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 | 17.3 | ||
Character | \(\chi\) | \(=\) | 224.17 |
Dual form | 224.3.n.a.145.3 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/224\mathbb{Z}\right)^\times\).
\(n\) | \(127\) | \(129\) | \(197\) |
\(\chi(n)\) | \(1\) | \(e\left(\frac{1}{6}\right)\) | \(-1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | −1.93494 | + | 3.35141i | −0.644980 | + | 1.11714i | 0.339326 | + | 0.940669i | \(0.389801\pi\) |
−0.984306 | + | 0.176469i | \(0.943532\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 2.33882 | + | 4.05096i | 0.467764 | + | 0.810191i | 0.999322 | − | 0.0368311i | \(-0.0117264\pi\) |
−0.531557 | + | 0.847022i | \(0.678393\pi\) | |||||||
\(6\) | 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 | \(-0.102473\pi\) |
0.200306 | + | 0.979733i | \(0.435806\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −12.7102 | −0.977705 | −0.488853 | − | 0.872366i | \(-0.662584\pi\) | ||||
−0.488853 | + | 0.872366i | \(0.662584\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −18.1019 | −1.20679 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −16.9068 | − | 9.76116i | −0.994519 | − | 0.574186i | −0.0878969 | − | 0.996130i | \(-0.528015\pi\) |
−0.906622 | + | 0.421944i | \(0.861348\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −8.86233 | − | 15.3500i | −0.466439 | − | 0.807895i | 0.532827 | − | 0.846224i | \(-0.321130\pi\) |
−0.999265 | + | 0.0383291i | \(0.987796\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 10.8032 | − | 24.8418i | 0.514438 | − | 1.18294i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 4.43038 | + | 7.67364i | 0.192625 | + | 0.333636i | 0.946119 | − | 0.323818i | \(-0.104967\pi\) |
−0.753494 | + | 0.657454i | \(0.771633\pi\) | |||||||
\(24\) | 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 | 0.0364685 | − | 0.999335i | \(-0.488389\pi\) |
−0.847215 | + | 0.531250i | \(0.821722\pi\) | |||||||
\(32\) | 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 | \(-0.719459\pi\) |
0.350163 | + | 0.936689i | \(0.386126\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 24.5934 | − | 42.5970i | 0.630600 | − | 1.09223i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 22.0903i | 0.538788i | 0.963030 | + | 0.269394i | \(0.0868233\pi\) | ||||
−0.963030 | + | 0.269394i | \(0.913177\pi\) | |||||||
\(42\) | 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 | −0.0585708 | − | 0.998283i | \(-0.518654\pi\) |
0.835253 | + | 0.549865i | \(0.185321\pi\) | |||||||
\(48\) | 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 | \(-0.222545\pi\) |
−0.174645 | + | 0.984631i | \(0.555878\pi\) | |||||||
\(54\) | 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 | \(-0.826840\pi\) |
0.876044 | + | 0.482231i | \(0.160173\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 14.6224 | + | 25.3268i | 0.239712 | + | 0.415194i | 0.960632 | − | 0.277825i | \(-0.0896136\pi\) |
−0.720919 | + | 0.693019i | \(0.756280\pi\) | |||||||
\(62\) | 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 | \(-0.431517\pi\) |
−0.739315 | + | 0.673360i | \(0.764850\pi\) | |||||||
\(68\) | 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 | 0.879233 | − | 0.476391i | \(-0.158055\pi\) |
0.0270498 | + | 0.999634i | \(0.491389\pi\) | |||||||
\(74\) | 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 | 0.866211 | + | 0.499679i | \(0.166549\pi\) |
−0.000370612 | 1.00000i | \(0.500118\pi\) | ||||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 49.5358 | − | 85.7985i | 0.611553 | − | 1.05924i | ||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −49.9942 | −0.602340 | −0.301170 | − | 0.953571i | \(-0.597377\pi\) | ||||
−0.301170 | + | 0.953571i | \(0.597377\pi\) | |||||||
