Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1323,2,Mod(440,1323)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1323, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([1, 3]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1323.440");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1323 = 3^{3} \cdot 7^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1323.o (of order \(6\), degree \(2\), not minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(10.5642081874\) |
Analytic rank: | \(0\) |
Dimension: | \(48\) |
Relative dimension: | \(24\) over \(\Q(\zeta_{6})\) |
Twist minimal: | no (minimal twist has level 441) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 440.2 | ||
Character | \(\chi\) | \(=\) | 1323.440 |
Dual form | 1323.2.o.e.881.2 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/1323\mathbb{Z}\right)^\times\).
\(n\) | \(785\) | \(1081\) |
\(\chi(n)\) | \(e\left(\frac{1}{6}\right)\) | \(-1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −2.23278 | − | 1.28910i | −1.57882 | − | 0.911529i | −0.995025 | − | 0.0996245i | \(-0.968236\pi\) |
−0.583790 | − | 0.811905i | \(-0.698431\pi\) | |||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 2.32354 | + | 4.02449i | 1.16177 | + | 2.01225i | ||||
\(5\) | −1.16595 | − | 2.01948i | −0.521427 | − | 0.903138i | −0.999689 | − | 0.0249208i | \(-0.992067\pi\) |
0.478263 | − | 0.878217i | \(-0.341267\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 0 | 0 | ||||||||
\(8\) | − | 6.82470i | − | 2.41290i | ||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 6.01207i | 1.90118i | ||||||||
\(11\) | 3.78114 | + | 2.18304i | 1.14006 | + | 0.658212i | 0.946444 | − | 0.322867i | \(-0.104647\pi\) |
0.193612 | + | 0.981078i | \(0.437980\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −1.14392 | + | 0.660445i | −0.317267 | + | 0.183174i | −0.650174 | − | 0.759785i | \(-0.725304\pi\) |
0.332906 | + | 0.942960i | \(0.391971\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −4.15061 | + | 7.18908i | −1.03765 | + | 1.79727i | ||||
\(17\) | −5.78655 | −1.40344 | −0.701722 | − | 0.712451i | \(-0.747585\pi\) | ||||
−0.701722 | + | 0.712451i | \(0.747585\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 0.675357i | 0.154937i | 0.996995 | + | 0.0774687i | \(0.0246838\pi\) | ||||
−0.996995 | + | 0.0774687i | \(0.975316\pi\) | |||||||
\(20\) | 5.41825 | − | 9.38468i | 1.21156 | − | 2.09848i | ||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −5.62830 | − | 9.74851i | −1.19996 | − | 2.07839i | ||||
\(23\) | 4.81799 | − | 2.78167i | 1.00462 | − | 0.580018i | 0.0950080 | − | 0.995477i | \(-0.469712\pi\) |
0.909612 | + | 0.415459i | \(0.136379\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −0.218858 | + | 0.379074i | −0.0437717 | + | 0.0758147i | ||||
\(26\) | 3.40551 | 0.667875 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −3.86926 | − | 2.23392i | −0.718503 | − | 0.414828i | 0.0956983 | − | 0.995410i | \(-0.469492\pi\) |
−0.814202 | + | 0.580582i | \(0.802825\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 3.47965 | − | 2.00898i | 0.624964 | − | 0.360823i | −0.153835 | − | 0.988097i | \(-0.549162\pi\) |
0.778799 | + | 0.627273i | \(0.215829\pi\) | |||||||
\(32\) | 6.71411 | − | 3.87639i | 1.18690 | − | 0.685256i | ||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 12.9201 | + | 7.45942i | 2.21578 | + | 1.27928i | ||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 3.01658 | 0.495923 | 0.247961 | − | 0.968770i | \(-0.420239\pi\) | ||||
0.247961 | + | 0.968770i | \(0.420239\pi\) | |||||||
\(38\) | 0.870601 | − | 1.50792i | 0.141230 | − | 0.244618i | ||||
\(39\) | 0 | 0 | ||||||||
\(40\) | −13.7823 | + | 7.95723i | −2.17918 | + | 1.25815i | ||||
\(41\) | 3.29501 | + | 5.70713i | 0.514594 | + | 0.891303i | 0.999857 | + | 0.0169348i | \(0.00539076\pi\) |
−0.485262 | + | 0.874369i | \(0.661276\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 3.89217 | − | 6.74143i | 0.593550 | − | 1.02806i | −0.400200 | − | 0.916428i | \(-0.631059\pi\) |
0.993750 | − | 0.111631i | \(-0.0356074\pi\) | |||||||
\(44\) | 20.2896i | 3.05877i | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −14.3434 | −2.11481 | ||||||||
\(47\) | −0.246705 | + | 0.427306i | −0.0359856 | + | 0.0623289i | −0.883457 | − | 0.468512i | \(-0.844790\pi\) |
0.847472 | + | 0.530841i | \(0.178124\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 0 | 0 | ||||||||
\(50\) | 0.977326 | − | 0.564259i | 0.138215 | − | 0.0797983i | ||||
\(51\) | 0 | 0 | ||||||||
\(52\) | −5.31591 | − | 3.06914i | −0.737184 | − | 0.425614i | ||||
\(53\) | 4.14566i | 0.569451i | 0.958609 | + | 0.284725i | \(0.0919024\pi\) | ||||
−0.958609 | + | 0.284725i | \(0.908098\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | − | 10.1812i | − | 1.37284i | ||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 5.75947 | + | 9.97570i | 0.756256 | + | 1.30987i | ||||
\(59\) | −2.15699 | − | 3.73602i | −0.280816 | − | 0.486388i | 0.690770 | − | 0.723075i | \(-0.257272\pi\) |
−0.971586 | + | 0.236687i | \(0.923939\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 1.77661 | + | 1.02572i | 0.227471 | + | 0.131330i | 0.609405 | − | 0.792859i | \(-0.291408\pi\) |
−0.381934 | + | 0.924190i | \(0.624742\pi\) | |||||||
\(62\) | −10.3591 | −1.31560 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | −3.38572 | −0.423215 | ||||||||
\(65\) | 2.66751 | + | 1.54009i | 0.330863 | + | 0.191024i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 2.41218 | + | 4.17802i | 0.294695 | + | 0.510427i | 0.974914 | − | 0.222582i | \(-0.0714486\pi\) |
−0.680219 | + | 0.733009i | \(0.738115\pi\) | |||||||
\(68\) | −13.4453 | − | 23.2879i | −1.63048 | − | 2.82408i | ||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 1.17135i | 0.139014i | 0.997581 | + | 0.0695068i | \(0.0221426\pi\) | ||||
−0.997581 | + | 0.0695068i | \(0.977857\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | − | 15.1153i | − | 1.76911i | −0.466432 | − | 0.884557i | \(-0.654461\pi\) | ||
0.466432 | − | 0.884557i | \(-0.345539\pi\) | |||||||
\(74\) | −6.73536 | − | 3.88866i | −0.782970 | − | 0.452048i | ||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −2.71797 | + | 1.56922i | −0.311772 | + | 0.180002i | ||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 5.30428 | − | 9.18728i | 0.596778 | − | 1.03365i | −0.396515 | − | 0.918028i | \(-0.629781\pi\) |
0.993293 | − | 0.115622i | \(-0.0368861\pi\) | |||||||
\(80\) | 19.3576 | 2.16424 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | − | 16.9904i | − | 1.87627i | ||||||
\(83\) | 5.32432 | − | 9.22199i | 0.584420 | − | 1.01225i | −0.410527 | − | 0.911848i | \(-0.634655\pi\) |
0.994947 | − | 0.100397i | \(-0.0320113\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 6.74680 | + | 11.6858i | 0.731793 | + | 1.26750i | ||||
\(86\) | −17.3807 | + | 10.0348i | −1.87421 | + | 1.08208i | ||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 14.8986 | − | 25.8051i | 1.58820 | − | 2.75084i | ||||
\(89\) | −3.32535 | −0.352486 | −0.176243 | − | 0.984347i | \(-0.556395\pi\) | ||||
−0.176243 | + | 0.984347i | \(0.556395\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | 22.3896 | + | 12.9266i | 2.33428 | + | 1.34770i | ||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 1.10168 | − | 0.636053i | 0.113629 | − | 0.0656039i | ||||
\(95\) | 1.36387 | − | 0.787429i | 0.139930 | − | 0.0807886i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −12.7531 | − | 7.36299i | −1.29488 | − | 0.747598i | −0.315363 | − | 0.948971i | \(-0.602126\pi\) |
−0.979515 | + | 0.201373i | \(0.935460\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | −2.03411 | −0.203411 | ||||||||
\(101\) | 0.832092 | − | 1.44123i | 0.0827963 | − | 0.143407i | −0.821654 | − | 0.569987i | \(-0.806948\pi\) |
0.904450 | + | 0.426580i | \(0.140282\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 1.40783 | − | 0.812812i | 0.138718 | − | 0.0800887i | −0.429035 | − | 0.903288i | \(-0.641146\pi\) |
0.567753 | + | 0.823199i | \(0.307813\pi\) | |||||||
