative dimension: | \(6\) over \(\Q(\zeta_{6})\) |
Coefficient field: | 12.0.32905425960566784.37 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{12} + 36x^{10} + 432x^{8} + 2040x^{6} + 3780x^{4} + 2592x^{2} + 576 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 2^{2} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 607.3 | ||
Root | \(-4.06501i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1344.607 |
Dual form | 1344.2.bb.g.31.3 |
$q$-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 \(\left(\mathbb{Z}/1344\mathbb{Z}\right)^\times\).
\(n\) | \(127\) | \(449\) | \(577\) | \(1093\) |
\(\chi(n)\) | \(-1\) | \(1\) | \(e\left(\frac{5}{6}\right)\) | \(-1\) |
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 | ||||||||
\(3\) | −0.866025 | + | 0.500000i | −0.500000 | + | 0.288675i | ||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 1.29211 | − | 2.23800i | 0.577850 | − | 1.00087i | −0.417875 | − | 0.908504i | \(-0.637225\pi\) |
0.995726 | − | 0.0923617i | \(-0.0294416\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −1.56777 | + | 2.13122i | −0.592559 | + | 0.805527i | ||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0.500000 | − | 0.866025i | 0.166667 | − | 0.288675i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 0.195786 | + | 0.339111i | 0.0590316 | + | 0.102246i | 0.894031 | − | 0.448005i | \(-0.147865\pi\) |
−0.834999 | + | 0.550251i | \(0.814532\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 1.67822 | 0.465455 | 0.232727 | − | 0.972542i | \(-0.425235\pi\) | ||||
0.232727 | + | 0.972542i | \(0.425235\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 2.58423i | 0.667244i | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 0.678221 | − | 0.391571i | 0.164493 | − | 0.0949700i | −0.415494 | − | 0.909596i | \(-0.636391\pi\) |
0.579986 | + | 0.814626i | \(0.303058\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 4.19734 | + | 2.42334i | 0.962936 | + | 0.555951i | 0.897075 | − | 0.441877i | \(-0.145687\pi\) |
0.0658606 | + | 0.997829i | \(0.479021\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0.292113 | − | 2.62958i | 0.0637442 | − | 0.573821i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −4.47601 | − | 2.58423i | −0.933313 | − | 0.538848i | −0.0454549 | − | 0.998966i | \(-0.514474\pi\) |
−0.887858 | + | 0.460118i | \(0.847807\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −0.839111 | − | 1.45338i | −0.167822 | − | 0.290676i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 1.00000i | 0.192450i | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | − | 1.79505i | − | 0.333333i | −0.986013 | − | 0.166666i | \(-0.946700\pi\) | ||
0.986013 | − | 0.166666i | \(-0.0533002\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 1.17619 | + | 2.03723i | 0.211251 | + | 0.365897i | 0.952106 | − | 0.305768i | \(-0.0989130\pi\) |
−0.740856 | + | 0.671664i | \(0.765580\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −0.339111 | − | 0.195786i | −0.0590316 | − | 0.0340819i | ||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 2.74396 | + | 6.26245i | 0.463814 | + | 1.05855i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 4.83911 | + | 2.79386i | 0.795545 | + | 0.459308i | 0.841911 | − | 0.539616i | \(-0.181431\pi\) |
−0.0463661 | + | 0.998925i | \(0.514764\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −1.45338 | + | 0.839111i | −0.232727 | + | 0.134365i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 4.24724i | 0.663308i | 0.943401 | + | 0.331654i | \(0.107607\pi\) | ||||
−0.943401 | + | 0.331654i | \(0.892393\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 11.0756 | 1.68902 | 0.844510 | − | 0.535540i | \(-0.179892\pi\) | ||||
0.844510 | + | 0.535540i | \(0.179892\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −1.29211 | − | 2.23800i | −0.192617 | − | 0.333622i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 6.59963 | − | 11.4309i | 0.962655 | − | 1.66737i | 0.246868 | − | 0.969049i | \(-0.420599\pi\) |
0.715787 | − | 0.698319i | \(-0.246068\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −2.08423 | − | 6.68251i | −0.297746 | − | 0.954645i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −0.391571 | + | 0.678221i | −0.0548309 | + | 0.0949700i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 8.23278 | − | 4.75320i | 1.13086 | − | 0.652902i | 0.186708 | − | 0.982415i | \(-0.440218\pi\) |
0.944151 | + | 0.329513i | \(0.106885\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 1.01191 | 0.136446 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −4.84667 | −0.641957 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −0.132786 | + | 0.0766640i | −0.0172873 | + | 0.00998080i | −0.508619 | − | 0.860992i | \(-0.669844\pi\) |
0.491331 | + | 0.870973i | \(0.336510\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 2.26245 | − | 3.91867i | 0.289677 | − | 0.501735i | −0.684056 | − | 0.729430i | \(-0.739786\pi\) |
0.973733 | + | 0.227695i | \(0.0731189\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 1.06181 | + | 2.42334i | 0.133776 | + | 0.305312i | ||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 2.16845 | − | 3.75587i | 0.268963 | − | 0.465858i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 2.46529 | + | 4.27001i | 0.301183 | + | 0.521665i | 0.976404 | − | 0.215951i | \(-0.0692851\pi\) |
−0.675221 | + | 0.737615i | \(0.735952\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 5.16845 | 0.622208 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | − | 0.524893i | − | 0.0622934i | −0.999515 | − | 0.0311467i | \(-0.990084\pi\) | ||
0.999515 | − | 0.0311467i | \(-0.00991590\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −10.2700 | + | 5.92939i | −1.20201 | + | 0.693983i | −0.961003 | − | 0.276540i | \(-0.910812\pi\) |
−0.241011 | + | 0.970522i | \(0.577479\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 1.45338 | + | 0.839111i | 0.167822 | + | 0.0968921i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −1.02967 | − | 0.114383i | −0.117341 | − | 0.0130351i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −2.51667 | − | 1.45300i | −0.283148 | − | 0.163476i | 0.351700 | − | 0.936113i | \(-0.385604\pi\) |
−0.634848 | + | 0.772637i | \(0.718937\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −0.500000 | − | 0.866025i | −0.0555556 | − | 0.0962250i | ||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 12.3716i | 1.35796i | 0.734159 | + | 0.678978i | \(0.237577\pi\) | ||||
−0.734159 | + | 0.678978i | \(0.762423\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | − | 2.02382i | − | 0.219514i | ||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0.897525 | + | 1.55456i | 0.0962248 | + | 0.166666i | ||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 10.8618 | + | 6.27106i | 1.15135 | + | 0.664731i | 0.949215 | − | 0.314627i | \(-0.101879\pi\) |
0.202133 | + | 0.979358i | \(0.435213\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −2.63106 | + | 3.57666i | −0.275810 | + | 0.374936i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −2.03723 | − | 1.17619i | −0.211251 | − | 0.121966i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 10.8469 | − | 6.26245i | 1.11287 | − | 0.642513i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 12.0245i | 1.22091i | 0.792052 | + | 0.610454i | \(0.209013\pi\) | ||||
−0.792052 | + | 0.610454i | \(0.790987\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0.391571 | 0.0393544 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −5.58423 | − | 9.67216i | −0.555651 | − | 0.962416i | −0.997853 | − | 0.0655003i | \(-0.979136\pi\) |
0.442201 | − | 0.896916i | \(-0.354198\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 0.278669 | − | 0.482668i | 0.0274580 | − | 0.0475587i | −0.851970 | − | 0.523591i | \(-0.824592\pi\) |
0.879428 | + | 0.476032i | \(0.157925\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −5.50756 | − | 4.05146i | −0.537483 | − | 0.395382i | ||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 6.79542 | − | 11.7700i | 0.656938 | − | 1.13785i | −0.324466 | − | 0.945897i | \(-0.605185\pi\) |
