Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1344,4,Mod(1,1344)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1344, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 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("1344.1");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1344 = 2^{6} \cdot 3 \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 1344.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: | \(79.2985670477\) |
Analytic rank: | \(1\) |
Dimension: | \(2\) |
Coefficient field: | \(\Q(\sqrt{43}) \) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{2} - 43 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 2 \) |
Twist minimal: | no (minimal twist has level 672) |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.1 | ||
Root | \(-6.55744\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1344.1 |
$q$-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 | ||||||||
\(3\) | −3.00000 | −0.577350 | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −21.1149 | −1.88857 | −0.944286 | − | 0.329126i | \(-0.893246\pi\) | ||||
−0.944286 | + | 0.329126i | \(0.893246\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −7.00000 | −0.377964 | ||||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 9.00000 | 0.333333 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −11.1149 | −0.304660 | −0.152330 | − | 0.988330i | \(-0.548678\pi\) | ||||
−0.152330 | + | 0.988330i | \(0.548678\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −26.0000 | −0.554700 | −0.277350 | − | 0.960769i | \(-0.589456\pi\) | ||||
−0.277350 | + | 0.960769i | \(0.589456\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 63.3446 | 1.09037 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 67.3446 | 0.960792 | 0.480396 | − | 0.877052i | \(-0.340493\pi\) | ||||
0.480396 | + | 0.877052i | \(0.340493\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 42.2298 | 0.509904 | 0.254952 | − | 0.966954i | \(-0.417940\pi\) | ||||
0.254952 | + | 0.966954i | \(0.417940\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 21.0000 | 0.218218 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −122.264 | −1.10842 | −0.554212 | − | 0.832376i | \(-0.686980\pi\) | ||||
−0.554212 | + | 0.832376i | \(0.686980\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 320.838 | 2.56670 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −27.0000 | −0.192450 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 16.2298 | 0.103924 | 0.0519619 | − | 0.998649i | \(-0.483453\pi\) | ||||
0.0519619 | + | 0.998649i | \(0.483453\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 279.149 | 1.61731 | 0.808655 | − | 0.588283i | \(-0.200196\pi\) | ||||
0.808655 | + | 0.588283i | \(0.200196\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 33.3446 | 0.175896 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 147.804 | 0.713813 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 123.838 | 0.550239 | 0.275120 | − | 0.961410i | \(-0.411283\pi\) | ||||
0.275120 | + | 0.961410i | \(0.411283\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 78.0000 | 0.320256 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −32.2636 | −0.122896 | −0.0614480 | − | 0.998110i | \(-0.519572\pi\) | ||||
−0.0614480 | + | 0.998110i | \(0.519572\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −281.838 | −0.999532 | −0.499766 | − | 0.866160i | \(-0.666581\pi\) | ||||
−0.499766 | + | 0.866160i | \(0.666581\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −190.034 | −0.629524 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 250.689 | 0.778017 | 0.389008 | − | 0.921234i | \(-0.372818\pi\) | ||||
0.389008 | + | 0.921234i | \(0.372818\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 49.0000 | 0.142857 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −202.034 | −0.554714 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 27.8380 | 0.0721481 | 0.0360740 | − | 0.999349i | \(-0.488515\pi\) | ||||
0.0360740 | + | 0.999349i | \(0.488515\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 234.689 | 0.575373 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −126.689 | −0.294393 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 677.906 | 1.49586 | 0.747931 | − | 0.663777i | \(-0.231048\pi\) | ||||
0.747931 | + | 0.663777i | \(0.231048\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −73.9322 | −0.155181 | −0.0775906 | − | 0.996985i | \(-0.524723\pi\) | ||||
−0.0775906 | + | 0.996985i | \(0.524723\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −63.0000 | −0.125988 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 548.987 | 1.04759 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 845.446 | 1.54161 | 0.770804 | − | 0.637073i | \(-0.219855\pi\) | ||||
0.770804 | + | 0.637073i | \(0.219855\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 366.791 | 0.639948 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −739.250 | −1.23567 | −0.617837 | − | 0.786306i | \(-0.711991\pi\) | ||||
−0.617837 | + | 0.786306i | \(0.711991\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −702.203 | −1.12585 | −0.562923 | − | 0.826510i | \(-0.690323\pi\) | ||||
−0.562923 | + | 0.826510i | \(0.690323\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −962.514 | −1.48189 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 77.8041 | 0.115151 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −250.689 | −0.357022 | −0.178511 | − | 0.983938i | \(-0.557128\pi\) | ||||
−0.178511 | + | 0.983938i | \(0.557128\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 81.0000 | 0.111111 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −699.352 | −0.924866 | −0.462433 | − | 0.886654i | \(-0.653023\pi\) | ||||
−0.462433 | + | 0.886654i | \(0.653023\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −1421.97 | −1.81453 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −48.6893 | −0.0600004 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 489.574 | 0.583087 | 0.291544 | − | 0.956558i | \(-0.405831\pi\) | ||||
0.291544 | + | 0.956558i | \(0.405831\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 182.000 | 0.209657 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −837.446 | −0.933754 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −891.676 | −0.962990 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 1184.37 | 1.23973 | 0.619866 | − | 0.784707i | \(-0.287187\pi\) | ||||
0.619866 | + | 0.784707i | \(0.287187\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −100.034 | −0.101553 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −1554.56 | −1.53153 | −0.765765 | − | 0.643120i | \(-0.777640\pi\) | ||||
