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 | 440.13 | ||
Character | \(\chi\) | \(=\) | 1323.440 |
Dual form | 1323.2.o.e.881.13 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0.367369 | + | 0.212101i | 0.259769 | + | 0.149978i | 0.624229 | − | 0.781241i | \(-0.285413\pi\) |
−0.364460 | + | 0.931219i | \(0.618746\pi\) | |||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | −0.910027 | − | 1.57621i | −0.455013 | − | 0.788106i | ||||
\(5\) | 1.80381 | + | 3.12430i | 0.806690 | + | 1.39723i | 0.915144 | + | 0.403126i | \(0.132077\pi\) |
−0.108454 | + | 0.994101i | \(0.534590\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 0 | 0 | ||||||||
\(8\) | − | 1.62047i | − | 0.572923i | ||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 1.53036i | 0.483942i | ||||||||
\(11\) | −3.20952 | − | 1.85302i | −0.967706 | − | 0.558705i | −0.0691700 | − | 0.997605i | \(-0.522035\pi\) |
−0.898536 | + | 0.438899i | \(0.855368\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −5.23479 | + | 3.02231i | −1.45187 | + | 0.838238i | −0.998588 | − | 0.0531292i | \(-0.983080\pi\) |
−0.453283 | + | 0.891367i | \(0.649747\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −1.47635 | + | 2.55711i | −0.369088 | + | 0.639279i | ||||
\(17\) | −1.06422 | −0.258110 | −0.129055 | − | 0.991637i | \(-0.541194\pi\) | ||||
−0.129055 | + | 0.991637i | \(0.541194\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 3.65191i | 0.837806i | 0.908031 | + | 0.418903i | \(0.137585\pi\) | ||||
−0.908031 | + | 0.418903i | \(0.862415\pi\) | |||||||
\(20\) | 3.28304 | − | 5.68639i | 0.734109 | − | 1.27151i | ||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −0.786052 | − | 1.36148i | −0.167587 | − | 0.290269i | ||||
\(23\) | −0.314574 | + | 0.181620i | −0.0655933 | + | 0.0378703i | −0.532438 | − | 0.846469i | \(-0.678724\pi\) |
0.466845 | + | 0.884339i | \(0.345391\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −4.00749 | + | 6.94117i | −0.801497 | + | 1.38823i | ||||
\(26\) | −2.56413 | −0.502868 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 0.857560 | + | 0.495112i | 0.159245 | + | 0.0919401i | 0.577505 | − | 0.816387i | \(-0.304027\pi\) |
−0.418260 | + | 0.908327i | \(0.637360\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −0.939786 | + | 0.542586i | −0.168791 | + | 0.0974513i | −0.582015 | − | 0.813178i | \(-0.697736\pi\) |
0.413225 | + | 0.910629i | \(0.364402\pi\) | |||||||
\(32\) | −3.89147 | + | 2.24674i | −0.687921 | + | 0.397171i | ||||
\(33\) | 0 | 0 | ||||||||
\(34\) | −0.390960 | − | 0.225721i | −0.0670490 | − | 0.0387108i | ||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −8.00373 | −1.31580 | −0.657902 | − | 0.753103i | \(-0.728556\pi\) | ||||
−0.657902 | + | 0.753103i | \(0.728556\pi\) | |||||||
\(38\) | −0.774573 | + | 1.34160i | −0.125652 | + | 0.217636i | ||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 5.06283 | − | 2.92303i | 0.800504 | − | 0.462171i | ||||
\(41\) | −2.09005 | − | 3.62007i | −0.326411 | − | 0.565360i | 0.655386 | − | 0.755294i | \(-0.272506\pi\) |
−0.981797 | + | 0.189934i | \(0.939173\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −1.89758 | + | 3.28670i | −0.289378 | + | 0.501217i | −0.973661 | − | 0.227999i | \(-0.926782\pi\) |
0.684284 | + | 0.729216i | \(0.260115\pi\) | |||||||
\(44\) | 6.74518i | 1.01687i | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −0.154086 | −0.0227188 | ||||||||
\(47\) | 2.83849 | − | 4.91640i | 0.414036 | − | 0.717131i | −0.581291 | − | 0.813696i | \(-0.697452\pi\) |
0.995327 | + | 0.0965648i | \(0.0307855\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 0 | 0 | ||||||||
\(50\) | −2.94445 | + | 1.69998i | −0.416408 | + | 0.240413i | ||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 9.52760 | + | 5.50076i | 1.32124 | + | 0.762819i | ||||
\(53\) | − | 4.53177i | − | 0.622487i | −0.950330 | − | 0.311243i | \(-0.899255\pi\) | ||
0.950330 | − | 0.311243i | \(-0.100745\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | − | 13.3700i | − | 1.80281i | ||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 0.210027 | + | 0.363778i | 0.0275779 | + | 0.0477664i | ||||
\(59\) | 5.62746 | + | 9.74705i | 0.732633 | + | 1.26896i | 0.955754 | + | 0.294167i | \(0.0950422\pi\) |
−0.223121 | + | 0.974791i | \(0.571624\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −0.0238258 | − | 0.0137558i | −0.00305058 | − | 0.00176126i | 0.498474 | − | 0.866905i | \(-0.333894\pi\) |
−0.501525 | + | 0.865143i | \(0.667227\pi\) | |||||||
\(62\) | −0.460331 | −0.0584621 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 3.99926 | 0.499908 | ||||||||
\(65\) | −18.8852 | − | 10.9034i | −2.34242 | − | 1.35240i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 4.86489 | + | 8.42624i | 0.594341 | + | 1.02943i | 0.993640 | + | 0.112608i | \(0.0359204\pi\) |
−0.399298 | + | 0.916821i | \(0.630746\pi\) | |||||||
\(68\) | 0.968464 | + | 1.67743i | 0.117444 | + | 0.203418i | ||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 5.55775i | 0.659584i | 0.944054 | + | 0.329792i | \(0.106979\pi\) | ||||
−0.944054 | + | 0.329792i | \(0.893021\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | − | 2.25814i | − | 0.264296i | −0.991230 | − | 0.132148i | \(-0.957813\pi\) | ||
0.991230 | − | 0.132148i | \(-0.0421874\pi\) | |||||||
\(74\) | −2.94032 | − | 1.69759i | −0.341805 | − | 0.197341i | ||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 5.75619 | − | 3.32334i | 0.660280 | − | 0.381213i | ||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −3.26604 | + | 5.65694i | −0.367458 | + | 0.636456i | −0.989167 | − | 0.146792i | \(-0.953105\pi\) |
0.621710 | + | 0.783248i | \(0.286438\pi\) | |||||||
\(80\) | −10.6522 | −1.19096 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | − | 1.77320i | − | 0.195817i | ||||||
\(83\) | 1.52977 | − | 2.64964i | 0.167914 | − | 0.290836i | −0.769772 | − | 0.638319i | \(-0.779630\pi\) |
0.937686 | + | 0.347483i | \(0.112964\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −1.91965 | − | 3.32492i | −0.208215 | − | 0.360639i | ||||
\(86\) | −1.39422 | + | 0.804954i | −0.150343 | + | 0.0868004i | ||||
\(87\) | 0 | 0 | ||||||||
\(88\) | −3.00276 | + | 5.20093i | −0.320095 | + | 0.554421i | ||||
\(89\) | −14.9590 | −1.58565 | −0.792827 | − | 0.609446i | \(-0.791392\pi\) | ||||
−0.792827 | + | 0.609446i | \(0.791392\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | 0.572542 | + | 0.330557i | 0.0596916 | + | 0.0344630i | ||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 2.08554 | − | 1.20409i | 0.215107 | − | 0.124192i | ||||
\(95\) | −11.4097 | + | 6.58737i | −1.17061 | + | 0.675850i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −1.67018 | − | 0.964277i | −0.169581 | − | 0.0979075i | 0.412807 | − | 0.910818i | \(-0.364548\pi\) |
−0.582388 | + | 0.812911i | \(0.697882\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 14.5877 | 1.45877 | ||||||||
\(101\) | −3.21811 | + | 5.57394i | −0.320214 | + | 0.554627i | −0.980532 | − | 0.196359i | \(-0.937088\pi\) |
0.660318 | + | 0.750986i | \(0.270422\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −8.41917 | + | 4.86081i | −0.829565 | + | 0.478950i | −0.853704 | − | 0.520759i | \(-0.825649\pi\) |
0.0241385 | + | 0.999709i | \(0.492316\pi\) | |||||||
\(104\) | 4.89756 | + | 8.48283i | 0.480246 | + | 0.831810i | ||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0.961191 | − | 1.66483i | 0.0933591 | − | 0.161703i | ||||
\(107\) | − | 3.96223i | − | 0.383043i | −0.981488 | − | 0.191522i | \(-0.938658\pi\) | ||
0.981488 | − | 0.191522i | \(-0.0613422\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −17.3253 | −1.65946 | −0.829729 | − | 0.558166i | \(-0.811505\pi\) | ||||
−0.829729 | + | 0.558166i | \(0.811505\pi\) | |||||||
\(110\) | 2.83578 | − | 4.91172i | 0.270381 | − | 0.468314i | ||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 8.50273 | − | 4.90905i | 0.799869 | − | 0.461805i | −0.0435562 | − | 0.999051i | \(-0.513869\pi\) |
