Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [76,5,Mod(13,76)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(76, base_ring=CyclotomicField(18))
chi = DirichletCharacter(H, H._module([0, 5]))
N = Newforms(chi, 5, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("76.13");
S:= CuspForms(chi, 5);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 76 = 2^{2} \cdot 19 \) |
Weight: | \( k \) | \(=\) | \( 5 \) |
Character orbit: | \([\chi]\) | \(=\) | 76.j (of order \(18\), degree \(6\), 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: | \(7.85611719437\) |
Analytic rank: | \(0\) |
Dimension: | \(42\) |
Relative dimension: | \(7\) over \(\Q(\zeta_{18})\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{18}]$ |
Embedding invariants
Embedding label | 13.2 | ||
Character | \(\chi\) | \(=\) | 76.13 |
Dual form | 76.5.j.a.41.2 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/76\mathbb{Z}\right)^\times\).
\(n\) | \(21\) | \(39\) |
\(\chi(n)\) | \(e\left(\frac{5}{18}\right)\) | \(1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | −4.13985 | + | 11.3741i | −0.459983 | + | 1.26379i | 0.465514 | + | 0.885040i | \(0.345869\pi\) |
−0.925498 | + | 0.378754i | \(0.876353\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −6.25205 | − | 35.4571i | −0.250082 | − | 1.41828i | −0.808388 | − | 0.588650i | \(-0.799660\pi\) |
0.558306 | − | 0.829635i | \(-0.311451\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −25.8702 | + | 44.8086i | −0.527964 | + | 0.914461i | 0.471504 | + | 0.881864i | \(0.343711\pi\) |
−0.999469 | + | 0.0325971i | \(0.989622\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −50.1832 | − | 42.1087i | −0.619546 | − | 0.519861i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −31.3514 | − | 54.3022i | −0.259102 | − | 0.448778i | 0.706899 | − | 0.707314i | \(-0.250093\pi\) |
−0.966002 | + | 0.258536i | \(0.916760\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −109.766 | − | 301.581i | −0.649506 | − | 1.78450i | −0.619558 | − | 0.784951i | \(-0.712688\pi\) |
−0.0299481 | − | 0.999551i | \(-0.509534\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 429.177 | + | 75.6755i | 1.90745 | + | 0.336335i | ||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 342.075 | − | 287.035i | 1.18365 | − | 0.993202i | 0.183704 | − | 0.982982i | \(-0.441191\pi\) |
0.999948 | − | 0.0102204i | \(-0.00325333\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −162.907 | − | 322.153i | −0.451265 | − | 0.892390i | ||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −402.560 | − | 479.753i | −0.912835 | − | 1.08787i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −90.4845 | + | 513.163i | −0.171048 | + | 0.970062i | 0.771559 | + | 0.636158i | \(0.219477\pi\) |
−0.942607 | + | 0.333904i | \(0.891634\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −630.811 | + | 229.596i | −1.00930 | + | 0.367354i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −162.378 | + | 93.7490i | −0.222741 | + | 0.128599i | ||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −524.868 | + | 625.513i | −0.624099 | + | 0.743773i | −0.981770 | − | 0.190075i | \(-0.939127\pi\) |
0.357670 | + | 0.933848i | \(0.383571\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −1072.59 | − | 619.262i | −1.11612 | − | 0.644393i | −0.175714 | − | 0.984441i | \(-0.556223\pi\) |
−0.940408 | + | 0.340048i | \(0.889557\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 747.431 | − | 131.792i | 0.686346 | − | 0.121021i | ||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 1750.52 | + | 637.139i | 1.42900 | + | 0.520113i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 532.840i | 0.389219i | 0.980881 | + | 0.194609i | \(0.0623439\pi\) | ||||
−0.980881 | + | 0.194609i | \(0.937656\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 3884.64 | 2.55401 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −355.017 | + | 975.401i | −0.211194 | + | 0.580251i | −0.999381 | − | 0.0351853i | \(-0.988798\pi\) |
0.788187 | + | 0.615436i | \(0.211020\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −79.7398 | − | 452.227i | −0.0431259 | − | 0.244579i | 0.955623 | − | 0.294594i | \(-0.0951843\pi\) |
−0.998748 | + | 0.0500145i | \(0.984073\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −1179.31 | + | 2042.62i | −0.582374 | + | 1.00870i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −2408.38 | − | 2020.87i | −1.09026 | − | 0.914836i | −0.0935268 | − | 0.995617i | \(-0.529814\pi\) |
−0.996732 | + | 0.0807812i | \(0.974259\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −138.039 | − | 239.091i | −0.0574924 | − | 0.0995797i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 1848.64 | + | 5079.10i | 0.710742 | + | 1.95275i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −1797.47 | − | 316.942i | −0.639895 | − | 0.112831i | −0.155719 | − | 0.987801i | \(-0.549769\pi\) |
−0.484176 | + | 0.874971i | \(0.660881\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −1729.39 | + | 1451.13i | −0.571699 | + | 0.479712i | ||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 4338.62 | − | 519.262i | 1.33537 | − | 0.159822i | ||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −365.255 | − | 435.294i | −0.104928 | − | 0.125049i | 0.711024 | − | 0.703167i | \(-0.248231\pi\) |
−0.815953 | + | 0.578119i | \(0.803787\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 93.8036 | − | 531.987i | 0.0252093 | − | 0.142969i | −0.969605 | − | 0.244674i | \(-0.921319\pi\) |
0.994815 | + | 0.101706i | \(0.0324300\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 3185.09 | − | 1159.28i | 0.802491 | − | 0.292083i | ||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −10006.9 | + | 5777.50i | −2.36850 | + | 1.36746i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 4282.23 | − | 5103.37i | 0.953939 | − | 1.13686i | −0.0365584 | − | 0.999332i | \(-0.511640\pi\) |
0.990498 | − | 0.137529i | \(-0.0439160\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −5462.20 | − | 3153.60i | −1.14728 | − | 0.662382i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −1606.46 | + | 283.262i | −0.318678 | + | 0.0561915i | −0.330699 | − | 0.943736i | \(-0.607285\pi\) |
0.0120212 | + | 0.999928i | \(0.496173\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 7746.45 | + | 2819.48i | 1.45364 | + | 0.529082i | 0.943605 | − | 0.331072i | \(-0.107410\pi\) |
0.510034 | + | 0.860154i | \(0.329633\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | − | 8125.43i | − | 1.44452i | ||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 3244.27 | 0.547187 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −2379.76 | + | 6538.35i | −0.381311 | + | 1.04764i | 0.589493 | + | 0.807773i | \(0.299327\pi\) |
−0.970805 | + | 0.239871i | \(0.922895\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −1315.52 | − | 7460.68i | −0.200506 | − | 1.13713i | ||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 3687.63 | − | 6387.16i | 0.535292 | − | 0.927153i | −0.463857 | − | 0.885910i | \(-0.653535\pi\) |
0.999149 | − | 0.0412433i | \(-0.0131319\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −12316.1 | − | 10334.4i | −1.70465 | − | 1.43037i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −4941.80 | − | 8559.45i | −0.652900 | − | 1.13086i | ||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 2153.49 | + | 5916.67i | 0.271871 | + | 0.746960i | 0.998220 | + | 0.0596339i | \(0.0189933\pi\) |
−0.726349 | + | 0.687326i | \(0.758784\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 16353.1 | + | 2883.49i | 1.97477 | + | 0.348206i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 11484.0 | − | 9636.18i | 1.32778 | − | 1.11414i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −10404.1 | + | 7790.32i | −1.15281 | + | 0.863193i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −2695.42 | − | 3212.28i | −0.286473 | − | 0.341405i | 0.603546 | − | 0.797328i | \(-0.293754\pi\) |
−0.890019 | + | 0.455923i | \(0.849309\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −713.283 | + | 4045.23i | −0.0727765 | + | 0.412736i | ||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 3566.13 | − | 1297.97i | 0.349587 | − | 0.127239i | −0.161258 | − | 0.986912i | \(-0.551555\pi\) |
0.510844 | + | 0.859673i | \(0.329333\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 2896.28 | − | 1672.17i | 0.273003 | − | 0.157618i | −0.357249 | − | 0.934009i | \(-0.616285\pi\) |
