Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [6016,2,Mod(1,6016)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(6016, 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("6016.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 6016 = 2^{7} \cdot 47 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 6016.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: | \(48.0380018560\) |
Analytic rank: | \(0\) |
Dimension: | \(13\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{13} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{13} - 4 x^{12} - 22 x^{11} + 96 x^{10} + 163 x^{9} - 840 x^{8} - 438 x^{7} + 3358 x^{6} + 5 x^{5} + \cdots - 832 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 2 \) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.1 | ||
Root | \(3.29402\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 6016.1 |
$q$-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 | ||||||||
\(3\) | −3.29402 | −1.90181 | −0.950903 | − | 0.309490i | \(-0.899842\pi\) | ||||
−0.950903 | + | 0.309490i | \(0.899842\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −3.40346 | −1.52207 | −0.761037 | − | 0.648708i | \(-0.775310\pi\) | ||||
−0.761037 | + | 0.648708i | \(0.775310\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −1.01019 | −0.381817 | −0.190909 | − | 0.981608i | \(-0.561143\pi\) | ||||
−0.190909 | + | 0.981608i | \(0.561143\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 7.85059 | 2.61686 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −5.72520 | −1.72621 | −0.863106 | − | 0.505023i | \(-0.831484\pi\) | ||||
−0.863106 | + | 0.505023i | \(0.831484\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 2.46556 | 0.683822 | 0.341911 | − | 0.939732i | \(-0.388926\pi\) | ||||
0.341911 | + | 0.939732i | \(0.388926\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 11.2111 | 2.89469 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 5.23012 | 1.26849 | 0.634246 | − | 0.773132i | \(-0.281311\pi\) | ||||
0.634246 | + | 0.773132i | \(0.281311\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 4.81048 | 1.10360 | 0.551799 | − | 0.833977i | \(-0.313941\pi\) | ||||
0.551799 | + | 0.833977i | \(0.313941\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 3.32760 | 0.726142 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 5.25423 | 1.09558 | 0.547791 | − | 0.836615i | \(-0.315469\pi\) | ||||
0.547791 | + | 0.836615i | \(0.315469\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 6.58356 | 1.31671 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −15.9780 | −3.07496 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 5.28804 | 0.981964 | 0.490982 | − | 0.871170i | \(-0.336638\pi\) | ||||
0.490982 | + | 0.871170i | \(0.336638\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −8.08188 | −1.45155 | −0.725774 | − | 0.687933i | \(-0.758518\pi\) | ||||
−0.725774 | + | 0.687933i | \(0.758518\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 18.8589 | 3.28292 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 3.43816 | 0.581154 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −4.26903 | −0.701824 | −0.350912 | − | 0.936408i | \(-0.614128\pi\) | ||||
−0.350912 | + | 0.936408i | \(0.614128\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −8.12160 | −1.30050 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −12.5727 | −1.96352 | −0.981760 | − | 0.190123i | \(-0.939111\pi\) | ||||
−0.981760 | + | 0.190123i | \(0.939111\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −3.79762 | −0.579131 | −0.289566 | − | 0.957158i | \(-0.593511\pi\) | ||||
−0.289566 | + | 0.957158i | \(0.593511\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −26.7192 | −3.98306 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −1.00000 | −0.145865 | ||||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −5.97951 | −0.854216 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −17.2281 | −2.41242 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 4.27708 | 0.587502 | 0.293751 | − | 0.955882i | \(-0.405096\pi\) | ||||
0.293751 | + | 0.955882i | \(0.405096\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 19.4855 | 2.62742 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −15.8458 | −2.09883 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 4.14200 | 0.539243 | 0.269621 | − | 0.962966i | \(-0.413101\pi\) | ||||
0.269621 | + | 0.962966i | \(0.413101\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 5.15979 | 0.660643 | 0.330322 | − | 0.943868i | \(-0.392843\pi\) | ||||
0.330322 | + | 0.943868i | \(0.392843\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −7.93062 | −0.999164 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −8.39143 | −1.04083 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 5.15333 | 0.629579 | 0.314789 | − | 0.949162i | \(-0.398066\pi\) | ||||
0.314789 | + | 0.949162i | \(0.398066\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −17.3075 | −2.08358 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 10.5001 | 1.24613 | 0.623065 | − | 0.782170i | \(-0.285887\pi\) | ||||
0.623065 | + | 0.782170i | \(0.285887\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −5.30202 | −0.620554 | −0.310277 | − | 0.950646i | \(-0.600422\pi\) | ||||
−0.310277 | + | 0.950646i | \(0.600422\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −21.6864 | −2.50413 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 5.78356 | 0.659097 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −14.3486 | −1.61435 | −0.807173 | − | 0.590315i | \(-0.799003\pi\) | ||||
−0.807173 | + | 0.590315i | \(0.799003\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 29.0800 | 3.23111 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −9.84381 | −1.08050 | −0.540250 | − | 0.841505i | \(-0.681670\pi\) | ||||
−0.540250 | + | 0.841505i | \(0.681670\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −17.8005 | −1.93074 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −17.4189 | −1.86750 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −7.70282 | −0.816497 | −0.408248 | − | 0.912871i | \(-0.633860\pi\) | ||||
−0.408248 | + | 0.912871i | \(0.633860\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −2.49069 | −0.261095 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 26.6219 | 2.76056 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −16.3723 | −1.67976 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −10.2647 | −1.04222 | −0.521110 | − | 0.853490i | \(-0.674482\pi\) | ||||
−0.521110 | + | 0.853490i | \(0.674482\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −44.9462 | −4.51726 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 19.7066 | 1.96088 | 0.980438 | − | 0.196828i | \(-0.0630640\pi\) | ||||