0.981404 | − | 0.191952i | \(-0.0614819\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 14.9136 | − | 8.61035i | 1.42846 | − | 0.824722i | 0.431461 | − | 0.902132i | \(-0.357998\pi\) |
0.996999 | + | 0.0774095i | \(0.0246649\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −5.58772 | −0.530363 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 17.6933 | 1.66445 | 0.832225 | − | 0.554438i | \(-0.187067\pi\) | ||||
0.832225 | + | 0.554438i | \(0.187067\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −11.5670 | + | 6.67822i | −1.07863 | + | 0.622747i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0.839111 | − | 1.45338i | 0.0775758 | − | 0.134365i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −0.228766 | + | 2.05933i | −0.0209709 | + | 0.188779i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 5.42334 | − | 9.39349i | 0.493031 | − | 0.853954i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −2.12362 | − | 3.67822i | −0.191481 | − | 0.331654i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 8.58423 | 0.767796 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 14.7873i | 1.31216i | 0.754690 | + | 0.656082i | \(0.227788\pi\) | ||||
−0.754690 | + | 0.656082i | \(0.772212\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −9.59179 | + | 5.53782i | −0.844510 | + | 0.487578i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 3.88865 | + | 2.24511i | 0.339753 | + | 0.196157i | 0.660163 | − | 0.751122i | \(-0.270487\pi\) |
−0.320410 | + | 0.947279i | \(0.603821\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −11.7451 | + | 5.14625i | −1.01843 | + | 0.446236i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 2.23800 | + | 1.29211i | 0.192617 | + | 0.111207i | ||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 6.52489 | + | 11.3014i | 0.557459 | + | 0.965548i | 0.997708 | + | 0.0676717i | \(0.0215571\pi\) |
−0.440248 | + | 0.897876i | \(0.645110\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | − | 17.1836i | − | 1.45749i | −0.684784 | − | 0.728746i | \(-0.740104\pi\) | ||
0.684784 | − | 0.728746i | \(-0.259896\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 13.1993i | 1.11158i | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 0.328571 | + | 0.569103i | 0.0274765 | + | 0.0475907i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −4.01733 | − | 2.31941i | −0.333621 | − | 0.192616i | ||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 5.14625 | + | 4.74511i | 0.424456 | + | 0.391370i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 5.32178 | + | 3.07253i | 0.435977 | + | 0.251712i | 0.701890 | − | 0.712286i | \(-0.252340\pi\) |
−0.265913 | + | 0.963997i | \(0.585673\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −3.97006 | + | 2.29211i | −0.323079 | + | 0.186529i | −0.652764 | − | 0.757561i | \(-0.726391\pi\) |
0.329685 | + | 0.944091i | \(0.393057\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | − | 0.783142i | − | 0.0633133i | ||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 6.07910 | 0.488285 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −7.67822 | − | 13.2991i | −0.612789 | − | 1.06138i | −0.990768 | − | 0.135567i | \(-0.956714\pi\) |
0.377979 | − | 0.925814i | \(-0.376619\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −4.75320 | + | 8.23278i | −0.376953 | + | 0.652902i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 12.5249 | − | 5.48792i | 0.987100 | − | 0.432509i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −8.00311 | + | 13.8618i | −0.626852 | + | 1.08574i | 0.361328 | + | 0.932439i | \(0.382324\pi\) |
−0.988180 | + | 0.153301i | \(0.951010\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −0.876338 | + | 0.505954i | −0.0682228 | + | 0.0393885i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 4.24724 | 0.328662 | 0.164331 | − | 0.986405i | \(-0.447454\pi\) | ||||
0.164331 | + | 0.986405i | \(0.447454\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −10.1836 | −0.783352 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 4.19734 | − | 2.42334i | 0.320979 | − | 0.185317i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −9.26245 | + | 16.0430i | −0.704211 | + | 1.21973i | 0.262765 | + | 0.964860i | \(0.415366\pi\) |
−0.966976 | + | 0.254869i | \(0.917968\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 4.41301 | + | 0.490230i | 0.333592 | + | 0.0370579i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0.0766640 | − | 0.132786i | 0.00576242 | − | 0.00998080i | ||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −8.66025 | − | 15.0000i | −0.647298 | − | 1.12115i | −0.983766 | − | 0.179458i | \(-0.942566\pi\) |
0.336468 | − | 0.941695i | \(-0.390768\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −17.1836 | −1.27724 | −0.638622 | − | 0.769520i | \(-0.720495\pi\) | ||||
−0.638622 | + | 0.769520i | \(0.720495\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 4.52489i | 0.334490i | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 12.5054 | − | 7.21997i | 0.919412 | − | 0.530823i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 0.265572 | + | 0.153328i | 0.0194205 | + | 0.0112125i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −2.13122 | − | 1.56777i | −0.155024 | − | 0.114038i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −15.3229 | − | 8.84667i | −1.10873 | − | 0.640123i | −0.170226 | − | 0.985405i | \(-0.554450\pi\) |
−0.938499 | + | 0.345282i | \(0.887783\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −3.08423 | − | 5.34204i | −0.222007 | − | 0.384528i | 0.733410 | − | 0.679787i | \(-0.237928\pi\) |
−0.955417 | + | 0.295258i | \(0.904594\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 4.33690i | 0.310572i | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 25.6154i | 1.82502i | 0.409054 | + | 0.912510i | \(0.365859\pi\) | ||||
−0.409054 | + | 0.912510i | \(0.634141\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 0.0629997 | + | 0.109119i | 0.00446593 | + | 0.00773521i | 0.868250 | − | 0.496127i | \(-0.165245\pi\) |
−0.863784 | + | 0.503863i | \(0.831912\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −4.27001 | − | 2.46529i | −0.301183 | − | 0.173888i | ||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 3.82565 | + | 2.81422i | 0.268508 | + | 0.197519i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 9.50535 | + | 5.48792i | 0.663883 | + | 0.383293i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −4.47601 | + | 2.58423i | −0.311104 | + | 0.179616i | ||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 1.89782i | 0.131275i | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 8.82602 | 0.607608 | 0.303804 | − | 0.952735i | \(-0.401743\pi\) | ||||
0.303804 | + | 0.952735i | \(0.401743\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0.262447 | + | 0.454571i | 0.0179825 | + | 0.0311467i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 14.3110 | − | 24.7873i | 0.976001 | − | 1.69048i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −6.18578 | − | 0.687162i | −0.419918 | − | 0.0466476i | ||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 5.92939 | − | 10.2700i | 0.400671 | − | 0.693983i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 1.13821 | − | 0.657143i | 0.0765640 | − | 0.0442042i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −19.1156 | −1.28007 | −0.640036 | − | 0.768345i | \(-0.721081\pi\) | ||||
−0.640036 | + | 0.768345i | \(0.721081\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −1.67822 | −0.111881 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −19.9317 | + | 11.5076i | −1.32291 | + | 0.763784i | −0.984192 | − | 0.177104i | \(-0.943327\pi\) |
−0.338720 | + | 0.940887i | \(0.609994\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −3.10156 | + | 5.37205i | −0.204957 | + | 0.354995i | −0.950119 | − | 0.311888i | \(-0.899039\pi\) |
0.745162 | + | 0.666883i | \(0.232372\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0.948908 | − | 0.415775i | 0.0624336 | − | 0.0273560i | ||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −9.00000 | + | 15.5885i | −0.589610 | + | 1.02123i | 0.404674 | + | 0.914461i | \(0.367385\pi\) |