0.630251 | + | 0.776391i | \(0.282952\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −14493.8 | + | 17273.1i | −1.31463 | + | 1.56672i | ||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 8891.77 | + | 5133.67i | 0.776642 | + | 0.448394i | 0.835239 | − | 0.549887i | \(-0.185329\pi\) |
−0.0585971 | + | 0.998282i | \(0.518663\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −20233.7 | + | 3567.75i | −1.70303 | + | 0.300290i | −0.938751 | − | 0.344596i | \(-0.888016\pi\) |
−0.764279 | + | 0.644886i | \(0.776905\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −6060.61 | − | 2205.88i | −0.491892 | − | 0.179034i | ||||
\(112\) | 0 | 0 | ||||||||
\(113\) | − | 9155.56i | − | 0.717015i | −0.933527 | − | 0.358507i | \(-0.883286\pi\) | ||
0.933527 | − | 0.358507i | \(-0.116714\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 18761.0 | 1.41860 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −7190.75 | + | 19756.4i | −0.525294 | + | 1.44323i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 4012.07 | + | 22753.6i | 0.283318 | + | 1.60678i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 5354.68 | − | 9274.58i | 0.365732 | − | 0.633466i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −9624.64 | − | 8076.03i | −0.636172 | − | 0.533811i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 833.406 | + | 1443.50i | 0.0533380 | + | 0.0923841i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −1123.59 | − | 3087.05i | −0.0696630 | − | 0.191397i | 0.899975 | − | 0.435941i | \(-0.143584\pi\) |
−0.969638 | + | 0.244543i | \(0.921362\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 5473.81 | + | 965.180i | 0.328935 | + | 0.0580001i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −10134.1 | + | 8503.54i | −0.590532 | + | 0.495515i | −0.888387 | − | 0.459096i | \(-0.848173\pi\) |
0.297855 | + | 0.954611i | \(0.403729\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 18649.6 | + | 1034.55i | 1.05431 | + | 0.0584853i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 4339.26 | + | 5171.33i | 0.238094 | + | 0.283749i | ||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −742.666 | + | 4211.87i | −0.0395688 | + | 0.224406i | −0.998179 | − | 0.0603146i | \(-0.980790\pi\) |
0.958611 | + | 0.284720i | \(0.0919007\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −6529.51 | + | 2376.55i | −0.337949 | + | 0.123003i | −0.505419 | − | 0.862874i | \(-0.668662\pi\) |
0.167471 | + | 0.985877i | \(0.446440\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 32956.0 | − | 19027.2i | 1.65766 | − | 0.957053i | ||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −12935.2 | + | 15415.5i | −0.632558 | + | 0.753853i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 25460.4 | + | 14699.6i | 1.21096 | + | 0.699147i | ||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 3290.92 | − | 580.277i | 0.152294 | − | 0.0268535i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 41071.4 | + | 14948.8i | 1.84998 | + | 0.673337i | 0.985255 | + | 0.171090i | \(0.0547290\pi\) |
0.864724 | + | 0.502247i | \(0.167493\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | − | 22893.0i | − | 1.00403i | −0.864858 | − | 0.502017i | \(-0.832591\pi\) | ||
0.864858 | − | 0.502017i | \(-0.167409\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −29253.1 | −1.24965 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −15251.3 | + | 41902.7i | −0.634811 | + | 1.74413i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −4649.04 | − | 26366.0i | −0.188610 | − | 1.06966i | −0.921229 | − | 0.389021i | \(-0.872813\pi\) |
0.732619 | − | 0.680639i | \(-0.238298\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 11046.2 | − | 19132.5i | 0.436936 | − | 0.756796i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −20653.2 | − | 17330.1i | −0.796777 | − | 0.668575i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −17362.1 | − | 30072.0i | −0.653472 | − | 1.13185i | −0.982275 | − | 0.187448i | \(-0.939978\pi\) |
0.328803 | − | 0.944399i | \(-0.393355\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −9345.95 | − | 25677.8i | −0.343285 | − | 0.943169i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −45243.1 | − | 7977.57i | −1.62226 | − | 0.286047i | −0.712650 | − | 0.701520i | \(-0.752505\pi\) |
−0.909606 | + | 0.415473i | \(0.863616\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −57023.4 | + | 47848.3i | −1.99655 | + | 1.67530i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −5390.25 | + | 23026.5i | −0.184339 | + | 0.787472i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 33628.3 | + | 40076.7i | 1.12360 | + | 1.33906i | 0.934032 | + | 0.357191i | \(0.116265\pi\) |
0.189571 | + | 0.981867i | \(0.439290\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 6031.35 | − | 34205.5i | 0.196942 | − | 1.11691i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 6463.20 | − | 2352.41i | 0.206301 | − | 0.0750874i | ||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −3772.59 | + | 2178.10i | −0.117743 | + | 0.0679787i | −0.557715 | − | 0.830033i | \(-0.688322\pi\) |
0.439972 | + | 0.898011i | \(0.354988\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 22208.2 | − | 26466.7i | 0.677886 | − | 0.807873i | −0.311948 | − | 0.950099i | \(-0.600982\pi\) |
0.989834 | + | 0.142226i | \(0.0454261\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 5662.56 | + | 3269.28i | 0.169087 | + | 0.0976226i | ||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 18893.0 | − | 3331.34i | 0.552023 | − | 0.0973365i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −26311.2 | − | 9576.49i | −0.752415 | − | 0.273857i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | − | 9701.24i | − | 0.271584i | ||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 2319.58 | 0.0635833 | 0.0317917 | − | 0.999495i | \(-0.489879\pi\) | ||||
0.0317917 | + | 0.999495i | \(0.489879\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 11685.7 | − | 32106.2i | 0.313719 | − | 0.861935i | −0.678179 | − | 0.734896i | \(-0.737231\pi\) |
0.991898 | − | 0.127038i | \(-0.0405471\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −24287.0 | − | 137738.i | −0.638710 | − | 3.62231i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 6488.54 | − | 11238.5i | 0.167192 | − | 0.289585i | −0.770240 | − | 0.637755i | \(-0.779863\pi\) |
0.937431 | + | 0.348170i | \(0.113197\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 39079.4 | + | 32791.5i | 0.986828 | + | 0.828047i | 0.985105 | − | 0.171952i | \(-0.0550074\pi\) |
0.00172223 | + | 0.999999i | \(0.499452\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 40318.6 | + | 69833.9i | 0.997961 | + | 1.72852i | ||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −14449.9 | − | 39700.7i | −0.350649 | − | 0.963400i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 36804.5 | + | 6489.63i | 0.875776 | + | 0.154423i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 26149.4 | − | 21942.0i | 0.610270 | − | 0.512077i | ||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −12386.2 | + | 18946.1i | −0.283561 | + | 0.433738i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 17233.3 | + | 20537.9i | 0.387083 | + | 0.461308i | 0.924037 | − | 0.382304i | \(-0.124869\pi\) |
−0.536953 | + | 0.843612i | \(0.680425\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 3428.63 | − | 19444.7i | 0.0755721 | − | 0.428591i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −15536.1 | + | 5654.69i | −0.336098 | + | 0.122330i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 55496.5 | − | 32040.9i | 1.17854 | − | 0.680433i | ||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −64138.3 | + | 76437.0i | −1.33730 | + | 1.59373i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −124113. | − | 71656.6i | −2.54116 | − | 1.46714i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 36556.3 | − | 6445.86i | 0.735110 | − | 0.129620i | 0.206454 | − | 0.978456i | \(-0.433808\pi\) |
0.528655 | + | 0.848837i | \(0.322696\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 41324.2 | + | 15040.8i | 0.816280 | + | 0.297101i | ||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 58042.3i | 1.12640i | 0.826320 | + | 0.563200i | \(0.190430\pi\) | ||||
