NUT00A – astro-fortran

public subroutine NUT00A(date1, date2, dpsi, deps)

Nutation, IAU 2000A model (MHB2000 luni-solar and planetary nutation with free core nutation omitted).
Status: canonical model.
Notes

The TT date DATE1+DATE2 is a Julian Date, apportioned in any convenient way between the two arguments. For example, JD(TT)=2450123.7 could be expressed in any of these ways, among others:
```
    DATE1          DATE2

 2450123.7D0        0D0        (JD method)
  2451545D0      -1421.3D0     (J2000 method)
 2400000.5D0     50123.2D0     (MJD method)
 2450123.5D0       0.2D0       (date & time method)
```
The JD method is the most natural and convenient to use in cases where the loss of several decimal digits of resolution is acceptable. The J2000 method is best matched to the way the argument is handled internally and will deliver the optimum resolution. The MJD method and the date & time methods are both good compromises between resolution and convenience.
The nutation components in longitude and obliquity are in radians and with respect to the equinox and ecliptic of date. The obliquity at J2000.0 is assumed to be the Lieske et al. (1977) value of 84381.448 arcsec.

Both the luni-solar and planetary nutations are included. The latter are due to direct planetary nutations and the perturbations of the lunar and terrestrial orbits.
The routine computes the MHB2000 nutation series with the associated corrections for planetary nutations. It is an implementation of the nutation part of the IAU 2000A precession- nutation model, formally adopted by the IAU General Assembly in 2000, namely MHB2000 (Mathews et al. 2002), but with the free core nutation (FCN - see Note 4) omitted.
The full MHB2000 model also contains contributions to the nutations in longitude and obliquity due to the free-excitation of the free-core-nutation during the period 1979-2000. These FCN terms, which are time-dependent and unpredictable, are NOT included in the present routine and, if required, must be independently computed. With the FCN corrections included, the present routine delivers a pole which is at current epochs accurate to a few hundred microarcseconds. The omission of FCN introduces further errors of about that size.
The present routine provides classical nutation. The MHB2000 algorithm, from which it is adapted, deals also with (i) the offsets between the GCRS and mean poles and (ii) the adjustments in longitude and obliquity due to the changed precession rates. These additional functions, namely frame bias and precession adjustments, are supported by the SOFA routines BI00 and PR00.
The MHB2000 algorithm also provides "total" nutations, comprising the arithmetic sum of the frame bias, precession adjustments, luni-solar nutation and planetary nutation. These total nutations can be used in combination with an existing IAU 1976 precession implementation, such as PMAT76, to deliver GCRS-to-true predictions of sub-mas accuracy at current epochs. However, there are three shortcomings in the MHB2000 model that must be taken into account if more accurate or definitive results are required (see Wallace 2002):

(i) The MHB2000 total nutations are simply arithmetic sums, yet in reality the various components are successive Euler rotations. This slight lack of rigor leads to cross terms that exceed 1 mas after a century. The rigorous procedure is to form the GCRS-to-true rotation matrix by applying the bias, precession and nutation in that order.

(ii) Although the precession adjustments are stated to be with respect to Lieske et al. (1977), the MHB2000 model does not specify which set of Euler angles are to be used and how the adjustments are to be applied. The most literal and straightforward procedure is to adopt the 4-rotation epsilon_0, psi_A, omega_A, xi_A option, and to add DPSIPR to psi_A and DEPSPR to both omega_A and eps_A.

(iii) The MHB2000 model predates the determination by Chapront et al. (2002) of a 14.6 mas displacement between the J2000.0 mean equinox and the origin of the ICRS frame. It should, however, be noted that neglecting this displacement when calculating star coordinates does not lead to a 14.6 mas change in right ascension, only a small second-order distortion in the pattern of the precession-nutation effect.

For these reasons, the SOFA routines do not generate the "total nutations" directly, though they can of course easily be generated by calling BI00, PR00 and the present routine and adding the results.
The MHB2000 model contains 41 instances where the same frequency appears multiple times, of which 38 are duplicates and three are triplicates. To keep the present code close to the original MHB algorithm, this small inefficiency has not been corrected.
References

Chapront, J., Chapront-Touze, M. & Francou, G. 2002, Astron.Astrophys. 387, 700
Lieske, J.H., Lederle, T., Fricke, W. & Morando, B. 1977, Astron.Astrophys. 58, 1-16
Mathews, P.M., Herring, T.A., Buffet, B.A. 2002, J.Geophys.Res. 107, B4. The MHB_2000 code itself was obtained on 9th September 2002 from ftp//maia.usno.navy.mil/conv2000/chapter5/IAU2000A.
Simon, J.-L., Bretagnon, P., Chapront, J., Chapront-Touze, M., Francou, G., Laskar, J. 1994, Astron.Astrophys. 282, 663-683
Souchay, J., Loysel, B., Kinoshita, H., Folgueira, M. 1999, Astron.Astrophys.Supp.Ser. 135, 111
Wallace, P.T., "Software for Implementing the IAU 2000 Resolutions", in IERS Workshop 5.1 (2002)
History

IAU SOFA revision: 2009 December 15
Arguments

Type	Intent		Name
real(kind=wp),	intent(in)	::	date1	TT as a 2-part Julian Date (Note 1)
real(kind=wp),	intent(in)	::	date2	TT as a 2-part Julian Date (Note 1)
real(kind=wp),	intent(out)	::	dpsi	nutation, luni-solar + planetary (Note 2)
real(kind=wp),	intent(out)	::	deps	nutation, luni-solar + planetary (Note 2)
Calls

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Called by

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Source Code

NUT00A
Source Code

    subroutine NUT00A ( date1, date2, dpsi, deps )

    implicit none

    real(wp),intent(in) :: date1 !! TT as a 2-part Julian Date (Note 1)
    real(wp),intent(in) :: date2 !! TT as a 2-part Julian Date (Note 1)
    real(wp),intent(out) :: dpsi !! nutation, luni-solar + planetary (Note 2)
    real(wp),intent(out) :: deps !! nutation, luni-solar + planetary (Note 2)

    !  Arcseconds in a full circle
    real(wp),parameter :: turnas = 1296000.0_wp

    !  Units of 0.1 microarcsecond to radians
    real(wp),parameter :: u2r = das2r/1.0e7_wp

    !  Miscellaneous
    integer :: i, j
    real(wp) :: t, el, elp, f, d, om, arg, dp, de, sarg, carg, &
                al, alsu, af, ad, aom, alme, alve, alea, alma, &
                alju, alsa, alur, alne, apa, dpsils, depsls, &
                dpsipl, depspl

    !  -------------------------
    !  Luni-Solar nutation model
    !  -------------------------

    !  Number of terms in the luni-solar nutation model
    integer,parameter :: nls = 678

    !  ---------------
    !  Planetary terms
    !  ---------------

    !  Number of terms in the planetary nutation model
    integer,parameter :: npl = 687

    !  ----------------------------------------
    !  Tables of argument and term coefficients
    !  ----------------------------------------

    !
    !  Luni-Solar argument multipliers
    !               L     L'    F     D     Om

