Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [648,4,Mod(1,648)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(648, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 0]))
N = Newforms(chi, 4, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("648.1");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 648 = 2^{3} \cdot 3^{4} \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 648.a (trivial) |
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: | yes |
Analytic conductor: | \(38.2332376837\) |
Analytic rank: | \(0\) |
Dimension: | \(2\) |
Coefficient field: | \(\Q(\sqrt{129}) \) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{2} - x - 32 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 2 \) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.1 | ||
Root | \(6.17891\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 648.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
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 | 0 | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −13.3578 | −1.19476 | −0.597380 | − | 0.801959i | \(-0.703791\pi\) | ||||
−0.597380 | + | 0.801959i | \(0.703791\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −14.3578 | −0.775249 | −0.387625 | − | 0.921817i | \(-0.626704\pi\) | ||||
−0.387625 | + | 0.921817i | \(0.626704\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −39.0735 | −1.07101 | −0.535504 | − | 0.844533i | \(-0.679878\pi\) | ||||
−0.535504 | + | 0.844533i | \(0.679878\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −76.7891 | −1.63827 | −0.819133 | − | 0.573604i | \(-0.805545\pi\) | ||||
−0.819133 | + | 0.573604i | \(0.805545\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 62.4313 | 0.890694 | 0.445347 | − | 0.895358i | \(-0.353080\pi\) | ||||
0.445347 | + | 0.895358i | \(0.353080\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −39.7891 | −0.480434 | −0.240217 | − | 0.970719i | \(-0.577219\pi\) | ||||
−0.240217 | + | 0.970719i | \(0.577219\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 128.505 | 1.16500 | 0.582502 | − | 0.812829i | \(-0.302074\pi\) | ||||
0.582502 | + | 0.812829i | \(0.302074\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 53.4313 | 0.427450 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −64.9360 | −0.415804 | −0.207902 | − | 0.978150i | \(-0.566663\pi\) | ||||
−0.207902 | + | 0.978150i | \(0.566663\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −9.13747 | −0.0529399 | −0.0264700 | − | 0.999650i | \(-0.508427\pi\) | ||||
−0.0264700 | + | 0.999650i | \(0.508427\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 191.789 | 0.926236 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 319.505 | 1.41963 | 0.709814 | − | 0.704389i | \(-0.248779\pi\) | ||||
0.709814 | + | 0.704389i | \(0.248779\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −17.5782 | −0.0669573 | −0.0334786 | − | 0.999439i | \(-0.510659\pi\) | ||||
−0.0334786 | + | 0.999439i | \(0.510659\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −450.945 | −1.59927 | −0.799634 | − | 0.600488i | \(-0.794973\pi\) | ||||
−0.799634 | + | 0.600488i | \(0.794973\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 581.597 | 1.80499 | 0.902496 | − | 0.430698i | \(-0.141732\pi\) | ||||
0.902496 | + | 0.430698i | \(0.141732\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −136.853 | −0.398989 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −329.450 | −0.853839 | −0.426919 | − | 0.904290i | \(-0.640401\pi\) | ||||
−0.426919 | + | 0.904290i | \(0.640401\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 521.936 | 1.27960 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 241.853 | 0.533671 | 0.266836 | − | 0.963742i | \(-0.414022\pi\) | ||||
0.266836 | + | 0.963742i | \(0.414022\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 497.524 | 1.04428 | 0.522142 | − | 0.852858i | \(-0.325133\pi\) | ||||
0.522142 | + | 0.852858i | \(0.325133\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 1025.73 | 1.95733 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −578.064 | −1.05406 | −0.527028 | − | 0.849848i | \(-0.676694\pi\) | ||||
−0.527028 | + | 0.849848i | \(0.676694\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 660.927 | 1.10475 | 0.552377 | − | 0.833594i | \(-0.313721\pi\) | ||||
0.552377 | + | 0.833594i | \(0.313721\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 696.559 | 1.11680 | 0.558398 | − | 0.829573i | \(-0.311416\pi\) | ||||
0.558398 | + | 0.829573i | \(0.311416\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 561.009 | 0.830298 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 730.268 | 1.04002 | 0.520010 | − | 0.854160i | \(-0.325928\pi\) | ||||
0.520010 | + | 0.854160i | \(0.325928\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −1090.48 | −1.44212 | −0.721058 | − | 0.692875i | \(-0.756344\pi\) | ||||
−0.721058 | + | 0.692875i | \(0.756344\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −833.945 | −1.06417 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 317.588 | 0.378250 | 0.189125 | − | 0.981953i | \(-0.439435\pi\) | ||||
