Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [6039,2,Mod(1,6039)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(6039, 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("6039.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 6039 = 3^{2} \cdot 11 \cdot 61 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 6039.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: | \(48.2216577807\) |
Analytic rank: | \(0\) |
Dimension: | \(25\) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.17 | ||
Character | \(\chi\) | \(=\) | 6039.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 1.56609 | 1.10739 | 0.553696 | − | 0.832719i | \(-0.313217\pi\) | ||||
0.553696 | + | 0.832719i | \(0.313217\pi\) | |||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 0.452630 | 0.226315 | ||||||||
\(5\) | 1.36136 | 0.608819 | 0.304409 | − | 0.952541i | \(-0.401541\pi\) | ||||
0.304409 | + | 0.952541i | \(0.401541\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 3.35990 | 1.26992 | 0.634962 | − | 0.772543i | \(-0.281016\pi\) | ||||
0.634962 | + | 0.772543i | \(0.281016\pi\) | |||||||
\(8\) | −2.42332 | −0.856772 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 2.13201 | 0.674200 | ||||||||
\(11\) | 1.00000 | 0.301511 | ||||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 6.49192 | 1.80053 | 0.900267 | − | 0.435337i | \(-0.143371\pi\) | ||||
0.900267 | + | 0.435337i | \(0.143371\pi\) | |||||||
\(14\) | 5.26190 | 1.40630 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −4.70039 | −1.17510 | ||||||||
\(17\) | 3.12895 | 0.758883 | 0.379442 | − | 0.925216i | \(-0.376116\pi\) | ||||
0.379442 | + | 0.925216i | \(0.376116\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −0.766546 | −0.175858 | −0.0879289 | − | 0.996127i | \(-0.528025\pi\) | ||||
−0.0879289 | + | 0.996127i | \(0.528025\pi\) | |||||||
\(20\) | 0.616192 | 0.137785 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 1.56609 | 0.333891 | ||||||||
\(23\) | −0.696071 | −0.145141 | −0.0725704 | − | 0.997363i | \(-0.523120\pi\) | ||||
−0.0725704 | + | 0.997363i | \(0.523120\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −3.14670 | −0.629340 | ||||||||
\(26\) | 10.1669 | 1.99390 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 1.52079 | 0.287403 | ||||||||
\(29\) | −1.69575 | −0.314893 | −0.157447 | − | 0.987527i | \(-0.550326\pi\) | ||||
−0.157447 | + | 0.987527i | \(0.550326\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −0.344190 | −0.0618184 | −0.0309092 | − | 0.999522i | \(-0.509840\pi\) | ||||
−0.0309092 | + | 0.999522i | \(0.509840\pi\) | |||||||
\(32\) | −2.51458 | −0.444520 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 4.90022 | 0.840380 | ||||||||
\(35\) | 4.57404 | 0.773153 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 5.23948 | 0.861366 | 0.430683 | − | 0.902503i | \(-0.358273\pi\) | ||||
0.430683 | + | 0.902503i | \(0.358273\pi\) | |||||||
\(38\) | −1.20048 | −0.194743 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | −3.29901 | −0.521619 | ||||||||
\(41\) | 8.27551 | 1.29242 | 0.646208 | − | 0.763161i | \(-0.276354\pi\) | ||||
0.646208 | + | 0.763161i | \(0.276354\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −1.26225 | −0.192491 | −0.0962456 | − | 0.995358i | \(-0.530683\pi\) | ||||
−0.0962456 | + | 0.995358i | \(0.530683\pi\) | |||||||
\(44\) | 0.452630 | 0.0682365 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −1.09011 | −0.160728 | ||||||||
\(47\) | −2.80853 | −0.409666 | −0.204833 | − | 0.978797i | \(-0.565665\pi\) | ||||
−0.204833 | + | 0.978797i | \(0.565665\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 4.28895 | 0.612707 | ||||||||
\(50\) | −4.92801 | −0.696925 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 2.93844 | 0.407488 | ||||||||
\(53\) | 13.4721 | 1.85054 | 0.925270 | − | 0.379309i | \(-0.123838\pi\) | ||||
0.925270 | + | 0.379309i | \(0.123838\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 1.36136 | 0.183566 | ||||||||
\(56\) | −8.14211 | −1.08804 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | −2.65570 | −0.348710 | ||||||||
\(59\) | 7.04704 | 0.917446 | 0.458723 | − | 0.888579i | \(-0.348307\pi\) | ||||
0.458723 | + | 0.888579i | \(0.348307\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −1.00000 | −0.128037 | ||||||||
\(62\) | −0.539032 | −0.0684571 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 5.46272 | 0.682840 | ||||||||
\(65\) | 8.83784 | 1.09620 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −11.9010 | −1.45393 | −0.726967 | − | 0.686672i | \(-0.759071\pi\) | ||||
−0.726967 | + | 0.686672i | \(0.759071\pi\) | |||||||
\(68\) | 1.41626 | 0.171747 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 7.16334 | 0.856183 | ||||||||
\(71\) | 1.74910 | 0.207580 | 0.103790 | − | 0.994599i | \(-0.466903\pi\) | ||||
0.103790 | + | 0.994599i | \(0.466903\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −9.19391 | −1.07607 | −0.538033 | − | 0.842924i | \(-0.680832\pi\) | ||||
−0.538033 | + | 0.842924i | \(0.680832\pi\) | |||||||
\(74\) | 8.20549 | 0.953868 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −0.346962 | −0.0397993 | ||||||||
\(77\) | 3.35990 | 0.382896 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −11.9855 | −1.34847 | −0.674236 | − | 0.738516i | \(-0.735527\pi\) | ||||
−0.674236 | + | 0.738516i | \(0.735527\pi\) | |||||||
\(80\) | −6.39892 | −0.715421 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 12.9602 | 1.43121 | ||||||||
\(83\) | −1.29768 | −0.142439 | −0.0712196 | − | 0.997461i | \(-0.522689\pi\) | ||||
−0.0712196 | + | 0.997461i | \(0.522689\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 4.25963 | 0.462022 | ||||||||
\(86\) | −1.97679 | −0.213163 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | −2.42332 | −0.258326 | ||||||||
\(89\) | −1.41865 | −0.150377 | −0.0751885 | − | 0.997169i | \(-0.523956\pi\) | ||||
−0.0751885 | + | 0.997169i | \(0.523956\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 21.8122 | 2.28654 | ||||||||
\(92\) | −0.315063 | −0.0328476 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | −4.39840 | −0.453660 | ||||||||
\(95\) | −1.04355 | −0.107065 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −5.21258 | −0.529257 | −0.264628 | − | 0.964350i | \(-0.585249\pi\) | ||||
−0.264628 | + | 0.964350i | \(0.585249\pi\) | |||||||
\(98\) | 6.71687 | 0.678506 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | −1.42429 | −0.142429 | ||||||||
\(101\) | 11.6285 | 1.15708 | 0.578539 | − | 0.815655i | \(-0.303623\pi\) | ||||
0.578539 | + | 0.815655i | \(0.303623\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −4.41364 | −0.434889 | −0.217445 | − | 0.976073i | \(-0.569772\pi\) | ||||
−0.217445 | + | 0.976073i | \(0.569772\pi\) | |||||||
\(104\) | −15.7320 | −1.54265 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 21.0985 | 2.04927 | ||||||||
