Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1024,4,Mod(1,1024)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1024, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([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("1024.1");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1024 = 2^{10} \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 1024.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: | \(60.4179558459\) |
Analytic rank: | \(0\) |
Dimension: | \(10\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{10} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{10} - 36x^{8} + 405x^{6} - 1380x^{4} + 420x^{2} - 32 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{11}]\) |
Coefficient ring index: | \( 2^{22} \) |
Twist minimal: | no (minimal twist has level 16) |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.4 | ||
Root | \(3.82089\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1024.1 |
$q$-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 | ||||||||
\(3\) | −2.80518 | −0.539857 | −0.269929 | − | 0.962880i | \(-0.587000\pi\) | ||||
−0.269929 | + | 0.962880i | \(0.587000\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −0.844070 | −0.0754959 | −0.0377480 | − | 0.999287i | \(-0.512018\pi\) | ||||
−0.0377480 | + | 0.999287i | \(0.512018\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −29.0828 | −1.57033 | −0.785163 | − | 0.619289i | \(-0.787421\pi\) | ||||
−0.785163 | + | 0.619289i | \(0.787421\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −19.1310 | −0.708554 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −17.1532 | −0.470171 | −0.235086 | − | 0.971975i | \(-0.575537\pi\) | ||||
−0.235086 | + | 0.971975i | \(0.575537\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −68.6824 | −1.46531 | −0.732657 | − | 0.680598i | \(-0.761720\pi\) | ||||
−0.732657 | + | 0.680598i | \(0.761720\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 2.36777 | 0.0407570 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −86.7193 | −1.23721 | −0.618604 | − | 0.785703i | \(-0.712301\pi\) | ||||
−0.618604 | + | 0.785703i | \(0.712301\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −77.5614 | −0.936517 | −0.468258 | − | 0.883592i | \(-0.655118\pi\) | ||||
−0.468258 | + | 0.883592i | \(0.655118\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 81.5826 | 0.847752 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 70.2145 | 0.636554 | 0.318277 | − | 0.947998i | \(-0.396896\pi\) | ||||
0.318277 | + | 0.947998i | \(0.396896\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −124.288 | −0.994300 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 129.406 | 0.922375 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −89.6641 | −0.574145 | −0.287072 | − | 0.957909i | \(-0.592682\pi\) | ||||
−0.287072 | + | 0.957909i | \(0.592682\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −8.86868 | −0.0513826 | −0.0256913 | − | 0.999670i | \(-0.508179\pi\) | ||||
−0.0256913 | + | 0.999670i | \(0.508179\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 48.1178 | 0.253825 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 24.5480 | 0.118553 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −30.7089 | −0.136446 | −0.0682231 | − | 0.997670i | \(-0.521733\pi\) | ||||
−0.0682231 | + | 0.997670i | \(0.521733\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 192.667 | 0.791060 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −153.274 | −0.583840 | −0.291920 | − | 0.956443i | \(-0.594294\pi\) | ||||
−0.291920 | + | 0.956443i | \(0.594294\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 171.050 | 0.606625 | 0.303312 | − | 0.952891i | \(-0.401907\pi\) | ||||
0.303312 | + | 0.952891i | \(0.401907\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 16.1479 | 0.0534930 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 99.9792 | 0.310286 | 0.155143 | − | 0.987892i | \(-0.450416\pi\) | ||||
0.155143 | + | 0.987892i | \(0.450416\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 502.812 | 1.46592 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 243.263 | 0.667915 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −550.315 | −1.42626 | −0.713128 | − | 0.701034i | \(-0.752722\pi\) | ||||
−0.713128 | + | 0.701034i | \(0.752722\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 14.4785 | 0.0354960 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 217.574 | 0.505585 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −459.364 | −1.01363 | −0.506814 | − | 0.862055i | \(-0.669177\pi\) | ||||
−0.506814 | + | 0.862055i | \(0.669177\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 0.479693 | 0.00100686 | 0.000503430 | − | 1.00000i | \(-0.499840\pi\) | ||||
0.000503430 | 1.00000i | \(0.499840\pi\) | ||||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 556.383 | 1.11266 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 57.9728 | 0.110625 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −799.438 | −1.45771 | −0.728857 | − | 0.684666i | \(-0.759948\pi\) | ||||
−0.728857 | + | 0.684666i | \(0.759948\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −196.964 | −0.343648 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 419.500 | 0.701205 | 0.350602 | − | 0.936524i | \(-0.385977\pi\) | ||||
0.350602 | + | 0.936524i | \(0.385977\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 374.833 | 0.600971 | 0.300485 | − | 0.953786i | \(-0.402851\pi\) | ||||
0.300485 | + | 0.953786i | \(0.402851\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 348.649 | 0.536780 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 498.864 | 0.738322 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 705.750 | 1.00510 | 0.502551 | − | 0.864547i | \(-0.332395\pi\) | ||||
0.502551 | + | 0.864547i | \(0.332395\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 153.530 | 0.210604 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −1339.39 | −1.77129 | −0.885646 | − | 0.464361i | \(-0.846284\pi\) | ||||
−0.885646 | + | 0.464361i | \(0.846284\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 73.1972 | 0.0934041 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 251.524 | 0.309956 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 4.72918 | 0.00563249 | 0.00281625 | − | 0.999996i | \(-0.499104\pi\) | ||||
0.00281625 | + | 0.999996i | \(0.499104\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 1997.48 | 2.30102 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 24.8782 | 0.0277393 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 65.4673 | 0.0707032 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 379.542 | 0.397285 | 0.198643 | − | 0.980072i | \(-0.436347\pi\) | ||||
0.198643 | + | 0.980072i | \(0.436347\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 328.157 | 0.333142 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −552.964 | −0.544772 | −0.272386 | − | 0.962188i | \(-0.587813\pi\) | ||||
