Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1944,2,Mod(649,1944)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1944, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 0, 4]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1944.649");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1944 = 2^{3} \cdot 3^{5} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1944.i (of order \(3\), 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: | \(15.5229181529\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Relative dimension: | \(2\) over \(\Q(\zeta_{3})\) |
Coefficient field: | \(\Q(\zeta_{12})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} - x^{2} + 1 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{13}]\) |
Coefficient ring index: | \( 3 \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{3}]$ |
Embedding invariants
Embedding label | 649.2 | ||
Root | \(0.866025 + 0.500000i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1944.649 |
Dual form | 1944.2.i.k.1297.2 |
$q$-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 \(\left(\mathbb{Z}/1944\mathbb{Z}\right)^\times\).
\(n\) | \(487\) | \(973\) | \(1217\) |
\(\chi(n)\) | \(1\) | \(1\) | \(e\left(\frac{2}{3}\right)\) |
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 | 0 | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 0.366025 | + | 0.633975i | 0.163692 | + | 0.283522i | 0.936190 | − | 0.351495i | \(-0.114326\pi\) |
−0.772498 | + | 0.635017i | \(0.780993\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −1.73205 | + | 3.00000i | −0.654654 | + | 1.13389i | 0.327327 | + | 0.944911i | \(0.393852\pi\) |
−0.981981 | + | 0.188982i | \(0.939481\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −3.09808 | + | 5.36603i | −0.934105 | + | 1.61792i | −0.157883 | + | 0.987458i | \(0.550467\pi\) |
−0.776222 | + | 0.630460i | \(0.782866\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 1.23205 | + | 2.13397i | 0.341709 | + | 0.591858i | 0.984750 | − | 0.173974i | \(-0.0556608\pi\) |
−0.643041 | + | 0.765832i | \(0.722327\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 0.732051 | 0.177548 | 0.0887742 | − | 0.996052i | \(-0.471705\pi\) | ||||
0.0887742 | + | 0.996052i | \(0.471705\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −4.46410 | −1.02414 | −0.512068 | − | 0.858945i | \(-0.671120\pi\) | ||||
−0.512068 | + | 0.858945i | \(0.671120\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −4.36603 | − | 7.56218i | −0.910379 | − | 1.57682i | −0.813529 | − | 0.581524i | \(-0.802457\pi\) |
−0.0968500 | − | 0.995299i | \(-0.530877\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 2.23205 | − | 3.86603i | 0.446410 | − | 0.773205i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −1.26795 | + | 2.19615i | −0.235452 | + | 0.407815i | −0.959404 | − | 0.282035i | \(-0.908990\pi\) |
0.723952 | + | 0.689851i | \(0.242324\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −1.23205 | − | 2.13397i | −0.221283 | − | 0.383273i | 0.733915 | − | 0.679241i | \(-0.237691\pi\) |
−0.955198 | + | 0.295968i | \(0.904358\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −2.53590 | −0.428645 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 2.53590 | 0.416899 | 0.208450 | − | 0.978033i | \(-0.433158\pi\) | ||||
0.208450 | + | 0.978033i | \(0.433158\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −4.73205 | − | 8.19615i | −0.739022 | − | 1.28002i | −0.952936 | − | 0.303171i | \(-0.901955\pi\) |
0.213914 | − | 0.976853i | \(-0.431379\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 2.96410 | − | 5.13397i | 0.452021 | − | 0.782924i | −0.546490 | − | 0.837465i | \(-0.684036\pi\) |
0.998511 | + | 0.0545417i | \(0.0173698\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 3.46410 | − | 6.00000i | 0.505291 | − | 0.875190i | −0.494690 | − | 0.869069i | \(-0.664718\pi\) |
0.999981 | − | 0.00612051i | \(-0.00194823\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −2.50000 | − | 4.33013i | −0.357143 | − | 0.618590i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −7.66025 | −1.05222 | −0.526108 | − | 0.850418i | \(-0.676349\pi\) | ||||
−0.526108 | + | 0.850418i | \(0.676349\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −4.53590 | −0.611620 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −0.901924 | − | 1.56218i | −0.117420 | − | 0.203378i | 0.801324 | − | 0.598230i | \(-0.204129\pi\) |
−0.918745 | + | 0.394852i | \(0.870796\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 0.767949 | − | 1.33013i | 0.0983258 | − | 0.170305i | −0.812666 | − | 0.582730i | \(-0.801985\pi\) |
0.910992 | + | 0.412424i | \(0.135318\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −0.901924 | + | 1.56218i | −0.111870 | + | 0.193764i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 1.76795 | + | 3.06218i | 0.215989 | + | 0.374105i | 0.953578 | − | 0.301146i | \(-0.0973690\pi\) |
−0.737589 | + | 0.675250i | \(0.764036\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −6.19615 | −0.735348 | −0.367674 | − | 0.929955i | \(-0.619846\pi\) | ||||
−0.367674 | + | 0.929955i | \(0.619846\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 11.3923 | 1.33337 | 0.666684 | − | 0.745340i | \(-0.267713\pi\) | ||||
0.666684 | + | 0.745340i | \(0.267713\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −10.7321 | − | 18.5885i | −1.22303 | − | 2.11835i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −6.96410 | + | 12.0622i | −0.783523 | + | 1.35710i | 0.146355 | + | 0.989232i | \(0.453246\pi\) |
−0.929878 | + | 0.367869i | \(0.880088\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −6.36603 | + | 11.0263i | −0.698762 | + | 1.21029i | 0.270134 | + | 0.962823i | \(0.412932\pi\) |
−0.968896 | + | 0.247469i | \(0.920401\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0.267949 | + | 0.464102i | 0.0290632 | + | 0.0503389i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −12.0000 | −1.27200 | −0.635999 | − | 0.771690i | \(-0.719412\pi\) | ||||
