1 /*
2 * - - - - - - - - - - -
3 * g a l _ n u t 0 0 a
4 * - - - - - - - - - - -
5 *
6 * This routine is part of the General Astrodynamics Library
7 *
8 * Description:
9 *
10 * Nutation, IAU 2000A model (MHB2000 luni-solar and planetary nutation
11 * with free core nutation omitted).
12 *
13 * This routine is an independent translation of a FORTRAN routine
14 * that is part of IAU's SOFA software collection.
15 *
16 * Status:
17 *
18 * canonical model.
19 *
20 * Given:
21 *
22 * date1,date2 d TT as a 2-part Julian Date (Note 1)
23 *
24 * Returned:
25 *
26 * *dpsi,*deps d nutation, luni-solar + planetary (Note 2)
27 *
28 * Notes:
29 *
30 * 1) The TT date date1+date2 is a Julian Date, apportioned in any
31 * convenient way between the two arguments. For example,
32 * JD(TT)=2450123.7 could be expressed in any of these ways,
33 * among others:
34 *
35 * date1 date2
36 *
37 * 2450123.7 0.0 (JD method)
38 * 2451545.0 -1421.3 (J2000 method)
39 * 2400000.5 50123.2 (MJD method)
40 * 2450123.5 0.2 (date & time method)
41 *
42 * The JD method is the most natural and convenient to use in
43 * cases where the loss of several decimal digits of resolution
44 * is acceptable. The J2000 method is best matched to the way
45 * the argument is handled internally and will deliver the
46 * optimum resolution. The MJD method and the date & time methods
47 * are both good compromises between resolution and convenience.
48 *
49 * 2) The nutation components in longitude and obliquity are in radians
50 * and with respect to the equinox and ecliptic of date. The
51 * obliquity at J2000 is assumed to be the Lieske et al. (1977) value
52 * of 84381.448 arcsec.
53 *
54 * Both the luni-solar and planetary nutations are included. The
55 * latter are due to direct planetary nutations and the perturbations
56 * of the lunar and terrestrial orbits.
57 *
58 * 3) The routine computes the MHB2000 nutation series with the
59 * associated corrections for planetary nutations. It is an
60 * implementation of the nutation part of the IAU 2000A precession-
61 * nutation model, formally adopted by the IAU General Assembly in
62 * 2000, namely MHB2000 (Mathews et al. 2002), but with the free core
63 * nutation (FCN - see Note 4) omitted.
64 *
65 * 4) The full MHB2000 model also contains contributions to the
66 * nutations in longitude and obliquity due to the free-excitation of
67 * the free-core-nutation during the period 1979-2000. These FCN
68 * terms, which are time-dependent and unpredictable, are NOT
69 * included in the present routine and, if required, must be
70 * independently computed. With the FCN corrections included, the
71 * present routine delivers a pole which is at current epochs
72 * accurate to a few hundred microarcseconds. The omission of FCN
73 * introduces further errors of about that size.
74 *
75 * 5) The present routine provides classical nutation. The MHB2000
76 * algorithm, from which it is adapted, deals also with (i) the
77 * offsets between the GCRS and mean poles and (ii) the adjustments
78 * in longitude and obliquity due to the changed precession rates.
79 * These additional functions, namely frame bias and precession
80 * adjustments, are supported by the SOFA routines gal_bi00 and
81 * gal_pr00.
82 *
83 * 6) The MHB2000 algorithm also provides "total" nutations, comprising
84 * the arithmetic sum of the frame bias, precession adjustments,
85 * luni-solar nutation and planetary nutation. These total nutations
86 * can be used in combination with an existing IAU 1976 precession
87 * implementation, such as gal_pmat76, to deliver GCRS-to-true
88 * predictions of sub-mas accuracy at current epochs. However, there
89 * are three shortcomings in the MHB2000 model that must be taken
90 * into account if more accurate or definitive results are required
91 * (see Wallace 2002):
92 *
93 * (i) The MHB2000 total nutations are simply arithmetic sums,
94 * yet in reality the various components are successive Euler
95 * rotations. This slight lack of rigor leads to cross terms
96 * that exceed 1 mas after a century. The rigorous procedure
97 * is to form the GCRS-to-true rotation matrix by applying the
98 * bias, precession and nutation in that order.
99 *
100 * (ii) Although the precession adjustments are stated to be with
101 * respect to Lieske et al. (1977), the MHB2000 model does
102 * not specify which set of Euler angles are to be used and
103 * how the adjustments are to be applied. The most literal and
104 * straightforward procedure is to adopt the 4-rotation
105 * epsilon_0, psi_A, omega_A, xi_A option, and to add dpsipr to
106 * psi_A and depspr to both omega_A and eps_A.
107 *
108 * (iii) The MHB2000 model predates the determination by Chapront
109 * et al. (2002) of a 14.6 mas displacement between the J2000
110 * mean equinox and the origin of the ICRS frame. It should,
111 * however, be noted that neglecting this displacement when
112 * calculating star coordinates does not lead to a 14.6 mas
113 * change in right ascension, only a small second-order
114 * distortion in the pattern of the precession-nutation effect.
115 *
116 * For these reasons, the SOFA routines do not generate the "total
117 * nutations" directly, though they can of course easily be generated
118 * by calling gal_bi00, gal_pr00 and the present routine and adding
119 * the results.
120 *
121 * Called:
122 *
123 * gal_fal03 mean anomaly of the Moon
124 * gal_faf03 mean argument of the latitude of the Moon
125 * gal_faom03 mean longitude of the Moon's ascending node
126 * gal_fame03 mean longitude of Mercury
127 * gal_fave03 mean longitude of Venus
128 * gal_fae03 mean longitude of Earth
129 * gal_fama03 mean longitude of Mars
130 * gal_faju03 mean longitude of Jupiter
131 * gal_fasa03 mean longitude of Saturn
132 * gal_faur03 mean longitude of Uranus
133 * gal_fapa03 general accumulated precession in longitude
134 *
135 * References:
136 *
137 * Chapront, J., Chapront-Touze, M. & Francou, G. 2002,
138 * Astron.Astrophys. 387, 700
139 *
140 * Lieske, J.H., Lederle, T., Fricke, W. & Morando, B. 1977,
141 * Astron.Astrophys. 58, 1-16
142 *
143 * Mathews, P.M., Herring, T.A., Buffet, B.A. 2002, J.Geophys.Res.
144 * 107, B4. The MHB_2000 code itself was obtained on 9th September
145 * 2002 from ftp//maia.usno.navy.mil/conv2000/chapter5/IAU2000A.
146 *
147 * Simon, J.-L., Bretagnon, P., Chapront, J., Chapront-Touze, M.,
148 * Francou, G., Laskar, J. 1994, Astron.Astrophys. 282, 663-683
149 *
150 * Souchay, J., Loysel, B., Kinoshita, H., Folgueira, M. 1999,
151 * Astron.Astrophys.Supp.Ser. 135, 111
152 *
153 * Wallace, P.T., "Software for Implementing the IAU 2000
154 * Resolutions", in IERS Workshop 5.1 (2002)
155 *
156 * This revision:
157 *
