Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [224,3,Mod(17,224)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(224, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 3, 1]))
N = Newforms(chi, 3, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("224.17");
S:= CuspForms(chi, 3);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 224 = 2^{5} \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 3 \) |
Character orbit: | \([\chi]\) | \(=\) | 224.n (of order \(6\), degree \(2\), not minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(6.10355792167\) |
Analytic rank: | \(0\) |
Dimension: | \(28\) |
Relative dimension: | \(14\) over \(\Q(\zeta_{6})\) |
Twist minimal: | no (minimal twist has level 56) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 145.12 | ||
Character | \(\chi\) | \(=\) | 224.145 |
Dual form | 224.3.n.a.17.12 |
$q$-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 \(\left(\mathbb{Z}/224\mathbb{Z}\right)^\times\).
\(n\) | \(127\) | \(129\) | \(197\) |
\(\chi(n)\) | \(1\) | \(e\left(\frac{5}{6}\right)\) | \(-1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | 1.93494 | + | 3.35141i | 0.644980 | + | 1.11714i | 0.984306 | + | 0.176469i | \(0.0564676\pi\) |
−0.339326 | + | 0.940669i | \(0.610199\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −2.33882 | + | 4.05096i | −0.467764 | + | 0.810191i | −0.999322 | − | 0.0368311i | \(-0.988274\pi\) |
0.531557 | + | 0.847022i | \(0.321607\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −6.95505 | − | 0.792023i | −0.993578 | − | 0.113146i | ||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −2.98798 | + | 5.17534i | −0.331998 | + | 0.575037i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −12.6383 | + | 7.29671i | −1.14893 | + | 0.663337i | −0.948627 | − | 0.316396i | \(-0.897527\pi\) |
−0.200306 | + | 0.979733i | \(0.564194\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 12.7102 | 0.977705 | 0.488853 | − | 0.872366i | \(-0.337416\pi\) | ||||
0.488853 | + | 0.872366i | \(0.337416\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −18.1019 | −1.20679 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −16.9068 | + | 9.76116i | −0.994519 | + | 0.574186i | −0.906622 | − | 0.421944i | \(-0.861348\pi\) |
−0.0878969 | + | 0.996130i | \(0.528015\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 8.86233 | − | 15.3500i | 0.466439 | − | 0.807895i | −0.532827 | − | 0.846224i | \(-0.678870\pi\) |
0.999265 | + | 0.0383291i | \(0.0122035\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −10.8032 | − | 24.8418i | −0.514438 | − | 1.18294i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 4.43038 | − | 7.67364i | 0.192625 | − | 0.333636i | −0.753494 | − | 0.657454i | \(-0.771633\pi\) |
0.946119 | + | 0.323818i | \(0.104967\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 1.55984 | + | 2.70172i | 0.0623936 | + | 0.108069i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 11.7027 | 0.433432 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 35.4981i | 1.22407i | 0.790830 | + | 0.612036i | \(0.209649\pi\) | ||||
−0.790830 | + | 0.612036i | \(0.790351\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −25.1331 | + | 14.5106i | −0.810747 | + | 0.468085i | −0.847215 | − | 0.531250i | \(-0.821722\pi\) |
0.0364685 | + | 0.999335i | \(0.488389\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −48.9086 | − | 28.2374i | −1.48208 | − | 0.855678i | ||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 19.4751 | − | 26.3222i | 0.556430 | − | 0.752063i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 10.5802 | + | 6.10847i | 0.285951 | + | 0.165094i | 0.636114 | − | 0.771595i | \(-0.280541\pi\) |
−0.350163 | + | 0.936689i | \(0.613874\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 24.5934 | + | 42.5970i | 0.630600 | + | 1.09223i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | − | 22.0903i | − | 0.538788i | −0.963030 | − | 0.269394i | \(-0.913177\pi\) | ||
0.963030 | − | 0.269394i | \(-0.0868233\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 79.8001i | 1.85582i | 0.372809 | + | 0.927908i | \(0.378395\pi\) | ||||
−0.372809 | + | 0.927908i | \(0.621605\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −13.9767 | − | 24.2084i | −0.310593 | − | 0.537964i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 36.5041 | + | 21.0756i | 0.776682 | + | 0.448418i | 0.835253 | − | 0.549865i | \(-0.185321\pi\) |
−0.0585708 | + | 0.998283i | \(0.518654\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 47.7454 | + | 11.0171i | 0.974396 | + | 0.224839i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −65.4273 | − | 37.7745i | −1.28289 | − | 0.740676i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −31.3096 | + | 18.0766i | −0.590748 | + | 0.341068i | −0.765393 | − | 0.643563i | \(-0.777455\pi\) |
0.174645 | + | 0.984631i | \(0.444122\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | − | 68.2627i | − | 1.24114i | ||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 68.5923 | 1.20337 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −1.20348 | − | 2.08449i | −0.0203979 | − | 0.0353303i | 0.855646 | − | 0.517561i | \(-0.173160\pi\) |
−0.876044 | + | 0.482231i | \(0.839827\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −14.6224 | + | 25.3268i | −0.239712 | + | 0.415194i | −0.960632 | − | 0.277825i | \(-0.910386\pi\) |
0.720919 | + | 0.693019i | \(0.243720\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 24.8805 | − | 33.6282i | 0.394929 | − | 0.533780i | ||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −29.7268 | + | 51.4883i | −0.457335 | + | 0.792128i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 35.2303 | − | 20.3402i | 0.525825 | − | 0.303585i | −0.213490 | − | 0.976945i | \(-0.568483\pi\) |
0.739315 | + | 0.673360i | \(0.235150\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 34.2900 | 0.496957 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 22.6174 | 0.318554 | 0.159277 | − | 0.987234i | \(-0.449084\pi\) | ||||
0.159277 | + | 0.987234i | \(0.449084\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 66.1587 | − | 38.1967i | 0.906283 | − | 0.523243i | 0.0270498 | − | 0.999634i | \(-0.491389\pi\) |
0.879233 | + | 0.476391i | \(0.158055\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −6.03639 | + | 10.4553i | −0.0804852 | + | 0.139404i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 93.6789 | − | 40.7391i | 1.21661 | − | 0.529080i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 68.4014 | − | 118.475i | 0.865840 | − | 1.49968i | −0.000370612 | − | 1.00000i | \(-0.500118\pi\) |
0.866211 | − | 0.499679i | \(-0.166549\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 49.5358 | + | 85.7985i | 0.611553 | + | 1.05924i | ||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 49.9942 | 0.602340 | 0.301170 | − | 0.953571i | \(-0.402623\pi\) | ||||
0.301170 | + | 0.953571i | \(0.402623\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | − | 91.3184i | − | 1.07433i | ||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −118.969 | + | 68.6866i | −1.36746 | + | 0.789502i | ||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 0.970023 | + | 0.560043i | 0.0108991 | + | 0.00629262i | 0.505440 | − | 0.862862i | \(-0.331330\pi\) |
−0.494541 | + | 0.869155i | \(0.664664\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −88.3998 | − | 10.0667i | −0.971427 | − | 0.110624i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −97.2622 | − | 56.1544i | −1.04583 | − | 0.603810i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 41.4548 | + | 71.8018i | 0.436366 | + | 0.755809i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | − | 158.827i | − | 1.63740i | −0.574225 | − | 0.818698i | \(-0.694696\pi\) | ||
0.574225 | − | 0.818698i | \(-0.305304\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | − | 87.2097i | − | 0.880906i | ||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 34.8122 | + | 60.2965i | 0.344675 | + | 0.596995i | 0.985295 | − | 0.170864i | \(-0.0546557\pi\) |
−0.640620 | + | 0.767858i | \(0.721322\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −16.9911 | − | 9.80983i | −0.164962 | − | 0.0952411i | 0.415246 | − | 0.909709i | \(-0.363696\pi\) |