\(84\) | 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 | −0.494541 | − | 0.869155i | \(-0.664664\pi\) |
0.505440 | + | 0.862862i | \(0.331330\pi\) | |||||||
\(90\) | 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 | \(0.305304\pi\) | ||||
−0.574225 | + | 0.818698i | \(0.694696\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | − | 87.2097i | − | 0.880906i | ||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −34.8122 | + | 60.2965i | −0.344675 | + | 0.596995i | −0.985295 | − | 0.170864i | \(-0.945344\pi\) |
0.640620 | + | 0.767858i | \(0.278678\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −16.9911 | + | 9.80983i | −0.164962 | + | 0.0952411i | −0.580208 | − | 0.814468i | \(-0.697029\pi\) |
0.415246 | + | 0.909709i | \(0.363696\pi\) | |||||||
\(104\) | 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 | \(-0.733723\pi\) |
0.307852 | + | 0.951434i | \(0.400390\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −49.0210 | − | 28.3023i | −0.449734 | − | 0.259654i | 0.257984 | − | 0.966149i | \(-0.416942\pi\) |
−0.707718 | + | 0.706495i | \(0.750275\pi\) | |||||||
\(110\) | 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 | \(-0.0138639\pi\) |
−0.537233 | + | 0.843434i | \(0.680531\pi\) | |||||||
\(132\) | 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 | −0.469306 | − | 0.883036i | \(-0.655496\pi\) |
0.999384 | − | 0.0350869i | \(-0.0111708\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 86.3503 | 0.621225 | 0.310613 | − | 0.950537i | \(-0.399466\pi\) | ||||
0.310613 | + | 0.950537i | \(0.399466\pi\) | |||||||
\(140\) | 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 | \(-0.929213\pi\) |
−0.296680 | + | 0.954977i | \(0.595879\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 41.6552 | − | 72.1490i | 0.275862 | − | 0.477808i | −0.694490 | − | 0.719502i | \(-0.744370\pi\) |
0.970352 | + | 0.241695i | \(0.0777033\pi\) | |||||||
\(152\) | 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 | \(-0.797329\pi\) |
0.916927 | + | 0.399056i | \(0.130662\pi\) | |||||||
\(158\) | 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 | \(-0.676877\pi\) |
0.471969 | + | 0.881615i | \(0.343543\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −228.777 | − | 132.084i | −1.38653 | − | 0.800511i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 78.8843i | 0.472361i | 0.971709 | + | 0.236181i | \(0.0758957\pi\) | ||||
−0.971709 | + | 0.236181i | \(0.924104\pi\) | |||||||
\(168\) | 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 | −0.997946 | − | 0.0640660i | \(-0.979593\pi\) |
0.443490 | − | 0.896279i | \(-0.353740\pi\) | |||||||
\(174\) | 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 | \(-0.270773\pi\) |
−0.321261 | + | 0.946991i | \(0.604107\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 343.635 | 1.89853 | 0.949267 | − | 0.314472i | \(-0.101827\pi\) | ||||
0.949267 | + | 0.314472i | \(0.101827\pi\) | |||||||
\(182\) | 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 | 0.623009 | − | 0.782215i | \(-0.285910\pi\) |
−0.988922 | + | 0.148434i | \(0.952577\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −11.4616 | + | 19.8521i | −0.0593867 | + | 0.102861i | −0.894190 | − | 0.447687i | \(-0.852248\pi\) |
0.834804 | + | 0.550548i | \(0.185581\pi\) | |||||||
\(194\) | 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 | 0.635671 | − | 0.771960i | \(-0.280723\pi\) |
−0.350701 | + | 0.936487i | \(0.614057\pi\) | |||||||
\(200\) | 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 | \(0.197205\pi\) | ||||
−0.814148 | + | 0.580658i | \(0.802795\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −18.6431 | −0.0828581 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −58.6721 | + | 101.623i | −0.258468 | + | 0.447679i | −0.965832 | − | 0.259171i | \(-0.916551\pi\) |