    !  Coefficients for fundamental arguments
    integer,dimension(5,nls),parameter :: nals = reshape([&
              0,    0,    0,    0,    1, &
              0,    0,    2,   -2,    2, &
              0,    0,    2,    0,    2, &
              0,    0,    0,    0,    2, &
              0,    1,    0,    0,    0, &
              0,    1,    2,   -2,    2, &
              1,    0,    0,    0,    0, &
              0,    0,    2,    0,    1, &
              1,    0,    2,    0,    2, &
              0,   -1,    2,   -2,    2, &
              0,    0,    2,   -2,    1, &
             -1,    0,    2,    0,    2, &
             -1,    0,    0,    2,    0, &
              1,    0,    0,    0,    1, &
             -1,    0,    0,    0,    1, &
             -1,    0,    2,    2,    2, &
              1,    0,    2,    0,    1, &
             -2,    0,    2,    0,    1, &
              0,    0,    0,    2,    0, &
              0,    0,    2,    2,    2, &
              0,   -2,    2,   -2,    2, &
             -2,    0,    0,    2,    0, &
              2,    0,    2,    0,    2, &
              1,    0,    2,   -2,    2, &
             -1,    0,    2,    0,    1, &
              2,    0,    0,    0,    0, &
              0,    0,    2,    0,    0, &
              0,    1,    0,    0,    1, &
             -1,    0,    0,    2,    1, &
              0,    2,    2,   -2,    2, &
              0,    0,   -2,    2,    0, &
              1,    0,    0,   -2,    1, &
              0,   -1,    0,    0,    1, &
             -1,    0,    2,    2,    1, &
              0,    2,    0,    0,    0, &
              1,    0,    2,    2,    2, &
             -2,    0,    2,    0,    0, &
              0,    1,    2,    0,    2, &
              0,    0,    2,    2,    1, &
              0,   -1,    2,    0,    2, &
              0,    0,    0,    2,    1, &
              1,    0,    2,   -2,    1, &
              2,    0,    2,   -2,    2, &
             -2,    0,    0,    2,    1, &
              2,    0,    2,    0,    1, &
              0,   -1,    2,   -2,    1, &
              0,    0,    0,   -2,    1, &
             -1,   -1,    0,    2,    0, &
              2,    0,    0,   -2,    1, &
              1,    0,    0,    2,    0, &
              0,    1,    2,   -2,    1, &
              1,   -1,    0,    0,    0, &
             -2,    0,    2,    0,    2, &
              3,    0,    2,    0,    2, &
              0,   -1,    0,    2,    0, &
              1,   -1,    2,    0,    2, &
              0,    0,    0,    1,    0, &
             -1,   -1,    2,    2,    2, &
             -1,    0,    2,    0,    0, &
              0,   -1,    2,    2,    2, &
             -2,    0,    0,    0,    1, &
              1,    1,    2,    0,    2, &
              2,    0,    0,    0,    1, &
             -1,    1,    0,    1,    0, &
              1,    1,    0,    0,    0, &
              1,    0,    2,    0,    0, &
             -1,    0,    2,   -2,    1, &
              1,    0,    0,    0,    2, &
             -1,    0,    0,    1,    0, &
              0,    0,    2,    1,    2, &
             -1,    0,    2,    4,    2, &
             -1,    1,    0,    1,    1, &
              0,   -2,    2,   -2,    1, &
              1,    0,    2,    2,    1, &
             -2,    0,    2,    2,    2, &
             -1,    0,    0,    0,    2, &
              1,    1,    2,   -2,    2, &
             -2,    0,    2,    4,    2, &
             -1,    0,    4,    0,    2, &
              2,    0,    2,   -2,    1, &
              2,    0,    2,    2,    2, &
              1,    0,    0,    2,    1, &
              3,    0,    0,    0,    0, &
              3,    0,    2,   -2,    2, &
              0,    0,    4,   -2,    2, &
              0,    1,    2,    0,    1, &
              0,    0,   -2,    2,    1, &
              0,    0,    2,   -2,    3, &
             -1,    0,    0,    4,    0, &
              2,    0,   -2,    0,    1, &
             -2,    0,    0,    4,    0, &
             -1,   -1,    0,    2,    1, &
             -1,    0,    0,    1,    1, &
              0,    1,    0,    0,    2, &
              0,    0,   -2,    0,    1, &
              0,   -1,    2,    0,    1, &
              0,    0,    2,   -1,    2, &
              0,    0,    2,    4,    2, &
             -2,   -1,    0,    2,    0, &
              1,    1,    0,   -2,    1, &
             -1,    1,    0,    2,    0, &
             -1,    1,    0,    1,    2, &
              1,   -1,    0,    0,    1, &
              1,   -1,    2,    2,    2, &
             -1,    1,    2,    2,    2, &
              3,    0,    2,    0,    1, &
              0,    1,   -2,    2,    0, &
             -1,    0,    0,   -2,    1, &
              0,    1,    2,    2,    2, &
             -1,   -1,    2,    2,    1, &
              0,   -1,    0,    0,    2, &
              1,    0,    2,   -4,    1, &
             -1,    0,   -2,    2,    0, &
              0,   -1,    2,    2,    1, &
              2,   -1,    2,    0,    2, &
              0,    0,    0,    2,    2, &
              1,   -1,    2,    0,    1, &
             -1,    1,    2,    0,    2, &
              0,    1,    0,    2,    0, &
              0,   -1,   -2,    2,    0, &
              0,    3,    2,   -2,    2, &
              0,    0,    0,    1,    1, &
             -1,    0,    2,    2,    0, &
              2,    1,    2,    0,    2, &
              1,    1,    0,    0,    1, &
              1,    1,    2,    0,    1, &
              2,    0,    0,    2,    0, &
              1,    0,   -2,    2,    0, &
             -1,    0,    0,    2,    2, &
              0,    1,    0,    1,    0, &
              0,    1,    0,   -2,    1, &
             -1,    0,    2,   -2,    2, &
              0,    0,    0,   -1,    1, &
             -1,    1,    0,    0,    1, &
              1,    0,    2,   -1,    2, &
              1,   -1,    0,    2,    0, &
              0,    0,    0,    4,    0, &
              1,    0,    2,    1,    2, &
              0,    0,    2,    1,    1, &
              1,    0,    0,   -2,    2, &
             -1,    0,    2,    4,    1, &
              1,    0,   -2,    0,    1, &
              1,    1,    2,   -2,    1, &
              0,    0,    2,    2,    0, &
             -1,    0,    2,   -1,    1, &
             -2,    0,    2,    2,    1, &
              4,    0,    2,    0,    2, &
              2,   -1,    0,    0,    0, &
              2,    1,    2,   -2,    2, &
              0,    1,    2,    1,    2, &
              1,    0,    4,   -2,    2, &
             -1,   -1,    0,    0,    1, &
              0,    1,    0,    2,    1, &
             -2,    0,    2,    4,    1, &
              2,    0,    2,    0,    0, &
              1,    0,    0,    1,    0, &
             -1,    0,    0,    4,    1, &
             -1,    0,    4,    0,    1, &
              2,    0,    2,    2,    1, &
              0,    0,    2,   -3,    2, &
             -1,   -2,    0,    2,    0, &
              2,    1,    0,    0,    0, &
              0,    0,    4,    0,    2, &
              0,    0,    0,    0,    3, &
              0,    3,    0,    0,    0, &
              0,    0,    2,   -4,    1, &
              0,   -1,    0,    2,    1, &
              0,    0,    0,    4,    1, &
             -1,   -1,    2,    4,    2, &
              1,    0,    2,    4,    2, &
             -2,    2,    0,    2,    0, &
             -2,   -1,    2,    0,    1, &
             -2,    0,    0,    2,    2, &
             -1,   -1,    2,    0,    2, &
              0,    0,    4,   -2,    1, &
              3,    0,    2,   -2,    1, &
             -2,   -1,    0,    2,    1, &
              1,    0,    0,   -1,    1, &
              0,   -2,    0,    2,    0, &
             -2,    0,    0,    4,    1, &
             -3,    0,    0,    0,    1, &
              1,    1,    2,    2,    2, &
              0,    0,    2,    4,    1, &
              3,    0,    2,    2,    2, &
             -1,    1,    2,   -2,    1, &
              2,    0,    0,   -4,    1, &
              0,    0,    0,   -2,    2, &
              2,    0,    2,   -4,    1, &
             -1,    1,    0,    2,    1, &
              0,    0,    2,   -1,    1, &
              0,   -2,    2,    2,    2, &
              2,    0,    0,    2,    1, &
              4,    0,    2,   -2,    2, &
              2,    0,    0,   -2,    2, &
              0,    2,    0,    0,    1, &
              1,    0,    0,   -4,    1, &
              0,    2,    2,   -2,    1, &
             -3,    0,    0,    4,    0, &
             -1,    1,    2,    0,    1, &
             -1,   -1,    0,    4,    0, &
             -1,   -2,    2,    2,    2, &
             -2,   -1,    2,    4,    2, &
              1,   -1,    2,    2,    1, &
             -2,    1,    0,    2,    0, &
             -2,    1,    2,    0,    1, &
              2,    1,    0,   -2,    1, &
             -3,    0,    2,    0,    1, &
             -2,    0,    2,   -2,    1, &
             -1,    1,    0,    2,    2, &
              0,   -1,    2,   -1,    2, &
             -1,    0,    4,   -2,    2, &
              0,   -2,    2,    0,    2, &
             -1,    0,    2,    1,    2, &
              2,    0,    0,    0,    2, &
              0,    0,    2,    0,    3, &
             -2,    0,    4,    0,    2, &
             -1,    0,   -2,    0,    1, &
             -1,    1,    2,    2,    1, &
              3,    0,    0,    0,    1, &
             -1,    0,    2,    3,    2, &
              2,   -1,    2,    0,    1, &
              0,    1,    2,    2,    1, &
              0,   -1,    2,    4,    2, &
              2,   -1,    2,    2,    2, &
              0,    2,   -2,    2,    0, &
             -1,   -1,    2,   -1,    1, &
              0,   -2,    0,    0,    1, &
              1,    0,    2,   -4,    2, &
              1,   -1,    0,   -2,    1, &
             -1,   -1,    2,    0,    1, &
              1,   -1,    2,   -2,    2, &
             -2,   -1,    0,    4,    0, &
             -1,    0,    0,    3,    0, &
             -2,   -1,    2,    2,    2, &
              0,    2,    2,    0,    2, &
              1,    1,    0,    2,    0, &
              2,    0,    2,   -1,    2, &
              1,    0,    2,    1,    1, &
              4,    0,    0,    0,    0, &
              2,    1,    2,    0,    1, &
              3,   -1,    2,    0,    2, &
             -2,    2,    0,    2,    1, &
              1,    0,    2,   -3,    1, &
              1,    1,    2,   -4,    1, &
             -1,   -1,    2,   -2,    1, &
              0,   -1,    0,   -1,    1, &
              0,   -1,    0,   -2,    1, &
             -2,    0,    0,    0,    2, &
             -2,    0,   -2,    2,    0, &
             -1,    0,   -2,    4,    0, &
              1,   -2,    0,    0,    0, &
              0,    1,    0,    1,    1, &
             -1,    2,    0,    2,    0, &
              1,   -1,    2,   -2,    1, &
              1,    2,    2,   -2,    2, &
              2,   -1,    2,   -2,    2, &
              1,    0,    2,   -1,    1, &
              2,    1,    2,   -2,    1, &
             -2,    0,    0,   -2,    1, &
              1,   -2,    2,    0,    2, &
              0,    1,    2,    1,    1, &
              1,    0,    4,   -2,    1, &
             -2,    0,    4,    2,    2, &
              1,    1,    2,    1,    2, &
              1,    0,    0,    4,    0, &
              1,    0,    2,    2,    0, &
              2,    0,    2,    1,    2, &
              3,    1,    2,    0,    2, &
              4,    0,    2,    0,    1, &
             -2,   -1,    2,    0,    0, &
              0,    1,   -2,    2,    1, &
              1,    0,   -2,    1,    0, &
              0,   -1,   -2,    2,    1, &
              2,   -1,    0,   -2,    1, &
             -1,    0,    2,   -1,    2, &
              1,    0,    2,   -3,    2, &
              0,    1,    2,   -2,    3, &
              0,    0,    2,   -3,    1, &
             -1,    0,   -2,    2,    1, &
              0,    0,    2,   -4,    2, &
             -2,    1,    0,    0,    1, &
             -1,    0,    0,   -1,    1, &
              2,    0,    2,   -4,    2, &
              0,    0,    4,   -4,    4, &
              0,    0,    4,   -4,    2, &
             -1,   -2,    0,    2,    1, &
             -2,    0,    0,    3,    0, &
              1,    0,   -2,    2,    1, &
             -3,    0,    2,    2,    2, &
             -3,    0,    2,    2,    1, &
             -2,    0,    2,    2,    0, &
              2,   -1,    0,    0,    1, &
             -2,    1,    2,    2,    2, &
              1,    1,    0,    1,    0, &
              0,    1,    4,   -2,    2, &
             -1,    1,    0,   -2,    1, &
              0,    0,    0,   -4,    1, &
              1,   -1,    0,    2,    1, &
              1,    1,    0,    2,    1, &
             -1,    2,    2,    2,    2, &
              3,    1,    2,   -2,    2, &
              0,   -1,    0,    4,    0, &
              2,   -1,    0,    2,    0, &
              0,    0,    4,    0,    1, &
              2,    0,    4,   -2,    2, &
             -1,   -1,    2,    4,    1, &
              1,    0,    0,    4,    1, &
              1,   -2,    2,    2,    2, &
              0,    0,    2,    3,    2, &
             -1,    1,    2,    4,    2, &
              3,    0,    0,    2,    0, &
             -1,    0,    4,    2,    2, &
              1,    1,    2,    2,    1, &
             -2,    0,    2,    6,    2, &
              2,    1,    2,    2,    2, &
             -1,    0,    2,    6,    2, &
              1,    0,    2,    4,    1, &
              2,    0,    2,    4,    2, &
              1,    1,   -2,    1,    0, &
             -3,    1,    2,    1,    2, &
              2,    0,   -2,    0,    2, &
             -1,    0,    0,    1,    2, &
             -4,    0,    2,    2,    1, &
             -1,   -1,    0,    1,    0, &
              0,    0,   -2,    2,    2, &
              1,    0,    0,   -1,    2, &
              0,   -1,    2,   -2,    3, &
             -2,    1,    2,    0,    0, &
              0,    0,    2,   -2,    4, &
             -2,   -2,    0,    2,    0, &
             -2,    0,   -2,    4,    0, &
              0,   -2,   -2,    2,    0, &
              1,    2,    0,   -2,    1, &
              3,    0,    0,   -4,    1, &
             -1,    1,    2,   -2,    2, &
              1,   -1,    2,   -4,    1, &
              1,    1,    0,   -2,    2, &
             -3,    0,    2,    0,    0, &