−0.826320 | + | 0.563200i | \(0.809570\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −47979.8 | −0.914930 | −0.457465 | − | 0.889228i | \(-0.651242\pi\) | ||||
−0.457465 | + | 0.889228i | \(0.651242\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −13430.8 | + | 36900.8i | −0.251697 | + | 0.691532i | ||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 15332.4 | + | 86954.6i | 0.282422 | + | 1.60170i | 0.714350 | + | 0.699789i | \(0.246723\pi\) |
−0.431927 | + | 0.901909i | \(0.642166\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −56597.0 | + | 98028.8i | −1.02484 | + | 1.77508i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −64516.3 | − | 54135.6i | −1.14861 | − | 0.963798i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −21266.4 | − | 36834.6i | −0.372305 | − | 0.644851i | 0.617615 | − | 0.786481i | \(-0.288099\pi\) |
−0.989920 | + | 0.141629i | \(0.954766\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −378.914 | − | 1041.06i | −0.00652390 | − | 0.0179243i | 0.936388 | − | 0.350967i | \(-0.114147\pi\) |
−0.942912 | + | 0.333042i | \(0.891925\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 75348.3 | + | 13285.9i | 1.27603 | + | 0.224999i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −7614.45 | + | 6389.28i | −0.126855 | + | 0.106444i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −79273.4 | + | 84491.2i | −1.29937 | + | 1.38490i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 57382.3 | + | 68385.5i | 0.925505 | + | 1.10297i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −5413.15 | + | 30699.5i | −0.0859217 | + | 0.487286i | 0.911232 | + | 0.411893i | \(0.135132\pi\) |
−0.997154 | + | 0.0753931i | \(0.975979\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 30702.7 | − | 11174.9i | 0.479662 | − | 0.174583i | ||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 168532. | − | 97302.2i | 2.59181 | − | 1.49638i | ||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 50379.6 | − | 60040.0i | 0.762760 | − | 0.909023i | −0.235259 | − | 0.971933i | \(-0.575594\pi\) |
0.998019 | + | 0.0629103i | \(0.0200382\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −23875.8 | − | 13784.7i | −0.355925 | − | 0.205494i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 52679.1 | − | 9288.75i | 0.773317 | − | 0.136357i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 82030.2 | + | 29856.6i | 1.18594 | + | 0.431647i | 0.858296 | − | 0.513155i | \(-0.171523\pi\) |
0.327643 | + | 0.944802i | \(0.393746\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 65714.5i | 0.935771i | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −76212.2 | −1.06906 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 2186.85 | − | 6008.31i | 0.0302213 | − | 0.0830325i | −0.923664 | − | 0.383202i | \(-0.874821\pi\) |
0.953886 | + | 0.300170i | \(0.0970434\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 718.640 | + | 4075.61i | 0.00978527 | + | 0.0554950i | 0.989309 | − | 0.145832i | \(-0.0465858\pi\) |
−0.979524 | + | 0.201327i | \(0.935475\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −100497. | + | 174065.i | −1.34842 | + | 2.33554i | ||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 32244.4 | + | 27056.3i | 0.426372 | + | 0.357769i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −57251.9 | − | 99163.2i | −0.746157 | − | 1.29238i | −0.949652 | − | 0.313306i | \(-0.898563\pi\) |
0.203495 | − | 0.979076i | \(-0.434770\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 27749.9 | + | 76242.1i | 0.356494 | + | 0.979460i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −75809.1 | − | 13367.2i | −0.960082 | − | 0.169288i | −0.328420 | − | 0.944532i | \(-0.606516\pi\) |
−0.631663 | + | 0.775243i | \(0.717627\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 16680.1 | − | 13996.3i | 0.208270 | − | 0.174759i | −0.532686 | − | 0.846313i | \(-0.678817\pi\) |
0.740956 | + | 0.671554i | \(0.234373\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −45536.8 | − | 150589.i | −0.560625 | − | 1.85397i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −34522.0 | − | 41141.7i | −0.419114 | − | 0.499480i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 20123.0 | − | 114123.i | 0.240934 | − | 1.36640i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 47695.6 | − | 17359.8i | 0.563239 | − | 0.205002i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −6337.52 | + | 3658.97i | −0.0738217 | + | 0.0426210i | −0.536456 | − | 0.843928i | \(-0.680237\pi\) |
0.462635 | + | 0.886549i | \(0.346904\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −13150.7 | + | 15672.4i | −0.151114 | + | 0.180090i | ||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 10181.6 | + | 5878.32i | 0.115425 | + | 0.0666408i | ||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 164692. | − | 29039.7i | 1.84218 | − | 0.324825i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 22326.5 | + | 8126.20i | 0.246427 | + | 0.0896921i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 45935.1i | 0.500333i | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −19449.2 | −0.209075 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 15214.4 | − | 41801.2i | 0.161428 | − | 0.443519i | −0.832437 | − | 0.554119i | \(-0.813055\pi\) |
0.993865 | + | 0.110600i | \(0.0352773\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 7029.33 | + | 39865.3i | 0.0736202 | + | 0.417521i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −27129.2 | + | 46989.2i | −0.280489 | + | 0.485822i | −0.971505 | − | 0.237018i | \(-0.923830\pi\) |
0.691016 | + | 0.722840i | \(0.257163\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −133986. | − | 112427.i | −1.36763 | − | 1.14758i | −0.973541 | − | 0.228510i | \(-0.926614\pi\) |
−0.394093 | − | 0.919071i | \(-0.628941\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −61017.9 | − | 105686.i | −0.614945 | − | 1.06512i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 17422.9 | + | 47869.1i | 0.173381 | + | 0.476361i | 0.995697 | − | 0.0926706i | \(-0.0295404\pi\) |
−0.822316 | + | 0.569032i | \(0.807318\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 50422.0 | + | 8890.77i | 0.495495 | + | 0.0873691i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −95201.7 | + | 79883.7i | −0.923920 | + | 0.775261i | ||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −148196. | − | 63440.5i | −1.42046 | − | 0.608081i | ||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 138484. | + | 165039.i | 1.31109 | + | 1.56250i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 43184.4 | − | 244911.i | 0.403861 | − | 2.29041i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 152858. | − | 55635.7i | 1.41220 | − | 0.513998i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 42178.2 | − | 24351.6i | 0.384975 | − | 0.222265i | −0.295006 | − | 0.955495i | \(-0.595322\pi\) |
0.679980 | + | 0.733230i | \(0.261988\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 22437.2 | − | 26739.7i | 0.202340 | − | 0.241139i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −207723. | − | 119929.i | −1.85095 | − | 1.06865i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −172939. | + | 30493.9i | −1.52277 | + | 0.268505i | −0.871520 | − | 0.490360i | \(-0.836865\pi\) |
−0.651248 | + | 0.758865i | \(0.725754\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 104137. | + | 37902.7i | 0.906159 | + | 0.329815i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 77658.9i | 0.667855i | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −109944. | −0.934513 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −77667.7 | + | 213390.i | −0.652533 | + | 1.79282i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −35555.2 | − | 201644.i | −0.295287 | − | 1.67466i | −0.666034 | − | 0.745921i | \(-0.732009\pi\) |
0.370747 | − | 0.928734i | \(-0.379102\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 14177.9 | − | 24556.8i | 0.116402 | − | 0.201614i | −0.801937 | − | 0.597408i | \(-0.796197\pi\) |
0.918339 | + | 0.395794i | \(0.129531\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 46096.6 | + | 38679.6i | 0.374158 | + | 0.313955i | ||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 31647.8 | + | 54815.5i | 0.253976 | + | 0.439900i | 0.964617 | − | 0.263655i | \(-0.0849281\pi\) |