−0.635999 | + | 0.771690i | \(0.719412\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −8.53590 | −0.894805 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −1.63397 | − | 2.83013i | −0.167642 | − | 0.290365i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −5.96410 | + | 10.3301i | −0.605563 | + | 1.04887i | 0.386400 | + | 0.922332i | \(0.373719\pi\) |
−0.991962 | + | 0.126534i | \(0.959615\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −2.19615 | + | 3.80385i | −0.218525 | + | 0.378497i | −0.954357 | − | 0.298667i | \(-0.903458\pi\) |
0.735832 | + | 0.677164i | \(0.236791\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 9.42820 | + | 16.3301i | 0.928988 | + | 1.60906i | 0.785018 | + | 0.619473i | \(0.212654\pi\) |
0.143971 | + | 0.989582i | \(0.454013\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 9.46410 | 0.914929 | 0.457465 | − | 0.889228i | \(-0.348758\pi\) | ||||
0.457465 | + | 0.889228i | \(0.348758\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 16.4641 | 1.57697 | 0.788487 | − | 0.615051i | \(-0.210865\pi\) | ||||
0.788487 | + | 0.615051i | \(0.210865\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −3.46410 | − | 6.00000i | −0.325875 | − | 0.564433i | 0.655814 | − | 0.754923i | \(-0.272326\pi\) |
−0.981689 | + | 0.190490i | \(0.938992\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 3.19615 | − | 5.53590i | 0.298043 | − | 0.516225i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −1.26795 | + | 2.19615i | −0.116233 | + | 0.201321i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −13.6962 | − | 23.7224i | −1.24510 | − | 2.15658i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 6.92820 | 0.619677 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 1.92820 | 0.171100 | 0.0855502 | − | 0.996334i | \(-0.472735\pi\) | ||||
0.0855502 | + | 0.996334i | \(0.472735\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −7.63397 | − | 13.2224i | −0.666983 | − | 1.15525i | −0.978743 | − | 0.205088i | \(-0.934252\pi\) |
0.311760 | − | 0.950161i | \(-0.399082\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 7.73205 | − | 13.3923i | 0.670454 | − | 1.16126i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −9.46410 | + | 16.3923i | −0.808573 | + | 1.40049i | 0.105280 | + | 0.994443i | \(0.466426\pi\) |
−0.913852 | + | 0.406046i | \(0.866907\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 1.73205 | + | 3.00000i | 0.146911 | + | 0.254457i | 0.930084 | − | 0.367347i | \(-0.119734\pi\) |
−0.783174 | + | 0.621803i | \(0.786400\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −15.2679 | −1.27677 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −1.85641 | −0.154166 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 10.0263 | + | 17.3660i | 0.821385 | + | 1.42268i | 0.904651 | + | 0.426153i | \(0.140131\pi\) |
−0.0832663 | + | 0.996527i | \(0.526535\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 1.76795 | − | 3.06218i | 0.143874 | − | 0.249196i | −0.785078 | − | 0.619396i | \(-0.787377\pi\) |
0.928952 | + | 0.370200i | \(0.120711\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 0.901924 | − | 1.56218i | 0.0724443 | − | 0.125477i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −2.69615 | − | 4.66987i | −0.215176 | − | 0.372696i | 0.738151 | − | 0.674636i | \(-0.235699\pi\) |
−0.953327 | + | 0.301939i | \(0.902366\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 30.2487 | 2.38393 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −22.3923 | −1.75390 | −0.876950 | − | 0.480581i | \(-0.840426\pi\) | ||||
−0.876950 | + | 0.480581i | \(0.840426\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −2.19615 | − | 3.80385i | −0.169943 | − | 0.294351i | 0.768456 | − | 0.639902i | \(-0.221025\pi\) |
−0.938400 | + | 0.345552i | \(0.887692\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 3.46410 | − | 6.00000i | 0.266469 | − | 0.461538i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −3.46410 | + | 6.00000i | −0.263371 | + | 0.456172i | −0.967135 | − | 0.254262i | \(-0.918168\pi\) |
0.703765 | + | 0.710433i | \(0.251501\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 7.73205 | + | 13.3923i | 0.584488 | + | 1.01236i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 2.53590 | 0.189542 | 0.0947710 | − | 0.995499i | \(-0.469788\pi\) | ||||
0.0947710 | + | 0.995499i | \(0.469788\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −11.3205 | −0.841447 | −0.420723 | − | 0.907189i | \(-0.638224\pi\) | ||||
−0.420723 | + | 0.907189i | \(0.638224\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 0.928203 | + | 1.60770i | 0.0682429 | + | 0.118200i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −2.26795 | + | 3.92820i | −0.165849 | + | 0.287259i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −9.46410 | + | 16.3923i | −0.684798 | + | 1.18611i | 0.288702 | + | 0.957419i | \(0.406776\pi\) |
−0.973500 | + | 0.228686i | \(0.926557\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 1.42820 | + | 2.47372i | 0.102804 | + | 0.178062i | 0.912839 | − | 0.408320i | \(-0.133885\pi\) |
−0.810035 | + | 0.586382i | \(0.800552\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −23.3205 | −1.66152 | −0.830759 | − | 0.556633i | \(-0.812093\pi\) | ||||
−0.830759 | + | 0.556633i | \(0.812093\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −11.0000 | −0.779769 | −0.389885 | − | 0.920864i | \(-0.627485\pi\) | ||||
−0.389885 | + | 0.920864i | \(0.627485\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −4.39230 | − | 7.60770i | −0.308279 | − | 0.533956i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 3.46410 | − | 6.00000i | 0.241943 | − | 0.419058i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 13.8301 | − | 23.9545i | 0.956650 | − | 1.65697i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −7.42820 | − | 12.8660i | −0.511379 | − | 0.885734i | −0.999913 | − | 0.0131891i | \(-0.995802\pi\) |