0.843425 | + | 0.537246i | \(0.180535\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −1.13487 | − | 0.655216i | −0.105827 | − | 0.0610992i | ||||
\(116\) | − | 1.80226i | − | 0.167336i | ||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 4.77435i | 0.439515i | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 1.36734 | + | 2.36830i | 0.124303 | + | 0.215300i | ||||
\(122\) | −0.00583524 | − | 0.0101069i | −0.000528298 | − | 0.000915039i | ||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 1.71046 | + | 0.987535i | 0.153604 | + | 0.0886833i | ||||
\(125\) | −10.8769 | −0.972858 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −11.7328 | −1.04112 | −0.520560 | − | 0.853825i | \(-0.674277\pi\) | ||||
−0.520560 | + | 0.853825i | \(0.674277\pi\) | |||||||
\(128\) | 9.25214 | + | 5.34173i | 0.817782 | + | 0.472146i | ||||
\(129\) | 0 | 0 | ||||||||
\(130\) | −4.62522 | − | 8.01111i | −0.405659 | − | 0.702621i | ||||
\(131\) | 10.5013 | + | 18.1888i | 0.917502 | + | 1.58916i | 0.803197 | + | 0.595714i | \(0.203131\pi\) |
0.114305 | + | 0.993446i | \(0.463536\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | 4.12738i | 0.356552i | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 1.72453i | 0.147877i | ||||||||
\(137\) | 9.76185 | + | 5.63600i | 0.834011 | + | 0.481516i | 0.855224 | − | 0.518259i | \(-0.173420\pi\) |
−0.0212131 | + | 0.999775i | \(0.506753\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −2.80312 | + | 1.61838i | −0.237758 | + | 0.137269i | −0.614146 | − | 0.789193i | \(-0.710499\pi\) |
0.376388 | + | 0.926462i | \(0.377166\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | −1.17880 | + | 2.04175i | −0.0989229 | + | 0.171340i | ||||
\(143\) | 22.4015 | 1.87331 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 3.57236i | 0.296668i | ||||||||
\(146\) | 0.478954 | − | 0.829572i | 0.0396385 | − | 0.0686559i | ||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 7.28360 | + | 12.6156i | 0.598709 | + | 1.03699i | ||||
\(149\) | 15.5066 | − | 8.95277i | 1.27035 | − | 0.733439i | 0.295299 | − | 0.955405i | \(-0.404581\pi\) |
0.975055 | + | 0.221966i | \(0.0712472\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 9.29945 | − | 16.1071i | 0.756778 | − | 1.31078i | −0.187707 | − | 0.982225i | \(-0.560106\pi\) |
0.944485 | − | 0.328553i | \(-0.106561\pi\) | |||||||
\(152\) | 5.91782 | 0.479998 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −3.39040 | − | 1.95745i | −0.272323 | − | 0.157226i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 6.64220 | − | 3.83488i | 0.530106 | − | 0.306057i | −0.210954 | − | 0.977496i | \(-0.567657\pi\) |
0.741059 | + | 0.671439i | \(0.234324\pi\) | |||||||
\(158\) | −2.39968 | + | 1.38546i | −0.190908 | + | 0.110221i | ||||
\(159\) | 0 | 0 | ||||||||
\(160\) | −14.0390 | − | 8.10540i | −1.10988 | − | 0.640788i | ||||
\(161\) | 0 | 0 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −3.99313 | −0.312766 | −0.156383 | − | 0.987696i | \(-0.549983\pi\) | ||||
−0.156383 | + | 0.987696i | \(0.549983\pi\) | |||||||
\(164\) | −3.80400 | + | 6.58872i | −0.297042 | + | 0.514492i | ||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 1.12398 | − | 0.648930i | 0.0872377 | − | 0.0503667i | ||||
\(167\) | 4.26254 | + | 7.38293i | 0.329845 | + | 0.571308i | 0.982481 | − | 0.186363i | \(-0.0596702\pi\) |
−0.652636 | + | 0.757672i | \(0.726337\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 11.7687 | − | 20.3840i | 0.905285 | − | 1.56800i | ||||
\(170\) | − | 1.62863i | − | 0.124910i | ||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 6.90738 | 0.526683 | ||||||||
\(173\) | −0.217445 | + | 0.376626i | −0.0165320 | + | 0.0286343i | −0.874173 | − | 0.485615i | \(-0.838596\pi\) |
0.857641 | + | 0.514249i | \(0.171929\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 9.47675 | − | 5.47140i | 0.714337 | − | 0.412423i | ||||
\(177\) | 0 | 0 | ||||||||
\(178\) | −5.49549 | − | 3.17282i | −0.411904 | − | 0.237813i | ||||
\(179\) | − | 17.4172i | − | 1.30183i | −0.759153 | − | 0.650913i | \(-0.774386\pi\) | ||
0.759153 | − | 0.650913i | \(-0.225614\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 17.7421i | 1.31876i | 0.751809 | + | 0.659381i | \(0.229182\pi\) | ||||
−0.751809 | + | 0.659381i | \(0.770818\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0.294309 | + | 0.509759i | 0.0216968 | + | 0.0375799i | ||||
\(185\) | −14.4372 | − | 25.0060i | −1.06145 | − | 1.83848i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 3.41562 | + | 1.97201i | 0.249775 | + | 0.144208i | ||||
\(188\) | −10.3324 | −0.753567 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | −5.58874 | −0.405450 | ||||||||
\(191\) | −0.215525 | − | 0.124433i | −0.0155948 | − | 0.00900367i | 0.492182 | − | 0.870492i | \(-0.336199\pi\) |
−0.507777 | + | 0.861488i | \(0.669533\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 4.14876 | + | 7.18586i | 0.298634 | + | 0.517250i | 0.975824 | − | 0.218559i | \(-0.0701356\pi\) |
−0.677190 | + | 0.735809i | \(0.736802\pi\) | |||||||
\(194\) | −0.409047 | − | 0.708491i | −0.0293679 | − | 0.0508667i | ||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | − | 22.5819i | − | 1.60889i | −0.594026 | − | 0.804446i | \(-0.702462\pi\) | ||
0.594026 | − | 0.804446i | \(-0.297538\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 6.12003i | 0.433837i | 0.976190 | + | 0.216919i | \(0.0696007\pi\) | ||||
−0.976190 | + | 0.216919i | \(0.930399\pi\) | |||||||
\(200\) | 11.2480 | + | 6.49401i | 0.795351 | + | 0.459196i | ||||
\(201\) | 0 | 0 | ||||||||
\(202\) | −2.36447 | + | 1.36513i | −0.166364 | + | 0.0960500i | ||||
\(203\) | 0 | 0 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 7.54011 | − | 13.0599i | 0.526624 | − | 0.912140i | ||||
\(206\) | −4.12392 | −0.287327 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | − | 17.8479i | − | 1.23753i | ||||||
\(209\) | 6.76705 | − | 11.7209i | 0.468087 | − | 0.810750i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 1.95472 | + | 3.38567i | 0.134568 | + | 0.233079i | 0.925432 | − | 0.378913i | \(-0.123702\pi\) |
−0.790864 | + | 0.611992i | \(0.790369\pi\) | |||||||
\(212\) | −7.14303 | + | 4.12403i | −0.490586 | + | 0.283240i | ||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0.840392 | − | 1.45560i | 0.0574480 | − | 0.0995029i | ||||
\(215\) | −13.6915 | −0.933752 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | −6.36476 | − | 3.67470i | −0.431076 | − | 0.248882i | ||||
\(219\) | 0 | 0 | ||||||||
\(220\) | −21.0739 | + | 12.1670i | −1.42080 | + | 0.820302i | ||||
\(221\) | 5.57095 | − | 3.21639i | 0.374742 | − | 0.216358i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 22.3165 | + | 12.8845i | 1.49443 | + | 0.862807i | 0.999980 | − | 0.00640186i | \(-0.00203779\pi\) |
0.494446 | + | 0.869209i | \(0.335371\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 4.16485 | 0.277042 | ||||||||
\(227\) | 12.3051 | − | 21.3130i | 0.816718 | − | 1.41460i | −0.0913703 | − | 0.995817i | \(-0.529125\pi\) |
0.908088 | − | 0.418779i | \(-0.137542\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 3.94267 | − | 2.27630i | 0.260539 | − | 0.150422i | −0.364042 | − | 0.931383i | \(-0.618603\pi\) |
0.624580 | + | 0.780961i | \(0.285270\pi\) | |||||||
\(230\) | −0.277943 | − | 0.481412i | −0.0183270 | − | 0.0317433i | ||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0.802315 | − | 1.38965i | 0.0526746 | − | 0.0912351i | ||||
\(233\) | 26.1353i | 1.71218i | 0.516826 | + | 0.856090i | \(0.327113\pi\) | ||||
−0.516826 | + | 0.856090i | \(0.672887\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 20.4804 | 1.33599 | ||||||||
\(236\) | 10.2423 | − | 17.7402i | 0.666716 | − | 1.15479i | ||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −14.8933 | + | 8.59865i | −0.963367 | + | 0.556200i | −0.897208 | − | 0.441609i | \(-0.854408\pi\) |
−0.0661594 | + | 0.997809i | \(0.521075\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −14.4927 | − | 8.36738i | −0.933559 | − | 0.538991i | −0.0456237 | − | 0.998959i | \(-0.514528\pi\) |
−0.887935 | + | 0.459968i | \(0.847861\pi\) | |||||||