−0.580208 | + | 0.814468i | \(0.697029\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 125.900 | + | 14.3371i | 1.19904 | + | 0.136544i | ||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 38.7540 | + | 22.3747i | 0.362187 | + | 0.209109i | 0.670040 | − | 0.742325i | \(-0.266277\pi\) |
−0.307852 | + | 0.951434i | \(0.599610\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 49.0210 | − | 28.3023i | 0.449734 | − | 0.259654i | −0.257984 | − | 0.966149i | \(-0.583058\pi\) |
0.707718 | + | 0.706495i | \(0.249725\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 47.2781i | 0.425929i | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −188.632 | −1.66931 | −0.834657 | − | 0.550770i | \(-0.814334\pi\) | ||||
−0.834657 | + | 0.550770i | \(0.814334\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 20.7237 | + | 35.8945i | 0.180206 | + | 0.312126i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −37.9777 | + | 65.7794i | −0.324596 | + | 0.562217i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 125.319 | − | 54.4987i | 1.05310 | − | 0.457972i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 45.9838 | − | 79.6463i | 0.380032 | − | 0.658234i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 74.0337 | − | 42.7434i | 0.601900 | − | 0.347507i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −131.534 | −1.05227 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −45.8547 | −0.361060 | −0.180530 | − | 0.983569i | \(-0.557781\pi\) | ||||
−0.180530 | + | 0.983569i | \(0.557781\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −267.443 | + | 154.408i | −2.07320 | + | 1.19696i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −60.4982 | + | 104.786i | −0.461818 | + | 0.799893i | −0.999052 | − | 0.0435409i | \(-0.986136\pi\) |
0.537233 | + | 0.843434i | \(0.319469\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −73.7955 | + | 99.7409i | −0.554854 | + | 0.749932i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −27.3704 | + | 47.4069i | −0.202744 | + | 0.351163i | ||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 72.6207 | + | 125.783i | 0.530078 | + | 0.918122i | 0.999384 | + | 0.0350869i | \(0.0111708\pi\) |
−0.469306 | + | 0.883036i | \(0.655496\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −86.3503 | −0.621225 | −0.310613 | − | 0.950537i | \(-0.600534\pi\) | ||||
−0.310613 | + | 0.950537i | \(0.600534\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 163.120i | 1.15688i | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −160.634 | + | 92.7424i | −1.12332 | + | 0.648548i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −143.801 | − | 83.0236i | −0.991732 | − | 0.572577i | ||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 55.4615 | + | 181.332i | 0.377289 | + | 1.23355i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 189.536 | + | 109.429i | 1.27205 | + | 0.734421i | 0.975374 | − | 0.220556i | \(-0.0707873\pi\) |
0.296680 | + | 0.954977i | \(0.404121\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 41.6552 | + | 72.1490i | 0.275862 | + | 0.477808i | 0.970352 | − | 0.241695i | \(-0.0777033\pi\) |
−0.694490 | + | 0.719502i | \(0.744370\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | − | 116.665i | − | 0.762514i | ||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | − | 135.751i | − | 0.875813i | ||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −17.7207 | − | 30.6932i | −0.112871 | − | 0.195498i | 0.804056 | − | 0.594554i | \(-0.202671\pi\) |
−0.916927 | + | 0.399056i | \(0.869338\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −121.164 | − | 69.9543i | −0.762041 | − | 0.439964i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −36.8912 | + | 49.8616i | −0.229138 | + | 0.309699i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 9.05412 | + | 5.22740i | 0.0555468 | + | 0.0320699i | 0.527516 | − | 0.849545i | \(-0.323123\pi\) |
−0.471969 | + | 0.881615i | \(0.656457\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 228.777 | − | 132.084i | 1.38653 | − | 0.800511i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | − | 78.8843i | − | 0.472361i | −0.971709 | − | 0.236181i | \(-0.924104\pi\) | ||
0.971709 | − | 0.236181i | \(-0.0758957\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −7.45163 | −0.0440925 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 52.9610 | + | 91.7311i | 0.309713 | + | 0.536439i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 95.9208 | − | 166.140i | 0.554456 | − | 0.960345i | −0.443490 | − | 0.896279i | \(-0.646260\pi\) |
0.997946 | − | 0.0640660i | \(-0.0204068\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −8.70893 | − | 20.0260i | −0.0497653 | − | 0.114434i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 4.65732 | − | 8.06671i | 0.0263125 | − | 0.0455746i | ||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −60.5426 | + | 34.9543i | −0.338227 | + | 0.195275i | −0.659488 | − | 0.751715i | \(-0.729227\pi\) |
0.321261 | + | 0.946991i | \(0.395893\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −343.635 | −1.89853 | −0.949267 | − | 0.314472i | \(-0.898173\pi\) | ||||
−0.949267 | + | 0.314472i | \(0.898173\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −113.174 | −0.618438 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −49.4903 | + | 28.5732i | −0.267515 | + | 0.154450i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 142.449 | − | 246.728i | 0.761757 | − | 1.31940i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −81.3925 | − | 9.26878i | −0.430648 | − | 0.0490411i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −69.8895 | + | 121.052i | −0.365913 | + | 0.633781i | −0.988922 | − | 0.148434i | \(-0.952577\pi\) |
0.623009 | + | 0.782215i | \(0.285910\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −11.4616 | − | 19.8521i | −0.0593867 | − | 0.102861i | 0.834804 | − | 0.550548i | \(-0.185581\pi\) |
−0.894190 | + | 0.447687i | \(0.852248\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −230.078 | −1.17989 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | − | 287.788i | − | 1.46085i | −0.682992 | − | 0.730426i | \(-0.739322\pi\) | ||
0.682992 | − | 0.730426i | \(-0.260678\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 56.7091 | − | 32.7410i | 0.284970 | − | 0.164528i | −0.350701 | − | 0.936487i | \(-0.614057\pi\) |
0.635671 | + | 0.771960i | \(0.280723\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 136.337 | + | 78.7141i | 0.678293 | + | 0.391613i | ||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 28.1153 | − | 246.891i | 0.138499 | − | 1.21621i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 89.4868 | + | 51.6652i | 0.436521 | + | 0.252026i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 26.4758 | + | 45.8574i | 0.127902 | + | 0.221533i | ||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 258.663i | 1.23762i | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 17.8985i | 0.0848270i | 0.999100 | + | 0.0424135i | \(0.0135047\pi\) | ||||
−0.999100 | + | 0.0424135i | \(0.986495\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 43.7632 | + | 75.8001i | 0.205461 | + | 0.355869i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −323.267 | − | 186.638i | −1.50357 | − | 0.868084i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 186.295 | − | 81.0161i | 0.858502 | − | 0.373346i | ||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 256.026 | + | 147.817i | 1.16907 | + | 0.674962i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −214.889 | + | 124.066i | −0.972346 | + | 0.561384i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | − | 258.973i | − | 1.16132i | −0.814148 | − | 0.580658i | \(-0.802795\pi\) | ||
0.814148 | − | 0.580658i | \(-0.197205\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −18.6431 | −0.0828581 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 58.6721 | + | 101.623i | 0.258468 | + | 0.447679i | 0.965832 | − | 0.259171i | \(-0.0834492\pi\) |
−0.707364 | + | 0.706849i | \(0.750116\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 43.5475 | − | 75.4264i | 0.190164 | − | 0.329373i | −0.755141 | − | 0.655563i | \(-0.772431\pi\) |
0.945304 | + | 0.326190i | \(0.105765\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 317.797 | + | 235.129i | 1.37574 | + | 1.01787i | ||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 155.825 | − | 269.897i | 0.668778 | − | 1.15836i | −0.309468 | − | 0.950910i | \(-0.600151\pi\) |