−0.272386 | + | 0.962188i | \(0.587813\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 307.935 | 0.294580 | 0.147290 | − | 0.989093i | \(-0.452945\pi\) | ||||
0.147290 | + | 0.989093i | \(0.452945\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −68.8615 | −0.0640018 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 850.801 | 0.768692 | 0.384346 | − | 0.923189i | \(-0.374427\pi\) | ||||
0.384346 | + | 0.923189i | \(0.374427\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −1341.93 | −1.17921 | −0.589605 | − | 0.807692i | \(-0.700717\pi\) | ||||
−0.589605 | + | 0.807692i | \(0.700717\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 86.1439 | 0.0736614 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −1824.02 | −1.51849 | −0.759244 | − | 0.650807i | \(-0.774431\pi\) | ||||
−0.759244 | + | 0.650807i | \(0.774431\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −59.2660 | −0.0480573 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 1313.96 | 1.03825 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 2522.04 | 1.94282 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −1036.77 | −0.778939 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 429.962 | 0.315190 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 210.416 | 0.150562 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 988.748 | 0.690844 | 0.345422 | − | 0.938447i | \(-0.387736\pi\) | ||||
0.345422 | + | 0.938447i | \(0.387736\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −479.826 | −0.327491 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −1122.28 | −0.748505 | −0.374252 | − | 0.927327i | \(-0.622101\pi\) | ||||
−0.374252 | + | 0.927327i | \(0.622101\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 2255.71 | 1.47064 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −109.227 | −0.0696356 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −1595.30 | −0.994856 | −0.497428 | − | 0.867505i | \(-0.665722\pi\) | ||||
−0.497428 | + | 0.867505i | \(0.665722\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 392.721 | 0.239641 | 0.119821 | − | 0.992796i | \(-0.461768\pi\) | ||||
0.119821 | + | 0.992796i | \(0.461768\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −280.460 | −0.167510 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 1178.12 | 0.688948 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 75.6828 | 0.0433456 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −1410.48 | −0.791390 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 839.014 | 0.461307 | 0.230653 | − | 0.973036i | \(-0.425914\pi\) | ||||
0.230653 | + | 0.973036i | \(0.425914\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −160.655 | −0.0865821 | −0.0432911 | − | 0.999063i | \(-0.513784\pi\) | ||||
−0.0432911 | + | 0.999063i | \(0.513784\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 1659.02 | 0.876629 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 7.48579 | 0.00387918 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 998.098 | 0.507369 | 0.253684 | − | 0.967287i | \(-0.418358\pi\) | ||||
0.253684 | + | 0.967287i | \(0.418358\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 1543.73 | 0.769975 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −2042.04 | −0.999598 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −2648.31 | −1.27259 | −0.636294 | − | 0.771447i | \(-0.719533\pi\) | ||||
−0.636294 | + | 0.771447i | \(0.719533\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −40.6148 | −0.0191628 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 3852.19 | 1.78498 | 0.892490 | − | 0.451066i | \(-0.148956\pi\) | ||||
0.892490 | + | 0.451066i | \(0.148956\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 2520.28 | 1.14715 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 1483.83 | 0.663573 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 3713.17 | 1.63183 | 0.815917 | − | 0.578170i | \(-0.196233\pi\) | ||||
0.815917 | + | 0.578170i | \(0.196233\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 3614.64 | 1.56138 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 1288.60 | 0.547215 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −1749.01 | −0.730318 | −0.365159 | − | 0.930945i | \(-0.618985\pi\) | ||||
−0.365159 | + | 0.930945i | \(0.618985\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −2227.25 | −0.914640 | −0.457320 | − | 0.889302i | \(-0.651191\pi\) | ||||
−0.457320 | + | 0.889302i | \(0.651191\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −1.34563 | −0.000543560 0 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 25.9204 | 0.0103011 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 1487.51 | 0.581699 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −3763.48 | −1.44843 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 3585.92 | 1.35847 | 0.679236 | − | 0.733920i | \(-0.262311\pi\) | ||||
0.679236 | + | 0.733920i | \(0.262311\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 523.601 | 0.195283 | 0.0976415 | − | 0.995222i | \(-0.468870\pi\) | ||||
0.0976415 | + | 0.995222i | \(0.468870\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −162.624 | −0.0597218 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −1591.89 | −0.575724 | −0.287862 | − | 0.957672i | \(-0.592944\pi\) | ||||
−0.287862 | + | 0.957672i | \(0.592944\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 2312.48 | 0.823757 | 0.411878 | − | 0.911239i | \(-0.364873\pi\) | ||||
0.411878 | + | 0.911239i | \(0.364873\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 2242.57 | 0.786957 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 2607.69 | 0.901595 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 129.374 | 0.0440775 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −1343.27 | −0.451033 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 1330.43 | 0.440323 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 2006.19 | 0.654558 | 0.327279 | − | 0.944928i | \(-0.393868\pi\) | ||||
0.327279 | + | 0.944928i | \(0.393868\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −1176.77 | −0.378550 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −144.378 | −0.0457977 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 257.926 | 0.0806875 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −1051.47 | −0.324438 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 5956.10 | 1.81290 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −4315.08 | −1.29578 | −0.647890 | − | 0.761734i | \(-0.724349\pi\) | ||||
−0.647890 | + | 0.761734i | \(0.724349\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 2377.74 | 0.704516 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −991.651 | −0.289948 | −0.144974 | − | 0.989435i | \(-0.546310\pi\) | ||||
