Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [112,3,Mod(17,112)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(112, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 0, 1]))
N = Newforms(chi, 3, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("112.17");
S:= CuspForms(chi, 3);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 112 = 2^{4} \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 3 \) |
Character orbit: | \([\chi]\) | \(=\) | 112.s (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: | \(3.05177896084\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Relative dimension: | \(2\) over \(\Q(\zeta_{6})\) |
Coefficient field: | \(\Q(\sqrt{2}, \sqrt{-3})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} + 2x^{2} + 4 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 3 \) |
Twist minimal: | no (minimal twist has level 14) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 17.1 | ||
Root | \(-0.707107 - 1.22474i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 112.17 |
Dual form | 112.3.s.b.33.1 |
$q$-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 \(\left(\mathbb{Z}/112\mathbb{Z}\right)^\times\).
\(n\) | \(15\) | \(17\) | \(85\) |
\(\chi(n)\) | \(1\) | \(e\left(\frac{1}{6}\right)\) | \(1\) |
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 | ||||||||
\(3\) | −0.621320 | − | 0.358719i | −0.207107 | − | 0.119573i | 0.392859 | − | 0.919599i | \(-0.371486\pi\) |
−0.599966 | + | 0.800025i | \(0.704819\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −5.74264 | + | 3.31552i | −1.14853 | + | 0.663103i | −0.948528 | − | 0.316693i | \(-0.897428\pi\) |
−0.200000 | + | 0.979796i | \(0.564094\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −6.24264 | + | 3.16693i | −0.891806 | + | 0.452418i | ||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −4.24264 | − | 7.34847i | −0.471405 | − | 0.816497i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −2.37868 | + | 4.11999i | −0.216244 | + | 0.374545i | −0.953657 | − | 0.300897i | \(-0.902714\pi\) |
0.737413 | + | 0.675442i | \(0.236047\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 15.2913i | 1.17625i | 0.808769 | + | 0.588126i | \(0.200134\pi\) | ||||
−0.808769 | + | 0.588126i | \(0.799866\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 4.75736 | 0.317157 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −3.25736 | − | 1.88064i | −0.191609 | − | 0.110626i | 0.401126 | − | 0.916023i | \(-0.368619\pi\) |
−0.592736 | + | 0.805397i | \(0.701952\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −3.62132 | + | 2.09077i | −0.190596 | + | 0.110041i | −0.592261 | − | 0.805746i | \(-0.701765\pi\) |
0.401666 | + | 0.915786i | \(0.368431\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 5.01472 | + | 0.271680i | 0.238796 | + | 0.0129371i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −13.8640 | − | 24.0131i | −0.602781 | − | 1.04405i | −0.992398 | − | 0.123070i | \(-0.960726\pi\) |
0.389617 | − | 0.920977i | \(-0.372607\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 9.48528 | − | 16.4290i | 0.379411 | − | 0.657160i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 12.5446i | 0.464616i | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 3.51472 | 0.121197 | 0.0605986 | − | 0.998162i | \(-0.480699\pi\) | ||||
0.0605986 | + | 0.998162i | \(0.480699\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 42.3198 | + | 24.4334i | 1.36516 | + | 0.788173i | 0.990305 | − | 0.138913i | \(-0.0443607\pi\) |
0.374850 | + | 0.927085i | \(0.377694\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 2.95584 | − | 1.70656i | 0.0895710 | − | 0.0517139i | ||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 25.3492 | − | 38.8841i | 0.724264 | − | 1.11097i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 1.47056 | + | 2.54709i | 0.0397449 | + | 0.0688403i | 0.885214 | − | 0.465185i | \(-0.154012\pi\) |
−0.845469 | + | 0.534025i | \(0.820679\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 5.48528 | − | 9.50079i | 0.140648 | − | 0.243610i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | − | 27.9590i | − | 0.681927i | −0.940077 | − | 0.340963i | \(-0.889247\pi\) | ||
0.940077 | − | 0.340963i | \(-0.110753\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 10.4853 | 0.243844 | 0.121922 | − | 0.992540i | \(-0.461094\pi\) | ||||
0.121922 | + | 0.992540i | \(0.461094\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 48.7279 | + | 28.1331i | 1.08284 | + | 0.625180i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −45.6213 | + | 26.3395i | −0.970666 | + | 0.560415i | −0.899439 | − | 0.437046i | \(-0.856025\pi\) |
−0.0712271 | + | 0.997460i | \(0.522691\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 28.9411 | − | 39.5400i | 0.590635 | − | 0.806939i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 1.34924 | + | 2.33696i | 0.0264557 | + | 0.0458227i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −27.9853 | + | 48.4719i | −0.528024 | + | 0.914565i | 0.471442 | + | 0.881897i | \(0.343734\pi\) |
−0.999466 | + | 0.0326677i | \(0.989600\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | − | 31.5462i | − | 0.573567i | ||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 3.00000 | 0.0526316 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −33.5330 | − | 19.3603i | −0.568356 | − | 0.328141i | 0.188136 | − | 0.982143i | \(-0.439755\pi\) |
−0.756492 | + | 0.654002i | \(0.773089\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −78.3823 | + | 45.2540i | −1.28495 | + | 0.741869i | −0.977750 | − | 0.209774i | \(-0.932727\pi\) |
−0.307205 | + | 0.951643i | \(0.599394\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 49.7574 | + | 32.4377i | 0.789799 | + | 0.514884i | ||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −50.6985 | − | 87.8124i | −0.779977 | − | 1.35096i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −17.3198 | + | 29.9988i | −0.258505 | + | 0.447743i | −0.965842 | − | 0.259134i | \(-0.916563\pi\) |
0.707337 | + | 0.706877i | \(0.249896\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 19.8931i | 0.288306i | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −36.4264 | −0.513048 | −0.256524 | − | 0.966538i | \(-0.582577\pi\) | ||||
−0.256524 | + | 0.966538i | \(0.582577\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 45.5589 | + | 26.3034i | 0.624094 | + | 0.360321i | 0.778461 | − | 0.627693i | \(-0.216001\pi\) |
−0.154367 | + | 0.988014i | \(0.549334\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −11.7868 | + | 6.80511i | −0.157157 | + | 0.0907348i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 1.80152 | − | 33.2528i | 0.0233963 | − | 0.431854i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −16.8934 | − | 29.2602i | −0.213840 | − | 0.370383i | 0.739073 | − | 0.673626i | \(-0.235264\pi\) |
−0.952913 | + | 0.303243i | \(0.901931\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −33.6838 | + | 58.3420i | −0.415849 | + | 0.720272i | ||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 127.577i | 1.53708i | 0.639803 | + | 0.768539i | \(0.279016\pi\) | ||||
−0.639803 | + | 0.768539i | \(0.720984\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 24.9411 | 0.293425 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −2.18377 | − | 1.26080i | −0.0251008 | − | 0.0144919i | ||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −43.5883 | + | 25.1657i | −0.489756 | + | 0.282761i | −0.724473 | − | 0.689303i | \(-0.757917\pi\) |
0.234717 | + | 0.972064i | \(0.424584\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −48.4264 | − | 95.4580i | −0.532158 | − | 1.04899i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −17.5294 | − | 30.3619i | −0.188489 | − | 0.326472i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 13.8640 | − | 24.0131i | 0.145936 | − | 0.252769i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 101.792i | 1.04940i | 0.851287 | + | 0.524700i | \(0.175823\pi\) | ||||
−0.851287 | + | 0.524700i | \(0.824177\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 40.3675 | 0.407753 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −51.6838 | − | 29.8396i | −0.511720 | − | 0.295442i | 0.221820 | − | 0.975088i | \(-0.428800\pi\) |
−0.733541 | + | 0.679646i | \(0.762134\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −104.077 | + | 60.0890i | −1.01046 | + | 0.583388i | −0.911326 | − | 0.411686i | \(-0.864940\pi\) |
