Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1152,2,Mod(191,1152)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1152, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([3, 3, 1]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1152.191");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1152 = 2^{7} \cdot 3^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1152.p (of order \(6\), degree \(2\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(9.19876631285\) |
Analytic rank: | \(0\) |
Dimension: | \(24\) |
Relative dimension: | \(12\) over \(\Q(\zeta_{6})\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 191.8 | ||
Character | \(\chi\) | \(=\) | 1152.191 |
Dual form | 1152.2.p.g.959.8 |
$q$-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 \(\left(\mathbb{Z}/1152\mathbb{Z}\right)^\times\).
\(n\) | \(127\) | \(641\) | \(901\) |
\(\chi(n)\) | \(-1\) | \(e\left(\frac{1}{6}\right)\) | \(-1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | 0.765007 | − | 1.55395i | 0.441677 | − | 0.897174i | ||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 0.781546 | + | 1.35368i | 0.349518 | + | 0.605383i | 0.986164 | − | 0.165774i | \(-0.0530121\pi\) |
−0.636646 | + | 0.771156i | \(0.719679\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −0.954503 | − | 0.551083i | −0.360768 | − | 0.208290i | 0.308649 | − | 0.951176i | \(-0.400123\pi\) |
−0.669418 | + | 0.742886i | \(0.733456\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −1.82953 | − | 2.37757i | −0.609843 | − | 0.792522i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −2.15418 | − | 1.24372i | −0.649509 | − | 0.374994i | 0.138759 | − | 0.990326i | \(-0.455689\pi\) |
−0.788268 | + | 0.615332i | \(0.789022\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 5.48986 | − | 3.16957i | 1.52261 | − | 0.879081i | 0.522971 | − | 0.852351i | \(-0.324824\pi\) |
0.999643 | − | 0.0267307i | \(-0.00850965\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 2.70144 | − | 0.178912i | 0.697508 | − | 0.0461950i | ||||
\(16\) | 0 | 0 | ||||||||
\(17\) | − | 0.874622i | − | 0.212127i | −0.994359 | − | 0.106064i | \(-0.966175\pi\) | ||
0.994359 | − | 0.106064i | \(-0.0338247\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −6.45410 | −1.48067 | −0.740337 | − | 0.672236i | \(-0.765334\pi\) | ||||
−0.740337 | + | 0.672236i | \(0.765334\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −1.58656 | + | 1.06167i | −0.346215 | + | 0.231675i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −1.52981 | − | 2.64970i | −0.318987 | − | 0.552501i | 0.661290 | − | 0.750130i | \(-0.270009\pi\) |
−0.980277 | + | 0.197629i | \(0.936676\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 1.27837 | − | 2.21421i | 0.255675 | − | 0.442841i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −5.09422 | + | 1.02415i | −0.980384 | + | 0.197097i | ||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −0.767807 | + | 1.32988i | −0.142578 | + | 0.246953i | −0.928467 | − | 0.371415i | \(-0.878873\pi\) |
0.785889 | + | 0.618368i | \(0.212206\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 6.29677 | − | 3.63544i | 1.13093 | − | 0.652945i | 0.186764 | − | 0.982405i | \(-0.440200\pi\) |
0.944169 | + | 0.329460i | \(0.106867\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −3.58063 | + | 2.39604i | −0.623309 | + | 0.417097i | ||||
\(34\) | 0 | 0 | ||||||||
\(35\) | − | 1.72279i | − | 0.291204i | ||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 1.74638i | 0.287103i | 0.989643 | + | 0.143551i | \(0.0458522\pi\) | ||||
−0.989643 | + | 0.143551i | \(0.954148\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −0.725582 | − | 10.9557i | −0.116186 | − | 1.75432i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 7.45339 | − | 4.30322i | 1.16402 | − | 0.672049i | 0.211759 | − | 0.977322i | \(-0.432081\pi\) |
0.952265 | + | 0.305273i | \(0.0987476\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 2.66223 | − | 4.61112i | 0.405986 | − | 0.703189i | −0.588449 | − | 0.808534i | \(-0.700261\pi\) |
0.994436 | + | 0.105345i | \(0.0335947\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 1.78859 | − | 4.33477i | 0.266628 | − | 0.646189i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 1.73458 | − | 3.00438i | 0.253015 | − | 0.438234i | −0.711340 | − | 0.702848i | \(-0.751911\pi\) |
0.964354 | + | 0.264614i | \(0.0852446\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −2.89262 | − | 5.01016i | −0.413231 | − | 0.715737i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −1.35912 | − | 0.669092i | −0.190315 | − | 0.0936916i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −11.1315 | −1.52903 | −0.764514 | − | 0.644607i | \(-0.777021\pi\) | ||||
−0.764514 | + | 0.644607i | \(0.777021\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | − | 3.88808i | − | 0.524269i | ||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −4.93743 | + | 10.0294i | −0.653979 | + | 1.32842i | ||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −1.76786 | + | 1.02067i | −0.230155 | + | 0.132880i | −0.610644 | − | 0.791905i | \(-0.709089\pi\) |
0.380488 | + | 0.924786i | \(0.375756\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 6.23086 | + | 3.59739i | 0.797780 | + | 0.460599i | 0.842694 | − | 0.538392i | \(-0.180968\pi\) |
−0.0449142 | + | 0.998991i | \(0.514301\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0.436057 | + | 3.27762i | 0.0549380 | + | 0.412941i | ||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 8.58115 | + | 4.95433i | 1.06436 | + | 0.614509i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 1.14096 | + | 1.97621i | 0.139391 | + | 0.241432i | 0.927266 | − | 0.374403i | \(-0.122152\pi\) |
−0.787875 | + | 0.615835i | \(0.788819\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −5.28782 | + | 0.350205i | −0.636579 | + | 0.0421597i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 13.1244 | 1.55758 | 0.778788 | − | 0.627287i | \(-0.215835\pi\) | ||||
0.778788 | + | 0.627287i | \(0.215835\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −4.92960 | −0.576966 | −0.288483 | − | 0.957485i | \(-0.593151\pi\) | ||||
−0.288483 | + | 0.957485i | \(0.593151\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −2.46281 | − | 3.68041i | −0.284380 | − | 0.424977i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 1.37078 | + | 2.37426i | 0.156215 | + | 0.270572i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 3.31959 | + | 1.91656i | 0.373483 | + | 0.215630i | 0.674979 | − | 0.737837i | \(-0.264153\pi\) |
−0.301496 | + | 0.953467i | \(0.597486\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −2.30564 | + | 8.69966i | −0.256182 | + | 0.966628i | ||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −11.2198 | − | 6.47775i | −1.23153 | − | 0.711026i | −0.264183 | − | 0.964472i | \(-0.585102\pi\) |
−0.967349 | + | 0.253447i | \(0.918436\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 1.18396 | − | 0.683557i | 0.128418 | − | 0.0741422i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 1.47919 | + | 2.21050i | 0.158586 | + | 0.236991i | ||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 13.3358i | 1.41359i | 0.707416 | + | 0.706797i | \(0.249861\pi\) | ||||
−0.707416 | + | 0.706797i | \(0.750139\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −6.98679 | −0.732414 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −0.832229 | − | 12.5660i | −0.0862982 | − | 1.30303i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −5.04418 | − | 8.73677i | −0.517522 | − | 0.896374i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 4.65272 | − | 8.05875i | 0.472412 | − | 0.818242i | −0.527089 | − | 0.849810i | \(-0.676717\pi\) |
0.999502 | + | 0.0315680i | \(0.0100501\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0.984118 | + | 7.39712i | 0.0989076 | + | 0.743438i | ||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −9.15459 | + | 15.8562i | −0.910916 | + | 1.57775i | −0.0981434 | + | 0.995172i | \(0.531290\pi\) |
−0.812773 | + | 0.582581i | \(0.802043\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −14.0766 | + | 8.12710i | −1.38700 | + | 0.800787i | −0.992977 | − | 0.118311i | \(-0.962252\pi\) |
−0.394028 | + | 0.919098i | \(0.628919\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −2.67712 | − | 1.31794i | −0.261261 | − | 0.128618i | ||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 5.80067i | 0.560772i | 0.959887 | + | 0.280386i | \(0.0904624\pi\) | ||||
