Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [280,2,Mod(9,280)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(280, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 0, 3, 2]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("280.9");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 280 = 2^{3} \cdot 5 \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 280.bg (of order \(6\), degree \(2\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(2.23581125660\) |
Analytic rank: | \(0\) |
Dimension: | \(24\) |
Relative dimension: | \(12\) over \(\Q(\zeta_{6})\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 249.3 | ||
Character | \(\chi\) | \(=\) | 280.249 |
Dual form | 280.2.bg.a.9.3 |
$q$-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 \(\left(\mathbb{Z}/280\mathbb{Z}\right)^\times\).
\(n\) | \(57\) | \(71\) | \(141\) | \(241\) |
\(\chi(n)\) | \(-1\) | \(1\) | \(1\) | \(e\left(\frac{2}{3}\right)\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | −1.82577 | − | 1.05411i | −1.05411 | − | 0.608589i | −0.130311 | − | 0.991473i | \(-0.541598\pi\) |
−0.923796 | + | 0.382884i | \(0.874931\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 1.46656 | + | 1.68796i | 0.655867 | + | 0.754877i | ||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −1.44930 | + | 2.21349i | −0.547784 | + | 0.836620i | ||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0.722285 | + | 1.25103i | 0.240762 | + | 0.417011i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −0.887326 | + | 1.53689i | −0.267539 | + | 0.463391i | −0.968226 | − | 0.250078i | \(-0.919544\pi\) |
0.700687 | + | 0.713469i | \(0.252877\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 1.44457i | 0.400652i | 0.979729 | + | 0.200326i | \(0.0642001\pi\) | ||||
−0.979729 | + | 0.200326i | \(0.935800\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −0.898317 | − | 4.62773i | −0.231945 | − | 1.19487i | ||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 5.08189 | + | 2.93403i | 1.23254 | + | 0.711607i | 0.967559 | − | 0.252647i | \(-0.0813010\pi\) |
0.264981 | + | 0.964254i | \(0.414634\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 3.58102 | + | 6.20251i | 0.821543 | + | 1.42295i | 0.904533 | + | 0.426404i | \(0.140220\pi\) |
−0.0829897 | + | 0.996550i | \(0.526447\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 4.97934 | − | 2.51359i | 1.08658 | − | 0.548511i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 0.574733 | − | 0.331822i | 0.119840 | − | 0.0691898i | −0.438882 | − | 0.898545i | \(-0.644625\pi\) |
0.558722 | + | 0.829355i | \(0.311292\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −0.698386 | + | 4.95099i | −0.139677 | + | 0.990197i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 3.27918i | 0.631079i | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −6.45763 | −1.19915 | −0.599576 | − | 0.800318i | \(-0.704664\pi\) | ||||
−0.599576 | + | 0.800318i | \(0.704664\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 5.03658 | − | 8.72362i | 0.904597 | − | 1.56681i | 0.0831406 | − | 0.996538i | \(-0.473505\pi\) |
0.821457 | − | 0.570271i | \(-0.193162\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 3.24010 | − | 1.87067i | 0.564029 | − | 0.325642i | ||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −5.86176 | + | 0.799863i | −0.990818 | + | 0.135201i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −4.34489 | + | 2.50852i | −0.714295 | + | 0.412399i | −0.812649 | − | 0.582753i | \(-0.801976\pi\) |
0.0983541 | + | 0.995151i | \(0.468642\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 1.52273 | − | 2.63745i | 0.243832 | − | 0.422330i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −1.92363 | −0.300421 | −0.150211 | − | 0.988654i | \(-0.547995\pi\) | ||||
−0.150211 | + | 0.988654i | \(0.547995\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | − | 5.81995i | − | 0.887535i | −0.896142 | − | 0.443767i | \(-0.853642\pi\) | ||
0.896142 | − | 0.443767i | \(-0.146358\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −1.05241 | + | 3.05391i | −0.156885 | + | 0.455249i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −3.20709 | + | 1.85161i | −0.467802 | + | 0.270085i | −0.715319 | − | 0.698798i | \(-0.753719\pi\) |
0.247517 | + | 0.968883i | \(0.420385\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −2.79905 | − | 6.41602i | −0.399864 | − | 0.916574i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −6.18557 | − | 10.7137i | −0.866153 | − | 1.50022i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −0.513002 | − | 0.296182i | −0.0704662 | − | 0.0406837i | 0.464353 | − | 0.885650i | \(-0.346287\pi\) |
−0.534819 | + | 0.844967i | \(0.679620\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −3.89553 | + | 0.756185i | −0.525273 | + | 0.101964i | ||||
\(56\) | 0 | 0 | ||||||||
\(57\) | − | 15.0991i | − | 1.99993i | ||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −3.79538 | + | 6.57379i | −0.494116 | + | 0.855835i | −0.999977 | − | 0.00678044i | \(-0.997842\pi\) |
0.505861 | + | 0.862615i | \(0.331175\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −4.36055 | − | 7.55270i | −0.558312 | − | 0.967024i | −0.997638 | − | 0.0686963i | \(-0.978116\pi\) |
0.439326 | − | 0.898328i | \(-0.355217\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −3.81596 | − | 0.214357i | −0.480765 | − | 0.0270065i | ||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −2.43837 | + | 2.11855i | −0.302442 | + | 0.262774i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 1.87782 | + | 1.08416i | 0.229412 | + | 0.132451i | 0.610301 | − | 0.792170i | \(-0.291049\pi\) |
−0.380889 | + | 0.924621i | \(0.624382\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −1.39911 | −0.168433 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 6.49826 | 0.771201 | 0.385601 | − | 0.922666i | \(-0.373994\pi\) | ||||
0.385601 | + | 0.922666i | \(0.373994\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 13.4511 | + | 7.76600i | 1.57433 | + | 0.908941i | 0.995628 | + | 0.0934035i | \(0.0297746\pi\) |
0.578704 | + | 0.815538i | \(0.303559\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 6.49396 | − | 8.30318i | 0.749858 | − | 0.958768i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −2.11589 | − | 4.19151i | −0.241128 | − | 0.477666i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −1.35360 | − | 2.34451i | −0.152292 | − | 0.263778i | 0.779778 | − | 0.626057i | \(-0.215332\pi\) |
−0.932070 | + | 0.362279i | \(0.881999\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 5.62346 | − | 9.74012i | 0.624829 | − | 1.08224i | ||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 6.35340i | 0.697376i | 0.937239 | + | 0.348688i | \(0.113373\pi\) | ||||
−0.937239 | + | 0.348688i | \(0.886627\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 2.50040 | + | 12.8809i | 0.271207 | + | 1.39713i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 11.7901 | + | 6.80704i | 1.26404 | + | 0.729791i | ||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 2.93079 | + | 5.07627i | 0.310663 | + | 0.538084i | 0.978506 | − | 0.206218i | \(-0.0661157\pi\) |
−0.667843 | + | 0.744302i | \(0.732782\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −3.19754 | − | 2.09362i | −0.335193 | − | 0.219471i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −18.3913 | + | 10.6182i | −1.90709 | + | 1.10106i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −5.21777 | + | 15.1410i | −0.535332 | + | 1.55343i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | − | 14.7748i | − | 1.50015i | −0.661351 | − | 0.750076i | \(-0.730017\pi\) | ||
0.661351 | − | 0.750076i | \(-0.269983\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −2.56361 | −0.257652 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −1.74093 | + | 3.01538i | −0.173229 | + | 0.300041i | −0.939547 | − | 0.342420i | \(-0.888753\pi\) |
0.766318 | + | 0.642461i | \(0.222087\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 6.99628 | − | 4.03930i | 0.689364 | − | 0.398004i | −0.114010 | − | 0.993480i | \(-0.536370\pi\) |
0.803374 | + | 0.595475i | \(0.203036\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 11.5454 | + | 4.71856i | 1.12671 | + | 0.460484i | ||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 0.112276 | − | 0.0648226i | 0.0108541 | − | 0.00626664i | −0.494563 | − | 0.869142i | \(-0.664672\pi\) |