0.978246 | − | 0.207448i | \(-0.0665159\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −170.753 | + | 98.5843i | −0.726608 | + | 0.419507i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 529.410 | 2.23380 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 140.823 | 0.589218 | 0.294609 | − | 0.955618i | \(-0.404811\pi\) | ||||
0.294609 | + | 0.955618i | \(0.404811\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −41.6447 | + | 24.0436i | −0.172799 | + | 0.0997658i | −0.583905 | − | 0.811822i | \(-0.698476\pi\) |
0.411106 | + | 0.911588i | \(0.365143\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −139.035 | + | 240.816i | −0.572162 | + | 0.991014i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −156.298 | + | 167.647i | −0.637950 | + | 0.684275i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 112.642 | − | 195.101i | 0.456039 | − | 0.789883i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 96.7357 | + | 167.551i | 0.388497 | + | 0.672896i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −152.080 | −0.605895 | −0.302947 | − | 0.953007i | \(-0.597971\pi\) | ||||
−0.302947 | + | 0.953007i | \(0.597971\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 129.309i | 0.511101i | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 306.046 | − | 176.696i | 1.20018 | − | 0.692924i | ||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 126.153 | + | 72.8347i | 0.490869 | + | 0.283403i | 0.724935 | − | 0.688817i | \(-0.241870\pi\) |
−0.234066 | + | 0.972221i | \(0.575203\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −68.7477 | − | 50.8645i | −0.265435 | − | 0.196388i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −183.714 | − | 106.068i | −0.703887 | − | 0.406389i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 176.696 | + | 306.047i | 0.671850 | + | 1.16368i | 0.977379 | + | 0.211495i | \(0.0678333\pi\) |
−0.305529 | + | 0.952183i | \(0.598833\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | − | 169.112i | − | 0.638158i | ||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 4.33460i | 0.0162345i | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 66.6490 | + | 115.439i | 0.247766 | + | 0.429143i | 0.962906 | − | 0.269838i | \(-0.0869703\pi\) |
−0.715140 | + | 0.698981i | \(0.753637\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 326.342 | + | 188.414i | 1.20421 | + | 0.695253i | 0.961489 | − | 0.274842i | \(-0.0886255\pi\) |
0.242725 | + | 0.970095i | \(0.421959\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −137.310 | − | 315.743i | −0.502969 | − | 1.15657i | ||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −39.4273 | − | 22.7634i | −0.143372 | − | 0.0827759i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −67.4788 | + | 38.9589i | −0.243606 | + | 0.140646i | −0.616833 | − | 0.787094i | \(-0.711585\pi\) |
0.373227 | + | 0.927740i | \(0.378251\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | − | 173.430i | − | 0.621613i | ||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 324.564 | 1.15503 | 0.577516 | − | 0.816380i | \(-0.304022\pi\) | ||||
0.577516 | + | 0.816380i | \(0.304022\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −149.741 | − | 259.359i | −0.529119 | − | 0.916462i | −0.999423 | − | 0.0339572i | \(-0.989189\pi\) |
0.470304 | − | 0.882505i | \(-0.344144\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −160.425 | + | 277.864i | −0.562895 | + | 0.974963i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −17.4960 | + | 153.639i | −0.0609618 | + | 0.535328i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 46.0604 | − | 79.7789i | 0.159378 | − | 0.276052i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 532.296 | − | 307.321i | 1.82920 | − | 1.05609i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −81.7250 | −0.278925 | −0.139463 | − | 0.990227i | \(-0.544537\pi\) | ||||
−0.139463 | + | 0.990227i | \(0.544537\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 11.2589 | 0.0381657 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −147.901 | + | 85.3908i | −0.497984 | + | 0.287511i | ||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 56.3108 | − | 97.5332i | 0.188331 | − | 0.326198i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 63.2035 | − | 555.013i | 0.209979 | − | 1.84390i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −134.719 | + | 233.340i | −0.444617 | + | 0.770099i | ||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −68.3986 | − | 118.470i | −0.224258 | − | 0.388425i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 361.930 | 1.17892 | 0.589462 | − | 0.807796i | \(-0.299340\pi\) | ||||
0.589462 | + | 0.807796i | \(0.299340\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | − | 75.9257i | − | 0.245714i | ||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −163.508 | + | 94.4017i | −0.525751 | + | 0.303542i | −0.739284 | − | 0.673393i | \(-0.764836\pi\) |
0.213534 | + | 0.976936i | \(0.431503\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −22.2463 | − | 12.8439i | −0.0710745 | − | 0.0410349i | 0.464042 | − | 0.885813i | \(-0.346399\pi\) |
−0.535116 | + | 0.844779i | \(0.679732\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 78.0351 | + | 179.440i | 0.247730 | + | 0.569651i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −432.257 | − | 249.564i | −1.36359 | − | 0.787268i | −0.373489 | − | 0.927635i | \(-0.621838\pi\) |
−0.990100 | + | 0.140367i | \(0.955172\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −259.019 | − | 448.634i | −0.811972 | − | 1.40638i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 173.174i | 0.539484i | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 346.027i | 1.07129i | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 19.8258 | + | 34.3393i | 0.0610025 | + | 0.105659i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 189.705 | + | 109.526i | 0.580138 | + | 0.334943i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −237.195 | − | 175.494i | −0.720958 | − | 0.533417i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −216.384 | − | 124.930i | −0.653729 | − | 0.377431i | 0.136154 | − | 0.990688i | \(-0.456526\pi\) |
−0.789883 | + | 0.613257i | \(0.789859\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −63.2268 | + | 36.5040i | −0.189870 | + | 0.109622i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 190.288i | 0.568025i | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −84.4039 | −0.250457 | −0.125228 | − | 0.992128i | \(-0.539966\pi\) | ||||
−0.125228 | + | 0.992128i | \(0.539966\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −364.992 | − | 632.185i | −1.07667 | − | 1.86485i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 211.760 | − | 366.778i | 0.620996 | − | 1.07560i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −323.346 | − | 114.440i | −0.942699 | − | 0.333645i | ||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −80.1982 | + | 138.907i | −0.232459 | + | 0.402630i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −326.707 | + | 188.624i | −0.941518 | + | 0.543586i | −0.890436 | − | 0.455109i | \(-0.849600\pi\) |
−0.0510824 | + | 0.998694i | \(0.516267\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 400.193 | 1.14668 | 0.573342 | − | 0.819316i | \(-0.305647\pi\) | ||||
0.573342 | + | 0.819316i | \(0.305647\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 148.743 | 0.423768 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 256.293 | − | 147.971i | 0.726043 | − | 0.419181i | −0.0909296 | − | 0.995857i | \(-0.528984\pi\) |
0.816973 | + | 0.576676i | \(0.195650\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −52.8980 | + | 91.6220i | −0.149008 | + | 0.258090i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 425.132 | + | 314.543i | 1.19085 | + | 0.881074i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −102.587 | + | 177.686i | −0.285757 | + | 0.494946i | −0.972793 | − | 0.231678i | \(-0.925578\pi\) |