0.488534 | − | 0.872545i | \(-0.337532\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 4.33975 | 0.295968 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 8.53590 | 0.579455 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 0.901924 | + | 1.56218i | 0.0606700 | + | 0.105083i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −6.96410 | + | 12.0622i | −0.466351 | + | 0.807743i | −0.999261 | − | 0.0384284i | \(-0.987765\pi\) |
0.532911 | + | 0.846172i | \(0.321098\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 10.3923 | − | 18.0000i | 0.689761 | − | 1.19470i | −0.282153 | − | 0.959369i | \(-0.591049\pi\) |
0.971915 | − | 0.235333i | \(-0.0756180\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 8.16025 | + | 14.1340i | 0.539245 | + | 0.933999i | 0.998945 | + | 0.0459251i | \(0.0146236\pi\) |
−0.459700 | + | 0.888074i | \(0.652043\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −17.1244 | −1.12185 | −0.560927 | − | 0.827865i | \(-0.689555\pi\) | ||||
−0.560927 | + | 0.827865i | \(0.689555\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 5.07180 | 0.330848 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 0.562178 | + | 0.973721i | 0.0363643 | + | 0.0629847i | 0.883635 | − | 0.468177i | \(-0.155089\pi\) |
−0.847270 | + | 0.531162i | \(0.821756\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −5.66025 | + | 9.80385i | −0.364609 | + | 0.631521i | −0.988713 | − | 0.149820i | \(-0.952131\pi\) |
0.624104 | + | 0.781341i | \(0.285464\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 1.83013 | − | 3.16987i | 0.116923 | − | 0.202516i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −5.50000 | − | 9.52628i | −0.349957 | − | 0.606143i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −22.5885 | −1.42577 | −0.712885 | − | 0.701281i | \(-0.752612\pi\) | ||||
−0.712885 | + | 0.701281i | \(0.752612\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 54.1051 | 3.40156 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 2.16987 | + | 3.75833i | 0.135353 | + | 0.234438i | 0.925732 | − | 0.378180i | \(-0.123450\pi\) |
−0.790379 | + | 0.612618i | \(0.790116\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −4.39230 | + | 7.60770i | −0.272925 | + | 0.472719i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 2.90192 | − | 5.02628i | 0.178940 | − | 0.309934i | −0.762578 | − | 0.646897i | \(-0.776066\pi\) |
0.941518 | + | 0.336963i | \(0.109400\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −2.80385 | − | 4.85641i | −0.172239 | − | 0.298327i | ||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 15.2679 | 0.930903 | 0.465452 | − | 0.885073i | \(-0.345892\pi\) | ||||
0.465452 | + | 0.885073i | \(0.345892\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −10.4641 | −0.635649 | −0.317824 | − | 0.948150i | \(-0.602952\pi\) | ||||
−0.317824 | + | 0.948150i | \(0.602952\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 13.8301 | + | 23.9545i | 0.833988 | + | 1.44451i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 0.303848 | − | 0.526279i | 0.0182564 | − | 0.0316211i | −0.856753 | − | 0.515727i | \(-0.827522\pi\) |
0.875009 | + | 0.484106i | \(0.160855\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 4.36603 | − | 7.56218i | 0.260455 | − | 0.451122i | −0.705908 | − | 0.708304i | \(-0.749461\pi\) |
0.966363 | + | 0.257182i | \(0.0827940\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 11.2321 | + | 19.4545i | 0.667676 | + | 1.15645i | 0.978552 | + | 0.205999i | \(0.0660442\pi\) |
−0.310876 | + | 0.950450i | \(0.600622\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 32.7846 | 1.93521 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −16.4641 | −0.968477 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −5.66025 | − | 9.80385i | −0.330676 | − | 0.572747i | 0.651969 | − | 0.758246i | \(-0.273943\pi\) |
−0.982644 | + | 0.185499i | \(0.940610\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0.660254 | − | 1.14359i | 0.0384415 | − | 0.0665826i | ||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 10.7583 | − | 18.6340i | 0.622170 | − | 1.07763i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 10.2679 | + | 17.7846i | 0.591835 | + | 1.02509i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 1.12436 | 0.0643804 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −20.5359 | −1.17205 | −0.586023 | − | 0.810295i | \(-0.699307\pi\) | ||||
−0.586023 | + | 0.810295i | \(0.699307\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 14.1962 | + | 24.5885i | 0.804990 | + | 1.39428i | 0.916298 | + | 0.400498i | \(0.131163\pi\) |
−0.111308 | + | 0.993786i | \(0.535504\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −3.80385 | + | 6.58846i | −0.215006 | + | 0.372402i | −0.953274 | − | 0.302106i | \(-0.902310\pi\) |
0.738268 | + | 0.674507i | \(0.235644\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 9.46410 | − | 16.3923i | 0.531557 | − | 0.920684i | −0.467765 | − | 0.883853i | \(-0.654941\pi\) |
0.999322 | − | 0.0368305i | \(-0.0117262\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −7.85641 | − | 13.6077i | −0.439874 | − | 0.761885i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −3.26795 | −0.181834 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 11.0000 | 0.610170 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 12.0000 | + | 20.7846i | 0.661581 | + | 1.14589i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −10.2321 | + | 17.7224i | −0.562404 | + | 0.974113i | 0.434882 | + | 0.900488i | \(0.356790\pi\) |
−0.997286 | + | 0.0736253i | \(0.976543\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −1.29423 | + | 2.24167i | −0.0707113 | + | 0.122476i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −16.7321 | − | 28.9808i | −0.911453 | − | 1.57868i | −0.812013 | − | 0.583639i | \(-0.801628\pi\) |
−0.0994397 | − | 0.995044i | \(-0.531705\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 15.2679 | 0.826806 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −6.92820 | −0.374088 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 1.26795 | + | 2.19615i | 0.0680671 | + | 0.117896i | 0.898050 | − | 0.439893i | \(-0.144983\pi\) |
