Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [504,2,Mod(323,504)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(504, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1, 1, 1, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("504.323");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 504 = 2^{3} \cdot 3^{2} \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 504.j (of order \(2\), degree \(1\), 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: | \(4.02446026187\) |
Analytic rank: | \(0\) |
Dimension: | \(24\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 323.6 | ||
Character | \(\chi\) | \(=\) | 504.323 |
Dual form | 504.2.j.a.323.5 |
$q$-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 \(\left(\mathbb{Z}/504\mathbb{Z}\right)^\times\).
\(n\) | \(73\) | \(127\) | \(253\) | \(281\) |
\(\chi(n)\) | \(1\) | \(-1\) | \(-1\) | \(-1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −0.937511 | + | 1.05881i | −0.662920 | + | 0.748690i | ||||
\(3\) | 0 | 0 | ||||||||
\(4\) | −0.242146 | − | 1.98529i | −0.121073 | − | 0.992644i | ||||
\(5\) | −4.34020 | −1.94099 | −0.970497 | − | 0.241112i | \(-0.922488\pi\) | ||||
−0.970497 | + | 0.241112i | \(0.922488\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 1.00000i | 0.377964i | ||||||||
\(8\) | 2.32905 | + | 1.60484i | 0.823444 | + | 0.567398i | ||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 4.06898 | − | 4.59543i | 1.28673 | − | 1.45320i | ||||
\(11\) | 1.12627i | 0.339584i | 0.985480 | + | 0.169792i | \(0.0543096\pi\) | ||||
−0.985480 | + | 0.169792i | \(0.945690\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | − | 0.491523i | − | 0.136324i | −0.997674 | − | 0.0681620i | \(-0.978287\pi\) | ||
0.997674 | − | 0.0681620i | \(-0.0217135\pi\) | |||||||
\(14\) | −1.05881 | − | 0.937511i | −0.282978 | − | 0.250560i | ||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −3.88273 | + | 0.961458i | −0.970683 | + | 0.240365i | ||||
\(17\) | − | 5.96280i | − | 1.44619i | −0.690748 | − | 0.723096i | \(-0.742719\pi\) | ||
0.690748 | − | 0.723096i | \(-0.257281\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 2.34308 | 0.537539 | 0.268769 | − | 0.963205i | \(-0.413383\pi\) | ||||
0.268769 | + | 0.963205i | \(0.413383\pi\) | |||||||
\(20\) | 1.05096 | + | 8.61654i | 0.235002 | + | 1.92672i | ||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −1.19251 | − | 1.05589i | −0.254243 | − | 0.225117i | ||||
\(23\) | 6.68189 | 1.39327 | 0.696636 | − | 0.717425i | \(-0.254679\pi\) | ||||
0.696636 | + | 0.717425i | \(0.254679\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 13.8373 | 2.76746 | ||||||||
\(26\) | 0.520429 | + | 0.460809i | 0.102064 | + | 0.0903720i | ||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 1.98529 | − | 0.242146i | 0.375184 | − | 0.0457613i | ||||
\(29\) | 4.70295 | 0.873315 | 0.436658 | − | 0.899628i | \(-0.356162\pi\) | ||||
0.436658 | + | 0.899628i | \(0.356162\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | − | 8.07383i | − | 1.45010i | −0.688694 | − | 0.725052i | \(-0.741816\pi\) | ||
0.688694 | − | 0.725052i | \(-0.258184\pi\) | |||||||
\(32\) | 2.62210 | − | 5.01244i | 0.463527 | − | 0.886083i | ||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 6.31346 | + | 5.59019i | 1.08275 | + | 0.958710i | ||||
\(35\) | − | 4.34020i | − | 0.733627i | ||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 0.750286i | 0.123346i | 0.998096 | + | 0.0616731i | \(0.0196436\pi\) | ||||
−0.998096 | + | 0.0616731i | \(0.980356\pi\) | |||||||
\(38\) | −2.19666 | + | 2.48087i | −0.356345 | + | 0.402450i | ||||
\(39\) | 0 | 0 | ||||||||
\(40\) | −10.1085 | − | 6.96533i | −1.59830 | − | 1.10132i | ||||
\(41\) | 3.41271i | 0.532976i | 0.963838 | + | 0.266488i | \(0.0858633\pi\) | ||||
−0.963838 | + | 0.266488i | \(0.914137\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −7.30336 | −1.11375 | −0.556876 | − | 0.830595i | \(-0.688000\pi\) | ||||
−0.556876 | + | 0.830595i | \(0.688000\pi\) | |||||||
\(44\) | 2.23598 | − | 0.272723i | 0.337086 | − | 0.0411145i | ||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −6.26435 | + | 7.07484i | −0.923628 | + | 1.04313i | ||||
\(47\) | 9.47430 | 1.38197 | 0.690984 | − | 0.722870i | \(-0.257177\pi\) | ||||
0.690984 | + | 0.722870i | \(0.257177\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −1.00000 | −0.142857 | ||||||||
\(50\) | −12.9726 | + | 14.6510i | −1.83461 | + | 2.07197i | ||||
\(51\) | 0 | 0 | ||||||||
\(52\) | −0.975815 | + | 0.119020i | −0.135321 | + | 0.0165052i | ||||
\(53\) | −3.12323 | −0.429008 | −0.214504 | − | 0.976723i | \(-0.568814\pi\) | ||||
−0.214504 | + | 0.976723i | \(0.568814\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | − | 4.88825i | − | 0.659132i | ||||||
\(56\) | −1.60484 | + | 2.32905i | −0.214456 | + | 0.311233i | ||||
\(57\) | 0 | 0 | ||||||||
\(58\) | −4.40906 | + | 4.97951i | −0.578938 | + | 0.653842i | ||||
\(59\) | − | 9.47430i | − | 1.23345i | −0.787179 | − | 0.616724i | \(-0.788459\pi\) | ||
0.787179 | − | 0.616724i | \(-0.211541\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 1.64644i | 0.210805i | 0.994430 | + | 0.105403i | \(0.0336131\pi\) | ||||
−0.994430 | + | 0.105403i | \(0.966387\pi\) | |||||||
\(62\) | 8.54863 | + | 7.56931i | 1.08568 | + | 0.961303i | ||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 2.84896 | + | 7.47552i | 0.356120 | + | 0.934440i | ||||
\(65\) | 2.13331i | 0.264604i | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 9.48557 | 1.15885 | 0.579423 | − | 0.815027i | \(-0.303278\pi\) | ||||
0.579423 | + | 0.815027i | \(0.303278\pi\) | |||||||
\(68\) | −11.8379 | + | 1.44387i | −1.43555 | + | 0.175095i | ||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 4.59543 | + | 4.06898i | 0.549259 | + | 0.486336i | ||||
\(71\) | −9.14438 | −1.08524 | −0.542619 | − | 0.839979i | \(-0.682567\pi\) | ||||
−0.542619 | + | 0.839979i | \(0.682567\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 2.65767 | 0.311057 | 0.155529 | − | 0.987831i | \(-0.450292\pi\) | ||||
0.155529 | + | 0.987831i | \(0.450292\pi\) | |||||||
\(74\) | −0.794408 | − | 0.703401i | −0.0923480 | − | 0.0817687i | ||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −0.567367 | − | 4.65168i | −0.0650814 | − | 0.533585i | ||||
\(77\) | −1.12627 | −0.128351 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 5.74652i | 0.646534i | 0.946308 | + | 0.323267i | \(0.104781\pi\) | ||||
−0.946308 | + | 0.323267i | \(0.895219\pi\) | |||||||
\(80\) | 16.8518 | − | 4.17292i | 1.88409 | − | 0.466546i | ||||
\(81\) | 0 | 0 | ||||||||
\(82\) | −3.61340 | − | 3.19946i | −0.399034 | − | 0.353321i | ||||
\(83\) | − | 12.8786i | − | 1.41361i | −0.707408 | − | 0.706805i | \(-0.750136\pi\) | ||
0.707408 | − | 0.706805i | \(-0.249864\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 25.8797i | 2.80705i | ||||||||
\(86\) | 6.84698 | − | 7.73285i | 0.738329 | − | 0.833855i | ||||
\(87\) | 0 | 0 | ||||||||
\(88\) | −1.80749 | + | 2.62315i | −0.192679 | + | 0.279629i | ||||
\(89\) | 12.9777i | 1.37563i | 0.725884 | + | 0.687817i | \(0.241431\pi\) | ||||
−0.725884 | + | 0.687817i | \(0.758569\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 0.491523 | 0.0515257 | ||||||||
\(92\) | −1.61799 | − | 13.2655i | −0.168687 | − | 1.38302i | ||||
\(93\) | 0 | 0 | ||||||||
\(94\) | −8.88226 | + | 10.0315i | −0.916135 | + | 1.03467i | ||||
\(95\) | −10.1694 | −1.04336 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −7.51246 | −0.762775 | −0.381387 | − | 0.924415i | \(-0.624554\pi\) | ||||
−0.381387 | + | 0.924415i | \(0.624554\pi\) | |||||||
\(98\) | 0.937511 | − | 1.05881i | 0.0947029 | − | 0.106956i | ||||
\(99\) | 0 | 0 | ||||||||
\(100\) | −3.35065 | − | 27.4710i | −0.335065 | − | 2.74710i | ||||
\(101\) | 12.2496 | 1.21888 | 0.609440 | − | 0.792832i | \(-0.291394\pi\) | ||||
0.609440 | + | 0.792832i | \(0.291394\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | − | 4.29883i | − | 0.423577i | −0.977316 | − | 0.211788i | \(-0.932071\pi\) | ||
0.977316 | − | 0.211788i | \(-0.0679288\pi\) | |||||||
\(104\) | 0.788818 | − | 1.14478i | 0.0773500 | − | 0.112255i | ||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 2.92806 | − | 3.30690i | 0.284398 | − | 0.321194i | ||||