0.687035 | + | 0.726624i | \(0.258912\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 23.4181 | + | 40.5613i | 0.0648701 | + | 0.112358i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 355.904 | 0.980451 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 357.341i | 0.979017i | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 306.216 | − | 176.794i | 0.834377 | − | 0.481728i | −0.0209719 | − | 0.999780i | \(-0.506676\pi\) |
0.855349 | + | 0.518052i | \(0.173343\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 114.325 | + | 66.0054i | 0.309823 | + | 0.178876i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 232.077 | − | 100.926i | 0.625545 | − | 0.272037i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 310.062 | + | 179.014i | 0.831264 | + | 0.479931i | 0.854285 | − | 0.519804i | \(-0.173995\pi\) |
−0.0230210 | + | 0.999735i | \(0.507328\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −254.510 | − | 440.824i | −0.678693 | − | 1.17553i | ||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 451.187i | 1.19678i | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 514.679i | 1.35799i | 0.734142 | + | 0.678996i | \(0.237585\pi\) | ||||
−0.734142 | + | 0.678996i | \(0.762415\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −88.7260 | − | 153.678i | −0.232877 | − | 0.403354i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −450.193 | − | 259.919i | −1.17544 | − | 0.678639i | −0.220483 | − | 0.975391i | \(-0.570763\pi\) |
−0.954955 | + | 0.296752i | \(0.904097\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −54.0657 | + | 474.771i | −0.140430 | + | 1.23317i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −412.992 | − | 238.441i | −1.06716 | − | 0.616127i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 91.3278 | − | 52.7281i | 0.234776 | − | 0.135548i | −0.377997 | − | 0.925807i | \(-0.623387\pi\) |
0.612773 | + | 0.790259i | \(0.290054\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 172.982i | 0.442410i | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −468.241 | −1.19145 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 319.957 | + | 554.182i | 0.810018 | + | 1.40299i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −185.762 | + | 321.749i | −0.467914 | + | 0.810450i | −0.999328 | − | 0.0366619i | \(-0.988328\pi\) |
0.531414 | + | 0.847112i | \(0.321661\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −477.063 | − | 54.3267i | −1.19565 | − | 0.136157i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −149.636 | + | 259.177i | −0.373157 | + | 0.646327i | −0.990049 | − | 0.140721i | \(-0.955058\pi\) |
0.616893 | + | 0.787047i | \(0.288391\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −319.446 | + | 184.433i | −0.792671 | + | 0.457649i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −463.421 | −1.14425 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −178.287 | −0.438052 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −17.6410 | + | 10.1850i | −0.0431320 | + | 0.0249023i | −0.521411 | − | 0.853306i | \(-0.674594\pi\) |
0.478279 | + | 0.878208i | \(0.341261\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −281.033 | + | 486.764i | −0.683780 | + | 1.18434i | ||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 6.71929 | + | 15.4509i | 0.0162695 | + | 0.0374113i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −116.927 | + | 202.524i | −0.281753 | + | 0.488010i | ||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −167.083 | − | 289.396i | −0.400678 | − | 0.693994i | ||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 183.085 | 0.436956 | 0.218478 | − | 0.975842i | \(-0.429891\pi\) | ||||
0.218478 | + | 0.975842i | \(0.429891\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 293.022i | 0.696014i | 0.937492 | + | 0.348007i | \(0.113141\pi\) | ||||
−0.937492 | + | 0.348007i | \(0.886859\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −218.147 | + | 125.947i | −0.515714 | + | 0.297748i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −52.7438 | − | 30.4517i | −0.124103 | − | 0.0716510i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 121.759 | − | 164.568i | 0.285150 | − | 0.385405i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −621.636 | − | 358.902i | −1.44903 | − | 0.836601i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −37.6108 | − | 65.1439i | −0.0872641 | − | 0.151146i | 0.819090 | − | 0.573666i | \(-0.194479\pi\) |
−0.906354 | + | 0.422520i | \(0.861146\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | − | 506.209i | − | 1.16907i | −0.811367 | − | 0.584536i | \(-0.801276\pi\) | ||
0.811367 | − | 0.584536i | \(-0.198724\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | − | 642.583i | − | 1.47720i | ||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −78.5269 | − | 136.013i | −0.179696 | − | 0.311242i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 141.358 | + | 81.6130i | 0.322000 | + | 0.185907i | 0.652284 | − | 0.757975i | \(-0.273811\pi\) |
−0.330284 | + | 0.943882i | \(0.607144\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −199.680 | + | 214.180i | −0.452788 | + | 0.485668i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 98.4732 | + | 56.8535i | 0.222287 | + | 0.128338i | 0.607009 | − | 0.794695i | \(-0.292369\pi\) |
−0.384722 | + | 0.923033i | \(0.625703\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −4.53742 | + | 2.61968i | −0.0101964 | + | 0.00588692i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 846.952i | 1.89475i | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 391.120 | 0.871091 | 0.435546 | − | 0.900167i | \(-0.356555\pi\) | ||||
0.435546 | + | 0.900167i | \(0.356555\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 161.186 | + | 279.183i | 0.357398 | + | 0.619031i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −161.201 | + | 279.208i | −0.355851 | + | 0.616353i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 247.531 | − | 334.559i | 0.544025 | − | 0.735296i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −286.893 | + | 496.913i | −0.627774 | + | 1.08734i | 0.360223 | + | 0.932866i | \(0.382701\pi\) |
−0.987997 | + | 0.154471i | \(0.950633\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −197.855 | + | 114.231i | −0.431056 | + | 0.248870i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 847.131 | 1.83759 | 0.918797 | − | 0.394729i | \(-0.129162\pi\) | ||||
0.918797 | + | 0.394729i | \(0.129162\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −109.055 | −0.235539 | −0.117770 | − | 0.993041i | \(-0.537574\pi\) | ||||
−0.117770 | + | 0.993041i | \(0.537574\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 454.958 | − | 262.670i | 0.978404 | − | 0.564882i | ||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 321.205 | − | 556.343i | 0.687805 | − | 1.19131i | −0.284741 | − | 0.958604i | \(-0.591908\pi\) |
0.972546 | − | 0.232709i | \(-0.0747590\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −261.138 | + | 113.564i | −0.556798 | + | 0.242141i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 68.5771 | − | 118.779i | 0.145599 | − | 0.252185i | ||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −582.278 | − | 1008.53i | −1.23103 | − | 2.13221i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 55.2952 | 0.116411 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | − | 216.050i | − | 0.452936i | ||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 367.909 | − | 212.412i | 0.768077 | − | 0.443449i | −0.0641112 | − | 0.997943i | \(-0.520421\pi\) |
0.832188 | + | 0.554493i | \(0.187088\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 134.476 | + | 77.6397i | 0.279576 | + | 0.161413i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −238.489 | − | 27.1585i | −0.493766 | − | 0.0562288i | ||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 643.403 | + | 371.469i | 1.32660 | + | 0.765915i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 388.616 | + | 673.103i | 0.797980 | + | 1.38214i | 0.920929 | + | 0.389729i | \(0.127431\pi\) |
−0.122949 | + | 0.992413i | \(0.539235\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 40.4588i | 0.0827379i | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | − | 476.370i | − | 0.970203i | −0.874458 | − | 0.485102i | \(-0.838783\pi\) | ||
