Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [168,4,Mod(25,168)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(168, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 0, 0, 4]))
N = Newforms(chi, 4, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("168.25");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 168 = 2^{3} \cdot 3 \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 168.q (of order \(3\), degree \(2\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(9.91232088096\) |
Analytic rank: | \(0\) |
Dimension: | \(8\) |
Relative dimension: | \(4\) over \(\Q(\zeta_{3})\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{8} + \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{8} + 173x^{6} + 9457x^{4} + 168048x^{2} + 746496 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 2^{6}\cdot 7 \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{3}]$ |
Embedding invariants
Embedding label | 25.3 | ||
Root | \(2.57353i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 168.25 |
Dual form | 168.4.q.f.121.3 |
$q$-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 \(\left(\mathbb{Z}/168\mathbb{Z}\right)^\times\).
\(n\) | \(73\) | \(85\) | \(113\) | \(127\) |
\(\chi(n)\) | \(e\left(\frac{2}{3}\right)\) | \(1\) | \(1\) | \(1\) |
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 | ||||||||
\(3\) | −1.50000 | + | 2.59808i | −0.288675 | + | 0.500000i | ||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −0.0642956 | − | 0.111363i | −0.00575077 | − | 0.00996063i | 0.863136 | − | 0.504972i | \(-0.168497\pi\) |
−0.868886 | + | 0.495011i | \(0.835164\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −0.866259 | − | 18.5000i | −0.0467736 | − | 0.998906i | ||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −4.50000 | − | 7.79423i | −0.166667 | − | 0.288675i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −27.0033 | + | 46.7711i | −0.740163 | + | 1.28200i | 0.212257 | + | 0.977214i | \(0.431919\pi\) |
−0.952421 | + | 0.304787i | \(0.901415\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −50.2350 | −1.07175 | −0.535873 | − | 0.844299i | \(-0.680017\pi\) | ||||
−0.535873 | + | 0.844299i | \(0.680017\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0.385773 | 0.00664042 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 65.7436 | − | 113.871i | 0.937951 | − | 1.62458i | 0.168666 | − | 0.985673i | \(-0.446054\pi\) |
0.769285 | − | 0.638906i | \(-0.220613\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −45.7547 | − | 79.2495i | −0.552466 | − | 0.956899i | −0.998096 | − | 0.0616814i | \(-0.980354\pi\) |
0.445630 | − | 0.895217i | \(-0.352980\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 49.3638 | + | 25.4994i | 0.512955 | + | 0.264972i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −89.7436 | − | 155.441i | −0.813602 | − | 1.40920i | −0.910328 | − | 0.413888i | \(-0.864170\pi\) |
0.0967260 | − | 0.995311i | \(-0.469163\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 62.4917 | − | 108.239i | 0.499934 | − | 0.865911i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 27.0000 | 0.192450 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −69.8961 | −0.447565 | −0.223782 | − | 0.974639i | \(-0.571841\pi\) | ||||
−0.223782 | + | 0.974639i | \(0.571841\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −163.423 | + | 283.058i | −0.946829 | + | 1.63996i | −0.194783 | + | 0.980846i | \(0.562400\pi\) |
−0.752046 | + | 0.659110i | \(0.770933\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −81.0099 | − | 140.313i | −0.427334 | − | 0.740163i | ||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −2.00452 | + | 1.28594i | −0.00968074 | + | 0.00621037i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −150.849 | − | 261.278i | −0.670254 | − | 1.16091i | −0.977832 | − | 0.209391i | \(-0.932852\pi\) |
0.307578 | − | 0.951523i | \(-0.400481\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 75.3525 | − | 130.514i | 0.309386 | − | 0.535873i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 296.048 | 1.12768 | 0.563840 | − | 0.825884i | \(-0.309324\pi\) | ||||
0.563840 | + | 0.825884i | \(0.309324\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −144.302 | −0.511764 | −0.255882 | − | 0.966708i | \(-0.582366\pi\) | ||||
−0.255882 | + | 0.966708i | \(0.582366\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −0.578660 | + | 1.00227i | −0.00191692 | + | 0.00332021i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 180.043 | + | 311.843i | 0.558764 | + | 0.967808i | 0.997600 | + | 0.0692409i | \(0.0220577\pi\) |
−0.438836 | + | 0.898567i | \(0.644609\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −341.499 | + | 32.0516i | −0.995624 | + | 0.0934448i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 197.231 | + | 341.614i | 0.541526 | + | 0.937951i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −0.917567 | + | 1.58927i | −0.00237807 | + | 0.00411893i | −0.867212 | − | 0.497939i | \(-0.834090\pi\) |
0.864834 | + | 0.502058i | \(0.167424\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 6.94477 | 0.0170260 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 274.528 | 0.637932 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 26.6193 | − | 46.1060i | 0.0587379 | − | 0.101737i | −0.835161 | − | 0.550005i | \(-0.814626\pi\) |
0.893899 | + | 0.448268i | \(0.147959\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 54.0605 | + | 93.6356i | 0.113471 | + | 0.196538i | 0.917168 | − | 0.398502i | \(-0.130470\pi\) |
−0.803696 | + | 0.595040i | \(0.797136\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −140.295 | + | 90.0018i | −0.280564 | + | 0.179987i | ||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 3.22989 | + | 5.59433i | 0.00616336 | + | 0.0106753i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −421.004 | + | 729.199i | −0.767668 | + | 1.32964i | 0.171156 | + | 0.985244i | \(0.445250\pi\) |
−0.938824 | + | 0.344396i | \(0.888084\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 538.462 | 0.939466 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −241.111 | −0.403023 | −0.201511 | − | 0.979486i | \(-0.564585\pi\) | ||||
−0.201511 | + | 0.979486i | \(0.564585\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 103.492 | − | 179.253i | 0.165929 | − | 0.287397i | −0.771056 | − | 0.636767i | \(-0.780271\pi\) |
0.936985 | + | 0.349370i | \(0.113605\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 187.475 | + | 324.717i | 0.288637 | + | 0.499934i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 888.656 | + | 459.045i | 1.31522 | + | 0.679390i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −279.981 | − | 484.942i | −0.398738 | − | 0.690635i | 0.594832 | − | 0.803850i | \(-0.297219\pi\) |
−0.993571 | + | 0.113215i | \(0.963885\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −40.5000 | + | 70.1481i | −0.0555556 | + | 0.0962250i | ||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 986.652 | 1.30481 | 0.652404 | − | 0.757871i | \(-0.273760\pi\) | ||||
0.652404 | + | 0.757871i | \(0.273760\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −16.9081 | −0.0215758 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 104.844 | − | 181.595i | 0.129201 | − | 0.223782i | ||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 221.683 | + | 383.966i | 0.264026 | + | 0.457307i | 0.967308 | − | 0.253604i | \(-0.0816161\pi\) |
−0.703282 | + | 0.710911i | \(0.748283\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 43.5165 | + | 929.348i | 0.0501294 | + | 1.07057i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −490.270 | − | 849.173i | −0.546652 | − | 0.946829i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −5.88365 | + | 10.1908i | −0.00635421 | + | 0.0110058i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −740.815 | −0.775447 | −0.387723 | − | 0.921776i | \(-0.626738\pi\) | ||||
−0.387723 | + | 0.921776i | \(0.626738\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 486.059 | 0.493442 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −371.888 | + | 644.130i | −0.366379 | + | 0.634587i | −0.988996 | − | 0.147939i | \(-0.952736\pi\) |