\(107\) | − | 18.4871i | − | 1.78721i | −0.448853 | − | 0.893606i | \(-0.648167\pi\) | ||
0.448853 | − | 0.893606i | \(-0.351833\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 8.41691i | 0.806194i | 0.915157 | + | 0.403097i | \(0.132066\pi\) | ||||
−0.915157 | + | 0.403097i | \(0.867934\pi\) | |||||||
\(110\) | 5.17572 | + | 4.58279i | 0.493485 | + | 0.436952i | ||||
\(111\) | 0 | 0 | ||||||||
\(112\) | −0.961458 | − | 3.88273i | −0.0908493 | − | 0.366884i | ||||
\(113\) | − | 14.1717i | − | 1.33317i | −0.745431 | − | 0.666583i | \(-0.767756\pi\) | ||
0.745431 | − | 0.666583i | \(-0.232244\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −29.0007 | −2.70433 | ||||||||
\(116\) | −1.13880 | − | 9.33670i | −0.105735 | − | 0.866891i | ||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 10.0315 | + | 8.88226i | 0.923470 | + | 0.817678i | ||||
\(119\) | 5.96280 | 0.546609 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 9.73151 | 0.884682 | ||||||||
\(122\) | −1.74326 | − | 1.54356i | −0.157828 | − | 0.139747i | ||||
\(123\) | 0 | 0 | ||||||||
\(124\) | −16.0289 | + | 1.95505i | −1.43944 | + | 0.175568i | ||||
\(125\) | −38.3556 | −3.43063 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | − | 17.0394i | − | 1.51200i | −0.654570 | − | 0.756001i | \(-0.727150\pi\) | ||
0.654570 | − | 0.756001i | \(-0.272850\pi\) | |||||||
\(128\) | −10.5861 | − | 3.99189i | −0.935685 | − | 0.352836i | ||||
\(129\) | 0 | 0 | ||||||||
\(130\) | −2.25876 | − | 2.00000i | −0.198107 | − | 0.175412i | ||||
\(131\) | 4.87851i | 0.426237i | 0.977026 | + | 0.213119i | \(0.0683621\pi\) | ||||
−0.977026 | + | 0.213119i | \(0.931638\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 2.34308i | 0.203171i | ||||||||
\(134\) | −8.89283 | + | 10.0434i | −0.768223 | + | 0.867617i | ||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 9.56936 | − | 13.8877i | 0.820566 | − | 1.19086i | ||||
\(137\) | 10.0039i | 0.854692i | 0.904088 | + | 0.427346i | \(0.140551\pi\) | ||||
−0.904088 | + | 0.427346i | \(0.859449\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 3.60637 | 0.305888 | 0.152944 | − | 0.988235i | \(-0.451125\pi\) | ||||
0.152944 | + | 0.988235i | \(0.451125\pi\) | |||||||
\(140\) | −8.61654 | + | 1.05096i | −0.728230 | + | 0.0888224i | ||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 8.57295 | − | 9.68213i | 0.719426 | − | 0.812507i | ||||
\(143\) | 0.553590 | 0.0462935 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −20.4117 | −1.69510 | ||||||||
\(146\) | −2.49160 | + | 2.81396i | −0.206206 | + | 0.232885i | ||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 1.48953 | − | 0.181679i | 0.122439 | − | 0.0149339i | ||||
\(149\) | 8.87078 | 0.726722 | 0.363361 | − | 0.931648i | \(-0.381629\pi\) | ||||
0.363361 | + | 0.931648i | \(0.381629\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 0.393631i | 0.0320333i | 0.999872 | + | 0.0160166i | \(0.00509847\pi\) | ||||
−0.999872 | + | 0.0160166i | \(0.994902\pi\) | |||||||
\(152\) | 5.45715 | + | 3.76027i | 0.442633 | + | 0.304998i | ||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 1.05589 | − | 1.19251i | 0.0850864 | − | 0.0960950i | ||||
\(155\) | 35.0420i | 2.81464i | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | − | 12.8320i | − | 1.02411i | −0.858954 | − | 0.512054i | \(-0.828885\pi\) | ||
0.858954 | − | 0.512054i | \(-0.171115\pi\) | |||||||
\(158\) | −6.08445 | − | 5.38742i | −0.484053 | − | 0.428600i | ||||
\(159\) | 0 | 0 | ||||||||
\(160\) | −11.3804 | + | 21.7550i | −0.899703 | + | 1.71988i | ||||
\(161\) | 6.68189i | 0.526607i | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −7.51948 | −0.588971 | −0.294485 | − | 0.955656i | \(-0.595148\pi\) | ||||
−0.294485 | + | 0.955656i | \(0.595148\pi\) | |||||||
\(164\) | 6.77521 | − | 0.826374i | 0.529055 | − | 0.0645290i | ||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 13.6360 | + | 12.0738i | 1.05836 | + | 0.937111i | ||||
\(167\) | −4.30627 | −0.333229 | −0.166615 | − | 0.986022i | \(-0.553284\pi\) | ||||
−0.166615 | + | 0.986022i | \(0.553284\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 12.7584 | 0.981416 | ||||||||
\(170\) | −27.4016 | − | 24.2625i | −2.10161 | − | 1.86085i | ||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 1.76848 | + | 14.4993i | 0.134845 | + | 1.10556i | ||||
\(173\) | −8.33156 | −0.633437 | −0.316718 | − | 0.948520i | \(-0.602581\pi\) | ||||
−0.316718 | + | 0.948520i | \(0.602581\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 13.8373i | 1.04600i | ||||||||
\(176\) | −1.08287 | − | 4.37302i | −0.0816240 | − | 0.329629i | ||||
\(177\) | 0 | 0 | ||||||||
\(178\) | −13.7409 | − | 12.1667i | −1.02992 | − | 0.911936i | ||||
\(179\) | − | 4.40770i | − | 0.329447i | −0.986340 | − | 0.164723i | \(-0.947327\pi\) | ||
0.986340 | − | 0.164723i | \(-0.0526731\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | − | 14.3110i | − | 1.06373i | −0.846830 | − | 0.531864i | \(-0.821492\pi\) | ||
0.846830 | − | 0.531864i | \(-0.178508\pi\) | |||||||
\(182\) | −0.460809 | + | 0.520429i | −0.0341574 | + | 0.0385767i | ||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 15.5625 | + | 10.7234i | 1.14728 | + | 0.790539i | ||||
\(185\) | − | 3.25639i | − | 0.239414i | ||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 6.71575 | 0.491104 | ||||||||
\(188\) | −2.29416 | − | 18.8092i | −0.167319 | − | 1.37180i | ||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 9.53394 | − | 10.7675i | 0.691665 | − | 0.781153i | ||||
\(191\) | 11.5050 | 0.832471 | 0.416236 | − | 0.909257i | \(-0.363349\pi\) | ||||
0.416236 | + | 0.909257i | \(0.363349\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 0.0619465 | 0.00445901 | 0.00222950 | − | 0.999998i | \(-0.499290\pi\) | ||||
0.00222950 | + | 0.999998i | \(0.499290\pi\) | |||||||
\(194\) | 7.04301 | − | 7.95425i | 0.505659 | − | 0.571082i | ||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0.242146 | + | 1.98529i | 0.0172961 | + | 0.141806i | ||||
\(197\) | 15.0637 | 1.07324 | 0.536620 | − | 0.843824i | \(-0.319701\pi\) | ||||
0.536620 | + | 0.843824i | \(0.319701\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | − | 9.80891i | − | 0.695335i | −0.937618 | − | 0.347667i | \(-0.886974\pi\) | ||
0.937618 | − | 0.347667i | \(-0.113026\pi\) | |||||||
\(200\) | 32.2278 | + | 22.2067i | 2.27885 | + | 1.57025i | ||||
\(201\) | 0 | 0 | ||||||||
\(202\) | −11.4841 | + | 12.9700i | −0.808021 | + | 0.912564i | ||||
\(203\) | 4.70295i | 0.330082i | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | − | 14.8118i | − | 1.03450i | ||||||
\(206\) | 4.55164 | + | 4.03021i | 0.317128 | + | 0.280798i | ||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0.472579 | + | 1.90845i | 0.0327675 | + | 0.132327i | ||||
\(209\) | 2.63895i | 0.182540i | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 7.17510 | 0.493954 | 0.246977 | − | 0.969021i | \(-0.420563\pi\) | ||||
0.246977 | + | 0.969021i | \(0.420563\pi\) | |||||||
\(212\) | 0.756277 | + | 6.20050i | 0.0519413 | + | 0.425852i | ||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 19.5742 | + | 17.3318i | 1.33807 | + | 1.18478i | ||||
\(215\) | 31.6980 | 2.16179 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 8.07383 | 0.548088 | ||||||||
\(218\) | −8.91189 | − | 7.89095i | −0.603589 | − | 0.534442i | ||||
\(219\) | 0 | 0 | ||||||||
\(220\) | −9.70458 | + | 1.18367i | −0.654283 | + | 0.0798030i | ||||
\(221\) | −2.93086 | −0.197151 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 2.06283i | 0.138138i | 0.997612 | + | 0.0690688i | \(0.0220028\pi\) | ||||
−0.997612 | + | 0.0690688i | \(0.977997\pi\) | |||||||
\(224\) | 5.01244 | + | 2.62210i | 0.334908 | + | 0.175197i | ||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 15.0051 | + | 13.2862i | 0.998127 | + | 0.883783i | ||||
\(227\) | 20.5663i | 1.36504i | 0.730869 | + | 0.682518i | \(0.239115\pi\) | ||||
−0.730869 | + | 0.682518i | \(0.760885\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 14.9296i | 0.986577i | 0.869866 | + | 0.493289i | \(0.164205\pi\) | ||||
−0.869866 | + | 0.493289i | \(0.835795\pi\) | |||||||
\(230\) | 27.1885 | − | 30.7062i | 1.79276 | − | 2.02471i | ||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 10.9534 | + | 7.54749i | 0.719126 | + | 0.495517i | ||||