0.874458 | − | 0.485102i | \(-0.161217\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −346.502 | − | 600.160i | −0.702845 | − | 1.21736i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 353.283 | + | 203.968i | 0.713702 | + | 0.412056i | ||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −157.305 | − | 17.9135i | −0.316509 | − | 0.0360432i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 377.065 | + | 217.698i | 0.755641 | + | 0.436269i | 0.827728 | − | 0.561129i | \(-0.189633\pi\) |
−0.0720876 | + | 0.997398i | \(0.522966\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 264.374 | − | 152.636i | 0.527693 | − | 0.304663i | ||||
\(502\) | 0 | 0 | ||||||||
\(503\) | − | 375.404i | − | 0.746329i | −0.927765 | − | 0.373165i | \(-0.878273\pi\) | ||
0.927765 | − | 0.373165i | \(-0.121727\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −325.678 | −0.644907 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −14.4185 | − | 24.9735i | −0.0284388 | − | 0.0492574i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 73.9117 | − | 128.019i | 0.145210 | − | 0.251510i | −0.784242 | − | 0.620456i | \(-0.786948\pi\) |
0.929451 | + | 0.368945i | \(0.120281\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −490.389 | + | 213.261i | −0.959666 | + | 0.417340i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 103.713 | − | 179.636i | 0.202169 | − | 0.350167i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 79.4784 | − | 45.8869i | 0.154327 | − | 0.0891007i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −615.131 | −1.18981 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 742.404 | 1.43045 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 755.302 | − | 436.074i | 1.44972 | − | 0.836994i | 0.451253 | − | 0.892396i | \(-0.350977\pi\) |
0.998464 | + | 0.0554019i | \(0.0176440\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 178.600 | − | 309.344i | 0.341491 | − | 0.591480i | −0.643219 | − | 0.765683i | \(-0.722401\pi\) |
0.984710 | + | 0.174202i | \(0.0557347\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 50.2642 | − | 67.9364i | 0.0957414 | − | 0.129403i | ||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 283.281 | − | 490.657i | 0.537535 | − | 0.931038i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 225.244 | + | 390.133i | 0.425791 | + | 0.737492i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 14.3839 | 0.0270883 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | − | 280.771i | − | 0.526776i | ||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −181.278 | + | 104.661i | −0.338836 | + | 0.195627i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −234.293 | − | 135.269i | −0.436299 | − | 0.251897i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −683.808 | + | 209.147i | −1.26866 | + | 0.388028i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 807.198 | + | 466.036i | 1.49205 | + | 0.861434i | 0.999958 | − | 0.00911085i | \(-0.00290011\pi\) |
0.492089 | + | 0.870545i | \(0.336233\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −664.912 | − | 1151.66i | −1.22452 | − | 2.12092i | ||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 264.776i | 0.485827i | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | − | 151.397i | − | 0.276778i | −0.990378 | − | 0.138389i | \(-0.955808\pi\) | ||
0.990378 | − | 0.138389i | \(-0.0441924\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −87.3832 | − | 151.352i | −0.159168 | − | 0.275687i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 544.896 | + | 314.596i | 0.988922 | + | 0.570954i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −569.569 | + | 769.821i | −1.02996 | + | 1.39208i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −191.522 | − | 110.575i | −0.345084 | − | 0.199234i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −775.593 | + | 447.789i | −1.39245 | + | 0.803929i | −0.993586 | − | 0.113082i | \(-0.963928\pi\) |
−0.398861 | + | 0.917011i | \(0.630594\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 1014.27i | 1.81444i | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 1102.52 | 1.96527 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 139.958 | + | 242.414i | 0.248592 | + | 0.430575i | 0.963136 | − | 0.269017i | \(-0.0866987\pi\) |
−0.714543 | + | 0.699591i | \(0.753365\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 441.177 | − | 764.142i | 0.780845 | − | 1.35246i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −276.569 | − | 635.966i | −0.487776 | − | 1.12163i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −160.963 | + | 278.796i | −0.282887 | + | 0.489975i | −0.972095 | − | 0.234589i | \(-0.924626\pi\) |
0.689207 | + | 0.724564i | \(0.257959\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 712.583 | − | 411.410i | 1.24796 | − | 0.720508i | 0.277255 | − | 0.960796i | \(-0.410575\pi\) |
0.970702 | + | 0.240288i | \(0.0772419\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −540.928 | −0.944027 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 27.6427 | 0.0480742 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 833.162 | − | 481.027i | 1.44396 | − | 0.833668i | 0.445845 | − | 0.895110i | \(-0.352903\pi\) |
0.998111 | + | 0.0614420i | \(0.0195699\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 44.3551 | − | 76.8253i | 0.0766064 | − | 0.132686i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −347.712 | − | 39.5966i | −0.598472 | − | 0.0681524i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 263.800 | − | 456.914i | 0.452486 | − | 0.783729i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −177.646 | − | 307.692i | −0.303669 | − | 0.525970i | ||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −885.638 | −1.50875 | −0.754377 | − | 0.656442i | \(-0.772061\pi\) | ||||
−0.754377 | + | 0.656442i | \(0.772061\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 514.392i | 0.873331i | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 964.496 | − | 556.852i | 1.63197 | − | 0.942220i | ||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 290.818 | + | 167.904i | 0.490418 | + | 0.283143i | 0.724748 | − | 0.689014i | \(-0.241956\pi\) |
−0.234330 | + | 0.972157i | \(0.575290\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −72.3263 | + | 635.124i | −0.121557 | + | 1.06743i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 219.457 | + | 126.704i | 0.367600 | + | 0.212234i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −30.1532 | − | 52.2269i | −0.0503393 | − | 0.0871902i | 0.839758 | − | 0.542961i | \(-0.182697\pi\) |
−0.890097 | + | 0.455771i | \(0.849364\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 509.153i | 0.847176i | 0.905855 | + | 0.423588i | \(0.139230\pi\) | ||||
−0.905855 | + | 0.423588i | \(0.860770\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 243.105i | 0.403159i | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 215.096 | + | 372.557i | 0.355530 | + | 0.615797i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 900.363 | + | 519.825i | 1.48330 | + | 0.856384i | 0.999820 | − | 0.0189717i | \(-0.00603923\pi\) |
0.483480 | + | 0.875355i | \(0.339373\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 881.835 | − | 383.493i | 1.44800 | − | 0.629709i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 463.973 | + | 267.875i | 0.759366 | + | 0.438420i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −172.277 | + | 99.4641i | −0.281039 | + | 0.162258i | −0.633894 | − | 0.773420i | \(-0.718544\pi\) |
0.352855 | + | 0.935678i | \(0.385211\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 399.876i | 0.650206i | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 136.689 | 0.221538 | 0.110769 | − | 0.993846i | \(-0.464669\pi\) | ||||
0.110769 | + | 0.993846i | \(0.464669\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −230.938 | − | 399.997i | −0.373083 | − | 0.646199i | 0.616955 | − | 0.786998i | \(-0.288366\pi\) |
−0.990038 | + | 0.140799i | \(0.955033\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 51.8472 | − | 89.8019i | 0.0834898 | − | 0.144609i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −6.30299 | − | 4.66341i | −0.0101172 | − | 0.00748541i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 268.638 | − | 465.294i | 0.429821 | − | 0.744471i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −866.888 | + | 500.498i | −1.38260 | + | 0.798242i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −238.503 | −0.379178 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −1042.33 | −1.65187 | −0.825933 | − | 0.563768i | \(-0.809351\pi\) | ||||