0.189125 | + | 0.981953i | \(0.439435\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 1102.52 | 1.27006 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 531.495 | 0.574003 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −1485.65 | −1.55511 | −0.777553 | − | 0.628817i | \(-0.783539\pi\) | ||||
−0.777553 | + | 0.628817i | \(0.783539\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 1003.27 | 0.988402 | 0.494201 | − | 0.869348i | \(-0.335461\pi\) | ||||
0.494201 | + | 0.869348i | \(0.335461\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −1717.60 | −1.64311 | −0.821553 | − | 0.570133i | \(-0.806892\pi\) | ||||
−0.821553 | + | 0.570133i | \(0.806892\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 1006.27 | 0.909161 | 0.454581 | − | 0.890706i | \(-0.349789\pi\) | ||||
0.454581 | + | 0.890706i | \(0.349789\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 1724.94 | 1.51577 | 0.757885 | − | 0.652388i | \(-0.226233\pi\) | ||||
0.757885 | + | 0.652388i | \(0.226233\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 627.019 | 0.521991 | 0.260995 | − | 0.965340i | \(-0.415949\pi\) | ||||
0.260995 | + | 0.965340i | \(0.415949\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −1716.54 | −1.39190 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −896.377 | −0.690510 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 195.735 | 0.147058 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 956.002 | 0.684059 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −1990.05 | −1.39046 | −0.695230 | − | 0.718788i | \(-0.744697\pi\) | ||||
−0.695230 | + | 0.718788i | \(0.744697\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −156.414 | −0.104321 | −0.0521603 | − | 0.998639i | \(-0.516611\pi\) | ||||
−0.0521603 | + | 0.998639i | \(0.516611\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 571.284 | 0.372456 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 2119.31 | 1.32164 | 0.660822 | − | 0.750543i | \(-0.270208\pi\) | ||||
0.660822 | + | 0.750543i | \(0.270208\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −2686.77 | −1.63949 | −0.819745 | − | 0.572729i | \(-0.805885\pi\) | ||||
−0.819745 | + | 0.572729i | \(0.805885\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 3000.41 | 1.75460 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 867.403 | 0.496785 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 1551.56 | 0.853080 | 0.426540 | − | 0.904469i | \(-0.359732\pi\) | ||||
0.426540 | + | 0.904469i | \(0.359732\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −18.1092 | −0.00975962 | −0.00487981 | − | 0.999988i | \(-0.501553\pi\) | ||||
−0.00487981 | + | 0.999988i | \(0.501553\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 122.057 | 0.0632505 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 3741.51 | 1.90194 | 0.950971 | − | 0.309280i | \(-0.100088\pi\) | ||||
0.950971 | + | 0.309280i | \(0.100088\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −1845.05 | −0.903168 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 2608.90 | 1.25365 | 0.626826 | − | 0.779160i | \(-0.284354\pi\) | ||||
0.626826 | + | 0.779160i | \(0.284354\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 1562.89 | 0.724193 | 0.362097 | − | 0.932141i | \(-0.382061\pi\) | ||||
0.362097 | + | 0.932141i | \(0.382061\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 3699.56 | 1.68392 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 1502.77 | 0.660425 | 0.330212 | − | 0.943907i | \(-0.392880\pi\) | ||||
0.330212 | + | 0.943907i | \(0.392880\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −767.156 | −0.331380 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −4126.50 | −1.72307 | −0.861534 | − | 0.507700i | \(-0.830496\pi\) | ||||
−0.861534 | + | 0.507700i | \(0.830496\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 1582.33 | 0.649800 | 0.324900 | − | 0.945748i | \(-0.394669\pi\) | ||||
0.324900 | + | 0.945748i | \(0.394669\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −4267.89 | −1.69611 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −2439.40 | −0.953941 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −2575.88 | −0.975833 | −0.487916 | − | 0.872890i | \(-0.662243\pi\) | ||||
−0.487916 | + | 0.872890i | \(0.662243\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −1395.30 | −0.520392 | −0.260196 | − | 0.965556i | \(-0.583787\pi\) | ||||
−0.260196 | + | 0.965556i | \(0.583787\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −5047.62 | −1.82552 | −0.912761 | − | 0.408494i | \(-0.866054\pi\) | ||||
−0.912761 | + | 0.408494i | \(0.866054\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −2441.47 | −0.869704 | −0.434852 | − | 0.900502i | \(-0.643199\pi\) | ||||
−0.434852 | + | 0.900502i | \(0.643199\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 932.339 | 0.322352 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 234.806 | 0.0799978 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 1554.70 | 0.514548 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 4266.16 | 1.39192 | 0.695959 | − | 0.718081i | \(-0.254979\pi\) | ||||
