Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [3380,2,Mod(1,3380)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(3380, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("3380.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 3380 = 2^{2} \cdot 5 \cdot 13^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 3380.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: | \(26.9894358832\) |
Analytic rank: | \(0\) |
Dimension: | \(9\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{9} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{9} - x^{8} - 19x^{7} + 16x^{6} + 106x^{5} - 87x^{4} - 153x^{3} + 149x^{2} - 26x + 1 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.3 | ||
Root | \(1.40883\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 3380.1 |
$q$-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 | ||||||||
\(3\) | −1.40883 | −0.813388 | −0.406694 | − | 0.913564i | \(-0.633318\pi\) | ||||
−0.406694 | + | 0.913564i | \(0.633318\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 1.00000 | 0.447214 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −2.17051 | −0.820374 | −0.410187 | − | 0.912001i | \(-0.634537\pi\) | ||||
−0.410187 | + | 0.912001i | \(0.634537\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −1.01520 | −0.338400 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −5.73367 | −1.72877 | −0.864384 | − | 0.502833i | \(-0.832291\pi\) | ||||
−0.864384 | + | 0.502833i | \(0.832291\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 0 | 0 | ||||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −1.40883 | −0.363758 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −5.24468 | −1.27202 | −0.636011 | − | 0.771680i | \(-0.719417\pi\) | ||||
−0.636011 | + | 0.771680i | \(0.719417\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −7.00804 | −1.60776 | −0.803878 | − | 0.594795i | \(-0.797233\pi\) | ||||
−0.803878 | + | 0.594795i | \(0.797233\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 3.05787 | 0.667283 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −8.19819 | −1.70944 | −0.854721 | − | 0.519088i | \(-0.826272\pi\) | ||||
−0.854721 | + | 0.519088i | \(0.826272\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 1.00000 | 0.200000 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 5.65673 | 1.08864 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 9.54822 | 1.77306 | 0.886530 | − | 0.462672i | \(-0.153109\pi\) | ||||
0.886530 | + | 0.462672i | \(0.153109\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −2.41917 | −0.434496 | −0.217248 | − | 0.976116i | \(-0.569708\pi\) | ||||
−0.217248 | + | 0.976116i | \(0.569708\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 8.07777 | 1.40616 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −2.17051 | −0.366883 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 7.16094 | 1.17725 | 0.588626 | − | 0.808406i | \(-0.299669\pi\) | ||||
0.588626 | + | 0.808406i | \(0.299669\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 7.16158 | 1.11845 | 0.559225 | − | 0.829016i | \(-0.311099\pi\) | ||||
0.559225 | + | 0.829016i | \(0.311099\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 7.76780 | 1.18458 | 0.592290 | − | 0.805725i | \(-0.298224\pi\) | ||||
0.592290 | + | 0.805725i | \(0.298224\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −1.01520 | −0.151337 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −5.41944 | −0.790506 | −0.395253 | − | 0.918572i | \(-0.629343\pi\) | ||||
−0.395253 | + | 0.918572i | \(0.629343\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −2.28890 | −0.326986 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 7.38886 | 1.03465 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 3.94223 | 0.541508 | 0.270754 | − | 0.962649i | \(-0.412727\pi\) | ||||
0.270754 | + | 0.962649i | \(0.412727\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −5.73367 | −0.773128 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 9.87313 | 1.30773 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −0.993988 | −0.129406 | −0.0647031 | − | 0.997905i | \(-0.520610\pi\) | ||||
−0.0647031 | + | 0.997905i | \(0.520610\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −4.28702 | −0.548897 | −0.274448 | − | 0.961602i | \(-0.588495\pi\) | ||||
−0.274448 | + | 0.961602i | \(0.588495\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 2.20350 | 0.277615 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 11.6322 | 1.42110 | 0.710548 | − | 0.703648i | \(-0.248447\pi\) | ||||
0.710548 | + | 0.703648i | \(0.248447\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 11.5499 | 1.39044 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 5.19073 | 0.616026 | 0.308013 | − | 0.951382i | \(-0.400336\pi\) | ||||
0.308013 | + | 0.951382i | \(0.400336\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −3.06083 | −0.358243 | −0.179121 | − | 0.983827i | \(-0.557326\pi\) | ||||
−0.179121 | + | 0.983827i | \(0.557326\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −1.40883 | −0.162678 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 12.4450 | 1.41824 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 7.33131 | 0.824837 | 0.412419 | − | 0.910994i | \(-0.364684\pi\) | ||||
0.412419 | + | 0.910994i | \(0.364684\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −4.92377 | −0.547085 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 2.86146 | 0.314086 | 0.157043 | − | 0.987592i | \(-0.449804\pi\) | ||||
0.157043 | + | 0.987592i | \(0.449804\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −5.24468 | −0.568866 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −13.4518 | −1.44219 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −12.2808 | −1.30176 | −0.650881 | − | 0.759180i | \(-0.725600\pi\) | ||||
−0.650881 | + | 0.759180i | \(0.725600\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 3.40820 | 0.353414 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −7.00804 | −0.719010 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −7.35295 | −0.746579 | −0.373289 | − | 0.927715i | \(-0.621770\pi\) | ||||
−0.373289 | + | 0.927715i | \(0.621770\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 5.82083 | 0.585015 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −13.4407 | −1.33740 | −0.668699 | − | 0.743533i | \(-0.733148\pi\) | ||||
−0.668699 | + | 0.743533i | \(0.733148\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 7.68074 | 0.756806 | 0.378403 | − | 0.925641i | \(-0.376473\pi\) | ||||