−0.765765 | + | 0.643120i | \(0.777640\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 1780.01 | 1.70282 | 0.851408 | − | 0.524504i | \(-0.175749\pi\) | ||||
0.851408 | + | 0.524504i | \(0.175749\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −443.412 | −0.412120 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 1140.37 | 1.03032 | 0.515159 | − | 0.857095i | \(-0.327733\pi\) | ||||
0.515159 | + | 0.857095i | \(0.327733\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −2089.68 | −1.83628 | −0.918141 | − | 0.396255i | \(-0.870310\pi\) | ||||
−0.918141 | + | 0.396255i | \(0.870310\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −371.514 | −0.317681 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −332.298 | −0.276636 | −0.138318 | − | 0.990388i | \(-0.544170\pi\) | ||||
−0.138318 | + | 0.990388i | \(0.544170\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 2581.58 | 2.09334 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −234.000 | −0.184900 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −471.412 | −0.363145 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −1207.46 | −0.907182 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 96.7909 | 0.0709540 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −4135.10 | −2.95883 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 1261.72 | 0.881569 | 0.440785 | − | 0.897613i | \(-0.354700\pi\) | ||||
0.440785 | + | 0.897613i | \(0.354700\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 845.514 | 0.577080 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −2639.03 | −1.76010 | −0.880049 | − | 0.474882i | \(-0.842491\pi\) | ||||
−0.880049 | + | 0.474882i | \(0.842491\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −295.608 | −0.192725 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 570.102 | 0.363456 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −2000.18 | −1.24735 | −0.623674 | − | 0.781685i | \(-0.714361\pi\) | ||||
−0.623674 | + | 0.781685i | \(0.714361\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 2014.89 | 1.22950 | 0.614752 | − | 0.788721i | \(-0.289256\pi\) | ||||
0.614752 | + | 0.788721i | \(0.289256\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −752.068 | −0.449188 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 288.987 | 0.168995 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −342.689 | −0.196268 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −147.000 | −0.0824786 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −140.810 | −0.0774201 | −0.0387100 | − | 0.999250i | \(-0.512325\pi\) | ||||
−0.0387100 | + | 0.999250i | \(0.512325\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −2493.00 | −1.34356 | −0.671780 | − | 0.740751i | \(-0.734470\pi\) | ||||
−0.671780 | + | 0.740751i | \(0.734470\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 606.102 | 0.320264 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −5894.19 | −3.05441 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −2681.28 | −1.36299 | −0.681496 | − | 0.731822i | \(-0.738670\pi\) | ||||
−0.681496 | + | 0.731822i | \(0.738670\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −83.5141 | −0.0416547 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 855.846 | 0.418945 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 3625.26 | 1.74204 | 0.871019 | − | 0.491250i | \(-0.163460\pi\) | ||||
0.871019 | + | 0.491250i | \(0.163460\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −704.068 | −0.332192 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 1242.82 | 0.575884 | 0.287942 | − | 0.957648i | \(-0.407029\pi\) | ||||
0.287942 | + | 0.957648i | \(0.407029\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −1521.00 | −0.692308 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 380.068 | 0.169968 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −249.778 | −0.109770 | −0.0548851 | − | 0.998493i | \(-0.517479\pi\) | ||||
−0.0548851 | + | 0.998493i | \(0.517479\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −2245.87 | −0.970123 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −2033.72 | −0.863636 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −3529.48 | −1.47378 | −0.736888 | − | 0.676015i | \(-0.763705\pi\) | ||||
−0.736888 | + | 0.676015i | \(0.763705\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 2359.73 | 0.969047 | 0.484524 | − | 0.874778i | \(-0.338993\pi\) | ||||
0.484524 | + | 0.874778i | \(0.338993\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 221.797 | 0.0895939 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −2614.82 | −1.03917 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −748.527 | −0.292715 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 189.000 | 0.0727393 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 686.859 | 0.260206 | 0.130103 | − | 0.991500i | \(-0.458469\pi\) | ||||
0.130103 | + | 0.991500i | \(0.458469\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −1456.89 | −0.543365 | −0.271682 | − | 0.962387i | \(-0.587580\pi\) | ||||
−0.271682 | + | 0.962387i | \(0.587580\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −1646.96 | −0.604827 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 4741.71 | 1.71489 | 0.857443 | − | 0.514579i | \(-0.172052\pi\) | ||||
0.857443 | + | 0.514579i | \(0.172052\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −563.269 | −0.200649 | −0.100324 | − | 0.994955i | \(-0.531988\pi\) | ||||
−0.100324 | + | 0.994955i | \(0.531988\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −2536.34 | −0.890048 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −113.608 | −0.0392795 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 681.243 | 0.232098 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −1100.37 | −0.369474 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −469.379 | −0.155347 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 3241.19 | 1.05750 | 0.528751 | − | 0.848777i | \(-0.322661\pi\) | ||||
0.528751 | + | 0.848777i | \(0.322661\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 2217.75 | 0.713417 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 5950.98 | 1.88769 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −1954.04 | −0.611286 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 2106.61 | 0.650007 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −1750.96 | −0.532952 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −2656.65 | −0.797768 | −0.398884 | − | 0.917001i | \(-0.630602\pi\) | ||||
−0.398884 | + | 0.917001i | \(0.630602\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 2887.54 | 0.855568 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 3125.02 | 0.913721 | 0.456860 | − | 0.889538i | \(-0.348974\pi\) | ||||