0.505417 | + | 0.862875i | \(0.331339\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 6.13241 | − | 10.6217i | 0.587379 | − | 1.01737i | −0.407196 | − | 0.913341i | \(-0.633493\pi\) |
0.994574 | − | 0.104029i | \(-0.0331734\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 10.5770 | 1.00393 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | − | 11.7467i | − | 1.10503i | −0.833501 | − | 0.552517i | \(-0.813667\pi\) | ||
0.833501 | − | 0.552517i | \(-0.186333\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 1.40298 | + | 0.483486i | 0.130829 | + | 0.0450853i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −1.80721 | + | 1.04339i | −0.167076 | + | 0.0964615i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −13.8596 | + | 6.99641i | −1.27051 | + | 0.641359i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 3.92531 | + | 6.79883i | 0.356846 | + | 0.618075i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 3.51211 | + | 2.02772i | 0.316676 | + | 0.182833i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −9.38127 | + | 6.08209i | −0.839086 | + | 0.543999i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | − | 12.6983i | − | 1.12679i | −0.826187 | − | 0.563395i | \(-0.809495\pi\) | ||
0.826187 | − | 0.563395i | \(-0.190505\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −6.13486 | + | 10.6259i | −0.540144 | + | 0.935557i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 0.115466 | + | 0.199993i | 0.0100883 | + | 0.0174734i | 0.871025 | − | 0.491238i | \(-0.163455\pi\) |
−0.860937 | + | 0.508711i | \(0.830122\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −18.9192 | − | 1.06276i | −1.64050 | − | 0.0921533i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −5.53511 | + | 4.80913i | −0.476386 | + | 0.413904i | ||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −14.5594 | − | 8.40586i | −1.24389 | − | 0.718161i | −0.274008 | − | 0.961728i | \(-0.588349\pi\) |
−0.969884 | + | 0.243566i | \(0.921683\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 20.5531 | 1.74329 | 0.871644 | − | 0.490139i | \(-0.163054\pi\) | ||||
0.871644 | + | 0.490139i | \(0.163054\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 7.80719 | 0.657484 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −2.22015 | − | 1.28180i | −0.185658 | − | 0.107190i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −9.47053 | − | 10.9002i | −0.786485 | − | 0.905212i | ||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −1.65276 | + | 14.6647i | −0.136317 | + | 1.20952i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 10.6363 | + | 18.4225i | 0.871356 | + | 1.50923i | 0.860595 | + | 0.509290i | \(0.170092\pi\) |
0.0107608 | + | 0.999942i | \(0.496575\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −3.23995 | + | 5.61176i | −0.263663 | + | 0.456678i | −0.967213 | − | 0.253968i | \(-0.918264\pi\) |
0.703549 | + | 0.710647i | \(0.251597\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 8.47683i | 0.685311i | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 22.1116 | − | 4.29221i | 1.77604 | − | 0.344759i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −4.71976 | − | 2.72495i | −0.376678 | − | 0.217475i | 0.299694 | − | 0.954035i | \(-0.403115\pi\) |
−0.676372 | + | 0.736560i | \(0.736449\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0.624415 | + | 1.08152i | 0.0495193 | + | 0.0857699i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −0.0984771 | + | 1.75308i | −0.00776108 | + | 0.138162i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 5.42930 | − | 3.13461i | 0.425255 | − | 0.245521i | −0.272068 | − | 0.962278i | \(-0.587708\pi\) |
0.697323 | + | 0.716757i | \(0.254374\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 7.90942 | + | 2.72569i | 0.615748 | + | 0.212194i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 18.5728i | 1.43720i | 0.695422 | + | 0.718602i | \(0.255218\pi\) | ||||
−0.695422 | + | 0.718602i | \(0.744782\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 10.9132 | 0.839478 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −5.17304 | + | 8.95997i | −0.395592 | + | 0.685186i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 12.0960 | − | 6.98361i | 0.919639 | − | 0.530954i | 0.0361190 | − | 0.999347i | \(-0.488500\pi\) |
0.883520 | + | 0.468394i | \(0.155167\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −9.94677 | − | 8.72134i | −0.751905 | − | 0.659271i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 13.8590 | − | 8.00148i | 1.04170 | − | 0.601428i | ||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 3.96270 | − | 6.86359i | 0.296186 | − | 0.513009i | −0.679074 | − | 0.734070i | \(-0.737619\pi\) |
0.975260 | + | 0.221061i | \(0.0709519\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −11.6887 | −0.868815 | −0.434407 | − | 0.900717i | \(-0.643042\pi\) | ||||
−0.434407 | + | 0.900717i | \(0.643042\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 18.3860i | 1.35913i | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −10.6063 | − | 3.65507i | −0.779793 | − | 0.268726i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −9.01858 | + | 5.20688i | −0.659504 | + | 0.380765i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −7.25843 | − | 4.75252i | −0.527973 | − | 0.345695i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 6.48908 | + | 11.2394i | 0.469533 | + | 0.813255i | 0.999393 | − | 0.0348297i | \(-0.0110889\pi\) |
−0.529860 | + | 0.848085i | \(0.677756\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 18.5375 | + | 10.7026i | 1.33436 | + | 0.770393i | 0.985965 | − | 0.166955i | \(-0.0533935\pi\) |
0.348395 | + | 0.937348i | \(0.386727\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 6.68508 | − | 1.29768i | 0.478728 | − | 0.0929289i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | − | 8.42871i | − | 0.600521i | −0.953857 | − | 0.300261i | \(-0.902926\pi\) | ||
0.953857 | − | 0.300261i | \(-0.0970736\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 2.10741 | − | 3.65013i | 0.149390 | − | 0.258751i | −0.781612 | − | 0.623765i | \(-0.785602\pi\) |
0.931002 | + | 0.365014i | \(0.118936\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −2.28564 | − | 3.95885i | −0.161217 | − | 0.279236i | ||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 9.35906 | − | 14.2939i | 0.656877 | − | 1.00323i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −2.82113 | − | 3.24701i | −0.197036 | − | 0.226781i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0.830243 | + | 0.479341i | 0.0577058 | + | 0.0333165i | ||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −12.7101 | −0.879179 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −0.629004 | −0.0433025 | −0.0216512 | − | 0.999766i | \(-0.506892\pi\) | ||||
−0.0216512 | + | 0.999766i | \(0.506892\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −11.8643 | − | 6.84986i | −0.812929 | − | 0.469345i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 9.82382 | − | 8.53533i | 0.669979 | − | 0.582105i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 12.0101 | + | 23.7916i | 0.815298 | + | 1.61508i | ||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −16.3724 | − | 28.3578i | −1.10634 | − | 1.91624i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −4.23841 | + | 7.34115i | −0.285107 | + | 0.493819i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | − | 21.4138i | − | 1.43398i | −0.697086 | − | 0.716988i | \(-0.745520\pi\) | ||
0.697086 | − | 0.716988i | \(-0.254480\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −6.69829 | + | 2.70232i | −0.446552 | + | 0.180155i | ||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 19.0953 | + | 11.0247i | 1.26740 | + | 0.731732i | 0.974495 | − | 0.224411i | \(-0.0720457\pi\) |
0.292902 | + | 0.956142i | \(0.405379\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 5.81797 | + | 10.0770i | 0.384462 | + | 0.665908i | 0.991694 | − | 0.128616i | \(-0.0410535\pi\) |
−0.607232 | + | 0.794524i | \(0.707720\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −0.555172 | + | 9.88309i | −0.0365276 | + | 0.650260i | ||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 9.71624 | − | 5.60967i | 0.636532 | − | 0.367502i | −0.146745 | − | 0.989174i | \(-0.546880\pi\) |
