Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1148,2,Mod(113,1148)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1148, base_ring=CyclotomicField(10))
chi = DirichletCharacter(H, H._module([0, 0, 7]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1148.113");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1148 = 2^{2} \cdot 7 \cdot 41 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1148.ba (of order \(10\), degree \(4\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(9.16682615204\) |
Analytic rank: | \(0\) |
Dimension: | \(80\) |
Relative dimension: | \(20\) over \(\Q(\zeta_{10})\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{10}]$ |
Embedding invariants
Embedding label | 113.8 | ||
Character | \(\chi\) | \(=\) | 1148.113 |
Dual form | 1148.2.ba.a.701.13 |
$q$-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 \(\left(\mathbb{Z}/1148\mathbb{Z}\right)^\times\).
\(n\) | \(493\) | \(575\) | \(785\) |
\(\chi(n)\) | \(1\) | \(1\) | \(e\left(\frac{7}{10}\right)\) |
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 | ||||||||
\(3\) | − | 0.904348i | − | 0.522126i | −0.965322 | − | 0.261063i | \(-0.915927\pi\) | ||
0.965322 | − | 0.261063i | \(-0.0840730\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 0.129544 | + | 0.398696i | 0.0579339 | + | 0.178302i | 0.975836 | − | 0.218505i | \(-0.0701181\pi\) |
−0.917902 | + | 0.396807i | \(0.870118\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −0.587785 | − | 0.809017i | −0.222162 | − | 0.305780i | ||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 2.18215 | 0.727385 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 1.99111 | + | 0.646951i | 0.600343 | + | 0.195063i | 0.593393 | − | 0.804913i | \(-0.297788\pi\) |
0.00694948 | + | 0.999976i | \(0.497788\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −1.84603 | + | 2.54084i | −0.511996 | + | 0.704702i | −0.984254 | − | 0.176758i | \(-0.943439\pi\) |
0.472258 | + | 0.881460i | \(0.343439\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0.360560 | − | 0.117153i | 0.0930961 | − | 0.0302488i | ||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 0.218991 | + | 0.0711543i | 0.0531130 | + | 0.0172575i | 0.335453 | − | 0.942057i | \(-0.391111\pi\) |
−0.282340 | + | 0.959314i | \(0.591111\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 1.62945 | + | 2.24275i | 0.373822 | + | 0.514522i | 0.953935 | − | 0.300014i | \(-0.0969914\pi\) |
−0.580112 | + | 0.814536i | \(0.696991\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −0.731633 | + | 0.531562i | −0.159655 | + | 0.115996i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 6.51499 | + | 4.73342i | 1.35847 | + | 0.986986i | 0.998541 | + | 0.0540065i | \(0.0171992\pi\) |
0.359929 | + | 0.932980i | \(0.382801\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 3.90291 | − | 2.83563i | 0.780582 | − | 0.567126i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | − | 4.68647i | − | 0.901912i | ||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −6.06473 | + | 1.97055i | −1.12619 | + | 0.365922i | −0.812128 | − | 0.583480i | \(-0.801691\pi\) |
−0.314064 | + | 0.949402i | \(0.601691\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 1.52993 | − | 4.70863i | 0.274783 | − | 0.845695i | −0.714494 | − | 0.699642i | \(-0.753343\pi\) |
0.989277 | − | 0.146053i | \(-0.0466571\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0.585069 | − | 1.80066i | 0.101847 | − | 0.313454i | ||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0.246408 | − | 0.339151i | 0.0416505 | − | 0.0573270i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −1.51532 | − | 4.66367i | −0.249117 | − | 0.766703i | −0.994932 | − | 0.100550i | \(-0.967940\pi\) |
0.745815 | − | 0.666153i | \(-0.232060\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 2.29780 | + | 1.66945i | 0.367943 | + | 0.267326i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 2.22688 | − | 6.00342i | 0.347780 | − | 0.937576i | ||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 8.75738 | + | 6.36261i | 1.33549 | + | 0.970289i | 0.999597 | + | 0.0283886i | \(0.00903760\pi\) |
0.335892 | + | 0.941901i | \(0.390962\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0.282685 | + | 0.870016i | 0.0421402 | + | 0.129694i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 0.514310 | − | 0.707887i | 0.0750199 | − | 0.103256i | −0.769858 | − | 0.638215i | \(-0.779673\pi\) |
0.844878 | + | 0.534959i | \(0.179673\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −0.309017 | + | 0.951057i | −0.0441453 | + | 0.135865i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0.0643483 | − | 0.198044i | 0.00901056 | − | 0.0277317i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −1.28343 | + | 0.417011i | −0.176292 | + | 0.0572809i | −0.395833 | − | 0.918322i | \(-0.629544\pi\) |
0.219541 | + | 0.975603i | \(0.429544\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0.877657i | 0.118343i | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 2.02823 | − | 1.47359i | 0.268645 | − | 0.195182i | ||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 1.10026 | + | 0.799383i | 0.143241 | + | 0.104071i | 0.657098 | − | 0.753805i | \(-0.271784\pi\) |
−0.513857 | + | 0.857876i | \(0.671784\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −2.01068 | + | 1.46085i | −0.257442 | + | 0.187042i | −0.709018 | − | 0.705190i | \(-0.750862\pi\) |
0.451577 | + | 0.892232i | \(0.350862\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −1.28264 | − | 1.76540i | −0.161597 | − | 0.222420i | ||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −1.25216 | − | 0.406853i | −0.155312 | − | 0.0504639i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 3.04069 | − | 0.987979i | 0.371479 | − | 0.120701i | −0.117327 | − | 0.993093i | \(-0.537433\pi\) |
0.488806 | + | 0.872392i | \(0.337433\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 4.28066 | − | 5.89182i | 0.515331 | − | 0.709292i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 9.37008 | + | 3.04452i | 1.11202 | + | 0.361318i | 0.806718 | − | 0.590936i | \(-0.201241\pi\) |
0.305305 | + | 0.952254i | \(0.401241\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 12.9116 | 1.51119 | 0.755593 | − | 0.655042i | \(-0.227349\pi\) | ||||
0.755593 | + | 0.655042i | \(0.227349\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −2.56440 | − | 3.52959i | −0.296111 | − | 0.407562i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −0.646951 | − | 1.99111i | −0.0737270 | − | 0.226908i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | − | 9.73942i | − | 1.09577i | −0.836553 | − | 0.547885i | \(-0.815433\pi\) | ||
0.836553 | − | 0.547885i | \(-0.184567\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 2.30826 | 0.256474 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 4.97099 | 0.545637 | 0.272819 | − | 0.962066i | \(-0.412044\pi\) | ||||
0.272819 | + | 0.962066i | \(0.412044\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0.0965282i | 0.0104700i | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 1.78206 | + | 5.48463i | 0.191057 | + | 0.588014i | ||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −3.59722 | − | 4.95116i | −0.381305 | − | 0.524821i | 0.574625 | − | 0.818417i | \(-0.305148\pi\) |
−0.955930 | + | 0.293596i | \(0.905148\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 3.14065 | 0.329230 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −4.25824 | − | 1.38359i | −0.441559 | − | 0.143471i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −0.683089 | + | 0.940192i | −0.0700835 | + | 0.0964616i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −13.7927 | + | 4.48154i | −1.40044 | + | 0.455031i | −0.909334 | − | 0.416068i | \(-0.863408\pi\) |
−0.491108 | + | 0.871099i | \(0.663408\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 4.34491 | + | 1.41175i | 0.436680 | + | 0.141886i | ||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −1.37232 | − | 1.88884i | −0.136551 | − | 0.187946i | 0.735265 | − | 0.677780i | \(-0.237058\pi\) |
−0.871816 | + | 0.489833i | \(0.837058\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −11.0964 | + | 8.06201i | −1.09336 | + | 0.794373i | −0.979964 | − | 0.199176i | \(-0.936173\pi\) |