−0.994283 | + | 0.106773i | \(0.965948\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −17.0549 | − | 29.5400i | −1.11254 | − | 1.92698i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 2.90600 | 0.188765 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | − | 10.8618i | − | 0.702591i | −0.936265 | − | 0.351296i | \(-0.885741\pi\) | ||
0.936265 | − | 0.351296i | \(-0.114259\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −2.66089 | + | 1.53627i | −0.171403 | + | 0.0989595i | −0.583247 | − | 0.812295i | \(-0.698218\pi\) |
0.411844 | + | 0.911254i | \(0.364885\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 0.866025 | + | 0.500000i | 0.0555556 | + | 0.0320750i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −17.6486 | − | 3.97006i | −1.12752 | − | 0.253638i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 7.04407 | + | 4.06689i | 0.448203 | + | 0.258770i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −6.18578 | − | 10.7141i | −0.392008 | − | 0.678978i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | − | 21.0844i | − | 1.33084i | −0.746470 | − | 0.665419i | \(-0.768253\pi\) | ||
0.746470 | − | 0.665419i | \(-0.231747\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | − | 2.02382i | − | 0.127236i | ||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 1.01191 | + | 1.75268i | 0.0633681 | + | 0.109757i | ||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −23.8271 | − | 13.7566i | −1.48630 | − | 0.858113i | −0.486418 | − | 0.873726i | \(-0.661697\pi\) |
−0.999878 | + | 0.0156133i | \(0.995030\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −13.5409 | + | 5.93311i | −0.841393 | + | 0.368665i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −1.55456 | − | 0.897525i | −0.0962248 | − | 0.0555554i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 4.47601 | − | 2.58423i | 0.276003 | − | 0.159350i | −0.355610 | − | 0.934635i | \(-0.615727\pi\) |
0.631612 | + | 0.775284i | \(0.282393\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | − | 24.5667i | − | 1.50912i | ||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −12.5421 | −0.767565 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −4.86122 | − | 8.41987i | −0.296394 | − | 0.513369i | 0.678915 | − | 0.734217i | \(-0.262451\pi\) |
−0.975308 | + | 0.220849i | \(0.929117\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −5.70211 | + | 9.87634i | −0.346378 | + | 0.599945i | −0.985603 | − | 0.169075i | \(-0.945922\pi\) |
0.639225 | + | 0.769020i | \(0.279255\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0.490230 | − | 4.41301i | 0.0296701 | − | 0.267088i | ||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 0.328571 | − | 0.569103i | 0.0198136 | − | 0.0343182i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 0.373550 | − | 0.215669i | 0.0224444 | − | 0.0129583i | −0.488736 | − | 0.872432i | \(-0.662542\pi\) |
0.511180 | + | 0.859474i | \(0.329208\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 2.35239 | 0.140834 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 13.0498 | 0.778485 | 0.389242 | − | 0.921135i | \(-0.372737\pi\) | ||||
0.389242 | + | 0.921135i | \(0.372737\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −21.1922 | + | 12.2353i | −1.25975 | + | 0.727316i | −0.973025 | − | 0.230698i | \(-0.925899\pi\) |
−0.286722 | + | 0.958014i | \(0.592566\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −6.26245 | + | 10.8469i | −0.370955 | + | 0.642513i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −9.05183 | − | 6.65868i | −0.534312 | − | 0.393049i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −8.19334 | + | 14.1913i | −0.481961 | + | 0.834782i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −6.01227 | − | 10.4136i | −0.352446 | − | 0.610454i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 6.92113 | 0.404337 | 0.202168 | − | 0.979351i | \(-0.435201\pi\) | ||||
0.202168 | + | 0.979351i | \(0.435201\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0.396234i | 0.0230696i | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −0.339111 | + | 0.195786i | −0.0196772 | + | 0.0113606i | ||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −7.51173 | − | 4.33690i | −0.434415 | − | 0.250810i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −17.3640 | + | 23.6047i | −1.00084 | + | 1.36055i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 9.67216 | + | 5.58423i | 0.555651 | + | 0.320805i | ||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −5.84667 | − | 10.1267i | −0.334779 | − | 0.579855i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | − | 12.8467i | − | 0.733198i | −0.930379 | − | 0.366599i | \(-0.880522\pi\) | ||
0.930379 | − | 0.366599i | \(-0.119478\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0.557337i | 0.0317058i | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −8.39468 | − | 14.5400i | −0.476019 | − | 0.824489i | 0.523604 | − | 0.851962i | \(-0.324587\pi\) |
−0.999623 | + | 0.0274732i | \(0.991254\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 2.06910 | + | 1.19460i | 0.116953 | + | 0.0675226i | 0.557335 | − | 0.830288i | \(-0.311824\pi\) |
−0.440383 | + | 0.897810i | \(0.645157\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 6.79542 | + | 0.754885i | 0.382878 | + | 0.0425330i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −23.0599 | − | 13.3136i | −1.29517 | − | 0.747769i | −0.315607 | − | 0.948890i | \(-0.602208\pi\) |
−0.979566 | + | 0.201121i | \(0.935542\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 0.608721 | − | 0.351445i | 0.0340818 | − | 0.0196771i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 13.5908i | 0.758566i | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 3.79563 | 0.211195 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −1.40821 | − | 2.43910i | −0.0781136 | − | 0.135297i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −8.61035 | + | 14.9136i | −0.476154 | + | 0.824722i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 14.0151 | + | 31.9863i | 0.772679 | + | 1.76346i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 14.4239 | − | 24.9829i | 0.792808 | − | 1.37318i | −0.131414 | − | 0.991328i | \(-0.541952\pi\) |
0.924222 | − | 0.381856i | \(-0.124715\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 4.83911 | − | 2.79386i | 0.265182 | − | 0.153103i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 12.7417 | 0.696155 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 9.14891 | 0.498373 | 0.249186 | − | 0.968456i | \(-0.419837\pi\) | ||||
0.249186 | + | 0.968456i | \(0.419837\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −15.3229 | + | 8.84667i | −0.832225 | + | 0.480485i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −0.460564 | + | 0.797720i | −0.0249409 | + | 0.0431989i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 17.5095 | + | 6.03466i | 0.945425 | + | 0.325841i | ||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 6.67822 | − | 11.5670i | 0.359543 | − | 0.622747i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −17.0549 | − | 29.5400i | −0.915557 | − | 1.58579i | −0.806084 | − | 0.591801i | \(-0.798417\pi\) |
−0.109473 | − | 0.993990i | \(-0.534916\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −12.0302 | −0.643964 | −0.321982 | − | 0.946746i | \(-0.604349\pi\) | ||||
−0.321982 | + | 0.946746i | \(0.604349\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 1.67822i | 0.0895768i | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 15.6782 | − | 9.05183i | 0.834468 | − | 0.481780i | −0.0209123 | − | 0.999781i | \(-0.506657\pi\) |
0.855380 | + | 0.518001i | \(0.173324\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −1.17471 | − | 0.678221i | −0.0623473 | − | 0.0359962i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −0.831549 | − | 1.89782i | −0.0440102 | − | 0.100443i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 0.909142 | + | 0.524893i | 0.0479827 | + | 0.0277028i | 0.523799 | − | 0.851842i | \(-0.324514\pi\) |
