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 | 1.13 | ||
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 | \(-0.100158\pi\) | ||||
0.950903 | + | 0.309490i | \(0.100158\pi\) | |||||||
\(4\) | 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 | \(-0.438857\pi\) | ||||
0.190909 | + | 0.981608i | \(0.438857\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 7.85059 | 2.61686 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 5.72520 | 1.72621 | 0.863106 | − | 0.505023i | \(-0.168516\pi\) | ||||
0.863106 | + | 0.505023i | \(0.168516\pi\) | |||||||
\(12\) | 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 | \(-0.686059\pi\) | ||||
−0.551799 | + | 0.833977i | \(0.686059\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 3.32760 | 0.726142 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −5.25423 | −1.09558 | −0.547791 | − | 0.836615i | \(-0.684531\pi\) | ||||
−0.547791 | + | 0.836615i | \(0.684531\pi\) | |||||||
\(24\) | 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 | \(-0.241482\pi\) | ||||
0.725774 | + | 0.687933i | \(0.241482\pi\) | |||||||
\(32\) | 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 | \(-0.406489\pi\) | ||||
0.289566 | + | 0.957158i | \(0.406489\pi\) | |||||||
\(44\) | 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 | \(-0.586899\pi\) | ||||
−0.269621 | + | 0.962966i | \(0.586899\pi\) | |||||||
\(60\) | 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 | \(-0.601934\pi\) | ||||
−0.314789 | + | 0.949162i | \(0.601934\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −17.3075 | −2.08358 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −10.5001 | −1.24613 | −0.623065 | − | 0.782170i | \(-0.714113\pi\) | ||||
−0.623065 | + | 0.782170i | \(0.714113\pi\) | |||||||
\(72\) | 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 | \(-0.200997\pi\) | ||||
0.807173 | + | 0.590315i | \(0.200997\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 29.0800 | 3.23111 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 9.84381 | 1.08050 | 0.540250 | − | 0.841505i | \(-0.318330\pi\) | ||||
0.540250 | + | 0.841505i | \(0.318330\pi\) | |||||||
\(84\) | 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 | \(-0.388184\pi\) | ||||
0.344100 | + | 0.938933i | \(0.388184\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −11.3254 | −1.10524 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 6.50926 | 0.629273 | 0.314637 | − | 0.949212i | \(-0.398117\pi\) | ||||
0.314637 | + | 0.949212i | \(0.398117\pi\) | |||||||
\(108\) | 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 | \(-0.473914\pi\) | ||||
0.0818612 | + | 0.996644i | \(0.473914\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 12.5094 | 1.10140 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −10.5001 | −0.917396 | −0.458698 | − | 0.888592i | \(-0.651684\pi\) | ||||
−0.458698 | + | 0.888592i | \(0.651684\pi\) | |||||||
\(132\) | 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 | \(-0.608953\pi\) | ||||
−0.335641 | + | 0.941990i | \(0.608953\pi\) | |||||||
\(140\) | 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 | \(-0.512294\pi\) | ||||
−0.0386144 | + | 0.999254i | \(0.512294\pi\) | |||||||
\(152\) | 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 | \(-0.403602\pi\) | ||||
0.298235 | + | 0.954492i | \(0.403602\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −64.1857 | −4.99685 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 7.71566 | 0.597056 | 0.298528 | − | 0.954401i | \(-0.403504\pi\) | ||||
0.298528 | + | 0.954401i | \(0.403504\pi\) | |||||||
\(168\) | 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 | \(-0.339233\pi\) | ||||
0.483863 | + | 0.875144i | \(0.339233\pi\) | |||||||
\(180\) | 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 | \(-0.409550\pi\) | ||||
0.280347 | + | 0.959899i | \(0.409550\pi\) | |||||||
\(192\) | 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 | \(-0.776494\pi\) | ||||
−0.763447 | + | 0.645871i | \(0.776494\pi\) | |||||||
\(200\) | 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 | \(-0.374733\pi\) | ||||
0.383458 | + | 0.923558i | \(0.374733\pi\) | |||||||
\(212\) | 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 | \(-0.530583\pi\) | ||||
−0.0959327 | + | 0.995388i | \(0.530583\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 51.6848 | 3.44565 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −7.92238 | −0.525827 | −0.262913 | − | 0.964819i | \(-0.584683\pi\) | ||||
−0.262913 | + | 0.964819i | \(0.584683\pi\) | |||||||
\(228\) | 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 | \(-0.474494\pi\) | ||||
0.0800450 | + | 0.996791i | \(0.474494\pi\) | |||||||
\(240\) | 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 | \(-0.327953\pi\) | ||||
0.514566 | + | 0.857451i | \(0.327953\pi\) | |||||||
\(252\) | 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 | \(-0.509642\pi\) | ||||
−0.0302862 | + | 0.999541i | \(0.509642\pi\) | |||||||