−0.113397 | + | 0.993550i | \(0.536173\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −0.306710 | − | 0.222838i | −0.0299319 | − | 0.0217468i | ||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 2.42990 | − | 1.76543i | 0.234908 | − | 0.170670i | −0.464104 | − | 0.885781i | \(-0.653624\pi\) |
0.699012 | + | 0.715110i | \(0.253624\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 2.03889i | 0.195290i | 0.995221 | + | 0.0976452i | \(0.0311310\pi\) | ||||
−0.995221 | + | 0.0976452i | \(0.968869\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −4.21758 | + | 1.37038i | −0.400315 | + | 0.130070i | ||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 1.05355 | − | 3.24251i | 0.0991101 | − | 0.305029i | −0.889193 | − | 0.457532i | \(-0.848733\pi\) |
0.988303 | + | 0.152503i | \(0.0487334\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −1.04322 | + | 3.21069i | −0.0972804 | + | 0.299398i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −4.02832 | + | 5.54451i | −0.372418 | + | 0.512590i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −0.0711543 | − | 0.218991i | −0.00652271 | − | 0.0200748i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −5.35321 | − | 3.88933i | −0.486655 | − | 0.353576i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −5.42918 | − | 2.01387i | −0.489532 | − | 0.181585i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 3.33191 | + | 2.42077i | 0.298015 | + | 0.216520i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 0.959438 | + | 2.95285i | 0.0851364 | + | 0.262023i | 0.984558 | − | 0.175060i | \(-0.0560118\pi\) |
−0.899421 | + | 0.437082i | \(0.856012\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 5.75402 | − | 7.91972i | 0.506613 | − | 0.697293i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 2.24384 | − | 6.90582i | 0.196045 | − | 0.603364i | −0.803918 | − | 0.594740i | \(-0.797255\pi\) |
0.999963 | − | 0.00862407i | \(-0.00274516\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 0.856654 | − | 2.63651i | 0.0742814 | − | 0.228615i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 1.86848 | − | 0.607105i | 0.160813 | − | 0.0522513i | ||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 2.72152i | 0.232515i | 0.993219 | + | 0.116258i | \(0.0370898\pi\) | ||||
−0.993219 | + | 0.116258i | \(0.962910\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −4.70343 | + | 3.41724i | −0.398940 | + | 0.289847i | −0.769109 | − | 0.639118i | \(-0.779300\pi\) |
0.370169 | + | 0.928964i | \(0.379300\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −0.640177 | − | 0.465116i | −0.0539126 | − | 0.0391698i | ||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −5.31945 | + | 3.86481i | −0.444835 | + | 0.323191i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −1.57130 | − | 2.16271i | −0.130489 | − | 0.179603i | ||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0.860086 | + | 0.279459i | 0.0709387 | + | 0.0230494i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 7.41892 | − | 2.41055i | 0.607782 | − | 0.197480i | 0.0110736 | − | 0.999939i | \(-0.496475\pi\) |
0.596708 | + | 0.802458i | \(0.296475\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 7.26959 | − | 10.0057i | 0.591591 | − | 0.814255i | −0.403315 | − | 0.915061i | \(-0.632142\pi\) |
0.994906 | + | 0.100806i | \(0.0321422\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0.477871 | + | 0.155270i | 0.0386336 | + | 0.0125528i | ||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 2.07551 | 0.166709 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 0.609904 | + | 0.839460i | 0.0486756 | + | 0.0669962i | 0.832661 | − | 0.553783i | \(-0.186816\pi\) |
−0.783985 | + | 0.620779i | \(0.786816\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0.377123 | + | 1.16067i | 0.0299078 | + | 0.0920468i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | − | 8.05297i | − | 0.634663i | ||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −16.4606 | −1.28930 | −0.644648 | − | 0.764480i | \(-0.722996\pi\) | ||||
−0.644648 | + | 0.764480i | \(0.722996\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0.793707 | 0.0617900 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 16.2288i | 1.25583i | 0.778284 | + | 0.627913i | \(0.216091\pi\) | ||||
−0.778284 | + | 0.627913i | \(0.783909\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 0.969174 | + | 2.98281i | 0.0745518 | + | 0.229447i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 3.55572 | + | 4.89403i | 0.271913 | + | 0.374256i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 1.36678 | 0.103915 | 0.0519573 | − | 0.998649i | \(-0.483454\pi\) | ||||
0.0519573 | + | 0.998649i | \(0.483454\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −4.58814 | − | 1.49078i | −0.346831 | − | 0.112692i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0.722921 | − | 0.995015i | 0.0543380 | − | 0.0747899i | ||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 8.96777 | − | 2.91380i | 0.670282 | − | 0.217788i | 0.0459464 | − | 0.998944i | \(-0.485370\pi\) |
0.624336 | + | 0.781156i | \(0.285370\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −15.7972 | − | 5.13283i | −1.17420 | − | 0.381520i | −0.343990 | − | 0.938973i | \(-0.611779\pi\) |
−0.830208 | + | 0.557453i | \(0.811779\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 1.32111 | + | 1.81836i | 0.0976596 | + | 0.134417i | ||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 1.66309 | − | 1.20830i | 0.122273 | − | 0.0888362i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 0.390001 | + | 0.283352i | 0.0285197 | + | 0.0207208i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −3.79143 | + | 2.75464i | −0.275786 | + | 0.200370i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 0.0658133i | 0.00476208i | 0.999997 | + | 0.00238104i | \(0.000757910\pi\) | ||||
−0.999997 | + | 0.00238104i | \(0.999242\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −13.8948 | + | 4.51469i | −1.00017 | + | 0.324974i | −0.762933 | − | 0.646478i | \(-0.776241\pi\) |
−0.237235 | + | 0.971452i | \(0.576241\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −0.367937 | + | 1.13239i | −0.0263485 | + | 0.0810923i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −5.32298 | + | 16.3825i | −0.379247 | + | 1.16720i | 0.561322 | + | 0.827598i | \(0.310293\pi\) |
−0.940569 | + | 0.339604i | \(0.889707\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −5.30008 | + | 7.29493i | −0.375713 | + | 0.517124i | −0.954442 | − | 0.298395i | \(-0.903549\pi\) |
0.578730 | + | 0.815519i | \(0.303549\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −0.893477 | − | 2.74984i | −0.0630210 | − | 0.193959i | ||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 5.15897 | + | 3.74821i | 0.362088 | + | 0.263073i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 2.68202 | + | 0.110140i | 0.187320 | + | 0.00769252i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 14.2167 | + | 10.3291i | 0.988130 | + | 0.717919i | ||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 1.79347 | + | 5.51974i | 0.124057 | + | 0.381809i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −13.0346 | + | 17.9406i | −0.897341 | + | 1.23508i | 0.0739671 | + | 0.997261i | \(0.476434\pi\) |
−0.971308 | + | 0.237824i | \(0.923566\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 2.75331 | − | 8.47381i | 0.188654 | − | 0.580616i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −1.40228 | + | 4.31577i | −0.0956347 | + | 0.294333i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −4.70863 | + | 1.52993i | −0.319643 | + | 0.103858i | ||||
\(218\) | 0 | 0 | ||||||||
\(219\) | − | 11.6766i | − | 0.789028i | ||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −0.585054 | + | 0.425067i | −0.0393550 | + | 0.0285931i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −17.6106 | − | 12.7948i | −1.17929 | − | 0.856805i | −0.187199 | − | 0.982322i | \(-0.559941\pi\) |
−0.992091 | + | 0.125517i | \(0.959941\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 8.51675 | − | 6.18778i | 0.567783 | − | 0.412519i | ||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 15.4912 | + | 21.3218i | 1.02818 | + | 1.41517i | 0.906302 | + | 0.422630i | \(0.138893\pi\) |