−0.475817 | + | 0.879544i | \(0.657847\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 2.24511 | + | 3.88865i | 0.118164 | + | 0.204666i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 10.8467i | 0.569303i | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 30.6458i | 1.60407i | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −5.26063 | − | 9.11168i | −0.274603 | − | 0.475626i | 0.695432 | − | 0.718592i | \(-0.255213\pi\) |
−0.970035 | + | 0.242966i | \(0.921880\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 3.67822 | + | 2.12362i | 0.191481 | + | 0.110551i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −2.77694 | + | 24.9978i | −0.144172 | + | 1.29782i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 24.5918 | + | 14.1981i | 1.27331 | + | 0.735148i | 0.975610 | − | 0.219510i | \(-0.0704458\pi\) |
0.297704 | + | 0.954658i | \(0.403779\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −7.43416 | + | 4.29211i | −0.383898 | + | 0.221644i | ||||
\(376\) | 0 | 0 | ||||||||
\(377\) | − | 3.01249i | − | 0.155151i | ||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 31.0771 | 1.59632 | 0.798162 | − | 0.602443i | \(-0.205806\pi\) | ||||
0.798162 | + | 0.602443i | \(0.205806\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −7.39367 | − | 12.8062i | −0.378789 | − | 0.656082i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −5.48792 | + | 9.50535i | −0.280420 | + | 0.485701i | −0.971488 | − | 0.237088i | \(-0.923807\pi\) |
0.691069 | + | 0.722789i | \(0.257140\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −1.58643 | + | 2.15660i | −0.0808522 | + | 0.109911i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 5.53782 | − | 9.59179i | 0.281503 | − | 0.487578i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 0.287115 | − | 0.165766i | 0.0145573 | − | 0.00840468i | −0.492704 | − | 0.870197i | \(-0.663991\pi\) |
0.507261 | + | 0.861792i | \(0.330658\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −4.04763 | −0.204698 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −4.49023 | −0.226502 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −6.50365 | + | 3.75489i | −0.327234 | + | 0.188929i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −18.2700 | + | 31.6446i | −0.916945 | + | 1.58820i | −0.112918 | + | 0.993604i | \(0.536020\pi\) |
−0.804028 | + | 0.594592i | \(0.797314\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 7.59844 | − | 10.3293i | 0.380398 | − | 0.517114i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −9.81201 | + | 16.9949i | −0.489988 | + | 0.848685i | −0.999934 | − | 0.0115222i | \(-0.996332\pi\) |
0.509945 | + | 0.860207i | \(0.329666\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 1.97391 | + | 3.41892i | 0.0983276 | + | 0.170308i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −2.58423 | −0.128411 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 2.18799i | 0.108455i | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 17.3965 | − | 10.0438i | 0.860200 | − | 0.496636i | −0.00387959 | − | 0.999992i | \(-0.501235\pi\) |
0.864079 | + | 0.503356i | \(0.167902\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −11.3014 | − | 6.52489i | −0.557459 | − | 0.321849i | ||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 0.0447891 | − | 0.403188i | 0.00220393 | − | 0.0198396i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 27.6876 | + | 15.9855i | 1.35913 | + | 0.784695i | ||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 8.59179 | + | 14.8814i | 0.420742 | + | 0.728746i | ||||
\(418\) | 0 | 0 | ||||||||
\(419\) | − | 4.64356i | − | 0.226853i | −0.993546 | − | 0.113426i | \(-0.963817\pi\) | ||
0.993546 | − | 0.113426i | \(-0.0361826\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 15.1969i | 0.740651i | 0.928902 | + | 0.370325i | \(0.120754\pi\) | ||||
−0.928902 | + | 0.370325i | \(0.879246\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −6.59963 | − | 11.4309i | −0.320885 | − | 0.555789i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −1.13821 | − | 0.657143i | −0.0552111 | − | 0.0318761i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 4.80458 | + | 10.9653i | 0.232510 | + | 0.530650i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −0.569103 | − | 0.328571i | −0.0274765 | − | 0.0158636i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −2.58115 | + | 1.49023i | −0.124330 | + | 0.0717818i | −0.560875 | − | 0.827900i | \(-0.689535\pi\) |
0.436545 | + | 0.899682i | \(0.356202\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 25.9672i | 1.24790i | 0.781463 | + | 0.623952i | \(0.214474\pi\) | ||||
−0.781463 | + | 0.623952i | \(0.785526\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 4.63882 | 0.222414 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −12.5249 | − | 21.6938i | −0.599147 | − | 1.03775i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −13.6422 | + | 23.6290i | −0.651108 | + | 1.12775i | 0.331747 | + | 0.943368i | \(0.392362\pi\) |
−0.982854 | + | 0.184383i | \(0.940971\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −6.82934 | − | 1.53627i | −0.325207 | − | 0.0731555i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −0.0300194 | + | 0.0519951i | −0.00142627 | + | 0.00247036i | −0.866738 | − | 0.498764i | \(-0.833787\pi\) |
0.865311 | + | 0.501235i | \(0.167121\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 28.0693 | − | 16.2058i | 1.33061 | − | 0.768230i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −6.14506 | −0.290651 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 3.28712 | 0.155129 | 0.0775643 | − | 0.996987i | \(-0.475286\pi\) | ||||
0.0775643 | + | 0.996987i | \(0.475286\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −1.44029 | + | 0.831549i | −0.0678204 | + | 0.0391561i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 2.29211 | − | 3.97006i | 0.107693 | − | 0.186529i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 4.60497 | + | 10.5098i | 0.215884 | + | 0.492706i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 4.17822 | − | 7.23689i | 0.195449 | − | 0.338527i | −0.751599 | − | 0.659621i | \(-0.770717\pi\) |
0.947048 | + | 0.321093i | \(0.104050\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0.391571 | + | 0.678221i | 0.0182770 | + | 0.0316567i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 3.81201 | 0.177543 | 0.0887715 | − | 0.996052i | \(-0.471706\pi\) | ||||
0.0887715 | + | 0.996052i | \(0.471706\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | − | 25.8965i | − | 1.20351i | −0.798681 | − | 0.601755i | \(-0.794468\pi\) | ||
0.798681 | − | 0.601755i | \(-0.205532\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −5.26466 | + | 3.03955i | −0.244143 | + | 0.140956i | ||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 6.37087 | + | 3.67822i | 0.294809 | + | 0.170208i | 0.640108 | − | 0.768285i | \(-0.278889\pi\) |
−0.345300 | + | 0.938492i | \(0.612223\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −12.9653 | − | 1.44029i | −0.598684 | − | 0.0665062i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 13.2991 | + | 7.67822i | 0.612789 | + | 0.353794i | ||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 2.16845 | + | 3.75587i | 0.0997055 | + | 0.172695i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | − | 8.13379i | − | 0.373204i | ||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | − | 9.50640i | − | 0.435268i | ||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 18.3324 | + | 31.7527i | 0.837629 | + | 1.45082i | 0.891871 | + | 0.452289i | \(0.149392\pi\) |
−0.0542420 | + | 0.998528i | \(0.517274\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 8.12110 | + | 4.68872i | 0.370290 | + | 0.213787i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −8.10292 | + | 11.0151i | −0.368695 | + | 0.501205i | ||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 26.9110 | + | 15.5371i | 1.22197 | + | 0.705502i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −12.6172 | + | 7.28455i | −0.571740 | + | 0.330095i | −0.757844 | − | 0.652436i | \(-0.773747\pi\) |
