Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1344,2,Mod(239,1344)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1344, base_ring=CyclotomicField(4))
chi = DirichletCharacter(H, H._module([2, 3, 2, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1344.239");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1344 = 2^{6} \cdot 3 \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1344.s (of order \(4\), degree \(2\), 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: | \(10.7318940317\) |
Analytic rank: | \(0\) |
Dimension: | \(48\) |
Relative dimension: | \(24\) over \(\Q(i)\) |
Twist minimal: | no (minimal twist has level 336) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{4}]$ |
Embedding invariants
Embedding label | 239.10 | ||
Character | \(\chi\) | \(=\) | 1344.239 |
Dual form | 1344.2.s.d.911.10 |
$q$-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 \(\left(\mathbb{Z}/1344\mathbb{Z}\right)^\times\).
\(n\) | \(127\) | \(449\) | \(577\) | \(1093\) |
\(\chi(n)\) | \(-1\) | \(-1\) | \(1\) | \(e\left(\frac{3}{4}\right)\) |
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 | ||||||||
\(3\) | −0.490427 | + | 1.66117i | −0.283148 | + | 0.959076i | ||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −2.27018 | − | 2.27018i | −1.01525 | − | 1.01525i | −0.999882 | − | 0.0153719i | \(-0.995107\pi\) |
−0.0153719 | − | 0.999882i | \(-0.504893\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −1.00000 | −0.377964 | ||||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −2.51896 | − | 1.62936i | −0.839654 | − | 0.543122i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −1.28969 | + | 1.28969i | −0.388855 | + | 0.388855i | −0.874279 | − | 0.485424i | \(-0.838665\pi\) |
0.485424 | + | 0.874279i | \(0.338665\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −2.15412 | − | 2.15412i | −0.597446 | − | 0.597446i | 0.342186 | − | 0.939632i | \(-0.388833\pi\) |
−0.939632 | + | 0.342186i | \(0.888833\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 4.88450 | − | 2.65779i | 1.26117 | − | 0.686238i | ||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 6.50745i | 1.57829i | 0.614208 | + | 0.789144i | \(0.289476\pi\) | ||||
−0.614208 | + | 0.789144i | \(0.710524\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 3.42567 | − | 3.42567i | 0.785903 | − | 0.785903i | −0.194917 | − | 0.980820i | \(-0.562444\pi\) |
0.980820 | + | 0.194917i | \(0.0624437\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0.490427 | − | 1.66117i | 0.107020 | − | 0.362497i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 5.60715i | 1.16917i | 0.811332 | + | 0.584586i | \(0.198743\pi\) | ||||
−0.811332 | + | 0.584586i | \(0.801257\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 5.30740i | 1.06148i | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 3.94202 | − | 3.38534i | 0.758642 | − | 0.651508i | ||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 3.59282 | − | 3.59282i | 0.667171 | − | 0.667171i | −0.289889 | − | 0.957060i | \(-0.593619\pi\) |
0.957060 | + | 0.289889i | \(0.0936185\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | − | 0.730914i | − | 0.131276i | −0.997843 | − | 0.0656380i | \(-0.979092\pi\) | ||
0.997843 | − | 0.0656380i | \(-0.0209083\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −1.50989 | − | 2.77489i | −0.262838 | − | 0.483046i | ||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 2.27018 | + | 2.27018i | 0.383730 | + | 0.383730i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 7.94100 | − | 7.94100i | 1.30549 | − | 1.30549i | 0.380859 | − | 0.924633i | \(-0.375628\pi\) |
0.924633 | − | 0.380859i | \(-0.124372\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 4.63480 | − | 2.52192i | 0.742162 | − | 0.403830i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 3.23899 | 0.505846 | 0.252923 | − | 0.967486i | \(-0.418608\pi\) | ||||
0.252923 | + | 0.967486i | \(0.418608\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 8.55003 | + | 8.55003i | 1.30387 | + | 1.30387i | 0.925762 | + | 0.378106i | \(0.123424\pi\) |
0.378106 | + | 0.925762i | \(0.376576\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 2.01954 | + | 9.41743i | 0.301056 | + | 1.40387i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 7.39702 | 1.07897 | 0.539483 | − | 0.841996i | \(-0.318620\pi\) | ||||
0.539483 | + | 0.841996i | \(0.318620\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 1.00000 | 0.142857 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −10.8100 | − | 3.19143i | −1.51370 | − | 0.446890i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 0.785056 | + | 0.785056i | 0.107836 | + | 0.107836i | 0.758966 | − | 0.651130i | \(-0.225705\pi\) |
−0.651130 | + | 0.758966i | \(0.725705\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 5.85564 | 0.789574 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 4.01057 | + | 7.37066i | 0.531214 | + | 0.976268i | ||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −4.42285 | + | 4.42285i | −0.575805 | + | 0.575805i | −0.933745 | − | 0.357939i | \(-0.883479\pi\) |
0.357939 | + | 0.933745i | \(0.383479\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −1.23526 | − | 1.23526i | −0.158159 | − | 0.158159i | 0.623591 | − | 0.781751i | \(-0.285673\pi\) |
−0.781751 | + | 0.623591i | \(0.785673\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 2.51896 | + | 1.62936i | 0.317359 | + | 0.205281i | ||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 9.78048i | 1.21312i | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 2.62374 | − | 2.62374i | 0.320540 | − | 0.320540i | −0.528434 | − | 0.848974i | \(-0.677221\pi\) |
0.848974 | + | 0.528434i | \(0.177221\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −9.31443 | − | 2.74990i | −1.12133 | − | 0.331049i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | − | 1.31590i | − | 0.156169i | −0.996947 | − | 0.0780843i | \(-0.975120\pi\) | ||
0.996947 | − | 0.0780843i | \(-0.0248803\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | − | 10.4065i | − | 1.21799i | −0.793175 | − | 0.608993i | \(-0.791574\pi\) | ||
0.793175 | − | 0.608993i | \(-0.208426\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −8.81649 | − | 2.60289i | −1.01804 | − | 0.300556i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 1.28969 | − | 1.28969i | 0.146974 | − | 0.146974i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 9.74158i | 1.09601i | 0.836474 | + | 0.548006i | \(0.184613\pi\) | ||||
−0.836474 | + | 0.548006i | \(0.815387\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 3.69034 | + | 8.20862i | 0.410038 | + | 0.912068i | ||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 0.603062 | + | 0.603062i | 0.0661946 | + | 0.0661946i | 0.739429 | − | 0.673234i | \(-0.235096\pi\) |
−0.673234 | + | 0.739429i | \(0.735096\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 14.7731 | − | 14.7731i | 1.60236 | − | 1.60236i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 4.20627 | + | 7.73031i | 0.450959 | + | 0.828776i | ||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 0.657476 | 0.0696923 | 0.0348462 | − | 0.999393i | \(-0.488906\pi\) | ||||
0.0348462 | + | 0.999393i | \(0.488906\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 2.15412 | + | 2.15412i | 0.225813 | + | 0.225813i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 1.21417 | + | 0.358460i | 0.125904 | + | 0.0371706i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −15.5538 | −1.59578 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 8.66806 | 0.880108 | 0.440054 | − | 0.897971i | \(-0.354959\pi\) | ||||
0.440054 | + | 0.897971i | \(0.354959\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 5.35005 | − | 1.14730i | 0.537700 | − | 0.115308i | ||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −6.86450 | − | 6.86450i | −0.683044 | − | 0.683044i | 0.277641 | − | 0.960685i | \(-0.410447\pi\) |
−0.960685 | + | 0.277641i | \(0.910447\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −8.38381 | −0.826081 | −0.413041 | − | 0.910713i | \(-0.635533\pi\) | ||||
