%%==================================================================%%
%%                                                                  %%
%%       Find below the Tables 3 to 8 of the paper entitled :       %%
%%                                                                  %%
%%                                                                  %%
%%       THEORY OF MOTION AND EPHEMERIDES OF HYPERION               %%
%%                                                                  %%
%%  by  DURIEZ \& VIENNE, to appear in Astron. Astrophys 1997.      %%
%%                                                                  %%
%%  e-mail: duriez@gat.univ-lille1.fr and vienne@gat.univ-lille1.fr %%
%%                                                                  %%
%%                                                                  %%
%%                                                                  %%
%%   These Tables  contain the full series of the representation    %%
%%  of the Hyperion's motion, with terms larger than 1 km for the   %%
%%    long-period part and than 5 km for the short-period part.     %%
%%                                                                  %%
%%==================================================================%%
%
%%==================================================================%%
%%                                                                  %%
%%                                                                  %%
%%                                                                  %%
%%                    text in    Plain TeX                          %%
%%                                                                  %%
%%                                                                  %%
%%==================================================================%%
\baselineskip10.5pt
%
\def\eps{\varepsilon}
\def\crs{\cr\noalign{\smallskip}}
\def\crm{\cr\noalign{\medskip}}
%
%
\def\sst{\scriptscriptstyle}
\def\st{\scriptstyle}
\def\Sp{\vphantom0^{\prime\prime}\!\!.}
\def\sqi{\sqrt{\st-1}\,}
\def\Day{{\hbox{$^{\rm \,d}$\ }}}
\def\Ud{$\,${\hbox{\rm d\ }}}
\def\Uy{$\,${\hbox{\rm y\ }}}
\def\Deg{\hbox{$^\circ$}}
\def\Dp{\hbox{$\vphantom0^{\circ}\!\!.$}}
\def\abs#1{\vert#1\vert}
\def\tenp#1{\,\hbox{$\st10^{\st#1}$}}
\def\f{\hfill}
\def\pho{\phantom{0}}
\font\katorz=cmr10 at 14pt

\null
\centerline{\bf \katorz Theory of motion and ephemerides of Hyperion}
\bigskip
\bigskip
\centerline{\bf L. Duriez  and A. Vienne  }
\bigskip
\centerline{ Universit\'e des Sciences et Technologies de Lille}
\centerline{  Laboratoire d'Astronomie}
\centerline{ 1 Impasse de l'Observatoire}
\centerline{ F-59000 Lille, France}
\centerline{ e-mail: duriez@gat.univ-lille1.fr and vienne@gat.univ-lille1.fr}

\bigskip
\bigskip
\noindent
{\bf Abstract.}
    In this paper, we present a new theory of motion for Hyperion, defined
    like in TASS1.6 for the other Saturn's satellites (Vienne \& Duriez 1995,
    =1995A\&A...297..588V), by the osculating saturnicentric orbital elements
    referred to the equatorial plane of Saturn and to the node of this plane
    in the mean ecliptic for J2000.0. These elements are expressed as
    semi-numerical trigonometric series in which the argument of each term
    is	given as an integer combination of 7 natural fundamental arguments
    (Table 3). These series (Tables 4 to 7) collect all the perturbations
    caused by Titan on the orbital elements of Hyperion, whose amplitudes
    are larger than 1~km in the long-period terms and than 5~km in the
    short-period ones. Taking also account of the perturbations from other
    satellites and Sun (Table 8), these series have been fitted to 8136
    Earth-based observations of Hyperion in the interval [1874-1985]. The
    resulting series allows to produce new ephemerides for Hyperion, which
    have been compared to those previously given by Taylor (1992)
    (=1992A\&A...265..825T): Using the same set of observations and the same
    way to weight them, the root mean square (o-c) residual of the present
    theory is 0.156 arcseconds while the ephemerides of Taylor gives
    0.203 arcseconds.

\bigskip
\bigskip
\noindent
Find below the Tables 3 to 8 of the paper of
DURIEZ \& VIENNE, to appear in Astron. Astrophys 1997.
These tables  contain the full series of the representation of
 the Hyperion's motion, with terms larger than 1 km for the long-period part
 and than 5 km for the short-period part. These series have been adjusted
 to observations over one century, as explained in the paper cited above.

\noindent
(ask for an offprint to duriez@gat.univ-lille1.fr).

\bigskip
\bigskip


%  Fundamental arguments
%
\bigskip
\noindent{\bf Table 3.} Fundamental arguments of
 the Titan-Hyperion interaction. Each one is in
 the form : $\omega^*_k t+\varphi^*_k$ where 
 $t=(\hbox{Julian Date)}-2\,451\,545.0$. The
 columns $\eps(T^*_k)$ and $\eps(\varphi^*_k)$ give
 the estimated error on each period and on each
 phase, issued from the fit of the theory to
 observations
 \smallskip
 \halign{
$\ #$\hfil&\quad\hfil$#$\hfil
&\quad\hfil$#$\quad&\quad\hfil$#$\hfil\quad
&\quad\hfil$#$\quad&\quad\hfil$#$\quad&
\quad\hfil$#$\cr
\noalign{\hrule\medskip}
k&\hfill\hbox{argument}\hfill
 &\hfill\hbox{$\omega^*_k$ (rad$/$d)}\hfill
 &\hfill\hbox{$\varphi^*_k$ (rad)}\hfill
 &\hfill\hbox{period (d)}\hfill
 &\hfill\hbox{$\eps(T^*_k)$ (d)}\hfill
 &\hfill\hbox{$\eps(\varphi^*_k)$ (rad)}\cr
\noalign{\medskip\hrule\medskip}
 1&\psi      &  0.098733765027&  1.379026808&      63.6377&  0.00008& 0.00011\cr
 2&\tau      &  0.009810539955&  1.803677249&     640.4525&  0.03454& 0.00100\cr
 3&\varpi^*_7& -0.000892481124&  3.382691058&   -7040.1324&  3.98970& 0.00038\cr
 4&\varpi^*_6&  0.000024646231&  2.860542690&  254934.9313&  0.00504& 0.00063\cr
 5&\Omega^*_7& -0.000113616050&  3.864510578&  -55301.9163& 15.97624& 0.00537\cr
 6&\Omega^*_6& -0.000024636367&  6.141812995& -255037.0101&  0.01695& 0.00915\cr
 7&\Omega_0  &  0.000000000000&  3.221557438&&& 0.00001\cr
\noalign{\medskip\hrule}
 }

\vfil\eject
\bigskip
\def\PS{\psi}
\def\TO{\tau}
\def\PH{\varpi^*_7}
\def\PT{\varpi^*_6}
\def\NH{\Omega^*_7}
\def\NT{\Omega^*_6}
\def\NO{\Omega_0}
\def\A{\rlap{\ *}}
\def\qhfil{\quad\hfil}
\def\Cdots{\noalign{\vskip-1.3mm}\cdots\cr\noalign{\vskip-1.3mm}}

% series p :