−0.825933 | + | 0.563768i | \(0.809351\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −59.9853 | + | 34.6325i | −0.0947635 | + | 0.0547117i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 107.246 | − | 185.755i | 0.168891 | − | 0.292528i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 606.852 | + | 140.029i | 0.952672 | + | 0.219826i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −67.5803 | + | 117.052i | −0.105759 | + | 0.183181i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −61.3334 | − | 106.233i | −0.0956840 | − | 0.165730i | 0.814210 | − | 0.580571i | \(-0.197170\pi\) |
−0.909894 | + | 0.414841i | \(0.863837\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −720.813 | −1.12102 | −0.560508 | − | 0.828149i | \(-0.689394\pi\) | ||||
−0.560508 | + | 0.828149i | \(0.689394\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | − | 1444.53i | − | 2.23959i | ||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −510.825 | + | 294.925i | −0.789528 | + | 0.455834i | −0.839796 | − | 0.542901i | \(-0.817326\pi\) |
0.0502683 | + | 0.998736i | \(0.483992\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 30.4198 | + | 17.5629i | 0.0468717 | + | 0.0270614i | ||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 631.988 | + | 467.590i | 0.970796 | + | 0.718265i | ||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −215.294 | − | 124.300i | −0.329700 | − | 0.190352i | 0.326008 | − | 0.945367i | \(-0.394296\pi\) |
−0.655708 | + | 0.755015i | \(0.727630\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −282.989 | − | 490.151i | −0.432044 | − | 0.748322i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 456.524i | 0.694862i | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 640.918i | 0.972562i | 0.873802 | + | 0.486281i | \(0.161647\pi\) | ||||
−0.873802 | + | 0.486281i | \(0.838353\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 483.321 | + | 837.137i | 0.731197 | + | 1.26647i | 0.956372 | + | 0.292152i | \(0.0943712\pi\) |
−0.225175 | + | 0.974318i | \(0.572295\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −831.593 | − | 480.120i | −1.25429 | − | 0.724163i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −231.451 | − | 532.218i | −0.348047 | − | 0.800328i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 272.399 | + | 157.270i | 0.408395 | + | 0.235787i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 867.927 | − | 501.098i | 1.29735 | − | 0.749025i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | − | 426.783i | − | 0.636040i | ||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −754.537 | −1.12115 | −0.560577 | − | 0.828102i | \(-0.689421\pi\) | ||||
−0.560577 | + | 0.828102i | \(0.689421\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 18.2543 | + | 31.6173i | 0.0270433 | + | 0.0468404i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −380.978 | + | 659.874i | −0.562745 | + | 0.974703i | 0.434511 | + | 0.900667i | \(0.356921\pi\) |
−0.997256 | + | 0.0740362i | \(0.976412\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −125.795 | + | 1104.65i | −0.185265 | + | 1.62688i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −227.054 | + | 393.269i | −0.333413 | + | 0.577488i | ||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 657.604 | − | 379.668i | 0.962817 | − | 0.555883i | 0.0657781 | − | 0.997834i | \(-0.479047\pi\) |
0.897039 | + | 0.441952i | \(0.145714\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −679.387 | −0.991806 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 337.047 | 0.490607 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −397.951 | + | 229.757i | −0.577577 | + | 0.333464i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 245.076 | − | 424.484i | 0.354669 | − | 0.614304i | −0.632393 | − | 0.774648i | \(-0.717927\pi\) |
0.987061 | + | 0.160344i | \(0.0512604\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −69.0721 | + | 606.548i | −0.0996711 | + | 0.875249i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 201.958 | − | 349.801i | 0.290587 | − | 0.503311i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 215.627 | + | 373.477i | 0.309364 | + | 0.535835i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 1206.05 | 1.72539 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | − | 577.533i | − | 0.823870i | −0.911213 | − | 0.411935i | \(-0.864853\pi\) | ||
0.911213 | − | 0.411935i | \(-0.135147\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 187.530 | − | 108.271i | 0.266757 | − | 0.154012i | ||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −660.793 | − | 381.509i | −0.937295 | − | 0.541148i | ||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −194.364 | − | 446.937i | −0.274914 | − | 0.632160i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −615.814 | − | 355.540i | −0.868567 | − | 0.501467i | −0.00169497 | − | 0.999999i | \(-0.500540\pi\) |
−0.866872 | + | 0.498531i | \(0.833873\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 408.764 | + | 708.000i | 0.574914 | + | 0.995781i | ||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 257.150i | 0.360659i | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | − | 867.631i | − | 1.21347i | ||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 272.484 | + | 471.957i | 0.380034 | + | 0.658238i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 150.440 | + | 86.8564i | 0.209235 | + | 0.120802i | 0.600956 | − | 0.799282i | \(-0.294787\pi\) |
−0.391721 | + | 0.920084i | \(0.628120\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 110.404 | + | 81.6852i | 0.153127 | + | 0.113294i | ||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −161.160 | − | 93.0457i | −0.222904 | − | 0.128694i | ||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −95.9059 | + | 55.3713i | −0.132284 | + | 0.0763742i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | − | 1056.57i | − | 1.45333i | −0.686993 | − | 0.726664i | \(-0.741070\pi\) | ||
0.686993 | − | 0.726664i | \(-0.258930\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −184.457 | −0.253028 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −778.941 | − | 1349.17i | −1.06558 | − | 1.84564i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 115.299 | − | 199.703i | 0.157297 | − | 0.272446i | −0.776596 | − | 0.629999i | \(-0.783055\pi\) |
0.933893 | + | 0.357553i | \(0.116389\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | −864.283 | − | 199.431i | −1.17589 | − | 0.271334i | ||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −296.833 | + | 514.130i | −0.402758 | + | 0.697598i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −77.4971 | + | 44.7430i | −0.104868 | + | 0.0605453i | −0.551517 | − | 0.834164i | \(-0.685951\pi\) |
0.446649 | + | 0.894709i | \(0.352617\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 871.820 | 1.17654 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 236.120 | 0.317793 | 0.158897 | − | 0.987295i | \(-0.449206\pi\) | ||||
0.158897 | + | 0.987295i | \(0.449206\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −886.581 | + | 511.868i | −1.19004 | + | 0.687071i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −149.382 | + | 258.737i | −0.199976 | + | 0.346368i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −251.815 | − | 186.311i | −0.336202 | − | 0.248746i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −717.692 | + | 1243.08i | −0.955649 | + | 1.65523i | −0.222772 | + | 0.974871i | \(0.571510\pi\) |
−0.732877 | + | 0.680361i | \(0.761823\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −294.265 | − | 509.682i | −0.390790 | − | 0.676868i | ||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −389.696 | −0.516154 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | − | 692.645i | − | 0.914987i | −0.889213 | − | 0.457494i | \(-0.848747\pi\) | ||
0.889213 | − | 0.457494i | \(-0.151253\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −433.367 | + | 250.204i | −0.570971 | + | 0.329650i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −999.810 | − | 577.241i | −1.31381 | − | 0.758529i | −0.331086 | − | 0.943601i | \(-0.607415\pi\) |