−0.413041 | + | 0.910713i | \(0.635533\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −4.88450 | + | 2.65779i | −0.476679 | + | 0.259374i | ||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −10.4659 | + | 10.4659i | −1.01178 | + | 1.01178i | −0.0118454 | + | 0.999930i | \(0.503771\pi\) |
−0.999930 | + | 0.0118454i | \(0.996229\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 9.36493 | + | 9.36493i | 0.896998 | + | 0.896998i | 0.995169 | − | 0.0981718i | \(-0.0312995\pi\) |
−0.0981718 | + | 0.995169i | \(0.531299\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 9.29685 | + | 17.0858i | 0.882418 | + | 1.62171i | ||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 3.62807i | 0.341300i | 0.985332 | + | 0.170650i | \(0.0545868\pi\) | ||||
−0.985332 | + | 0.170650i | \(0.945413\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 12.7292 | − | 12.7292i | 1.18701 | − | 1.18701i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 1.91630 | + | 8.93600i | 0.177162 | + | 0.826134i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | − | 6.50745i | − | 0.596537i | ||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 7.67341i | 0.697583i | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −1.58849 | + | 5.38052i | −0.143229 | + | 0.485145i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 0.697856 | − | 0.697856i | 0.0624181 | − | 0.0624181i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | − | 3.31704i | − | 0.294339i | −0.989111 | − | 0.147170i | \(-0.952984\pi\) | ||
0.989111 | − | 0.147170i | \(-0.0470163\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −18.3962 | + | 10.0099i | −1.61970 | + | 0.881321i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −1.98650 | − | 1.98650i | −0.173562 | − | 0.173562i | 0.614981 | − | 0.788542i | \(-0.289164\pi\) |
−0.788542 | + | 0.614981i | \(0.789164\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −3.42567 | + | 3.42567i | −0.297043 | + | 0.297043i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −16.6344 | − | 1.26376i | −1.43166 | − | 0.108768i | ||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 13.4203 | 1.14657 | 0.573286 | − | 0.819355i | \(-0.305668\pi\) | ||||
0.573286 | + | 0.819355i | \(0.305668\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −14.1855 | − | 14.1855i | −1.20320 | − | 1.20320i | −0.973189 | − | 0.230008i | \(-0.926125\pi\) |
−0.230008 | − | 0.973189i | \(-0.573875\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −3.62770 | + | 12.2877i | −0.305507 | + | 1.03481i | ||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 5.55629 | 0.464640 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −16.3127 | −1.35470 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −0.490427 | + | 1.66117i | −0.0404498 | + | 0.137011i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 0.311090 | + | 0.311090i | 0.0254855 | + | 0.0254855i | 0.719735 | − | 0.694249i | \(-0.244263\pi\) |
−0.694249 | + | 0.719735i | \(0.744263\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 20.1035 | 1.63600 | 0.817999 | − | 0.575220i | \(-0.195084\pi\) | ||||
0.817999 | + | 0.575220i | \(0.195084\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 10.6030 | − | 16.3920i | 0.857203 | − | 1.32522i | ||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −1.65930 | + | 1.65930i | −0.133279 | + | 0.133279i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 7.95586 | + | 7.95586i | 0.634947 | + | 0.634947i | 0.949305 | − | 0.314358i | \(-0.101789\pi\) |
−0.314358 | + | 0.949305i | \(0.601789\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −1.68912 | + | 0.919097i | −0.133956 | + | 0.0728891i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | − | 5.60715i | − | 0.441906i | ||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 12.2408 | − | 12.2408i | 0.958775 | − | 0.958775i | −0.0404083 | − | 0.999183i | \(-0.512866\pi\) |
0.999183 | + | 0.0404083i | \(0.0128659\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −2.87176 | + | 9.72720i | −0.223567 | + | 0.757262i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 3.00323i | 0.232397i | 0.993226 | + | 0.116198i | \(0.0370708\pi\) | ||||
−0.993226 | + | 0.116198i | \(0.962929\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | − | 3.71951i | − | 0.286116i | ||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −14.2108 | + | 3.04747i | −1.08673 | + | 0.233046i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 16.3777 | − | 16.3777i | 1.24517 | − | 1.24517i | 0.287349 | − | 0.957826i | \(-0.407226\pi\) |
0.957826 | − | 0.287349i | \(-0.0927738\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | − | 5.30740i | − | 0.401202i | ||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −5.17801 | − | 9.51618i | −0.389203 | − | 0.715280i | ||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −5.60043 | − | 5.60043i | −0.418596 | − | 0.418596i | 0.466124 | − | 0.884720i | \(-0.345650\pi\) |
−0.884720 | + | 0.466124i | \(0.845650\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −11.8857 | + | 11.8857i | −0.883454 | + | 0.883454i | −0.993884 | − | 0.110430i | \(-0.964777\pi\) |
0.110430 | + | 0.993884i | \(0.464777\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 2.65779 | − | 1.44617i | 0.196469 | − | 0.106904i | ||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −36.0549 | −2.65081 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −8.39258 | − | 8.39258i | −0.613726 | − | 0.613726i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −3.94202 | + | 3.38534i | −0.286740 | + | 0.246247i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −1.49917 | −0.108476 | −0.0542382 | − | 0.998528i | \(-0.517273\pi\) | ||||
−0.0542382 | + | 0.998528i | \(0.517273\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 2.29555 | 0.165237 | 0.0826186 | − | 0.996581i | \(-0.473672\pi\) | ||||
0.0826186 | + | 0.996581i | \(0.473672\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −16.2470 | − | 4.79661i | −1.16347 | − | 0.343492i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 4.21633 | + | 4.21633i | 0.300401 | + | 0.300401i | 0.841171 | − | 0.540770i | \(-0.181867\pi\) |
−0.540770 | + | 0.841171i | \(0.681867\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 4.09403 | 0.290218 | 0.145109 | − | 0.989416i | \(-0.453647\pi\) | ||||
0.145109 | + | 0.989416i | \(0.453647\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 3.07172 | + | 5.64522i | 0.216662 | + | 0.398183i | ||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −3.59282 | + | 3.59282i | −0.252167 | + | 0.252167i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −7.35309 | − | 7.35309i | −0.513562 | − | 0.513562i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 9.13610 | − | 14.1242i | 0.635003 | − | 0.981701i | ||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 8.83609i | 0.611205i | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −9.76923 | + | 9.76923i | −0.672541 | + | 0.672541i | −0.958301 | − | 0.285760i | \(-0.907754\pi\) |
0.285760 | + | 0.958301i | \(0.407754\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 2.18593 | + | 0.645353i | 0.149778 | + | 0.0442189i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | − | 38.8202i | − | 2.64751i | ||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 0.730914i | 0.0496177i | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 17.2869 | + | 5.10362i | 1.16814 | + | 0.344871i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 14.0178 | − | 14.0178i | 0.942942 | − | 0.942942i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | − | 5.84418i | − | 0.391355i | −0.980668 | − | 0.195678i | \(-0.937309\pi\) | ||
0.980668 | − | 0.195678i | \(-0.0626906\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 8.64769 | − | 13.3691i | 0.576513 | − | 0.891276i | ||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 6.43042 | + | 6.43042i | 0.426802 | + | 0.426802i | 0.887538 | − | 0.460735i | \(-0.152414\pi\) |
−0.460735 | + | 0.887538i | \(0.652414\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 0.741920 | − | 0.741920i | 0.0490275 | − | 0.0490275i | −0.682168 | − | 0.731195i | \(-0.738963\pi\) |