\noindent{\bf Table 4.} Series for $p_7$ : Each term
 is in the form $\alpha \cos(\omega t+\varphi)$
with $t=(\hbox{Julian Date)}-2\,451\,545.0$.
Each argument is also identified
 as an integer
 combination of the seven fundamental arguments
 given in Table 3;
 the values of $\omega $ and $\varphi$ are in
 fact computed from these combinations. The
 osculating semi-major axis is then
$a_7=A_7(1+p_7)^{-2/3} $ where $A_7$ is a kind of mean
 value of $a_7$, computed from the third Kepler's
 law : $A_7=(k^2(M_s+m_7)/N_7^2)^{1/3}$ with $k$
the gaussian constant, with  $M_s=
M_\odot/3498.790 $ (from Campbell \& Anderson 1989)
 $m_7=3\ 10^{-8}\ M_s$ (from Burns 1986)
and with the mean mean motion  $N_7=
 0.2953088139$~rad/d.
The amplitudes in km represent $-(2/3)A_7p_7$
with $A_7=
 1482333.4$~km.
 The estimated error $\varepsilon(\alpha)$ on
 each amplitude comes from the fit of the theory
 to observations 
\medskip
 \halign{
$#$\hfil&\qhfil$#$&\qhfil$#$&\qhfil$#$&\qhfil$#$&
\quad\quad$#$\hfil
&\quad\qhfil$#$&\qhfil$#$\cr
\noalign{\hrule\medskip}
\hbox{n\Deg}
 &\hfill\hbox{amplitude $\alpha $}\hfill
 &\hfill\hbox{phase $\varphi$}\hfill
 &\hfill\hbox{frequency $\omega $}\hfill
 &\hfill\hbox{period}\hfill
 &\hfill\hbox{argument}\hfill
 &\hfill\hbox{amplitude}\hfill
 &\hfill\hbox{$\varepsilon(\alpha)$}\hfill
 \cr 
 &\hfill\hbox{(rad)}\hfill
 &\hfill\hbox{(deg)}\hfill
 &\hfill\hbox{(rad/d)}\hfill
 &\hfill\hbox{(d)}\hfill
 & 
 &\hfill\hbox{(km)}\hfill
 &\hfill\hbox{(km)}\hfill
\cr
\noalign{\medskip\hrule\medskip}
   0& -0.0015747&   0.000&   0.0000000000&&&   1556.14&   0.53\cr
   1&  0.0052692& 103.343&   0.0098105400&    640.45&\TO                      &  -5207.14&   5.30\cr
   2& -0.0009448&  79.012&   0.0987337650&     63.64&\PS                      &    933.67&   0.26\cr
   3& -0.0006016& 335.669&   0.0889232251&     70.66&\PS-\TO                  &    594.52&   0.61\cr
   4&  0.0005148& 182.356&   0.1085443050&     57.89&\PS+\TO                  &   -508.75&   0.52\cr
   5& -0.0001310&  73.426&   0.0107276673&    585.70&\TO-\PH+\PT              &    129.44&   0.23\cr
   6&  0.0001186& 133.260&   0.0088934126&    706.50&\TO+\PH-\PT              &   -117.21&   0.21\cr
  7& -0.0000759& 232.326&   0.0791126851&     79.42&\PS -2\TO                &     74.98&   0.15\cr
  8& -0.0000439& 285.699&   0.1183548449&     53.09&\PS+ 2\TO                &     43.42&   0.09\cr
  9& -0.0000299& 310.029&   0.0294316199&    213.48&  3\TO                   &     29.51&   0.09\cr
 10&  0.0000242& 206.686&   0.0196210799&    320.23&  2\TO                   &    -23.94&   0.05\cr
 11&  0.0000172&   5.586&   0.0880060977&     71.39&\PS-\TO+\PH-\PT          &    -17.01&   0.03\cr
 12& -0.0000134& 305.752&   0.0898403524&     69.94&\PS-\TO-\PH+\PT          &     13.23&   0.02\cr
 13& -0.0000130& 152.439&   0.1094614323&     57.40&\PS+\TO-\PH+\PT          &     12.88&   0.02\cr
 14&  0.0000129&  66.505&   0.0099241560&    633.12&\TO-\NH+\NO              &    -12.75&   0.09\cr
 15& -0.0000128& 140.182&   0.0096969239&    647.96&\TO+\NH-\NO              &     12.61&   0.09\cr
 16& -0.0000121& 108.929&   0.0978166377&     64.23&\PS+\PH-\PT              &     11.92&   0.01\cr
  17&  0.0000101& 212.272&   0.1076271776&     58.38&\PS+\TO+\PH-\PT          &    -10.01&   0.02\cr
 18& -0.0000096& 330.083&   0.0009171274&   6850.94&-\PH+\PT                 &      9.48&   0.01\cr
 19&  0.0000077& 128.983&   0.0693021452&     90.66&\PS -3\TO                &     -7.63&   0.02\cr
 20& -0.0000050&  29.042&   0.1281653849&     49.02&\PS+ 3\TO                &      4.97&   0.01\cr
 21& -0.0000047& 158.556&   0.0113682701&    552.69&\TO -2\PH+ 2\NH          &      4.67&   0.06\cr
 22& -0.0000045& 233.823&   0.0098995196&    634.70&\TO-\NH+\NT              &      4.44&   0.05\cr
 23&  0.0000044& 332.863&   0.0097215603&    646.31&\TO+\NH-\NT              &     -4.39&   0.05\cr
 24&  0.0000039&  48.131&   0.0082528098&    761.34&\TO+ 2\PH -2\NH          &     -3.88&   0.05\cr
 25&  0.0000038& 262.243&   0.0781955578&     80.35&\PS -2\TO+\PH-\PT        &     -3.80&   0.01\cr
 26& -0.0000035& 202.409&   0.0800298125&     78.51&\PS -2\TO-\PH+\PT        &      3.46&   0.01\cr
 27&  0.0000028&  43.509&   0.0116447947&    539.57&\TO -2\PH+ 2\PT          &     -2.78&   0.01\cr
 28&  0.0000026&  49.096&   0.0996508924&     63.05&\PS-\PH+\PT              &     -2.59&   0.00\cr
 29&  0.0000022& 280.112&   0.0303487472&    207.03&  3\TO-\PH+\PT           &     -2.14&   0.01\cr
 30&  0.0000022& 255.782&   0.1192719723&     52.68&\PS+ 2\TO-\PH+\PT        &     -2.16&   0.01\cr
 31& -0.0000022& 339.946&   0.0285144925&    220.35&  3\TO+\PH-\PT           &      2.15&   0.01\cr
 32& -0.0000021& 315.616&   0.1174377176&     53.50&\PS+ 2\TO+\PH-\PT        &      2.06&   0.01\cr
 33&  0.0000018& 296.025&   0.0098351763&    638.85&\TO-\NT+\NO              &     -1.74&   0.02\cr
 34& -0.0000017& 270.661&   0.0097859036&    642.06&\TO+\NT-\NO              &      1.71&   0.02\cr
 35&  0.0000016&  25.640&   0.0594916052&    105.61&\PS -4\TO                &     -1.61&   0.01\cr
 36& -0.0000014&  12.508&   0.0888096090&     70.75&\PS-\TO+\NH-\NO          &      1.41&   0.01\cr
 37&  0.0000014& 298.831&   0.0890368411&     70.57&\PS-\TO-\NH+\NO          &     -1.37&   0.01\cr
 38&  0.0000014& 145.517&   0.1086579210&     57.83&\PS+\TO-\NH+\NO          &     -1.36&   0.01\cr
  39& -0.0000013& 219.194&   0.1084306889&     57.95&\PS+\TO+\NH-\NO          &      1.33&   0.01\crs
  40&  0.0009846& 158.025&   0.1974675301&     31.82&  2\PS                   &   -972.98&   0.20\cr
  41&  0.0005722& 237.037&   0.2962012951&     21.21&  3\PS                   &   -565.48&   0.15\cr
  42&  0.0003064& 316.050&   0.3949350601&     15.91&  4\PS                   &   -302.81&   0.12\cr
  43&  0.0002329&  35.062&   0.4936688251&     12.73&  5\PS                   &   -230.13&   0.07\cr
  44&  0.0001830& 114.074&   0.5924025902&     10.61&  6\PS                   &   -180.87&   0.05\cr
  45&  0.0001428& 193.087&   0.6911363552&      9.09&  7\PS                   &   -141.13&   0.04\cr
  46&  0.0001031& 272.099&   0.7898701202&      7.95&  8\PS                   &   -101.85&   0.04\cr
 47&  0.0000916& 133.694&   0.2863907551&     21.94&  3\PS-\TO               &    -90.54&   0.10\cr
 48&  0.0000842& 212.707&   0.3851245202&     16.31&  4\PS-\TO               &    -83.21&   0.10\cr
 49&  0.0000748& 351.112&   0.8886038852&      7.07&  9\PS                   &    -73.90&   0.03\cr
 50&  0.0000625& 291.719&   0.4838582852&     12.99&  5\PS-\TO               &    -61.72&   0.07\cr
 51& -0.0000593& 340.380&   0.3060118350&     20.53&  3\PS+\TO               &     58.55&   0.07\cr
 52& -0.0000587& 187.942&   0.1965504027&     31.97&  2\PS+\PH-\PT           &     57.97&   0.03\cr
 53& -0.0000584&  59.393&   0.4047456001&     15.52&  4\PS+\TO               &     57.70&   0.07\cr
 54&  0.0000552&  70.124&   0.9873376503&      6.36& 10\PS                   &    -54.52&   0.03\cr
 55&  0.0000529&  10.731&   0.5825920502&     10.78&  6\PS-\TO               &    -52.29&   0.06\cr
 56&  0.0000479&  89.744&   0.6813258152&      9.22&  7\PS-\TO               &    -47.29&   0.05\cr
 57&  0.0000465&  54.682&   0.1876569901&     33.48&  2\PS-\TO               &    -45.94&   0.05\cr
 58& -0.0000451& 138.405&   0.5034793651&     12.48&  5\PS+\TO               &     44.57&   0.05\cr
 59&  0.0000439& 168.756&   0.7800595803&      8.05&  8\PS-\TO               &    -43.41&   0.05\cr
 60&  0.0000427&  64.979&   0.4927516978&     12.75&  5\PS+\PH-\PT           &    -42.23&   0.03\cr
 61&  0.0000415& 149.137&   1.0860714153&      5.79& 11\PS                   &    -41.05&   0.02\cr
 62& -0.0000406& 217.418&   0.6022131301&     10.43&  6\PS+\TO               &     40.09&   0.05\cr
 63& -0.0000386& 296.430&   0.7009468951&      8.96&  7\PS+\TO               &     38.12&   0.04\cr
 64&  0.0000382& 247.769&   0.8787933453&      7.15&  9\PS-\TO               &    -37.70&   0.04\cr
 65& -0.0000362& 311.339&   0.1778464501&     35.33&  2\PS -2\TO             &     35.73&   0.07\cr
 66& -0.0000362&  15.442&   0.7996806602&      7.86&  8\PS+\TO               &     35.77&   0.04\cr
 67&  0.0000321& 326.781&   0.9775271103&      6.43& 10\PS-\TO               &    -31.73&   0.03\cr
 68& -0.0000319&  94.455&   0.8984144252&      6.99&  9\PS+\TO               &     31.54&   0.03\cr
 69&  0.0000311& 228.149&   1.1848051803&      5.30& 12\PS                   &    -30.70&   0.02\cr
 70& -0.0000280&   4.711&   0.2170886100&     28.94&  2\PS+ 2\TO             &     27.64&   0.06\cr
 71& -0.0000272& 173.467&   0.9971481902&      6.30& 10\PS+\TO               &     26.91&   0.03\cr
 72&  0.0000267&  45.793&   1.0762608753&      5.84& 11\PS-\TO               &    -26.39&   0.02\cr
 73& -0.0000230& 252.480&   1.0958819553&      5.73& 11\PS+\TO               &     22.70&   0.02\cr
 74&  0.0000230& 307.161&   1.2835389454&      4.90& 13\PS                   &    -22.73&   0.02\cr
 75&  0.0000223& 124.806&   1.1749946404&      5.35& 12\PS-\TO               &    -22.06&   0.02\cr
 76& -0.0000194& 331.492&   1.1946157203&      5.26& 12\PS+\TO               &     19.18&   0.02\cr
 77&  0.0000186& 203.818&   1.2737284054&      4.93& 13\PS-\TO               &    -18.40&   0.01\cr
 78&  0.0000168&  26.174&   1.3822727104&      4.55& 14\PS                   &    -16.64&   0.02\cr
 79& -0.0000164&  50.505&   1.2933494853&      4.86& 13\PS+\TO               &     16.17&   0.01\cr
  80&  0.0000154& 282.831&   1.3724621704&      4.58& 14\PS-\TO               &    -15.26&   0.01\cr
 81& -0.0000137& 129.517&   1.3920832503&      4.51& 14\PS+\TO               &     13.51&   0.01\cr
 82& -0.0000134&  83.723&   0.3158223750&     19.89&  3\PS+ 2\TO             &     13.21&   0.03\cr
 83& -0.0000132&  30.351&   0.2765802152&     22.72&  3\PS -2\TO             &     13.05&   0.03\cr
 84&  0.0000127&   1.843&   1.4711959355&      4.27& 15\PS-\TO               &    -12.56&   0.01\cr
 85&  0.0000122& 105.186&   1.4810064754&      4.24& 15\PS                   &    -12.10&   0.02\cr
 86& -0.0000113& 208.529&   1.4908170154&      4.21& 15\PS+\TO               &     11.18&   0.01\cr
 87& -0.0000109& 266.954&   0.2952841677&     21.28&  3\PS+\PH-\PT           &     10.77&   0.01\cr
 88&  0.0000104&  80.856&   1.5699297005&      4.00& 16\PS-\TO               &    -10.27&   0.01\cr
 89& -0.0000093& 287.542&   1.5895507804&      3.95& 16\PS+\TO               &      9.19&   0.01\cr
 90&  0.0000088& 184.199&   1.5797402404&      3.98& 16\PS                   &     -8.74&   0.01\cr
 91&  0.0000085& 159.868&   1.6686634655&      3.77& 17\PS-\TO               &     -8.36&   0.00\cr
 92& -0.0000079& 261.368&   0.2072780700&     30.31&  2\PS+\TO               &      7.81&   0.02\cr
 93& -0.0000076&   6.554&   1.6882845454&      3.72& 17\PS+\TO               &      7.52&   0.00\cr
 94&  0.0000074& 223.438&   0.9677165704&      6.49& 10\PS -2\TO             &     -7.34&   0.02\cr
 95&  0.0000074& 144.426&   0.8689828053&      7.23&  9\PS -2\TO             &     -7.27&   0.02\cr
 96&  0.0000072& 302.450&   1.0664503354&      5.89& 11\PS -2\TO             &     -7.08&   0.01\cr
 97&  0.0000070&  65.413&   0.7702490403&      8.16&  8\PS -2\TO             &     -6.87&   0.01\cr
 98&  0.0000069& 238.880&   1.7673972305&      3.56& 18\PS-\TO               &     -6.80&   0.00\cr
 99&  0.0000066& 346.401&   0.6715152753&      9.36&  7\PS -2\TO             &     -6.54&   0.01\cr
100&  0.0000063& 263.211&   1.6784740055&      3.74& 17\PS                   &     -6.26&   0.01\cr
101& -0.0000062&  85.567&   1.7870183104&      3.52& 18\PS+\TO               &      6.11&   0.00\cr
102&  0.0000061& 100.475&   1.2639178654&      4.97& 13\PS -2\TO             &     -6.06&   0.01\cr
103&  0.0000056& 179.488&   1.3626516305&      4.61& 14\PS -2\TO             &     -5.52&   0.01\cr
 104&  0.0000055& 317.893&   1.8661309956&      3.37& 19\PS-\TO               &     -5.47&   0.00\cr
\noalign{\medskip\hrule}
 }