0.707364 | + | 0.706849i | \(0.249884\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −43.5475 | − | 75.4264i | −0.190164 | − | 0.329373i | 0.755141 | − | 0.655563i | \(-0.227569\pi\) |
−0.945304 | + | 0.326190i | \(0.894235\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 317.797 | − | 235.129i | 1.37574 | − | 1.01787i | ||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 155.825 | + | 269.897i | 0.668778 | + | 1.15836i | 0.978246 | + | 0.207448i | \(0.0665159\pi\) |
−0.309468 | + | 0.950910i | \(0.600151\pi\) | |||||||
\(234\) | 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 | 0.411106 | − | 0.911588i | \(-0.365143\pi\) |
−0.583905 | + | 0.811822i | \(0.698476\pi\) | |||||||
\(242\) | 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 | \(-0.402029\pi\) | ||||
0.302947 | + | 0.953007i | \(0.402029\pi\) | |||||||
\(252\) | 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 | −0.234066 | − | 0.972221i | \(-0.575203\pi\) |
0.724935 | + | 0.688817i | \(0.241870\pi\) | |||||||
\(258\) | 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 | −0.305529 | − | 0.952183i | \(-0.598833\pi\) |
0.977379 | − | 0.211495i | \(-0.0678333\pi\) | |||||||
\(264\) | 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 | \(-0.913030\pi\) |
0.715140 | + | 0.698981i | \(0.246363\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 326.342 | − | 188.414i | 1.20421 | − | 0.695253i | 0.242725 | − | 0.970095i | \(-0.421959\pi\) |
0.961489 | + | 0.274842i | \(0.0886255\pi\) | |||||||
\(272\) | 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 | \(-0.288415\pi\) |
−0.373227 | + | 0.927740i | \(0.621749\pi\) | |||||||
\(278\) | 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 | −0.470304 | − | 0.882505i | \(-0.655856\pi\) |
0.999423 | − | 0.0339572i | \(-0.0108110\pi\) | |||||||
\(284\) | 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 | \(-0.455463\pi\) | ||||
0.139463 | + | 0.990227i | \(0.455463\pi\) | |||||||
\(294\) | 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 | \(-0.700660\pi\) | ||||
−0.589462 | + | 0.807796i | \(0.700660\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | − | 75.9257i | − | 0.245714i | ||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −163.508 | − | 94.4017i | −0.525751 | − | 0.303542i | 0.213534 | − | 0.976936i | \(-0.431503\pi\) |
−0.739284 | + | 0.673393i | \(0.764836\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −22.2463 | + | 12.8439i | −0.0710745 | + | 0.0410349i | −0.535116 | − | 0.844779i | \(-0.679732\pi\) |
0.464042 | + | 0.885813i | \(0.346399\pi\) | |||||||
\(314\) | 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 | \(-0.378162\pi\) |
0.990100 | + | 0.140367i | \(0.0448282\pi\) | |||||||
\(318\) | 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 | \(-0.543474\pi\) |
0.789883 | + | 0.613257i | \(0.210141\pi\) | |||||||
\(332\) | 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 | \(-0.150400\pi\) |
0.0510824 | + | 0.998694i | \(0.483733\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −400.193 | −1.14668 | −0.573342 | − | 0.819316i | \(-0.694353\pi\) | ||||
−0.573342 | + | 0.819316i | \(0.694353\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 148.743 | 0.423768 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 256.293 | + | 147.971i | 0.726043 | + | 0.419181i | 0.816973 | − | 0.576676i | \(-0.195650\pi\) |
−0.0909296 | + | 0.995857i | \(0.528984\pi\) | |||||||
\(354\) | 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 | 0.687035 | − | 0.726624i | \(-0.258912\pi\) |
−0.972793 | + | 0.231678i | \(0.925578\pi\) | |||||||
\(360\) | 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 | 0.855349 | − | 0.518052i | \(-0.173343\pi\) |
−0.0209719 | + | 0.999780i | \(0.506676\pi\) | |||||||