−0.0991322 | + | 0.995074i | \(0.531607\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −29.6985 | + | 15.0662i | −0.282843 | + | 0.143488i | ||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −56.8051 | − | 98.3893i | −0.530889 | − | 0.919526i | −0.999350 | − | 0.0360423i | \(-0.988525\pi\) |
0.468462 | − | 0.883484i | \(-0.344808\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 72.6543 | − | 125.841i | 0.666553 | − | 1.15450i | −0.312308 | − | 0.949981i | \(-0.601102\pi\) |
0.978862 | − | 0.204524i | \(-0.0655645\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | − | 2.11008i | − | 0.0190097i | ||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 34.5442 | 0.305700 | 0.152850 | − | 0.988249i | \(-0.451155\pi\) | ||||
0.152850 | + | 0.988249i | \(0.451155\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 159.231 | + | 91.9323i | 1.38462 | + | 0.799412i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 112.368 | − | 64.8754i | 0.960406 | − | 0.554491i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 26.2904 | + | 1.42432i | 0.220927 | + | 0.0119691i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 49.1838 | + | 85.1888i | 0.406477 | + | 0.704040i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −10.0294 | + | 17.3715i | −0.0815401 | + | 0.141232i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | − | 39.9814i | − | 0.319851i | ||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 247.338 | 1.94754 | 0.973772 | − | 0.227526i | \(-0.0730636\pi\) | ||||
0.973772 | + | 0.227526i | \(0.0730636\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −6.51472 | − | 3.76127i | −0.0505017 | − | 0.0291572i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 127.864 | − | 73.8223i | 0.976061 | − | 0.563529i | 0.0749822 | − | 0.997185i | \(-0.476110\pi\) |
0.901079 | + | 0.433656i | \(0.142777\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 15.9853 | − | 24.5204i | 0.120190 | − | 0.184364i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −41.5919 | − | 72.0393i | −0.308088 | − | 0.533624i | ||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 16.2868 | − | 28.2096i | 0.118882 | − | 0.205909i | −0.800443 | − | 0.599409i | \(-0.795402\pi\) |
0.919325 | + | 0.393500i | \(0.128736\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | − | 68.5857i | − | 0.493422i | −0.969089 | − | 0.246711i | \(-0.920650\pi\) | ||
0.969089 | − | 0.246711i | \(-0.0793499\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 37.7939 | 0.268042 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −63.0000 | − | 36.3731i | −0.440559 | − | 0.254357i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −20.1838 | + | 11.6531i | −0.139198 | + | 0.0803662i | ||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −32.1655 | + | 14.1853i | −0.218813 | + | 0.0964984i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −46.1985 | − | 80.0181i | −0.310057 | − | 0.537034i | 0.668317 | − | 0.743876i | \(-0.267015\pi\) |
−0.978374 | + | 0.206842i | \(0.933681\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −45.8934 | + | 79.4897i | −0.303930 | + | 0.526422i | −0.977022 | − | 0.213136i | \(-0.931632\pi\) |
0.673093 | + | 0.739558i | \(0.264965\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 31.9155i | 0.208598i | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −324.037 | −2.09056 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 7.32338 | + | 4.22815i | 0.0466457 | + | 0.0269309i | 0.523142 | − | 0.852246i | \(-0.324760\pi\) |
−0.476496 | + | 0.879177i | \(0.658093\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 34.7756 | − | 20.0777i | 0.218715 | − | 0.126275i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 162.595 | + | 105.999i | 1.00991 | + | 0.658378i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 110.989 | + | 192.238i | 0.680913 | + | 1.17938i | 0.974703 | + | 0.223506i | \(0.0717503\pi\) |
−0.293789 | + | 0.955870i | \(0.594916\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −11.3162 | + | 19.6003i | −0.0685832 | + | 0.118790i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | − | 168.841i | − | 1.01102i | −0.862820 | − | 0.505511i | \(-0.831304\pi\) | ||
0.862820 | − | 0.505511i | \(-0.168696\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −64.8234 | −0.383570 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 30.7279 | + | 17.7408i | 0.179695 | + | 0.103747i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −142.323 | + | 82.1704i | −0.822678 | + | 0.474974i | −0.851339 | − | 0.524616i | \(-0.824209\pi\) |
0.0286608 | + | 0.999589i | \(0.490876\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −7.18377 | + | 132.599i | −0.0410501 | + | 0.757711i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 13.8898 | + | 24.0579i | 0.0784736 | + | 0.135920i | ||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 92.5919 | − | 160.374i | 0.517273 | − | 0.895943i | −0.482526 | − | 0.875882i | \(-0.660280\pi\) |
0.999799 | − | 0.0200614i | \(-0.00638618\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | − | 155.086i | − | 0.856830i | −0.903582 | − | 0.428415i | \(-0.859072\pi\) | ||
0.903582 | − | 0.428415i | \(-0.140928\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 64.9340 | 0.354831 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −16.8898 | − | 9.75135i | −0.0912964 | − | 0.0527100i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 15.4964 | − | 8.94687i | 0.0828686 | − | 0.0478442i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −39.7279 | − | 78.3116i | −0.210201 | − | 0.414347i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 124.048 | + | 214.857i | 0.649465 | + | 1.12491i | 0.983251 | + | 0.182257i | \(0.0583402\pi\) |
−0.333786 | + | 0.942649i | \(0.608326\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −77.1690 | + | 133.661i | −0.399840 | + | 0.692543i | −0.993706 | − | 0.112021i | \(-0.964268\pi\) |
0.593866 | + | 0.804564i | \(0.297601\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 72.7461i | 0.373057i | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −181.103 | −0.919303 | −0.459651 | − | 0.888099i | \(-0.652026\pi\) | ||||
−0.459651 | + | 0.888099i | \(0.652026\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −301.989 | − | 174.353i | −1.51753 | − | 0.876147i | −0.999788 | − | 0.0206121i | \(-0.993439\pi\) |
−0.517744 | − | 0.855535i | \(-0.673228\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 21.5223 | − | 12.4259i | 0.107076 | − | 0.0618204i | ||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −21.9411 | + | 11.1309i | −0.108084 | + | 0.0548318i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 92.6985 | + | 160.558i | 0.452188 | + | 0.783212i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −117.640 | + | 203.758i | −0.568307 | + | 0.984337i | ||||
\(208\) | 0 | 0 | ||||||||
\(209\) | − | 19.8931i | − | 0.0951823i | ||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −364.073 | −1.72547 | −0.862733 | − | 0.505660i | \(-0.831249\pi\) | ||||
−0.862733 | + | 0.505660i | \(0.831249\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 22.6325 | + | 13.0669i | 0.106256 | + | 0.0613468i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −60.2132 | + | 34.7641i | −0.280061 | + | 0.161694i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −341.566 | − | 18.5048i | −1.57404 | − | 0.0852757i | ||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −18.8711 | − | 32.6857i | −0.0861694 | − | 0.149250i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 28.7574 | − | 49.8092i | 0.130124 | − | 0.225381i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | − | 123.231i | − | 0.552603i | −0.961071 | − | 0.276302i | \(-0.910891\pi\) | ||
0.961071 | − | 0.276302i | \(-0.0891089\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −160.971 | −0.715425 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 66.1432 | + | 38.1878i | 0.291380 | + | 0.168228i | 0.638564 | − | 0.769569i | \(-0.279529\pi\) |
−0.347184 | + | 0.937797i | \(0.612862\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 309.419 | − | 178.643i | 1.35117 | − | 0.780101i | 0.362760 | − | 0.931883i | \(-0.381834\pi\) |
0.988414 | + | 0.151782i | \(0.0485012\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −13.0477 | + | 20.0144i | −0.0564837 | + | 0.0866423i | ||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 136.537 | + | 236.488i | 0.585994 | + | 1.01497i | 0.994751 | + | 0.102328i | \(0.0326291\pi\) |