\(107\) | 4.86398 | 0.470219 | 0.235110 | − | 0.971969i | \(-0.424455\pi\) | ||||
0.235110 | + | 0.971969i | \(0.424455\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 5.03958 | 0.482704 | 0.241352 | − | 0.970438i | \(-0.422409\pi\) | ||||
0.241352 | + | 0.970438i | \(0.422409\pi\) | |||||||
\(110\) | 2.13201 | 0.203279 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | −15.7928 | −1.49228 | ||||||||
\(113\) | −5.27857 | −0.496566 | −0.248283 | − | 0.968688i | \(-0.579866\pi\) | ||||
−0.248283 | + | 0.968688i | \(0.579866\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −0.947603 | −0.0883645 | ||||||||
\(116\) | −0.767549 | −0.0712651 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 11.0363 | 1.01597 | ||||||||
\(119\) | 10.5130 | 0.963724 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 1.00000 | 0.0909091 | ||||||||
\(122\) | −1.56609 | −0.141787 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | −0.155791 | −0.0139904 | ||||||||
\(125\) | −11.0906 | −0.991972 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −7.24882 | −0.643229 | −0.321615 | − | 0.946871i | \(-0.604226\pi\) | ||||
−0.321615 | + | 0.946871i | \(0.604226\pi\) | |||||||
\(128\) | 13.5843 | 1.20069 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 13.8408 | 1.21392 | ||||||||
\(131\) | −0.0866722 | −0.00757259 | −0.00378629 | − | 0.999993i | \(-0.501205\pi\) | ||||
−0.00378629 | + | 0.999993i | \(0.501205\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −2.57552 | −0.223326 | ||||||||
\(134\) | −18.6380 | −1.61007 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −7.58245 | −0.650190 | ||||||||
\(137\) | −19.1955 | −1.63999 | −0.819993 | − | 0.572374i | \(-0.806023\pi\) | ||||
−0.819993 | + | 0.572374i | \(0.806023\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 14.1692 | 1.20182 | 0.600910 | − | 0.799317i | \(-0.294805\pi\) | ||||
0.600910 | + | 0.799317i | \(0.294805\pi\) | |||||||
\(140\) | 2.07035 | 0.174976 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 2.73925 | 0.229873 | ||||||||
\(143\) | 6.49192 | 0.542882 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −2.30853 | −0.191713 | ||||||||
\(146\) | −14.3985 | −1.19163 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 2.37155 | 0.194940 | ||||||||
\(149\) | 1.84097 | 0.150818 | 0.0754090 | − | 0.997153i | \(-0.475974\pi\) | ||||
0.0754090 | + | 0.997153i | \(0.475974\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 1.00745 | 0.0819850 | 0.0409925 | − | 0.999159i | \(-0.486948\pi\) | ||||
0.0409925 | + | 0.999159i | \(0.486948\pi\) | |||||||
\(152\) | 1.85758 | 0.150670 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 5.26190 | 0.424016 | ||||||||
\(155\) | −0.468567 | −0.0376362 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 22.8792 | 1.82596 | 0.912979 | − | 0.408007i | \(-0.133776\pi\) | ||||
0.912979 | + | 0.408007i | \(0.133776\pi\) | |||||||
\(158\) | −18.7703 | −1.49329 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | −3.42325 | −0.270632 | ||||||||
\(161\) | −2.33873 | −0.184318 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 7.76465 | 0.608174 | 0.304087 | − | 0.952644i | \(-0.401649\pi\) | ||||
0.304087 | + | 0.952644i | \(0.401649\pi\) | |||||||
\(164\) | 3.74574 | 0.292493 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −2.03228 | −0.157736 | ||||||||
\(167\) | −9.83034 | −0.760695 | −0.380347 | − | 0.924844i | \(-0.624196\pi\) | ||||
−0.380347 | + | 0.924844i | \(0.624196\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 29.1450 | 2.24193 | ||||||||
\(170\) | 6.67096 | 0.511639 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | −0.571332 | −0.0435637 | ||||||||
\(173\) | 15.9889 | 1.21561 | 0.607807 | − | 0.794085i | \(-0.292049\pi\) | ||||
0.607807 | + | 0.794085i | \(0.292049\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −10.5726 | −0.799214 | ||||||||
\(176\) | −4.70039 | −0.354305 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | −2.22174 | −0.166526 | ||||||||
\(179\) | 15.4714 | 1.15639 | 0.578194 | − | 0.815899i | \(-0.303757\pi\) | ||||
0.578194 | + | 0.815899i | \(0.303757\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 4.75922 | 0.353750 | 0.176875 | − | 0.984233i | \(-0.443401\pi\) | ||||
0.176875 | + | 0.984233i | \(0.443401\pi\) | |||||||
\(182\) | 34.1598 | 2.53210 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 1.68680 | 0.124353 | ||||||||
\(185\) | 7.13282 | 0.524415 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 3.12895 | 0.228812 | ||||||||
\(188\) | −1.27122 | −0.0927135 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | −1.63428 | −0.118563 | ||||||||
\(191\) | −20.8442 | −1.50823 | −0.754116 | − | 0.656742i | \(-0.771934\pi\) | ||||
−0.754116 | + | 0.656742i | \(0.771934\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −10.9933 | −0.791316 | −0.395658 | − | 0.918398i | \(-0.629483\pi\) | ||||
−0.395658 | + | 0.918398i | \(0.629483\pi\) | |||||||
\(194\) | −8.16335 | −0.586094 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 1.94131 | 0.138665 | ||||||||
\(197\) | 9.78826 | 0.697385 | 0.348692 | − | 0.937237i | \(-0.386626\pi\) | ||||
0.348692 | + | 0.937237i | \(0.386626\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −11.5773 | −0.820695 | −0.410347 | − | 0.911929i | \(-0.634593\pi\) | ||||
−0.410347 | + | 0.911929i | \(0.634593\pi\) | |||||||
\(200\) | 7.62545 | 0.539201 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 18.2112 | 1.28134 | ||||||||
\(203\) | −5.69756 | −0.399891 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 11.2659 | 0.786847 | ||||||||
\(206\) | −6.91215 | −0.481592 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | −30.5145 | −2.11580 | ||||||||
\(209\) | −0.766546 | −0.0530231 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −11.0359 | −0.759746 | −0.379873 | − | 0.925039i | \(-0.624032\pi\) | ||||
−0.379873 | + | 0.925039i | \(0.624032\pi\) | |||||||
\(212\) | 6.09789 | 0.418805 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 7.61742 | 0.520716 | ||||||||
\(215\) | −1.71838 | −0.117192 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −1.15645 | −0.0785046 | ||||||||
\(218\) | 7.89242 | 0.534542 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0.616192 | 0.0415437 | ||||||||
\(221\) | 20.3129 | 1.36640 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 7.01627 | 0.469844 | 0.234922 | − | 0.972014i | \(-0.424517\pi\) | ||||
0.234922 | + | 0.972014i | \(0.424517\pi\) | |||||||
\(224\) | −8.44875 | −0.564506 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −8.26670 | −0.549893 | ||||||||
\(227\) | 1.47103 | 0.0976358 | 0.0488179 | − | 0.998808i | \(-0.484455\pi\) | ||||
0.0488179 | + | 0.998808i | \(0.484455\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 7.81248 | 0.516263 | 0.258132 | − | 0.966110i | \(-0.416893\pi\) | ||||