0.121882 | + | 0.992545i | \(0.461107\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −15.7367 | − | 5.11315i | −1.03991 | − | 0.337887i | −0.261208 | − | 0.965283i | \(-0.584121\pi\) |
−0.778700 | + | 0.627396i | \(0.784121\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −1.80066 | + | 0.585069i | −0.118475 | + | 0.0384947i | ||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −12.5681 | + | 17.2985i | −0.823361 | + | 1.13326i | 0.165761 | + | 0.986166i | \(0.446992\pi\) |
−0.989123 | + | 0.147094i | \(0.953008\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0.348858 | + | 0.113351i | 0.0227570 | + | 0.00739419i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −8.80783 | −0.572130 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 15.5801 | + | 21.4442i | 1.00779 | + | 1.38711i | 0.920419 | + | 0.390933i | \(0.127848\pi\) |
0.0873746 | + | 0.996176i | \(0.472152\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 1.10831 | + | 3.41103i | 0.0713927 | + | 0.219724i | 0.980386 | − | 0.197086i | \(-0.0631479\pi\) |
−0.908993 | + | 0.416810i | \(0.863148\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | − | 16.1469i | − | 1.03582i | ||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −0.419214 | −0.0267826 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −8.70649 | −0.553981 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | − | 4.49551i | − | 0.284891i | ||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −5.97814 | − | 18.3988i | −0.377337 | − | 1.16132i | −0.941889 | − | 0.335925i | \(-0.890951\pi\) |
0.564552 | − | 0.825398i | \(-0.309049\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 9.90979 | + | 13.6397i | 0.623023 | + | 0.857517i | ||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0.0872951 | 0.00546663 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −18.9898 | − | 6.17015i | −1.18455 | − | 0.384883i | −0.350494 | − | 0.936565i | \(-0.613986\pi\) |
−0.834055 | + | 0.551682i | \(0.813986\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −2.88231 | + | 3.96716i | −0.179098 | + | 0.246507i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −13.2342 | + | 4.30004i | −0.819175 | + | 0.266166i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −22.5399 | − | 7.32366i | −1.38987 | − | 0.451596i | −0.483969 | − | 0.875085i | \(-0.660805\pi\) |
−0.905901 | + | 0.423489i | \(0.860805\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −0.332521 | − | 0.457676i | −0.0204266 | − | 0.0281148i | ||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −4.47757 | + | 3.25314i | −0.274023 | + | 0.199089i | ||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −16.7376 | − | 12.1606i | −1.02051 | − | 0.741443i | −0.0541217 | − | 0.998534i | \(-0.517236\pi\) |
−0.966387 | + | 0.257091i | \(0.917236\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −5.53287 | + | 4.01986i | −0.336098 | + | 0.244189i | −0.743014 | − | 0.669276i | \(-0.766604\pi\) |
0.406916 | + | 0.913466i | \(0.366604\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | − | 2.84024i | − | 0.171899i | ||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 9.60564 | − | 3.12106i | 0.579242 | − | 0.188207i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −3.48978 | + | 10.7404i | −0.209681 | + | 0.645331i | 0.789808 | + | 0.613354i | \(0.210180\pi\) |
−0.999489 | + | 0.0319765i | \(0.989820\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 3.33854 | − | 10.2750i | 0.199873 | − | 0.615146i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 15.9780 | − | 21.9919i | 0.953170 | − | 1.31193i | 0.00306492 | − | 0.999995i | \(-0.499024\pi\) |
0.950105 | − | 0.311930i | \(-0.100976\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 8.99516 | + | 27.6843i | 0.534707 | + | 1.64566i | 0.744282 | + | 0.667866i | \(0.232792\pi\) |
−0.209575 | + | 0.977793i | \(0.567208\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0.850260 | + | 0.617750i | 0.0503651 | + | 0.0365924i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −6.16579 | + | 1.72714i | −0.363955 | + | 0.101950i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −13.7104 | − | 9.96119i | −0.806494 | − | 0.585952i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 4.05287 | + | 12.4734i | 0.237583 | + | 0.731206i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 8.83366 | − | 12.1585i | 0.516068 | − | 0.710307i | −0.468860 | − | 0.883273i | \(-0.655335\pi\) |
0.984928 | + | 0.172966i | \(0.0553351\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −0.176179 | + | 0.542223i | −0.0102575 | + | 0.0315695i | ||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 3.03192 | − | 9.33129i | 0.175930 | − | 0.541456i | ||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −24.0537 | + | 7.81553i | −1.39106 | + | 0.451984i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | − | 10.8247i | − | 0.623927i | ||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −1.70817 | + | 1.24106i | −0.0981316 | + | 0.0712968i | ||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −0.842906 | − | 0.612407i | −0.0482647 | − | 0.0350663i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −8.54457 | + | 6.20799i | −0.487664 | + | 0.354309i | −0.804285 | − | 0.594243i | \(-0.797452\pi\) |
0.316621 | + | 0.948552i | \(0.397452\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 7.29086 | + | 10.0350i | 0.414763 | + | 0.570872i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 8.81263 | + | 2.86340i | 0.499719 | + | 0.162368i | 0.548021 | − | 0.836464i | \(-0.315381\pi\) |
−0.0483028 | + | 0.998833i | \(0.515381\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −14.4665 | + | 4.70046i | −0.817697 | + | 0.265686i | −0.687854 | − | 0.725849i | \(-0.741447\pi\) |
−0.129843 | + | 0.991535i | \(0.541447\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0.537700 | − | 0.740080i | 0.0302959 | − | 0.0416988i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −17.0786 | − | 5.54919i | −0.959232 | − | 0.311673i | −0.212771 | − | 0.977102i | \(-0.568249\pi\) |
−0.746461 | + | 0.665429i | \(0.768249\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −13.3504 | −0.747479 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −1.59656 | − | 2.19748i | −0.0891114 | − | 0.122651i | ||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 0.197253 | + | 0.607084i | 0.0109755 | + | 0.0337790i | ||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 15.1513i | 0.840444i | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 1.84387 | 0.101966 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −0.874997 | −0.0482401 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 6.86868i | 0.377537i | 0.982022 | + | 0.188768i | \(0.0604496\pi\) | ||||
−0.982022 | + | 0.188768i | \(0.939550\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −3.30666 | − | 10.1769i | −0.181204 | − | 0.557688i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 0.787807 | + | 1.08432i | 0.0430425 | + | 0.0592429i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 32.9405 | 1.79438 | 0.897192 | − | 0.441640i | \(-0.145603\pi\) | ||||
0.897192 | + | 0.441640i | \(0.145603\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −2.93235 | − | 0.952780i | −0.159264 | − | 0.0517479i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 6.09251 | − | 8.38562i | 0.329928 | − | 0.454107i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 0.951057 | − | 0.309017i | 0.0513522 | − | 0.0166853i | ||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 2.90358 | + | 0.943430i | 0.156323 | + | 0.0507926i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 2.00308 | + | 2.75700i | 0.107531 | + | 0.148004i | 0.859391 | − | 0.511319i | \(-0.170843\pi\) |
−0.751860 | + | 0.659323i | \(0.770843\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 16.9999 | − | 12.3512i | 0.909986 | − | 0.661143i | −0.0310254 | − | 0.999519i | \(-0.509877\pi\) |
0.941011 | + | 0.338375i | \(0.109877\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 11.9076 | + | 8.65136i | 0.635579 | + | 0.461775i | ||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 17.7763 | − | 12.9152i | 0.946135 | − | 0.687407i | −0.00375494 | − | 0.999993i | \(-0.501195\pi\) |