\vfill\eject
% series q :
\bigskip
\noindent{\bf Table 5.} Series for $q_7$ : Each term
 is in the form $\alpha \sin(\omega t+\varphi)$
with $t=(\hbox{Julian Date)}-2\,451\,545.0$.
Each argument is also identified as an integer
 combination of the seven fundamental arguments
 given in Table 3; $\omega $ and $\varphi$ are in
 fact computed from these combinations.
 The mean longitude is then $\lambda _7= 
( 4.3486836\pm 0.0001432)+( 0.2953088139\pm 0.0000001286)
 \,t + q_7$.
The amplitudes in km represent $A_7q_7$ 
with $A_7=
 1482333.4$~km.
% The probable error (p.e.) on
% each amplitude comes from the fit of the theory
% to observations
\medskip
 \halign{
$#$\hfil&\qhfil$#$&\qhfil$#$&\qhfil$#$&\qhfil$#$&
\quad\quad$#$\hfil
&\qhfil$#$&\qhfil$#$\cr
\noalign{\hrule\medskip}
\hbox{n\Deg}
 &\hfill\hbox{amplitude $\alpha $}\hfill
 &\hfill\hbox{phase $\varphi$}\hfill
 &\hfill\hbox{frequency $\omega $}\hfill
 &\hfill\hbox{period}\hfill
 &\hfill\hbox{argument}\hfill
 &\hfill\hbox{amplitude}\hfill
 &\hfill\hbox{$\varepsilon(\alpha)$}\hfill
 \cr 
 &\hfill\hbox{(rad)}\hfill
 &\hfill\hbox{(deg)}\hfill
 &\hfill\hbox{(rad/d)}\hfill
 &\hfill\hbox{(d)}\hfill
 & 
 &\hfill\hbox{(km)}\hfill
 &\hfill\hbox{(km)}\hfill
\cr
\noalign{\medskip\hrule\medskip}
   1&  0.1591300& 103.343&   0.0098105400&    640.45&\TO                      & 235883.78& 229.13\cr
   2&  0.0040425& 133.260&   0.0088934126&    706.50&\TO+\PH-\PT              &   5992.32&  10.19\cr
   3& -0.0036745&  73.426&   0.0107276673&    585.70&\TO-\PH+\PT              &  -5446.77&   9.42\cr
   4&  0.0018763&  79.012&   0.0987337650&     63.64&\PS                      &   2781.35&   1.52\cr
   5& -0.0015590& 335.669&   0.0889232251&     70.66&\PS-\TO                  &  -2311.02&   2.38\cr
   6&  0.0015341& 330.083&   0.0009171274&   6850.94&-\PH+\PT                 &   2274.02&   2.53\cr
   7&  0.0011322& 182.356&   0.1085443050&     57.89&\PS+\TO                  &   1678.35&   1.72\cr
   8& -0.0003899& 140.182&   0.0096969239&    647.96&\TO+\NH-\NO              &   -577.96&   3.88\cr
   9&  0.0003851&  66.505&   0.0099241560&    633.12&\TO-\NH+\NO              &    570.90&   3.83\cr
  10& -0.0003603& 323.161&   0.0001136161&  55301.92&-\NH+\NO                 &   -534.05&   3.23\cr
  11& -0.0003109& 232.326&   0.0791126851&     79.42&\PS -2\TO                &   -460.84&   0.96\cr
  12& -0.0003037& 310.029&   0.0294316199&    213.48&  3\TO                   &   -450.16&   1.33\cr
  13& -0.0001967& 192.682&   0.0000246364& 255037.01&-\NT+\NO                 &   -291.58&   2.57\cr
  14&  0.0001585& 206.686&   0.0196210799&    320.23&  2\TO                   &    234.91&   0.46\cr
  15&  0.0001444&  48.131&   0.0082528098&    761.34&\TO+ 2\PH -2\NH          &    214.01&   2.70\cr
  16& -0.0001337& 285.699&   0.1183548449&     53.09&\PS+ 2\TO                &   -198.12&   0.41\cr
  17&  0.0001354& 332.863&   0.0097215603&    646.31&\TO+\NH-\NT              &    200.76&   2.25\cr
  18& -0.0001344& 233.823&   0.0098995196&    634.70&\TO-\NH+\NT              &   -199.26&   2.23\cr
  19& -0.0001248& 158.556&   0.0113682701&    552.69&\TO -2\PH+ 2\NH          &   -185.04&   2.33\cr
  20& -0.0000934&  55.212&   0.0015577301&   4033.55& -2\PH+ 2\NH             &   -138.50&   1.71\cr
  21&  0.0000856& 130.480&   0.0000889797&  70613.71&-\NH+\NT                 &    126.87&   1.33\cr
  22&  0.0000722&  43.509&   0.0116447947&    539.57&\TO -2\PH+ 2\PT          &    107.09&   0.25\cr
 23&  0.0000530& 296.025&   0.0098351763&    638.85&\TO-\NT+\NO              &     78.52&   0.77\cr
 24& -0.0000525& 270.661&   0.0097859036&    642.06&\TO+\NT-\NO              &    -77.79&   0.76\cr
 25&  0.0000419&  49.096&   0.0996508924&     63.05&\PS-\PH+\PT              &     62.10&   0.04\cr
 26&  0.0000410&   5.586&   0.0880060977&     71.39&\PS-\TO+\PH-\PT          &     60.76&   0.11\cr
 27&  0.0000376& 300.166&   0.0018342547&   3425.47& -2\PH+ 2\PT             &     55.80&   0.08\cr
 28& -0.0000353& 152.439&   0.1094614323&     57.40&\PS+\TO-\PH+\PT          &    -52.35&   0.09\cr
 29& -0.0000295&  84.969&   0.0081391938&    771.97&\TO+ 2\PH-\NH-\NO        &    -43.70&   0.30\cr
 30&  0.0000284& 212.272&   0.1076271776&     58.38&\PS+\TO+\PH-\PT          &     42.11&   0.07\cr
 31&  0.0000268& 128.983&   0.0693021452&     90.66&\PS -3\TO                &     39.68&   0.12\cr
 32&  0.0000247& 121.717&   0.0114818862&    547.23&\TO -2\PH+\NH+\NO        &     36.54&   0.24\cr
 33&  0.0000238&  18.374&   0.0016713462&   3759.36& -2\PH+\NH+\NO           &     35.33&   0.22\cr
 34& -0.0000236& 305.752&   0.0898403524&     69.94&\PS-\TO-\PH+\PT          &    -34.96&   0.07\cr
 35& -0.0000231& 339.946&   0.0285144925&    220.35&  3\TO+\PH-\PT           &    -34.22&   0.12\cr
 36&  0.0000217& 280.112&   0.0303487472&    207.03&  3\TO-\PH+\PT           &     32.22&   0.11\cr
 37&  0.0000164& 163.177&   0.0079762852&    787.73&\TO+ 2\PH -2\PT          &     24.35&   0.11\cr
 38&  0.0000155& 262.243&   0.0781955578&     80.35&\PS -2\TO+\PH-\PT        &     23.03&   0.06\cr
 39& -0.0000134& 202.409&   0.0800298125&     78.51&\PS -2\TO-\PH+\PT        &    -19.83&   0.05\cr
 40& -0.0000113&  36.588&   0.0108412834&    579.56&\TO-\PH+\PT-\NH+\NO      &    -16.79&   0.13\cr
 41&  0.0000109& 110.265&   0.0106140513&    591.97&\TO-\PH+\PT+\NH-\NO      &     16.14&   0.12\cr
 42& -0.0000100&  29.042&   0.1281653849&     49.02&\PS+ 3\TO                &    -14.84&   0.05\cr
 43&  0.0000088&  25.640&   0.0594916052&    105.61&\PS -4\TO                &     13.04&   0.05\cr
 44&  0.0000082& 277.651&   0.0081638301&    769.64&\TO+ 2\PH-\NH-\NT        &     12.16&   0.15\cr
 45&  0.0000077&  96.421&   0.0090070287&    697.59&\TO+\PH-\PT-\NH+\NO      &     11.45&   0.09\cr
 46& -0.0000072& 170.098&   0.0087797965&    715.64&\TO+\PH-\PT+\NH-\NO      &    -10.70&   0.08\cr
  47& -0.0000070& 188.472&   0.0104511427&    601.20&\TO-\PH-\PT+ 2\NH        &    -10.35&   0.13\cr
 48& -0.0000069& 289.035&   0.0114572498&    548.40&\TO -2\PH+\NH+\NT        &    -10.20&   0.12\cr
 49&  0.0000067& 255.782&   0.1192719723&     52.68&\PS+ 2\TO-\PH+\PT        &      9.86&   0.02\cr
 50& -0.0000063& 315.616&   0.1174377176&     53.50&\PS+ 2\TO+\PH-\PT        &     -9.33&   0.02\cr
 51&  0.0000061& 108.929&   0.0978166377&     64.23&\PS+\PH-\PT              &      9.06&   0.02\cr
 52&  0.0000060&  85.129&   0.0006406028&   9808.24&-\PH-\PT+ 2\NH           &      8.92&   0.11\cr
 53&  0.0000054& 128.639&   0.0122853975&    511.44&\TO -3\PH+\PT+ 2\NH      &      8.07&   0.10\cr
 54& -0.0000056& 185.692&   0.0016467098&   3815.60& -2\PH+\NH+\NT           &     -8.24&   0.09\cr
 55& -0.0000040& 151.474&   0.0180633498&    347.84&  2\TO+ 2\PH -2\NH       &     -5.87&   0.08\cr
 56&  0.0000039& 203.906&   0.0108166470&    580.88&\TO-\PH+\PT-\NH+\NT      &      5.84&   0.07\cr
 57& -0.0000038& 302.946&   0.0106386876&    590.60&\TO-\PH+\PT+\NH-\NT      &     -5.60&   0.07\cr
 58& -0.0000036&  12.508&   0.0888096090&     70.75&\PS-\TO+\NH-\NO          &     -5.36&   0.04\cr
 59&  0.0000035& 298.831&   0.0890368411&     70.57&\PS-\TO-\NH+\NO          &      5.20&   0.04\cr
 60&  0.0000030& 145.517&   0.1086579210&     57.83&\PS+\TO-\NH+\NO          &      4.39&   0.03\cr
 61& -0.0000029& 219.194&   0.1084306889&     57.95&\PS+\TO+\NH-\NO          &     -4.26&   0.03\cr
 62& -0.0000027& 263.740&   0.0089823923&    699.50&\TO+\PH-\PT-\NH+\NT      &     -3.98&   0.05\cr
 63&  0.0000025&   2.780&   0.0088044329&    713.64&\TO+\PH-\PT+\NH-\NT      &      3.75&   0.05\cr
 64& -0.0000022& 273.191&   0.0295452359&    212.66&  3\TO-\NH+\NO           &     -3.30&   0.03\cr
 65&  0.0000022& 346.868&   0.0293180038&    214.31&  3\TO+\NH-\NO           &      3.27&   0.03\cr
 66&  0.0000021& 156.715&   0.0490526998&    128.09&  5\TO                   &      3.09&   0.02\cr
 67& -0.0000021& 158.900&   0.0683850178&     91.88&\PS -3\TO+\PH-\PT        &     -3.08&   0.01\cr
 68&  0.0000021&  25.296&   0.0024748575&   2538.81& -3\PH+\PT+ 2\NH         &      3.04&   0.04\cr
 69&  0.0000019&  99.066&   0.0702192725&     89.48&\PS -3\TO-\PH+\PT        &      2.86&   0.01\cr
 70&  0.0000019& 266.520&   0.0177868252&    353.25&  2\TO+ 2\PH -2\PT       &      2.77&   0.01\cr
 71&  0.0000018& 280.457&   0.0873654949&     71.92&\PS-\TO+ 2\PH -2\NH      &      2.66&   0.03\cr
 72&  0.0000017& 132.385&   0.1379759248&     45.54&\PS+ 4\TO                &      2.56&   0.01\cr
 73&  0.0000017& 261.899&   0.0211788101&    296.67&  2\TO -2\PH+ 2\NH       &      2.49&   0.03\cr
 74&  0.0000015& 121.808&   0.0080255777&    782.90&\TO+ 2\PH -2\NO          &      2.28&   0.00\cr
 75& -0.0000015& 269.165&   0.0789990691&     79.53&\PS -2\TO+\NH-\NO        &     -2.26&   0.02\cr
 76& -0.0000015& 341.535&   0.0017849622&   3520.07& -2\PH+ 2\NO             &     -2.22&   0.00\cr
 77& -0.0000015& 266.108&   0.0107523037&    584.36&\TO-\PH+\PT-\NT+\NO      &     -2.26&   0.03\cr
 78&  0.0000015& 195.488&   0.0792263012&     79.31&\PS -2\TO-\NH+\NO        &      2.19&   0.02\cr
 79&  0.0000015& 151.634&   0.0105647588&    594.73&\TO-\PH-\PT+\NH+\NO      &      2.15&   0.02\cr
 80&  0.0000015& 240.745&   0.0107030309&    587.05&\TO-\PH+\PT+\NT-\NO      &      2.20&   0.02\cr
 81& -0.0000012&  84.879&   0.0115955022&    541.86&\TO -2\PH+ 2\NO          &     -1.84&   0.00\cr
 82& -0.0000012&  13.592&   0.0125619220&    500.18&\TO -3\PH+ 3\PT          &     -1.81&   0.00\cr
 83&  0.0000012& 205.190&   0.0888342454&     70.73&\PS-\TO+\NH-\NT          &      1.84&   0.02\cr
 84& -0.0000012& 106.149&   0.0890122048&     70.59&\PS-\TO-\NH+\NT          &     -1.81&   0.02\cr
 85& -0.0000012& 146.852&   0.0214553346&    292.85&  2\TO -2\PH+ 2\PT       &     -1.76&   0.01\cr
 86& -0.0000012& 237.568&   0.1101020351&     57.07&\PS+\TO -2\PH+ 2\NH      &     -1.78&   0.02\cr
 87& -0.0000011&  35.503&   0.0870889704&     72.15&\PS-\TO+ 2\PH -2\PT      &     -1.67&   0.00\cr
 88& -0.0000011&  91.800&   0.0123990135&    506.75&\TO -3\PH+\PT+\NH+\NO    &     -1.63&   0.01\cr
 89&  0.0000010& 325.942&   0.0089180490&    704.55&\TO+\PH-\PT-\NT+\NO      &      1.52&   0.02\cr
 90& -0.0000010& 312.835&   0.1086332847&     57.84&\PS+\TO-\NH+\NT          &     -1.51&   0.02\cr
 91& -0.0000010& 300.578&   0.0088687762&    708.46&\TO+\PH-\PT+\NT-\NO      &     -1.50&   0.02\cr
 92&  0.0000010&  51.876&   0.1084553253&     57.93&\PS+\TO+\NH-\NT          &      1.48&   0.02\cr
 93& -0.0000011& 282.297&   0.0496810653&    126.47&\PS -5\TO                &     -1.57&   0.02\cr
 94&  0.0000009& 188.312&   0.0179497337&    350.04&  2\TO+ 2\PH-\NH-\NO     &      1.40&   0.01\cr
 95& -0.0000009& 250.195&   0.0312658746&    200.96&  3\TO -2\PH+ 2\PT       &     -1.37&   0.01\cr
 96& -0.0000009&  55.557&   0.0585744779&    107.27&\PS -4\TO+\PH-\PT        &     -1.32&   0.01\cr
 97& -0.0000009& 254.817&   0.0278738897&    225.41&  3\TO+ 2\PH -2\NH       &     -1.27&   0.02\cr
 98&  0.0000008& 169.848&   0.0197346960&    318.38&  2\TO-\NH+\NO           &      1.25&   0.01\cr
 99& -0.0000009& 314.489&   0.0080502141&    780.50&\TO+ 2\PH-\NT-\NO        &     -1.27&   0.01\cr
100& -0.0000008&  30.882&   0.0904809552&     69.44&\PS-\TO -2\PH+ 2\NH      &     -1.22&   0.02\cr
101&  0.0000008&  18.214&   0.0091699372&    685.19&\TO+\PH+\PT -2\NH        &      1.19&   0.02\cr