0.695959 | + | 0.718081i | \(0.254979\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 6023.65 | 1.91074 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 131.194 | 0.0410416 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −4794.04 | −1.45919 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 1751.15 | 0.525855 | 0.262927 | − | 0.964816i | \(-0.415312\pi\) | ||||
0.262927 | + | 0.964816i | \(0.415312\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −2200.05 | −0.643269 | −0.321635 | − | 0.946864i | \(-0.604232\pi\) | ||||
−0.321635 | + | 0.946864i | \(0.604232\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −1191.29 | −0.343767 | −0.171884 | − | 0.985117i | \(-0.554985\pi\) | ||||
−0.171884 | + | 0.985117i | \(0.554985\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −2644.52 | −0.743555 | −0.371778 | − | 0.928322i | \(-0.621252\pi\) | ||||
−0.371778 | + | 0.928322i | \(0.621252\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −7768.87 | −2.15653 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −1437.52 | −0.389061 | −0.194530 | − | 0.980896i | \(-0.562318\pi\) | ||||
−0.194530 | + | 0.980896i | \(0.562318\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 3267.08 | 0.873240 | 0.436620 | − | 0.899646i | \(-0.356175\pi\) | ||||
0.436620 | + | 0.899646i | \(0.356175\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 1828.06 | 0.476695 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 3055.37 | 0.787078 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 1871.89 | 0.470727 | 0.235364 | − | 0.971907i | \(-0.424372\pi\) | ||||
0.235364 | + | 0.971907i | \(0.424372\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −5021.12 | −1.24773 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 4690.82 | 1.13854 | 0.569271 | − | 0.822150i | \(-0.307225\pi\) | ||||
0.569271 | + | 0.822150i | \(0.307225\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −4587.39 | −1.10057 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −4593.38 | −1.07696 | −0.538479 | − | 0.842639i | \(-0.681001\pi\) | ||||
−0.538479 | + | 0.842639i | \(0.681001\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 4400.73 | 1.02013 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −83.0074 | −0.0188143 | −0.00940716 | − | 0.999956i | \(-0.502994\pi\) | ||||
−0.00940716 | + | 0.999956i | \(0.502994\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −3464.08 | −0.776487 | −0.388244 | − | 0.921557i | \(-0.626918\pi\) | ||||
−0.388244 | + | 0.921557i | \(0.626918\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −2087.74 | −0.457803 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −1270.70 | −0.275628 | −0.137814 | − | 0.990458i | \(-0.544008\pi\) | ||||
−0.137814 | + | 0.990458i | \(0.544008\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −7651.80 | −1.62444 | −0.812221 | − | 0.583350i | \(-0.801742\pi\) | ||||
−0.812221 | + | 0.583350i | \(0.801742\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −7.45013 | −0.00156489 | −0.000782446 | − | 1.00000i | \(-0.500249\pi\) | ||||
−0.000782446 | 1.00000i | \(0.500249\pi\) | ||||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 252.384 | 0.0519086 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −1015.34 | −0.206663 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 2814.02 | 0.561082 | 0.280541 | − | 0.959842i | \(-0.409486\pi\) | ||||
0.280541 | + | 0.959842i | \(0.409486\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −3230.63 | −0.637609 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −9867.76 | −1.90859 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 6474.59 | 1.23983 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −6645.83 | −1.24767 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −5096.55 | −0.947477 | −0.473739 | − | 0.880666i | \(-0.657096\pi\) | ||||
−0.473739 | + | 0.880666i | \(0.657096\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −7784.81 | −1.41941 | −0.709705 | − | 0.704499i | \(-0.751172\pi\) | ||||
−0.709705 | + | 0.704499i | \(0.751172\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −246.469 | −0.0445088 | −0.0222544 | − | 0.999752i | \(-0.507084\pi\) | ||||
−0.0222544 | + | 0.999752i | \(0.507084\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 59.3201 | 0.0105102 | 0.00525512 | − | 0.999986i | \(-0.498327\pi\) | ||||
0.00525512 | + | 0.999986i | \(0.498327\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 2537.27 | 0.445329 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −2484.08 | −0.427920 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −4102.94 | −0.700277 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −8350.46 | −1.39932 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 4409.10 | 0.732163 | 0.366082 | − | 0.930583i | \(-0.380699\pi\) | ||||
0.366082 | + | 0.930583i | \(0.380699\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 7721.67 | 1.25934 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 6032.30 | 0.975075 | 0.487537 | − | 0.873102i | \(-0.337895\pi\) | ||||
0.487537 | + | 0.873102i | \(0.337895\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 357.032 | 0.0566991 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 6889.64 | 1.08456 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 6240.78 | 0.965484 | 0.482742 | − | 0.875763i | \(-0.339641\pi\) | ||||