             -3,    0,    2,    0,    2, &
             -2,    0,    0,    1,    0, &
              0,    0,   -2,    1,    0, &
             -3,    0,    0,    2,    1, &
             -1,   -1,   -2,    2,    0, &
              0,    1,    2,   -4,    1, &
              2,    1,    0,   -4,    1, &
              0,    2,    0,   -2,    1, &
              1,    0,    0,   -3,    1, &
             -2,    0,    2,   -2,    2, &
             -2,   -1,    0,    0,    1, &
             -4,    0,    0,    2,    0, &
              1,    1,    0,   -4,    1, &
             -1,    0,    2,   -4,    1, &
              0,    0,    4,   -4,    1, &
              0,    3,    2,   -2,    2, &
             -3,   -1,    0,    4,    0, &
             -3,    0,    0,    4,    1, &
              1,   -1,   -2,    2,    0, &
             -1,   -1,    0,    2,    2, &
              1,   -2,    0,    0,    1, &
              1,   -1,    0,    0,    2, &
              0,    0,    0,    1,    2, &
             -1,   -1,    2,    0,    0, &
              1,   -2,    2,   -2,    2, &
              0,   -1,    2,   -1,    1, &
             -1,    0,    2,    0,    3, &
              1,    1,    0,    0,    2, &
             -1,    1,    2,    0,    0, &
              1,    2,    0,    0,    0, &
             -1,    2,    2,    0,    2, &
             -1,    0,    4,   -2,    1, &
              3,    0,    2,   -4,    2, &
              1,    2,    2,   -2,    1, &
              1,    0,    4,   -4,    2, &
             -2,   -1,    0,    4,    1, &
              0,   -1,    0,    2,    2, &
             -2,    1,    0,    4,    0, &
             -2,   -1,    2,    2,    1, &
              2,    0,   -2,    2,    0, &
              1,    0,    0,    1,    1, &
              0,    1,    0,    2,    2, &
              1,   -1,    2,   -1,    2, &
             -2,    0,    4,    0,    1, &
              2,    1,    0,    0,    1, &
              0,    1,    2,    0,    0, &
              0,   -1,    4,   -2,    2, &
              0,    0,    4,   -2,    4, &
              0,    2,    2,    0,    1, &
             -3,    0,    0,    6,    0, &
             -1,   -1,    0,    4,    1, &
              1,   -2,    0,    2,    0, &
             -1,    0,    0,    4,    2, &
             -1,   -2,    2,    2,    1, &
             -1,    0,    0,   -2,    2, &
              1,    0,   -2,   -2,    1, &
              0,    0,   -2,   -2,    1, &
             -2,    0,   -2,    0,    1, &
              0,    0,    0,    3,    1, &
              0,    0,    0,    3,    0, &
             -1,    1,    0,    4,    0, &
             -1,   -1,    2,    2,    0, &
             -2,    0,    2,    3,    2, &
              1,    0,    0,    2,    2, &
              0,   -1,    2,    1,    2, &
              3,   -1,    0,    0,    0, &
              2,    0,    0,    1,    0, &
              1,   -1,    2,    0,    0, &
              0,    0,    2,    1,    0, &
              1,    0,    2,    0,    3, &
              3,    1,    0,    0,    0, &
              3,   -1,    2,   -2,    2, &
              2,    0,    2,   -1,    1, &
              1,    1,    2,    0,    0, &
              0,    0,    4,   -1,    2, &
              1,    2,    2,    0,    2, &
             -2,    0,    0,    6,    0, &
              0,   -1,    0,    4,    1, &
             -2,   -1,    2,    4,    1, &
              0,   -2,    2,    2,    1, &
              0,   -1,    2,    2,    0, &
             -1,    0,    2,    3,    1, &
             -2,    1,    2,    4,    2, &
              2,    0,    0,    2,    2, &
              2,   -2,    2,    0,    2, &
             -1,    1,    2,    3,    2, &
              3,    0,    2,   -1,    2, &
              4,    0,    2,   -2,    1, &
             -1,    0,    0,    6,    0, &
             -1,   -2,    2,    4,    2, &
             -3,    0,    2,    6,    2, &
             -1,    0,    2,    4,    0, &
              3,    0,    0,    2,    1, &
              3,   -1,    2,    0,    1, &
              3,    0,    2,    0,    0, &
              1,    0,    4,    0,    2, &
              5,    0,    2,   -2,    2, &
              0,   -1,    2,    4,    1, &
              2,   -1,    2,    2,    1, &
              0,    1,    2,    4,    2, &
              1,   -1,    2,    4,    2, &
              3,   -1,    2,    2,    2, &
              3,    0,    2,    2,    1, &
              5,    0,    2,    0,    2, &
              0,    0,    2,    6,    2, &
              4,    0,    2,    2,    2, &
              0,   -1,    1,   -1,    1, &
             -1,    0,    1,    0,    3, &
              0,   -2,    2,   -2,    3, &
              1,    0,   -1,    0,    1, &
              2,   -2,    0,   -2,    1, &
             -1,    0,    1,    0,    2, &
             -1,    0,    1,    0,    1, &
             -1,   -1,    2,   -1,    2, &
             -2,    2,    0,    2,    2, &
             -1,    0,    1,    0,    0, &
             -4,    1,    2,    2,    2, &
             -3,    0,    2,    1,    1, &
             -2,   -1,    2,    0,    2, &
              1,    0,   -2,    1,    1, &
              2,   -1,   -2,    0,    1, &
             -4,    0,    2,    2,    0, &
             -3,    1,    0,    3,    0, &
             -1,    0,   -1,    2,    0, &
              0,   -2,    0,    0,    2, &
              0,   -2,    0,    0,    2, &
             -3,    0,    0,    3,    0, &
             -2,   -1,    0,    2,    2, &
             -1,    0,   -2,    3,    0, &
             -4,    0,    0,    4,    0, &
              2,    1,   -2,    0,    1, &
              2,   -1,    0,   -2,    2, &
              0,    0,    1,   -1,    0, &
             -1,    2,    0,    1,    0, &
             -2,    1,    2,    0,    2, &
              1,    1,    0,   -1,    1, &
              1,    0,    1,   -2,    1, &
              0,    2,    0,    0,    2, &
              1,   -1,    2,   -3,    1, &
             -1,    1,    2,   -1,    1, &
             -2,    0,    4,   -2,    2, &
             -2,    0,    4,   -2,    1, &
             -2,   -2,    0,    2,    1, &
             -2,    0,   -2,    4,    0, &
              1,    2,    2,   -4,    1, &
              1,    1,    2,   -4,    2, &
             -1,    2,    2,   -2,    1, &
              2,    0,    0,   -3,    1, &
             -1,    2,    0,    0,    1, &
              0,    0,    0,   -2,    0, &
             -1,   -1,    2,   -2,    2, &
             -1,    1,    0,    0,    2, &
              0,    0,    0,   -1,    2, &
             -2,    1,    0,    1,    0, &
              1,   -2,    0,   -2,    1, &
              1,    0,   -2,    0,    2, &
             -3,    1,    0,    2,    0, &
             -1,    1,   -2,    2,    0, &
             -1,   -1,    0,    0,    2, &
             -3,    0,    0,    2,    0, &
             -3,   -1,    0,    2,    0, &
              2,    0,    2,   -6,    1, &
              0,    1,    2,   -4,    2, &
              2,    0,    0,   -4,    2, &
             -2,    1,    2,   -2,    1, &
              0,   -1,    2,   -4,    1, &
              0,    1,    0,   -2,    2, &
             -1,    0,    0,   -2,    0, &
              2,    0,   -2,   -2,    1, &
             -4,    0,    2,    0,    1, &
             -1,   -1,    0,   -1,    1, &
              0,    0,   -2,    0,    2, &
             -3,    0,    0,    1,    0, &
             -1,    0,   -2,    1,    0, &
             -2,    0,   -2,    2,    1, &
              0,    0,   -4,    2,    0, &
             -2,   -1,   -2,    2,    0, &
              1,    0,    2,   -6,    1, &
             -1,    0,    2,   -4,    2, &
              1,    0,    0,   -4,    2, &
              2,    1,    2,   -4,    2, &
              2,    1,    2,   -4,    1, &
              0,    1,    4,   -4,    4, &
              0,    1,    4,   -4,    2, &
             -1,   -1,   -2,    4,    0, &
             -1,   -3,    0,    2,    0, &
             -1,    0,   -2,    4,    1, &
             -2,   -1,    0,    3,    0, &
              0,    0,   -2,    3,    0, &
             -2,    0,    0,    3,    1, &
              0,   -1,    0,    1,    0, &
             -3,    0,    2,    2,    0, &
              1,    1,   -2,    2,    0, &
             -1,    1,    0,    2,    2, &
              1,   -2,    2,   -2,    1, &
              0,    0,    1,    0,    2, &
              0,    0,    1,    0,    1, &
              0,    0,    1,    0,    0, &
             -1,    2,    0,    2,    1, &
              0,    0,    2,    0,    2, &
             -2,    0,    2,    0,    2, &
              2,    0,    0,   -1,    1, &
              3,    0,    0,   -2,    1, &
              1,    0,    2,   -2,    3, &
              1,    2,    0,    0,    1, &
              2,    0,    2,   -3,    2, &
             -1,    1,    4,   -2,    2, &
             -2,   -2,    0,    4,    0, &
              0,   -3,    0,    2,    0, &
              0,    0,   -2,    4,    0, &
             -1,   -1,    0,    3,    0, &
             -2,    0,    0,    4,    2, &
             -1,    0,    0,    3,    1, &
              2,   -2,    0,    0,    0, &
              1,   -1,    0,    1,    0, &
             -1,    0,    0,    2,    0, &
              0,   -2,    2,    0,    1, &
             -1,    0,    1,    2,    1, &
             -1,    1,    0,    3,    0, &
             -1,   -1,    2,    1,    2, &
              0,   -1,    2,    0,    0, &
             -2,    1,    2,    2,    1, &
              2,   -2,    2,   -2,    2, &
              1,    1,    0,    1,    1, &
              1,    0,    1,    0,    1, &
              1,    0,    1,    0,    0, &
              0,    2,    0,    2,    0, &
              2,   -1,    2,   -2,    1, &
              0,   -1,    4,   -2,    1, &
              0,    0,    4,   -2,    3, &
              0,    1,    4,   -2,    1, &
              4,    0,    2,   -4,    2, &
              2,    2,    2,   -2,    2, &
              2,    0,    4,   -4,    2, &
             -1,   -2,    0,    4,    0, &
             -1,   -3,    2,    2,    2, &
             -3,    0,    2,    4,    2, &
             -3,    0,    2,   -2,    1, &
             -1,   -1,    0,   -2,    1, &
             -3,    0,    0,    0,    2, &
             -3,    0,   -2,    2,    0, &
              0,    1,    0,   -4,    1, &
             -2,    1,    0,   -2,    1, &
             -4,    0,    0,    0,    1, &
             -1,    0,    0,   -4,    1, &
             -3,    0,    0,   -2,    1, &
              0,    0,    0,    3,    2, &
             -1,    1,    0,    4,    1, &
              1,   -2,    2,    0,    1, &
              0,    1,    0,    3,    0, &
             -1,    0,    2,    2,    3, &
              0,    0,    2,    2,    2, &
             -2,    0,    2,    2,    2, &
             -1,    1,    2,    2,    0, &
              3,    0,    0,    0,    2, &
              2,    1,    0,    1,    0, &
              2,   -1,    2,   -1,    2, &
              0,    0,    2,    0,    1, &
              0,    0,    3,    0,    3, &
              0,    0,    3,    0,    2, &
             -1,    2,    2,    2,    1, &
             -1,    0,    4,    0,    0, &
              1,    2,    2,    0,    1, &
              3,    1,    2,   -2,    1, &
              1,    1,    4,   -2,    2, &
             -2,   -1,    0,    6,    0, &
              0,   -2,    0,    4,    0, &
             -2,    0,    0,    6,    1, &
             -2,   -2,    2,    4,    2, &
              0,   -3,    2,    2,    2, &
              0,    0,    0,    4,    2, &
             -1,   -1,    2,    3,    2, &
             -2,    0,    2,    4,    0, &
              2,   -1,    0,    2,    1, &
              1,    0,    0,    3,    0, &
              0,    1,    0,    4,    1, &
              0,    1,    0,    4,    0, &
              1,   -1,    2,    1,    2, &
              0,    0,    2,    2,    3, &
              1,    0,    2,    2,    2, &
             -1,    0,    2,    2,    2, &
             -2,    0,    4,    2,    1, &
              2,    1,    0,    2,    1, &
              2,    1,    0,    2,    0, &
              2,   -1,    2,    0,    0, &
              1,    0,    2,    1,    0, &
              0,    1,    2,    2,    0, &
              2,    0,    2,    0,    3, &
              3,    0,    2,    0,    2, &
              1,    0,    2,    0,    2, &
              1,    0,    3,    0,    3, &
              1,    1,    2,    1,    1, &
              0,    2,    2,    2,    2, &
              2,    1,    2,    0,    0, &
              2,    0,    4,   -2,    1, &
              4,    1,    2,   -2,    2, &
             -1,   -1,    0,    6,    0, &
             -3,   -1,    2,    6,    2, &
             -1,    0,    0,    6,    1, &
             -3,    0,    2,    6,    1, &
              1,   -1,    0,    4,    1, &
              1,   -1,    0,    4,    0, &
             -2,    0,    2,    5,    2, &
              1,   -2,    2,    2,    1, &
              3,   -1,    0,    2,    0, &
              1,   -1,    2,    2,    0, &
              0,    0,    2,    3,    1, &
             -1,    1,    2,    4,    1, &
              0,    1,    2,    3,    2, &
             -1,    0,    4,    2,    1, &
              2,    0,    2,    1,    1, &
              5,    0,    0,    0,    0, &
              2,    1,    2,    1,    2, &
              1,    0,    4,    0,    1, &
              3,    1,    2,    0,    1, &
              3,    0,    4,   -2,    2, &
             -2,   -1,    2,    6,    2, &
              0,    0,    0,    6,    0, &
              0,   -2,    2,    4,    2, &
             -2,    0,    2,    6,    1, &
              2,    0,    0,    4,    1, &
              2,    0,    0,    4,    0, &
              2,   -2,    2,    2,    2, &
              0,    0,    2,    4,    0, &
              1,    0,    2,    3,    2, &
              4,    0,    0,    2,    0, &
              2,    0,    2,    2,    0, &
              0,    0,    4,    2,    2, &
              4,   -1,    2,    0,    2, &
              3,    0,    2,    1,    2, &
              2,    1,    2,    2,    1, &
              4,    1,    2,    0,    2, &
             -1,   -1,    2,    6,    2, &
             -1,    0,    2,    6,    1, &
              1,   -1,    2,    4,    1, &
              1,    1,    2,    4,    2, &
              3,    1,    2,    2,    2, &
              5,    0,    2,    0,    1, &
              2,   -1,    2,    4,    2, &
              2,    0,    2,    4,    1 ], [5,nls])