102& -0.0000008&  58.959&   0.1272482575&     49.38&\PS+ 3\TO+\PH-\PT        &     -1.16&   0.00\cr
103&  0.0000008& 355.723&   0.0604087326&    104.01&\PS -4\TO-\PH+\PT        &      1.17&   0.00\cr
104&  0.0000008&   5.242&   0.0309893500&    202.75&  3\TO -2\PH+ 2\NH       &      1.18&   0.02\cr
105&  0.0000008& 122.522&   0.1103785597&     56.92&\PS+\TO -2\PH+ 2\PT      &      1.13&   0.00\cr
106&  0.0000008& 127.143&   0.1069865748&     58.73&\PS+\TO+ 2\PH -2\NH      &      1.12&   0.01\cr
107&  0.0000008&  80.509&   0.0295205995&    212.84&  3\TO-\NH+\NT           &      1.15&   0.01\cr
108& -0.0000008& 179.549&   0.0293426402&    214.13&  3\TO+\NH-\NT           &     -1.13&   0.01\cr
109& -0.0000007& 243.525&   0.0195074639&    322.09&  2\TO+\NH-\NO           &     -1.08&   0.01\cr
110&  0.0000007&  48.291&   0.0007542188&   8330.72&-\PH-\PT+\NH+\NO         &      1.04&   0.01\cr
 111& -0.0000007& 248.860&   0.1184684610&     53.04&\PS+ 2\TO-\NH+\NO        &     -1.02&   0.01\crs
 112&  0.0024777& 158.025&   0.1974675301&     31.82&  2\PS                   &   3672.78&   0.85\cr
 113&  0.0011774& 237.037&   0.2962012951&     21.21&  3\PS                   &   1745.35&   0.43\cr
 114&  0.0007098& 316.050&   0.3949350601&     15.91&  4\PS                   &   1052.09&   0.23\cr
 115&  0.0004277&  35.062&   0.4936688251&     12.73&  5\PS                   &    633.97&   0.17\cr
 116&  0.0002883& 114.074&   0.5924025902&     10.61&  6\PS                   &    427.37&   0.12\cr
 117&  0.0002445&  54.682&   0.1876569901&     33.48&  2\PS-\TO               &    362.46&   0.40\cr
 118&  0.0002080& 133.694&   0.2863907551&     21.94&  3\PS-\TO               &    308.27&   0.35\cr
 119&  0.0001998& 193.087&   0.6911363552&      9.09&  7\PS                   &    296.12&   0.10\cr
 120&  0.0001532& 212.707&   0.3851245202&     16.31&  4\PS-\TO               &    227.10&   0.26\cr
 121&  0.0001392& 272.099&   0.7898701202&      7.95&  8\PS                   &    206.31&   0.08\cr
 122& -0.0001347& 340.380&   0.3060118350&     20.53&  3\PS+\TO               &   -199.68&   0.23\cr
 123& -0.0001169& 261.368&   0.2072780700&     30.31&  2\PS+\TO               &   -173.23&   0.18\cr
 124&  0.0001158& 291.719&   0.4838582852&     12.99&  5\PS-\TO               &    171.71&   0.19\cr
 125& -0.0001110&  59.393&   0.4047456001&     15.52&  4\PS+\TO               &   -164.57&   0.19\cr
 126&  0.0000988& 351.112&   0.8886038852&      7.07&  9\PS                   &    146.40&   0.06\cr
 127&  0.0000936&  10.731&   0.5825920502&     10.78&  6\PS-\TO               &    138.76&   0.15\cr
 128& -0.0000879& 138.405&   0.5034793651&     12.48&  5\PS+\TO               &   -130.26&   0.15\cr
 129&  0.0000763&  89.744&   0.6813258152&      9.22&  7\PS-\TO               &    113.05&   0.12\cr
 130& -0.0000742& 217.418&   0.6022131301&     10.43&  6\PS+\TO               &   -110.04&   0.12\cr
 131&  0.0000707&  70.124&   0.9873376503&      6.36& 10\PS                   &    104.78&   0.05\cr
 132& -0.0000695& 187.942&   0.1965504027&     31.97&  2\PS+\PH-\PT           &   -102.98&   0.06\cr
133& -0.0000651& 311.339&   0.1778464501&     35.33&  2\PS -2\TO             &    -96.57&   0.20\cr
134& -0.0000625& 296.430&   0.7009468951&      8.96&  7\PS+\TO               &    -92.58&   0.10\cr
135&  0.0000624& 168.756&   0.7800595803&      8.05&  8\PS-\TO               &     92.44&   0.09\cr
136& -0.0000521&  15.442&   0.7996806602&      7.86&  8\PS+\TO               &    -77.26&   0.08\cr
137&  0.0000509& 149.137&   1.0860714153&      5.79& 11\PS                   &     75.41&   0.04\cr
138&  0.0000506& 247.769&   0.8787933453&      7.15&  9\PS-\TO               &     74.99&   0.07\cr
139& -0.0000481&   4.711&   0.2170886100&     28.94&  2\PS+ 2\TO             &    -71.35&   0.15\cr
140& -0.0000430&  94.455&   0.8984144252&      6.99&  9\PS+\TO               &    -63.76&   0.06\cr
141&  0.0000410& 326.781&   0.9775271103&      6.43& 10\PS-\TO               &     60.84&   0.06\cr
142&  0.0000367& 228.149&   1.1848051803&      5.30& 12\PS                   &     54.33&   0.04\cr
143& -0.0000354& 173.467&   0.9971481902&      6.30& 10\PS+\TO               &    -52.45&   0.05\cr
144&  0.0000333&  45.793&   1.0762608753&      5.84& 11\PS-\TO               &     49.31&   0.04\cr
145& -0.0000290& 252.480&   1.0958819553&      5.73& 11\PS+\TO               &    -43.02&   0.04\cr
146&  0.0000269& 124.806&   1.1749946404&      5.35& 12\PS-\TO               &     39.93&   0.03\cr
147&  0.0000267& 345.967&   0.3940179328&     15.95&  4\PS+\PH-\PT           &     39.56&   0.02\cr
148&  0.0000264& 307.161&   1.2835389454&      4.90& 13\PS                   &     39.14&   0.04\cr
149& -0.0000237& 331.492&   1.1946157203&      5.26& 12\PS+\TO               &    -35.19&   0.03\cr
150&  0.0000218& 203.818&   1.2737284054&      4.93& 13\PS-\TO               &     32.26&   0.03\cr
151& -0.0000193&  50.505&   1.2933494853&      4.86& 13\PS+\TO               &    -28.68&   0.02\cr
152&  0.0000190&  26.174&   1.3822727104&      4.55& 14\PS                   &     28.13&   0.03\cr
153&  0.0000175& 282.831&   1.3724621704&      4.58& 14\PS-\TO               &     26.01&   0.02\cr
154&  0.0000157& 128.108&   0.1983846574&     31.67&  2\PS-\PH+\PT           &     23.31&   0.02\cr
155& -0.0000157& 129.517&   1.3920832503&      4.51& 14\PS+\TO               &    -23.30&   0.02\cr
156& -0.0000154&  83.723&   0.3158223750&     19.89&  3\PS+ 2\TO             &    -22.83&   0.05\cr
157&  0.0000141&   1.843&   1.4711959355&      4.27& 15\PS-\TO               &     20.91&   0.01\cr
158&  0.0000136& 105.186&   1.4810064754&      4.24& 15\PS                   &     20.12&   0.03\cr
159& -0.0000127& 208.529&   1.4908170154&      4.21& 15\PS+\TO               &    -18.88&   0.01\cr
160&  0.0000116& 346.401&   0.6715152753&      9.36&  7\PS -2\TO             &     17.25&   0.04\cr
161&  0.0000114& 267.388&   0.5727815103&     10.97&  6\PS -2\TO             &     16.89&   0.04\cr
162&  0.0000114&  65.413&   0.7702490403&      8.16&  8\PS -2\TO             &     16.89&   0.04\cr
163&  0.0000114& 266.954&   0.2952841677&     21.28&  3\PS+\PH-\PT           &     16.83&   0.01\cr
164&  0.0000113&  80.856&   1.5699297005&      4.00& 16\PS-\TO               &     16.77&   0.01\cr
165&  0.0000109& 144.426&   0.8689828053&      7.23&  9\PS -2\TO             &     16.09&   0.03\cr
 166& -0.0000106&  30.351&   0.2765802152&     22.72&  3\PS -2\TO             &    -15.67&   0.03\cr
167&  0.0000104& 188.376&   0.4740477452&     13.25&  5\PS -2\TO             &     15.37&   0.04\cr
168& -0.0000103& 287.542&   1.5895507804&      3.95& 16\PS+\TO               &    -15.23&   0.01\cr
169&  0.0000103&  24.765&   0.1885741175&     33.32&  2\PS-\TO-\PH+\PT       &     15.23&   0.03\cr
170&  0.0000101& 223.438&   0.9677165704&      6.49& 10\PS -2\TO             &     14.92&   0.03\cr
171&  0.0000096& 184.199&   1.5797402404&      3.98& 16\PS                   &     14.28&   0.02\cr
172&  0.0000092& 302.450&   1.0664503354&      5.89& 11\PS -2\TO             &     13.60&   0.03\cr
173&  0.0000091& 159.868&   1.6686634655&      3.77& 17\PS-\TO               &     13.44&   0.01\cr
174&  0.0000089& 207.120&   0.2971184224&     21.15&  3\PS-\PH+\PT           &     13.12&   0.01\cr
175&  0.0000083&  21.463&   1.1651841004&      5.39& 12\PS -2\TO             &     12.23&   0.03\cr
176& -0.0000083&   6.554&   1.6882845454&      3.72& 17\PS+\TO               &    -12.24&   0.01\cr
177&  0.0000079& 103.777&   0.2873078825&     21.87&  3\PS-\TO-\PH+\PT       &     11.72&   0.02\cr
178& -0.0000079& 291.285&   0.2063609427&     30.45&  2\PS+\TO+\PH-\PT       &    -11.64&   0.02\cr
179&  0.0000073& 100.475&   1.2639178654&      4.97& 13\PS -2\TO             &     10.88&   0.02\cr
180&  0.0000072& 238.880&   1.7673972305&      3.56& 18\PS-\TO               &     10.72&   0.01\cr
181&  0.0000068& 263.211&   1.6784740055&      3.74& 17\PS                   &     10.03&   0.02\cr
182& -0.0000066&  85.567&   1.7870183104&      3.52& 18\PS+\TO               &     -9.81&   0.00\cr
183&  0.0000065& 197.798&   0.9082249652&      6.92&  9\PS+ 2\TO             &      9.70&   0.02\cr
184&  0.0000065& 179.488&   1.3626516305&      4.61& 14\PS -2\TO             &      9.59&   0.02\cr
185&  0.0000064& 276.810&   1.0069587302&      6.24& 10\PS+ 2\TO             &      9.53&   0.02\cr
186&  0.0000063& 118.786&   0.8094912001&      7.76&  8\PS+ 2\TO             &      9.38&   0.02\cr
187& -0.0000063& 163.611&   0.2854736278&     22.01&  3\PS-\TO+\PH-\PT       &     -9.40&   0.02\cr
188&  0.0000061& 355.823&   1.1056924952&      5.68& 11\PS+ 2\TO             &      9.08&   0.02\cr
189&  0.0000057& 317.893&   1.8661309956&      3.37& 19\PS-\TO               &      8.52&   0.00\cr
190&  0.0000057&  74.835&   1.2044262602&      5.22& 12\PS+ 2\TO             &      8.46&   0.02\cr
191&  0.0000058& 182.790&   0.3860416475&     16.28&  4\PS-\TO-\PH+\PT       &      8.53&   0.02\cr
192&  0.0000056&  39.773&   0.7107574351&      8.84&  7\PS+ 2\TO             &      8.37&   0.02\cr
193&  0.0000056& 258.500&   1.4613853955&      4.30& 15\PS -2\TO             &      8.37&   0.02\cr
194&  0.0000054& 109.363&   0.3753139802&     16.74&  4\PS -2\TO             &      8.05&   0.02\cr
195&  0.0000054& 286.133&   0.3958521875&     15.87&  4\PS-\PH+\PT           &      7.93&   0.01\cr
196&  0.0000053&  64.979&   0.4927516978&     12.75&  5\PS+\PH-\PT           &      7.78&   0.01\cr
197& -0.0000053& 164.579&   1.8857520755&      3.33& 19\PS+\TO               &     -7.82&   0.00\cr
198&  0.0000052& 153.848&   1.3031600253&      4.82& 13\PS+ 2\TO             &      7.75&   0.02\cr
199&  0.0000049& 337.512&   1.5601191605&      4.03& 16\PS -2\TO             &      7.25&   0.02\cr
200&  0.0000047& 232.860&   1.4018937903&      4.48& 14\PS+ 2\TO             &      7.00&   0.01\cr
201&  0.0000047& 342.223&   1.7772077705&      3.54& 18\PS                   &      6.96&   0.02\cr
202&  0.0000046&  36.905&   1.9648647606&      3.20& 20\PS-\TO               &      6.76&   0.00\cr
203& -0.0000044& 287.008&   0.2667696752&     23.55&  3\PS -3\TO             &     -6.55&   0.02\cr
204&  0.0000043& 320.761&   0.6120236701&     10.27&  6\PS+ 2\TO             &      6.43&   0.01\cr
205& -0.0000044& 207.996&   0.1680359102&     37.39&  2\PS -3\TO             &     -6.49&   0.02\cr
206&  0.0000043&  56.525&   1.6588529256&      3.79& 17\PS -2\TO             &      6.32&   0.01\cr
207&  0.0000043& 261.802&   0.4847754125&     12.96&  5\PS-\TO-\PH+\PT       &      6.36&   0.01\cr
208&  0.0000042& 311.872&   1.5006275553&      4.19& 15\PS+ 2\TO             &      6.26&   0.01\cr
209& -0.0000042& 243.591&   1.9844858405&      3.17& 20\PS+\TO               &     -6.22&   0.00\cr
210&  0.0000037&  30.885&   1.5993613203&      3.93& 16\PS+ 2\TO             &      5.53&   0.01\cr
211&  0.0000036& 115.918&   2.0635985256&      3.04& 21\PS-\TO               &      5.39&   0.01\cr
212&  0.0000034&   5.145&   0.4945859525&     12.70&  5\PS-\PH+\PT           &      5.05&   0.00\cr
213& -0.0000035& 242.623&   0.3842073928&     16.35&  4\PS-\TO+\PH-\PT       &     -5.19&   0.01\cr
 214&  0.0000035& 340.815&   0.5835091776&     10.77&  6\PS-\TO-\PH+\PT       &      5.12&   0.01\cr
\noalign{\medskip\hrule}
 }