0.378403 | + | 0.925641i | \(0.376473\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 3.05787 | 0.298418 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −8.06583 | −0.779754 | −0.389877 | − | 0.920867i | \(-0.627482\pi\) | ||||
−0.389877 | + | 0.920867i | \(0.627482\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −7.34155 | −0.703193 | −0.351597 | − | 0.936152i | \(-0.614361\pi\) | ||||
−0.351597 | + | 0.936152i | \(0.614361\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −10.0885 | −0.957562 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −0.260722 | −0.0245267 | −0.0122633 | − | 0.999925i | \(-0.503904\pi\) | ||||
−0.0122633 | + | 0.999925i | \(0.503904\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −8.19819 | −0.764485 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 11.3836 | 1.04353 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 21.8750 | 1.98864 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −10.0894 | −0.909734 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 1.00000 | 0.0894427 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 12.6915 | 1.12619 | 0.563096 | − | 0.826392i | \(-0.309610\pi\) | ||||
0.563096 | + | 0.826392i | \(0.309610\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −10.9435 | −0.963522 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 0.587367 | 0.0513185 | 0.0256592 | − | 0.999671i | \(-0.491832\pi\) | ||||
0.0256592 | + | 0.999671i | \(0.491832\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 15.2110 | 1.31896 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 5.65673 | 0.486854 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 15.5251 | 1.32640 | 0.663200 | − | 0.748443i | \(-0.269198\pi\) | ||||
0.663200 | + | 0.748443i | \(0.269198\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 18.8204 | 1.59632 | 0.798161 | − | 0.602444i | \(-0.205806\pi\) | ||||
0.798161 | + | 0.602444i | \(0.205806\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 7.63506 | 0.642988 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 0 | 0 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 9.54822 | 0.792936 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 3.22467 | 0.265966 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −16.9576 | −1.38922 | −0.694609 | − | 0.719387i | \(-0.744423\pi\) | ||||
−0.694609 | + | 0.719387i | \(0.744423\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −10.9444 | −0.890640 | −0.445320 | − | 0.895371i | \(-0.646910\pi\) | ||||
−0.445320 | + | 0.895371i | \(0.646910\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 5.32440 | 0.430453 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −2.41917 | −0.194313 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 10.0706 | 0.803718 | 0.401859 | − | 0.915702i | \(-0.368364\pi\) | ||||
0.401859 | + | 0.915702i | \(0.368364\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −5.55394 | −0.440456 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 17.7942 | 1.40238 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −19.5144 | −1.52849 | −0.764243 | − | 0.644928i | \(-0.776887\pi\) | ||||
−0.764243 | + | 0.644928i | \(0.776887\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 8.07777 | 0.628853 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −13.4061 | −1.03740 | −0.518698 | − | 0.854958i | \(-0.673583\pi\) | ||||
−0.518698 | + | 0.854958i | \(0.673583\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 0 | 0 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 7.11457 | 0.544064 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 15.1841 | 1.15443 | 0.577214 | − | 0.816593i | \(-0.304140\pi\) | ||||
0.577214 | + | 0.816593i | \(0.304140\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −2.17051 | −0.164075 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 1.40036 | 0.105257 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 1.24513 | 0.0930655 | 0.0465327 | − | 0.998917i | \(-0.485183\pi\) | ||||
0.0465327 | + | 0.998917i | \(0.485183\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −4.69219 | −0.348768 | −0.174384 | − | 0.984678i | \(-0.555793\pi\) | ||||
−0.174384 | + | 0.984678i | \(0.555793\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 6.03968 | 0.446466 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 7.16094 | 0.526483 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 30.0713 | 2.19903 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −12.2780 | −0.893091 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 11.1007 | 0.803218 | 0.401609 | − | 0.915811i | \(-0.368451\pi\) | ||||
0.401609 | + | 0.915811i | \(0.368451\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −6.30549 | −0.453879 | −0.226940 | − | 0.973909i | \(-0.572872\pi\) | ||||
−0.226940 | + | 0.973909i | \(0.572872\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −15.9703 | −1.13783 | −0.568917 | − | 0.822395i | \(-0.692637\pi\) | ||||
−0.568917 | + | 0.822395i | \(0.692637\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −12.0075 | −0.851191 | −0.425596 | − | 0.904914i | \(-0.639935\pi\) | ||||
−0.425596 | + | 0.904914i | \(0.639935\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −16.3878 | −1.15590 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −20.7245 | −1.45457 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 7.16158 | 0.500186 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 8.32281 | 0.578475 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 40.1818 | 2.77943 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −1.02582 | −0.0706203 | −0.0353102 | − | 0.999376i | \(-0.511242\pi\) | ||||
−0.0353102 | + | 0.999376i | \(0.511242\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −7.31285 | −0.501068 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 7.76780 | 0.529760 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 5.25083 | 0.356450 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 4.31219 | 0.291391 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 0 | 0 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 2.17108 | 0.145387 | 0.0726933 | − | 0.997354i | \(-0.476841\pi\) | ||||
0.0726933 | + | 0.997354i | \(0.476841\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −1.01520 | −0.0676800 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 6.48039 | 0.430119 | 0.215059 | − | 0.976601i | \(-0.431006\pi\) | ||||