    !
    !  Luni-Solar nutation coefficients, unit 1e-7 arcsec
    !  longitude (sin, t*sin, cos), obliquity (cos, t*cos, sin)
    !
    real(wp),dimension(6,nls),parameter :: cls = reshape([&
     -172064161.0_wp, -174666.0_wp,  33386.0_wp, 92052331.0_wp,  9086.0_wp, 15377.0_wp, &
      -13170906.0_wp,   -1675.0_wp, -13696.0_wp,  5730336.0_wp, -3015.0_wp, -4587.0_wp, &
       -2276413.0_wp,    -234.0_wp,   2796.0_wp,   978459.0_wp,  -485.0_wp,  1374.0_wp, &
        2074554.0_wp,     207.0_wp,   -698.0_wp,  -897492.0_wp,   470.0_wp,  -291.0_wp, &
        1475877.0_wp,   -3633.0_wp,  11817.0_wp,    73871.0_wp,  -184.0_wp, -1924.0_wp, &
        -516821.0_wp,    1226.0_wp,   -524.0_wp,   224386.0_wp,  -677.0_wp,  -174.0_wp, &
         711159.0_wp,      73.0_wp,   -872.0_wp,    -6750.0_wp,     0.0_wp,   358.0_wp, &
        -387298.0_wp,    -367.0_wp,    380.0_wp,   200728.0_wp,    18.0_wp,   318.0_wp, &
        -301461.0_wp,     -36.0_wp,    816.0_wp,   129025.0_wp,   -63.0_wp,   367.0_wp, &
         215829.0_wp,    -494.0_wp,    111.0_wp,   -95929.0_wp,   299.0_wp,   132.0_wp, &
         128227.0_wp,     137.0_wp,    181.0_wp,   -68982.0_wp,    -9.0_wp,    39.0_wp, &
         123457.0_wp,      11.0_wp,     19.0_wp,   -53311.0_wp,    32.0_wp,    -4.0_wp, &
         156994.0_wp,      10.0_wp,   -168.0_wp,    -1235.0_wp,     0.0_wp,    82.0_wp, &
          63110.0_wp,      63.0_wp,     27.0_wp,   -33228.0_wp,     0.0_wp,    -9.0_wp, &
         -57976.0_wp,     -63.0_wp,   -189.0_wp,    31429.0_wp,     0.0_wp,   -75.0_wp, &
         -59641.0_wp,     -11.0_wp,    149.0_wp,    25543.0_wp,   -11.0_wp,    66.0_wp, &
         -51613.0_wp,     -42.0_wp,    129.0_wp,    26366.0_wp,     0.0_wp,    78.0_wp, &
          45893.0_wp,      50.0_wp,     31.0_wp,   -24236.0_wp,   -10.0_wp,    20.0_wp, &
          63384.0_wp,      11.0_wp,   -150.0_wp,    -1220.0_wp,     0.0_wp,    29.0_wp, &
         -38571.0_wp,      -1.0_wp,    158.0_wp,    16452.0_wp,   -11.0_wp,    68.0_wp, &
          32481.0_wp,       0.0_wp,      0.0_wp,   -13870.0_wp,     0.0_wp,     0.0_wp, &
         -47722.0_wp,       0.0_wp,    -18.0_wp,      477.0_wp,     0.0_wp,   -25.0_wp, &
         -31046.0_wp,      -1.0_wp,    131.0_wp,    13238.0_wp,   -11.0_wp,    59.0_wp, &
          28593.0_wp,       0.0_wp,     -1.0_wp,   -12338.0_wp,    10.0_wp,    -3.0_wp, &
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           3579.0_wp,       0.0_wp,      5.0_wp,    -1900.0_wp,     0.0_wp,     1.0_wp, &
           4725.0_wp,       0.0_wp,     -6.0_wp,      -41.0_wp,     0.0_wp,     3.0_wp, &
          -3075.0_wp,       0.0_wp,     -2.0_wp,     1313.0_wp,     0.0_wp,    -1.0_wp, &
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          -2819.0_wp,       0.0_wp,      7.0_wp,     1207.0_wp,     0.0_wp,     3.0_wp, &
          -4056.0_wp,       0.0_wp,      5.0_wp,       40.0_wp,     0.0_wp,    -2.0_wp, &
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          -3389.0_wp,       0.0_wp,      5.0_wp,       35.0_wp,     0.0_wp,    -2.0_wp, &
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          -1987.0_wp,       0.0_wp,     -6.0_wp,     1073.0_wp,     0.0_wp,    -2.0_wp, &
          -1981.0_wp,       0.0_wp,      0.0_wp,      854.0_wp,     0.0_wp,     0.0_wp, &
           4026.0_wp,       0.0_wp,   -353.0_wp,     -553.0_wp,     0.0_wp,  -139.0_wp, &
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           -970.0_wp,       0.0_wp,      2.0_wp,      496.0_wp,     0.0_wp,     1.0_wp, &
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           -949.0_wp,       0.0_wp,      1.0_wp,        8.0_wp,     0.0_wp,    -1.0_wp, &
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           -875.0_wp,       0.0_wp,      1.0_wp,       29.0_wp,     0.0_wp,     0.0_wp, &
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           -103.0_wp,       0.0_wp,      0.0_wp,        2.0_wp,     0.0_wp,     0.0_wp, &
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            -38.0_wp,       0.0_wp,      0.0_wp,       19.0_wp,     0.0_wp,     0.0_wp, &
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            -60.0_wp,       0.0_wp,      0.0_wp,        0.0_wp,     0.0_wp,     0.0_wp, &
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            -14.0_wp,       0.0_wp,      0.0_wp,        7.0_wp,     0.0_wp,     0.0_wp, &
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            -16.0_wp,       0.0_wp,      0.0_wp,        8.0_wp,     0.0_wp,     0.0_wp, &
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            -18.0_wp,       0.0_wp,      0.0_wp,       10.0_wp,     0.0_wp,     0.0_wp, &
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            -26.0_wp,       0.0_wp,      0.0_wp,       11.0_wp,     0.0_wp,     0.0_wp, &
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            -10.0_wp,       0.0_wp,      0.0_wp,        5.0_wp,     0.0_wp,     0.0_wp, &
            -20.0_wp,       0.0_wp,      0.0_wp,       11.0_wp,     0.0_wp,     0.0_wp, &
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              8.0_wp,       0.0_wp,      0.0_wp,       -4.0_wp,     0.0_wp,     0.0_wp, &
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            -13.0_wp,       0.0_wp,      0.0_wp,        6.0_wp,     0.0_wp,     0.0_wp, &
            -14.0_wp,       0.0_wp,      0.0_wp,        8.0_wp,     0.0_wp,     0.0_wp, &
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            -17.0_wp,       0.0_wp,      0.0_wp,        9.0_wp,     0.0_wp,     0.0_wp, &
            -12.0_wp,       0.0_wp,      0.0_wp,        6.0_wp,     0.0_wp,     0.0_wp, &
            -10.0_wp,       0.0_wp,      0.0_wp,        5.0_wp,     0.0_wp,     0.0_wp, &
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            -15.0_wp,       0.0_wp,      0.0_wp,        0.0_wp,     0.0_wp,     0.0_wp, &
            -22.0_wp,       0.0_wp,      0.0_wp,        0.0_wp,     0.0_wp,     0.0_wp, &
             28.0_wp,       0.0_wp,      0.0_wp,       -1.0_wp,     0.0_wp,     0.0_wp, &
             15.0_wp,       0.0_wp,      0.0_wp,       -7.0_wp,     0.0_wp,     0.0_wp, &
             23.0_wp,       0.0_wp,      0.0_wp,      -10.0_wp,     0.0_wp,     0.0_wp, &
             12.0_wp,       0.0_wp,      0.0_wp,       -5.0_wp,     0.0_wp,     0.0_wp, &
             29.0_wp,       0.0_wp,      0.0_wp,       -1.0_wp,     0.0_wp,     0.0_wp, &
            -25.0_wp,       0.0_wp,      0.0_wp,        1.0_wp,     0.0_wp,     0.0_wp, &
             22.0_wp,       0.0_wp,      0.0_wp,        0.0_wp,     0.0_wp,     0.0_wp, &
            -18.0_wp,       0.0_wp,      0.0_wp,        0.0_wp,     0.0_wp,     0.0_wp, &
             15.0_wp,       0.0_wp,      0.0_wp,        3.0_wp,     0.0_wp,     0.0_wp, &
            -23.0_wp,       0.0_wp,      0.0_wp,        0.0_wp,     0.0_wp,     0.0_wp, &
             12.0_wp,       0.0_wp,      0.0_wp,       -5.0_wp,     0.0_wp,     0.0_wp, &
             -8.0_wp,       0.0_wp,      0.0_wp,        4.0_wp,     0.0_wp,     0.0_wp, &
            -19.0_wp,       0.0_wp,      0.0_wp,        0.0_wp,     0.0_wp,     0.0_wp, &
            -10.0_wp,       0.0_wp,      0.0_wp,        4.0_wp,     0.0_wp,     0.0_wp, &
             21.0_wp,       0.0_wp,      0.0_wp,       -9.0_wp,     0.0_wp,     0.0_wp, &
             23.0_wp,       0.0_wp,      0.0_wp,       -1.0_wp,     0.0_wp,     0.0_wp, &
            -16.0_wp,       0.0_wp,      0.0_wp,        8.0_wp,     0.0_wp,     0.0_wp, &
            -19.0_wp,       0.0_wp,      0.0_wp,        9.0_wp,     0.0_wp,     0.0_wp, &
            -22.0_wp,       0.0_wp,      0.0_wp,       10.0_wp,     0.0_wp,     0.0_wp, &
             27.0_wp,       0.0_wp,      0.0_wp,       -1.0_wp,     0.0_wp,     0.0_wp, &
             16.0_wp,       0.0_wp,      0.0_wp,       -8.0_wp,     0.0_wp,     0.0_wp, &
             19.0_wp,       0.0_wp,      0.0_wp,       -8.0_wp,     0.0_wp,     0.0_wp, &
              9.0_wp,       0.0_wp,      0.0_wp,       -4.0_wp,     0.0_wp,     0.0_wp, &
             -9.0_wp,       0.0_wp,      0.0_wp,        4.0_wp,     0.0_wp,     0.0_wp, &
             -9.0_wp,       0.0_wp,      0.0_wp,        4.0_wp,     0.0_wp,     0.0_wp, &
             -8.0_wp,       0.0_wp,      0.0_wp,        4.0_wp,     0.0_wp,     0.0_wp, &
             18.0_wp,       0.0_wp,      0.0_wp,       -9.0_wp,     0.0_wp,     0.0_wp, &
             16.0_wp,       0.0_wp,      0.0_wp,       -1.0_wp,     0.0_wp,     0.0_wp, &
            -10.0_wp,       0.0_wp,      0.0_wp,        4.0_wp,     0.0_wp,     0.0_wp, &
            -23.0_wp,       0.0_wp,      0.0_wp,        9.0_wp,     0.0_wp,     0.0_wp, &
             16.0_wp,       0.0_wp,      0.0_wp,       -1.0_wp,     0.0_wp,     0.0_wp, &
            -12.0_wp,       0.0_wp,      0.0_wp,        6.0_wp,     0.0_wp,     0.0_wp, &
             -8.0_wp,       0.0_wp,      0.0_wp,        4.0_wp,     0.0_wp,     0.0_wp, &
             30.0_wp,       0.0_wp,      0.0_wp,       -2.0_wp,     0.0_wp,     0.0_wp, &
             24.0_wp,       0.0_wp,      0.0_wp,      -10.0_wp,     0.0_wp,     0.0_wp, &
             10.0_wp,       0.0_wp,      0.0_wp,       -4.0_wp,     0.0_wp,     0.0_wp, &
            -16.0_wp,       0.0_wp,      0.0_wp,        7.0_wp,     0.0_wp,     0.0_wp, &
            -16.0_wp,       0.0_wp,      0.0_wp,        7.0_wp,     0.0_wp,     0.0_wp, &
             17.0_wp,       0.0_wp,      0.0_wp,       -7.0_wp,     0.0_wp,     0.0_wp, &
            -24.0_wp,       0.0_wp,      0.0_wp,       10.0_wp,     0.0_wp,     0.0_wp, &
            -12.0_wp,       0.0_wp,      0.0_wp,        5.0_wp,     0.0_wp,     0.0_wp, &
            -24.0_wp,       0.0_wp,      0.0_wp,       11.0_wp,     0.0_wp,     0.0_wp, &
            -23.0_wp,       0.0_wp,      0.0_wp,        9.0_wp,     0.0_wp,     0.0_wp, &
            -13.0_wp,       0.0_wp,      0.0_wp,        5.0_wp,     0.0_wp,     0.0_wp, &
            -15.0_wp,       0.0_wp,      0.0_wp,        7.0_wp,     0.0_wp,     0.0_wp, &
              0.0_wp,       0.0_wp,  -1988.0_wp,        0.0_wp,     0.0_wp, -1679.0_wp, &
              0.0_wp,       0.0_wp,    -63.0_wp,        0.0_wp,     0.0_wp,   -27.0_wp, &
             -4.0_wp,       0.0_wp,      0.0_wp,        0.0_wp,     0.0_wp,     0.0_wp, &
              0.0_wp,       0.0_wp,      5.0_wp,        0.0_wp,     0.0_wp,     4.0_wp, &
              5.0_wp,       0.0_wp,      0.0_wp,       -3.0_wp,     0.0_wp,     0.0_wp, &
              0.0_wp,       0.0_wp,    364.0_wp,        0.0_wp,     0.0_wp,   176.0_wp, &
              0.0_wp,       0.0_wp,  -1044.0_wp,        0.0_wp,     0.0_wp,  -891.0_wp, &
             -3.0_wp,       0.0_wp,      0.0_wp,        1.0_wp,     0.0_wp,     0.0_wp, &
              4.0_wp,       0.0_wp,      0.0_wp,       -2.0_wp,     0.0_wp,     0.0_wp, &
              0.0_wp,       0.0_wp,    330.0_wp,        0.0_wp,     0.0_wp,     0.0_wp, &
              5.0_wp,       0.0_wp,      0.0_wp,       -2.0_wp,     0.0_wp,     0.0_wp, &
              3.0_wp,       0.0_wp,      0.0_wp,       -2.0_wp,     0.0_wp,     0.0_wp, &
             -3.0_wp,       0.0_wp,      0.0_wp,        1.0_wp,     0.0_wp,     0.0_wp, &
             -5.0_wp,       0.0_wp,      0.0_wp,        2.0_wp,     0.0_wp,     0.0_wp, &
              3.0_wp,       0.0_wp,      0.0_wp,       -1.0_wp,     0.0_wp,     0.0_wp, &
              3.0_wp,       0.0_wp,      0.0_wp,        0.0_wp,     0.0_wp,     0.0_wp, &
              3.0_wp,       0.0_wp,      0.0_wp,        0.0_wp,     0.0_wp,     0.0_wp, &
              0.0_wp,       0.0_wp,      5.0_wp,        0.0_wp,     0.0_wp,     0.0_wp, &
              0.0_wp,       0.0_wp,      0.0_wp,        1.0_wp,     0.0_wp,     0.0_wp, &
              4.0_wp,       0.0_wp,      0.0_wp,       -2.0_wp,     0.0_wp,     0.0_wp, &
              6.0_wp,       0.0_wp,      0.0_wp,        0.0_wp,     0.0_wp,     0.0_wp, &
              5.0_wp,       0.0_wp,      0.0_wp,       -2.0_wp,     0.0_wp,     0.0_wp, &
             -7.0_wp,       0.0_wp,      0.0_wp,        0.0_wp,     0.0_wp,     0.0_wp, &
            -12.0_wp,       0.0_wp,      0.0_wp,        0.0_wp,     0.0_wp,     0.0_wp, &
              5.0_wp,       0.0_wp,      0.0_wp,       -3.0_wp,     0.0_wp,     0.0_wp, &
              3.0_wp,       0.0_wp,      0.0_wp,       -1.0_wp,     0.0_wp,     0.0_wp, &
             -5.0_wp,       0.0_wp,      0.0_wp,        0.0_wp,     0.0_wp,     0.0_wp, &
              3.0_wp,       0.0_wp,      0.0_wp,        0.0_wp,     0.0_wp,     0.0_wp, &
             -7.0_wp,       0.0_wp,      0.0_wp,        3.0_wp,     0.0_wp,     0.0_wp, &
              7.0_wp,       0.0_wp,      0.0_wp,       -4.0_wp,     0.0_wp,     0.0_wp, &
              0.0_wp,       0.0_wp,    -12.0_wp,        0.0_wp,     0.0_wp,   -10.0_wp, &
              4.0_wp,       0.0_wp,      0.0_wp,       -2.0_wp,     0.0_wp,     0.0_wp, &
              3.0_wp,       0.0_wp,      0.0_wp,       -2.0_wp,     0.0_wp,     0.0_wp, &
             -3.0_wp,       0.0_wp,      0.0_wp,        2.0_wp,     0.0_wp,     0.0_wp, &
             -7.0_wp,       0.0_wp,      0.0_wp,        3.0_wp,     0.0_wp,     0.0_wp, &
             -4.0_wp,       0.0_wp,      0.0_wp,        2.0_wp,     0.0_wp,     0.0_wp, &
             -3.0_wp,       0.0_wp,      0.0_wp,        1.0_wp,     0.0_wp,     0.0_wp, &
              0.0_wp,       0.0_wp,      0.0_wp,        0.0_wp,     0.0_wp,     0.0_wp, &
             -3.0_wp,       0.0_wp,      0.0_wp,        1.0_wp,     0.0_wp,     0.0_wp, &
              7.0_wp,       0.0_wp,      0.0_wp,       -3.0_wp,     0.0_wp,     0.0_wp, &
             -4.0_wp,       0.0_wp,      0.0_wp,        2.0_wp,     0.0_wp,     0.0_wp, &
              4.0_wp,       0.0_wp,      0.0_wp,       -2.0_wp,     0.0_wp,     0.0_wp, &
             -5.0_wp,       0.0_wp,      0.0_wp,        3.0_wp,     0.0_wp,     0.0_wp, &
              5.0_wp,       0.0_wp,      0.0_wp,        0.0_wp,     0.0_wp,     0.0_wp, &
             -5.0_wp,       0.0_wp,      0.0_wp,        2.0_wp,     0.0_wp,     0.0_wp, &
              5.0_wp,       0.0_wp,      0.0_wp,       -2.0_wp,     0.0_wp,     0.0_wp, &
             -8.0_wp,       0.0_wp,      0.0_wp,        3.0_wp,     0.0_wp,     0.0_wp, &
              9.0_wp,       0.0_wp,      0.0_wp,        0.0_wp,     0.0_wp,     0.0_wp, &
              6.0_wp,       0.0_wp,      0.0_wp,       -3.0_wp,     0.0_wp,     0.0_wp, &
             -5.0_wp,       0.0_wp,      0.0_wp,        2.0_wp,     0.0_wp,     0.0_wp, &
              3.0_wp,       0.0_wp,      0.0_wp,        0.0_wp,     0.0_wp,     0.0_wp, &
             -7.0_wp,       0.0_wp,      0.0_wp,        0.0_wp,     0.0_wp,     0.0_wp, &
             -3.0_wp,       0.0_wp,      0.0_wp,        1.0_wp,     0.0_wp,     0.0_wp, &
              5.0_wp,       0.0_wp,      0.0_wp,        0.0_wp,     0.0_wp,     0.0_wp, &
              3.0_wp,       0.0_wp,      0.0_wp,        0.0_wp,     0.0_wp,     0.0_wp, &
             -3.0_wp,       0.0_wp,      0.0_wp,        2.0_wp,     0.0_wp,     0.0_wp, &
              4.0_wp,       0.0_wp,      0.0_wp,       -2.0_wp,     0.0_wp,     0.0_wp, &
              3.0_wp,       0.0_wp,      0.0_wp,       -1.0_wp,     0.0_wp,     0.0_wp, &
             -5.0_wp,       0.0_wp,      0.0_wp,        2.0_wp,     0.0_wp,     0.0_wp, &
              4.0_wp,       0.0_wp,      0.0_wp,       -2.0_wp,     0.0_wp,     0.0_wp, &
              9.0_wp,       0.0_wp,      0.0_wp,       -3.0_wp,     0.0_wp,     0.0_wp, &