−0.959887 | + | 0.280386i | \(0.909538\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | − | 7.34771i | − | 0.703783i | −0.936041 | − | 0.351892i | \(-0.885539\pi\) | ||
0.936041 | − | 0.351892i | \(-0.114461\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 2.71379 | + | 1.33599i | 0.257581 | + | 0.126807i | ||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −0.260651 | + | 0.150487i | −0.0245200 | + | 0.0141566i | −0.512210 | − | 0.858860i | \(-0.671173\pi\) |
0.487690 | + | 0.873017i | \(0.337840\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 2.39123 | − | 4.14173i | 0.222983 | − | 0.386218i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −17.5797 | − | 7.25368i | −1.62525 | − | 0.670603i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −0.481989 | + | 0.834830i | −0.0441839 | + | 0.0765287i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −2.40634 | − | 4.16791i | −0.218758 | − | 0.378901i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −0.985097 | − | 14.8742i | −0.0888232 | − | 1.34116i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 11.8119 | 1.05649 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | − | 18.6505i | − | 1.65497i | −0.561490 | − | 0.827484i | \(-0.689772\pi\) | ||
0.561490 | − | 0.827484i | \(-0.310228\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −5.12883 | − | 7.66451i | −0.451568 | − | 0.674823i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 7.75570 | − | 4.47775i | 0.677618 | − | 0.391223i | −0.121339 | − | 0.992611i | \(-0.538719\pi\) |
0.798957 | + | 0.601388i | \(0.205385\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 6.16046 | + | 3.55675i | 0.534180 | + | 0.308409i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −5.36773 | − | 6.09552i | −0.461981 | − | 0.524618i | ||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 8.59826 | + | 4.96421i | 0.734599 | + | 0.424121i | 0.820102 | − | 0.572217i | \(-0.193917\pi\) |
−0.0855034 | + | 0.996338i | \(0.527250\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 0.970830 | + | 1.68153i | 0.0823448 | + | 0.142625i | 0.904257 | − | 0.426989i | \(-0.140426\pi\) |
−0.821912 | + | 0.569615i | \(0.807092\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −3.34170 | − | 4.99383i | −0.281422 | − | 0.420556i | ||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −15.7682 | −1.31860 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −2.40030 | −0.199334 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −9.99841 | + | 0.662181i | −0.824655 | + | 0.0546158i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 9.65962 | + | 16.7310i | 0.791347 | + | 1.37065i | 0.925133 | + | 0.379643i | \(0.123953\pi\) |
−0.133786 | + | 0.991010i | \(0.542713\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 9.90266 | + | 5.71730i | 0.805867 | + | 0.465267i | 0.845519 | − | 0.533946i | \(-0.179291\pi\) |
−0.0396516 | + | 0.999214i | \(0.512625\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −2.07947 | + | 1.60015i | −0.168115 | + | 0.129364i | ||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 9.84243 | + | 5.68253i | 0.790563 | + | 0.456432i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 15.2905 | − | 8.82799i | 1.22032 | − | 0.704551i | 0.255332 | − | 0.966854i | \(-0.417815\pi\) |
0.964986 | + | 0.262303i | \(0.0844820\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −8.51566 | + | 17.2978i | −0.675336 | + | 1.37180i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 3.37220i | 0.265767i | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 5.64209 | 0.441922 | 0.220961 | − | 0.975283i | \(-0.429081\pi\) | ||||
0.220961 | + | 0.975283i | \(0.429081\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −6.04189 | − | 2.97441i | −0.470361 | − | 0.231557i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 11.6305 | + | 20.1446i | 0.899993 | + | 1.55883i | 0.827501 | + | 0.561465i | \(0.189762\pi\) |
0.0724922 | + | 0.997369i | \(0.476905\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 13.5924 | − | 23.5427i | 1.04557 | − | 1.81098i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 11.8080 | + | 15.3451i | 0.902979 | + | 1.17347i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −5.69231 | + | 9.85937i | −0.432778 | + | 0.749594i | −0.997111 | − | 0.0759531i | \(-0.975800\pi\) |
0.564333 | + | 0.825547i | \(0.309133\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −2.44042 | + | 1.40898i | −0.184479 | + | 0.106509i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0.233654 | + | 3.52799i | 0.0175625 | + | 0.265180i | ||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 10.6783i | 0.798133i | 0.916922 | + | 0.399066i | \(0.130666\pi\) | ||||
−0.916922 | + | 0.399066i | \(0.869334\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 5.74638i | 0.427125i | 0.976929 | + | 0.213562i | \(0.0685067\pi\) | ||||
−0.976929 | + | 0.213562i | \(0.931493\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 10.3568 | − | 6.93043i | 0.765598 | − | 0.512312i | ||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −2.36403 | + | 1.36487i | −0.173807 | + | 0.100348i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −1.08778 | + | 1.88409i | −0.0795464 | + | 0.137778i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 5.42684 | + | 1.82979i | 0.394745 | + | 0.133097i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −8.87439 | + | 15.3709i | −0.642129 | + | 1.11220i | 0.342828 | + | 0.939398i | \(0.388615\pi\) |
−0.984957 | + | 0.172801i | \(0.944718\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −10.5823 | − | 18.3291i | −0.761732 | − | 1.31936i | −0.941957 | − | 0.335733i | \(-0.891016\pi\) |
0.180225 | − | 0.983625i | \(-0.442317\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 14.2634 | − | 9.54460i | 1.02143 | − | 0.683503i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −5.51688 | −0.393061 | −0.196531 | − | 0.980498i | \(-0.562968\pi\) | ||||
−0.196531 | + | 0.980498i | \(0.562968\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 6.90420i | 0.489426i | 0.969596 | + | 0.244713i | \(0.0786938\pi\) | ||||
−0.969596 | + | 0.244713i | \(0.921306\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 3.94377 | − | 0.261191i | 0.278172 | − | 0.0184230i | ||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 1.46575 | − | 0.846250i | 0.102875 | − | 0.0593951i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 11.6503 | + | 6.72632i | 0.813694 | + | 0.469786i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −3.50102 | + | 8.48493i | −0.243338 | + | 0.589743i | ||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 13.9033 | + | 8.02707i | 0.961711 | + | 0.555244i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 3.74236 | + | 6.48196i | 0.257635 | + | 0.446237i | 0.965608 | − | 0.260003i | \(-0.0837235\pi\) |
−0.707973 | + | 0.706240i | \(0.750390\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 10.0402 | − | 20.3946i | 0.687946 | − | 1.39742i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 8.32262 | 0.567598 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −8.01372 | −0.544007 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −3.77117 | + | 7.66035i | −0.254832 | + | 0.517639i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −2.77218 | − | 4.80155i | −0.186477 | − | 0.322987i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 17.3052 | + | 9.99117i | 1.15884 | + | 0.669058i | 0.951026 | − | 0.309110i | \(-0.100031\pi\) |
0.207816 | + | 0.978168i | \(0.433364\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −7.60324 | + | 1.01154i | −0.506883 | + | 0.0674361i | ||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 18.3301 | + | 10.5829i | 1.21661 | + | 0.702409i | 0.964191 | − | 0.265209i | \(-0.0854410\pi\) |
0.252417 | + | 0.967618i | \(0.418774\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 3.97745 | − | 2.29638i | 0.262838 | − | 0.151749i | −0.362791 | − | 0.931871i | \(-0.618176\pi\) |
0.625628 | + | 0.780121i | \(0.284843\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 4.73814 | − | 0.313801i | 0.311747 | − | 0.0206466i | ||||
\(232\) | 0 | 0 | ||||||||
\(233\) | − | 19.1408i | − | 1.25396i | −0.779037 | − | 0.626979i | \(-0.784291\pi\) | ||