0.622617 | + | 0.782526i | \(0.286069\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −52.3253 | − | 90.6300i | −0.0500559 | − | 0.0866994i | 0.839912 | − | 0.542723i | \(-0.182607\pi\) |
−0.889968 | + | 0.456024i | \(0.849273\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −0.334180 | − | 7.13680i | −0.000310596 | − | 0.00663315i | ||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −256.850 | − | 444.878i | −0.232062 | − | 0.401943i | 0.726353 | − | 0.687322i | \(-0.241214\pi\) |
−0.958415 | + | 0.285379i | \(0.907881\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −487.519 | + | 844.408i | −0.428402 | + | 0.742015i | −0.996731 | − | 0.0807868i | \(-0.974257\pi\) |
0.568329 | + | 0.822801i | \(0.307590\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 905.093 | 0.773942 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 1926.07 | 1.60345 | 0.801723 | − | 0.597696i | \(-0.203917\pi\) | ||||
0.801723 | + | 0.597696i | \(0.203917\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −11.5402 | + | 19.9883i | −0.00935767 | + | 0.0162080i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 226.058 | + | 391.543i | 0.178624 | + | 0.309386i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −2163.57 | − | 1117.61i | −1.66667 | − | 0.860937i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −792.855 | − | 1373.27i | −0.595684 | − | 1.03175i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −444.071 | + | 769.154i | −0.325533 | + | 0.563840i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −32.1457 | −0.0230016 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −1125.95 | −0.786709 | −0.393355 | − | 0.919387i | \(-0.628686\pi\) | ||||
−0.393355 | + | 0.919387i | \(0.628686\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 216.453 | − | 374.908i | 0.147734 | − | 0.255882i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −746.621 | − | 1293.19i | −0.497959 | − | 0.862490i | 0.502038 | − | 0.864845i | \(-0.332584\pi\) |
−0.999997 | + | 0.00235541i | \(0.999250\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −1426.48 | + | 915.112i | −0.930010 | + | 0.596619i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −1.73598 | − | 3.00681i | −0.00110674 | − | 0.00191692i | ||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −730.386 | + | 1265.07i | −0.455483 | + | 0.788919i | −0.998716 | − | 0.0506627i | \(-0.983867\pi\) |
0.543233 | + | 0.839582i | \(0.317200\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 2225.85 | 1.35823 | 0.679116 | − | 0.734031i | \(-0.262363\pi\) | ||||
0.679116 | + | 0.734031i | \(0.262363\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −1080.26 | −0.645206 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 1356.51 | − | 2349.55i | 0.793267 | − | 1.37398i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 4.49401 | + | 7.78385i | 0.00257384 | + | 0.00445803i | ||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 428.976 | − | 935.318i | 0.240690 | − | 0.524787i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −197.340 | − | 341.804i | −0.108502 | − | 0.187930i | 0.806662 | − | 0.591013i | \(-0.201272\pi\) |
−0.915163 | + | 0.403083i | \(0.867939\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 1562.10 | − | 2705.64i | 0.841867 | − | 1.45816i | −0.0464473 | − | 0.998921i | \(-0.514790\pi\) |
0.888314 | − | 0.459236i | \(-0.151877\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −1183.39 | −0.625301 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 42.0296 | 0.0217800 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 1800.35 | − | 3118.30i | 0.915183 | − | 1.58514i | 0.108551 | − | 0.994091i | \(-0.465379\pi\) |
0.806633 | − | 0.591053i | \(-0.201288\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −2.75270 | − | 4.76782i | −0.00137298 | − | 0.00237807i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −2797.91 | + | 1794.91i | −1.36960 | + | 0.878624i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −987.012 | − | 1709.55i | −0.474287 | − | 0.821489i | 0.525280 | − | 0.850930i | \(-0.323961\pi\) |
−0.999567 | + | 0.0294409i | \(0.990627\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −10.4172 | + | 18.0430i | −0.00491499 | + | 0.00851302i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 1067.09 | 0.494453 | 0.247227 | − | 0.968958i | \(-0.420481\pi\) | ||||
0.247227 | + | 0.968958i | \(0.420481\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 326.559 | 0.148638 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −411.792 | + | 713.245i | −0.184155 | + | 0.318966i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 137.327 | + | 237.858i | 0.0603515 | + | 0.104532i | 0.894623 | − | 0.446823i | \(-0.147445\pi\) |
−0.834271 | + | 0.551355i | \(0.814111\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −2056.55 | − | 1062.33i | −0.888347 | − | 0.458885i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 79.8578 | + | 138.318i | 0.0339123 | + | 0.0587379i | ||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −277.166 | + | 480.066i | −0.115734 | + | 0.200457i | −0.918073 | − | 0.396412i | \(-0.870255\pi\) |
0.802339 | + | 0.596869i | \(0.203589\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −685.436 | −0.281481 | −0.140741 | − | 0.990047i | \(-0.544948\pi\) | ||||
−0.140741 | + | 0.990047i | \(0.544948\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −324.363 | −0.131025 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −19.3978 | + | 33.5980i | −0.00770895 | + | 0.0133523i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 3550.59 | + | 6149.80i | 1.38847 | + | 2.40491i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −23.3890 | − | 499.500i | −0.00900158 | − | 0.192239i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −2449.44 | − | 4242.55i | −0.927932 | − | 1.60722i | −0.786777 | − | 0.617237i | \(-0.788252\pi\) |
−0.141155 | − | 0.989988i | \(-0.545082\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −1570.13 | + | 2719.55i | −0.585598 | + | 1.01429i | 0.409202 | + | 0.912444i | \(0.365807\pi\) |
−0.994801 | + | 0.101842i | \(0.967526\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −19.3793 | −0.00711684 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −227.412 | −0.0822460 | −0.0411230 | − | 0.999154i | \(-0.513094\pi\) | ||||
−0.0411230 | + | 0.999154i | \(0.513094\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 607.250 | − | 1051.79i | 0.216316 | − | 0.374670i | −0.737363 | − | 0.675497i | \(-0.763929\pi\) |
0.953679 | + | 0.300827i | \(0.0972626\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −1263.01 | − | 2187.60i | −0.443213 | − | 0.767668i | ||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 60.5481 | + | 1293.08i | 0.0209342 | + | 0.447075i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −19.0345 | − | 32.9688i | −0.00648502 | − | 0.0112324i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −807.693 | + | 1398.96i | −0.271201 | + | 0.469733i | ||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 4942.11 | 1.63566 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 5116.07 | 1.66922 | 0.834608 | − | 0.550844i | \(-0.185694\pi\) | ||||
0.834608 | + | 0.550844i | \(0.185694\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 361.666 | − | 626.425i | 0.116343 | − | 0.201511i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 9.27799 | + | 16.0699i | 0.00294304 | + | 0.00509749i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 5378.13 | + | 2778.13i | 1.68245 | + | 0.869087i | ||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 310.475 | + | 537.759i | 0.0957989 | + | 0.165929i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −3302.63 | + | 5720.33i | −1.00524 | + | 1.74114i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 119.384 | 0.0358499 | 0.0179250 | − | 0.999839i | \(-0.494294\pi\) | ||||
0.0179250 | + | 0.999839i | \(0.494294\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −1124.85 | −0.333289 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −996.000 | + | 1725.12i | −0.291220 | + | 0.504407i | −0.974098 | − | 0.226124i | \(-0.927394\pi\) |