0.980438 | + | 0.196828i | \(0.0630640\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −6.98446 | −0.688199 | −0.344100 | − | 0.938933i | \(-0.611816\pi\) | ||||
−0.344100 | + | 0.938933i | \(0.611816\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −11.3254 | −1.10524 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −6.50926 | −0.629273 | −0.314637 | − | 0.949212i | \(-0.601883\pi\) | ||||
−0.314637 | + | 0.949212i | \(0.601883\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −16.5829 | −1.58835 | −0.794177 | − | 0.607686i | \(-0.792098\pi\) | ||||
−0.794177 | + | 0.607686i | \(0.792098\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 14.0623 | 1.33473 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 5.91614 | 0.556543 | 0.278272 | − | 0.960502i | \(-0.410238\pi\) | ||||
0.278272 | + | 0.960502i | \(0.410238\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −17.8826 | −1.66756 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 19.3561 | 1.78947 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −5.28344 | −0.484332 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 21.7779 | 1.97981 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 41.4147 | 3.73423 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −5.38958 | −0.482058 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −1.84506 | −0.163722 | −0.0818612 | − | 0.996644i | \(-0.526086\pi\) | ||||
−0.0818612 | + | 0.996644i | \(0.526086\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 12.5094 | 1.10140 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 10.5001 | 0.917396 | 0.458698 | − | 0.888592i | \(-0.348316\pi\) | ||||
0.458698 | + | 0.888592i | \(0.348316\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −4.85951 | −0.421373 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 54.3804 | 4.68032 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 11.4238 | 0.976004 | 0.488002 | − | 0.872843i | \(-0.337726\pi\) | ||||
0.488002 | + | 0.872843i | \(0.337726\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 7.91429 | 0.671281 | 0.335641 | − | 0.941990i | \(-0.391047\pi\) | ||||
0.335641 | + | 0.941990i | \(0.391047\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 3.29402 | 0.277407 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −14.1158 | −1.18042 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −17.9976 | −1.49462 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 19.6966 | 1.62455 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 18.0805 | 1.48121 | 0.740605 | − | 0.671940i | \(-0.234539\pi\) | ||||
0.740605 | + | 0.671940i | \(0.234539\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 0.949002 | 0.0772287 | 0.0386144 | − | 0.999254i | \(-0.487706\pi\) | ||||
0.0386144 | + | 0.999254i | \(0.487706\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 41.0596 | 3.31947 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 27.5064 | 2.20936 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −10.0579 | −0.802710 | −0.401355 | − | 0.915923i | \(-0.631461\pi\) | ||||
−0.401355 | + | 0.915923i | \(0.631461\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −14.0888 | −1.11731 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −5.30779 | −0.418312 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −7.61522 | −0.596470 | −0.298235 | − | 0.954492i | \(-0.596398\pi\) | ||||
−0.298235 | + | 0.954492i | \(0.596398\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −64.1857 | −4.99685 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −7.71566 | −0.597056 | −0.298528 | − | 0.954401i | \(-0.596496\pi\) | ||||
−0.298528 | + | 0.954401i | \(0.596496\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −6.92103 | −0.532387 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 37.7651 | 2.88797 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −9.15546 | −0.696077 | −0.348038 | − | 0.937480i | \(-0.613152\pi\) | ||||
−0.348038 | + | 0.937480i | \(0.613152\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −6.65067 | −0.502743 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −13.6439 | −1.02554 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −12.9473 | −0.967727 | −0.483863 | − | 0.875144i | \(-0.660767\pi\) | ||||
−0.483863 | + | 0.875144i | \(0.660767\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −0.263246 | −0.0195669 | −0.00978347 | − | 0.999952i | \(-0.503114\pi\) | ||||
−0.00978347 | + | 0.999952i | \(0.503114\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −16.9965 | −1.25641 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 14.5295 | 1.06823 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −29.9435 | −2.18968 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 16.1408 | 1.17407 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −7.74895 | −0.560695 | −0.280347 | − | 0.959899i | \(-0.590450\pi\) | ||||
−0.280347 | + | 0.959899i | \(0.590450\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 20.2678 | 1.45891 | 0.729455 | − | 0.684028i | \(-0.239774\pi\) | ||||
0.729455 | + | 0.684028i | \(0.239774\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 27.6416 | 1.97945 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −1.16480 | −0.0829889 | −0.0414944 | − | 0.999139i | \(-0.513212\pi\) | ||||
−0.0414944 | + | 0.999139i | \(0.513212\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 21.5395 | 1.52689 | 0.763447 | − | 0.645871i | \(-0.223506\pi\) | ||||
0.763447 | + | 0.645871i | \(0.223506\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −16.9752 | −1.19734 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −5.34194 | −0.374931 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 42.7906 | 2.98863 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 41.2488 | 2.86699 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −27.5409 | −1.90505 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −11.1401 | −0.766916 | −0.383458 | − | 0.923558i | \(-0.625267\pi\) | ||||
−0.383458 | + | 0.923558i | \(0.625267\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −34.5875 | −2.36990 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 12.9251 | 0.881481 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 8.16426 | 0.554226 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 17.4650 | 1.18017 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 12.8952 | 0.867423 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 2.86516 | 0.191865 | 0.0959327 | − | 0.995388i | \(-0.469417\pi\) | ||||