0.731195 | + | 0.682168i | \(0.238963\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 1.50989 | + | 2.77489i | 0.0993435 | + | 0.182574i | ||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 20.8459 | 1.36566 | 0.682831 | − | 0.730576i | \(-0.260749\pi\) | ||||
0.682831 | + | 0.730576i | \(0.260749\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −16.7925 | − | 16.7925i | −1.09542 | − | 1.09542i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −16.1824 | − | 4.77753i | −1.05116 | − | 0.310334i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 12.2887 | 0.794892 | 0.397446 | − | 0.917626i | \(-0.369897\pi\) | ||||
0.397446 | + | 0.917626i | \(0.369897\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 20.9833 | 1.35165 | 0.675826 | − | 0.737061i | \(-0.263787\pi\) | ||||
0.675826 | + | 0.737061i | \(0.263787\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −15.4457 | + | 2.10455i | −0.990845 | + | 0.135007i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −2.27018 | − | 2.27018i | −0.145036 | − | 0.145036i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −14.7586 | −0.939069 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −1.29754 | + | 0.706029i | −0.0822286 | + | 0.0447428i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 15.6696 | − | 15.6696i | 0.989056 | − | 0.989056i | −0.0108844 | − | 0.999941i | \(-0.503465\pi\) |
0.999941 | + | 0.0108844i | \(0.00346468\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −7.23148 | − | 7.23148i | −0.454639 | − | 0.454639i | ||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 17.2954 | + | 31.7857i | 1.08308 | + | 1.99049i | ||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 2.87847i | 0.179554i | 0.995962 | + | 0.0897771i | \(0.0286155\pi\) | ||||
−0.995962 | + | 0.0897771i | \(0.971385\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −7.94100 | + | 7.94100i | −0.493430 | + | 0.493430i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −14.9042 | + | 3.19617i | −0.922548 | + | 0.197838i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 3.38442i | 0.208692i | 0.994541 | + | 0.104346i | \(0.0332750\pi\) | ||||
−0.994541 | + | 0.104346i | \(0.966725\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | − | 3.56443i | − | 0.218961i | ||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −0.322444 | + | 1.09218i | −0.0197333 | + | 0.0668403i | ||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 21.9081 | − | 21.9081i | 1.33576 | − | 1.33576i | 0.435634 | − | 0.900124i | \(-0.356524\pi\) |
0.900124 | − | 0.435634i | \(-0.143476\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | − | 15.2450i | − | 0.926069i | −0.886340 | − | 0.463035i | \(-0.846761\pi\) | ||
0.886340 | − | 0.463035i | \(-0.153239\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −4.63480 | + | 2.52192i | −0.280511 | + | 0.152634i | ||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −6.84489 | − | 6.84489i | −0.412762 | − | 0.412762i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −9.03535 | + | 9.03535i | −0.542882 | + | 0.542882i | −0.924373 | − | 0.381491i | \(-0.875411\pi\) |
0.381491 | + | 0.924373i | \(0.375411\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −1.19093 | + | 1.84115i | −0.0712989 | + | 0.110226i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −6.55154 | −0.390832 | −0.195416 | − | 0.980720i | \(-0.562606\pi\) | ||||
−0.195416 | + | 0.980720i | \(0.562606\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 5.58014 | + | 5.58014i | 0.331705 | + | 0.331705i | 0.853234 | − | 0.521529i | \(-0.174638\pi\) |
−0.521529 | + | 0.853234i | \(0.674638\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 7.62799 | − | 25.8374i | 0.451843 | − | 1.53048i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −3.23899 | −0.191192 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −25.3469 | −1.49099 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −4.25105 | + | 14.3991i | −0.249201 | + | 0.844090i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −21.2015 | − | 21.2015i | −1.23860 | − | 1.23860i | −0.960572 | − | 0.278032i | \(-0.910318\pi\) |
−0.278032 | − | 0.960572i | \(-0.589682\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 20.0813 | 1.16918 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −0.717945 | + | 9.45000i | −0.0416594 | + | 0.548344i | ||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 12.0785 | − | 12.0785i | 0.698518 | − | 0.698518i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −8.55003 | − | 8.55003i | −0.492816 | − | 0.492816i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 14.7696 | − | 8.03656i | 0.848493 | − | 0.461688i | ||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 5.60854i | 0.321144i | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −18.6587 | + | 18.6587i | −1.06491 | + | 1.06491i | −0.0671654 | + | 0.997742i | \(0.521396\pi\) |
−0.997742 | + | 0.0671654i | \(0.978604\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 4.11165 | − | 13.9269i | 0.233903 | − | 0.792275i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | − | 2.15121i | − | 0.121984i | −0.998138 | − | 0.0609919i | \(-0.980574\pi\) | ||
0.998138 | − | 0.0609919i | \(-0.0194264\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | − | 11.1212i | − | 0.628606i | −0.949323 | − | 0.314303i | \(-0.898229\pi\) | ||
0.949323 | − | 0.314303i | \(-0.101771\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −2.01954 | − | 9.41743i | −0.113788 | − | 0.530612i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −13.7663 | + | 13.7663i | −0.773192 | + | 0.773192i | −0.978663 | − | 0.205471i | \(-0.934127\pi\) |
0.205471 | + | 0.978663i | \(0.434127\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 9.26724i | 0.518866i | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −12.2528 | − | 22.5184i | −0.683887 | − | 1.25685i | ||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 22.2924 | + | 22.2924i | 1.24038 | + | 1.24038i | ||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 11.4328 | − | 11.4328i | 0.634177 | − | 0.634177i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −20.1495 | + | 10.9639i | −1.11427 | + | 0.606306i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −7.39702 | −0.407811 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −1.82707 | − | 1.82707i | −0.100425 | − | 0.100425i | 0.655109 | − | 0.755534i | \(-0.272623\pi\) |
−0.755534 | + | 0.655109i | \(0.772623\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −32.9419 | + | 7.06429i | −1.80520 | + | 0.387121i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −11.9127 | −0.650859 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 25.8200 | 1.40650 | 0.703252 | − | 0.710941i | \(-0.251731\pi\) | ||||
0.703252 | + | 0.710941i | \(0.251731\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −6.02684 | − | 1.77930i | −0.327333 | − | 0.0966385i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 0.942651 | + | 0.942651i | 0.0510474 | + | 0.0510474i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −1.00000 | −0.0539949 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 14.9026 | + | 27.3882i | 0.802331 | + | 1.47453i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −11.7500 | + | 11.7500i | −0.630770 | + | 0.630770i | −0.948261 | − | 0.317491i | \(-0.897160\pi\) |
0.317491 | + | 0.948261i | \(0.397160\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −3.25078 | − | 3.25078i | −0.174010 | − | 0.174010i | 0.614728 | − | 0.788739i | \(-0.289266\pi\) |
−0.788739 | + | 0.614728i | \(0.789266\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −15.7840 | − | 1.19916i | −0.842488 | − | 0.0640064i | ||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 1.23082i | 0.0655098i | 0.999463 | + | 0.0327549i | \(0.0104281\pi\) | ||||