−0.829983 | + | 0.557788i | \(0.811650\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 14.1962 | − | 24.5885i | 0.759903 | − | 1.31619i | −0.182997 | − | 0.983113i | \(-0.558580\pi\) |
0.942900 | − | 0.333077i | \(-0.108087\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −9.83013 | + | 17.0263i | −0.523205 | + | 0.906217i | 0.476430 | + | 0.879212i | \(0.341930\pi\) |
−0.999635 | + | 0.0270052i | \(0.991403\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −2.26795 | − | 3.92820i | −0.120370 | − | 0.208487i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 20.7846 | 1.09697 | 0.548485 | − | 0.836160i | \(-0.315205\pi\) | ||||
0.548485 | + | 0.836160i | \(0.315205\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 0.928203 | 0.0488528 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 4.16987 | + | 7.22243i | 0.218261 | + | 0.378039i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 15.4282 | − | 26.7224i | 0.805346 | − | 1.39490i | −0.110712 | − | 0.993853i | \(-0.535313\pi\) |
0.916057 | − | 0.401047i | \(-0.131354\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 13.2679 | − | 22.9808i | 0.688838 | − | 1.19310i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 12.5000 | + | 21.6506i | 0.647225 | + | 1.12103i | 0.983783 | + | 0.179364i | \(0.0574041\pi\) |
−0.336557 | + | 0.941663i | \(0.609263\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −6.24871 | −0.321825 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 16.7846 | 0.862167 | 0.431084 | − | 0.902312i | \(-0.358131\pi\) | ||||
0.431084 | + | 0.902312i | \(0.358131\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 14.1962 | + | 24.5885i | 0.725390 | + | 1.25641i | 0.958813 | + | 0.284036i | \(0.0916737\pi\) |
−0.233424 | + | 0.972375i | \(0.574993\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 7.85641 | − | 13.6077i | 0.400400 | − | 0.693512i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −7.83013 | + | 13.5622i | −0.397003 | + | 0.687630i | −0.993355 | − | 0.115094i | \(-0.963283\pi\) |
0.596351 | + | 0.802723i | \(0.296616\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −3.19615 | − | 5.53590i | −0.161636 | − | 0.279962i | ||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −10.1962 | −0.513024 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −13.0000 | −0.652451 | −0.326226 | − | 0.945292i | \(-0.605777\pi\) | ||||
−0.326226 | + | 0.945292i | \(0.605777\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −8.19615 | − | 14.1962i | −0.409296 | − | 0.708922i | 0.585515 | − | 0.810662i | \(-0.300892\pi\) |
−0.994811 | + | 0.101740i | \(0.967559\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 3.03590 | − | 5.25833i | 0.151229 | − | 0.261936i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −7.85641 | + | 13.6077i | −0.389428 | + | 0.674508i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −11.6603 | − | 20.1962i | −0.576562 | − | 0.998635i | −0.995870 | − | 0.0907912i | \(-0.971060\pi\) |
0.419307 | − | 0.907844i | \(-0.362273\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 6.24871 | 0.307479 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −9.32051 | −0.457526 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 15.1244 | + | 26.1962i | 0.738873 | + | 1.27977i | 0.953003 | + | 0.302961i | \(0.0979751\pi\) |
−0.214130 | + | 0.976805i | \(0.568692\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −1.00000 | + | 1.73205i | −0.0487370 | + | 0.0844150i | −0.889365 | − | 0.457198i | \(-0.848853\pi\) |
0.840628 | + | 0.541613i | \(0.182186\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 1.63397 | − | 2.83013i | 0.0792594 | − | 0.137281i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 2.66025 | + | 4.60770i | 0.128739 | + | 0.222982i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 20.3397 | 0.979731 | 0.489866 | − | 0.871798i | \(-0.337046\pi\) | ||||
0.489866 | + | 0.871798i | \(0.337046\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −15.3923 | −0.739707 | −0.369853 | − | 0.929090i | \(-0.620592\pi\) | ||||
−0.369853 | + | 0.929090i | \(0.620592\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 19.4904 | + | 33.7583i | 0.932351 | + | 1.61488i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 11.1962 | − | 19.3923i | 0.534363 | − | 0.925544i | −0.464831 | − | 0.885400i | \(-0.653885\pi\) |
0.999194 | − | 0.0401446i | \(-0.0127819\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −14.2224 | + | 24.6340i | −0.675728 | + | 1.17040i | 0.300527 | + | 0.953773i | \(0.402837\pi\) |
−0.976255 | + | 0.216622i | \(0.930496\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −4.39230 | − | 7.60770i | −0.208215 | − | 0.360639i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 13.8038 | 0.651444 | 0.325722 | − | 0.945466i | \(-0.394393\pi\) | ||||
0.325722 | + | 0.945466i | \(0.394393\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 58.6410 | 2.76130 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −3.12436 | − | 5.41154i | −0.146472 | − | 0.253697i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −9.42820 | + | 16.3301i | −0.441033 | + | 0.763891i | −0.997766 | − | 0.0667999i | \(-0.978721\pi\) |
0.556734 | + | 0.830691i | \(0.312054\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 11.0981 | − | 19.2224i | 0.516889 | − | 0.895278i | −0.482919 | − | 0.875665i | \(-0.660423\pi\) |
0.999808 | − | 0.0196127i | \(-0.00624332\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −3.30385 | − | 5.72243i | −0.153543 | − | 0.265944i | 0.778985 | − | 0.627043i | \(-0.215735\pi\) |
−0.932527 | + | 0.361099i | \(0.882402\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 9.46410 | 0.437946 | 0.218973 | − | 0.975731i | \(-0.429729\pi\) | ||||
0.218973 | + | 0.975731i | \(0.429729\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −12.2487 | −0.565593 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 18.3660 | + | 31.8109i | 0.844471 | + | 1.46267i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −9.96410 | + | 17.2583i | −0.457184 | + | 0.791866i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 7.83013 | − | 13.5622i | 0.357768 | − | 0.619672i | −0.629820 | − | 0.776741i | \(-0.716871\pi\) |