0.682879 | + | 0.730532i | \(0.260728\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −351.738 | − | 609.228i | −0.101500 | − | 0.175803i | 0.810803 | − | 0.585319i | \(-0.199031\pi\) |
−0.912303 | + | 0.409516i | \(0.865698\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −2525.62 | + | 1620.23i | −0.719365 | + | 0.461486i | ||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −480.892 | − | 832.929i | −0.135211 | − | 0.234193i | 0.790467 | − | 0.612505i | \(-0.209838\pi\) |
−0.925678 | + | 0.378312i | \(0.876505\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 23.1519 | − | 40.1003i | 0.00642665 | − | 0.0111313i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 1679.89 | 0.460423 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −4464.71 | −1.20836 | −0.604179 | − | 0.796848i | \(-0.706499\pi\) | ||||
−0.604179 | + | 0.796848i | \(0.706499\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 217.656 | − | 376.991i | 0.0581761 | − | 0.100764i | −0.835471 | − | 0.549535i | \(-0.814805\pi\) |
0.893647 | + | 0.448771i | \(0.148138\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −121.500 | − | 210.444i | −0.0320750 | − | 0.0555556i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 25.5262 | + | 35.9697i | 0.00665638 | + | 0.00937966i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 2298.49 | + | 3981.10i | 0.592103 | + | 1.02555i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −1479.98 | + | 2563.40i | −0.376666 | + | 0.652404i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 863.003 | 0.217021 | 0.108510 | − | 0.994095i | \(-0.465392\pi\) | ||||
0.108510 | + | 0.994095i | \(0.465392\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 9693.49 | 2.40879 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 25.3621 | − | 43.9285i | 0.00622839 | − | 0.0107879i | ||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 268.346 | + | 464.790i | 0.0651322 | + | 0.112812i | 0.896753 | − | 0.442532i | \(-0.145920\pi\) |
−0.831620 | + | 0.555344i | \(0.812586\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −4702.96 | + | 3017.03i | −1.12829 | + | 0.723820i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 314.533 | + | 544.786i | 0.0745942 | + | 0.129201i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −185.954 | + | 322.082i | −0.0435986 | + | 0.0755149i | −0.887001 | − | 0.461767i | \(-0.847216\pi\) |
0.843403 | + | 0.537282i | \(0.180549\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0.235982 | 5.47029e−5 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −1330.10 | −0.304871 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 2252.80 | − | 3901.97i | 0.510616 | − | 0.884414i | −0.489308 | − | 0.872111i | \(-0.662751\pi\) |
0.999924 | − | 0.0123024i | \(-0.00391609\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 198.058 | + | 343.046i | 0.0443954 | + | 0.0768951i | 0.887369 | − | 0.461059i | \(-0.152531\pi\) |
−0.842974 | + | 0.537955i | \(0.819197\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −2479.79 | − | 1280.96i | −0.549757 | − | 0.283983i | ||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 3374.96 | + | 5845.61i | 0.740066 | + | 1.28183i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 3254.37 | − | 5636.73i | 0.705907 | − | 1.22267i | −0.260457 | − | 0.965486i | \(-0.583873\pi\) |
0.966363 | − | 0.257181i | \(-0.0827935\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 2941.62 | 0.631220 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 2785.80 | 0.591413 | 0.295707 | − | 0.955279i | \(-0.404445\pi\) | ||||
0.295707 | + | 0.955279i | \(0.404445\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −0.305923 | + | 0.529874i | −6.42588e−5 | + | 0.000111299i | −0.866058 | − | 0.499944i | \(-0.833354\pi\) |
0.865993 | + | 0.500056i | \(0.166687\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −17.6509 | − | 30.5723i | −0.00366860 | − | 0.00635421i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −256.454 | − | 5476.88i | −0.0527456 | − | 1.12645i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −6187.95 | − | 10717.8i | −1.25950 | − | 2.18153i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 1111.22 | − | 1924.69i | 0.223852 | − | 0.387723i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −4145.98 | −0.826657 | −0.413329 | − | 0.910582i | \(-0.635634\pi\) | ||||
−0.413329 | + | 0.910582i | \(0.635634\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −6.84601 | −0.00135115 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −729.089 | + | 1262.82i | −0.142445 | + | 0.246721i | ||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 4508.27 | + | 7808.56i | 0.871974 | + | 1.51030i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 125.003 | + | 2669.59i | 0.0239371 | + | 0.511204i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −1115.67 | − | 1932.39i | −0.211529 | − | 0.366379i | ||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 6.95171 | − | 12.0407i | 0.00130509 | − | 0.00226049i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 1960.53 | 0.364473 | 0.182236 | − | 0.983255i | \(-0.441666\pi\) | ||||
0.182236 | + | 0.983255i | \(0.441666\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 313.952 | 0.0577996 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −2603.78 | + | 4509.89i | −0.474749 | + | 0.822290i | −0.999582 | − | 0.0289155i | \(-0.990795\pi\) |
0.524833 | + | 0.851206i | \(0.324128\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 1995.86 | + | 3456.92i | 0.360423 | + | 0.624271i | 0.988030 | − | 0.154259i | \(-0.0492990\pi\) |
−0.627607 | + | 0.778530i | \(0.715966\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 19.0432 | + | 9.83698i | 0.00340624 | + | 0.00175953i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −902.519 | − | 1563.21i | −0.159907 | − | 0.276967i | 0.774928 | − | 0.632050i | \(-0.217786\pi\) |
−0.934835 | + | 0.355083i | \(0.884453\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 1887.43 | − | 3269.12i | 0.331271 | − | 0.573779i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 1541.10 | 0.267962 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −12032.3 | −2.07274 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −3139.27 | + | 5437.38i | −0.535802 | + | 0.928036i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −1462.56 | − | 2533.22i | −0.247338 | − | 0.428402i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 5613.13 | − | 3600.92i | 0.940614 | − | 0.603421i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −3453.09 | − | 5980.93i | −0.573411 | − | 0.993177i | −0.996212 | − | 0.0869547i | \(-0.972286\pi\) |
0.422801 | − | 0.906222i | \(-0.361047\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −1357.64 | + | 2351.50i | −0.223418 | + | 0.386971i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 108.275 | 0.0176587 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −6081.36 | −0.983006 | −0.491503 | − | 0.870876i | \(-0.663552\pi\) | ||||
−0.491503 | + | 0.870876i | \(0.663552\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −2889.10 | + | 5004.07i | −0.462875 | + | 0.801723i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −8825.94 | − | 15287.0i | −1.40162 | − | 2.42767i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 888.780 | + | 6289.97i | 0.139911 | + | 0.990164i | ||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −34.6207 | − | 59.9648i | −0.00540265 | − | 0.00935767i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 3893.51 | − | 6743.75i | 0.602347 | − | 1.04330i | −0.390117 | − | 0.920765i | \(-0.627566\pi\) |
0.992465 | − | 0.122531i | \(-0.0391011\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −1928.25 | −0.295751 | −0.147875 | − | 0.989006i | \(-0.547243\pi\) | ||||
−0.147875 | + | 0.989006i | \(0.547243\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −1356.35 | −0.206258 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 1702.14 | − | 2948.18i | 0.256645 | − | 0.444521i | −0.708696 | − | 0.705514i | \(-0.750716\pi\) |