−0.710641 | + | 0.703555i | \(0.751595\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 20087.3 | + | 55189.3i | 0.159391 | + | 0.437924i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −275412. | − | 48562.6i | −2.16096 | − | 0.381035i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 138189. | − | 115954.i | 1.07222 | − | 0.899699i | 0.0769680 | − | 0.997034i | \(-0.475476\pi\) |
0.995252 | + | 0.0973344i | \(0.0310316\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −77243.7 | + | 104962.i | −0.592719 | + | 0.805409i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 83322.9 | + | 99300.3i | 0.632340 | + | 0.753594i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 51539.3 | − | 292294.i | 0.386859 | − | 2.19399i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 155098. | − | 56451.0i | 1.15153 | − | 0.419121i | 0.305463 | − | 0.952204i | \(-0.401189\pi\) |
0.846063 | + | 0.533083i | \(0.178966\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 58888.8 | − | 33999.5i | 0.432494 | − | 0.249701i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 60702.6 | − | 72342.5i | 0.441021 | − | 0.525589i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 17104.7 | + | 9875.42i | 0.122942 | + | 0.0709803i | 0.560210 | − | 0.828351i | \(-0.310721\pi\) |
−0.437268 | + | 0.899331i | \(0.644054\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −19868.8 | + | 3503.40i | −0.141289 | + | 0.0249131i | ||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 246256. | + | 89629.7i | 1.73262 | + | 0.630622i | ||||
\(378\) | 0 | 0 | ||||||||
\(379\) | − | 62884.2i | − | 0.437787i | −0.975749 | − | 0.218894i | \(-0.929755\pi\) | ||
0.975749 | − | 0.218894i | \(-0.0702448\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 39764.1 | 0.273931 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −87776.5 | + | 241164.i | −0.598385 | + | 1.64405i | 0.156107 | + | 0.987740i | \(0.450105\pi\) |
−0.754492 | + | 0.656309i | \(0.772117\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −20283.3 | − | 115033.i | −0.136842 | − | 0.776067i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −15041.1 | + | 26052.0i | −0.100429 | + | 0.173948i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 57339.1 | + | 48113.2i | 0.378924 | + | 0.317955i | 0.812280 | − | 0.583268i | \(-0.198226\pi\) |
−0.433356 | + | 0.901223i | \(0.642671\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 116343. | + | 201513.i | 0.761006 | + | 1.31810i | ||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −54766.7 | − | 150470.i | −0.354594 | − | 0.974240i | ||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 246709. | + | 43501.5i | 1.58122 | + | 0.278811i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 76222.8 | − | 63958.5i | 0.483619 | − | 0.405805i | −0.368114 | − | 0.929781i | \(-0.619996\pi\) |
0.851733 | + | 0.523976i | \(0.175552\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −88973.8 | + | 207841.i | −0.558877 | + | 1.30553i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −17594.1 | − | 20967.9i | −0.109416 | − | 0.130396i | 0.708557 | − | 0.705653i | \(-0.249346\pi\) |
−0.817973 | + | 0.575257i | \(0.804902\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −69022.8 | + | 391448.i | −0.424994 | + | 2.41026i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −256309. | + | 93289.0i | −1.56262 | + | 0.568749i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 28934.4 | − | 16705.3i | 0.174673 | − | 0.100847i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −31610.0 | + | 37671.3i | −0.188963 | + | 0.225198i | −0.852206 | − | 0.523207i | \(-0.824735\pi\) |
0.663242 | + | 0.748405i | \(0.269180\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −44831.9 | − | 25883.7i | −0.265402 | − | 0.153230i | ||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 28954.1 | − | 5105.40i | 0.169750 | − | 0.0299316i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −249525. | − | 90819.8i | −1.44883 | − | 0.527333i | ||||
\(416\) | 0 | 0 | ||||||||
\(417\) | − | 84106.1i | − | 0.483677i | ||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 172898. | 0.984829 | 0.492415 | − | 0.870361i | \(-0.336114\pi\) | ||||
0.492415 | + | 0.870361i | \(0.336114\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −31024.7 | + | 85239.6i | −0.175042 | + | 0.480925i | −0.995926 | − | 0.0901699i | \(-0.971259\pi\) |
0.820884 | + | 0.571095i | \(0.193481\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 35764.0 | + | 202828.i | 0.199878 | + | 1.13357i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −149883. | + | 259604.i | −0.829800 | + | 1.43726i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 21410.9 | + | 17965.8i | 0.117430 | + | 0.0985353i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −121789. | − | 210945.i | −0.661749 | − | 1.14618i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −57800.6 | − | 158806.i | −0.311156 | − | 0.854894i | −0.992424 | − | 0.122860i | \(-0.960793\pi\) |
0.681268 | − | 0.732034i | \(-0.261429\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 62509.0 | + | 11022.0i | 0.333401 | + | 0.0587876i | 0.337843 | − | 0.941203i | \(-0.390303\pi\) |
−0.00444187 | + | 0.999990i | \(0.501414\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −272597. | + | 228736.i | −1.44060 | + | 1.20880i | ||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 180057. | − | 54447.9i | 0.942862 | − | 0.285114i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 78416.9 | + | 93453.6i | 0.406893 | + | 0.484916i | 0.930109 | − | 0.367284i | \(-0.119712\pi\) |
−0.523216 | + | 0.852200i | \(0.675268\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −3140.56 | + | 17811.0i | −0.0161484 | + | 0.0915823i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −39956.5 | + | 14543.0i | −0.203601 | + | 0.0741047i | −0.441808 | − | 0.897110i | \(-0.645663\pi\) |
0.238207 | + | 0.971214i | \(0.423440\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 196324. | − | 113348.i | 0.991411 | − | 0.572392i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −340059. | + | 405266.i | −1.70192 | + | 2.02827i | ||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 244799. | + | 141335.i | 1.21427 | + | 0.701061i | 0.963687 | − | 0.267034i | \(-0.0860436\pi\) |
0.250585 | + | 0.968094i | \(0.419377\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 64096.7 | − | 11302.0i | 0.315125 | − | 0.0555650i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 260388. | + | 94773.6i | 1.26889 | + | 0.461839i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | − | 597861.i | − | 2.88787i | ||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −245414. | −1.17508 | −0.587539 | − | 0.809196i | \(-0.699903\pi\) | ||||
−0.587539 | + | 0.809196i | \(0.699903\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −28636.3 | + | 78677.5i | −0.135922 | + | 0.373444i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −54578.8 | − | 309532.i | −0.256816 | − | 1.45648i | −0.791368 | − | 0.611340i | \(-0.790631\pi\) |
0.534552 | − | 0.845136i | \(-0.320480\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 207033. | − | 358592.i | 0.965779 | − | 1.67278i | 0.258272 | − | 0.966072i | \(-0.416847\pi\) |
0.707507 | − | 0.706706i | \(-0.249820\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −413469. | − | 346942.i | −1.91222 | − | 1.60454i | ||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −126489. | − | 219086.i | −0.579990 | − | 1.00457i | −0.995480 | − | 0.0949745i | \(-0.969723\pi\) |
0.415489 | − | 0.909598i | \(-0.363610\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 117892. | + | 323906.i | 0.535969 | + | 1.47256i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 319138. | + | 56272.6i | 1.43859 | + | 0.253662i | ||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −22057.0 | + | 18508.0i | −0.0985879 | + | 0.0827250i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 176729. | + | 165815.i | 0.783284 | + | 0.734913i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 76856.6 | + | 91594.2i | 0.337788 | + | 0.402560i | ||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −3378.29 | + | 19159.3i | −0.0147240 | + | 0.0835040i | −0.991284 | − | 0.131740i | \(-0.957944\pi\) |