−0.144974 | + | 0.989435i | \(0.546310\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −938.121 | −0.270711 | −0.135355 | − | 0.990797i | \(-0.543218\pi\) | ||||
−0.135355 | + | 0.990797i | \(0.543218\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −1399.40 | −0.398588 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −3490.15 | −0.981318 | −0.490659 | − | 0.871352i | \(-0.663244\pi\) | ||||
−0.490659 | + | 0.871352i | \(0.663244\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −84.3895 | −0.0234254 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −1979.76 | −0.542612 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −2950.43 | −0.798525 | −0.399263 | − | 0.916837i | \(-0.630734\pi\) | ||||
−0.399263 | + | 0.916837i | \(0.630734\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 1128.96 | 0.301755 | 0.150877 | − | 0.988552i | \(-0.451790\pi\) | ||||
0.150877 | + | 0.988552i | \(0.451790\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −3924.63 | −1.03607 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −424.409 | −0.110671 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 5327.11 | 1.37229 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 3757.23 | 0.956244 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 6536.30 | 1.64370 | 0.821848 | − | 0.569706i | \(-0.192943\pi\) | ||||
0.821848 | + | 0.569706i | \(0.192943\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −1204.40 | −0.299289 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −205.331 | −0.0504249 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 610.977 | 0.148295 | 0.0741473 | − | 0.997247i | \(-0.476377\pi\) | ||||
0.0741473 | + | 0.997247i | \(0.476377\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 893.101 | 0.214265 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 1715.36 | 0.406813 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −4973.57 | −1.16610 | −0.583048 | − | 0.812438i | \(-0.698140\pi\) | ||||
−0.583048 | + | 0.812438i | \(0.698140\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 464.505 | 0.107677 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −13.2662 | −0.00304074 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −1327.12 | −0.300803 | −0.150401 | − | 0.988625i | \(-0.548057\pi\) | ||||
−0.150401 | + | 0.988625i | \(0.548057\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 4010.64 | 0.898999 | 0.449500 | − | 0.893280i | \(-0.351602\pi\) | ||||
0.449500 | + | 0.893280i | \(0.351602\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −5603.29 | −1.24222 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 2131.93 | 0.467491 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 4999.23 | 1.08439 | 0.542193 | − | 0.840254i | \(-0.317594\pi\) | ||||
0.542193 | + | 0.840254i | \(0.317594\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 169.666 | 0.0364074 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −7468.35 | −1.58550 | −0.792748 | − | 0.609550i | \(-0.791350\pi\) | ||||
−0.792748 | + | 0.609550i | \(0.791350\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −3180.88 | −0.668140 | −0.334070 | − | 0.942548i | \(-0.608422\pi\) | ||||
−0.334070 | + | 0.942548i | \(0.608422\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −183.648 | −0.0381696 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 4457.66 | 0.916819 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 2607.24 | 0.530682 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −1064.68 | −0.214477 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −5590.09 | −1.11460 | −0.557298 | − | 0.830312i | \(-0.688162\pi\) | ||||
−0.557298 | + | 0.830312i | \(0.688162\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 387.736 | 0.0765249 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −2219.72 | −0.433674 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −4822.51 | −0.932752 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −4974.62 | −0.952599 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 1551.16 | 0.294099 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −0.404895 | −7.60138e−5 0 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −5452.13 | −1.01358 | −0.506791 | − | 0.862069i | \(-0.669168\pi\) | ||||
−0.506791 | + | 0.862069i | \(0.669168\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −863.814 | −0.159031 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −5194.39 | −0.947096 | −0.473548 | − | 0.880768i | \(-0.657027\pi\) | ||||
−0.473548 | + | 0.880768i | \(0.657027\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −4710.01 | −0.850561 | −0.425281 | − | 0.905062i | \(-0.639825\pi\) | ||||
−0.425281 | + | 0.905062i | \(0.639825\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −469.626 | −0.0840014 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −8033.04 | −1.42328 | −0.711641 | − | 0.702544i | \(-0.752048\pi\) | ||||
−0.711641 | + | 0.702544i | \(0.752048\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 1538.03 | 0.269946 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −2386.65 | −0.414984 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 6726.08 | 1.15867 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 8536.37 | 1.45696 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 3764.36 | 0.636605 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −2907.68 | −0.487251 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −2567.92 | −0.426423 | −0.213211 | − | 0.977006i | \(-0.568392\pi\) | ||||
−0.213211 | + | 0.977006i | \(0.568392\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 587.490 | 0.0966795 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 674.782 | 0.110052 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 2683.29 | 0.433733 | 0.216867 | − | 0.976201i | \(-0.430416\pi\) | ||||
0.216867 | + | 0.976201i | \(0.430416\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 5116.69 | 0.819766 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 152.126 | 0.0241586 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −4647.79 | −0.731653 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 166.252 | 0.0259440 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −7483.74 | −1.15778 | −0.578888 | − | 0.815407i | \(-0.696513\pi\) | ||||
−0.578888 | + | 0.815407i | \(0.696513\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −104.239 | −0.0159880 | −0.00799400 | − | 0.999968i | \(-0.502545\pi\) | ||||
−0.00799400 | + | 0.999968i | \(0.502545\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −8887.90 | −1.35157 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −5067.25 | −0.764030 | −0.382015 | − | 0.924156i | \(-0.624770\pi\) | ||||
−0.382015 | + | 0.924156i | \(0.624770\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −354.088 | −0.0529381 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −7074.79 | −1.04884 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −970.230 | −0.142637 | −0.0713186 | − | 0.997454i | \(-0.522721\pi\) | ||||