\(242\) | 1.16005i | 0.0745710i | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 0.0500727i | 0.00320558i | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −11.0372 | − | 19.1170i | −0.702281 | − | 1.21639i | ||||
\(248\) | 0.879245 | + | 1.52290i | 0.0558321 | + | 0.0967040i | ||||
\(249\) | 0 | 0 | ||||||||
\(250\) | −3.99583 | − | 2.30699i | −0.252719 | − | 0.145907i | ||||
\(251\) | 5.33468 | 0.336722 | 0.168361 | − | 0.985725i | \(-0.446153\pi\) | ||||
0.168361 | + | 0.985725i | \(0.446153\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 1.34618 | 0.0846334 | ||||||||
\(254\) | −4.31028 | − | 2.48854i | −0.270451 | − | 0.156145i | ||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −1.73330 | − | 3.00216i | −0.108331 | − | 0.187635i | ||||
\(257\) | −12.3100 | − | 21.3216i | −0.767878 | − | 1.33000i | −0.938712 | − | 0.344703i | \(-0.887979\pi\) |
0.170834 | − | 0.985300i | \(-0.445354\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | 39.6894i | 2.46143i | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 8.90932i | 0.550419i | ||||||||
\(263\) | 26.6568 | + | 15.3903i | 1.64373 | + | 0.949006i | 0.979492 | + | 0.201482i | \(0.0645757\pi\) |
0.664235 | + | 0.747524i | \(0.268758\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 14.1586 | − | 8.17447i | 0.869756 | − | 0.502154i | ||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 8.85436 | − | 15.3362i | 0.540866 | − | 0.936808i | ||||
\(269\) | 13.9809 | 0.852432 | 0.426216 | − | 0.904622i | \(-0.359846\pi\) | ||||
0.426216 | + | 0.904622i | \(0.359846\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | − | 6.46262i | − | 0.392576i | −0.980546 | − | 0.196288i | \(-0.937111\pi\) | ||
0.980546 | − | 0.196288i | \(-0.0628888\pi\) | |||||||
\(272\) | 1.57115 | − | 2.72132i | 0.0952652 | − | 0.165004i | ||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 2.39080 | + | 4.14099i | 0.144433 | + | 0.250166i | ||||
\(275\) | 25.7242 | − | 14.8519i | 1.55123 | − | 0.895601i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 9.55984 | − | 16.5581i | 0.574395 | − | 0.994881i | −0.421712 | − | 0.906730i | \(-0.638571\pi\) |
0.996107 | − | 0.0881515i | \(-0.0280960\pi\) | |||||||
\(278\) | −1.37304 | −0.0823494 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −20.0611 | − | 11.5823i | −1.19674 | − | 0.690940i | −0.236915 | − | 0.971530i | \(-0.576136\pi\) |
−0.959828 | + | 0.280591i | \(0.909470\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 13.8239 | − | 7.98126i | 0.821748 | − | 0.474436i | −0.0292708 | − | 0.999572i | \(-0.509319\pi\) |
0.851019 | + | 0.525135i | \(0.175985\pi\) | |||||||
\(284\) | 8.76020 | − | 5.05770i | 0.519822 | − | 0.300120i | ||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 8.22963 | + | 4.75138i | 0.486628 | + | 0.280955i | ||||
\(287\) | 0 | 0 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −15.8674 | −0.933379 | ||||||||
\(290\) | −0.757700 | + | 1.31237i | −0.0444937 | + | 0.0770653i | ||||
\(291\) | 0 | 0 | ||||||||
\(292\) | −3.55931 | + | 2.05497i | −0.208293 | + | 0.120258i | ||||
\(293\) | 3.34849 | + | 5.79975i | 0.195621 | + | 0.338825i | 0.947104 | − | 0.320927i | \(-0.103995\pi\) |
−0.751483 | + | 0.659752i | \(0.770661\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −20.3018 | + | 35.1637i | −1.18202 | + | 2.04731i | ||||
\(296\) | 12.9698i | 0.753855i | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 7.59555 | 0.439998 | ||||||||
\(299\) | 1.09782 | − | 1.90148i | 0.0634886 | − | 0.109966i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | 6.83266 | − | 3.94484i | 0.393175 | − | 0.227000i | ||||
\(303\) | 0 | 0 | ||||||||
\(304\) | −9.33836 | − | 5.39150i | −0.535591 | − | 0.309224i | ||||
\(305\) | − | 0.0992519i | − | 0.00568315i | ||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 8.59068i | 0.490296i | 0.969486 | + | 0.245148i | \(0.0788365\pi\) | ||||
−0.969486 | + | 0.245148i | \(0.921163\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | −0.830352 | − | 1.43821i | −0.0471608 | − | 0.0816849i | ||||
\(311\) | −2.11723 | − | 3.66714i | −0.120057 | − | 0.207945i | 0.799733 | − | 0.600356i | \(-0.204974\pi\) |
−0.919790 | + | 0.392411i | \(0.871641\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 3.10288 | + | 1.79145i | 0.175385 | + | 0.101259i | 0.585123 | − | 0.810945i | \(-0.301046\pi\) |
−0.409737 | + | 0.912204i | \(0.634380\pi\) | |||||||
\(314\) | 3.25352 | 0.183607 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 11.8887 | 0.668793 | ||||||||
\(317\) | 7.69566 | + | 4.44309i | 0.432231 | + | 0.249549i | 0.700297 | − | 0.713852i | \(-0.253051\pi\) |
−0.268065 | + | 0.963401i | \(0.586384\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −1.83490 | − | 3.17814i | −0.102735 | − | 0.177942i | ||||
\(320\) | 7.21392 | + | 12.4949i | 0.403271 | + | 0.698485i | ||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | − | 3.88642i | − | 0.216246i | ||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | − | 48.4474i | − | 2.68738i | ||||||
\(326\) | −1.46695 | − | 0.846946i | −0.0812470 | − | 0.0469080i | ||||
\(327\) | 0 | 0 | ||||||||
\(328\) | −5.86622 | + | 3.38686i | −0.323908 | + | 0.187008i | ||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −7.89126 | + | 13.6681i | −0.433743 | + | 0.751265i | −0.997192 | − | 0.0748861i | \(-0.976141\pi\) |
0.563449 | + | 0.826151i | \(0.309474\pi\) | |||||||
\(332\) | −5.56852 | −0.305612 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 3.61635i | 0.197878i | ||||||||
\(335\) | −17.5507 | + | 30.3987i | −0.958898 | + | 1.66086i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −6.79951 | − | 11.7771i | −0.370393 | − | 0.641539i | 0.619233 | − | 0.785207i | \(-0.287444\pi\) |
−0.989626 | + | 0.143668i | \(0.954110\pi\) | |||||||
\(338\) | 8.64691 | − | 4.99230i | 0.470330 | − | 0.271545i | ||||
\(339\) | 0 | 0 | ||||||||
\(340\) | −3.49386 | + | 6.05154i | −0.189481 | + | 0.328191i | ||||
\(341\) | 4.02168 | 0.217786 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 0 | 0 | ||||||||
\(344\) | 5.32600 | + | 3.07497i | 0.287159 | + | 0.165791i | ||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −0.159765 | + | 0.0922404i | −0.00858902 | + | 0.00495887i | ||||
\(347\) | −12.0065 | + | 6.93198i | −0.644545 | + | 0.372128i | −0.786363 | − | 0.617765i | \(-0.788038\pi\) |
0.141818 | + | 0.989893i | \(0.454705\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 1.55204 | + | 0.896072i | 0.0830789 | + | 0.0479656i | 0.540964 | − | 0.841046i | \(-0.318060\pi\) |
−0.457885 | + | 0.889011i | \(0.651393\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 16.6530 | 0.887607 | ||||||||
\(353\) | −3.88049 | + | 6.72121i | −0.206538 | + | 0.357734i | −0.950622 | − | 0.310352i | \(-0.899553\pi\) |
0.744084 | + | 0.668086i | \(0.232886\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −17.3641 | + | 10.0252i | −0.921589 | + | 0.532080i | ||||
\(356\) | 13.6131 | + | 23.5786i | 0.721494 | + | 1.24966i | ||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 3.69421 | − | 6.39855i | 0.195245 | − | 0.338174i | ||||
\(359\) | − | 22.5810i | − | 1.19178i | −0.803066 | − | 0.595890i | \(-0.796799\pi\) | ||
0.803066 | − | 0.595890i | \(-0.203201\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 5.66354 | 0.298081 | ||||||||
\(362\) | −3.76312 | + | 6.51791i | −0.197785 | + | 0.342574i | ||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 7.05511 | − | 4.07327i | 0.369281 | − | 0.213205i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 13.5263 | + | 7.80942i | 0.706068 | + | 0.407648i | 0.809603 | − | 0.586977i | \(-0.199682\pi\) |
−0.103536 | + | 0.994626i | \(0.533016\pi\) | |||||||
\(368\) | − | 1.07254i | − | 0.0559098i | ||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | − | 12.2486i | − | 0.636773i | ||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 12.6229 | + | 21.8635i | 0.653589 | + | 1.13205i | 0.982246 | + | 0.187600i | \(0.0600709\pi\) |
−0.328656 | + | 0.944450i | \(0.606596\pi\) | |||||||