−0.999463 | + | 0.0327549i | \(0.989572\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −2.98733 | + | 2.98733i | −0.158551 | + | 0.158551i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 10.8100 | + | 3.19143i | 0.572124 | + | 0.168908i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 8.68746i | 0.458507i | 0.973367 | + | 0.229253i | \(0.0736284\pi\) | ||||
−0.973367 | + | 0.229253i | \(0.926372\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | − | 4.47044i | − | 0.235286i | ||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −12.7468 | − | 3.76325i | −0.669035 | − | 0.197519i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −23.6246 | + | 23.6246i | −1.23657 | + | 1.23657i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 6.48836i | 0.338689i | 0.985557 | + | 0.169345i | \(0.0541651\pi\) | ||||
−0.985557 | + | 0.169345i | \(0.945835\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −8.15890 | − | 5.27750i | −0.424736 | − | 0.274736i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −0.785056 | − | 0.785056i | −0.0407581 | − | 0.0407581i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 8.51133 | − | 8.51133i | 0.440700 | − | 0.440700i | −0.451547 | − | 0.892247i | \(-0.649128\pi\) |
0.892247 | + | 0.451547i | \(0.149128\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0.817009 | + | 1.50150i | 0.0421901 | + | 0.0775373i | ||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −15.4788 | −0.797197 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 18.0451 | + | 18.0451i | 0.926916 | + | 0.926916i | 0.997505 | − | 0.0705899i | \(-0.0224882\pi\) |
−0.0705899 | + | 0.997505i | \(0.522488\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 5.51016 | + | 1.62676i | 0.282294 | + | 0.0833417i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −10.5037 | −0.536715 | −0.268357 | − | 0.963319i | \(-0.586481\pi\) | ||||
−0.268357 | + | 0.963319i | \(0.586481\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −5.85564 | −0.298431 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −7.60609 | − | 35.4683i | −0.386639 | − | 1.80296i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 14.1412 | + | 14.1412i | 0.716989 | + | 0.716989i | 0.967987 | − | 0.250998i | \(-0.0807589\pi\) |
−0.250998 | + | 0.967987i | \(0.580759\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −36.4883 | −1.84529 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 4.27415 | − | 2.32568i | 0.215603 | − | 0.117315i | ||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 22.1151 | − | 22.1151i | 1.11273 | − | 1.11273i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 12.4687 | + | 12.4687i | 0.625787 | + | 0.625787i | 0.947005 | − | 0.321218i | \(-0.104092\pi\) |
−0.321218 | + | 0.947005i | \(0.604092\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −4.01057 | − | 7.37066i | −0.200780 | − | 0.368994i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | − | 7.28320i | − | 0.363706i | −0.983326 | − | 0.181853i | \(-0.941791\pi\) | ||
0.983326 | − | 0.181853i | \(-0.0582094\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −1.57448 | + | 1.57448i | −0.0784304 | + | 0.0784304i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 10.2573 | − | 27.0127i | 0.509688 | − | 1.34227i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 20.4828i | 1.01530i | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | − | 33.5956i | − | 1.66119i | −0.556873 | − | 0.830597i | \(-0.687999\pi\) | ||
0.556873 | − | 0.830597i | \(-0.312001\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −6.58167 | + | 22.2934i | −0.324650 | + | 1.09965i | ||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 4.42285 | − | 4.42285i | 0.217634 | − | 0.217634i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | − | 2.73811i | − | 0.134409i | ||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 30.5214 | − | 16.6075i | 1.49464 | − | 0.813274i | ||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 15.3527 | + | 15.3527i | 0.750029 | + | 0.750029i | 0.974484 | − | 0.224456i | \(-0.0720604\pi\) |
−0.224456 | + | 0.974484i | \(0.572060\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −19.1550 | + | 19.1550i | −0.933560 | + | 0.933560i | −0.997926 | − | 0.0643664i | \(-0.979497\pi\) |
0.0643664 | + | 0.997926i | \(0.479497\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −18.6328 | − | 12.0524i | −0.905958 | − | 0.586010i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −34.5377 | −1.67532 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 1.23526 | + | 1.23526i | 0.0597786 | + | 0.0597786i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −2.72496 | + | 9.22993i | −0.131562 | + | 0.445625i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −28.7862 | −1.38658 | −0.693292 | − | 0.720657i | \(-0.743840\pi\) | ||||
−0.693292 | + | 0.720657i | \(0.743840\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −9.30076 | −0.446966 | −0.223483 | − | 0.974708i | \(-0.571743\pi\) | ||||
−0.223483 | + | 0.974708i | \(0.571743\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 8.00019 | − | 27.0981i | 0.383580 | − | 1.29926i | ||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 19.2083 | + | 19.2083i | 0.918856 | + | 0.918856i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 13.3333 | 0.636363 | 0.318182 | − | 0.948030i | \(-0.396928\pi\) | ||||
0.318182 | + | 0.948030i | \(0.396928\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −2.51896 | − | 1.62936i | −0.119951 | − | 0.0775888i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 16.3081 | − | 16.3081i | 0.774821 | − | 0.774821i | −0.204124 | − | 0.978945i | \(-0.565435\pi\) |
0.978945 | + | 0.204124i | \(0.0654347\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −1.49259 | − | 1.49259i | −0.0707554 | − | 0.0707554i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −0.669341 | + | 0.364206i | −0.0316587 | + | 0.0172264i | ||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 42.0919i | 1.98644i | 0.116250 | + | 0.993220i | \(0.462913\pi\) | ||||
−0.116250 | + | 0.993220i | \(0.537087\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −4.17729 | + | 4.17729i | −0.196701 | + | 0.196701i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −9.85929 | + | 33.3953i | −0.463230 | + | 1.56905i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | − | 9.78048i | − | 0.458516i | ||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | − | 7.09163i | − | 0.331733i | −0.986148 | − | 0.165866i | \(-0.946958\pi\) | ||
0.986148 | − | 0.165866i | \(-0.0530420\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 22.0299 | + | 25.6525i | 1.02827 | + | 1.19736i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −21.5049 | + | 21.5049i | −1.00158 | + | 1.00158i | −0.00158208 | + | 0.999999i | \(0.500504\pi\) |
−0.999999 | + | 0.00158208i | \(0.999496\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | − | 11.6751i | − | 0.542590i | −0.962496 | − | 0.271295i | \(-0.912548\pi\) | ||
0.962496 | − | 0.271295i | \(-0.0874519\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −1.94262 | − | 3.57015i | −0.0900867 | − | 0.165562i | ||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 17.1941 | + | 17.1941i | 0.795649 | + | 0.795649i | 0.982406 | − | 0.186757i | \(-0.0597977\pi\) |
−0.186757 | + | 0.982406i | \(0.559798\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −2.62374 | + | 2.62374i | −0.121153 | + | 0.121153i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −17.1178 | + | 9.31425i | −0.788746 | + | 0.429178i | ||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −22.0537 | −1.01403 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 18.1814 | + | 18.1814i | 0.834220 | + | 0.834220i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −0.698383 | − | 3.25667i | −0.0319768 | − | 0.149113i | ||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −2.98046 | −0.136181 | −0.0680904 | − | 0.997679i | \(-0.521691\pi\) | ||||
−0.0680904 | + | 0.997679i | \(0.521691\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −34.2118 | −1.55992 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 9.31443 | + | 2.74990i | 0.423821 | + | 0.125125i | ||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −19.6780 | − | 19.6780i | −0.893533 | − | 0.893533i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −23.8458 | −1.08056 | −0.540279 | − | 0.841486i | \(-0.681681\pi\) | ||||