−0.0713186 | + | 0.997454i | \(0.522721\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −843.224 | −0.122937 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 2908.32 | 0.420516 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −316.385 | −0.0453709 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −13451.4 | −1.91323 | −0.956617 | − | 0.291347i | \(-0.905896\pi\) | ||||
−0.956617 | + | 0.291347i | \(0.905896\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 2932.29 | 0.413682 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 16004.7 | 2.23969 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −8341.34 | −1.15790 | −0.578952 | − | 0.815362i | \(-0.696538\pi\) | ||||
−0.578952 | + | 0.815362i | \(0.696538\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −590.255 | −0.0812817 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 6158.35 | 0.841302 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −6288.62 | −0.852308 | −0.426154 | − | 0.904651i | \(-0.640132\pi\) | ||||
−0.426154 | + | 0.904651i | \(0.640132\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −2773.62 | −0.372957 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −6417.68 | −0.856209 | −0.428105 | − | 0.903729i | \(-0.640819\pi\) | ||||
−0.428105 | + | 0.903729i | \(0.640819\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −421.076 | −0.0557403 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −3272.35 | −0.429827 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 9271.04 | 1.20838 | 0.604191 | − | 0.796840i | \(-0.293497\pi\) | ||||
0.604191 | + | 0.796840i | \(0.293497\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −6088.96 | −0.787549 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 3148.20 | 0.404086 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −595.703 | −0.0758812 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 12590.0 | 1.59163 | 0.795814 | − | 0.605541i | \(-0.207043\pi\) | ||||
0.795814 | + | 0.605541i | \(0.207043\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −6327.66 | −0.793933 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 6425.77 | 0.800218 | 0.400109 | − | 0.916468i | \(-0.368972\pi\) | ||||
0.400109 | + | 0.916468i | \(0.368972\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 609.122 | 0.0752917 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −129.590 | −0.0158997 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 526.755 | 0.0641530 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 12796.0 | 1.54699 | 0.773496 | − | 0.633801i | \(-0.218506\pi\) | ||||
0.773496 | + | 0.633801i | \(0.218506\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 4475.09 | 0.537080 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 13359.6 | 1.59173 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 1130.54 | 0.133725 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −1101.65 | −0.129372 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 9256.33 | 1.07924 | 0.539620 | − | 0.841909i | \(-0.318568\pi\) | ||||
0.539620 | + | 0.841909i | \(0.318568\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −9036.83 | −1.04615 | −0.523074 | − | 0.852287i | \(-0.675215\pi\) | ||||
−0.523074 | + | 0.852287i | \(0.675215\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −1912.70 | −0.219855 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 10778.1 | 1.23016 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −13.9508 | −0.00158110 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −3304.85 | −0.371934 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 10639.3 | 1.18904 | 0.594519 | − | 0.804081i | \(-0.297342\pi\) | ||||
0.594519 | + | 0.804081i | \(0.297342\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −3806.14 | −0.422428 | −0.211214 | − | 0.977440i | \(-0.567742\pi\) | ||||
−0.211214 | + | 0.977440i | \(0.567742\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −212.304 | −0.0234004 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −5445.94 | −0.596143 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −14102.8 | −1.53323 | −0.766616 | − | 0.642106i | \(-0.778061\pi\) | ||||
−0.766616 | + | 0.642106i | \(0.778061\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −9619.28 | −1.03869 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −10836.3 | −1.16219 | −0.581095 | − | 0.813836i | \(-0.697375\pi\) | ||||
−0.581095 | + | 0.813836i | \(0.697375\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −3.99176 | −0.000425230 0 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −2353.58 | −0.249040 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 13679.4 | 1.43779 | 0.718897 | − | 0.695117i | \(-0.244647\pi\) | ||||
0.718897 | + | 0.695117i | \(0.244647\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 2629.14 | 0.274505 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 450.666 | 0.0467420 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −1686.01 | −0.173718 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −7913.48 | −0.810016 | −0.405008 | − | 0.914313i | \(-0.632731\pi\) | ||||
−0.405008 | + | 0.914313i | \(0.632731\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −11222.0 | −1.14117 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −820.548 | −0.0828996 | −0.0414498 | − | 0.999141i | \(-0.513198\pi\) | ||||
−0.0414498 | + | 0.999141i | \(0.513198\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −14236.5 | −1.42899 | −0.714497 | − | 0.699638i | \(-0.753344\pi\) | ||||
−0.714497 | + | 0.699638i | \(0.753344\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −20.9990 | −0.00209420 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −11801.0 | −1.16935 | −0.584674 | − | 0.811269i | \(-0.698777\pi\) | ||||
−0.584674 | + | 0.811269i | \(0.698777\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 23249.9 | 2.28909 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −2799.85 | −0.273907 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −2934.05 | −0.285217 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 9639.92 | 0.931179 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 10528.1 | 1.01058 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −5563.77 | −0.530720 | −0.265360 | − | 0.964149i | \(-0.585491\pi\) | ||||
−0.265360 | + | 0.964149i | \(0.585491\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 2109.16 | 0.199936 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 5728.29 | 0.539640 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −320.360 | −0.0299934 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −18150.5 | −1.68886 | −0.844432 | − | 0.535662i | \(-0.820062\pi\) | ||||
−0.844432 | + | 0.535662i | \(0.820062\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 7428.99 | 0.687015 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −16395.0 | −1.50692 | −0.753459 | − | 0.657495i | \(-0.771616\pi\) | ||||