0.482742 | + | 0.875763i | \(0.339641\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 5634.61 | 0.864223 | 0.432111 | − | 0.901820i | \(-0.357769\pi\) | ||||
0.432111 | + | 0.901820i | \(0.357769\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 3441.32 | 0.518875 | 0.259437 | − | 0.965760i | \(-0.416463\pi\) | ||||
0.259437 | + | 0.965760i | \(0.416463\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −8828.54 | −1.31992 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −7808.79 | −1.14800 | −0.574000 | − | 0.818855i | \(-0.694609\pi\) | ||||
−0.574000 | + | 0.818855i | \(0.694609\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −5275.83 | −0.769183 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −9304.51 | −1.33430 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 13608.1 | 1.93553 | 0.967763 | − | 0.251862i | \(-0.0810429\pi\) | ||||
0.967763 | + | 0.251862i | \(0.0810429\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 4730.18 | 0.661938 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −3748.17 | −0.520303 | −0.260151 | − | 0.965568i | \(-0.583772\pi\) | ||||
−0.260151 | + | 0.965568i | \(0.583772\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 4986.37 | 0.681197 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −10210.3 | −1.38382 | −0.691909 | − | 0.721985i | \(-0.743230\pi\) | ||||
−0.691909 | + | 0.721985i | \(0.743230\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −6129.49 | −0.817761 | −0.408880 | − | 0.912588i | \(-0.634081\pi\) | ||||
−0.408880 | + | 0.912588i | \(0.634081\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −7493.86 | −0.992007 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 4865.97 | 0.634227 | 0.317114 | − | 0.948388i | \(-0.397286\pi\) | ||||
0.317114 | + | 0.948388i | \(0.397286\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 8022.71 | 1.03766 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −9754.78 | −1.24257 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −438.311 | −0.0554110 | −0.0277055 | − | 0.999616i | \(-0.508820\pi\) | ||||
−0.0277055 | + | 0.999616i | \(0.508820\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 11753.7 | 1.46371 | 0.731857 | − | 0.681458i | \(-0.238654\pi\) | ||||
0.731857 | + | 0.681458i | \(0.238654\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 701.658 | 0.0867297 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −12484.2 | −1.52043 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 11246.5 | 1.35967 | 0.679833 | − | 0.733367i | \(-0.262052\pi\) | ||||
0.679833 | + | 0.733367i | \(0.262052\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −3472.48 | −0.413728 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 14566.4 | 1.72298 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 12316.4 | 1.43602 | 0.718012 | − | 0.696031i | \(-0.245052\pi\) | ||||
0.718012 | + | 0.696031i | \(0.245052\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −4702.60 | −0.544396 | −0.272198 | − | 0.962241i | \(-0.587751\pi\) | ||||
−0.272198 | + | 0.962241i | \(0.587751\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 3335.78 | 0.380727 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −7143.35 | −0.809581 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 2204.89 | 0.246417 | 0.123208 | − | 0.992381i | \(-0.460682\pi\) | ||||
0.123208 | + | 0.992381i | \(0.460682\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 9426.46 | 1.04620 | 0.523102 | − | 0.852270i | \(-0.324775\pi\) | ||||
0.523102 | + | 0.852270i | \(0.324775\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −5113.08 | −0.559707 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −7684.59 | −0.835457 | −0.417728 | − | 0.908572i | \(-0.637174\pi\) | ||||
−0.417728 | + | 0.908572i | \(0.637174\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 12394.3 | 1.32928 | 0.664640 | − | 0.747164i | \(-0.268585\pi\) | ||||
0.664640 | + | 0.747164i | \(0.268585\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −4242.28 | −0.451917 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 14568.7 | 1.53127 | 0.765635 | − | 0.643275i | \(-0.222425\pi\) | ||||
0.765635 | + | 0.643275i | \(0.222425\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 686.840 | 0.0717118 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −14727.3 | −1.51742 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −646.047 | −0.0661287 | −0.0330643 | − | 0.999453i | \(-0.510527\pi\) | ||||
−0.0330643 | + | 0.999453i | \(0.510527\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −19001.0 | −1.91966 | −0.959831 | − | 0.280579i | \(-0.909473\pi\) | ||||
−0.959831 | + | 0.280579i | \(0.909473\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 13665.7 | 1.37171 | 0.685853 | − | 0.727740i | \(-0.259429\pi\) | ||||
0.685853 | + | 0.727740i | \(0.259429\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −3762.83 | −0.372855 | −0.186427 | − | 0.982469i | \(-0.559691\pi\) | ||||
−0.186427 | + | 0.982469i | \(0.559691\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 8299.74 | 0.817156 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 17620.0 | 1.71283 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −2125.98 | −0.205361 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 6763.87 | 0.645197 | 0.322598 | − | 0.946536i | \(-0.395444\pi\) | ||||