0.0959327 | + | 0.995388i | \(0.469417\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 51.6848 | 3.44565 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 7.92238 | 0.525827 | 0.262913 | − | 0.964819i | \(-0.415317\pi\) | ||||
0.262913 | + | 0.964819i | \(0.415317\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −10.1286 | −0.669319 | −0.334659 | − | 0.942339i | \(-0.608621\pi\) | ||||
−0.334659 | + | 0.942339i | \(0.608621\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −19.0512 | −1.25347 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −5.45696 | −0.357497 | −0.178749 | − | 0.983895i | \(-0.557205\pi\) | ||||
−0.178749 | + | 0.983895i | \(0.557205\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 3.40346 | 0.222017 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 47.2647 | 3.07017 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −2.47493 | −0.160090 | −0.0800450 | − | 0.996791i | \(-0.525506\pi\) | ||||
−0.0800450 | + | 0.996791i | \(0.525506\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −17.7997 | −1.14658 | −0.573291 | − | 0.819352i | \(-0.694333\pi\) | ||||
−0.573291 | + | 0.819352i | \(0.694333\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −47.8563 | −3.06998 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 20.3510 | 1.30018 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 11.8605 | 0.754666 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 32.4258 | 2.05490 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −16.3045 | −1.02913 | −0.514566 | − | 0.857451i | \(-0.672047\pi\) | ||||
−0.514566 | + | 0.857451i | \(0.672047\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −30.0815 | −1.89121 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 58.6354 | 3.67189 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 0.476521 | 0.0297246 | 0.0148623 | − | 0.999890i | \(-0.495269\pi\) | ||||
0.0148623 | + | 0.999890i | \(0.495269\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 4.31255 | 0.267969 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 41.5142 | 2.56967 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 0.982319 | 0.0605724 | 0.0302862 | − | 0.999541i | \(-0.490358\pi\) | ||||
0.0302862 | + | 0.999541i | \(0.490358\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −14.5569 | −0.894221 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 25.3733 | 1.55282 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 10.2190 | 0.623064 | 0.311532 | − | 0.950236i | \(-0.399158\pi\) | ||||
0.311532 | + | 0.950236i | \(0.399158\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 5.62542 | 0.341720 | 0.170860 | − | 0.985295i | \(-0.445345\pi\) | ||||
0.170860 | + | 0.985295i | \(0.445345\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 8.20439 | 0.496552 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −37.6922 | −2.27292 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −12.2346 | −0.735107 | −0.367553 | − | 0.930002i | \(-0.619805\pi\) | ||||
−0.367553 | + | 0.930002i | \(0.619805\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −63.4475 | −3.79850 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −14.7699 | −0.881096 | −0.440548 | − | 0.897729i | \(-0.645216\pi\) | ||||
−0.440548 | + | 0.897729i | \(0.645216\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −19.4910 | −1.15862 | −0.579311 | − | 0.815107i | \(-0.696678\pi\) | ||||
−0.579311 | + | 0.815107i | \(0.696678\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 53.9307 | 3.19458 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 12.7008 | 0.749706 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 10.3542 | 0.609070 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 33.8121 | 1.98210 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −11.5024 | −0.671975 | −0.335988 | − | 0.941866i | \(-0.609070\pi\) | ||||
−0.335988 | + | 0.941866i | \(0.609070\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −14.0972 | −0.820768 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 91.4770 | 5.30803 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 12.9546 | 0.749184 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 3.83633 | 0.221122 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −64.9139 | −3.72920 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −17.5611 | −1.00555 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −27.1455 | −1.54927 | −0.774637 | − | 0.632407i | \(-0.782067\pi\) | ||||
−0.774637 | + | 0.632407i | \(0.782067\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 23.0070 | 1.30882 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 29.2076 | 1.65621 | 0.828105 | − | 0.560573i | \(-0.189419\pi\) | ||||
0.828105 | + | 0.560573i | \(0.189419\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 17.3355 | 0.979862 | 0.489931 | − | 0.871761i | \(-0.337022\pi\) | ||||
0.489931 | + | 0.871761i | \(0.337022\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 26.9916 | 1.52080 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 8.16893 | 0.458813 | 0.229406 | − | 0.973331i | \(-0.426322\pi\) | ||||
0.229406 | + | 0.973331i | \(0.426322\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −30.2750 | −1.69508 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 21.4416 | 1.19676 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 25.1594 | 1.39991 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 16.2321 | 0.900397 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 54.6245 | 3.02074 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 1.01019 | 0.0556938 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −8.54399 | −0.469620 | −0.234810 | − | 0.972041i | \(-0.575447\pi\) | ||||
−0.234810 | + | 0.972041i | \(0.575447\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −33.5144 | −1.83658 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −17.5392 | −0.958266 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 14.5188 | 0.790888 | 0.395444 | − | 0.918490i | \(-0.370591\pi\) | ||||
0.395444 | + | 0.918490i | \(0.370591\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −19.4879 | −1.05844 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 46.2703 | 2.50568 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 13.1118 | 0.707972 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 58.9056 | 3.17137 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −9.43033 | −0.506247 | −0.253123 | − | 0.967434i | \(-0.581458\pi\) | ||||
−0.253123 | + | 0.967434i | \(0.581458\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −7.36249 | −0.394105 | −0.197052 | − | 0.980393i | \(-0.563137\pi\) | ||||