\(233\) | 14.3687i | 0.941324i | 0.882314 | + | 0.470662i | \(0.155985\pi\) | ||||
−0.882314 | + | 0.470662i | \(0.844015\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −41.1203 | −2.68239 | ||||||||
\(236\) | −18.8092 | + | 2.29416i | −1.22437 | + | 0.149337i | ||||
\(237\) | 0 | 0 | ||||||||
\(238\) | −5.59019 | + | 6.31346i | −0.362358 | + | 0.409241i | ||||
\(239\) | 16.3432 | 1.05715 | 0.528577 | − | 0.848885i | \(-0.322726\pi\) | ||||
0.528577 | + | 0.848885i | \(0.322726\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 0.456020 | 0.0293748 | 0.0146874 | − | 0.999892i | \(-0.495325\pi\) | ||||
0.0146874 | + | 0.999892i | \(0.495325\pi\) | |||||||
\(242\) | −9.12340 | + | 10.3038i | −0.586474 | + | 0.662353i | ||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 3.26866 | − | 0.398679i | 0.209254 | − | 0.0255228i | ||||
\(245\) | 4.34020 | 0.277285 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | − | 1.15168i | − | 0.0732795i | ||||||
\(248\) | 12.9572 | − | 18.8044i | 0.822785 | − | 1.19408i | ||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 35.9588 | − | 40.6112i | 2.27424 | − | 2.56848i | ||||
\(251\) | 21.9739i | 1.38698i | 0.720465 | + | 0.693491i | \(0.243928\pi\) | ||||
−0.720465 | + | 0.693491i | \(0.756072\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 7.52564i | 0.473133i | ||||||||
\(254\) | 18.0414 | + | 15.9746i | 1.13202 | + | 1.00234i | ||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 14.1512 | − | 7.46617i | 0.884450 | − | 0.466635i | ||||
\(257\) | − | 13.7264i | − | 0.856230i | −0.903724 | − | 0.428115i | \(-0.859178\pi\) | ||
0.903724 | − | 0.428115i | \(-0.140822\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −0.750286 | −0.0466205 | ||||||||
\(260\) | 4.23523 | − | 0.516572i | 0.262658 | − | 0.0320364i | ||||
\(261\) | 0 | 0 | ||||||||
\(262\) | −5.16540 | − | 4.57365i | −0.319119 | − | 0.282561i | ||||
\(263\) | −28.3093 | −1.74563 | −0.872813 | − | 0.488055i | \(-0.837707\pi\) | ||||
−0.872813 | + | 0.488055i | \(0.837707\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 13.5554 | 0.832703 | ||||||||
\(266\) | −2.48087 | − | 2.19666i | −0.152112 | − | 0.134686i | ||||
\(267\) | 0 | 0 | ||||||||
\(268\) | −2.29689 | − | 18.8316i | −0.140305 | − | 1.15032i | ||||
\(269\) | −6.38645 | −0.389389 | −0.194694 | − | 0.980864i | \(-0.562372\pi\) | ||||
−0.194694 | + | 0.980864i | \(0.562372\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | − | 4.63869i | − | 0.281780i | −0.990025 | − | 0.140890i | \(-0.955004\pi\) | ||
0.990025 | − | 0.140890i | \(-0.0449965\pi\) | |||||||
\(272\) | 5.73298 | + | 23.1519i | 0.347613 | + | 1.40379i | ||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −10.5922 | − | 9.37878i | −0.639899 | − | 0.566593i | ||||
\(275\) | 15.5846i | 0.939786i | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | − | 22.9701i | − | 1.38014i | −0.723744 | − | 0.690069i | \(-0.757580\pi\) | ||
0.723744 | − | 0.690069i | \(-0.242420\pi\) | |||||||
\(278\) | −3.38101 | + | 3.81845i | −0.202780 | + | 0.229015i | ||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 6.96533 | − | 10.1085i | 0.416258 | − | 0.604101i | ||||
\(281\) | 13.1528i | 0.784630i | 0.919831 | + | 0.392315i | \(0.128326\pi\) | ||||
−0.919831 | + | 0.392315i | \(0.871674\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 29.1290 | 1.73154 | 0.865769 | − | 0.500443i | \(-0.166830\pi\) | ||||
0.865769 | + | 0.500443i | \(0.166830\pi\) | |||||||
\(284\) | 2.21427 | + | 18.1542i | 0.131393 | + | 1.07725i | ||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −0.518997 | + | 0.586145i | −0.0306889 | + | 0.0346595i | ||||
\(287\) | −3.41271 | −0.201446 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −18.5550 | −1.09147 | ||||||||
\(290\) | 19.1362 | − | 21.6121i | 1.12372 | − | 1.26910i | ||||
\(291\) | 0 | 0 | ||||||||
\(292\) | −0.643545 | − | 5.27624i | −0.0376606 | − | 0.308769i | ||||
\(293\) | −0.874951 | −0.0511152 | −0.0255576 | − | 0.999673i | \(-0.508136\pi\) | ||||
−0.0255576 | + | 0.999673i | \(0.508136\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 41.1203i | 2.39412i | ||||||||
\(296\) | −1.20409 | + | 1.74745i | −0.0699863 | + | 0.101569i | ||||
\(297\) | 0 | 0 | ||||||||
\(298\) | −8.31645 | + | 9.39244i | −0.481759 | + | 0.544090i | ||||
\(299\) | − | 3.28431i | − | 0.189936i | ||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | − | 7.30336i | − | 0.420959i | ||||||
\(302\) | −0.416780 | − | 0.369034i | −0.0239830 | − | 0.0212355i | ||||
\(303\) | 0 | 0 | ||||||||
\(304\) | −9.09754 | + | 2.25277i | −0.521780 | + | 0.129205i | ||||
\(305\) | − | 7.14588i | − | 0.409172i | ||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 17.0895 | 0.975350 | 0.487675 | − | 0.873025i | \(-0.337845\pi\) | ||||
0.487675 | + | 0.873025i | \(0.337845\pi\) | |||||||
\(308\) | 0.272723 | + | 2.23598i | 0.0155398 | + | 0.127407i | ||||
\(309\) | 0 | 0 | ||||||||
\(310\) | −37.1028 | − | 32.8523i | −2.10729 | − | 1.86588i | ||||
\(311\) | −20.9397 | −1.18738 | −0.593692 | − | 0.804692i | \(-0.702330\pi\) | ||||
−0.593692 | + | 0.804692i | \(0.702330\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −26.3947 | −1.49191 | −0.745957 | − | 0.665994i | \(-0.768008\pi\) | ||||
−0.745957 | + | 0.665994i | \(0.768008\pi\) | |||||||
\(314\) | 13.5866 | + | 12.0302i | 0.766739 | + | 0.678902i | ||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 11.4085 | − | 1.39150i | 0.641778 | − | 0.0782777i | ||||
\(317\) | 23.9039 | 1.34258 | 0.671288 | − | 0.741197i | \(-0.265741\pi\) | ||||
0.671288 | + | 0.741197i | \(0.265741\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 5.29681i | 0.296564i | ||||||||
\(320\) | −12.3650 | − | 32.4452i | −0.691227 | − | 1.81374i | ||||
\(321\) | 0 | 0 | ||||||||
\(322\) | −7.07484 | − | 6.26435i | −0.394265 | − | 0.349099i | ||||
\(323\) | − | 13.9713i | − | 0.777384i | ||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | − | 6.80136i | − | 0.377272i | ||||||
\(326\) | 7.04959 | − | 7.96168i | 0.390441 | − | 0.440957i | ||||
\(327\) | 0 | 0 | ||||||||
\(328\) | −5.47687 | + | 7.94838i | −0.302409 | + | 0.438876i | ||||
\(329\) | 9.47430i | 0.522335i | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −15.8718 | −0.872394 | −0.436197 | − | 0.899851i | \(-0.643675\pi\) | ||||
−0.436197 | + | 0.899851i | \(0.643675\pi\) | |||||||
\(332\) | −25.5677 | + | 3.11850i | −1.40321 | + | 0.171150i | ||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 4.03718 | − | 4.55951i | 0.220904 | − | 0.249485i | ||||
\(335\) | −41.1692 | −2.24932 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −8.80926 | −0.479871 | −0.239936 | − | 0.970789i | \(-0.577126\pi\) | ||||
−0.239936 | + | 0.970789i | \(0.577126\pi\) | |||||||
\(338\) | −11.9611 | + | 13.5087i | −0.650601 | + | 0.734776i | ||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 51.3787 | − | 6.26667i | 2.78640 | − | 0.339858i | ||||
\(341\) | 9.09335 | 0.492432 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | − | 1.00000i | − | 0.0539949i | ||||||
\(344\) | −17.0099 | − | 11.7208i | −0.917113 | − | 0.631941i | ||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 7.81093 | − | 8.82152i | 0.419918 | − | 0.474248i | ||||
\(347\) | − | 18.5105i | − | 0.993697i | −0.867837 | − | 0.496849i | \(-0.834490\pi\) | ||
0.867837 | − | 0.496849i | \(-0.165510\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | − | 3.03971i | − | 0.162712i | −0.996685 | − | 0.0813561i | \(-0.974075\pi\) | ||
0.996685 | − | 0.0813561i | \(-0.0259251\pi\) | |||||||
\(350\) | −14.6510 | − | 12.9726i | −0.783131 | − | 0.693416i | ||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 5.64538 | + | 2.95321i | 0.300900 | + | 0.157407i | ||||
\(353\) | 17.0150i | 0.905616i | 0.891608 | + | 0.452808i | \(0.149578\pi\) | ||||
−0.891608 | + | 0.452808i | \(0.850422\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 39.6884 | 2.10644 | ||||||||
\(356\) | 25.7645 | − | 3.14250i | 1.36551 | − | 0.166552i | ||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 4.66690 | + | 4.13227i | 0.246653 | + | 0.218397i | ||||
\(359\) | 10.7746 | 0.568661 | 0.284331 | − | 0.958726i | \(-0.408229\pi\) | ||||