158 * 2007 February 9 ( c version 2008 January 19 )
159 *
160 *
161 * Copyright (C) 2008 Paul C. L. Willmott. See notes at end.
162 *
163 *-----------------------------------------------------------------------
164 */
165
166 #include <math.h>
167 #include "gal_const.h"
168 #include "gal_nut00a.h"
169 #include "gal_fal03.h"
170 #include "gal_faf03.h"
171 #include "gal_faom03.h"
172 #include "gal_fame03.h"
173 #include "gal_fave03.h"
174 #include "gal_fae03.h"
175 #include "gal_fama03.h"
176 #include "gal_faju03.h"
177 #include "gal_fasa03.h"
178 #include "gal_faur03.h"
179 #include "gal_fapa03.h"
180
181 void
gal_nut00a(double date1,double date2,double * dpsi,double * deps)182 gal_nut00a
183 (
184 double date1,
185 double date2,
186 double *dpsi,
187 double *deps
188 )
189 {
190
191 /*
192 * Miscellaneous
193 */
194
195 int i ;
196
197 double t, el, elp, f, d, om, arg, dp, de, sarg, carg,
198 al, alsu, af, ad, aom, alme, alve, alea, alma,
199 alju, alsa, alur, alne, apa, dpsils, depsls,
200 dpsipl, depspl ;
201
202 /*
203 * ----------------------------------------
204 * Tables of argument and term coefficients
205 * ----------------------------------------
206 */
207
208 /*
209 * -------------------------
210 * Luni-Solar nutation model
211 * -------------------------
212 */
213
214 /*
215 * Number of terms in the luni-solar nutation model
216 */
217
218 #define NLS 678
219
220 /*
221 * Coefficients for fundamental arguments
222 */
223
224 static const int NALS[ NLS ][5] = {
225
226 /*
227 * Luni-Solar argument multipliers
228 * L L' F D Om
229 */
230
231 { 0, 0, 0, 0, 1, } ,
232 { 0, 0, 2, -2, 2, } ,
233 { 0, 0, 2, 0, 2, } ,
234 { 0, 0, 0, 0, 2, } ,
235 { 0, 1, 0, 0, 0, } ,
236 { 0, 1, 2, -2, 2, } ,
237 { 1, 0, 0, 0, 0, } ,
238 { 0, 0, 2, 0, 1, } ,
239 { 1, 0, 2, 0, 2, } ,
240 { 0, -1, 2, -2, 2, } ,
241 { 0, 0, 2, -2, 1, } ,
242 { -1, 0, 2, 0, 2, } ,
243 { -1, 0, 0, 2, 0, } ,
244 { 1, 0, 0, 0, 1, } ,
245 { -1, 0, 0, 0, 1, } ,
246 { -1, 0, 2, 2, 2, } ,
247 { 1, 0, 2, 0, 1, } ,
248 { -2, 0, 2, 0, 1, } ,
249 { 0, 0, 0, 2, 0, } ,
250 { 0, 0, 2, 2, 2, } ,
251 { 0, -2, 2, -2, 2, } ,
252 { -2, 0, 0, 2, 0, } ,
253 { 2, 0, 2, 0, 2, } ,
254 { 1, 0, 2, -2, 2, } ,
255 { -1, 0, 2, 0, 1, } ,
256 { 2, 0, 0, 0, 0, } ,
257 { 0, 0, 2, 0, 0, } ,
258 { 0, 1, 0, 0, 1, } ,
259 { -1, 0, 0, 2, 1, } ,
260 { 0, 2, 2, -2, 2, } ,
261 { 0, 0, -2, 2, 0, } ,
262 { 1, 0, 0, -2, 1, } ,
263 { 0, -1, 0, 0, 1, } ,
264 { -1, 0, 2, 2, 1, } ,
265 { 0, 2, 0, 0, 0, } ,
266 { 1, 0, 2, 2, 2, } ,
267 { -2, 0, 2, 0, 0, } ,
268 { 0, 1, 2, 0, 2, } ,
269 { 0, 0, 2, 2, 1, } ,
270 { 0, -1, 2, 0, 2, } ,
271 { 0, 0, 0, 2, 1, } ,
272 { 1, 0, 2, -2, 1, } ,
273 { 2, 0, 2, -2, 2, } ,
274 { -2, 0, 0, 2, 1, } ,
275 { 2, 0, 2, 0, 1, } ,
276 { 0, -1, 2, -2, 1, } ,
277 { 0, 0, 0, -2, 1, } ,
278 { -1, -1, 0, 2, 0, } ,
279 { 2, 0, 0, -2, 1, } ,
280 { 1, 0, 0, 2, 0, } ,
281 { 0, 1, 2, -2, 1, } ,
282 { 1, -1, 0, 0, 0, } ,
283 { -2, 0, 2, 0, 2, } ,
284 { 3, 0, 2, 0, 2, } ,
285 { 0, -1, 0, 2, 0, } ,
286 { 1, -1, 2, 0, 2, } ,
287 { 0, 0, 0, 1, 0, } ,
288 { -1, -1, 2, 2, 2, } ,
289 { -1, 0, 2, 0, 0, } ,
290 { 0, -1, 2, 2, 2, } ,
291 { -2, 0, 0, 0, 1, } ,
292 { 1, 1, 2, 0, 2, } ,
293 { 2, 0, 0, 0, 1, } ,
294 { -1, 1, 0, 1, 0, } ,
295 { 1, 1, 0, 0, 0, } ,
296 { 1, 0, 2, 0, 0, } ,
297 { -1, 0, 2, -2, 1, } ,
298 { 1, 0, 0, 0, 2, } ,
299 { -1, 0, 0, 1, 0, } ,
300 { 0, 0, 2, 1, 2, } ,
301 { -1, 0, 2, 4, 2, } ,
302 { -1, 1, 0, 1, 1, } ,
303 { 0, -2, 2, -2, 1, } ,
304 { 1, 0, 2, 2, 1, } ,
305 { -2, 0, 2, 2, 2, } ,
306 { -1, 0, 0, 0, 2, } ,
307 { 1, 1, 2, -2, 2, } ,
308 { -2, 0, 2, 4, 2, } ,
309 { -1, 0, 4, 0, 2, } ,
310 { 2, 0, 2, -2, 1, } ,
311 { 2, 0, 2, 2, 2, } ,
312 { 1, 0, 0, 2, 1, } ,
313 { 3, 0, 0, 0, 0, } ,
314 { 3, 0, 2, -2, 2, } ,
315 { 0, 0, 4, -2, 2, } ,
316 { 0, 1, 2, 0, 1, } ,
317 { 0, 0, -2, 2, 1, } ,
318 { 0, 0, 2, -2, 3, } ,
319 { -1, 0, 0, 4, 0, } ,
320 { 2, 0, -2, 0, 1, } ,
321 { -2, 0, 0, 4, 0, } ,
322 { -1, -1, 0, 2, 1, } ,
323 { -1, 0, 0, 1, 1, } ,
324 { 0, 1, 0, 0, 2, } ,
325 { 0, 0, -2, 0, 1, } ,
326 { 0, -1, 2, 0, 1, } ,
327 { 0, 0, 2, -1, 2, } ,
328 { 0, 0, 2, 4, 2, } ,
329 { -2, -1, 0, 2, 0, } ,
330 { 1, 1, 0, -2, 1, } ,
331 { -1, 1, 0, 2, 0, } ,
332 { -1, 1, 0, 1, 2, } ,
333 { 1, -1, 0, 0, 1, } ,
334 { 1, -1, 2, 2, 2, } ,
335 { -1, 1, 2, 2, 2, } ,
336 { 3, 0, 2, 0, 1, } ,
337 { 0, 1, -2, 2, 0, } ,
338 { -1, 0, 0, -2, 1, } ,
339 { 0, 1, 2, 2, 2, } ,
340 { -1, -1, 2, 2, 1, } ,
341 { 0, -1, 0, 0, 2, } ,
342 { 1, 0, 2, -4, 1, } ,
343 { -1, 0, -2, 2, 0, } ,
344 { 0, -1, 2, 2, 1, } ,
345 { 2, -1, 2, 0, 2, } ,
346 { 0, 0, 0, 2, 2, } ,
347 { 1, -1, 2, 0, 1, } ,
348 { -1, 1, 2, 0, 2, } ,
349 { 0, 1, 0, 2, 0, } ,
350 { 0, -1, -2, 2, 0, } ,
351 { 0, 3, 2, -2, 2, } ,
352 { 0, 0, 0, 1, 1, } ,
353 { -1, 0, 2, 2, 0, } ,
354 { 2, 1, 2, 0, 2, } ,
355 { 1, 1, 0, 0, 1, } ,
356 { 1, 1, 2, 0, 1, } ,
357 { 2, 0, 0, 2, 0, } ,
358 { 1, 0, -2, 2, 0, } ,
359 { -1, 0, 0, 2, 2, } ,
360 { 0, 1, 0, 1, 0, } ,
361 { 0, 1, 0, -2, 1, } ,
362 { -1, 0, 2, -2, 2, } ,
363 { 0, 0, 0, -1, 1, } ,
364 { -1, 1, 0, 0, 1, } ,
365 { 1, 0, 2, -1, 2, } ,
366 { 1, -1, 0, 2, 0, } ,
367 { 0, 0, 0, 4, 0, } ,
368 { 1, 0, 2, 1, 2, } ,
369 { 0, 0, 2, 1, 1, } ,
370 { 1, 0, 0, -2, 2, } ,
371 { -1, 0, 2, 4, 1, } ,
372 { 1, 0, -2, 0, 1, } ,
373 { 1, 1, 2, -2, 1, } ,
374 { 0, 0, 2, 2, 0, } ,
375 { -1, 0, 2, -1, 1, } ,
376 { -2, 0, 2, 2, 1, } ,
377 { 4, 0, 2, 0, 2, } ,
378 { 2, -1, 0, 0, 0, } ,
379 { 2, 1, 2, -2, 2, } ,
380 { 0, 1, 2, 1, 2, } ,
381 { 1, 0, 4, -2, 2, } ,
382 { -1, -1, 0, 0, 1, } ,
383 { 0, 1, 0, 2, 1, } ,
384 { -2, 0, 2, 4, 1, } ,
385 { 2, 0, 2, 0, 0, } ,
386 { 1, 0, 0, 1, 0, } ,
387 { -1, 0, 0, 4, 1, } ,
388 { -1, 0, 4, 0, 1, } ,
389 { 2, 0, 2, 2, 1, } ,
390 { 0, 0, 2, -3, 2, } ,
391 { -1, -2, 0, 2, 0, } ,
392 { 2, 1, 0, 0, 0, } ,
393 { 0, 0, 4, 0, 2, } ,
394 { 0, 0, 0, 0, 3, } ,
395 { 0, 3, 0, 0, 0, } ,
396 { 0, 0, 2, -4, 1, } ,
397 { 0, -1, 0, 2, 1, } ,
398 { 0, 0, 0, 4, 1, } ,
399 { -1, -1, 2, 4, 2, } ,
400 { 1, 0, 2, 4, 2, } ,
401 { -2, 2, 0, 2, 0, } ,
402 { -2, -1, 2, 0, 1, } ,
403 { -2, 0, 0, 2, 2, } ,
404 { -1, -1, 2, 0, 2, } ,
405 { 0, 0, 4, -2, 1, } ,
406 { 3, 0, 2, -2, 1, } ,
407 { -2, -1, 0, 2, 1, } ,
408 { 1, 0, 0, -1, 1, } ,
409 { 0, -2, 0, 2, 0, } ,
410 { -2, 0, 0, 4, 1, } ,
411 { -3, 0, 0, 0, 1, } ,
412 { 1, 1, 2, 2, 2, } ,
413 { 0, 0, 2, 4, 1, } ,
414 { 3, 0, 2, 2, 2, } ,
415 { -1, 1, 2, -2, 1, } ,
416 { 2, 0, 0, -4, 1, } ,
417 { 0, 0, 0, -2, 2, } ,
418 { 2, 0, 2, -4, 1, } ,
419 { -1, 1, 0, 2, 1, } ,
420 { 0, 0, 2, -1, 1, } ,
421 { 0, -2, 2, 2, 2, } ,
422 { 2, 0, 0, 2, 1, } ,
423 { 4, 0, 2, -2, 2, } ,
424 { 2, 0, 0, -2, 2, } ,
425 { 0, 2, 0, 0, 1, } ,
426 { 1, 0, 0, -4, 1, } ,
427 { 0, 2, 2, -2, 1, } ,
428 { -3, 0, 0, 4, 0, } ,
429 { -1, 1, 2, 0, 1, } ,
430 { -1, -1, 0, 4, 0, } ,
431 { -1, -2, 2, 2, 2, } ,
432 { -2, -1, 2, 4, 2, } ,