0.215059 | + | 0.976601i | \(0.431006\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −25.8710 | −1.70960 | −0.854801 | − | 0.518955i | \(-0.826321\pi\) | ||||
−0.854801 | + | 0.518955i | \(0.826321\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −17.5328 | −1.15358 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 26.4139 | 1.73043 | 0.865216 | − | 0.501400i | \(-0.167181\pi\) | ||||
0.865216 | + | 0.501400i | \(0.167181\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −5.41944 | −0.353525 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −10.3286 | −0.670913 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −0.157397 | −0.0101811 | −0.00509057 | − | 0.999987i | \(-0.501620\pi\) | ||||
−0.00509057 | + | 0.999987i | \(0.501620\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 11.5671 | 0.745103 | 0.372551 | − | 0.928012i | \(-0.378483\pi\) | ||||
0.372551 | + | 0.928012i | \(0.378483\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −10.0334 | −0.643646 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −2.28890 | −0.146232 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 0 | 0 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −4.03131 | −0.255474 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −1.54408 | −0.0974615 | −0.0487307 | − | 0.998812i | \(-0.515518\pi\) | ||||
−0.0487307 | + | 0.998812i | \(0.515518\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 47.0057 | 2.95523 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 7.38886 | 0.462709 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 14.9633 | 0.933388 | 0.466694 | − | 0.884419i | \(-0.345445\pi\) | ||||
0.466694 | + | 0.884419i | \(0.345445\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −15.5429 | −0.965787 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −9.69335 | −0.600003 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −15.1383 | −0.933470 | −0.466735 | − | 0.884397i | \(-0.654570\pi\) | ||||
−0.466735 | + | 0.884397i | \(0.654570\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 3.94223 | 0.242170 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 17.3015 | 1.05884 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −9.14065 | −0.557315 | −0.278658 | − | 0.960390i | \(-0.589889\pi\) | ||||
−0.278658 | + | 0.960390i | \(0.589889\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −4.39788 | −0.267152 | −0.133576 | − | 0.991039i | \(-0.542646\pi\) | ||||
−0.133576 | + | 0.991039i | \(0.542646\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −5.73367 | −0.345753 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 26.9216 | 1.61756 | 0.808780 | − | 0.588112i | \(-0.200128\pi\) | ||||
0.808780 | + | 0.588112i | \(0.200128\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 2.45594 | 0.147034 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 7.40886 | 0.441975 | 0.220988 | − | 0.975277i | \(-0.429072\pi\) | ||||
0.220988 | + | 0.975277i | \(0.429072\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −31.5220 | −1.87379 | −0.936894 | − | 0.349613i | \(-0.886313\pi\) | ||||
−0.936894 | + | 0.349613i | \(0.886313\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 9.87313 | 0.584834 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −15.5443 | −0.917549 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 10.5067 | 0.618042 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 10.3590 | 0.607258 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 9.19191 | 0.536997 | 0.268499 | − | 0.963280i | \(-0.413473\pi\) | ||||
0.268499 | + | 0.963280i | \(0.413473\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −0.993988 | −0.0578722 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −32.4338 | −1.88200 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 0 | 0 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −16.8601 | −0.971798 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 18.9356 | 1.08782 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −4.28702 | −0.245474 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 20.6454 | 1.17830 | 0.589148 | − | 0.808025i | \(-0.299463\pi\) | ||||
0.589148 | + | 0.808025i | \(0.299463\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −10.8209 | −0.615577 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 8.12701 | 0.460841 | 0.230420 | − | 0.973091i | \(-0.425990\pi\) | ||||
0.230420 | + | 0.973091i | \(0.425990\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −5.45768 | −0.308486 | −0.154243 | − | 0.988033i | \(-0.549294\pi\) | ||||
−0.154243 | + | 0.988033i | \(0.549294\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 2.20350 | 0.124153 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −10.7778 | −0.605342 | −0.302671 | − | 0.953095i | \(-0.597878\pi\) | ||||
−0.302671 | + | 0.953095i | \(0.597878\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −54.7464 | −3.06521 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 11.3634 | 0.634242 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 36.7550 | 2.04510 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 10.3430 | 0.571969 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 11.7629 | 0.648511 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 25.9764 | 1.42779 | 0.713896 | − | 0.700252i | \(-0.246929\pi\) | ||||
0.713896 | + | 0.700252i | \(0.246929\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −7.26979 | −0.398382 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 11.6322 | 0.635534 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 20.6275 | 1.12365 | 0.561824 | − | 0.827256i | \(-0.310100\pi\) | ||||
0.561824 | + | 0.827256i | \(0.310100\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0.367313 | 0.0199497 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 13.8707 | 0.751143 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 20.1616 | 1.08863 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 11.5499 | 0.621823 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 18.9341 | 1.01643 | 0.508217 | − | 0.861229i | \(-0.330305\pi\) | ||||
0.508217 | + | 0.861229i | \(0.330305\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −4.53125 | −0.242552 | −0.121276 | − | 0.992619i | \(-0.538699\pi\) | ||||
−0.121276 | + | 0.992619i | \(0.538699\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 18.8925 | 1.00554 | 0.502772 | − | 0.864419i | \(-0.332314\pi\) | ||||