\(368\) | 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 | \(-0.826005\pi\) |
0.0230210 | + | 0.999735i | \(0.492672\pi\) | |||||||
\(374\) | 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 | −0.954955 | − | 0.296752i | \(-0.904097\pi\) |
−0.220483 | + | 0.975391i | \(0.570763\pi\) | |||||||
\(384\) | 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 | \(-0.376613\pi\) |
−0.612773 | + | 0.790259i | \(0.709946\pi\) | |||||||
\(390\) | 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 | \(-0.0116725\pi\) |
−0.531414 | + | 0.847112i | \(0.678339\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −477.063 | + | 54.3267i | −1.19565 | + | 0.136157i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −149.636 | − | 259.177i | −0.373157 | − | 0.646327i | 0.616893 | − | 0.787047i | \(-0.288391\pi\) |
−0.990049 | + | 0.140721i | \(0.955058\pi\) | |||||||
\(402\) | 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 | 0.478279 | − | 0.878208i | \(-0.341261\pi\) |
−0.521411 | + | 0.853306i | \(0.674594\pi\) | |||||||
\(410\) | 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 | \(-0.570109\pi\) | ||||
−0.218478 | + | 0.975842i | \(0.570109\pi\) | |||||||
\(420\) | 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 | −0.906354 | − | 0.422520i | \(-0.861146\pi\) |
0.819090 | + | 0.573666i | \(0.194479\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 506.209i | 1.16907i | 0.811367 | + | 0.584536i | \(0.198724\pi\) | ||||
−0.811367 | + | 0.584536i | \(0.801276\pi\) | |||||||
\(434\) | 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 | −0.330284 | − | 0.943882i | \(-0.607144\pi\) |
0.652284 | + | 0.757975i | \(0.273811\pi\) | |||||||
\(440\) | 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 | \(-0.707631\pi\) |
0.384722 | + | 0.923033i | \(0.374297\pi\) | |||||||
\(444\) | 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 | −0.987997 | − | 0.154471i | \(-0.950633\pi\) |
0.360223 | − | 0.932866i | \(-0.382701\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 197.855 | + | 114.231i | 0.431056 | + | 0.248870i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −847.131 | −1.83759 | −0.918797 | − | 0.394729i | \(-0.870838\pi\) | ||||
−0.918797 | + | 0.394729i | \(0.870838\pi\) | |||||||
\(462\) | 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 | −0.972546 | − | 0.232709i | \(-0.925241\pi\) |
0.284741 | − | 0.958604i | \(-0.408092\pi\) | |||||||
\(468\) | 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 | 0.832188 | − | 0.554493i | \(-0.187088\pi\) |
−0.0641112 | + | 0.997943i | \(0.520421\pi\) | |||||||
\(480\) | 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 | −0.122949 | − | 0.992413i | \(-0.539235\pi\) |
0.920929 | − | 0.389729i | \(-0.127431\pi\) | |||||||
\(488\) | 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 | \(-0.810367\pi\) |
0.0720876 | + | 0.997398i | \(0.477034\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −264.374 | − | 152.636i | −0.527693 | − | 0.304663i | ||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 375.404i | 0.746329i | 0.927765 | + | 0.373165i | \(0.121727\pi\) | ||||
−0.927765 | + | 0.373165i | \(0.878273\pi\) | |||||||
\(504\) | 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 | \(-0.213052\pi\) |
−0.929451 | + | 0.368945i | \(0.879719\pi\) | |||||||
\(510\) | 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 | 0.998464 | − | 0.0554019i | \(-0.0176440\pi\) |
0.451253 | + | 0.892396i | \(0.350977\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −178.600 | − | 309.344i | −0.341491 | − | 0.591480i | 0.643219 | − | 0.765683i | \(-0.277599\pi\) |
−0.984710 | + | 0.174202i | \(0.944265\pi\) | |||||||
\(524\) | 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 | \(-0.997100\pi\) |
−0.492089 | + | 0.870545i | \(0.663767\pi\) | |||||||