% series z :
\bigskip
\noindent{\bf Table 6.} Series for $z_7= 
 e_7\,\exp\sqi\varpi_7$ :
 Each term
is in the form $\alpha\exp\sqi(\omega t+\varphi)$
with $t=(\hbox{Julian Date)}-2\,451\,545.0$.
Each argument is also identified as an integer
 combination of the seven fundamental arguments
 given in Table 3; $\omega $ and $\varphi$ are in
 fact computed from these combinations.
The amplitudes in km represent $A_7z_7$ 
with $A_7=
 1482333.4$~km.
\medskip
 \halign{
$#$\hfil&\qhfil$#$&\qhfil$#$&\qhfil$#$&\qhfil$#$&
\quad\quad$#$\hfil
&\qhfil$#$&\qhfil$#$\cr
\noalign{\hrule\medskip}
\hbox{n\Deg}
 &\hfill\hbox{amplitude $\alpha $}\hfill
 &\hfill\hbox{phase $\varphi$}\hfill
 &\hfill\hbox{frequency $\omega $}\hfill
 &\hfill\hbox{period}\hfill
 &\hfill\hbox{argument}\hfill
 &\hfill\hbox{amplitude}\hfill
 &\hfill\hbox{$\varepsilon(\alpha)$}\hfill
 \cr 
 &\hfill\hbox{(rad)}\hfill
 &\hfill\hbox{(deg)}\hfill
 &\hfill\hbox{(rad/d)}\hfill
 &\hfill\hbox{(d)}\hfill
 & 
 &\hfill\hbox{(km)}\hfill
 &\hfill\hbox{(km)}\hfill
\cr
\noalign{\medskip\hrule\medskip}
   1&  0.1030661& 193.814&  -0.0008924811&   7040.13&\PH                      & 152778.39&  46.77\cr
   2&  0.0244818& 163.897&   0.0000246462& 254934.93&\PT                      &  36290.25&  20.63\cr
   3& -0.0025006& 297.157&   0.0089180588&    704.55&\TO+\PH                  &  -3706.74&   4.04\cr
   4& -0.0016531&  90.471&  -0.0107030211&    587.05&-\TO+\PH                 &  -2450.48&   2.65\cr
   5& -0.0011220& 272.826&   0.0978412839&     64.22&\PS+\PH                  &  -1663.13&   0.38\cr
   6&  0.0007518& 114.802&  -0.0996262462&     63.07&-\PS+\PH                 &   1114.43&   0.39\cr
   7&  0.0002580& 218.145&  -0.0898157062&     69.96&-\PS+\TO+\PH             &    382.46&   0.43\cr
   8& -0.0001702&  11.458&  -0.1094367861&     57.41&-\PS-\TO+\PH             &   -252.33&   0.28\cr
   9& -0.0001630&  16.169&   0.1076518239&     58.37&\PS+\TO+\PH              &   -241.69&   0.27\cr
  10&  0.0001502& 169.483&   0.0880307439&     71.37&\PS-\TO+\PH              &    222.66&   0.25\cr
  11&  0.0001081& 267.240&   0.0098351862&    638.85&\TO+\PT                  &    160.20&   0.25\cr
  12&  0.0000856& 223.731&  -0.0018096085&   3472.12&  2\PH-\PT               &    126.94&   0.18\cr
  13& -0.0000764& 327.074&   0.0080009315&    785.31&\TO+ 2\PH-\PT            &   -113.28&   0.18\cr
 14&  0.0000641& 230.652&  -0.0010060972&   6245.11&\PH+\NH-\NO              &     95.02&   0.56\cr
 15& -0.0000638& 156.975&  -0.0007788651&   8067.10&\PH-\NH+\NO              &    -94.57&   0.56\cr
 16& -0.0000374&  40.500&   0.0187285988&    335.49&  2\TO+\PH               &    -55.42&   0.13\cr
 17&  0.0000318& 242.909&   0.0987584113&     63.62&\PS+\PT                  &     47.10&   0.03\cr
 18&  0.0000307& 120.388&  -0.0116201484&    540.71&-\TO+ 2\PH-\PT           &     45.48&   0.08\cr
 19&  0.0000273& 249.026&   0.0006652490&   9444.86&-\PH+ 2\NH               &     40.51&   0.48\cr
 20&  0.0000256& 321.488&  -0.0800051662&     78.53&-\PS+ 2\TO+\PH           &     37.94&   0.09\cr
 21&  0.0000202&  66.140&   0.0782202040&     80.33&\PS -2\TO+\PH            &     30.01&   0.06\cr
 22& -0.0000202&  63.334&  -0.0009814608&   6401.87&\PH+\NH-\NT              &    -29.93&   0.31\cr
 23&  0.0000201& 324.294&  -0.0008035014&   7819.76&\PH-\NH+\NT              &     29.77&   0.31\cr
 24& -0.0000181& 347.128&  -0.0205135610&    306.29& -2\TO+\PH               &    -26.85&   0.05\cr
 25&  0.0000124&  60.554&  -0.0097858937&    642.07&-\TO+\PT                 &     18.32&   0.03\cr
 26&  0.0000117& 143.843&   0.0285391387&    220.16&  3\TO+\PH               &     17.29&   0.05\cr
 27&  0.0000109& 243.785&  -0.0303241010&    207.20& -3\TO+\PH               &     16.11&   0.05\cr
 28& -0.0000104& 188.228&  -0.0888985788&     70.68&-\PS+\TO+\PT             &    -15.46&   0.02\cr
 29&  0.0000082&   1.132&  -0.0009171175&   6851.01&\PH+\NT-\NO              &     12.22&   0.11\cr
 30& -0.0000082&  26.496&  -0.0008678448&   7239.99&\PH-\NT+\NO              &    -12.16&   0.11\cr
 31&  0.0000080&  84.885&  -0.0987091188&     63.65&-\PS+\PT                 &     11.86&   0.01\cr
 32&  0.0000080& 119.513&   0.1174623638&     53.49&\PS+ 2\TO+\PH            &     11.81&   0.02\cr
 33&  0.0000072& 346.253&   0.1085689512&     57.87&\PS+\TO+\PT              &     10.73&   0.02\cr
 34&  0.0000073& 138.601&  -0.0024502113&   2564.34&  3\PH -2\NH             &     10.78&   0.13\cr
  35&  0.0000067& 248.061&  -0.0907328336&     69.25&-\PS+\TO+ 2\PH-\PT       &      9.96&   0.02\cr
 36&  0.0000067& 278.943&  -0.0002518783&  24945.32&-\PT+ 2\NH               &      9.99&   0.12\cr
 37&  0.0000052& 268.115&  -0.1192473261&     52.69&-\PS -2\TO+\PH           &      7.71&   0.02\cr
 38& -0.0000052& 212.188&   0.0007788651&   8067.10&-\PH+\NH+\NO             &     -7.72&   0.05\cr
 39&  0.0000050&  53.632&  -0.0105894050&    593.35&-\TO+\PH-\NH+\NO         &      7.48&   0.05\cr
 40& -0.0000050& 127.309&  -0.0108166371&    580.88&-\TO+\PH+\NH-\NO         &     -7.46&   0.05\cr
 41& -0.0000048&  46.086&   0.1067346965&     58.87&\PS+\TO+ 2\PH-\PT        &     -7.17&   0.01\cr
 42& -0.0000046& 260.319&   0.0090316749&    695.68&\TO+\PH-\NH+\NO          &     -6.84&   0.05\cr
 43&  0.0000044& 333.996&   0.0088044428&    713.64&\TO+\PH+\NH-\NO          &      6.59&   0.04\cr
 44& -0.0000042& 241.945&   0.0073603287&    853.66&\TO+ 3\PH -2\NH          &     -6.16&   0.08\cr
 45& -0.0000039& 322.797&   0.0684096640&     91.85&\PS -3\TO+\PH            &     -5.75&   0.02\cr
 46&  0.0000036&  41.375&  -0.1103539135&     56.94&-\PS-\TO+ 2\PH-\PT       &      5.35&   0.01\cr
 47& -0.0000031&  64.831&  -0.0701946263&     89.51&-\PS+ 3\TO+\PH           &     -4.61&   0.01\cr
 48& -0.0000027& 199.400&   0.0871136166&     72.13&\PS-\TO+ 2\PH-\PT        &     -3.98&   0.01\cr
 49&  0.0000025& 222.856&   0.1272729038&     49.37&\PS+ 3\TO+\PH            &      3.77&   0.01\cr
 50& -0.0000025& 302.743&   0.0969241565&     64.83&\PS+ 2\PH-\PT            &     -3.75&   0.00\cr
 51&  0.0000025&  10.583&   0.0196457261&    319.82&  2\TO+\PT               &      3.66&   0.01\cr
 52& -0.0000024&  70.417&   0.0178114714&    352.76&  2\TO+ 2\PH-\PT         &     -3.55&   0.01\cr
 53&  0.0000023& 164.772&  -0.1290578660&     48.69&-\PS -3\TO+\PH           &      3.44&   0.01\cr
 54& -0.0000023& 237.323&   0.0107523135&    584.36&\TO-\PH+ 2\PT            &     -3.34&   0.01\cr
 55& -0.0000020& 291.571&  -0.0790880389&     79.45&-\PS+ 2\TO+\PT           &     -3.02&   0.01\cr
 56&  0.0000020& 352.369&   0.0104757890&    599.78&\TO-\PH+ 2\NH            &      2.93&   0.04\cr
 57& -0.0000018& 175.440&  -0.0025638273&   2450.71&  3\PH-\NH-\NO           &     -2.69&   0.02\cr
 58& -0.0000018& 253.648&  -0.0027267358&   2304.29&  3\PH -2\PT             &     -2.61&   0.00\cr
 59&  0.0000017& 319.991&  -0.0107920008&    582.21&-\TO+\PH+\NH-\NT         &      2.53&   0.03\cr
 60& -0.0000017& 220.951&  -0.0106140414&    591.97&-\TO+\PH-\NH+\NT         &     -2.53&   0.03\cr
 61&  0.0000016&  67.637&   0.0090070385&    697.59&\TO+\PH-\NH+\NT          &      2.43&   0.03\cr
 62& -0.0000015& 317.211&  -0.0195964337&    320.63& -2\TO+\PT               &     -2.30&   0.01\cr
 63& -0.0000016& 166.677&   0.0088290791&    711.65&\TO+\PH+\NH-\NT          &     -2.36&   0.03\cr
 64&  0.0000015&  19.506&   0.0007542287&   8330.61&-\PH+\NH+\NT             &      2.23&   0.02\cr
 65&  0.0000014& 200.736&  -0.0000889698&  70621.54&\PT+\NH-\NO              &      2.06&   0.01\cr
 66& -0.0000013& 145.683&  -0.0091452909&    687.04&-\TO-\PH+ 2\NH           &     -1.98&   0.03\cr
 67&  0.0000013& 351.405&  -0.0809222936&     77.64&-\PS+ 2\TO+ 2\PH-\PT     &      1.90&   0.01\cr
 68&  0.0000013&  30.637&  -0.0088687664&    708.46&-\TO-\PH+ 2\PT           &      1.89&   0.00\cr
 69& -0.0000011& 113.926&   0.0294562661&    213.31&  3\TO+\PT               &     -1.60&   0.01\cr
 70& -0.0000011&  96.057&   0.0773030766&     81.28&\PS -2\TO+ 2\PH-\PT      &     -1.61&   0.00\cr
 71&  0.0000011&  17.045&  -0.0214306884&    293.19& -2\TO+ 2\PH-\PT         &      1.59&   0.00\cr
 72& -0.0000011& 242.105&  -0.0001382623&  45443.96&-\PT+\NH+\NO             &     -1.57&   0.01\cr
 73& -0.0000011& 108.685&  -0.0015330839&   4098.40&  2\PH+\PT -2\NH         &     -1.56&   0.02\cr
 74&  0.0000010& 144.718&  -0.1005433735&     62.49&-\PS+ 2\PH-\PT           &      1.51&   0.00\cr
 75&  0.0000009& 278.783&   0.0072467126&    867.04&\TO+ 3\PH-\NH-\NO        &      1.37&   0.01\cr
 76&  0.0000009& 173.760&   0.0276220114&    227.47&  3\TO+ 2\PH-\PT         &      1.26&   0.00\cr
 77& -0.0000008& 273.702&  -0.0312412283&    201.12& -3\TO+ 2\PH-\PT         &     -1.11&   0.00\cr
 78& -0.0000007& 168.174&  -0.0603840863&    104.05&-\PS+ 4\TO+\PH           &     -1.10&   0.01\cr
  79& -0.0000007& 139.566&   0.0889478713&     70.64&\PS-\TO+\PT              &     -1.02&   0.00\crs
  80&  0.0003778&  35.789&  -0.1983600112&     31.68& -2\PS+\PH               &    560.07&   0.17\cr
  81& -0.0003775& 351.839&   0.1965750489&     31.96&  2\PS+\PH               &   -559.65&   0.16\cr
  82& -0.0003598& 149.864&   0.3940425790&     15.95&  4\PS+\PH               &   -533.32&   0.05\cr
  83& -0.0002928&  70.851&   0.2953088140&     21.28&  3\PS+\PH               &   -434.02&   0.09\cr
  84&  0.0002217& 316.777&  -0.2970937762&     21.15& -3\PS+\PH               &    328.61&   0.10\cr
  85&  0.0001404& 237.764&  -0.3958275412&     15.87& -4\PS+\PH               &    208.10&   0.08\cr
  86&  0.0001283& 139.132&  -0.1885494712&     33.32& -2\PS+\TO+\PH           &    190.14&   0.21\cr
  87& -0.0000984& 292.446&  -0.2081705511&     30.18& -2\PS-\TO+\PH           &   -145.91&   0.16\cr
  88&  0.0000930& 158.752&  -0.4945613063&     12.70& -5\PS+\PH               &    137.90&   0.06\cr
  89&  0.0000861&  60.120&  -0.2872832363&     21.87& -3\PS+\TO+\PH           &    127.61&   0.13\cr
  90& -0.0000698& 213.434&  -0.3069043162&     20.47& -3\PS-\TO+\PH           &   -103.41&   0.11\cr
 91&  0.0000639& 341.107&  -0.3860170013&     16.28& -4\PS+\TO+\PH           &     94.78&   0.10\cr
 92&  0.0000639&  79.739&  -0.5932950713&     10.59& -6\PS+\PH               &     94.68&   0.05\cr
 93& -0.0000534& 134.421&  -0.4056380812&     15.49& -4\PS-\TO+\PH           &    -79.14&   0.08\cr
 94&  0.0000491& 262.095&  -0.4847507663&     12.96& -5\PS+\TO+\PH           &     72.76&   0.07\cr
 95&  0.0000481& 228.876&   0.4927763440&     12.75&  5\PS+\PH               &     71.32&   0.02\cr
 96&  0.0000449&   0.727&  -0.6920288363&      9.08& -7\PS+\PH               &     66.51&   0.04\cr
 97& -0.0000418&  55.409&  -0.5043718462&     12.46& -5\PS-\TO+\PH           &    -61.93&   0.06\cr
 98& -0.0000388&  46.520&   0.3842320390&     16.35&  4\PS-\TO+\PH           &    -57.52&   0.06\cr
 99&  0.0000382& 183.083&  -0.5834845313&     10.77& -6\PS+\TO+\PH           &     56.61&   0.05\cr
100& -0.0000355& 327.508&   0.2854982740&     22.01&  3\PS-\TO+\PH           &    -52.68&   0.05\cr
101&  0.0000342& 307.888&   0.5915101090&     10.62&  6\PS+\PH               &     50.63&   0.01\cr
102&  0.0000334& 253.207&   0.4038531189&     15.56&  4\PS+\TO+\PH           &     49.51&   0.05\cr
103& -0.0000330& 336.396&  -0.6031056112&     10.42& -6\PS-\TO+\PH           &    -48.93&   0.05\cr
104&  0.0000318& 281.715&  -0.7907626013&      7.95& -8\PS+\PH               &     47.15&   0.04\cr
105&  0.0000300& 104.070&  -0.6822182964&      9.21& -7\PS+\TO+\PH           &     44.52&   0.04\cr
106&  0.0000273&   5.872&  -0.1974428838&     31.82& -2\PS+\PT               &     40.46&   0.02\cr
107& -0.0000263& 257.384&  -0.7018393763&      8.95& -7\PS-\TO+\PH           &    -38.98&   0.03\cr
108&  0.0000247& 174.194&   0.3051193539&     20.59&  3\PS+\TO+\PH           &     36.67&   0.04\cr
109& -0.0000242& 248.496&   0.1867645090&     33.64&  2\PS-\TO+\PH           &    -35.83&   0.03\cr
110&  0.0000238&  25.058&  -0.7809520614&      8.05& -8\PS+\TO+\PH           &     35.34&   0.03\cr
111&  0.0000226& 202.702&  -0.8894963664&      7.06& -9\PS+\PH               &     33.50&   0.03\cr
112& -0.0000211& 178.371&  -0.8005731413&      7.85& -8\PS-\TO+\PH           &    -31.28&   0.03\cr
113&  0.0000190& 306.045&  -0.8796858264&      7.14& -9\PS+\TO+\PH           &     28.20&   0.02\cr
114&  0.0000171& 242.475&  -0.1787389313&     35.15& -2\PS+ 2\TO+\PH         &     25.29&   0.06\cr
115& -0.0000170&  99.359&  -0.8993069063&      6.99& -9\PS-\TO+\PH           &    -25.17&   0.02\cr
116&  0.0000168& 145.153&   0.1769539690&     35.51&  2\PS -2\TO+\PH         &     24.90&   0.05\cr
117&  0.0000160& 123.690&  -0.9882301314&      6.36&-10\PS+\PH               &     23.77&   0.03\cr
118&  0.0000152& 227.033&  -0.9784195914&      6.42&-10\PS+\TO+\PH           &     22.53&   0.02\cr
119&  0.0000138& 163.463&  -0.2774726963&     22.64& -3\PS+ 2\TO+\PH         &     20.45&   0.04\cr
120& -0.0000137&  20.347&  -0.9980406714&      6.30&-10\PS-\TO+\PH           &    -20.26&   0.01\cr
121&  0.0000128& 263.938&   0.9864451691&      6.37& 10\PS+\PH               &     18.96&   0.00\cr
122&  0.0000124& 198.525&   0.2161961288&     29.06&  2\PS+ 2\TO+\PH         &     18.44&   0.04\cr
123&  0.0000123& 184.926&   0.8877114041&      7.08&  9\PS+\PH               &     18.16&   0.00\cr
124&  0.0000123& 135.830&   0.7880605117&      7.97&  8\PS+ 2\PH-\PT         &     18.17&   0.01\cr
125& -0.0000122& 125.533&   0.4829658041&     13.01&  5\PS-\TO+\PH           &    -18.11&   0.02\cr
126&  0.0000121& 148.020&  -1.0771533565&      5.83&-11\PS+\TO+\PH           &     17.98&   0.01\cr
127&  0.0000120&  84.450&  -0.3762064613&     16.70& -4\PS+ 2\TO+\PH         &     17.76&   0.04\cr
128&  0.0000114&  44.677&  -1.0869638964&      5.78&-11\PS+\PH               &     16.83&   0.02\cr
129& -0.0000110& 301.334&  -1.0967744364&      5.73&-11\PS-\TO+\PH           &    -16.28&   0.01\cr
 130&  0.0000107&   5.438&  -0.4749402263&     13.23& -5\PS+ 2\TO+\PH         &     15.85&   0.03\cr
131&  0.0000107& 332.219&   0.5025868840&     12.50&  5\PS+\TO+\PH           &     15.82&   0.02\cr
132&  0.0000097& 342.950&   1.0851789342&      5.79& 11\PS+\PH               &     14.37&   0.00\cr
133&  0.0000097&  69.008&  -1.1758871215&      5.34&-12\PS+\TO+\PH           &     14.35&   0.01\cr
134&  0.0000096& 286.426&  -0.5736739914&     10.95& -6\PS+ 2\TO+\PH         &     14.18&   0.03\cr
135&  0.0000095& 105.913&   0.7889776391&      7.96&  8\PS+\PH               &     14.04&   0.01\cr
136& -0.0000088& 222.322&  -1.1955082014&      5.26&-12\PS-\TO+\PH           &    -13.04&   0.01\cr
137&  0.0000086& 321.922&   0.1974921763&     31.81&  2\PS+\PT               &     12.75&   0.01\cr
138&  0.0000085& 207.413&  -0.6724077564&      9.34& -7\PS+ 2\TO+\PH         &     12.58&   0.03\cr
139&  0.0000080& 325.665&  -1.1856976614&      5.30&-12\PS+\PH               &     11.85&   0.02\cr
140&  0.0000077& 349.996&  -1.2746208865&      4.93&-13\PS+\TO+\PH           &     11.42&   0.00\cr
141&  0.0000075& 128.401&  -0.7711415214&      8.15& -8\PS+ 2\TO+\PH         &     11.08&   0.02\cr
142&  0.0000074& 224.165&   0.2756877340&     22.79&  3\PS -2\TO+\PH         &     10.95&   0.02\cr
143&  0.0000071&  61.963&   1.1839126992&      5.31& 12\PS+\PH               &     10.59&   0.00\cr
144& -0.0000070& 143.309&  -1.2942419664&      4.85&-13\PS-\TO+\PH           &    -10.44&   0.01\cr
145&  0.0000068& 110.090&  -0.3167148561&     19.84& -3\PS -2\TO+\PH         &     10.05&   0.02\cr
146&  0.0000068&  31.078&  -0.4154486211&     15.12& -4\PS -2\TO+\PH         &     10.01&   0.02\cr
147&  0.0000067& 189.103&  -0.2179810911&     28.82& -2\PS -2\TO+\PH         &      9.86&   0.02\cr
148&  0.0000066& 312.066&  -0.5141823862&     12.22& -5\PS -2\TO+\PH         &      9.74&   0.02\cr
149&  0.0000066&  49.388&  -0.8698752865&      7.22& -9\PS+ 2\TO+\PH         &      9.71&   0.02\cr
150&  0.0000064& 277.537&   0.3149298939&     19.95&  3\PS+ 2\TO+\PH         &      9.55&   0.02\cr
151&  0.0000062& 233.053&  -0.6129161512&     10.25& -6\PS -2\TO+\PH         &      9.22&   0.02\cr
152& -0.0000062& 258.793&   0.4918592167&     12.77&  5\PS+ 2\PH-\PT         &     -9.21&   0.01\cr
153&  0.0000061& 270.983&  -1.3733546515&      4.58&-14\PS+\TO+\PH           &      9.08&   0.00\cr
154&  0.0000058& 154.041&  -0.7116499162&      8.83& -7\PS -2\TO+\PH         &      8.53&   0.02\cr
155&  0.0000057& 330.376&  -0.9686090515&      6.49&-10\PS+ 2\TO+\PH         &      8.48&   0.02\cr
156&  0.0000057& 283.558&   0.6804333341&      9.23&  7\PS-\TO+\PH           &      8.46&   0.01\cr
157& -0.0000056&  64.297&  -1.3929757315&      4.51&-14\PS-\TO+\PH           &     -8.33&   0.00\cr
158&  0.0000056& 246.653&  -1.2844314265&      4.89&-13\PS+\PH               &      8.28&   0.02\cr
159&  0.0000055& 140.975&   1.2826464642&      4.90& 13\PS+\PH               &      8.09&   0.00\cr
160&  0.0000052&  75.028&  -0.8103836813&      7.75& -8\PS -2\TO+\PH         &      7.76&   0.02\cr
161&  0.0000050& 251.364&  -1.0673428165&      5.89&-11\PS+ 2\TO+\PH         &      7.38&   0.01\cr
162&  0.0000050&  95.182&   0.2063855889&     30.44&  2\PS+\TO+\PH           &      7.34&   0.02\cr
163& -0.0000050& 262.529&  -0.2072534238&     30.32& -2\PS-\TO+\PT           &     -7.34&   0.01\cr
164&  0.0000049& 191.971&  -1.4720884166&      4.27&-15\PS+\TO+\PH           &      7.21&   0.00\cr
165&  0.0000047& 356.016&  -0.9091174463&      6.91& -9\PS -2\TO+\PH         &      6.98&   0.01\cr
166&  0.0000046& 286.860&  -0.2961766489&     21.21& -3\PS+\PT               &      6.89&   0.00\cr
167& -0.0000045& 345.285&  -1.4917094965&      4.21&-15\PS-\TO+\PH           &     -6.62&   0.00\cr
168&  0.0000044& 219.988&   1.3813802293&      4.55& 14\PS+\PH               &      6.56&   0.00\cr
169&  0.0000043& 172.351&  -1.1660765815&      5.39&-12\PS+ 2\TO+\PH         &      6.37&   0.01\cr
170&  0.0000042& 277.004&  -1.0078512113&      6.23&-10\PS -2\TO+\PH         &      6.23&   0.01\cr
171& -0.0000041& 130.244&   0.7000544140&      8.98&  7\PS+\TO+\PH           &     -6.07&   0.01\cr
172&  0.0000039&  26.901&   0.6902438741&      9.10&  7\PS+\PH               &      5.77&   0.02\cr
173&  0.0000038& 112.958&  -1.5708221816&      4.00&-16\PS+\TO+\PH           &      5.70&   0.00\cr
174&  0.0000038& 167.640&  -1.3831651915&      4.54&-14\PS+\PH               &      5.70&   0.01\cr
175&  0.0000037& 197.991&  -1.1065849763&      5.68&-11\PS -2\TO+\PH         &      5.52&   0.01\cr
176&  0.0000037&  93.339&  -1.2648103466&      4.97&-13\PS+ 2\TO+\PH         &      5.48&   0.01\cr
177& -0.0000035& 266.272&  -1.5904432615&      3.95&-16\PS-\TO+\PH           &     -5.25&   0.00\cr
178&  0.0000035& 299.000&   1.4801139943&      4.25& 15\PS+\PH               &      5.23&   0.00\cr
 179&  0.0000034&  40.934&   0.2962259413&     21.21&  3\PS+\PT               &      5.04&   0.01\cr
\noalign{\medskip\hrule}
 }