              4.0_wp,       0.0_wp,      0.0_wp,        0.0_wp,     0.0_wp,     0.0_wp, &
              4.0_wp,       0.0_wp,      0.0_wp,       -2.0_wp,     0.0_wp,     0.0_wp, &
             -3.0_wp,       0.0_wp,      0.0_wp,        2.0_wp,     0.0_wp,     0.0_wp, &
             -4.0_wp,       0.0_wp,      0.0_wp,        2.0_wp,     0.0_wp,     0.0_wp, &
              9.0_wp,       0.0_wp,      0.0_wp,       -3.0_wp,     0.0_wp,     0.0_wp, &
             -4.0_wp,       0.0_wp,      0.0_wp,        0.0_wp,     0.0_wp,     0.0_wp, &
             -4.0_wp,       0.0_wp,      0.0_wp,        0.0_wp,     0.0_wp,     0.0_wp, &
              3.0_wp,       0.0_wp,      0.0_wp,       -2.0_wp,     0.0_wp,     0.0_wp, &
              8.0_wp,       0.0_wp,      0.0_wp,        0.0_wp,     0.0_wp,     0.0_wp, &
              3.0_wp,       0.0_wp,      0.0_wp,        0.0_wp,     0.0_wp,     0.0_wp, &
             -3.0_wp,       0.0_wp,      0.0_wp,        2.0_wp,     0.0_wp,     0.0_wp, &
              3.0_wp,       0.0_wp,      0.0_wp,       -1.0_wp,     0.0_wp,     0.0_wp, &
              3.0_wp,       0.0_wp,      0.0_wp,       -1.0_wp,     0.0_wp,     0.0_wp, &
             -3.0_wp,       0.0_wp,      0.0_wp,        1.0_wp,     0.0_wp,     0.0_wp, &
              6.0_wp,       0.0_wp,      0.0_wp,       -3.0_wp,     0.0_wp,     0.0_wp, &
              3.0_wp,       0.0_wp,      0.0_wp,        0.0_wp,     0.0_wp,     0.0_wp, &
             -3.0_wp,       0.0_wp,      0.0_wp,        1.0_wp,     0.0_wp,     0.0_wp, &
             -7.0_wp,       0.0_wp,      0.0_wp,        0.0_wp,     0.0_wp,     0.0_wp, &
              9.0_wp,       0.0_wp,      0.0_wp,        0.0_wp,     0.0_wp,     0.0_wp, &
             -3.0_wp,       0.0_wp,      0.0_wp,        2.0_wp,     0.0_wp,     0.0_wp, &
             -3.0_wp,       0.0_wp,      0.0_wp,        0.0_wp,     0.0_wp,     0.0_wp, &
             -4.0_wp,       0.0_wp,      0.0_wp,        0.0_wp,     0.0_wp,     0.0_wp, &
             -5.0_wp,       0.0_wp,      0.0_wp,        3.0_wp,     0.0_wp,     0.0_wp, &
            -13.0_wp,       0.0_wp,      0.0_wp,        0.0_wp,     0.0_wp,     0.0_wp, &
             -7.0_wp,       0.0_wp,      0.0_wp,        0.0_wp,     0.0_wp,     0.0_wp, &
             10.0_wp,       0.0_wp,      0.0_wp,        0.0_wp,     0.0_wp,     0.0_wp, &
              3.0_wp,       0.0_wp,      0.0_wp,       -1.0_wp,     0.0_wp,     0.0_wp, &
             10.0_wp,       0.0_wp,     13.0_wp,        6.0_wp,     0.0_wp,    -5.0_wp, &
              0.0_wp,       0.0_wp,     30.0_wp,        0.0_wp,     0.0_wp,    14.0_wp, &
              0.0_wp,       0.0_wp,   -162.0_wp,        0.0_wp,     0.0_wp,  -138.0_wp, &
              0.0_wp,       0.0_wp,     75.0_wp,        0.0_wp,     0.0_wp,     0.0_wp, &
             -7.0_wp,       0.0_wp,      0.0_wp,        4.0_wp,     0.0_wp,     0.0_wp, &
             -4.0_wp,       0.0_wp,      0.0_wp,        2.0_wp,     0.0_wp,     0.0_wp, &
              4.0_wp,       0.0_wp,      0.0_wp,       -2.0_wp,     0.0_wp,     0.0_wp, &
              5.0_wp,       0.0_wp,      0.0_wp,       -2.0_wp,     0.0_wp,     0.0_wp, &
              5.0_wp,       0.0_wp,      0.0_wp,       -3.0_wp,     0.0_wp,     0.0_wp, &
             -3.0_wp,       0.0_wp,      0.0_wp,        0.0_wp,     0.0_wp,     0.0_wp, &
             -3.0_wp,       0.0_wp,      0.0_wp,        2.0_wp,     0.0_wp,     0.0_wp, &
             -4.0_wp,       0.0_wp,      0.0_wp,        2.0_wp,     0.0_wp,     0.0_wp, &
             -5.0_wp,       0.0_wp,      0.0_wp,        2.0_wp,     0.0_wp,     0.0_wp, &
              6.0_wp,       0.0_wp,      0.0_wp,        0.0_wp,     0.0_wp,     0.0_wp, &
              9.0_wp,       0.0_wp,      0.0_wp,        0.0_wp,     0.0_wp,     0.0_wp, &
              5.0_wp,       0.0_wp,      0.0_wp,        0.0_wp,     0.0_wp,     0.0_wp, &
             -7.0_wp,       0.0_wp,      0.0_wp,        0.0_wp,     0.0_wp,     0.0_wp, &
             -3.0_wp,       0.0_wp,      0.0_wp,        1.0_wp,     0.0_wp,     0.0_wp, &
             -4.0_wp,       0.0_wp,      0.0_wp,        2.0_wp,     0.0_wp,     0.0_wp, &
              7.0_wp,       0.0_wp,      0.0_wp,        0.0_wp,     0.0_wp,     0.0_wp, &
             -4.0_wp,       0.0_wp,      0.0_wp,        0.0_wp,     0.0_wp,     0.0_wp, &
              4.0_wp,       0.0_wp,      0.0_wp,        0.0_wp,     0.0_wp,     0.0_wp, &
             -6.0_wp,       0.0_wp,     -3.0_wp,        3.0_wp,     0.0_wp,     1.0_wp, &
              0.0_wp,       0.0_wp,     -3.0_wp,        0.0_wp,     0.0_wp,    -2.0_wp, &
             11.0_wp,       0.0_wp,      0.0_wp,        0.0_wp,     0.0_wp,     0.0_wp, &
              3.0_wp,       0.0_wp,      0.0_wp,       -1.0_wp,     0.0_wp,     0.0_wp, &
             11.0_wp,       0.0_wp,      0.0_wp,        0.0_wp,     0.0_wp,     0.0_wp, &
             -3.0_wp,       0.0_wp,      0.0_wp,        2.0_wp,     0.0_wp,     0.0_wp, &
             -1.0_wp,       0.0_wp,      3.0_wp,        3.0_wp,     0.0_wp,    -1.0_wp, &
              4.0_wp,       0.0_wp,      0.0_wp,       -2.0_wp,     0.0_wp,     0.0_wp, &
              0.0_wp,       0.0_wp,    -13.0_wp,        0.0_wp,     0.0_wp,   -11.0_wp, &
              3.0_wp,       0.0_wp,      6.0_wp,        0.0_wp,     0.0_wp,     0.0_wp, &
             -7.0_wp,       0.0_wp,      0.0_wp,        0.0_wp,     0.0_wp,     0.0_wp, &
              5.0_wp,       0.0_wp,      0.0_wp,       -3.0_wp,     0.0_wp,     0.0_wp, &
             -3.0_wp,       0.0_wp,      0.0_wp,        1.0_wp,     0.0_wp,     0.0_wp, &
              3.0_wp,       0.0_wp,      0.0_wp,        0.0_wp,     0.0_wp,     0.0_wp, &
              5.0_wp,       0.0_wp,      0.0_wp,       -3.0_wp,     0.0_wp,     0.0_wp, &
             -7.0_wp,       0.0_wp,      0.0_wp,        3.0_wp,     0.0_wp,     0.0_wp, &
              8.0_wp,       0.0_wp,      0.0_wp,       -3.0_wp,     0.0_wp,     0.0_wp, &
             -4.0_wp,       0.0_wp,      0.0_wp,        2.0_wp,     0.0_wp,     0.0_wp, &
             11.0_wp,       0.0_wp,      0.0_wp,        0.0_wp,     0.0_wp,     0.0_wp, &
             -3.0_wp,       0.0_wp,      0.0_wp,        1.0_wp,     0.0_wp,     0.0_wp, &
              3.0_wp,       0.0_wp,      0.0_wp,       -1.0_wp,     0.0_wp,     0.0_wp, &
             -4.0_wp,       0.0_wp,      0.0_wp,        2.0_wp,     0.0_wp,     0.0_wp, &
              8.0_wp,       0.0_wp,      0.0_wp,       -4.0_wp,     0.0_wp,     0.0_wp, &
              3.0_wp,       0.0_wp,      0.0_wp,       -1.0_wp,     0.0_wp,     0.0_wp, &
             11.0_wp,       0.0_wp,      0.0_wp,        0.0_wp,     0.0_wp,     0.0_wp, &
             -6.0_wp,       0.0_wp,      0.0_wp,        3.0_wp,     0.0_wp,     0.0_wp, &
             -4.0_wp,       0.0_wp,      0.0_wp,        2.0_wp,     0.0_wp,     0.0_wp, &
             -8.0_wp,       0.0_wp,      0.0_wp,        4.0_wp,     0.0_wp,     0.0_wp, &
             -7.0_wp,       0.0_wp,      0.0_wp,        3.0_wp,     0.0_wp,     0.0_wp, &
             -4.0_wp,       0.0_wp,      0.0_wp,        2.0_wp,     0.0_wp,     0.0_wp, &
              3.0_wp,       0.0_wp,      0.0_wp,       -1.0_wp,     0.0_wp,     0.0_wp, &
              6.0_wp,       0.0_wp,      0.0_wp,       -3.0_wp,     0.0_wp,     0.0_wp, &
             -6.0_wp,       0.0_wp,      0.0_wp,        3.0_wp,     0.0_wp,     0.0_wp, &
              6.0_wp,       0.0_wp,      0.0_wp,        0.0_wp,     0.0_wp,     0.0_wp, &
              6.0_wp,       0.0_wp,      0.0_wp,       -1.0_wp,     0.0_wp,     0.0_wp, &
              5.0_wp,       0.0_wp,      0.0_wp,       -2.0_wp,     0.0_wp,     0.0_wp, &
             -5.0_wp,       0.0_wp,      0.0_wp,        2.0_wp,     0.0_wp,     0.0_wp, &
             -4.0_wp,       0.0_wp,      0.0_wp,        0.0_wp,     0.0_wp,     0.0_wp, &
             -4.0_wp,       0.0_wp,      0.0_wp,        2.0_wp,     0.0_wp,     0.0_wp, &
              4.0_wp,       0.0_wp,      0.0_wp,        0.0_wp,     0.0_wp,     0.0_wp, &
              6.0_wp,       0.0_wp,      0.0_wp,       -3.0_wp,     0.0_wp,     0.0_wp, &
             -4.0_wp,       0.0_wp,      0.0_wp,        2.0_wp,     0.0_wp,     0.0_wp, &
              0.0_wp,       0.0_wp,    -26.0_wp,        0.0_wp,     0.0_wp,   -11.0_wp, &
              0.0_wp,       0.0_wp,    -10.0_wp,        0.0_wp,     0.0_wp,    -5.0_wp, &
              5.0_wp,       0.0_wp,      0.0_wp,       -3.0_wp,     0.0_wp,     0.0_wp, &
            -13.0_wp,       0.0_wp,      0.0_wp,        0.0_wp,     0.0_wp,     0.0_wp, &
              3.0_wp,       0.0_wp,      0.0_wp,       -2.0_wp,     0.0_wp,     0.0_wp, &
              4.0_wp,       0.0_wp,      0.0_wp,       -2.0_wp,     0.0_wp,     0.0_wp, &
              7.0_wp,       0.0_wp,      0.0_wp,       -3.0_wp,     0.0_wp,     0.0_wp, &
              4.0_wp,       0.0_wp,      0.0_wp,        0.0_wp,     0.0_wp,     0.0_wp, &
              5.0_wp,       0.0_wp,      0.0_wp,        0.0_wp,     0.0_wp,     0.0_wp, &
             -3.0_wp,       0.0_wp,      0.0_wp,        2.0_wp,     0.0_wp,     0.0_wp, &
             -6.0_wp,       0.0_wp,      0.0_wp,        2.0_wp,     0.0_wp,     0.0_wp, &
             -5.0_wp,       0.0_wp,      0.0_wp,        2.0_wp,     0.0_wp,     0.0_wp, &
             -7.0_wp,       0.0_wp,      0.0_wp,        3.0_wp,     0.0_wp,     0.0_wp, &
              5.0_wp,       0.0_wp,      0.0_wp,       -2.0_wp,     0.0_wp,     0.0_wp, &
             13.0_wp,       0.0_wp,      0.0_wp,        0.0_wp,     0.0_wp,     0.0_wp, &
             -4.0_wp,       0.0_wp,      0.0_wp,        2.0_wp,     0.0_wp,     0.0_wp, &
             -3.0_wp,       0.0_wp,      0.0_wp,        0.0_wp,     0.0_wp,     0.0_wp, &
              5.0_wp,       0.0_wp,      0.0_wp,       -2.0_wp,     0.0_wp,     0.0_wp, &
            -11.0_wp,       0.0_wp,      0.0_wp,        0.0_wp,     0.0_wp,     0.0_wp, &
              5.0_wp,       0.0_wp,      0.0_wp,       -2.0_wp,     0.0_wp,     0.0_wp, &
              4.0_wp,       0.0_wp,      0.0_wp,        0.0_wp,     0.0_wp,     0.0_wp, &
              4.0_wp,       0.0_wp,      0.0_wp,       -2.0_wp,     0.0_wp,     0.0_wp, &
             -4.0_wp,       0.0_wp,      0.0_wp,        2.0_wp,     0.0_wp,     0.0_wp, &
              6.0_wp,       0.0_wp,      0.0_wp,       -3.0_wp,     0.0_wp,     0.0_wp, &
              3.0_wp,       0.0_wp,      0.0_wp,       -2.0_wp,     0.0_wp,     0.0_wp, &
            -12.0_wp,       0.0_wp,      0.0_wp,        0.0_wp,     0.0_wp,     0.0_wp, &
              4.0_wp,       0.0_wp,      0.0_wp,        0.0_wp,     0.0_wp,     0.0_wp, &
             -3.0_wp,       0.0_wp,      0.0_wp,        0.0_wp,     0.0_wp,     0.0_wp, &
             -4.0_wp,       0.0_wp,      0.0_wp,        0.0_wp,     0.0_wp,     0.0_wp, &
              3.0_wp,       0.0_wp,      0.0_wp,        0.0_wp,     0.0_wp,     0.0_wp, &
              3.0_wp,       0.0_wp,      0.0_wp,       -1.0_wp,     0.0_wp,     0.0_wp, &
             -3.0_wp,       0.0_wp,      0.0_wp,        1.0_wp,     0.0_wp,     0.0_wp, &
              0.0_wp,       0.0_wp,     -5.0_wp,        0.0_wp,     0.0_wp,    -2.0_wp, &
             -7.0_wp,       0.0_wp,      0.0_wp,        4.0_wp,     0.0_wp,     0.0_wp, &
              6.0_wp,       0.0_wp,      0.0_wp,       -3.0_wp,     0.0_wp,     0.0_wp, &
             -3.0_wp,       0.0_wp,      0.0_wp,        0.0_wp,     0.0_wp,     0.0_wp, &
              5.0_wp,       0.0_wp,      0.0_wp,       -3.0_wp,     0.0_wp,     0.0_wp, &
              3.0_wp,       0.0_wp,      0.0_wp,       -1.0_wp,     0.0_wp,     0.0_wp, &
              3.0_wp,       0.0_wp,      0.0_wp,        0.0_wp,     0.0_wp,     0.0_wp, &
             -3.0_wp,       0.0_wp,      0.0_wp,        1.0_wp,     0.0_wp,     0.0_wp, &
             -5.0_wp,       0.0_wp,      0.0_wp,        3.0_wp,     0.0_wp,     0.0_wp, &
             -3.0_wp,       0.0_wp,      0.0_wp,        2.0_wp,     0.0_wp,     0.0_wp, &
             -3.0_wp,       0.0_wp,      0.0_wp,        2.0_wp,     0.0_wp,     0.0_wp, &
             12.0_wp,       0.0_wp,      0.0_wp,        0.0_wp,     0.0_wp,     0.0_wp, &
              3.0_wp,       0.0_wp,      0.0_wp,       -1.0_wp,     0.0_wp,     0.0_wp, &
             -4.0_wp,       0.0_wp,      0.0_wp,        2.0_wp,     0.0_wp,     0.0_wp, &
              4.0_wp,       0.0_wp,      0.0_wp,        0.0_wp,     0.0_wp,     0.0_wp, &
              6.0_wp,       0.0_wp,      0.0_wp,        0.0_wp,     0.0_wp,     0.0_wp, &
              5.0_wp,       0.0_wp,      0.0_wp,       -3.0_wp,     0.0_wp,     0.0_wp, &
              4.0_wp,       0.0_wp,      0.0_wp,       -2.0_wp,     0.0_wp,     0.0_wp, &
             -6.0_wp,       0.0_wp,      0.0_wp,        3.0_wp,     0.0_wp,     0.0_wp, &
              4.0_wp,       0.0_wp,      0.0_wp,       -2.0_wp,     0.0_wp,     0.0_wp, &
              6.0_wp,       0.0_wp,      0.0_wp,       -3.0_wp,     0.0_wp,     0.0_wp, &
              6.0_wp,       0.0_wp,      0.0_wp,        0.0_wp,     0.0_wp,     0.0_wp, &
             -6.0_wp,       0.0_wp,      0.0_wp,        3.0_wp,     0.0_wp,     0.0_wp, &
              3.0_wp,       0.0_wp,      0.0_wp,       -2.0_wp,     0.0_wp,     0.0_wp, &
              7.0_wp,       0.0_wp,      0.0_wp,       -4.0_wp,     0.0_wp,     0.0_wp, &
              4.0_wp,       0.0_wp,      0.0_wp,       -2.0_wp,     0.0_wp,     0.0_wp, &
             -5.0_wp,       0.0_wp,      0.0_wp,        2.0_wp,     0.0_wp,     0.0_wp, &
              5.0_wp,       0.0_wp,      0.0_wp,        0.0_wp,     0.0_wp,     0.0_wp, &
             -6.0_wp,       0.0_wp,      0.0_wp,        3.0_wp,     0.0_wp,     0.0_wp, &
             -6.0_wp,       0.0_wp,      0.0_wp,        3.0_wp,     0.0_wp,     0.0_wp, &
             -4.0_wp,       0.0_wp,      0.0_wp,        2.0_wp,     0.0_wp,     0.0_wp, &
             10.0_wp,       0.0_wp,      0.0_wp,        0.0_wp,     0.0_wp,     0.0_wp, &
             -4.0_wp,       0.0_wp,      0.0_wp,        2.0_wp,     0.0_wp,     0.0_wp, &
              7.0_wp,       0.0_wp,      0.0_wp,        0.0_wp,     0.0_wp,     0.0_wp, &
              7.0_wp,       0.0_wp,      0.0_wp,       -3.0_wp,     0.0_wp,     0.0_wp, &
              4.0_wp,       0.0_wp,      0.0_wp,        0.0_wp,     0.0_wp,     0.0_wp, &
             11.0_wp,       0.0_wp,      0.0_wp,        0.0_wp,     0.0_wp,     0.0_wp, &
              5.0_wp,       0.0_wp,      0.0_wp,       -2.0_wp,     0.0_wp,     0.0_wp, &
             -6.0_wp,       0.0_wp,      0.0_wp,        2.0_wp,     0.0_wp,     0.0_wp, &
              4.0_wp,       0.0_wp,      0.0_wp,       -2.0_wp,     0.0_wp,     0.0_wp, &
              3.0_wp,       0.0_wp,      0.0_wp,       -2.0_wp,     0.0_wp,     0.0_wp, &
              5.0_wp,       0.0_wp,      0.0_wp,       -2.0_wp,     0.0_wp,     0.0_wp, &
             -4.0_wp,       0.0_wp,      0.0_wp,        2.0_wp,     0.0_wp,     0.0_wp, &
             -4.0_wp,       0.0_wp,      0.0_wp,        2.0_wp,     0.0_wp,     0.0_wp, &
             -3.0_wp,       0.0_wp,      0.0_wp,        2.0_wp,     0.0_wp,     0.0_wp, &
              4.0_wp,       0.0_wp,      0.0_wp,       -2.0_wp,     0.0_wp,     0.0_wp, &
              3.0_wp,       0.0_wp,      0.0_wp,       -1.0_wp,     0.0_wp,     0.0_wp, &
             -3.0_wp,       0.0_wp,      0.0_wp,        1.0_wp,     0.0_wp,     0.0_wp, &
             -3.0_wp,       0.0_wp,      0.0_wp,        1.0_wp,     0.0_wp,     0.0_wp, &
             -3.0_wp,       0.0_wp,      0.0_wp,        2.0_wp,     0.0_wp,     0.0_wp], [6,nls])