0.284331 | + | 0.958726i | \(0.408229\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −13.5100 | −0.711052 | ||||||||
\(362\) | 15.1526 | + | 13.4167i | 0.796402 | + | 0.705167i | ||||
\(363\) | 0 | 0 | ||||||||
\(364\) | −0.119020 | − | 0.975815i | −0.00623836 | − | 0.0511466i | ||||
\(365\) | −11.5348 | −0.603760 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | − | 6.78051i | − | 0.353940i | −0.984216 | − | 0.176970i | \(-0.943370\pi\) | ||
0.984216 | − | 0.176970i | \(-0.0566295\pi\) | |||||||
\(368\) | −25.9440 | + | 6.42436i | −1.35242 | + | 0.334893i | ||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 3.44789 | + | 3.05290i | 0.179247 | + | 0.158713i | ||||
\(371\) | − | 3.12323i | − | 0.162150i | ||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 18.6952i | 0.968001i | 0.875068 | + | 0.484001i | \(0.160817\pi\) | ||||
−0.875068 | + | 0.484001i | \(0.839183\pi\) | |||||||
\(374\) | −6.29609 | + | 7.11068i | −0.325563 | + | 0.367685i | ||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 22.0661 | + | 15.2048i | 1.13797 | + | 0.784126i | ||||
\(377\) | − | 2.31161i | − | 0.119054i | ||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 28.5414 | 1.46607 | 0.733036 | − | 0.680190i | \(-0.238103\pi\) | ||||
0.733036 | + | 0.680190i | \(0.238103\pi\) | |||||||
\(380\) | 2.46248 | + | 20.1892i | 0.126323 | + | 1.03568i | ||||
\(381\) | 0 | 0 | ||||||||
\(382\) | −10.7861 | + | 12.1816i | −0.551862 | + | 0.623263i | ||||
\(383\) | −9.88924 | −0.505317 | −0.252658 | − | 0.967556i | \(-0.581305\pi\) | ||||
−0.252658 | + | 0.967556i | \(0.581305\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 4.88825 | 0.249128 | ||||||||
\(386\) | −0.0580756 | + | 0.0655895i | −0.00295597 | + | 0.00333842i | ||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 1.81911 | + | 14.9144i | 0.0923514 | + | 0.757163i | ||||
\(389\) | 10.5873 | 0.536798 | 0.268399 | − | 0.963308i | \(-0.413505\pi\) | ||||
0.268399 | + | 0.963308i | \(0.413505\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | − | 39.8428i | − | 2.01494i | ||||||
\(392\) | −2.32905 | − | 1.60484i | −0.117635 | − | 0.0810568i | ||||
\(393\) | 0 | 0 | ||||||||
\(394\) | −14.1223 | + | 15.9495i | −0.711473 | + | 0.803524i | ||||
\(395\) | − | 24.9410i | − | 1.25492i | ||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 11.8639i | 0.595432i | 0.954654 | + | 0.297716i | \(0.0962249\pi\) | ||||
−0.954654 | + | 0.297716i | \(0.903775\pi\) | |||||||
\(398\) | 10.3857 | + | 9.19596i | 0.520590 | + | 0.460952i | ||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −53.7265 | + | 13.3040i | −2.68633 | + | 0.665199i | ||||
\(401\) | 12.2757i | 0.613017i | 0.951868 | + | 0.306509i | \(0.0991608\pi\) | ||||
−0.951868 | + | 0.306509i | \(0.900839\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −3.96848 | −0.197684 | ||||||||
\(404\) | −2.96619 | − | 24.3190i | −0.147573 | − | 1.20991i | ||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −4.97951 | − | 4.40906i | −0.247129 | − | 0.218818i | ||||
\(407\) | −0.845027 | −0.0418864 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 1.87041 | 0.0924858 | 0.0462429 | − | 0.998930i | \(-0.485275\pi\) | ||||
0.0462429 | + | 0.998930i | \(0.485275\pi\) | |||||||
\(410\) | 15.6829 | + | 13.8863i | 0.774522 | + | 0.685794i | ||||
\(411\) | 0 | 0 | ||||||||
\(412\) | −8.53442 | + | 1.04095i | −0.420461 | + | 0.0512837i | ||||
\(413\) | 9.47430 | 0.466200 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 55.8957i | 2.74381i | ||||||||
\(416\) | −2.46373 | − | 1.28883i | −0.120794 | − | 0.0631899i | ||||
\(417\) | 0 | 0 | ||||||||
\(418\) | −2.79414 | − | 2.47404i | −0.136666 | − | 0.121009i | ||||
\(419\) | 4.70969i | 0.230083i | 0.993361 | + | 0.115042i | \(0.0367001\pi\) | ||||
−0.993361 | + | 0.115042i | \(0.963300\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 3.21062i | 0.156476i | 0.996935 | + | 0.0782381i | \(0.0249294\pi\) | ||||
−0.996935 | + | 0.0782381i | \(0.975071\pi\) | |||||||
\(422\) | −6.72674 | + | 7.59705i | −0.327452 | + | 0.369819i | ||||
\(423\) | 0 | 0 | ||||||||
\(424\) | −7.27416 | − | 5.01229i | −0.353264 | − | 0.243418i | ||||
\(425\) | − | 82.5091i | − | 4.00228i | ||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −1.64644 | −0.0796769 | ||||||||
\(428\) | −36.7021 | + | 4.47656i | −1.77406 | + | 0.216383i | ||||
\(429\) | 0 | 0 | ||||||||
\(430\) | −29.7173 | + | 33.5621i | −1.43309 | + | 1.61851i | ||||
\(431\) | −0.126718 | −0.00610381 | −0.00305190 | − | 0.999995i | \(-0.500971\pi\) | ||||
−0.00305190 | + | 0.999995i | \(0.500971\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −1.28232 | −0.0616245 | −0.0308123 | − | 0.999525i | \(-0.509809\pi\) | ||||
−0.0308123 | + | 0.999525i | \(0.509809\pi\) | |||||||
\(434\) | −7.56931 | + | 8.54863i | −0.363338 | + | 0.410348i | ||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 16.7100 | − | 2.03812i | 0.800263 | − | 0.0976083i | ||||
\(437\) | 15.6562 | 0.748937 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | − | 27.9888i | − | 1.33583i | −0.744236 | − | 0.667917i | \(-0.767186\pi\) | ||
0.744236 | − | 0.667917i | \(-0.232814\pi\) | |||||||
\(440\) | 7.84487 | − | 11.3850i | 0.373990 | − | 0.542758i | ||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 2.74771 | − | 3.10321i | 0.130695 | − | 0.147605i | ||||
\(443\) | − | 3.08184i | − | 0.146422i | −0.997316 | − | 0.0732112i | \(-0.976675\pi\) | ||
0.997316 | − | 0.0732112i | \(-0.0233247\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | − | 56.3258i | − | 2.67010i | ||||||
\(446\) | −2.18414 | − | 1.93393i | −0.103422 | − | 0.0915742i | ||||
\(447\) | 0 | 0 | ||||||||
\(448\) | −7.47552 | + | 2.84896i | −0.353185 | + | 0.134601i | ||||
\(449\) | − | 9.63488i | − | 0.454698i | −0.973813 | − | 0.227349i | \(-0.926994\pi\) | ||
0.973813 | − | 0.227349i | \(-0.0730058\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −3.84365 | −0.180990 | ||||||||
\(452\) | −28.1350 | + | 3.43163i | −1.32336 | + | 0.161410i | ||||
\(453\) | 0 | 0 | ||||||||
\(454\) | −21.7758 | − | 19.2812i | −1.02199 | − | 0.904910i | ||||
\(455\) | −2.13331 | −0.100011 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −8.42000 | −0.393871 | −0.196936 | − | 0.980416i | \(-0.563099\pi\) | ||||
−0.196936 | + | 0.980416i | \(0.563099\pi\) | |||||||
\(458\) | −15.8076 | − | 13.9967i | −0.738640 | − | 0.654022i | ||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 7.02241 | + | 57.5748i | 0.327421 | + | 2.68444i | ||||
\(461\) | −1.69743 | −0.0790570 | −0.0395285 | − | 0.999218i | \(-0.512586\pi\) | ||||
−0.0395285 | + | 0.999218i | \(0.512586\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | − | 26.7887i | − | 1.24498i | −0.782628 | − | 0.622489i | \(-0.786121\pi\) | ||
0.782628 | − | 0.622489i | \(-0.213879\pi\) | |||||||
\(464\) | −18.2603 | + | 4.52169i | −0.847712 | + | 0.209914i | ||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −15.2137 | − | 13.4708i | −0.704760 | − | 0.624023i | ||||
\(467\) | 13.5366i | 0.626400i | 0.949687 | + | 0.313200i | \(0.101401\pi\) | ||||
−0.949687 | + | 0.313200i | \(0.898599\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 9.48557i | 0.438003i | ||||||||
\(470\) | 38.5507 | − | 43.5385i | 1.77821 | − | 2.00828i | ||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 15.2048 | − | 22.0661i | 0.699856 | − | 1.01568i | ||||
\(473\) | − | 8.22559i | − | 0.378213i | ||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 32.4219 | 1.48762 | ||||||||
\(476\) | −1.44387 | − | 11.8379i | −0.0661795 | − | 0.542588i | ||||
\(477\) | 0 | 0 | ||||||||
\(478\) | −15.3219 | + | 17.3043i | −0.700809 | + | 0.791481i | ||||
\(479\) | −2.91420 | −0.133153 | −0.0665765 | − | 0.997781i | \(-0.521208\pi\) | ||||
−0.0665765 | + | 0.997781i | \(0.521208\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 0.368783 | 0.0168151 | ||||||||
\(482\) | −0.427524 | + | 0.482837i | −0.0194732 | + | 0.0219926i | ||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −2.35644 | − | 19.3198i | −0.107111 | − | 0.878174i | ||||
\(485\) | 32.6055 | 1.48054 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 29.7819i | 1.34955i | 0.738025 | + | 0.674774i | \(0.235759\pi\) | ||||