0.322598 | + | 0.946536i | \(0.395444\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −24534.5 | −2.32573 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 19845.1 | 1.85798 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −1447.72 | −0.134708 | −0.0673538 | − | 0.997729i | \(-0.521456\pi\) | ||||
−0.0673538 | + | 0.997729i | \(0.521456\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 7838.28 | 0.720441 | 0.360220 | − | 0.932867i | \(-0.382701\pi\) | ||||
0.360220 | + | 0.932867i | \(0.382701\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −4054.04 | −0.370354 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −9489.46 | −0.856460 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −4245.34 | −0.380857 | −0.190428 | − | 0.981701i | \(-0.560988\pi\) | ||||
−0.190428 | + | 0.981701i | \(0.560988\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 17914.9 | 1.58804 | 0.794021 | − | 0.607891i | \(-0.207984\pi\) | ||||
0.794021 | + | 0.607891i | \(0.207984\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −13401.4 | −1.18090 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 14520.3 | 1.26444 | 0.632220 | − | 0.774789i | \(-0.282144\pi\) | ||||
0.632220 | + | 0.774789i | \(0.282144\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −10001.1 | −0.865795 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 22943.3 | 1.96312 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −22725.0 | −1.93316 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −3372.49 | −0.283592 | −0.141796 | − | 0.989896i | \(-0.545288\pi\) | ||||
−0.141796 | + | 0.989896i | \(0.545288\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 4339.40 | 0.362808 | 0.181404 | − | 0.983409i | \(-0.441936\pi\) | ||||
0.181404 | + | 0.983409i | \(0.441936\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −570.464 | −0.0471533 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 4346.46 | 0.357234 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 1349.81 | 0.109694 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −13441.6 | −1.08623 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 5347.32 | 0.427320 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −3831.98 | −0.304528 | −0.152264 | − | 0.988340i | \(-0.548656\pi\) | ||||
−0.152264 | + | 0.988340i | \(0.548656\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −23041.4 | −1.81098 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 13402.7 | 1.04764 | 0.523818 | − | 0.851830i | \(-0.324507\pi\) | ||||
0.523818 | + | 0.851830i | \(0.324507\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 2583.74 | 0.199766 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −10485.0 | −0.806274 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −14810.0 | −1.12661 | −0.563304 | − | 0.826249i | \(-0.690470\pi\) | ||||
−0.563304 | + | 0.826249i | \(0.690470\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 34627.7 | 2.62003 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 12233.2 | 0.915753 | 0.457877 | − | 0.889016i | \(-0.348610\pi\) | ||||
0.457877 | + | 0.889016i | \(0.348610\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −8375.60 | −0.623654 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −9711.68 | −0.715527 | −0.357763 | − | 0.933812i | \(-0.616461\pi\) | ||||
−0.357763 | + | 0.933812i | \(0.616461\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 8529.61 | 0.625137 | 0.312568 | − | 0.949895i | \(-0.398811\pi\) | ||||
0.312568 | + | 0.949895i | \(0.398811\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 6866.17 | 0.497981 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 15314.0 | 1.10491 | 0.552453 | − | 0.833544i | \(-0.313692\pi\) | ||||
0.552453 | + | 0.833544i | \(0.313692\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 15656.9 | 1.11800 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 12872.8 | 0.914468 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 19675.1 | 1.38343 | 0.691717 | − | 0.722168i | \(-0.256854\pi\) | ||||
0.691717 | + | 0.722168i | \(0.256854\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 363.571 | 0.0254341 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 15635.9 | 1.08278 | 0.541391 | − | 0.840771i | \(-0.317898\pi\) | ||||
0.541391 | + | 0.840771i | \(0.317898\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 11973.6 | 0.824994 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −485.189 | −0.0330956 | −0.0165478 | − | 0.999863i | \(-0.505268\pi\) | ||||
−0.0165478 | + | 0.999863i | \(0.505268\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −14796.2 | −1.00425 | −0.502123 | − | 0.864796i | \(-0.667447\pi\) | ||||
−0.502123 | + | 0.864796i | \(0.667447\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −2614.59 | −0.175699 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 3547.98 | 0.237245 | 0.118623 | − | 0.992939i | \(-0.462152\pi\) | ||||