\(374\) | 0.836528 | + | 1.44891i | 0.0432558 | + | 0.0749213i | ||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −7.96689 | − | 4.59969i | −0.410861 | − | 0.237211i | ||||
\(377\) | −5.98553 | −0.308271 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 14.7721 | 0.758792 | 0.379396 | − | 0.925234i | \(-0.376132\pi\) | ||||
0.379396 | + | 0.925234i | \(0.376132\pi\) | |||||||
\(380\) | 20.7662 | + | 11.9894i | 1.06528 | + | 0.615041i | ||||
\(381\) | 0 | 0 | ||||||||
\(382\) | −0.0527847 | − | 0.0914258i | −0.00270070 | − | 0.00467775i | ||||
\(383\) | 5.29503 | + | 9.17127i | 0.270564 | + | 0.468630i | 0.969006 | − | 0.247036i | \(-0.0794566\pi\) |
−0.698443 | + | 0.715666i | \(0.746123\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 3.51982i | 0.179154i | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 3.51007i | 0.178197i | ||||||||
\(389\) | 11.7642 | + | 6.79207i | 0.596469 | + | 0.344371i | 0.767651 | − | 0.640868i | \(-0.221425\pi\) |
−0.171182 | + | 0.985239i | \(0.554759\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 0.334775 | − | 0.193282i | 0.0169303 | − | 0.00977471i | ||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 4.78963 | − | 8.29588i | 0.241298 | − | 0.417940i | ||||
\(395\) | −23.5653 | −1.18570 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 38.9108i | 1.95287i | 0.215801 | + | 0.976437i | \(0.430764\pi\) | ||||
−0.215801 | + | 0.976437i | \(0.569236\pi\) | |||||||
\(398\) | −1.29806 | + | 2.24831i | −0.0650660 | + | 0.112698i | ||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −11.8329 | − | 20.4952i | −0.591645 | − | 1.02476i | ||||
\(401\) | −24.8956 | + | 14.3735i | −1.24323 | + | 0.717778i | −0.969750 | − | 0.244101i | \(-0.921507\pi\) |
−0.273477 | + | 0.961878i | \(0.588174\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 3.27972 | − | 5.68065i | 0.163375 | − | 0.282973i | ||||
\(404\) | 11.7143 | 0.582807 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 25.6881 | + | 14.8310i | 1.27331 | + | 0.735147i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −16.3485 | + | 9.43879i | −0.808379 | + | 0.466718i | −0.846393 | − | 0.532559i | \(-0.821230\pi\) |
0.0380133 | + | 0.999277i | \(0.487897\pi\) | |||||||
\(410\) | 5.54001 | − | 3.19852i | 0.273601 | − | 0.157964i | ||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 15.3233 | + | 8.84693i | 0.754927 | + | 0.435857i | ||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 11.0377 | 0.541818 | ||||||||
\(416\) | 13.5807 | − | 23.5224i | 0.665848 | − | 1.15328i | ||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 4.97201 | − | 2.87059i | 0.243189 | − | 0.140405i | ||||
\(419\) | 3.31895 | + | 5.74860i | 0.162142 | + | 0.280837i | 0.935636 | − | 0.352965i | \(-0.114827\pi\) |
−0.773495 | + | 0.633802i | \(0.781493\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −9.70574 | + | 16.8108i | −0.473029 | + | 0.819310i | −0.999523 | − | 0.0308686i | \(-0.990173\pi\) |
0.526495 | + | 0.850178i | \(0.323506\pi\) | |||||||
\(422\) | 1.65839i | 0.0807290i | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | −7.34360 | −0.356637 | ||||||||
\(425\) | 4.26483 | − | 7.38690i | 0.206874 | − | 0.358317i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | −6.24532 | + | 3.60574i | −0.301879 | + | 0.174290i | ||||
\(429\) | 0 | 0 | ||||||||
\(430\) | −5.02983 | − | 2.90397i | −0.242560 | − | 0.140042i | ||||
\(431\) | 24.3185i | 1.17138i | 0.810535 | + | 0.585690i | \(0.199176\pi\) | ||||
−0.810535 | + | 0.585690i | \(0.800824\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 3.32148i | 0.159620i | 0.996810 | + | 0.0798101i | \(0.0254314\pi\) | ||||
−0.996810 | + | 0.0798101i | \(0.974569\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 15.7664 | + | 27.3083i | 0.755076 | + | 1.30783i | ||||
\(437\) | −0.663259 | − | 1.14880i | −0.0317280 | − | 0.0549544i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −23.3126 | − | 13.4595i | −1.11265 | − | 0.642389i | −0.173136 | − | 0.984898i | \(-0.555390\pi\) |
−0.939515 | + | 0.342509i | \(0.888723\pi\) | |||||||
\(440\) | −21.6657 | −1.03287 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 2.72879 | 0.129795 | ||||||||
\(443\) | −22.8837 | − | 13.2119i | −1.08724 | − | 0.627717i | −0.154397 | − | 0.988009i | \(-0.549344\pi\) |
−0.932839 | + | 0.360292i | \(0.882677\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −26.9833 | − | 46.7365i | −1.27913 | − | 2.21552i | ||||
\(446\) | 5.46560 | + | 9.46670i | 0.258804 | + | 0.448261i | ||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | − | 19.6314i | − | 0.926464i | −0.886237 | − | 0.463232i | \(-0.846690\pi\) | ||
0.886237 | − | 0.463232i | \(-0.153310\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 15.4916i | 0.729470i | ||||||||
\(452\) | −15.4754 | − | 8.93474i | −0.727902 | − | 0.420255i | ||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 9.04102 | − | 5.21983i | 0.424316 | − | 0.244979i | ||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 12.6244 | − | 21.8660i | 0.590543 | − | 1.02285i | −0.403617 | − | 0.914928i | \(-0.632247\pi\) |
0.994159 | − | 0.107922i | \(-0.0344196\pi\) | |||||||
\(458\) | 1.93122 | 0.0902399 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 2.38505i | 0.111204i | ||||||||
\(461\) | −7.23618 | + | 12.5334i | −0.337023 | + | 0.583740i | −0.983871 | − | 0.178878i | \(-0.942753\pi\) |
0.646849 | + | 0.762618i | \(0.276087\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −10.0168 | − | 17.3495i | −0.465519 | − | 0.806302i | 0.533706 | − | 0.845670i | \(-0.320799\pi\) |
−0.999225 | + | 0.0393681i | \(0.987466\pi\) | |||||||
\(464\) | −2.53212 | + | 1.46192i | −0.117551 | + | 0.0678679i | ||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −5.54331 | + | 9.60130i | −0.256789 | + | 0.444772i | ||||
\(467\) | −23.5630 | −1.09037 | −0.545183 | − | 0.838317i | \(-0.683540\pi\) | ||||
−0.545183 | + | 0.838317i | \(0.683540\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | 7.52386 | + | 4.34390i | 0.347050 | + | 0.200369i | ||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 15.7948 | − | 9.11914i | 0.727015 | − | 0.419742i | ||||
\(473\) | 12.1806 | − | 7.03248i | 0.560065 | − | 0.323354i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −25.3485 | − | 14.6350i | −1.16307 | − | 0.671499i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | −7.29511 | −0.333671 | ||||||||
\(479\) | −12.4674 | + | 21.5941i | −0.569648 | + | 0.986660i | 0.426952 | + | 0.904274i | \(0.359587\pi\) |
−0.996601 | + | 0.0823855i | \(0.973746\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 41.8978 | − | 24.1897i | 1.91038 | − | 1.10296i | ||||
\(482\) | −3.54945 | − | 6.14783i | −0.161673 | − | 0.280026i | ||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 2.48863 | − | 4.31043i | 0.113119 | − | 0.195929i | ||||
\(485\) | − | 6.95750i | − | 0.315924i | ||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −5.00662 | −0.226871 | −0.113436 | − | 0.993545i | \(-0.536186\pi\) | ||||
−0.113436 | + | 0.993545i | \(0.536186\pi\) | |||||||
\(488\) | −0.0222909 | + | 0.0386090i | −0.00100906 | + | 0.00174775i | ||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −18.6960 | + | 10.7942i | −0.843740 | + | 0.487134i | −0.858534 | − | 0.512757i | \(-0.828624\pi\) |
0.0147936 | + | 0.999891i | \(0.495291\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −0.912628 | − | 0.526906i | −0.0411027 | − | 0.0237307i | ||||
\(494\) | − | 9.36399i | − | 0.421306i | ||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | − | 3.20419i | − | 0.143872i | ||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −17.9065 | − | 31.0149i | −0.801604 | − | 1.38842i | −0.918560 | − | 0.395282i | \(-0.870647\pi\) |
0.116956 | − | 0.993137i | \(-0.462686\pi\) | |||||||
\(500\) | 9.89826 | + | 17.1443i | 0.442664 | + | 0.766716i | ||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 1.95979 | + | 1.13149i | 0.0874699 | + | 0.0505008i | ||||
\(503\) | 23.9969 | 1.06997 | 0.534984 | − | 0.844862i | \(-0.320318\pi\) | ||||