\(104\) | 4.50734 | + | 7.80694i | 0.441981 | + | 0.765533i | ||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 5.34416 | − | 9.25636i | 0.519071 | − | 0.899057i | ||||
\(107\) | − | 18.3130i | − | 1.77039i | −0.465221 | − | 0.885194i | \(-0.654025\pi\) | ||
0.465221 | − | 0.885194i | \(-0.345975\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −15.9736 | −1.52999 | −0.764995 | − | 0.644036i | \(-0.777259\pi\) | ||||
−0.764995 | + | 0.644036i | \(0.777259\pi\) | |||||||
\(110\) | −13.1246 | + | 22.7325i | −1.25138 | + | 2.16746i | ||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 5.07612 | − | 2.93070i | 0.477521 | − | 0.275697i | −0.241862 | − | 0.970311i | \(-0.577758\pi\) |
0.719383 | + | 0.694614i | \(0.244425\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −11.2350 | − | 6.48654i | −1.04767 | − | 0.604873i | ||||
\(116\) | − | 20.7624i | − | 1.92774i | ||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 11.1223i | 1.02389i | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 4.03134 | + | 6.98248i | 0.366485 | + | 0.634771i | ||||
\(122\) | −2.64451 | − | 4.58043i | −0.239423 | − | 0.414693i | ||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 16.1702 | + | 9.33589i | 1.45213 | + | 0.838388i | ||||
\(125\) | −10.6387 | −0.951559 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −16.5710 | −1.47044 | −0.735218 | − | 0.677831i | \(-0.762920\pi\) | ||||
−0.735218 | + | 0.677831i | \(0.762920\pi\) | |||||||
\(128\) | −5.86864 | − | 3.38826i | −0.518719 | − | 0.299483i | ||||
\(129\) | 0 | 0 | ||||||||
\(130\) | −3.97064 | − | 6.87735i | −0.348248 | − | 0.603183i | ||||
\(131\) | 3.55989 | + | 6.16591i | 0.311029 | + | 0.538718i | 0.978585 | − | 0.205841i | \(-0.0659930\pi\) |
−0.667556 | + | 0.744559i | \(0.732660\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | − | 12.4382i | − | 1.07449i | ||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 39.4914i | 3.38636i | ||||||||
\(137\) | 0.716584 | + | 0.413720i | 0.0612219 | + | 0.0353465i | 0.530298 | − | 0.847811i | \(-0.322080\pi\) |
−0.469077 | + | 0.883157i | \(0.655413\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −12.0735 | + | 6.97062i | −1.02406 | + | 0.591241i | −0.915277 | − | 0.402825i | \(-0.868028\pi\) |
−0.108782 | + | 0.994066i | \(0.534695\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 1.50998 | − | 2.61537i | 0.126715 | − | 0.219477i | ||||
\(143\) | −5.76711 | −0.482270 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 10.4185i | 0.865210i | ||||||||
\(146\) | −19.4851 | + | 33.7492i | −1.61260 | + | 2.79310i | ||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 7.00915 | + | 12.1402i | 0.576149 | + | 0.997919i | ||||
\(149\) | 9.46916 | − | 5.46702i | 0.775744 | − | 0.447876i | −0.0591761 | − | 0.998248i | \(-0.518847\pi\) |
0.834920 | + | 0.550372i | \(0.185514\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 6.97277 | − | 12.0772i | 0.567436 | − | 0.982828i | −0.429383 | − | 0.903123i | \(-0.641269\pi\) |
0.996818 | − | 0.0797050i | \(-0.0253978\pi\) | |||||||
\(152\) | 4.60911 | 0.373848 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −8.11417 | − | 4.68472i | −0.651746 | − | 0.376286i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −13.6641 | + | 7.88894i | −1.09051 | + | 0.629606i | −0.933712 | − | 0.358024i | \(-0.883450\pi\) |
−0.156798 | + | 0.987631i | \(0.550117\pi\) | |||||||
\(158\) | −23.6866 | + | 13.6755i | −1.88440 | + | 1.08796i | ||||
\(159\) | 0 | 0 | ||||||||
\(160\) | −15.6566 | − | 9.03932i | −1.23776 | − | 0.714621i | ||||
\(161\) | 0 | 0 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −6.76552 | −0.529916 | −0.264958 | − | 0.964260i | \(-0.585358\pi\) | ||||
−0.264958 | + | 0.964260i | \(0.585358\pi\) | |||||||
\(164\) | −15.3122 | + | 26.5215i | −1.19568 | + | 2.07098i | ||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −23.7761 | + | 13.7271i | −1.84538 | + | 1.06543i | ||||
\(167\) | −9.54631 | − | 16.5347i | −0.738716 | − | 1.27949i | −0.953074 | − | 0.302738i | \(-0.902099\pi\) |
0.214358 | − | 0.976755i | \(-0.431234\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −5.62763 | + | 9.74733i | −0.432894 | + | 0.749795i | ||||
\(170\) | − | 34.7891i | − | 2.66820i | ||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 36.1745 | 2.75828 | ||||||||
\(173\) | 10.9246 | − | 18.9219i | 0.830579 | − | 1.43860i | −0.0670016 | − | 0.997753i | \(-0.521343\pi\) |
0.897580 | − | 0.440851i | \(-0.145323\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | −31.3881 | + | 18.1219i | −2.36597 | + | 1.36599i | ||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 7.42478 | + | 4.28670i | 0.556511 | + | 0.321302i | ||||
\(179\) | 17.1896i | 1.28481i | 0.766364 | + | 0.642406i | \(0.222064\pi\) | ||||
−0.766364 | + | 0.642406i | \(0.777936\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | − | 16.6462i | − | 1.23730i | −0.785666 | − | 0.618650i | \(-0.787680\pi\) | ||
0.785666 | − | 0.618650i | \(-0.212320\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | −18.9840 | − | 32.8813i | −1.39952 | − | 2.42404i | ||||
\(185\) | −3.51717 | − | 6.09191i | −0.258587 | − | 0.447886i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −21.8797 | − | 12.6323i | −1.60000 | − | 0.923763i | ||||
\(188\) | −2.29292 | −0.167228 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | −4.06029 | −0.294565 | ||||||||
\(191\) | −0.826254 | − | 0.477038i | −0.0597857 | − | 0.0345173i | 0.469809 | − | 0.882768i | \(-0.344323\pi\) |
−0.529595 | + | 0.848251i | \(0.677656\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 0.847203 | + | 1.46740i | 0.0609830 | + | 0.105626i | 0.894905 | − | 0.446257i | \(-0.147243\pi\) |
−0.833922 | + | 0.551882i | \(0.813910\pi\) | |||||||
\(194\) | 18.9832 | + | 32.8799i | 1.36292 | + | 2.36064i | ||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | − | 12.7486i | − | 0.908301i | −0.890925 | − | 0.454150i | \(-0.849943\pi\) | ||
0.890925 | − | 0.454150i | \(-0.150057\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | − | 4.35807i | − | 0.308935i | −0.987998 | − | 0.154468i | \(-0.950634\pi\) | ||
0.987998 | − | 0.154468i | \(-0.0493662\pi\) | |||||||
\(200\) | 2.58706 | + | 1.49364i | 0.182933 | + | 0.105616i | ||||
\(201\) | 0 | 0 | ||||||||
\(202\) | −3.71576 | + | 2.14530i | −0.261440 | + | 0.150942i | ||||
\(203\) | 0 | 0 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 7.68361 | − | 13.3084i | 0.536646 | − | 0.929499i | ||||
\(206\) | −4.19117 | −0.292013 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | − | 10.9650i | − | 0.760287i | ||||||
\(209\) | −1.47433 | + | 2.55362i | −0.101982 | + | 0.176637i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −2.24368 | − | 3.88617i | −0.154461 | − | 0.267535i | 0.778401 | − | 0.627767i | \(-0.216031\pi\) |
−0.932863 | + | 0.360232i | \(0.882698\pi\) | |||||||
\(212\) | −16.6842 | + | 9.63263i | −1.14588 | + | 0.661571i | ||||
\(213\) | 0 | 0 | ||||||||
\(214\) | −23.6073 | + | 40.8890i | −1.61376 | + | 2.79512i | ||||
\(215\) | −18.1522 | −1.23797 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | 35.6655 | + | 20.5915i | 2.41557 | + | 1.39463i | ||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 40.9743 | − | 23.6565i | 2.76249 | − | 1.59492i | ||||
\(221\) | 6.61937 | − | 3.82170i | 0.445267 | − | 0.257075i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 18.0005 | + | 10.3926i | 1.20540 | + | 0.695939i | 0.961751 | − | 0.273924i | \(-0.0883218\pi\) |
0.243650 | + | 0.969863i | \(0.421655\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −15.1118 | −1.00522 | ||||||||
\(227\) | −14.1579 | + | 24.5223i | −0.939696 | + | 1.62760i | −0.173657 | + | 0.984806i | \(0.555558\pi\) |
−0.766039 | + | 0.642795i | \(0.777775\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 18.8670 | − | 10.8929i | 1.24677 | − | 0.719821i | 0.276303 | − | 0.961071i | \(-0.410891\pi\) |
0.970463 | + | 0.241250i | \(0.0775573\pi\) | |||||||
\(230\) | 16.7236 | + | 28.9661i | 1.10272 | + | 1.90997i | ||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −15.2458 | + | 26.4065i | −1.00094 | + | 1.73367i | ||||