−0.197052 | + | 0.980393i | \(0.563137\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −39.3946 | −2.10273 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −13.0551 | −0.694853 | −0.347426 | − | 0.937707i | \(-0.612944\pi\) | ||||
−0.347426 | + | 0.937707i | \(0.612944\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −35.7366 | −1.89670 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 17.4038 | 0.921105 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 27.7361 | 1.46386 | 0.731929 | − | 0.681381i | \(-0.238620\pi\) | ||||
0.731929 | + | 0.681381i | \(0.238620\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 4.14068 | 0.217931 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −71.7368 | −3.76521 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 18.0452 | 0.944530 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 36.6642 | 1.91386 | 0.956929 | − | 0.290323i | \(-0.0937627\pi\) | ||||
0.956929 | + | 0.290323i | \(0.0937627\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −98.7029 | −5.13827 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −4.32067 | −0.224318 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 9.01404 | 0.466729 | 0.233365 | − | 0.972389i | \(-0.425026\pi\) | ||||
0.233365 | + | 0.972389i | \(0.425026\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 17.7534 | 0.916781 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 13.0380 | 0.671489 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 11.2137 | 0.576010 | 0.288005 | − | 0.957629i | \(-0.407008\pi\) | ||||
0.288005 | + | 0.957629i | \(0.407008\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 6.07766 | 0.311368 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −12.3247 | −0.629760 | −0.314880 | − | 0.949131i | \(-0.601964\pi\) | ||||
−0.314880 | + | 0.949131i | \(0.601964\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −19.6841 | −1.00320 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −29.8135 | −1.51551 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 11.6693 | 0.591658 | 0.295829 | − | 0.955241i | \(-0.404404\pi\) | ||||
0.295829 | + | 0.955241i | \(0.404404\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 27.4803 | 1.38974 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −34.5875 | −1.74471 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 48.8350 | 2.45715 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 5.65277 | 0.283705 | 0.141852 | − | 0.989888i | \(-0.454694\pi\) | ||||
0.141852 | + | 0.989888i | \(0.454694\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 16.0073 | 0.801370 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 39.7695 | 1.98599 | 0.992997 | − | 0.118139i | \(-0.0376929\pi\) | ||||
0.992997 | + | 0.118139i | \(0.0376929\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −19.9263 | −0.992601 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −98.9727 | −4.91799 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 24.4410 | 1.21150 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −14.0369 | −0.694078 | −0.347039 | − | 0.937851i | \(-0.612813\pi\) | ||||
−0.347039 | + | 0.937851i | \(0.612813\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −37.6304 | −1.85617 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −4.18423 | −0.205892 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 33.5031 | 1.64460 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −26.0699 | −1.27665 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 38.8002 | 1.89551 | 0.947756 | − | 0.318996i | \(-0.103346\pi\) | ||||
0.947756 | + | 0.318996i | \(0.103346\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 8.76782 | 0.427317 | 0.213659 | − | 0.976908i | \(-0.431462\pi\) | ||||
0.213659 | + | 0.976908i | \(0.431462\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −7.85059 | −0.381709 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 34.4328 | 1.67024 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −5.21239 | −0.252245 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 46.4978 | 2.24493 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 15.9651 | 0.769011 | 0.384505 | − | 0.923123i | \(-0.374372\pi\) | ||||
0.384505 | + | 0.923123i | \(0.374372\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −35.6916 | −1.71523 | −0.857615 | − | 0.514292i | \(-0.828055\pi\) | ||||
−0.857615 | + | 0.514292i | \(0.828055\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 59.2846 | 2.84248 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 25.2753 | 1.20908 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −27.1930 | −1.29785 | −0.648925 | − | 0.760852i | \(-0.724781\pi\) | ||||
−0.648925 | + | 0.760852i | \(0.724781\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −46.9427 | −2.23537 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 16.9119 | 0.803507 | 0.401753 | − | 0.915748i | \(-0.368401\pi\) | ||||
0.401753 | + | 0.915748i | \(0.368401\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 26.2162 | 1.24277 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −59.5575 | −2.81697 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −5.54470 | −0.261671 | −0.130835 | − | 0.991404i | \(-0.541766\pi\) | ||||
−0.130835 | + | 0.991404i | \(0.541766\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 71.9810 | 3.38945 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −3.12604 | −0.146874 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 8.47697 | 0.397406 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −16.4027 | −0.767286 | −0.383643 | − | 0.923481i | \(-0.625331\pi\) | ||||
−0.383643 | + | 0.923481i | \(0.625331\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −83.5667 | −3.90056 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 8.06731 | 0.375732 | 0.187866 | − | 0.982195i | \(-0.439843\pi\) | ||||
0.187866 | + | 0.982195i | \(0.439843\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 35.3959 | 1.64499 | 0.822493 | − | 0.568776i | \(-0.192583\pi\) | ||||
0.822493 | + | 0.568776i | \(0.192583\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −90.6066 | −4.20178 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 0.348500 | 0.0161267 | 0.00806334 | − | 0.999967i | \(-0.497433\pi\) | ||||
0.00806334 | + | 0.999967i | \(0.497433\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −5.20586 | −0.240384 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 33.1311 | 1.52660 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 21.7421 | 0.999703 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 31.6700 | 1.45312 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 33.5776 | 1.53741 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −17.7205 | −0.809669 | −0.404835 | − | 0.914390i | \(-0.632671\pi\) | ||||