−0.408757 | + | 0.912643i | \(0.634038\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 174.658 | − | 302.516i | 0.743225 | − | 1.28730i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 24.2400i | 0.102278i | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 265.103 | 1.10922 | 0.554608 | − | 0.832112i | \(-0.312868\pi\) | ||||
0.554608 | + | 0.832112i | \(0.312868\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −75.8970 | − | 43.8191i | −0.314925 | − | 0.181822i | 0.334203 | − | 0.942501i | \(-0.391533\pi\) |
−0.649128 | + | 0.760679i | \(0.724866\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 139.632 | − | 80.6168i | 0.574619 | − | 0.331757i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −35.1030 | + | 323.019i | −0.143278 | + | 1.31844i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −31.9706 | − | 55.3746i | −0.129435 | − | 0.224189i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 45.7645 | − | 79.2664i | 0.183793 | − | 0.318339i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 495.655i | 1.97472i | 0.158491 | + | 0.987360i | \(0.449337\pi\) | ||||
−0.158491 | + | 0.987360i | \(0.550663\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 131.912 | 0.521390 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −15.4964 | − | 8.94687i | −0.0607703 | − | 0.0350858i | ||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 346.875 | − | 200.268i | 1.34971 | − | 0.779254i | 0.361499 | − | 0.932372i | \(-0.382265\pi\) |
0.988208 | + | 0.153119i | \(0.0489317\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −17.2466 | − | 11.2434i | −0.0665894 | − | 0.0434108i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −14.9117 | − | 25.8278i | −0.0571329 | − | 0.0989571i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −16.1726 | + | 28.0118i | −0.0614928 | + | 0.106509i | −0.895133 | − | 0.445799i | \(-0.852919\pi\) |
0.833640 | + | 0.552308i | \(0.186253\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | − | 371.142i | − | 1.40054i | ||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 36.1097 | 0.135242 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −265.838 | − | 153.482i | −0.988246 | − | 0.570564i | −0.0834963 | − | 0.996508i | \(-0.526609\pi\) |
−0.904749 | + | 0.425944i | \(0.859942\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 65.8051 | − | 37.9926i | 0.242823 | − | 0.140194i | −0.373650 | − | 0.927570i | \(-0.621894\pi\) |
0.616474 | + | 0.787376i | \(0.288561\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −4.15433 | + | 76.6815i | −0.0152173 | + | 0.280885i | ||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 45.1249 | + | 78.1586i | 0.164091 | + | 0.284213i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −139.206 | + | 241.111i | −0.502547 | + | 0.870438i | 0.497448 | + | 0.867494i | \(0.334270\pi\) |
−0.999996 | + | 0.00294398i | \(0.999063\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | − | 414.648i | − | 1.48619i | ||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 394.690 | 1.40459 | 0.702296 | − | 0.711885i | \(-0.252158\pi\) | ||||
0.702296 | + | 0.711885i | \(0.252158\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −126.783 | − | 73.1981i | −0.447996 | − | 0.258650i | 0.258988 | − | 0.965881i | \(-0.416611\pi\) |
−0.706983 | + | 0.707230i | \(0.749944\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −17.2279 | + | 9.94655i | −0.0604488 | + | 0.0349002i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 88.5442 | + | 174.538i | 0.308516 | + | 0.608146i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −137.426 | − | 238.030i | −0.475524 | − | 0.823632i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 36.5147 | − | 63.2453i | 0.125480 | − | 0.217338i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 299.678i | 1.02279i | 0.859345 | + | 0.511396i | \(0.170872\pi\) | ||||
−0.859345 | + | 0.511396i | \(0.829128\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 256.757 | 0.870364 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −51.6838 | − | 29.8396i | −0.174019 | − | 0.100470i | ||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 367.191 | − | 211.998i | 1.22806 | − | 0.709023i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −65.4558 | + | 33.2061i | −0.217461 | + | 0.110319i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 21.4081 | + | 37.0799i | 0.0706539 | + | 0.122376i | ||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 300.081 | − | 519.755i | 0.983871 | − | 1.70412i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 20.9886i | 0.0683666i | 0.999416 | + | 0.0341833i | \(0.0108830\pi\) | ||||
−0.999416 | + | 0.0341833i | \(0.989117\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 86.2203 | 0.279030 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −157.651 | − | 91.0197i | −0.506916 | − | 0.292668i | 0.224649 | − | 0.974440i | \(-0.427876\pi\) |
−0.731565 | + | 0.681772i | \(0.761210\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −84.8087 | + | 48.9643i | −0.270954 | + | 0.156435i | −0.629321 | − | 0.777145i | \(-0.716667\pi\) |
0.358367 | + | 0.933581i | \(0.383334\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −393.286 | − | 21.3068i | −1.24853 | − | 0.0676408i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 240.985 | + | 417.399i | 0.760206 | + | 1.31672i | 0.942744 | + | 0.333517i | \(0.108235\pi\) |
−0.182538 | + | 0.983199i | \(0.558431\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −8.36039 | + | 14.4806i | −0.0262081 | + | 0.0453938i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 81.5084i | 0.253920i | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 15.7279 | 0.0486933 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 251.220 | + | 145.042i | 0.772986 | + | 0.446283i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −90.2832 | + | 52.1250i | −0.276095 | + | 0.159404i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 201.382 | − | 308.907i | 0.612104 | − | 0.938928i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 112.504 | + | 194.862i | 0.339890 | + | 0.588707i | 0.984412 | − | 0.175879i | \(-0.0562768\pi\) |
−0.644522 | + | 0.764586i | \(0.722944\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 12.4781 | − | 21.6128i | 0.0374719 | − | 0.0649032i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | − | 229.696i | − | 0.685661i | ||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −264.368 | −0.784473 | −0.392237 | − | 0.919864i | \(-0.628299\pi\) | ||||
−0.392237 | + | 0.919864i | \(0.628299\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −21.4630 | − | 12.3917i | −0.0633126 | − | 0.0365536i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −201.331 | + | 116.238i | −0.590412 | + | 0.340875i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −55.4487 | + | 338.488i | −0.161658 | + | 0.986847i | ||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −65.9558 | − | 114.239i | −0.191176 | − | 0.331127i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −95.6285 | + | 165.633i | −0.275586 | + | 0.477330i | −0.970283 | − | 0.241973i | \(-0.922205\pi\) |
0.694697 | + | 0.719303i | \(0.255539\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 135.448i | 0.388104i | 0.980991 | + | 0.194052i | \(0.0621630\pi\) | ||||
−0.980991 | + | 0.194052i | \(0.937837\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −191.823 | −0.546505 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −301.802 | − | 174.245i | −0.854962 | − | 0.493612i | 0.00736010 | − | 0.999973i | \(-0.497657\pi\) |
−0.862322 | + | 0.506360i | \(0.830991\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 209.184 | − | 120.772i | 0.589250 | − | 0.340204i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −15.8238 | − | 10.3158i | −0.0443244 | − | 0.0288959i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 152.415 | + | 263.991i | 0.424555 | + | 0.735351i | 0.996379 | − | 0.0850256i | \(-0.0270972\pi\) |
−0.571824 | + | 0.820377i | \(0.693764\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −171.757 | + | 297.492i | −0.475782 | + | 0.824079i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | − | 70.5727i | − | 0.194415i | ||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −348.838 | −0.955720 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 82.2761 | + | 47.5021i | 0.224186 | + | 0.129434i | 0.607887 | − | 0.794024i | \(-0.292017\pi\) |