0.965341 | + | 0.260992i | \(0.0840497\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 15.5024 | + | 26.8509i | 0.00231769 | + | 0.00401436i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 6149.00 | − | 3944.69i | 0.911595 | − | 0.584805i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −2208.53 | − | 3825.28i | −0.324684 | − | 0.562369i | 0.656764 | − | 0.754096i | \(-0.271925\pi\) |
−0.981448 | + | 0.191727i | \(0.938591\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −757.484 | + | 1312.00i | −0.110436 | + | 0.191282i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 4757.13 | 0.687837 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −26.6162 | −0.00381687 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 2538.33 | − | 4396.51i | 0.361034 | − | 0.625329i | −0.627097 | − | 0.778941i | \(-0.715757\pi\) |
0.988131 | + | 0.153612i | \(0.0490905\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −1332.21 | − | 2307.46i | −0.187947 | − | 0.325533i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 30.1964 | + | 15.5983i | 0.00422566 | + | 0.00218281i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 3438.32 | + | 5955.35i | 0.477291 | + | 0.826692i | 0.999661 | − | 0.0260264i | \(-0.00828540\pi\) |
−0.522370 | + | 0.852719i | \(0.674952\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 48.2185 | − | 83.5169i | 0.00663998 | − | 0.0115008i | ||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 3511.23 | 0.479676 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −9285.61 | −1.25850 | −0.629248 | − | 0.777205i | \(-0.716637\pi\) | ||||
−0.629248 | + | 0.777205i | \(0.716637\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 1688.93 | − | 2925.31i | 0.227103 | − | 0.393355i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 3840.83 | + | 6652.51i | 0.512420 | + | 0.887538i | 0.999896 | + | 0.0144017i | \(0.00458437\pi\) |
−0.487476 | + | 0.873136i | \(0.662082\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −6.01597 | − | 128.478i | −0.000796369 | − | 0.0170074i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 649.360 | + | 1124.72i | 0.0852941 | + | 0.147734i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −4313.86 | + | 7471.83i | −0.562266 | + | 0.973873i | 0.435032 | + | 0.900415i | \(0.356737\pi\) |
−0.997298 | + | 0.0734585i | \(0.976596\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −23600.3 | −3.05247 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 4479.73 | 0.574993 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −36.0031 | + | 62.3592i | −0.00458611 | + | 0.00794337i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −2867.81 | − | 4967.19i | −0.362547 | − | 0.627949i | 0.625832 | − | 0.779957i | \(-0.284759\pi\) |
−0.988379 | + | 0.152008i | \(0.951426\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −237.812 | − | 5078.77i | −0.0298384 | − | 0.637234i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 3608.89 | + | 6250.79i | 0.449425 | + | 0.778427i | 0.998349 | − | 0.0574453i | \(-0.0182955\pi\) |
−0.548923 | + | 0.835873i | \(0.684962\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 8209.58 | − | 14219.4i | 1.01476 | − | 1.75762i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 10.4159 | 0.00127795 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 16293.7 | 1.98439 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 5401.46 | − | 9355.60i | 0.653019 | − | 1.13106i | −0.329367 | − | 0.944202i | \(-0.606835\pi\) |
0.982386 | − | 0.186861i | \(-0.0598313\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −2191.16 | − | 3795.20i | −0.262973 | − | 0.455483i | ||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −876.019 | − | 452.517i | −0.104373 | − | 0.0539150i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −63.4373 | − | 109.877i | −0.00750365 | − | 0.0129967i | ||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −3338.78 | + | 5782.93i | −0.392088 | + | 0.679116i | ||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 13257.1 | 1.54571 | 0.772856 | − | 0.634582i | \(-0.218828\pi\) | ||||
0.772856 | + | 0.634582i | \(0.218828\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −6252.11 | −0.723774 | −0.361887 | − | 0.932222i | \(-0.617867\pi\) | ||||
−0.361887 | + | 0.932222i | \(0.617867\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 1620.38 | − | 2806.59i | 0.186255 | − | 0.322603i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −8216.87 | − | 14232.0i | −0.937827 | − | 1.62436i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 1685.43 | − | 1081.23i | 0.191015 | − | 0.122540i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 4069.53 | + | 7048.64i | 0.457993 | + | 0.793267i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −2474.54 | + | 4286.03i | −0.276553 | + | 0.479004i | −0.970526 | − | 0.240997i | \(-0.922526\pi\) |
0.693973 | + | 0.720001i | \(0.255859\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −16602.8 | −1.84267 | −0.921337 | − | 0.388764i | \(-0.872902\pi\) | ||||
−0.921337 | + | 0.388764i | \(0.872902\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −26.9641 | −0.00297202 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −8212.38 | + | 14224.3i | −0.898974 | + | 1.55707i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 2354.19 | + | 4077.57i | 0.255944 | + | 0.443307i | 0.965151 | − | 0.261692i | \(-0.0842805\pi\) |
−0.709208 | + | 0.705000i | \(0.750947\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 1786.56 | + | 2517.49i | 0.192913 | + | 0.271838i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 850.218 | + | 1472.62i | 0.0911852 | + | 0.157937i | 0.908010 | − | 0.418948i | \(-0.137601\pi\) |
−0.816825 | + | 0.576886i | \(0.804268\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 28.5065 | − | 49.3746i | 0.00303671 | − | 0.00525973i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 1184.04 | 0.125287 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 10050.2 | 1.05635 | 0.528173 | − | 0.849137i | \(-0.322877\pi\) | ||||
0.528173 | + | 0.849137i | \(0.322877\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −7994.26 | + | 13846.5i | −0.834667 | + | 1.44569i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 4686.30 | + | 8116.91i | 0.486052 | + | 0.841867i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 100.697 | − | 64.5991i | 0.0103753 | − | 0.00665594i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 5495.95 | + | 9519.27i | 0.562560 | + | 0.974382i | 0.997272 | + | 0.0738128i | \(0.0235167\pi\) |
−0.434712 | + | 0.900569i | \(0.643150\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 1775.08 | − | 3074.52i | 0.180509 | − | 0.312650i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −548.440 | −0.0554086 | −0.0277043 | − | 0.999616i | \(-0.508820\pi\) | ||||
−0.0277043 | + | 0.999616i | \(0.508820\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 4028.04 | 0.404317 | 0.202159 | − | 0.979353i | \(-0.435204\pi\) | ||||
0.202159 | + | 0.979353i | \(0.435204\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −63.0444 | + | 109.196i | −0.00628734 | + | 0.0108900i | ||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −1035.35 | − | 1793.27i | −0.102591 | − | 0.177693i | 0.810160 | − | 0.586208i | \(-0.199380\pi\) |
−0.912751 | + | 0.408515i | \(0.866047\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 13854.9 | + | 7156.88i | 1.36409 | + | 0.704636i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 5401.06 | + | 9354.91i | 0.528381 | + | 0.915183i | ||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 3896.63 | − | 6749.16i | 0.378789 | − | 0.656082i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −11437.2 | −1.10479 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 16.5162 | 0.00158538 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 89.3926 | − | 154.832i | 0.00852704 | − | 0.0147693i | −0.861730 | − | 0.507366i | \(-0.830619\pi\) |
0.870257 | + | 0.492597i | \(0.163952\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 7577.89 | + | 13125.3i | 0.718341 | + | 1.24420i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −466.447 | − | 9961.54i | −0.0439422 | − | 0.938438i | ||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 47.6311 | + | 82.4995i | 0.00445942 | + | 0.00772393i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 8298.48 | − | 14373.4i | 0.772156 | − | 1.33741i | −0.164223 | − | 0.986423i | \(-0.552512\pi\) |