−0.982725 | + | 0.185071i | \(0.940748\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −363.359 | + | 158.018i | −0.476224 | + | 0.207101i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 472.603 | + | 272.858i | 0.617782 | + | 0.356677i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −15.2964 | − | 26.4942i | −0.0199432 | − | 0.0345426i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | − | 894.095i | − | 1.16267i | −0.813663 | − | 0.581336i | \(-0.802530\pi\) | ||
0.813663 | − | 0.581336i | \(-0.197470\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 563.723i | 0.731158i | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −464.538 | − | 804.603i | −0.600954 | − | 1.04088i | −0.992677 | − | 0.120800i | \(-0.961454\pi\) |
0.391722 | − | 0.920083i | \(-0.371879\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −78.4073 | − | 45.2685i | −0.101171 | − | 0.0584109i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 37.4454 | − | 328.822i | 0.0481922 | − | 0.423194i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −339.086 | − | 195.772i | −0.435284 | − | 0.251311i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −285.844 | + | 165.032i | −0.365998 | + | 0.211309i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 415.422i | 0.530552i | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 165.782 | 0.211188 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 693.013 | + | 1200.33i | 0.880576 | + | 1.52520i | 0.850702 | + | 0.525649i | \(0.176177\pi\) |
0.0298746 | + | 0.999554i | \(0.490489\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −683.794 | + | 1184.37i | −0.866659 | + | 1.50110i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 1311.95 | + | 149.401i | 1.65859 | + | 0.188876i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −185.854 | + | 321.908i | −0.234368 | + | 0.405937i | ||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 566.764 | − | 327.221i | 0.712910 | − | 0.411599i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 388.524 | 0.487484 | 0.243742 | − | 0.969840i | \(-0.421625\pi\) | ||||
0.243742 | + | 0.969840i | \(0.421625\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −822.890 | −1.02990 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −5.79682 | + | 3.34680i | −0.00723698 | + | 0.00417827i | ||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −557.421 | + | 965.481i | −0.694173 | + | 1.20234i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −115.705 | − | 266.062i | −0.143733 | − | 0.330512i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −257.924 | + | 446.737i | −0.319608 | + | 0.553577i | ||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −255.112 | − | 441.867i | −0.315342 | − | 0.546189i | 0.664168 | − | 0.747583i | \(-0.268786\pi\) |
−0.979510 | + | 0.201395i | \(0.935453\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −54.8689 | −0.0676558 | −0.0338279 | − | 0.999428i | \(-0.510770\pi\) | ||||
−0.0338279 | + | 0.999428i | \(0.510770\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 1458.28i | 1.79370i | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −42.3519 | + | 24.4519i | −0.0519656 | + | 0.0300023i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 1224.93 | + | 707.215i | 1.49931 | + | 0.865624i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 316.236 | − | 427.420i | 0.386124 | − | 0.521880i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 167.045 | + | 96.4438i | 0.203466 | + | 0.117471i | 0.598271 | − | 0.801294i | \(-0.295855\pi\) |
−0.394805 | + | 0.918765i | \(0.629188\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 71.3241 | + | 123.537i | 0.0866636 | + | 0.150106i | 0.906099 | − | 0.423066i | \(-0.139046\pi\) |
−0.819435 | + | 0.573172i | \(0.805713\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | − | 176.183i | − | 0.213555i | ||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 91.3639i | 0.110476i | 0.998473 | + | 0.0552382i | \(0.0175918\pi\) | ||||
−0.998473 | + | 0.0552382i | \(0.982408\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −232.999 | − | 403.567i | −0.281061 | − | 0.486812i | 0.690586 | − | 0.723251i | \(-0.257353\pi\) |
−0.971646 | + | 0.236439i | \(0.924020\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −261.135 | − | 150.766i | −0.314242 | − | 0.181428i | ||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −914.763 | + | 279.786i | −1.09815 | + | 0.335877i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 319.557 | + | 184.496i | 0.382703 | + | 0.220954i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −294.125 | + | 169.813i | −0.351403 | + | 0.202883i | ||||
\(838\) | 0 | 0 | ||||||||
\(839\) | − | 24.9426i | − | 0.0297289i | −0.999890 | − | 0.0148645i | \(-0.995268\pi\) | ||
0.999890 | − | 0.0148645i | \(-0.00473168\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −419.114 | −0.498352 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 628.011 | + | 1087.75i | 0.744972 | + | 1.29033i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 17.4280 | − | 30.1862i | 0.0206249 | − | 0.0357234i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −382.901 | + | 517.524i | −0.452068 | + | 0.611008i | ||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 579.479 | − | 1003.69i | 0.682543 | − | 1.18220i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 93.7484 | − | 54.1257i | 0.110163 | − | 0.0636025i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 1642.90 | 1.92603 | 0.963016 | − | 0.269445i | \(-0.0868403\pi\) | ||||
0.963016 | + | 0.269445i | \(0.0868403\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −495.465 | −0.579491 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −130.888 | + | 75.5681i | −0.152728 | + | 0.0881775i | −0.574416 | − | 0.818563i | \(-0.694771\pi\) |
0.421688 | + | 0.906741i | \(0.361438\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −450.007 | + | 779.435i | −0.523873 | + | 0.907374i | 0.475741 | + | 0.879585i | \(0.342180\pi\) |
−0.999614 | + | 0.0277890i | \(0.991153\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −548.762 | + | 238.646i | −0.637354 | + | 0.277173i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 207.932 | − | 360.149i | 0.240941 | − | 0.417322i | −0.720042 | − | 0.693931i | \(-0.755877\pi\) |
0.960983 | + | 0.276609i | \(0.0892107\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 448.683 | + | 777.142i | 0.518709 | + | 0.898430i | ||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 356.496 | 0.411184 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 1996.42i | 2.29737i | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 447.783 | − | 258.527i | 0.514102 | − | 0.296817i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 821.985 | + | 474.573i | 0.941564 | + | 0.543612i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 914.824 | + | 104.178i | 1.04551 | + | 0.119060i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −1488.56 | − | 859.419i | −1.69733 | − | 0.979954i | −0.948278 | − | 0.317442i | \(-0.897176\pi\) |
−0.749052 | − | 0.662511i | \(-0.769491\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −158.133 | − | 273.894i | −0.179901 | − | 0.311598i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 1094.47i | 1.24231i | 0.783689 | + | 0.621153i | \(0.213336\pi\) | ||||
−0.783689 | + | 0.621153i | \(0.786664\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | − | 527.301i | − | 0.597170i | −0.954383 | − | 0.298585i | \(-0.903485\pi\) | ||
0.954383 | − | 0.298585i | \(-0.0965146\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 21.7853 | + | 37.7332i | 0.0246161 | + | 0.0426363i | ||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −1459.99 | − | 842.925i | −1.64599 | − | 0.950310i | −0.978645 | − | 0.205558i | \(-0.934099\pi\) |