−0.738025 | + | 0.674774i | \(0.764241\pi\) | |||||||
\(488\) | −2.64228 | + | 3.83465i | −0.119610 | + | 0.173586i | ||||
\(489\) | 0 | 0 | ||||||||
\(490\) | −4.06898 | + | 4.59543i | −0.183818 | + | 0.207600i | ||||
\(491\) | − | 19.8773i | − | 0.897050i | −0.893770 | − | 0.448525i | \(-0.851950\pi\) | ||
0.893770 | − | 0.448525i | \(-0.148050\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | − | 28.0427i | − | 1.26298i | ||||||
\(494\) | 1.21940 | + | 1.07971i | 0.0548636 | + | 0.0485785i | ||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 7.76265 | + | 31.3485i | 0.348553 | + | 1.40759i | ||||
\(497\) | − | 9.14438i | − | 0.410181i | ||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −29.3452 | −1.31367 | −0.656837 | − | 0.754033i | \(-0.728106\pi\) | ||||
−0.656837 | + | 0.754033i | \(0.728106\pi\) | |||||||
\(500\) | 9.28766 | + | 76.1470i | 0.415357 | + | 3.40540i | ||||
\(501\) | 0 | 0 | ||||||||
\(502\) | −23.2662 | − | 20.6008i | −1.03842 | − | 0.919459i | ||||
\(503\) | −1.44916 | −0.0646150 | −0.0323075 | − | 0.999478i | \(-0.510286\pi\) | ||||
−0.0323075 | + | 0.999478i | \(0.510286\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −53.1657 | −2.36584 | ||||||||
\(506\) | −7.96821 | − | 7.05537i | −0.354230 | − | 0.313650i | ||||
\(507\) | 0 | 0 | ||||||||
\(508\) | −33.8281 | + | 4.12602i | −1.50088 | + | 0.183063i | ||||
\(509\) | −1.87334 | −0.0830342 | −0.0415171 | − | 0.999138i | \(-0.513219\pi\) | ||||
−0.0415171 | + | 0.999138i | \(0.513219\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 2.65767i | 0.117569i | ||||||||
\(512\) | −5.36167 | + | 21.9830i | −0.236955 | + | 0.971521i | ||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 14.5336 | + | 12.8687i | 0.641050 | + | 0.567612i | ||||
\(515\) | 18.6578i | 0.822160i | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 10.6707i | 0.469295i | ||||||||
\(518\) | 0.703401 | − | 0.794408i | 0.0309057 | − | 0.0349043i | ||||
\(519\) | 0 | 0 | ||||||||
\(520\) | −3.42362 | + | 4.96858i | −0.150136 | + | 0.217887i | ||||
\(521\) | 21.9333i | 0.960917i | 0.877017 | + | 0.480459i | \(0.159530\pi\) | ||||
−0.877017 | + | 0.480459i | \(0.840470\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −3.06684 | −0.134104 | −0.0670518 | − | 0.997749i | \(-0.521359\pi\) | ||||
−0.0670518 | + | 0.997749i | \(0.521359\pi\) | |||||||
\(524\) | 9.68524 | − | 1.18131i | 0.423102 | − | 0.0516058i | ||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 26.5403 | − | 29.9741i | 1.15721 | − | 1.30693i | ||||
\(527\) | −48.1427 | −2.09713 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 21.6477 | 0.941205 | ||||||||
\(530\) | −12.7084 | + | 14.3526i | −0.552016 | + | 0.623436i | ||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 4.65168 | − | 0.567367i | 0.201676 | − | 0.0245985i | ||||
\(533\) | 1.67743 | 0.0726575 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 80.2375i | 3.46897i | ||||||||
\(536\) | 22.0924 | + | 15.2229i | 0.954245 | + | 0.657527i | ||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 5.98737 | − | 6.76202i | 0.258134 | − | 0.291532i | ||||
\(539\) | − | 1.12627i | − | 0.0485121i | ||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | − | 21.5872i | − | 0.928106i | −0.885807 | − | 0.464053i | \(-0.846395\pi\) | ||
0.885807 | − | 0.464053i | \(-0.153605\pi\) | |||||||
\(542\) | 4.91148 | + | 4.34882i | 0.210966 | + | 0.186798i | ||||
\(543\) | 0 | 0 | ||||||||
\(544\) | −29.8882 | − | 15.6351i | −1.28145 | − | 0.670349i | ||||
\(545\) | − | 36.5310i | − | 1.56482i | ||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 31.1736 | 1.33289 | 0.666443 | − | 0.745556i | \(-0.267816\pi\) | ||||
0.666443 | + | 0.745556i | \(0.267816\pi\) | |||||||
\(548\) | 19.8606 | − | 2.42241i | 0.848404 | − | 0.103480i | ||||
\(549\) | 0 | 0 | ||||||||
\(550\) | −16.5011 | − | 14.6107i | −0.703609 | − | 0.623004i | ||||
\(551\) | 11.0194 | 0.469441 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −5.74652 | −0.244367 | ||||||||
\(554\) | 24.3209 | + | 21.5347i | 1.03329 | + | 0.914921i | ||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −0.873267 | − | 7.15968i | −0.0370348 | − | 0.303638i | ||||
\(557\) | −38.7541 | −1.64206 | −0.821032 | − | 0.570882i | \(-0.806602\pi\) | ||||
−0.821032 | + | 0.570882i | \(0.806602\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 3.58977i | 0.151831i | ||||||||
\(560\) | 4.17292 | + | 16.8518i | 0.176338 | + | 0.712119i | ||||
\(561\) | 0 | 0 | ||||||||
\(562\) | −13.9263 | − | 12.3309i | −0.587444 | − | 0.520147i | ||||
\(563\) | − | 26.4152i | − | 1.11327i | −0.830758 | − | 0.556634i | \(-0.812092\pi\) | ||
0.830758 | − | 0.556634i | \(-0.187908\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 61.5081i | 2.58767i | ||||||||
\(566\) | −27.3088 | + | 30.8420i | −1.14787 | + | 1.29639i | ||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −21.2977 | − | 14.6753i | −0.893632 | − | 0.615761i | ||||
\(569\) | − | 37.6248i | − | 1.57731i | −0.614833 | − | 0.788657i | \(-0.710777\pi\) | ||
0.614833 | − | 0.788657i | \(-0.289223\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 21.7106 | 0.908559 | 0.454280 | − | 0.890859i | \(-0.349897\pi\) | ||||
0.454280 | + | 0.890859i | \(0.349897\pi\) | |||||||
\(572\) | −0.134050 | − | 1.09904i | −0.00560489 | − | 0.0459530i | ||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 3.19946 | − | 3.61340i | 0.133543 | − | 0.150821i | ||||
\(575\) | 92.4594 | 3.85582 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 31.1816 | 1.29811 | 0.649054 | − | 0.760742i | \(-0.275165\pi\) | ||||
0.649054 | + | 0.760742i | \(0.275165\pi\) | |||||||
\(578\) | 17.3955 | − | 19.6461i | 0.723557 | − | 0.817172i | ||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 4.94261 | + | 40.5231i | 0.205231 | + | 1.68263i | ||||
\(581\) | 12.8786 | 0.534295 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | − | 3.51761i | − | 0.145685i | ||||||
\(584\) | 6.18986 | + | 4.26515i | 0.256138 | + | 0.176493i | ||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0.820276 | − | 0.926405i | 0.0338853 | − | 0.0382694i | ||||
\(587\) | − | 5.00948i | − | 0.206763i | −0.994642 | − | 0.103382i | \(-0.967034\pi\) | ||
0.994642 | − | 0.103382i | \(-0.0329663\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | − | 18.9176i | − | 0.779487i | ||||||
\(590\) | −43.5385 | − | 38.5507i | −1.79245 | − | 1.58711i | ||||
\(591\) | 0 | 0 | ||||||||
\(592\) | −0.721368 | − | 2.91316i | −0.0296481 | − | 0.119730i | ||||
\(593\) | 1.48006i | 0.0607789i | 0.999538 | + | 0.0303895i | \(0.00967476\pi\) | ||||
−0.999538 | + | 0.0303895i | \(0.990325\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −25.8797 | −1.06097 | ||||||||
\(596\) | −2.14802 | − | 17.6110i | −0.0879864 | − | 0.721376i | ||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 3.47745 | + | 3.07907i | 0.142203 | + | 0.125913i | ||||
\(599\) | 9.72452 | 0.397333 | 0.198667 | − | 0.980067i | \(-0.436339\pi\) | ||||
0.198667 | + | 0.980067i | \(0.436339\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −22.1582 | −0.903853 | −0.451926 | − | 0.892055i | \(-0.649263\pi\) | ||||
−0.451926 | + | 0.892055i | \(0.649263\pi\) | |||||||
\(602\) | 7.73285 | + | 6.84698i | 0.315168 | + | 0.279062i | ||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 0.781471 | − | 0.0953162i | 0.0317976 | − | 0.00387836i | ||||
\(605\) | −42.2367 | −1.71716 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 32.4508i | 1.31714i | 0.752522 | + | 0.658568i | \(0.228837\pi\) | ||||
−0.752522 | + | 0.658568i | \(0.771163\pi\) | |||||||
\(608\) | 6.14379 | − | 11.7445i | 0.249164 | − | 0.476304i | ||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 7.56611 | + | 6.69934i | 0.306343 | + | 0.271248i | ||||
\(611\) | − | 4.65684i | − | 0.188396i | ||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 18.5345i | 0.748603i | 0.927307 | + | 0.374302i | \(0.122118\pi\) | ||||
−0.927307 | + | 0.374302i | \(0.877882\pi\) | |||||||
\(614\) | −16.0216 | + | 18.0945i | −0.646579 | + | 0.730234i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −2.62315 | − | 1.80749i | −0.105690 | − | 0.0728260i | ||||
\(617\) | − | 25.8856i | − | 1.04212i | −0.853522 | − | 0.521058i | \(-0.825538\pi\) | ||