\(542\) | 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 | \(-0.0360722\pi\) |
0.398861 | + | 0.917011i | \(0.369406\pi\) | |||||||
\(558\) | 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 | \(-0.913301\pi\) |
0.714543 | + | 0.699591i | \(0.246635\pi\) | |||||||
\(564\) | 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 | 0.689207 | − | 0.724564i | \(-0.257959\pi\) |
−0.972095 | + | 0.234589i | \(0.924626\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −712.583 | − | 411.410i | −1.24796 | − | 0.720508i | −0.277255 | − | 0.960796i | \(-0.589425\pi\) |
−0.970702 | + | 0.240288i | \(0.922758\pi\) | |||||||
\(572\) | 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 | 0.998111 | − | 0.0614420i | \(-0.0195699\pi\) |
0.445845 | + | 0.895110i | \(0.352903\pi\) | |||||||
\(578\) | 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 | \(-0.227939\pi\) | ||||
0.754377 | + | 0.656442i | \(0.227939\pi\) | |||||||
\(588\) | 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 | −0.234330 | − | 0.972157i | \(-0.575290\pi\) |
0.724748 | + | 0.689014i | \(0.241956\pi\) | |||||||
\(594\) | 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 | −0.890097 | − | 0.455771i | \(-0.849364\pi\) |
0.839758 | + | 0.542961i | \(0.182697\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | − | 509.153i | − | 0.847176i | −0.905855 | − | 0.423588i | \(-0.860770\pi\) | ||
0.905855 | − | 0.423588i | \(-0.139230\pi\) | |||||||
\(602\) | 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 | 0.483480 | − | 0.875355i | \(-0.339373\pi\) |
0.999820 | + | 0.0189717i | \(0.00603923\pi\) | |||||||
\(608\) | 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 | \(-0.281456\pi\) |
−0.352855 | + | 0.935678i | \(0.614789\pi\) | |||||||
\(614\) | 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 | \(-0.711634\pi\) |
0.990038 | + | 0.140799i | \(0.0449673\pi\) | |||||||
\(620\) | 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 | −0.909894 | − | 0.414841i | \(-0.863837\pi\) |
0.814210 | + | 0.580571i | \(0.197170\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 720.813 | 1.12102 | 0.560508 | − | 0.828149i | \(-0.310606\pi\) | ||||
0.560508 | + | 0.828149i | \(0.310606\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | − | 1444.53i | − | 2.23959i | ||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −510.825 | − | 294.925i | −0.789528 | − | 0.455834i | 0.0502683 | − | 0.998736i | \(-0.483992\pi\) |
−0.839796 | + | 0.542901i | \(0.817326\pi\) | |||||||
\(648\) | 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 | \(-0.605704\pi\) |
0.655708 | + | 0.755015i | \(0.272370\pi\) | |||||||
\(654\) | 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 | 0.225175 | + | 0.974318i | \(0.427705\pi\) |
−0.956372 | + | 0.292152i | \(0.905629\pi\) | |||||||
\(662\) | 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 | 0.997256 | + | 0.0740362i | \(0.0235880\pi\) |
−0.434511 | + | 0.900667i | \(0.643079\pi\) | |||||||
\(678\) | 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 | \(-0.520953\pi\) |
−0.897039 | + | 0.441952i | \(0.854286\pi\) | |||||||
\(684\) | 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 | \(-0.282073\pi\) |
−0.987061 | + | 0.160344i | \(0.948740\pi\) | |||||||
\(692\) | 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 | \(-0.499460\pi\) |
0.866872 | + | 0.498531i | \(0.166127\pi\) | |||||||
\(710\) | 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 | −0.391721 | − | 0.920084i | \(-0.628120\pi\) |
0.600956 | + | 0.799282i | \(0.294787\pi\) | |||||||
\(720\) | 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 | \(0.258930\pi\) | ||||
−0.686993 | + | 0.726664i | \(0.741070\pi\) | |||||||
\(728\) | 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 | \(-0.216945\pi\) |