0.534984 | + | 0.844862i | \(0.320318\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −23.2195 | −1.03325 | ||||||||
\(506\) | 0.494543 | + | 0.285525i | 0.0219851 | + | 0.0126931i | ||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 10.6772 | + | 18.4934i | 0.473724 | + | 0.820514i | ||||
\(509\) | 9.07094 | + | 15.7113i | 0.402062 | + | 0.696392i | 0.993975 | − | 0.109610i | \(-0.0349602\pi\) |
−0.591912 | + | 0.806002i | \(0.701627\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | − | 22.8374i | − | 1.00928i | ||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | − | 10.4438i | − | 0.460658i | ||||||
\(515\) | −30.3732 | − | 17.5360i | −1.33840 | − | 0.772728i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −18.2203 | + | 10.5195i | −0.801330 | + | 0.462648i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | −17.6686 | + | 30.6029i | −0.774819 | + | 1.34203i | ||||
\(521\) | 0.839387 | 0.0367742 | 0.0183871 | − | 0.999831i | \(-0.494147\pi\) | ||||
0.0183871 | + | 0.999831i | \(0.494147\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | − | 16.2832i | − | 0.712015i | −0.934483 | − | 0.356008i | \(-0.884138\pi\) | ||
0.934483 | − | 0.356008i | \(-0.115862\pi\) | |||||||
\(524\) | 19.1129 | − | 33.1045i | 0.834951 | − | 1.44618i | ||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 6.52858 | + | 11.3078i | 0.284660 | + | 0.493045i | ||||
\(527\) | 1.00014 | − | 0.577428i | 0.0435666 | − | 0.0251532i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −11.4340 | + | 19.8043i | −0.497132 | + | 0.861057i | ||||
\(530\) | 6.93524 | 0.301247 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 21.8819 | + | 12.6335i | 0.947812 | + | 0.547219i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 12.3792 | − | 7.14713i | 0.535199 | − | 0.308997i | ||||
\(536\) | 13.6545 | − | 7.88342i | 0.589784 | − | 0.340512i | ||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 5.13615 | + | 2.96536i | 0.221435 | + | 0.127846i | ||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −1.86693 | −0.0802657 | −0.0401328 | − | 0.999194i | \(-0.512778\pi\) | ||||
−0.0401328 | + | 0.999194i | \(0.512778\pi\) | |||||||
\(542\) | 1.37072 | − | 2.37417i | 0.0588777 | − | 0.101979i | ||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 4.14136 | − | 2.39102i | 0.177559 | − | 0.102514i | ||||
\(545\) | −31.2515 | − | 54.1292i | −1.33867 | − | 2.31864i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 7.55792 | − | 13.0907i | 0.323153 | − | 0.559718i | −0.657984 | − | 0.753032i | \(-0.728590\pi\) |
0.981137 | + | 0.193315i | \(0.0619238\pi\) | |||||||
\(548\) | − | 20.5157i | − | 0.876386i | ||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 12.6004 | 0.537281 | ||||||||
\(551\) | −1.80811 | + | 3.13173i | −0.0770279 | + | 0.133416i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | 7.02398 | − | 4.05529i | 0.298420 | − | 0.172293i | ||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 5.10183 | + | 2.94554i | 0.216366 | + | 0.124919i | ||||
\(557\) | − | 6.32176i | − | 0.267862i | −0.990991 | − | 0.133931i | \(-0.957240\pi\) | ||
0.990991 | − | 0.133931i | \(-0.0427600\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | − | 22.9402i | − | 0.970269i | ||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | −4.91321 | − | 8.50992i | −0.207251 | − | 0.358970i | ||||
\(563\) | 4.82545 | + | 8.35793i | 0.203369 | + | 0.352245i | 0.949612 | − | 0.313429i | \(-0.101478\pi\) |
−0.746243 | + | 0.665673i | \(0.768144\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 30.6747 | + | 17.7100i | 1.29049 | + | 0.745066i | ||||
\(566\) | 6.77132 | 0.284620 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 9.00618 | 0.377891 | ||||||||
\(569\) | −13.4785 | − | 7.78184i | −0.565050 | − | 0.326232i | 0.190120 | − | 0.981761i | \(-0.439112\pi\) |
−0.755170 | + | 0.655529i | \(0.772446\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 20.9434 | + | 36.2750i | 0.876454 | + | 1.51806i | 0.855206 | + | 0.518288i | \(0.173431\pi\) |
0.0212481 | + | 0.999774i | \(0.493236\pi\) | |||||||
\(572\) | −20.3860 | − | 35.3096i | −0.852382 | − | 1.47637i | ||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | − | 2.91135i | − | 0.121412i | ||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 40.3472i | 1.67968i | 0.542837 | + | 0.839838i | \(0.317350\pi\) | ||||
−0.542837 | + | 0.839838i | \(0.682650\pi\) | |||||||
\(578\) | −5.82921 | − | 3.36549i | −0.242463 | − | 0.139986i | ||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 5.63080 | − | 3.25094i | 0.233806 | − | 0.134988i | ||||
\(581\) | 0 | 0 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −8.39744 | + | 14.5448i | −0.347787 | + | 0.602384i | ||||
\(584\) | −3.65926 | −0.151421 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 2.84086i | 0.117355i | ||||||||
\(587\) | −1.91520 | + | 3.31723i | −0.0790490 | + | 0.136917i | −0.902840 | − | 0.429977i | \(-0.858522\pi\) |
0.823791 | + | 0.566894i | \(0.191855\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −1.98148 | − | 3.43202i | −0.0816453 | − | 0.141414i | ||||
\(590\) | −14.9165 | + | 8.61204i | −0.614102 | + | 0.354552i | ||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 11.8163 | − | 20.4664i | 0.485647 | − | 0.841166i | ||||
\(593\) | 12.5143 | 0.513902 | 0.256951 | − | 0.966424i | \(-0.417282\pi\) | ||||
0.256951 | + | 0.966424i | \(0.417282\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | −28.2229 | − | 16.2945i | −1.15606 | − | 0.667449i | ||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0.806611 | − | 0.465697i | 0.0329848 | − | 0.0190438i | ||||
\(599\) | −6.62258 | + | 3.82355i | −0.270591 | + | 0.156226i | −0.629156 | − | 0.777279i | \(-0.716599\pi\) |
0.358565 | + | 0.933505i | \(0.383266\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −29.8513 | − | 17.2346i | −1.21766 | − | 0.703015i | −0.253242 | − | 0.967403i | \(-0.581497\pi\) |
−0.964416 | + | 0.264388i | \(0.914830\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | −33.8510 | −1.37738 | ||||||||
\(605\) | −4.93285 | + | 8.54394i | −0.200549 | + | 0.347361i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −10.7472 | + | 6.20488i | −0.436214 | + | 0.251848i | −0.701990 | − | 0.712186i | \(-0.747705\pi\) |
0.265776 | + | 0.964035i | \(0.414372\pi\) | |||||||
\(608\) | −8.20490 | − | 14.2113i | −0.332753 | − | 0.576344i | ||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0.0210514 | − | 0.0364621i | 0.000852346 | − | 0.00147631i | ||||
\(611\) | 34.3151i | 1.38824i | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −1.66896 | −0.0674088 | −0.0337044 | − | 0.999432i | \(-0.510730\pi\) | ||||
−0.0337044 | + | 0.999432i | \(0.510730\pi\) | |||||||
\(614\) | −1.82209 | + | 3.15595i | −0.0735335 | + | 0.127364i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 13.5698 | − | 7.83453i | 0.546300 | − | 0.315406i | −0.201329 | − | 0.979524i | \(-0.564526\pi\) |
0.747628 | + | 0.664118i | \(0.231193\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 3.10436 | + | 1.79230i | 0.124775 | + | 0.0720387i | 0.561088 | − | 0.827756i | \(-0.310383\pi\) |
−0.436314 | + | 0.899795i | \(0.643716\pi\) | |||||||
\(620\) | 7.12532i | 0.286160i | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | − | 1.79626i | − | 0.0720234i | ||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 0.417550 | + | 0.723218i | 0.0167020 | + | 0.0289287i | ||||
\(626\) | 0.759935 | + | 1.31625i | 0.0303731 | + | 0.0526078i | ||||
\(627\) | 0 | 0 | ||||||||
\(628\) | −12.0892 | − | 6.97968i | −0.482410 | − | 0.278520i | ||||
\(629\) | 8.51769 | 0.339622 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 23.1493 | 0.921557 | 0.460779 | − | 0.887515i | \(-0.347570\pi\) | ||||
0.460779 | + | 0.887515i | \(0.347570\pi\) | |||||||
\(632\) | 9.16691 | + | 5.29252i | 0.364640 | + | 0.210525i | ||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 1.88476 | + | 3.26451i | 0.0748536 | + | 0.129650i | ||||