0.502772 | + | 0.864419i | \(0.332314\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 5.19073 | 0.275495 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −16.0376 | −0.848799 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −20.4677 | −1.08024 | −0.540122 | − | 0.841587i | \(-0.681622\pi\) | ||||
−0.540122 | + | 0.841587i | \(0.681622\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 30.1127 | 1.58488 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −30.8181 | −1.61753 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −3.06083 | −0.160211 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 22.6792 | 1.18384 | 0.591922 | − | 0.805995i | \(-0.298369\pi\) | ||||
0.591922 | + | 0.805995i | \(0.298369\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −7.27044 | −0.378484 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −8.55665 | −0.444239 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 14.9049 | 0.771749 | 0.385874 | − | 0.922551i | \(-0.373900\pi\) | ||||
0.385874 | + | 0.922551i | \(0.373900\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −1.40883 | −0.0727516 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 0 | 0 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −15.7604 | −0.809555 | −0.404778 | − | 0.914415i | \(-0.632651\pi\) | ||||
−0.404778 | + | 0.914415i | \(0.632651\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −17.8802 | −0.916030 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −1.21077 | −0.0618675 | −0.0309338 | − | 0.999521i | \(-0.509848\pi\) | ||||
−0.0309338 | + | 0.999521i | \(0.509848\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 12.4450 | 0.634255 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −7.88588 | −0.400862 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −30.4592 | −1.54434 | −0.772172 | − | 0.635414i | \(-0.780829\pi\) | ||||
−0.772172 | + | 0.635414i | \(0.780829\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 42.9969 | 2.17445 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −0.827500 | −0.0417418 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 7.33131 | 0.368878 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 30.6666 | 1.53911 | 0.769557 | − | 0.638578i | \(-0.220477\pi\) | ||||
0.769557 | + | 0.638578i | \(0.220477\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −21.4297 | −1.07283 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 12.3885 | 0.618652 | 0.309326 | − | 0.950956i | \(-0.399896\pi\) | ||||
0.309326 | + | 0.950956i | \(0.399896\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 0 | 0 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −4.92377 | −0.244664 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −41.0585 | −2.03519 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −9.76935 | −0.483063 | −0.241532 | − | 0.970393i | \(-0.577650\pi\) | ||||
−0.241532 | + | 0.970393i | \(0.577650\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −21.8722 | −1.07888 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 2.15746 | 0.106162 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 2.86146 | 0.140464 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −26.5147 | −1.29843 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 5.65383 | 0.276208 | 0.138104 | − | 0.990418i | \(-0.455899\pi\) | ||||
0.138104 | + | 0.990418i | \(0.455899\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −17.8610 | −0.870494 | −0.435247 | − | 0.900311i | \(-0.643339\pi\) | ||||
−0.435247 | + | 0.900311i | \(0.643339\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 5.50182 | 0.267507 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −5.24468 | −0.254405 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 9.30501 | 0.450301 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 27.3930 | 1.31947 | 0.659737 | − | 0.751497i | \(-0.270668\pi\) | ||||
0.659737 | + | 0.751497i | \(0.270668\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −10.0057 | −0.480841 | −0.240421 | − | 0.970669i | \(-0.577285\pi\) | ||||
−0.240421 | + | 0.970669i | \(0.577285\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −13.4518 | −0.644965 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 57.4533 | 2.74836 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −1.38320 | −0.0660167 | −0.0330084 | − | 0.999455i | \(-0.510509\pi\) | ||||
−0.0330084 | + | 0.999455i | \(0.510509\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 2.32369 | 0.110652 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 15.6990 | 0.745883 | 0.372941 | − | 0.927855i | \(-0.378349\pi\) | ||||
0.372941 | + | 0.927855i | \(0.378349\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −12.2808 | −0.582166 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 23.8903 | 1.12997 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −29.7220 | −1.40267 | −0.701335 | − | 0.712832i | \(-0.747412\pi\) | ||||
−0.701335 | + | 0.712832i | \(0.747412\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −41.0622 | −1.93354 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 15.4187 | 0.724436 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 0.208226 | 0.00974041 | 0.00487021 | − | 0.999988i | \(-0.498450\pi\) | ||||
0.00487021 | + | 0.999988i | \(0.498450\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −29.6678 | −1.38477 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −6.24475 | −0.290847 | −0.145424 | − | 0.989369i | \(-0.546454\pi\) | ||||
−0.145424 | + | 0.989369i | \(0.546454\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 3.42664 | 0.159249 | 0.0796246 | − | 0.996825i | \(-0.474628\pi\) | ||||
0.0796246 | + | 0.996825i | \(0.474628\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 3.40820 | 0.158052 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 26.2665 | 1.21547 | 0.607733 | − | 0.794141i | \(-0.292079\pi\) | ||||
0.607733 | + | 0.794141i | \(0.292079\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −25.2477 | −1.16583 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −14.1877 | −0.653735 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −44.5380 | −2.04786 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −7.00804 | −0.321551 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −4.00216 | −0.183246 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 3.46962 | 0.158531 | 0.0792654 | − | 0.996854i | \(-0.474743\pi\) | ||||