0.186104 | + | 0.982530i | \(0.440414\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | − | 16.0062i | − | 0.723826i | ||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 4.18128 | 0.188699 | 0.0943493 | − | 0.995539i | \(-0.469923\pi\) | ||||
0.0943493 | + | 0.995539i | \(0.469923\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −0.702890 | − | 1.21744i | −0.0316566 | − | 0.0548308i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0.505954 | − | 0.876338i | 0.0227409 | − | 0.0393885i | ||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 1.11866 | + | 0.822909i | 0.0501790 | + | 0.0369125i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −2.46529 | + | 4.27001i | −0.110362 | + | 0.191152i | −0.915916 | − | 0.401370i | \(-0.868534\pi\) |
0.805555 | + | 0.592522i | \(0.201868\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −3.67822 | + | 2.12362i | −0.164331 | + | 0.0948764i | ||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −2.47543 | −0.110374 | −0.0551869 | − | 0.998476i | \(-0.517575\pi\) | ||||
−0.0551869 | + | 0.998476i | \(0.517575\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −28.8618 | −1.28433 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 8.81923 | − | 5.09179i | 0.391676 | − | 0.226134i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 5.07945 | − | 8.79787i | 0.225143 | − | 0.389959i | −0.731219 | − | 0.682142i | \(-0.761048\pi\) |
0.956362 | + | 0.292184i | \(0.0943818\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 3.46410 | − | 31.1836i | 0.153243 | − | 1.37948i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −2.42334 | + | 4.19734i | −0.106993 | + | 0.185317i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −0.720143 | − | 1.24732i | −0.0317333 | − | 0.0549636i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 5.16845 | 0.227308 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | − | 18.5249i | − | 0.813153i | ||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 17.3218 | − | 10.0007i | 0.758881 | − | 0.438140i | −0.0700129 | − | 0.997546i | \(-0.522304\pi\) |
0.828894 | + | 0.559406i | \(0.188971\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 18.0799 | + | 10.4385i | 0.790581 | + | 0.456442i | 0.840167 | − | 0.542328i | \(-0.182457\pi\) |
−0.0495863 | + | 0.998770i | \(0.515790\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | −4.06689 | + | 1.78195i | −0.177494 | + | 0.0777708i | ||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 1.59544 | + | 0.921127i | 0.0694984 | + | 0.0401249i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 1.85644 | + | 3.21545i | 0.0807149 | + | 0.139802i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0.153328i | 0.00665387i | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 7.12781i | 0.308740i | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −17.5609 | − | 30.4164i | −0.759223 | − | 1.31501i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 15.0000 | + | 8.66025i | 0.647298 | + | 0.373718i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 1.85805 | − | 2.01512i | 0.0800319 | − | 0.0867975i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −14.7356 | − | 8.50758i | −0.633532 | − | 0.365770i | 0.148587 | − | 0.988899i | \(-0.452528\pi\) |
−0.782119 | + | 0.623130i | \(0.785861\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 14.8814 | − | 8.59179i | 0.638622 | − | 0.368709i | ||||
\(544\) | 0 | 0 | ||||||||
\(545\) | − | 44.5022i | − | 1.90626i | ||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 15.0912 | 0.645251 | 0.322626 | − | 0.946527i | \(-0.395435\pi\) | ||||
0.322626 | + | 0.946527i | \(0.395435\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −2.26245 | − | 3.91867i | −0.0965589 | − | 0.167245i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 4.35001 | − | 7.53444i | 0.185317 | − | 0.320978i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 7.04222 | − | 3.08563i | 0.299466 | − | 0.131214i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −7.21997 | + | 12.5054i | −0.306471 | + | 0.530823i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 29.6290 | − | 17.1063i | 1.25542 | − | 0.724818i | 0.283241 | − | 0.959049i | \(-0.408590\pi\) |
0.972181 | + | 0.234231i | \(0.0752572\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 18.5874 | 0.786162 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −0.306656 | −0.0129470 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −21.3720 | + | 12.3391i | −0.900721 | + | 0.520032i | −0.877434 | − | 0.479697i | \(-0.840746\pi\) |
−0.0232870 | + | 0.999729i | \(0.507413\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 22.8618 | − | 39.5978i | 0.961803 | − | 1.66589i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 2.62958 | + | 0.292113i | 0.110432 | + | 0.0122676i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −16.8813 | + | 29.2393i | −0.707702 | + | 1.22578i | 0.258005 | + | 0.966144i | \(0.416935\pi\) |
−0.965707 | + | 0.259633i | \(0.916398\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −3.97154 | − | 6.87890i | −0.166204 | − | 0.287873i | 0.770878 | − | 0.636982i | \(-0.219818\pi\) |
−0.937082 | + | 0.349109i | \(0.886484\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 17.6933 | 0.739150 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 8.67380i | 0.361723i | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −28.3220 | + | 16.3517i | −1.17906 | + | 0.680731i | −0.955797 | − | 0.294027i | \(-0.905004\pi\) |
−0.223263 | + | 0.974758i | \(0.571671\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 5.34204 | + | 3.08423i | 0.222007 | + | 0.128176i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −26.3666 | − | 19.3957i | −1.09387 | − | 0.804670i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 3.22372 | + | 1.86122i | 0.133513 | + | 0.0770837i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −2.16845 | − | 3.75587i | −0.0896544 | − | 0.155286i | ||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 22.1836i | 0.915614i | 0.889052 | + | 0.457807i | \(0.151365\pi\) | ||||
−0.889052 | + | 0.457807i | \(0.848635\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 11.4013i | 0.469780i | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −12.8077 | − | 22.1836i | −0.526838 | − | 0.912510i | ||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −38.0800 | − | 21.9855i | −1.56376 | − | 0.902837i | −0.996871 | − | 0.0790422i | \(-0.974814\pi\) |
−0.566888 | − | 0.823795i | \(-0.691853\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 4.31320 | + | 3.17287i | 0.176824 | + | 0.130075i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −0.109119 | − | 0.0629997i | −0.00446593 | − | 0.00257840i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −8.95202 | + | 5.16845i | −0.365770 | + | 0.211177i | −0.671609 | − | 0.740906i | \(-0.734396\pi\) |
0.305839 | + | 0.952083i | \(0.401063\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | − | 6.88844i | − | 0.280985i | −0.990082 | − | 0.140493i | \(-0.955131\pi\) | ||
0.990082 | − | 0.140493i | \(-0.0448686\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 4.93058 | 0.200789 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −14.0151 | − | 24.2749i | −0.569796 | − | 0.986915i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −5.19763 | + | 9.00256i | −0.210965 | + | 0.365403i | −0.952017 | − | 0.306045i | \(-0.900994\pi\) |
0.741052 | + | 0.671448i | \(0.234327\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −4.72022 | − | 0.524357i | −0.191273 | − | 0.0212480i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 11.0756 | − | 19.1836i | 0.448072 | − | 0.776084i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 21.3274 | − | 12.3134i | 0.861404 | − | 0.497332i | −0.00307834 | − | 0.999995i | \(-0.500980\pi\) |
0.864482 | + | 0.502664i | \(0.167647\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −10.9758 | −0.442588 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −19.0498 | −0.766916 | −0.383458 | − | 0.923558i | \(-0.625267\pi\) | ||||
−0.383458 | + | 0.923558i | \(0.625267\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −21.5178 | + | 12.4233i | −0.864875 | + | 0.499336i | −0.865642 | − | 0.500664i | \(-0.833089\pi\) |