−0.383701 | + | 0.923457i | \(0.625351\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −205.456 | + | 118.620i | −0.556791 | + | 0.321463i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 21.1949 | − | 391.220i | 0.0571291 | − | 1.05450i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −126.779 | − | 219.588i | −0.339891 | − | 0.588708i | 0.644521 | − | 0.764586i | \(-0.277057\pi\) |
−0.984412 | + | 0.175879i | \(0.943723\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −14.3421 | + | 24.8412i | −0.0382456 | + | 0.0662433i | ||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 53.7446i | 0.142559i | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −508.250 | −1.34103 | −0.670514 | − | 0.741897i | \(-0.733926\pi\) | ||||
−0.670514 | + | 0.741897i | \(0.733926\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −153.676 | − | 88.7250i | −0.403350 | − | 0.232874i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −413.753 | + | 238.881i | −1.08030 | + | 0.623709i | −0.930976 | − | 0.365080i | \(-0.881042\pi\) |
−0.149320 | + | 0.988789i | \(0.547708\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 99.9045 | + | 196.932i | 0.259492 | + | 0.511511i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −44.4853 | − | 77.0508i | −0.114949 | − | 0.199098i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −85.1102 | + | 147.415i | −0.218792 | + | 0.378959i | −0.954439 | − | 0.298406i | \(-0.903545\pi\) |
0.735647 | + | 0.677365i | \(0.236878\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 104.292i | 0.266732i | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −105.926 | −0.269532 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 194.025 | + | 112.021i | 0.491204 | + | 0.283597i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 211.786 | − | 122.275i | 0.533467 | − | 0.307997i | −0.208960 | − | 0.977924i | \(-0.567008\pi\) |
0.742427 | + | 0.669927i | \(0.233675\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −18.7279 | + | 9.50079i | −0.0469371 | + | 0.0238115i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 208.786 | + | 361.629i | 0.520664 | + | 0.901817i | 0.999711 | + | 0.0240277i | \(0.00764899\pi\) |
−0.479047 | + | 0.877789i | \(0.659018\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −373.617 | + | 647.124i | −0.927090 | + | 1.60577i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | − | 446.716i | − | 1.10300i | ||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −13.9920 | −0.0343784 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 266.919 | + | 154.106i | 0.652614 | + | 0.376787i | 0.789457 | − | 0.613806i | \(-0.210362\pi\) |
−0.136843 | + | 0.990593i | \(0.543696\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −20.2386 | + | 11.6848i | −0.0492424 | + | 0.0284301i | ||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 270.647 | + | 14.6627i | 0.655320 | + | 0.0355029i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −422.985 | − | 732.631i | −1.01924 | − | 1.76538i | ||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −24.6030 | + | 42.6137i | −0.0590001 | + | 0.102191i | ||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 103.142i | 0.246163i | 0.992397 | + | 0.123081i | \(0.0392776\pi\) | ||||
−0.992397 | + | 0.123081i | \(0.960722\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −165.220 | −0.392447 | −0.196224 | − | 0.980559i | \(-0.562868\pi\) | ||||
−0.196224 | + | 0.980559i | \(0.562868\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 387.110 | + | 223.498i | 0.915153 | + | 0.528364i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −61.7939 | + | 35.6767i | −0.145398 | + | 0.0839453i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 345.996 | − | 530.736i | 0.810295 | − | 1.24294i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 26.0955 | + | 45.1987i | 0.0608286 | + | 0.105358i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 297.268 | − | 514.883i | 0.689717 | − | 1.19463i | −0.282212 | − | 0.959352i | \(-0.591068\pi\) |
0.971929 | − | 0.235273i | \(-0.0755984\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | − | 40.6267i | − | 0.0938261i | −0.998899 | − | 0.0469131i | \(-0.985062\pi\) | ||
0.998899 | − | 0.0469131i | \(-0.0149384\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 16.7208 | 0.0384386 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 100.412 | + | 57.9727i | 0.229775 | + | 0.132661i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −126.959 | + | 73.3001i | −0.289201 | + | 0.166971i | −0.637582 | − | 0.770383i | \(-0.720065\pi\) |
0.348380 | + | 0.937353i | \(0.386732\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −413.345 | − | 44.9190i | −0.937291 | − | 0.101857i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 53.6802 | + | 92.9768i | 0.121174 | + | 0.209880i | 0.920231 | − | 0.391376i | \(-0.128001\pi\) |
−0.799057 | + | 0.601256i | \(0.794667\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 166.875 | − | 289.035i | 0.374999 | − | 0.649518i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 66.2892i | 0.148298i | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 135.161 | 0.301028 | 0.150514 | − | 0.988608i | \(-0.451907\pi\) | ||||
0.150514 | + | 0.988608i | \(0.451907\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 115.191 | + | 66.5055i | 0.255412 | + | 0.147462i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 57.0290 | − | 32.9257i | 0.125892 | − | 0.0726837i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 594.588 | + | 387.622i | 1.30679 | + | 0.851918i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −79.8675 | − | 138.335i | −0.174765 | − | 0.302702i | 0.765315 | − | 0.643656i | \(-0.222583\pi\) |
−0.940080 | + | 0.340954i | \(0.889250\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 23.5919 | − | 40.8623i | 0.0513984 | − | 0.0890247i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 310.250i | 0.672993i | 0.941685 | + | 0.336497i | \(0.109242\pi\) | ||||
−0.941685 | + | 0.336497i | \(0.890758\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 326.014 | 0.704135 | 0.352067 | − | 0.935975i | \(-0.385479\pi\) | ||||
0.352067 | + | 0.935975i | \(0.385479\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 201.331 | + | 116.238i | 0.432969 | + | 0.249975i | ||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −515.769 | + | 297.779i | −1.10443 | + | 0.637643i | −0.937381 | − | 0.348306i | \(-0.886757\pi\) |
−0.167048 | + | 0.985949i | \(0.553424\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 13.1173 | − | 242.122i | 0.0279687 | − | 0.516252i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −3.03344 | − | 5.25408i | −0.00644043 | − | 0.0111551i | ||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −24.9411 | + | 43.1993i | −0.0527297 | + | 0.0913304i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 79.3262i | 0.167002i | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 474.926 | 0.995652 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −438.798 | − | 253.340i | −0.916071 | − | 0.528894i | −0.0336914 | − | 0.999432i | \(-0.510726\pi\) |
−0.882379 | + | 0.470539i | \(0.844060\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −38.9483 | + | 22.4868i | −0.0809735 | + | 0.0467501i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −63.0000 | − | 124.185i | −0.130435 | − | 0.257113i | ||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −337.492 | − | 584.554i | −0.695861 | − | 1.20527i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 105.651 | − | 182.992i | 0.216942 | − | 0.375755i | −0.736930 | − | 0.675970i | \(-0.763725\pi\) |
0.953872 | + | 0.300215i | \(0.0970584\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | − | 159.255i | − | 0.325676i | ||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 784.161 | 1.59707 | 0.798534 | − | 0.601949i | \(-0.205609\pi\) | ||||
0.798534 | + | 0.601949i | \(0.205609\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −11.4487 | − | 6.60991i | −0.0232225 | − | 0.0134075i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −231.816 | + | 133.839i | −0.468316 | + | 0.270382i | ||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 227.397 | − | 115.360i | 0.457539 | − | 0.232112i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −85.7462 | − | 148.517i | −0.171836 | − | 0.297629i | 0.767226 | − | 0.641377i | \(-0.221637\pi\) |