\(635\) | −21.1638 | − | 36.6568i | −0.839861 | − | 1.45468i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | − | 1.55674i | − | 0.0616318i | ||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 38.5419i | 1.52350i | ||||||||
\(641\) | −20.3567 | − | 11.7529i | −0.804041 | − | 0.464213i | 0.0408415 | − | 0.999166i | \(-0.486996\pi\) |
−0.844882 | + | 0.534953i | \(0.820329\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 4.83255 | − | 2.79007i | 0.190577 | − | 0.110030i | −0.401676 | − | 0.915782i | \(-0.631572\pi\) |
0.592253 | + | 0.805752i | \(0.298239\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0.824312 | − | 1.42775i | 0.0324321 | − | 0.0561741i | ||||
\(647\) | 3.90178 | 0.153395 | 0.0766974 | − | 0.997054i | \(-0.475562\pi\) | ||||
0.0766974 | + | 0.997054i | \(0.475562\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | − | 41.7111i | − | 1.63730i | ||||||
\(650\) | 10.2757 | − | 17.7981i | 0.403047 | − | 0.698098i | ||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 3.63386 | + | 6.29402i | 0.142313 | + | 0.246493i | ||||
\(653\) | 5.29484 | − | 3.05698i | 0.207203 | − | 0.119629i | −0.392808 | − | 0.919621i | \(-0.628496\pi\) |
0.600011 | + | 0.799992i | \(0.295163\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −37.8847 | + | 65.6183i | −1.48028 | + | 2.56392i | ||||
\(656\) | 12.3426 | 0.481896 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −24.7031 | − | 14.2623i | −0.962296 | − | 0.555582i | −0.0654174 | − | 0.997858i | \(-0.520838\pi\) |
−0.896879 | + | 0.442276i | \(0.854171\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −21.7672 | + | 12.5673i | −0.846648 | + | 0.488812i | −0.859518 | − | 0.511105i | \(-0.829236\pi\) |
0.0128707 | + | 0.999917i | \(0.495903\pi\) | |||||||
\(662\) | −5.79801 | + | 3.34748i | −0.225346 | + | 0.130104i | ||||
\(663\) | 0 | 0 | ||||||||
\(664\) | −4.29366 | − | 2.47895i | −0.166626 | − | 0.0962018i | ||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −0.359688 | −0.0139272 | ||||||||
\(668\) | 7.75804 | − | 13.4373i | 0.300168 | − | 0.519906i | ||||
\(669\) | 0 | 0 | ||||||||
\(670\) | −12.8952 | + | 7.44503i | −0.498184 | + | 0.287627i | ||||
\(671\) | 0.0509796 | + | 0.0882993i | 0.00196805 | + | 0.00340875i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 12.5278 | − | 21.6988i | 0.482912 | − | 0.836428i | −0.516895 | − | 0.856049i | \(-0.672912\pi\) |
0.999808 | + | 0.0196203i | \(0.00624575\pi\) | |||||||
\(674\) | − | 5.76872i | − | 0.222203i | ||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −42.8393 | −1.64767 | ||||||||
\(677\) | −16.8081 | + | 29.1126i | −0.645989 | + | 1.11889i | 0.338083 | + | 0.941116i | \(0.390222\pi\) |
−0.984072 | + | 0.177770i | \(0.943112\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | −5.38794 | + | 3.11073i | −0.206618 | + | 0.119291i | ||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 1.47744 | + | 0.853001i | 0.0565742 | + | 0.0326631i | ||||
\(683\) | 38.5467i | 1.47495i | 0.675375 | + | 0.737475i | \(0.263982\pi\) | ||||
−0.675375 | + | 0.737475i | \(0.736018\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 40.6652i | 1.55374i | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | −5.60297 | − | 9.70464i | −0.213611 | − | 0.369986i | ||||
\(689\) | 13.6964 | + | 23.7229i | 0.521792 | + | 0.903770i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 26.1768 | + | 15.1132i | 0.995812 | + | 0.574932i | 0.907006 | − | 0.421117i | \(-0.138362\pi\) |
0.0888052 | + | 0.996049i | \(0.471695\pi\) | |||||||
\(692\) | 0.791523 | 0.0300892 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −5.88111 | −0.223244 | ||||||||
\(695\) | −10.1126 | − | 5.83852i | −0.383593 | − | 0.221468i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 2.22426 | + | 3.85253i | 0.0842499 | + | 0.145925i | ||||
\(698\) | 0.380115 | + | 0.658378i | 0.0143876 | + | 0.0249200i | ||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 29.6057i | 1.11819i | 0.829103 | + | 0.559096i | \(0.188852\pi\) | ||||
−0.829103 | + | 0.559096i | \(0.811148\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | − | 29.2289i | − | 1.10239i | ||||||
\(704\) | −12.8357 | − | 7.41070i | −0.483764 | − | 0.279301i | ||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −2.85114 | + | 1.64611i | −0.107304 | + | 0.0619521i | ||||
\(707\) | 0 | 0 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −1.78201 | + | 3.08652i | −0.0669246 | + | 0.115917i | −0.897546 | − | 0.440921i | \(-0.854652\pi\) |
0.830622 | + | 0.556837i | \(0.187985\pi\) | |||||||
\(710\) | −8.50536 | −0.319200 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 24.2407i | 0.908458i | ||||||||
\(713\) | 0.197088 | − | 0.341367i | 0.00738102 | − | 0.0127843i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 40.4082 | + | 69.9891i | 1.51118 | + | 2.61744i | ||||
\(716\) | −27.4533 | + | 15.8501i | −1.02598 | + | 0.592348i | ||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 4.78944 | − | 8.29556i | 0.178740 | − | 0.309588i | ||||
\(719\) | −1.61282 | −0.0601480 | −0.0300740 | − | 0.999548i | \(-0.509574\pi\) | ||||
−0.0300740 | + | 0.999548i | \(0.509574\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | 2.08061 | + | 1.20124i | 0.0774322 | + | 0.0447055i | ||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 27.9654 | − | 16.1458i | 1.03933 | − | 0.600055i | ||||
\(725\) | −6.87332 | + | 3.96831i | −0.255269 | + | 0.147379i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −10.4930 | − | 6.05816i | −0.389166 | − | 0.224685i | 0.292633 | − | 0.956225i | \(-0.405469\pi\) |
−0.681799 | + | 0.731540i | \(0.738802\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 3.45577 | 0.127904 | ||||||||
\(731\) | 2.01943 | − | 3.49775i | 0.0746913 | − | 0.129369i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −34.9931 | + | 20.2033i | −1.29250 | + | 0.746225i | −0.979097 | − | 0.203396i | \(-0.934802\pi\) |
−0.313403 | + | 0.949620i | \(0.601469\pi\) | |||||||
\(734\) | 3.31277 | + | 5.73788i | 0.122276 | + | 0.211789i | ||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0.816104 | − | 1.41353i | 0.0300820 | − | 0.0521035i | ||||
\(737\) | − | 36.0589i | − | 1.32825i | ||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −20.4634 | −0.752760 | −0.376380 | − | 0.926465i | \(-0.622831\pi\) | ||||
−0.376380 | + | 0.926465i | \(0.622831\pi\) | |||||||
\(740\) | −26.2765 | + | 45.5123i | −0.965944 | + | 1.67306i | ||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −37.1209 | + | 21.4318i | −1.36184 | + | 0.786256i | −0.989868 | − | 0.141990i | \(-0.954650\pi\) |
−0.371967 | + | 0.928246i | \(0.621317\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 55.9422 | + | 32.2982i | 2.04956 | + | 1.18332i | ||||
\(746\) | 10.7093i | 0.392095i | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | − | 7.17832i | − | 0.262465i | ||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 21.5028 | + | 37.2440i | 0.784649 | + | 1.35905i | 0.929209 | + | 0.369556i | \(0.120490\pi\) |
−0.144559 | + | 0.989496i | \(0.546177\pi\) | |||||||
\(752\) | 8.38120 | + | 14.5167i | 0.305631 | + | 0.529368i | ||||
\(753\) | 0 | 0 | ||||||||
\(754\) | −2.19890 | − | 1.26953i | −0.0800792 | − | 0.0462337i | ||||
\(755\) | 67.0979 | 2.44194 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −13.0766 | −0.475276 | −0.237638 | − | 0.971354i | \(-0.576373\pi\) | ||||
−0.237638 | + | 0.971354i | \(0.576373\pi\) | |||||||
\(758\) | 5.42682 | + | 3.13317i | 0.197111 | + | 0.113802i | ||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 10.6746 | + | 18.4890i | 0.387210 | + | 0.670667i | ||||
\(761\) | 11.5916 | + | 20.0773i | 0.420196 | + | 0.727801i | 0.995958 | − | 0.0898160i | \(-0.0286279\pi\) |
−0.575762 | + | 0.817617i | \(0.695295\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | 0.452950i | 0.0163872i | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 4.49232i | 0.162314i | ||||||||
\(767\) | −58.9172 | − | 34.0159i | −2.12738 | − | 1.22824i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −11.4527 | + | 6.61219i | −0.412993 | + | 0.238442i | −0.692075 | − | 0.721826i | \(-0.743303\pi\) |