0.456860 | + | 0.889538i | \(0.348974\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 403.107 | 0.116324 | 0.0581618 | − | 0.998307i | \(-0.481476\pi\) | ||||
0.0581618 | + | 0.998307i | \(0.481476\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −233.412 | −0.0664823 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −1156.47 | −0.325163 | −0.162581 | − | 0.986695i | \(-0.551982\pi\) | ||||
−0.162581 | + | 0.986695i | \(0.551982\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −5293.27 | −1.46934 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 752.068 | 0.206127 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −3733.02 | −1.01033 | −0.505165 | − | 0.863023i | \(-0.668568\pi\) | ||||
−0.505165 | + | 0.863023i | \(0.668568\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 3153.04 | 0.842761 | 0.421380 | − | 0.906884i | \(-0.361546\pi\) | ||||
0.421380 | + | 0.906884i | \(0.361546\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −243.000 | −0.0641500 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −1034.63 | −0.269796 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −1097.97 | −0.282844 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 2098.06 | 0.533972 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −2441.45 | −0.613955 | −0.306978 | − | 0.951717i | \(-0.599318\pi\) | ||||
−0.306978 | + | 0.951717i | \(0.599318\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 1358.95 | 0.337692 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 4265.92 | 1.04762 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 2416.55 | 0.586538 | 0.293269 | − | 0.956030i | \(-0.405257\pi\) | ||||
0.293269 | + | 0.956030i | \(0.405257\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −866.866 | −0.207971 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 146.068 | 0.0346413 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −509.427 | −0.119440 | −0.0597198 | − | 0.998215i | \(-0.519021\pi\) | ||||
−0.0597198 | + | 0.998215i | \(0.519021\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −587.797 | −0.136257 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −1468.72 | −0.336646 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 8309.43 | 1.88340 | 0.941701 | − | 0.336452i | \(-0.109227\pi\) | ||||
0.941701 | + | 0.336452i | \(0.109227\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 1499.88 | 0.336204 | 0.168102 | − | 0.985770i | \(-0.446236\pi\) | ||||
0.168102 | + | 0.985770i | \(0.446236\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −546.000 | −0.121046 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −3566.08 | −0.781972 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −1724.03 | −0.373959 | −0.186980 | − | 0.982364i | \(-0.559870\pi\) | ||||
−0.186980 | + | 0.982364i | \(0.559870\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 2512.34 | 0.539103 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −8393.23 | −1.78184 | −0.890922 | − | 0.454156i | \(-0.849941\pi\) | ||||
−0.890922 | + | 0.454156i | \(0.849941\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 8049.99 | 1.69089 | 0.845445 | − | 0.534062i | \(-0.179335\pi\) | ||||
0.845445 | + | 0.534062i | \(0.179335\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 2675.03 | 0.555982 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 225.846 | 0.0464503 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −377.701 | −0.0768778 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −3553.10 | −0.715760 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −9886.67 | −1.97128 | −0.985641 | − | 0.168854i | \(-0.945993\pi\) | ||||
−0.985641 | + | 0.168854i | \(0.945993\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −14313.9 | −2.82504 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 300.102 | 0.0586319 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 3178.85 | 0.614843 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 1972.87 | 0.377788 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 4663.68 | 0.884230 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 1561.07 | 0.293071 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 1721.15 | 0.319970 | 0.159985 | − | 0.987119i | \(-0.448855\pi\) | ||||
0.159985 | + | 0.987119i | \(0.448855\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −5340.04 | −0.983122 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 4417.94 | 0.805525 | 0.402762 | − | 0.915305i | \(-0.368050\pi\) | ||||
0.402762 | + | 0.915305i | \(0.368050\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −8351.08 | −1.50809 | −0.754043 | − | 0.656825i | \(-0.771899\pi\) | ||||
−0.754043 | + | 0.656825i | \(0.771899\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 1330.24 | 0.237938 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −5002.52 | −0.886339 | −0.443170 | − | 0.896438i | \(-0.646146\pi\) | ||||
−0.443170 | + | 0.896438i | \(0.646146\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −180.392 | −0.0316614 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −3421.12 | −0.594854 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 2843.95 | 0.489912 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −8341.79 | −1.42375 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 6269.03 | 1.06018 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −1754.82 | −0.294063 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −1210.92 | −0.201083 | −0.100541 | − | 0.994933i | \(-0.532057\pi\) | ||||
−0.100541 | + | 0.994933i | \(0.532057\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 1114.54 | 0.183413 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −17851.5 | −2.91144 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 611.974 | 0.0989209 | 0.0494604 | − | 0.998776i | \(-0.484250\pi\) | ||||
0.0494604 | + | 0.998776i | \(0.484250\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 996.893 | 0.159716 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −3102.70 | −0.492730 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −343.000 | −0.0539949 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −7744.75 | −1.20859 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −8546.91 | −1.32225 | −0.661127 | − | 0.750274i | \(-0.729922\pi\) | ||||
−0.661127 | + | 0.750274i | \(0.729922\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 5144.82 | 0.789101 | 0.394550 | − | 0.918874i | \(-0.370900\pi\) | ||||
0.394550 | + | 0.918874i | \(0.370900\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 702.000 | 0.106752 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −9998.93 | −1.50762 | −0.753809 | − | 0.657093i | \(-0.771786\pi\) | ||||