433 { 1, -1, 2, 2, 1, } ,
434 { -2, 1, 0, 2, 0, } ,
435 { -2, 1, 2, 0, 1, } ,
436 { 2, 1, 0, -2, 1, } ,
437 { -3, 0, 2, 0, 1, } ,
438 { -2, 0, 2, -2, 1, } ,
439 { -1, 1, 0, 2, 2, } ,
440 { 0, -1, 2, -1, 2, } ,
441 { -1, 0, 4, -2, 2, } ,
442 { 0, -2, 2, 0, 2, } ,
443 { -1, 0, 2, 1, 2, } ,
444 { 2, 0, 0, 0, 2, } ,
445 { 0, 0, 2, 0, 3, } ,
446 { -2, 0, 4, 0, 2, } ,
447 { -1, 0, -2, 0, 1, } ,
448 { -1, 1, 2, 2, 1, } ,
449 { 3, 0, 0, 0, 1, } ,
450 { -1, 0, 2, 3, 2, } ,
451 { 2, -1, 2, 0, 1, } ,
452 { 0, 1, 2, 2, 1, } ,
453 { 0, -1, 2, 4, 2, } ,
454 { 2, -1, 2, 2, 2, } ,
455 { 0, 2, -2, 2, 0, } ,
456 { -1, -1, 2, -1, 1, } ,
457 { 0, -2, 0, 0, 1, } ,
458 { 1, 0, 2, -4, 2, } ,
459 { 1, -1, 0, -2, 1, } ,
460 { -1, -1, 2, 0, 1, } ,
461 { 1, -1, 2, -2, 2, } ,
462 { -2, -1, 0, 4, 0, } ,
463 { -1, 0, 0, 3, 0, } ,
464 { -2, -1, 2, 2, 2, } ,
465 { 0, 2, 2, 0, 2, } ,
466 { 1, 1, 0, 2, 0, } ,
467 { 2, 0, 2, -1, 2, } ,
468 { 1, 0, 2, 1, 1, } ,
469 { 4, 0, 0, 0, 0, } ,
470 { 2, 1, 2, 0, 1, } ,
471 { 3, -1, 2, 0, 2, } ,
472 { -2, 2, 0, 2, 1, } ,
473 { 1, 0, 2, -3, 1, } ,
474 { 1, 1, 2, -4, 1, } ,
475 { -1, -1, 2, -2, 1, } ,
476 { 0, -1, 0, -1, 1, } ,
477 { 0, -1, 0, -2, 1, } ,
478 { -2, 0, 0, 0, 2, } ,
479 { -2, 0, -2, 2, 0, } ,
480 { -1, 0, -2, 4, 0, } ,
481 { 1, -2, 0, 0, 0, } ,
482 { 0, 1, 0, 1, 1, } ,
483 { -1, 2, 0, 2, 0, } ,
484 { 1, -1, 2, -2, 1, } ,
485 { 1, 2, 2, -2, 2, } ,
486 { 2, -1, 2, -2, 2, } ,
487 { 1, 0, 2, -1, 1, } ,
488 { 2, 1, 2, -2, 1, } ,
489 { -2, 0, 0, -2, 1, } ,
490 { 1, -2, 2, 0, 2, } ,
491 { 0, 1, 2, 1, 1, } ,
492 { 1, 0, 4, -2, 1, } ,
493 { -2, 0, 4, 2, 2, } ,
494 { 1, 1, 2, 1, 2, } ,
495 { 1, 0, 0, 4, 0, } ,
496 { 1, 0, 2, 2, 0, } ,
497 { 2, 0, 2, 1, 2, } ,
498 { 3, 1, 2, 0, 2, } ,
499 { 4, 0, 2, 0, 1, } ,
500 { -2, -1, 2, 0, 0, } ,
501 { 0, 1, -2, 2, 1, } ,
502 { 1, 0, -2, 1, 0, } ,
503 { 0, -1, -2, 2, 1, } ,
504 { 2, -1, 0, -2, 1, } ,
505 { -1, 0, 2, -1, 2, } ,
506 { 1, 0, 2, -3, 2, } ,
507 { 0, 1, 2, -2, 3, } ,
508 { 0, 0, 2, -3, 1, } ,
509 { -1, 0, -2, 2, 1, } ,
510 { 0, 0, 2, -4, 2, } ,
511 { -2, 1, 0, 0, 1, } ,
512 { -1, 0, 0, -1, 1, } ,
513 { 2, 0, 2, -4, 2, } ,
514 { 0, 0, 4, -4, 4, } ,
515 { 0, 0, 4, -4, 2, } ,
516 { -1, -2, 0, 2, 1, } ,
517 { -2, 0, 0, 3, 0, } ,
518 { 1, 0, -2, 2, 1, } ,
519 { -3, 0, 2, 2, 2, } ,
520 { -3, 0, 2, 2, 1, } ,
521 { -2, 0, 2, 2, 0, } ,
522 { 2, -1, 0, 0, 1, } ,
523 { -2, 1, 2, 2, 2, } ,
524 { 1, 1, 0, 1, 0, } ,
525 { 0, 1, 4, -2, 2, } ,
526 { -1, 1, 0, -2, 1, } ,
527 { 0, 0, 0, -4, 1, } ,
528 { 1, -1, 0, 2, 1, } ,
529 { 1, 1, 0, 2, 1, } ,
530 { -1, 2, 2, 2, 2, } ,
531 { 3, 1, 2, -2, 2, } ,
532 { 0, -1, 0, 4, 0, } ,
533 { 2, -1, 0, 2, 0, } ,
534 { 0, 0, 4, 0, 1, } ,
535 { 2, 0, 4, -2, 2, } ,
536 { -1, -1, 2, 4, 1, } ,
537 { 1, 0, 0, 4, 1, } ,
538 { 1, -2, 2, 2, 2, } ,
539 { 0, 0, 2, 3, 2, } ,
540 { -1, 1, 2, 4, 2, } ,
541 { 3, 0, 0, 2, 0, } ,
542 { -1, 0, 4, 2, 2, } ,
543 { 1, 1, 2, 2, 1, } ,
544 { -2, 0, 2, 6, 2, } ,
545 { 2, 1, 2, 2, 2, } ,
546 { -1, 0, 2, 6, 2, } ,
547 { 1, 0, 2, 4, 1, } ,
548 { 2, 0, 2, 4, 2, } ,
549 { 1, 1, -2, 1, 0, } ,
550 { -3, 1, 2, 1, 2, } ,
551 { 2, 0, -2, 0, 2, } ,
552 { -1, 0, 0, 1, 2, } ,
553 { -4, 0, 2, 2, 1, } ,
554 { -1, -1, 0, 1, 0, } ,
555 { 0, 0, -2, 2, 2, } ,
556 { 1, 0, 0, -1, 2, } ,
557 { 0, -1, 2, -2, 3, } ,
558 { -2, 1, 2, 0, 0, } ,
559 { 0, 0, 2, -2, 4, } ,
560 { -2, -2, 0, 2, 0, } ,
561 { -2, 0, -2, 4, 0, } ,
562 { 0, -2, -2, 2, 0, } ,
563 { 1, 2, 0, -2, 1, } ,
564 { 3, 0, 0, -4, 1, } ,
565 { -1, 1, 2, -2, 2, } ,
566 { 1, -1, 2, -4, 1, } ,
567 { 1, 1, 0, -2, 2, } ,
568 { -3, 0, 2, 0, 0, } ,
569 { -3, 0, 2, 0, 2, } ,
570 { -2, 0, 0, 1, 0, } ,
571 { 0, 0, -2, 1, 0, } ,
572 { -3, 0, 0, 2, 1, } ,
573 { -1, -1, -2, 2, 0, } ,
574 { 0, 1, 2, -4, 1, } ,
575 { 2, 1, 0, -4, 1, } ,
576 { 0, 2, 0, -2, 1, } ,
577 { 1, 0, 0, -3, 1, } ,
578 { -2, 0, 2, -2, 2, } ,
579 { -2, -1, 0, 0, 1, } ,
580 { -4, 0, 0, 2, 0, } ,
581 { 1, 1, 0, -4, 1, } ,
582 { -1, 0, 2, -4, 1, } ,
583 { 0, 0, 4, -4, 1, } ,
584 { 0, 3, 2, -2, 2, } ,
585 { -3, -1, 0, 4, 0, } ,
586 { -3, 0, 0, 4, 1, } ,
587 { 1, -1, -2, 2, 0, } ,
588 { -1, -1, 0, 2, 2, } ,
589 { 1, -2, 0, 0, 1, } ,
590 { 1, -1, 0, 0, 2, } ,
591 { 0, 0, 0, 1, 2, } ,
592 { -1, -1, 2, 0, 0, } ,
593 { 1, -2, 2, -2, 2, } ,
594 { 0, -1, 2, -1, 1, } ,
595 { -1, 0, 2, 0, 3, } ,
596 { 1, 1, 0, 0, 2, } ,
597 { -1, 1, 2, 0, 0, } ,
598 { 1, 2, 0, 0, 0, } ,
599 { -1, 2, 2, 0, 2, } ,
600 { -1, 0, 4, -2, 1, } ,
601 { 3, 0, 2, -4, 2, } ,
602 { 1, 2, 2, -2, 1, } ,
603 { 1, 0, 4, -4, 2, } ,
604 { -2, -1, 0, 4, 1, } ,
605 { 0, -1, 0, 2, 2, } ,
606 { -2, 1, 0, 4, 0, } ,
607 { -2, -1, 2, 2, 1, } ,
608 { 2, 0, -2, 2, 0, } ,
609 { 1, 0, 0, 1, 1, } ,
610 { 0, 1, 0, 2, 2, } ,
611 { 1, -1, 2, -1, 2, } ,
612 { -2, 0, 4, 0, 1, } ,
613 { 2, 1, 0, 0, 1, } ,
614 { 0, 1, 2, 0, 0, } ,
615 { 0, -1, 4, -2, 2, } ,
616 { 0, 0, 4, -2, 4, } ,
617 { 0, 2, 2, 0, 1, } ,
618 { -3, 0, 0, 6, 0, } ,
619 { -1, -1, 0, 4, 1, } ,
620 { 1, -2, 0, 2, 0, } ,
621 { -1, 0, 0, 4, 2, } ,
622 { -1, -2, 2, 2, 1, } ,
623 { -1, 0, 0, -2, 2, } ,
624 { 1, 0, -2, -2, 1, } ,
625 { 0, 0, -2, -2, 1, } ,
626 { -2, 0, -2, 0, 1, } ,
627 { 0, 0, 0, 3, 1, } ,
628 { 0, 0, 0, 3, 0, } ,
629 { -1, 1, 0, 4, 0, } ,
630 { -1, -1, 2, 2, 0, } ,
631 { -2, 0, 2, 3, 2, } ,
632 { 1, 0, 0, 2, 2, } ,
633 { 0, -1, 2, 1, 2, } ,
634 { 3, -1, 0, 0, 0, } ,
635 { 2, 0, 0, 1, 0, } ,
636 { 1, -1, 2, 0, 0, } ,
637 { 0, 0, 2, 1, 0, } ,
638 { 1, 0, 2, 0, 3, } ,
639 { 3, 1, 0, 0, 0, } ,
640 { 3, -1, 2, -2, 2, } ,
641 { 2, 0, 2, -1, 1, } ,
642 { 1, 1, 2, 0, 0, } ,
643 { 0, 0, 4, -1, 2, } ,
644 { 1, 2, 2, 0, 2, } ,
645 { -2, 0, 0, 6, 0, } ,
646 { 0, -1, 0, 4, 1, } ,
647 { -2, -1, 2, 4, 1, } ,
648 { 0, -2, 2, 2, 1, } ,
649 { 0, -1, 2, 2, 0, } ,
650 { -1, 0, 2, 3, 1, } ,
651 { -2, 1, 2, 4, 2, } ,
652 { 2, 0, 0, 2, 2, } ,
653 { 2, -2, 2, 0, 2, } ,
654 { -1, 1, 2, 3, 2, } ,
655 { 3, 0, 2, -1, 2, } ,
656 { 4, 0, 2, -2, 1, } ,
657 { -1, 0, 0, 6, 0, } ,
658 { -1, -2, 2, 4, 2, } ,
659 { -3, 0, 2, 6, 2, } ,
660 { -1, 0, 2, 4, 0, } ,
661 { 3, 0, 0, 2, 1, } ,
662 { 3, -1, 2, 0, 1, } ,
663 { 3, 0, 2, 0, 0, } ,
664 { 1, 0, 4, 0, 2, } ,
665 { 5, 0, 2, -2, 2, } ,
666 { 0, -1, 2, 4, 1, } ,
667 { 2, -1, 2, 2, 1, } ,
668 { 0, 1, 2, 4, 2, } ,
669 { 1, -1, 2, 4, 2, } ,
670 { 3, -1, 2, 2, 2, } ,
671 { 3, 0, 2, 2, 1, } ,
672 { 5, 0, 2, 0, 2, } ,
673 { 0, 0, 2, 6, 2, } ,
674 { 4, 0, 2, 2, 2, } ,
675 { 0, -1, 1, -1, 1, } ,
676 { -1, 0, 1, 0, 3, } ,
677 { 0, -2, 2, -2, 3, } ,
678 { 1, 0, -1, 0, 1, } ,
679 { 2, -2, 0, -2, 1, } ,
680 { -1, 0, 1, 0, 2, } ,
681 { -1, 0, 1, 0, 1, } ,
682 { -1, -1, 2, -1, 2, } ,
683 { -2, 2, 0, 2, 2, } ,
684 { -1, 0, 1, 0, 0, } ,
685 { -4, 1, 2, 2, 2, } ,
686 { -3, 0, 2, 1, 1, } ,
687 { -2, -1, 2, 0, 2, } ,
688 { 1, 0, -2, 1, 1, } ,
689 { 2, -1, -2, 0, 1, } ,
690 { -4, 0, 2, 2, 0, } ,