0.258132 | + | 0.966110i | \(0.416893\pi\) | |||||||
\(230\) | −1.48403 | −0.0978540 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 4.10935 | 0.269792 | ||||||||
\(233\) | −6.56622 | −0.430167 | −0.215084 | − | 0.976596i | \(-0.569002\pi\) | ||||
−0.215084 | + | 0.976596i | \(0.569002\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −3.82342 | −0.249412 | ||||||||
\(236\) | 3.18970 | 0.207632 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 16.4643 | 1.06722 | ||||||||
\(239\) | −11.6820 | −0.755647 | −0.377823 | − | 0.925878i | \(-0.623327\pi\) | ||||
−0.377823 | + | 0.925878i | \(0.623327\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 23.4303 | 1.50928 | 0.754638 | − | 0.656141i | \(-0.227813\pi\) | ||||
0.754638 | + | 0.656141i | \(0.227813\pi\) | |||||||
\(242\) | 1.56609 | 0.100672 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | −0.452630 | −0.0289767 | ||||||||
\(245\) | 5.83880 | 0.373027 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −4.97636 | −0.316638 | ||||||||
\(248\) | 0.834082 | 0.0529642 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | −17.3688 | −1.09850 | ||||||||
\(251\) | 17.2071 | 1.08610 | 0.543051 | − | 0.839699i | \(-0.317269\pi\) | ||||
0.543051 | + | 0.839699i | \(0.317269\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −0.696071 | −0.0437616 | ||||||||
\(254\) | −11.3523 | −0.712306 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 10.3487 | 0.646794 | ||||||||
\(257\) | 21.5802 | 1.34614 | 0.673068 | − | 0.739581i | \(-0.264976\pi\) | ||||
0.673068 | + | 0.739581i | \(0.264976\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 17.6041 | 1.09387 | ||||||||
\(260\) | 4.00027 | 0.248086 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | −0.135736 | −0.00838582 | ||||||||
\(263\) | 11.4225 | 0.704339 | 0.352169 | − | 0.935936i | \(-0.385444\pi\) | ||||
0.352169 | + | 0.935936i | \(0.385444\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 18.3404 | 1.12664 | ||||||||
\(266\) | −4.03349 | −0.247309 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | −5.38673 | −0.329047 | ||||||||
\(269\) | 19.5550 | 1.19229 | 0.596144 | − | 0.802877i | \(-0.296699\pi\) | ||||
0.596144 | + | 0.802877i | \(0.296699\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 22.7236 | 1.38036 | 0.690179 | − | 0.723639i | \(-0.257532\pi\) | ||||
0.690179 | + | 0.723639i | \(0.257532\pi\) | |||||||
\(272\) | −14.7073 | −0.891761 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −30.0619 | −1.81611 | ||||||||
\(275\) | −3.14670 | −0.189753 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −22.6998 | −1.36390 | −0.681950 | − | 0.731398i | \(-0.738868\pi\) | ||||
−0.681950 | + | 0.731398i | \(0.738868\pi\) | |||||||
\(278\) | 22.1903 | 1.33088 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | −11.0843 | −0.662416 | ||||||||
\(281\) | −14.5156 | −0.865929 | −0.432965 | − | 0.901411i | \(-0.642532\pi\) | ||||
−0.432965 | + | 0.901411i | \(0.642532\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 8.44305 | 0.501888 | 0.250944 | − | 0.968002i | \(-0.419259\pi\) | ||||
0.250944 | + | 0.968002i | \(0.419259\pi\) | |||||||
\(284\) | 0.791697 | 0.0469785 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 10.1669 | 0.601182 | ||||||||
\(287\) | 27.8049 | 1.64127 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −7.20964 | −0.424097 | ||||||||
\(290\) | −3.61536 | −0.212301 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | −4.16144 | −0.243530 | ||||||||
\(293\) | 33.7697 | 1.97284 | 0.986422 | − | 0.164230i | \(-0.0525140\pi\) | ||||
0.986422 | + | 0.164230i | \(0.0525140\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 9.59355 | 0.558558 | ||||||||
\(296\) | −12.6969 | −0.737994 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 2.88312 | 0.167015 | ||||||||
\(299\) | −4.51884 | −0.261331 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −4.24104 | −0.244449 | ||||||||
\(302\) | 1.57775 | 0.0907895 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 3.60306 | 0.206650 | ||||||||
\(305\) | −1.36136 | −0.0779512 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −28.9927 | −1.65470 | −0.827352 | − | 0.561684i | \(-0.810154\pi\) | ||||
−0.827352 | + | 0.561684i | \(0.810154\pi\) | |||||||
\(308\) | 1.52079 | 0.0866552 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | −0.733816 | −0.0416780 | ||||||||
\(311\) | −11.0448 | −0.626293 | −0.313146 | − | 0.949705i | \(-0.601383\pi\) | ||||
−0.313146 | + | 0.949705i | \(0.601383\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 5.07426 | 0.286814 | 0.143407 | − | 0.989664i | \(-0.454194\pi\) | ||||
0.143407 | + | 0.989664i | \(0.454194\pi\) | |||||||
\(314\) | 35.8308 | 2.02205 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −5.42499 | −0.305179 | ||||||||
\(317\) | 10.8321 | 0.608391 | 0.304195 | − | 0.952610i | \(-0.401612\pi\) | ||||
0.304195 | + | 0.952610i | \(0.401612\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −1.69575 | −0.0949439 | ||||||||
\(320\) | 7.43672 | 0.415725 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | −3.66266 | −0.204112 | ||||||||
\(323\) | −2.39849 | −0.133455 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −20.4281 | −1.13315 | ||||||||
\(326\) | 12.1601 | 0.673487 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | −20.0542 | −1.10731 | ||||||||
\(329\) | −9.43638 | −0.520244 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 20.2052 | 1.11058 | 0.555289 | − | 0.831657i | \(-0.312608\pi\) | ||||
0.555289 | + | 0.831657i | \(0.312608\pi\) | |||||||
\(332\) | −0.587370 | −0.0322361 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | −15.3952 | −0.842386 | ||||||||
\(335\) | −16.2015 | −0.885182 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −12.1303 | −0.660782 | −0.330391 | − | 0.943844i | \(-0.607181\pi\) | ||||
−0.330391 | + | 0.943844i | \(0.607181\pi\) | |||||||
\(338\) | 45.6437 | 2.48269 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 1.92804 | 0.104563 | ||||||||
\(341\) | −0.344190 | −0.0186389 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −9.10888 | −0.491833 | ||||||||
\(344\) | 3.05883 | 0.164921 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 25.0400 | 1.34616 | ||||||||
\(347\) | −18.8939 | −1.01428 | −0.507139 | − | 0.861864i | \(-0.669297\pi\) | ||||
−0.507139 | + | 0.861864i | \(0.669297\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −33.9066 | −1.81498 | −0.907490 | − | 0.420075i | \(-0.862004\pi\) | ||||
−0.907490 | + | 0.420075i | \(0.862004\pi\) | |||||||
\(350\) | −16.5576 | −0.885042 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | −2.51458 | −0.134028 | ||||||||
\(353\) | 17.7095 | 0.942579 | 0.471290 | − | 0.881978i | \(-0.343789\pi\) | ||||
0.471290 | + | 0.881978i | \(0.343789\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 2.38116 | 0.126379 | ||||||||