    !
    !  Planetary argument multipliers
    !    :         L   L'  F   D   Om  Me  Ve  E  Ma  Ju  Sa  Ur  Ne  pre

    !  Coefficients for fundamental arguments

    integer,dimension(14,npl),parameter :: napl = reshape( [ &
             0,  0,  0,  0,  0,  0,  0,  8,-16,  4,  5,  0,  0,  0, &
             0,  0,  0,  0,  0,  0,  0, -8, 16, -4, -5,  0,  0,  2, &
             0,  0,  0,  0,  0,  0,  0,  8,-16,  4,  5,  0,  0,  2, &
             0,  0,  0,  0,  0,  0,  0,  0,  0,  0,  0, -1,  2,  2, &
             0,  0,  0,  0,  0,  0,  0, -4,  8, -1, -5,  0,  0,  2, &
             0,  0,  0,  0,  0,  0,  0,  4, -8,  3,  0,  0,  0,  1, &
             0,  0,  1, -1,  1,  0,  0,  3, -8,  3,  0,  0,  0,  0, &
            -1,  0,  0,  0,  0,  0, 10, -3,  0,  0,  0,  0,  0,  0, &
             0,  0,  0,  0,  0,  0,  0,  0,  0, -2,  6, -3,  0,  2, &
             0,  0,  0,  0,  0,  0,  0,  4, -8,  3,  0,  0,  0,  0, &
             0,  0,  1, -1,  1,  0,  0, -5,  8, -3,  0,  0,  0,  0, &
             0,  0,  0,  0,  0,  0,  0, -4,  8, -3,  0,  0,  0,  1, &
             0,  0,  0,  0,  0,  0,  0,  4, -8,  1,  5,  0,  0,  2, &
             0,  0,  0,  0,  0,  0, -5,  6,  4,  0,  0,  0,  0,  2, &
             0,  0,  0,  0,  0,  0,  0,  0,  0,  2, -5,  0,  0,  2, &
             0,  0,  0,  0,  0,  0,  0,  0,  0,  2, -5,  0,  0,  1, &
             0,  0,  1, -1,  1,  0,  0, -1,  0,  2, -5,  0,  0,  0, &
             0,  0,  0,  0,  0,  0,  0,  0,  0,  2, -5,  0,  0,  0, &
             0,  0,  1, -1,  1,  0,  0, -1,  0, -2,  5,  0,  0,  0, &
             0,  0,  0,  0,  0,  0,  0,  0,  0, -2,  5,  0,  0,  1, &
             0,  0,  0,  0,  0,  0,  0,  0,  0, -2,  5,  0,  0,  2, &
             2,  0, -1, -1,  0,  0,  0,  3, -7,  0,  0,  0,  0,  0, &
             1,  0,  0, -2,  0,  0, 19,-21,  3,  0,  0,  0,  0,  0, &
             0,  0,  1, -1,  1,  0,  2, -4,  0, -3,  0,  0,  0,  0, &
             1,  0,  0, -1,  1,  0,  0, -1,  0,  2,  0,  0,  0,  0, &
             0,  0,  1, -1,  1,  0,  0, -1,  0, -4, 10,  0,  0,  0, &
            -2,  0,  0,  2,  1,  0,  0,  2,  0,  0, -5,  0,  0,  0, &
             0,  0,  0,  0,  0,  0,  3, -7,  4,  0,  0,  0,  0,  0, &
             0,  0, -1,  1,  0,  0,  0,  1,  0,  1, -1,  0,  0,  0, &
            -2,  0,  0,  2,  1,  0,  0,  2,  0, -2,  0,  0,  0,  0, &
            -1,  0,  0,  0,  0,  0, 18,-16,  0,  0,  0,  0,  0,  0, &
            -2,  0,  1,  1,  2,  0,  0,  1,  0, -2,  0,  0,  0,  0, &
            -1,  0,  1, -1,  1,  0, 18,-17,  0,  0,  0,  0,  0,  0, &
            -1,  0,  0,  1,  1,  0,  0,  2, -2,  0,  0,  0,  0,  0, &
             0,  0,  0,  0,  0,  0, -8, 13,  0,  0,  0,  0,  0,  2, &
             0,  0,  2, -2,  2,  0, -8, 11,  0,  0,  0,  0,  0,  0, &
             0,  0,  0,  0,  0,  0, -8, 13,  0,  0,  0,  0,  0,  1, &
             0,  0,  1, -1,  1,  0, -8, 12,  0,  0,  0,  0,  0,  0, &
             0,  0,  0,  0,  0,  0,  8,-13,  0,  0,  0,  0,  0,  0, &
             0,  0,  1, -1,  1,  0,  8,-14,  0,  0,  0,  0,  0,  0, &
             0,  0,  0,  0,  0,  0,  8,-13,  0,  0,  0,  0,  0,  1, &
            -2,  0,  0,  2,  1,  0,  0,  2,  0, -4,  5,  0,  0,  0, &
            -2,  0,  0,  2,  2,  0,  3, -3,  0,  0,  0,  0,  0,  0, &
            -2,  0,  0,  2,  0,  0,  0,  2,  0, -3,  1,  0,  0,  0, &
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             0,  0,  0,  0,  0,  0,  3, -1,  0,  0,  0,  0,  0,  1, &
             0,  0,  0,  0,  0,  0,  3, -1,  0,  0,  0,  0,  0,  2, &
             0,  0,  0,  0,  0,  0,  0,  4,  0, -1,  0,  0,  0,  2, &
             0,  0,  0,  0,  0,  0,  0,  4,  0,  0, -2,  0,  0,  2, &
             0,  0,  0,  0,  0,  0,  0,  5, -2,  0,  0,  0,  0,  2, &
             0,  0,  0,  0,  0,  0,  0,  4,  0,  0,  0,  0,  0,  0, &
             0,  0,  0,  0,  0,  0,  8, -9,  0,  0,  0,  0,  0,  0, &
             0,  0,  0,  0,  0,  0,  5, -4,  0,  0,  0,  0,  0,  2, &
             0,  0,  0,  0,  0,  0,  2,  1,  0,  0,  0,  0,  0,  2, &
             0,  0,  0,  0,  0,  0,  2,  1,  0,  0,  0,  0,  0,  1, &
             0,  0,  0,  0,  0,  0,  2,  1,  0,  0,  0,  0,  0,  1, &
             0,  0,  0,  0,  0,  0, -7,  7,  0,  0,  0,  0,  0,  1, &
             0,  0,  0,  0,  0,  0,  7, -7,  0,  0,  0,  0,  0,  0, &
             0,  0,  0,  0,  0,  0,  4, -2,  0,  0,  0,  0,  0,  1, &
             0,  0,  0,  0,  0,  0,  4, -2,  0,  0,  0,  0,  0,  2, &
             0,  0,  0,  0,  0,  0,  4, -2,  0,  0,  0,  0,  0,  0, &
             0,  0,  0,  0,  0,  0,  4, -2,  0,  0,  0,  0,  0,  0, &
             0,  0,  0,  0,  0,  0,  0,  5,  0, -4,  0,  0,  0,  2, &
             0,  0,  0,  0,  0,  0,  0,  5,  0, -3,  0,  0,  0,  2, &
             0,  0,  0,  0,  0,  0,  0,  5,  0, -2,  0,  0,  0,  2, &
             0,  0,  0,  0,  0,  0,  3,  0,  0,  0,  0,  0,  0,  2, &
             0,  0,  0,  0,  0,  0, -8,  8,  0,  0,  0,  0,  0,  1, &
             0,  0,  0,  0,  0,  0,  8, -8,  0,  0,  0,  0,  0,  0, &
             0,  0,  0,  0,  0,  0,  5, -3,  0,  0,  0,  0,  0,  1, &
             0,  0,  0,  0,  0,  0,  5, -3,  0,  0,  0,  0,  0,  2, &
             0,  0,  0,  0,  0,  0, -9,  9,  0,  0,  0,  0,  0,  1, &
             0,  0,  0,  0,  0,  0, -9,  9,  0,  0,  0,  0,  0,  1, &
             0,  0,  0,  0,  0,  0, -9,  9,  0,  0,  0,  0,  0,  1, &
             0,  0,  0,  0,  0,  0,  9, -9,  0,  0,  0,  0,  0,  0, &
             0,  0,  0,  0,  0,  0,  6, -4,  0,  0,  0,  0,  0,  1, &
             0,  0,  0,  0,  0,  0,  0,  6,  0,  0,  0,  0,  0,  2, &
             0,  0,  0,  0,  0,  0,  0,  6,  0,  0,  0,  0,  0,  0, &
             0,  0,  0,  0,  0,  0,  0,  6,  0,  0,  0,  0,  0,  0, &
             0,  0,  0,  0,  0,  0,  0,  6,  0,  0,  0,  0,  0,  1, &
             0,  0,  0,  0,  0,  0,  0,  6,  0,  0,  0,  0,  0,  2, &
             0,  0,  0,  0,  0,  0,  0,  6,  0,  0,  0,  0,  0,  0, &
             0,  0,  0,  0,  0,  0,  0,  6,  0,  0,  0,  0,  0,  1, &
             0,  0,  0,  0,  0,  0,  0,  6,  0,  0,  0,  0,  0,  2, &
             0,  0,  0,  0,  0,  0,  0,  0,  0,  0,  0,  0,  0,  2, &
             1,  0,  0, -2,  0,  0,  0,  2,  0, -2,  0,  0,  0,  0, &
             1,  0,  0, -2,  0,  0,  2, -2,  0,  0,  0,  0,  0,  0, &
             1,  0,  0, -2,  0,  0,  0,  1,  0, -1,  0,  0,  0,  0, &
             1,  0,  0, -2,  0,  0,  1, -1,  0,  0,  0,  0,  0,  0, &
            -1,  0,  0,  0,  0,  0,  3, -3,  0,  0,  0,  0,  0,  0, &
            -1,  0,  0,  0,  0,  0,  0,  2,  0, -2,  0,  0,  0,  0, &
            -1,  0,  0,  2,  0,  0,  0,  4, -8,  3,  0,  0,  0,  0, &
             1,  0,  0, -2,  0,  0,  0,  4, -8,  3,  0,  0,  0,  0, &
            -2,  0,  0,  2,  0,  0,  0,  4, -8,  3,  0,  0,  0,  0, &
            -1,  0,  0,  0,  0,  0,  0,  2,  0, -3,  0,  0,  0,  0, &
            -1,  0,  0,  0,  0,  0,  0,  1,  0, -1,  0,  0,  0,  0, &
            -1,  0,  0,  0,  0,  0,  1, -1,  0,  0,  0,  0,  0,  0, &
            -1,  0,  0,  2,  0,  0,  2, -2,  0,  0,  0,  0,  0,  0, &
             1,  0, -1,  1,  0,  0,  0,  1,  0,  0,  0,  0,  0,  0, &
            -1,  0,  0,  2,  0,  0,  0,  2,  0, -3,  0,  0,  0,  0, &
            -2,  0,  0,  0,  0,  0,  0,  2,  0, -3,  0,  0,  0,  0, &
             1,  0,  0,  0,  0,  0,  0,  4, -8,  3,  0,  0,  0,  0, &
            -1,  0,  1, -1,  1,  0,  0, -1,  0,  0,  0,  0,  0,  0, &
             1,  0,  1, -1,  1,  0,  0, -1,  0,  0,  0,  0,  0,  0, &
            -1,  0,  0,  0,  0,  0,  0,  4, -8,  3,  0,  0,  0,  0, &
            -1,  0,  0,  2,  1,  0,  0,  2,  0, -2,  0,  0,  0,  0, &
             0,  0,  0,  0,  0,  0,  0,  2,  0, -2,  0,  0,  0,  0, &
            -1,  0,  0,  2,  0,  0,  0,  2,  0, -2,  0,  0,  0,  0, &
            -1,  0,  0,  2,  0,  0,  3, -3,  0,  0,  0,  0,  0,  0, &
             1,  0,  0, -2,  1,  0,  0, -2,  0,  2,  0,  0,  0,  0, &
             1,  0,  2, -2,  2,  0, -3,  3,  0,  0,  0,  0,  0,  0, &
             1,  0,  2, -2,  2,  0,  0, -2,  0,  2,  0,  0,  0,  0, &
             1,  0,  0,  0,  0,  0,  1, -1,  0,  0,  0,  0,  0,  0, &
             1,  0,  0,  0,  0,  0,  0,  1,  0, -1,  0,  0,  0,  0, &
             0,  0,  0, -2,  0,  0,  2, -2,  0,  0,  0,  0,  0,  0, &
             0,  0,  0, -2,  0,  0,  0,  1,  0, -1,  0,  0,  0,  0, &
             0,  0,  2,  0,  2,  0, -2,  2,  0,  0,  0,  0,  0,  0, &
             0,  0,  2,  0,  2,  0,  0, -1,  0,  1,  0,  0,  0,  0, &
             0,  0,  2,  0,  2,  0, -1,  1,  0,  0,  0,  0,  0,  0, &
             0,  0,  2,  0,  2,  0, -2,  3,  0,  0,  0,  0,  0,  0, &
             0,  0,  0,  2,  0,  0,  0,  2,  0, -2,  0,  0,  0,  0, &
             0,  0,  1,  1,  2,  0,  0,  1,  0,  0,  0,  0,  0,  0, &
             1,  0,  2,  0,  2,  0,  0,  1,  0,  0,  0,  0,  0,  0, &
            -1,  0,  2,  0,  2,  0, 10, -3,  0,  0,  0,  0,  0,  0, &
             0,  0,  1,  1,  1,  0,  0,  1,  0,  0,  0,  0,  0,  0, &
             1,  0,  2,  0,  2,  0,  0,  1,  0,  0,  0,  0,  0,  0, &
             0,  0,  2,  0,  2,  0,  0,  4, -8,  3,  0,  0,  0,  0, &
             0,  0,  2,  0,  2,  0,  0, -4,  8, -3,  0,  0,  0,  0, &
            -1,  0,  2,  0,  2,  0,  0, -4,  8, -3,  0,  0,  0,  0, &
             2,  0,  2, -2,  2,  0,  0, -2,  0,  3,  0,  0,  0,  0, &
             1,  0,  2,  0,  1,  0,  0, -2,  0,  3,  0,  0,  0,  0, &
             0,  0,  1,  1,  0,  0,  0,  1,  0,  0,  0,  0,  0,  0, &
            -1,  0,  2,  0,  1,  0,  0,  1,  0,  0,  0,  0,  0,  0, &
            -2,  0,  2,  2,  2,  0,  0,  2,  0, -2,  0,  0,  0,  0, &
             0,  0,  2,  0,  2,  0,  2, -3,  0,  0,  0,  0,  0,  0, &
             0,  0,  2,  0,  2,  0,  1, -1,  0,  0,  0,  0,  0,  0, &
             0,  0,  2,  0,  2,  0,  0,  1,  0, -1,  0,  0,  0,  0, &
             0,  0,  2,  0,  2,  0,  2, -2,  0,  0,  0,  0,  0,  0, &
            -1,  0,  2,  2,  2,  0,  0, -1,  0,  1,  0,  0,  0,  0, &
             1,  0,  2,  0,  2,  0, -1,  1,  0,  0,  0,  0,  0,  0, &
            -1,  0,  2,  2,  2,  0,  0,  2,  0, -3,  0,  0,  0,  0, &
             2,  0,  2,  0,  2,  0,  0,  2,  0, -3,  0,  0,  0,  0, &
             1,  0,  2,  0,  2,  0,  0, -4,  8, -3,  0,  0,  0,  0, &
             1,  0,  2,  0,  2,  0,  0,  4, -8,  3,  0,  0,  0,  0, &
             1,  0,  1,  1,  1,  0,  0,  1,  0,  0,  0,  0,  0,  0, &
             0,  0,  2,  0,  2,  0,  0,  1,  0,  0,  0,  0,  0,  0, &
             2,  0,  2,  0,  1,  0,  0,  1,  0,  0,  0,  0,  0,  0, &
            -1,  0,  2,  2,  2,  0,  0,  2,  0, -2,  0,  0,  0,  0, &
            -1,  0,  2,  2,  2,  0,  3, -3,  0,  0,  0,  0,  0,  0, &
             1,  0,  2,  0,  2,  0,  1, -1,  0,  0,  0,  0,  0,  0, &
             0,  0,  2,  2,  2,  0,  0,  2,  0, -2,  0,  0,  0,  0 ] , [14,npl])

    !
    !  Planetary nutation coefficients, unit 1e-7 arcsec
    !  longitude (sin, cos), obliquity (sin, cos)
    !