−0.540279 | + | 0.841486i | \(0.681681\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 14.3308 | + | 26.3373i | 0.648063 | + | 1.19101i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −3.63955 | + | 3.63955i | −0.164251 | + | 0.164251i | −0.784447 | − | 0.620196i | \(-0.787053\pi\) |
0.620196 | + | 0.784447i | \(0.287053\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 23.3801 | + | 23.3801i | 1.05299 | + | 1.05299i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −14.7501 | − | 9.54097i | −0.662969 | − | 0.428835i | ||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 1.31590i | 0.0590262i | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 4.83486 | − | 4.83486i | 0.216438 | − | 0.216438i | −0.590558 | − | 0.806996i | \(-0.701092\pi\) |
0.806996 | + | 0.590558i | \(0.201092\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −4.98887 | − | 1.47286i | −0.222886 | − | 0.0658027i | ||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 25.8257i | 1.15151i | 0.817622 | + | 0.575755i | \(0.195292\pi\) | ||||
−0.817622 | + | 0.575755i | \(0.804708\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 31.1673i | 1.38693i | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 6.17874 | + | 1.82415i | 0.274407 | + | 0.0810134i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −16.2497 | + | 16.2497i | −0.720254 | + | 0.720254i | −0.968657 | − | 0.248403i | \(-0.920094\pi\) |
0.248403 | + | 0.968657i | \(0.420094\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 10.4065i | 0.460356i | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 1.90701 | − | 25.1011i | 0.0841964 | − | 1.10824i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 19.0327 | + | 19.0327i | 0.838682 | + | 0.838682i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −9.53985 | + | 9.53985i | −0.419562 | + | 0.419562i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 19.1741 | + | 35.2382i | 0.841648 | + | 1.54679i | ||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 31.9912 | 1.40156 | 0.700780 | − | 0.713377i | \(-0.252835\pi\) | ||||
0.700780 | + | 0.713377i | \(0.252835\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 3.23155 | + | 3.23155i | 0.141306 | + | 0.141306i | 0.774221 | − | 0.632915i | \(-0.218142\pi\) |
−0.632915 | + | 0.774221i | \(0.718142\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 8.81649 | + | 2.60289i | 0.384783 | + | 0.113600i | ||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 4.75639 | 0.207192 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −8.44018 | −0.366964 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 18.3474 | − | 3.93455i | 0.796210 | − | 0.170745i | ||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −6.97719 | − | 6.97719i | −0.302216 | − | 0.302216i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 47.5188 | 2.05442 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 12.0499 | − | 6.55666i | 0.519990 | − | 0.282941i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −1.28969 | + | 1.28969i | −0.0555508 | + | 0.0555508i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −1.55521 | − | 1.55521i | −0.0668635 | − | 0.0668635i | 0.672884 | − | 0.739748i | \(-0.265055\pi\) |
−0.739748 | + | 0.672884i | \(0.765055\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −13.9150 | − | 25.5731i | −0.597151 | − | 1.09745i | ||||
\(544\) | 0 | 0 | ||||||||
\(545\) | − | 42.5201i | − | 1.82136i | ||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 28.9521 | − | 28.9521i | 1.23790 | − | 1.23790i | 0.277045 | − | 0.960857i | \(-0.410645\pi\) |
0.960857 | − | 0.277045i | \(-0.0893551\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 1.09889 | + | 5.12428i | 0.0468994 | + | 0.218699i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | − | 24.6157i | − | 1.04866i | ||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | − | 9.74158i | − | 0.414254i | ||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 17.6823 | − | 59.8933i | 0.750573 | − | 2.54233i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 4.99540 | − | 4.99540i | 0.211662 | − | 0.211662i | −0.593311 | − | 0.804973i | \(-0.702180\pi\) |
0.804973 | + | 0.593311i | \(0.202180\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | − | 36.8356i | − | 1.55798i | ||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 18.0574 | − | 9.82554i | 0.762386 | − | 0.414835i | ||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 9.20717 | + | 9.20717i | 0.388036 | + | 0.388036i | 0.873986 | − | 0.485950i | \(-0.161526\pi\) |
−0.485950 | + | 0.873986i | \(0.661526\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 8.23636 | − | 8.23636i | 0.346506 | − | 0.346506i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −3.69034 | − | 8.20862i | −0.154980 | − | 0.344729i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 24.4833 | 1.02639 | 0.513196 | − | 0.858272i | \(-0.328462\pi\) | ||||
0.513196 | + | 0.858272i | \(0.328462\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −3.81239 | − | 3.81239i | −0.159544 | − | 0.159544i | 0.622821 | − | 0.782364i | \(-0.285987\pi\) |
−0.782364 | + | 0.622821i | \(0.785987\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0.735236 | − | 2.49038i | 0.0307149 | − | 0.104037i | ||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −29.7594 | −1.24105 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 12.7113 | 0.529177 | 0.264589 | − | 0.964361i | \(-0.414764\pi\) | ||||
0.264589 | + | 0.964361i | \(0.414764\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −1.12580 | + | 3.81329i | −0.0467866 | + | 0.158475i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −0.603062 | − | 0.603062i | −0.0250192 | − | 0.0250192i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −2.02495 | −0.0838650 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 15.9360 | − | 24.6366i | 0.658871 | − | 1.01860i | ||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 24.1308 | − | 24.1308i | 0.995985 | − | 0.995985i | −0.00400654 | − | 0.999992i | \(-0.501275\pi\) |
0.999992 | + | 0.00400654i | \(0.00127533\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −2.50387 | − | 2.50387i | −0.103170 | − | 0.103170i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −9.07183 | + | 4.93623i | −0.373165 | + | 0.203049i | ||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 7.81607i | 0.320968i | 0.987038 | + | 0.160484i | \(0.0513054\pi\) | ||||
−0.987038 | + | 0.160484i | \(0.948695\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −14.7731 | + | 14.7731i | −0.605636 | + | 0.605636i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −2.00783 | + | 6.80088i | −0.0821749 | + | 0.278342i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | − | 36.8480i | − | 1.50557i | −0.658268 | − | 0.752784i | \(-0.728710\pi\) | ||
0.658268 | − | 0.752784i | \(-0.271290\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 46.9927i | 1.91687i | 0.285306 | + | 0.958436i | \(0.407905\pi\) | ||||
−0.285306 | + | 0.958436i | \(0.592095\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −10.8841 | + | 2.33407i | −0.443235 | + | 0.0950506i | ||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 17.4200 | − | 17.4200i | 0.708224 | − | 0.708224i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 44.8233i | 1.81932i | 0.415353 | + | 0.909660i | \(0.363658\pi\) | ||||
−0.415353 | + | 0.909660i | \(0.636342\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −4.20627 | − | 7.73031i | −0.170447 | − | 0.313248i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −15.9341 | − | 15.9341i | −0.644624 | − | 0.644624i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 32.0395 | − | 32.0395i | 1.29406 | − | 1.29406i | 0.361813 | − | 0.932251i | \(-0.382158\pi\) |
0.932251 | − | 0.361813i | \(-0.117842\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 15.8209 | − | 8.60856i | 0.637959 | − | 0.347131i | ||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 3.37809 | 0.135997 | 0.0679985 | − | 0.997685i | \(-0.478339\pi\) | ||||