0.0792654 | + | 0.996854i | \(0.474743\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 0 | 0 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −25.0690 | −1.14068 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −7.35295 | −0.333880 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 16.6306 | 0.753606 | 0.376803 | − | 0.926293i | \(-0.377023\pi\) | ||||
0.376803 | + | 0.926293i | \(0.377023\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 27.4925 | 1.24325 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 19.0416 | 0.859334 | 0.429667 | − | 0.902987i | \(-0.358631\pi\) | ||||
0.429667 | + | 0.902987i | \(0.358631\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −50.0774 | −2.25537 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 5.82083 | 0.261627 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −11.2665 | −0.505372 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −34.4954 | −1.54423 | −0.772114 | − | 0.635485i | \(-0.780800\pi\) | ||||
−0.772114 | + | 0.635485i | \(0.780800\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 18.8869 | 0.843805 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −23.5640 | −1.05067 | −0.525333 | − | 0.850897i | \(-0.676059\pi\) | ||||
−0.525333 | + | 0.850897i | \(0.676059\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −13.4407 | −0.598102 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 25.8268 | 1.14475 | 0.572377 | − | 0.819991i | \(-0.306022\pi\) | ||||
0.572377 | + | 0.819991i | \(0.306022\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 6.64355 | 0.293893 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −39.6426 | −1.75026 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 7.68074 | 0.338454 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 31.0733 | 1.36660 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −21.3918 | −0.938998 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −24.7194 | −1.08298 | −0.541489 | − | 0.840708i | \(-0.682139\pi\) | ||||
−0.541489 | + | 0.840708i | \(0.682139\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −22.6317 | −0.989613 | −0.494807 | − | 0.869003i | \(-0.664761\pi\) | ||||
−0.494807 | + | 0.869003i | \(0.664761\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 3.05787 | 0.133457 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 12.6878 | 0.552689 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 44.2104 | 1.92219 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 1.00910 | 0.0437911 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 0 | 0 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −8.06583 | −0.348716 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −1.75418 | −0.0756983 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 13.1238 | 0.565282 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −16.2447 | −0.698413 | −0.349206 | − | 0.937046i | \(-0.613549\pi\) | ||||
−0.349206 | + | 0.937046i | \(0.613549\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 6.61049 | 0.283683 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −7.34155 | −0.314478 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −24.2073 | −1.03503 | −0.517515 | − | 0.855674i | \(-0.673143\pi\) | ||||
−0.517515 | + | 0.855674i | \(0.673143\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 4.35219 | 0.185747 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −66.9143 | −2.85065 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −15.9127 | −0.676675 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −10.0885 | −0.428235 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −16.6266 | −0.704492 | −0.352246 | − | 0.935907i | \(-0.614582\pi\) | ||||
−0.352246 | + | 0.935907i | \(0.614582\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 0 | 0 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −42.3653 | −1.78867 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −2.94274 | −0.124022 | −0.0620109 | − | 0.998075i | \(-0.519751\pi\) | ||||
−0.0620109 | + | 0.998075i | \(0.519751\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −0.260722 | −0.0109687 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 10.6871 | 0.448815 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −45.8747 | −1.92317 | −0.961583 | − | 0.274514i | \(-0.911483\pi\) | ||||
−0.961583 | + | 0.274514i | \(0.911483\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −2.07821 | −0.0869705 | −0.0434853 | − | 0.999054i | \(-0.513846\pi\) | ||||
−0.0434853 | + | 0.999054i | \(0.513846\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −15.6390 | −0.653328 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −8.19819 | −0.341888 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 42.5167 | 1.76999 | 0.884997 | − | 0.465597i | \(-0.154161\pi\) | ||||
0.884997 | + | 0.465597i | \(0.154161\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 8.88336 | 0.369180 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −6.21082 | −0.257668 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −22.6035 | −0.936141 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 8.29519 | 0.342379 | 0.171190 | − | 0.985238i | \(-0.445239\pi\) | ||||
0.171190 | + | 0.985238i | \(0.445239\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 16.9537 | 0.698563 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 22.4994 | 0.925500 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 20.8549 | 0.856407 | 0.428203 | − | 0.903682i | \(-0.359147\pi\) | ||||
0.428203 | + | 0.903682i | \(0.359147\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 11.3836 | 0.466683 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 16.9166 | 0.692349 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −19.1748 | −0.783461 | −0.391730 | − | 0.920080i | \(-0.628123\pi\) | ||||
−0.391730 | + | 0.920080i | \(0.628123\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 46.9333 | 1.91445 | 0.957225 | − | 0.289345i | \(-0.0934375\pi\) | ||||
0.957225 | + | 0.289345i | \(0.0934375\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −11.8090 | −0.480899 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 21.8750 | 0.889345 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 7.58350 | 0.307805 | 0.153902 | − | 0.988086i | \(-0.450816\pi\) | ||||
0.153902 | + | 0.988086i | \(0.450816\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 29.1972 | 1.18313 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 0 | 0 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −14.1514 | −0.571569 | −0.285785 | − | 0.958294i | \(-0.592254\pi\) | ||||