    !  Longitude and obliquity coefficients
    integer,dimension(4,npl),parameter :: icpl = reshape([ &
           1440,          0,          0,          0, &
             56,       -117,        -42,        -40, &
            125,        -43,          0,        -54, &
              0,          5,          0,          0, &
              3,         -7,         -3,          0, &
              3,          0,          0,         -2, &
           -114,          0,          0,         61, &
           -219,         89,          0,          0, &
             -3,          0,          0,          0, &
           -462,       1604,          0,          0, &
             99,          0,          0,        -53, &
             -3,          0,          0,          2, &
              0,          6,          2,          0, &
              3,          0,          0,          0, &
            -12,          0,          0,          0, &
             14,       -218,        117,          8, &
             31,       -481,       -257,        -17, &
           -491,        128,          0,          0, &
          -3084,       5123,       2735,       1647, &
          -1444,       2409,      -1286,       -771, &
             11,        -24,        -11,         -9, &
             26,         -9,          0,          0, &
            103,        -60,          0,          0, &
              0,        -13,         -7,          0, &
            -26,        -29,        -16,         14, &
              9,        -27,        -14,         -5, &
             12,          0,          0,         -6, &
             -7,          0,          0,          0, &
              0,         24,          0,          0, &
            284,          0,          0,       -151, &
            226,        101,          0,          0, &
              0,         -8,         -2,          0, &
              0,         -6,         -3,          0, &
              5,          0,          0,         -3, &
            -41,        175,         76,         17, &
              0,         15,          6,          0, &
            425,        212,       -133,        269, &
           1200,        598,        319,       -641, &
            235,        334,          0,          0, &
             11,        -12,         -7,         -6, &
              5,         -6,          3,          3, &
             -5,          0,          0,          3, &
              6,          0,          0,         -3, &
             15,          0,          0,          0, &
             13,          0,          0,         -7, &
             -6,         -9,          0,          0, &
            266,        -78,          0,          0, &
           -460,       -435,       -232,        246, &
              0,         15,          7,          0, &
             -3,          0,          0,          2, &
              0,        131,          0,          0, &
              4,          0,          0,          0, &
              0,          3,          0,          0, &
              0,          4,          2,          0, &
              0,          3,          0,          0, &
            -17,        -19,        -10,          9, &
             -9,        -11,          6,         -5, &
             -6,          0,          0,          3, &
            -16,          8,          0,          0, &
              0,          3,          0,          0, &
             11,         24,         11,         -5, &
             -3,         -4,         -2,          1, &
              3,          0,          0,         -1, &
              0,         -8,         -4,          0, &
              0,          3,          0,          0, &
              0,          5,          0,          0, &
              0,          3,          2,          0, &
             -6,          4,          2,          3, &
             -3,         -5,          0,          0, &
             -5,          0,          0,          2, &
              4,         24,         13,         -2, &
            -42,         20,          0,          0, &
            -10,        233,          0,          0, &
             -3,          0,          0,          1, &
             78,        -18,          0,          0, &
              0,          3,          1,          0, &
              0,         -3,         -1,          0, &
              0,         -4,         -2,          1, &
              0,         -8,         -4,         -1, &
              0,         -5,          3,          0, &
             -7,          0,          0,          3, &
            -14,          8,          3,          6, &
              0,          8,         -4,          0, &
              0,         19,         10,          0, &
             45,        -22,          0,          0, &
             -3,          0,          0,          0, &
              0,         -3,          0,          0, &
              0,          3,          0,          0, &
              3,          5,          3,         -2, &
             89,        -16,         -9,        -48, &
              0,          3,          0,          0, &
             -3,          7,          4,          2, &
           -349,        -62,          0,          0, &
            -15,         22,          0,          0, &
             -3,          0,          0,          0, &
            -53,          0,          0,          0, &
              5,          0,          0,         -3, &
              0,         -8,          0,          0, &
             15,         -7,         -4,         -8, &
             -3,          0,          0,          1, &
            -21,        -78,          0,          0, &
             20,        -70,        -37,        -11, &
              0,          6,          3,          0, &
              5,          3,          2,         -2, &
            -17,         -4,         -2,          9, &
              0,          6,          3,          0, &
             32,         15,         -8,         17, &
            174,         84,         45,        -93, &
             11,         56,          0,          0, &
            -66,        -12,         -6,         35, &
             47,          8,          4,        -25, &
              0,          8,          4,          0, &
             10,        -22,        -12,         -5, &
             -3,          0,          0,          2, &
            -24,         12,          0,          0, &
              5,         -6,          0,          0, &
              3,          0,          0,         -2, &
              4,          3,          1,         -2, &
              0,         29,         15,          0, &
             -5,         -4,         -2,          2, &
              8,         -3,         -1,         -5, &
              0,         -3,          0,          0, &
             10,          0,          0,          0, &
              3,          0,          0,         -2, &
             -5,          0,          0,          3, &
             46,         66,         35,        -25, &
            -14,          7,          0,          0, &
              0,          3,          2,          0, &
             -5,          0,          0,          0, &
            -68,        -34,        -18,         36, &
              0,         14,          7,          0, &
             10,         -6,         -3,         -5, &
             -5,         -4,         -2,          3, &
             -3,          5,          2,          1, &
             76,         17,          9,        -41, &
             84,        298,        159,        -45, &
              3,          0,          0,         -1, &
             -3,          0,          0,          2, &
             -3,          0,          0,          1, &
            -82,        292,        156,         44, &
            -73,         17,          9,         39, &
             -9,        -16,          0,          0, &
              3,          0,         -1,         -2, &
             -3,          0,          0,          0, &
             -9,         -5,         -3,          5, &
           -439,          0,          0,          0, &
             57,        -28,        -15,        -30, &
              0,         -6,         -3,          0, &
             -4,          0,          0,          2, &
            -40,         57,         30,         21, &
             23,          7,          3,        -13, &
            273,         80,         43,       -146, &
           -449,        430,          0,          0, &
             -8,        -47,        -25,          4, &
              6,         47,         25,         -3, &
              0,         23,         13,          0, &
             -3,          0,          0,          2, &
              3,         -4,         -2,         -2, &
            -48,       -110,        -59,         26, &
             51,        114,         61,        -27, &
           -133,          0,          0,         57, &
              0,          4,          0,          0, &
            -21,         -6,         -3,         11, &
              0,         -3,         -1,          0, &
            -11,        -21,        -11,          6, &
            -18,       -436,       -233,          9, &
             35,         -7,          0,          0, &
              0,          5,          3,          0, &
             11,         -3,         -1,         -6, &
             -5,         -3,         -1,          3, &
            -53,         -9,         -5,         28, &
              0,          3,          2,          1, &
              4,          0,          0,         -2, &
              0,         -4,          0,          0, &
            -50,        194,        103,         27, &
            -13,         52,         28,          7, &
            -91,        248,          0,          0, &
              6,         49,         26,         -3, &
             -6,        -47,        -25,          3, &
              0,          5,          3,          0, &
             52,         23,         10,        -23, &
             -3,          0,          0,          1, &
              0,          5,          3,          0, &
             -4,          0,          0,          0, &
             -4,          8,          3,          2, &
             10,          0,          0,          0, &
              3,          0,          0,         -2, &
              0,          8,          4,          0, &
              0,          8,          4,          1, &
             -4,          0,          0,          0, &
             -4,          0,          0,          0, &
             -8,          4,          2,          4, &
              8,         -4,         -2,         -4, &
              0,         15,          7,          0, &
           -138,          0,          0,          0, &
              0,         -7,         -3,          0, &
              0,         -7,         -3,          0, &
             54,          0,          0,        -29, &
              0,         10,          4,          0, &
             -7,          0,          0,          3, &
            -37,         35,         19,         20, &
              0,          4,          0,          0, &
             -4,          9,          0,          0, &
              8,          0,          0,         -4, &
             -9,        -14,         -8,          5, &
             -3,         -9,         -5,          3, &
           -145,         47,          0,          0, &
            -10,         40,         21,          5, &
             11,        -49,        -26,         -7, &
          -2150,          0,          0,        932, &
            -12,          0,          0,          5, &
             85,          0,          0,        -37, &
              4,          0,          0,         -2, &
              3,          0,          0,         -2, &
            -86,        153,          0,          0, &
             -6,          9,          5,          3, &
              9,        -13,         -7,         -5, &
             -8,         12,          6,          4, &
            -51,          0,          0,         22, &
            -11,       -268,       -116,          5, &
              0,         12,          5,          0, &
              0,          7,          3,          0, &
             31,          6,          3,        -17, &
            140,         27,         14,        -75, &
             57,         11,          6,        -30, &
            -14,        -39,          0,          0, &
              0,         -6,         -2,          0, &
              4,         15,          8,         -2, &
              0,          4,          0,          0, &
             -3,          0,          0,          1, &
              0,         11,          5,          0, &
              9,          6,          0,          0, &
             -4,         10,          4,          2, &
              5,          3,          0,          0, &
             16,          0,          0,         -9, &
             -3,          0,          0,          0, &
              0,          3,          2,         -1, &
              7,          0,          0,         -3, &
            -25,         22,          0,          0, &
             42,        223,        119,        -22, &
            -27,       -143,        -77,         14, &
              9,         49,         26,         -5, &
          -1166,          0,          0,        505, &
             -5,          0,          0,          2, &
             -6,          0,          0,          3, &
             -8,          0,          1,          4, &
              0,         -4,          0,          0, &
            117,          0,          0,        -63, &
             -4,          8,          4,          2, &
              3,          0,          0,         -2, &
             -5,          0,          0,          2, &
              0,         31,          0,          0, &
             -5,          0,          1,          3, &
              4,          0,          0,         -2, &
             -4,          0,          0,          2, &
            -24,        -13,         -6,         10, &
              3,          0,          0,          0, &
              0,        -32,        -17,          0, &
              8,         12,          5,         -3, &
              3,          0,          0,         -1, &
              7,         13,          0,          0, &
             -3,         16,          0,          0, &
             50,          0,          0,        -27, &
              0,         -5,         -3,          0, &
             13,          0,          0,          0, &
              0,          5,          3,          1, &
             24,          5,          2,        -11, &
              5,        -11,         -5,         -2, &
             30,         -3,         -2,        -16, &
             18,          0,          0,         -9, &
              8,        614,          0,          0, &
              3,         -3,         -1,         -2, &
              6,         17,          9,         -3, &
             -3,         -9,         -5,          2, &
              0,          6,          3,         -1, &
           -127,         21,          9,         55, &
              3,          5,          0,          0, &
             -6,        -10,         -4,          3, &
              5,          0,          0,          0, &
             16,          9,          4,         -7, &
              3,          0,          0,         -2, &
              0,         22,          0,          0, &
              0,         19,         10,          0, &
              7,          0,          0,         -4, &
              0,         -5,         -2,          0, &
              0,          3,          1,          0, &
             -9,          3,          1,          4, &
             17,          0,          0,         -7, &
              0,         -3,         -2,         -1, &
            -20,         34,          0,          0, &
            -10,          0,          1,          5, &
             -4,          0,          0,          2, &
             22,        -87,          0,          0, &
             -4,          0,          0,          2, &
             -3,         -6,         -2,          1, &
            -16,         -3,         -1,          7, &
              0,         -3,         -2,          0, &
              4,          0,          0,          0, &
            -68,         39,          0,          0, &
             27,          0,          0,        -14, &
              0,         -4,          0,          0, &
            -25,          0,          0,          0, &
            -12,         -3,         -2,          6, &
              3,          0,          0,         -1, &
              3,         66,         29,         -1, &
            490,          0,          0,       -213, &
            -22,         93,         49,         12, &
             -7,         28,         15,          4, &
             -3,         13,          7,          2, &
            -46,         14,          0,          0, &
             -5,          0,          0,          0, &
              2,          1,          0,          0, &
              0,         -3,          0,          0, &
            -28,          0,          0,         15, &
              5,          0,          0,         -2, &
              0,          3,          0,          0, &
            -11,          0,          0,          5, &
              0,          3,          1,          0, &
             -3,          0,          0,          1, &
             25,        106,         57,        -13, &
              5,         21,         11,         -3, &
           1485,          0,          0,          0, &
             -7,        -32,        -17,          4, &
              0,          5,          3,          0, &
             -6,         -3,         -2,          3, &
             30,         -6,         -2,        -13, &
             -4,          4,          0,          0, &
            -19,          0,          0,         10, &
              0,          4,          2,         -1, &
              0,          3,          0,          0, &
              4,          0,          0,         -2, &
              0,         -3,         -1,          0, &
             -3,          0,          0,          0, &
              5,          3,          1,         -2, &
              0,         11,          0,          0, &
            118,          0,          0,        -52, &
              0,         -5,         -3,          0, &
            -28,         36,          0,          0, &
              5,         -5,          0,          0, &
             14,        -59,        -31,         -8, &
              0,          9,          5,          1, &
           -458,          0,          0,        198, &
              0,        -45,        -20,          0, &
              9,          0,          0,         -5, &
              0,         -3,          0,          0, &
              0,         -4,         -2,         -1, &
             11,          0,          0,         -6, &
              6,          0,          0,         -2, &
            -16,         23,          0,          0, &
              0,         -4,         -2,          0, &
             -5,          0,          0,          2, &
           -166,        269,          0,          0, &
             15,          0,          0,         -8, &
             10,          0,          0,         -4, &
            -78,         45,          0,          0, &
              0,         -5,         -2,          0, &
              7,          0,          0,         -4, &
             -5,        328,          0,          0, &
              3,          0,          0,         -2, &
              5,          0,          0,         -2, &
              0,          3,          1,          0, &
             -3,          0,          0,          0, &
             -3,          0,          0,          0, &
              0,         -4,         -2,          0, &
          -1223,        -26,          0,          0, &
              0,          7,          3,          0, &
              3,          0,          0,          0, &
              0,          3,          2,          0, &
             -6,         20,          0,          0, &
           -368,          0,          0,          0, &
            -75,          0,          0,          0, &
             11,          0,          0,         -6, &
              3,          0,          0,         -2, &
             -3,          0,          0,          1, &
            -13,        -30,          0,          0, &
             21,          3,          0,          0, &
             -3,          0,          0,          1, &
             -4,          0,          0,          2, &
              8,        -27,          0,          0, &
            -19,        -11,          0,          0, &
             -4,          0,          0,          2, &
              0,          5,          2,          0, &
             -6,          0,          0,          2, &
             -8,          0,          0,          0, &
             -1,          0,          0,          0, &
            -14,          0,          0,          6, &
              6,          0,          0,          0, &
            -74,          0,          0,         32, &
              0,         -3,         -1,          0, &
              4,          0,          0,         -2, &
              8,         11,          0,          0, &
              0,          3,          2,          0, &
           -262,          0,          0,        114, &
              0,         -4,          0,          0, &
             -7,          0,          0,          4, &
              0,        -27,        -12,          0, &
            -19,         -8,         -4,          8, &
            202,          0,          0,        -87, &
             -8,         35,         19,          5, &
              0,          4,          2,          0, &
             16,         -5,          0,          0, &
              5,          0,          0,         -3, &
              0,         -3,          0,          0, &
              1,          0,          0,          0, &
            -35,        -48,        -21,         15, &
             -3,         -5,         -2,          1, &
              6,          0,          0,         -3, &
              3,          0,          0,         -1, &
              0,         -5,          0,          0, &
             12,         55,         29,         -6, &
              0,          5,          3,          0, &
           -598,          0,          0,          0, &
             -3,        -13,         -7,          1, &
             -5,         -7,         -3,          2, &
              3,          0,          0,         -1, &
              5,         -7,          0,          0, &
              4,          0,          0,         -2, &
             16,         -6,          0,          0, &
              8,         -3,          0,          0, &
              8,        -31,        -16,         -4, &
              0,          3,          1,          0, &
            113,          0,          0,        -49, &
              0,        -24,        -10,          0, &
              4,          0,          0,         -2, &
             27,          0,          0,          0, &
             -3,          0,          0,          1, &
              0,         -4,         -2,          0, &
              5,          0,          0,         -2, &
              0,         -3,          0,          0, &
            -13,          0,          0,          6, &
              5,          0,          0,         -2, &
            -18,        -10,         -4,          8, &
             -4,        -28,          0,          0, &
             -5,          6,          3,          2, &
             -3,          0,          0,          1, &
             -5,         -9,         -4,          2, &
             17,          0,          0,         -7, &
             11,          4,          0,          0, &
              0,         -6,         -2,          0, &
             83,         15,          0,          0, &
             -4,          0,          0,          2, &
              0,       -114,        -49,          0, &
            117,          0,          0,        -51, &
             -5,         19,         10,          2, &
             -3,          0,          0,          0, &
             -3,          0,          0,          2, &
              0,         -3,         -1,          0, &
              3,          0,          0,          0, &
              0,         -6,         -2,          0, &
            393,          3,          0,          0, &
             -4,         21,         11,          2, &
             -6,          0,         -1,          3, &
             -3,          8,          4,          1, &
              8,          0,          0,          0, &
             18,        -29,        -13,         -8, &
              8,         34,         18,         -4, &
             89,          0,          0,          0, &
              3,         12,          6,         -1, &
             54,        -15,         -7,        -24, &
              0,          3,          0,          0, &
              3,          0,          0,         -1, &
              0,         35,          0,          0, &
           -154,        -30,        -13,         67, &
             15,          0,          0,          0, &
              0,          4,          2,          0, &
              0,          9,          0,          0, &
             80,        -71,        -31,        -35, &
              0,        -20,         -9,          0, &
             11,          5,          2,         -5, &
             61,        -96,        -42,        -27, &
             14,          9,          4,         -6, &
            -11,         -6,         -3,          5, &
              0,         -3,         -1,          0, &
            123,       -415,       -180,        -53, &
              0,          0,          0,        -35, &
             -5,          0,          0,          0, &
              7,        -32,        -17,         -4, &
              0,         -9,         -5,          0, &
              0,         -4,          2,          0, &
            -89,          0,          0,         38, &
              0,        -86,        -19,         -6, &
              0,          0,        -19,          6, &
           -123,       -416,       -180,         53, &
              0,         -3,         -1,          0, &
             12,         -6,         -3,         -5, &
            -13,          9,          4,          6, &
              0,        -15,         -7,          0, &
              3,          0,          0,         -1, &
            -62,        -97,        -42,         27, &
            -11,          5,          2,          5, &
              0,        -19,         -8,          0, &
             -3,          0,          0,          1, &
              0,          4,          2,          0, &
              0,          3,          0,          0, &
              0,          4,          2,          0, &
            -85,        -70,        -31,         37, &
            163,        -12,         -5,        -72, &
            -63,        -16,         -7,         28, &
            -21,        -32,        -14,          9, &
              0,         -3,         -1,          0, &
              3,          0,          0,         -2, &
              0,          8,          0,          0, &
              3,         10,          4,         -1, &
              3,          0,          0,         -1, &
              0,         -7,         -3,          0, &
              0,         -4,         -2,          0, &
              6,         19,          0,          0, &
              5,       -173,        -75,         -2, &
              0,         -7,         -3,          0, &
              7,        -12,         -5,         -3, &
             -3,          0,          0,          2, &
              3,         -4,         -2,         -1, &
             74,          0,          0,        -32, &
             -3,         12,          6,          2, &
             26,        -14,         -6,        -11, &
             19,          0,          0,         -8, &
              6,         24,         13,         -3, &
             83,          0,          0,          0, &
              0,        -10,         -5,          0, &
             11,         -3,         -1,         -5, &
              3,          0,          1,         -1, &
              3,          0,          0,         -1, &
             -4,          0,          0,          0, &
              5,        -23,        -12,         -3, &
           -339,          0,          0,        147, &
              0,        -10,         -5,          0, &
              5,          0,          0,          0, &
              3,          0,          0,         -1, &
              0,         -4,         -2,          0, &
             18,         -3,          0,          0, &
              9,        -11,         -5,         -4, &
             -8,          0,          0,          4, &
              3,          0,          0,         -1, &
              0,          9,          0,          0, &
              6,         -9,         -4,         -2, &
             -4,        -12,          0,          0, &
             67,        -91,        -39,        -29, &
             30,        -18,         -8,        -13, &
              0,          0,          0,          0, &
              0,       -114,        -50,          0, &
              0,          0,          0,         23, &
            517,         16,          7,       -224, &
              0,         -7,         -3,          0, &
            143,         -3,         -1,        -62, &
             29,          0,          0,        -13, &
             -4,          0,          0,          2, &
             -6,          0,          0,          3, &
              5,         12,          5,         -2, &
            -25,          0,          0,         11, &
             -3,          0,          0,          1, &
              0,          4,          2,          0, &
            -22,         12,          5,         10, &
             50,          0,          0,        -22, &
              0,          7,          4,          0, &
              0,          3,          1,          0, &
             -4,          4,          2,          2, &
             -5,        -11,         -5,          2, &
              0,          4,          2,          0, &
              4,         17,          9,         -2, &
             59,          0,          0,          0, &
              0,         -4,         -2,          0, &
             -8,          0,          0,          4, &
             -3,          0,          0,          0, &
              4,        -15,         -8,         -2, &
            370,         -8,          0,       -160, &
              0,          0,         -3,          0, &
              0,          3,          1,          0, &
             -6,          3,          1,          3, &
              0,          6,          0,          0, &
            -10,          0,          0,          4, &
              0,          9,          4,          0, &
              4,         17,          7,         -2, &
             34,          0,          0,        -15, &
              0,          5,          3,          0, &
             -5,          0,          0,          2, &
            -37,         -7,         -3,         16, &
              3,         13,          7,         -2, &
             40,          0,          0,          0, &
              0,         -3,         -2,          0, &
           -184,         -3,         -1,         80, &
             -3,          0,          0,          1, &
             -3,          0,          0,          0, &
              0,        -10,         -6,         -1, &
             31,         -6,          0,        -13, &
             -3,        -32,        -14,          1, &
             -7,          0,          0,          3, &
              0,         -8,         -4,          0, &
              3,         -4,          0,          0, &
              0,          4,          0,          0, &
              0,          3,          1,          0, &
             19,        -23,        -10,          2, &
              0,          0,          0,        -10, &
              0,          3,          2,          0, &
              0,          9,          5,         -1, &
             28,          0,          0,          0, &
              0,         -7,         -4,          0, &
              8,         -4,          0,         -4, &
              0,          0,         -2,          0, &
              0,          3,          0,          0, &
             -3,          0,          0,          1, &
             -9,          0,          1,          4, &
              3,         12,          5,         -1, &
             17,         -3,         -1,          0, &
              0,          7,          4,          0, &
             19,          0,          0,          0, &
              0,         -5,         -3,          0, &
             14,         -3,          0,         -1, &
              0,          0,         -1,          0, &
              0,          0,          0,         -5, &
              0,          5,          3,          0, &
             13,          0,          0,          0, &
              0,         -3,         -2,          0, &
              2,          9,          4,          3, &
              0,          0,          0,         -4, &
              8,          0,          0,          0, &
              0,          4,          2,          0, &
              6,          0,          0,         -3, &
              6,          0,          0,          0, &
              0,          3,          1,          0, &
              5,          0,          0,         -2, &
              3,          0,          0,         -1, &
             -3,          0,          0,          0, &
              6,          0,          0,          0, &
              7,          0,          0,          0, &
             -4,          0,          0,          0, &
              4,          0,          0,          0, &
              6,          0,          0,          0, &
              0,         -4,          0,          0, &
              0,         -4,          0,          0, &
              5,          0,          0,          0, &
             -3,          0,          0,          0, &
              4,          0,          0,          0, &
             -5,          0,          0,          0, &
              4,          0,          0,          0, &
              0,          3,          0,          0, &
             13,          0,          0,          0, &
             21,         11,          0,          0, &
              0,         -5,          0,          0, &
              0,         -5,         -2,          0, &
              0,          5,          3,          0, &
              0,         -5,          0,          0, &
             -3,          0,          0,          2, &
             20,         10,          0,          0, &
            -34,          0,          0,          0, &
            -19,          0,          0,          0, &
              3,          0,          0,         -2, &
             -3,          0,          0,          1, &
             -6,          0,          0,          3, &
             -4,          0,          0,          0, &
              3,          0,          0,          0, &
              3,          0,          0,          0, &
              4,          0,          0,          0, &
              3,          0,          0,         -1, &
              6,          0,          0,         -3, &
             -8,          0,          0,          3, &
              0,          3,          1,          0, &
             -3,          0,          0,          0, &
              0,         -3,         -2,          0, &
            126,        -63,        -27,        -55, &
             -5,          0,          1,          2, &
             -3,         28,         15,          2, &
              5,          0,          1,         -2, &
              0,          9,          4,          1, &
              0,          9,          4,         -1, &
           -126,        -63,        -27,         55, &
              3,          0,          0,         -1, &
             21,        -11,         -6,        -11, &
              0,         -4,          0,          0, &
            -21,        -11,         -6,         11, &
             -3,          0,          0,          1, &
              0,          3,          1,          0, &
              8,          0,          0,         -4, &
             -6,          0,          0,          3, &
             -3,          0,          0,          1, &
              3,          0,          0,         -1, &
             -3,          0,          0,          1, &
             -5,          0,          0,          2, &
             24,        -12,         -5,        -11, &
              0,          3,          1,          0, &
              0,          3,          1,          0, &
              0,          3,          2,          0, &
            -24,        -12,         -5,         10, &
              4,          0,         -1,         -2, &
             13,          0,          0,         -6, &
              7,          0,          0,         -3, &
              3,          0,          0,         -1, &
              3,          0,          0,         -1 ], [4,npl])