0.976560 | + | 0.215244i | \(0.0690547\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 160695. | − | 58488.0i | 0.694562 | − | 0.252800i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 282617. | − | 163169.i | 1.21145 | − | 0.699428i | ||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −97046.3 | + | 115655.i | −0.412568 | + | 0.491679i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −138308. | − | 79852.2i | −0.583162 | − | 0.336689i | 0.179227 | − | 0.983808i | \(-0.442640\pi\) |
−0.762389 | + | 0.647119i | \(0.775974\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 413920. | − | 72985.3i | 1.73101 | − | 0.305223i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −61049.3 | − | 22220.1i | −0.253232 | − | 0.0921687i | 0.212285 | − | 0.977208i | \(-0.431909\pi\) |
−0.465517 | + | 0.885039i | \(0.654132\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 364628.i | 1.50022i | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 147892. | 0.603577 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 28866.9 | − | 79311.1i | 0.116866 | − | 0.321086i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −10083.2 | − | 57184.4i | −0.0404944 | − | 0.229655i | 0.957843 | − | 0.287291i | \(-0.0927548\pi\) |
−0.998338 | + | 0.0576361i | \(0.981644\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 278038. | − | 481575.i | 1.10772 | − | 1.91862i | ||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −280926. | − | 235725.i | −1.11034 | − | 0.931686i | −0.112263 | − | 0.993678i | \(-0.535810\pi\) |
−0.998077 | + | 0.0619926i | \(0.980254\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −68317.8 | − | 118330.i | −0.267887 | − | 0.463993i | ||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −308165. | − | 846677.i | −1.19886 | − | 3.29384i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −327355. | − | 57721.5i | −1.26352 | − | 0.222793i | −0.498553 | − | 0.866859i | \(-0.666135\pi\) |
−0.764970 | + | 0.644066i | \(0.777246\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −326739. | + | 274167.i | −1.25129 | + | 1.04996i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 56654.0 | + | 37038.2i | 0.215276 | + | 0.140739i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −77398.0 | − | 92239.4i | −0.291820 | − | 0.347778i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −34231.7 | + | 194137.i | −0.128070 | + | 0.726321i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −595054. | + | 216582.i | −2.20913 | + | 0.804058i | ||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −154075. | + | 88955.0i | −0.567617 | + | 0.327714i | −0.756197 | − | 0.654344i | \(-0.772945\pi\) |
0.188580 | + | 0.982058i | \(0.439612\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −7225.72 | + | 8611.28i | −0.0264167 | + | 0.0314821i | −0.779091 | − | 0.626911i | \(-0.784319\pi\) |
0.752674 | + | 0.658393i | \(0.228763\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 364089. | + | 210207.i | 1.32096 | + | 0.762655i | ||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −544658. | + | 96037.9i | −1.96111 | + | 0.345797i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 7815.74 | + | 2844.70i | 0.0279292 | + | 0.0101654i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 37224.9i | 0.132021i | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 333131. | 1.17263 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 126433. | − | 347372.i | 0.441727 | − | 1.21363i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −9156.13 | − | 51927.0i | −0.0317514 | − | 0.180071i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −8655.44 | + | 14991.7i | −0.0297928 | + | 0.0516027i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −381628. | − | 320224.i | −1.30391 | − | 1.09411i | −0.989456 | − | 0.144833i | \(-0.953736\pi\) |
−0.314450 | − | 0.949274i | \(-0.601820\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 209098. | + | 362168.i | 0.709169 | + | 1.22832i | ||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 253004. | + | 695123.i | 0.851794 | + | 2.34028i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 276.343 | + | 48.7267i | 0.000923578 | + | 0.000162852i | 0.174110 | − | 0.984726i | \(-0.444295\pi\) |
−0.173186 | + | 0.984889i | \(0.555406\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −27108.7 | + | 22746.9i | −0.0899422 | + | 0.0754704i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 287015. | + | 67187.2i | 0.945370 | + | 0.221301i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −231409. | − | 275783.i | −0.756711 | − | 0.901813i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −40323.0 | + | 228683.i | −0.130908 | + | 0.742416i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 107948. | − | 39289.8i | 0.347940 | − | 0.126640i | −0.162138 | − | 0.986768i | \(-0.551839\pi\) |
0.510078 | + | 0.860128i | \(0.329617\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −127630. | + | 73687.4i | −0.408442 | + | 0.235814i | ||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 217849. | − | 259622.i | 0.692196 | − | 0.824928i | ||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 43650.6 | + | 25201.7i | 0.137713 | + | 0.0795084i | 0.567273 | − | 0.823530i | \(-0.307998\pi\) |
−0.429561 | + | 0.903038i | \(0.641332\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −324630. | + | 57241.0i | −1.01693 | + | 0.179312i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 368335. | + | 134063.i | 1.14572 | + | 0.417007i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | − | 51452.5i | − | 0.158921i | −0.996838 | − | 0.0794606i | \(-0.974680\pi\) | ||
0.996838 | − | 0.0794606i | \(-0.0253198\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −313784. | −0.962406 | −0.481203 | − | 0.876609i | \(-0.659800\pi\) | ||||
−0.481203 | + | 0.876609i | \(0.659800\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −9602.73 | + | 26383.3i | −0.0292473 | + | 0.0803562i | ||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −60741.8 | − | 344484.i | −0.183718 | − | 1.04192i | ||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 292982. | − | 507460.i | 0.880014 | − | 1.52423i | 0.0286892 | − | 0.999588i | \(-0.490867\pi\) |
0.851324 | − | 0.524640i | \(-0.175800\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 316804. | + | 265830.i | 0.945002 | + | 0.792951i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 190800. | + | 330475.i | 0.565230 | + | 0.979008i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 39142.4 | + | 107543.i | 0.115162 | + | 0.316406i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 745463. | + | 131445.i | 2.17828 | + | 0.384090i | ||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 86046.8 | − | 72201.8i | 0.249723 | − | 0.209542i | −0.509330 | − | 0.860571i | \(-0.670107\pi\) |
0.759053 | + | 0.651029i | \(0.225662\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −24764.2 | + | 446421.i | −0.0713828 | + | 1.28681i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 100967. | + | 120327.i | 0.289070 | + | 0.344500i | ||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 66008.9 | − | 374355.i | 0.187712 | − | 1.06457i | −0.734708 | − | 0.678383i | \(-0.762681\pi\) |
0.922421 | − | 0.386187i | \(-0.126208\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 781693. | − | 284513.i | 2.20802 | − | 0.803652i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −534758. | + | 308743.i | −1.50040 | + | 0.866259i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −37860.1 | + | 45119.9i | −0.105518 | + | 0.125752i | −0.816219 | − | 0.577743i | \(-0.803934\pi\) |
0.710700 | + | 0.703495i | \(0.248378\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −276837. | − | 159832.i | −0.766435 | − | 0.442502i | 0.0651661 | − | 0.997874i | \(-0.479242\pi\) |
−0.831602 | + | 0.555373i | \(0.812576\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −429793. | + | 75784.0i | −1.18202 | + | 0.208422i | ||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −362328. | − | 131876.i | −0.989899 | − | 0.360294i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | − | 350213.i | − | 0.950507i | −0.879849 | − | 0.475253i | \(-0.842356\pi\) | ||
0.879849 | − | 0.475253i | \(-0.157644\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 511382. | 1.37883 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −345097. | + | 948146.i | −0.924397 | + | 2.53976i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −12206.6 | − | 69227.1i | −0.0324844 | − | 0.184228i | 0.964248 | − | 0.265001i | \(-0.0853722\pi\) |