0.279082 | + | 0.960267i | \(0.409970\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 7.55096 | − | 13.0787i | 0.271765 | − | 0.470711i | ||||
\(773\) | 19.6319 | 0.706110 | 0.353055 | − | 0.935603i | \(-0.385143\pi\) | ||||
0.353055 | + | 0.935603i | \(0.385143\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | − | 8.69762i | − | 0.312428i | ||||||
\(776\) | −1.56258 | + | 2.70647i | −0.0560935 | + | 0.0971567i | ||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 2.88120 | + | 4.99039i | 0.103296 | + | 0.178914i | ||||
\(779\) | 13.2202 | − | 7.63267i | 0.473662 | − | 0.273469i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 10.2986 | − | 17.8377i | 0.368513 | − | 0.638284i | ||||
\(782\) | 0.163981 | 0.00586395 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 23.9626 | + | 13.8348i | 0.855262 | + | 0.493786i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −14.8621 | + | 8.58063i | −0.529776 | + | 0.305866i | −0.740925 | − | 0.671588i | \(-0.765613\pi\) |
0.211149 | + | 0.977454i | \(0.432279\pi\) | |||||||
\(788\) | −35.5938 | + | 20.5501i | −1.26798 | + | 0.732067i | ||||
\(789\) | 0 | 0 | ||||||||
\(790\) | −8.65715 | − | 4.99821i | −0.308008 | − | 0.177828i | ||||
\(791\) | 0 | 0 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 0.166298 | 0.00590540 | ||||||||
\(794\) | −8.25299 | + | 14.2946i | −0.292888 | + | 0.507297i | ||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 9.64647 | − | 5.56939i | 0.341910 | − | 0.197402i | ||||
\(797\) | −11.2772 | − | 19.5326i | −0.399458 | − | 0.691882i | 0.594201 | − | 0.804317i | \(-0.297468\pi\) |
−0.993659 | + | 0.112435i | \(0.964135\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −3.02076 | + | 5.23211i | −0.106867 | + | 0.185099i | ||||
\(800\) | − | 36.0151i | − | 1.27333i | ||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | −12.1945 | −0.430603 | ||||||||
\(803\) | −4.18438 | + | 7.24755i | −0.147663 | + | 0.255761i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 2.40974 | − | 1.39126i | 0.0848794 | − | 0.0490051i | ||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 9.03240 | + | 5.21486i | 0.317759 | + | 0.183458i | ||||
\(809\) | − | 48.2178i | − | 1.69525i | −0.530598 | − | 0.847624i | \(-0.678033\pi\) | ||
0.530598 | − | 0.847624i | \(-0.321967\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | − | 11.2304i | − | 0.394354i | −0.980368 | − | 0.197177i | \(-0.936823\pi\) | ||
0.980368 | − | 0.197177i | \(-0.0631774\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 6.29134 | + | 10.8969i | 0.220511 | + | 0.381937i | ||||
\(815\) | −7.20287 | − | 12.4757i | −0.252305 | − | 0.437006i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −12.0027 | − | 6.92978i | −0.419922 | − | 0.242442i | ||||
\(818\) | −8.00789 | −0.279989 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −27.4468 | −0.958484 | ||||||||
\(821\) | 34.6778 | + | 20.0212i | 1.21026 | + | 0.698746i | 0.962817 | − | 0.270156i | \(-0.0870752\pi\) |
0.247447 | + | 0.968902i | \(0.420409\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −4.98922 | − | 8.64158i | −0.173913 | − | 0.301227i | 0.765871 | − | 0.642994i | \(-0.222308\pi\) |
−0.939785 | + | 0.341767i | \(0.888975\pi\) | |||||||
\(824\) | 7.87680 | + | 13.6430i | 0.274401 | + | 0.475277i | ||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | − | 20.8802i | − | 0.726077i | −0.931774 | − | 0.363038i | \(-0.881739\pi\) | ||
0.931774 | − | 0.363038i | \(-0.118261\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 16.0646i | 0.557945i | 0.960299 | + | 0.278973i | \(0.0899939\pi\) | ||||
−0.960299 | + | 0.278973i | \(0.910006\pi\) | |||||||
\(830\) | 4.05490 | + | 2.34110i | 0.140748 | + | 0.0812607i | ||||
\(831\) | 0 | 0 | ||||||||
\(832\) | −20.9353 | + | 12.0870i | −0.725801 | + | 0.419042i | ||||
\(833\) | 0 | 0 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −15.3776 | + | 26.6349i | −0.532165 | + | 0.921737i | ||||
\(836\) | −24.6328 | −0.851943 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 2.81581i | 0.0972705i | ||||||||
\(839\) | −10.1943 | + | 17.6570i | −0.351946 | + | 0.609589i | −0.986590 | − | 0.163216i | \(-0.947813\pi\) |
0.634644 | + | 0.772805i | \(0.281147\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −14.0097 | − | 24.2656i | −0.483094 | − | 0.836743i | ||||
\(842\) | −7.13117 | + | 4.11719i | −0.245756 | + | 0.141888i | ||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 3.55769 | − | 6.16210i | 0.122461 | − | 0.212108i | ||||
\(845\) | 84.9142 | 2.92114 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | 11.5883 | + | 6.69048i | 0.397942 | + | 0.229752i | ||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 3.13353 | − | 1.80914i | 0.107479 | − | 0.0620531i | ||||
\(851\) | 2.51777 | − | 1.45363i | 0.0863079 | − | 0.0498299i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −7.80792 | − | 4.50790i | −0.267338 | − | 0.154348i | 0.360339 | − | 0.932821i | \(-0.382661\pi\) |
−0.627677 | + | 0.778474i | \(0.715994\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −6.42068 | −0.219454 | ||||||||
\(857\) | −16.1658 | + | 28.0000i | −0.552213 | + | 0.956461i | 0.445902 | + | 0.895082i | \(0.352883\pi\) |
−0.998115 | + | 0.0613789i | \(0.980450\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −38.1416 | + | 22.0211i | −1.30138 | + | 0.751349i | −0.980640 | − | 0.195819i | \(-0.937263\pi\) |
−0.320735 | + | 0.947169i | \(0.603930\pi\) | |||||||
\(860\) | 12.4596 | + | 21.5807i | 0.424870 | + | 0.735896i | ||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −5.15796 | + | 8.93385i | −0.175681 | + | 0.304288i | ||||
\(863\) | 6.12763i | 0.208587i | 0.994547 | + | 0.104293i | \(0.0332581\pi\) | ||||
−0.994547 | + | 0.104293i | \(0.966742\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −1.56892 | −0.0533449 | ||||||||
\(866\) | −0.704488 | + | 1.22021i | −0.0239395 | + | 0.0414644i | ||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 20.9648 | − | 12.1040i | 0.711182 | − | 0.410601i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −50.9334 | − | 29.4064i | −1.72581 | − | 0.996398i | ||||
\(872\) | 28.0751i | 0.950742i | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | − | 0.562710i | − | 0.0190340i | ||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 1.13204 | + | 1.96075i | 0.0382263 | + | 0.0662099i | 0.884506 | − | 0.466530i | \(-0.154496\pi\) |
−0.846279 | + | 0.532740i | \(0.821163\pi\) | |||||||
\(878\) | −5.70956 | − | 9.88924i | −0.192688 | − | 0.333746i | ||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 34.1886 | + | 19.7388i | 1.15250 | + | 0.665394i | ||||
\(881\) | −19.2955 | −0.650083 | −0.325041 | − | 0.945700i | \(-0.605378\pi\) | ||||
−0.325041 | + | 0.945700i | \(0.605378\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −0.833572 | −0.0280519 | −0.0140260 | − | 0.999902i | \(-0.504465\pi\) | ||||
−0.0140260 | + | 0.999902i | \(0.504465\pi\) | |||||||
\(884\) | −10.1394 | − | 5.85400i | −0.341026 | − | 0.196891i | ||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −5.60451 | − | 9.70729i | −0.188287 | − | 0.326123i | ||||
\(887\) | −28.7740 | − | 49.8380i | −0.966136 | − | 1.67340i | −0.706532 | − | 0.707681i | \(-0.749741\pi\) |
−0.259604 | − | 0.965715i | \(-0.583592\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | − | 22.8927i | − | 0.767365i | ||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | − | 46.9008i | − | 1.57035i | ||||||
\(893\) | 17.9543 | + | 10.3659i | 0.600817 | + | 0.346882i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 54.4166 | − | 31.4174i | 1.81895 | − | 1.05017i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 4.16384 | − | 7.21198i | 0.138949 | − | 0.240667i | ||||
\(899\) | −1.07456 | −0.0358387 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 4.82278i | 0.160670i | ||||||||
\(902\) | −3.28577 | + | 5.69112i | −0.109404 | + | 0.189494i | ||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −7.95498 | − | 13.7784i | −0.264579 | − | 0.458263i | ||||