−0.939062 | + | 0.343748i | \(0.888303\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −60.5665 | + | 104.904i | −0.120891 | + | 0.209390i | ||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 20.0883i | 0.0399370i | 0.999801 | + | 0.0199685i | \(0.00635659\pi\) | ||||
−0.999801 | + | 0.0199685i | \(0.993643\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 395.735 | 0.783634 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 40.2761 | + | 23.2534i | 0.0794400 | + | 0.0458647i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −412.890 | + | 238.382i | −0.811178 | + | 0.468334i | −0.847365 | − | 0.531011i | \(-0.821812\pi\) |
0.0361865 | + | 0.999345i | \(0.488479\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −367.709 | − | 19.9211i | −0.719587 | − | 0.0389846i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −26.2279 | − | 45.4281i | −0.0511266 | − | 0.0885538i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 398.452 | − | 690.139i | 0.773693 | − | 1.34008i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | − | 250.613i | − | 0.484744i | ||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 117.905 | 0.227176 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 739.823 | + | 427.137i | 1.42001 | + | 0.819841i | 0.996299 | − | 0.0859587i | \(-0.0273953\pi\) |
0.423707 | + | 0.905799i | \(0.360729\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 513.554 | − | 296.501i | 0.981940 | − | 0.566923i | 0.0790845 | − | 0.996868i | \(-0.474800\pi\) |
0.902855 | + | 0.429945i | \(0.141467\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 52.0294 | − | 79.8098i | 0.0991037 | − | 0.152019i | ||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −91.9005 | − | 159.176i | −0.174384 | − | 0.302043i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −119.919 | + | 207.706i | −0.226690 | + | 0.392638i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 328.555i | 0.618748i | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 427.529 | 0.802118 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 652.422 | + | 376.676i | 1.21948 | + | 0.704068i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −115.058 | + | 66.4290i | −0.214262 | + | 0.123704i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 94.0629 | + | 213.290i | 0.174514 | + | 0.395715i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −427.595 | − | 740.617i | −0.790380 | − | 1.36898i | −0.925732 | − | 0.378180i | \(-0.876550\pi\) |
0.135352 | − | 0.990798i | \(-0.456783\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −55.6325 | + | 96.3583i | −0.102454 | + | 0.177455i | ||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 963.546i | 1.76797i | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −415.897 | −0.760323 | −0.380161 | − | 0.924920i | \(-0.624132\pi\) | ||||
−0.380161 | + | 0.924920i | \(0.624132\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 665.095 | + | 383.993i | 1.21147 | + | 0.699441i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −12.7279 | + | 7.34847i | −0.0230997 | + | 0.0133366i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 198.124 | + | 129.161i | 0.358272 | + | 0.233564i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 6.99600 | + | 12.1174i | 0.0126054 | + | 0.0218332i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 292.110 | − | 505.950i | 0.524435 | − | 0.908348i | −0.475160 | − | 0.879899i | \(-0.657610\pi\) |
0.999595 | − | 0.0284485i | \(-0.00905667\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 160.333i | 0.286822i | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −12.8377 | −0.0228835 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −789.076 | − | 455.573i | −1.40156 | − | 0.809189i | −0.407004 | − | 0.913426i | \(-0.633427\pi\) |
−0.994552 | + | 0.104237i | \(0.966760\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −198.375 | + | 114.532i | −0.351106 | + | 0.202711i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 25.5107 | − | 470.882i | 0.0449924 | − | 0.830480i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −350.000 | − | 606.217i | −0.615113 | − | 1.06541i | −0.990365 | − | 0.138485i | \(-0.955777\pi\) |
0.375251 | − | 0.926923i | \(-0.377556\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −281.231 | + | 487.107i | −0.492525 | + | 0.853077i | −0.999963 | − | 0.00861055i | \(-0.997259\pi\) |
0.507438 | + | 0.861688i | \(0.330592\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | − | 177.993i | − | 0.310634i | ||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −526.014 | −0.914807 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −573.014 | − | 330.830i | −0.993092 | − | 0.573362i | −0.0868946 | − | 0.996218i | \(-0.527694\pi\) |
−0.906197 | + | 0.422856i | \(0.861028\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 95.8934 | − | 55.3641i | 0.165619 | − | 0.0956202i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −404.029 | − | 796.420i | −0.695402 | − | 1.37077i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −133.136 | − | 230.598i | −0.228364 | − | 0.395538i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −430.191 | + | 745.113i | −0.735369 | + | 1.27370i | ||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 823.029i | 1.40209i | 0.713116 | + | 0.701046i | \(0.247283\pi\) | ||||
−0.713116 | + | 0.701046i | \(0.752717\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −204.338 | −0.346924 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 112.523 | + | 64.9650i | 0.190394 | + | 0.109924i | ||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −538.890 | + | 311.128i | −0.908752 | + | 0.524668i | −0.880029 | − | 0.474919i | \(-0.842477\pi\) |
−0.0287225 | + | 0.999587i | \(0.509144\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −155.698 | + | 78.9868i | −0.261678 | + | 0.132751i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 125.088 | + | 216.659i | 0.209527 | + | 0.362912i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −256.422 | + | 444.137i | −0.428084 | + | 0.741463i | −0.996703 | − | 0.0811377i | \(-0.974145\pi\) |
0.568619 | + | 0.822601i | \(0.307478\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 680.160i | 1.13171i | 0.824504 | + | 0.565857i | \(0.191454\pi\) | ||||
−0.824504 | + | 0.565857i | \(0.808546\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 293.927 | 0.487441 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −564.889 | − | 326.139i | −0.933701 | − | 0.539073i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −33.5482 | + | 19.3690i | −0.0552688 | + | 0.0319095i | −0.527380 | − | 0.849630i | \(-0.676825\pi\) |
0.472111 | + | 0.881539i | \(0.343492\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 17.6253 | + | 0.954877i | 0.0289414 | + | 0.00156794i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −402.765 | − | 697.609i | −0.659189 | − | 1.14175i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −200.552 | + | 347.366i | −0.327164 | + | 0.566665i | −0.981948 | − | 0.189151i | \(-0.939426\pi\) |
0.654784 | + | 0.755816i | \(0.272760\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | − | 133.011i | − | 0.216278i | ||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −959.044 | −1.55437 | −0.777183 | − | 0.629275i | \(-0.783352\pi\) | ||||
−0.777183 | + | 0.629275i | \(0.783352\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 869.951 | + | 502.267i | 1.40541 | + | 0.811416i | 0.994941 | − | 0.100457i | \(-0.0320303\pi\) |
0.410473 | + | 0.911873i | \(0.365364\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 301.235 | − | 173.918i | 0.485081 | − | 0.280061i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 192.408 | − | 295.142i | 0.308841 | − | 0.473743i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 369.691 | + | 640.323i | 0.591505 | + | 1.02452i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −7.13604 | + | 12.3600i | −0.0113812 | + | 0.0197129i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | − | 11.0624i | − | 0.0175873i | ||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 386.514 | 0.612542 | 0.306271 | − | 0.951944i | \(-0.400919\pi\) | ||||