\(356\) | −0.642125 | −0.0340326 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 24.2296 | 1.28057 | ||||||||
\(359\) | 11.8177 | 0.623713 | 0.311857 | − | 0.950129i | \(-0.399049\pi\) | ||||
0.311857 | + | 0.950129i | \(0.399049\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −18.4124 | −0.969074 | ||||||||
\(362\) | 7.45336 | 0.391740 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 9.87287 | 0.517479 | ||||||||
\(365\) | −12.5162 | −0.655129 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 7.22914 | 0.377358 | 0.188679 | − | 0.982039i | \(-0.439579\pi\) | ||||
0.188679 | + | 0.982039i | \(0.439579\pi\) | |||||||
\(368\) | 3.27180 | 0.170555 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 11.1706 | 0.580733 | ||||||||
\(371\) | 45.2651 | 2.35005 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −18.2438 | −0.944631 | −0.472315 | − | 0.881430i | \(-0.656582\pi\) | ||||
−0.472315 | + | 0.881430i | \(0.656582\pi\) | |||||||
\(374\) | 4.90022 | 0.253384 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 6.80595 | 0.350990 | ||||||||
\(377\) | −11.0087 | −0.566977 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −30.8681 | −1.58559 | −0.792794 | − | 0.609490i | \(-0.791374\pi\) | ||||
−0.792794 | + | 0.609490i | \(0.791374\pi\) | |||||||
\(380\) | −0.472340 | −0.0242305 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | −32.6438 | −1.67020 | ||||||||
\(383\) | 31.8273 | 1.62630 | 0.813148 | − | 0.582056i | \(-0.197752\pi\) | ||||
0.813148 | + | 0.582056i | \(0.197752\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 4.57404 | 0.233114 | ||||||||
\(386\) | −17.2165 | −0.876296 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | −2.35937 | −0.119779 | ||||||||
\(389\) | −23.8104 | −1.20724 | −0.603618 | − | 0.797273i | \(-0.706275\pi\) | ||||
−0.603618 | + | 0.797273i | \(0.706275\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −2.17798 | −0.110145 | ||||||||
\(392\) | −10.3935 | −0.524950 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 15.3293 | 0.772278 | ||||||||
\(395\) | −16.3166 | −0.820975 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 0.237691 | 0.0119294 | 0.00596470 | − | 0.999982i | \(-0.498101\pi\) | ||||
0.00596470 | + | 0.999982i | \(0.498101\pi\) | |||||||
\(398\) | −18.1311 | −0.908830 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 14.7907 | 0.739535 | ||||||||
\(401\) | −7.74372 | −0.386703 | −0.193352 | − | 0.981130i | \(-0.561936\pi\) | ||||
−0.193352 | + | 0.981130i | \(0.561936\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −2.23445 | −0.111306 | ||||||||
\(404\) | 5.26340 | 0.261864 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −8.92288 | −0.442835 | ||||||||
\(407\) | 5.23948 | 0.259711 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −26.4977 | −1.31023 | −0.655114 | − | 0.755530i | \(-0.727380\pi\) | ||||
−0.655114 | + | 0.755530i | \(0.727380\pi\) | |||||||
\(410\) | 17.6434 | 0.871348 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | −1.99775 | −0.0984219 | ||||||||
\(413\) | 23.6774 | 1.16509 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −1.76661 | −0.0867196 | ||||||||
\(416\) | −16.3245 | −0.800373 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | −1.20048 | −0.0587173 | ||||||||
\(419\) | 4.24640 | 0.207450 | 0.103725 | − | 0.994606i | \(-0.466924\pi\) | ||||
0.103725 | + | 0.994606i | \(0.466924\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −4.39859 | −0.214374 | −0.107187 | − | 0.994239i | \(-0.534184\pi\) | ||||
−0.107187 | + | 0.994239i | \(0.534184\pi\) | |||||||
\(422\) | −17.2832 | −0.841335 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | −32.6473 | −1.58549 | ||||||||
\(425\) | −9.84588 | −0.477595 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −3.35990 | −0.162597 | ||||||||
\(428\) | 2.20159 | 0.106418 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | −2.69113 | −0.129778 | ||||||||
\(431\) | −20.3462 | −0.980043 | −0.490022 | − | 0.871710i | \(-0.663011\pi\) | ||||
−0.490022 | + | 0.871710i | \(0.663011\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −6.50313 | −0.312521 | −0.156260 | − | 0.987716i | \(-0.549944\pi\) | ||||
−0.156260 | + | 0.987716i | \(0.549944\pi\) | |||||||
\(434\) | −1.81109 | −0.0869353 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 2.28107 | 0.109243 | ||||||||
\(437\) | 0.533571 | 0.0255241 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 8.54133 | 0.407655 | 0.203828 | − | 0.979007i | \(-0.434662\pi\) | ||||
0.203828 | + | 0.979007i | \(0.434662\pi\) | |||||||
\(440\) | −3.29901 | −0.157274 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 31.8118 | 1.51313 | ||||||||
\(443\) | −7.02111 | −0.333583 | −0.166791 | − | 0.985992i | \(-0.553341\pi\) | ||||
−0.166791 | + | 0.985992i | \(0.553341\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −1.93130 | −0.0915523 | ||||||||
\(446\) | 10.9881 | 0.520301 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 18.3542 | 0.867154 | ||||||||
\(449\) | −6.70573 | −0.316463 | −0.158232 | − | 0.987402i | \(-0.550579\pi\) | ||||
−0.158232 | + | 0.987402i | \(0.550579\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 8.27551 | 0.389678 | ||||||||
\(452\) | −2.38924 | −0.112380 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 2.30376 | 0.108121 | ||||||||
\(455\) | 29.6943 | 1.39209 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 3.04900 | 0.142626 | 0.0713132 | − | 0.997454i | \(-0.477281\pi\) | ||||
0.0713132 | + | 0.997454i | \(0.477281\pi\) | |||||||
\(458\) | 12.2350 | 0.571705 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | −0.428914 | −0.0199982 | ||||||||
\(461\) | −25.0006 | −1.16439 | −0.582197 | − | 0.813048i | \(-0.697807\pi\) | ||||
−0.582197 | + | 0.813048i | \(0.697807\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 1.57111 | 0.0730158 | 0.0365079 | − | 0.999333i | \(-0.488377\pi\) | ||||
0.0365079 | + | 0.999333i | \(0.488377\pi\) | |||||||
\(464\) | 7.97069 | 0.370030 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −10.2833 | −0.476363 | ||||||||
\(467\) | −4.67308 | −0.216245 | −0.108122 | − | 0.994138i | \(-0.534484\pi\) | ||||
−0.108122 | + | 0.994138i | \(0.534484\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −39.9861 | −1.84639 | ||||||||
\(470\) | −5.98780 | −0.276197 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | −17.0772 | −0.786042 | ||||||||
\(473\) | −1.26225 | −0.0580383 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 2.41209 | 0.110674 | ||||||||
\(476\) | 4.75849 | 0.218105 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | −18.2951 | −0.836796 | ||||||||
\(479\) | 22.7806 | 1.04087 | 0.520437 | − | 0.853900i | \(-0.325769\pi\) | ||||
0.520437 | + | 0.853900i | \(0.325769\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 34.0143 | 1.55092 | ||||||||