0.949889 | + | 0.312586i | \(0.101195\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 4.13021i | 0.219209i | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −0.198044 | + | 0.0643483i | −0.0104816 | + | 0.00340567i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 7.34445 | − | 22.6039i | 0.387625 | − | 1.19299i | −0.546932 | − | 0.837177i | \(-0.684205\pi\) |
0.934558 | − | 0.355811i | \(-0.115795\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 3.49651 | − | 10.7612i | 0.184027 | − | 0.566377i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −3.51731 | + | 4.84116i | −0.184611 | + | 0.254095i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 1.67262 | + | 5.14779i | 0.0875489 | + | 0.269448i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −20.6653 | − | 15.0142i | −1.07872 | − | 0.783734i | −0.101259 | − | 0.994860i | \(-0.532287\pi\) |
−0.977459 | + | 0.211126i | \(0.932287\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 4.85940 | − | 13.1004i | 0.252970 | − | 0.681979i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 1.09175 | + | 0.793202i | 0.0566808 | + | 0.0411810i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 1.79347 | + | 5.51973i | 0.0928623 | + | 0.285801i | 0.986691 | − | 0.162609i | \(-0.0519908\pi\) |
−0.893828 | + | 0.448409i | \(0.851991\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 2.18922 | − | 3.01320i | 0.113051 | − | 0.155601i | ||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 6.18881 | − | 19.0472i | 0.318740 | − | 0.980981i | ||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −3.77756 | + | 11.6261i | −0.194040 | + | 0.597195i | 0.805946 | + | 0.591989i | \(0.201657\pi\) |
−0.999986 | + | 0.00520598i | \(0.998343\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 2.67040 | − | 0.867666i | 0.136809 | − | 0.0444519i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | − | 17.3466i | − | 0.886367i | −0.896431 | − | 0.443184i | \(-0.853849\pi\) | ||
0.896431 | − | 0.443184i | \(-0.146151\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0.710039 | − | 0.515874i | 0.0361870 | − | 0.0262914i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 19.1100 | + | 13.8842i | 0.971414 | + | 0.705774i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −7.28912 | + | 5.29586i | −0.369573 | + | 0.268511i | −0.757034 | − | 0.653376i | \(-0.773352\pi\) |
0.387461 | + | 0.921886i | \(0.373352\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 1.08992 | + | 1.50014i | 0.0551195 | + | 0.0758655i | ||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −6.24527 | − | 2.02921i | −0.315032 | − | 0.102360i | ||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 3.88307 | − | 1.26169i | 0.195378 | − | 0.0634823i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −13.0340 | + | 17.9398i | −0.654160 | + | 0.900374i | −0.999271 | − | 0.0381879i | \(-0.987841\pi\) |
0.345110 | + | 0.938562i | \(0.387841\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −2.38432 | − | 0.774714i | −0.119365 | − | 0.0387842i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −6.47571 | −0.323382 | −0.161691 | − | 0.986841i | \(-0.551695\pi\) | ||||
−0.161691 | + | 0.986841i | \(0.551695\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 9.13959 | + | 12.5796i | 0.455275 | + | 0.626633i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0.299022 | + | 0.920295i | 0.0148585 | + | 0.0457298i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | − | 10.2662i | − | 0.508878i | ||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −36.8721 | −1.82321 | −0.911603 | − | 0.411072i | \(-0.865155\pi\) | ||||
−0.911603 | + | 0.411072i | \(0.865155\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 2.46120 | 0.121402 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | − | 1.35999i | − | 0.0669208i | ||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 0.643963 | + | 1.98191i | 0.0316109 | + | 0.0972883i | ||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 3.09038 | + | 4.25354i | 0.151336 | + | 0.208297i | ||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −28.0131 | −1.36853 | −0.684264 | − | 0.729234i | \(-0.739876\pi\) | ||||
−0.684264 | + | 0.729234i | \(0.739876\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −25.8734 | − | 8.40679i | −1.26099 | − | 0.409722i | −0.399145 | − | 0.916888i | \(-0.630693\pi\) |
−0.861848 | + | 0.507166i | \(0.830693\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 1.12230 | − | 1.54472i | 0.0545683 | − | 0.0751069i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 1.05647 | − | 0.343267i | 0.0512462 | − | 0.0166509i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 2.36370 | + | 0.768013i | 0.114387 | + | 0.0371667i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 3.49513 | + | 4.81063i | 0.168746 | + | 0.232260i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 25.7348 | − | 18.6974i | 1.23960 | − | 0.900623i | 0.242029 | − | 0.970269i | \(-0.422187\pi\) |
0.997572 | + | 0.0696460i | \(0.0221870\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −6.94748 | − | 5.04764i | −0.333874 | − | 0.242574i | 0.408198 | − | 0.912893i | \(-0.366157\pi\) |
−0.742073 | + | 0.670319i | \(0.766157\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −1.95584 | + | 1.42100i | −0.0937754 | + | 0.0681318i | ||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 22.3244i | 1.06792i | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 7.89212 | − | 2.56430i | 0.376670 | − | 0.122388i | −0.114562 | − | 0.993416i | \(-0.536547\pi\) |
0.491232 | + | 0.871029i | \(0.336547\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −0.674323 | + | 2.07535i | −0.0321106 | + | 0.0988263i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −4.54535 | + | 13.9891i | −0.215956 | + | 0.664644i | 0.783128 | + | 0.621860i | \(0.213623\pi\) |
−0.999084 | + | 0.0427839i | \(0.986377\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 1.50801 | − | 2.07559i | 0.0714863 | − | 0.0983925i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −2.17998 | − | 6.70928i | −0.103109 | − | 0.317338i | ||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 9.71423 | + | 7.05780i | 0.458443 | + | 0.333078i | 0.792920 | − | 0.609326i | \(-0.208560\pi\) |
−0.334477 | + | 0.942404i | \(0.608560\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 8.31788 | − | 10.5128i | 0.391674 | − | 0.495028i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −9.04866 | − | 6.57424i | −0.425143 | − | 0.308885i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0.406853 | + | 1.25216i | 0.0190736 | + | 0.0587024i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −0.599903 | + | 0.825696i | −0.0280623 | + | 0.0386244i | −0.822818 | − | 0.568306i | \(-0.807599\pi\) |
0.794755 | + | 0.606930i | \(0.207599\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0.333463 | − | 1.02629i | 0.0155647 | − | 0.0479032i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −0.546117 | + | 1.68078i | −0.0254352 | + | 0.0782815i | −0.962968 | − | 0.269614i | \(-0.913104\pi\) |
0.937533 | + | 0.347896i | \(0.113104\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 21.9651 | − | 7.13690i | 1.02081 | − | 0.331680i | 0.249657 | − | 0.968334i | \(-0.419682\pi\) |
0.771149 | + | 0.636654i | \(0.219682\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | − | 1.87698i | − | 0.0870428i | ||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 20.9101 | − | 15.1921i | 0.967603 | − | 0.703005i | 0.0126990 | − | 0.999919i | \(-0.495958\pi\) |
0.954904 | + | 0.296915i | \(0.0959577\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −2.58656 | − | 1.87925i | −0.119436 | − | 0.0867756i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0.759164 | − | 0.551565i | 0.0349804 | − | 0.0254148i | ||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 13.3206 | + | 18.3343i | 0.612483 | + | 0.843011i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 12.7192 | + | 4.13272i | 0.583598 | + | 0.189622i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −2.80064 | + | 0.909983i | −0.128232 | + | 0.0416653i | ||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −15.2401 | + | 20.9762i | −0.696338 | + | 0.958427i | 0.303646 | + | 0.952785i | \(0.401796\pi\) |