691 { -3, 1, 0, 3, 0, } ,
692 { -1, 0, -1, 2, 0, } ,
693 { 0, -2, 0, 0, 2, } ,
694 { 0, -2, 0, 0, 2, } ,
695 { -3, 0, 0, 3, 0, } ,
696 { -2, -1, 0, 2, 2, } ,
697 { -1, 0, -2, 3, 0, } ,
698 { -4, 0, 0, 4, 0, } ,
699 { 2, 1, -2, 0, 1, } ,
700 { 2, -1, 0, -2, 2, } ,
701 { 0, 0, 1, -1, 0, } ,
702 { -1, 2, 0, 1, 0, } ,
703 { -2, 1, 2, 0, 2, } ,
704 { 1, 1, 0, -1, 1, } ,
705 { 1, 0, 1, -2, 1, } ,
706 { 0, 2, 0, 0, 2, } ,
707 { 1, -1, 2, -3, 1, } ,
708 { -1, 1, 2, -1, 1, } ,
709 { -2, 0, 4, -2, 2, } ,
710 { -2, 0, 4, -2, 1, } ,
711 { -2, -2, 0, 2, 1, } ,
712 { -2, 0, -2, 4, 0, } ,
713 { 1, 2, 2, -4, 1, } ,
714 { 1, 1, 2, -4, 2, } ,
715 { -1, 2, 2, -2, 1, } ,
716 { 2, 0, 0, -3, 1, } ,
717 { -1, 2, 0, 0, 1, } ,
718 { 0, 0, 0, -2, 0, } ,
719 { -1, -1, 2, -2, 2, } ,
720 { -1, 1, 0, 0, 2, } ,
721 { 0, 0, 0, -1, 2, } ,
722 { -2, 1, 0, 1, 0, } ,
723 { 1, -2, 0, -2, 1, } ,
724 { 1, 0, -2, 0, 2, } ,
725 { -3, 1, 0, 2, 0, } ,
726 { -1, 1, -2, 2, 0, } ,
727 { -1, -1, 0, 0, 2, } ,
728 { -3, 0, 0, 2, 0, } ,
729 { -3, -1, 0, 2, 0, } ,
730 { 2, 0, 2, -6, 1, } ,
731 { 0, 1, 2, -4, 2, } ,
732 { 2, 0, 0, -4, 2, } ,
733 { -2, 1, 2, -2, 1, } ,
734 { 0, -1, 2, -4, 1, } ,
735 { 0, 1, 0, -2, 2, } ,
736 { -1, 0, 0, -2, 0, } ,
737 { 2, 0, -2, -2, 1, } ,
738 { -4, 0, 2, 0, 1, } ,
739 { -1, -1, 0, -1, 1, } ,
740 { 0, 0, -2, 0, 2, } ,
741 { -3, 0, 0, 1, 0, } ,
742 { -1, 0, -2, 1, 0, } ,
743 { -2, 0, -2, 2, 1, } ,
744 { 0, 0, -4, 2, 0, } ,
745 { -2, -1, -2, 2, 0, } ,
746 { 1, 0, 2, -6, 1, } ,
747 { -1, 0, 2, -4, 2, } ,
748 { 1, 0, 0, -4, 2, } ,
749 { 2, 1, 2, -4, 2, } ,
750 { 2, 1, 2, -4, 1, } ,
751 { 0, 1, 4, -4, 4, } ,
752 { 0, 1, 4, -4, 2, } ,
753 { -1, -1, -2, 4, 0, } ,
754 { -1, -3, 0, 2, 0, } ,
755 { -1, 0, -2, 4, 1, } ,
756 { -2, -1, 0, 3, 0, } ,
757 { 0, 0, -2, 3, 0, } ,
758 { -2, 0, 0, 3, 1, } ,
759 { 0, -1, 0, 1, 0, } ,
760 { -3, 0, 2, 2, 0, } ,
761 { 1, 1, -2, 2, 0, } ,
762 { -1, 1, 0, 2, 2, } ,
763 { 1, -2, 2, -2, 1, } ,
764 { 0, 0, 1, 0, 2, } ,
765 { 0, 0, 1, 0, 1, } ,
766 { 0, 0, 1, 0, 0, } ,
767 { -1, 2, 0, 2, 1, } ,
768 { 0, 0, 2, 0, 2, } ,
769 { -2, 0, 2, 0, 2, } ,
770 { 2, 0, 0, -1, 1, } ,
771 { 3, 0, 0, -2, 1, } ,
772 { 1, 0, 2, -2, 3, } ,
773 { 1, 2, 0, 0, 1, } ,
774 { 2, 0, 2, -3, 2, } ,
775 { -1, 1, 4, -2, 2, } ,
776 { -2, -2, 0, 4, 0, } ,
777 { 0, -3, 0, 2, 0, } ,
778 { 0, 0, -2, 4, 0, } ,
779 { -1, -1, 0, 3, 0, } ,
780 { -2, 0, 0, 4, 2, } ,
781 { -1, 0, 0, 3, 1, } ,
782 { 2, -2, 0, 0, 0, } ,
783 { 1, -1, 0, 1, 0, } ,
784 { -1, 0, 0, 2, 0, } ,
785 { 0, -2, 2, 0, 1, } ,
786 { -1, 0, 1, 2, 1, } ,
787 { -1, 1, 0, 3, 0, } ,
788 { -1, -1, 2, 1, 2, } ,
789 { 0, -1, 2, 0, 0, } ,
790 { -2, 1, 2, 2, 1, } ,
791 { 2, -2, 2, -2, 2, } ,
792 { 1, 1, 0, 1, 1, } ,
793 { 1, 0, 1, 0, 1, } ,
794 { 1, 0, 1, 0, 0, } ,
795 { 0, 2, 0, 2, 0, } ,
796 { 2, -1, 2, -2, 1, } ,
797 { 0, -1, 4, -2, 1, } ,
798 { 0, 0, 4, -2, 3, } ,
799 { 0, 1, 4, -2, 1, } ,
800 { 4, 0, 2, -4, 2, } ,
801 { 2, 2, 2, -2, 2, } ,
802 { 2, 0, 4, -4, 2, } ,
803 { -1, -2, 0, 4, 0, } ,
804 { -1, -3, 2, 2, 2, } ,
805 { -3, 0, 2, 4, 2, } ,
806 { -3, 0, 2, -2, 1, } ,
807 { -1, -1, 0, -2, 1, } ,
808 { -3, 0, 0, 0, 2, } ,
809 { -3, 0, -2, 2, 0, } ,
810 { 0, 1, 0, -4, 1, } ,
811 { -2, 1, 0, -2, 1, } ,
812 { -4, 0, 0, 0, 1, } ,
813 { -1, 0, 0, -4, 1, } ,
814 { -3, 0, 0, -2, 1, } ,
815 { 0, 0, 0, 3, 2, } ,
816 { -1, 1, 0, 4, 1, } ,
817 { 1, -2, 2, 0, 1, } ,
818 { 0, 1, 0, 3, 0, } ,
819 { -1, 0, 2, 2, 3, } ,
820 { 0, 0, 2, 2, 2, } ,
821 { -2, 0, 2, 2, 2, } ,
822 { -1, 1, 2, 2, 0, } ,
823 { 3, 0, 0, 0, 2, } ,
824 { 2, 1, 0, 1, 0, } ,
825 { 2, -1, 2, -1, 2, } ,
826 { 0, 0, 2, 0, 1, } ,
827 { 0, 0, 3, 0, 3, } ,
828 { 0, 0, 3, 0, 2, } ,
829 { -1, 2, 2, 2, 1, } ,
830 { -1, 0, 4, 0, 0, } ,
831 { 1, 2, 2, 0, 1, } ,
832 { 3, 1, 2, -2, 1, } ,
833 { 1, 1, 4, -2, 2, } ,
834 { -2, -1, 0, 6, 0, } ,
835 { 0, -2, 0, 4, 0, } ,
836 { -2, 0, 0, 6, 1, } ,
837 { -2, -2, 2, 4, 2, } ,
838 { 0, -3, 2, 2, 2, } ,
839 { 0, 0, 0, 4, 2, } ,
840 { -1, -1, 2, 3, 2, } ,
841 { -2, 0, 2, 4, 0, } ,
842 { 2, -1, 0, 2, 1, } ,
843 { 1, 0, 0, 3, 0, } ,
844 { 0, 1, 0, 4, 1, } ,
845 { 0, 1, 0, 4, 0, } ,
846 { 1, -1, 2, 1, 2, } ,
847 { 0, 0, 2, 2, 3, } ,
848 { 1, 0, 2, 2, 2, } ,
849 { -1, 0, 2, 2, 2, } ,
850 { -2, 0, 4, 2, 1, } ,
851 { 2, 1, 0, 2, 1, } ,
852 { 2, 1, 0, 2, 0, } ,
853 { 2, -1, 2, 0, 0, } ,
854 { 1, 0, 2, 1, 0, } ,
855 { 0, 1, 2, 2, 0, } ,
856 { 2, 0, 2, 0, 3, } ,
857 { 3, 0, 2, 0, 2, } ,
858 { 1, 0, 2, 0, 2, } ,
859 { 1, 0, 3, 0, 3, } ,
860 { 1, 1, 2, 1, 1, } ,
861 { 0, 2, 2, 2, 2, } ,
862 { 2, 1, 2, 0, 0, } ,
863 { 2, 0, 4, -2, 1, } ,
864 { 4, 1, 2, -2, 2, } ,
865 { -1, -1, 0, 6, 0, } ,
866 { -3, -1, 2, 6, 2, } ,
867 { -1, 0, 0, 6, 1, } ,
868 { -3, 0, 2, 6, 1, } ,
869 { 1, -1, 0, 4, 1, } ,
870 { 1, -1, 0, 4, 0, } ,
871 { -2, 0, 2, 5, 2, } ,
872 { 1, -2, 2, 2, 1, } ,
873 { 3, -1, 0, 2, 0, } ,
874 { 1, -1, 2, 2, 0, } ,
875 { 0, 0, 2, 3, 1, } ,
876 { -1, 1, 2, 4, 1, } ,
877 { 0, 1, 2, 3, 2, } ,
878 { -1, 0, 4, 2, 1, } ,
879 { 2, 0, 2, 1, 1, } ,
880 { 5, 0, 0, 0, 0, } ,
881 { 2, 1, 2, 1, 2, } ,
882 { 1, 0, 4, 0, 1, } ,
883 { 3, 1, 2, 0, 1, } ,
884 { 3, 0, 4, -2, 2, } ,
885 { -2, -1, 2, 6, 2, } ,
886 { 0, 0, 0, 6, 0, } ,
887 { 0, -2, 2, 4, 2, } ,
888 { -2, 0, 2, 6, 1, } ,
889 { 2, 0, 0, 4, 1, } ,
890 { 2, 0, 0, 4, 0, } ,
891 { 2, -2, 2, 2, 2, } ,
892 { 0, 0, 2, 4, 0, } ,
893 { 1, 0, 2, 3, 2, } ,
894 { 4, 0, 0, 2, 0, } ,
895 { 2, 0, 2, 2, 0, } ,
896 { 0, 0, 4, 2, 2, } ,
897 { 4, -1, 2, 0, 2, } ,
898 { 3, 0, 2, 1, 2, } ,
899 { 2, 1, 2, 2, 1, } ,
900 { 4, 1, 2, 0, 2, } ,
901 { -1, -1, 2, 6, 2, } ,
902 { -1, 0, 2, 6, 1, } ,
903 { 1, -1, 2, 4, 1, } ,
904 { 1, 1, 2, 4, 2, } ,
905 { 3, 1, 2, 2, 2, } ,
906 { 5, 0, 2, 0, 1, } ,
907 { 2, -1, 2, 4, 2, } ,
908 { 2, 0, 2, 4, 1, } ,
909
910 } ;
911
912 /*
913 * Longitude and obliquity coefficients
914 */
915
916 static const double CLS[ NLS ][6] = {
917
918 /*
919 * Luni-Solar nutation coefficients, unit 1e-7 arcsec
920 * longitude (sin, t*sin, cos), obliquity (cos, t*cos, sin)
921 */
922
923 { -172064161e0, -174666e0, 33386e0, 92052331e0, 9086e0, 15377e0, } ,
924 { -13170906e0, -1675e0, -13696e0, 5730336e0, -3015e0, -4587e0, } ,
925 { -2276413e0, -234e0, 2796e0, 978459e0, -485e0, 1374e0, } ,
926 { 2074554e0, 207e0, -698e0, -897492e0, 470e0, -291e0, } ,
927 { 1475877e0, -3633e0, 11817e0, 73871e0, -184e0, -1924e0, } ,
928 { -516821e0, 1226e0, -524e0, 224386e0, -677e0, -174e0, } ,
929 { 711159e0, 73e0, -872e0, -6750e0, 0e0, 358e0, } ,
930 { -387298e0, -367e0, 380e0, 200728e0, 18e0, 318e0, } ,
931 { -301461e0, -36e0, 816e0, 129025e0, -63e0, 367e0, } ,
932 { 215829e0, -494e0, 111e0, -95929e0, 299e0, 132e0, } ,
933 { 128227e0, 137e0, 181e0, -68982e0, -9e0, 39e0, } ,
934 { 123457e0, 11e0, 19e0, -53311e0, 32e0, -4e0, } ,
935 { 156994e0, 10e0, -168e0, -1235e0, 0e0, 82e0, } ,
936 { 63110e0, 63e0, 27e0, -33228e0, 0e0, -9e0, } ,