0.118623 | + | 0.992939i | \(0.462152\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −44660.3 | −2.95706 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 20450.9 | 1.34748 | 0.673740 | − | 0.738968i | \(-0.264687\pi\) | ||||
0.673740 | + | 0.738968i | \(0.264687\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −15305.2 | −0.998646 | −0.499323 | − | 0.866416i | \(-0.666418\pi\) | ||||
−0.499323 | + | 0.866416i | \(0.666418\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −4151.19 | −0.269548 | −0.134774 | − | 0.990876i | \(-0.543031\pi\) | ||||
−0.134774 | + | 0.990876i | \(0.543031\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −4559.86 | −0.293238 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −19449.0 | −1.24474 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 19947.1 | 1.26446 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 25954.4 | 1.63745 | 0.818724 | − | 0.574187i | \(-0.194682\pi\) | ||||
0.818724 | + | 0.574187i | \(0.194682\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 26582.7 | 1.66126 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 10508.8 | 0.653650 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 17261.3 | 1.06362 | 0.531811 | − | 0.846863i | \(-0.321512\pi\) | ||||
0.531811 | + | 0.846863i | \(0.321512\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 2860.36 | 0.175430 | 0.0877152 | − | 0.996146i | \(-0.472043\pi\) | ||||
0.0877152 | + | 0.996146i | \(0.472043\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 28384.9 | 1.72477 | 0.862384 | − | 0.506255i | \(-0.168971\pi\) | ||||
0.862384 | + | 0.506255i | \(0.168971\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −9450.04 | −0.571566 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 11036.4 | 0.661393 | 0.330696 | − | 0.943737i | \(-0.392716\pi\) | ||||
0.330696 | + | 0.943737i | \(0.392716\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 2089.36 | 0.124638 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 21294.9 | 1.25877 | 0.629387 | − | 0.777092i | \(-0.283306\pi\) | ||||
0.629387 | + | 0.777092i | \(0.283306\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 12324.7 | 0.725229 | 0.362615 | − | 0.931939i | \(-0.381884\pi\) | ||||
0.362615 | + | 0.931939i | \(0.381884\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −7631.11 | −0.444995 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −8344.58 | −0.484413 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −19440.0 | −1.11844 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 3050.94 | 0.174748 | 0.0873738 | − | 0.996176i | \(-0.472153\pi\) | ||||
0.0873738 | + | 0.996176i | \(0.472153\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 1685.47 | 0.0956835 | 0.0478418 | − | 0.998855i | \(-0.484766\pi\) | ||||
0.0478418 | + | 0.998855i | \(0.484766\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 21330.7 | 1.20559 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −34715.5 | −1.94488 | −0.972440 | − | 0.233155i | \(-0.925095\pi\) | ||||
−0.972440 | + | 0.233155i | \(0.925095\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −28309.4 | −1.57905 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 25298.2 | 1.39882 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −8295.37 | −0.456687 | −0.228343 | − | 0.973581i | \(-0.573331\pi\) | ||||
−0.228343 | + | 0.973581i | \(0.573331\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 35889.4 | 1.95880 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −1097.43 | −0.0596385 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 23420.5 | 1.26188 | 0.630942 | − | 0.775830i | \(-0.282669\pi\) | ||||
0.630942 | + | 0.775830i | \(0.282669\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −12712.8 | −0.682037 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −14404.7 | −0.766258 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −5282.67 | −0.279823 | −0.139912 | − | 0.990164i | \(-0.544682\pi\) | ||||
−0.139912 | + | 0.990164i | \(0.544682\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −1174.21 | −0.0616752 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −40079.0 | −2.09632 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 714.975 | 0.0370849 | 0.0185425 | − | 0.999828i | \(-0.494097\pi\) | ||||
0.0185425 | + | 0.999828i | \(0.494097\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 24660.9 | 1.27382 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −3469.61 | −0.177735 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 25795.5 | 1.31596 | 0.657979 | − | 0.753036i | \(-0.271412\pi\) | ||||
0.657979 | + | 0.753036i | \(0.271412\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −28153.1 | −1.42446 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 3631.55 | 0.182994 | 0.0914969 | − | 0.995805i | \(-0.470835\pi\) | ||||
0.0914969 | + | 0.995805i | \(0.470835\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 22587.0 | 1.12890 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −24758.3 | −1.23241 | −0.616203 | − | 0.787588i | \(-0.711330\pi\) | ||||
−0.616203 | + | 0.787588i | \(0.711330\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −8845.33 | −0.436748 | −0.218374 | − | 0.975865i | \(-0.570075\pi\) | ||||