0.936379 | − | 0.350991i | \(-0.114155\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 5922.07 | 0.547659 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −4547.22 | −0.417949 | −0.208975 | − | 0.977921i | \(-0.567013\pi\) | ||||
−0.208975 | + | 0.977921i | \(0.567013\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −4595.22 | + | 7959.16i | −0.419794 | + | 0.727105i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −31.2515 | − | 54.1291i | −0.00283767 | − | 0.00491499i | ||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 208.864 | + | 4460.55i | 0.0188508 | + | 0.402581i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −512.984 | − | 888.515i | −0.0460207 | − | 0.0797102i | 0.842097 | − | 0.539325i | \(-0.181321\pi\) |
−0.888118 | + | 0.459615i | \(0.847987\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −1600.63 | + | 2772.37i | −0.142736 | + | 0.247227i | ||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 6745.26 | 0.597925 | 0.298962 | − | 0.954265i | \(-0.403359\pi\) | ||||
0.298962 | + | 0.954265i | \(0.403359\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 95.6431 | 0.00842785 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −489.838 | + | 848.424i | −0.0429082 | + | 0.0743192i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 3000.51 | + | 5197.03i | 0.261287 | + | 0.452563i | 0.966584 | − | 0.256349i | \(-0.0825197\pi\) |
−0.705297 | + | 0.708912i | \(0.749186\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −3405.83 | − | 1759.32i | −0.294843 | − | 0.152304i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −1235.38 | − | 2139.74i | −0.106322 | − | 0.184155i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −6.72856 | + | 11.6542i | −0.000575720 | + | 0.000997177i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −19447.0 | −1.65431 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −823.964 | −0.0696879 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −2347.61 | + | 4066.17i | −0.197410 | + | 0.341924i | −0.947688 | − | 0.319199i | \(-0.896586\pi\) |
0.750278 | + | 0.661122i | \(0.229920\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −385.884 | − | 668.370i | −0.0322629 | − | 0.0558810i | 0.849443 | − | 0.527680i | \(-0.176938\pi\) |
−0.881706 | + | 0.471799i | \(0.843605\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 5844.85 | − | 3749.58i | 0.485886 | − | 0.311705i | ||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 21488.1 | + | 37218.5i | 1.77616 | + | 3.07640i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −10024.3 | + | 17362.7i | −0.823895 | + | 1.42703i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −479.147 | −0.0391586 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −14872.0 | −1.20859 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −33.0286 | + | 57.2073i | −0.00266907 | + | 0.00462297i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −831.498 | − | 1440.20i | −0.0668190 | − | 0.115734i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 7722.52 | − | 16837.8i | 0.617129 | − | 1.34556i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −1692.83 | − | 2932.07i | −0.134529 | − | 0.233012i | 0.790888 | − | 0.611961i | \(-0.209619\pi\) |
−0.925418 | + | 0.378949i | \(0.876286\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 1028.15 | − | 1780.82i | 0.0812566 | − | 0.140741i | ||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 125.381 | 0.00985457 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 4988.75 | 0.389952 | 0.194976 | − | 0.980808i | \(-0.437537\pi\) | ||||
0.194976 | + | 0.980808i | \(0.437537\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 486.545 | − | 842.720i | 0.0378237 | − | 0.0655126i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 3198.08 | + | 5539.23i | 0.247264 | + | 0.428274i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −8728.88 | + | 5599.73i | −0.671229 | + | 0.430606i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −58.1934 | − | 100.794i | −0.00445076 | − | 0.00770895i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 10103.6 | − | 17500.0i | 0.768591 | − | 1.33124i | −0.169736 | − | 0.985490i | \(-0.554291\pi\) |
0.938327 | − | 0.345749i | \(-0.112375\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 7249.02 | 0.548481 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −21303.5 | −1.60327 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 5845.20 | − | 10124.2i | 0.437559 | − | 0.757875i | −0.559941 | − | 0.828532i | \(-0.689176\pi\) |
0.997501 | + | 0.0706574i | \(0.0225097\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −123.838 | − | 214.493i | −0.00922104 | − | 0.0159713i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 1332.82 | + | 688.483i | 0.0987183 | + | 0.0509940i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 8964.45 | + | 15526.9i | 0.660473 | + | 1.14397i | 0.980491 | + | 0.196562i | \(0.0629777\pi\) |
−0.320018 | + | 0.947411i | \(0.603689\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 7836.84 | − | 13573.8i | 0.574364 | − | 0.994827i | −0.421747 | − | 0.906714i | \(-0.638583\pi\) |
0.996110 | − | 0.0881136i | \(-0.0280838\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 14696.6 | 1.07148 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −22432.9 | −1.62699 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 6826.50 | − | 11823.8i | 0.492532 | − | 0.853090i | −0.507431 | − | 0.861692i | \(-0.669405\pi\) |
0.999963 | + | 0.00860205i | \(0.00273815\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −4710.39 | − | 8158.64i | −0.338095 | − | 0.585598i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −854.696 | − | 18253.0i | −0.0610306 | − | 1.30338i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −49.5547 | − | 85.8312i | −0.00352032 | − | 0.00609737i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 29.0690 | − | 50.3490i | 0.00205445 | − | 0.00355842i | ||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −18021.5 | −1.26717 | −0.633583 | − | 0.773675i | \(-0.718417\pi\) | ||||
−0.633583 | + | 0.773675i | \(0.718417\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 29909.6 | 2.09236 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 341.118 | − | 590.834i | 0.0237424 | − | 0.0411230i | ||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −10568.7 | − | 18305.5i | −0.731877 | − | 1.26765i | −0.956080 | − | 0.293105i | \(-0.905311\pi\) |
0.224204 | − | 0.974542i | \(-0.428022\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 14.6468 | + | 312.800i | 0.00100918 | + | 0.0215522i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 1821.75 | + | 3155.36i | 0.124890 | + | 0.216316i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −4684.80 | + | 8114.30i | −0.319559 | + | 0.553492i | −0.980396 | − | 0.197037i | \(-0.936868\pi\) |
0.660837 | + | 0.750529i | \(0.270201\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −22750.0 | −1.54408 | −0.772040 | − | 0.635573i | \(-0.780764\pi\) | ||||
−0.772040 | + | 0.635573i | \(0.780764\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 7578.06 | 0.511779 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −101.954 | + | 176.590i | −0.00685128 | + | 0.0118668i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 2986.82 | + | 5173.33i | 0.199722 | + | 0.345929i | 0.948438 | − | 0.316962i | \(-0.102663\pi\) |
−0.748716 | + | 0.662891i | \(0.769329\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −3450.34 | − | 1782.31i | −0.229581 | − | 0.118592i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −9044.45 | − | 15665.4i | −0.598853 | − | 1.03724i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 11673.7 | − | 20219.4i | 0.769162 | − | 1.33223i | −0.168856 | − | 0.985641i | \(-0.554007\pi\) |
0.938018 | − | 0.346586i | \(-0.112659\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 114.207 | 0.00748826 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 28199.1 | 1.83996 | 0.919979 | − | 0.391968i | \(-0.128206\pi\) | ||||