0.779037 | − | 0.626979i | \(-0.215709\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 5.42262 | 0.353733 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 5.51775 | − | 3.69229i | 0.358416 | − | 0.239840i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −12.0889 | − | 20.9385i | −0.781964 | − | 1.35440i | −0.930796 | − | 0.365539i | \(-0.880885\pi\) |
0.148832 | − | 0.988862i | \(-0.452449\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −5.04705 | + | 8.74174i | −0.325109 | + | 0.563105i | −0.981534 | − | 0.191286i | \(-0.938734\pi\) |
0.656426 | + | 0.754391i | \(0.272068\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 11.7550 | + | 10.2381i | 0.754084 | + | 0.656778i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 4.52142 | − | 7.83133i | 0.288863 | − | 0.500325i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −35.4321 | + | 20.4568i | −2.25449 | + | 1.30163i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −18.6493 | + | 12.4795i | −1.18185 | + | 0.790856i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | − | 17.6233i | − | 1.11237i | −0.831057 | − | 0.556187i | \(-0.812264\pi\) | ||
0.831057 | − | 0.556187i | \(-0.187736\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 7.61058i | 0.478473i | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −0.156481 | − | 2.36273i | −0.00979920 | − | 0.147960i | ||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 16.6994 | − | 9.64142i | 1.04168 | − | 0.601415i | 0.121372 | − | 0.992607i | \(-0.461271\pi\) |
0.920309 | + | 0.391192i | \(0.127937\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 0.962399 | − | 1.66692i | 0.0598005 | − | 0.103578i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 4.56660 | − | 0.607544i | 0.282666 | − | 0.0376061i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 0.912358 | − | 1.58025i | 0.0562584 | − | 0.0974424i | −0.836525 | − | 0.547929i | \(-0.815416\pi\) |
0.892783 | + | 0.450487i | \(0.148750\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −8.69977 | − | 15.0684i | −0.534422 | − | 0.925647i | ||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 20.7232 | + | 10.2020i | 1.26824 | + | 0.624352i | ||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −2.48843 | −0.151722 | −0.0758610 | − | 0.997118i | \(-0.524171\pi\) | ||||
−0.0758610 | + | 0.997118i | \(0.524171\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | − | 8.04111i | − | 0.488463i | −0.969717 | − | 0.244231i | \(-0.921464\pi\) | ||
0.969717 | − | 0.244231i | \(-0.0785356\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −5.34494 | + | 10.8571i | −0.323490 | + | 0.657103i | ||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −5.50769 | + | 3.17987i | −0.332126 | + | 0.191753i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 4.27917 | + | 2.47058i | 0.257110 | + | 0.148443i | 0.623016 | − | 0.782209i | \(-0.285907\pi\) |
−0.365905 | + | 0.930652i | \(0.619241\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −20.1636 | − | 8.31984i | −1.20717 | − | 0.498096i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 12.4468 | + | 7.18614i | 0.742511 | + | 0.428689i | 0.822982 | − | 0.568068i | \(-0.192309\pi\) |
−0.0804703 | + | 0.996757i | \(0.525642\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 16.3639 | + | 28.3432i | 0.972736 | + | 1.68483i | 0.687214 | + | 0.726455i | \(0.258833\pi\) |
0.285522 | + | 0.958372i | \(0.407833\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −17.4353 | + | 1.15472i | −1.03278 | + | 0.0683996i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −9.48571 | −0.559924 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 16.2350 | 0.955002 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −8.96354 | − | 13.3951i | −0.525452 | − | 0.785234i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −2.68074 | − | 4.64317i | −0.156610 | − | 0.271257i | 0.777034 | − | 0.629459i | \(-0.216723\pi\) |
−0.933644 | + | 0.358202i | \(0.883390\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −2.76332 | − | 1.59540i | −0.160887 | − | 0.0928880i | ||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 12.2476 | + | 4.12957i | 0.710679 | + | 0.239622i | ||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −16.7969 | − | 9.69767i | −0.971387 | − | 0.560831i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −5.08222 | + | 2.93422i | −0.292934 | + | 0.169126i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 17.6365 | + | 26.3559i | 1.01319 | + | 1.51411i | ||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 11.2461i | 0.643950i | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −11.1124 | −0.634219 | −0.317110 | − | 0.948389i | \(-0.602712\pi\) | ||||
−0.317110 | + | 0.948389i | \(0.602712\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 1.86047 | + | 28.0916i | 0.105838 | + | 1.59807i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 10.4892 | + | 18.1679i | 0.594790 | + | 1.03021i | 0.993576 | + | 0.113163i | \(0.0360981\pi\) |
−0.398787 | + | 0.917044i | \(0.630569\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −11.3679 | + | 19.6898i | −0.642553 | + | 1.11293i | 0.342308 | + | 0.939588i | \(0.388791\pi\) |
−0.984861 | + | 0.173347i | \(0.944542\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −4.09604 | + | 3.15189i | −0.230785 | + | 0.177589i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −14.6224 | + | 25.3267i | −0.821276 | + | 1.42249i | 0.0834573 | + | 0.996511i | \(0.473404\pi\) |
−0.904733 | + | 0.425980i | \(0.859930\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 3.30799 | − | 1.90987i | 0.185212 | − | 0.106932i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 9.01396 | + | 4.43755i | 0.503110 | + | 0.247680i | ||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 5.64490i | 0.314091i | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | − | 16.2076i | − | 0.899035i | ||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −11.4180 | − | 5.62105i | −0.631416 | − | 0.310845i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −3.31133 | + | 1.91180i | −0.182559 | + | 0.105401i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 13.2737 | − | 22.9908i | 0.729591 | − | 1.26369i | −0.227465 | − | 0.973786i | \(-0.573044\pi\) |
0.957056 | − | 0.289903i | \(-0.0936229\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 4.15213 | − | 3.19505i | 0.227535 | − | 0.175088i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −1.78343 | + | 3.08899i | −0.0974392 | + | 0.168770i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 4.28240 | + | 7.41733i | 0.233277 | + | 0.404048i | 0.958771 | − | 0.284181i | \(-0.0917217\pi\) |
−0.725493 | + | 0.688229i | \(0.758388\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0.0344497 | + | 0.520163i | 0.00187105 | + | 0.0282514i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −18.0858 | −0.979402 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 14.0914i | 0.760866i | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −4.60674 | − | 6.88430i | −0.248019 | − | 0.370638i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 11.8860 | − | 6.86239i | 0.638075 | − | 0.368393i | −0.145798 | − | 0.989314i | \(-0.546575\pi\) |
0.783872 | + | 0.620922i | \(0.213242\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −11.2390 | − | 6.48885i | −0.601611 | − | 0.347340i | 0.168064 | − | 0.985776i | \(-0.446248\pi\) |
−0.769675 | + | 0.638436i | \(0.779582\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −24.7205 | + | 21.7689i | −1.31948 | + | 1.16194i | ||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −22.9788 | − | 13.2668i | −1.22304 | − | 0.706120i | −0.257472 | − | 0.966286i | \(-0.582889\pi\) |
−0.965564 | + | 0.260166i | \(0.916223\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 10.2573 | + | 17.7662i | 0.544401 | + | 0.942930i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0.928560 | + | 1.38764i | 0.0491446 | + | 0.0734416i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −5.61198 | −0.296189 | −0.148095 | − | 0.988973i | \(-0.547314\pi\) | ||||