−0.218374 | + | 0.975865i | \(0.570075\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −20725.5 | −1.01922 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −14447.9 | −0.704827 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 1660.40 | 0.0806775 | 0.0403387 | − | 0.999186i | \(-0.487156\pi\) | ||||
0.0403387 | + | 0.999186i | \(0.487156\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 241.899 | 0.0116604 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 19937.2 | 0.957239 | 0.478619 | − | 0.878022i | \(-0.341137\pi\) | ||||
0.478619 | + | 0.878022i | \(0.341137\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −8443.74 | −0.402215 | −0.201107 | − | 0.979569i | \(-0.564454\pi\) | ||||
−0.201107 | + | 0.979569i | \(0.564454\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −24766.3 | −1.17510 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −18571.7 | −0.874295 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 17107.9 | 0.802243 | 0.401122 | − | 0.916025i | \(-0.368620\pi\) | ||||
0.401122 | + | 0.916025i | \(0.368620\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 9821.05 | 0.456971 | 0.228486 | − | 0.973547i | \(-0.426623\pi\) | ||||
0.228486 | + | 0.973547i | \(0.426623\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −488.226 | −0.0226292 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 699.419 | 0.0321685 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −25824.7 | −1.18320 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −49978.4 | −2.27236 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −5245.57 | −0.237591 | −0.118796 | − | 0.992919i | \(-0.537903\pi\) | ||||
−0.118796 | + | 0.992919i | \(0.537903\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −9002.62 | −0.404673 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −38204.4 | −1.71082 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 9218.52 | 0.409707 | 0.204854 | − | 0.978793i | \(-0.434328\pi\) | ||||
0.204854 | + | 0.978793i | \(0.434328\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 36309.8 | 1.60770 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −27217.0 | −1.19610 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 24645.8 | 1.07907 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −16397.4 | −0.712611 | −0.356305 | − | 0.934370i | \(-0.615964\pi\) | ||||
−0.356305 | + | 0.934370i | \(0.615964\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 8468.88 | 0.366686 | 0.183343 | − | 0.983049i | \(-0.441308\pi\) | ||||
0.183343 | + | 0.983049i | \(0.441308\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −34849.3 | −1.49781 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 17942.7 | 0.768342 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 5233.46 | 0.222471 | 0.111236 | − | 0.993794i | \(-0.464519\pi\) | ||||
0.111236 | + | 0.993794i | \(0.464519\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −3124.68 | −0.132344 | −0.0661722 | − | 0.997808i | \(-0.521079\pi\) | ||||
−0.0661722 | + | 0.997808i | \(0.521079\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −11037.6 | −0.464103 | −0.232052 | − | 0.972703i | \(-0.574544\pi\) | ||||
−0.232052 | + | 0.972703i | \(0.574544\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −23941.9 | −1.00306 | −0.501529 | − | 0.865141i | \(-0.667229\pi\) | ||||
−0.501529 | + | 0.865141i | \(0.667229\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −8543.91 | −0.355377 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −20876.8 | −0.865237 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −21259.4 | −0.874798 | −0.437399 | − | 0.899268i | \(-0.644100\pi\) | ||||
−0.437399 | + | 0.899268i | \(0.644100\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −20172.3 | −0.827107 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −49418.1 | −2.01187 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −2810.32 | −0.114007 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 41057.9 | 1.65387 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 8828.74 | 0.354385 | 0.177192 | − | 0.984176i | \(-0.443299\pi\) | ||||
0.177192 | + | 0.984176i | \(0.443299\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 38014.8 | 1.51524 | 0.757621 | − | 0.652695i | \(-0.226362\pi\) | ||||
0.757621 | + | 0.652695i | \(0.226362\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 4917.61 | 0.195328 | 0.0976640 | − | 0.995219i | \(-0.468863\pi\) | ||||
0.0976640 | + | 0.995219i | \(0.468863\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 20474.1 | 0.807585 | 0.403792 | − | 0.914851i | \(-0.367692\pi\) | ||||
0.403792 | + | 0.914851i | \(0.367692\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −20073.7 | −0.789049 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −28534.1 | −1.11387 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 44389.0 | 1.72682 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −13726.1 | −0.530316 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 14280.7 | 0.549858 | 0.274929 | − | 0.961464i | \(-0.411346\pi\) | ||||
0.274929 | + | 0.961464i | \(0.411346\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −12505.2 | −0.478217 | −0.239109 | − | 0.970993i | \(-0.576855\pi\) | ||||