−0.753809 | + | 0.657093i | \(0.771786\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 15609.2 | 2.33366 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 1414.24 | 0.209662 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 3832.83 | 0.563480 | 0.281740 | − | 0.959491i | \(-0.409089\pi\) | ||||
0.281740 | + | 0.959491i | \(0.409089\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −5075.65 | −0.739998 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 3622.38 | 0.523762 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 14826.9 | 2.12624 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 5782.49 | 0.822462 | 0.411231 | − | 0.911531i | \(-0.365099\pi\) | ||||
0.411231 | + | 0.911531i | \(0.365099\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −290.373 | −0.0409653 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −194.866 | −0.0272694 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 9914.87 | 1.37633 | 0.688167 | − | 0.725552i | \(-0.258416\pi\) | ||||
0.688167 | + | 0.725552i | \(0.258416\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 12405.3 | 1.70828 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −421.974 | −0.0576465 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −9678.39 | −1.31173 | −0.655865 | − | 0.754879i | \(-0.727696\pi\) | ||||
−0.655865 | + | 0.754879i | \(0.727696\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −3785.15 | −0.508974 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −8619.74 | −1.14999 | −0.574997 | − | 0.818155i | \(-0.694997\pi\) | ||||
−0.574997 | + | 0.818155i | \(0.694997\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −1642.82 | −0.217470 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −2536.54 | −0.333177 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 9220.61 | 1.20181 | 0.600904 | − | 0.799321i | \(-0.294807\pi\) | ||||
0.600904 | + | 0.799321i | \(0.294807\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −8233.80 | −1.06496 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 7917.08 | 1.01619 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 5293.27 | 0.674262 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 12551.5 | 1.58676 | 0.793379 | − | 0.608728i | \(-0.208320\pi\) | ||||
0.793379 | + | 0.608728i | \(0.208320\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 886.825 | 0.111270 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −11057.6 | −1.37703 | −0.688514 | − | 0.725223i | \(-0.741737\pi\) | ||||
−0.688514 | + | 0.725223i | \(0.741737\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −7257.87 | −0.897122 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −1710.31 | −0.209841 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −1376.44 | −0.167636 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −10535.3 | −1.27368 | −0.636842 | − | 0.770995i | \(-0.719759\pi\) | ||||
−0.636842 | + | 0.770995i | \(0.719759\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 6000.53 | 0.720157 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −4745.34 | −0.565382 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 14766.7 | 1.74668 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −6044.68 | −0.709854 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 4846.31 | 0.565055 | 0.282527 | − | 0.959259i | \(-0.408827\pi\) | ||||
0.282527 | + | 0.959259i | \(0.408827\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −9326.47 | −1.07968 | −0.539839 | − | 0.841768i | \(-0.681515\pi\) | ||||
−0.539839 | + | 0.841768i | \(0.681515\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 2256.20 | 0.259339 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 21606.7 | 2.46607 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 517.525 | 0.0586530 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −866.960 | −0.0975693 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 15498.1 | 1.73205 | 0.866027 | − | 0.499998i | \(-0.166666\pi\) | ||||
0.866027 | + | 0.499998i | \(0.166666\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 3861.65 | 0.428589 | 0.214294 | − | 0.976769i | \(-0.431255\pi\) | ||||
0.214294 | + | 0.976769i | \(0.431255\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 1028.07 | 0.113315 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −5163.16 | −0.565189 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −4826.85 | −0.524767 | −0.262384 | − | 0.964964i | \(-0.584509\pi\) | ||||
−0.262384 | + | 0.964964i | \(0.584509\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 441.000 | 0.0476190 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −4796.48 | −0.514419 | −0.257209 | − | 0.966356i | \(-0.582803\pi\) | ||||
−0.257209 | + | 0.966356i | \(0.582803\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −10337.3 | −1.10120 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 422.430 | 0.0446985 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −10161.7 | −1.06806 | −0.534029 | − | 0.845466i | \(-0.679323\pi\) | ||||
−0.534029 | + | 0.845466i | \(0.679323\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 358.606 | 0.0374415 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 7479.01 | 0.775705 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −3842.91 | −0.395952 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 10037.3 | 1.02741 | 0.513704 | − | 0.857968i | \(-0.328273\pi\) | ||||
0.513704 | + | 0.857968i | \(0.328273\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −1818.31 | −0.184905 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 12646.4 | 1.27766 | 0.638831 | − | 0.769347i | \(-0.279418\pi\) | ||||
0.638831 | + | 0.769347i | \(0.279418\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −17077.8 | −1.71419 | −0.857097 | − | 0.515155i | \(-0.827734\pi\) | ||||
−0.857097 | + | 0.515155i | \(0.827734\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 17682.6 | 1.76346 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 899.992 | 0.0891792 | 0.0445896 | − | 0.999005i | \(-0.485802\pi\) | ||||
0.0445896 | + | 0.999005i | \(0.485802\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −5918.12 | −0.582673 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 8043.85 | 0.786924 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 3132.60 | 0.304518 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 13548.9 | 1.30877 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 250.542 | 0.0240494 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −5953.85 | −0.567929 | −0.283965 | − | 0.958835i | \(-0.591650\pi\) | ||||