0.306271 | + | 0.951944i | \(0.400919\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 226.206 | + | 130.600i | 0.357356 | + | 0.206319i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −1420.37 | + | 820.053i | −2.23681 | + | 1.29142i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 604.617 | + | 442.547i | 0.949164 | + | 0.694736i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 154.544 | + | 267.678i | 0.241853 | + | 0.418902i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 496.074 | − | 859.225i | 0.773906 | − | 1.34044i | −0.161502 | − | 0.986872i | \(-0.551634\pi\) |
0.935407 | − | 0.353572i | \(-0.115033\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | − | 944.986i | − | 1.46965i | −0.678256 | − | 0.734826i | \(-0.737264\pi\) | ||
0.678256 | − | 0.734826i | \(-0.262736\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 49.8823 | 0.0773368 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −2.50357 | − | 1.44544i | −0.00386951 | − | 0.00223406i | 0.498064 | − | 0.867140i | \(-0.334044\pi\) |
−0.501934 | + | 0.864906i | \(0.667378\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 159.529 | − | 92.1039i | 0.245807 | − | 0.141917i | ||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 205.584 | + | 134.024i | 0.315797 | + | 0.205874i | ||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 161.529 | + | 279.777i | 0.247365 | + | 0.428449i | 0.962794 | − | 0.270237i | \(-0.0871019\pi\) |
−0.715429 | + | 0.698686i | \(0.753769\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −489.518 | + | 847.870i | −0.747356 | + | 1.29446i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | − | 446.384i | − | 0.679428i | ||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −295.955 | −0.449098 | −0.224549 | − | 0.974463i | \(-0.572091\pi\) | ||||
−0.224549 | + | 0.974463i | \(0.572091\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 17.9710 | + | 10.3756i | 0.0271876 | + | 0.0156968i | 0.513532 | − | 0.858070i | \(-0.328337\pi\) |
−0.486345 | + | 0.873767i | \(0.661670\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −35.7351 | + | 20.6316i | −0.0538990 | + | 0.0311186i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −10.5000 | + | 193.811i | −0.0157895 | + | 0.291445i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −48.7279 | − | 84.3992i | −0.0730554 | − | 0.126536i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −44.2052 | + | 76.5656i | −0.0660765 | + | 0.114448i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | − | 430.579i | − | 0.641698i | ||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 627.044 | 0.931714 | 0.465857 | − | 0.884860i | \(-0.345746\pi\) | ||||
0.465857 | + | 0.884860i | \(0.345746\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 206.095 | + | 118.989i | 0.305327 | + | 0.176280i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −94.6097 | + | 54.6230i | −0.139749 | + | 0.0806838i | −0.568244 | − | 0.822860i | \(-0.692377\pi\) |
0.428496 | + | 0.903544i | \(0.359044\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −322.368 | − | 635.450i | −0.474768 | − | 0.935861i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −27.3974 | − | 47.4537i | −0.0402311 | − | 0.0696824i | ||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 396.783 | − | 687.248i | 0.580941 | − | 1.00622i | −0.414427 | − | 0.910083i | \(-0.636018\pi\) |
0.995368 | − | 0.0961370i | \(-0.0306487\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 215.996i | 0.315323i | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −256.331 | −0.373116 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −741.198 | − | 427.931i | −1.07576 | − | 0.621090i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −159.253 | + | 91.9447i | −0.230467 | + | 0.133060i | −0.610788 | − | 0.791794i | \(-0.709147\pi\) |
0.380320 | + | 0.924855i | \(0.375814\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −252.000 | + | 127.841i | −0.363636 | + | 0.184475i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 227.397 | + | 393.863i | 0.327190 | + | 0.566710i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −52.5807 | + | 91.0725i | −0.0754386 | + | 0.130664i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | − | 195.913i | − | 0.280277i | ||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −1043.82 | −1.48905 | −0.744525 | − | 0.667595i | \(-0.767324\pi\) | ||||
−0.744525 | + | 0.667595i | \(0.767324\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −10.6508 | − | 6.14922i | −0.0151504 | − | 0.00874711i | ||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −217.037 | + | 125.306i | −0.307854 | + | 0.177740i | ||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 417.143 | + | 22.5993i | 0.590019 | + | 0.0319651i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 490.279 | + | 849.188i | 0.691507 | + | 1.19773i | 0.971344 | + | 0.237678i | \(0.0763864\pi\) |
−0.279836 | + | 0.960048i | \(0.590280\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −143.345 | + | 248.281i | −0.201611 | + | 0.349200i | ||||
\(712\) | 0 | 0 | ||||||||
\(713\) | − | 1354.97i | − | 1.90038i | ||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 482.382 | 0.674660 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −164.714 | − | 95.0975i | −0.229726 | − | 0.132632i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 674.187 | − | 389.242i | 0.937673 | − | 0.541366i | 0.0484429 | − | 0.998826i | \(-0.484574\pi\) |
0.889230 | + | 0.457460i | \(0.151241\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 459.419 | − | 704.719i | 0.637197 | − | 0.977419i | ||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 31.4376 | + | 54.4514i | 0.0434821 | + | 0.0753132i | ||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 33.3381 | − | 57.7433i | 0.0459836 | − | 0.0796459i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 735.255i | 1.01135i | 0.862723 | + | 0.505677i | \(0.168757\pi\) | ||||
−0.862723 | + | 0.505677i | \(0.831243\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 490.632 | 0.673021 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −34.1543 | − | 19.7190i | −0.0467227 | − | 0.0269754i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −414.705 | + | 239.430i | −0.565764 | + | 0.326644i | −0.755456 | − | 0.655200i | \(-0.772585\pi\) |
0.189692 | + | 0.981844i | \(0.439251\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 137.683 | − | 188.106i | 0.187324 | − | 0.255926i | ||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −82.3965 | − | 142.715i | −0.111800 | − | 0.193643i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −9.95227 | + | 17.2378i | −0.0134672 | + | 0.0233259i | −0.872680 | − | 0.488292i | \(-0.837620\pi\) |
0.859213 | + | 0.511618i | \(0.170954\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 45.8739i | 0.0619080i | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −43.3095 | −0.0582901 | −0.0291450 | − | 0.999575i | \(-0.509278\pi\) | ||||
−0.0291450 | + | 0.999575i | \(0.509278\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 530.603 | + | 306.344i | 0.712218 | + | 0.411199i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 937.499 | − | 541.265i | 1.25502 | − | 0.724585i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 666.206 | + | 434.311i | 0.889460 | + | 0.579855i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 112.665 | + | 195.142i | 0.150020 | + | 0.259842i | 0.931235 | − | 0.364420i | \(-0.118733\pi\) |
−0.781215 | + | 0.624263i | \(0.785400\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 177.801 | − | 307.961i | 0.236124 | − | 0.408978i | ||||
\(754\) | 0 | 0 | ||||||||
\(755\) | − | 608.641i | − | 0.806147i | ||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 935.779 | 1.23617 | 0.618084 | − | 0.786112i | \(-0.287909\pi\) | ||||
0.618084 | + | 0.786112i | \(0.287909\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −81.9594 | − | 47.3193i | −0.107983 | − | 0.0623443i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 1214.79 | − | 701.357i | 1.59630 | − | 0.921625i | 0.604110 | − | 0.796901i | \(-0.293529\pi\) |
0.992191 | − | 0.124724i | \(-0.0398046\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −55.0254 | + | 1015.67i | −0.0721172 | + | 1.33115i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −105.816 | − | 183.279i | −0.138322 | − | 0.239581i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 296.044 | − | 512.763i | 0.385976 | − | 0.668530i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 1.72330i | 0.00224097i | 0.999999 | + | 0.00112048i | \(0.000356661\pi\) | ||||