0.0679985 | + | 0.997685i | \(0.478339\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 0.353620 | + | 0.353620i | 0.0142132 | + | 0.0142132i | 0.714178 | − | 0.699964i | \(-0.246801\pi\) |
−0.699964 | + | 0.714178i | \(0.746801\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 18.9821 | + | 22.1035i | 0.761726 | + | 0.886983i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −0.657476 | −0.0263412 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 23.3685 | 0.934740 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −14.6782 | − | 4.33346i | −0.586192 | − | 0.173062i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 51.6756 | + | 51.6756i | 2.06044 | + | 2.06044i | ||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 5.49410 | 0.218717 | 0.109358 | − | 0.994002i | \(-0.465120\pi\) | ||||
0.109358 | + | 0.994002i | \(0.465120\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −11.4372 | − | 21.0194i | −0.454589 | − | 0.835447i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −7.53026 | + | 7.53026i | −0.298829 | + | 0.298829i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −2.15412 | − | 2.15412i | −0.0853494 | − | 0.0853494i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −2.14408 | + | 3.31470i | −0.0848185 | + | 0.131128i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | − | 12.3855i | − | 0.489198i | −0.969624 | − | 0.244599i | \(-0.921344\pi\) | ||
0.969624 | − | 0.244599i | \(-0.0786563\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 8.45364 | − | 8.45364i | 0.333379 | − | 0.333379i | −0.520489 | − | 0.853868i | \(-0.674250\pi\) |
0.853868 | + | 0.520489i | \(0.174250\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 64.4869 | + | 19.0385i | 2.53917 | + | 0.749639i | ||||
\(646\) | 0 | 0 | ||||||||
\(647\) | − | 31.5511i | − | 1.24040i | −0.784443 | − | 0.620200i | \(-0.787051\pi\) | ||
0.784443 | − | 0.620200i | \(-0.212949\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | − | 11.4082i | − | 0.447810i | ||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −1.21417 | − | 0.358460i | −0.0475871 | − | 0.0140492i | ||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 24.3917 | − | 24.3917i | 0.954521 | − | 0.954521i | −0.0444889 | − | 0.999010i | \(-0.514166\pi\) |
0.999010 | + | 0.0444889i | \(0.0141659\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 9.01943i | 0.352418i | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −16.9560 | + | 26.2135i | −0.661515 | + | 1.02269i | ||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −8.56243 | − | 8.56243i | −0.333545 | − | 0.333545i | 0.520386 | − | 0.853931i | \(-0.325788\pi\) |
−0.853931 | + | 0.520386i | \(0.825788\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −8.35402 | + | 8.35402i | −0.324934 | + | 0.324934i | −0.850656 | − | 0.525722i | \(-0.823795\pi\) |
0.525722 | + | 0.850656i | \(0.323795\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 16.4113 | + | 30.1607i | 0.637361 | + | 1.17135i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 15.5538 | 0.603149 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 20.1455 | + | 20.1455i | 0.780038 | + | 0.780038i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 9.70817 | + | 2.86615i | 0.375340 | + | 0.110812i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 3.18621 | 0.123002 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 38.6443 | 1.48963 | 0.744813 | − | 0.667273i | \(-0.232538\pi\) | ||||
0.744813 | + | 0.667273i | \(0.232538\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 17.9673 | + | 20.9219i | 0.691563 | + | 0.805283i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −14.6806 | − | 14.6806i | −0.564223 | − | 0.564223i | 0.366281 | − | 0.930504i | \(-0.380631\pi\) |
−0.930504 | + | 0.366281i | \(0.880631\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −8.66806 | −0.332649 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −13.8357 | + | 7.52836i | −0.530184 | + | 0.288487i | ||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 11.0844 | − | 11.0844i | 0.424132 | − | 0.424132i | −0.462492 | − | 0.886624i | \(-0.653044\pi\) |
0.886624 | + | 0.462492i | \(0.153044\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −30.4664 | − | 30.4664i | −1.16406 | − | 1.16406i | ||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0.868597 | + | 1.59631i | 0.0331390 | + | 0.0609031i | ||||
\(688\) | 0 | 0 | ||||||||
\(689\) | − | 3.38221i | − | 0.128852i | ||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −31.1872 | + | 31.1872i | −1.18642 | + | 1.18642i | −0.208364 | + | 0.978051i | \(0.566814\pi\) |
−0.978051 | + | 0.208364i | \(0.933186\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −5.35005 | + | 1.14730i | −0.203231 | + | 0.0435824i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 64.4071i | 2.44310i | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 21.0776i | 0.798371i | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −10.2234 | + | 34.6286i | −0.386685 | + | 1.30977i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −22.3603 | + | 22.3603i | −0.844537 | + | 0.844537i | −0.989445 | − | 0.144909i | \(-0.953711\pi\) |
0.144909 | + | 0.989445i | \(0.453711\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | − | 54.4065i | − | 2.05198i | ||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 36.1308 | − | 19.6597i | 1.36076 | − | 0.740428i | ||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 6.86450 | + | 6.86450i | 0.258166 | + | 0.258166i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −17.5606 | + | 17.5606i | −0.659501 | + | 0.659501i | −0.955262 | − | 0.295761i | \(-0.904427\pi\) |
0.295761 | + | 0.955262i | \(0.404427\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 15.8726 | − | 24.5387i | 0.595268 | − | 0.920272i | ||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 4.09835 | 0.153484 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −12.6138 | − | 12.6138i | −0.471728 | − | 0.471728i | ||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −6.02673 | + | 20.4136i | −0.225072 | + | 0.762361i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −6.22460 | −0.232138 | −0.116069 | − | 0.993241i | \(-0.537029\pi\) | ||||
−0.116069 | + | 0.993241i | \(0.537029\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 8.38381 | 0.312229 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −10.2908 | + | 34.8568i | −0.382718 | + | 1.29634i | ||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 19.0686 | + | 19.0686i | 0.708189 | + | 0.708189i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −32.0728 | −1.18952 | −0.594758 | − | 0.803905i | \(-0.702752\pi\) | ||||
−0.594758 | + | 0.803905i | \(0.702752\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 4.07900 | − | 26.6901i | 0.151074 | − | 0.988522i | ||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −55.6389 | + | 55.6389i | −2.05788 | + | 2.05788i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −13.0287 | − | 13.0287i | −0.481226 | − | 0.481226i | 0.424297 | − | 0.905523i | \(-0.360521\pi\) |
−0.905523 | + | 0.424297i | \(0.860521\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 4.88450 | − | 2.65779i | 0.180168 | − | 0.0980340i | ||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 6.76760i | 0.249288i | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 6.57440 | − | 6.57440i | 0.241843 | − | 0.241843i | −0.575769 | − | 0.817612i | \(-0.695297\pi\) |
0.817612 | + | 0.575769i | \(0.195297\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 7.23803 | − | 24.5166i | 0.265896 | − | 0.900639i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | − | 18.1728i | − | 0.666694i | −0.942804 | − | 0.333347i | \(-0.891822\pi\) | ||
0.942804 | − | 0.333347i | \(-0.108178\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | − | 1.41246i | − | 0.0517485i | ||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −0.536482 | − | 2.50170i | −0.0196289 | − | 0.0915323i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 10.4659 | − | 10.4659i | 0.382415 | − | 0.382415i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | − | 12.6900i | − | 0.463065i | −0.972827 | − | 0.231532i | \(-0.925626\pi\) | ||