0.919979 | + | 0.391968i | \(0.128206\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 1487.78 | − | 2576.91i | 0.0966057 | − | 0.167326i | −0.813672 | − | 0.581324i | \(-0.802535\pi\) |
0.910278 | + | 0.413998i | \(0.135868\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −2423.08 | − | 4196.89i | −0.156578 | − | 0.271201i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 6911.33 | − | 4433.75i | 0.444457 | − | 0.285127i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −7809.40 | − | 13526.3i | −0.499802 | − | 0.865682i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −7413.16 | + | 12840.0i | −0.472174 | + | 0.817830i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −39669.4 | −2.51466 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −2631.33 | −0.166009 | −0.0830044 | − | 0.996549i | \(-0.526452\pi\) | ||||
−0.0830044 | + | 0.996549i | \(0.526452\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −7674.10 | + | 13291.9i | −0.481861 | + | 0.834608i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 72.3937 | + | 125.390i | 0.00452418 | + | 0.00783611i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 17155.2 | − | 1610.11i | 1.06706 | − | 0.100149i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 1085.00 | + | 1879.27i | 0.0671704 | + | 0.116343i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −7247.12 | + | 12552.4i | −0.446559 | + | 0.773462i | −0.998159 | − | 0.0606460i | \(-0.980684\pi\) |
0.551601 | + | 0.834108i | \(0.314017\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −15176.0 | −0.930767 | −0.465383 | − | 0.885109i | \(-0.654084\pi\) | ||||
−0.465383 | + | 0.885109i | \(0.654084\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −55.6679 | −0.00339833 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 3784.59 | − | 6555.10i | 0.229965 | − | 0.398312i | −0.727832 | − | 0.685755i | \(-0.759472\pi\) |
0.957798 | + | 0.287443i | \(0.0928053\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 1437.62 | + | 2490.02i | 0.0869513 | + | 0.150604i | ||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −15285.0 | + | 9805.60i | −0.920224 | + | 0.590341i | ||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 6966.75 | + | 12066.8i | 0.417504 | + | 0.723138i | 0.995688 | − | 0.0927688i | \(-0.0295717\pi\) |
−0.578184 | + | 0.815906i | \(0.696238\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −96.0089 | + | 166.292i | −0.00572729 | + | 0.00991996i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −1862.85 | −0.110619 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −17015.5 | −1.00581 | −0.502904 | − | 0.864342i | \(-0.667735\pi\) | ||||
−0.502904 | + | 0.864342i | \(0.667735\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 8267.70 | − | 14320.1i | 0.486500 | − | 0.842642i | −0.513380 | − | 0.858161i | \(-0.671607\pi\) |
0.999880 | + | 0.0155194i | \(0.00494019\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −9907.90 | − | 17161.0i | −0.580378 | − | 1.00524i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 193.626 | + | 100.020i | 0.0112910 | + | 0.00583247i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 6272.73 | + | 10864.7i | 0.364140 | + | 0.630708i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −179.076 | + | 310.168i | −0.0103490 | + | 0.0179250i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −5839.25 | −0.335949 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 4571.05 | 0.261814 | 0.130907 | − | 0.991395i | \(-0.458211\pi\) | ||||
0.130907 | + | 0.991395i | \(0.458211\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 1687.28 | − | 2922.45i | 0.0962123 | − | 0.166645i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −13142.3 | − | 22763.1i | −0.746083 | − | 1.29225i | −0.949687 | − | 0.313201i | \(-0.898599\pi\) |
0.203604 | − | 0.979053i | \(-0.434735\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 641.737 | + | 13705.1i | 0.0362704 | + | 0.774598i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −2988.00 | − | 5175.37i | −0.168136 | − | 0.291220i | ||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −3398.61 | + | 5886.57i | −0.190402 | + | 0.329785i | −0.945383 | − | 0.325961i | \(-0.894312\pi\) |
0.754982 | + | 0.655746i | \(0.227646\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 187.842 | 0.0104775 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 2110.43 | 0.117202 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 46.0940 | − | 79.8372i | 0.00254868 | − | 0.00441445i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −13879.3 | − | 24039.7i | −0.764103 | − | 1.32346i | −0.940720 | − | 0.339185i | \(-0.889849\pi\) |
0.176617 | − | 0.984280i | \(-0.443485\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −421.053 | − | 8992.09i | −0.0230801 | − | 0.492902i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −143.112 | − | 247.878i | −0.00781088 | − | 0.0135288i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 19463.2 | − | 33711.3i | 1.05771 | − | 1.83200i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 2885.35 | 0.156129 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −21638.3 | −1.16586 | −0.582929 | − | 0.812523i | \(-0.698093\pi\) | ||||
−0.582929 | + | 0.812523i | \(0.698093\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −13804.1 | + | 23909.4i | −0.740584 | + | 1.28273i | ||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 69.4557 | + | 120.301i | 0.00371043 | + | 0.00642665i | ||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 12238.5 | + | 6321.95i | 0.651029 | + | 0.336296i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 8144.36 | + | 14106.4i | 0.431408 | + | 0.747220i | 0.996995 | − | 0.0774687i | \(-0.0246838\pi\) |
−0.565587 | + | 0.824688i | \(0.691350\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −2519.83 | + | 4364.47i | −0.132913 | + | 0.230212i | ||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 58664.8 | 3.08137 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −348.871 | −0.0182476 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 6697.06 | − | 11599.6i | 0.348823 | − | 0.604179i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 1695.87 | + | 2937.33i | 0.0879628 | + | 0.152356i | 0.906650 | − | 0.421884i | \(-0.138631\pi\) |
−0.818687 | + | 0.574240i | \(0.805298\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −1631.33 | + | 1046.53i | −0.0842632 | + | 0.0540564i | ||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 652.967 | + | 1130.97i | 0.0335880 | + | 0.0581761i | ||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −4367.93 | + | 7565.48i | −0.223753 | + | 0.387551i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 23158.7 | 1.18144 | 0.590722 | − | 0.806875i | \(-0.298843\pi\) | ||||
0.590722 | + | 0.806875i | \(0.298843\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 729.000 | 0.0370370 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −9486.94 | + | 16431.9i | −0.480010 | + | 0.831402i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 13814.6 | + | 23927.6i | 0.696116 | + | 1.20571i | 0.969803 | + | 0.243890i | \(0.0784236\pi\) |
−0.273686 | + | 0.961819i | \(0.588243\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | −131.741 | + | 12.3646i | −0.00661136 | + | 0.000620512i | ||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −22737.0 | − | 39381.6i | −1.13640 | − | 1.96830i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 4730.82 | − | 8194.03i | 0.235489 | − | 0.407879i | −0.723926 | − | 0.689878i | \(-0.757664\pi\) |
0.959415 | + | 0.281999i | \(0.0909976\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −13790.9 | −0.683701 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −14316.9 | −0.706913 | −0.353457 | − | 0.935451i | \(-0.614994\pi\) | ||||
−0.353457 | + | 0.935451i | \(0.614994\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −25.3762 | + | 43.9529i | −0.00124794 | + | 0.00216149i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −4439.93 | − | 7690.19i | −0.217468 | − | 0.376666i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −8007.73 | + | 5137.10i | −0.390649 | + | 0.250608i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 3743.03 | + | 6483.13i | 0.181871 | + | 0.315010i | 0.942518 | − | 0.334156i | \(-0.108451\pi\) |