−0.999984 | + | 0.00564216i | \(0.998204\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 14.6470 | + | 4.75909i | 0.667844 | + | 0.216996i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −7.28269 | −0.331374 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −3.57354 | − | 4.91856i | −0.162266 | − | 0.223340i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −0.0406868 | − | 0.125221i | −0.00184369 | − | 0.00567430i | 0.950130 | − | 0.311853i | \(-0.100950\pi\) |
−0.951974 | + | 0.306178i | \(0.900950\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 14.8861i | 0.673174i | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 24.8763 | 1.12265 | 0.561327 | − | 0.827594i | \(-0.310291\pi\) | ||||
0.561327 | + | 0.827594i | \(0.310291\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −1.46833 | −0.0661303 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 1.91518i | 0.0860811i | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −3.04452 | − | 9.37008i | −0.136566 | − | 0.420306i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 2.57033 | + | 3.53776i | 0.115064 | + | 0.158372i | 0.862664 | − | 0.505777i | \(-0.168794\pi\) |
−0.747600 | + | 0.664149i | \(0.768794\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 14.6765 | 0.655699 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −4.68339 | − | 1.52173i | −0.208822 | − | 0.0678504i | 0.202738 | − | 0.979233i | \(-0.435016\pi\) |
−0.411560 | + | 0.911383i | \(0.635016\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 0.575296 | − | 0.791827i | 0.0256003 | − | 0.0352358i | ||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 2.69750 | − | 0.876470i | 0.119800 | − | 0.0389254i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 7.74645 | + | 2.51698i | 0.343355 | + | 0.111563i | 0.475618 | − | 0.879652i | \(-0.342224\pi\) |
−0.132263 | + | 0.991215i | \(0.542224\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −7.58923 | − | 10.4457i | −0.335728 | − | 0.462090i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 10.5106 | − | 7.63639i | 0.464054 | − | 0.337155i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −4.65176 | − | 3.37970i | −0.204981 | − | 0.148928i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 1.48202 | − | 1.07675i | 0.0651791 | − | 0.0473554i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | − | 1.23605i | − | 0.0542565i | ||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 37.4349 | − | 12.1633i | 1.64005 | − | 0.532886i | 0.663503 | − | 0.748174i | \(-0.269069\pi\) |
0.976551 | + | 0.215288i | \(0.0690691\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 11.9880 | − | 36.8953i | 0.524199 | − | 1.61332i | −0.241694 | − | 0.970352i | \(-0.577703\pi\) |
0.765894 | − | 0.642967i | \(-0.222297\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | −1.34818 | + | 4.14928i | −0.0588395 | + | 0.181089i | ||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 0.670079 | − | 0.922285i | 0.0291891 | − | 0.0401754i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 12.9325 | + | 39.8021i | 0.562282 | + | 1.73053i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 2.40093 | + | 1.74438i | 0.104192 | + | 0.0756996i | ||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 11.1428 | + | 16.7406i | 0.482650 | + | 0.725117i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 1.01865 | + | 0.740092i | 0.0440400 | + | 0.0319970i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −2.63509 | − | 8.10998i | −0.113713 | − | 0.349971i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −1.23057 | + | 1.69374i | −0.0530046 | + | 0.0729546i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −2.72788 | + | 8.39557i | −0.117281 | + | 0.360954i | −0.992416 | − | 0.122925i | \(-0.960772\pi\) |
0.875135 | + | 0.483879i | \(0.160772\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −4.64186 | + | 14.2862i | −0.199201 | + | 0.613079i | ||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −0.812898 | + | 0.264127i | −0.0348207 | + | 0.0113139i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | − | 10.3796i | − | 0.443799i | −0.975070 | − | 0.221899i | \(-0.928774\pi\) | ||
0.975070 | − | 0.221899i | \(-0.0712257\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −4.38762 | + | 3.18779i | −0.187259 | + | 0.136052i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −14.3016 | − | 10.3908i | −0.609271 | − | 0.442661i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −7.87936 | + | 5.72469i | −0.335064 | + | 0.243439i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −1.09273 | − | 1.50401i | −0.0463837 | − | 0.0638416i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 38.9391 | + | 12.6521i | 1.64990 | + | 0.536086i | 0.978719 | − | 0.205204i | \(-0.0657859\pi\) |
0.671184 | + | 0.741290i | \(0.265786\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −32.3328 | + | 10.5055i | −1.36753 | + | 0.444337i | ||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0.256249 | − | 0.352697i | 0.0108188 | − | 0.0148909i | ||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 1.02495 | + | 0.333025i | 0.0431963 | + | 0.0140353i | 0.330535 | − | 0.943794i | \(-0.392771\pi\) |
−0.287339 | + | 0.957829i | \(0.592771\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 1.42926 | 0.0601292 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −1.35676 | − | 1.86742i | −0.0569787 | − | 0.0784245i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −6.39945 | − | 19.6955i | −0.268279 | − | 0.825677i | −0.990920 | − | 0.134454i | \(-0.957072\pi\) |
0.722641 | − | 0.691223i | \(-0.242928\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | − | 10.8456i | − | 0.453876i | −0.973909 | − | 0.226938i | \(-0.927129\pi\) | ||
0.973909 | − | 0.226938i | \(-0.0728715\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0.0595181 | 0.00248641 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 38.8496 | 1.62014 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 13.3323i | 0.555033i | 0.960721 | + | 0.277516i | \(0.0895113\pi\) | ||||
−0.960721 | + | 0.277516i | \(0.910489\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 4.08285 | + | 12.5657i | 0.169677 | + | 0.522213i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −2.92187 | − | 4.02162i | −0.121220 | − | 0.166845i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −2.82524 | −0.117009 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −2.73242 | − | 0.887816i | −0.112972 | − | 0.0367067i | ||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −18.8332 | + | 25.9217i | −0.777330 | + | 1.06990i | 0.218241 | + | 0.975895i | \(0.429968\pi\) |
−0.995571 | + | 0.0940081i | \(0.970032\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 13.0532 | − | 4.24125i | 0.537849 | − | 0.174758i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 14.8154 | + | 4.81383i | 0.609426 | + | 0.198014i | ||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −0.396731 | − | 0.546054i | −0.0162918 | − | 0.0224237i | 0.800793 | − | 0.598941i | \(-0.204411\pi\) |
−0.817085 | + | 0.576517i | \(0.804411\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0.0780930 | − | 0.0567379i | 0.00320150 | − | 0.00232603i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 6.59716 | + | 4.79311i | 0.270004 | + | 0.196169i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −4.08326 | + | 2.96667i | −0.166838 | + | 0.121215i | −0.668071 | − | 0.744097i | \(-0.732880\pi\) |
0.501233 | + | 0.865312i | \(0.332880\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | − | 27.6469i | − | 1.12774i | −0.825863 | − | 0.563871i | \(-0.809311\pi\) | ||
0.825863 | − | 0.563871i | \(-0.190689\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 6.63525 | − | 2.15592i | 0.270208 | − | 0.0877960i | ||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 0.857184 | − | 2.63814i | 0.0348495 | − | 0.107256i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 4.01401 | − | 12.3538i | 0.162924 | − | 0.501427i | −0.835954 | − | 0.548800i | \(-0.815085\pi\) |
0.998877 | + | 0.0473728i | \(0.0150849\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 3.38968 | − | 4.66550i | 0.137357 | − | 0.189056i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 0.849197 | + | 2.61356i | 0.0343548 | + | 0.105733i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 5.02586 | + | 3.65150i | 0.202993 | + | 0.147483i | 0.684638 | − | 0.728884i | \(-0.259960\pi\) |