\(905\) | −55.4317 | + | 32.0035i | −1.84261 | + | 1.06383i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 5.05621 | − | 8.75761i | 0.167889 | − | 0.290792i | −0.769789 | − | 0.638299i | \(-0.779638\pi\) |
0.937677 | + | 0.347507i | \(0.112972\pi\) | |||||||
\(908\) | −44.7918 | −1.48647 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 16.9986 | + | 9.81416i | 0.563190 | + | 0.325158i | 0.754425 | − | 0.656387i | \(-0.227916\pi\) |
−0.191235 | + | 0.981544i | \(0.561249\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −9.81965 | + | 5.66937i | −0.324983 | + | 0.187629i | ||||
\(914\) | 9.27560 | − | 5.35527i | 0.306810 | − | 0.177137i | ||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −7.17586 | − | 4.14299i | −0.237097 | − | 0.136888i | ||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 17.0487 | 0.562384 | 0.281192 | − | 0.959652i | \(-0.409270\pi\) | ||||
0.281192 | + | 0.959652i | \(0.409270\pi\) | |||||||
\(920\) | −1.06176 | + | 1.83902i | −0.0350051 | + | 0.0606306i | ||||
\(921\) | 0 | 0 | ||||||||
\(922\) | −5.31670 | + | 3.06960i | −0.175096 | + | 0.101092i | ||||
\(923\) | −16.7972 | − | 29.0937i | −0.552888 | − | 0.957630i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 32.0748 | − | 55.5552i | 1.05461 | − | 1.82664i | ||||
\(926\) | − | 8.49825i | − | 0.279270i | ||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | −4.44956 | −0.146064 | ||||||||
\(929\) | 4.32511 | − | 7.49131i | 0.141902 | − | 0.245782i | −0.786311 | − | 0.617831i | \(-0.788011\pi\) |
0.928213 | + | 0.372049i | \(0.121345\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | 41.1948 | − | 23.7838i | 1.34938 | − | 0.779065i | ||||
\(933\) | 0 | 0 | ||||||||
\(934\) | −8.65632 | − | 4.99773i | −0.283244 | − | 0.163531i | ||||
\(935\) | 14.2285i | 0.465323i | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | − | 34.9586i | − | 1.14205i | −0.820933 | − | 0.571025i | \(-0.806546\pi\) | ||
0.820933 | − | 0.571025i | \(-0.193454\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | −18.6377 | − | 32.2815i | −0.607895 | − | 1.05291i | ||||
\(941\) | −20.5472 | − | 35.5887i | −0.669818 | − | 1.16016i | −0.977955 | − | 0.208817i | \(-0.933039\pi\) |
0.308136 | − | 0.951342i | \(-0.400295\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 1.31495 | + | 0.759187i | 0.0428207 | + | 0.0247225i | ||||
\(944\) | −33.2324 | −1.08162 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 5.96637 | 0.193983 | ||||||||
\(947\) | 29.2164 | + | 16.8681i | 0.949405 | + | 0.548139i | 0.892896 | − | 0.450263i | \(-0.148670\pi\) |
0.0565088 | + | 0.998402i | \(0.482003\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 6.82481 | + | 11.8209i | 0.221543 | + | 0.383723i | ||||
\(950\) | −6.20818 | − | 10.7529i | −0.201420 | − | 0.348869i | ||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 18.7823i | 0.608420i | 0.952605 | + | 0.304210i | \(0.0983925\pi\) | ||||
−0.952605 | + | 0.304210i | \(0.901608\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | − | 0.897817i | − | 0.0290527i | ||||||
\(956\) | 27.1066 | + | 15.6500i | 0.876690 | + | 0.506157i | ||||
\(957\) | 0 | 0 | ||||||||
\(958\) | −9.16024 | + | 5.28867i | −0.295954 | + | 0.170869i | ||||
\(959\) | 0 | 0 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −14.9112 | + | 25.8270i | −0.481006 | + | 0.833128i | ||||
\(962\) | 20.5226 | 0.661676 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 30.4582i | 0.980992i | ||||||||
\(965\) | −14.9672 | + | 25.9239i | −0.481810 | + | 0.834520i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −17.5860 | − | 30.4599i | −0.565529 | − | 0.979525i | −0.997000 | − | 0.0773981i | \(-0.975339\pi\) |
0.431471 | − | 0.902127i | \(-0.357995\pi\) | |||||||
\(968\) | 3.83776 | − | 2.21573i | 0.123350 | − | 0.0712163i | ||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 1.47569 | − | 2.55597i | 0.0473816 | − | 0.0820673i | ||||
\(971\) | 39.5962 | 1.27070 | 0.635351 | − | 0.772223i | \(-0.280855\pi\) | ||||
0.635351 | + | 0.772223i | \(0.280855\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 0 | 0 | ||||||||
\(974\) | −1.83928 | − | 1.06191i | −0.0589342 | − | 0.0340257i | ||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0.0703505 | − | 0.0406169i | 0.00225187 | − | 0.00130012i | ||||
\(977\) | 30.3364 | − | 17.5147i | 0.970546 | − | 0.560345i | 0.0711433 | − | 0.997466i | \(-0.477335\pi\) |
0.899403 | + | 0.437121i | \(0.144002\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 48.0113 | + | 27.7193i | 1.53445 | + | 0.885914i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | −9.15779 | −0.292237 | ||||||||
\(983\) | −22.0865 | + | 38.2550i | −0.704451 | + | 1.22015i | 0.262438 | + | 0.964949i | \(0.415474\pi\) |
−0.966889 | + | 0.255197i | \(0.917860\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 70.5524 | − | 40.7335i | 2.24799 | − | 1.29788i | ||||
\(986\) | −0.223514 | − | 0.387138i | −0.00711814 | − | 0.0123290i | ||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −20.0883 | + | 34.7940i | −0.639094 | + | 1.10694i | ||||
\(989\) | − | 1.37855i | − | 0.0438353i | ||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 26.8886 | 0.854146 | 0.427073 | − | 0.904217i | \(-0.359545\pi\) | ||||
0.427073 | + | 0.904217i | \(0.359545\pi\) | |||||||
\(992\) | 2.43810 | − | 4.22291i | 0.0774097 | − | 0.134078i | ||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −19.1208 | + | 11.0394i | −0.606170 | + | 0.349972i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 26.9780 | + | 15.5757i | 0.854401 | + | 0.493289i | 0.862133 | − | 0.506681i | \(-0.169128\pi\) |
−0.00773220 | + | 0.999970i | \(0.502461\pi\) | |||||||
\(998\) | − | 15.1919i | − | 0.480891i | ||||||
\(999\) | 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.440.13 | 48 | ||
3.2 | odd | 2 | 441.2.o.e.146.11 | ✓ | 48 | ||
7.2 | even | 3 | 1323.2.i.d.521.3 | 48 | |||
7.3 | odd | 6 | 1323.2.s.d.656.11 | 48 | |||
7.4 | even | 3 | 1323.2.s.d.656.12 | 48 | |||
7.5 | odd | 6 | 1323.2.i.d.521.19 | 48 | |||
7.6 | odd | 2 | inner | 1323.2.o.e.440.14 | 48 | ||
9.4 | even | 3 | 441.2.o.e.293.12 | yes | 48 | ||
9.5 | odd | 6 | inner | 1323.2.o.e.881.14 | 48 | ||
21.2 | odd | 6 | 441.2.i.d.227.13 | 48 | |||
21.5 | even | 6 | 441.2.i.d.227.14 | 48 | |||
21.11 | odd | 6 | 441.2.s.d.362.14 | 48 | |||
21.17 | even | 6 | 441.2.s.d.362.13 | 48 | |||
21.20 | even | 2 | 441.2.o.e.146.12 | yes | 48 | ||
63.4 | even | 3 | 441.2.i.d.68.12 | 48 | |||
63.5 | even | 6 | 1323.2.s.d.962.12 | 48 | |||
63.13 | odd | 6 | 441.2.o.e.293.11 | yes | 48 | ||
63.23 | odd | 6 | 1323.2.s.d.962.11 | 48 | |||
63.31 | odd | 6 | 441.2.i.d.68.11 | 48 | |||
63.32 | odd | 6 | 1323.2.i.d.1097.19 | 48 | |||
63.40 | odd | 6 | 441.2.s.d.374.14 | 48 | |||
63.41 | even | 6 | inner | 1323.2.o.e.881.13 | 48 | ||
63.58 | even | 3 | 441.2.s.d.374.13 | 48 | |||
63.59 | even | 6 | 1323.2.i.d.1097.3 | 48 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
441.2.i.d.68.11 | 48 | 63.31 | odd | 6 | |||
441.2.i.d.68.12 | 48 | 63.4 | even | 3 | |||
441.2.i.d.227.13 | 48 | 21.2 | odd | 6 | |||
441.2.i.d.227.14 | 48 | 21.5 | even | 6 | |||
441.2.o.e.146.11 | ✓ | 48 | 3.2 | odd | 2 | ||
441.2.o.e.146.12 | yes | 48 | 21.20 | even | 2 | ||
441.2.o.e.293.11 | yes | 48 | 63.13 | odd | 6 | ||
441.2.o.e.293.12 | yes | 48 | 9.4 | even | 3 | ||
441.2.s.d.362.13 | 48 | 21.17 | even | 6 | |||
441.2.s.d.362.14 | 48 | 21.11 | odd | 6 | |||
441.2.s.d.374.13 | 48 | 63.58 | even | 3 | |||
441.2.s.d.374.14 | 48 | 63.40 | odd | 6 | |||
1323.2.i.d.521.3 | 48 | 7.2 | even | 3 | |||
1323.2.i.d.521.19 | 48 | 7.5 | odd | 6 | |||
1323.2.i.d.1097.3 | 48 | 63.59 | even | 6 | |||
1323.2.i.d.1097.19 | 48 | 63.32 | odd | 6 | |||
1323.2.o.e.440.13 | 48 | 1.1 | even | 1 | trivial | ||
1323.2.o.e.440.14 | 48 | 7.6 | odd | 2 | inner | ||
1323.2.o.e.881.13 | 48 | 63.41 | even | 6 | inner | ||
1323.2.o.e.881.14 | 48 | 9.5 | odd | 6 | inner | ||
1323.2.s.d.656.11 | 48 | 7.3 | odd | 6 | |||
1323.2.s.d.656.12 | 48 | 7.4 | even | 3 | |||
1323.2.s.d.962.11 | 48 | 63.23 | odd | 6 | |||
1323.2.s.d.962.12 | 48 | 63.5 | even | 6 |