−0.404835 | + | 0.914390i | \(0.632671\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −10.5255 | −0.479923 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 17.4840 | 0.795548 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 34.9354 | 1.58634 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −1.44876 | −0.0656495 | −0.0328247 | − | 0.999461i | \(-0.510450\pi\) | ||||
−0.0328247 | + | 0.999461i | \(0.510450\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 25.0847 | 1.13437 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −2.15520 | −0.0972627 | −0.0486313 | − | 0.998817i | \(-0.515486\pi\) | ||||
−0.0486313 | + | 0.998817i | \(0.515486\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 27.6571 | 1.24561 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 152.973 | 6.87561 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −10.6071 | −0.475794 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 22.5468 | 1.00933 | 0.504666 | − | 0.863314i | \(-0.331616\pi\) | ||||
0.504666 | + | 0.863314i | \(0.331616\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 25.4156 | 1.13548 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 12.1442 | 0.541483 | 0.270742 | − | 0.962652i | \(-0.412731\pi\) | ||||
0.270742 | + | 0.962652i | \(0.412731\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −67.0705 | −2.98460 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 22.7980 | 1.01250 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 1.45073 | 0.0643027 | 0.0321513 | − | 0.999483i | \(-0.489764\pi\) | ||||
0.0321513 | + | 0.999483i | \(0.489764\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 5.35606 | 0.236938 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −76.8616 | −3.39352 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 23.7713 | 1.04749 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 5.72520 | 0.251794 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 30.1583 | 1.32380 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −14.2519 | −0.624388 | −0.312194 | − | 0.950018i | \(-0.601064\pi\) | ||||
−0.312194 | + | 0.950018i | \(0.601064\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 1.78280 | 0.0779565 | 0.0389782 | − | 0.999240i | \(-0.487590\pi\) | ||||
0.0389782 | + | 0.999240i | \(0.487590\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 21.9075 | 0.956120 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −42.2692 | −1.84128 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 4.60691 | 0.200300 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 32.5172 | 1.41113 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −30.9986 | −1.34270 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 22.1540 | 0.957801 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 42.6487 | 1.84043 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 34.2339 | 1.47456 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −1.55369 | −0.0667982 | −0.0333991 | − | 0.999442i | \(-0.510633\pi\) | ||||
−0.0333991 | + | 0.999442i | \(0.510633\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 0.867140 | 0.0372125 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 56.4393 | 2.41759 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −23.8059 | −1.01787 | −0.508933 | − | 0.860806i | \(-0.669960\pi\) | ||||
−0.508933 | + | 0.860806i | \(0.669960\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 40.5074 | 1.72881 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 25.4380 | 1.08369 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 14.4949 | 0.616385 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −47.8605 | −2.03156 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 24.3308 | 1.03093 | 0.515465 | − | 0.856911i | \(-0.327619\pi\) | ||||
0.515465 | + | 0.856911i | \(0.327619\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −9.36324 | −0.396023 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 98.6345 | 4.16435 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 6.88333 | 0.290098 | 0.145049 | − | 0.989424i | \(-0.453666\pi\) | ||||
0.145049 | + | 0.989424i | \(0.453666\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −20.1353 | −0.847101 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −29.3764 | −1.23369 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 6.32305 | 0.265076 | 0.132538 | − | 0.991178i | \(-0.457687\pi\) | ||||
0.132538 | + | 0.991178i | \(0.457687\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −6.32641 | −0.264752 | −0.132376 | − | 0.991200i | \(-0.542261\pi\) | ||||
−0.132376 | + | 0.991200i | \(0.542261\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 25.5252 | 1.06633 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 34.5915 | 1.44257 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 24.5472 | 1.02191 | 0.510957 | − | 0.859606i | \(-0.329291\pi\) | ||||
0.510957 | + | 0.859606i | \(0.329291\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −66.7627 | −2.77456 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 9.94416 | 0.412553 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −24.4871 | −1.01415 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −65.8777 | −2.72371 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −34.4747 | −1.42293 | −0.711463 | − | 0.702724i | \(-0.751967\pi\) | ||||
−0.711463 | + | 0.702724i | \(0.751967\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −38.8777 | −1.60193 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 3.83689 | 0.157829 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −16.5677 | −0.680354 | −0.340177 | − | 0.940361i | \(-0.610487\pi\) | ||||
−0.340177 | + | 0.940361i | \(0.610487\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 17.9820 | 0.737189 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −70.9515 | −2.90385 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 3.33391 | 0.136220 | 0.0681099 | − | 0.997678i | \(-0.478303\pi\) | ||||
0.0681099 | + | 0.997678i | \(0.478303\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −22.6444 | −0.923684 | −0.461842 | − | 0.886962i | \(-0.652811\pi\) | ||||
−0.461842 | + | 0.886962i | \(0.652811\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 40.4566 | 1.64752 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −74.1202 | −3.01341 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 39.5991 | 1.60728 | 0.803639 | − | 0.595117i | \(-0.202894\pi\) | ||||
0.803639 | + | 0.595117i | \(0.202894\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 17.5965 | 0.713045 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −2.46556 | −0.0997457 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −5.24650 | −0.211904 | −0.105952 | − | 0.994371i | \(-0.533789\pi\) | ||||