\vfill\eject
% series zt :
\bigskip
\noindent{\bf Table 7.} Series for $\zeta_7= 
 \sin(i_7/2)\exp\sqi\Omega_7$ : 
 Each term
is in the form $\alpha\exp\sqi(\omega t+\varphi)$
with $t=(\hbox{Julian Date)}-2\,451\,545.0$.
Each argument is also identified as an integer
 combination of the seven fundamental arguments
 given in Table 3; $\omega $ and $\varphi$ are in
 fact computed from these combinations. The
amplitudes in km represent $2A_7\zeta_7$ 
with $A_7=
 1482333.4$~km.
\medskip
 \halign{
$#$\hfil&\qhfil$#$&\qhfil$#$&\qhfil$#$&\qhfil$#$&
\quad\quad$#$\hfil
&\qhfil$#$&\qhfil$#$\cr
\noalign{\hrule\medskip}
\hbox{n\Deg}
 &\hfill\hbox{amplitude $\alpha $}\hfill
 &\hfill\hbox{phase $\varphi$}\hfill
 &\hfill\hbox{frequency $\omega $}\hfill
 &\hfill\hbox{period}\hfill
 &\hfill\hbox{argument}\hfill
 &\hfill\hbox{amplitude}\hfill
 &\hfill\hbox{$\varepsilon(\alpha)$}\hfill
 \cr 
 &\hfill\hbox{(rad)}\hfill
 &\hfill\hbox{(deg)}\hfill
 &\hfill\hbox{(rad/d)}\hfill
 &\hfill\hbox{(d)}\hfill
 & 
 &\hfill\hbox{(km)}\hfill
 &\hfill\hbox{(km)}\hfill
\cr
\noalign{\medskip\hrule\medskip}
   0&  0.0049552& 184.582&   0.0000000000&& \NO &  14690.65&   0.59\cr
   1&  0.0059485& 221.420&  -0.0001136161&  55301.92&\NH                      &  17635.36& 102.71\cr
   2&  0.0015359& 351.900&  -0.0000246364& 255037.01&\NT                      &   4553.41&  40.15\cr
   3& -0.0001497& 166.208&  -0.0016713462&   3759.36&  2\PH-\NH               &   -443.91&   2.76\cr
   4& -0.0000491& 136.291&  -0.0007542188&   8330.72&\PH+\PT-\NH              &   -145.62&   0.95\cr
  5&  0.0000219& 251.337&  -0.0010307434&   6095.78&\PH-\PT+\NH              &     64.90&   0.42\cr
  6&  0.0000150& 203.046&  -0.0017849622&   3520.07&  2\PH-\NO               &     44.37&   0.04\cr
  7&  0.0000140& 269.551&   0.0081391938&    771.97&\TO+ 2\PH-\NH            &     41.63&   0.28\cr
  8& -0.0000131& 191.503&   0.0008035113&   7819.66&-\PH+\PT+\NH             &    -38.96&   0.25\cr
  9&  0.0000084&  62.865&  -0.0114818862&    547.23&-\TO+ 2\PH-\NH           &     24.87&   0.17\cr
 10&  0.0000075& 106.374&   0.0001629085&  38568.80&  2\PT-\NH               &     22.14&   0.15\cr
 11& -0.0000049& 300.433&   0.0986201490&     63.71&\PS+\NH                  &    -14.57&   0.09\cr
 12&  0.0000045& 173.129&  -0.0008678349&   7240.07&\PH+\PT-\NO              &     13.37&   0.01\cr
 13& -0.0000041&  35.728&  -0.0017603259&   3569.33&  2\PH-\NT               &    -12.29&   0.12\cr
 14&  0.0000038& 142.408&  -0.0988473811&     63.56&-\PS+\NH                 &     11.38&   0.07\cr
  15&  0.0000036& 118.077&  -0.0099241560&    633.12&-\TO+\NH                 &     10.57&   0.07\cr
 16&  0.0000030& 245.220&   0.0970624188&     64.73&\PS+ 2\PH-\NH            &      8.98&   0.06\cr
 17& -0.0000027& 214.499&  -0.0009171274&   6850.94&\PH-\PT+\NO              &     -7.95&   0.01\cr
 18& -0.0000020&  87.195&  -0.1004051112&     62.58&-\PS+ 2\PH-\NH           &     -5.94&   0.04\cr
 19& -0.0000016& 306.389&   0.0080255777&    782.90&\TO+ 2\PH-\NO            &     -4.63&   0.00\cr
 20& -0.0000014& 143.212&   0.0000492925& 127467.47&  2\PT-\NO               &     -4.15&   0.01\cr
 21&  0.0000013& 154.665&   0.0009171274&   6850.94&-\PH+\PT+\NO             &      3.72&   0.00\cr
 22& -0.0000013&   5.811&  -0.0008431985&   7451.61&\PH+\PT-\NT              &     -3.77&   0.04\cr
 23&  0.0000012&  12.894&   0.0179497337&    350.04&  2\TO+ 2\PH-\NH         &      3.62&   0.03\cr
 24& -0.0000012& 190.538&  -0.0905945713&     69.35&-\PS+\TO+ 2\PH-\NH       &     -3.53&   0.02\cr
 25& -0.0000011& 141.877&   0.0872518789&     72.01&\PS-\TO+ 2\PH-\NH        &     -3.33&   0.02\cr
 26&  0.0000011& 348.563&   0.1068729588&     58.79&\PS+\TO+ 2\PH-\NH        &      3.31&   0.02\cr
 27& -0.0000009&  99.703&  -0.0115955022&    541.86&-\TO+ 2\PH-\NO           &     -2.63&   0.00\cr
 28&  0.0000008& 343.852&  -0.1102156512&     57.01&-\PS-\TO+ 2\PH-\NH       &      2.46&   0.02\cr
 29&  0.0000008&  32.948&  -0.0105647588&    594.73&-\TO+\PH+\PT-\NH         &      2.46&   0.02\cr
 30&  0.0000008& 258.259&  -0.0002272321&  27650.96&  2\NH-\NO               &      2.32&   0.03\cr
 31& -0.0000008& 197.089&   0.0888096090&     70.75&\PS-\TO+\NH              &     -2.26&   0.02\cr
 32&  0.0000007&  68.106&   0.0195074639&    322.09&  2\TO+\NH               &      2.20&   0.02\cr
 33& -0.0000007&  14.734&  -0.0197346960&    318.38& -2\TO+\NH               &     -2.16&   0.02\cr
 34&  0.0000007&  21.817&  -0.0009417637&   6671.72&\PH-\PT+\NT              &      2.12&   0.02\cr
 35&  0.0000007& 239.634&   0.0090563211&    693.79&\TO+\PH+\PT-\NH          &      2.05&   0.02\cr
 36&  0.0000007& 196.125&  -0.0025884736&   2427.37&  3\PH-\PT-\NH           &      1.95&   0.01\cr
 37& -0.0000006& 354.680&   0.0087797965&    715.64&\TO+\PH-\PT+\NH          &     -1.86&   0.01\cr
 38& -0.0000006& 319.522&  -0.0212924261&    295.09& -2\TO+ 2\PH-\NH         &     -1.65&   0.01\cr
 39&  0.0000005& 263.594&   0.0987337650&     63.64&\PS+\NO                  &      1.61&   0.00\cr
 40& -0.0000005& 147.994&  -0.0108412834&    579.56&-\TO+\PH-\PT+\NH         &     -1.34&   0.01\cr
 41& -0.0000004& 105.569&  -0.0987337650&     63.64&-\PS+\NO                 &     -1.26&   0.00\cr
 42&  0.0000004& 215.303&   0.0979795462&     64.13&\PS+\PH+\PT-\NH          &      1.25&   0.01\cr
 43&  0.0000004& 139.071&   0.0080502141&    780.50&\TO+ 2\PH-\NT            &      1.27&   0.01\cr
 44& -0.0000004&  81.239&  -0.0098105400&    640.45&-\TO+\NO                 &     -1.22&   0.00\cr
 45&  0.0000004&  88.160&  -0.0090070287&    697.59&-\TO-\PH+\PT+\NH         &      1.16&   0.01\cr
 46&  0.0000004& 245.751&  -0.0890368411&     70.57&-\PS+\TO+\NH             &      1.06&   0.01\cr
  47& -0.0000004& 321.983&   0.0008924910&   7040.05&-\PH+\PT+\NT             &     -1.04&   0.01\crs
  48&  0.0000031&  63.395&  -0.1975811461&     31.80& -2\PS+\NH               &      9.33&   0.05\cr
  49& -0.0000022&  19.445&   0.1973539140&     31.84&  2\PS+\NH               &     -6.43&   0.04\cr
  50&  0.0000018& 324.233&   0.1957961839&     32.09&  2\PS+ 2\PH-\NH         &      5.44&   0.03\cr
  51&  0.0000018& 344.383&  -0.2963149111&     21.20& -3\PS+\NH               &      5.28&   0.03\cr
\noalign{\medskip\hrule}
 }