−0.999999 | + | 0.00112048i | \(0.999643\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −287.360 | −0.372711 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 194.213 | + | 112.129i | 0.251245 | + | 0.145057i | 0.620334 | − | 0.784337i | \(-0.286997\pi\) |
−0.369089 | + | 0.929394i | \(0.620330\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 802.831 | − | 463.514i | 1.03591 | − | 0.598083i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 6.68247 | + | 13.1725i | 0.00860034 | + | 0.0169530i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 58.4558 | + | 101.248i | 0.0750396 | + | 0.129972i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 86.6468 | − | 150.077i | 0.110943 | − | 0.192160i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 44.0908i | 0.0563101i | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −56.0740 | −0.0714319 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −60.7979 | − | 35.1017i | −0.0772528 | − | 0.0446019i | 0.460876 | − | 0.887465i | \(-0.347535\pi\) |
−0.538129 | + | 0.842863i | \(0.680869\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 20.0968 | − | 11.6029i | 0.0254712 | − | 0.0147058i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −215.647 | + | 109.399i | −0.272625 | + | 0.138305i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −691.992 | − | 1198.57i | −0.872625 | − | 1.51143i | ||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −133.136 | + | 230.598i | −0.167467 | + | 0.290061i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 1305.38i | 1.63787i | 0.573889 | + | 0.818933i | \(0.305434\pi\) | ||||
−0.573889 | + | 0.818933i | \(0.694566\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 198.140 | 0.247985 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 369.859 | + | 213.538i | 0.461747 | + | 0.266590i | ||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −216.740 | + | 125.135i | −0.269913 | + | 0.155834i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −1285.17 | − | 69.6258i | −1.59648 | − | 0.0864917i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 110.114 | + | 190.723i | 0.136448 | + | 0.236335i | ||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −381.382 | + | 660.573i | −0.471424 | + | 0.816531i | −0.999466 | − | 0.0326879i | \(-0.989593\pi\) |
0.528041 | + | 0.849219i | \(0.322927\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | − | 1214.98i | − | 1.49813i | −0.662498 | − | 0.749064i | \(-0.730504\pi\) | ||
0.662498 | − | 0.749064i | \(-0.269496\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −54.5147 | −0.0670538 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −1274.74 | − | 735.970i | −1.56410 | − | 0.903031i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −37.9706 | + | 21.9223i | −0.0464756 | + | 0.0268327i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −496.014 | + | 760.854i | −0.605634 | + | 0.929004i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 291.684 | + | 505.211i | 0.355279 | + | 0.615361i | 0.987166 | − | 0.159700i | \(-0.0510527\pi\) |
−0.631887 | + | 0.775061i | \(0.717719\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 515.371 | − | 892.648i | 0.626210 | − | 1.08463i | −0.362096 | − | 0.932141i | \(-0.617939\pi\) |
0.988306 | − | 0.152486i | \(-0.0487280\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | − | 64.7487i | − | 0.0784833i | ||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −152.102 | −0.183920 | −0.0919599 | − | 0.995763i | \(-0.529313\pi\) | ||||
−0.0919599 | + | 0.995763i | \(0.529313\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 532.095 | + | 307.205i | 0.641852 | + | 0.370573i | 0.785327 | − | 0.619081i | \(-0.212495\pi\) |
−0.143476 | + | 0.989654i | \(0.545828\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 172.983 | − | 99.8715i | 0.208162 | − | 0.120182i | ||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −168.632 | + | 74.3682i | −0.202439 | + | 0.0892776i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 559.794 | + | 969.592i | 0.670412 | + | 1.16119i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −306.507 | + | 530.886i | −0.366197 | + | 0.634272i | ||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 1546.14i | 1.84284i | 0.388568 | + | 0.921420i | \(0.372970\pi\) | ||||
−0.388568 | + | 0.921420i | \(0.627030\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −828.647 | −0.985311 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −245.229 | − | 141.583i | −0.290901 | − | 0.167952i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 372.257 | − | 214.923i | 0.440541 | − | 0.254347i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −576.823 | − | 376.041i | −0.681019 | − | 0.443969i | ||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 52.5152 | + | 90.9589i | 0.0618553 | + | 0.107137i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 40.7756 | − | 70.6255i | 0.0479150 | − | 0.0829912i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | − | 1235.15i | − | 1.44800i | −0.689798 | − | 0.724002i | \(-0.742301\pi\) | ||
0.689798 | − | 0.724002i | \(-0.257699\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −235.279 | −0.275180 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −953.219 | − | 550.341i | −1.11227 | − | 0.642172i | −0.172857 | − | 0.984947i | \(-0.555300\pi\) |
−0.939417 | + | 0.342775i | \(0.888633\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −512.488 | + | 295.885i | −0.596610 | + | 0.344453i | −0.767707 | − | 0.640801i | \(-0.778602\pi\) |
0.171096 | + | 0.985254i | \(0.445269\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 7.59589 | − | 140.207i | 0.00882217 | − | 0.162841i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −32.3635 | − | 56.0553i | −0.0375012 | − | 0.0649540i | 0.846666 | − | 0.532125i | \(-0.178606\pi\) |
−0.884167 | + | 0.467171i | \(0.845273\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 544.875 | − | 943.751i | 0.629913 | − | 1.09104i | ||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 197.190i | 0.227440i | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 160.736 | 0.184967 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −458.720 | − | 264.842i | −0.526659 | − | 0.304067i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 748.014 | − | 431.866i | 0.856832 | − | 0.494692i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 126.618 | + | 249.589i | 0.144706 | + | 0.285245i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 152.096 | + | 263.438i | 0.173427 | + | 0.300385i | 0.939616 | − | 0.342231i | \(-0.111182\pi\) |
−0.766188 | + | 0.642616i | \(0.777849\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 107.500 | − | 186.196i | 0.122299 | − | 0.211827i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 863.732i | 0.980400i | 0.871610 | + | 0.490200i | \(0.163076\pi\) | ||||
−0.871610 | + | 0.490200i | \(0.836924\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 567.456 | 0.642645 | 0.321323 | − | 0.946970i | \(-0.395873\pi\) | ||||
0.321323 | + | 0.946970i | \(0.395873\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −159.529 | − | 92.1039i | −0.180258 | − | 0.104072i | ||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 770.555 | − | 444.880i | 0.868721 | − | 0.501556i | 0.00179783 | − | 0.999998i | \(-0.499428\pi\) |
0.866923 | + | 0.498442i | \(0.166094\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −1544.04 | + | 783.302i | −1.73683 | + | 0.881105i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −160.246 | − | 277.554i | −0.179849 | − | 0.311508i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 110.140 | − | 190.767i | 0.123337 | − | 0.213625i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 1227.96i | 1.37202i | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −304.191 | −0.339120 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 148.742 | + | 85.8764i | 0.165453 | + | 0.0955243i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 182.316 | − | 105.260i | 0.202349 | − | 0.116826i | ||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 52.5807 | + | 2.84864i | 0.0582289 | + | 0.00315464i | ||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 514.191 | + | 890.605i | 0.568167 | + | 0.984094i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 186.989 | − | 323.874i | 0.206162 | − | 0.357083i | −0.744340 | − | 0.667800i | \(-0.767236\pi\) |