−0.481645 | + | 0.876366i | \(0.659960\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0.0996050 | − | 2.42548i | 0.00401646 | − | 0.0978046i | ||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 30.4908 | + | 22.1528i | 1.22751 | + | 0.891840i | 0.996701 | − | 0.0811586i | \(-0.0258620\pi\) |
0.230811 | + | 0.972999i | \(0.425862\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −3.53321 | − | 10.8741i | −0.142012 | − | 0.437067i | 0.854603 | − | 0.519282i | \(-0.173801\pi\) |
−0.996615 | + | 0.0822150i | \(0.973801\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 22.1830 | − | 30.5323i | 0.890174 | − | 1.22522i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −1.89117 | + | 5.82043i | −0.0757682 | + | 0.233191i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 6.92037 | − | 21.2987i | 0.276815 | − | 0.851948i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 4.99177 | − | 1.62192i | 0.199352 | − | 0.0647734i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | − | 1.12912i | − | 0.0450210i | ||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −20.2384 | + | 14.7041i | −0.805678 | + | 0.585359i | −0.912574 | − | 0.408911i | \(-0.865909\pi\) |
0.106897 | + | 0.994270i | \(0.465909\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 16.2246 | + | 11.7878i | 0.644869 | + | 0.468525i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −1.05300 | + | 0.765048i | −0.0417870 | + | 0.0303600i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −1.84603 | − | 2.54084i | −0.0731423 | − | 0.100672i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 20.4470 | + | 6.64362i | 0.808869 | + | 0.262818i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −27.1521 | + | 8.82226i | −1.07244 | + | 0.348458i | −0.791439 | − | 0.611248i | \(-0.790668\pi\) |
−0.281006 | + | 0.959706i | \(0.590668\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 25.8556 | − | 35.5872i | 1.01965 | − | 1.40342i | 0.107195 | − | 0.994238i | \(-0.465813\pi\) |
0.912451 | − | 0.409185i | \(-0.134187\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 3.90296 | + | 1.26815i | 0.153679 | + | 0.0499333i | ||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 36.0356 | 1.41670 | 0.708352 | − | 0.705859i | \(-0.249439\pi\) | ||||
0.708352 | + | 0.705859i | \(0.249439\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 1.67357 | + | 2.30347i | 0.0656934 | + | 0.0904193i | ||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 1.38359 | + | 4.25824i | 0.0542270 | + | 0.166894i | ||||
\(652\) | 0 | 0 | ||||||||
\(653\) | − | 2.51651i | − | 0.0984786i | −0.998787 | − | 0.0492393i | \(-0.984320\pi\) | ||
0.998787 | − | 0.0492393i | \(-0.0156797\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 3.04400 | 0.118939 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 28.1750 | 1.09921 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | − | 11.9875i | − | 0.466967i | −0.972361 | − | 0.233483i | \(-0.924988\pi\) | ||
0.972361 | − | 0.233483i | \(-0.0750125\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 13.5361 | + | 41.6598i | 0.526493 | + | 1.62038i | 0.761344 | + | 0.648348i | \(0.224540\pi\) |
−0.234851 | + | 0.972031i | \(0.575460\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0.384408 | + | 0.529093i | 0.0149292 | + | 0.0205483i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 1.16214 | 0.0450659 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −48.8391 | − | 15.8688i | −1.89106 | − | 0.614442i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −11.5710 | + | 15.9261i | −0.447360 | + | 0.615738i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −4.94859 | + | 1.60790i | −0.191038 | + | 0.0620721i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −23.5399 | − | 7.64859i | −0.907397 | − | 0.294831i | −0.182111 | − | 0.983278i | \(-0.558293\pi\) |
−0.725287 | + | 0.688447i | \(0.758293\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −13.2891 | − | 18.2909i | −0.511497 | − | 0.704016i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −7.70855 | + | 5.60059i | −0.296264 | + | 0.215248i | −0.725980 | − | 0.687716i | \(-0.758614\pi\) |
0.429716 | + | 0.902964i | \(0.358614\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 11.7328 | + | 8.52439i | 0.450264 | + | 0.327136i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 19.2823 | − | 14.0094i | 0.738899 | − | 0.536841i | ||||
\(682\) | 0 | 0 | ||||||||
\(683\) | − | 39.8358i | − | 1.52427i | −0.647416 | − | 0.762137i | \(-0.724150\pi\) | ||
0.647416 | − | 0.762137i | \(-0.275850\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −1.08506 | + | 0.352557i | −0.0414580 | + | 0.0134705i | ||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −4.62407 | + | 14.2314i | −0.176419 | + | 0.542963i | ||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 1.30969 | − | 4.03080i | 0.0498951 | − | 0.153561i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −4.51589 | + | 6.21559i | −0.171793 | + | 0.236452i | −0.886228 | − | 0.463249i | \(-0.846684\pi\) |
0.714436 | + | 0.699701i | \(0.246684\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −1.41175 | − | 4.34491i | −0.0536279 | − | 0.165050i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −1.97174 | − | 1.43256i | −0.0747925 | − | 0.0543399i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 0.914834 | − | 1.15624i | 0.0346518 | − | 0.0437957i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 15.6438 | + | 11.3659i | 0.591704 | + | 0.429898i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −13.5647 | − | 41.7478i | −0.512331 | − | 1.57679i | −0.788087 | − | 0.615564i | \(-0.788928\pi\) |
0.275756 | − | 0.961228i | \(-0.411072\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 7.99031 | − | 10.9977i | 0.301360 | − | 0.414787i | ||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0.102509 | − | 0.315489i | 0.00386069 | − | 0.0118820i | ||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −0.721472 | + | 2.22046i | −0.0271337 | + | 0.0835091i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −41.0018 | + | 13.3223i | −1.53985 | + | 0.500329i | −0.951336 | − | 0.308156i | \(-0.900288\pi\) |
−0.588518 | + | 0.808484i | \(0.700288\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | − | 21.2529i | − | 0.797047i | ||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 32.2554 | − | 23.4349i | 1.20797 | − | 0.877644i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −2.22999 | − | 1.62018i | −0.0833967 | − | 0.0605913i | ||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 19.3930 | − | 14.0898i | 0.724245 | − | 0.526195i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −9.13692 | − | 12.5759i | −0.340750 | − | 0.469002i | 0.603910 | − | 0.797052i | \(-0.293608\pi\) |
−0.944660 | + | 0.328050i | \(0.893608\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 13.0446 | + | 4.23845i | 0.485806 | + | 0.157848i | ||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 3.08476 | − | 1.00230i | 0.114724 | − | 0.0372759i | ||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −18.0823 | + | 24.8882i | −0.671561 | + | 0.924324i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −10.8239 | − | 3.51688i | −0.401435 | − | 0.130434i | 0.101339 | − | 0.994852i | \(-0.467687\pi\) |
−0.502774 | + | 0.864418i | \(0.667687\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −7.67761 | −0.284356 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 1.46506 | + | 2.01648i | 0.0541871 | + | 0.0745821i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 5.09849 | + | 15.6915i | 0.188317 | + | 0.579580i | 0.999990 | − | 0.00453239i | \(-0.00144271\pi\) |
−0.811673 | + | 0.584112i | \(0.801443\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0.379115i | 0.0139839i | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 6.69352 | 0.246559 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −10.8437 | −0.398892 | −0.199446 | − | 0.979909i | \(-0.563914\pi\) | ||||