−0.283965 | + | 0.958835i | \(0.591650\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −3219.79 | −0.305218 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −2567.54 | −0.241878 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −25007.7 | −2.34132 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 13309.9 | 1.23846 | 0.619229 | − | 0.785211i | \(-0.287445\pi\) | ||||
0.619229 | + | 0.785211i | \(0.287445\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −10875.8 | −1.00577 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 1894.37 | 0.174117 | 0.0870587 | − | 0.996203i | \(-0.472253\pi\) | ||||
0.0870587 | + | 0.996203i | \(0.472253\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 1092.99 | 0.0998492 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 2112.20 | 0.191791 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 5174.75 | 0.467041 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 5338.14 | 0.478894 | 0.239447 | − | 0.970909i | \(-0.423034\pi\) | ||||
0.239447 | + | 0.970909i | \(0.423034\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −3728.47 | −0.332487 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 6895.58 | 0.611250 | 0.305625 | − | 0.952152i | \(-0.401135\pi\) | ||||
0.305625 | + | 0.952152i | \(0.401135\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 32824.4 | 2.89241 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 4563.00 | 0.399704 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −1638.74 | −0.142703 | −0.0713516 | − | 0.997451i | \(-0.522731\pi\) | ||||
−0.0713516 | + | 0.997451i | \(0.522731\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 4915.42 | 0.425529 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −1140.20 | −0.0981310 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −37584.8 | −3.21589 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −2786.38 | −0.237031 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 749.333 | 0.0633759 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 13423.8 | 1.12880 | 0.564401 | − | 0.825501i | \(-0.309107\pi\) | ||||
0.564401 | + | 0.825501i | \(0.309107\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −15758.4 | −1.31753 | −0.658763 | − | 0.752350i | \(-0.728920\pi\) | ||||
−0.658763 | + | 0.752350i | \(0.728920\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 6737.60 | 0.560101 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 18799.2 | 1.55390 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 2781.40 | 0.228602 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 6101.15 | 0.498620 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 838.855 | 0.0681704 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −24078.8 | −1.94583 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 10588.4 | 0.850884 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −544.629 | −0.0435229 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 12144.5 | 0.965127 | 0.482564 | − | 0.875861i | \(-0.339706\pi\) | ||||
0.482564 | + | 0.875861i | \(0.339706\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −7079.20 | −0.559480 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 44123.3 | 3.46795 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 11271.8 | 0.881070 | 0.440535 | − | 0.897735i | \(-0.354789\pi\) | ||||
0.440535 | + | 0.897735i | \(0.354789\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −665.390 | −0.0517270 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 685.379 | 0.0529911 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 1754.82 | 0.134942 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 7844.47 | 0.599963 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 13000.5 | 0.988954 | 0.494477 | − | 0.869191i | \(-0.335360\pi\) | ||||
0.494477 | + | 0.869191i | \(0.335360\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 7327.79 | 0.554441 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 2245.58 | 0.168999 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −18246.0 | −1.36586 | −0.682929 | − | 0.730485i | \(-0.739294\pi\) | ||||
−0.682929 | + | 0.730485i | \(0.739294\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 7016.42 | 0.522448 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −567.000 | −0.0419961 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 10249.3 | 0.755140 | 0.377570 | − | 0.925981i | \(-0.376760\pi\) | ||||
0.377570 | + | 0.925981i | \(0.376760\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −1383.57 | −0.101402 | −0.0507011 | − | 0.998714i | \(-0.516146\pi\) | ||||
−0.0507011 | + | 0.998714i | \(0.516146\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −2060.58 | −0.150230 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −39226.8 | −2.84499 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −346.308 | −0.0249861 | −0.0124931 | − | 0.999922i | \(-0.503977\pi\) | ||||
−0.0124931 | + | 0.999922i | \(0.503977\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 4370.68 | 0.313712 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 4895.46 | 0.349566 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −309.416 | −0.0219806 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 4940.88 | 0.349197 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −8208.65 | −0.577184 | −0.288592 | − | 0.957452i | \(-0.593187\pi\) | ||||
−0.288592 | + | 0.957452i | \(0.593187\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 11788.4 | 0.824672 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −14225.1 | −0.990090 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 19522.9 | 1.35196 | 0.675978 | − | 0.736922i | \(-0.263721\pi\) | ||||
0.675978 | + | 0.736922i | \(0.263721\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 9953.82 | 0.685826 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 1689.81 | 0.115845 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −294.580 | −0.0200938 | −0.0100469 | − | 0.999950i | \(-0.503198\pi\) | ||||
−0.0100469 | + | 0.999950i | \(0.503198\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 1132.24 | 0.0768473 | 0.0384236 | − | 0.999262i | \(-0.487766\pi\) | ||||
0.0384236 | + | 0.999262i | \(0.487766\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 7609.02 | 0.513869 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 25495.4 | 1.71328 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −2175.61 | −0.145478 | −0.0727390 | − | 0.997351i | \(-0.523174\pi\) | ||||
−0.0727390 | + | 0.997351i | \(0.523174\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 340.825 | 0.0226780 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −6517.92 | −0.431566 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −23243.3 | −1.53147 | −0.765734 | − | 0.643158i | \(-0.777624\pi\) | ||||