−0.667341 | − | 0.744752i | \(-0.732568\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 318.921 | + | 36.3180i | 0.358742 | + | 0.0408526i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −1252.09 | − | 722.896i | −1.40527 | − | 0.811331i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 647.023 | − | 373.559i | 0.724549 | − | 0.418319i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | − | 327.007i | − | 0.365371i | ||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 435.832 | 0.485878 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −515.099 | − | 892.178i | −0.572969 | − | 0.992412i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 352.897 | − | 611.236i | 0.391673 | − | 0.678398i | ||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 1982.37 | − | 862.096i | 2.19532 | − | 0.954702i | ||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 803.700 | − | 1392.05i | 0.888066 | − | 1.53818i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −1439.38 | + | 831.024i | −1.58696 | + | 0.916234i | −0.593160 | + | 0.805085i | \(0.702120\pi\) |
−0.993804 | + | 0.111149i | \(0.964547\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −416.073 | −0.457726 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 1220.19 | 1.33940 | 0.669698 | − | 0.742633i | \(-0.266423\pi\) | ||||
0.669698 | + | 0.742633i | \(0.266423\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −631.840 | + | 364.793i | −0.692048 | + | 0.399554i | ||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 264.694 | − | 458.464i | 0.289283 | − | 0.501053i | ||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 503.761 | − | 680.875i | 0.549357 | − | 0.742503i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −38.1217 | + | 66.0288i | −0.0414817 | + | 0.0718485i | −0.886021 | − | 0.463645i | \(-0.846541\pi\) |
0.844539 | + | 0.535494i | \(0.179875\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 700.312 | + | 1212.98i | 0.760382 | + | 1.31702i | ||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 287.471 | 0.311452 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 38.1129i | 0.0412032i | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 101.538 | − | 58.6232i | 0.109534 | − | 0.0632397i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 200.762 | + | 115.910i | 0.216106 | + | 0.124769i | 0.604146 | − | 0.796874i | \(-0.293514\pi\) |
−0.388040 | + | 0.921643i | \(0.626848\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 592.249 | − | 635.255i | 0.636142 | − | 0.682336i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −632.758 | − | 365.323i | −0.678197 | − | 0.391557i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 666.323 | + | 1154.11i | 0.712645 | + | 1.23434i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | − | 985.061i | − | 1.05129i | −0.850703 | − | 0.525646i | \(-0.823824\pi\) | ||
0.850703 | − | 0.525646i | \(-0.176176\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | − | 99.4088i | − | 0.105867i | ||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −704.239 | − | 1219.78i | −0.748394 | − | 1.29626i | −0.948592 | − | 0.316501i | \(-0.897492\pi\) |
0.200198 | − | 0.979756i | \(-0.435842\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −169.513 | − | 97.8683i | −0.179759 | − | 0.103784i | ||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 227.910 | − | 308.040i | 0.241175 | − | 0.325968i | ||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −144.121 | − | 83.2085i | −0.152187 | − | 0.0878654i | 0.421972 | − | 0.906609i | \(-0.361338\pi\) |
−0.574160 | + | 0.818743i | \(0.694671\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 840.888 | − | 485.487i | 0.886078 | − | 0.511577i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | − | 1931.56i | − | 2.03109i | ||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 815.618 | 0.855843 | 0.427921 | − | 0.903816i | \(-0.359246\pi\) | ||||
0.427921 | + | 0.903816i | \(0.359246\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −326.918 | − | 566.238i | −0.342322 | − | 0.592920i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 1002.37 | − | 1736.16i | 1.04741 | − | 1.81417i | ||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −405.458 | − | 932.343i | −0.422792 | − | 0.972203i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −59.3833 | + | 102.855i | −0.0617933 | + | 0.107029i | ||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −231.593 | + | 133.710i | −0.240491 | + | 0.138848i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 107.227 | 0.111116 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 86.3395 | 0.0892860 | 0.0446430 | − | 0.999003i | \(-0.485785\pi\) | ||||
0.0446430 | + | 0.999003i | \(0.485785\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −1159.68 | + | 669.540i | −1.19678 | + | 0.690960i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −339.651 | + | 588.292i | −0.349795 | + | 0.605862i | −0.986213 | − | 0.165482i | \(-0.947082\pi\) |
0.636418 | + | 0.771344i | \(0.280415\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 600.571 | + | 68.3915i | 0.617236 | + | 0.0702893i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −76.7235 | + | 132.889i | −0.0786908 | + | 0.136296i | ||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 107.029 | + | 185.379i | 0.109548 | + | 0.189743i | 0.915587 | − | 0.402119i | \(-0.131726\pi\) |
−0.806039 | + | 0.591862i | \(0.798393\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −16.3459 | −0.0166965 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 338.267i | 0.344818i | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −1559.10 | + | 900.146i | −1.58606 | + | 0.915713i | −0.592114 | + | 0.805854i | \(0.701707\pi\) |
−0.993947 | + | 0.109859i | \(0.964960\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 1165.82 | + | 673.084i | 1.18357 | + | 0.683334i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 129.195 | − | 1134.51i | 0.130897 | − | 1.14945i | ||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 612.357 | + | 353.544i | 0.619168 | + | 0.357477i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 205.714 | + | 356.306i | 0.207582 | + | 0.359542i | 0.950952 | − | 0.309338i | \(-0.100107\pi\) |
−0.743370 | + | 0.668880i | \(0.766774\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | − | 966.925i | − | 0.973741i | ||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 306.302i | 0.307841i | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 806.000 | + | 1396.03i | 0.808425 | + | 1.40023i | 0.913954 | + | 0.405817i | \(0.133013\pi\) |
−0.105529 | + | 0.994416i | \(0.533654\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 123.816 | + | 71.4854i | 0.123940 | + | 0.0715569i |
(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 | 224.3.n.a.145.12 | 28 | ||
4.3 | odd | 2 | 56.3.j.a.5.11 | yes | 28 | ||
7.2 | even | 3 | 1568.3.h.a.881.6 | 28 | |||
7.3 | odd | 6 | inner | 224.3.n.a.17.3 | 28 | ||
7.5 | odd | 6 | 1568.3.h.a.881.24 | 28 | |||
8.3 | odd | 2 | 56.3.j.a.5.9 | ✓ | 28 | ||
8.5 | even | 2 | inner | 224.3.n.a.145.3 | 28 | ||
28.3 | even | 6 | 56.3.j.a.45.9 | yes | 28 | ||
28.11 | odd | 6 | 392.3.j.e.325.9 | 28 | |||
28.19 | even | 6 | 392.3.h.a.293.1 | 28 | |||
28.23 | odd | 6 | 392.3.h.a.293.2 | 28 | |||
28.27 | even | 2 | 392.3.j.e.117.11 | 28 | |||
56.3 | even | 6 | 56.3.j.a.45.11 | yes | 28 | ||
56.5 | odd | 6 | 1568.3.h.a.881.5 | 28 | |||
56.11 | odd | 6 | 392.3.j.e.325.11 | 28 | |||
56.19 | even | 6 | 392.3.h.a.293.4 | 28 | |||
56.27 | even | 2 | 392.3.j.e.117.9 | 28 | |||
56.37 | even | 6 | 1568.3.h.a.881.23 | 28 | |||
56.45 | odd | 6 | inner | 224.3.n.a.17.12 | 28 | ||
56.51 | odd | 6 | 392.3.h.a.293.3 | 28 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
56.3.j.a.5.9 | ✓ | 28 | 8.3 | odd | 2 | ||
56.3.j.a.5.11 | yes | 28 | 4.3 | odd | 2 | ||
56.3.j.a.45.9 | yes | 28 | 28.3 | even | 6 | ||
56.3.j.a.45.11 | yes | 28 | 56.3 | even | 6 | ||
224.3.n.a.17.3 | 28 | 7.3 | odd | 6 | inner | ||
224.3.n.a.17.12 | 28 | 56.45 | odd | 6 | inner | ||
224.3.n.a.145.3 | 28 | 8.5 | even | 2 | inner | ||
224.3.n.a.145.12 | 28 | 1.1 | even | 1 | trivial | ||
392.3.h.a.293.1 | 28 | 28.19 | even | 6 | |||
392.3.h.a.293.2 | 28 | 28.23 | odd | 6 | |||
392.3.h.a.293.3 | 28 | 56.51 | odd | 6 | |||
392.3.h.a.293.4 | 28 | 56.19 | even | 6 | |||
392.3.j.e.117.9 | 28 | 56.27 | even | 2 | |||
392.3.j.e.117.11 | 28 | 28.27 | even | 2 | |||
392.3.j.e.325.9 | 28 | 28.11 | odd | 6 | |||
392.3.j.e.325.11 | 28 | 56.11 | odd | 6 | |||
1568.3.h.a.881.5 | 28 | 56.5 | odd | 6 | |||
1568.3.h.a.881.6 | 28 | 7.2 | even | 3 | |||
1568.3.h.a.881.23 | 28 | 56.37 | even | 6 | |||
1568.3.h.a.881.24 | 28 | 7.5 | odd | 6 |