−0.285785 | + | 0.958294i | \(0.592254\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −10.0894 | −0.406846 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 13.2765 | 0.534493 | 0.267246 | − | 0.963628i | \(-0.413886\pi\) | ||||
0.267246 | + | 0.963628i | \(0.413886\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −28.0262 | −1.12647 | −0.563234 | − | 0.826298i | \(-0.690443\pi\) | ||||
−0.563234 | + | 0.826298i | \(0.690443\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −46.3750 | −1.86096 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 26.6556 | 1.06793 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 1.00000 | 0.0400000 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −56.6093 | −2.26076 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −37.5569 | −1.49749 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 18.1132 | 0.721074 | 0.360537 | − | 0.932745i | \(-0.382594\pi\) | ||||
0.360537 | + | 0.932745i | \(0.382594\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 1.44520 | 0.0574417 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 12.6915 | 0.503648 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −5.26963 | −0.208463 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 11.1409 | 0.440038 | 0.220019 | − | 0.975496i | \(-0.429388\pi\) | ||||
0.220019 | + | 0.975496i | \(0.429388\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 4.70617 | 0.185593 | 0.0927965 | − | 0.995685i | \(-0.470419\pi\) | ||||
0.0927965 | + | 0.995685i | \(0.470419\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −10.9435 | −0.430900 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 6.21648 | 0.244395 | 0.122197 | − | 0.992506i | \(-0.461006\pi\) | ||||
0.122197 | + | 0.992506i | \(0.461006\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 5.69920 | 0.223713 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −7.39752 | −0.289932 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 33.0832 | 1.29465 | 0.647323 | − | 0.762215i | \(-0.275888\pi\) | ||||
0.647323 | + | 0.762215i | \(0.275888\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 0.587367 | 0.0229503 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 3.10735 | 0.121229 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −10.1051 | −0.393640 | −0.196820 | − | 0.980440i | \(-0.563061\pi\) | ||||
−0.196820 | + | 0.980440i | \(0.563061\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 28.5808 | 1.11166 | 0.555832 | − | 0.831295i | \(-0.312400\pi\) | ||||
0.555832 | + | 0.831295i | \(0.312400\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 15.2110 | 0.589857 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −78.2781 | −3.03094 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −3.05869 | −0.118256 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 24.5804 | 0.948915 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −27.0625 | −1.04318 | −0.521590 | − | 0.853196i | \(-0.674661\pi\) | ||||
−0.521590 | + | 0.853196i | \(0.674661\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 5.65673 | 0.217728 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −48.4114 | −1.86060 | −0.930301 | − | 0.366798i | \(-0.880454\pi\) | ||||
−0.930301 | + | 0.366798i | \(0.880454\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 15.9596 | 0.612474 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −9.12976 | −0.349853 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −20.6854 | −0.791507 | −0.395753 | − | 0.918357i | \(-0.629516\pi\) | ||||
−0.395753 | + | 0.918357i | \(0.629516\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 15.5251 | 0.593184 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 36.4478 | 1.39057 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 0 | 0 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −28.3098 | −1.07696 | −0.538478 | − | 0.842639i | \(-0.681001\pi\) | ||||
−0.538478 | + | 0.842639i | \(0.681001\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −12.6341 | −0.479931 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 18.8204 | 0.713897 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −37.5602 | −1.42269 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −37.2127 | −1.40751 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −12.7481 | −0.481490 | −0.240745 | − | 0.970588i | \(-0.577392\pi\) | ||||
−0.240745 | + | 0.970588i | \(0.577392\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −50.1842 | −1.89273 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 7.63506 | 0.287553 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 29.1731 | 1.09717 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 44.3115 | 1.66415 | 0.832077 | − | 0.554660i | \(-0.187152\pi\) | ||||
0.832077 | + | 0.554660i | \(0.187152\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −7.44275 | −0.279125 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 19.8328 | 0.742746 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 0.221745 | 0.00828122 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 7.49703 | 0.279592 | 0.139796 | − | 0.990180i | \(-0.455355\pi\) | ||||
0.139796 | + | 0.990180i | \(0.455355\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −16.6711 | −0.620864 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −16.2961 | −0.606058 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 9.54822 | 0.354612 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 23.3642 | 0.866530 | 0.433265 | − | 0.901267i | \(-0.357361\pi\) | ||||
0.433265 | + | 0.901267i | \(0.357361\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 28.9067 | 1.07062 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −40.7397 | −1.50681 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −27.2189 | −1.00535 | −0.502677 | − | 0.864474i | \(-0.667652\pi\) | ||||
−0.502677 | + | 0.864474i | \(0.667652\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 3.22467 | 0.118944 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −66.6951 | −2.45675 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 35.2389 | 1.29628 | 0.648141 | − | 0.761520i | \(-0.275547\pi\) | ||||
0.648141 | + | 0.761520i | \(0.275547\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −9.76023 | −0.358068 | −0.179034 | − | 0.983843i | \(-0.557297\pi\) | ||||