937 { -57976e0, -63e0, -189e0, 31429e0, 0e0, -75e0, } ,
938 { -59641e0, -11e0, 149e0, 25543e0, -11e0, 66e0, } ,
939 { -51613e0, -42e0, 129e0, 26366e0, 0e0, 78e0, } ,
940 { 45893e0, 50e0, 31e0, -24236e0, -10e0, 20e0, } ,
941 { 63384e0, 11e0, -150e0, -1220e0, 0e0, 29e0, } ,
942 { -38571e0, -1e0, 158e0, 16452e0, -11e0, 68e0, } ,
943 { 32481e0, 0e0, 0e0, -13870e0, 0e0, 0e0, } ,
944 { -47722e0, 0e0, -18e0, 477e0, 0e0, -25e0, } ,
945 { -31046e0, -1e0, 131e0, 13238e0, -11e0, 59e0, } ,
946 { 28593e0, 0e0, -1e0, -12338e0, 10e0, -3e0, } ,
947 { 20441e0, 21e0, 10e0, -10758e0, 0e0, -3e0, } ,
948 { 29243e0, 0e0, -74e0, -609e0, 0e0, 13e0, } ,
949 { 25887e0, 0e0, -66e0, -550e0, 0e0, 11e0, } ,
950 { -14053e0, -25e0, 79e0, 8551e0, -2e0, -45e0, } ,
951 { 15164e0, 10e0, 11e0, -8001e0, 0e0, -1e0, } ,
952 { -15794e0, 72e0, -16e0, 6850e0, -42e0, -5e0, } ,
953 { 21783e0, 0e0, 13e0, -167e0, 0e0, 13e0, } ,
954 { -12873e0, -10e0, -37e0, 6953e0, 0e0, -14e0, } ,
955 { -12654e0, 11e0, 63e0, 6415e0, 0e0, 26e0, } ,
956 { -10204e0, 0e0, 25e0, 5222e0, 0e0, 15e0, } ,
957 { 16707e0, -85e0, -10e0, 168e0, -1e0, 10e0, } ,
958 { -7691e0, 0e0, 44e0, 3268e0, 0e0, 19e0, } ,
959 { -11024e0, 0e0, -14e0, 104e0, 0e0, 2e0, } ,
960 { 7566e0, -21e0, -11e0, -3250e0, 0e0, -5e0, } ,
961 { -6637e0, -11e0, 25e0, 3353e0, 0e0, 14e0, } ,
962 { -7141e0, 21e0, 8e0, 3070e0, 0e0, 4e0, } ,
963 { -6302e0, -11e0, 2e0, 3272e0, 0e0, 4e0, } ,
964 { 5800e0, 10e0, 2e0, -3045e0, 0e0, -1e0, } ,
965 { 6443e0, 0e0, -7e0, -2768e0, 0e0, -4e0, } ,
966 { -5774e0, -11e0, -15e0, 3041e0, 0e0, -5e0, } ,
967 { -5350e0, 0e0, 21e0, 2695e0, 0e0, 12e0, } ,
968 { -4752e0, -11e0, -3e0, 2719e0, 0e0, -3e0, } ,
969 { -4940e0, -11e0, -21e0, 2720e0, 0e0, -9e0, } ,
970 { 7350e0, 0e0, -8e0, -51e0, 0e0, 4e0, } ,
971 { 4065e0, 0e0, 6e0, -2206e0, 0e0, 1e0, } ,
972 { 6579e0, 0e0, -24e0, -199e0, 0e0, 2e0, } ,
973 { 3579e0, 0e0, 5e0, -1900e0, 0e0, 1e0, } ,
974 { 4725e0, 0e0, -6e0, -41e0, 0e0, 3e0, } ,
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1225 { 47e0, 0e0, 0e0, -1e0, 0e0, 0e0, } ,
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1303 { 22e0, 0e0, 0e0, -9e0, 0e0, 0e0, } ,
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1313 { -13e0, 0e0, 0e0, 6e0, 0e0, 0e0, } ,
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1413 { -8e0, 0e0, 0e0, 3e0, 0e0, 0e0, } ,
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1416 { -5e0, 0e0, 0e0, 2e0, 0e0, 0e0, } ,
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1422 { -3e0, 0e0, 0e0, 2e0, 0e0, 0e0, } ,
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1425 { -5e0, 0e0, 0e0, 2e0, 0e0, 0e0, } ,
1426 { 4e0, 0e0, 0e0, -2e0, 0e0, 0e0, } ,
1427 { 9e0, 0e0, 0e0, -3e0, 0e0, 0e0, } ,
1428 { 4e0, 0e0, 0e0, 0e0, 0e0, 0e0, } ,
1429 { 4e0, 0e0, 0e0, -2e0, 0e0, 0e0, } ,
1430 { -3e0, 0e0, 0e0, 2e0, 0e0, 0e0, } ,
1431 { -4e0, 0e0, 0e0, 2e0, 0e0, 0e0, } ,
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1434 { -4e0, 0e0, 0e0, 0e0, 0e0, 0e0, } ,
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1436 { 8e0, 0e0, 0e0, 0e0, 0e0, 0e0, } ,
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1438 { -3e0, 0e0, 0e0, 2e0, 0e0, 0e0, } ,
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1440 { 3e0, 0e0, 0e0, -1e0, 0e0, 0e0, } ,
1441 { -3e0, 0e0, 0e0, 1e0, 0e0, 0e0, } ,
1442 { 6e0, 0e0, 0e0, -3e0, 0e0, 0e0, } ,
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1444 { -3e0, 0e0, 0e0, 1e0, 0e0, 0e0, } ,
1445 { -7e0, 0e0, 0e0, 0e0, 0e0, 0e0, } ,
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1447 { -3e0, 0e0, 0e0, 2e0, 0e0, 0e0, } ,
1448 { -3e0, 0e0, 0e0, 0e0, 0e0, 0e0, } ,
1449 { -4e0, 0e0, 0e0, 0e0, 0e0, 0e0, } ,
1450 { -5e0, 0e0, 0e0, 3e0, 0e0, 0e0, } ,
1451 { -13e0, 0e0, 0e0, 0e0, 0e0, 0e0, } ,
1452 { -7e0, 0e0, 0e0, 0e0, 0e0, 0e0, } ,
1453 { 10e0, 0e0, 0e0, 0e0, 0e0, 0e0, } ,
1454 { 3e0, 0e0, 0e0, -1e0, 0e0, 0e0, } ,
1455 { 10e0, 0e0, 13e0, 6e0, 0e0, -5e0, } ,
1456 { 0e0, 0e0, 30e0, 0e0, 0e0, 14e0, } ,
1457 { 0e0, 0e0, -162e0, 0e0, 0e0, -138e0, } ,
1458 { 0e0, 0e0, 75e0, 0e0, 0e0, 0e0, } ,
1459 { -7e0, 0e0, 0e0, 4e0, 0e0, 0e0, } ,
1460 { -4e0, 0e0, 0e0, 2e0, 0e0, 0e0, } ,
1461 { 4e0, 0e0, 0e0, -2e0, 0e0, 0e0, } ,
1462 { 5e0, 0e0, 0e0, -2e0, 0e0, 0e0, } ,
1463 { 5e0, 0e0, 0e0, -3e0, 0e0, 0e0, } ,
1464 { -3e0, 0e0, 0e0, 0e0, 0e0, 0e0, } ,
1465 { -3e0, 0e0, 0e0, 2e0, 0e0, 0e0, } ,
1466 { -4e0, 0e0, 0e0, 2e0, 0e0, 0e0, } ,
1467 { -5e0, 0e0, 0e0, 2e0, 0e0, 0e0, } ,
1468 { 6e0, 0e0, 0e0, 0e0, 0e0, 0e0, } ,
1469 { 9e0, 0e0, 0e0, 0e0, 0e0, 0e0, } ,
1470 { 5e0, 0e0, 0e0, 0e0, 0e0, 0e0, } ,
1471 { -7e0, 0e0, 0e0, 0e0, 0e0, 0e0, } ,
1472 { -3e0, 0e0, 0e0, 1e0, 0e0, 0e0, } ,
1473 { -4e0, 0e0, 0e0, 2e0, 0e0, 0e0, } ,
1474 { 7e0, 0e0, 0e0, 0e0, 0e0, 0e0, } ,
1475 { -4e0, 0e0, 0e0, 0e0, 0e0, 0e0, } ,
1476 { 4e0, 0e0, 0e0, 0e0, 0e0, 0e0, } ,
1477 { -6e0, 0e0, -3e0, 3e0, 0e0, 1e0, } ,
1478 { 0e0, 0e0, -3e0, 0e0, 0e0, -2e0, } ,
1479 { 11e0, 0e0, 0e0, 0e0, 0e0, 0e0, } ,
1480 { 3e0, 0e0, 0e0, -1e0, 0e0, 0e0, } ,
1481 { 11e0, 0e0, 0e0, 0e0, 0e0, 0e0, } ,
1482 { -3e0, 0e0, 0e0, 2e0, 0e0, 0e0, } ,
1483 { -1e0, 0e0, 3e0, 3e0, 0e0, -1e0, } ,
1484 { 4e0, 0e0, 0e0, -2e0, 0e0, 0e0, } ,
1485 { 0e0, 0e0, -13e0, 0e0, 0e0, -11e0, } ,
1486 { 3e0, 0e0, 6e0, 0e0, 0e0, 0e0, } ,
1487 { -7e0, 0e0, 0e0, 0e0, 0e0, 0e0, } ,
1488 { 5e0, 0e0, 0e0, -3e0, 0e0, 0e0, } ,
1489 { -3e0, 0e0, 0e0, 1e0, 0e0, 0e0, } ,
1490 { 3e0, 0e0, 0e0, 0e0, 0e0, 0e0, } ,
1491 { 5e0, 0e0, 0e0, -3e0, 0e0, 0e0, } ,
1492 { -7e0, 0e0, 0e0, 3e0, 0e0, 0e0, } ,
1493 { 8e0, 0e0, 0e0, -3e0, 0e0, 0e0, } ,
1494 { -4e0, 0e0, 0e0, 2e0, 0e0, 0e0, } ,
1495 { 11e0, 0e0, 0e0, 0e0, 0e0, 0e0, } ,
1496 { -3e0, 0e0, 0e0, 1e0, 0e0, 0e0, } ,
1497 { 3e0, 0e0, 0e0, -1e0, 0e0, 0e0, } ,
1498 { -4e0, 0e0, 0e0, 2e0, 0e0, 0e0, } ,
1499 { 8e0, 0e0, 0e0, -4e0, 0e0, 0e0, } ,
1500 { 3e0, 0e0, 0e0, -1e0, 0e0, 0e0, } ,
1501 { 11e0, 0e0, 0e0, 0e0, 0e0, 0e0, } ,
1502 { -6e0, 0e0, 0e0, 3e0, 0e0, 0e0, } ,
1503 { -4e0, 0e0, 0e0, 2e0, 0e0, 0e0, } ,
1504 { -8e0, 0e0, 0e0, 4e0, 0e0, 0e0, } ,
1505 { -7e0, 0e0, 0e0, 3e0, 0e0, 0e0, } ,
1506 { -4e0, 0e0, 0e0, 2e0, 0e0, 0e0, } ,
1507 { 3e0, 0e0, 0e0, -1e0, 0e0, 0e0, } ,
1508 { 6e0, 0e0, 0e0, -3e0, 0e0, 0e0, } ,
1509 { -6e0, 0e0, 0e0, 3e0, 0e0, 0e0, } ,
1510 { 6e0, 0e0, 0e0, 0e0, 0e0, 0e0, } ,
1511 { 6e0, 0e0, 0e0, -1e0, 0e0, 0e0, } ,
1512 { 5e0, 0e0, 0e0, -2e0, 0e0, 0e0, } ,
1513 { -5e0, 0e0, 0e0, 2e0, 0e0, 0e0, } ,
1514 { -4e0, 0e0, 0e0, 0e0, 0e0, 0e0, } ,
1515 { -4e0, 0e0, 0e0, 2e0, 0e0, 0e0, } ,
1516 { 4e0, 0e0, 0e0, 0e0, 0e0, 0e0, } ,
1517 { 6e0, 0e0, 0e0, -3e0, 0e0, 0e0, } ,
1518 { -4e0, 0e0, 0e0, 2e0, 0e0, 0e0, } ,
1519 { 0e0, 0e0, -26e0, 0e0, 0e0, -11e0, } ,
1520 { 0e0, 0e0, -10e0, 0e0, 0e0, -5e0, } ,
1521 { 5e0, 0e0, 0e0, -3e0, 0e0, 0e0, } ,
1522 { -13e0, 0e0, 0e0, 0e0, 0e0, 0e0, } ,
1523 { 3e0, 0e0, 0e0, -2e0, 0e0, 0e0, } ,