−0.765734 | + | 0.643158i | \(0.777624\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −2043.73 | −0.134002 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −23917.8 | −1.56060 | −0.780302 | − | 0.625403i | \(-0.784935\pi\) | ||||
−0.780302 | + | 0.625403i | \(0.784935\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 14915.1 | 0.968482 | 0.484241 | − | 0.874935i | \(-0.339096\pi\) | ||||
0.484241 | + | 0.874935i | \(0.339096\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 3301.12 | 0.213316 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −3427.02 | −0.220386 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 47207.3 | 3.02127 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 1408.14 | 0.0896898 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 8339.83 | 0.528666 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 14782.3 | 0.932604 | 0.466302 | − | 0.884626i | \(-0.345586\pi\) | ||||
0.466302 | + | 0.884626i | \(0.345586\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −9723.57 | −0.610549 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −26641.0 | −1.66491 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −1274.00 | −0.0792429 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −6653.25 | −0.411891 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 3820.66 | 0.235424 | 0.117712 | − | 0.993048i | \(-0.462444\pi\) | ||||
0.117712 | + | 0.993048i | \(0.462444\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 31644.8 | 1.94082 | 0.970411 | − | 0.241460i | \(-0.0776264\pi\) | ||||
0.970411 | + | 0.241460i | \(0.0776264\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −17852.9 | −1.08986 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −28264.2 | −1.71744 | −0.858718 | − | 0.512448i | \(-0.828739\pi\) | ||||
−0.858718 | + | 0.512448i | \(0.828739\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −7534.84 | −0.455729 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 5862.12 | 0.352926 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 10647.4 | 0.638076 | 0.319038 | − | 0.947742i | \(-0.396640\pi\) | ||||
0.319038 | + | 0.947742i | \(0.396640\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 55722.8 | 3.32407 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −6319.83 | −0.375282 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −22956.8 | −1.35701 | −0.678505 | − | 0.734595i | \(-0.737372\pi\) | ||||
−0.678505 | + | 0.734595i | \(0.737372\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −11133.8 | −0.655149 | −0.327575 | − | 0.944825i | \(-0.606231\pi\) | ||||
−0.327575 | + | 0.944825i | \(0.606231\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 5252.88 | 0.307700 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 6241.73 | 0.363976 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −1984.31 | −0.115192 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 7969.94 | 0.460592 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 821.747 | 0.0472775 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 5327.32 | 0.305131 | 0.152565 | − | 0.988293i | \(-0.451247\pi\) | ||||
0.152565 | + | 0.988293i | \(0.451247\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −8662.63 | −0.493962 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −15023.5 | −0.852878 | −0.426439 | − | 0.904516i | \(-0.640232\pi\) | ||||
−0.426439 | + | 0.904516i | \(0.640232\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −8290.56 | −0.468575 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −9375.05 | −0.527537 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 14635.9 | 0.819954 | 0.409977 | − | 0.912096i | \(-0.365537\pi\) | ||||
0.409977 | + | 0.912096i | \(0.365537\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 42233.5 | 2.35571 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −1209.32 | −0.0671594 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −723.789 | −0.0400206 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 7115.23 | 0.391717 | 0.195858 | − | 0.980632i | \(-0.437251\pi\) | ||||
0.195858 | + | 0.980632i | \(0.437251\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 700.237 | 0.0383836 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −42544.2 | −2.32201 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −2172.78 | −0.118078 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 3469.41 | 0.187733 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −14927.8 | −0.804299 | −0.402149 | − | 0.915574i | \(-0.631737\pi\) | ||||
−0.402149 | + | 0.915574i | \(0.631737\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 5229.65 | 0.280569 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 15879.8 | 0.848324 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 10881.9 | 0.578864 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −888.426 | −0.0470600 | −0.0235300 | − | 0.999723i | \(-0.507491\pi\) | ||||
−0.0235300 | + | 0.999723i | \(0.507491\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −2256.20 | −0.119007 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −34129.7 | −1.79266 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −6101.92 | −0.319159 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 11199.1 | 0.583315 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 24155.9 | 1.25294 | 0.626470 | − | 0.779445i | \(-0.284499\pi\) | ||||
0.626470 | + | 0.779445i | \(0.284499\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −12460.1 | −0.643604 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −9459.13 | −0.486568 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 5207.12 | 0.266742 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −11284.0 | −0.575654 | −0.287827 | − | 0.957682i | \(-0.592933\pi\) | ||||
−0.287827 | + | 0.957682i | \(0.592933\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 729.000 | 0.0370370 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −18980.3 | −0.960343 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −19307.2 | −0.972887 | −0.486444 | − | 0.873712i | \(-0.661706\pi\) | ||||
−0.486444 | + | 0.873712i | \(0.661706\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 3103.89 | 0.155767 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −9397.03 | −0.469666 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −16139.9 | −0.803406 | −0.401703 | − | 0.915770i | \(-0.631582\pi\) | ||||
−0.401703 | + | 0.915770i | \(0.631582\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 3293.92 | 0.163300 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 6613.88 | 0.326568 | 0.163284 | − | 0.986579i | \(-0.447791\pi\) | ||||