−0.179034 | + | 0.983843i | \(0.557297\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −16.9576 | −0.621277 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −2.90496 | −0.106287 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 17.5069 | 0.639690 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 53.1333 | 1.93886 | 0.969431 | − | 0.245363i | \(-0.0789073\pi\) | ||||
0.969431 | + | 0.245363i | \(0.0789073\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 2.17534 | 0.0792740 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −10.9444 | −0.398306 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −33.6611 | −1.22343 | −0.611716 | − | 0.791077i | \(-0.709520\pi\) | ||||
−0.611716 | + | 0.791077i | \(0.709520\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −66.2231 | −2.40375 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −38.2985 | −1.38832 | −0.694160 | − | 0.719821i | \(-0.744224\pi\) | ||||
−0.694160 | + | 0.719821i | \(0.744224\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 15.9349 | 0.576882 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 5.32440 | 0.192504 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 0 | 0 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −28.9380 | −1.04353 | −0.521765 | − | 0.853089i | \(-0.674726\pi\) | ||||
−0.521765 | + | 0.853089i | \(0.674726\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −21.0808 | −0.759206 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 22.4859 | 0.808762 | 0.404381 | − | 0.914591i | \(-0.367487\pi\) | ||||
0.404381 | + | 0.914591i | \(0.367487\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −2.41917 | −0.0868992 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 21.8972 | 0.785559 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −50.1887 | −1.79820 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −29.7619 | −1.06497 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 54.0117 | 1.93022 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 10.0706 | 0.359434 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 16.0779 | 0.573117 | 0.286558 | − | 0.958063i | \(-0.407489\pi\) | ||||
0.286558 | + | 0.958063i | \(0.407489\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 21.3273 | 0.759273 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 0.565899 | 0.0201211 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 0 | 0 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −5.55394 | −0.196978 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −51.8604 | −1.83699 | −0.918494 | − | 0.395434i | \(-0.870594\pi\) | ||||
−0.918494 | + | 0.395434i | \(0.870594\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 28.4232 | 1.00554 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 12.4675 | 0.440516 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 17.5498 | 0.619319 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 17.7942 | 0.627164 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 12.8776 | 0.453314 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 26.9372 | 0.947060 | 0.473530 | − | 0.880778i | \(-0.342980\pi\) | ||||
0.473530 | + | 0.880778i | \(0.342980\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 36.5575 | 1.28371 | 0.641854 | − | 0.766827i | \(-0.278166\pi\) | ||||
0.641854 | + | 0.766827i | \(0.278166\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 6.19586 | 0.217298 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −19.5144 | −0.683560 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −54.4371 | −1.90451 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 2.59771 | 0.0906607 | 0.0453304 | − | 0.998972i | \(-0.485566\pi\) | ||||
0.0453304 | + | 0.998972i | \(0.485566\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −7.85046 | −0.273650 | −0.136825 | − | 0.990595i | \(-0.543690\pi\) | ||||
−0.136825 | + | 0.990595i | \(0.543690\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 8.07777 | 0.281232 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 7.12878 | 0.247892 | 0.123946 | − | 0.992289i | \(-0.460445\pi\) | ||||
0.123946 | + | 0.992289i | \(0.460445\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 51.3687 | 1.78411 | 0.892054 | − | 0.451929i | \(-0.149264\pi\) | ||||
0.892054 | + | 0.451929i | \(0.149264\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −37.9279 | −1.31570 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 12.0046 | 0.415933 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −13.4061 | −0.463938 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −13.6846 | −0.473009 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 0.322289 | 0.0111266 | 0.00556332 | − | 0.999985i | \(-0.498229\pi\) | ||||
0.00556332 | + | 0.999985i | \(0.498229\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 62.1685 | 2.14374 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −10.4378 | −0.359497 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −47.4798 | −1.63143 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 44.4091 | 1.52412 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −58.7068 | −2.01244 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 18.1009 | 0.619763 | 0.309881 | − | 0.950775i | \(-0.399711\pi\) | ||||
0.309881 | + | 0.950775i | \(0.399711\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 7.11457 | 0.243313 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −44.3079 | −1.51353 | −0.756764 | − | 0.653688i | \(-0.773221\pi\) | ||||
−0.756764 | + | 0.653688i | \(0.773221\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 14.5314 | 0.495807 | 0.247903 | − | 0.968785i | \(-0.420258\pi\) | ||||
0.247903 | + | 0.968785i | \(0.420258\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 21.8992 | 0.746323 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −23.5161 | −0.800496 | −0.400248 | − | 0.916407i | \(-0.631076\pi\) | ||||
−0.400248 | + | 0.916407i | \(0.631076\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 15.1841 | 0.516276 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −14.8022 | −0.502707 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −42.0354 | −1.42595 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 0 | 0 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 7.46471 | 0.252642 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −2.17051 | −0.0733765 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 27.6427 | 0.933428 | 0.466714 | − | 0.884408i | \(-0.345438\pi\) | ||||