0.000766513 | 1.00000i | \(0.499756\pi\) | ||||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 2.58423 | − | 4.47601i | 0.103701 | − | 0.179616i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −30.3938 | + | 13.3174i | −1.21770 | + | 0.533549i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 15.2873 | − | 26.4784i | 0.611494 | − | 1.05914i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −0.948908 | − | 1.64356i | −0.0378958 | − | 0.0656374i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 4.37598 | 0.174482 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | − | 13.6833i | − | 0.544726i | −0.962195 | − | 0.272363i | \(-0.912195\pi\) | ||
0.962195 | − | 0.272363i | \(-0.0878051\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −7.64356 | + | 4.41301i | −0.303804 | + | 0.175401i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 33.0941 | + | 19.1069i | 1.31330 | + | 0.758235i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −3.49779 | − | 11.2147i | −0.138588 | − | 0.444344i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −0.454571 | − | 0.262447i | −0.0179825 | − | 0.0103822i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −17.5400 | − | 30.3802i | −0.692789 | − | 1.19995i | −0.970920 | − | 0.239403i | \(-0.923048\pi\) |
0.278131 | − | 0.960543i | \(-0.410285\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 19.8965i | 0.784640i | 0.919829 | + | 0.392320i | \(0.128327\pi\) | ||||
−0.919829 | + | 0.392320i | \(0.871673\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 28.6220i | 1.12699i | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 17.9011 | + | 31.0056i | 0.703764 | + | 1.21896i | 0.967136 | + | 0.254261i | \(0.0818321\pi\) |
−0.263372 | + | 0.964694i | \(0.584835\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −0.0519951 | − | 0.0300194i | −0.00204099 | − | 0.00117836i | ||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 5.70063 | − | 2.49779i | 0.223425 | − | 0.0978962i | ||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 32.9564 | + | 19.0274i | 1.28968 | + | 0.744598i | 0.978598 | − | 0.205784i | \(-0.0659743\pi\) |
0.311085 | + | 0.950382i | \(0.399308\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 10.0492 | − | 5.80188i | 0.392653 | − | 0.226698i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 11.8588i | 0.462655i | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 24.0491 | 0.936820 | 0.468410 | − | 0.883511i | \(-0.344827\pi\) | ||||
0.468410 | + | 0.883511i | \(0.344827\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −16.2107 | − | 28.0777i | −0.630522 | − | 1.09210i | −0.987445 | − | 0.157963i | \(-0.949507\pi\) |
0.356923 | − | 0.934134i | \(-0.383826\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −0.657143 | + | 1.13821i | −0.0255213 | + | 0.0442042i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −3.65868 | + | 32.9352i | −0.141878 | + | 1.27717i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −4.63882 | + | 8.03466i | −0.179616 | + | 0.311103i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 16.5546 | − | 9.55778i | 0.640036 | − | 0.369525i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 1.77182 | 0.0684003 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 22.0800 | 0.851123 | 0.425561 | − | 0.904930i | \(-0.360077\pi\) | ||||
0.425561 | + | 0.904930i | \(0.360077\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 1.45338 | − | 0.839111i | 0.0559407 | − | 0.0322974i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 3.06433 | − | 5.30757i | 0.117772 | − | 0.203987i | −0.801113 | − | 0.598514i | \(-0.795758\pi\) |
0.918884 | + | 0.394527i | \(0.129092\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −25.6270 | − | 18.8517i | −0.983474 | − | 0.723461i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 11.5076 | − | 19.9317i | 0.440971 | − | 0.763784i | ||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 11.3974 | + | 19.7409i | 0.436110 | + | 0.755365i | 0.997386 | − | 0.0722639i | \(-0.0230224\pi\) |
−0.561275 | + | 0.827629i | \(0.689689\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 33.7236 | 1.28851 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | − | 6.20311i | − | 0.236664i | ||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 13.8164 | − | 7.97692i | 0.526364 | − | 0.303896i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −5.60378 | − | 3.23534i | −0.213178 | − | 0.123078i | 0.389610 | − | 0.920980i | \(-0.372610\pi\) |
−0.602787 | + | 0.797902i | \(0.705943\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −0.613892 | + | 0.834526i | −0.0233198 | + | 0.0317010i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −38.4569 | − | 22.2031i | −1.45875 | − | 0.842212i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 1.66310 | + | 2.88057i | 0.0629943 | + | 0.109109i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | − | 18.0000i | − | 0.680823i | ||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | − | 41.8445i | − | 1.58044i | −0.612821 | − | 0.790222i | \(-0.709965\pi\) | ||
0.612821 | − | 0.790222i | \(-0.290035\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 13.5409 | + | 23.4536i | 0.510706 | + | 0.884569i | ||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 29.5400 | + | 17.0549i | 1.11254 | + | 0.642326i | ||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 29.3683 | + | 3.26245i | 1.10451 | + | 0.122697i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 13.3564 | + | 7.71135i | 0.501612 | + | 0.289606i | 0.729379 | − | 0.684110i | \(-0.239809\pi\) |
−0.227767 | + | 0.973716i | \(0.573143\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −2.51667 | + | 1.45300i | −0.0943826 | + | 0.0544918i | ||||
\(712\) | 0 | 0 | ||||||||
\(713\) | − | 12.1582i | − | 0.455328i | ||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 1.69821 | 0.0635093 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 5.43090 | + | 9.40659i | 0.202821 | + | 0.351296i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −3.68991 | + | 6.39111i | −0.137610 | + | 0.238348i | −0.926592 | − | 0.376069i | \(-0.877275\pi\) |
0.788981 | + | 0.614417i | \(0.210609\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 0.591787 | + | 1.35062i | 0.0220393 | + | 0.0502996i | ||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 1.53627 | − | 2.66089i | 0.0571343 | − | 0.0989595i | ||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −2.60889 | + | 1.50625i | −0.0968919 | + | 0.0559406i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 26.7271 | 0.991253 | 0.495627 | − | 0.868536i | \(-0.334938\pi\) | ||||
0.495627 | + | 0.868536i | \(0.334938\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −1.00000 | −0.0370370 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 7.51173 | − | 4.33690i | 0.277832 | − | 0.160406i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −1.14577 | + | 1.98453i | −0.0423199 | + | 0.0733001i | −0.886409 | − | 0.462902i | \(-0.846808\pi\) |
0.844090 | + | 0.536202i | \(0.180142\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 17.2691 | − | 5.38611i | 0.636981 | − | 0.198670i | ||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −0.965337 | + | 1.67201i | −0.0355586 | + | 0.0615894i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 5.14625 | + | 8.91357i | 0.189308 | + | 0.327891i | 0.945020 | − | 0.327013i | \(-0.106042\pi\) |
−0.755712 | + | 0.654904i | \(0.772709\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −8.13379 | −0.298802 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 41.0800i | 1.50708i | 0.657402 | + | 0.753540i | \(0.271655\pi\) | ||||
−0.657402 | + | 0.753540i | \(0.728345\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 13.7527 | − | 7.94011i | 0.503859 | − | 0.290903i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 10.7141 | + | 6.18578i | 0.392008 | + | 0.226326i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 14.4309 | + | 32.9352i | 0.527294 | + | 1.20342i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −20.0524 | − | 11.5772i | −0.731722 | − | 0.422460i | 0.0873301 | − | 0.996179i | \(-0.472167\pi\) |