\(482\) | 36.6938 | 1.67136 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0.452630 | 0.0205741 | ||||||||
\(485\) | −7.09619 | −0.322221 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −32.7483 | −1.48397 | −0.741983 | − | 0.670419i | \(-0.766114\pi\) | ||||
−0.741983 | + | 0.670419i | \(0.766114\pi\) | |||||||
\(488\) | 2.42332 | 0.109698 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 9.14407 | 0.413087 | ||||||||
\(491\) | −39.7785 | −1.79518 | −0.897590 | − | 0.440831i | \(-0.854684\pi\) | ||||
−0.897590 | + | 0.440831i | \(0.854684\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −5.30593 | −0.238967 | ||||||||
\(494\) | −7.79341 | −0.350642 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 1.61783 | 0.0726425 | ||||||||
\(497\) | 5.87682 | 0.263611 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 0.606793 | 0.0271638 | 0.0135819 | − | 0.999908i | \(-0.495677\pi\) | ||||
0.0135819 | + | 0.999908i | \(0.495677\pi\) | |||||||
\(500\) | −5.01993 | −0.224498 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 26.9478 | 1.20274 | ||||||||
\(503\) | 17.8924 | 0.797783 | 0.398891 | − | 0.916998i | \(-0.369395\pi\) | ||||
0.398891 | + | 0.916998i | \(0.369395\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 15.8306 | 0.704450 | ||||||||
\(506\) | −1.09011 | −0.0484612 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | −3.28104 | −0.145572 | ||||||||
\(509\) | −34.3179 | −1.52112 | −0.760558 | − | 0.649270i | \(-0.775074\pi\) | ||||
−0.760558 | + | 0.649270i | \(0.775074\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −30.8906 | −1.36652 | ||||||||
\(512\) | −10.9615 | −0.484436 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 33.7965 | 1.49070 | ||||||||
\(515\) | −6.00855 | −0.264769 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −2.80853 | −0.123519 | ||||||||
\(518\) | 27.5696 | 1.21134 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | −21.4169 | −0.939193 | ||||||||
\(521\) | −14.6255 | −0.640756 | −0.320378 | − | 0.947290i | \(-0.603810\pi\) | ||||
−0.320378 | + | 0.947290i | \(0.603810\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −13.0719 | −0.571593 | −0.285797 | − | 0.958290i | \(-0.592258\pi\) | ||||
−0.285797 | + | 0.958290i | \(0.592258\pi\) | |||||||
\(524\) | −0.0392305 | −0.00171379 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 17.8886 | 0.779978 | ||||||||
\(527\) | −1.07696 | −0.0469129 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −22.5155 | −0.978934 | ||||||||
\(530\) | 28.7227 | 1.24763 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | −1.16576 | −0.0505420 | ||||||||
\(533\) | 53.7239 | 2.32704 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 6.62163 | 0.286278 | ||||||||
\(536\) | 28.8398 | 1.24569 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 30.6248 | 1.32033 | ||||||||
\(539\) | 4.28895 | 0.184738 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −29.1984 | −1.25534 | −0.627669 | − | 0.778480i | \(-0.715991\pi\) | ||||
−0.627669 | + | 0.778480i | \(0.715991\pi\) | |||||||
\(542\) | 35.5871 | 1.52860 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | −7.86802 | −0.337338 | ||||||||
\(545\) | 6.86068 | 0.293879 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −34.5379 | −1.47673 | −0.738366 | − | 0.674400i | \(-0.764402\pi\) | ||||
−0.738366 | + | 0.674400i | \(0.764402\pi\) | |||||||
\(548\) | −8.68848 | −0.371153 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | −4.92801 | −0.210131 | ||||||||
\(551\) | 1.29987 | 0.0553764 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −40.2700 | −1.71246 | ||||||||
\(554\) | −35.5499 | −1.51037 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 6.41342 | 0.271990 | ||||||||
\(557\) | −33.0302 | −1.39953 | −0.699767 | − | 0.714371i | \(-0.746713\pi\) | ||||
−0.699767 | + | 0.714371i | \(0.746713\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −8.19442 | −0.346587 | ||||||||
\(560\) | −21.4997 | −0.908530 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | −22.7327 | −0.958922 | ||||||||
\(563\) | −20.8159 | −0.877285 | −0.438642 | − | 0.898662i | \(-0.644541\pi\) | ||||
−0.438642 | + | 0.898662i | \(0.644541\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −7.18603 | −0.302319 | ||||||||
\(566\) | 13.2226 | 0.555786 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −4.23863 | −0.177849 | ||||||||
\(569\) | −5.73465 | −0.240409 | −0.120204 | − | 0.992749i | \(-0.538355\pi\) | ||||
−0.120204 | + | 0.992749i | \(0.538355\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 3.24657 | 0.135865 | 0.0679323 | − | 0.997690i | \(-0.478360\pi\) | ||||
0.0679323 | + | 0.997690i | \(0.478360\pi\) | |||||||
\(572\) | 2.93844 | 0.122862 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 43.5449 | 1.81753 | ||||||||
\(575\) | 2.19033 | 0.0913429 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 21.8389 | 0.909165 | 0.454583 | − | 0.890705i | \(-0.349788\pi\) | ||||
0.454583 | + | 0.890705i | \(0.349788\pi\) | |||||||
\(578\) | −11.2909 | −0.469641 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | −1.04491 | −0.0433875 | ||||||||
\(581\) | −4.36009 | −0.180887 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 13.4721 | 0.557959 | ||||||||
\(584\) | 22.2797 | 0.921943 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 52.8862 | 2.18471 | ||||||||
\(587\) | 5.80443 | 0.239574 | 0.119787 | − | 0.992800i | \(-0.461779\pi\) | ||||
0.119787 | + | 0.992800i | \(0.461779\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 0.263838 | 0.0108712 | ||||||||
\(590\) | 15.0243 | 0.618542 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | −24.6276 | −1.01219 | ||||||||
\(593\) | −27.9671 | −1.14847 | −0.574235 | − | 0.818690i | \(-0.694701\pi\) | ||||
−0.574235 | + | 0.818690i | \(0.694701\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 14.3120 | 0.586733 | ||||||||
\(596\) | 0.833278 | 0.0341324 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | −7.07690 | −0.289396 | ||||||||
\(599\) | 1.61130 | 0.0658358 | 0.0329179 | − | 0.999458i | \(-0.489520\pi\) | ||||
0.0329179 | + | 0.999458i | \(0.489520\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −15.5337 | −0.633632 | −0.316816 | − | 0.948487i | \(-0.602614\pi\) | ||||
−0.316816 | + | 0.948487i | \(0.602614\pi\) | |||||||
\(602\) | −6.64183 | −0.270701 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 0.456002 | 0.0185544 | ||||||||
\(605\) | 1.36136 | 0.0553471 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −35.6663 | −1.44765 | −0.723826 | − | 0.689982i | \(-0.757618\pi\) | ||||
−0.723826 | + | 0.689982i | \(0.757618\pi\) | |||||||
\(608\) | 1.92754 | 0.0781722 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | −2.13201 | −0.0863225 | ||||||||