\(264\) | 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 | \(-0.554655\pi\) | ||||
−0.170860 | + | 0.985295i | \(0.554655\pi\) | |||||||
\(272\) | 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 | \(-0.303322\pi\) | ||||
0.579311 | + | 0.815107i | \(0.303322\pi\) | |||||||
\(284\) | 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 | \(-0.217933\pi\) | ||||
0.774637 | + | 0.632407i | \(0.217933\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 23.0070 | 1.30882 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −29.2076 | −1.65621 | −0.828105 | − | 0.560573i | \(-0.810581\pi\) | ||||
−0.828105 | + | 0.560573i | \(0.810581\pi\) | |||||||
\(312\) | 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 | \(-0.424553\pi\) | ||||
0.234810 | + | 0.972041i | \(0.424553\pi\) | |||||||
\(332\) | 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 | \(-0.418542\pi\) | ||||
0.253123 | + | 0.967434i | \(0.418542\pi\) | |||||||
\(348\) | 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 | \(-0.761380\pi\) | ||||
−0.731929 | + | 0.681381i | \(0.761380\pi\) | |||||||
\(360\) | 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 | \(-0.906237\pi\) | ||||
−0.956929 | + | 0.290323i | \(0.906237\pi\) | |||||||
\(368\) | 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 | \(-0.592992\pi\) | ||||
−0.288005 | + | 0.957629i | \(0.592992\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 6.07766 | 0.311368 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 12.3247 | 0.629760 | 0.314880 | − | 0.949131i | \(-0.398036\pi\) | ||||
0.314880 | + | 0.949131i | \(0.398036\pi\) | |||||||
\(384\) | 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 | \(-0.896654\pi\) | ||||
−0.947756 | + | 0.318996i | \(0.896654\pi\) | |||||||
\(420\) | 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 | \(-0.625628\pi\) | ||||
−0.384505 | + | 0.923123i | \(0.625628\pi\) | |||||||
\(432\) | 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 | \(-0.275219\pi\) | ||||
0.648925 | + | 0.760852i | \(0.275219\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −46.9427 | −2.23537 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −16.9119 | −0.803507 | −0.401753 | − | 0.915748i | \(-0.631599\pi\) | ||||
−0.401753 | + | 0.915748i | \(0.631599\pi\) | |||||||
\(444\) | 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 | \(-0.807417\pi\) | ||||
−0.822493 | + | 0.568776i | \(0.807417\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −90.6066 | −4.20178 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −0.348500 | −0.0161267 | −0.00806334 | − | 0.999967i | \(-0.502567\pi\) | ||||
−0.00806334 | + | 0.999967i | \(0.502567\pi\) | |||||||
\(468\) | 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 | \(-0.367329\pi\) | ||||
0.404835 | + | 0.914390i | \(0.367329\pi\) | |||||||
\(480\) | 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 | \(-0.489550\pi\) | ||||
0.0328247 | + | 0.999461i | \(0.489550\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 25.0847 | 1.13437 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 2.15520 | 0.0972627 | 0.0486313 | − | 0.998817i | \(-0.484514\pi\) | ||||
0.0486313 | + | 0.998817i | \(0.484514\pi\) | |||||||
\(492\) | 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 | \(-0.668384\pi\) | ||||
−0.504666 | + | 0.863314i | \(0.668384\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 25.4156 | 1.13548 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −12.1442 | −0.541483 | −0.270742 | − | 0.962652i | \(-0.587269\pi\) | ||||
−0.270742 | + | 0.962652i | \(0.587269\pi\) | |||||||
\(504\) | 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 | \(-0.512410\pi\) | ||||
−0.0389782 | + | 0.999240i | \(0.512410\pi\) | |||||||
\(524\) | 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 | \(-0.330040\pi\) | ||||
0.508933 | + | 0.860806i | \(0.330040\pi\) | |||||||
\(548\) | 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 | \(-0.546334\pi\) | ||||
−0.145049 | + | 0.989424i | \(0.546334\pi\) | |||||||
\(564\) | 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 | \(-0.457739\pi\) | ||||
0.132376 | + | 0.991200i | \(0.457739\pi\) | |||||||
\(572\) | 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 | \(-0.248033\pi\) | ||||
0.711463 | + | 0.702724i | \(0.248033\pi\) | |||||||
\(588\) | 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 | \(-0.521697\pi\) | ||||
−0.0681099 | + | 0.997678i | \(0.521697\pi\) | |||||||
\(600\) | 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 | \(-0.797106\pi\) | ||||
−0.803639 | + | 0.595117i | \(0.797106\pi\) | |||||||
\(608\) | 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 | \(-0.504814\pi\) | ||||
−0.0151226 | + | 0.999886i | \(0.504814\pi\) | |||||||
\(620\) | 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 | \(-0.603914\pi\) | ||||
−0.320686 | + | 0.947185i | \(0.603914\pi\) | |||||||
\(632\) | 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 | \(-0.390180\pi\) | ||||