0.972827 | − | 0.231532i | \(-0.0743739\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 18.3450 | + | 33.7146i | 0.668531 | + | 1.22863i | ||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −45.6384 | − | 45.6384i | −1.66095 | − | 1.66095i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −20.3686 | + | 20.3686i | −0.740311 | + | 0.740311i | −0.972638 | − | 0.232327i | \(-0.925366\pi\) |
0.232327 | + | 0.972638i | \(0.425366\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 15.5592 | − | 8.46619i | 0.564764 | − | 0.307303i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −24.1751 | −0.876346 | −0.438173 | − | 0.898891i | \(-0.644374\pi\) | ||||
−0.438173 | + | 0.898891i | \(0.644374\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −9.36493 | − | 9.36493i | −0.339033 | − | 0.339033i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −61.2835 | + | 13.1421i | −2.21571 | + | 0.475153i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 19.0547 | 0.688025 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 21.7492 | 0.784298 | 0.392149 | − | 0.919902i | \(-0.371732\pi\) | ||||
0.392149 | + | 0.919902i | \(0.371732\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −4.78163 | − | 1.41168i | −0.172206 | − | 0.0508404i | ||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 25.0813 | + | 25.0813i | 0.902112 | + | 0.902112i | 0.995619 | − | 0.0935069i | \(-0.0298077\pi\) |
−0.0935069 | + | 0.995619i | \(0.529808\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 3.87926 | 0.139347 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −9.29685 | − | 17.0858i | −0.333523 | − | 0.612950i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 11.0957 | − | 11.0957i | 0.397546 | − | 0.397546i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 1.69710 | + | 1.69710i | 0.0607270 | + | 0.0607270i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 2.00006 | − | 26.3259i | 0.0714762 | − | 0.940811i | ||||
\(784\) | 0 | 0 | ||||||||
\(785\) | − | 36.1224i | − | 1.28926i | ||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 12.7875 | − | 12.7875i | 0.455824 | − | 0.455824i | −0.441458 | − | 0.897282i | \(-0.645538\pi\) |
0.897282 | + | 0.441458i | \(0.145538\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −5.62209 | − | 1.65981i | −0.200152 | − | 0.0590909i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | − | 3.62807i | − | 0.128999i | ||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 5.32182i | 0.188983i | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 5.92112 | + | 1.74809i | 0.210000 | + | 0.0619985i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 15.0855 | − | 15.0855i | 0.534356 | − | 0.534356i | −0.387510 | − | 0.921866i | \(-0.626665\pi\) |
0.921866 | + | 0.387510i | \(0.126665\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 48.1357i | 1.70292i | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −1.65616 | − | 1.07127i | −0.0585175 | − | 0.0378514i | ||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 13.4211 | + | 13.4211i | 0.473621 | + | 0.473621i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −12.7292 | + | 12.7292i | −0.448646 | + | 0.448646i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 25.6487 | + | 47.1373i | 0.902876 | + | 1.65931i | ||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −46.1180 | −1.62142 | −0.810712 | − | 0.585445i | \(-0.800920\pi\) | ||||
−0.810712 | + | 0.585445i | \(0.800920\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 33.5469 | + | 33.5469i | 1.17799 | + | 1.17799i | 0.980255 | + | 0.197737i | \(0.0633592\pi\) |
0.197737 | + | 0.980255i | \(0.436641\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 25.3246 | + | 7.47658i | 0.888171 | + | 0.262215i | ||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −55.5776 | −1.94680 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 58.5792 | 2.04943 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −1.91630 | − | 8.93600i | −0.0669610 | − | 0.312249i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −32.2408 | − | 32.2408i | −1.12521 | − | 1.12521i | −0.990945 | − | 0.134265i | \(-0.957133\pi\) |
−0.134265 | − | 0.990945i | \(-0.542867\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 15.6995 | 0.547252 | 0.273626 | − | 0.961836i | \(-0.411777\pi\) | ||||
0.273626 | + | 0.961836i | \(0.411777\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 14.7274 | − | 8.01360i | 0.512744 | − | 0.278998i | ||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 17.5343 | − | 17.5343i | 0.609728 | − | 0.609728i | −0.333147 | − | 0.942875i | \(-0.608111\pi\) |
0.942875 | + | 0.333147i | \(0.108111\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −14.8343 | − | 14.8343i | −0.515216 | − | 0.515216i | 0.400904 | − | 0.916120i | \(-0.368696\pi\) |
−0.916120 | + | 0.400904i | \(0.868696\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −10.5781 | − | 19.4404i | −0.366949 | − | 0.674381i | ||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 6.50745i | 0.225470i | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 6.81785 | − | 6.81785i | 0.235942 | − | 0.235942i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −2.47439 | − | 2.88128i | −0.0855274 | − | 0.0995915i | ||||
\(838\) | 0 | 0 | ||||||||
\(839\) | − | 1.23295i | − | 0.0425661i | −0.999773 | − | 0.0212830i | \(-0.993225\pi\) | ||
0.999773 | − | 0.0212830i | \(-0.00677511\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 3.18322i | 0.109766i | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 3.21306 | − | 10.8832i | 0.110663 | − | 0.374838i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −8.44395 | + | 8.44395i | −0.290481 | + | 0.290481i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | − | 7.67341i | − | 0.263662i | ||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −12.0062 | + | 6.53290i | −0.412052 | + | 0.224209i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 44.5264 | + | 44.5264i | 1.52635 | + | 1.52635i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −3.79105 | + | 3.79105i | −0.129803 | + | 0.129803i | −0.769024 | − | 0.639220i | \(-0.779257\pi\) |
0.639220 | + | 0.769024i | \(0.279257\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 39.1793 | + | 25.3427i | 1.33990 | + | 0.866703i | ||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −27.4939 | −0.939175 | −0.469588 | − | 0.882886i | \(-0.655597\pi\) | ||||
−0.469588 | + | 0.882886i | \(0.655597\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −21.1302 | − | 21.1302i | −0.720954 | − | 0.720954i | 0.247846 | − | 0.968800i | \(-0.420277\pi\) |
−0.968800 | + | 0.247846i | \(0.920277\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 1.58849 | − | 5.38052i | 0.0541356 | − | 0.183367i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 2.27110 | 0.0773092 | 0.0386546 | − | 0.999253i | \(-0.487693\pi\) | ||||
0.0386546 | + | 0.999253i | \(0.487693\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −74.3606 | −2.52834 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 12.4308 | − | 42.1055i | 0.422173 | − | 1.42998i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −12.5636 | − | 12.5636i | −0.426191 | − | 0.426191i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −11.3037 | −0.383011 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −21.8345 | − | 14.1234i | −0.738986 | − | 0.478006i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −0.697856 | + | 0.697856i | −0.0235918 | + | 0.0235918i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −22.9389 | − | 22.9389i | −0.774591 | − | 0.774591i | 0.204314 | − | 0.978905i | \(-0.434504\pi\) |
−0.978905 | + | 0.204314i | \(0.934504\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 45.6170 | − | 24.8214i | 1.53862 | − | 0.837207i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 11.5927i | 0.390569i | 0.980747 | + | 0.195284i | \(0.0625629\pi\) | ||||