1524 { 4e0, 0e0, 0e0, -2e0, 0e0, 0e0, } ,
1525 { 7e0, 0e0, 0e0, -3e0, 0e0, 0e0, } ,
1526 { 4e0, 0e0, 0e0, 0e0, 0e0, 0e0, } ,
1527 { 5e0, 0e0, 0e0, 0e0, 0e0, 0e0, } ,
1528 { -3e0, 0e0, 0e0, 2e0, 0e0, 0e0, } ,
1529 { -6e0, 0e0, 0e0, 2e0, 0e0, 0e0, } ,
1530 { -5e0, 0e0, 0e0, 2e0, 0e0, 0e0, } ,
1531 { -7e0, 0e0, 0e0, 3e0, 0e0, 0e0, } ,
1532 { 5e0, 0e0, 0e0, -2e0, 0e0, 0e0, } ,
1533 { 13e0, 0e0, 0e0, 0e0, 0e0, 0e0, } ,
1534 { -4e0, 0e0, 0e0, 2e0, 0e0, 0e0, } ,
1535 { -3e0, 0e0, 0e0, 0e0, 0e0, 0e0, } ,
1536 { 5e0, 0e0, 0e0, -2e0, 0e0, 0e0, } ,
1537 { -11e0, 0e0, 0e0, 0e0, 0e0, 0e0, } ,
1538 { 5e0, 0e0, 0e0, -2e0, 0e0, 0e0, } ,
1539 { 4e0, 0e0, 0e0, 0e0, 0e0, 0e0, } ,
1540 { 4e0, 0e0, 0e0, -2e0, 0e0, 0e0, } ,
1541 { -4e0, 0e0, 0e0, 2e0, 0e0, 0e0, } ,
1542 { 6e0, 0e0, 0e0, -3e0, 0e0, 0e0, } ,
1543 { 3e0, 0e0, 0e0, -2e0, 0e0, 0e0, } ,
1544 { -12e0, 0e0, 0e0, 0e0, 0e0, 0e0, } ,
1545 { 4e0, 0e0, 0e0, 0e0, 0e0, 0e0, } ,
1546 { -3e0, 0e0, 0e0, 0e0, 0e0, 0e0, } ,
1547 { -4e0, 0e0, 0e0, 0e0, 0e0, 0e0, } ,
1548 { 3e0, 0e0, 0e0, 0e0, 0e0, 0e0, } ,
1549 { 3e0, 0e0, 0e0, -1e0, 0e0, 0e0, } ,
1550 { -3e0, 0e0, 0e0, 1e0, 0e0, 0e0, } ,
1551 { 0e0, 0e0, -5e0, 0e0, 0e0, -2e0, } ,
1552 { -7e0, 0e0, 0e0, 4e0, 0e0, 0e0, } ,
1553 { 6e0, 0e0, 0e0, -3e0, 0e0, 0e0, } ,
1554 { -3e0, 0e0, 0e0, 0e0, 0e0, 0e0, } ,
1555 { 5e0, 0e0, 0e0, -3e0, 0e0, 0e0, } ,
1556 { 3e0, 0e0, 0e0, -1e0, 0e0, 0e0, } ,
1557 { 3e0, 0e0, 0e0, 0e0, 0e0, 0e0, } ,
1558 { -3e0, 0e0, 0e0, 1e0, 0e0, 0e0, } ,
1559 { -5e0, 0e0, 0e0, 3e0, 0e0, 0e0, } ,
1560 { -3e0, 0e0, 0e0, 2e0, 0e0, 0e0, } ,
1561 { -3e0, 0e0, 0e0, 2e0, 0e0, 0e0, } ,
1562 { 12e0, 0e0, 0e0, 0e0, 0e0, 0e0, } ,
1563 { 3e0, 0e0, 0e0, -1e0, 0e0, 0e0, } ,
1564 { -4e0, 0e0, 0e0, 2e0, 0e0, 0e0, } ,
1565 { 4e0, 0e0, 0e0, 0e0, 0e0, 0e0, } ,
1566 { 6e0, 0e0, 0e0, 0e0, 0e0, 0e0, } ,
1567 { 5e0, 0e0, 0e0, -3e0, 0e0, 0e0, } ,
1568 { 4e0, 0e0, 0e0, -2e0, 0e0, 0e0, } ,
1569 { -6e0, 0e0, 0e0, 3e0, 0e0, 0e0, } ,
1570 { 4e0, 0e0, 0e0, -2e0, 0e0, 0e0, } ,
1571 { 6e0, 0e0, 0e0, -3e0, 0e0, 0e0, } ,
1572 { 6e0, 0e0, 0e0, 0e0, 0e0, 0e0, } ,
1573 { -6e0, 0e0, 0e0, 3e0, 0e0, 0e0, } ,
1574 { 3e0, 0e0, 0e0, -2e0, 0e0, 0e0, } ,
1575 { 7e0, 0e0, 0e0, -4e0, 0e0, 0e0, } ,
1576 { 4e0, 0e0, 0e0, -2e0, 0e0, 0e0, } ,
1577 { -5e0, 0e0, 0e0, 2e0, 0e0, 0e0, } ,
1578 { 5e0, 0e0, 0e0, 0e0, 0e0, 0e0, } ,
1579 { -6e0, 0e0, 0e0, 3e0, 0e0, 0e0, } ,
1580 { -6e0, 0e0, 0e0, 3e0, 0e0, 0e0, } ,
1581 { -4e0, 0e0, 0e0, 2e0, 0e0, 0e0, } ,
1582 { 10e0, 0e0, 0e0, 0e0, 0e0, 0e0, } ,
1583 { -4e0, 0e0, 0e0, 2e0, 0e0, 0e0, } ,
1584 { 7e0, 0e0, 0e0, 0e0, 0e0, 0e0, } ,
1585 { 7e0, 0e0, 0e0, -3e0, 0e0, 0e0, } ,
1586 { 4e0, 0e0, 0e0, 0e0, 0e0, 0e0, } ,
1587 { 11e0, 0e0, 0e0, 0e0, 0e0, 0e0, } ,
1588 { 5e0, 0e0, 0e0, -2e0, 0e0, 0e0, } ,
1589 { -6e0, 0e0, 0e0, 2e0, 0e0, 0e0, } ,
1590 { 4e0, 0e0, 0e0, -2e0, 0e0, 0e0, } ,
1591 { 3e0, 0e0, 0e0, -2e0, 0e0, 0e0, } ,
1592 { 5e0, 0e0, 0e0, -2e0, 0e0, 0e0, } ,
1593 { -4e0, 0e0, 0e0, 2e0, 0e0, 0e0, } ,
1594 { -4e0, 0e0, 0e0, 2e0, 0e0, 0e0, } ,
1595 { -3e0, 0e0, 0e0, 2e0, 0e0, 0e0, } ,
1596 { 4e0, 0e0, 0e0, -2e0, 0e0, 0e0, } ,
1597 { 3e0, 0e0, 0e0, -1e0, 0e0, 0e0, } ,
1598 { -3e0, 0e0, 0e0, 1e0, 0e0, 0e0, } ,
1599 { -3e0, 0e0, 0e0, 1e0, 0e0, 0e0, } ,
1600 { -3e0, 0e0, 0e0, 2e0, 0e0, 0e0, } ,
1601 } ;
1602
1603 /*
1604 * ---------------
1605 * Planetary terms
1606 * ---------------
1607 */
1608
1609 /*
1610 * Number of terms in the planetary nutation model
1611 */
1612
1613 #define NPL 687
1614
1615 /*
1616 * Coefficients for fundamental arguments
1617 */
1618
1619 static const int NAPL[ NPL ][14] = {
1620
1621 /*
1622 * Planetary argument multipliers
1623 * L L' F D Om Me Ve E Ma Ju Sa Ur Ne pre
1624 */
1625
1626 { 0, 0, 0, 0, 0, 0, 0, 8,-16, 4, 5, 0, 0, 0, } ,
1627 { 0, 0, 0, 0, 0, 0, 0, -8, 16, -4, -5, 0, 0, 2, } ,
1628 { 0, 0, 0, 0, 0, 0, 0, 8,-16, 4, 5, 0, 0, 2, } ,
1629 { 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, 2, 2, } ,
1630 { 0, 0, 0, 0, 0, 0, 0, -4, 8, -1, -5, 0, 0, 2, } ,
1631 { 0, 0, 0, 0, 0, 0, 0, 4, -8, 3, 0, 0, 0, 1, } ,
1632 { 0, 0, 1, -1, 1, 0, 0, 3, -8, 3, 0, 0, 0, 0, } ,
1633 { -1, 0, 0, 0, 0, 0, 10, -3, 0, 0, 0, 0, 0, 0, } ,
1634 { 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 6, -3, 0, 2, } ,
1635 { 0, 0, 0, 0, 0, 0, 0, 4, -8, 3, 0, 0, 0, 0, } ,
1636 { 0, 0, 1, -1, 1, 0, 0, -5, 8, -3, 0, 0, 0, 0, } ,
1637 { 0, 0, 0, 0, 0, 0, 0, -4, 8, -3, 0, 0, 0, 1, } ,
1638 { 0, 0, 0, 0, 0, 0, 0, 4, -8, 1, 5, 0, 0, 2, } ,
1639 { 0, 0, 0, 0, 0, 0, -5, 6, 4, 0, 0, 0, 0, 2, } ,
1640 { 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, -5, 0, 0, 2, } ,
1641 { 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, -5, 0, 0, 1, } ,
1642 { 0, 0, 1, -1, 1, 0, 0, -1, 0, 2, -5, 0, 0, 0, } ,
1643 { 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, -5, 0, 0, 0, } ,
1644 { 0, 0, 1, -1, 1, 0, 0, -1, 0, -2, 5, 0, 0, 0, } ,
1645 { 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 5, 0, 0, 1, } ,
1646 { 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 5, 0, 0, 2, } ,
1647 { 2, 0, -1, -1, 0, 0, 0, 3, -7, 0, 0, 0, 0, 0, } ,
1648 { 1, 0, 0, -2, 0, 0, 19,-21, 3, 0, 0, 0, 0, 0, } ,
1649 { 0, 0, 1, -1, 1, 0, 2, -4, 0, -3, 0, 0, 0, 0, } ,
1650 { 1, 0, 0, -1, 1, 0, 0, -1, 0, 2, 0, 0, 0, 0, } ,
1651 { 0, 0, 1, -1, 1, 0, 0, -1, 0, -4, 10, 0, 0, 0, } ,
1652 { -2, 0, 0, 2, 1, 0, 0, 2, 0, 0, -5, 0, 0, 0, } ,
1653 { 0, 0, 0, 0, 0, 0, 3, -7, 4, 0, 0, 0, 0, 0, } ,
1654 { 0, 0, -1, 1, 0, 0, 0, 1, 0, 1, -1, 0, 0, 0, } ,
1655 { -2, 0, 0, 2, 1, 0, 0, 2, 0, -2, 0, 0, 0, 0, } ,
1656 { -1, 0, 0, 0, 0, 0, 18,-16, 0, 0, 0, 0, 0, 0, } ,
1657 { -2, 0, 1, 1, 2, 0, 0, 1, 0, -2, 0, 0, 0, 0, } ,
1658 { -1, 0, 1, -1, 1, 0, 18,-17, 0, 0, 0, 0, 0, 0, } ,
1659 { -1, 0, 0, 1, 1, 0, 0, 2, -2, 0, 0, 0, 0, 0, } ,
1660 { 0, 0, 0, 0, 0, 0, -8, 13, 0, 0, 0, 0, 0, 2, } ,
1661 { 0, 0, 2, -2, 2, 0, -8, 11, 0, 0, 0, 0, 0, 0, } ,
1662 { 0, 0, 0, 0, 0, 0, -8, 13, 0, 0, 0, 0, 0, 1, } ,
1663 { 0, 0, 1, -1, 1, 0, -8, 12, 0, 0, 0, 0, 0, 0, } ,
1664 { 0, 0, 0, 0, 0, 0, 8,-13, 0, 0, 0, 0, 0, 0, } ,
1665 { 0, 0, 1, -1, 1, 0, 8,-14, 0, 0, 0, 0, 0, 0, } ,
1666 { 0, 0, 0, 0, 0, 0, 8,-13, 0, 0, 0, 0, 0, 1, } ,
1667 { -2, 0, 0, 2, 1, 0, 0, 2, 0, -4, 5, 0, 0, 0, } ,
1668 { -2, 0, 0, 2, 2, 0, 3, -3, 0, 0, 0, 0, 0, 0, } ,
1669 { -2, 0, 0, 2, 0, 0, 0, 2, 0, -3, 1, 0, 0, 0, } ,
1670 { 0, 0, 0, 0, 1, 0, 3, -5, 0, 2, 0, 0, 0, 0, } ,
1671 { -2, 0, 0, 2, 0, 0, 0, 2, 0, -4, 3, 0, 0, 0, } ,
1672 { 0, 0, -1, 1, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, } ,
1673 { 0, 0, 0, 0, 1, 0, 0, -1, 2, 0, 0, 0, 0, 0, } ,
1674 { 0, 0, 1, -1, 2, 0, 0, -2, 2, 0, 0, 0, 0, 0, } ,
1675 { -1, 0, 1, 0, 1, 0, 3, -5, 0, 0, 0, 0, 0, 0, } ,
1676 { -1, 0, 0, 1, 0, 0, 3, -4, 0, 0, 0, 0, 0, 0, } ,
1677 { -2, 0, 0, 2, 0, 0, 0, 2, 0, -2, -2, 0, 0, 0, } ,
1678 { -2, 0, 2, 0, 2, 0, 0, -5, 9, 0, 0, 0, 0, 0, } ,