\(233\) | 15.2335i | 0.997978i | 0.866608 | + | 0.498989i | \(0.166295\pi\) | ||||
−0.866608 | + | 0.498989i | \(0.833705\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 1.15058 | 0.0750554 | ||||||||
\(236\) | 10.0237 | − | 17.3616i | 0.652489 | − | 1.13014i | ||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 4.95125 | − | 2.85861i | 0.320270 | − | 0.184908i | −0.331243 | − | 0.943545i | \(-0.607468\pi\) |
0.651513 | + | 0.758638i | \(0.274135\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −3.87212 | − | 2.23557i | −0.249425 | − | 0.144006i | 0.370076 | − | 0.929002i | \(-0.379332\pi\) |
−0.619501 | + | 0.784996i | \(0.712665\pi\) | |||||||
\(242\) | − | 20.7871i | − | 1.33625i | ||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 9.53325i | 0.610304i | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −0.446036 | − | 0.772557i | −0.0283806 | − | 0.0491566i | ||||
\(248\) | −13.7107 | − | 23.7476i | −0.870629 | − | 1.50797i | ||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 23.7540 | + | 13.7144i | 1.50234 | + | 0.867374i | ||||
\(251\) | 11.6265 | 0.733861 | 0.366931 | − | 0.930248i | \(-0.380409\pi\) | ||||
0.366931 | + | 0.930248i | \(0.380409\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 24.2900 | 1.52710 | ||||||||
\(254\) | 36.9993 | + | 21.3616i | 2.32155 | + | 1.34034i | ||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 12.1213 | + | 20.9947i | 0.757582 | + | 1.31217i | ||||
\(257\) | −1.05140 | − | 1.82108i | −0.0655846 | − | 0.113596i | 0.831369 | − | 0.555721i | \(-0.187558\pi\) |
−0.896953 | + | 0.442126i | \(0.854225\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | 14.3138i | 0.887705i | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | − | 18.3562i | − | 1.13405i | ||||||
\(263\) | 1.90773 | + | 1.10143i | 0.117636 | + | 0.0679170i | 0.557663 | − | 0.830067i | \(-0.311698\pi\) |
−0.440028 | + | 0.897984i | \(0.645031\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 8.37207 | − | 4.83362i | 0.514292 | − | 0.296927i | ||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | −11.2096 | + | 19.4156i | −0.684737 | + | 1.18600i | ||||
\(269\) | 27.8623 | 1.69880 | 0.849398 | − | 0.527753i | \(-0.176965\pi\) | ||||
0.849398 | + | 0.527753i | \(0.176965\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | − | 11.4804i | − | 0.697382i | −0.937238 | − | 0.348691i | \(-0.886626\pi\) | ||
0.937238 | − | 0.348691i | \(-0.113374\pi\) | |||||||
\(272\) | 24.0177 | − | 41.5999i | 1.45629 | − | 2.52237i | ||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −1.06665 | − | 1.84749i | −0.0644387 | − | 0.111611i | ||||
\(275\) | −1.65507 | + | 0.955553i | −0.0998043 | + | 0.0576220i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 5.10000 | − | 8.83346i | 0.306429 | − | 0.530751i | −0.671149 | − | 0.741322i | \(-0.734199\pi\) |
0.977579 | + | 0.210571i | \(0.0675323\pi\) | |||||||
\(278\) | 35.9432 | 2.15573 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −9.45116 | − | 5.45663i | −0.563809 | − | 0.325515i | 0.190864 | − | 0.981617i | \(-0.438871\pi\) |
−0.754673 | + | 0.656101i | \(0.772204\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 10.2766 | − | 5.93322i | 0.610882 | − | 0.352693i | −0.162428 | − | 0.986720i | \(-0.551933\pi\) |
0.773311 | + | 0.634027i | \(0.218599\pi\) | |||||||
\(284\) | −4.71409 | + | 2.72168i | −0.279730 | + | 0.161502i | ||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 12.8767 | + | 7.43437i | 0.761415 | + | 0.439603i | ||||
\(287\) | 0 | 0 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 16.4841 | 0.969655 | ||||||||
\(290\) | 13.4305 | − | 23.2622i | 0.788664 | − | 1.36601i | ||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 60.8315 | − | 35.1211i | 3.55989 | − | 2.05531i | ||||
\(293\) | −9.55012 | − | 16.5413i | −0.557924 | − | 0.966353i | −0.997670 | − | 0.0682302i | \(-0.978265\pi\) |
0.439746 | − | 0.898122i | \(-0.355069\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −5.02987 | + | 8.71199i | −0.292850 | + | 0.507232i | ||||
\(296\) | − | 20.5872i | − | 1.19661i | ||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | −28.1901 | −1.63301 | ||||||||
\(299\) | −3.67427 | + | 6.36403i | −0.212489 | + | 0.368041i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | −31.1373 | + | 17.9772i | −1.79175 | + | 1.03447i | ||||
\(303\) | 0 | 0 | ||||||||
\(304\) | −4.85519 | − | 2.80315i | −0.278464 | − | 0.160771i | ||||
\(305\) | − | 4.78375i | − | 0.273917i | ||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | − | 2.35488i | − | 0.134400i | −0.997740 | − | 0.0672001i | \(-0.978593\pi\) | ||
0.997740 | − | 0.0672001i | \(-0.0214066\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 12.0781 | + | 20.9199i | 0.685991 | + | 1.18817i | ||||
\(311\) | −3.92483 | − | 6.79801i | −0.222557 | − | 0.385480i | 0.733027 | − | 0.680200i | \(-0.238107\pi\) |
−0.955584 | + | 0.294720i | \(0.904774\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −26.0268 | − | 15.0266i | −1.47112 | − | 0.849352i | −0.471647 | − | 0.881787i | \(-0.656340\pi\) |
−0.999474 | + | 0.0324349i | \(0.989674\pi\) | |||||||
\(314\) | 40.6785 | 2.29562 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 49.2989 | 2.77328 | ||||||||
\(317\) | 9.61906 | + | 5.55356i | 0.540260 | + | 0.311919i | 0.745184 | − | 0.666859i | \(-0.232361\pi\) |
−0.204924 | + | 0.978778i | \(0.565695\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −9.75347 | − | 16.8935i | −0.546089 | − | 0.945854i | ||||
\(320\) | 3.94757 | + | 6.83739i | 0.220676 | + | 0.382222i | ||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | − | 3.90798i | − | 0.217446i | ||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | − | 0.578175i | − | 0.0320714i | ||||||
\(326\) | 15.1059 | + | 8.72141i | 0.836640 | + | 0.483034i | ||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 38.9494 | − | 22.4875i | 2.15062 | − | 1.24166i | ||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 8.63362 | − | 14.9539i | 0.474547 | − | 0.821939i | −0.525028 | − | 0.851085i | \(-0.675945\pi\) |
0.999575 | + | 0.0291457i | \(0.00927866\pi\) | |||||||
\(332\) | 49.4851 | 2.71585 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 49.2245i | 2.69345i | ||||||||
\(335\) | 5.62495 | − | 9.74270i | 0.307324 | − | 0.532300i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −3.82962 | − | 6.63309i | −0.208612 | − | 0.361327i | 0.742665 | − | 0.669663i | \(-0.233561\pi\) |
−0.951278 | + | 0.308336i | \(0.900228\pi\) | |||||||
\(338\) | 25.1305 | − | 14.5091i | 1.36692 | − | 0.789192i | ||||
\(339\) | 0 | 0 | ||||||||
\(340\) | −31.3530 | + | 54.3049i | −1.70035 | + | 2.94510i | ||||
\(341\) | 17.5427 | 0.949992 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 0 | 0 | ||||||||
\(344\) | −46.0082 | − | 26.5629i | −2.48060 | − | 1.43217i | ||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −48.7843 | + | 28.1656i | −2.62266 | + | 1.51419i | ||||
\(347\) | 11.4014 | − | 6.58262i | 0.612061 | − | 0.353374i | −0.161711 | − | 0.986838i | \(-0.551701\pi\) |
0.773772 | + | 0.633465i | \(0.218368\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −1.05185 | − | 0.607283i | −0.0563040 | − | 0.0325071i | 0.471584 | − | 0.881821i | \(-0.343682\pi\) |
−0.527888 | + | 0.849314i | \(0.677016\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 33.8493 | 1.80417 | ||||||||
\(353\) | 13.4114 | − | 23.2292i | 0.713816 | − | 1.23637i | −0.249598 | − | 0.968349i | \(-0.580299\pi\) |
0.963414 | − | 0.268016i | \(-0.0863681\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 2.36551 | − | 1.36573i | 0.125548 | − | 0.0724854i | ||||
\(356\) | −7.72659 | − | 13.3829i | −0.409509 | − | 0.709290i | ||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 22.1591 | − | 38.3807i | 1.17114 | − | 2.02848i | ||||
\(359\) | 7.45024i | 0.393208i | 0.980483 | + | 0.196604i | \(0.0629914\pi\) | ||||
−0.980483 | + | 0.196604i | \(0.937009\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 18.5439 | 0.975994 | ||||||||