−0.753459 | + | 0.657495i | \(0.771616\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 7775.61 | 0.710336 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −276.988 | −0.0251509 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −12200.3 | −1.10112 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 4397.61 | 0.394517 | 0.197259 | − | 0.980351i | \(-0.436796\pi\) | ||||
0.197259 | + | 0.980351i | \(0.436796\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −10806.1 | −0.963635 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 6221.21 | 0.551471 | 0.275736 | − | 0.961233i | \(-0.411079\pi\) | ||||
0.275736 | + | 0.961233i | \(0.411079\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 466.740 | 0.0411281 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −7069.83 | −0.619295 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −19516.8 | −1.69954 | −0.849770 | − | 0.527154i | \(-0.823259\pi\) | ||||
−0.849770 | + | 0.527154i | \(0.823259\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −10901.2 | −0.943720 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −10036.9 | −0.863820 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −259.919 | −0.0222396 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −1714.96 | −0.145888 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −10416.1 | −0.880957 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 6874.63 | 0.578086 | 0.289043 | − | 0.957316i | \(-0.406663\pi\) | ||||
0.289043 | + | 0.957316i | \(0.406663\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −3261.91 | −0.272722 | −0.136361 | − | 0.990659i | \(-0.543541\pi\) | ||||
−0.136361 | + | 0.990659i | \(0.543541\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | −10139.7 | −0.842920 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 769.086 | 0.0635710 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −7236.92 | −0.594799 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 8788.08 | 0.718211 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 10527.3 | 0.855509 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −718.136 | −0.0580332 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 4906.28 | 0.394267 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −8624.83 | −0.689235 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 18724.1 | 1.48801 | 0.744005 | − | 0.668174i | \(-0.232924\pi\) | ||||
0.744005 | + | 0.668174i | \(0.232924\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 6247.82 | 0.493775 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 1132.69 | 0.0890256 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 18768.5 | 1.46706 | 0.733530 | − | 0.679657i | \(-0.237871\pi\) | ||||
0.733530 | + | 0.679657i | \(0.237871\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −9.17700 | −0.000713415 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 6954.47 | 0.537696 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −20525.2 | −1.57834 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −72.7115 | −0.00556114 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −12021.7 | −0.914497 | −0.457249 | − | 0.889339i | \(-0.651165\pi\) | ||||
−0.457249 | + | 0.889339i | \(0.651165\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −11748.1 | −0.888896 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −4172.74 | −0.314034 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 24504.4 | 1.83434 | 0.917172 | − | 0.398491i | \(-0.130466\pi\) | ||||
0.917172 | + | 0.398491i | \(0.130466\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 1539.60 | 0.114640 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −4465.09 | −0.330716 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 8998.54 | 0.662985 | 0.331492 | − | 0.943458i | \(-0.392448\pi\) | ||||
0.331492 | + | 0.943458i | \(0.392448\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −13928.9 | −1.02085 | −0.510427 | − | 0.859921i | \(-0.670513\pi\) | ||||
−0.510427 | + | 0.859921i | \(0.670513\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −10059.1 | −0.733380 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −8726.79 | −0.632926 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −20584.4 | −1.48516 | −0.742580 | − | 0.669757i | \(-0.766398\pi\) | ||||
−0.742580 | + | 0.669757i | \(0.766398\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −1468.79 | −0.105425 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 38953.3 | 2.78151 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 9439.66 | 0.670585 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −1109.08 | −0.0783840 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 3658.25 | 0.257227 | 0.128613 | − | 0.991695i | \(-0.458947\pi\) | ||||
0.128613 | + | 0.991695i | \(0.458947\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 687.867 | 0.0481207 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 4465.54 | 0.310809 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 6035.89 | 0.417984 | 0.208992 | − | 0.977917i | \(-0.432982\pi\) | ||||
0.208992 | + | 0.977917i | \(0.432982\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −2128.78 | −0.146675 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −6486.93 | −0.444711 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 5427.20 | 0.370199 | 0.185100 | − | 0.982720i | \(-0.440739\pi\) | ||||
0.185100 | + | 0.982720i | \(0.440739\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −17725.7 | −1.20307 | −0.601535 | − | 0.798847i | \(-0.705444\pi\) | ||||
−0.601535 | + | 0.798847i | \(0.705444\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 15294.0 | 1.03287 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 875.105 | 0.0588067 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 13487.6 | 0.901884 | 0.450942 | − | 0.892553i | \(-0.351088\pi\) | ||||
0.450942 | + | 0.892553i | \(0.351088\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −7315.03 | −0.486732 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −6866.81 | −0.454667 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −23830.0 | −1.57012 | −0.785062 | − | 0.619417i | \(-0.787369\pi\) | ||||
−0.785062 | + | 0.619417i | \(0.787369\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −362.918 | −0.0237956 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −535.243 | −0.0349239 | −0.0174620 | − | 0.999848i | \(-0.505559\pi\) | ||||
−0.0174620 | + | 0.999848i | \(0.505559\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 27847.2 | 1.80820 | 0.904098 | − | 0.427324i | \(-0.140544\pi\) | ||||
0.904098 | + | 0.427324i | \(0.140544\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 9086.16 | 0.587142 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −137.538 | −0.00884485 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 15358.3 | 0.982934 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −3732.08 | −0.237711 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 2663.05 | 0.168812 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −11880.2 | −0.749511 | −0.374755 | − | 0.927124i | \(-0.622273\pi\) | ||||