    !  Interval between fundamental date J2000.0 and given date (JC).
    t = ( ( date1-dj00 ) + date2 ) / djc

    !  -------------------
    !  LUNI-SOLAR NUTATION
    !  -------------------

    !
    !  Fundamental (Delaunay) arguments
    !

    !  Mean anomaly of the Moon (IERS 2003).
    el = FAL03 ( t )

    !  Mean anomaly of the Sun (MHB2000).
    elp = mod (       1287104.79305_wp + &
                t*( 129596581.0481_wp + &
                t*(       - 0.5532_wp + &
                t*(         0.000136_wp + &
                t*(       - 0.00001149_wp )))), turnas ) * das2r

    !  Mean longitude of the Moon minus that of the ascending node
    !  (IERS 2003.
    f = FAF03 ( t )

    !  Mean elongation of the Moon from the Sun (MHB2000).
    d = mod (        1072260.70369_wp + &
              t*( 1602961601.2090_wp + &
              t*(        - 6.3706_wp + &
              t*(          0.006593_wp + &
              t*(        - 0.00003169_wp )))), turnas ) * das2r

    !  Mean longitude of the ascending node of the Moon (IERS 2003).
    om = FAOM03 ( t )

    !  Initialize the nutation values.
    dp = 0.0_wp
    de = 0.0_wp

    !  Summation of luni-solar nutation series (in reverse order).
    do i = nls, 1, -1

       !  Argument and functions.
       arg = mod ( real ( nals(1,i), wp ) * el  + &
                   real ( nals(2,i), wp ) * elp + &
                   real ( nals(3,i), wp ) * f   + &
                   real ( nals(4,i), wp ) * d   + &
                   real ( nals(5,i), wp ) * om, d2pi )
       sarg = sin(arg)
       carg = cos(arg)

       !  Term.
       dp = dp + ( cls(1,i) + cls(2,i) * t ) * sarg &
               +   cls(3,i)                  * carg
       de = de + ( cls(4,i) + cls(5,i) * t ) * carg &
               +   cls(6,i)                  * sarg

    end do

    !  Convert from 0.1 microarcsec units to radians.
    dpsils = dp * u2r
    depsls = de * u2r

    !  ------------------
    !  PLANETARY NUTATION
    !  ------------------

    !  n.b.  The MHB2000 code computes the luni-solar and planetary nutation
    !        in different routines, using slightly different Delaunay
    !        arguments in the two cases.  This behaviour is faithfully
    !        reproduced here.  Use of the IERS 2003 expressions for both
    !        cases leads to negligible changes, well below
    !        0.1 microarcsecond.

    !  Mean anomaly of the Moon (MHB2000).
    al = mod ( 2.35555598_wp + 8328.6914269554_wp * t, d2pi )

    !  Mean anomaly of the Sun (MHB2000).
    alsu = mod ( 6.24006013_wp + 628.301955_wp * t, d2pi )

    !  Mean longitude of the Moon minus that of the ascending node
    ! (MHB2000).
    af = mod ( 1.627905234_wp + 8433.466158131_wp * t, d2pi )

    !  Mean elongation of the Moon from the Sun (MHB2000).
    ad = mod ( 5.198466741_wp + 7771.3771468121_wp * t, d2pi )

    !  Mean longitude of the ascending node of the Moon (MHB2000).
    aom = mod ( 2.18243920_wp - 33.757045_wp * t, d2pi )

    !  General accumulated precession in longitude (IERS 2003).
    apa = FAPA03 ( t )

    !  Planetary longitudes, Mercury through Uranus (IERS 2003).
    alme = FAME03 ( t )
    alve = FAVE03 ( t )
    alea = FAE03 ( t )
    alma = FAMA03 ( t )
    alju = FAJU03 ( t )
    alsa = FASA03 ( t )
    alur = FAUR03 ( t )

    !  Neptune longitude (MHB2000).
    alne = mod ( 5.321159000_wp + 3.8127774000_wp * t, d2pi )

    !  Initialize the nutation values.
    dp = 0.0_wp
    de = 0.0_wp

    !  Summation of planetary nutation series (in reverse order).
    do i = npl, 1, -1

       !  Argument and functions.
       arg = mod ( real ( napl( 1,i), wp ) * al   + &
                   real ( napl( 2,i), wp ) * alsu + &
                   real ( napl( 3,i), wp ) * af   + &
                   real ( napl( 4,i), wp ) * ad   + &
                   real ( napl( 5,i), wp ) * aom  + &
                   real ( napl( 6,i), wp ) * alme + &
                   real ( napl( 7,i), wp ) * alve + &
                   real ( napl( 8,i), wp ) * alea + &
                   real ( napl( 9,i), wp ) * alma + &
                   real ( napl(10,i), wp ) * alju + &
                   real ( napl(11,i), wp ) * alsa + &
                   real ( napl(12,i), wp ) * alur + &
                   real ( napl(13,i), wp ) * alne + &
                   real ( napl(14,i), wp ) * apa, d2pi )
       sarg = sin(arg)
       carg = cos(arg)

       !  Term.
       dp = dp + real(icpl(1,i), wp) * sarg + real(icpl(2,i), wp) * carg
       de = de + real(icpl(3,i), wp) * sarg + real(icpl(4,i), wp) * carg

    end do

    !  Convert from 0.1 microarcsec units to radians.
    dpsipl = dp * u2r
    depspl = de * u2r

    !  -------
    !  RESULTS
    !  -------

    !  Add luni-solar and planetary components.
    dpsi = dpsils + dpsipl
    deps = depsls + depspl

    end subroutine NUT00A
NUT00A Subroutine

Contents

Source Code

public subroutine NUT00A(date1, date2, dpsi, deps)

Notes

References

History

Arguments

Calls

Called by

Contents

Source Code

Source Code