0.853522 | − | 0.521058i | \(-0.174462\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −21.0528 | −0.846183 | −0.423091 | − | 0.906087i | \(-0.639055\pi\) | ||||
−0.423091 | + | 0.906087i | \(0.639055\pi\) | |||||||
\(620\) | 69.5685 | − | 8.48528i | 2.79394 | − | 0.340777i | ||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 19.6312 | − | 22.1712i | 0.787141 | − | 0.888982i | ||||
\(623\) | −12.9777 | −0.519941 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 97.2845 | 3.89138 | ||||||||
\(626\) | 24.7453 | − | 27.9469i | 0.989021 | − | 1.11698i | ||||
\(627\) | 0 | 0 | ||||||||
\(628\) | −25.4753 | + | 3.10722i | −1.01657 | + | 0.123992i | ||||
\(629\) | 4.47380 | 0.178382 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 35.5468i | 1.41510i | 0.706666 | + | 0.707548i | \(0.250199\pi\) | ||||
−0.706666 | + | 0.707548i | \(0.749801\pi\) | |||||||
\(632\) | −9.22226 | + | 13.3839i | −0.366842 | + | 0.532384i | ||||
\(633\) | 0 | 0 | ||||||||
\(634\) | −22.4102 | + | 25.3096i | −0.890021 | + | 1.00517i | ||||
\(635\) | 73.9543i | 2.93479i | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 0.491523i | 0.0194749i | ||||||||
\(638\) | −5.60830 | − | 4.96581i | −0.222035 | − | 0.196598i | ||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 45.9456 | + | 17.3256i | 1.81616 | + | 0.684854i | ||||
\(641\) | 44.8131i | 1.77001i | 0.465581 | + | 0.885005i | \(0.345845\pi\) | ||||
−0.465581 | + | 0.885005i | \(0.654155\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −35.5002 | −1.39999 | −0.699995 | − | 0.714148i | \(-0.746814\pi\) | ||||
−0.699995 | + | 0.714148i | \(0.746814\pi\) | |||||||
\(644\) | 13.2655 | − | 1.61799i | 0.522733 | − | 0.0637579i | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 14.7929 | + | 13.0983i | 0.582020 | + | 0.515344i | ||||
\(647\) | −8.53449 | −0.335525 | −0.167763 | − | 0.985827i | \(-0.553654\pi\) | ||||
−0.167763 | + | 0.985827i | \(0.553654\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 10.6707 | 0.418860 | ||||||||
\(650\) | 7.20133 | + | 6.37635i | 0.282459 | + | 0.250101i | ||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 1.82081 | + | 14.9283i | 0.0713084 | + | 0.584638i | ||||
\(653\) | −18.0406 | −0.705984 | −0.352992 | − | 0.935626i | \(-0.614836\pi\) | ||||
−0.352992 | + | 0.935626i | \(0.614836\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | − | 21.1737i | − | 0.827324i | ||||||
\(656\) | −3.28118 | − | 13.2506i | −0.128109 | − | 0.517351i | ||||
\(657\) | 0 | 0 | ||||||||
\(658\) | −10.0315 | − | 8.88226i | −0.391067 | − | 0.346267i | ||||
\(659\) | − | 11.6857i | − | 0.455212i | −0.973753 | − | 0.227606i | \(-0.926910\pi\) | ||
0.973753 | − | 0.227606i | \(-0.0730897\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | − | 3.24527i | − | 0.126227i | −0.998006 | − | 0.0631133i | \(-0.979897\pi\) | ||
0.998006 | − | 0.0631133i | \(-0.0201029\pi\) | |||||||
\(662\) | 14.8800 | − | 16.8052i | 0.578328 | − | 0.653152i | ||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 20.6681 | − | 29.9949i | 0.802079 | − | 1.16403i | ||||
\(665\) | − | 10.1694i | − | 0.394353i | ||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 31.4246 | 1.21676 | ||||||||
\(668\) | 1.04275 | + | 8.54918i | 0.0403450 | + | 0.330778i | ||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 38.5966 | − | 43.5903i | 1.49112 | − | 1.68404i | ||||
\(671\) | −1.85434 | −0.0715861 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −30.3154 | −1.16857 | −0.584287 | − | 0.811547i | \(-0.698626\pi\) | ||||
−0.584287 | + | 0.811547i | \(0.698626\pi\) | |||||||
\(674\) | 8.25878 | − | 9.32731i | 0.318116 | − | 0.359275i | ||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −3.08939 | − | 25.3291i | −0.118823 | − | 0.974196i | ||||
\(677\) | 25.5344 | 0.981368 | 0.490684 | − | 0.871338i | \(-0.336747\pi\) | ||||
0.490684 | + | 0.871338i | \(0.336747\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | − | 7.51246i | − | 0.288302i | ||||||
\(680\) | −41.5329 | + | 60.2752i | −1.59271 | + | 2.31145i | ||||
\(681\) | 0 | 0 | ||||||||
\(682\) | −8.52512 | + | 9.62810i | −0.326444 | + | 0.368679i | ||||
\(683\) | − | 42.9534i | − | 1.64357i | −0.569799 | − | 0.821784i | \(-0.692979\pi\) | ||
0.569799 | − | 0.821784i | \(-0.307021\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | − | 43.4189i | − | 1.65895i | ||||||
\(686\) | 1.05881 | + | 0.937511i | 0.0404255 | + | 0.0357943i | ||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 28.3570 | − | 7.02188i | 1.08110 | − | 0.267707i | ||||
\(689\) | 1.53514i | 0.0584842i | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 30.2219 | 1.14970 | 0.574848 | − | 0.818260i | \(-0.305061\pi\) | ||||
0.574848 | + | 0.818260i | \(0.305061\pi\) | |||||||
\(692\) | 2.01745 | + | 16.5405i | 0.0766921 | + | 0.628777i | ||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 19.5991 | + | 17.3538i | 0.743971 | + | 0.658742i | ||||
\(695\) | −15.6523 | −0.593727 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 20.3493 | 0.770785 | ||||||||
\(698\) | 3.21847 | + | 2.84977i | 0.121821 | + | 0.107865i | ||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 27.4710 | − | 3.35065i | 1.03831 | − | 0.126643i | ||||
\(701\) | −47.5750 | −1.79688 | −0.898441 | − | 0.439094i | \(-0.855300\pi\) | ||||
−0.898441 | + | 0.439094i | \(0.855300\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 1.75798i | 0.0663034i | ||||||||
\(704\) | −8.41949 | + | 3.20871i | −0.317321 | + | 0.120933i | ||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −18.0156 | − | 15.9517i | −0.678026 | − | 0.600351i | ||||
\(707\) | 12.2496i | 0.460694i | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | − | 5.97537i | − | 0.224410i | −0.993685 | − | 0.112205i | \(-0.964209\pi\) | ||
0.993685 | − | 0.112205i | \(-0.0357913\pi\) | |||||||
\(710\) | −37.2083 | + | 42.0224i | −1.39640 | + | 1.57707i | ||||
\(711\) | 0 | 0 | ||||||||
\(712\) | −20.8272 | + | 30.2257i | −0.780531 | + | 1.13276i | ||||
\(713\) | − | 53.9485i | − | 2.02039i | ||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −2.40269 | −0.0898555 | ||||||||
\(716\) | −8.75055 | + | 1.06731i | −0.327023 | + | 0.0398871i | ||||
\(717\) | 0 | 0 | ||||||||
\(718\) | −10.1013 | + | 11.4082i | −0.376977 | + | 0.425751i | ||||
\(719\) | −15.5907 | −0.581434 | −0.290717 | − | 0.956809i | \(-0.593894\pi\) | ||||
−0.290717 | + | 0.956809i | \(0.593894\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 4.29883 | 0.160097 | ||||||||
\(722\) | 12.6658 | − | 14.3045i | 0.471371 | − | 0.532357i | ||||
\(723\) | 0 | 0 | ||||||||
\(724\) | −28.4114 | + | 3.46535i | −1.05590 | + | 0.128789i | ||||
\(725\) | 65.0761 | 2.41687 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | − | 37.3382i | − | 1.38480i | −0.721515 | − | 0.692399i | \(-0.756554\pi\) | ||
0.721515 | − | 0.692399i | \(-0.243446\pi\) | |||||||
\(728\) | 1.14478 | + | 0.788818i | 0.0424285 | + | 0.0292355i | ||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 10.8140 | − | 12.2132i | 0.400245 | − | 0.452029i | ||||
\(731\) | 43.5485i | 1.61070i | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | − | 2.18169i | − | 0.0805825i | −0.999188 | − | 0.0402912i | \(-0.987171\pi\) | ||
0.999188 | − | 0.0402912i | \(-0.0128286\pi\) | |||||||
\(734\) | 7.17925 | + | 6.35680i | 0.264991 | + | 0.234634i | ||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 17.5206 | − | 33.4926i | 0.645819 | − | 1.23455i | ||||
\(737\) | 10.6834i | 0.393526i | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −9.14831 | −0.336526 | −0.168263 | − | 0.985742i | \(-0.553816\pi\) | ||||
−0.168263 | + | 0.985742i | \(0.553816\pi\) | |||||||
\(740\) | −6.46486 | + | 0.788521i | −0.237653 | + | 0.0289866i | ||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 3.30690 | + | 2.92806i | 0.121400 | + | 0.107493i | ||||
\(743\) | −19.6022 | −0.719134 | −0.359567 | − | 0.933119i | \(-0.617076\pi\) | ||||
−0.359567 | + | 0.933119i | \(0.617076\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −38.5009 | −1.41056 | ||||||||
\(746\) | −19.7946 | − | 17.5270i | −0.724733 | − | 0.641708i | ||||
\(747\) | 0 | 0 | ||||||||
\(748\) | −1.62619 | − | 13.3327i | −0.0594594 | − | 0.487491i | ||||