\(362\) | −21.4585 | + | 37.1673i | −1.12784 | + | 1.95347i | ||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −30.5250 | + | 17.6236i | −1.59775 | + | 0.922463i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 30.3000 | + | 17.4937i | 1.58165 | + | 0.913166i | 0.994619 | + | 0.103601i | \(0.0330365\pi\) |
0.587031 | + | 0.809565i | \(0.300297\pi\) | |||||||
\(368\) | 46.1825i | 2.40743i | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 18.1359i | 0.942840i | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 15.0495 | + | 26.0665i | 0.779233 | + | 1.34967i | 0.932384 | + | 0.361469i | \(0.117725\pi\) |
−0.153151 | + | 0.988203i | \(0.548942\pi\) | |||||||
\(374\) | 32.5684 | + | 56.4102i | 1.68407 | + | 2.91690i | ||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 2.91623 | + | 1.68369i | 0.150393 | + | 0.0868295i | ||||
\(377\) | 5.90152 | 0.303944 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −27.0996 | −1.39201 | −0.696006 | − | 0.718036i | \(-0.745041\pi\) | ||||
−0.696006 | + | 0.718036i | \(0.745041\pi\) | |||||||
\(380\) | 6.33801 | + | 3.65925i | 0.325133 | + | 0.187716i | ||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 1.22990 | + | 2.13024i | 0.0629270 | + | 0.108993i | ||||
\(383\) | −1.83015 | − | 3.16992i | −0.0935164 | − | 0.161975i | 0.815472 | − | 0.578796i | \(-0.196477\pi\) |
−0.908988 | + | 0.416821i | \(0.863144\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | − | 4.36851i | − | 0.222351i | ||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | − | 68.4329i | − | 3.47415i | ||||||
\(389\) | −10.5387 | − | 6.08449i | −0.534331 | − | 0.308496i | 0.208447 | − | 0.978034i | \(-0.433159\pi\) |
−0.742778 | + | 0.669537i | \(0.766492\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −27.8795 | + | 16.0962i | −1.40993 | + | 0.814022i | ||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | −16.4342 | + | 28.4649i | −0.827943 | + | 1.43404i | ||||
\(395\) | −24.7380 | −1.24470 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 26.7741i | 1.34375i | 0.740663 | + | 0.671876i | \(0.234511\pi\) | ||||
−0.740663 | + | 0.671876i | \(0.765489\pi\) | |||||||
\(398\) | −5.61797 | + | 9.73061i | −0.281603 | + | 0.487752i | ||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −1.81679 | − | 3.14678i | −0.0908397 | − | 0.157339i | ||||
\(401\) | −6.69428 | + | 3.86494i | −0.334296 | + | 0.193006i | −0.657747 | − | 0.753239i | \(-0.728490\pi\) |
0.323451 | + | 0.946245i | \(0.395157\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −2.65364 | + | 4.59624i | −0.132187 | + | 0.228955i | ||||
\(404\) | 7.73361 | 0.384761 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 11.4061 | + | 6.58532i | 0.565380 | + | 0.326422i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −7.84660 | + | 4.53024i | −0.387989 | + | 0.224006i | −0.681289 | − | 0.732015i | \(-0.738580\pi\) |
0.293299 | + | 0.956021i | \(0.405247\pi\) | |||||||
\(410\) | −34.3116 | + | 19.8098i | −1.69453 | + | 0.978338i | ||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 6.54231 | + | 3.77720i | 0.322316 | + | 0.186090i | ||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −24.8315 | −1.21893 | ||||||||
\(416\) | −5.12029 | + | 8.86860i | −0.251043 | + | 0.434819i | ||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 6.58372 | − | 3.80111i | 0.322020 | − | 0.185919i | ||||
\(419\) | 3.30466 | + | 5.72384i | 0.161443 | + | 0.279628i | 0.935386 | − | 0.353627i | \(-0.115052\pi\) |
−0.773943 | + | 0.633255i | \(0.781718\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 6.39209 | − | 11.0714i | 0.311531 | − | 0.539588i | −0.667163 | − | 0.744912i | \(-0.732491\pi\) |
0.978694 | + | 0.205324i | \(0.0658248\pi\) | |||||||
\(422\) | 11.5693i | 0.563184i | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 28.2929 | 1.37403 | ||||||||
\(425\) | 1.26643 | − | 2.19353i | 0.0614311 | − | 0.106402i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | 73.7007 | − | 42.5511i | 3.56246 | − | 2.05679i | ||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 40.5299 | + | 23.4000i | 1.95453 | + | 1.12845i | ||||
\(431\) | 21.9112i | 1.05542i | 0.849424 | + | 0.527712i | \(0.176950\pi\) | ||||
−0.849424 | + | 0.527712i | \(0.823050\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | − | 8.21181i | − | 0.394635i | −0.980340 | − | 0.197317i | \(-0.936777\pi\) | ||
0.980340 | − | 0.197317i | \(-0.0632229\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −37.1153 | − | 64.2855i | −1.77750 | − | 3.07872i | ||||
\(437\) | 1.87862 | + | 3.25386i | 0.0898665 | + | 0.155653i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 32.7996 | + | 18.9368i | 1.56544 | + | 0.903806i | 0.996690 | + | 0.0812949i | \(0.0259056\pi\) |
0.568749 | + | 0.822511i | \(0.307428\pi\) | |||||||
\(440\) | −69.4838 | −3.31251 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | −19.7061 | −0.937326 | ||||||||
\(443\) | −17.7210 | − | 10.2312i | −0.841950 | − | 0.486100i | 0.0159769 | − | 0.999872i | \(-0.494914\pi\) |
−0.857926 | + | 0.513773i | \(0.828248\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 3.87718 | + | 6.71547i | 0.183796 | + | 0.318344i | ||||
\(446\) | −26.7941 | − | 46.4087i | −1.26874 | − | 2.19752i | ||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 35.7054i | 1.68504i | 0.538665 | + | 0.842520i | \(0.318929\pi\) | ||||
−0.538665 | + | 0.842520i | \(0.681071\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 28.7726i | 1.35485i | ||||||||
\(452\) | 23.5892 | + | 13.6192i | 1.10954 | + | 0.640594i | ||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 63.2232 | − | 36.5019i | 2.96721 | − | 1.71312i | ||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 0.127090 | − | 0.220126i | 0.00594501 | − | 0.0102971i | −0.863038 | − | 0.505140i | \(-0.831441\pi\) |
0.868983 | + | 0.494843i | \(0.164774\pi\) | |||||||
\(458\) | −56.1678 | −2.62455 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | − | 60.2870i | − | 2.81090i | ||||||
\(461\) | 12.2175 | − | 21.1613i | 0.569025 | − | 0.985581i | −0.427637 | − | 0.903950i | \(-0.640654\pi\) |
0.996663 | − | 0.0816304i | \(-0.0260127\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 0.409986 | + | 0.710116i | 0.0190536 | + | 0.0330019i | 0.875395 | − | 0.483408i | \(-0.160601\pi\) |
−0.856341 | + | 0.516410i | \(0.827268\pi\) | |||||||
\(464\) | 32.1196 | − | 18.5443i | 1.49112 | − | 0.860896i | ||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 19.6374 | − | 34.0130i | 0.909686 | − | 1.57562i | ||||
\(467\) | 1.81925 | 0.0841848 | 0.0420924 | − | 0.999114i | \(-0.486598\pi\) | ||||
0.0420924 | + | 0.999114i | \(0.486598\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | −2.56899 | − | 1.48321i | −0.118499 | − | 0.0684152i | ||||
\(471\) | 0 | 0 | ||||||||
\(472\) | −25.4972 | + | 14.7208i | −1.17360 | + | 0.677581i | ||||
\(473\) | 29.4336 | − | 16.9935i | 1.35336 | − | 0.781363i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −0.256010 | − | 0.147807i | −0.0117465 | − | 0.00678187i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | −14.7401 | −0.674196 | ||||||||
\(479\) | 0.681074 | − | 1.17965i | 0.0311191 | − | 0.0538998i | −0.850046 | − | 0.526708i | \(-0.823426\pi\) |
0.881166 | + | 0.472808i | \(0.156760\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −3.45074 | + | 1.99228i | −0.157340 | + | 0.0908403i | ||||
\(482\) | 5.76373 | + | 9.98308i | 0.262531 | + | 0.454717i | ||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −18.7340 | + | 32.4482i | −0.851544 | + | 1.47492i | ||||
\(485\) | 34.3394i | 1.55927i | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 31.6121 | 1.43248 | 0.716241 | − | 0.697853i | \(-0.245861\pi\) | ||||
0.716241 | + | 0.697853i | \(0.245861\pi\) | |||||||
\(488\) | 7.00026 | − | 12.1248i | 0.316887 | − | 0.548864i | ||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 1.97415 | − | 1.13977i | 0.0890919 | − | 0.0514373i | −0.454792 | − | 0.890598i | \(-0.650286\pi\) |
0.543884 | + | 0.839160i | \(0.316953\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 22.3897 | + | 12.9267i | 1.00838 | + | 0.582188i | ||||