−0.980747 | + | 0.195284i | \(0.937437\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −34.7982 | + | 34.7982i | −1.17105 | + | 1.17105i | −0.189093 | + | 0.981959i | \(0.560555\pi\) |
−0.981959 | + | 0.189093i | \(0.939445\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −9.84841 | + | 33.3584i | −0.331051 | + | 1.12133i | ||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 14.8054i | 0.497115i | 0.968617 | + | 0.248558i | \(0.0799565\pi\) | ||||
−0.968617 | + | 0.248558i | \(0.920043\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 3.31704i | 0.111250i | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −15.3459 | − | 5.82716i | −0.514108 | − | 0.195217i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 25.3398 | − | 25.3398i | 0.847963 | − | 0.847963i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 25.4279i | 0.849962i | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 14.1408 | + | 25.9880i | 0.472147 | + | 0.867716i | ||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −2.62605 | − | 2.62605i | −0.0875836 | − | 0.0875836i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −5.10871 | + | 5.10871i | −0.170196 | + | 0.170196i | ||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 18.3962 | − | 10.0099i | 0.612188 | − | 0.333108i | ||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 53.9651 | 1.79386 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 7.13712 | + | 7.13712i | 0.236984 | + | 0.236984i | 0.815600 | − | 0.578616i | \(-0.196407\pi\) |
−0.578616 | + | 0.815600i | \(0.696407\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 6.10664 | + | 28.4762i | 0.202545 | + | 0.944496i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 16.9295 | 0.560901 | 0.280450 | − | 0.959869i | \(-0.409516\pi\) | ||||
0.280450 | + | 0.959869i | \(0.409516\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −1.55552 | −0.0514803 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −9.31672 | − | 2.75058i | −0.308001 | − | 0.0909313i | ||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 1.98650 | + | 1.98650i | 0.0656001 | + | 0.0656001i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −12.9874 | −0.428414 | −0.214207 | − | 0.976788i | \(-0.568717\pi\) | ||||
−0.214207 | + | 0.976788i | \(0.568717\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −21.8445 | − | 40.1459i | −0.719800 | − | 1.32285i | ||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −2.83461 | + | 2.83461i | −0.0933023 | + | 0.0933023i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 42.1461 | + | 42.1461i | 1.38575 | + | 1.38575i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 21.1185 | + | 13.6603i | 0.693622 | + | 0.448662i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 34.0965i | 1.11867i | 0.828942 | + | 0.559335i | \(0.188943\pi\) | ||||
−0.828942 | + | 0.559335i | \(0.811057\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 3.42567 | − | 3.42567i | 0.112272 | − | 0.112272i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 3.57352 | + | 1.05501i | 0.116992 | + | 0.0345395i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 38.1053i | 1.24618i | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 16.6312i | 0.543317i | 0.962394 | + | 0.271659i | \(0.0875722\pi\) | ||||
−0.962394 | + | 0.271659i | \(0.912428\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 18.4741 | + | 5.45413i | 0.602881 | + | 0.177989i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −8.04851 | + | 8.04851i | −0.262374 | + | 0.262374i | −0.826018 | − | 0.563644i | \(-0.809399\pi\) |
0.563644 | + | 0.826018i | \(0.309399\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 18.1615i | 0.591421i | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 16.6344 | + | 1.26376i | 0.541117 | + | 0.0411103i | ||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −6.31033 | − | 6.31033i | −0.205058 | − | 0.205058i | 0.597105 | − | 0.802163i | \(-0.296318\pi\) |
−0.802163 | + | 0.597105i | \(0.796318\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −22.4168 | + | 22.4168i | −0.727681 | + | 0.727681i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −16.1168 | − | 29.6195i | −0.522622 | − | 0.960478i | ||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 50.9888 | 1.65169 | 0.825845 | − | 0.563897i | \(-0.190698\pi\) | ||||
0.825845 | + | 0.563897i | \(0.190698\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 3.40339 | + | 3.40339i | 0.110131 | + | 0.110131i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −15.3945 | − | 4.54491i | −0.497632 | − | 0.146916i | ||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −13.4203 | −0.433364 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 30.4658 | 0.982767 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 43.4159 | − | 9.31042i | 1.39906 | − | 0.300024i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −5.21130 | − | 5.21130i | −0.167758 | − | 0.167758i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −26.3341 | −0.846849 | −0.423424 | − | 0.905931i | \(-0.639172\pi\) | ||||
−0.423424 | + | 0.905931i | \(0.639172\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −47.9642 | + | 26.0986i | −1.54083 | + | 0.838408i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −10.1620 | + | 10.1620i | −0.326114 | + | 0.326114i | −0.851107 | − | 0.524993i | \(-0.824068\pi\) |
0.524993 | + | 0.851107i | \(0.324068\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 14.1855 | + | 14.1855i | 0.454766 | + | 0.454766i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 13.3848 | + | 24.5987i | 0.428658 | + | 0.787790i | ||||
\(976\) | 0 | 0 | ||||||||
\(977\) | − | 40.0377i | − | 1.28092i | −0.767992 | − | 0.640460i | \(-0.778744\pi\) | ||
0.767992 | − | 0.640460i | \(-0.221256\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −0.847939 | + | 0.847939i | −0.0271002 | + | 0.0271002i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −8.33102 | − | 38.8488i | −0.265989 | − | 1.24035i | ||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 29.8253i | 0.951280i | 0.879640 | + | 0.475640i | \(0.157783\pi\) | ||||
−0.879640 | + | 0.475640i | \(0.842217\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | − | 19.1436i | − | 0.609966i | ||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 3.62770 | − | 12.2877i | 0.115471 | − | 0.391122i | ||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −47.9414 | + | 47.9414i | −1.52445 | + | 1.52445i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 47.9793i | 1.52411i | 0.647511 | + | 0.762056i | \(0.275810\pi\) | ||||
−0.647511 | + | 0.762056i | \(0.724190\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 3.93112 | − | 2.13903i | 0.124750 | − | 0.0678800i | ||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −9.29418 | − | 9.29418i | −0.294645 | − | 0.294645i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 24.4353 | − | 24.4353i | 0.773873 | − | 0.773873i | −0.204908 | − | 0.978781i | \(-0.565690\pi\) |
0.978781 | + | 0.204908i | \(0.0656896\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 4.42060 | − | 58.1865i | 0.139862 | − | 1.84094i |
(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.s.d.239.10 | 48 | ||
3.2 | odd | 2 | inner | 1344.2.s.d.239.2 | 48 | ||
4.3 | odd | 2 | 336.2.s.d.323.11 | yes | 48 | ||
12.11 | even | 2 | 336.2.s.d.323.14 | yes | 48 | ||
16.5 | even | 4 | 336.2.s.d.155.14 | yes | 48 | ||
16.11 | odd | 4 | inner | 1344.2.s.d.911.2 | 48 | ||
48.5 | odd | 4 | 336.2.s.d.155.11 | ✓ | 48 | ||
48.11 | even | 4 | inner | 1344.2.s.d.911.10 | 48 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
336.2.s.d.155.11 | ✓ | 48 | 48.5 | odd | 4 | ||
336.2.s.d.155.14 | yes | 48 | 16.5 | even | 4 | ||
336.2.s.d.323.11 | yes | 48 | 4.3 | odd | 2 | ||
336.2.s.d.323.14 | yes | 48 | 12.11 | even | 2 | ||
1344.2.s.d.239.2 | 48 | 3.2 | odd | 2 | inner | ||
1344.2.s.d.239.10 | 48 | 1.1 | even | 1 | trivial | ||
1344.2.s.d.911.2 | 48 | 16.11 | odd | 4 | inner | ||
1344.2.s.d.911.10 | 48 | 48.11 | even | 4 | inner |