\(611\) | −18.2327 | −0.737618 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 42.4297 | 1.71372 | 0.856859 | − | 0.515550i | \(-0.172412\pi\) | ||||
0.856859 | + | 0.515550i | \(0.172412\pi\) | |||||||
\(614\) | −45.4052 | −1.83240 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −8.14211 | −0.328055 | ||||||||
\(617\) | 7.26110 | 0.292321 | 0.146160 | − | 0.989261i | \(-0.453308\pi\) | ||||
0.146160 | + | 0.989261i | \(0.453308\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 15.5594 | 0.625385 | 0.312692 | − | 0.949854i | \(-0.398769\pi\) | ||||
0.312692 | + | 0.949854i | \(0.398769\pi\) | |||||||
\(620\) | −0.212087 | −0.00851763 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | −17.2971 | −0.693551 | ||||||||
\(623\) | −4.76654 | −0.190967 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 0.635214 | 0.0254086 | ||||||||
\(626\) | 7.94674 | 0.317616 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 10.3558 | 0.413242 | ||||||||
\(629\) | 16.3941 | 0.653676 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −5.24432 | −0.208773 | −0.104387 | − | 0.994537i | \(-0.533288\pi\) | ||||
−0.104387 | + | 0.994537i | \(0.533288\pi\) | |||||||
\(632\) | 29.0446 | 1.15533 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 16.9640 | 0.673726 | ||||||||
\(635\) | −9.86826 | −0.391610 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 27.8435 | 1.10320 | ||||||||
\(638\) | −2.65570 | −0.105140 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 18.4931 | 0.731002 | ||||||||
\(641\) | −2.17971 | −0.0860935 | −0.0430468 | − | 0.999073i | \(-0.513706\pi\) | ||||
−0.0430468 | + | 0.999073i | \(0.513706\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −4.84766 | −0.191173 | −0.0955865 | − | 0.995421i | \(-0.530473\pi\) | ||||
−0.0955865 | + | 0.995421i | \(0.530473\pi\) | |||||||
\(644\) | −1.05858 | −0.0417139 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −3.75624 | −0.147787 | ||||||||
\(647\) | 40.2387 | 1.58195 | 0.790973 | − | 0.611851i | \(-0.209575\pi\) | ||||
0.790973 | + | 0.611851i | \(0.209575\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 7.04704 | 0.276620 | ||||||||
\(650\) | −31.9922 | −1.25484 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 3.51451 | 0.137639 | ||||||||
\(653\) | 6.85500 | 0.268257 | 0.134129 | − | 0.990964i | \(-0.457177\pi\) | ||||
0.134129 | + | 0.990964i | \(0.457177\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −0.117992 | −0.00461033 | ||||||||
\(656\) | −38.8981 | −1.51871 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | −14.7782 | −0.576114 | ||||||||
\(659\) | −26.8314 | −1.04520 | −0.522601 | − | 0.852577i | \(-0.675038\pi\) | ||||
−0.522601 | + | 0.852577i | \(0.675038\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 30.6381 | 1.19168 | 0.595842 | − | 0.803102i | \(-0.296819\pi\) | ||||
0.595842 | + | 0.803102i | \(0.296819\pi\) | |||||||
\(662\) | 31.6431 | 1.22984 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 3.14470 | 0.122038 | ||||||||
\(665\) | −3.50621 | −0.135965 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 1.18036 | 0.0457039 | ||||||||
\(668\) | −4.44951 | −0.172157 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | −25.3730 | −0.980243 | ||||||||
\(671\) | −1.00000 | −0.0386046 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 31.9283 | 1.23075 | 0.615373 | − | 0.788236i | \(-0.289005\pi\) | ||||
0.615373 | + | 0.788236i | \(0.289005\pi\) | |||||||
\(674\) | −18.9972 | −0.731744 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 13.1919 | 0.507381 | ||||||||
\(677\) | −23.5546 | −0.905275 | −0.452638 | − | 0.891695i | \(-0.649517\pi\) | ||||
−0.452638 | + | 0.891695i | \(0.649517\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −17.5137 | −0.672116 | ||||||||
\(680\) | −10.3224 | −0.395848 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | −0.539032 | −0.0206406 | ||||||||
\(683\) | −17.5832 | −0.672802 | −0.336401 | − | 0.941719i | \(-0.609210\pi\) | ||||
−0.336401 | + | 0.941719i | \(0.609210\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −26.1320 | −0.998454 | ||||||||
\(686\) | −14.2653 | −0.544652 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 5.93306 | 0.226196 | ||||||||
\(689\) | 87.4600 | 3.33196 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −17.1914 | −0.653992 | −0.326996 | − | 0.945026i | \(-0.606036\pi\) | ||||
−0.326996 | + | 0.945026i | \(0.606036\pi\) | |||||||
\(692\) | 7.23706 | 0.275112 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −29.5895 | −1.12320 | ||||||||
\(695\) | 19.2894 | 0.731690 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 25.8937 | 0.980793 | ||||||||
\(698\) | −53.1007 | −2.00989 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | −4.78548 | −0.180874 | ||||||||
\(701\) | 38.0758 | 1.43810 | 0.719052 | − | 0.694956i | \(-0.244576\pi\) | ||||
0.719052 | + | 0.694956i | \(0.244576\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −4.01631 | −0.151478 | ||||||||
\(704\) | 5.46272 | 0.205884 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 27.7346 | 1.04380 | ||||||||
\(707\) | 39.0706 | 1.46940 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 7.43128 | 0.279088 | 0.139544 | − | 0.990216i | \(-0.455436\pi\) | ||||
0.139544 | + | 0.990216i | \(0.455436\pi\) | |||||||
\(710\) | 3.72910 | 0.139951 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 3.43785 | 0.128839 | ||||||||
\(713\) | 0.239581 | 0.00897237 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 8.83784 | 0.330516 | ||||||||
\(716\) | 7.00283 | 0.261708 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 18.5075 | 0.690694 | ||||||||
\(719\) | 22.8101 | 0.850671 | 0.425336 | − | 0.905036i | \(-0.360156\pi\) | ||||
0.425336 | + | 0.905036i | \(0.360156\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −14.8294 | −0.552276 | ||||||||
\(722\) | −28.8354 | −1.07314 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 2.15417 | 0.0800590 | ||||||||
\(725\) | 5.33602 | 0.198175 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −16.7830 | −0.622447 | −0.311223 | − | 0.950337i | \(-0.600739\pi\) | ||||
−0.311223 | + | 0.950337i | \(0.600739\pi\) | |||||||
\(728\) | −52.8579 | −1.95904 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | −19.6015 | −0.725484 | ||||||||
\(731\) | −3.94952 | −0.146078 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 12.5004 | 0.461713 | 0.230857 | − | 0.972988i | \(-0.425847\pi\) | ||||
0.230857 | + | 0.972988i | \(0.425847\pi\) | |||||||
\(734\) | 11.3215 | 0.417883 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 1.75033 | 0.0645180 | ||||||||
\(737\) | −11.9010 | −0.438378 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −30.0947 | −1.10705 | −0.553526 | − | 0.832832i | \(-0.686718\pi\) | ||||
−0.553526 | + | 0.832832i | \(0.686718\pi\) | |||||||