0.987588 | + | 0.157069i | \(0.0502047\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 3.12436 | + | 5.41154i | 0.142458 | + | 0.246745i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −8.73205 | −0.396502 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −4.07180 | −0.184511 | −0.0922554 | − | 0.995735i | \(-0.529408\pi\) | ||||
−0.0922554 | + | 0.995735i | \(0.529408\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −0.928203 | − | 1.60770i | −0.0418892 | − | 0.0725543i | 0.844321 | − | 0.535838i | \(-0.180004\pi\) |
−0.886210 | + | 0.463284i | \(0.846671\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −0.928203 | + | 1.60770i | −0.0418042 | + | 0.0724069i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 10.7321 | − | 18.5885i | 0.481398 | − | 0.833806i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 14.6603 | + | 25.3923i | 0.656283 | + | 1.13672i | 0.981570 | + | 0.191100i | \(0.0612056\pi\) |
−0.325287 | + | 0.945615i | \(0.605461\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −21.4641 | −0.957037 | −0.478518 | − | 0.878077i | \(-0.658826\pi\) | ||||
−0.478518 | + | 0.878077i | \(0.658826\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −3.21539 | −0.143083 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 16.3923 | + | 28.3923i | 0.726576 | + | 1.25847i | 0.958322 | + | 0.285690i | \(0.0922229\pi\) |
−0.231746 | + | 0.972776i | \(0.574444\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −19.7321 | + | 34.1769i | −0.872895 | + | 1.51190i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −6.90192 | + | 11.9545i | −0.304135 | + | 0.526777i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 21.4641 | + | 37.1769i | 0.943990 | + | 1.63504i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 17.8038 | 0.780001 | 0.390000 | − | 0.920815i | \(-0.372475\pi\) | ||||
0.390000 | + | 0.920815i | \(0.372475\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −12.8564 | −0.562171 | −0.281086 | − | 0.959683i | \(-0.590695\pi\) | ||||
−0.281086 | + | 0.959683i | \(0.590695\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −0.901924 | − | 1.56218i | −0.0392884 | − | 0.0680495i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −26.6244 | + | 46.1147i | −1.15758 | + | 2.00499i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 11.6603 | − | 20.1962i | 0.505062 | − | 0.874792i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 3.46410 | + | 6.00000i | 0.149766 | + | 0.259403i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 30.9808 | 1.33444 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −4.39230 | −0.188840 | −0.0944200 | − | 0.995532i | \(-0.530100\pi\) | ||||
−0.0944200 | + | 0.995532i | \(0.530100\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 6.02628 | + | 10.4378i | 0.258137 | + | 0.447107i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 3.83975 | − | 6.65064i | 0.164176 | − | 0.284361i | −0.772187 | − | 0.635396i | \(-0.780837\pi\) |
0.936362 | + | 0.351035i | \(0.114170\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 5.66025 | − | 9.80385i | 0.241135 | − | 0.417658i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −24.1244 | − | 41.7846i | −1.02587 | − | 1.77686i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 6.19615 | 0.262539 | 0.131270 | − | 0.991347i | \(-0.458095\pi\) | ||||
0.131270 | + | 0.991347i | \(0.458095\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 14.6077 | 0.617840 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −6.56218 | − | 11.3660i | −0.276563 | − | 0.479021i | 0.693965 | − | 0.720008i | \(-0.255862\pi\) |
−0.970528 | + | 0.240987i | \(0.922529\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 2.53590 | − | 4.39230i | 0.106686 | − | 0.184786i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 13.2942 | − | 23.0263i | 0.557323 | − | 0.965312i | −0.440396 | − | 0.897804i | \(-0.645162\pi\) |
0.997719 | − | 0.0675081i | \(-0.0215048\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 1.73205 | + | 3.00000i | 0.0724841 | + | 0.125546i | 0.899989 | − | 0.435912i | \(-0.143574\pi\) |
−0.827505 | + | 0.561458i | \(0.810241\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −38.9808 | −1.62561 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −14.8564 | −0.618480 | −0.309240 | − | 0.950984i | \(-0.600075\pi\) | ||||
−0.309240 | + | 0.950984i | \(0.600075\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −22.0526 | − | 38.1962i | −0.914894 | − | 1.58464i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 23.7321 | − | 41.1051i | 0.982881 | − | 1.70240i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 2.90192 | − | 5.02628i | 0.119775 | − | 0.207457i | −0.799903 | − | 0.600129i | \(-0.795116\pi\) |
0.919679 | + | 0.392672i | \(0.128449\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 5.50000 | + | 9.52628i | 0.226624 | + | 0.392524i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −26.5885 | −1.09186 | −0.545929 | − | 0.837832i | \(-0.683823\pi\) | ||||
−0.545929 | + | 0.837832i | \(0.683823\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −1.85641 | −0.0761052 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −7.85641 | − | 13.6077i | −0.321004 | − | 0.555995i | 0.659691 | − | 0.751537i | \(-0.270687\pi\) |
−0.980695 | + | 0.195541i | \(0.937354\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −6.16025 | + | 10.6699i | −0.251282 | + | 0.435233i | −0.963879 | − | 0.266340i | \(-0.914185\pi\) |
0.712597 | + | 0.701574i | \(0.247519\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 10.0263 | − | 17.3660i | 0.407626 | − | 0.706029i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 6.39230 | + | 11.0718i | 0.259456 | + | 0.449390i | 0.966096 | − | 0.258182i | \(-0.0831235\pi\) |
−0.706641 | + | 0.707573i | \(0.749790\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 17.0718 | 0.690651 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −19.9282 | −0.804893 | −0.402446 | − | 0.915444i | \(-0.631840\pi\) | ||||