−0.105952 | + | 0.994371i | \(0.533789\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −140.953 | −5.68378 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 3.90461 | 0.157194 | 0.0785969 | − | 0.996906i | \(-0.474956\pi\) | ||||
0.0785969 | + | 0.996906i | \(0.474956\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 0.752490 | 0.0302451 | 0.0151226 | − | 0.999886i | \(-0.495186\pi\) | ||||
0.0151226 | + | 0.999886i | \(0.495186\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −83.9518 | −3.36887 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 7.78134 | 0.311753 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −14.5746 | −0.582982 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 90.7204 | 3.62303 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −22.3276 | −0.890258 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 16.1111 | 0.641373 | 0.320686 | − | 0.947185i | \(-0.396086\pi\) | ||||
0.320686 | + | 0.947185i | \(0.396086\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 36.6958 | 1.45853 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 6.27958 | 0.249198 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −14.7428 | −0.584132 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 82.4318 | 3.26095 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 3.57148 | 0.141065 | 0.0705325 | − | 0.997509i | \(-0.477530\pi\) | ||||
0.0705325 | + | 0.997509i | \(0.477530\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −17.1521 | −0.676411 | −0.338206 | − | 0.941072i | \(-0.609820\pi\) | ||||
−0.338206 | + | 0.941072i | \(0.609820\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −42.5754 | −1.67641 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 16.7145 | 0.657114 | 0.328557 | − | 0.944484i | \(-0.393438\pi\) | ||||
0.328557 | + | 0.944484i | \(0.393438\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −23.7138 | −0.930847 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −26.8933 | −1.05403 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −40.0870 | −1.56873 | −0.784364 | − | 0.620301i | \(-0.787010\pi\) | ||||
−0.784364 | + | 0.620301i | \(0.787010\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −35.7366 | −1.39635 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −41.6240 | −1.62391 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −18.5765 | −0.723638 | −0.361819 | − | 0.932248i | \(-0.617844\pi\) | ||||
−0.361819 | + | 0.932248i | \(0.617844\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 25.8030 | 1.00362 | 0.501811 | − | 0.864977i | \(-0.332667\pi\) | ||||
0.501811 | + | 0.864977i | \(0.332667\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −42.4770 | −1.64967 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 16.5392 | 0.641361 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 27.7845 | 1.07582 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −9.43791 | −0.364891 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −29.5408 | −1.14041 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −10.0161 | −0.386092 | −0.193046 | − | 0.981190i | \(-0.561837\pi\) | ||||
−0.193046 | + | 0.981190i | \(0.561837\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −105.192 | −4.04883 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −48.0177 | −1.84547 | −0.922736 | − | 0.385433i | \(-0.874052\pi\) | ||||
−0.922736 | + | 0.385433i | \(0.874052\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 10.3693 | 0.397937 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −26.0965 | −1.00002 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 20.3988 | 0.780537 | 0.390268 | − | 0.920701i | \(-0.372382\pi\) | ||||
0.390268 | + | 0.920701i | \(0.372382\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −38.8806 | −1.48555 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 33.3639 | 1.27291 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 10.5454 | 0.401747 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 3.07747 | 0.117072 | 0.0585362 | − | 0.998285i | \(-0.481357\pi\) | ||||
0.0585362 | + | 0.998285i | \(0.481357\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 45.4043 | 1.72477 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −26.9360 | −1.02174 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −65.7566 | −2.49071 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 17.9754 | 0.679890 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 11.7014 | 0.441956 | 0.220978 | − | 0.975279i | \(-0.429075\pi\) | ||||
0.220978 | + | 0.975279i | \(0.429075\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −20.5361 | −0.774533 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −11.2111 | −0.422234 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −19.9074 | −0.748696 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 39.4191 | 1.48042 | 0.740209 | − | 0.672377i | \(-0.234727\pi\) | ||||
0.740209 | + | 0.672377i | \(0.234727\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −112.645 | −4.22452 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −42.4640 | −1.59029 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 48.0426 | 1.79669 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 8.15248 | 0.304460 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 41.1251 | 1.53371 | 0.766854 | − | 0.641822i | \(-0.221821\pi\) | ||||
0.766854 | + | 0.641822i | \(0.221821\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 7.05566 | 0.262766 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 58.6327 | 2.18057 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 34.8141 | 1.29296 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −29.8097 | −1.10558 | −0.552790 | − | 0.833321i | \(-0.686437\pi\) | ||||
−0.552790 | + | 0.833321i | \(0.686437\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 70.3999 | 2.60740 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −19.8620 | −0.734623 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −2.39218 | −0.0883573 | −0.0441786 | − | 0.999024i | \(-0.514067\pi\) | ||||
−0.0441786 | + | 0.999024i | \(0.514067\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | −67.0368 | −2.47269 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −29.5038 | −1.08679 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 29.4914 | 1.08486 | 0.542428 | − | 0.840102i | \(-0.317505\pi\) | ||||
0.542428 | + | 0.840102i | \(0.317505\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −39.0688 | −1.43523 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 18.1362 | 0.665353 | 0.332677 | − | 0.943041i | \(-0.392048\pi\) | ||||