0.783277 | + | 0.621672i | \(0.213546\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −7.82883 | − | 2.69791i | −0.510697 | − | 0.175992i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 5.70737i | 0.370733i | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −22.8279 | −1.47662 | −0.738308 | − | 0.674464i | \(-0.764375\pi\) | ||||
−0.738308 | + | 0.674464i | \(0.764375\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −2.10135 | + | 3.63965i | −0.135360 | + | 0.234450i | −0.925735 | − | 0.378173i | \(-0.876552\pi\) |
0.790375 | + | 0.612623i | \(0.209886\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −12.0147 | + | 6.93670i | −0.770744 | + | 0.444989i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 6.72497 | − | 14.1342i | 0.429643 | − | 0.902999i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −8.95997 | + | 5.17304i | −0.570109 | + | 0.329153i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 6.69717 | − | 11.5998i | 0.424416 | − | 0.735109i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −16.9587 | −1.07042 | −0.535211 | − | 0.844718i | \(-0.679768\pi\) | ||||
−0.535211 | + | 0.844718i | \(0.679768\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 1.17774i | 0.0740438i | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 9.01275 | − | 26.1533i | 0.564400 | − | 1.63778i | ||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −23.3223 | + | 13.4651i | −1.45480 | + | 0.839932i | −0.998748 | − | 0.0500191i | \(-0.984072\pi\) |
−0.456056 | + | 0.889951i | \(0.650738\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 0.744470 | − | 13.2530i | 0.0462591 | − | 0.823499i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −4.66425 | − | 8.07872i | −0.288710 | − | 0.500060i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −19.0110 | − | 10.9760i | −1.17227 | − | 0.676809i | −0.218055 | − | 0.975937i | \(-0.569971\pi\) |
−0.954213 | + | 0.299127i | \(0.903304\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −0.252408 | − | 1.30029i | −0.0155053 | − | 0.0798764i | ||||
\(266\) | 0 | 0 | ||||||||
\(267\) | − | 12.3575i | − | 0.756264i | ||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 12.0427 | − | 20.8586i | 0.734256 | − | 1.27177i | −0.220793 | − | 0.975321i | \(-0.570864\pi\) |
0.955049 | − | 0.296448i | \(-0.0958023\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −1.03365 | − | 1.79034i | −0.0627900 | − | 0.108755i | 0.832922 | − | 0.553391i | \(-0.186666\pi\) |
−0.895712 | + | 0.444636i | \(0.853333\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 3.63106 | + | 7.19301i | 0.219762 | + | 0.435341i | ||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −6.98944 | − | 5.46648i | −0.421479 | − | 0.329641i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 14.7880 | + | 8.53786i | 0.888525 | + | 0.512990i | 0.873460 | − | 0.486896i | \(-0.161871\pi\) |
0.0150652 | + | 0.999887i | \(0.495204\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 14.5514 | 0.871169 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −13.2035 | −0.787655 | −0.393828 | − | 0.919184i | \(-0.628849\pi\) | ||||
−0.393828 | + | 0.919184i | \(0.628849\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −23.0353 | − | 13.2994i | −1.36931 | − | 0.790570i | −0.378468 | − | 0.925615i | \(-0.623549\pi\) |
−0.990840 | + | 0.135045i | \(0.956882\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 25.4867 | − | 22.1438i | 1.50970 | − | 1.31169i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 2.78793 | − | 4.25794i | 0.164566 | − | 0.251338i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 8.71708 | + | 15.0984i | 0.512769 | + | 0.888142i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −15.5742 | + | 26.9753i | −0.912977 | + | 1.58132i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | − | 0.472681i | − | 0.0276143i | −0.999905 | − | 0.0138071i | \(-0.995605\pi\) | ||
0.999905 | − | 0.0138071i | \(-0.00439509\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −16.6624 | + | 3.23445i | −0.970124 | + | 0.188317i | ||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −5.03975 | − | 2.90970i | −0.292436 | − | 0.168838i | ||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 0.479341 | + | 0.830243i | 0.0277210 | + | 0.0480142i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 12.8824 | + | 8.43487i | 0.742529 | + | 0.486178i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 6.35706 | − | 3.67025i | 0.365204 | − | 0.210850i | ||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 6.35359 | − | 18.4369i | 0.363806 | − | 1.05570i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | − | 15.2073i | − | 0.867929i | −0.900930 | − | 0.433965i | \(-0.857114\pi\) | ||
0.900930 | − | 0.433965i | \(-0.142886\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −17.0314 | −0.968885 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 8.29030 | − | 14.3592i | 0.470100 | − | 0.814237i | −0.529316 | − | 0.848425i | \(-0.677551\pi\) |
0.999415 | + | 0.0341882i | \(0.0108846\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −1.02148 | + | 0.589752i | −0.0577375 | + | 0.0333348i | −0.528591 | − | 0.848877i | \(-0.677279\pi\) |
0.470853 | + | 0.882211i | \(0.343946\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −5.23452 | − | 6.75553i | −0.294932 | − | 0.380631i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 23.7540 | − | 13.7144i | 1.33416 | − | 0.770278i | 0.348226 | − | 0.937411i | \(-0.386784\pi\) |
0.985934 | + | 0.167133i | \(0.0534509\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 5.73002 | − | 9.92469i | 0.320820 | − | 0.555676i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −0.273320 | −0.0152552 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 42.0273i | 2.33846i | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −7.15204 | − | 1.00887i | −0.396724 | − | 0.0559619i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −22.3927 | + | 12.9284i | −1.23832 | + | 0.714945i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 0.549515 | − | 9.78239i | 0.0302957 | − | 0.539320i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −2.60580 | − | 4.51337i | −0.143228 | − | 0.248078i | 0.785483 | − | 0.618884i | \(-0.212415\pi\) |
−0.928710 | + | 0.370806i | \(0.879081\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −6.27649 | − | 3.62374i | −0.343950 | − | 0.198580i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 0.923929 | + | 4.75967i | 0.0504796 | + | 0.260048i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 9.52496i | 0.518858i | 0.965762 | + | 0.259429i | \(0.0835343\pi\) | ||||
−0.965762 | + | 0.259429i | \(0.916466\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −12.3823 | + | 21.4467i | −0.672512 | + | 1.16483i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 8.93818 | + | 15.4814i | 0.484030 | + | 0.838364i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 18.2584 | + | 3.10308i | 0.985863 | + | 0.167551i | ||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −2.05188 | − | 2.36163i | −0.110469 | − | 0.127146i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −23.6235 | − | 13.6390i | −1.26818 | − | 0.732182i | −0.293534 | − | 0.955949i | \(-0.594831\pi\) |
−0.974643 | + | 0.223767i | \(0.928165\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −6.78145 | −0.363003 | −0.181501 | − | 0.983391i | \(-0.558096\pi\) | ||||
−0.181501 | + | 0.983391i | \(0.558096\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −4.73701 | −0.252843 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 13.5785 | + | 7.83957i | 0.722713 | + | 0.417258i | 0.815750 | − | 0.578404i | \(-0.196324\pi\) |
−0.0930377 | + | 0.995663i | \(0.529658\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 9.53010 | + | 10.9688i | 0.505805 | + | 0.582162i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 32.6794 | + | 1.83573i | 1.72958 | + | 0.0971572i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −3.16733 | − | 5.48598i | −0.167165 | − | 0.289539i | 0.770257 | − | 0.637734i | \(-0.220128\pi\) |
−0.937422 | + | 0.348195i | \(0.886795\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −16.1475 | + | 27.9682i | −0.849866 | + | 1.47201i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | − | 16.5508i | − | 0.868691i | ||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 6.61823 | + | 34.0942i | 0.346414 | + | 1.78457i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 11.0504 | + | 6.37993i | 0.576824 | + | 0.333030i | 0.759870 | − | 0.650075i | \(-0.225262\pi\) |