0.163284 | + | 0.986579i | \(0.447791\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 2973.18 | 0.146213 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −6294.17 | −0.308289 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −7982.61 | −0.389424 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 5167.07 | 0.251064 | 0.125532 | − | 0.992090i | \(-0.459936\pi\) | ||||
0.125532 | + | 0.992090i | \(0.459936\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 7324.34 | 0.354467 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 52639.4 | 2.53741 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 21745.4 | 1.04405 | 0.522027 | − | 0.852929i | \(-0.325176\pi\) | ||||
0.522027 | + | 0.852929i | \(0.325176\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −4076.84 | −0.194967 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 3002.22 | 0.143010 | 0.0715049 | − | 0.997440i | \(-0.477220\pi\) | ||||
0.0715049 | + | 0.997440i | \(0.477220\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 14627.7 | 0.694049 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −12797.8 | −0.604842 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −17625.6 | −0.829755 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −4008.18 | −0.187957 | −0.0939784 | − | 0.995574i | \(-0.529958\pi\) | ||||
−0.0939784 | + | 0.995574i | \(0.529958\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −7249.65 | −0.338638 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −3816.48 | −0.177580 | −0.0887900 | − | 0.996050i | \(-0.528300\pi\) | ||||
−0.0887900 | + | 0.996050i | \(0.528300\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 89561.5 | 4.15116 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 2600.60 | 0.120072 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −1362.49 | −0.0626651 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 8216.68 | 0.376461 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −438.203 | −0.0200001 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 56615.0 | 2.57411 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −22492.0 | −1.01874 | −0.509372 | − | 0.860546i | \(-0.670122\pi\) | ||||
−0.509372 | + | 0.860546i | \(0.670122\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 1528.28 | 0.0689585 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 2326.08 | 0.104559 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 1922.24 | 0.0860790 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 1763.39 | 0.0786679 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −41001.1 | −1.82225 | −0.911124 | − | 0.412132i | \(-0.864784\pi\) | ||||
−0.911124 | + | 0.412132i | \(0.864784\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 16882.6 | 0.747513 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 4406.17 | 0.194362 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 7804.90 | 0.343000 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −18071.1 | −0.791207 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −24928.3 | −1.08738 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −30507.0 | −1.32579 | −0.662897 | − | 0.748710i | \(-0.730673\pi\) | ||||
−0.662897 | + | 0.748710i | \(0.730673\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −3799.66 | −0.164518 | −0.0822590 | − | 0.996611i | \(-0.526213\pi\) | ||||
−0.0822590 | + | 0.996611i | \(0.526213\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −4499.64 | −0.194107 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −76546.9 | −3.28996 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −11902.0 | −0.509665 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 1638.00 | 0.0698857 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −27444.1 | −1.16663 | −0.583316 | − | 0.812245i | \(-0.698245\pi\) | ||||
−0.583316 | + | 0.812245i | \(0.698245\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −9422.95 | −0.399105 | −0.199553 | − | 0.979887i | \(-0.563949\pi\) | ||||
−0.199553 | + | 0.979887i | \(0.563949\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 10698.2 | 0.451472 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −5531.49 | −0.232586 | −0.116293 | − | 0.993215i | \(-0.537101\pi\) | ||||
−0.116293 | + | 0.993215i | \(0.537101\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −47025.9 | −1.97018 | −0.985088 | − | 0.172050i | \(-0.944961\pi\) | ||||
−0.985088 | + | 0.172050i | \(0.944961\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 5172.08 | 0.215905 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 3299.89 | 0.137256 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −26242.1 | −1.08760 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −7537.02 | −0.311251 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −25249.1 | −1.03897 | −0.519484 | − | 0.854480i | \(-0.673876\pi\) | ||||
−0.519484 | + | 0.854480i | \(0.673876\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −24125.6 | −0.989200 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 25179.7 | 1.02875 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 32115.7 | 1.30747 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 8452.22 | 0.342883 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −24150.0 | −0.976236 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −15140.9 | −0.609898 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 5220.44 | 0.209548 | 0.104774 | − | 0.994496i | \(-0.466588\pi\) | ||||
0.104774 | + | 0.994496i | \(0.466588\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −8025.08 | −0.320997 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −16752.7 | −0.667751 | −0.333876 | − | 0.942617i | \(-0.608357\pi\) | ||||
−0.333876 | + | 0.942617i | \(0.608357\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −46840.6 | −1.86051 | −0.930257 | − | 0.366908i | \(-0.880416\pi\) | ||||
−0.930257 | + | 0.366908i | \(0.880416\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −677.537 | −0.0268181 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −2861.77 | −0.112881 | −0.0564403 | − | 0.998406i | \(-0.517975\pi\) | ||||
−0.0564403 | + | 0.998406i | \(0.517975\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 5274.03 | 0.207309 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 1133.10 | 0.0443854 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 2786.38 | 0.108770 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −21981.6 | −0.855130 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 10659.3 | 0.413244 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 28945.7 | 1.11833 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 28321.1 | 1.09046 | 0.545231 | − | 0.838286i | \(-0.316442\pi\) | ||||