−0.374755 | + | 0.927124i | \(0.622273\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −5627.72 | −0.353368 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −834.573 | −0.0521560 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −34534.4 | −2.14804 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −8025.45 | −0.496842 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 18341.0 | 1.13015 | 0.565074 | − | 0.825040i | \(-0.308848\pi\) | ||||
0.565074 | + | 0.825040i | \(0.308848\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −9936.56 | −0.609424 | −0.304712 | − | 0.952445i | \(-0.598560\pi\) | ||||
−0.304712 | + | 0.952445i | \(0.598560\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 405.007 | 0.0247242 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 21429.7 | 1.30215 | 0.651073 | − | 0.759015i | \(-0.274319\pi\) | ||||
0.651073 | + | 0.759015i | \(0.274319\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 7879.56 | 0.476579 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −723.530 | −0.0435597 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 12277.1 | 0.735742 | 0.367871 | − | 0.929877i | \(-0.380087\pi\) | ||||
0.367871 | + | 0.929877i | \(0.380087\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 947.284 | 0.0565091 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −7170.92 | −0.425821 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −5871.25 | −0.347058 | −0.173529 | − | 0.984829i | \(-0.555517\pi\) | ||||
−0.173529 | + | 0.984829i | \(0.555517\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −17308.5 | −1.01849 | −0.509246 | − | 0.860621i | \(-0.670076\pi\) | ||||
−0.509246 | + | 0.860621i | \(0.670076\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −16707.9 | −0.978706 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −1903.98 | −0.111027 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −6295.72 | −0.365474 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 12104.6 | 0.699536 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −8.22827 | −0.000473396 0 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 6528.62 | 0.373937 | 0.186969 | − | 0.982366i | \(-0.440134\pi\) | ||||
0.186969 | + | 0.982366i | \(0.440134\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −16083.5 | −0.917118 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −20110.9 | −1.14169 | −0.570847 | − | 0.821057i | \(-0.693385\pi\) | ||||
−0.570847 | + | 0.821057i | \(0.693385\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −11038.2 | −0.623867 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 2781.76 | 0.156530 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −30291.8 | −1.69705 | −0.848524 | − | 0.529157i | \(-0.822508\pi\) | ||||
−0.848524 | + | 0.529157i | \(0.822508\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 1346.54 | 0.0751076 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 2631.60 | 0.146145 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 37797.0 | 2.08991 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −23387.1 | −1.28753 | −0.643767 | − | 0.765222i | \(-0.722629\pi\) | ||||
−0.643767 | + | 0.765222i | \(0.722629\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −9543.74 | −0.523141 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −331.484 | −0.0180920 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 13291.8 | 0.722331 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 9790.49 | 0.529772 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 4280.14 | 0.230612 | 0.115306 | − | 0.993330i | \(-0.463215\pi\) | ||||
0.115306 | + | 0.993330i | \(0.463215\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 2381.82 | 0.127784 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 236.728 | 0.0126464 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 16081.8 | 0.855470 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 5630.18 | 0.298231 | 0.149115 | − | 0.988820i | \(-0.452357\pi\) | ||||
0.149115 | + | 0.988820i | \(0.452357\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −13501.7 | −0.712170 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −622.710 | −0.0327078 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −994.419 | −0.0520128 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 8276.49 | 0.431090 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 5682.25 | 0.294732 | 0.147366 | − | 0.989082i | \(-0.452921\pi\) | ||||
0.147366 | + | 0.989082i | \(0.452921\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −8955.64 | −0.462587 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −3166.94 | −0.162904 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 11144.1 | 0.570872 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 18883.0 | 0.963317 | 0.481658 | − | 0.876359i | \(-0.340035\pi\) | ||||
0.481658 | + | 0.876359i | \(0.340035\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 6863.99 | 0.348727 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −14833.3 | −0.750521 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 35302.3 | 1.77888 | 0.889441 | − | 0.457049i | \(-0.151094\pi\) | ||||
0.889441 | + | 0.457049i | \(0.151094\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 1190.54 | 0.0597467 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 13712.9 | 0.685375 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −8771.48 | −0.436623 | −0.218311 | − | 0.975879i | \(-0.570055\pi\) | ||||
−0.218311 | + | 0.975879i | \(0.570055\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −14943.5 | −0.740841 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 30.9140 | 0.00152641 | 0.000763205 | − | 1.00000i | \(-0.499757\pi\) | ||||
0.000763205 | 1.00000i | \(0.499757\pi\) | ||||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −708.187 | −0.0348268 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 25623.8 | 1.25506 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −24743.7 | −1.20710 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 16318.5 | 0.792905 | 0.396453 | − | 0.918055i | \(-0.370241\pi\) | ||||
0.396453 | + | 0.918055i | \(0.370241\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −18335.5 | −0.887361 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 135.604 | 0.00653660 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −13936.5 | −0.669129 | −0.334564 | − | 0.942373i | \(-0.608589\pi\) | ||||
−0.334564 | + | 0.942373i | \(0.608589\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 3378.57 | 0.161573 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −3823.42 | −0.182127 | −0.0910637 | − | 0.995845i | \(-0.529027\pi\) | ||||