\(740\) | 3.22853 | 0.118683 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 70.8891 | 2.60242 | ||||||||
\(743\) | −38.8598 | −1.42563 | −0.712813 | − | 0.701354i | \(-0.752579\pi\) | ||||
−0.712813 | + | 0.701354i | \(0.752579\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 2.50622 | 0.0918209 | ||||||||
\(746\) | −28.5715 | −1.04608 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 1.41626 | 0.0517836 | ||||||||
\(749\) | 16.3425 | 0.597142 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 30.7717 | 1.12288 | 0.561438 | − | 0.827519i | \(-0.310248\pi\) | ||||
0.561438 | + | 0.827519i | \(0.310248\pi\) | |||||||
\(752\) | 13.2012 | 0.481397 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | −17.2406 | −0.627865 | ||||||||
\(755\) | 1.37150 | 0.0499140 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −22.9285 | −0.833351 | −0.416676 | − | 0.909055i | \(-0.636805\pi\) | ||||
−0.416676 | + | 0.909055i | \(0.636805\pi\) | |||||||
\(758\) | −48.3421 | −1.75587 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 2.52884 | 0.0917307 | ||||||||
\(761\) | 12.8001 | 0.464001 | 0.232001 | − | 0.972716i | \(-0.425473\pi\) | ||||
0.232001 | + | 0.972716i | \(0.425473\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 16.9325 | 0.612998 | ||||||||
\(764\) | −9.43470 | −0.341335 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 49.8443 | 1.80095 | ||||||||
\(767\) | 45.7488 | 1.65189 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 30.0017 | 1.08189 | 0.540945 | − | 0.841058i | \(-0.318067\pi\) | ||||
0.540945 | + | 0.841058i | \(0.318067\pi\) | |||||||
\(770\) | 7.16334 | 0.258149 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | −4.97590 | −0.179087 | ||||||||
\(773\) | 25.4863 | 0.916680 | 0.458340 | − | 0.888777i | \(-0.348444\pi\) | ||||
0.458340 | + | 0.888777i | \(0.348444\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 1.08306 | 0.0389048 | ||||||||
\(776\) | 12.6317 | 0.453452 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −37.2892 | −1.33688 | ||||||||
\(779\) | −6.34356 | −0.227282 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 1.74910 | 0.0625878 | ||||||||
\(782\) | −3.41090 | −0.121974 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | −20.1597 | −0.719989 | ||||||||
\(785\) | 31.1468 | 1.11168 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 17.9205 | 0.638796 | 0.319398 | − | 0.947621i | \(-0.396519\pi\) | ||||
0.319398 | + | 0.947621i | \(0.396519\pi\) | |||||||
\(788\) | 4.43046 | 0.157829 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | −25.5531 | −0.909140 | ||||||||
\(791\) | −17.7355 | −0.630601 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −6.49192 | −0.230535 | ||||||||
\(794\) | 0.372246 | 0.0132105 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −5.24024 | −0.185736 | ||||||||
\(797\) | −2.75839 | −0.0977072 | −0.0488536 | − | 0.998806i | \(-0.515557\pi\) | ||||
−0.0488536 | + | 0.998806i | \(0.515557\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −8.78775 | −0.310888 | ||||||||
\(800\) | 7.91264 | 0.279754 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | −12.1273 | −0.428232 | ||||||||
\(803\) | −9.19391 | −0.324446 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −3.18386 | −0.112216 | ||||||||
\(806\) | −3.49935 | −0.123259 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | −28.1795 | −0.991351 | ||||||||
\(809\) | −3.91072 | −0.137494 | −0.0687468 | − | 0.997634i | \(-0.521900\pi\) | ||||
−0.0687468 | + | 0.997634i | \(0.521900\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −54.0477 | −1.89787 | −0.948936 | − | 0.315468i | \(-0.897839\pi\) | ||||
−0.948936 | + | 0.315468i | \(0.897839\pi\) | |||||||
\(812\) | −2.57889 | −0.0905013 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 8.20549 | 0.287602 | ||||||||
\(815\) | 10.5705 | 0.370268 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 0.967573 | 0.0338511 | ||||||||
\(818\) | −41.4978 | −1.45094 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 5.09930 | 0.178075 | ||||||||
\(821\) | 10.4632 | 0.365169 | 0.182585 | − | 0.983190i | \(-0.441554\pi\) | ||||
0.182585 | + | 0.983190i | \(0.441554\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −41.4188 | −1.44377 | −0.721884 | − | 0.692015i | \(-0.756723\pi\) | ||||
−0.721884 | + | 0.692015i | \(0.756723\pi\) | |||||||
\(824\) | 10.6957 | 0.372601 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 37.0808 | 1.29021 | ||||||||
\(827\) | 25.7169 | 0.894264 | 0.447132 | − | 0.894468i | \(-0.352445\pi\) | ||||
0.447132 | + | 0.894468i | \(0.352445\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −56.0823 | −1.94782 | −0.973909 | − | 0.226938i | \(-0.927129\pi\) | ||||
−0.973909 | + | 0.226938i | \(0.927129\pi\) | |||||||
\(830\) | −2.76667 | −0.0960325 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 35.4635 | 1.22948 | ||||||||
\(833\) | 13.4199 | 0.464973 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −13.3826 | −0.463125 | ||||||||
\(836\) | −0.346962 | −0.0119999 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 6.65023 | 0.229728 | ||||||||
\(839\) | −18.3203 | −0.632486 | −0.316243 | − | 0.948678i | \(-0.602422\pi\) | ||||
−0.316243 | + | 0.948678i | \(0.602422\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −26.1244 | −0.900842 | ||||||||
\(842\) | −6.88857 | −0.237396 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | −4.99520 | −0.171942 | ||||||||
\(845\) | 39.6769 | 1.36493 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 3.35990 | 0.115448 | ||||||||
\(848\) | −63.3242 | −2.17456 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | −15.4195 | −0.528885 | ||||||||
\(851\) | −3.64705 | −0.125019 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 47.0478 | 1.61088 | 0.805442 | − | 0.592674i | \(-0.201928\pi\) | ||||
0.805442 | + | 0.592674i | \(0.201928\pi\) | |||||||
\(854\) | −5.26190 | −0.180059 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −11.7870 | −0.402870 | ||||||||
\(857\) | −55.0112 | −1.87915 | −0.939573 | − | 0.342350i | \(-0.888777\pi\) | ||||
−0.939573 | + | 0.342350i | \(0.888777\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 45.6370 | 1.55711 | 0.778557 | − | 0.627574i | \(-0.215952\pi\) | ||||
0.778557 | + | 0.627574i | \(0.215952\pi\) | |||||||
\(860\) | −0.777789 | −0.0265224 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −31.8640 | −1.08529 | ||||||||
\(863\) | 53.4991 | 1.82113 | 0.910565 | − | 0.413365i | \(-0.135647\pi\) | ||||
0.910565 | + | 0.413365i | \(0.135647\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 21.7666 | 0.740088 | ||||||||
\(866\) | −10.1845 | −0.346082 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | −0.523442 | −0.0177668 | ||||||||
\(869\) | −11.9855 | −0.406580 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −77.2601 | −2.61786 | ||||||||