−0.996733 | + | 0.0807729i | \(0.974261\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −226179. | + | 391754.i | −0.598002 | + | 1.03577i | ||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 542281. | + | 455027.i | 1.42447 | + | 1.19527i | 0.948892 | + | 0.315600i | \(0.102206\pi\) |
0.475579 | + | 0.879673i | \(0.342239\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −167678. | − | 290427.i | −0.437617 | − | 0.757976i | 0.559888 | − | 0.828568i | \(-0.310844\pi\) |
−0.997505 | + | 0.0705929i | \(0.977511\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −33415.8 | − | 91809.2i | −0.0866501 | − | 0.238069i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −320829. | − | 56570.8i | −0.826604 | − | 0.145753i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −275429. | + | 231113.i | −0.705099 | + | 0.591648i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −164219. | − | 219317.i | −0.417723 | − | 0.557876i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 152944. | + | 182272.i | 0.386573 | + | 0.460700i | ||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −40019.6 | + | 226962.i | −0.100511 | + | 0.570026i | 0.892408 | + | 0.451230i | \(0.149015\pi\) |
−0.992919 | + | 0.118796i | \(0.962096\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −304944. | + | 110991.i | −0.761050 | + | 0.277000i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −102433. | + | 59139.8i | −0.254035 | + | 0.146667i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −56953.2 | + | 67874.2i | −0.140359 | + | 0.167273i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 92545.0 | + | 53430.9i | 0.226648 | + | 0.130855i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 391871. | − | 69097.5i | 0.953734 | − | 0.168169i | 0.324935 | − | 0.945736i | \(-0.394658\pi\) |
0.628800 | + | 0.777567i | \(0.283547\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 131116. | + | 47722.2i | 0.317126 | + | 0.115425i | 0.495679 | − | 0.868506i | \(-0.334919\pi\) |
−0.178553 | + | 0.983930i | \(0.557141\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | − | 200120.i | − | 0.481028i | ||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 27790.7 | 0.0663883 | 0.0331941 | − | 0.999449i | \(-0.489432\pi\) | ||||
0.0331941 | + | 0.999449i | \(0.489432\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −12186.2 | + | 33481.2i | −0.0289320 | + | 0.0794899i | ||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 134691. | + | 763870.i | 0.317816 | + | 1.80243i | ||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −319447. | + | 553298.i | −0.749155 | + | 1.29758i | 0.199073 | + | 0.979985i | \(0.436207\pi\) |
−0.948228 | + | 0.317590i | \(0.897126\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 364870. | + | 306162.i | 0.850463 | + | 0.713623i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −270017. | − | 467683.i | −0.625548 | − | 1.08348i | ||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 26699.8 | + | 73357.1i | 0.0614805 | + | 0.168916i | 0.966630 | − | 0.256178i | \(-0.0824632\pi\) |
−0.905149 | + | 0.425094i | \(0.860241\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −49357.5 | − | 8703.06i | −0.112967 | − | 0.0199191i | 0.116879 | − | 0.993146i | \(-0.462711\pi\) |
−0.229846 | + | 0.973227i | \(0.573822\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 1.32884e6 | − | 1.11503e6i | 3.02305 | − | 2.53664i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −79916.4 | − | 667731.i | −0.180714 | − | 1.50993i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −273498. | − | 325942.i | −0.614755 | − | 0.732636i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −78021.4 | + | 442481.i | −0.174326 | + | 0.988650i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −31828.9 | + | 11584.8i | −0.0706931 | + | 0.0257302i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −615226. | + | 355201.i | −1.35833 | + | 0.784231i | −0.989398 | − | 0.145227i | \(-0.953609\pi\) |
−0.368929 | + | 0.929457i | \(0.620276\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 80905.4 | − | 96419.3i | 0.177570 | − | 0.211620i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −318414. | − | 183836.i | −0.694727 | − | 0.401101i | 0.110653 | − | 0.993859i | \(-0.464706\pi\) |
−0.805380 | + | 0.592758i | \(0.798039\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 213669. | − | 37675.6i | 0.463449 | − | 0.0817186i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −660182. | − | 240286.i | −1.42354 | − | 0.518126i | ||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 47025.2i | 0.100807i | 0.998729 | + | 0.0504033i | \(0.0160507\pi\) | ||||
−0.998729 | + | 0.0504033i | \(0.983949\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 153984. | 0.328167 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 198629. | − | 545730.i | 0.420853 | − | 1.15628i | ||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 101718. | + | 576871.i | 0.214269 | + | 1.21518i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 153603. | − | 266049.i | 0.321695 | − | 0.557192i | −0.659143 | − | 0.752018i | \(-0.729081\pi\) |
0.980838 | + | 0.194826i | \(0.0624141\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −162808. | − | 136612.i | −0.339008 | − | 0.284461i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 125088. | + | 216659.i | 0.258968 | + | 0.448546i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 158532. | + | 435563.i | 0.326326 | + | 0.896573i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −1.05251e6 | − | 185586.i | −2.15413 | − | 0.379830i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 46126.4 | − | 38704.6i | 0.0938671 | − | 0.0787639i | −0.594646 | − | 0.803987i | \(-0.702708\pi\) |
0.688514 | + | 0.725223i | \(0.258264\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 171656. | − | 86803.3i | 0.347335 | − | 0.175641i | ||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −880691. | − | 1.04957e6i | −1.77193 | − | 2.11170i | ||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −34096.7 | + | 193372.i | −0.0682140 | + | 0.386861i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 233239. | − | 84891.9i | 0.463989 | − | 0.168878i | −0.0994384 | − | 0.995044i | \(-0.531705\pi\) |
0.563428 | + | 0.826165i | \(0.309482\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 394746. | − | 227907.i | 0.780869 | − | 0.450835i | ||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 414835. | − | 494382.i | 0.816012 | − | 0.972486i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 627462. | + | 362265.i | 1.22737 | + | 0.708622i | ||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 507002. | − | 89398.1i | 0.986214 | − | 0.173896i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −520380. | − | 189403.i | −1.00661 | − | 0.366377i | −0.214482 | − | 0.976728i | \(-0.568806\pi\) |
−0.792131 | + | 0.610351i | \(0.791029\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 173038.i | 0.332867i | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 13409.8 | 0.0256535 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 187477. | − | 515088.i | 0.356674 | − | 0.979954i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 67242.9 | + | 381353.i | 0.127226 | + | 0.721537i | 0.979961 | + | 0.199192i | \(0.0638317\pi\) |
−0.852734 | + | 0.522345i | \(0.825057\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −156228. | + | 270595.i | −0.293971 | + | 0.509172i | ||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −157082. | − | 131808.i | −0.293963 | − | 0.246664i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 2211.44 | + | 3830.33i | 0.00411593 | + | 0.00712900i | 0.868076 | − | 0.496431i | \(-0.165357\pi\) |
−0.863960 | + | 0.503560i | \(0.832023\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | −41149.9 | − | 113059.i | −0.0761718 | − | 0.209280i | ||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −411378. | − | 72537.0i | −0.757366 | − | 0.133544i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 305398. | − | 256259.i | 0.559213 | − | 0.469236i | −0.318833 | − | 0.947811i | \(-0.603291\pi\) |
0.878047 | + | 0.478575i | \(0.158847\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −632835. | − | 1.25145e6i | −1.15253 | − | 2.27917i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 474303. | + | 565252.i | 0.859168 | + | 1.02392i | 0.999429 | + | 0.0338014i | \(0.0107614\pi\) |