−0.148095 | + | 0.988973i | \(0.547314\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 22.6555 | 1.19239 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −8.31759 | + | 0.550863i | −0.436560 | + | 0.0289128i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −3.85270 | − | 6.67308i | −0.201660 | − | 0.349285i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 20.8358 | + | 12.0295i | 1.08762 | + | 0.627937i | 0.932941 | − | 0.360029i | \(-0.117233\pi\) |
0.154677 | + | 0.987965i | \(0.450566\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −23.8674 | − | 9.84806i | −1.24249 | − | 0.512670i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 10.6250 | + | 6.13437i | 0.551625 | + | 0.318481i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 14.8743 | − | 8.58769i | 0.770163 | − | 0.444654i | −0.0627699 | − | 0.998028i | \(-0.519993\pi\) |
0.832933 | + | 0.553374i | \(0.186660\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 9.03617 | − | 18.3551i | 0.466626 | − | 0.947853i | ||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 9.73448i | 0.501351i | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −30.5262 | −1.56803 | −0.784013 | − | 0.620745i | \(-0.786830\pi\) | ||||
−0.784013 | + | 0.620745i | \(0.786830\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −28.9820 | − | 14.2678i | −1.48479 | − | 0.730961i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 8.10743 | + | 14.0425i | 0.414270 | + | 0.717537i | 0.995352 | − | 0.0963082i | \(-0.0307034\pi\) |
−0.581081 | + | 0.813846i | \(0.697370\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −2.14266 | + | 3.71119i | −0.109200 | + | 0.189140i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −15.8339 | + | 2.10655i | −0.804881 | + | 0.107082i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 12.8869 | − | 22.3207i | 0.653391 | − | 1.13171i | −0.328903 | − | 0.944364i | \(-0.606679\pi\) |
0.982295 | − | 0.187343i | \(-0.0599877\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −2.31749 | + | 1.33800i | −0.117200 | + | 0.0676657i | ||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −1.02505 | − | 15.4775i | −0.0517070 | − | 0.780736i | ||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 5.99153i | 0.301466i | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | − | 9.36711i | − | 0.470122i | −0.971981 | − | 0.235061i | \(-0.924471\pi\) | ||
0.971981 | − | 0.235061i | \(-0.0755290\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 10.2398 | − | 6.85213i | 0.512631 | − | 0.343035i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −4.16389 | + | 2.40402i | −0.207935 | + | 0.120051i | −0.600351 | − | 0.799736i | \(-0.704973\pi\) |
0.392416 | + | 0.919788i | \(0.371639\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 23.0456 | − | 39.9161i | 1.14798 | − | 1.98836i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −13.5785 | + | 3.67809i | −0.674720 | + | 0.182766i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 2.17200 | − | 3.76201i | 0.107662 | − | 0.186476i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 18.1532 | + | 31.4422i | 0.897616 | + | 1.55472i | 0.830534 | + | 0.556968i | \(0.188036\pi\) |
0.0670820 | + | 0.997747i | \(0.478631\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 14.2919 | − | 9.56363i | 0.704966 | − | 0.471739i | ||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 2.24990 | 0.110710 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | − | 20.2506i | − | 0.994065i | ||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 3.35570 | − | 0.222244i | 0.164330 | − | 0.0108833i | ||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −7.72947 | + | 4.46261i | −0.377609 | + | 0.218013i | −0.676778 | − | 0.736188i | \(-0.736624\pi\) |
0.299168 | + | 0.954200i | \(0.403291\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −0.670604 | − | 0.387173i | −0.0326832 | − | 0.0188697i | 0.483569 | − | 0.875306i | \(-0.339340\pi\) |
−0.516253 | + | 0.856436i | \(0.672673\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −10.3166 | + | 1.37253i | −0.501610 | + | 0.0667345i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −1.93659 | − | 1.11809i | −0.0939386 | − | 0.0542355i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −3.96492 | − | 6.86744i | −0.191876 | − | 0.332339i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −12.0628 | + | 24.5030i | −0.582396 | + | 1.18302i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −20.8535 | −1.00448 | −0.502238 | − | 0.864730i | \(-0.667490\pi\) | ||||
−0.502238 | + | 0.864730i | \(0.667490\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −5.02013 | −0.241252 | −0.120626 | − | 0.992698i | \(-0.538490\pi\) | ||||
−0.120626 | + | 0.992698i | \(0.538490\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −1.83625 | + | 3.72996i | −0.0880414 | + | 0.178838i | ||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 9.87354 | + | 17.1015i | 0.472315 | + | 0.818074i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −22.7559 | − | 13.1381i | −1.08608 | − | 0.627049i | −0.153550 | − | 0.988141i | \(-0.549071\pi\) |
−0.932530 | + | 0.361092i | \(0.882404\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −6.61985 | + | 16.0436i | −0.315231 | + | 0.763982i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 25.6178 | + | 14.7905i | 1.21714 | + | 0.702716i | 0.964305 | − | 0.264793i | \(-0.0853037\pi\) |
0.252835 | + | 0.967509i | \(0.418637\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −18.0524 | + | 10.4226i | −0.855765 | + | 0.494076i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 33.3888 | − | 2.21129i | 1.57923 | − | 0.104591i | ||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 1.43585i | 0.0677617i | 0.999426 | + | 0.0338809i | \(0.0107867\pi\) | ||||
−0.999426 | + | 0.0338809i | \(0.989213\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −21.4079 | −1.00806 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 16.4600 | − | 11.0145i | 0.773359 | − | 0.517505i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −5.46049 | − | 9.45785i | −0.255992 | − | 0.443391i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 2.66816 | − | 4.62138i | 0.124811 | − | 0.216179i | −0.796848 | − | 0.604180i | \(-0.793501\pi\) |
0.921659 | + | 0.388001i | \(0.126834\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0.895741 | + | 4.45552i | 0.0418096 | + | 0.207966i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −4.71373 | + | 8.16442i | −0.219540 | + | 0.380255i | −0.954668 | − | 0.297674i | \(-0.903789\pi\) |
0.735127 | + | 0.677929i | \(0.237122\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 13.0444 | − | 7.53117i | 0.606223 | − | 0.350003i | −0.165262 | − | 0.986250i | \(-0.552847\pi\) |
0.771486 | + | 0.636246i | \(0.219514\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 16.3599 | − | 10.9475i | 0.758672 | − | 0.507677i | ||||
\(466\) | 0 | 0 | ||||||||
\(467\) | − | 22.9660i | − | 1.06274i | −0.847140 | − | 0.531369i | \(-0.821678\pi\) | ||
0.847140 | − | 0.531369i | \(-0.178322\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | − | 2.51506i | − | 0.116135i | ||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −2.02091 | − | 30.5142i | −0.0931188 | − | 1.40602i | ||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −11.4698 | + | 6.62212i | −0.527384 | + | 0.304485i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −8.25075 | + | 14.2907i | −0.378571 | + | 0.655703i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 20.3654 | + | 26.4658i | 0.932467 | + | 1.21179i | ||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 15.2716 | − | 26.4512i | 0.697779 | − | 1.20859i | −0.271456 | − | 0.962451i | \(-0.587505\pi\) |
0.969235 | − | 0.246137i | \(-0.0791614\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 5.53527 | + | 9.58737i | 0.252387 | + | 0.437146i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 5.24024 | + | 2.57976i | 0.238439 | + | 0.117383i | ||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 14.5453 | 0.660466 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | − | 25.2482i | − | 1.14411i | −0.820217 | − | 0.572053i | \(-0.806147\pi\) | ||
0.820217 | − | 0.572053i | \(-0.193853\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 4.31623 | − | 8.76753i | 0.195187 | − | 0.396481i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −28.5831 | + | 16.5025i | −1.28994 | + | 0.744746i | −0.978643 | − | 0.205568i | \(-0.934096\pi\) |