\(749\) | 18.4871 | 0.675502 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | − | 27.9656i | − | 1.02048i | −0.860032 | − | 0.510240i | \(-0.829556\pi\) | ||
0.860032 | − | 0.510240i | \(-0.170444\pi\) | |||||||
\(752\) | −36.7861 | + | 9.10914i | −1.34145 | + | 0.332176i | ||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 2.44755 | + | 2.16716i | 0.0891344 | + | 0.0789232i | ||||
\(755\) | − | 1.70844i | − | 0.0621764i | ||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | − | 34.1370i | − | 1.24073i | −0.784312 | − | 0.620366i | \(-0.786984\pi\) | ||
0.784312 | − | 0.620366i | \(-0.213016\pi\) | |||||||
\(758\) | −26.7579 | + | 30.2198i | −0.971889 | + | 1.09763i | ||||
\(759\) | 0 | 0 | ||||||||
\(760\) | −23.6851 | − | 16.3203i | −0.859149 | − | 0.592000i | ||||
\(761\) | 49.4689i | 1.79325i | 0.442795 | + | 0.896623i | \(0.353987\pi\) | ||||
−0.442795 | + | 0.896623i | \(0.646013\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −8.41691 | −0.304713 | ||||||||
\(764\) | −2.78588 | − | 22.8407i | −0.100790 | − | 0.826347i | ||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 9.27127 | − | 10.4708i | 0.334985 | − | 0.378325i | ||||
\(767\) | −4.65684 | −0.168149 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 3.30479 | 0.119174 | 0.0595868 | − | 0.998223i | \(-0.481022\pi\) | ||||
0.0595868 | + | 0.998223i | \(0.481022\pi\) | |||||||
\(770\) | −4.58279 | + | 5.17572i | −0.165152 | + | 0.186520i | ||||
\(771\) | 0 | 0 | ||||||||
\(772\) | −0.0150001 | − | 0.122982i | −0.000539865 | − | 0.00442621i | ||||
\(773\) | −20.4350 | −0.734995 | −0.367498 | − | 0.930024i | \(-0.619785\pi\) | ||||
−0.367498 | + | 0.930024i | \(0.619785\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | − | 111.720i | − | 4.01310i | ||||||
\(776\) | −17.4969 | − | 12.0563i | −0.628102 | − | 0.432797i | ||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −9.92572 | + | 11.2099i | −0.355854 | + | 0.401895i | ||||
\(779\) | 7.99625i | 0.286495i | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | − | 10.2991i | − | 0.368530i | ||||||
\(782\) | 42.1858 | + | 37.3531i | 1.50856 | + | 1.33574i | ||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 3.88273 | − | 0.961458i | 0.138669 | − | 0.0343378i | ||||
\(785\) | 55.6935i | 1.98779i | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 38.8368 | 1.38438 | 0.692192 | − | 0.721713i | \(-0.256645\pi\) | ||||
0.692192 | + | 0.721713i | \(0.256645\pi\) | |||||||
\(788\) | −3.64760 | − | 29.9057i | −0.129940 | − | 1.06535i | ||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 26.4077 | + | 23.3825i | 0.939545 | + | 0.831911i | ||||
\(791\) | 14.1717 | 0.503889 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 0.809264 | 0.0287378 | ||||||||
\(794\) | −12.5616 | − | 11.1225i | −0.445794 | − | 0.394724i | ||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −19.4735 | + | 2.37519i | −0.690220 | + | 0.0841862i | ||||
\(797\) | 20.3591 | 0.721157 | 0.360578 | − | 0.932729i | \(-0.382579\pi\) | ||||
0.360578 | + | 0.932729i | \(0.382579\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | − | 56.4933i | − | 1.99859i | ||||||
\(800\) | 36.2829 | − | 69.3587i | 1.28279 | − | 2.45220i | ||||
\(801\) | 0 | 0 | ||||||||
\(802\) | −12.9976 | − | 11.5086i | −0.458960 | − | 0.406382i | ||||
\(803\) | 2.99327i | 0.105630i | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | − | 29.0007i | − | 1.02214i | ||||||
\(806\) | 3.72049 | − | 4.20185i | 0.131049 | − | 0.148004i | ||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 28.5299 | + | 19.6587i | 1.00368 | + | 0.691590i | ||||
\(809\) | 51.7428i | 1.81918i | 0.415505 | + | 0.909591i | \(0.363605\pi\) | ||||
−0.415505 | + | 0.909591i | \(0.636395\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −53.4436 | −1.87666 | −0.938329 | − | 0.345744i | \(-0.887627\pi\) | ||||
−0.938329 | + | 0.345744i | \(0.887627\pi\) | |||||||
\(812\) | 9.33670 | − | 1.13880i | 0.327654 | − | 0.0399640i | ||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0.792222 | − | 0.894721i | 0.0277674 | − | 0.0313600i | ||||
\(815\) | 32.6360 | 1.14319 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −17.1123 | −0.598685 | ||||||||
\(818\) | −1.75353 | + | 1.98040i | −0.0613108 | + | 0.0692432i | ||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −29.4058 | + | 3.58663i | −1.02689 | + | 0.125250i | ||||
\(821\) | 24.1628 | 0.843289 | 0.421644 | − | 0.906761i | \(-0.361453\pi\) | ||||
0.421644 | + | 0.906761i | \(0.361453\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 23.3024i | 0.812270i | 0.913813 | + | 0.406135i | \(0.133124\pi\) | ||||
−0.913813 | + | 0.406135i | \(0.866876\pi\) | |||||||
\(824\) | 6.89895 | − | 10.0122i | 0.240336 | − | 0.348792i | ||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −8.88226 | + | 10.0315i | −0.309053 | + | 0.349039i | ||||
\(827\) | − | 24.6097i | − | 0.855764i | −0.903835 | − | 0.427882i | \(-0.859260\pi\) | ||
0.903835 | − | 0.427882i | \(-0.140740\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 50.5634i | 1.75614i | 0.478534 | + | 0.878069i | \(0.341168\pi\) | ||||
−0.478534 | + | 0.878069i | \(0.658832\pi\) | |||||||
\(830\) | −59.1827 | − | 52.4028i | −2.05426 | − | 1.81893i | ||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 3.67439 | − | 1.40033i | 0.127387 | − | 0.0485477i | ||||
\(833\) | 5.96280i | 0.206599i | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 18.6901 | 0.646796 | ||||||||
\(836\) | 5.23907 | − | 0.639010i | 0.181197 | − | 0.0221006i | ||||
\(837\) | 0 | 0 | ||||||||
\(838\) | −4.98665 | − | 4.41538i | −0.172261 | − | 0.152527i | ||||
\(839\) | 10.4578 | 0.361042 | 0.180521 | − | 0.983571i | \(-0.442222\pi\) | ||||
0.180521 | + | 0.983571i | \(0.442222\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −6.88230 | −0.237321 | ||||||||
\(842\) | −3.39943 | − | 3.01000i | −0.117152 | − | 0.103731i | ||||
\(843\) | 0 | 0 | ||||||||
\(844\) | −1.73742 | − | 14.2446i | −0.0598045 | − | 0.490321i | ||||
\(845\) | −55.3740 | −1.90492 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 9.73151i | 0.334379i | ||||||||
\(848\) | 12.1267 | − | 3.00285i | 0.416431 | − | 0.103118i | ||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 87.3612 | + | 77.3532i | 2.99646 | + | 2.65319i | ||||
\(851\) | 5.01333i | 0.171855i | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 48.5133i | 1.66106i | 0.556971 | + | 0.830532i | \(0.311963\pi\) | ||||
−0.556971 | + | 0.830532i | \(0.688037\pi\) | |||||||
\(854\) | 1.54356 | − | 1.74326i | 0.0528194 | − | 0.0596533i | ||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 29.6688 | − | 43.0573i | 1.01406 | − | 1.47167i | ||||
\(857\) | − | 26.0672i | − | 0.890437i | −0.895422 | − | 0.445219i | \(-0.853126\pi\) | ||
0.895422 | − | 0.445219i | \(-0.146874\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 20.1390 | 0.687133 | 0.343567 | − | 0.939128i | \(-0.388365\pi\) | ||||
0.343567 | + | 0.939128i | \(0.388365\pi\) | |||||||
\(860\) | −7.67555 | − | 62.9297i | −0.261734 | − | 2.14588i | ||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0.118800 | − | 0.134170i | 0.00404634 | − | 0.00456986i | ||||
\(863\) | 12.6122 | 0.429323 | 0.214662 | − | 0.976689i | \(-0.431135\pi\) | ||||
0.214662 | + | 0.976689i | \(0.431135\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 36.1606 | 1.22950 | ||||||||
\(866\) | 1.20219 | − | 1.35773i | 0.0408522 | − | 0.0461377i | ||||
\(867\) | 0 | 0 | ||||||||
\(868\) | −1.95505 | − | 16.0289i | −0.0663586 | − | 0.544056i | ||||
\(869\) | −6.47215 | −0.219553 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | − | 4.66238i | − | 0.157979i | ||||||
\(872\) | −13.5078 | + | 19.6034i | −0.457433 | + | 0.663855i | ||||
\(873\) | 0 | 0 | ||||||||
\(874\) | −14.6779 | + | 16.5769i | −0.496486 | + | 0.560722i | ||||
\(875\) | − | 38.3556i | − | 1.29666i | ||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 44.9111i | 1.51654i | 0.651940 | + | 0.758270i | \(0.273955\pi\) | ||||
−0.651940 | + | 0.758270i | \(0.726045\pi\) | |||||||
\(878\) | 29.6348 | + | 26.2398i | 1.00012 | + | 0.885551i | ||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 4.69985 | + | 18.9798i | 0.158432 | + | 0.639808i | ||||