\(494\) | 2.29993i | 0.103479i | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 33.3540i | 1.49764i | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −13.5195 | − | 23.4164i | −0.605215 | − | 1.04826i | −0.992017 | − | 0.126101i | \(-0.959754\pi\) |
0.386802 | − | 0.922163i | \(-0.373580\pi\) | |||||||
\(500\) | −24.7196 | − | 42.8156i | −1.10549 | − | 1.91477i | ||||
\(501\) | 0 | 0 | ||||||||
\(502\) | −25.9595 | − | 14.9877i | −1.15863 | − | 0.668936i | ||||
\(503\) | 0.276948 | 0.0123485 | 0.00617426 | − | 0.999981i | \(-0.498035\pi\) | ||||
0.00617426 | + | 0.999981i | \(0.498035\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −3.88070 | −0.172689 | ||||||||
\(506\) | −54.2342 | − | 31.3121i | −2.41100 | − | 1.39199i | ||||
\(507\) | 0 | 0 | ||||||||
\(508\) | −38.5033 | − | 66.6897i | −1.70831 | − | 2.95888i | ||||
\(509\) | 9.21476 | + | 15.9604i | 0.408437 | + | 0.707434i | 0.994715 | − | 0.102676i | \(-0.0327406\pi\) |
−0.586278 | + | 0.810110i | \(0.699407\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | − | 48.9492i | − | 2.16327i | ||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 5.42143i | 0.239129i | ||||||||
\(515\) | −3.28291 | − | 1.89539i | −0.144662 | − | 0.0835208i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −1.86565 | + | 1.07713i | −0.0820512 | + | 0.0473723i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 10.5106 | − | 18.2049i | 0.460921 | − | 0.798339i | ||||
\(521\) | 23.2527 | 1.01872 | 0.509360 | − | 0.860554i | \(-0.329882\pi\) | ||||
0.509360 | + | 0.860554i | \(0.329882\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 13.3052i | 0.581798i | 0.956754 | + | 0.290899i | \(0.0939543\pi\) | ||||
−0.956754 | + | 0.290899i | \(0.906046\pi\) | |||||||
\(524\) | −16.5431 | + | 28.6535i | −0.722689 | + | 1.25173i | ||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −2.83970 | − | 4.91850i | −0.123817 | − | 0.214457i | ||||
\(527\) | −20.1352 | + | 11.6251i | −0.877102 | + | 0.506395i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 3.97534 | − | 6.88549i | 0.172841 | − | 0.299369i | ||||
\(530\) | −24.9240 | −1.08263 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −7.53848 | − | 4.35235i | −0.326528 | − | 0.188521i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −36.9828 | + | 21.3520i | −1.59890 | + | 0.923128i | ||||
\(536\) | 28.5138 | − | 16.4624i | 1.23161 | − | 0.711069i | ||||
\(537\) | 0 | 0 | ||||||||
\(538\) | −62.2105 | − | 35.9172i | −2.68208 | − | 1.54850i | ||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −30.1692 | −1.29707 | −0.648537 | − | 0.761183i | \(-0.724619\pi\) | ||||
−0.648537 | + | 0.761183i | \(0.724619\pi\) | |||||||
\(542\) | −14.7993 | + | 25.6331i | −0.635684 | + | 1.10104i | ||||
\(543\) | 0 | 0 | ||||||||
\(544\) | −38.8515 | + | 22.4309i | −1.66574 | + | 0.961718i | ||||
\(545\) | 18.6243 | + | 32.2582i | 0.797778 | + | 1.38179i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −0.572061 | + | 0.990840i | −0.0244596 | + | 0.0423652i | −0.877996 | − | 0.478668i | \(-0.841120\pi\) |
0.853537 | + | 0.521033i | \(0.174453\pi\) | |||||||
\(548\) | 3.84518i | 0.164258i | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 4.92720 | 0.210097 | ||||||||
\(551\) | 1.50869 | − | 2.61313i | 0.0642724 | − | 0.111323i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | −22.7744 | + | 13.1488i | −0.967591 | + | 0.558639i | ||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −56.1065 | − | 32.3931i | −2.37944 | − | 1.37377i | ||||
\(557\) | − | 9.64623i | − | 0.408724i | −0.978895 | − | 0.204362i | \(-0.934488\pi\) | ||
0.978895 | − | 0.204362i | \(-0.0655120\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 10.2822i | 0.434893i | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 14.0683 | + | 24.3669i | 0.593434 | + | 1.02786i | ||||
\(563\) | −1.54395 | − | 2.67420i | −0.0650698 | − | 0.112704i | 0.831655 | − | 0.555292i | \(-0.187394\pi\) |
−0.896725 | + | 0.442588i | \(0.854060\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −11.8370 | − | 6.83407i | −0.497985 | − | 0.287512i | ||||
\(566\) | −30.5940 | −1.28596 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 7.99411 | 0.335425 | ||||||||
\(569\) | −7.30588 | − | 4.21805i | −0.306278 | − | 0.176830i | 0.338982 | − | 0.940793i | \(-0.389918\pi\) |
−0.645260 | + | 0.763963i | \(0.723251\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 17.0208 | + | 29.4808i | 0.712297 | + | 1.23373i | 0.963993 | + | 0.265928i | \(0.0856782\pi\) |
−0.251696 | + | 0.967806i | \(0.580988\pi\) | |||||||
\(572\) | −13.4001 | − | 23.2097i | −0.560288 | − | 0.970447i | ||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 2.43516i | 0.101553i | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | − | 18.1052i | − | 0.753730i | −0.926268 | − | 0.376865i | \(-0.877002\pi\) | ||
0.926268 | − | 0.376865i | \(-0.122998\pi\) | |||||||
\(578\) | −36.8055 | − | 21.2497i | −1.53091 | − | 0.883869i | ||||
\(579\) | 0 | 0 | ||||||||
\(580\) | −41.9292 | + | 24.2078i | −1.74102 | + | 1.00518i | ||||
\(581\) | 0 | 0 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −9.05015 | + | 15.6753i | −0.374819 | + | 0.649206i | ||||
\(584\) | −103.157 | −4.26869 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 49.2441i | 2.03426i | ||||||||
\(587\) | −4.04900 | + | 7.01308i | −0.167120 | + | 0.289461i | −0.937406 | − | 0.348238i | \(-0.886780\pi\) |
0.770286 | + | 0.637699i | \(0.220113\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 1.35678 | + | 2.35001i | 0.0559050 | + | 0.0968304i | ||||
\(590\) | 22.4612 | − | 12.9680i | 0.924713 | − | 0.533883i | ||||
\(591\) | 0 | 0 | ||||||||
\(592\) | −12.5207 | + | 21.6864i | −0.514596 | + | 0.891306i | ||||
\(593\) | −6.66433 | −0.273671 | −0.136836 | − | 0.990594i | \(-0.543693\pi\) | ||||
−0.136836 | + | 0.990594i | \(0.543693\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 44.0040 | + | 25.4057i | 1.80247 | + | 1.04066i | ||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 16.4077 | − | 9.47299i | 0.670961 | − | 0.387380i | ||||
\(599\) | 3.10562 | − | 1.79303i | 0.126892 | − | 0.0732614i | −0.435210 | − | 0.900329i | \(-0.643326\pi\) |
0.562103 | + | 0.827068i | \(0.309993\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 4.86949 | + | 2.81140i | 0.198631 | + | 0.114679i | 0.596017 | − | 0.802972i | \(-0.296749\pi\) |
−0.397386 | + | 0.917652i | \(0.630083\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 64.8061 | 2.63692 | ||||||||
\(605\) | 9.40064 | − | 16.2824i | 0.382190 | − | 0.661973i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −1.93239 | + | 1.11566i | −0.0784332 | + | 0.0452834i | −0.538704 | − | 0.842495i | \(-0.681086\pi\) |
0.460270 | + | 0.887779i | \(0.347752\pi\) | |||||||
\(608\) | 2.61795 | + | 4.53442i | 0.106172 | + | 0.183895i | ||||
\(609\) | 0 | 0 | ||||||||
\(610\) | −6.16672 | + | 10.6811i | −0.249683 | + | 0.432464i | ||||
\(611\) | − | 0.651740i | − | 0.0263666i | ||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −6.82038 | −0.275473 | −0.137736 | − | 0.990469i | \(-0.543983\pi\) | ||||
−0.137736 | + | 0.990469i | \(0.543983\pi\) | |||||||
\(614\) | −3.03567 | + | 5.25793i | −0.122510 | + | 0.212193i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 2.35139 | − | 1.35757i | 0.0946632 | − | 0.0546538i | −0.451921 | − | 0.892058i | \(-0.649261\pi\) |
0.546584 | + | 0.837404i | \(0.315928\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 23.1886 | + | 13.3880i | 0.932029 | + | 0.538107i | 0.887453 | − | 0.460899i | \(-0.152473\pi\) |
0.0445762 | + | 0.999006i | \(0.485806\pi\) | |||||||
\(620\) | − | 43.5406i | − | 1.74863i | ||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 20.2380i | 0.811469i | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 13.4985 | + | 23.3801i | 0.539940 | + | 0.935203i | ||||
\(626\) | 38.7414 | + | 67.1021i | 1.54842 | + | 2.68194i | ||||
\(627\) | 0 | 0 | ||||||||
\(628\) | −63.4980 | − | 36.6606i | −2.53385 | − | 1.46292i | ||||
\(629\) | −17.4556 | −0.696000 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −11.1620 | −0.444354 | −0.222177 | − | 0.975006i | \(-0.571316\pi\) | ||||