−0.311295 | + | 0.950313i | \(0.600763\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 1.16314 | + | 0.671541i | 0.0523853 | + | 0.0302447i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −9.24417 | + | 7.11336i | −0.415495 | + | 0.319722i | ||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −12.5273 | − | 7.23262i | −0.561924 | − | 0.324427i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 8.61075 | + | 14.9143i | 0.385470 | + | 0.667654i | 0.991834 | − | 0.127533i | \(-0.0407060\pi\) |
−0.606364 | + | 0.795187i | \(0.707373\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 40.2011 | − | 2.66246i | 1.79605 | − | 0.118950i | ||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 39.7159 | 1.77084 | 0.885421 | − | 0.464789i | \(-0.153870\pi\) | ||||
0.885421 | + | 0.464789i | \(0.153870\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −28.6189 | −1.27353 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −26.1859 | − | 39.1322i | −1.16296 | − | 1.73792i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −16.7472 | − | 29.0071i | −0.742309 | − | 1.28572i | −0.951442 | − | 0.307829i | \(-0.900398\pi\) |
0.209133 | − | 0.977887i | \(-0.432936\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 4.70532 | + | 2.71662i | 0.208151 | + | 0.120176i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 32.8787 | − | 6.60995i | 1.45163 | − | 0.291836i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −22.0029 | − | 12.7034i | −0.969566 | − | 0.559779i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −7.47320 | + | 4.31465i | −0.328671 | + | 0.189758i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 10.9663 | + | 16.3881i | 0.481368 | + | 0.719356i | ||||
\(520\) | 0 | 0 | ||||||||
\(521\) | − | 19.2115i | − | 0.841671i | −0.907137 | − | 0.420836i | \(-0.861737\pi\) | ||
0.907137 | − | 0.420836i | \(-0.138263\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −21.9153 | −0.958290 | −0.479145 | − | 0.877736i | \(-0.659053\pi\) | ||||
−0.479145 | + | 0.877736i | \(0.659053\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0.322545 | + | 4.87018i | 0.0140770 | + | 0.212552i | ||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −3.17964 | − | 5.50729i | −0.138507 | − | 0.239901i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 6.81938 | − | 11.8115i | 0.296495 | − | 0.513544i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 5.66106 | + | 2.33585i | 0.245669 | + | 0.101367i | ||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 27.2787 | − | 47.2481i | 1.18157 | − | 2.04654i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −7.85223 | + | 4.53349i | −0.339481 | + | 0.196000i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 16.5935 | + | 8.16896i | 0.716064 | + | 0.352517i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 14.3904i | 0.619837i | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 18.1171i | 0.778913i | 0.921045 | + | 0.389456i | \(0.127337\pi\) | ||||
−0.921045 | + | 0.389456i | \(0.872663\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 8.92959 | + | 4.39602i | 0.383205 | + | 0.188651i | ||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 9.94643 | − | 5.74257i | 0.426058 | − | 0.245985i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −4.95910 | + | 8.58941i | −0.212036 | + | 0.367257i | −0.952352 | − | 0.305003i | \(-0.901343\pi\) |
0.740316 | + | 0.672259i | \(0.234676\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −2.84652 | − | 21.3958i | −0.121486 | − | 0.913151i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 4.95551 | − | 8.58319i | 0.211112 | − | 0.365656i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −2.11237 | − | 3.65873i | −0.0898271 | − | 0.155585i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0.312448 | + | 4.71773i | 0.0132627 | + | 0.200256i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 9.59817 | 0.406687 | 0.203344 | − | 0.979107i | \(-0.434819\pi\) | ||||
0.203344 | + | 0.979107i | \(0.434819\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | − | 33.7525i | − | 1.42758i | ||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 2.09563 | + | 3.13170i | 0.0884775 | + | 0.132221i | ||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −13.9909 | + | 8.07768i | −0.589648 | + | 0.340433i | −0.764958 | − | 0.644080i | \(-0.777240\pi\) |
0.175310 | + | 0.984513i | \(0.443907\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −0.407422 | − | 0.235225i | −0.0171404 | − | 0.00989599i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 6.99497 | − | 7.03325i | 0.293761 | − | 0.295369i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −22.7099 | − | 13.1116i | −0.952048 | − | 0.549665i | −0.0583315 | − | 0.998297i | \(-0.518578\pi\) |
−0.893717 | + | 0.448632i | \(0.851911\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 3.52667 | + | 6.10837i | 0.147587 | + | 0.255628i | 0.930335 | − | 0.366711i | \(-0.119516\pi\) |
−0.782748 | + | 0.622338i | \(0.786183\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 17.0967 | + | 25.5492i | 0.714223 | + | 1.06733i | ||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −7.82266 | −0.326227 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −19.1200 | −0.795978 | −0.397989 | − | 0.917390i | \(-0.630292\pi\) | ||||
−0.397989 | + | 0.917390i | \(0.630292\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −36.5781 | + | 2.42252i | −1.52013 | + | 0.100676i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 7.13956 | + | 12.3661i | 0.296199 | + | 0.513031i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 23.9792 | + | 13.8444i | 0.993118 | + | 0.573377i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −3.92023 | − | 29.4664i | −0.162081 | − | 1.21828i | ||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −20.9418 | − | 12.0908i | −0.864361 | − | 0.499039i | 0.00110929 | − | 0.999999i | \(-0.499647\pi\) |
−0.865470 | + | 0.500960i | \(0.832980\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −40.6400 | + | 23.4635i | −1.67454 | + | 0.966798i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −4.22045 | + | 8.57296i | −0.173606 | + | 0.352644i | ||||
\(592\) | 0 | 0 | ||||||||
\(593\) | − | 15.8938i | − | 0.652681i | −0.945252 | − | 0.326340i | \(-0.894184\pi\) | ||
0.945252 | − | 0.326340i | \(-0.105816\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −1.50679 | −0.0617722 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 10.7288 | + | 5.28176i | 0.439100 | + | 0.216168i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −0.540573 | − | 0.936300i | −0.0220872 | − | 0.0382562i | 0.854771 | − | 0.519006i | \(-0.173698\pi\) |
−0.876858 | + | 0.480750i | \(0.840364\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −7.09881 | + | 12.2955i | −0.289566 | + | 0.501544i | −0.973706 | − | 0.227807i | \(-0.926844\pi\) |
0.684140 | + | 0.729351i | \(0.260178\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 2.61113 | − | 6.32824i | 0.106334 | − | 0.257706i | ||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 3.76133 | − | 6.51482i | 0.152920 | − | 0.264865i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −3.34733 | + | 1.93258i | −0.135864 | + | 0.0784411i | −0.566391 | − | 0.824136i | \(-0.691661\pi\) |
0.430527 | + | 0.902578i | \(0.358328\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −0.193725 | − | 2.92509i | −0.00785011 | − | 0.118531i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | − | 21.9915i | − | 0.889682i | ||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 5.87436i | 0.237263i | 0.992938 | + | 0.118632i | \(0.0378507\pi\) | ||||
−0.992938 | + | 0.118632i | \(0.962149\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 19.3649 | − | 12.9584i | 0.780870 | − | 0.522532i | ||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 21.7236 | − | 12.5421i | 0.874559 | − | 0.504927i | 0.00569811 | − | 0.999984i | \(-0.498186\pi\) |
0.868860 | + | 0.495057i | \(0.164853\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 18.8316 | − | 32.6172i | 0.756904 | − | 1.31100i | −0.187518 | − | 0.982261i | \(-0.560044\pi\) |