−0.933893 | + | 0.357553i | \(0.883611\pi\) | |||||||
\(734\) | 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 | \(-0.314049\pi\) |
−0.446649 | + | 0.894709i | \(0.647383\pi\) | |||||||
\(740\) | 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 | −0.732877 | − | 0.680361i | \(-0.761823\pi\) |
−0.222772 | − | 0.974871i | \(-0.571510\pi\) | |||||||
\(752\) | 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 | −0.982725 | − | 0.185071i | \(-0.940748\pi\) |
−0.331086 | + | 0.943601i | \(0.607415\pi\) | |||||||
\(762\) | 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 | \(0.197470\pi\) | ||||
−0.813663 | + | 0.581336i | \(0.802530\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 563.723i | 0.731158i | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 464.538 | − | 804.603i | 0.600954 | − | 1.04088i | −0.391722 | − | 0.920083i | \(-0.628121\pi\) |
0.992677 | − | 0.120800i | \(-0.0385460\pi\) | |||||||
\(774\) | 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 | −0.0298746 | + | 0.999554i | \(0.509511\pi\) |
−0.850702 | + | 0.525649i | \(0.823823\pi\) | |||||||
\(788\) | 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 | \(-0.578375\pi\) | ||||
−0.243742 | + | 0.969840i | \(0.578375\pi\) | |||||||
\(798\) | 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 | −0.979510 | − | 0.201395i | \(-0.935453\pi\) |
0.664168 | + | 0.747583i | \(0.268786\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 54.8689 | 0.0676558 | 0.0338279 | − | 0.999428i | \(-0.489230\pi\) | ||||
0.0338279 | + | 0.999428i | \(0.489230\pi\) | |||||||
\(812\) | 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 | \(-0.704145\pi\) |
0.394805 | + | 0.918765i | \(0.370812\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 71.3241 | − | 123.537i | 0.0866636 | − | 0.150106i | −0.819435 | − | 0.573172i | \(-0.805713\pi\) |
0.906099 | + | 0.423066i | \(0.139046\pi\) | |||||||
\(824\) | 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 | \(-0.742647\pi\) |
0.971646 | + | 0.236439i | \(0.0759804\pi\) | |||||||
\(830\) | 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 | \(0.00473168\pi\) | ||||
−0.999890 | + | 0.0148645i | \(0.995268\pi\) | |||||||
\(840\) | 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 | \(-0.913160\pi\) | ||||
−0.963016 | + | 0.269445i | \(0.913160\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −495.465 | −0.579491 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −130.888 | − | 75.5681i | −0.152728 | − | 0.0881775i | 0.421688 | − | 0.906741i | \(-0.361438\pi\) |
−0.574416 | + | 0.818563i | \(0.694771\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 450.007 | + | 779.435i | 0.523873 | + | 0.907374i | 0.999614 | + | 0.0277890i | \(0.00884664\pi\) |
−0.475741 | + | 0.879585i | \(0.657820\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 548.762 | + | 238.646i | 0.637354 | + | 0.277173i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 207.932 | + | 360.149i | 0.240941 | + | 0.417322i | 0.960983 | − | 0.276609i | \(-0.0892107\pi\) |
−0.720042 | + | 0.693931i | \(0.755877\pi\) | |||||||
\(864\) | 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 | 0.749052 | − | 0.662511i | \(-0.230509\pi\) |
0.948278 | − | 0.317442i | \(-0.102824\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −158.133 | + | 273.894i | −0.179901 | + | 0.311598i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | − | 1094.47i | − | 1.24231i | −0.783689 | − | 0.621153i | \(-0.786664\pi\) | ||
0.783689 | − | 0.621153i | \(-0.213336\pi\) | |||||||
\(882\) | 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 | −0.667341 | + | 0.744752i | \(0.732568\pi\) |
−0.978645 | + | 0.205558i | \(0.934099\pi\) | |||||||