−0.402446 | + | 0.915444i | \(0.631840\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 4.73205 | + | 8.19615i | 0.190505 | + | 0.329965i | 0.945418 | − | 0.325861i | \(-0.105654\pi\) |
−0.754913 | + | 0.655825i | \(0.772321\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −0.500000 | + | 0.866025i | −0.0200967 | + | 0.0348085i | −0.875899 | − | 0.482495i | \(-0.839731\pi\) |
0.855802 | + | 0.517303i | \(0.173064\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 20.7846 | − | 36.0000i | 0.832718 | − | 1.44231i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −8.62436 | − | 14.9378i | −0.344974 | − | 0.597513i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 1.85641 | 0.0740198 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 28.0000 | 1.11466 | 0.557331 | − | 0.830290i | \(-0.311825\pi\) | ||||
0.557331 | + | 0.830290i | \(0.311825\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 0.705771 | + | 1.22243i | 0.0280077 | + | 0.0485107i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 6.16025 | − | 10.6699i | 0.244078 | − | 0.422756i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −15.0981 | + | 26.1506i | −0.596338 | + | 1.03289i | 0.397018 | + | 0.917811i | \(0.370045\pi\) |
−0.993357 | + | 0.115077i | \(0.963288\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −12.8038 | − | 22.1769i | −0.504934 | − | 0.874572i | −0.999984 | − | 0.00570722i | \(-0.998183\pi\) |
0.495049 | − | 0.868865i | \(-0.335150\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −25.1244 | −0.987740 | −0.493870 | − | 0.869536i | \(-0.664418\pi\) | ||||
−0.493870 | + | 0.869536i | \(0.664418\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 11.1769 | 0.438732 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −4.39230 | − | 7.60770i | −0.171884 | − | 0.297712i | 0.767194 | − | 0.641415i | \(-0.221652\pi\) |
−0.939079 | + | 0.343703i | \(0.888319\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 5.58846 | − | 9.67949i | 0.218359 | − | 0.378209i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 6.00000 | − | 10.3923i | 0.233727 | − | 0.404827i | −0.725175 | − | 0.688565i | \(-0.758241\pi\) |
0.958902 | + | 0.283738i | \(0.0915745\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 14.3564 | + | 24.8660i | 0.558399 | + | 0.967176i | 0.997630 | + | 0.0688021i | \(0.0219177\pi\) |
−0.439231 | + | 0.898374i | \(0.644749\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 11.3205 | 0.438990 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 22.1436 | 0.857403 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 4.75833 | + | 8.24167i | 0.183693 | + | 0.318166i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 8.62436 | − | 14.9378i | 0.332444 | − | 0.575811i | −0.650546 | − | 0.759467i | \(-0.725460\pi\) |
0.982991 | + | 0.183656i | \(0.0587933\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −22.9545 | + | 39.7583i | −0.882212 | + | 1.52804i | −0.0333368 | + | 0.999444i | \(0.510613\pi\) |
−0.848876 | + | 0.528593i | \(0.822720\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −20.6603 | − | 35.7846i | −0.792868 | − | 1.37329i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −0.0525589 | −0.00201111 | −0.00100555 | − | 0.999999i | \(-0.500320\pi\) | ||||
−0.00100555 | + | 0.999999i | \(0.500320\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −13.8564 | −0.529426 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −9.43782 | − | 16.3468i | −0.359552 | − | 0.622763i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 16.0885 | − | 27.8660i | 0.612034 | − | 1.06007i | −0.378863 | − | 0.925453i | \(-0.623685\pi\) |
0.990897 | − | 0.134621i | \(-0.0429817\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −1.26795 | + | 2.19615i | −0.0480961 | + | 0.0833048i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −3.46410 | − | 6.00000i | −0.131212 | − | 0.227266i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 23.3205 | 0.880803 | 0.440402 | − | 0.897801i | \(-0.354836\pi\) | ||||
0.440402 | + | 0.897801i | \(0.354836\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −11.3205 | −0.426961 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −7.60770 | − | 13.1769i | −0.286117 | − | 0.495569i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 0.0358984 | − | 0.0621778i | 0.00134819 | − | 0.00233514i | −0.865351 | − | 0.501167i | \(-0.832904\pi\) |
0.866699 | + | 0.498832i | \(0.166238\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −10.7583 | + | 18.6340i | −0.402903 | + | 0.697848i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −5.58846 | − | 9.67949i | −0.208996 | − | 0.361992i | ||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −12.7321 | −0.474825 | −0.237413 | − | 0.971409i | \(-0.576299\pi\) | ||||
−0.237413 | + | 0.971409i | \(0.576299\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −65.3205 | −2.43266 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 5.66025 | + | 9.80385i | 0.210217 | + | 0.364106i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 11.1962 | − | 19.3923i | 0.415242 | − | 0.719221i | −0.580212 | − | 0.814466i | \(-0.697030\pi\) |
0.995454 | + | 0.0952450i | \(0.0303635\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 2.16987 | − | 3.75833i | 0.0802557 | − | 0.139007i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 18.9641 | + | 32.8468i | 0.700455 | + | 1.21322i | 0.968307 | + | 0.249764i | \(0.0803529\pi\) |
−0.267852 | + | 0.963460i | \(0.586314\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −21.9090 | −0.807027 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −14.6077 | −0.537353 | −0.268676 | − | 0.963231i | \(-0.586586\pi\) | ||||
−0.268676 | + | 0.963231i | \(0.586586\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 6.02628 | + | 10.4378i | 0.221083 | + | 0.382927i | 0.955137 | − | 0.296164i | \(-0.0957076\pi\) |