0.545231 | + | 0.838286i | \(0.316442\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 29660.0 | 1.13812 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −17763.2 | −0.679293 | −0.339647 | − | 0.940553i | \(-0.610307\pi\) | ||||
−0.339647 | + | 0.940553i | \(0.610307\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 5366.85 | 0.204540 | 0.102270 | − | 0.994757i | \(-0.467389\pi\) | ||||
0.102270 | + | 0.994757i | \(0.467389\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 42941.7 | 1.63104 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 50485.4 | 1.91109 | 0.955544 | − | 0.294849i | \(-0.0952693\pi\) | ||||
0.955544 | + | 0.294849i | \(0.0952693\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −8832.02 | −0.333202 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −900.305 | −0.0338511 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 10586.5 | 0.396714 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 74524.5 | 2.78333 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −9536.56 | −0.354980 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 4530.52 | 0.168077 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 1874.74 | 0.0693193 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −5918.60 | −0.218116 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −49825.5 | −1.83012 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 14517.9 | 0.531487 | 0.265744 | − | 0.964044i | \(-0.414382\pi\) | ||||
0.265744 | + | 0.964044i | \(0.414382\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −13991.1 | −0.510510 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −39837.6 | −1.44883 | −0.724413 | − | 0.689367i | \(-0.757889\pi\) | ||||
−0.724413 | + | 0.689367i | \(0.757889\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 7773.21 | 0.281770 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −4683.21 | −0.169204 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 18473.2 | 0.665255 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −3406.72 | −0.122282 | −0.0611411 | − | 0.998129i | \(-0.519474\pi\) | ||||
−0.0611411 | + | 0.998129i | \(0.519474\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −5163.44 | −0.184735 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 19220.5 | 0.685429 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 39732.0 | 1.41230 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 16020.1 | 0.567605 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −7453.31 | −0.263224 | −0.131612 | − | 0.991301i | \(-0.542015\pi\) | ||||
−0.131612 | + | 0.991301i | \(0.542015\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 2069.26 | 0.0728434 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −13253.8 | −0.465070 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 15805.1 | 0.552814 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −13599.3 | −0.474140 | −0.237070 | − | 0.971493i | \(-0.576187\pi\) | ||||
−0.237070 | + | 0.971493i | \(0.576187\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 25053.3 | 0.870694 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 1430.50 | 0.0495569 | 0.0247784 | − | 0.999693i | \(-0.492112\pi\) | ||||
0.0247784 | + | 0.999693i | \(0.492112\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 3944.67 | 0.136221 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | −3990.71 | −0.137373 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −7382.05 | −0.253310 | −0.126655 | − | 0.991947i | \(-0.540424\pi\) | ||||
−0.126655 | + | 0.991947i | \(0.540424\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 18257.3 | 0.624506 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 15007.6 | 0.511728 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 19941.7 | 0.677833 | 0.338916 | − | 0.940816i | \(-0.389940\pi\) | ||||
0.338916 | + | 0.940816i | \(0.389940\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −14502.9 | −0.491418 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 541.175 | 0.0182797 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 14001.2 | 0.471453 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 48133.0 | 1.61569 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 10263.4 | 0.343439 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 30762.1 | 1.02618 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 6161.51 | 0.204903 | 0.102451 | − | 0.994738i | \(-0.467331\pi\) | ||||
0.102451 | + | 0.994738i | \(0.467331\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −8531.84 | −0.282851 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −35313.3 | −1.16710 | −0.583552 | − | 0.812076i | \(-0.698338\pi\) | ||||
−0.583552 | + | 0.812076i | \(0.698338\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −14104.2 | −0.464709 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 25025.4 | 0.822003 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 9684.81 | 0.317139 | 0.158569 | − | 0.987348i | \(-0.449312\pi\) | ||||
0.158569 | + | 0.987348i | \(0.449312\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −5441.56 | −0.177643 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −18807.1 | −0.612094 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −52986.8 | −1.71924 | −0.859621 | − | 0.510932i | \(-0.829301\pi\) | ||||
−0.859621 | + | 0.510932i | \(0.829301\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −100121. | −3.23869 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 5264.47 | 0.169777 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 34458.5 | 1.10790 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −6415.80 | −0.205656 | −0.102828 | − | 0.994699i | \(-0.532789\pi\) | ||||
−0.102828 | + | 0.994699i | \(0.532789\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 3632.77 | 0.116095 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 11893.4 | 0.378940 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 20825.7 | 0.661540 | 0.330770 | − | 0.943711i | \(-0.392692\pi\) | ||||
0.330770 | + | 0.943711i | \(0.392692\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −3343.63 | −0.105894 |
(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 | 1344.4.a.bc.1.1 | 2 | ||
4.3 | odd | 2 | 1344.4.a.bk.1.1 | 2 | |||
8.3 | odd | 2 | 672.4.a.i.1.2 | ✓ | 2 | ||
8.5 | even | 2 | 672.4.a.n.1.2 | yes | 2 | ||
24.5 | odd | 2 | 2016.4.a.g.1.1 | 2 | |||
24.11 | even | 2 | 2016.4.a.h.1.1 | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
672.4.a.i.1.2 | ✓ | 2 | 8.3 | odd | 2 | ||
672.4.a.n.1.2 | yes | 2 | 8.5 | even | 2 | ||
1344.4.a.bc.1.1 | 2 | 1.1 | even | 1 | trivial | ||
1344.4.a.bk.1.1 | 2 | 4.3 | odd | 2 | |||
2016.4.a.g.1.1 | 2 | 24.5 | odd | 2 | |||
2016.4.a.h.1.1 | 2 | 24.11 | even | 2 |