−0.0910637 | + | 0.995845i | \(0.529027\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 39027.2 | 1.85174 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −1400.33 | −0.0661819 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 31550.2 | 1.48528 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 31689.1 | 1.48601 | 0.743003 | − | 0.669288i | \(-0.233401\pi\) | ||||
0.743003 | + | 0.669288i | \(0.233401\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −1713.90 | −0.0800578 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −1846.74 | −0.0859282 | −0.0429641 | − | 0.999077i | \(-0.513680\pi\) | ||||
−0.0429641 | + | 0.999077i | \(0.513680\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 1102.27 | 0.0510898 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −2505.31 | −0.115672 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 11888.2 | 0.546776 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −7195.77 | −0.329686 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −11603.0 | −0.529577 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −842.465 | −0.0383043 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 20364.0 | 0.922363 | 0.461181 | − | 0.887306i | \(-0.347426\pi\) | ||||
0.461181 | + | 0.887306i | \(0.347426\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 13951.7 | 0.629525 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 53047.6 | 2.38452 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −32.9465 | −0.00147537 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −1303.02 | −0.0581300 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 7880.27 | 0.350230 | 0.175115 | − | 0.984548i | \(-0.443970\pi\) | ||||
0.175115 | + | 0.984548i | \(0.443970\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −8670.13 | −0.383889 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −90.4737 | −0.00399093 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −6429.58 | −0.282559 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 1723.62 | 0.0754656 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 3722.81 | 0.162390 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 5081.28 | 0.220826 | 0.110413 | − | 0.993886i | \(-0.464783\pi\) | ||||
0.110413 | + | 0.993886i | \(0.464783\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −6354.33 | −0.275130 | −0.137565 | − | 0.990493i | \(-0.543928\pi\) | ||||
−0.137565 | + | 0.990493i | \(0.543928\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −11250.6 | −0.485331 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 2235.36 | 0.0960752 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −13266.9 | −0.568114 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −38213.7 | −1.63040 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −2991.83 | −0.127181 | −0.0635904 | − | 0.997976i | \(-0.520255\pi\) | ||||
−0.0635904 | + | 0.997976i | \(0.520255\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 24432.6 | 1.03483 | 0.517416 | − | 0.855734i | \(-0.326894\pi\) | ||||
0.517416 | + | 0.855734i | \(0.326894\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −5980.44 | −0.252378 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 29771.2 | 1.25181 | 0.625904 | − | 0.779900i | \(-0.284730\pi\) | ||||
0.625904 | + | 0.779900i | \(0.284730\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −35980.5 | −1.50742 | −0.753711 | − | 0.657206i | \(-0.771738\pi\) | ||||
−0.753711 | + | 0.657206i | \(0.771738\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −14023.7 | −0.585413 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −43603.5 | −1.81365 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −3251.52 | −0.134759 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −1147.66 | −0.0473941 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 18757.2 | 0.771837 | 0.385919 | − | 0.922533i | \(-0.373885\pi\) | ||||
0.385919 | + | 0.922533i | \(0.373885\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −16349.4 | −0.670358 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 20950.1 | 0.855941 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −2127.29 | −0.0866048 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 30152.2 | 1.22319 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 8922.94 | 0.360700 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −2156.21 | −0.0868553 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 8626.94 | 0.346285 | 0.173142 | − | 0.984897i | \(-0.444608\pi\) | ||||
0.173142 | + | 0.984897i | \(0.444608\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −1252.45 | −0.0500971 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −2079.04 | −0.0828687 | −0.0414344 | − | 0.999141i | \(-0.513193\pi\) | ||||
−0.0414344 | + | 0.999141i | \(0.513193\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 11740.7 | 0.466343 | 0.233171 | − | 0.972436i | \(-0.425090\pi\) | ||||
0.233171 | + | 0.972436i | \(0.425090\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −12504.5 | −0.494951 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 43830.8 | 1.72887 | 0.864436 | − | 0.502743i | \(-0.167676\pi\) | ||||
0.864436 | + | 0.502743i | \(0.167676\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −3134.18 | −0.123197 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −7313.78 | −0.286493 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −12105.9 | −0.472570 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 54907.3 | 2.13601 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −7261.01 | −0.281498 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −6119.50 | −0.236431 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −3628.71 | −0.139718 | −0.0698591 | − | 0.997557i | \(-0.522255\pi\) | ||||
−0.0698591 | + | 0.997557i | \(0.522255\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 15681.2 | 0.601723 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −26429.8 | −1.01072 | −0.505360 | − | 0.862909i | \(-0.668640\pi\) | ||||
−0.505360 | + | 0.862909i | \(0.668640\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −29286.1 | −1.11614 | −0.558071 | − | 0.829793i | \(-0.688458\pi\) | ||||
−0.558071 | + | 0.829793i | \(0.688458\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −1087.67 | −0.0413125 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −22350.0 | −0.846042 | −0.423021 | − | 0.906120i | \(-0.639030\pi\) | ||||
−0.423021 | + | 0.906120i | \(0.639030\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −28755.6 | −1.08485 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −2633.53 | −0.0990197 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −7754.53 | −0.290588 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 1476.28 | 0.0551360 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 13528.0 | 0.503553 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 795.202 | 0.0295011 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 47723.0 | 1.76457 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 13954.7 | 0.514267 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 1879.95 | 0.0690516 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 5779.79 | 0.211593 | 0.105796 | − | 0.994388i | \(-0.466261\pi\) | ||||