−0.183046 | + | 0.983104i | \(0.558596\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −1.38941 | − | 2.40653i | −0.0723299 | − | 0.125279i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 1.39909 | − | 0.706266i | 0.0726370 | − | 0.0366675i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −1.44553 | + | 0.834577i | −0.0748467 | + | 0.0432127i | −0.536956 | − | 0.843610i | \(-0.680426\pi\) |
0.462110 | + | 0.886823i | \(0.347093\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 23.5392 | − | 1.21562i | 1.21556 | − | 0.0627742i | ||||
\(376\) | 0 | 0 | ||||||||
\(377\) | − | 9.32850i | − | 0.480442i | ||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 21.5557 | 1.10724 | 0.553621 | − | 0.832768i | \(-0.313245\pi\) | ||||
0.553621 | + | 0.832768i | \(0.313245\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −13.3854 | + | 23.1841i | −0.685753 | + | 1.18776i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −4.36845 | + | 2.52213i | −0.223217 | + | 0.128875i | −0.607439 | − | 0.794366i | \(-0.707803\pi\) |
0.384222 | + | 0.923241i | \(0.374470\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 3.97199 | − | 9.71864i | 0.202431 | − | 0.495308i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 7.28096 | − | 4.20366i | 0.370112 | − | 0.213684i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −6.25975 | + | 10.8422i | −0.317382 | + | 0.549722i | −0.979941 | − | 0.199288i | \(-0.936137\pi\) |
0.662559 | + | 0.749010i | \(0.269470\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 3.89431 | 0.196944 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | − | 0.486853i | − | 0.0245585i | ||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 1.97228 | − | 5.72319i | 0.0992362 | − | 0.287965i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −19.3934 | + | 11.1968i | −0.973326 | + | 0.561950i | −0.900249 | − | 0.435376i | \(-0.856615\pi\) |
−0.0730773 | + | 0.997326i | \(0.523282\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 33.4217 | + | 21.8832i | 1.67318 | + | 1.09553i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 7.69654 | + | 13.3308i | 0.384347 | + | 0.665708i | 0.991678 | − | 0.128740i | \(-0.0410933\pi\) |
−0.607331 | + | 0.794449i | \(0.707760\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 12.6019 | + | 7.27570i | 0.627744 | + | 0.362428i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 24.6881 | − | 4.79235i | 1.22676 | − | 0.238134i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | − | 8.90351i | − | 0.441330i | ||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 15.4851 | − | 26.8209i | 0.765687 | − | 1.32621i | −0.174196 | − | 0.984711i | \(-0.555733\pi\) |
0.939883 | − | 0.341498i | \(-0.110934\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 17.7214 | + | 30.6943i | 0.874130 | + | 1.51404i | ||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −9.05035 | − | 17.9284i | −0.445339 | − | 0.882200i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −10.7243 | + | 9.31766i | −0.526433 | + | 0.457386i | ||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −37.5251 | − | 21.6651i | −1.83761 | − | 1.06095i | ||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −0.434578 | −0.0212305 | −0.0106153 | − | 0.999944i | \(-0.503379\pi\) | ||||
−0.0106153 | + | 0.999944i | \(0.503379\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −27.3152 | −1.33126 | −0.665630 | − | 0.746282i | \(-0.731837\pi\) | ||||
−0.665630 | + | 0.746282i | \(0.731837\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −4.63286 | − | 2.67478i | −0.225257 | − | 0.130052i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −18.0755 | + | 23.1113i | −0.876789 | + | 1.12106i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 23.0376 | + | 1.29411i | 1.11487 | + | 0.0626263i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 2.70232 | + | 4.68055i | 0.130469 | + | 0.225979i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 10.2637 | − | 17.7773i | 0.494386 | − | 0.856302i | −0.505593 | − | 0.862772i | \(-0.668726\pi\) |
0.999979 | + | 0.00646986i | \(0.00205944\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 16.0082i | 0.769304i | 0.923062 | + | 0.384652i | \(0.125679\pi\) | ||||
−0.923062 | + | 0.384652i | \(0.874321\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 5.80100 | + | 29.8842i | 0.278137 | + | 1.43284i | ||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 4.11627 | + | 2.37653i | 0.196908 | + | 0.113685i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 4.03479 | + | 6.98846i | 0.192570 | + | 0.333541i | 0.946101 | − | 0.323871i | \(-0.104984\pi\) |
−0.753531 | + | 0.657412i | \(0.771651\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 6.00495 | − | 8.13590i | 0.285950 | − | 0.387424i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 6.22857 | − | 3.59607i | 0.295928 | − | 0.170854i | −0.344684 | − | 0.938719i | \(-0.612014\pi\) |
0.640612 | + | 0.767864i | \(0.278681\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −4.27034 | + | 12.3917i | −0.202433 | + | 0.587423i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | − | 44.8470i | − | 2.12119i | ||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 4.16729 | 0.196667 | 0.0983334 | − | 0.995154i | \(-0.468649\pi\) | ||||
0.0983334 | + | 0.995154i | \(0.468649\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 1.70689 | − | 2.95642i | 0.0803743 | − | 0.139212i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 11.8308 | − | 6.83051i | 0.555859 | − | 0.320925i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −1.15546 | − | 8.46772i | −0.0541687 | − | 0.396973i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −7.94968 | + | 4.58975i | −0.371871 | + | 0.214700i | −0.674275 | − | 0.738480i | \(-0.735544\pi\) |
0.302405 | + | 0.953180i | \(0.402211\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −9.62122 | + | 16.6644i | −0.449080 | + | 0.777829i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 27.3537 | 1.27399 | 0.636995 | − | 0.770868i | \(-0.280177\pi\) | ||||
0.636995 | + | 0.770868i | \(0.280177\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 12.8660i | 0.597932i | 0.954264 | + | 0.298966i | \(0.0966418\pi\) | ||||
−0.954264 | + | 0.298966i | \(0.903358\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −44.8950 | − | 15.4714i | −2.08196 | − | 0.717468i | ||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −12.0386 | + | 6.95048i | −0.557079 | + | 0.321630i | −0.751972 | − | 0.659195i | \(-0.770897\pi\) |
0.194893 | + | 0.980824i | \(0.437564\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −5.12130 | + | 2.58526i | −0.236480 | + | 0.119376i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 5.74478 | + | 9.95026i | 0.264706 | + | 0.458484i | ||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 8.94465 | + | 5.16419i | 0.411275 | + | 0.237450i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −33.2095 | + | 13.3978i | −1.52376 | + | 0.614735i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | − | 0.855710i | − | 0.0391803i | ||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −0.185972 | + | 0.322113i | −0.00849729 | + | 0.0147177i | −0.870243 | − | 0.492623i | \(-0.836038\pi\) |
0.861745 | + | 0.507341i | \(0.169371\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −3.62374 | − | 6.27649i | −0.165228 | − | 0.286184i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 2.02773 | − | 3.09690i | 0.0922648 | − | 0.140914i | ||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 24.9392 | − | 21.6682i | 1.13243 | − | 0.983901i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −16.6572 | − | 9.61701i | −0.754808 | − | 0.435788i | 0.0726206 | − | 0.997360i | \(-0.476864\pi\) |
−0.827428 | + | 0.561571i | \(0.810197\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −13.2168 | −0.597686 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 15.2267 | 0.687170 | 0.343585 | − | 0.939122i | \(-0.388359\pi\) | ||||
0.343585 | + | 0.939122i | \(0.388359\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −32.8170 | − | 18.9469i | −1.47800 | − | 0.853325i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −3.75969 | − | 4.32726i | −0.168986 | − | 0.194496i | ||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −9.41793 | + | 14.3838i | −0.422452 | + | 0.645202i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 6.97149 | + | 12.0750i | 0.312087 | + | 0.540550i | 0.978814 | − | 0.204752i | \(-0.0656387\pi\) |