1679 { 0, 0, 1, -1, 1, 0, 0, -1, 0, 0, 0, -1, 0, 0, } ,
1680 { 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, } ,
1681 { 0, 0, 1, -1, 1, 0, 0, -1, 0, 0, 0, 0, 2, 0, } ,
1682 { 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 1, } ,
1683 { 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 2, } ,
1684 { -1, 0, 0, 1, 0, 0, 0, 3, -4, 0, 0, 0, 0, 0, } ,
1685 { 0, 0, -1, 1, 0, 0, 0, 1, 0, 0, 2, 0, 0, 0, } ,
1686 { 0, 0, 1, -1, 2, 0, 0, -1, 0, 0, 2, 0, 0, 0, } ,
1687 { 0, 0, 0, 0, 1, 0, 0, -9, 17, 0, 0, 0, 0, 0, } ,
1688 { 0, 0, 0, 0, 2, 0, -3, 5, 0, 0, 0, 0, 0, 0, } ,
1689 { 0, 0, 1, -1, 1, 0, 0, -1, 0, -1, 2, 0, 0, 0, } ,
1690 { 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, -2, 0, 0, 0, } ,
1691 { 1, 0, 0, -2, 0, 0, 17,-16, 0, -2, 0, 0, 0, 0, } ,
1692 { 0, 0, 1, -1, 1, 0, 0, -1, 0, 1, -3, 0, 0, 0, } ,
1693 { -2, 0, 0, 2, 1, 0, 0, 5, -6, 0, 0, 0, 0, 0, } ,
1694 { 0, 0, -2, 2, 0, 0, 0, 9,-13, 0, 0, 0, 0, 0, } ,
1695 { 0, 0, 1, -1, 2, 0, 0, -1, 0, 0, 1, 0, 0, 0, } ,
1696 { 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, } ,
1697 { 0, 0, -1, 1, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, } ,
1698 { 0, 0, -2, 2, 0, 0, 5, -6, 0, 0, 0, 0, 0, 0, } ,
1699 { 0, 0, -1, 1, 1, 0, 5, -7, 0, 0, 0, 0, 0, 0, } ,
1700 { -2, 0, 0, 2, 0, 0, 6, -8, 0, 0, 0, 0, 0, 0, } ,
1701 { 2, 0, 1, -3, 1, 0, -6, 7, 0, 0, 0, 0, 0, 0, } ,
1702 { 0, 0, 0, 0, 2, 0, 0, 0, 0, 1, 0, 0, 0, 0, } ,
1703 { 0, 0, -1, 1, 1, 0, 0, 1, 0, 1, 0, 0, 0, 0, } ,
1704 { 0, 0, 1, -1, 1, 0, 0, -1, 0, 0, 0, 2, 0, 0, } ,
1705 { 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 1, } ,
1706 { 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 2, } ,
1707 { 0, 0, 0, 0, 0, 0, 0, -8, 15, 0, 0, 0, 0, 2, } ,
1708 { 0, 0, 0, 0, 0, 0, 0, -8, 15, 0, 0, 0, 0, 1, } ,
1709 { 0, 0, 1, -1, 1, 0, 0, -9, 15, 0, 0, 0, 0, 0, } ,
1710 { 0, 0, 0, 0, 0, 0, 0, 8,-15, 0, 0, 0, 0, 0, } ,
1711 { 1, 0, -1, -1, 0, 0, 0, 8,-15, 0, 0, 0, 0, 0, } ,
1712 { 2, 0, 0, -2, 0, 0, 2, -5, 0, 0, 0, 0, 0, 0, } ,
1713 { -2, 0, 0, 2, 0, 0, 0, 2, 0, -5, 5, 0, 0, 0, } ,
1714 { 2, 0, 0, -2, 1, 0, 0, -6, 8, 0, 0, 0, 0, 0, } ,
1715 { 2, 0, 0, -2, 1, 0, 0, -2, 0, 3, 0, 0, 0, 0, } ,
1716 { -2, 0, 1, 1, 0, 0, 0, 1, 0, -3, 0, 0, 0, 0, } ,
1717 { -2, 0, 1, 1, 1, 0, 0, 1, 0, -3, 0, 0, 0, 0, } ,
1718 { -2, 0, 0, 2, 0, 0, 0, 2, 0, -3, 0, 0, 0, 0, } ,
1719 { -2, 0, 0, 2, 0, 0, 0, 6, -8, 0, 0, 0, 0, 0, } ,
1720 { -2, 0, 0, 2, 0, 0, 0, 2, 0, -1, -5, 0, 0, 0, } ,
1721 { -1, 0, 0, 1, 0, 0, 0, 1, 0, -1, 0, 0, 0, 0, } ,
1722 { -1, 0, 1, 1, 1, 0, -20,20, 0, 0, 0, 0, 0, 0, } ,
1723 { 1, 0, 0, -2, 0, 0, 20,-21, 0, 0, 0, 0, 0, 0, } ,
1724 { 0, 0, 0, 0, 1, 0, 0, 8,-15, 0, 0, 0, 0, 0, } ,
1725 { 0, 0, 2, -2, 1, 0, 0,-10, 15, 0, 0, 0, 0, 0, } ,
1726 { 0, 0, -1, 1, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, } ,
1727 { 0, 0, 0, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, } ,
1728 { 0, 0, 1, -1, 2, 0, 0, -1, 0, 1, 0, 0, 0, 0, } ,
1729 { 0, 0, 1, -1, 1, 0, 0, -1, 0, -2, 4, 0, 0, 0, } ,
1730 { 2, 0, 0, -2, 1, 0, -6, 8, 0, 0, 0, 0, 0, 0, } ,
1731 { 0, 0, -2, 2, 1, 0, 5, -6, 0, 0, 0, 0, 0, 0, } ,
1732 { 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, 0, 0, 1, } ,
1733 { 0, 0, 1, -1, 1, 0, 0, -1, 0, 0, -1, 0, 0, 0, } ,
1734 { 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, } ,
1735 { 0, 0, 1, -1, 1, 0, 0, -1, 0, 0, 1, 0, 0, 0, } ,
1736 { 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 1, } ,
1737 { 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 2, } ,
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1903 { 0, 0, 0, 0, 0, 0, 0, -4, 8, 0, 0, 0, 0, 2, } ,
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1910 { 0, 0, 0, 0, 0, 0, 0, -5, 10, 0, 0, 0, 0, 2, } ,
1911 { 0, 0, 0, 0, 1, 0, -1, 2, 0, 0, 0, 0, 0, 0, } ,
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1913 { 0, 0, 0, 0, 0, 0, 0, -3, 5, 0, 0, 0, 0, 2, } ,
1914 { 0, 0, 0, 0, 0, 0, 0, -3, 5, 0, 0, 0, 0, 1, } ,
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1917 { 0, 0, 1, -1, 1, 0, 1, -3, 0, 0, 0, 0, 0, 0, } ,
1918 { 0, 0, 0, 0, 0, 0, 1, -2, 0, 0, 0, 0, 0, 0, } ,
1919 { 0, 0, 0, 0, 0, 0, -1, 2, 0, 0, 0, 0, 0, 1, } ,
1920 { 0, 0, 0, 0, 0, 0, -1, 2, 0, 0, 0, 0, 0, 2, } ,
1921 { 0, 0, 0, 0, 0, 0, -7, 11, 0, 0, 0, 0, 0, 2, } ,
1922 { 0, 0, 0, 0, 0, 0, -7, 11, 0, 0, 0, 0, 0, 1, } ,
1923 { 0, 0, -2, 2, 0, 0, 4, -4, 0, 0, 0, 0, 0, 0, } ,
1924 { 0, 0, 0, 0, 0, 0, 0, 2, -3, 0, 0, 0, 0, 0, } ,
1925 { 0, 0, 2, -2, 1, 0, -4, 4, 0, 0, 0, 0, 0, 0, } ,
1926 { 0, 0, -1, 1, 0, 0, 4, -5, 0, 0, 0, 0, 0, 0, } ,
1927 { 0, 0, 0, 0, 0, 0, 0, 1, -1, 0, 0, 0, 0, 0, } ,
1928 { 0, 0, 0, 0, 0, 0, -4, 7, 0, 0, 0, 0, 0, 1, } ,
1929 { 0, 0, 1, -1, 1, 0, -4, 6, 0, 0, 0, 0, 0, 0, } ,
1930 { 0, 0, 0, 0, 0, 0, -4, 7, 0, 0, 0, 0, 0, 2, } ,
1931 { 0, 0, 0, 0, 0, 0, -4, 6, 0, 0, 0, 0, 0, 2, } ,
1932 { 0, 0, 0, 0, 0, 0, -4, 6, 0, 0, 0, 0, 0, 1, } ,
1933 { 0, 0, 1, -1, 1, 0, -4, 5, 0, 0, 0, 0, 0, 0, } ,
1934 { 0, 0, 0, 0, 0, 0, -4, 6, 0, 0, 0, 0, 0, 1, } ,
1935 { 0, 0, 0, 0, 0, 0, 4, -6, 0, 0, 0, 0, 0, 0, } ,
1936 { -2, 0, 0, 2, 0, 0, 2, -2, 0, 0, 0, 0, 0, 0, } ,
1937 { 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, } ,
1938 { 0, 0, -1, 1, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, } ,
1939 { 0, 0, 0, 0, 1, 0, 1, -1, 0, 0, 0, 0, 0, 0, } ,
1940 { 0, 0, 0, 0, 0, 0, 0, -1, 0, 5, 0, 0, 0, 2, } ,
1941 { 0, 0, 0, 0, 0, 0, 0, 1, -3, 0, 0, 0, 0, 0, } ,
1942 { 0, 0, 0, 0, 0, 0, 0, -1, 3, 0, 0, 0, 0, 2, } ,
1943 { 0, 0, 0, 0, 0, 0, 0, -7, 12, 0, 0, 0, 0, 2, } ,
1944 { 0, 0, 0, 0, 0, 0, -1, 1, 0, 0, 0, 0, 0, 2, } ,
1945 { 0, 0, 0, 0, 0, 0, -1, 1, 0, 0, 0, 0, 0, 1, } ,
1946 { 0, 0, 1, -1, 1, 0, -1, 0, 0, 0, 0, 0, 0, 0, } ,
1947 { 0, 0, 0, 0, 0, 0, 1, -1, 0, 0, 0, 0, 0, 0, } ,
1948 { 0, 0, 0, 0, 0, 0, 1, -1, 0, 0, 0, 0, 0, 1, } ,
1949 { 0, 0, 1, -1, 1, 0, 1, -2, 0, 0, 0, 0, 0, 0, } ,
1950 { 0, 0, 0, 0, 0, 0, 0, -2, 5, 0, 0, 0, 0, 2, } ,
1951 { 0, 0, 0, 0, 0, 0, 0, -1, 0, 4, 0, 0, 0, 2, } ,
1952 { 0, 0, 0, 0, 0, 0, 0, 1, 0, -4, 0, 0, 0, 0, } ,
1953 { 0, 0, 0, 0, 1, 0, -1, 1, 0, 0, 0, 0, 0, 0, } ,
1954 { 0, 0, 0, 0, 0, 0, 0, -6, 10, 0, 0, 0, 0, 2, } ,
1955 { 0, 0, 0, 0, 0, 0, 0, -6, 10, 0, 0, 0, 0, 0, } ,
1956 { 0, 0, 2, -2, 1, 0, 0, -3, 0, 3, 0, 0, 0, 0, } ,
1957 { 0, 0, 0, 0, 0, 0, 0, -3, 7, 0, 0, 0, 0, 2, } ,
1958 { -2, 0, 0, 2, 0, 0, 4, -4, 0, 0, 0, 0, 0, 0, } ,
1959 { 0, 0, 0, 0, 0, 0, 0, -5, 8, 0, 0, 0, 0, 2, } ,
1960 { 0, 0, 0, 0, 0, 0, 0, 5, -8, 0, 0, 0, 0, 0, } ,
1961 { 0, 0, 0, 0, 0, 0, 0, -1, 0, 3, 0, 0, 0, 2, } ,
1962 { 0, 0, 0, 0, 0, 0, 0, -1, 0, 3, 0, 0, 0, 1, } ,
1963 { 0, 0, 0, 0, 0, 0, 0, 1, 0, -3, 0, 0, 0, 0, } ,
1964 { 0, 0, 0, 0, 0, 0, 2, -4, 0, 0, 0, 0, 0, 0, } ,
1965 { 0, 0, 0, 0, 0, 0, -2, 4, 0, 0, 0, 0, 0, 1, } ,
1966 { 0, 0, 1, -1, 1, 0, -2, 3, 0, 0, 0, 0, 0, 0, } ,