−0.819052 | + | 0.573720i | \(0.805500\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 10.5422 | + | 18.2597i | 0.384180 | + | 0.665419i | ||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 11.8467i | 0.431145i | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 0.205533i | 0.00747022i | 0.999993 | + | 0.00373511i | \(0.00118893\pi\) | ||||
−0.999993 | + | 0.00373511i | \(0.998811\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 1.01191 | + | 1.75268i | 0.0367299 | + | 0.0636181i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −20.0347 | − | 11.5670i | −0.726256 | − | 0.419304i | 0.0907949 | − | 0.995870i | \(-0.471059\pi\) |
−0.817051 | + | 0.576566i | \(0.804393\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −5.03039 | + | 45.2831i | −0.182112 | + | 1.63936i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −1.75268 | − | 1.01191i | −0.0633681 | − | 0.0365856i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −0.222844 | + | 0.128659i | −0.00804644 | + | 0.00464561i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | − | 3.42433i | − | 0.123485i | −0.998092 | − | 0.0617423i | \(-0.980334\pi\) | ||
0.998092 | − | 0.0617423i | \(-0.0196657\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 27.5132 | 0.990864 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 13.4656 | + | 23.3230i | 0.484323 | + | 0.838871i | 0.999838 | − | 0.0180091i | \(-0.00573279\pi\) |
−0.515515 | + | 0.856880i | \(0.672399\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 1.97391 | − | 3.41892i | 0.0709051 | − | 0.122811i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 8.76024 | − | 11.9087i | 0.314272 | − | 0.427222i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −10.2925 | + | 17.8271i | −0.368767 | + | 0.638723i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 0.177997 | − | 0.102767i | 0.00636923 | − | 0.00367727i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 1.79505 | 0.0641499 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −39.6845 | −1.41640 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 26.9161 | − | 15.5400i | 0.959455 | − | 0.553942i | 0.0634499 | − | 0.997985i | \(-0.479790\pi\) |
0.896005 | + | 0.444043i | \(0.146456\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −2.58423 | + | 4.47601i | −0.0920009 | + | 0.159350i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −27.7390 | + | 37.7085i | −0.986286 | + | 1.34076i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 3.79689 | − | 6.57640i | 0.134831 | − | 0.233535i | ||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 12.2833 | + | 21.2754i | 0.435645 | + | 0.754559i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −5.25803 | −0.186249 | −0.0931245 | − | 0.995654i | \(-0.529685\pi\) | ||||
−0.0931245 | + | 0.995654i | \(0.529685\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | − | 10.3369i | − | 0.365693i | ||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 10.8618 | − | 6.27106i | 0.383783 | − | 0.221577i | ||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −4.02144 | − | 2.32178i | −0.141913 | − | 0.0819338i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 3.90159 | − | 35.1218i | 0.137513 | − | 1.23788i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 8.41987 | + | 4.86122i | 0.296394 | + | 0.171123i | ||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 7.18357 | + | 12.4423i | 0.252561 | + | 0.437448i | 0.964230 | − | 0.265066i | \(-0.0853938\pi\) |
−0.711669 | + | 0.702515i | \(0.752060\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 16.0000i | 0.561836i | 0.959732 | + | 0.280918i | \(0.0906389\pi\) | ||||
−0.959732 | + | 0.280918i | \(0.909361\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | − | 11.4042i | − | 0.399963i | ||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 20.6818 | + | 35.8220i | 0.724453 | + | 1.25479i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 46.4882 | + | 26.8400i | 1.62642 | + | 0.939013i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 1.78195 | + | 4.06689i | 0.0622665 | + | 0.142109i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 3.94009 | + | 2.27481i | 0.137510 | + | 0.0793914i | 0.567177 | − | 0.823596i | \(-0.308036\pi\) |
−0.429667 | + | 0.902988i | \(0.641369\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −8.89198 | + | 5.13379i | −0.309955 | + | 0.178953i | −0.646906 | − | 0.762569i | \(-0.723938\pi\) |
0.336951 | + | 0.941522i | \(0.390604\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0.657143i | 0.0228788i | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 13.9224 | 0.484128 | 0.242064 | − | 0.970260i | \(-0.422176\pi\) | ||||
0.242064 | + | 0.970260i | \(0.422176\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −16.0227 | − | 27.7521i | −0.556491 | − | 0.963870i | −0.997786 | − | 0.0665083i | \(-0.978814\pi\) |
0.441295 | − | 0.897362i | \(-0.354519\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −0.215669 | + | 0.373550i | −0.00748147 | + | 0.0129583i | ||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −4.03025 | − | 3.71610i | −0.139640 | − | 0.128755i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 5.48792 | − | 9.50535i | 0.189917 | − | 0.328946i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −2.03723 | + | 1.17619i | −0.0704169 | + | 0.0406552i | ||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 24.6267 | 0.850208 | 0.425104 | − | 0.905144i | \(-0.360237\pi\) | ||||
0.425104 | + | 0.905144i | \(0.360237\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 25.7778 | 0.888889 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −11.3014 | + | 6.52489i | −0.389242 | + | 0.224729i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −13.1583 | + | 22.7909i | −0.452660 | + | 0.784030i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 11.5171 | + | 26.2851i | 0.395733 | + | 0.903168i | ||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 12.2353 | − | 21.1922i | 0.419916 | − | 0.727316i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −14.4399 | − | 25.0107i | −0.494995 | − | 0.857356i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 19.5205 | 0.668368 | 0.334184 | − | 0.942508i | \(-0.391539\pi\) | ||||
0.334184 | + | 0.942508i | \(0.391539\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | − | 12.5249i | − | 0.428342i | ||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −28.4018 | + | 16.3978i | −0.970187 | + | 0.560138i | −0.899293 | − | 0.437346i | \(-0.855919\pi\) |
−0.0708940 | + | 0.997484i | \(0.522585\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 13.5908 | + | 7.84667i | 0.463713 | + | 0.267725i | 0.713604 | − | 0.700549i | \(-0.247061\pi\) |
−0.249891 | + | 0.968274i | \(0.580395\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 11.1685 | + | 1.24067i | 0.380620 | + | 0.0422821i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −42.7101 | − | 24.6587i | −1.45387 | − | 0.839391i | −0.455170 | − | 0.890404i | \(-0.650422\pi\) |
−0.998698 | + | 0.0510131i | \(0.983755\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 23.9363 | + | 41.4588i | 0.813857 | + | 1.40964i | ||||
\(866\) | 0 | 0 | ||||||||
\(867\) | − | 16.3867i | − | 0.556521i | ||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | − | 1.13791i | − | 0.0386009i | ||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 4.13730 | + | 7.16602i | 0.140187 | + | 0.242811i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 10.4136 | + | 6.01227i | 0.352446 | + | 0.203485i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −13.4580 | + | 18.2949i | −0.454965 | + | 0.618481i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −36.7925 | − | 21.2421i | −1.24239 | − | 0.717296i | −0.272812 | − | 0.962067i | \(-0.587954\pi\) |
−0.969581 | + | 0.244771i | \(0.921287\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −5.99387 | + | 3.46056i | −0.202168 | + | 0.116722i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | − | 16.9890i | − | 0.572373i | −0.958174 | − | 0.286187i | \(-0.907612\pi\) | ||