−0.222177 | + | 0.975006i | \(0.571316\pi\) | |||||||
\(632\) | −62.7004 | − | 36.2001i | −2.49409 | − | 1.43996i | ||||
\(633\) | 0 | 0 | ||||||||
\(634\) | −14.3182 | − | 24.7998i | −0.568647 | − | 0.984926i | ||||
\(635\) | 19.3208 | + | 33.4647i | 0.766724 | + | 1.32801i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | 50.2927i | 1.99111i | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 15.8021i | 0.624633i | ||||||||
\(641\) | −38.6251 | − | 22.3002i | −1.52560 | − | 0.880805i | −0.999539 | − | 0.0303565i | \(-0.990336\pi\) |
−0.526059 | − | 0.850448i | \(-0.676331\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −23.6268 | + | 13.6410i | −0.931751 | + | 0.537947i | −0.887365 | − | 0.461068i | \(-0.847466\pi\) |
−0.0443860 | + | 0.999014i | \(0.514133\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −5.03777 | + | 8.72568i | −0.198208 | + | 0.343307i | ||||
\(647\) | 44.9350 | 1.76658 | 0.883288 | − | 0.468831i | \(-0.155325\pi\) | ||||
0.883288 | + | 0.468831i | \(0.155325\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | − | 18.8352i | − | 0.739347i | ||||||
\(650\) | −0.745324 | + | 1.29094i | −0.0292340 | + | 0.0506348i | ||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −15.7200 | − | 27.2278i | −0.615642 | − | 1.06632i | ||||
\(653\) | 24.0549 | − | 13.8881i | 0.941343 | − | 0.543484i | 0.0509617 | − | 0.998701i | \(-0.483771\pi\) |
0.890381 | + | 0.455216i | \(0.150438\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 8.30128 | − | 14.3782i | 0.324358 | − | 0.561804i | ||||
\(656\) | −54.7053 | −2.13588 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −0.801975 | − | 0.463021i | −0.0312405 | − | 0.0180367i | 0.484298 | − | 0.874903i | \(-0.339075\pi\) |
−0.515539 | + | 0.856866i | \(0.672408\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 28.3028 | − | 16.3406i | 1.10085 | − | 0.635577i | 0.164408 | − | 0.986392i | \(-0.447429\pi\) |
0.936445 | + | 0.350815i | \(0.114095\pi\) | |||||||
\(662\) | −38.5540 | + | 22.2592i | −1.49844 | + | 0.865126i | ||||
\(663\) | 0 | 0 | ||||||||
\(664\) | −62.9373 | − | 36.3369i | −2.44244 | − | 1.41014i | ||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −24.8561 | −0.962430 | ||||||||
\(668\) | 44.3625 | − | 76.8382i | 1.71644 | − | 2.97296i | ||||
\(669\) | 0 | 0 | ||||||||
\(670\) | −25.1186 | + | 14.5022i | −0.970415 | + | 0.560269i | ||||
\(671\) | 4.47839 | + | 7.75681i | 0.172886 | + | 0.299448i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −15.6947 | + | 27.1840i | −0.604987 | + | 1.04787i | 0.387067 | + | 0.922052i | \(0.373488\pi\) |
−0.992054 | + | 0.125816i | \(0.959845\pi\) | |||||||
\(674\) | 19.7470i | 0.760625i | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −52.3041 | −2.01170 | ||||||||
\(677\) | −10.7882 | + | 18.6858i | −0.414626 | + | 0.718153i | −0.995389 | − | 0.0959196i | \(-0.969421\pi\) |
0.580763 | + | 0.814072i | \(0.302754\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | 79.7521 | − | 46.0449i | 3.05835 | − | 1.76574i | ||||
\(681\) | 0 | 0 | ||||||||
\(682\) | −39.1691 | − | 22.6143i | −1.49986 | − | 0.865946i | ||||
\(683\) | − | 36.2593i | − | 1.38742i | −0.720253 | − | 0.693711i | \(-0.755974\pi\) | ||
0.720253 | − | 0.693711i | \(-0.244026\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | − | 1.92950i | − | 0.0737224i | ||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 32.3098 | + | 55.9622i | 1.23180 | + | 2.13354i | ||||
\(689\) | −2.73798 | − | 4.74232i | −0.104309 | − | 0.180668i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −6.16389 | − | 3.55872i | −0.234485 | − | 0.135380i | 0.378154 | − | 0.925743i | \(-0.376559\pi\) |
−0.612640 | + | 0.790362i | \(0.709892\pi\) | |||||||
\(692\) | 101.535 | 3.85977 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −33.9426 | −1.28844 | ||||||||
\(695\) | 28.1540 | + | 16.2547i | 1.06794 | + | 0.616577i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −19.0667 | − | 33.0246i | −0.722204 | − | 1.25089i | ||||
\(698\) | 1.56569 | + | 2.71186i | 0.0592624 | + | 0.102645i | ||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 29.4609i | 1.11272i | 0.830940 | + | 0.556362i | \(0.187803\pi\) | ||||
−0.830940 | + | 0.556362i | \(0.812197\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 2.03727i | 0.0768370i | ||||||||
\(704\) | −12.8019 | − | 7.39117i | −0.482489 | − | 0.278565i | ||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −59.8894 | + | 34.5772i | −2.25397 | + | 1.30133i | ||||
\(707\) | 0 | 0 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 19.0361 | − | 32.9715i | 0.714916 | − | 1.23827i | −0.248076 | − | 0.968740i | \(-0.579798\pi\) |
0.962992 | − | 0.269530i | \(-0.0868683\pi\) | |||||||
\(710\) | −7.04224 | −0.264290 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 22.6945i | 0.850513i | ||||||||
\(713\) | 11.1766 | − | 19.3585i | 0.418568 | − | 0.724980i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 6.72414 | + | 11.6466i | 0.251469 | + | 0.435556i | ||||
\(716\) | −69.1795 | + | 39.9408i | −2.58536 | + | 1.49266i | ||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 9.60408 | − | 16.6348i | 0.358421 | − | 0.620803i | ||||
\(719\) | −38.2114 | −1.42505 | −0.712523 | − | 0.701649i | \(-0.752447\pi\) | ||||
−0.712523 | + | 0.701649i | \(0.752447\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | −41.4045 | − | 23.9049i | −1.54091 | − | 0.889647i | ||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 66.9924 | − | 38.6781i | 2.48975 | − | 1.43746i | ||||
\(725\) | 1.69364 | − | 0.977823i | 0.0629002 | − | 0.0363154i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 17.7563 | + | 10.2516i | 0.658546 | + | 0.380212i | 0.791723 | − | 0.610881i | \(-0.209184\pi\) |
−0.133177 | + | 0.991092i | \(0.542518\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 90.8743 | 3.36341 | ||||||||
\(731\) | −22.5222 | + | 39.0096i | −0.833014 | + | 1.44282i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 0.900627 | − | 0.519977i | 0.0332654 | − | 0.0192058i | −0.483275 | − | 0.875469i | \(-0.660553\pi\) |
0.516540 | + | 0.856263i | \(0.327220\pi\) | |||||||
\(734\) | −45.1023 | − | 78.1194i | −1.66475 | − | 2.88344i | ||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 21.5657 | − | 37.3528i | 0.794921 | − | 1.37684i | ||||
\(737\) | 21.0636i | 0.775887i | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 24.1609 | 0.888774 | 0.444387 | − | 0.895835i | \(-0.353422\pi\) | ||||
0.444387 | + | 0.895835i | \(0.353422\pi\) | |||||||
\(740\) | 16.3446 | − | 28.3096i | 0.600839 | − | 1.04068i | ||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 13.1637 | − | 7.60008i | 0.482930 | − | 0.278820i | −0.238707 | − | 0.971092i | \(-0.576723\pi\) |
0.721637 | + | 0.692272i | \(0.243390\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −22.0810 | − | 12.7485i | −0.808987 | − | 0.467069i | ||||
\(746\) | − | 77.6010i | − | 2.84118i | ||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | − | 117.406i | − | 4.29281i | ||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −1.52037 | − | 2.63336i | −0.0554791 | − | 0.0960926i | 0.836952 | − | 0.547276i | \(-0.184335\pi\) |
−0.892431 | + | 0.451184i | \(0.851002\pi\) | |||||||
\(752\) | −2.04795 | − | 3.54716i | −0.0746812 | − | 0.129352i | ||||
\(753\) | 0 | 0 | ||||||||
\(754\) | −13.1768 | − | 7.60763i | −0.479871 | − | 0.277053i | ||||
\(755\) | −32.5195 | −1.18350 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 43.3700 | 1.57631 | 0.788155 | − | 0.615477i | \(-0.211036\pi\) | ||||
0.788155 | + | 0.615477i | \(0.211036\pi\) | |||||||
\(758\) | 60.5075 | + | 34.9340i | 2.19773 | + | 1.26886i | ||||
\(759\) | 0 | 0 | ||||||||
\(760\) | −5.37397 | − | 9.30799i | −0.194934 | − | 0.337636i | ||||
\(761\) | −14.6319 | − | 25.3432i | −0.530406 | − | 0.918690i | −0.999371 | − | 0.0354731i | \(-0.988706\pi\) |
0.468965 | − | 0.883217i | \(-0.344627\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | − | 4.43367i | − | 0.160405i | ||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 9.43698i | 0.340972i | ||||||||