−0.666727 | + | 0.745302i | \(0.732305\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 19.5777 | − | 33.9095i | 0.874666 | − | 1.51497i | ||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 41.6394i | 1.85661i | 0.371821 | + | 0.928305i | \(0.378734\pi\) | ||||
−0.371821 | + | 0.928305i | \(0.621266\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −7.64300 | + | 1.48363i | −0.340109 | + | 0.0660207i | ||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −19.9250 | − | 11.5037i | −0.884900 | − | 0.510897i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −15.5832 | − | 26.9908i | −0.690712 | − | 1.19635i | −0.971605 | − | 0.236609i | \(-0.923964\pi\) |
0.280893 | − | 0.959739i | \(-0.409369\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −36.6846 | + | 18.5186i | −1.62283 | + | 0.819213i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −20.3392 | + | 11.7428i | −0.897996 | + | 0.518458i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 17.0786 | + | 5.88551i | 0.752575 | + | 0.259347i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | − | 6.57193i | − | 0.289033i | ||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −29.4459 | −1.29253 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 4.95959 | − | 8.59026i | 0.217284 | − | 0.376346i | −0.736693 | − | 0.676227i | \(-0.763614\pi\) |
0.953977 | + | 0.299881i | \(0.0969470\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 16.6572 | − | 9.61701i | 0.728367 | − | 0.420523i | −0.0894577 | − | 0.995991i | \(-0.528513\pi\) |
0.817824 | + | 0.575468i | \(0.195180\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 8.96727 | + | 26.4081i | 0.391364 | + | 1.15254i | ||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 51.1908 | − | 29.5550i | 2.22990 | − | 1.28744i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −11.2798 | + | 19.5372i | −0.490426 | + | 0.849442i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −10.9654 | −0.475857 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | − | 2.77882i | − | 0.120364i | ||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 0.274078 | + | 0.0944505i | 0.0118494 | + | 0.00408345i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −14.4699 | + | 8.35421i | −0.624423 | + | 0.360511i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 12.3444 | + | 1.39126i | 0.531711 | + | 0.0599257i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 1.80279 | + | 3.12253i | 0.0775081 | + | 0.134248i | 0.902174 | − | 0.431372i | \(-0.141970\pi\) |
−0.824666 | + | 0.565620i | \(0.808637\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 21.3409 | + | 12.3212i | 0.915824 | + | 0.528751i | ||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 26.9224 | − | 5.22608i | 1.15323 | − | 0.223861i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | − | 11.1011i | − | 0.474647i | −0.971431 | − | 0.237324i | \(-0.923730\pi\) | ||
0.971431 | − | 0.237324i | \(-0.0762702\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 6.29912 | − | 10.9104i | 0.268840 | − | 0.465645i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −23.1249 | − | 40.0536i | −0.985156 | − | 1.70634i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 7.15132 | + | 0.401717i | 0.304105 | + | 0.0170828i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 15.5119 | + | 17.8535i | 0.658441 | + | 0.757840i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 21.5074 | + | 12.4173i | 0.911298 | + | 0.526138i | 0.880848 | − | 0.473398i | \(-0.156973\pi\) |
0.0304492 | + | 0.999536i | \(0.490306\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 8.40733 | 0.355592 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 21.9545 | 0.926918 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −2.44929 | − | 1.41410i | −0.103225 | − | 0.0595970i | 0.447499 | − | 0.894285i | \(-0.352315\pi\) |
−0.550724 | + | 0.834688i | \(0.685648\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 19.8279 | − | 17.2272i | 0.834165 | − | 0.724756i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 13.4095 | + | 26.5638i | 0.563148 | + | 1.11558i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −12.5659 | − | 21.7648i | −0.526791 | − | 0.912429i | −0.999513 | − | 0.0312168i | \(-0.990062\pi\) |
0.472722 | − | 0.881212i | \(-0.343272\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 17.6047 | − | 30.4922i | 0.736733 | − | 1.27606i | −0.217226 | − | 0.976121i | \(-0.569701\pi\) |
0.953959 | − | 0.299937i | \(-0.0969657\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | − | 27.3607i | − | 1.14301i | ||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 1.24146 | + | 3.07724i | 0.0517726 | + | 0.128330i | ||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 24.1071 | + | 13.9182i | 1.00359 | + | 0.579424i | 0.909309 | − | 0.416122i | \(-0.136611\pi\) |
0.0942822 | + | 0.995546i | \(0.469944\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −22.5635 | − | 39.0811i | −0.937705 | − | 1.62415i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −14.0632 | − | 9.20799i | −0.583439 | − | 0.382012i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 0.910399 | − | 0.525619i | 0.0377049 | − | 0.0217689i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −4.41158 | − | 1.52028i | −0.182396 | − | 0.0628560i | ||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 4.74640i | 0.195905i | 0.995191 | + | 0.0979524i | \(0.0312293\pi\) | ||||
−0.995191 | + | 0.0979524i | \(0.968771\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 72.1445 | 2.97266 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −8.88477 | + | 15.3889i | −0.365471 | + | 0.633014i | ||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 6.47860 | − | 3.74042i | 0.266044 | − | 0.153601i | −0.361044 | − | 0.932549i | \(-0.617580\pi\) |
0.627089 | + | 0.778948i | \(0.284246\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −32.1356 | − | 13.1338i | −1.31743 | − | 0.538432i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −7.69527 | + | 4.44286i | −0.314946 | + | 0.181834i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −2.28083 | + | 3.95051i | −0.0931920 | + | 0.161413i | −0.908853 | − | 0.417117i | \(-0.863040\pi\) |
0.815661 | + | 0.578531i | \(0.196374\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −4.96538 | −0.202542 | −0.101271 | − | 0.994859i | \(-0.532291\pi\) | ||||
−0.101271 | + | 0.994859i | \(0.532291\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 3.13229i | 0.127557i | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −5.71941 | + | 16.5967i | −0.232527 | + | 0.674750i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −3.81333 | + | 2.20162i | −0.154778 | + | 0.0893612i | −0.575389 | − | 0.817880i | \(-0.695149\pi\) |
0.420611 | + | 0.907241i | \(0.361816\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −32.1548 | + | 16.2319i | −1.30298 | + | 0.657749i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −2.67478 | − | 4.63286i | −0.108210 | − | 0.187425i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −36.9750 | − | 21.3475i | −1.49340 | − | 0.862218i | −0.493434 | − | 0.869783i | \(-0.664258\pi\) |
−0.999971 | + | 0.00756572i | \(0.997592\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 1.72803 | + | 8.90206i | 0.0696810 | + | 0.358966i | ||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 23.2135i | 0.934541i | 0.884114 | + | 0.467270i | \(0.154763\pi\) | ||||
−0.884114 | + | 0.467270i | \(0.845237\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −14.0067 | + | 24.2603i | −0.562977 | + | 0.975104i | 0.434258 | + | 0.900789i | \(0.357011\pi\) |
−0.997235 | + | 0.0743159i | \(0.976323\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 1.08811 | + | 1.88465i | 0.0436642 | + | 0.0756286i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −15.4839 | − | 0.869788i | −0.620348 | − | 0.0348473i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −24.0245 | − | 6.91539i | −0.960981 | − | 0.276616i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 23.2058 | + | 13.3978i | 0.926749 | + | 0.535059i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −29.4403 | −1.17386 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −28.8446 | −1.14829 | −0.574144 | − | 0.818755i | \(-0.694665\pi\) | ||||