−0.760647 | + | 0.649166i | \(0.775118\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −1294.50 | + | 2242.15i | −0.0626486 | + | 0.108510i | ||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −401.744 | −0.0193655 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −17416.8 | −0.836227 | −0.418114 | − | 0.908395i | \(-0.637309\pi\) | ||||
−0.418114 | + | 0.908395i | \(0.637309\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −14540.2 | + | 25184.4i | −0.695359 | + | 1.20440i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 16615.5 | + | 28778.9i | 0.791474 | + | 1.37087i | 0.925054 | + | 0.379835i | \(0.124019\pi\) |
−0.133580 | + | 0.991038i | \(0.542647\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 16043.9 | + | 8287.62i | 0.761240 | + | 0.393227i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 76.0864 | + | 131.786i | 0.00359596 | + | 0.00622839i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −1337.22 | + | 2316.13i | −0.0629521 | + | 0.109036i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 13714.2 | 0.643103 | 0.321552 | − | 0.946892i | \(-0.395796\pi\) | ||||
0.321552 | + | 0.946892i | \(0.395796\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −1610.08 | −0.0752082 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −7604.65 | + | 13171.6i | −0.353842 | + | 0.612873i | −0.986919 | − | 0.161216i | \(-0.948458\pi\) |
0.633077 | + | 0.774089i | \(0.281792\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 20425.2 | + | 35377.5i | 0.946704 | + | 1.63974i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −784.045 | − | 16744.2i | −0.0362001 | − | 0.773095i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −13545.6 | − | 23461.6i | −0.623004 | − | 1.07907i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 6510.79 | − | 11277.0i | 0.298303 | − | 0.516675i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −1887.20 | −0.0861339 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −463.019 | −0.0210520 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 6610.74 | − | 11450.1i | 0.299425 | − | 0.518619i | −0.676580 | − | 0.736369i | \(-0.736539\pi\) |
0.976004 | + | 0.217750i | \(0.0698719\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −557.862 | − | 966.246i | −0.0251716 | − | 0.0435986i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −1668.47 | − | 35632.3i | −0.0749989 | − | 1.60169i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −2715.73 | − | 4703.79i | −0.121612 | − | 0.210639i | ||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −0.353973 | + | 0.613099i | −1.57914e−5 | + | 2.73514e-5i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 13373.9 | 0.594387 | 0.297194 | − | 0.954817i | \(-0.403949\pi\) | ||||
0.297194 | + | 0.954817i | \(0.403949\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 47346.6 | 2.09637 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 1995.15 | − | 3455.69i | 0.0880088 | − | 0.152436i | ||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 5589.23 | + | 9680.84i | 0.245629 | + | 0.425441i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 379.780 | + | 196.179i | 0.0166279 | + | 0.00858933i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 6758.41 | + | 11705.9i | 0.294805 | + | 0.510616i | ||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 5614.64 | − | 9724.84i | 0.244005 | − | 0.422630i | −0.717846 | − | 0.696202i | \(-0.754872\pi\) |
0.961851 | + | 0.273572i | \(0.0882052\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −4301.42 | −0.186243 | −0.0931215 | − | 0.995655i | \(-0.529685\pi\) | ||||
−0.0931215 | + | 0.995655i | \(0.529685\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −1188.35 | −0.0512634 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −126.921 | + | 219.834i | −0.00545503 | + | 0.00944838i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 6602.50 | + | 11435.9i | 0.282732 | + | 0.489707i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 7047.72 | − | 4521.24i | 0.300693 | − | 0.192900i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 20455.3 | + | 35429.6i | 0.869543 | + | 1.50609i | 0.862464 | + | 0.506118i | \(0.168920\pi\) |
0.00707888 | + | 0.999975i | \(0.497747\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −14021.6 | + | 24286.1i | −0.593879 | + | 1.02863i | 0.399825 | + | 0.916592i | \(0.369071\pi\) |
−0.993704 | + | 0.112038i | \(0.964262\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −20249.8 | −0.854554 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 17598.9 | 0.739993 | 0.369996 | − | 0.929033i | \(-0.379359\pi\) | ||||
0.369996 | + | 0.929033i | \(0.379359\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 7282.76 | − | 12614.1i | 0.305116 | − | 0.528476i | −0.672172 | − | 0.740395i | \(-0.734638\pi\) |
0.977287 | + | 0.211920i | \(0.0679716\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 9763.11 | + | 16910.2i | 0.407555 | + | 0.705907i | ||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −18801.6 | + | 40994.1i | −0.782039 | + | 1.70512i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −68.6090 | − | 118.834i | −0.00284349 | − | 0.00492506i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −4412.43 | + | 7642.56i | −0.182217 | + | 0.315610i | ||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 711.056 | 0.0292591 | 0.0146295 | − | 0.999893i | \(-0.495343\pi\) | ||||
0.0146295 | + | 0.999893i | \(0.495343\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −19503.5 | −0.799686 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −4178.70 | + | 7237.73i | −0.170726 | + | 0.295707i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −20.9963 | − | 36.3666i | −0.000854785 | − | 0.00148053i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −24718.6 | + | 15857.4i | −1.00276 | + | 0.643291i | ||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −0.917769 | − | 1.58962i | −3.70998e−5 | − | 6.42588e-5i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −27075.4 | + | 46896.0i | −1.09064 | + | 1.88904i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −7459.48 | −0.299423 | −0.149712 | − | 0.988730i | \(-0.547834\pi\) | ||||
−0.149712 | + | 0.988730i | \(0.547834\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 105.906 | 0.00423614 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −1780.46 | + | 3083.85i | −0.0709678 | + | 0.122920i | −0.899326 | − | 0.437279i | \(-0.855942\pi\) |
0.828358 | + | 0.560199i | \(0.189275\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −6759.57 | − | 11707.9i | −0.268491 | − | 0.465039i | 0.699982 | − | 0.714161i | \(-0.253191\pi\) |
−0.968472 | + | 0.249121i | \(0.919858\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 14614.0 | + | 7549.03i | 0.578449 | + | 0.298804i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −10198.0 | − | 17663.4i | −0.402251 | − | 0.696719i | 0.591746 | − | 0.806124i | \(-0.298439\pi\) |
−0.993997 | + | 0.109405i | \(0.965105\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 17.6591 | − | 30.5864i | 0.000694135 | − | 0.00120228i | ||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 37127.7 | 1.45435 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 30241.6 | 1.18053 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 21149.1 | − | 36631.4i | 0.822745 | − | 1.42504i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 3333.67 | + | 5774.08i | 0.129241 | + | 0.223852i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 27.8465 | + | 594.694i | 0.00107587 | + | 0.0229764i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −3598.63 | − | 6233.01i | −0.138560 | − | 0.239993i | 0.788392 | − | 0.615174i | \(-0.210914\pi\) |
−0.926952 | + | 0.375181i | \(0.877581\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 6218.96 | − | 10771.6i | 0.238635 | − | 0.413329i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 11588.3 | 0.443156 | 0.221578 | − | 0.975143i | \(-0.428879\pi\) | ||||