\(888\) | 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 | 0.993804 | + | 0.111149i | \(0.0354530\pi\) |
0.593160 | + | 0.805085i | \(0.297880\pi\) | |||||||
\(908\) | 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 | 0.844539 | − | 0.535494i | \(-0.179875\pi\) |
−0.886021 | + | 0.463645i | \(0.846541\pi\) | |||||||
\(920\) | 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 | −0.388040 | − | 0.921643i | \(-0.626848\pi\) |
0.604146 | + | 0.796874i | \(0.293514\pi\) | |||||||
\(930\) | 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 | \(0.176176\pi\) | ||||
−0.850703 | + | 0.525646i | \(0.823824\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | − | 99.4088i | − | 0.105867i | ||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 704.239 | − | 1219.78i | 0.748394 | − | 1.29626i | −0.200198 | − | 0.979756i | \(-0.564158\pi\) |
0.948592 | − | 0.316501i | \(-0.102508\pi\) | |||||||
\(942\) | 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 | \(-0.638662\pi\) |
0.574160 | + | 0.818743i | \(0.305329\pi\) | |||||||
\(948\) | 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 | \(-0.0529180\pi\) |
−0.636418 | + | 0.771344i | \(0.719585\pi\) | |||||||
\(972\) | 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 | −0.806039 | − | 0.591862i | \(-0.798393\pi\) |
0.915587 | + | 0.402119i | \(0.131726\pi\) | |||||||
\(978\) | 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 | −0.993947 | − | 0.109859i | \(-0.964960\pi\) |
−0.592114 | − | 0.805854i | \(-0.701707\pi\) | |||||||
\(984\) | 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 | −0.743370 | − | 0.668880i | \(-0.766774\pi\) |
0.950952 | + | 0.309338i | \(0.100107\pi\) | |||||||
\(992\) | 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 | 0.105529 | + | 0.994416i | \(0.466346\pi\) |
−0.913954 | + | 0.405817i | \(0.866987\pi\) | |||||||
\(998\) | 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.17.3 | 28 | ||
4.3 | odd | 2 | 56.3.j.a.45.9 | yes | 28 | ||
7.3 | odd | 6 | 1568.3.h.a.881.6 | 28 | |||
7.4 | even | 3 | 1568.3.h.a.881.24 | 28 | |||
7.5 | odd | 6 | inner | 224.3.n.a.145.12 | 28 | ||
8.3 | odd | 2 | 56.3.j.a.45.11 | yes | 28 | ||
8.5 | even | 2 | inner | 224.3.n.a.17.12 | 28 | ||
28.3 | even | 6 | 392.3.h.a.293.2 | 28 | |||
28.11 | odd | 6 | 392.3.h.a.293.1 | 28 | |||
28.19 | even | 6 | 56.3.j.a.5.11 | yes | 28 | ||
28.23 | odd | 6 | 392.3.j.e.117.11 | 28 | |||
28.27 | even | 2 | 392.3.j.e.325.9 | 28 | |||
56.3 | even | 6 | 392.3.h.a.293.3 | 28 | |||
56.5 | odd | 6 | inner | 224.3.n.a.145.3 | 28 | ||
56.11 | odd | 6 | 392.3.h.a.293.4 | 28 | |||
56.19 | even | 6 | 56.3.j.a.5.9 | ✓ | 28 | ||
56.27 | even | 2 | 392.3.j.e.325.11 | 28 | |||
56.45 | odd | 6 | 1568.3.h.a.881.23 | 28 | |||
56.51 | odd | 6 | 392.3.j.e.117.9 | 28 | |||
56.53 | even | 6 | 1568.3.h.a.881.5 | 28 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
56.3.j.a.5.9 | ✓ | 28 | 56.19 | even | 6 | ||
56.3.j.a.5.11 | yes | 28 | 28.19 | even | 6 | ||
56.3.j.a.45.9 | yes | 28 | 4.3 | odd | 2 | ||
56.3.j.a.45.11 | yes | 28 | 8.3 | odd | 2 | ||
224.3.n.a.17.3 | 28 | 1.1 | even | 1 | trivial | ||
224.3.n.a.17.12 | 28 | 8.5 | even | 2 | inner | ||
224.3.n.a.145.3 | 28 | 56.5 | odd | 6 | inner | ||
224.3.n.a.145.12 | 28 | 7.5 | odd | 6 | inner | ||
392.3.h.a.293.1 | 28 | 28.11 | odd | 6 | |||
392.3.h.a.293.2 | 28 | 28.3 | even | 6 | |||
392.3.h.a.293.3 | 28 | 56.3 | even | 6 | |||
392.3.h.a.293.4 | 28 | 56.11 | odd | 6 | |||
392.3.j.e.117.9 | 28 | 56.51 | odd | 6 | |||
392.3.j.e.117.11 | 28 | 28.23 | odd | 6 | |||
392.3.j.e.325.9 | 28 | 28.27 | even | 2 | |||
392.3.j.e.325.11 | 28 | 56.27 | even | 2 | |||
1568.3.h.a.881.5 | 28 | 56.53 | even | 6 | |||
1568.3.h.a.881.6 | 28 | 7.3 | odd | 6 | |||
1568.3.h.a.881.23 | 28 | 56.45 | odd | 6 | |||
1568.3.h.a.881.24 | 28 | 7.4 | even | 3 |