−0.574144 | + | 0.818755i | \(0.694665\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 1.14842 | + | 0.663038i | 0.0456454 | + | 0.0263534i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 21.4341 | − | 18.6228i | 0.850588 | − | 0.739025i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 9.26839 | − | 4.04342i | 0.367227 | − | 0.160206i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 4.69359 | + | 8.12954i | 0.185676 | + | 0.321600i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 20.5927 | − | 35.6676i | 0.813363 | − | 1.40879i | −0.0971347 | − | 0.995271i | \(-0.530968\pi\) |
0.910498 | − | 0.413514i | \(-0.135699\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 7.64360i | 0.301434i | 0.988577 | + | 0.150717i | \(0.0481583\pi\) | ||||
−0.988577 | + | 0.150717i | \(0.951842\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −26.9332 | + | 5.22816i | −1.06049 | + | 0.205859i | ||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −19.1717 | − | 11.0688i | −0.753717 | − | 0.435159i | 0.0733183 | − | 0.997309i | \(-0.476641\pi\) |
−0.827035 | + | 0.562150i | \(0.809974\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −6.73548 | − | 11.6662i | −0.264391 | − | 0.457938i | ||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 3.15123 | − | 56.0978i | 0.123507 | − | 2.19865i | ||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 15.8506 | − | 9.15132i | 0.620280 | − | 0.358119i | −0.156698 | − | 0.987647i | \(-0.550085\pi\) |
0.776978 | + | 0.629528i | \(0.216752\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −0.168241 | + | 0.488203i | −0.00657371 | + | 0.0190757i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 22.4370i | 0.875353i | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 28.1377 | 1.09609 | 0.548044 | − | 0.836449i | \(-0.315373\pi\) | ||||
0.548044 | + | 0.836449i | \(0.315373\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 11.6371 | − | 20.1560i | 0.452630 | − | 0.783979i | −0.545918 | − | 0.837838i | \(-0.683819\pi\) |
0.998549 | + | 0.0538598i | \(0.0171524\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 15.4767 | − | 8.93548i | 0.601066 | − | 0.347025i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −25.9523 | − | 33.4933i | −1.00639 | − | 1.29882i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −3.71142 | + | 2.14279i | −0.143707 | + | 0.0829691i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −22.5725 | + | 39.0967i | −0.872702 | + | 1.51156i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 15.4769 | 0.597480 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 19.0282i | 0.733484i | 0.930323 | + | 0.366742i | \(0.119527\pi\) | ||||
−0.930323 | + | 0.366742i | \(0.880473\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −16.2352 | − | 2.29013i | −0.624892 | − | 0.0881472i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −35.2928 | + | 20.3763i | −1.35641 | + | 0.783124i | −0.989138 | − | 0.146989i | \(-0.953042\pi\) |
−0.367273 | + | 0.930113i | \(0.619708\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 32.7038 | + | 21.4131i | 1.25506 | + | 0.821760i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −23.2423 | − | 40.2569i | −0.890648 | − | 1.54265i | ||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −27.6456 | − | 15.9612i | −1.05783 | − | 0.610738i | −0.132999 | − | 0.991116i | \(-0.542461\pi\) |
−0.924831 | + | 0.380378i | \(0.875794\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −7.16353 | − | 36.9033i | −0.273704 | − | 1.41000i | ||||
\(686\) | 0 | 0 | ||||||||
\(687\) | − | 24.5311i | − | 0.935918i | ||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 0.427855 | − | 0.741067i | 0.0163000 | − | 0.0282324i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 6.05622 | + | 10.4897i | 0.230389 | + | 0.399046i | 0.957923 | − | 0.287026i | \(-0.0926667\pi\) |
−0.727533 | + | 0.686072i | \(0.759333\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 3.71544 | − | 5.67451i | 0.141138 | − | 0.215557i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 30.1424 | + | 34.6927i | 1.14337 | + | 1.31597i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −9.77570 | − | 5.64400i | −0.370281 | − | 0.213782i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −23.6528 | −0.894631 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −9.83067 | −0.371299 | −0.185650 | − | 0.982616i | \(-0.559439\pi\) | ||||
−0.185650 | + | 0.982616i | \(0.559439\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −31.1183 | − | 17.9662i | −1.17365 | − | 0.677606i | ||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 11.4497 | + | 13.1782i | 0.431222 | + | 0.496319i | ||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −4.15137 | − | 8.22371i | −0.156128 | − | 0.309284i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −4.61102 | − | 7.98651i | −0.173170 | − | 0.299940i | 0.766356 | − | 0.642416i | \(-0.222068\pi\) |
−0.939527 | + | 0.342476i | \(0.888734\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 1.95537 | − | 3.38681i | 0.0733322 | − | 0.127015i | ||||
\(712\) | 0 | 0 | ||||||||
\(713\) | − | 6.68501i | − | 0.250356i | ||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −1.09236 | − | 5.62736i | −0.0408520 | − | 0.210451i | ||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 41.6785 | + | 24.0631i | 1.55651 | + | 0.898653i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −16.2886 | − | 28.2128i | −0.607464 | − | 1.05216i | −0.991657 | − | 0.128906i | \(-0.958854\pi\) |
0.384193 | − | 0.923253i | \(-0.374480\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −1.19877 | + | 21.3403i | −0.0446445 | + | 0.794756i | ||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 7.67316 | − | 4.43010i | 0.285368 | − | 0.164757i | ||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 4.50992 | − | 31.9717i | 0.167494 | − | 1.18740i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 28.4462i | 1.05501i | 0.849552 | + | 0.527505i | \(0.176872\pi\) | ||||
−0.849552 | + | 0.527505i | \(0.823128\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −4.49268 | −0.166396 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 17.0759 | − | 29.5764i | 0.631576 | − | 1.09392i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −8.32604 | + | 4.80704i | −0.307529 | + | 0.177552i | −0.645820 | − | 0.763489i | \(-0.723484\pi\) |
0.338291 | + | 0.941042i | \(0.390151\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | −27.1772 | + | 18.7169i | −1.00244 | + | 0.690382i | ||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −3.33248 | + | 1.92401i | −0.122753 | + | 0.0708717i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 1.94205 | − | 3.36372i | 0.0714393 | − | 0.123736i | −0.828093 | − | 0.560591i | \(-0.810574\pi\) |
0.899532 | + | 0.436854i | \(0.143907\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 21.8118 | 0.801275 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | − | 16.8174i | − | 0.616971i | −0.951229 | − | 0.308486i | \(-0.900178\pi\) | ||
0.951229 | − | 0.308486i | \(-0.0998222\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −15.4977 | + | 44.9713i | −0.567791 | + | 1.64762i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −7.94832 | + | 4.58897i | −0.290814 | + | 0.167901i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −0.0192378 | + | 0.342469i | −0.000702935 | + | 0.0125135i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 16.6827 | + | 28.8953i | 0.608760 | + | 1.05440i | 0.991445 | + | 0.130525i | \(0.0416662\pi\) |
−0.382685 | + | 0.923879i | \(0.625000\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 30.9626 | + | 17.8763i | 1.12834 | + | 0.651448i | ||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −14.2240 | + | 2.76111i | −0.517664 | + | 0.100487i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | − | 31.2781i | − | 1.13682i | −0.822744 | − | 0.568412i | \(-0.807558\pi\) | ||
0.822744 | − | 0.568412i | \(-0.192442\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 1.24146 | − | 2.15028i | 0.0450622 | − | 0.0780501i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −1.41224 | − | 2.44608i | −0.0511937 | − | 0.0886702i | 0.839293 | − | 0.543679i | \(-0.182969\pi\) |