\(881\) | 46.5834i | 1.56943i | 0.619854 | + | 0.784717i | \(0.287192\pi\) | ||||
−0.619854 | + | 0.784717i | \(0.712808\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −29.5508 | −0.994463 | −0.497232 | − | 0.867618i | \(-0.665650\pi\) | ||||
−0.497232 | + | 0.867618i | \(0.665650\pi\) | |||||||
\(884\) | 0.709695 | + | 5.81859i | 0.0238696 | + | 0.195700i | ||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 3.26307 | + | 2.88926i | 0.109625 | + | 0.0970664i | ||||
\(887\) | 22.8412 | 0.766932 | 0.383466 | − | 0.923555i | \(-0.374730\pi\) | ||||
0.383466 | + | 0.923555i | \(0.374730\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 17.0394 | 0.571483 | ||||||||
\(890\) | 59.6382 | + | 52.8060i | 1.99908 | + | 1.77006i | ||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 4.09532 | − | 0.499507i | 0.137121 | − | 0.0167247i | ||||
\(893\) | 22.1990 | 0.742862 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 19.1303i | 0.639454i | ||||||||
\(896\) | 3.99189 | − | 10.5861i | 0.133360 | − | 0.353656i | ||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 10.2015 | + | 9.03281i | 0.340428 | + | 0.301429i | ||||
\(899\) | − | 37.9708i | − | 1.26640i | ||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 18.6232i | 0.620428i | ||||||||
\(902\) | 3.60346 | − | 4.06968i | 0.119982 | − | 0.135506i | ||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 22.7434 | − | 33.0067i | 0.756435 | − | 1.09779i | ||||
\(905\) | 62.1125i | 2.06469i | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 24.9022 | 0.826864 | 0.413432 | − | 0.910535i | \(-0.364330\pi\) | ||||
0.413432 | + | 0.910535i | \(0.364330\pi\) | |||||||
\(908\) | 40.8301 | − | 4.98005i | 1.35499 | − | 0.165269i | ||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 2.00000 | − | 2.25876i | 0.0662994 | − | 0.0748772i | ||||
\(911\) | 12.2059 | 0.404401 | 0.202200 | − | 0.979344i | \(-0.435191\pi\) | ||||
0.202200 | + | 0.979344i | \(0.435191\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 14.5048 | 0.480040 | ||||||||
\(914\) | 7.89384 | − | 8.91516i | 0.261105 | − | 0.294887i | ||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 29.6396 | − | 3.61515i | 0.979319 | − | 0.119448i | ||||
\(917\) | −4.87851 | −0.161103 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 29.0260i | 0.957480i | 0.877957 | + | 0.478740i | \(0.158906\pi\) | ||||
−0.877957 | + | 0.478740i | \(0.841094\pi\) | |||||||
\(920\) | −67.5442 | − | 46.5416i | −2.22687 | − | 1.53443i | ||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 1.59136 | − | 1.79725i | 0.0524085 | − | 0.0591892i | ||||
\(923\) | 4.49467i | 0.147944i | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 10.3819i | 0.341356i | ||||||||
\(926\) | 28.3641 | + | 25.1147i | 0.932103 | + | 0.825322i | ||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 12.3316 | − | 23.5732i | 0.404805 | − | 0.773830i | ||||
\(929\) | 0.717723i | 0.0235477i | 0.999931 | + | 0.0117739i | \(0.00374782\pi\) | ||||
−0.999931 | + | 0.0117739i | \(0.996252\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −2.34308 | −0.0767913 | ||||||||
\(932\) | 28.5260 | − | 3.47932i | 0.934399 | − | 0.113969i | ||||
\(933\) | 0 | 0 | ||||||||
\(934\) | −14.3327 | − | 12.6907i | −0.468979 | − | 0.415253i | ||||
\(935\) | −29.1477 | −0.953230 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −36.3608 | −1.18785 | −0.593927 | − | 0.804519i | \(-0.702423\pi\) | ||||
−0.593927 | + | 0.804519i | \(0.702423\pi\) | |||||||
\(938\) | −10.0434 | − | 8.89283i | −0.327928 | − | 0.290361i | ||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 9.95711 | + | 81.6356i | 0.324765 | + | 2.66266i | ||||
\(941\) | 22.6783 | 0.739290 | 0.369645 | − | 0.929173i | \(-0.379479\pi\) | ||||
0.369645 | + | 0.929173i | \(0.379479\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 22.8034i | 0.742580i | ||||||||
\(944\) | 9.10914 | + | 36.7861i | 0.296477 | + | 1.19729i | ||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 8.70931 | + | 7.71158i | 0.283164 | + | 0.250725i | ||||
\(947\) | − | 14.8231i | − | 0.481685i | −0.970564 | − | 0.240842i | \(-0.922576\pi\) | ||
0.970564 | − | 0.240842i | \(-0.0774237\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | − | 1.30631i | − | 0.0424046i | ||||||
\(950\) | −30.3959 | + | 34.3285i | −0.986172 | + | 1.11376i | ||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 13.8877 | + | 9.56936i | 0.450102 | + | 0.310145i | ||||
\(953\) | 3.80423i | 0.123231i | 0.998100 | + | 0.0616155i | \(0.0196253\pi\) | ||||
−0.998100 | + | 0.0616155i | \(0.980375\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −49.9339 | −1.61582 | ||||||||
\(956\) | −3.95744 | − | 32.4460i | −0.127993 | − | 1.04938i | ||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 2.73209 | − | 3.08557i | 0.0882699 | − | 0.0996904i | ||||
\(959\) | −10.0039 | −0.323043 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −34.1868 | −1.10280 | ||||||||
\(962\) | −0.345738 | + | 0.390470i | −0.0111470 | + | 0.0125893i | ||||
\(963\) | 0 | 0 | ||||||||
\(964\) | −0.110423 | − | 0.905330i | −0.00355649 | − | 0.0291587i | ||||
\(965\) | −0.268860 | −0.00865491 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 11.2095i | 0.360474i | 0.983623 | + | 0.180237i | \(0.0576865\pi\) | ||||
−0.983623 | + | 0.180237i | \(0.942313\pi\) | |||||||
\(968\) | 22.6652 | + | 15.6175i | 0.728486 | + | 0.501967i | ||||
\(969\) | 0 | 0 | ||||||||
\(970\) | −30.5681 | + | 34.5230i | −0.981481 | + | 1.10847i | ||||
\(971\) | 50.7626i | 1.62905i | 0.580129 | + | 0.814525i | \(0.303002\pi\) | ||||
−0.580129 | + | 0.814525i | \(0.696998\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 3.60637i | 0.115615i | ||||||||
\(974\) | −31.5333 | − | 27.9209i | −1.01039 | − | 0.894642i | ||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −1.58298 | − | 6.39269i | −0.0506701 | − | 0.204625i | ||||
\(977\) | − | 28.4952i | − | 0.911644i | −0.890071 | − | 0.455822i | \(-0.849345\pi\) | ||
0.890071 | − | 0.455822i | \(-0.150655\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −14.6164 | −0.467144 | ||||||||
\(980\) | −1.05096 | − | 8.61654i | −0.0335717 | − | 0.275245i | ||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 21.0462 | + | 18.6352i | 0.671612 | + | 0.594673i | ||||
\(983\) | −19.8866 | −0.634283 | −0.317142 | − | 0.948378i | \(-0.602723\pi\) | ||||
−0.317142 | + | 0.948378i | \(0.602723\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −65.3792 | −2.08315 | ||||||||
\(986\) | 29.6918 | + | 26.2904i | 0.945581 | + | 0.837256i | ||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −2.28641 | + | 0.278874i | −0.0727404 | + | 0.00887216i | ||||
\(989\) | −48.8003 | −1.55176 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | − | 14.1816i | − | 0.450493i | −0.974302 | − | 0.225246i | \(-0.927681\pi\) | ||
0.974302 | − | 0.225246i | \(-0.0723187\pi\) | |||||||
\(992\) | −40.4696 | − | 21.1704i | −1.28491 | − | 0.672162i | ||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 9.68213 | + | 8.57295i | 0.307099 | + | 0.271918i | ||||
\(995\) | 42.5726i | 1.34964i | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 26.5442i | 0.840663i | 0.907371 | + | 0.420331i | \(0.138086\pi\) | ||||
−0.907371 | + | 0.420331i | \(0.861914\pi\) | |||||||
\(998\) | 27.5115 | − | 31.0709i | 0.870861 | − | 0.983534i | ||||
\(999\) | 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 | 504.2.j.a.323.6 | yes | 24 | |
3.2 | odd | 2 | inner | 504.2.j.a.323.19 | yes | 24 | |
4.3 | odd | 2 | 2016.2.j.a.1583.2 | 24 | |||
8.3 | odd | 2 | inner | 504.2.j.a.323.20 | yes | 24 | |
8.5 | even | 2 | 2016.2.j.a.1583.24 | 24 | |||
12.11 | even | 2 | 2016.2.j.a.1583.23 | 24 | |||
24.5 | odd | 2 | 2016.2.j.a.1583.1 | 24 | |||
24.11 | even | 2 | inner | 504.2.j.a.323.5 | ✓ | 24 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
504.2.j.a.323.5 | ✓ | 24 | 24.11 | even | 2 | inner | |
504.2.j.a.323.6 | yes | 24 | 1.1 | even | 1 | trivial | |
504.2.j.a.323.19 | yes | 24 | 3.2 | odd | 2 | inner | |
504.2.j.a.323.20 | yes | 24 | 8.3 | odd | 2 | inner | |
2016.2.j.a.1583.1 | 24 | 24.5 | odd | 2 | |||
2016.2.j.a.1583.2 | 24 | 4.3 | odd | 2 | |||
2016.2.j.a.1583.23 | 24 | 12.11 | even | 2 | |||
2016.2.j.a.1583.24 | 24 | 8.5 | even | 2 |