\(767\) | 4.93487 | + | 2.84915i | 0.178188 | + | 0.102877i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 29.6496 | − | 17.1182i | 1.06919 | − | 0.617299i | 0.141232 | − | 0.989977i | \(-0.454894\pi\) |
0.927961 | + | 0.372678i | \(0.121560\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | −3.93702 | + | 6.81912i | −0.141697 | + | 0.245426i | ||||
\(773\) | 33.9854 | 1.22237 | 0.611185 | − | 0.791488i | \(-0.290693\pi\) | ||||
0.611185 | + | 0.791488i | \(0.290693\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 1.75873i | 0.0631753i | ||||||||
\(776\) | −50.2502 | + | 87.0359i | −1.80388 | + | 3.12441i | ||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 15.6870 | + | 27.1707i | 0.562406 | + | 0.974117i | ||||
\(779\) | −3.85435 | + | 2.22531i | −0.138096 | + | 0.0797299i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −2.55710 | + | 4.42904i | −0.0915004 | + | 0.158483i | ||||
\(782\) | 82.9985 | 2.96802 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 31.8631 | + | 18.3962i | 1.13724 | + | 0.656587i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −23.8225 | + | 13.7539i | −0.849180 | + | 0.490274i | −0.860374 | − | 0.509663i | \(-0.829770\pi\) |
0.0111939 | + | 0.999937i | \(0.496437\pi\) | |||||||
\(788\) | 51.3067 | − | 29.6219i | 1.82773 | − | 1.05524i | ||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 55.2346 | + | 31.8897i | 1.96516 | + | 1.13458i | ||||
\(791\) | 0 | 0 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −2.70974 | −0.0962255 | ||||||||
\(794\) | 34.5144 | − | 59.7807i | 1.22487 | − | 2.12154i | ||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 17.5390 | − | 10.1262i | 0.621654 | − | 0.358912i | ||||
\(797\) | 21.0873 | + | 36.5243i | 0.746952 | + | 1.29376i | 0.949277 | + | 0.314440i | \(0.101817\pi\) |
−0.202326 | + | 0.979318i | \(0.564850\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 1.42757 | − | 2.47262i | 0.0505038 | − | 0.0874751i | ||||
\(800\) | 3.39352i | 0.119979i | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 19.9292 | 0.703723 | ||||||||
\(803\) | 32.9974 | − | 57.1531i | 1.16445 | − | 2.01689i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 11.8500 | − | 6.84160i | 0.417398 | − | 0.240985i | ||||
\(807\) | 0 | 0 | ||||||||
\(808\) | −9.83594 | − | 5.67878i | −0.346027 | − | 0.199779i | ||||
\(809\) | 4.83100i | 0.169849i | 0.996387 | + | 0.0849245i | \(0.0270649\pi\) | ||||
−0.996387 | + | 0.0849245i | \(0.972935\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | − | 6.46035i | − | 0.226853i | −0.993546 | − | 0.113427i | \(-0.963817\pi\) | ||
0.993546 | − | 0.113427i | \(-0.0361827\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | −16.9782 | − | 29.4071i | −0.595086 | − | 1.03072i | ||||
\(815\) | 7.88823 | + | 13.6628i | 0.276313 | + | 0.478587i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 4.55287 | + | 2.62860i | 0.159285 | + | 0.0919631i | ||||
\(818\) | 23.3597 | 0.816751 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 71.4128 | 2.49384 | ||||||||
\(821\) | −14.5455 | − | 8.39783i | −0.507640 | − | 0.293086i | 0.224223 | − | 0.974538i | \(-0.428016\pi\) |
−0.731863 | + | 0.681452i | \(0.761349\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 7.51749 | + | 13.0207i | 0.262043 | + | 0.453872i | 0.966785 | − | 0.255592i | \(-0.0822703\pi\) |
−0.704741 | + | 0.709464i | \(0.748937\pi\) | |||||||
\(824\) | −5.54719 | − | 9.60802i | −0.193246 | − | 0.334711i | ||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | − | 29.2462i | − | 1.01699i | −0.861065 | − | 0.508495i | \(-0.830202\pi\) | ||
0.861065 | − | 0.508495i | \(-0.169798\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 1.50423i | 0.0522440i | 0.999659 | + | 0.0261220i | \(0.00831584\pi\) | ||||
−0.999659 | + | 0.0261220i | \(0.991684\pi\) | |||||||
\(830\) | 55.4433 | + | 32.0102i | 1.92446 | + | 1.11109i | ||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 3.87301 | − | 2.23608i | 0.134272 | − | 0.0775222i | ||||
\(833\) | 0 | 0 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −22.2610 | + | 38.5571i | −0.770373 | + | 1.33432i | ||||
\(836\) | −13.7027 | −0.473917 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | − | 17.0401i | − | 0.588641i | ||||||
\(839\) | −22.9477 | + | 39.7466i | −0.792243 | + | 1.37221i | 0.132331 | + | 0.991206i | \(0.457754\pi\) |
−0.924575 | + | 0.381000i | \(0.875580\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −4.51923 | − | 7.82753i | −0.155835 | − | 0.269915i | ||||
\(842\) | −28.5443 | + | 16.4800i | −0.983701 | + | 0.567940i | ||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 10.4266 | − | 18.0593i | 0.358897 | − | 0.621628i | ||||
\(845\) | 26.2460 | 0.902891 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | −29.8035 | − | 17.2071i | −1.02346 | − | 0.590893i | ||||
\(849\) | 0 | 0 | ||||||||
\(850\) | −5.65534 | + | 3.26511i | −0.193977 | + | 0.111992i | ||||
\(851\) | 14.5338 | − | 8.39112i | 0.498214 | − | 0.287644i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 24.3086 | + | 14.0346i | 0.832310 | + | 0.480534i | 0.854643 | − | 0.519216i | \(-0.173776\pi\) |
−0.0223330 | + | 0.999751i | \(0.507109\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −124.981 | −4.27176 | ||||||||
\(857\) | −8.55426 | + | 14.8164i | −0.292208 | + | 0.506119i | −0.974332 | − | 0.225118i | \(-0.927723\pi\) |
0.682123 | + | 0.731237i | \(0.261057\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −4.50996 | + | 2.60383i | −0.153878 | + | 0.0888414i | −0.574962 | − | 0.818180i | \(-0.694983\pi\) |
0.421084 | + | 0.907022i | \(0.361650\pi\) | |||||||
\(860\) | −42.1775 | − | 73.0535i | −1.43824 | − | 2.49110i | ||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 28.2456 | − | 48.9228i | 0.962049 | − | 1.66632i | ||||
\(863\) | − | 44.7024i | − | 1.52169i | −0.648935 | − | 0.760844i | \(-0.724785\pi\) | ||
0.648935 | − | 0.760844i | \(-0.275215\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −50.9497 | −1.73234 | ||||||||
\(866\) | −10.5858 | + | 18.3352i | −0.359721 | + | 0.623055i | ||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 40.1124 | − | 23.1589i | 1.36072 | − | 0.785613i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −5.51871 | − | 3.18623i | −0.186994 | − | 0.107961i | ||||
\(872\) | 109.015i | 3.69171i | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | − | 9.68688i | − | 0.327664i | ||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 2.87432 | + | 4.97846i | 0.0970587 | + | 0.168111i | 0.910466 | − | 0.413584i | \(-0.135723\pi\) |
−0.813407 | + | 0.581695i | \(0.802390\pi\) | |||||||
\(878\) | −48.8229 | − | 84.5637i | −1.64769 | − | 2.85389i | ||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 73.1936 | + | 42.2584i | 2.46736 | + | 1.42453i | ||||
\(881\) | 9.98120 | 0.336275 | 0.168138 | − | 0.985764i | \(-0.446225\pi\) | ||||
0.168138 | + | 0.985764i | \(0.446225\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −32.0942 | −1.08006 | −0.540028 | − | 0.841647i | \(-0.681586\pi\) | ||||
−0.540028 | + | 0.841647i | \(0.681586\pi\) | |||||||
\(884\) | 30.7608 | + | 17.7597i | 1.03460 | + | 0.597325i | ||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 26.3781 | + | 45.6881i | 0.886188 | + | 1.53492i | ||||
\(887\) | 4.26812 | + | 7.39260i | 0.143309 | + | 0.248219i | 0.928741 | − | 0.370729i | \(-0.120892\pi\) |
−0.785432 | + | 0.618949i | \(0.787559\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | − | 19.9922i | − | 0.670141i | ||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 96.5904i | 3.23409i | ||||||||
\(893\) | −0.288584 | − | 0.166614i | −0.00965709 | − | 0.00557552i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 34.7140 | − | 20.0422i | 1.16036 | − | 0.669935i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 46.0277 | − | 79.7223i | 1.53596 | − | 2.66037i | ||||
\(899\) | −17.9516 | −0.598718 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | − | 23.9891i | − | 0.799192i | ||||||
\(902\) | 37.0906 | − | 64.2429i | 1.23498 | − | 2.13905i | ||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −20.0011 | − | 34.6430i | −0.665228 | − | 1.15221i | ||||