−0.890487 | + | 0.455009i | \(0.849636\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 14.6232 | + | 28.9680i | 0.529394 | + | 1.04871i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −14.3085 | + | 12.4318i | −0.517325 | + | 0.449473i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −9.49630 | − | 5.48269i | −0.342892 | − | 0.197969i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 29.1637 | 1.05167 | 0.525836 | − | 0.850586i | \(-0.323753\pi\) | ||||
0.525836 | + | 0.850586i | \(0.323753\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 56.7748 | 2.04469 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 35.3151 | + | 20.3892i | 1.27020 | + | 0.733348i | 0.975025 | − | 0.222096i | \(-0.0712899\pi\) |
0.295171 | + | 0.955444i | \(0.404623\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 39.6730 | + | 31.0285i | 1.42510 | + | 1.11458i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −15.3293 | + | 23.4121i | −0.549935 | + | 0.839903i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −6.88858 | − | 11.9314i | −0.246809 | − | 0.427486i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −5.76607 | + | 9.98713i | −0.206326 | + | 0.357367i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | − | 21.1758i | − | 0.756760i | ||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −2.32222 | − | 11.9631i | −0.0828837 | − | 0.426980i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 7.14650 | + | 4.12603i | 0.254745 | + | 0.147077i | 0.621935 | − | 0.783069i | \(-0.286347\pi\) |
−0.367190 | + | 0.930146i | \(0.619680\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 23.1398 | + | 40.0793i | 0.823798 | + | 1.42686i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 26.0011 | + | 17.0245i | 0.924494 | + | 0.605321i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 10.9104 | − | 6.29912i | 0.387440 | − | 0.223688i | ||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −0.909810 | + | 2.64010i | −0.0322676 | + | 0.0936346i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 39.6687i | 1.40514i | 0.711616 | + | 0.702569i | \(0.247964\pi\) | ||||
−0.711616 | + | 0.702569i | \(0.752036\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −21.7307 | −0.768779 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −4.23373 | + | 7.33303i | −0.149591 | + | 0.259100i | ||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −23.8710 | + | 13.7819i | −0.842390 | + | 0.486354i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −3.10354 | + | 2.40477i | −0.109385 | + | 0.0847571i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −43.9743 | + | 25.3886i | −1.54797 | + | 0.893721i | ||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −16.1578 | + | 27.9861i | −0.568078 | + | 0.983940i | 0.428678 | + | 0.903457i | \(0.358980\pi\) |
−0.996756 | + | 0.0804828i | \(0.974354\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 7.67248 | 0.269417 | 0.134709 | − | 0.990885i | \(-0.456990\pi\) | ||||
0.134709 | + | 0.990885i | \(0.456990\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 4.35833i | 0.152853i | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 13.2535 | + | 4.56731i | 0.464249 | + | 0.159986i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 36.0983 | − | 20.8414i | 1.26292 | − | 0.729148i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0.309654 | − | 5.51242i | 0.0108202 | − | 0.192619i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −8.52811 | − | 14.7711i | −0.297633 | − | 0.515515i | 0.677961 | − | 0.735098i | \(-0.262864\pi\) |
−0.975594 | + | 0.219582i | \(0.929530\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 28.6675 | + | 16.5512i | 0.999288 | + | 0.576939i | 0.908037 | − | 0.418889i | \(-0.137580\pi\) |
0.0912502 | + | 0.995828i | \(0.470914\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 6.99884 | + | 17.3481i | 0.243668 | + | 0.603985i | ||||
\(826\) | 0 | 0 | ||||||||
\(827\) | − | 20.1051i | − | 0.699123i | −0.936913 | − | 0.349561i | \(-0.886331\pi\) | ||
0.936913 | − | 0.349561i | \(-0.113669\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 9.48334 | − | 16.4256i | 0.329370 | − | 0.570486i | −0.653017 | − | 0.757343i | \(-0.726497\pi\) |
0.982387 | + | 0.186858i | \(0.0598303\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −17.9996 | − | 31.1763i | −0.624400 | − | 1.08149i | ||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 4.60033 | − | 40.8180i | 0.159392 | − | 1.41426i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −31.3500 | + | 27.2381i | −1.08491 | + | 0.942614i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 28.6063 | + | 16.5159i | 0.988779 | + | 0.570872i | ||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −4.15025 | −0.143283 | −0.0716413 | − | 0.997430i | \(-0.522824\pi\) | ||||
−0.0716413 | + | 0.997430i | \(0.522824\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 12.7010 | 0.437967 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 24.1065 | + | 13.9179i | 0.830273 | + | 0.479358i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 16.0049 | + | 18.4210i | 0.550586 | + | 0.633702i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −20.7381 | − | 1.16494i | −0.712569 | − | 0.0400278i | ||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 28.0381 | + | 48.5634i | 0.962265 | + | 1.66669i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −1.66477 | + | 2.88346i | −0.0570675 | + | 0.0988439i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 1.53140i | 0.0524340i | 0.999656 | + | 0.0262170i | \(0.00834609\pi\) | ||||
−0.999656 | + | 0.0262170i | \(0.991654\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −22.7106 | + | 4.40850i | −0.776686 | + | 0.150767i | ||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 20.6317 | + | 11.9117i | 0.704766 | + | 0.406897i | 0.809120 | − | 0.587643i | \(-0.199944\pi\) |
−0.104354 | + | 0.994540i | \(0.533278\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 7.34165 | + | 12.7161i | 0.250494 | + | 0.433868i | 0.963662 | − | 0.267125i | \(-0.0860737\pi\) |
−0.713168 | + | 0.700993i | \(0.752740\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −9.57843 | + | 4.83524i | −0.326432 | + | 0.164784i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −36.6611 | + | 21.1663i | −1.24796 | + | 0.720508i | −0.970702 | − | 0.240288i | \(-0.922758\pi\) |
−0.277255 | + | 0.960796i | \(0.589425\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 29.5275 | + | 10.1755i | 1.00397 | + | 0.345979i | ||||
\(866\) | 0 | 0 | ||||||||
\(867\) | − | 36.7549i | − | 1.24826i | ||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 4.80434 | 0.162976 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −1.56615 | + | 2.71264i | −0.0530668 | + | 0.0919144i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 18.4838 | − | 10.6716i | 0.625581 | − | 0.361179i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 0.133659 | − | 29.5801i | 0.00451849 | − | 0.999990i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −9.17470 | + | 5.29702i | −0.309808 | + | 0.178868i | −0.646840 | − | 0.762625i | \(-0.723910\pi\) |
0.337033 | + | 0.941493i | \(0.390577\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −0.498256 | + | 0.863005i | −0.0168058 | + | 0.0291084i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 27.1174 | 0.913609 | 0.456805 | − | 0.889567i | \(-0.348994\pi\) | ||||
0.456805 | + | 0.889567i | \(0.348994\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | − | 21.7240i | − | 0.731072i | −0.930797 | − | 0.365536i | \(-0.880886\pi\) | ||
0.930797 | − | 0.365536i | \(-0.119114\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 33.8312 | + | 11.6586i | 1.13722 | + | 0.391901i | ||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 18.3256 | − | 10.5803i | 0.615312 | − | 0.355251i | −0.159729 | − | 0.987161i | \(-0.551062\pi\) |