0.332677 | + | 0.943041i | \(0.392048\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −61.5362 | −2.25451 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −77.2798 | −2.82752 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 6.57561 | 0.240267 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 36.7238 | 1.34007 | 0.670035 | − | 0.742329i | \(-0.266279\pi\) | ||||
0.670035 | + | 0.742329i | \(0.266279\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 53.7075 | 1.95721 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −3.22989 | −0.117548 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −16.3203 | −0.593173 | −0.296587 | − | 0.955006i | \(-0.595848\pi\) | ||||
−0.296587 | + | 0.955006i | \(0.595848\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 99.0891 | 3.59671 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 34.0552 | 1.23450 | 0.617250 | − | 0.786767i | \(-0.288247\pi\) | ||||
0.617250 | + | 0.786767i | \(0.288247\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 16.7519 | 0.606461 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −139.745 | −5.05248 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 10.2123 | 0.368746 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −1.76745 | −0.0637360 | −0.0318680 | − | 0.999492i | \(-0.510146\pi\) | ||||
−0.0318680 | + | 0.999492i | \(0.510146\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −1.56967 | −0.0565303 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −15.3189 | −0.550984 | −0.275492 | − | 0.961303i | \(-0.588841\pi\) | ||||
−0.275492 | + | 0.961303i | \(0.588841\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −53.2075 | −1.91127 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −14.2056 | −0.509624 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −60.4805 | −2.16694 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −60.1150 | −2.15108 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −84.4920 | −3.01950 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 34.2318 | 1.22178 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 49.6113 | 1.76845 | 0.884226 | − | 0.467059i | \(-0.154686\pi\) | ||||
0.884226 | + | 0.467059i | \(0.154686\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −3.23578 | −0.115197 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −5.97644 | −0.212498 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 12.7218 | 0.451763 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 47.9507 | 1.70063 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 28.4624 | 1.00819 | 0.504096 | − | 0.863648i | \(-0.331826\pi\) | ||||
0.504096 | + | 0.863648i | \(0.331826\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −5.23012 | −0.185028 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −60.4717 | −2.13666 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 30.3551 | 1.07121 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 18.0649 | 0.636702 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −33.6617 | −1.18495 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 55.0741 | 1.93630 | 0.968151 | − | 0.250366i | \(-0.0805509\pi\) | ||||
0.968151 | + | 0.250366i | \(0.0805509\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −14.1223 | −0.495902 | −0.247951 | − | 0.968773i | \(-0.579757\pi\) | ||||
−0.247951 | + | 0.968773i | \(0.579757\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −18.5303 | −0.649885 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 25.9181 | 0.907872 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −18.2684 | −0.639129 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −19.5534 | −0.683250 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −42.8827 | −1.49662 | −0.748308 | − | 0.663352i | \(-0.769133\pi\) | ||||
−0.748308 | + | 0.663352i | \(0.769133\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 39.9210 | 1.39156 | 0.695779 | − | 0.718256i | \(-0.255059\pi\) | ||||
0.695779 | + | 0.718256i | \(0.255059\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 124.159 | 4.32266 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −48.2874 | −1.67912 | −0.839558 | − | 0.543270i | \(-0.817186\pi\) | ||||
−0.839558 | + | 0.543270i | \(0.817186\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −7.12920 | −0.247607 | −0.123804 | − | 0.992307i | \(-0.539509\pi\) | ||||
−0.123804 | + | 0.992307i | \(0.539509\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 40.3011 | 1.39803 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −31.2736 | −1.08356 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 26.2600 | 0.908764 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 129.132 | 4.46345 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −33.3109 | −1.15002 | −0.575010 | − | 0.818146i | \(-0.695002\pi\) | ||||
−0.575010 | + | 0.818146i | \(0.695002\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −1.03666 | −0.0357471 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 48.6523 | 1.67567 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 23.5555 | 0.810333 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −21.9999 | −0.755924 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 64.2039 | 2.20347 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −22.4305 | −0.768906 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −9.10908 | −0.311889 | −0.155944 | − | 0.987766i | \(-0.549842\pi\) | ||||
−0.155944 | + | 0.987766i | \(0.549842\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −128.532 | −4.39570 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −7.22096 | −0.246663 | −0.123332 | − | 0.992366i | \(-0.539358\pi\) | ||||
−0.123332 | + | 0.992366i | \(0.539358\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −15.4990 | −0.528818 | −0.264409 | − | 0.964411i | \(-0.585177\pi\) | ||||
−0.264409 | + | 0.964411i | \(0.585177\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −41.8368 | −1.42580 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −8.22895 | −0.280117 | −0.140058 | − | 0.990143i | \(-0.544729\pi\) | ||||
−0.140058 | + | 0.990143i | \(0.544729\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 31.1603 | 1.05948 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −34.1069 | −1.15833 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 82.1486 | 2.78670 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 12.7058 | 0.430520 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −80.5837 | −2.72735 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 5.44452 | 0.184058 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −27.2276 | −0.919411 | −0.459706 | − | 0.888071i | \(-0.652045\pi\) | ||||