0.338206 | + | 0.941072i | \(0.390180\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −42.5754 | −1.67641 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −16.7145 | −0.657114 | −0.328557 | − | 0.944484i | \(-0.606562\pi\) | ||||
−0.328557 | + | 0.944484i | \(0.606562\pi\) | |||||||
\(648\) | 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 | \(-0.382156\pi\) | ||||
0.361819 | + | 0.932248i | \(0.382156\pi\) | |||||||
\(660\) | 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 | \(-0.627618\pi\) | ||||
−0.390268 | + | 0.920701i | \(0.627618\pi\) | |||||||
\(684\) | 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 | \(-0.518643\pi\) | ||||
−0.0585362 | + | 0.998285i | \(0.518643\pi\) | |||||||
\(692\) | 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 | \(-0.778179\pi\) | ||||
−0.766854 | + | 0.641822i | \(0.778179\pi\) | |||||||
\(720\) | 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 | \(-0.313563\pi\) | ||||
0.552790 | + | 0.833321i | \(0.313563\pi\) | |||||||
\(728\) | 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 | \(-0.682495\pi\) | ||||
−0.542428 | + | 0.840102i | \(0.682495\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −39.0688 | −1.43523 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −18.1362 | −0.665353 | −0.332677 | − | 0.943041i | \(-0.607952\pi\) | ||||
−0.332677 | + | 0.943041i | \(0.607952\pi\) | |||||||
\(744\) | 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 | \(-0.733721\pi\) | ||||
−0.670035 | + | 0.742329i | \(0.733721\pi\) | |||||||
\(752\) | 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 | \(-0.845314\pi\) | ||||
−0.884226 | + | 0.467059i | \(0.845314\pi\) | |||||||
\(788\) | 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 | \(-0.420243\pi\) | ||||
0.247951 | + | 0.968773i | \(0.420243\pi\) | |||||||
\(812\) | 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 | \(-0.744941\pi\) | ||||
−0.695779 | + | 0.718256i | \(0.744941\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 124.159 | 4.32266 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 48.2874 | 1.67912 | 0.839558 | − | 0.543270i | \(-0.182814\pi\) | ||||
0.839558 | + | 0.543270i | \(0.182814\pi\) | |||||||
\(828\) | 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 | \(-0.304998\pi\) | ||||
0.575010 | + | 0.818146i | \(0.304998\pi\) | |||||||
\(840\) | 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 | \(-0.414823\pi\) | ||||
0.264409 | + | 0.964411i | \(0.414823\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −41.8368 | −1.42580 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 8.22895 | 0.280117 | 0.140058 | − | 0.990143i | \(-0.455271\pi\) | ||||
0.140058 | + | 0.990143i | \(0.455271\pi\) | |||||||
\(864\) | 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 | \(-0.646028\pi\) | ||||
−0.442837 | + | 0.896602i | \(0.646028\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 46.4364 | 1.56094 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 52.0204 | 1.74667 | 0.873337 | − | 0.487116i | \(-0.161951\pi\) | ||||
0.873337 | + | 0.487116i | \(0.161951\pi\) | |||||||
\(888\) | 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 | \(-0.779050\pi\) | ||||
−0.768608 | + | 0.639720i | \(0.779050\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 154.708 | 5.13135 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −34.5338 | −1.14416 | −0.572079 | − | 0.820199i | \(-0.693863\pi\) | ||||
−0.572079 | + | 0.820199i | \(0.693863\pi\) | |||||||
\(912\) | 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 | \(-0.699029\pi\) | ||||
−0.585315 | + | 0.810806i | \(0.699029\pi\) | |||||||
\(920\) | 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 | \(-0.412993\pi\) | ||||
0.269949 | + | 0.962875i | \(0.412993\pi\) | |||||||
\(948\) | 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 | \(-0.718996\pi\) | ||||
−0.634990 | + | 0.772520i | \(0.718996\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −82.8756 | −2.66235 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −10.5070 | −0.337185 | −0.168592 | − | 0.985686i | \(-0.553922\pi\) | ||||
−0.168592 | + | 0.985686i | \(0.553922\pi\) | |||||||
\(972\) | 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 | \(-0.0573152\pi\) | ||||
0.983833 | + | 0.179089i | \(0.0573152\pi\) | |||||||
\(984\) | 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 | \(-0.817779\pi\) | ||||
−0.840569 | + | 0.541705i | \(0.817779\pi\) | |||||||
\(992\) | 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.p.1.13 | yes | 13 | |
4.3 | odd | 2 | 6016.2.a.n.1.1 | yes | 13 | ||
8.3 | odd | 2 | 6016.2.a.o.1.13 | yes | 13 | ||
8.5 | even | 2 | 6016.2.a.m.1.1 | ✓ | 13 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
6016.2.a.m.1.1 | ✓ | 13 | 8.5 | even | 2 | ||
6016.2.a.n.1.1 | yes | 13 | 4.3 | odd | 2 | ||
6016.2.a.o.1.13 | yes | 13 | 8.3 | odd | 2 | ||
6016.2.a.p.1.13 | yes | 13 | 1.1 | even | 1 | trivial |