\def\L#1{\lambda_{o#1}}
\def\PR#1{\varpi_{#1}^{*}}
\def\ND#1{\Omega_{#1}^{*}}
\def\LS{\lambda_{9}}
\def\PRS{\varpi_{9}}
\def\NDS{\Omega_{9}}
\def\NDz{\Omega_{0}}


\vfill\eject
% solar perturbations :
\bigskip
\noindent{\bf Table 8.} 
Solar and short-period perturbations of Hyperion:
These are expressed as $\alpha \cos(\omega t+\phi)$ for $p_7$, as
$\alpha \sin(\omega t+\phi)$ for $q_7$ and as 
$\alpha \exp\sqi(\omega t+\phi)$ for $z_7$ and $\zeta_7$, with 
$t=(\hbox{Julian Date})-2\,451\,545.0$. We give also for each term,
the combination of arguments
from which the frequency and the phase are computed: $\lambda_9$,
 $\varpi_9$ and $\Omega_9$ concern the elements of the Sun
in the saturnicentric Saturn-equatorial reference frame referred to the mean
ecliptic for the J2000.0 epoch, $\L{i}$  refers to the linear part of the mean
 longitude of the satellite $i$ and other arguments to the fundamental arguments
 given in Table 3. Amplitudes in kilometres are computed like in Tables 4 to 7.
\medskip
 \halign{
$#$\hfil&\qhfil$#$&\qhfil$#$&\qhfil$#$&\qhfil$#$&
\quad\quad$#$\qhfil
&\qhfil$#$\cr
\noalign{\hrule\medskip}
 &\hfill\hbox{amplitude $\alpha $}\hfill
 &\hfill\hbox{phase $\varphi$}\hfill
 &\hfill\hbox{frequency $\omega $}\hfill
 &\hfill\hbox{period}\hfill
 &\hfill\hbox{argument}\hfill
 &\hfill\hbox{amplitude}\hfill
 \cr 
 &\hfill\hbox{(rad)}\hfill
 &\hfill\hbox{(deg)}\hfill
 &\hfill\hbox{(rad/d)}\hfill
 &\hfill\hbox{(d)}\hfill
 & &\hfill\hbox{(km)}\hfill
\cr
\noalign{\medskip\hrule\medskip}
%
% perturbations of p_7
%
p_7&  -0.0000268&  123.098&  1.0955449042&        5.74&  \L5-\L7                  &    26.45\cr
&  -0.0000131&  247.802&  2.0004088347&        3.14&  \L4-\L7                  &    12.93\cr
&  -0.0000125&   55.315&  0.2962012606&       21.21&  \L7-\PR7                 &    12.35\cr
&  -0.0000088&   16.193&  0.5894496611&       10.66&  2\L7-2\LS                &     8.68\cr
&  -0.0000030&   85.277&  0.2952841655&       21.28&  \L7-\PR6                 &     2.93\cr
%
% perturbations of q_7
%
\noalign{\medskip\hrule\medskip}
q_7&  -0.0002989&  112.955&  0.0011679623&     5379.61&  2\LS-2\NDS               &  -443.05\cr
&  -0.0002231&  317.020&  0.0005839811&    10759.23&  \LS-\PRS                 &  -330.68\cr
&  -0.0000409&   69.976&  0.0017519434&     3586.41&  3\LS-2\NDS-\PRS          &   -60.67\cr
&  -0.0000233&   94.436&  0.0029528601&     2127.83&  2\LS-2\PR7               &   -34.51\cr
&   0.0000175&  155.935&  0.0005839811&    10759.23&  \LS+\PRS-2\NDS           &    26.00\cr
&  -0.0000160&  124.398&  0.0020357649&     3086.40&  2\LS-\PR7-\PR6           &   -23.72\cr
&  -0.0000137&  274.041&  0.0011679623&     5379.61&  2\LS-2\PRS               &   -20.28\cr
&   0.0000129&   76.654&  0.0012815784&     4902.69&  2\LS-\NDS-\ND7           &    19.10\cr
&   0.0000118&  112.958&  0.0011679623&     5379.61&  2\LS-\NDS-\NDz           &    17.56\cr
&   0.0000037&  307.094&  0.0011925987&     5268.48&  2\LS-\NDS-\ND6           &     5.49\cr
&  -0.0000035&  154.360&  0.0011186698&     5616.66&  2\LS-2\PR6               &    -5.11\cr
&   0.0000146&   55.315&  0.2962012606&       21.21&  \L7-\PR7                 &    21.64\cr
&   0.0000134&  123.098&  1.0955449042&        5.74&  \L5-\L7                  &    19.86\cr
&  -0.0000102&   16.193&  0.5894496611&       10.66&  2\L7-2\LS                &   -15.19\cr
&   0.0000073&  247.802&  2.0004088347&        3.14&  \L4-\L7                  &    10.75\cr
&   0.0000035&   85.277&  0.2952841655&       21.28&  \L7-\PR6                 &     5.13\cr
%%
% perturbations of z_7
%%
\noalign{\medskip\hrule\medskip}
z_7&   0.0001928&  288.280&  0.0020604112&     3049.48&  2\LS-\PR7                &   285.74\cr
&   0.0000823&  318.242&  0.0011433161&     5495.58&  2\LS-\PR6                &   122.02\cr
&   0.0000517&  306.799&  0.0002755134&    22805.37&  2\LS-2\NDS+\PR7          &    76.69\cr
&   0.0000327&  245.300&  0.0026443923&     2376.04&  3\LS-\PRS-\PR7           &    48.46\cr
&  -0.0000163&  150.864& -0.0003084677&   -20369.02&  \LS-\PRS+\PR7            &   -24.20\cr
&   0.0000128&  218.304&  0.0003084677&    20369.02&  -\LS+\PRS+2\NDS-\PR7     &    19.02\cr
&   0.0000119&  275.262&  0.0017272972&     3637.58&  3\LS-\PRS-\PR6           &    17.58\cr
&  -0.0000084&  331.259&  0.0014764300&     4255.66&  \LS+\PRS-\PR7            &   -12.40\cr
&  -0.0000069&   80.888& -0.0020604112&    -3049.48&  -2\LS+2\NDS+\PR7         &   -10.25\cr
&  -0.0000030&   50.926& -0.0011433161&    -5495.58&  -2\LS+2\NDS+\PR6         &    -4.38\cr
&   0.0000029&  120.902&  0.0006086274&    10323.53&  \LS-\PRS+\PR6            &     4.28\cr
&   0.0000028&  276.837&  0.0011926085&     5268.44&  2\LS-2\NDS+\PR6          &     4.20\cr
&  -0.0000015&  248.266& -0.0006086274&   -10323.53&  -\LS+\PRS+2\NDS-\PR6     &    -2.28\cr
&   0.0000404&  249.158&  0.2953088117&       21.28&  \L7                      &    59.92\cr
&   0.0000111&   12.256&  1.3908537159&        4.52&  \L5                      &    16.43\cr
&   0.0000088&  232.965& -0.2941408494&      -21.36&  2\LS-\L7                 &    13.05\cr
%%
% perturbations of \zeta_7
%%
\noalign{\medskip\hrule\medskip}
\zeta_7&  -0.0001609&  297.539&  0.0011679623&     5379.61&  2\LS-\NDS                &  -477.05\cr
&  -0.0000247&  227.564& -0.0005839811&   -10759.23&  -\LS+\PRS+\NDS           &   -73.10\cr
&   0.0000247&  141.604&  0.0005839811&    10759.23&  \LS-\PRS+\NDS            &    73.10\cr
&  -0.0000221&  254.560&  0.0017519434&     3586.41&  3\LS-\PRS-\NDS           &   -65.62\cr
&   0.0000095&  340.519&  0.0005839811&    10759.23&  \LS+\PRS-\NDS            &    28.12\cr
&  -0.0000091&   71.629& -0.0011679623&    -5379.61&  -2\LS+3\NDS              &   -27.05\cr
&   0.0000040&  261.238&  0.0012815784&     4902.69&  2\LS-\ND7                &    11.81\cr
&   0.0000037&  297.541&  0.0011679623&     5379.61&  2\LS-\NDz                &    10.85\cr
&   0.0000011&  131.678&  0.0011925987&     5268.48&  2\LS-\ND6                &     3.39\cr
\noalign{\medskip\hrule}
 }