−0.459706 | + | 0.888071i | \(0.652045\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 37.8890 | 1.27797 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 35.2731 | 1.18838 | 0.594191 | − | 0.804324i | \(-0.297472\pi\) | ||||
0.594191 | + | 0.804324i | \(0.297472\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 26.3181 | 0.885674 | 0.442837 | − | 0.896602i | \(-0.353972\pi\) | ||||
0.442837 | + | 0.896602i | \(0.353972\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 46.4364 | 1.56094 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −52.0204 | −1.74667 | −0.873337 | − | 0.487116i | \(-0.838049\pi\) | ||||
−0.873337 | + | 0.487116i | \(0.838049\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 1.86386 | 0.0625120 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −166.489 | −5.57758 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −4.81048 | −0.160976 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 44.0657 | 1.47295 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −42.6727 | −1.42480 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −42.7373 | −1.42537 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 22.3696 | 0.745241 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −12.6370 | −0.420532 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 0.895949 | 0.0297824 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 46.2955 | 1.53722 | 0.768608 | − | 0.639720i | \(-0.220950\pi\) | ||||
0.768608 | + | 0.639720i | \(0.220950\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 154.708 | 5.13135 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 34.5338 | 1.14416 | 0.572079 | − | 0.820199i | \(-0.306137\pi\) | ||||
0.572079 | + | 0.820199i | \(0.306137\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 56.3578 | 1.86517 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 57.8468 | 1.91236 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −10.6071 | −0.350278 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 35.4876 | 1.17063 | 0.585315 | − | 0.810806i | \(-0.300971\pi\) | ||||
0.585315 | + | 0.810806i | \(0.300971\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 89.4178 | 2.94642 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 25.8885 | 0.852131 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −28.1054 | −0.924100 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −54.8321 | −1.80092 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −27.0523 | −0.887557 | −0.443779 | − | 0.896136i | \(-0.646362\pi\) | ||||
−0.443779 | + | 0.896136i | \(0.646362\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −28.7643 | −0.942711 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −96.2105 | −3.14979 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 101.912 | 3.33286 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −51.6534 | −1.68744 | −0.843722 | − | 0.536780i | \(-0.819640\pi\) | ||||
−0.843722 | + | 0.536780i | \(0.819640\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −57.1036 | −1.86351 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 45.5605 | 1.48523 | 0.742615 | − | 0.669718i | \(-0.233585\pi\) | ||||
0.742615 | + | 0.669718i | \(0.233585\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −66.0596 | −2.15120 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | −54.9347 | −1.78703 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −16.6145 | −0.539898 | −0.269949 | − | 0.962875i | \(-0.587007\pi\) | ||||
−0.269949 | + | 0.962875i | \(0.587007\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −13.0724 | −0.424349 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −26.9086 | −0.872572 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 4.18754 | 0.135648 | 0.0678239 | − | 0.997697i | \(-0.478394\pi\) | ||||
0.0678239 | + | 0.997697i | \(0.478394\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 26.3733 | 0.853419 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 99.7267 | 3.22371 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −11.5403 | −0.372655 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 34.3167 | 1.10699 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −51.1015 | −1.64672 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −68.9808 | −2.22057 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 39.4921 | 1.26998 | 0.634990 | − | 0.772520i | \(-0.281004\pi\) | ||||
0.634990 | + | 0.772520i | \(0.281004\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −82.8756 | −2.66235 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 10.5070 | 0.337185 | 0.168592 | − | 0.985686i | \(-0.446078\pi\) | ||||
0.168592 | + | 0.985686i | \(0.446078\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −7.99496 | −0.256307 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −53.4690 | −1.71238 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −43.7558 | −1.39987 | −0.699937 | − | 0.714205i | \(-0.746788\pi\) | ||||
−0.699937 | + | 0.714205i | \(0.746788\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 44.1001 | 1.40945 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −130.186 | −4.15651 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −61.6919 | −1.96767 | −0.983833 | − | 0.179089i | \(-0.942685\pi\) | ||||
−0.983833 | + | 0.179089i | \(0.942685\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 3.96437 | 0.126315 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −3.32760 | −0.105919 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −19.9536 | −0.634486 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 52.9225 | 1.68114 | 0.840569 | − | 0.541705i | \(-0.182221\pi\) | ||||
0.840569 | + | 0.541705i | \(0.182221\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 28.1441 | 0.893127 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −73.3088 | −2.32405 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −58.6863 | −1.85861 | −0.929306 | − | 0.369310i | \(-0.879594\pi\) | ||||
−0.929306 | + | 0.369310i | \(0.879594\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 68.2104 | 2.15808 |
(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 | 6016.2.a.n.1.1 | yes | 13 | |
4.3 | odd | 2 | 6016.2.a.p.1.13 | yes | 13 | ||
8.3 | odd | 2 | 6016.2.a.m.1.1 | ✓ | 13 | ||
8.5 | even | 2 | 6016.2.a.o.1.13 | yes | 13 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
6016.2.a.m.1.1 | ✓ | 13 | 8.3 | odd | 2 | ||
6016.2.a.n.1.1 | yes | 13 | 1.1 | even | 1 | trivial | |
6016.2.a.o.1.13 | yes | 13 | 8.5 | even | 2 | ||
6016.2.a.p.1.13 | yes | 13 | 4.3 | odd | 2 |