\(905\) | −33.6166 | + | 19.4085i | −1.11745 | + | 0.645162i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −16.0272 | + | 27.7599i | −0.532175 | + | 0.921754i | 0.467120 | + | 0.884194i | \(0.345292\pi\) |
−0.999294 | + | 0.0375597i | \(0.988042\pi\) | |||||||
\(908\) | −131.586 | −4.36685 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −26.3261 | − | 15.1994i | −0.872221 | − | 0.503577i | −0.00413539 | − | 0.999991i | \(-0.501316\pi\) |
−0.868086 | + | 0.496414i | \(0.834650\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 40.2640 | − | 23.2464i | 1.33254 | − | 0.769344i | ||||
\(914\) | −0.567527 | + | 0.327662i | −0.0187721 | + | 0.0108381i | ||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 87.6765 | + | 50.6201i | 2.89691 | + | 1.67253i | ||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −17.4431 | −0.575393 | −0.287697 | − | 0.957722i | \(-0.592889\pi\) | ||||
−0.287697 | + | 0.957722i | \(0.592889\pi\) | |||||||
\(920\) | −44.2687 | + | 76.6757i | −1.45950 | + | 2.52792i | ||||
\(921\) | 0 | 0 | ||||||||
\(922\) | −54.5580 | + | 31.4991i | −1.79677 | + | 1.03737i | ||||
\(923\) | −0.773612 | − | 1.33994i | −0.0254637 | − | 0.0441045i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −0.660203 | + | 1.14351i | −0.0217074 | + | 0.0375982i | ||||
\(926\) | − | 2.11405i | − | 0.0694718i | ||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | −34.6382 | −1.13705 | ||||||||
\(929\) | 5.21392 | − | 9.03077i | 0.171063 | − | 0.296290i | −0.767729 | − | 0.640775i | \(-0.778613\pi\) |
0.938792 | + | 0.344485i | \(0.111946\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | −61.3070 | + | 35.3956i | −2.00818 | + | 1.15942i | ||||
\(933\) | 0 | 0 | ||||||||
\(934\) | −4.06199 | − | 2.34519i | −0.132912 | − | 0.0767369i | ||||
\(935\) | 58.9142i | 1.92670i | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 51.3201i | 1.67655i | 0.545245 | + | 0.838277i | \(0.316437\pi\) | ||||
−0.545245 | + | 0.838277i | \(0.683563\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 2.67342 | + | 4.63049i | 0.0871973 | + | 0.151030i | ||||
\(941\) | 24.6673 | + | 42.7251i | 0.804133 | + | 1.39280i | 0.916875 | + | 0.399174i | \(0.130703\pi\) |
−0.112742 | + | 0.993624i | \(0.535963\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 31.7506 | + | 18.3312i | 1.03394 | + | 0.596947i | ||||
\(944\) | 35.8114 | 1.16556 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −87.6252 | −2.84894 | ||||||||
\(947\) | 38.0468 | + | 21.9663i | 1.23636 | + | 0.713810i | 0.968347 | − | 0.249607i | \(-0.0803013\pi\) |
0.268008 | + | 0.963417i | \(0.413635\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 9.98283 | + | 17.2908i | 0.324056 | + | 0.561282i | ||||
\(950\) | 0.381076 | + | 0.660044i | 0.0123637 | + | 0.0214146i | ||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | − | 21.0833i | − | 0.682956i | −0.939890 | − | 0.341478i | \(-0.889072\pi\) | ||
0.939890 | − | 0.341478i | \(-0.110928\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 2.22480i | 0.0719929i | ||||||||
\(956\) | 23.0089 | + | 13.2842i | 0.744161 | + | 0.429641i | ||||
\(957\) | 0 | 0 | ||||||||
\(958\) | −3.04138 | + | 1.75594i | −0.0982625 | + | 0.0567319i | ||||
\(959\) | 0 | 0 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −7.42801 | + | 12.8657i | −0.239613 | + | 0.415022i | ||||
\(962\) | 10.2730 | 0.331215 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | − | 20.7778i | − | 0.669207i | ||||||
\(965\) | 1.97558 | − | 3.42181i | 0.0635963 | − | 0.110152i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −27.6671 | − | 47.9209i | −0.889716 | − | 1.54103i | −0.840212 | − | 0.542259i | \(-0.817569\pi\) |
−0.0495039 | − | 0.998774i | \(-0.515764\pi\) | |||||||
\(968\) | 47.6533 | − | 27.5127i | 1.53164 | − | 0.884290i | ||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 44.2668 | − | 76.6723i | 1.42132 | − | 2.46180i | ||||
\(971\) | −6.83465 | −0.219334 | −0.109667 | − | 0.993968i | \(-0.534979\pi\) | ||||
−0.109667 | + | 0.993968i | \(0.534979\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 0 | 0 | ||||||||
\(974\) | −70.5830 | − | 40.7511i | −2.26162 | − | 1.30575i | ||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −14.7480 | + | 8.51477i | −0.472072 | + | 0.272551i | ||||
\(977\) | −31.1982 | + | 18.0123i | −0.998118 | + | 0.576264i | −0.907691 | − | 0.419639i | \(-0.862157\pi\) |
−0.0904272 | + | 0.995903i | \(0.528823\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −12.5736 | − | 7.25938i | −0.401854 | − | 0.232011i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | −5.87711 | −0.187546 | ||||||||
\(983\) | −20.6863 | + | 35.8298i | −0.659791 | + | 1.14279i | 0.320878 | + | 0.947120i | \(0.396022\pi\) |
−0.980670 | + | 0.195671i | \(0.937311\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −25.7455 | + | 14.8642i | −0.820321 | + | 0.473612i | ||||
\(986\) | −33.3275 | − | 57.7249i | −1.06136 | − | 1.83833i | ||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 2.07277 | − | 3.59014i | 0.0659435 | − | 0.114218i | ||||
\(989\) | − | 43.3068i | − | 1.37708i | ||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −21.6734 | −0.688478 | −0.344239 | − | 0.938882i | \(-0.611863\pi\) | ||||
−0.344239 | + | 0.938882i | \(0.611863\pi\) | |||||||
\(992\) | 15.5752 | − | 26.9770i | 0.494512 | − | 0.856520i | ||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −8.80102 | + | 5.08127i | −0.279011 | + | 0.161087i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −11.8699 | − | 6.85308i | −0.375923 | − | 0.217039i | 0.300120 | − | 0.953901i | \(-0.402973\pi\) |
−0.676043 | + | 0.736862i | \(0.736307\pi\) | |||||||
\(998\) | 69.7117i | 2.20669i | ||||||||
\(999\) | 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 | 1323.2.o.e.440.2 | 48 | ||
3.2 | odd | 2 | 441.2.o.e.146.23 | ✓ | 48 | ||
7.2 | even | 3 | 1323.2.i.d.521.2 | 48 | |||
7.3 | odd | 6 | 1323.2.s.d.656.24 | 48 | |||
7.4 | even | 3 | 1323.2.s.d.656.23 | 48 | |||
7.5 | odd | 6 | 1323.2.i.d.521.14 | 48 | |||
7.6 | odd | 2 | inner | 1323.2.o.e.440.1 | 48 | ||
9.4 | even | 3 | 441.2.o.e.293.24 | yes | 48 | ||
9.5 | odd | 6 | inner | 1323.2.o.e.881.1 | 48 | ||
21.2 | odd | 6 | 441.2.i.d.227.2 | 48 | |||
21.5 | even | 6 | 441.2.i.d.227.1 | 48 | |||
21.11 | odd | 6 | 441.2.s.d.362.2 | 48 | |||
21.17 | even | 6 | 441.2.s.d.362.1 | 48 | |||
21.20 | even | 2 | 441.2.o.e.146.24 | yes | 48 | ||
63.4 | even | 3 | 441.2.i.d.68.23 | 48 | |||
63.5 | even | 6 | 1323.2.s.d.962.23 | 48 | |||
63.13 | odd | 6 | 441.2.o.e.293.23 | yes | 48 | ||
63.23 | odd | 6 | 1323.2.s.d.962.24 | 48 | |||
63.31 | odd | 6 | 441.2.i.d.68.24 | 48 | |||
63.32 | odd | 6 | 1323.2.i.d.1097.14 | 48 | |||
63.40 | odd | 6 | 441.2.s.d.374.2 | 48 | |||
63.41 | even | 6 | inner | 1323.2.o.e.881.2 | 48 | ||
63.58 | even | 3 | 441.2.s.d.374.1 | 48 | |||
63.59 | even | 6 | 1323.2.i.d.1097.2 | 48 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
441.2.i.d.68.23 | 48 | 63.4 | even | 3 | |||
441.2.i.d.68.24 | 48 | 63.31 | odd | 6 | |||
441.2.i.d.227.1 | 48 | 21.5 | even | 6 | |||
441.2.i.d.227.2 | 48 | 21.2 | odd | 6 | |||
441.2.o.e.146.23 | ✓ | 48 | 3.2 | odd | 2 | ||
441.2.o.e.146.24 | yes | 48 | 21.20 | even | 2 | ||
441.2.o.e.293.23 | yes | 48 | 63.13 | odd | 6 | ||
441.2.o.e.293.24 | yes | 48 | 9.4 | even | 3 | ||
441.2.s.d.362.1 | 48 | 21.17 | even | 6 | |||
441.2.s.d.362.2 | 48 | 21.11 | odd | 6 | |||
441.2.s.d.374.1 | 48 | 63.58 | even | 3 | |||
441.2.s.d.374.2 | 48 | 63.40 | odd | 6 | |||
1323.2.i.d.521.2 | 48 | 7.2 | even | 3 | |||
1323.2.i.d.521.14 | 48 | 7.5 | odd | 6 | |||
1323.2.i.d.1097.2 | 48 | 63.59 | even | 6 | |||
1323.2.i.d.1097.14 | 48 | 63.32 | odd | 6 | |||
1323.2.o.e.440.1 | 48 | 7.6 | odd | 2 | inner | ||
1323.2.o.e.440.2 | 48 | 1.1 | even | 1 | trivial | ||
1323.2.o.e.881.1 | 48 | 9.5 | odd | 6 | inner | ||
1323.2.o.e.881.2 | 48 | 63.41 | even | 6 | inner | ||
1323.2.s.d.656.23 | 48 | 7.4 | even | 3 | |||
1323.2.s.d.656.24 | 48 | 7.3 | odd | 6 | |||
1323.2.s.d.962.23 | 48 | 63.5 | even | 6 | |||
1323.2.s.d.962.24 | 48 | 63.23 | odd | 6 |