0.105796 | + | 0.994388i | \(0.466261\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 10578.7 | 0.386000 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 20024.6 | 0.728259 | 0.364130 | − | 0.931348i | \(-0.381367\pi\) | ||||
0.364130 | + | 0.931348i | \(0.381367\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 22974.8 | 0.832810 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 1.13580 | 4.10366e−5 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 32639.1 | 1.17540 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −26977.7 | −0.968349 | −0.484175 | − | 0.874971i | \(-0.660880\pi\) | ||||
−0.484175 | + | 0.874971i | \(0.660880\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 15294.2 | 0.547189 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −28812.3 | −1.02748 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 3816.73 | 0.135668 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −5891.10 | −0.208726 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −34371.4 | −1.21387 | −0.606937 | − | 0.794750i | \(-0.707602\pi\) | ||||
−0.606937 | + | 0.794750i | \(0.707602\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −38998.8 | −1.37286 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 14571.2 | 0.511297 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −1255.57 | −0.0439159 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 32901.8 | 1.14712 | 0.573561 | − | 0.819163i | \(-0.305561\pi\) | ||||
0.573561 | + | 0.819163i | \(0.305561\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 13212.4 | 0.459181 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 47208.7 | 1.63545 | 0.817726 | − | 0.575607i | \(-0.195234\pi\) | ||||
0.817726 | + | 0.575607i | \(0.195234\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −10762.1 | −0.371646 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 3176.65 | 0.109351 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 19250.2 | 0.660557 | 0.330279 | − | 0.943884i | \(-0.392857\pi\) | ||||
0.330279 | + | 0.943884i | \(0.392857\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −25744.4 | −0.880611 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 22534.1 | 0.768369 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −4572.49 | −0.155422 | −0.0777112 | − | 0.996976i | \(-0.524761\pi\) | ||||
−0.0777112 | + | 0.996976i | \(0.524761\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −3026.77 | −0.102559 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −4314.44 | −0.145732 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 46395.7 | 1.56225 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −29712.3 | −0.997360 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −16276.7 | −0.544660 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −441.956 | −0.0147431 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −33060.9 | −1.09945 | −0.549725 | − | 0.835346i | \(-0.685268\pi\) | ||||
−0.549725 | + | 0.835346i | \(0.685268\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −18867.9 | −0.625514 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 21995.9 | 0.726964 | 0.363482 | − | 0.931601i | \(-0.381588\pi\) | ||||
0.363482 | + | 0.931601i | \(0.381588\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −11421.4 | −0.376315 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −23946.1 | −0.786551 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −1241.54 | −0.0406555 | −0.0203277 | − | 0.999793i | \(-0.506471\pi\) | ||||
−0.0203277 | + | 0.999793i | \(0.506471\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −81.1205 | −0.00264823 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 25672.5 | 0.835534 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −10797.7 | −0.350349 | −0.175175 | − | 0.984537i | \(-0.556049\pi\) | ||||
−0.175175 | + | 0.984537i | \(0.556049\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 1343.67 | 0.0434648 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 8156.56 | 0.263046 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 12010.2 | 0.386149 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −10204.8 | −0.327112 | −0.163556 | − | 0.986534i | \(-0.552296\pi\) | ||||
−0.163556 | + | 0.986534i | \(0.552296\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 7203.49 | 0.230207 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −1951.90 | −0.0621903 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 21279.2 | 0.675947 | 0.337973 | − | 0.941156i | \(-0.390259\pi\) | ||||
0.337973 | + | 0.941156i | \(0.390259\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −3973.90 | −0.125855 |
(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 | 1024.4.a.n.1.4 | 10 | ||
4.3 | odd | 2 | 1024.4.a.m.1.7 | 10 | |||
8.3 | odd | 2 | 1024.4.a.m.1.4 | 10 | |||
8.5 | even | 2 | inner | 1024.4.a.n.1.7 | 10 | ||
16.3 | odd | 4 | 1024.4.b.k.513.7 | 10 | |||
16.5 | even | 4 | 1024.4.b.j.513.7 | 10 | |||
16.11 | odd | 4 | 1024.4.b.k.513.4 | 10 | |||
16.13 | even | 4 | 1024.4.b.j.513.4 | 10 | |||
32.3 | odd | 8 | 128.4.e.a.33.4 | 10 | |||
32.5 | even | 8 | 16.4.e.a.5.4 | ✓ | 10 | ||
32.11 | odd | 8 | 128.4.e.a.97.4 | 10 | |||
32.13 | even | 8 | 16.4.e.a.13.4 | yes | 10 | ||
32.19 | odd | 8 | 64.4.e.a.17.2 | 10 | |||
32.21 | even | 8 | 128.4.e.b.97.2 | 10 | |||
32.27 | odd | 8 | 64.4.e.a.49.2 | 10 | |||
32.29 | even | 8 | 128.4.e.b.33.2 | 10 | |||
96.5 | odd | 8 | 144.4.k.a.37.2 | 10 | |||
96.59 | even | 8 | 576.4.k.a.433.3 | 10 | |||
96.77 | odd | 8 | 144.4.k.a.109.2 | 10 | |||
96.83 | even | 8 | 576.4.k.a.145.3 | 10 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
16.4.e.a.5.4 | ✓ | 10 | 32.5 | even | 8 | ||
16.4.e.a.13.4 | yes | 10 | 32.13 | even | 8 | ||
64.4.e.a.17.2 | 10 | 32.19 | odd | 8 | |||
64.4.e.a.49.2 | 10 | 32.27 | odd | 8 | |||
128.4.e.a.33.4 | 10 | 32.3 | odd | 8 | |||
128.4.e.a.97.4 | 10 | 32.11 | odd | 8 | |||
128.4.e.b.33.2 | 10 | 32.29 | even | 8 | |||
128.4.e.b.97.2 | 10 | 32.21 | even | 8 | |||
144.4.k.a.37.2 | 10 | 96.5 | odd | 8 | |||
144.4.k.a.109.2 | 10 | 96.77 | odd | 8 | |||
576.4.k.a.145.3 | 10 | 96.83 | even | 8 | |||
576.4.k.a.433.3 | 10 | 96.59 | even | 8 | |||
1024.4.a.m.1.4 | 10 | 8.3 | odd | 2 | |||
1024.4.a.m.1.7 | 10 | 4.3 | odd | 2 | |||
1024.4.a.n.1.4 | 10 | 1.1 | even | 1 | trivial | ||
1024.4.a.n.1.7 | 10 | 8.5 | even | 2 | inner | ||
1024.4.b.j.513.4 | 10 | 16.13 | even | 4 | |||
1024.4.b.j.513.7 | 10 | 16.5 | even | 4 | |||
1024.4.b.k.513.4 | 10 | 16.11 | odd | 4 | |||
1024.4.b.k.513.7 | 10 | 16.3 | odd | 4 |