0.775042 | + | 0.631910i | \(0.217729\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 28.1075 | + | 18.4036i | 0.942695 | + | 0.617238i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 9.97969 | + | 17.2853i | 0.334332 | + | 0.579080i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −22.9693 | − | 13.2613i | −0.768638 | − | 0.443774i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 17.3970 | − | 3.37704i | 0.581517 | − | 0.112882i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | − | 2.02111i | − | 0.0674828i | ||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −32.5244 | + | 56.3340i | −1.08475 | + | 1.87884i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −1.73801 | − | 3.01033i | −0.0579016 | − | 0.100288i | ||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −14.6290 | − | 28.9795i | −0.486823 | − | 0.964378i | ||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −17.1422 | − | 19.7300i | −0.569827 | − | 0.655848i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −32.7913 | − | 18.9321i | −1.08882 | − | 0.628630i | −0.155557 | − | 0.987827i | \(-0.549717\pi\) |
−0.933262 | + | 0.359197i | \(0.883051\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −5.02978 | −0.166827 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −30.1221 | −0.997990 | −0.498995 | − | 0.866605i | \(-0.666297\pi\) | ||||
−0.498995 | + | 0.866605i | \(0.666297\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −9.76450 | − | 5.63753i | −0.323158 | − | 0.186575i | ||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −31.0347 | + | 26.9642i | −1.02597 | + | 0.891408i | ||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −0.610026 | − | 0.0342675i | −0.0201448 | − | 0.00113161i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −23.0566 | − | 39.9352i | −0.760566 | − | 1.31734i | −0.942559 | − | 0.334040i | \(-0.891588\pi\) |
0.181993 | − | 0.983300i | \(-0.441745\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −16.0302 | + | 27.7651i | −0.528212 | + | 0.914891i | ||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 9.38718i | 0.308983i | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −9.38525 | − | 23.2634i | −0.308585 | − | 0.764896i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 10.1066 | + | 5.83506i | 0.331945 | + | 0.191648i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 13.7587 | + | 23.8308i | 0.451408 | + | 0.781862i | 0.998474 | − | 0.0552279i | \(-0.0175885\pi\) |
−0.547066 | + | 0.837090i | \(0.684255\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 29.7720 | − | 40.3371i | 0.975738 | − | 1.32199i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −30.2723 | + | 17.4777i | −0.991071 | + | 0.572195i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −22.0153 | − | 7.58675i | −0.719978 | − | 0.248113i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | − | 50.4704i | − | 1.64880i | −0.566010 | − | 0.824399i | \(-0.691514\pi\) | ||
0.566010 | − | 0.824399i | \(-0.308486\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 2.48665 | 0.0811487 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −0.928314 | + | 1.60789i | −0.0302622 | + | 0.0524156i | −0.880760 | − | 0.473563i | \(-0.842968\pi\) |
0.850498 | + | 0.525979i | \(0.176301\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −1.10558 | + | 0.638305i | −0.0360025 | + | 0.0207861i | ||||
\(944\) | 0 | 0 | ||||||||
\(945\) | −2.62289 | − | 19.2218i | −0.0853228 | − | 0.625284i | ||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 31.3232 | − | 18.0844i | 1.01787 | − | 0.587666i | 0.104381 | − | 0.994537i | \(-0.466714\pi\) |
0.913485 | + | 0.406872i | \(0.133380\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −11.2185 | + | 19.4311i | −0.364169 | + | 0.630759i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −57.8258 | −1.87513 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 17.3367i | 0.561590i | 0.959768 | + | 0.280795i | \(0.0905981\pi\) | ||||
−0.959768 | + | 0.280795i | \(0.909402\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −9.45498 | + | 27.4366i | −0.305956 | + | 0.887827i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −20.9234 | + | 12.0801i | −0.676357 | + | 0.390495i | ||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 39.7072 | − | 20.0444i | 1.28221 | − | 0.647267i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −35.2344 | − | 61.0277i | −1.13659 | − | 1.96864i | ||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0.162191 | + | 0.0936408i | 0.00522652 | + | 0.00301753i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 9.12086 | + | 46.9866i | 0.293611 | + | 1.51255i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | − | 23.4618i | − | 0.754480i | −0.926116 | − | 0.377240i | \(-0.876873\pi\) | ||
0.926116 | − | 0.377240i | \(-0.123127\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 44.3013 | − | 76.7322i | 1.42316 | − | 2.46499i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 28.2777 | + | 48.9783i | 0.907473 | + | 1.57179i | 0.817563 | + | 0.575840i | \(0.195325\pi\) |
0.0899104 | + | 0.995950i | \(0.471342\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −29.7876 | + | 45.4940i | −0.954946 | + | 1.45847i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 11.9945 | + | 9.38098i | 0.384132 | + | 0.300432i | ||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −25.0960 | − | 14.4892i | −0.802891 | − | 0.463549i | 0.0415899 | − | 0.999135i | \(-0.486758\pi\) |
−0.844481 | + | 0.535585i | \(0.820091\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −10.4022 | −0.332457 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 17.7174 | 0.565673 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 35.7911 | + | 20.6640i | 1.14156 | + | 0.659079i | 0.946816 | − | 0.321776i | \(-0.104280\pi\) |
0.194742 | + | 0.980854i | \(0.437613\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 14.2273 | − | 12.3612i | 0.453319 | − | 0.393862i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −11.3150 | + | 17.2811i | −0.360160 | + | 0.550064i | ||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −1.93119 | − | 3.34492i | −0.0614083 | − | 0.106362i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 14.5449 | − | 25.1924i | 0.462032 | − | 0.800264i | −0.537030 | − | 0.843563i | \(-0.680454\pi\) |
0.999062 | + | 0.0432996i | \(0.0137870\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 10.9872i | 0.348667i | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 9.25191 | − | 1.79595i | 0.293305 | − | 0.0569353i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −18.5965 | − | 10.7367i | −0.588957 | − | 0.340035i | 0.175728 | − | 0.984439i | \(-0.443772\pi\) |
−0.764685 | + | 0.644404i | \(0.777105\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −8.22590 | − | 14.2477i | −0.260256 | − | 0.450777i |
(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 | 280.2.bg.a.249.3 | yes | 24 | |
4.3 | odd | 2 | 560.2.bw.f.529.10 | 24 | |||
5.2 | odd | 4 | 1400.2.q.n.1201.2 | 12 | |||
5.3 | odd | 4 | 1400.2.q.o.1201.5 | 12 | |||
5.4 | even | 2 | inner | 280.2.bg.a.249.10 | yes | 24 | |
7.2 | even | 3 | inner | 280.2.bg.a.9.10 | yes | 24 | |
7.3 | odd | 6 | 1960.2.g.e.1569.3 | 12 | |||
7.4 | even | 3 | 1960.2.g.f.1569.10 | 12 | |||
20.19 | odd | 2 | 560.2.bw.f.529.3 | 24 | |||
28.23 | odd | 6 | 560.2.bw.f.289.3 | 24 | |||
35.2 | odd | 12 | 1400.2.q.n.401.2 | 12 | |||
35.3 | even | 12 | 9800.2.a.cy.1.5 | 6 | |||
35.4 | even | 6 | 1960.2.g.f.1569.3 | 12 | |||
35.9 | even | 6 | inner | 280.2.bg.a.9.3 | ✓ | 24 | |
35.17 | even | 12 | 9800.2.a.cw.1.2 | 6 | |||
35.18 | odd | 12 | 9800.2.a.cv.1.2 | 6 | |||
35.23 | odd | 12 | 1400.2.q.o.401.5 | 12 | |||
35.24 | odd | 6 | 1960.2.g.e.1569.10 | 12 | |||
35.32 | odd | 12 | 9800.2.a.cx.1.5 | 6 | |||
140.79 | odd | 6 | 560.2.bw.f.289.10 | 24 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
280.2.bg.a.9.3 | ✓ | 24 | 35.9 | even | 6 | inner | |
280.2.bg.a.9.10 | yes | 24 | 7.2 | even | 3 | inner | |
280.2.bg.a.249.3 | yes | 24 | 1.1 | even | 1 | trivial | |
280.2.bg.a.249.10 | yes | 24 | 5.4 | even | 2 | inner | |
560.2.bw.f.289.3 | 24 | 28.23 | odd | 6 | |||
560.2.bw.f.289.10 | 24 | 140.79 | odd | 6 | |||
560.2.bw.f.529.3 | 24 | 20.19 | odd | 2 | |||
560.2.bw.f.529.10 | 24 | 4.3 | odd | 2 | |||
1400.2.q.n.401.2 | 12 | 35.2 | odd | 12 | |||
1400.2.q.n.1201.2 | 12 | 5.2 | odd | 4 | |||
1400.2.q.o.401.5 | 12 | 35.23 | odd | 12 | |||
1400.2.q.o.1201.5 | 12 | 5.3 | odd | 4 | |||
1960.2.g.e.1569.3 | 12 | 7.3 | odd | 6 | |||
1960.2.g.e.1569.10 | 12 | 35.24 | odd | 6 | |||
1960.2.g.f.1569.3 | 12 | 35.4 | even | 6 | |||
1960.2.g.f.1569.10 | 12 | 7.4 | even | 3 | |||
9800.2.a.cv.1.2 | 6 | 35.18 | odd | 12 | |||
9800.2.a.cw.1.2 | 6 | 35.17 | even | 12 | |||
9800.2.a.cx.1.5 | 6 | 35.32 | odd | 12 | |||
9800.2.a.cy.1.5 | 6 | 35.3 | even | 12 |