0.958174 | − | 0.286187i | \(-0.0923877\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −35.1247 | −1.18204 | −0.591021 | − | 0.806656i | \(-0.701275\pi\) | ||||
−0.591021 | + | 0.806656i | \(0.701275\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −0.198117 | − | 0.343149i | −0.00665963 | − | 0.0115348i | ||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 17.6491 | − | 30.5691i | 0.592598 | − | 1.02641i | −0.401283 | − | 0.915954i | \(-0.631436\pi\) |
0.993881 | − | 0.110456i | \(-0.0352311\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −31.5151 | − | 23.1831i | −1.05698 | − | 0.777535i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0.195786 | − | 0.339111i | 0.00655906 | − | 0.0113606i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 55.4018 | − | 31.9863i | 1.85395 | − | 1.07038i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −44.7601 | −1.49617 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 8.67380 | 0.289610 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 3.65693 | − | 2.11133i | 0.121965 | − | 0.0704167i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 3.72243 | − | 6.44744i | 0.124012 | − | 0.214795i | ||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 3.23534 | − | 29.1242i | 0.107665 | − | 0.969194i | ||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −22.2031 | + | 38.4569i | −0.738056 | + | 1.27835i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −12.4660 | − | 21.5918i | −0.413928 | − | 0.716944i | 0.581388 | − | 0.813627i | \(-0.302510\pi\) |
−0.995315 | + | 0.0966832i | \(0.969177\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −11.1685 | −0.370434 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 19.2680i | 0.638378i | 0.947691 | + | 0.319189i | \(0.103410\pi\) | ||||
−0.947691 | + | 0.319189i | \(0.896590\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −4.19533 | + | 2.42217i | −0.138845 | + | 0.0801623i | ||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 10.1267 | + | 5.84667i | 0.334779 | + | 0.193285i | ||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −10.8813 | + | 4.76778i | −0.359333 | + | 0.157446i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 43.5634 | + | 25.1513i | 1.43702 | + | 0.829666i | 0.997642 | − | 0.0686339i | \(-0.0218641\pi\) |
0.439382 | + | 0.898300i | \(0.355197\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 6.42334 | + | 11.1255i | 0.211656 | + | 0.366599i | ||||
\(922\) | 0 | 0 | ||||||||
\(923\) | − | 0.880887i | − | 0.0289947i | ||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | − | 9.37744i | − | 0.308328i | ||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −0.278669 | − | 0.482668i | −0.00915268 | − | 0.0158529i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −23.7129 | − | 13.6906i | −0.777995 | − | 0.449175i | 0.0577246 | − | 0.998333i | \(-0.481615\pi\) |
−0.835719 | + | 0.549157i | \(0.814949\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 7.44577 | − | 33.0996i | 0.244025 | − | 1.08479i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 14.5400 | + | 8.39468i | 0.476019 | + | 0.274830i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 0.686298 | − | 0.396234i | 0.0224443 | − | 0.0129582i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 20.6712i | 0.675300i | 0.941272 | + | 0.337650i | \(0.109632\pi\) | ||||
−0.941272 | + | 0.337650i | \(0.890368\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −2.38919 | −0.0779684 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 7.95079 | + | 13.7712i | 0.259188 | + | 0.448928i | 0.966025 | − | 0.258450i | \(-0.0832116\pi\) |
−0.706836 | + | 0.707377i | \(0.749878\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 10.9758 | − | 19.0107i | 0.357422 | − | 0.619074i | ||||
\(944\) | 0 | 0 | ||||||||
\(945\) | −6.26245 | + | 2.74396i | −0.203717 | + | 0.0892610i | ||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 19.3046 | − | 33.4365i | 0.627314 | − | 1.08654i | −0.360775 | − | 0.932653i | \(-0.617488\pi\) |
0.988089 | − | 0.153886i | \(-0.0491790\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −17.2353 | + | 9.95083i | −0.559483 | + | 0.323018i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 26.6273 | 0.863449 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −14.4062 | −0.466664 | −0.233332 | − | 0.972397i | \(-0.574963\pi\) | ||||
−0.233332 | + | 0.972397i | \(0.574963\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −39.5978 | + | 22.8618i | −1.28135 | + | 0.739790i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −0.351445 | + | 0.608721i | −0.0113606 | + | 0.0196771i | ||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −34.3154 | − | 3.81201i | −1.10810 | − | 0.123096i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 12.7331 | − | 22.0544i | 0.410746 | − | 0.711433i | ||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −6.79542 | − | 11.7700i | −0.218979 | − | 0.379283i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −15.9407 | −0.513148 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | − | 45.8371i | − | 1.47402i | −0.675880 | − | 0.737011i | \(-0.736236\pi\) | ||
0.675880 | − | 0.737011i | \(-0.263764\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −3.28712 | + | 1.89782i | −0.105597 | + | 0.0609667i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −24.8623 | − | 14.3542i | −0.797868 | − | 0.460649i | 0.0448572 | − | 0.998993i | \(-0.485717\pi\) |
−0.842725 | + | 0.538344i | \(0.819050\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 36.6220 | + | 26.9398i | 1.17405 | + | 0.863651i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 2.43910 | + | 1.40821i | 0.0781136 | + | 0.0450989i | ||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −19.8618 | − | 34.4016i | −0.635435 | − | 1.10061i | −0.986423 | − | 0.164226i | \(-0.947487\pi\) |
0.350988 | − | 0.936380i | \(-0.385846\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 4.91113i | 0.156960i | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | − | 17.2207i | − | 0.549815i | ||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 7.38573 | + | 12.7925i | 0.235568 | + | 0.408016i | 0.959438 | − | 0.281921i | \(-0.0909715\pi\) |
−0.723869 | + | 0.689937i | \(0.757638\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 57.3274 | + | 33.0980i | 1.82660 | + | 1.05459i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −28.1306 | − | 20.6933i | −0.895406 | − | 0.658676i | ||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −49.5747 | − | 28.6220i | −1.57638 | − | 0.910125i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 30.1791 | − | 17.4239i | 0.958671 | − | 0.553489i | 0.0629072 | − | 0.998019i | \(-0.479963\pi\) |
0.895764 | + | 0.444530i | \(0.146629\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 28.8478i | 0.915456i | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 0.325611 | 0.0103226 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 7.10156 | + | 12.3003i | 0.224909 | + | 0.389553i | 0.956292 | − | 0.292413i | \(-0.0944583\pi\) |
−0.731383 | + | 0.681966i | \(0.761125\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −2.79386 | + | 4.83911i | −0.0883939 | + | 0.153103i |
(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 | 1344.2.bb.g.607.3 | yes | 12 | |
4.3 | odd | 2 | inner | 1344.2.bb.g.607.6 | yes | 12 | |
7.3 | odd | 6 | 1344.2.bb.f.31.1 | ✓ | 12 | ||
8.3 | odd | 2 | 1344.2.bb.f.607.1 | yes | 12 | ||
8.5 | even | 2 | 1344.2.bb.f.607.4 | yes | 12 | ||
28.3 | even | 6 | 1344.2.bb.f.31.4 | yes | 12 | ||
56.3 | even | 6 | inner | 1344.2.bb.g.31.3 | yes | 12 | |
56.45 | odd | 6 | inner | 1344.2.bb.g.31.6 | yes | 12 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1344.2.bb.f.31.1 | ✓ | 12 | 7.3 | odd | 6 | ||
1344.2.bb.f.31.4 | yes | 12 | 28.3 | even | 6 | ||
1344.2.bb.f.607.1 | yes | 12 | 8.3 | odd | 2 | ||
1344.2.bb.f.607.4 | yes | 12 | 8.5 | even | 2 | ||
1344.2.bb.g.31.3 | yes | 12 | 56.3 | even | 6 | inner | |
1344.2.bb.g.31.6 | yes | 12 | 56.45 | odd | 6 | inner | |
1344.2.bb.g.607.3 | yes | 12 | 1.1 | even | 1 | trivial | |
1344.2.bb.g.607.6 | yes | 12 | 4.3 | odd | 2 | inner |