−0.140261 | + | 0.990115i | \(0.544794\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 273260. | − | 1.54973e6i | 0.492338 | − | 2.79219i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −454012. | + | 165247.i | −0.813629 | + | 0.296137i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −460065. | + | 265618.i | −0.820078 | + | 0.473472i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 542438. | − | 646452.i | 0.961768 | − | 1.14619i | −0.0274331 | − | 0.999624i | \(-0.508733\pi\) |
0.989201 | − | 0.146567i | \(-0.0468222\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −326771. | − | 188661.i | −0.576307 | − | 0.332731i | ||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −811720. | + | 143128.i | −1.42401 | + | 0.251091i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 787851. | + | 286754.i | 1.37484 | + | 0.500401i | 0.920610 | − | 0.390483i | \(-0.127692\pi\) |
0.454231 | + | 0.890884i | \(0.349914\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 395479.i | 0.686499i | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 258202. | 0.445851 | 0.222925 | − | 0.974836i | \(-0.428439\pi\) | ||||
0.222925 | + | 0.974836i | \(0.428439\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 363585. | − | 998942.i | 0.624535 | − | 1.71590i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 182892. | + | 1.03723e6i | 0.312516 | + | 1.77236i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −91183.6 | + | 157935.i | −0.154998 | + | 0.268464i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 202961. | + | 170305.i | 0.343211 | + | 0.287988i | 0.798057 | − | 0.602582i | \(-0.205861\pi\) |
−0.454846 | + | 0.890570i | \(0.650306\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 474340. | + | 821581.i | 0.797960 | + | 1.38211i | ||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 66157.2 | + | 181765.i | 0.110718 | + | 0.304195i | 0.982661 | − | 0.185413i | \(-0.0593622\pi\) |
−0.871943 | + | 0.489608i | \(0.837140\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 818784. | + | 144374.i | 1.36322 | + | 0.240372i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 255632. | − | 214500.i | 0.423421 | − | 0.355293i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 372063. | − | 44529.8i | 0.613114 | − | 0.0733797i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 65746.3 | + | 78353.4i | 0.107788 | + | 0.128456i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 26585.8 | − | 150775.i | 0.0433636 | − | 0.245927i | ||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −905798. | + | 329683.i | −1.46991 | + | 0.535005i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 90304.7 | − | 52137.4i | 0.145801 | − | 0.0841783i | −0.425325 | − | 0.905041i | \(-0.639840\pi\) |
0.571126 | + | 0.820862i | \(0.306507\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −679186. | + | 809422.i | −1.09102 | + | 1.30023i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 410248. | + | 236857.i | 0.655682 | + | 0.378558i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −170734. | + | 30104.9i | −0.271502 | + | 0.0478731i | ||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −747446. | − | 272048.i | −1.18262 | − | 0.430439i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 1.02433e6i | 1.61259i | 0.591515 | + | 0.806294i | \(0.298530\pi\) | ||||
−0.591515 | + | 0.806294i | \(0.701470\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −1.40391e6 | −2.19910 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 141074. | − | 387598.i | 0.219878 | − | 0.604111i | ||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −89758.1 | − | 509043.i | −0.139201 | − | 0.789448i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −485351. | + | 840653.i | −0.748970 | + | 1.29725i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 59286.2 | + | 49747.0i | 0.0910346 | + | 0.0763871i | ||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 69501.1 | + | 120379.i | 0.106193 | + | 0.183931i | 0.914225 | − | 0.405207i | \(-0.132801\pi\) |
−0.808032 | + | 0.589138i | \(0.799467\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −33162.9 | − | 91114.3i | −0.0504209 | − | 0.138530i | 0.911926 | − | 0.410355i | \(-0.134595\pi\) |
−0.962347 | + | 0.271825i | \(0.912373\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −49331.6 | − | 8698.50i | −0.0746353 | − | 0.0131602i | ||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −957719. | + | 803621.i | −1.44186 | + | 1.20986i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −132696. | + | 99359.3i | −0.198799 | + | 0.148855i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −699231. | − | 833311.i | −1.04244 | − | 1.24234i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −97133.2 | + | 550870.i | −0.144106 | + | 0.817265i | 0.823975 | + | 0.566626i | \(0.191752\pi\) |
−0.968081 | + | 0.250639i | \(0.919359\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 42360.5 | − | 15418.0i | 0.0625405 | − | 0.0227629i | −0.310560 | − | 0.950554i | \(-0.600517\pi\) |
0.373101 | + | 0.927791i | \(0.378294\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −441229. | + | 254744.i | −0.648270 | + | 0.374279i | ||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 388588. | − | 463101.i | 0.568170 | − | 0.677118i | −0.403085 | − | 0.915163i | \(-0.632062\pi\) |
0.971254 | + | 0.238044i | \(0.0765064\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −637152. | − | 367860.i | −0.927116 | − | 0.535271i | −0.0412175 | − | 0.999150i | \(-0.513124\pi\) |
−0.885898 | + | 0.463880i | \(0.846457\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 1.36491e6 | − | 240671.i | 1.97653 | − | 0.348515i | ||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −115847. | − | 42165.0i | −0.166954 | − | 0.0607662i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 1.65407e6i | 2.37235i | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 232221. | 0.331475 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 327167. | − | 898883.i | 0.464777 | − | 1.27697i | −0.457076 | − | 0.889427i | \(-0.651103\pi\) |
0.921854 | − | 0.387538i | \(-0.126674\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 7037.72 | + | 39912.9i | 0.00995039 | + | 0.0564315i | ||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 465879. | − | 806925.i | 0.655568 | − | 1.13548i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 2.05308e6 | + | 1.72273e6i | 2.87536 | + | 2.41271i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 277054. | + | 479871.i | 0.386187 | + | 0.668895i | ||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 90142.4 | + | 247664.i | 0.125059 | + | 0.343596i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −273434. | − | 48213.8i | −0.377566 | − | 0.0665751i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 358823. | − | 301088.i | 0.493153 | − | 0.413805i | −0.362002 | − | 0.932177i | \(-0.617907\pi\) |
0.855155 | + | 0.518373i | \(0.173462\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 850152. | + | 47160.3i | 1.16296 | + | 0.0645125i | ||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 21649.4 | + | 25800.7i | 0.0294770 | + | 0.0351293i | 0.780582 | − | 0.625054i | \(-0.214923\pi\) |
−0.751105 | + | 0.660183i | \(0.770479\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −129727. | + | 735720.i | −0.175811 | + | 0.997072i | 0.761393 | + | 0.648290i | \(0.224516\pi\) |
−0.937204 | + | 0.348782i | \(0.886596\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 610867. | − | 222338.i | 0.824025 | − | 0.299921i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −837032. | + | 483261.i | −1.12388 | + | 0.648873i | −0.942389 | − | 0.334519i | \(-0.891426\pi\) |
−0.181493 | + | 0.983392i | \(0.558093\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 1.21076e6 | − | 1.44292e6i | 1.61817 | − | 1.92846i | ||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 1.21475e6 | + | 701336.i | 1.61603 | + | 0.933014i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 429655. | − | 75759.8i | 0.568959 | − | 0.100323i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −2.00912e6 | − | 731261.i | −2.64832 | − | 0.963910i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 274704.i | 0.360442i | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −86241.7 | −0.112642 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 476224. | − | 1.30842e6i | 0.619174 | − | 1.70117i | −0.0898265 | − | 0.995957i | \(-0.528631\pi\) |