−0.734054 | + | 0.679091i | \(0.762374\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −7.33975 | + | 12.7128i | −0.268907 | + | 0.465761i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −16.3923 | + | 28.3923i | −0.598962 | + | 1.03743i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 10.2679 | + | 17.7846i | 0.374683 | + | 0.648970i | 0.990280 | − | 0.139092i | \(-0.0444183\pi\) |
−0.615597 | + | 0.788061i | \(0.711085\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 2.58846 | 0.0942036 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −0.0717968 | −0.00260950 | −0.00130475 | − | 0.999999i | \(-0.500415\pi\) | ||||
−0.00130475 | + | 0.999999i | \(0.500415\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −17.0981 | − | 29.6147i | −0.619805 | − | 1.07353i | −0.989521 | − | 0.144389i | \(-0.953878\pi\) |
0.369716 | − | 0.929145i | \(-0.379455\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −28.5167 | + | 49.3923i | −1.03237 | + | 1.78812i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 2.22243 | − | 3.84936i | 0.0802474 | − | 0.138993i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 15.2846 | + | 26.4737i | 0.551177 | + | 0.954667i | 0.998190 | + | 0.0601393i | \(0.0191545\pi\) |
−0.447013 | + | 0.894528i | \(0.647512\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −33.4641 | −1.20362 | −0.601810 | − | 0.798639i | \(-0.705554\pi\) | ||||
−0.601810 | + | 0.798639i | \(0.705554\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −11.0000 | −0.395132 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 21.1244 | + | 36.5885i | 0.756859 | + | 1.31092i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 19.1962 | − | 33.2487i | 0.686892 | − | 1.18973i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 1.97372 | − | 3.41858i | 0.0704451 | − | 0.122015i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −23.8205 | − | 41.2583i | −0.849109 | − | 1.47070i | −0.882004 | − | 0.471242i | \(-0.843806\pi\) |
0.0328946 | − | 0.999459i | \(-0.489527\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 24.0000 | 0.853342 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 3.78461 | 0.134395 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −4.36603 | − | 7.56218i | −0.154653 | − | 0.267866i | 0.778280 | − | 0.627918i | \(-0.216092\pi\) |
−0.932932 | + | 0.360051i | \(0.882759\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 2.53590 | − | 4.39230i | 0.0897136 | − | 0.155389i | ||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −35.2942 | + | 61.1314i | −1.24551 | + | 2.15728i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 11.0718 | + | 19.1769i | 0.390230 | + | 0.675897i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −4.33975 | −0.152577 | −0.0762887 | − | 0.997086i | \(-0.524307\pi\) | ||||
−0.0762887 | + | 0.997086i | \(0.524307\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 45.7846 | 1.60772 | 0.803858 | − | 0.594822i | \(-0.202777\pi\) | ||||
0.803858 | + | 0.594822i | \(0.202777\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −8.19615 | − | 14.1962i | −0.287099 | − | 0.497270i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −13.2321 | + | 22.9186i | −0.462931 | + | 0.801820i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 12.9282 | − | 22.3923i | 0.451197 | − | 0.781497i | −0.547263 | − | 0.836960i | \(-0.684330\pi\) |
0.998461 | + | 0.0554637i | \(0.0176637\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −21.0885 | − | 36.5263i | −0.735097 | − | 1.27323i | −0.954681 | − | 0.297632i | \(-0.903803\pi\) |
0.219583 | − | 0.975594i | \(-0.429530\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 21.5167 | 0.748208 | 0.374104 | − | 0.927387i | \(-0.377950\pi\) | ||||
0.374104 | + | 0.927387i | \(0.377950\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 13.2487 | 0.460147 | 0.230073 | − | 0.973173i | \(-0.426103\pi\) | ||||
0.230073 | + | 0.973173i | \(0.426103\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −1.83013 | − | 3.16987i | −0.0634101 | − | 0.109830i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 1.60770 | − | 2.78461i | 0.0556366 | − | 0.0963654i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −5.66025 | + | 9.80385i | −0.195414 | + | 0.338466i | −0.947036 | − | 0.321127i | \(-0.895938\pi\) |
0.751622 | + | 0.659594i | \(0.229272\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 11.2846 | + | 19.5455i | 0.389124 | + | 0.673983i | ||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 5.07180 | 0.174475 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 94.8897 | 3.26045 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −11.0718 | − | 19.1769i | −0.379536 | − | 0.657376i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −15.8923 | + | 27.5263i | −0.544142 | + | 0.942482i | 0.454518 | + | 0.890737i | \(0.349811\pi\) |
−0.998660 | + | 0.0517444i | \(0.983522\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −6.58846 | + | 11.4115i | −0.225057 | + | 0.389811i | −0.956337 | − | 0.292267i | \(-0.905590\pi\) |
0.731279 | + | 0.682078i | \(0.238924\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −16.2679 | − | 28.1769i | −0.555055 | − | 0.961384i | −0.997899 | − | 0.0647852i | \(-0.979364\pi\) |
0.442844 | − | 0.896599i | \(-0.353970\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −15.9474 | −0.542857 | −0.271429 | − | 0.962459i | \(-0.587496\pi\) | ||||
−0.271429 | + | 0.962459i | \(0.587496\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −5.07180 | −0.172446 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −43.1506 | − | 74.7391i | −1.46379 | − | 2.53535i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −4.35641 | + | 7.54552i | −0.147611 | + | 0.255670i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −12.0000 | + | 20.7846i | −0.405674 | + | 0.702648i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 22.7321 | + | 39.3731i | 0.767607 | + | 1.32953i | 0.938857 | + | 0.344306i | \(0.111886\pi\) |
−0.171250 | + | 0.985228i | \(0.554781\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −15.6603 | −0.527607 | −0.263804 | − | 0.964576i | \(-0.584977\pi\) | ||||