\(872\) | −12.2125 | −0.413567 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 0.835618 | 0.0282652 | ||||||||
\(875\) | −37.2633 | −1.25973 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −7.59394 | −0.256429 | −0.128214 | − | 0.991746i | \(-0.540925\pi\) | ||||
−0.128214 | + | 0.991746i | \(0.540925\pi\) | |||||||
\(878\) | 13.3765 | 0.451434 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | −6.39892 | −0.215707 | ||||||||
\(881\) | −18.4709 | −0.622300 | −0.311150 | − | 0.950361i | \(-0.600714\pi\) | ||||
−0.311150 | + | 0.950361i | \(0.600714\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 43.3310 | 1.45820 | 0.729102 | − | 0.684405i | \(-0.239938\pi\) | ||||
0.729102 | + | 0.684405i | \(0.239938\pi\) | |||||||
\(884\) | 9.19424 | 0.309236 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −10.9957 | −0.369407 | ||||||||
\(887\) | 33.1903 | 1.11442 | 0.557211 | − | 0.830371i | \(-0.311872\pi\) | ||||
0.557211 | + | 0.830371i | \(0.311872\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −24.3553 | −0.816852 | ||||||||
\(890\) | −3.02458 | −0.101384 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 3.17577 | 0.106333 | ||||||||
\(893\) | 2.15287 | 0.0720429 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 21.0622 | 0.704031 | ||||||||
\(896\) | 45.6418 | 1.52478 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | −10.5018 | −0.350448 | ||||||||
\(899\) | 0.583661 | 0.0194662 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 42.1537 | 1.40434 | ||||||||
\(902\) | 12.9602 | 0.431526 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 12.7916 | 0.425444 | ||||||||
\(905\) | 6.47901 | 0.215370 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −35.1466 | −1.16702 | −0.583511 | − | 0.812105i | \(-0.698322\pi\) | ||||
−0.583511 | + | 0.812105i | \(0.698322\pi\) | |||||||
\(908\) | 0.665833 | 0.0220964 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 46.5038 | 1.54159 | ||||||||
\(911\) | −2.35749 | −0.0781070 | −0.0390535 | − | 0.999237i | \(-0.512434\pi\) | ||||
−0.0390535 | + | 0.999237i | \(0.512434\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −1.29768 | −0.0429470 | ||||||||
\(914\) | 4.77501 | 0.157943 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 3.53616 | 0.116838 | ||||||||
\(917\) | −0.291210 | −0.00961661 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −54.1630 | −1.78667 | −0.893335 | − | 0.449390i | \(-0.851641\pi\) | ||||
−0.893335 | + | 0.449390i | \(0.851641\pi\) | |||||||
\(920\) | 2.29634 | 0.0757082 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | −39.1531 | −1.28944 | ||||||||
\(923\) | 11.3550 | 0.373756 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −16.4871 | −0.542092 | ||||||||
\(926\) | 2.46050 | 0.0808570 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 4.26411 | 0.139976 | ||||||||
\(929\) | 3.87710 | 0.127203 | 0.0636017 | − | 0.997975i | \(-0.479741\pi\) | ||||
0.0636017 | + | 0.997975i | \(0.479741\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −3.28768 | −0.107749 | ||||||||
\(932\) | −2.97207 | −0.0973533 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | −7.31846 | −0.239467 | ||||||||
\(935\) | 4.25963 | 0.139305 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 5.02820 | 0.164264 | 0.0821321 | − | 0.996621i | \(-0.473827\pi\) | ||||
0.0821321 | + | 0.996621i | \(0.473827\pi\) | |||||||
\(938\) | −62.6217 | −2.04467 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | −1.73059 | −0.0564457 | ||||||||
\(941\) | −19.4123 | −0.632824 | −0.316412 | − | 0.948622i | \(-0.602478\pi\) | ||||
−0.316412 | + | 0.948622i | \(0.602478\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −5.76034 | −0.187583 | ||||||||
\(944\) | −33.1238 | −1.07809 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −1.97679 | −0.0642711 | ||||||||
\(947\) | −57.0998 | −1.85549 | −0.927746 | − | 0.373211i | \(-0.878257\pi\) | ||||
−0.927746 | + | 0.373211i | \(0.878257\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −59.6861 | −1.93749 | ||||||||
\(950\) | 3.77754 | 0.122560 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | −25.4763 | −0.825691 | ||||||||
\(953\) | −25.4030 | −0.822884 | −0.411442 | − | 0.911436i | \(-0.634975\pi\) | ||||
−0.411442 | + | 0.911436i | \(0.634975\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −28.3764 | −0.918239 | ||||||||
\(956\) | −5.28763 | −0.171014 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 35.6765 | 1.15265 | ||||||||
\(959\) | −64.4951 | −2.08266 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −30.8815 | −0.996178 | ||||||||
\(962\) | 53.2694 | 1.71747 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 10.6052 | 0.341572 | ||||||||
\(965\) | −14.9659 | −0.481768 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 30.7013 | 0.987287 | 0.493644 | − | 0.869664i | \(-0.335665\pi\) | ||||
0.493644 | + | 0.869664i | \(0.335665\pi\) | |||||||
\(968\) | −2.42332 | −0.0778883 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | −11.1133 | −0.356825 | ||||||||
\(971\) | 48.6547 | 1.56140 | 0.780701 | − | 0.624904i | \(-0.214862\pi\) | ||||
0.780701 | + | 0.624904i | \(0.214862\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 47.6073 | 1.52622 | ||||||||
\(974\) | −51.2866 | −1.64333 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 4.70039 | 0.150456 | ||||||||
\(977\) | 50.1834 | 1.60551 | 0.802755 | − | 0.596309i | \(-0.203367\pi\) | ||||
0.802755 | + | 0.596309i | \(0.203367\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −1.41865 | −0.0453404 | ||||||||
\(980\) | 2.64282 | 0.0844217 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | −62.2967 | −1.98797 | ||||||||
\(983\) | 7.93819 | 0.253189 | 0.126594 | − | 0.991955i | \(-0.459595\pi\) | ||||
0.126594 | + | 0.991955i | \(0.459595\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 13.3253 | 0.424581 | ||||||||
\(986\) | −8.30956 | −0.264630 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −2.25245 | −0.0716599 | ||||||||
\(989\) | 0.878616 | 0.0279384 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −39.0515 | −1.24051 | −0.620256 | − | 0.784400i | \(-0.712971\pi\) | ||||
−0.620256 | + | 0.784400i | \(0.712971\pi\) | |||||||
\(992\) | 0.865494 | 0.0274795 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 9.20361 | 0.291921 | ||||||||
\(995\) | −15.7609 | −0.499654 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −24.2028 | −0.766512 | −0.383256 | − | 0.923642i | \(-0.625197\pi\) | ||||
−0.383256 | + | 0.923642i | \(0.625197\pi\) | |||||||
\(998\) | 0.950290 | 0.0300809 | ||||||||
\(999\) | 0 | 0 |
(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 | 6039.2.a.o.1.17 | yes | 25 | |
3.2 | odd | 2 | 6039.2.a.n.1.9 | ✓ | 25 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
6039.2.a.n.1.9 | ✓ | 25 | 3.2 | odd | 2 | ||
6039.2.a.o.1.17 | yes | 25 | 1.1 | even | 1 | trivial |