0.944422 | − | 0.328735i | \(-0.106622\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 10.5069 | + | 11.9314i | 0.421626 | + | 0.478792i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 7.34914 | − | 12.7291i | 0.294437 | − | 0.509980i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 2.83966 | + | 4.91844i | 0.113586 | + | 0.196737i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 23.1098 | − | 15.4643i | 0.922916 | − | 0.617584i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 1.52742 | 0.0609022 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 1.34576i | 0.0535740i | 0.999641 | + | 0.0267870i | \(0.00852759\pi\) | ||||
−0.999641 | + | 0.0267870i | \(0.991472\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 12.9356 | − | 0.856706i | 0.514143 | − | 0.0340510i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 25.2468 | − | 14.5762i | 1.00189 | − | 0.578441i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −31.7601 | − | 18.3367i | −1.25838 | − | 0.726527i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −24.0114 | − | 31.2041i | −0.949878 | − | 1.23441i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −12.5197 | − | 7.22823i | −0.494497 | − | 0.285498i | 0.231941 | − | 0.972730i | \(-0.425492\pi\) |
−0.726438 | + | 0.687232i | \(0.758826\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −12.0008 | − | 20.7861i | −0.473267 | − | 0.819722i | 0.526265 | − | 0.850321i | \(-0.323592\pi\) |
−0.999532 | + | 0.0305983i | \(0.990259\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 6.36686 | − | 12.9329i | 0.250695 | − | 0.509234i | ||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −8.55443 | −0.336309 | −0.168155 | − | 0.985761i | \(-0.553781\pi\) | ||||
−0.168155 | + | 0.985761i | \(0.553781\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 5.07771 | 0.199317 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −6.13055 | + | 12.4529i | −0.240275 | + | 0.488069i | ||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −6.58668 | − | 11.4085i | −0.257757 | − | 0.446448i | 0.707884 | − | 0.706329i | \(-0.249650\pi\) |
−0.965641 | + | 0.259881i | \(0.916317\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 12.1229 | + | 6.99914i | 0.473679 | + | 0.273479i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 9.01884 | + | 11.7204i | 0.351859 | + | 0.457258i | ||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −10.6191 | − | 6.13093i | −0.413661 | − | 0.238827i | 0.278701 | − | 0.960378i | \(-0.410096\pi\) |
−0.692361 | + | 0.721551i | \(0.743430\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −12.6734 | + | 7.31697i | −0.492937 | + | 0.284597i | −0.725792 | − | 0.687914i | \(-0.758526\pi\) |
0.232855 | + | 0.972511i | \(0.425193\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −9.58211 | + | 0.634610i | −0.372138 | + | 0.0246462i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 11.1190i | 0.431178i | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 4.69838 | 0.181922 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 28.7644 | − | 19.2482i | 1.11210 | − | 0.744177i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −8.94826 | − | 15.4988i | −0.345444 | − | 0.598326i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −6.35891 | + | 11.0140i | −0.245118 | + | 0.424557i | −0.962165 | − | 0.272468i | \(-0.912160\pi\) |
0.717047 | + | 0.697025i | \(0.245493\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −4.24465 | + | 12.5889i | −0.163376 | + | 0.484547i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 13.3262 | − | 23.0816i | 0.512167 | − | 0.887099i | −0.487734 | − | 0.872992i | \(-0.662176\pi\) |
0.999901 | − | 0.0141062i | \(-0.00449029\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −8.88207 | + | 5.12807i | −0.340863 | + | 0.196797i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 30.4679 | − | 20.3881i | 1.16753 | − | 0.781272i | ||||
\(682\) | 0 | 0 | ||||||||
\(683\) | − | 22.4974i | − | 0.860841i | −0.902629 | − | 0.430420i | \(-0.858365\pi\) | ||
0.902629 | − | 0.430420i | \(-0.141635\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 15.5190i | 0.592951i | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −0.525691 | − | 7.93752i | −0.0200564 | − | 0.302835i | ||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −61.1103 | + | 35.2821i | −2.32812 | + | 1.34414i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −5.25993 | + | 9.11047i | −0.200097 | + | 0.346579i | −0.948560 | − | 0.316599i | \(-0.897459\pi\) |
0.748462 | + | 0.663177i | \(0.230793\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 3.13708 | − | 7.60290i | 0.119168 | − | 0.288810i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −1.51750 | + | 2.62838i | −0.0575619 | + | 0.0997002i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −3.76369 | − | 6.51890i | −0.142560 | − | 0.246921i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −29.7439 | − | 14.6429i | −1.12502 | − | 0.553844i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 30.8786 | 1.16627 | 0.583134 | − | 0.812376i | \(-0.301826\pi\) | ||||
0.583134 | + | 0.812376i | \(0.301826\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | − | 11.2713i | − | 0.425105i | ||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 4.14834 | − | 8.42648i | 0.156235 | − | 0.317360i | ||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 17.4762 | − | 10.0899i | 0.657259 | − | 0.379469i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −8.71948 | − | 5.03419i | −0.327467 | − | 0.189063i | 0.327249 | − | 0.944938i | \(-0.393878\pi\) |
−0.654716 | + | 0.755875i | \(0.727212\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −1.51652 | − | 11.3989i | −0.0568741 | − | 0.427494i | ||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −19.2657 | − | 11.1230i | −0.721506 | − | 0.416561i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −12.3236 | − | 21.3450i | −0.460875 | − | 0.798259i | ||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −41.7855 | + | 2.76740i | −1.56051 | + | 0.103350i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 2.52664 | 0.0942280 | 0.0471140 | − | 0.998890i | \(-0.484998\pi\) | ||||
0.0471140 | + | 0.998890i | \(0.484998\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 17.9148 | 0.667183 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 9.72322 | + | 14.5304i | 0.361610 | + | 0.540390i | ||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 1.96309 | + | 3.40017i | 0.0729072 | + | 0.126279i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 30.9471 | + | 17.8673i | 1.14776 | + | 0.662662i | 0.948341 | − | 0.317252i | \(-0.102760\pi\) |
0.199423 | + | 0.979914i | \(0.436093\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 24.9022 | − | 10.4345i | 0.922305 | − | 0.386462i | ||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −4.03299 | − | 2.32845i | −0.149165 | − | 0.0861207i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 3.78054 | − | 2.18269i | 0.139637 | − | 0.0806196i | −0.428554 | − | 0.903516i | \(-0.640977\pi\) |
0.568191 | + | 0.822897i | \(0.307643\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | −8.71059 | − | 13.0171i | −0.321295 | − | 0.480143i | ||||
\(736\) | 0 | 0 | ||||||||
\(737\) | − | 5.67614i | − | 0.209083i | ||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −40.4265 | −1.48711 | −0.743556 | − | 0.668674i | \(-0.766862\pi\) | ||||
−0.743556 | + | 0.668674i | \(0.766862\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 4.68298 | + | 70.7094i | 0.172034 | + | 2.59757i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 9.83837 | + | 17.0406i | 0.360935 | + | 0.625158i | 0.988115 | − | 0.153717i | \(-0.0491243\pi\) |
−0.627180 | + | 0.778874i | \(0.715791\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −15.0989 | + | 26.1520i | −0.553180 | + | 0.958136i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 5.12567 | + | 38.5270i | 0.187538 | + | 1.40963i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 3.19665 | − | 5.53676i | 0.116803 | − | 0.202309i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −26.3391 | + | 15.2069i | −0.961126 | + | 0.554906i | −0.896519 | − | 0.443005i | \(-0.853913\pi\) |
−0.0646065 | + | 0.997911i | \(0.520579\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −27.3858 | − | 13.4820i | −0.997994 | − | 0.491310i | ||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 17.8733i | 0.650477i | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | − | 5.71127i | − | 0.207580i | −0.994599 | − | 0.103790i | \(-0.966903\pi\) | ||