0.709000 | − | 0.705208i | \(-0.249147\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −15381.3 | − | 87231.4i | −0.0199074 | − | 0.112900i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 306465. | − | 530813.i | 0.394847 | − | 0.683895i | −0.598235 | − | 0.801321i | \(-0.704131\pi\) |
0.993082 | + | 0.117426i | \(0.0374643\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 1.05100e6 | + | 881896.i | 1.34798 | + | 1.13109i | 0.979499 | + | 0.201450i | \(0.0645654\pi\) |
0.368478 | + | 0.929637i | \(0.379879\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −123818. | − | 214459.i | −0.158087 | − | 0.273815i | ||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −311606. | − | 856129.i | −0.396057 | − | 1.08816i | −0.964188 | − | 0.265220i | \(-0.914555\pi\) |
0.568131 | − | 0.822938i | \(-0.307667\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 167394. | + | 29516.1i | 0.211805 | + | 0.0373469i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −363888. | + | 305338.i | −0.458366 | + | 0.384614i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −258688. | + | 1.10508e6i | −0.324394 | + | 1.38577i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 100816. | + | 120147.i | 0.125858 | + | 0.149992i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −351500. | + | 1.99345e6i | −0.436858 | + | 2.47754i | ||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 950326. | − | 345890.i | 1.17585 | − | 0.427976i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −705842. | + | 407518.i | −0.869477 | + | 0.501993i | ||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −184857. | + | 220304.i | −0.226705 | + | 0.270176i | ||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −1.07728e6 | − | 621968.i | −1.31532 | − | 0.759401i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −1.39765e6 | + | 246443.i | −1.69896 | + | 0.299572i | −0.937330 | − | 0.348442i | \(-0.886711\pi\) |
−0.761628 | + | 0.648014i | \(0.775600\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −233616. | − | 85029.2i | −0.282732 | − | 0.102906i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | − | 994499.i | − | 1.19831i | −0.800635 | − | 0.599153i | \(-0.795504\pi\) | ||
0.800635 | − | 0.599153i | \(-0.204496\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −462449. | −0.554782 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 80516.7 | − | 221218.i | 0.0961709 | − | 0.264227i | ||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −118859. | − | 674084.i | −0.141349 | − | 0.801633i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −105274. | + | 182340.i | −0.124649 | + | 0.215899i | −0.921596 | − | 0.388151i | \(-0.873114\pi\) |
0.796947 | + | 0.604050i | \(0.206447\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 412468. | + | 346102.i | 0.486263 | + | 0.408023i | ||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 261761. | + | 453384.i | 0.307257 | + | 0.532185i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −122338. | − | 336122.i | −0.142981 | − | 0.392838i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −215758. | − | 38043.9i | −0.251077 | − | 0.0442717i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −8081.27 | + | 6780.99i | −0.00936372 | + | 0.00785709i | −0.647457 | − | 0.762102i | \(-0.724168\pi\) |
0.638094 | + | 0.769959i | \(0.279723\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −54536.3 | + | 83419.3i | −0.0629196 | + | 0.0962425i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −422151. | − | 503100.i | −0.484958 | − | 0.577951i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −175056. | + | 992791.i | −0.200241 | + | 1.13562i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 31055.5 | − | 11303.3i | 0.0353720 | − | 0.0128744i | −0.324274 | − | 0.945963i | \(-0.605120\pi\) |
0.359646 | + | 0.933089i | \(0.382898\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 1.83345e6 | − | 1.05854e6i | 2.07940 | − | 1.20054i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −894179. | + | 1.06564e6i | −1.00982 | + | 1.20346i | −0.0308387 | + | 0.999524i | \(0.509818\pi\) |
−0.978984 | + | 0.203936i | \(0.934627\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −468416. | − | 270440.i | −0.526755 | − | 0.304122i | ||||
\(944\) | 0 | 0 | ||||||||
\(945\) | −343978. | + | 60652.6i | −0.385183 | + | 0.0679181i | ||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −385244. | − | 140217.i | −0.429572 | − | 0.156351i | 0.118180 | − | 0.992992i | \(-0.462294\pi\) |
−0.547752 | + | 0.836641i | \(0.684516\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | − | 2.64566e6i | − | 2.93767i | ||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −616598. | −0.681775 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 60967.8 | − | 167508.i | 0.0671297 | − | 0.184437i | −0.901592 | − | 0.432588i | \(-0.857601\pi\) |
0.968721 | + | 0.248151i | \(0.0798228\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −14502.1 | − | 82245.7i | −0.0159010 | − | 0.0901793i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −309865. | + | 536701.i | −0.338336 | + | 0.586015i | ||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −169515. | − | 142240.i | −0.184319 | − | 0.154662i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 305210. | + | 528640.i | 0.330486 | + | 0.572418i | ||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −230046. | − | 632045.i | −0.248063 | − | 0.681547i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −1.21145e6 | − | 213612.i | −1.30092 | − | 0.229388i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −1.11852e6 | + | 938550.i | −1.19616 | + | 1.00370i | −0.196434 | + | 0.980517i | \(0.562936\pi\) |
−0.999731 | + | 0.0231844i | \(0.992620\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 1.33509e6 | − | 1.42296e6i | 1.42188 | − | 1.51547i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −274314. | − | 326915.i | −0.290944 | − | 0.346734i | 0.600697 | − | 0.799477i | \(-0.294890\pi\) |
−0.891641 | + | 0.452743i | \(0.850445\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 62430.3 | − | 354060.i | 0.0659431 | − | 0.373982i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −2.45048e6 | + | 891900.i | −2.57775 | + | 0.938225i | ||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 1.57184e6 | − | 907502.i | 1.64672 | − | 0.950733i | 0.668353 | − | 0.743844i | \(-0.267000\pi\) |
0.978365 | − | 0.206889i | \(-0.0663338\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 253773. | − | 302435.i | 0.264777 | − | 0.315549i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 1.16563e6 | + | 672974.i | 1.21121 | + | 0.699295i | ||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 1.50159e6 | − | 264772.i | 1.55398 | − | 0.274009i | 0.670297 | − | 0.742093i | \(-0.266167\pi\) |
0.883684 | + | 0.468084i | \(0.155056\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −439051. | − | 159802.i | −0.452525 | − | 0.164706i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 1.96895e6i | 2.02116i | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 239281. | 0.244634 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 119897. | − | 329413.i | 0.122084 | − | 0.335424i | −0.863563 | − | 0.504241i | \(-0.831772\pi\) |
0.985647 | + | 0.168817i | \(0.0539946\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 102367. | + | 580553.i | 0.103815 | + | 0.588767i | ||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 918365. | − | 1.59066e6i | 0.927618 | − | 1.60668i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −17591.6 | − | 14761.1i | −0.0176976 | − | 0.0148501i | 0.633896 | − | 0.773418i | \(-0.281455\pi\) |
−0.651594 | + | 0.758568i | \(0.725899\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −49953.3 | − | 86521.6i | −0.0500533 | − | 0.0866949i |
(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 | 76.5.j.a.13.2 | ✓ | 42 | |
19.3 | odd | 18 | inner | 76.5.j.a.41.2 | yes | 42 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
76.5.j.a.13.2 | ✓ | 42 | 1.1 | even | 1 | trivial | |
76.5.j.a.41.2 | yes | 42 | 19.3 | odd | 18 | inner |