\bye





We present here a new theory of motion for Hyperion, the seventh
major satellite of Saturn.  The Hyperion's motion is defined like in TASS1.6
for the other satellites (Vienne \& Duriez 1995), by the osculating
saturnicentric orbital elements referred to the equatorial plane of Saturn
and to the node of this plane in the mean ecliptic for J$2000.0$. These
elements are expressed as semi-numerical trigonometric series in which the
argument of each term is  given as an integer combination of 7 natural
fundamental arguments. These series collect all the perturbations caused by
Titan on the orbital elements of Hyperion, whose amplitudes are larger than
1~km in the long-period terms and than 5~km in the short-period ones.
 However, the
 convergence of these series is so slow that, in spite of several hundreds of
 terms, their internal accuracy over one century is about 200~km only.
 These
series have been constructed in such a way that the fundamental arguments and
the amplitude of each term depend explicitly on 13 parameters (the twelve
initial conditions of the motions of Titan and Hyperion and the mass of
Titan). Taking also account of the perturbations from other satellites and Sun, 
we have fitted these series to 8136 Earth-based
observations of Hyperion in the interval [1874-1985], giving a set of better
values for these parameters. In particular the mass of Titan is found equal to
$(237.399\pm0.005)\,10^{-6}$ (in units of the Saturn's mass) and we discuss
this value in comparison with that [$(236.638\pm0.008)\ 10^{-6}$] obtained by
 Campbell \& Anderson from their analysis of the Voyager missions to Saturn.
The resulting fitted series allows us to produce new ephemerides for Hyperion.
 Their comparison
to those from Taylor (1992) shows that, with the same set of observations and
the same way to weight them, we obtain a root mean square (o$-$c) residual of
$0\Sp156$ while  the ephemerides of Taylor gives $0\Sp203$.