0.994599 | − | 0.103790i | \(-0.0330969\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 11.8265 | + | 5.82214i | 0.429274 | + | 0.211330i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −32.8500 | + | 18.9660i | −1.19081 | + | 0.687516i | −0.958491 | − | 0.285123i | \(-0.907966\pi\) |
−0.232322 | + | 0.972639i | \(0.574632\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −4.04920 | + | 7.01342i | −0.146591 | + | 0.253903i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −3.79128 | − | 1.56434i | −0.137074 | − | 0.0565590i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −6.47019 | + | 11.2067i | −0.233625 | + | 0.404651i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 20.7986 | + | 36.0243i | 0.750018 | + | 1.29907i | 0.947813 | + | 0.318826i | \(0.103289\pi\) |
−0.197795 | + | 0.980243i | \(0.563378\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −2.20712 | − | 33.3258i | −0.0794876 | − | 1.20020i | ||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −20.0762 | −0.722090 | −0.361045 | − | 0.932548i | \(-0.617580\pi\) | ||||
−0.361045 | + | 0.932548i | \(0.617580\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | − | 18.5898i | − | 0.667765i | ||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −1.85408 | − | 2.77073i | −0.0665146 | − | 0.0993993i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −48.1049 | + | 27.7734i | −1.72354 | + | 0.995085i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −28.2723 | − | 16.3230i | −1.01166 | − | 0.584083i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 2.54939 | − | 7.56106i | 0.0911077 | − | 0.270210i | ||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 23.9005 | + | 13.7990i | 0.853045 | + | 0.492506i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −4.62218 | − | 8.00585i | −0.164763 | − | 0.285378i | 0.771808 | − | 0.635855i | \(-0.219353\pi\) |
−0.936571 | + | 0.350478i | \(0.886019\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −1.75767 | − | 2.62666i | −0.0625748 | − | 0.0935116i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 0.331723 | 0.0117947 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 45.6088 | 1.61961 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −30.0710 | + | 1.99156i | −1.06651 | + | 0.0706334i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −5.18050 | − | 8.97288i | −0.183503 | − | 0.317836i | 0.759568 | − | 0.650428i | \(-0.225410\pi\) |
−0.943071 | + | 0.332592i | \(0.892077\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −2.62770 | − | 1.51710i | −0.0929613 | − | 0.0536713i | ||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 31.7068 | − | 24.3983i | 1.12030 | − | 0.862071i | ||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 10.6192 | + | 6.13102i | 0.374745 | + | 0.216359i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −4.56487 | + | 2.63553i | −0.160891 | + | 0.0928902i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −1.90366 | + | 3.86689i | −0.0670121 | + | 0.136121i | ||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 12.1122i | 0.425841i | 0.977070 | + | 0.212921i | \(0.0682976\pi\) | ||||
−0.977070 | + | 0.212921i | \(0.931702\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 43.7534 | 1.53639 | 0.768196 | − | 0.640215i | \(-0.221155\pi\) | ||||
0.768196 | + | 0.640215i | \(0.221155\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −12.4955 | − | 6.15150i | −0.438236 | − | 0.215743i | ||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 4.40955 | + | 7.63756i | 0.154460 | + | 0.267532i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −17.1823 | + | 29.7606i | −0.601133 | + | 1.04119i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 12.7825 | + | 16.6115i | 0.446658 | + | 0.580454i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 1.09747 | − | 1.90088i | 0.0383021 | − | 0.0663411i | −0.846239 | − | 0.532804i | \(-0.821138\pi\) |
0.884541 | + | 0.466463i | \(0.154472\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 11.3278 | − | 6.54013i | 0.394864 | − | 0.227975i | −0.289402 | − | 0.957208i | \(-0.593456\pi\) |
0.684265 | + | 0.729233i | \(0.260123\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0.727938 | + | 10.9913i | 0.0253436 | + | 0.382668i | ||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 5.42534i | 0.188658i | 0.995541 | + | 0.0943289i | \(0.0300705\pi\) | ||||
−0.995541 | + | 0.0943289i | \(0.969929\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | − | 1.91806i | − | 0.0666169i | −0.999445 | − | 0.0333085i | \(-0.989396\pi\) | ||
0.999445 | − | 0.0333085i | \(-0.0106044\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 7.11275 | − | 4.75961i | 0.246739 | − | 0.165109i | ||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −4.38199 | + | 2.52995i | −0.151827 | + | 0.0876574i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −18.1795 | + | 31.4878i | −0.629127 | + | 1.08968i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −28.3539 | + | 24.9686i | −0.980055 | + | 0.863040i | ||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 8.35203 | − | 14.4661i | 0.288344 | − | 0.499427i | −0.685071 | − | 0.728477i | \(-0.740229\pi\) |
0.973415 | + | 0.229050i | \(0.0735620\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 13.3209 | + | 23.0726i | 0.459343 | + | 0.795605i | ||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 20.6888 | − | 13.8442i | 0.712559 | − | 0.476820i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 42.4923 | 1.46178 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 5.30437i | 0.182260i | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 56.5625 | − | 3.74605i | 1.94122 | − | 0.128564i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 4.62738 | − | 2.67162i | 0.158625 | − | 0.0915820i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −38.1750 | − | 22.0403i | −1.30709 | − | 0.754646i | −0.325477 | − | 0.945550i | \(-0.605525\pi\) |
−0.981609 | + | 0.190904i | \(0.938858\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −11.5438 | + | 27.9770i | −0.394789 | + | 0.956795i | ||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −35.6626 | − | 20.5898i | −1.21821 | − | 0.703334i | −0.253676 | − | 0.967289i | \(-0.581640\pi\) |
−0.964535 | + | 0.263955i | \(0.914973\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 20.7385 | + | 35.9201i | 0.707587 | + | 1.22558i | 0.965750 | + | 0.259476i | \(0.0835498\pi\) |
−0.258162 | + | 0.966102i | \(0.583117\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −7.25663 | + | 14.7403i | −0.247305 | + | 0.502349i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −1.67319 | −0.0569560 | −0.0284780 | − | 0.999594i | \(-0.509066\pi\) | ||||
−0.0284780 | + | 0.999594i | \(0.509066\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −17.7952 | −0.605055 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 12.4199 | − | 25.2285i | 0.421802 | − | 0.856803i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −4.76732 | − | 8.25724i | −0.161720 | − | 0.280108i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 12.5275 | + | 7.23273i | 0.424477 | + | 0.245072i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −27.6725 | + | 3.68157i | −0.936572 | + | 0.124602i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −11.2745 | − | 6.50932i | −0.381147 | − | 0.220055i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 6.16758 | − | 3.56085i | 0.208264 | − | 0.120241i | −0.392240 | − | 0.919863i | \(-0.628300\pi\) |
0.600504 | + | 0.799621i | \(0.294966\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −9.26605 | + | 0.613678i | −0.312536 | + | 0.0206988i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | − | 24.8828i | − | 0.838323i | −0.907912 | − | 0.419162i | \(-0.862324\pi\) | ||
0.907912 | − | 0.419162i | \(-0.137676\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 13.2594 | 0.446213 | 0.223107 | − | 0.974794i | \(-0.428380\pi\) | ||||
0.223107 | + | 0.974794i | \(0.428380\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −4.59314 | + | 3.07357i | −0.154397 | + | 0.103317i | ||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −16.8122 | − | 29.1195i | −0.564497 | − | 0.977738i | −0.997096 | − | 0.0761517i | \(-0.975737\pi\) |