0.950502 | + | 0.310717i | \(0.100569\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 506.395i | 0.557091i | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −1133.75 | −1.24451 | −0.622256 | − | 0.782814i | \(-0.713784\pi\) | ||||
−0.622256 | + | 0.782814i | \(0.713784\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −525.618 | − | 303.466i | −0.575704 | − | 0.332383i | ||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −372.893 | + | 215.290i | −0.407533 | + | 0.235289i | ||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −564.419 | + | 865.782i | −0.615506 | + | 0.944146i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 228.151 | + | 395.169i | 0.248260 | + | 0.429999i | 0.963043 | − | 0.269347i | \(-0.0868078\pi\) |
−0.714783 | + | 0.699346i | \(0.753475\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 7.52900 | − | 13.0406i | 0.00817481 | − | 0.0141592i | ||||
\(922\) | 0 | 0 | ||||||||
\(923\) | − | 557.007i | − | 0.603474i | ||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 55.7948 | 0.0603187 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 883.124 | + | 509.872i | 0.952669 | + | 0.550024i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −824.058 | + | 475.770i | −0.887037 | + | 0.512131i | −0.872972 | − | 0.487770i | \(-0.837811\pi\) |
−0.0140650 | + | 0.999901i | \(0.504477\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −22.1360 | + | 203.696i | −0.0237766 | + | 0.218793i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 65.3011 | + | 113.105i | 0.0699904 | + | 0.121227i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −59.3269 | + | 102.757i | −0.0634513 | + | 0.109901i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | − | 1295.71i | − | 1.38283i | −0.722460 | − | 0.691413i | \(-0.756989\pi\) | ||
0.722460 | − | 0.691413i | \(-0.243011\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 70.2578 | 0.0748219 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −1175.10 | − | 678.446i | −1.24878 | − | 0.720984i | −0.277915 | − | 0.960606i | \(-0.589643\pi\) |
−0.970866 | + | 0.239622i | \(0.922977\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −671.382 | + | 387.622i | −0.711964 | + | 0.411052i | ||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 487.786 | + | 317.997i | 0.516176 | + | 0.336504i | ||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −354.731 | − | 614.412i | −0.374584 | − | 0.648799i | 0.615681 | − | 0.787996i | \(-0.288881\pi\) |
−0.990265 | + | 0.139197i | \(0.955548\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −402.213 | + | 696.654i | −0.423828 | + | 0.734092i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | − | 345.784i | − | 0.363601i | ||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 936.603 | 0.982794 | 0.491397 | − | 0.870936i | \(-0.336486\pi\) | ||||
0.491397 | + | 0.870936i | \(0.336486\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −1424.72 | − | 822.564i | −1.49186 | − | 0.861324i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 10.3890 | − | 5.99807i | 0.0108558 | − | 0.00626757i | ||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −12.3350 | + | 227.681i | −0.0128623 | + | 0.237415i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 713.477 | + | 1235.78i | 0.742432 | + | 1.28593i | ||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −482.007 | + | 834.861i | −0.500527 | + | 0.866938i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | − | 1023.42i | − | 1.06054i | ||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −1374.37 | −1.42127 | −0.710635 | − | 0.703561i | \(-0.751592\pi\) | ||||
−0.710635 | + | 0.703561i | \(0.751592\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −9.77208 | − | 5.64191i | −0.0100847 | − | 0.00582241i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 27.2466 | − | 15.7309i | 0.0280604 | − | 0.0162007i | −0.485904 | − | 0.874012i | \(-0.661510\pi\) |
0.513965 | + | 0.857811i | \(0.328176\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 217.206 | + | 428.156i | 0.223233 | + | 0.440037i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −104.059 | − | 180.235i | −0.106727 | − | 0.184857i | ||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 270.949 | − | 469.297i | 0.277327 | − | 0.480345i | −0.693392 | − | 0.720560i | \(-0.743885\pi\) |
0.970720 | + | 0.240215i | \(0.0772181\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | − | 239.445i | − | 0.244581i | ||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −1232.98 | −1.25687 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −19.4161 | − | 11.2099i | −0.0197519 | − | 0.0114038i | 0.490092 | − | 0.871671i | \(-0.336963\pi\) |
−0.509843 | + | 0.860267i | \(0.670297\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 1040.01 | − | 600.448i | 1.05584 | − | 0.609592i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −235.934 | + | 119.691i | −0.239042 | + | 0.121267i | ||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −145.368 | − | 251.784i | −0.146984 | − | 0.254584i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 339.017 | − | 587.195i | 0.342096 | − | 0.592528i | −0.642726 | − | 0.766097i | \(-0.722196\pi\) |
0.984822 | + | 0.173568i | \(0.0555298\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | − | 161.429i | − | 0.162567i | ||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 2312.28 | 2.32390 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 758.779 | + | 438.081i | 0.761062 | + | 0.439400i | 0.829677 | − | 0.558244i | \(-0.188525\pi\) |
−0.0686147 | + | 0.997643i | \(0.521858\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −31.9523 | + | 18.4477i | −0.0319843 | + | 0.0184661i |
(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 | 112.3.s.b.17.1 | 4 | ||
3.2 | odd | 2 | 1008.3.cg.l.577.2 | 4 | |||
4.3 | odd | 2 | 14.3.d.a.3.1 | ✓ | 4 | ||
7.2 | even | 3 | 784.3.s.c.705.2 | 4 | |||
7.3 | odd | 6 | 784.3.c.e.97.2 | 4 | |||
7.4 | even | 3 | 784.3.c.e.97.3 | 4 | |||
7.5 | odd | 6 | inner | 112.3.s.b.33.1 | 4 | ||
7.6 | odd | 2 | 784.3.s.c.129.2 | 4 | |||
8.3 | odd | 2 | 448.3.s.d.129.1 | 4 | |||
8.5 | even | 2 | 448.3.s.c.129.2 | 4 | |||
12.11 | even | 2 | 126.3.n.c.73.2 | 4 | |||
20.3 | even | 4 | 350.3.i.a.199.2 | 8 | |||
20.7 | even | 4 | 350.3.i.a.199.3 | 8 | |||
20.19 | odd | 2 | 350.3.k.a.101.2 | 4 | |||
21.5 | even | 6 | 1008.3.cg.l.145.2 | 4 | |||
28.3 | even | 6 | 98.3.b.b.97.4 | 4 | |||
28.11 | odd | 6 | 98.3.b.b.97.3 | 4 | |||
28.19 | even | 6 | 14.3.d.a.5.1 | yes | 4 | ||
28.23 | odd | 6 | 98.3.d.a.19.1 | 4 | |||
28.27 | even | 2 | 98.3.d.a.31.1 | 4 | |||
56.5 | odd | 6 | 448.3.s.c.257.2 | 4 | |||
56.19 | even | 6 | 448.3.s.d.257.1 | 4 | |||
84.11 | even | 6 | 882.3.c.f.685.2 | 4 | |||
84.23 | even | 6 | 882.3.n.b.19.2 | 4 | |||
84.47 | odd | 6 | 126.3.n.c.19.2 | 4 | |||
84.59 | odd | 6 | 882.3.c.f.685.1 | 4 | |||
84.83 | odd | 2 | 882.3.n.b.325.2 | 4 | |||
140.19 | even | 6 | 350.3.k.a.201.2 | 4 | |||
140.47 | odd | 12 | 350.3.i.a.299.2 | 8 | |||
140.103 | odd | 12 | 350.3.i.a.299.3 | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
14.3.d.a.3.1 | ✓ | 4 | 4.3 | odd | 2 | ||
14.3.d.a.5.1 | yes | 4 | 28.19 | even | 6 | ||
98.3.b.b.97.3 | 4 | 28.11 | odd | 6 | |||
98.3.b.b.97.4 | 4 | 28.3 | even | 6 | |||
98.3.d.a.19.1 | 4 | 28.23 | odd | 6 | |||
98.3.d.a.31.1 | 4 | 28.27 | even | 2 | |||
112.3.s.b.17.1 | 4 | 1.1 | even | 1 | trivial | ||
112.3.s.b.33.1 | 4 | 7.5 | odd | 6 | inner | ||
126.3.n.c.19.2 | 4 | 84.47 | odd | 6 | |||
126.3.n.c.73.2 | 4 | 12.11 | even | 2 | |||
350.3.i.a.199.2 | 8 | 20.3 | even | 4 | |||
350.3.i.a.199.3 | 8 | 20.7 | even | 4 | |||
350.3.i.a.299.2 | 8 | 140.47 | odd | 12 | |||
350.3.i.a.299.3 | 8 | 140.103 | odd | 12 | |||
350.3.k.a.101.2 | 4 | 20.19 | odd | 2 | |||
350.3.k.a.201.2 | 4 | 140.19 | even | 6 | |||
448.3.s.c.129.2 | 4 | 8.5 | even | 2 | |||
448.3.s.c.257.2 | 4 | 56.5 | odd | 6 | |||
448.3.s.d.129.1 | 4 | 8.3 | odd | 2 | |||
448.3.s.d.257.1 | 4 | 56.19 | even | 6 | |||
784.3.c.e.97.2 | 4 | 7.3 | odd | 6 | |||
784.3.c.e.97.3 | 4 | 7.4 | even | 3 | |||
784.3.s.c.129.2 | 4 | 7.6 | odd | 2 | |||
784.3.s.c.705.2 | 4 | 7.2 | even | 3 | |||
882.3.c.f.685.1 | 4 | 84.59 | odd | 6 | |||
882.3.c.f.685.2 | 4 | 84.11 | even | 6 | |||
882.3.n.b.19.2 | 4 | 84.23 | even | 6 | |||
882.3.n.b.325.2 | 4 | 84.83 | odd | 2 | |||
1008.3.cg.l.145.2 | 4 | 21.5 | even | 6 | |||
1008.3.cg.l.577.2 | 4 | 3.2 | odd | 2 |