−0.263804 | + | 0.964576i | \(0.584977\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 11.6795 | 0.393046 | 0.196523 | − | 0.980499i | \(-0.437035\pi\) | ||||
0.196523 | + | 0.980499i | \(0.437035\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −14.5622 | − | 25.2224i | −0.488950 | − | 0.846886i | 0.510969 | − | 0.859599i | \(-0.329287\pi\) |
−0.999919 | + | 0.0127127i | \(0.995953\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −3.33975 | + | 5.78461i | −0.112011 | + | 0.194010i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −15.4641 | + | 26.7846i | −0.517486 | + | 0.896313i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 0.928203 | + | 1.60770i | 0.0310264 | + | 0.0537393i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 6.24871 | 0.208406 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −5.60770 | −0.186819 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −4.14359 | − | 7.17691i | −0.137738 | − | 0.238569i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −3.50000 | + | 6.06218i | −0.116216 | + | 0.201291i | −0.918265 | − | 0.395966i | \(-0.870410\pi\) |
0.802049 | + | 0.597258i | \(0.203743\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −6.90192 | + | 11.9545i | −0.228671 | + | 0.396070i | −0.957414 | − | 0.288717i | \(-0.906771\pi\) |
0.728744 | + | 0.684787i | \(0.240105\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −39.4449 | − | 68.3205i | −1.30543 | − | 2.26108i | ||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 52.8897 | 1.74657 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 4.00000 | 0.131948 | 0.0659739 | − | 0.997821i | \(-0.478985\pi\) | ||||
0.0659739 | + | 0.997821i | \(0.478985\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −7.63397 | − | 13.2224i | −0.251275 | − | 0.435222i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 5.66025 | − | 9.80385i | 0.186108 | − | 0.322349i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −25.2942 | + | 43.8109i | −0.829877 | + | 1.43739i | 0.0682577 | + | 0.997668i | \(0.478256\pi\) |
−0.898134 | + | 0.439721i | \(0.855077\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 11.1603 | + | 19.3301i | 0.365763 | + | 0.633519i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −3.32051 | −0.108592 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −16.3923 | −0.535513 | −0.267757 | − | 0.963487i | \(-0.586282\pi\) | ||||
−0.267757 | + | 0.963487i | \(0.586282\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 3.46410 | + | 6.00000i | 0.112926 | + | 0.195594i | 0.916949 | − | 0.399004i | \(-0.130644\pi\) |
−0.804022 | + | 0.594599i | \(0.797311\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −41.3205 | + | 71.5692i | −1.34558 | + | 2.33061i | ||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −9.12436 | + | 15.8038i | −0.296502 | + | 0.513556i | −0.975333 | − | 0.220738i | \(-0.929153\pi\) |
0.678831 | + | 0.734294i | \(0.262487\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 14.0359 | + | 24.3109i | 0.455625 | + | 0.789165i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −3.21539 | −0.104157 | −0.0520784 | − | 0.998643i | \(-0.516585\pi\) | ||||
−0.0520784 | + | 0.998643i | \(0.516585\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −13.8564 | −0.448383 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −32.7846 | − | 56.7846i | −1.05867 | − | 1.83367i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 12.4641 | − | 21.5885i | 0.402068 | − | 0.696402i | ||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −1.04552 | + | 1.81089i | −0.0336564 | + | 0.0582946i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 21.6244 | + | 37.4545i | 0.695392 | + | 1.20445i | 0.970048 | + | 0.242912i | \(0.0781027\pi\) |
−0.274656 | + | 0.961543i | \(0.588564\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −46.6410 | −1.49678 | −0.748391 | − | 0.663258i | \(-0.769173\pi\) | ||||
−0.748391 | + | 0.663258i | \(0.769173\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −12.0000 | −0.384702 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 5.66025 | + | 9.80385i | 0.181088 | + | 0.313653i | 0.942251 | − | 0.334907i | \(-0.108705\pi\) |
−0.761164 | + | 0.648560i | \(0.775372\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 37.1769 | − | 64.3923i | 1.18818 | − | 2.05799i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 20.1962 | − | 34.9808i | 0.644157 | − | 1.11571i | −0.340338 | − | 0.940303i | \(-0.610542\pi\) |
0.984495 | − | 0.175410i | \(-0.0561251\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −8.53590 | − | 14.7846i | −0.271976 | − | 0.471077i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −51.7654 | −1.64604 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 13.9282 | 0.442444 | 0.221222 | − | 0.975223i | \(-0.428995\pi\) | ||||
0.221222 | + | 0.975223i | \(0.428995\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −4.02628 | − | 6.97372i | −0.127642 | − | 0.221082i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −5.00000 | + | 8.66025i | −0.158352 | + | 0.274273i | −0.934274 | − | 0.356555i | \(-0.883951\pi\) |
0.775923 | + | 0.630828i | \(0.217285\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 0 | 0 |
(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 | 1944.2.i.k.649.2 | 4 | ||
3.2 | odd | 2 | 1944.2.i.n.649.1 | 4 | |||
9.2 | odd | 6 | 1944.2.a.k.1.2 | ✓ | 2 | ||
9.4 | even | 3 | inner | 1944.2.i.k.1297.2 | 4 | ||
9.5 | odd | 6 | 1944.2.i.n.1297.1 | 4 | |||
9.7 | even | 3 | 1944.2.a.n.1.1 | yes | 2 | ||
36.7 | odd | 6 | 3888.2.a.bc.1.1 | 2 | |||
36.11 | even | 6 | 3888.2.a.w.1.2 | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1944.2.a.k.1.2 | ✓ | 2 | 9.2 | odd | 6 | ||
1944.2.a.n.1.1 | yes | 2 | 9.7 | even | 3 | ||
1944.2.i.k.649.2 | 4 | 1.1 | even | 1 | trivial | ||
1944.2.i.k.1297.2 | 4 | 9.4 | even | 3 | inner | ||
1944.2.i.n.649.1 | 4 | 3.2 | odd | 2 | |||
1944.2.i.n.1297.1 | 4 | 9.5 | odd | 6 | |||
3888.2.a.w.1.2 | 2 | 36.11 | even | 6 | |||
3888.2.a.bc.1.1 | 2 | 36.7 | odd | 6 |