0.432599 | − | 0.901587i | \(-0.357597\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −10.2780 | + | 17.8020i | −0.344713 | + | 0.597060i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 15.7867 | − | 15.8731i | 0.528873 | − | 0.531767i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −11.1952 | + | 19.3906i | −0.374632 | + | 0.648882i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −14.4550 | + | 8.34557i | −0.483176 | + | 0.278962i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −27.9194 | + | 18.6827i | −0.932202 | + | 0.623798i | ||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 11.1653i | 0.372382i | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 9.73584i | 0.324348i | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0.671705 | + | 10.1422i | 0.0223529 | + | 0.337512i | ||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −7.77874 | + | 4.49106i | −0.258574 | + | 0.149288i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 10.7148 | − | 18.5585i | 0.355778 | − | 0.616226i | −0.631473 | − | 0.775398i | \(-0.717549\pi\) |
0.987251 | + | 0.159173i | \(0.0508826\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 54.4478 | − | 7.24378i | 1.80592 | − | 0.240261i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −14.6331 | + | 25.3452i | −0.484816 | + | 0.839725i | −0.999848 | − | 0.0174455i | \(-0.994447\pi\) |
0.515032 | + | 0.857171i | \(0.327780\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 16.1130 | + | 27.9085i | 0.533261 | + | 0.923636i | ||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 17.4759 | + | 8.60334i | 0.577735 | + | 0.284418i | ||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −9.87045 | −0.325951 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | − | 41.2334i | − | 1.36016i | −0.733136 | − | 0.680082i | \(-0.761944\pi\) | ||
0.733136 | − | 0.680082i | \(-0.238056\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −8.50107 | + | 17.2682i | −0.280120 | + | 0.569005i | ||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 72.0510 | − | 41.5987i | 2.37159 | − | 1.36924i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 3.86684 | + | 2.23252i | 0.127141 | + | 0.0734049i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 45.0762 | + | 18.5992i | 1.48050 | + | 0.610877i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −14.4159 | − | 8.32305i | −0.472972 | − | 0.273070i | 0.244511 | − | 0.969646i | \(-0.421373\pi\) |
−0.717483 | + | 0.696576i | \(0.754706\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 18.6692 | + | 32.3361i | 0.611860 | + | 1.05977i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 36.2563 | − | 2.40121i | 1.18698 | − | 0.0786120i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −3.40060 | −0.111212 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −6.27457 | −0.204981 | −0.102491 | − | 0.994734i | \(-0.532681\pi\) | ||||
−0.102491 | + | 0.994734i | \(0.532681\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 21.9005 | + | 32.7280i | 0.714695 | + | 1.06804i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −23.9585 | − | 41.4974i | −0.781025 | − | 1.35278i | −0.931345 | − | 0.364138i | \(-0.881364\pi\) |
0.150320 | − | 0.988637i | \(-0.451970\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −22.8045 | − | 13.1662i | −0.742616 | − | 0.428750i | ||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 1.76439 | + | 8.77625i | 0.0573954 | + | 0.285492i | ||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 15.0765 | + | 8.70441i | 0.489920 | + | 0.282855i | 0.724541 | − | 0.689232i | \(-0.242052\pi\) |
−0.234622 | + | 0.972087i | \(0.575385\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −27.0628 | + | 15.6247i | −0.878496 | + | 0.507200i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 28.1703 | + | 42.0976i | 0.913484 | + | 1.36511i | ||||
\(952\) | 0 | 0 | ||||||||
\(953\) | − | 4.44379i | − | 0.143948i | −0.997406 | − | 0.0719742i | \(-0.977070\pi\) | ||
0.997406 | − | 0.0719742i | \(-0.0229299\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −27.7430 | −0.897742 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −0.437209 | − | 6.60151i | −0.0141330 | − | 0.213397i | ||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −5.47138 | − | 9.47670i | −0.176680 | − | 0.306019i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 10.9329 | − | 18.9363i | 0.352673 | − | 0.610848i | ||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 13.7915 | − | 10.6125i | 0.444424 | − | 0.341983i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 16.5411 | − | 28.6501i | 0.532478 | − | 0.922278i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −30.2987 | + | 17.4930i | −0.974342 | + | 0.562536i | −0.900557 | − | 0.434738i | \(-0.856841\pi\) |
−0.0737845 | + | 0.997274i | \(0.523508\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 8.77190 | + | 4.31839i | 0.281794 | + | 0.138727i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 40.1769i | 1.28934i | 0.764461 | + | 0.644670i | \(0.223005\pi\) | ||||
−0.764461 | + | 0.644670i | \(0.776995\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | − | 2.14003i | − | 0.0686063i | ||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −25.1858 | − | 12.3989i | −0.806591 | − | 0.397083i | ||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 19.2404 | − | 11.1084i | 0.615554 | − | 0.355390i | −0.159582 | − | 0.987185i | \(-0.551015\pi\) |
0.775136 | + | 0.631794i | \(0.217681\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 16.5860 | − | 28.7277i | 0.530090 | − | 0.918143i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −17.4697 | + | 13.4429i | −0.557764 | + | 0.429198i | ||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −24.9905 | + | 43.2848i | −0.797073 | + | 1.38057i | 0.124441 | + | 0.992227i | \(0.460286\pi\) |
−0.921514 | + | 0.388344i | \(0.873047\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −4.31169 | − | 7.46807i | −0.137382 | − | 0.237952i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0.437650 | + | 6.60818i | 0.0139306 | + | 0.210341i | ||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −16.2908 | −0.518017 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 47.8498i | 1.52000i | 0.649925 | + | 0.759999i | \(0.274800\pi\) | ||||
−0.649925 | + | 0.759999i | \(0.725200\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −25.5721 | − | 38.2149i | −0.811506 | − | 1.21271i | ||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −9.34606 | + | 5.39595i | −0.296290 | + | 0.171063i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −4.23642 | − | 2.44590i | −0.134169 | − | 0.0774623i | 0.431413 | − | 0.902154i | \(-0.358015\pi\) |
−0.565582 | + | 0.824692i | \(0.691348\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −1.78855 | − | 8.89644i | −0.0565871 | − | 0.281471i |
(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 | 1152.2.p.g.191.8 | yes | 24 | |
3.2 | odd | 2 | 3456.2.p.g.575.4 | 24 | |||
4.3 | odd | 2 | 1152.2.p.f.191.5 | ✓ | 24 | ||
8.3 | odd | 2 | 1152.2.p.f.191.8 | yes | 24 | ||
8.5 | even | 2 | inner | 1152.2.p.g.191.5 | yes | 24 | |
9.4 | even | 3 | 3456.2.p.f.2879.9 | 24 | |||
9.5 | odd | 6 | 1152.2.p.f.959.8 | yes | 24 | ||
12.11 | even | 2 | 3456.2.p.f.575.4 | 24 | |||
24.5 | odd | 2 | 3456.2.p.g.575.9 | 24 | |||
24.11 | even | 2 | 3456.2.p.f.575.9 | 24 | |||
36.23 | even | 6 | inner | 1152.2.p.g.959.5 | yes | 24 | |
36.31 | odd | 6 | 3456.2.p.g.2879.9 | 24 | |||
72.5 | odd | 6 | 1152.2.p.f.959.5 | yes | 24 | ||
72.13 | even | 6 | 3456.2.p.f.2879.4 | 24 | |||
72.59 | even | 6 | inner | 1152.2.p.g.959.8 | yes | 24 | |
72.67 | odd | 6 | 3456.2.p.g.2879.4 | 24 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1152.2.p.f.191.5 | ✓ | 24 | 4.3 | odd | 2 | ||
1152.2.p.f.191.8 | yes | 24 | 8.3 | odd | 2 | ||
1152.2.p.f.959.5 | yes | 24 | 72.5 | odd | 6 | ||
1152.2.p.f.959.8 | yes | 24 | 9.5 | odd | 6 | ||
1152.2.p.g.191.5 | yes | 24 | 8.5 | even | 2 | inner | |
1152.2.p.g.191.8 | yes | 24 | 1.1 | even | 1 | trivial | |
1152.2.p.g.959.5 | yes | 24 | 36.23 | even | 6 | inner | |
1152.2.p.g.959.8 | yes | 24 | 72.59 | even | 6 | inner | |
3456.2.p.f.575.4 | 24 | 12.11 | even | 2 | |||
3456.2.p.f.575.9 | 24 | 24.11 | even | 2 | |||
3456.2.p.f.2879.4 | 24 | 72.13 | even | 6 | |||
3456.2.p.f.2879.9 | 24 | 9.4 | even | 3 | |||
3456.2.p.g.575.4 | 24 | 3.2 | odd | 2 | |||
3456.2.p.g.575.9 | 24 | 24.5 | odd | 2 | |||
3456.2.p.g.2879.4 | 24 | 72.67 | odd | 6 | |||
3456.2.p.g.2879.9 | 24 | 36.31 | odd | 6 |