−0.239109 | + | 0.970993i | \(0.576855\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −34255.9 | −1.30555 | −0.652776 | − | 0.757551i | \(-0.726396\pi\) | ||||
−0.652776 | + | 0.757551i | \(0.726396\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 24372.4 | 0.922600 | 0.461300 | − | 0.887244i | \(-0.347383\pi\) | ||||
0.461300 | + | 0.887244i | \(0.347383\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 28572.8 | 1.07795 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −23141.2 | −0.867179 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 55121.0 | 2.05865 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 593.350 | 0.0220126 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −20568.0 | −0.760510 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −21136.5 | −0.776355 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −42836.1 | −1.56819 | −0.784095 | − | 0.620641i | \(-0.786873\pi\) | ||||
−0.784095 | + | 0.620641i | \(0.786873\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 36145.3 | 1.31454 | 0.657271 | − | 0.753655i | \(-0.271711\pi\) | ||||
0.657271 | + | 0.753655i | \(0.271711\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 42608.8 | 1.54452 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 2245.77 | 0.0808744 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −23283.2 | −0.835738 | −0.417869 | − | 0.908507i | \(-0.637223\pi\) | ||||
−0.417869 | + | 0.908507i | \(0.637223\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −50751.9 | −1.80988 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 17071.5 | 0.606820 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 39190.5 | 1.38407 | 0.692033 | − | 0.721866i | \(-0.256715\pi\) | ||||
0.692033 | + | 0.721866i | \(0.256715\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 5445.26 | 0.191688 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 32585.1 | 1.13973 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −36892.8 | −1.28627 | −0.643135 | − | 0.765753i | \(-0.722366\pi\) | ||||
−0.643135 | + | 0.765753i | \(0.722366\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −26605.8 | −0.921705 | −0.460853 | − | 0.887477i | \(-0.652456\pi\) | ||||
−0.460853 | + | 0.887477i | \(0.652456\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −2258.88 | −0.0780055 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −12841.3 | −0.440641 | −0.220321 | − | 0.975427i | \(-0.570710\pi\) | ||||
−0.220321 | + | 0.975427i | \(0.570710\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −53488.2 | −1.82961 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −33977.5 | −1.15492 | −0.577460 | − | 0.816419i | \(-0.695956\pi\) | ||||
−0.577460 | + | 0.816419i | \(0.695956\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 34408.1 | 1.16589 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −30428.7 | −1.02460 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −29707.5 | −0.997197 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 18638.1 | 0.621744 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 49342.9 | 1.64091 | 0.820455 | − | 0.571712i | \(-0.193720\pi\) | ||||
0.820455 | + | 0.571712i | \(0.193720\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −43375.7 | −1.43356 | −0.716782 | − | 0.697297i | \(-0.754386\pi\) | ||||
−0.716782 | + | 0.697297i | \(0.754386\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 38576.2 | 1.27101 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 39694.6 | 1.29984 | 0.649919 | − | 0.760004i | \(-0.274803\pi\) | ||||
0.649919 | + | 0.760004i | \(0.274803\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −12409.2 | −0.405108 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −9058.89 | −0.293931 | −0.146965 | − | 0.989142i | \(-0.546951\pi\) | ||||
−0.146965 | + | 0.989142i | \(0.546951\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 67425.2 | 2.18106 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −57948.6 | −1.86315 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −33006.3 | −1.05800 | −0.529001 | − | 0.848621i | \(-0.677433\pi\) | ||||
−0.529001 | + | 0.848621i | \(0.677433\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 32612.7 | 1.03909 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 44324.4 | 1.40799 | 0.703996 | − | 0.710204i | \(-0.251397\pi\) | ||||
0.703996 | + | 0.710204i | \(0.251397\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 0 | 0 |
(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 | 648.4.a.d.1.1 | ✓ | 2 | |
3.2 | odd | 2 | 648.4.a.e.1.2 | yes | 2 | ||
4.3 | odd | 2 | 1296.4.a.n.1.1 | 2 | |||
9.2 | odd | 6 | 648.4.i.p.433.1 | 4 | |||
9.4 | even | 3 | 648.4.i.q.217.2 | 4 | |||
9.5 | odd | 6 | 648.4.i.p.217.1 | 4 | |||
9.7 | even | 3 | 648.4.i.q.433.2 | 4 | |||
12.11 | even | 2 | 1296.4.a.p.1.2 | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
648.4.a.d.1.1 | ✓ | 2 | 1.1 | even | 1 | trivial | |
648.4.a.e.1.2 | yes | 2 | 3.2 | odd | 2 | ||
648.4.i.p.217.1 | 4 | 9.5 | odd | 6 | |||
648.4.i.p.433.1 | 4 | 9.2 | odd | 6 | |||
648.4.i.q.217.2 | 4 | 9.4 | even | 3 | |||
648.4.i.q.433.2 | 4 | 9.7 | even | 3 | |||
1296.4.a.n.1.1 | 2 | 4.3 | odd | 2 | |||
1296.4.a.p.1.2 | 2 | 12.11 | even | 2 |