0.466714 | + | 0.884408i | \(0.345438\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −12.9498 | −0.436787 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −11.7134 | −0.394635 | −0.197318 | − | 0.980340i | \(-0.563223\pi\) | ||||
−0.197318 | + | 0.980340i | \(0.563223\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −5.53015 | −0.186105 | −0.0930523 | − | 0.995661i | \(-0.529662\pi\) | ||||
−0.0930523 | + | 0.995661i | \(0.529662\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 1.40036 | 0.0470726 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −15.0601 | −0.505668 | −0.252834 | − | 0.967510i | \(-0.581363\pi\) | ||||
−0.252834 | + | 0.967510i | \(0.581363\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −27.5471 | −0.923899 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 28.2313 | 0.945783 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 37.9797 | 1.27094 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 1.24513 | 0.0416202 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −23.0988 | −0.770388 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −20.6758 | −0.688810 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 23.7530 | 0.790449 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −4.69219 | −0.155974 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 47.0337 | 1.56173 | 0.780865 | − | 0.624700i | \(-0.214779\pi\) | ||||
0.780865 | + | 0.624700i | \(0.214779\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 13.6450 | 0.452575 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 18.2632 | 0.605086 | 0.302543 | − | 0.953136i | \(-0.402164\pi\) | ||||
0.302543 | + | 0.953136i | \(0.402164\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −16.4067 | −0.542982 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 6.03968 | 0.199666 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −1.27488 | −0.0421004 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 23.9725 | 0.790780 | 0.395390 | − | 0.918513i | \(-0.370610\pi\) | ||||
0.395390 | + | 0.918513i | \(0.370610\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −29.0859 | −0.958412 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 0 | 0 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 7.16094 | 0.235450 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −7.79749 | −0.256103 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 31.2931 | 1.02669 | 0.513347 | − | 0.858181i | \(-0.328405\pi\) | ||||
0.513347 | + | 0.858181i | \(0.328405\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 16.0407 | 0.525713 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −11.4496 | −0.374842 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 30.0713 | 0.983437 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −0.100918 | −0.00329684 | −0.00164842 | − | 0.999999i | \(-0.500525\pi\) | ||||
−0.00164842 | + | 0.999999i | \(0.500525\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 7.68894 | 0.250919 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 32.1209 | 1.04711 | 0.523555 | − | 0.851992i | \(-0.324605\pi\) | ||||
0.523555 | + | 0.851992i | \(0.324605\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −58.7120 | −1.91193 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | −12.2780 | −0.399403 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 11.3926 | 0.370209 | 0.185104 | − | 0.982719i | \(-0.440738\pi\) | ||||
0.185104 | + | 0.982719i | \(0.440738\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 0 | 0 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 15.1841 | 0.492378 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 20.0389 | 0.649125 | 0.324562 | − | 0.945864i | \(-0.394783\pi\) | ||||
0.324562 | + | 0.945864i | \(0.394783\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 11.1007 | 0.359210 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 77.1283 | 2.49320 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −33.6973 | −1.08814 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −25.1476 | −0.811213 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 8.18844 | 0.263869 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −6.30549 | −0.202981 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 17.7835 | 0.571878 | 0.285939 | − | 0.958248i | \(-0.407694\pi\) | ||||
0.285939 | + | 0.958248i | \(0.407694\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −51.7815 | −1.66346 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 10.0669 | 0.323062 | 0.161531 | − | 0.986868i | \(-0.448357\pi\) | ||||
0.161531 | + | 0.986868i | \(0.448357\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −40.8497 | −1.30958 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −6.91072 | −0.221094 | −0.110547 | − | 0.993871i | \(-0.535260\pi\) | ||||
−0.110547 | + | 0.993871i | \(0.535260\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 70.4141 | 2.25044 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 7.45315 | 0.237961 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −29.7862 | −0.950033 | −0.475017 | − | 0.879977i | \(-0.657558\pi\) | ||||
−0.475017 | + | 0.879977i | \(0.657558\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −15.9703 | −0.508855 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −16.5720 | −0.527491 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −63.6820 | −2.02497 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −19.6830 | −0.625252 | −0.312626 | − | 0.949876i | \(-0.601209\pi\) | ||||
−0.312626 | + | 0.949876i | \(0.601209\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −36.5963 | −1.16135 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −12.0075 | −0.380664 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 19.3853 | 0.613940 | 0.306970 | − | 0.951719i | \(-0.400685\pi\) | ||||
0.306970 | + | 0.951719i | \(0.400685\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 40.5075 | 1.28160 |
(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 | 3380.2.a.s.1.3 | yes | 9 | |
13.5 | odd | 4 | 3380.2.f.j.3041.5 | 18 | |||
13.8 | odd | 4 | 3380.2.f.j.3041.6 | 18 | |||
13.12 | even | 2 | 3380.2.a.r.1.3 | ✓ | 9 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
3380.2.a.r.1.3 | ✓ | 9 | 13.12 | even | 2 | ||
3380.2.a.s.1.3 | yes | 9 | 1.1 | even | 1 | trivial | |
3380.2.f.j.3041.5 | 18 | 13.5 | odd | 4 | |||
3380.2.f.j.3041.6 | 18 | 13.8 | odd | 4 |