−0.199446 | + | 0.979909i | \(0.563914\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 7.87369i | 0.289247i | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 0.875666 | + | 2.69502i | 0.0321251 | + | 0.0988708i | 0.965833 | − | 0.259164i | \(-0.0834470\pi\) |
−0.933708 | + | 0.358035i | \(0.883447\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 1.92216 | + | 2.64562i | 0.0704223 | + | 0.0969280i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 10.8475 | 0.396888 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −2.85652 | − | 0.928141i | −0.104375 | − | 0.0339135i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −0.578661 | + | 0.796458i | −0.0211156 | + | 0.0290632i | −0.819444 | − | 0.573159i | \(-0.805718\pi\) |
0.798329 | + | 0.602222i | \(0.205718\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −16.6389 | + | 5.40632i | −0.606356 | + | 0.197017i | ||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 4.93098 | + | 1.60217i | 0.179457 | + | 0.0583090i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 9.66954 | + | 13.3090i | 0.351445 | + | 0.483723i | 0.947740 | − | 0.319042i | \(-0.103361\pi\) |
−0.596295 | + | 0.802765i | \(0.703361\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 12.3350 | − | 8.96189i | 0.447732 | − | 0.325296i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 10.0609 | + | 7.30964i | 0.364706 | + | 0.264974i | 0.755012 | − | 0.655711i | \(-0.227631\pi\) |
−0.390306 | + | 0.920685i | \(0.627631\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 1.64950 | − | 1.19843i | 0.0597158 | − | 0.0433861i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0.210640i | 0.00761569i | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −4.06221 | + | 1.31989i | −0.146678 | + | 0.0476585i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 7.63007 | − | 23.4829i | 0.275147 | − | 0.846816i | −0.714033 | − | 0.700112i | \(-0.753133\pi\) |
0.989180 | − | 0.146704i | \(-0.0468666\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −5.57996 | + | 17.1733i | −0.200957 | + | 0.618483i | ||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −31.3381 | + | 43.1332i | −1.12715 | + | 1.55139i | −0.333786 | + | 0.942649i | \(0.608326\pi\) |
−0.793367 | + | 0.608744i | \(0.791674\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −7.38077 | − | 22.7157i | −0.265125 | − | 0.815971i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 3.58769 | + | 2.60661i | 0.128708 | + | 0.0935116i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 17.0928 | − | 4.78795i | 0.612412 | − | 0.171546i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 16.6872 | + | 12.1240i | 0.597116 | + | 0.433830i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 9.23493 | + | 28.4222i | 0.330029 | + | 1.01573i | ||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −0.255680 | + | 0.351913i | −0.00912561 | + | 0.0125603i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −0.435269 | + | 1.33962i | −0.0155157 | + | 0.0477523i | −0.958515 | − | 0.285043i | \(-0.907992\pi\) |
0.942999 | + | 0.332796i | \(0.107992\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −6.62313 | + | 20.3839i | −0.235790 | + | 0.725686i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −3.24251 | + | 1.05355i | −0.115290 | + | 0.0374601i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | − | 7.80559i | − | 0.277185i | ||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −0.413899 | + | 0.300715i | −0.0146795 | + | 0.0106653i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −25.8845 | − | 18.8062i | −0.916878 | − | 0.666151i | 0.0258673 | − | 0.999665i | \(-0.491765\pi\) |
−0.942745 | + | 0.333515i | \(0.891765\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 0.162998 | − | 0.118425i | 0.00576647 | − | 0.00418958i | ||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −7.84970 | − | 10.8042i | −0.277356 | − | 0.381747i | ||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 25.7084 | + | 8.35316i | 0.907229 | + | 0.294777i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 3.21069 | − | 1.04322i | 0.113162 | − | 0.0367685i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −10.9974 | + | 15.1366i | −0.387126 | + | 0.532834i | ||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −15.8118 | − | 5.13757i | −0.555914 | − | 0.180627i | 0.0175681 | − | 0.999846i | \(-0.494408\pi\) |
−0.573482 | + | 0.819218i | \(0.694408\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −10.3052 | −0.361864 | −0.180932 | − | 0.983496i | \(-0.557911\pi\) | ||||
−0.180932 | + | 0.983496i | \(0.557911\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 3.63536 | + | 5.00364i | 0.127497 | + | 0.175485i | ||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −2.13238 | − | 6.56278i | −0.0746939 | − | 0.229884i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 30.0082i | 1.04985i | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 6.85339 | 0.239477 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −21.8993 | −0.764290 | −0.382145 | − | 0.924102i | \(-0.624815\pi\) | ||||
−0.382145 | + | 0.924102i | \(0.624815\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | − | 30.3056i | − | 1.05639i | −0.849124 | − | 0.528193i | \(-0.822870\pi\) | ||
0.849124 | − | 0.528193i | \(-0.177130\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −2.82253 | − | 8.68684i | −0.0982677 | − | 0.302437i | ||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 7.12452 | + | 9.80605i | 0.247744 | + | 0.340990i | 0.914719 | − | 0.404089i | \(-0.132412\pi\) |
−0.666976 | + | 0.745079i | \(0.732412\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 41.4703 | 1.44032 | 0.720161 | − | 0.693807i | \(-0.244068\pi\) | ||||
0.720161 | + | 0.693807i | \(0.244068\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 9.71310 | + | 3.15598i | 0.336944 | + | 0.109480i | ||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −0.135344 | + | 0.186284i | −0.00468938 | + | 0.00645437i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −6.47038 | + | 2.10235i | −0.223917 | + | 0.0727549i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −22.0669 | − | 7.16996i | −0.762742 | − | 0.247830i | ||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 10.4229 | + | 14.3458i | 0.359837 | + | 0.495274i | 0.950103 | − | 0.311935i | \(-0.100977\pi\) |
−0.590266 | + | 0.807209i | \(0.700977\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 9.43638 | − | 6.85593i | 0.325392 | − | 0.236411i | ||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −19.8883 | − | 14.4497i | −0.684990 | − | 0.497674i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −1.06368 | + | 0.772811i | −0.0365918 | + | 0.0265855i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 6.61693i | 0.227360i | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 25.0362 | − | 8.13476i | 0.859240 | − | 0.279184i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 12.2028 | − | 37.5564i | 0.418308 | − | 1.28742i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −7.92907 | + | 24.4032i | −0.271486 | + | 0.835548i | 0.718642 | + | 0.695381i | \(0.244764\pi\) |
−0.990128 | + | 0.140168i | \(0.955236\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −1.49061 | + | 2.05164i | −0.0509777 | + | 0.0701647i | ||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −13.9963 | − | 43.0763i | −0.478105 | − | 1.47146i | −0.841723 | − | 0.539909i | \(-0.818459\pi\) |
0.363618 | − | 0.931548i | \(-0.381541\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −28.4020 | − | 20.6352i | −0.969062 | − | 0.704065i | −0.0138246 | − | 0.999904i | \(-0.504401\pi\) |
−0.955238 | + | 0.295840i | \(0.904401\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 1.56193 | + | 5.57602i | 0.0532305 | + | 0.190030i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 8.65756 | + | 6.29008i | 0.294707 | + | 0.214117i | 0.725307 | − | 0.688426i | \(-0.241698\pi\) |
−0.430600 | + | 0.902543i | \(0.641698\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 0.177059 | + | 0.544931i | 0.00602018 | + | 0.0185282i | ||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −9.00838 | + | 12.3990i | −0.305941 | + | 0.421091i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 6.30093 | − | 19.3923i | 0.213745 | − | 0.657838i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −3.10290 | + | 9.54974i | −0.105138 | + | 0.323581i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −30.0979 | + | 9.77940i | −1.01866 | + | 0.330983i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | − | 4.11846i | − | 0.139229i | ||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −17.1642 | + | 12.4705i | −0.579595 | + | 0.421100i | −0.838578 | − | 0.544782i | \(-0.816613\pi\) |