0.221578 | + | 0.975143i | \(0.428879\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 21959.0 | 0.836898 | 0.418449 | − | 0.908240i | \(-0.362574\pi\) | ||||
0.418449 | + | 0.908240i | \(0.362574\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 10.2690 | − | 17.7864i | 0.000390044 | − | 0.000675576i | ||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −6259.45 | − | 10841.7i | −0.236947 | − | 0.410404i | 0.722890 | − | 0.690963i | \(-0.242813\pi\) |
−0.959837 | + | 0.280559i | \(0.909480\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 975.366 | + | 20830.1i | 0.0367972 | + | 0.785848i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −2187.27 | − | 3788.46i | −0.0822404 | − | 0.142445i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 16475.6 | − | 28536.6i | 0.617396 | − | 1.06936i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 71.2822 | 0.00266224 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −27049.6 | −1.00687 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 11422.7 | − | 19784.6i | 0.423768 | − | 0.733987i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 120.648 | + | 208.969i | 0.00446102 | + | 0.00772672i | ||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −7123.30 | − | 3679.61i | −0.262512 | − | 0.135603i | ||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 44.0705 | + | 76.3324i | 0.00161873 | + | 0.00280373i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −14135.0 | + | 24482.6i | −0.517470 | + | 0.896285i | 0.482324 | + | 0.875993i | \(0.339793\pi\) |
−0.999794 | + | 0.0202920i | \(0.993540\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 6693.99 | 0.244253 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −7908.58 | −0.287621 | −0.143811 | − | 0.989605i | \(-0.545936\pi\) | ||||
−0.143811 | + | 0.989605i | \(0.545936\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −26642.8 | + | 46146.8i | −0.965771 | + | 1.67277i | ||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 20.8551 | + | 36.1221i | 0.000753496 | + | 0.00130509i | ||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −23277.2 | + | 14932.7i | −0.838255 | + | 0.537756i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −15725.3 | − | 27237.0i | −0.564451 | − | 0.977658i | −0.997101 | − | 0.0760955i | \(-0.975755\pi\) |
0.432650 | − | 0.901562i | \(-0.357579\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −2940.79 | + | 5093.60i | −0.105214 | + | 0.182236i | ||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 12112.2 | 0.431938 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −37707.2 | −1.34033 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −470.927 | + | 815.670i | −0.0166853 | + | 0.0288998i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 1734.59 | + | 3004.40i | 0.0612596 | + | 0.106105i | 0.895029 | − | 0.446009i | \(-0.147155\pi\) |
−0.833769 | + | 0.552113i | \(0.813822\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 18165.3 | + | 25597.1i | 0.639465 | + | 0.901087i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −7811.35 | − | 13529.7i | −0.274097 | − | 0.474749i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 456.574 | − | 790.810i | 0.0159696 | − | 0.0276601i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 50935.7 | 1.77588 | 0.887939 | − | 0.459962i | \(-0.152137\pi\) | ||||
0.887939 | + | 0.459962i | \(0.152137\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −11975.1 | −0.416181 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −23947.5 | + | 41478.2i | −0.829612 | + | 1.43693i | 0.0687311 | + | 0.997635i | \(0.478105\pi\) |
−0.898343 | + | 0.439295i | \(0.855228\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −26568.4 | − | 46017.8i | −0.917482 | − | 1.58913i | ||||
\(944\) | 0 | 0 | ||||||||
\(945\) | −54.1221 | + | 34.7203i | −0.00186306 | + | 0.00119519i | ||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −5269.44 | − | 9126.94i | −0.180817 | − | 0.313184i | 0.761342 | − | 0.648351i | \(-0.224541\pi\) |
−0.942159 | + | 0.335166i | \(0.891208\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −5198.91 | + | 9004.78i | −0.177833 | + | 0.308016i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 5415.11 | 0.184645 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 31123.5 | 1.05791 | 0.528955 | − | 0.848650i | \(-0.322584\pi\) | ||||
0.528955 | + | 0.848650i | \(0.322584\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −314.976 | + | 545.554i | −0.0106726 | + | 0.0184856i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 5662.28 | + | 9807.35i | 0.191260 | + | 0.331271i | ||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 24036.4 | + | 12416.3i | 0.809360 | + | 0.418084i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −38518.9 | − | 66716.7i | −1.29297 | − | 2.23949i | ||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −2311.65 | + | 4003.90i | −0.0773540 | + | 0.133981i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 403.810 | 0.0134706 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −1626.14 | −0.0540776 | −0.0270388 | − | 0.999634i | \(-0.508608\pi\) | ||||
−0.0270388 | + | 0.999634i | \(0.508608\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 18048.5 | − | 31260.9i | 0.598349 | − | 1.03637i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −17750.0 | − | 30744.0i | −0.586638 | − | 1.01609i | −0.994669 | − | 0.103119i | \(-0.967118\pi\) |
0.408031 | − | 0.912968i | \(-0.366216\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −1928.16 | − | 41178.2i | −0.0635294 | − | 1.35675i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −9417.82 | − | 16312.1i | −0.309345 | − | 0.535802i | ||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −13285.1 | + | 23010.5i | −0.435034 | + | 0.753501i | −0.997298 | − | 0.0734563i | \(-0.976597\pi\) |
0.562264 | + | 0.826958i | \(0.309930\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −23944.7 | −0.781691 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 8775.34 | 0.285602 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 26925.8 | − | 46636.9i | 0.873652 | − | 1.51321i | 0.0154597 | − | 0.999880i | \(-0.495079\pi\) |
0.858192 | − | 0.513329i | \(-0.171588\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 14.6216 | + | 25.3254i | 0.000472978 | + | 0.000819221i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 935.782 | + | 19984.7i | 0.0301786 | + | 0.644499i | ||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 12950.2 | + | 22430.4i | 0.416372 | + | 0.721178i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −1414.87 | + | 2450.63i | −0.0453531 | + | 0.0785539i | −0.887811 | − | 0.460209i | \(-0.847775\pi\) |
0.842458 | + | 0.538762i | \(0.181108\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 20718.6 | 0.662118 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −156.174 | −0.00497593 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −6452.14 | + | 11175.4i | −0.204956 | + | 0.354994i | −0.950119 | − | 0.311888i | \(-0.899038\pi\) |
0.745163 | + | 0.666883i | \(0.232372\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −4072.92 | − | 7054.50i | −0.128990 | − | 0.223418i |
(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 | 168.4.q.f.25.3 | ✓ | 8 | |
3.2 | odd | 2 | 504.4.s.j.361.2 | 8 | |||
4.3 | odd | 2 | 336.4.q.m.193.3 | 8 | |||
7.2 | even | 3 | inner | 168.4.q.f.121.3 | yes | 8 | |
7.3 | odd | 6 | 1176.4.a.ba.1.3 | 4 | |||
7.4 | even | 3 | 1176.4.a.bd.1.2 | 4 | |||
21.2 | odd | 6 | 504.4.s.j.289.2 | 8 | |||
28.3 | even | 6 | 2352.4.a.cp.1.3 | 4 | |||
28.11 | odd | 6 | 2352.4.a.cm.1.2 | 4 | |||
28.23 | odd | 6 | 336.4.q.m.289.3 | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
168.4.q.f.25.3 | ✓ | 8 | 1.1 | even | 1 | trivial | |
168.4.q.f.121.3 | yes | 8 | 7.2 | even | 3 | inner | |
336.4.q.m.193.3 | 8 | 4.3 | odd | 2 | |||
336.4.q.m.289.3 | 8 | 28.23 | odd | 6 | |||
504.4.s.j.289.2 | 8 | 21.2 | odd | 6 | |||
504.4.s.j.361.2 | 8 | 3.2 | odd | 2 | |||
1176.4.a.ba.1.3 | 4 | 7.3 | odd | 6 | |||
1176.4.a.bd.1.2 | 4 | 7.4 | even | 3 | |||
2352.4.a.cm.1.2 | 4 | 28.11 | odd | 6 | |||
2352.4.a.cp.1.3 | 4 | 28.3 | even | 6 |