0.258983 | + | 0.965882i | \(0.416613\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −10.9955 | − | 7.98870i | −0.370869 | − | 0.269452i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 12.8305 | − | 9.32192i | 0.432271 | − | 0.314063i | −0.350285 | − | 0.936643i | \(-0.613915\pi\) |
0.782556 | + | 0.622580i | \(0.213915\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −23.2574 | − | 32.0110i | −0.782672 | − | 1.07726i | −0.994982 | − | 0.100054i | \(-0.968099\pi\) |
0.212310 | − | 0.977202i | \(-0.431901\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0.490359 | + | 0.159327i | 0.0164832 | + | 0.00535572i | ||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −26.5802 | + | 8.63642i | −0.892474 | + | 0.289982i | −0.719127 | − | 0.694878i | \(-0.755458\pi\) |
−0.173347 | + | 0.984861i | \(0.555458\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 1.82496 | − | 2.51184i | 0.0612072 | − | 0.0842445i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 4.59601 | + | 1.49333i | 0.153972 | + | 0.0500286i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 2.42566 | 0.0811716 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 2.32344 | + | 3.19794i | 0.0776641 | + | 0.106896i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 7.06796 | + | 21.7529i | 0.235992 | + | 0.726309i | ||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 31.5714i | 1.05296i | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −0.310731 | −0.0103519 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −9.78932 | −0.325768 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | − | 6.96322i | − | 0.231465i | ||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −9.06012 | − | 27.8842i | −0.300836 | − | 0.925879i | −0.981198 | − | 0.193003i | \(-0.938177\pi\) |
0.680362 | − | 0.732876i | \(-0.261823\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −2.99462 | − | 4.12174i | −0.0993252 | − | 0.136709i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 37.5554 | 1.24427 | 0.622133 | − | 0.782912i | \(-0.286266\pi\) | ||||
0.622133 | + | 0.782912i | \(0.286266\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 9.89780 | + | 3.21599i | 0.327569 | + | 0.106434i | ||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −0.553829 | + | 0.762280i | −0.0183090 | + | 0.0252002i | ||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −6.90582 | + | 2.24384i | −0.228050 | + | 0.0740980i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −35.4527 | − | 11.5193i | −1.16948 | − | 0.379986i | −0.341029 | − | 0.940053i | \(-0.610775\pi\) |
−0.828447 | + | 0.560067i | \(0.810775\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 5.61419 | + | 7.72726i | 0.184994 | + | 0.254622i | ||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −25.0331 | + | 18.1876i | −0.823974 | + | 0.598652i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −19.1386 | − | 13.9050i | −0.629273 | − | 0.457194i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −24.2141 | + | 17.5926i | −0.795294 | + | 0.577815i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | − | 58.1072i | − | 1.90644i | −0.302285 | − | 0.953218i | \(-0.597749\pi\) | ||
0.302285 | − | 0.953218i | \(-0.402251\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −2.63651 | + | 0.856654i | −0.0864082 | + | 0.0280757i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 2.58951 | − | 7.96969i | 0.0847767 | − | 0.260916i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −0.0624491 | + | 0.192199i | −0.00204230 | + | 0.00628556i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −10.9093 | + | 15.0154i | −0.356391 | + | 0.490531i | −0.949139 | − | 0.314858i | \(-0.898043\pi\) |
0.592747 | + | 0.805388i | \(0.298043\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 4.25085 | + | 13.0828i | 0.138721 | + | 0.426941i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −18.8335 | − | 13.6833i | −0.613955 | − | 0.446064i | 0.236850 | − | 0.971546i | \(-0.423885\pi\) |
−0.850805 | + | 0.525482i | \(0.823885\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 42.9248 | − | 28.5715i | 1.39782 | − | 0.930415i | ||||
\(944\) | 0 | 0 | ||||||||
\(945\) | −1.58942 | − | 1.15478i | −0.0517039 | − | 0.0375651i | ||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 8.96380 | + | 27.5878i | 0.291284 | + | 0.896481i | 0.984444 | + | 0.175697i | \(0.0562180\pi\) |
−0.693160 | + | 0.720784i | \(0.743782\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −23.8351 | + | 32.8062i | −0.773721 | + | 1.06494i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −5.01839 | + | 15.4450i | −0.162733 | + | 0.500839i | ||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −3.92059 | + | 12.0663i | −0.127000 | + | 0.390867i | −0.994260 | − | 0.106989i | \(-0.965879\pi\) |
0.867260 | + | 0.497856i | \(0.165879\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −0.0262395 | + | 0.00852573i | −0.000849090 | + | 0.000275886i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 12.0734i | 0.390278i | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 2.20176 | − | 1.59967i | 0.0710984 | − | 0.0516560i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 5.24899 | + | 3.81361i | 0.169322 | + | 0.123020i | ||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 5.30243 | − | 3.85244i | 0.170868 | − | 0.124143i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −3.59997 | − | 4.95494i | −0.115887 | − | 0.159505i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −35.0959 | − | 11.4034i | −1.12861 | − | 0.366707i | −0.315562 | − | 0.948905i | \(-0.602193\pi\) |
−0.813047 | + | 0.582198i | \(0.802193\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0.549015 | − | 0.178386i | 0.0176369 | − | 0.00573058i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 6.80947 | − | 9.37243i | 0.218526 | − | 0.300776i | −0.685653 | − | 0.727928i | \(-0.740483\pi\) |
0.904179 | + | 0.427153i | \(0.140483\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 5.52922 | + | 1.79655i | 0.177259 | + | 0.0575948i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 13.7021 | 0.438817 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 20.2483 | + | 27.8693i | 0.647799 | + | 0.891619i | 0.999001 | − | 0.0446807i | \(-0.0142270\pi\) |
−0.351202 | + | 0.936300i | \(0.614227\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −3.95932 | − | 12.1855i | −0.126540 | − | 0.389451i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 4.44918i | 0.142051i | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −35.8823 | −1.14447 | −0.572234 | − | 0.820090i | \(-0.693923\pi\) | ||||
−0.572234 | + | 0.820090i | \(0.693923\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −7.22118 | −0.230086 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0.791302i | 0.0251874i | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 26.9374 | + | 82.9047i | 0.856559 | + | 2.63622i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 5.93454 | + | 8.16820i | 0.188517 | + | 0.259471i | 0.892805 | − | 0.450443i | \(-0.148734\pi\) |
−0.704288 | + | 0.709914i | \(0.748734\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 6.21168 | 0.197122 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −3.59505 | − | 1.16810i | −0.113971 | − | 0.0370314i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −3.71495 | + | 5.11319i | −0.117654 | + | 0.161936i | −0.863782 | − | 0.503866i | \(-0.831911\pi\) |
0.746128 | + | 0.665802i | \(0.231911\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −21.8562 | + | 7.10150i | −0.691499 | + | 0.224682i |
(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 | 1148.2.ba.a.113.8 | ✓ | 80 | |
41.4 | even | 10 | inner | 1148.2.ba.a.701.13 | yes | 80 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1148.2.ba.a.113.8 | ✓ | 80 | 1.1 | even | 1 | trivial | |
1148.2.ba.a.701.13 | yes | 80 | 41.4 | even | 10 | inner |