1967 { 0, 0, 0, 0, 0, 0, -2, 4, 0, 0, 0, 0, 0, 2, } ,
1968 { 0, 0, 0, 0, 0, 0, -6, 9, 0, 0, 0, 0, 0, 2, } ,
1969 { 0, 0, 0, 0, 0, 0, -6, 9, 0, 0, 0, 0, 0, 1, } ,
1970 { 0, 0, 0, 0, 0, 0, 6, -9, 0, 0, 0, 0, 0, 0, } ,
1971 { 0, 0, 0, 0, 1, 0, 0, 1, 0, -2, 0, 0, 0, 0, } ,
1972 { 0, 0, 2, -2, 1, 0, -2, 2, 0, 0, 0, 0, 0, 0, } ,
1973 { 0, 0, 0, 0, 0, 0, 0, -4, 6, 0, 0, 0, 0, 2, } ,
1974 { 0, 0, 0, 0, 0, 0, 0, 4, -6, 0, 0, 0, 0, 0, } ,
1975 { 0, 0, 0, 0, 1, 0, 3, -4, 0, 0, 0, 0, 0, 0, } ,
1976 { 0, 0, 0, 0, 0, 0, 0, -1, 0, 2, 0, 0, 0, 2, } ,
1977 { 0, 0, 0, 0, 0, 0, 0, 1, 0, -2, 0, 0, 0, 0, } ,
1978 { 0, 0, 0, 0, 1, 0, 0, 1, 0, -1, 0, 0, 0, 0, } ,
1979 { 0, 0, 0, 0, 0, 0, -5, 9, 0, 0, 0, 0, 0, 2, } ,
1980 { 0, 0, 0, 0, 0, 0, 0, 3, -4, 0, 0, 0, 0, 0, } ,
1981 { 0, 0, 0, 0, 0, 0, -3, 4, 0, 0, 0, 0, 0, 2, } ,
1982 { 0, 0, 0, 0, 0, 0, -3, 4, 0, 0, 0, 0, 0, 1, } ,
1983 { 0, 0, 0, 0, 0, 0, 3, -4, 0, 0, 0, 0, 0, 0, } ,
1984 { 0, 0, 0, 0, 0, 0, 3, -4, 0, 0, 0, 0, 0, 1, } ,
1985 { 0, 0, 0, 0, 1, 0, 0, 2, -2, 0, 0, 0, 0, 0, } ,
1986 { 0, 0, 0, 0, 1, 0, 0, -1, 0, 2, 0, 0, 0, 0, } ,
1987 { 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, -3, 0, 0, 0, } ,
1988 { 0, 0, 0, 0, 0, 0, 0, 1, 0, 1, -5, 0, 0, 0, } ,
1989 { 0, 0, 0, 0, 0, 0, 0, -1, 0, 1, 0, 0, 0, 1, } ,
1990 { 0, 0, 0, 0, 0, 0, 0, 1, 0, -1, 0, 0, 0, 0, } ,
1991 { 0, 0, 0, 0, 0, 0, 0, 1, 0, -1, 0, 0, 0, 1, } ,
1992 { 0, 0, 0, 0, 0, 0, 0, 1, 0, -3, 5, 0, 0, 0, } ,
1993 { 0, 0, 0, 0, 1, 0, -3, 4, 0, 0, 0, 0, 0, 0, } ,
1994 { 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, -2, 0, 0, 0, } ,
1995 { 0, 0, 0, 0, 0, 0, 0, 2, -2, 0, 0, 0, 0, 0, } ,
1996 { 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, -1, 0, 0, 0, } ,
1997 { 0, 0, 0, 0, 1, 0, 0, -1, 0, 1, 0, 0, 0, 0, } ,
1998 { 0, 0, 0, 0, 1, 0, 0, -2, 2, 0, 0, 0, 0, 0, } ,
1999 { 0, 0, 0, 0, 0, 0, -8, 14, 0, 0, 0, 0, 0, 2, } ,
2000 { 0, 0, 0, 0, 0, 0, 0, 1, 0, 2, -5, 0, 0, 0, } ,
2001 { 0, 0, 0, 0, 0, 0, 0, 5, -8, 3, 0, 0, 0, 0, } ,
2002 { 0, 0, 0, 0, 0, 0, 0, 5, -8, 3, 0, 0, 0, 2, } ,
2003 { 0, 0, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, 1, } ,
2004 { 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, } ,
2005 { 0, 0, 0, 0, 0, 0, 0, 3, -8, 3, 0, 0, 0, 0, } ,
2006 { 0, 0, 0, 0, 0, 0, 0, -3, 8, -3, 0, 0, 0, 2, } ,
2007 { 0, 0, 0, 0, 0, 0, 0, 1, 0, -2, 5, 0, 0, 2, } ,
2008 { 0, 0, 0, 0, 0, 0, -8, 12, 0, 0, 0, 0, 0, 2, } ,
2009 { 0, 0, 0, 0, 0, 0, -8, 12, 0, 0, 0, 0, 0, 0, } ,
2010 { 0, 0, 0, 0, 0, 0, 0, 1, 0, 1, -2, 0, 0, 0, } ,
2011 { 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 2, } ,
2012 { 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, } ,
2013 { 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 2, } ,
2014 { 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 2, 0, 0, 2, } ,
2015 { 0, 0, 2, -2, 1, 0, -5, 5, 0, 0, 0, 0, 0, 0, } ,
2016 { 0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, } ,
2017 { 0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 1, } ,
2018 { 0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 2, } ,
2019 { 0, 0, 0, 0, 0, 0, 3, -6, 0, 0, 0, 0, 0, 0, } ,
2020 { 0, 0, 0, 0, 0, 0, -3, 6, 0, 0, 0, 0, 0, 1, } ,
2021 { 0, 0, 0, 0, 0, 0, -3, 6, 0, 0, 0, 0, 0, 2, } ,
2022 { 0, 0, 0, 0, 0, 0, 0, -1, 4, 0, 0, 0, 0, 2, } ,
2023 { 0, 0, 0, 0, 0, 0, -5, 7, 0, 0, 0, 0, 0, 2, } ,
2024 { 0, 0, 0, 0, 0, 0, -5, 7, 0, 0, 0, 0, 0, 1, } ,
2025 { 0, 0, 1, -1, 1, 0, -5, 6, 0, 0, 0, 0, 0, 0, } ,
2026 { 0, 0, 0, 0, 0, 0, 5, -7, 0, 0, 0, 0, 0, 0, } ,
2027 { 0, 0, 2, -2, 1, 0, 0, -1, 0, 1, 0, 0, 0, 0, } ,
2028 { 0, 0, 0, 0, 0, 0, 0, -1, 0, 1, 0, 0, 0, 0, } ,
2029 { 0, 0, 0, 0, 0, -1, 0, 3, 0, 0, 0, 0, 0, 2, } ,
2030 { 0, 0, 0, 0, 0, 0, 0, 1, 0, 2, 0, 0, 0, 2, } ,
2031 { 0, 0, 0, 0, 0, 0, 0, -2, 6, 0, 0, 0, 0, 2, } ,
2032 { 0, 0, 0, 0, 1, 0, 2, -2, 0, 0, 0, 0, 0, 0, } ,
2033 { 0, 0, 0, 0, 0, 0, 0, -6, 9, 0, 0, 0, 0, 2, } ,
2034 { 0, 0, 0, 0, 0, 0, 0, 6, -9, 0, 0, 0, 0, 0, } ,
2035 { 0, 0, 0, 0, 0, 0, -2, 2, 0, 0, 0, 0, 0, 1, } ,
2036 { 0, 0, 1, -1, 1, 0, -2, 1, 0, 0, 0, 0, 0, 0, } ,
2037 { 0, 0, 0, 0, 0, 0, 2, -2, 0, 0, 0, 0, 0, 0, } ,
2038 { 0, 0, 0, 0, 0, 0, 2, -2, 0, 0, 0, 0, 0, 1, } ,
2039 { 0, 0, 0, 0, 0, 0, 0, 1, 0, 3, 0, 0, 0, 2, } ,
2040 { 0, 0, 0, 0, 0, 0, 0, -5, 7, 0, 0, 0, 0, 2, } ,
2041 { 0, 0, 0, 0, 0, 0, 0, 5, -7, 0, 0, 0, 0, 0, } ,
2042 { 0, 0, 0, 0, 1, 0, -2, 2, 0, 0, 0, 0, 0, 0, } ,
2043 { 0, 0, 0, 0, 0, 0, 0, 4, -5, 0, 0, 0, 0, 0, } ,
2044 { 0, 0, 0, 0, 0, 0, 1, -3, 0, 0, 0, 0, 0, 0, } ,
2045 { 0, 0, 0, 0, 0, 0, -1, 3, 0, 0, 0, 0, 0, 1, } ,
2046 { 0, 0, 1, -1, 1, 0, -1, 2, 0, 0, 0, 0, 0, 0, } ,
2047 { 0, 0, 0, 0, 0, 0, -1, 3, 0, 0, 0, 0, 0, 2, } ,
2048 { 0, 0, 0, 0, 0, 0, -7, 10, 0, 0, 0, 0, 0, 2, } ,
2049 { 0, 0, 0, 0, 0, 0, -7, 10, 0, 0, 0, 0, 0, 1, } ,
2050 { 0, 0, 0, 0, 0, 0, 0, 3, -3, 0, 0, 0, 0, 0, } ,
2051 { 0, 0, 0, 0, 0, 0, -4, 8, 0, 0, 0, 0, 0, 2, } ,
2052 { 0, 0, 0, 0, 0, 0, -4, 5, 0, 0, 0, 0, 0, 2, } ,
2053 { 0, 0, 0, 0, 0, 0, -4, 5, 0, 0, 0, 0, 0, 1, } ,
2054 { 0, 0, 0, 0, 0, 0, 4, -5, 0, 0, 0, 0, 0, 0, } ,
2055 { 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 2, } ,
2056 { 0, 0, 0, 0, 0, 0, 0, -2, 0, 5, 0, 0, 0, 2, } ,
2057 { 0, 0, 0, 0, 0, 0, 0, 0, 3, 0, 0, 0, 0, 2, } ,
2058 { 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, } ,
2059 { 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 2, } ,
2060 { 0, 0, 0, 0, 0, 0, -9, 13, 0, 0, 0, 0, 0, 2, } ,
2061 { 0, 0, 0, 0, 0, 0, 0, -1, 5, 0, 0, 0, 0, 2, } ,
2062 { 0, 0, 0, 0, 0, 0, 0, -2, 0, 4, 0, 0, 0, 2, } ,
2063 { 0, 0, 0, 0, 0, 0, 0, 2, 0, -4, 0, 0, 0, 0, } ,
2064 { 0, 0, 0, 0, 0, 0, 0, -2, 7, 0, 0, 0, 0, 2, } ,
2065 { 0, 0, 0, 0, 0, 0, 0, 2, 0, -3, 0, 0, 0, 0, } ,
2066 { 0, 0, 0, 0, 0, 0, -2, 5, 0, 0, 0, 0, 0, 1, } ,
2067 { 0, 0, 0, 0, 0, 0, -2, 5, 0, 0, 0, 0, 0, 2, } ,
2068 { 0, 0, 0, 0, 0, 0, -6, 8, 0, 0, 0, 0, 0, 2, } ,
2069 { 0, 0, 0, 0, 0, 0, -6, 8, 0, 0, 0, 0, 0, 1, } ,
2070 { 0, 0, 0, 0, 0, 0, 6, -8, 0, 0, 0, 0, 0, 0, } ,
2071 { 0, 0, 0, 0, 1, 0, 0, 2, 0, -2, 0, 0, 0, 0, } ,
2072 { 0, 0, 0, 0, 0, 0, 0, -3, 9, 0, 0, 0, 0, 2, } ,
2073 { 0, 0, 0, 0, 0, 0, 0, 5, -6, 0, 0, 0, 0, 0, } ,
2074 { 0, 0, 0, 0, 0, 0, 0, 5, -6, 0, 0, 0, 0, 2, } ,
2075 { 0, 0, 0, 0, 0, 0, 0, 2, 0, -2, 0, 0, 0, 0, } ,
2076 { 0, 0, 0, 0, 0, 0, 0, 2, 0, -2, 0, 0, 0, 1, } ,
2077 { 0, 0, 0, 0, 0, 0, 0, 2, 0, -2, 0, 0, 0, 2, } ,
2078 { 0, 0, 0, 0, 0, 0, -5, 10, 0, 0, 0, 0, 0, 2, } ,
2079 { 0, 0, 0, 0, 0, 0, 0, 4, -4, 0, 0, 0, 0, 0, } ,
2080 { 0, 0, 0, 0, 0, 0, 0, 4, -4, 0, 0, 0, 0, 2, } ,
2081 { 0, 0, 0, 0, 0, 0, -3, 3, 0, 0, 0, 0, 0, 1, } ,
2082 { 0, 0, 0, 0, 0, 0, 3, -3, 0, 0, 0, 0, 0, 0, } ,
2083 { 0, 0, 0, 0, 0, 0, 3, -3, 0, 0, 0, 0, 0, 1, } ,
2084 { 0, 0, 0, 0, 0, 0, 3, -3, 0, 0, 0, 0, 0, 2, } ,
2085 { 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, -3, 0, 0, 0, } ,
2086 { 0, 0, 0, 0, 0, 0, 0, -5, 13, 0, 0, 0, 0, 2, } ,
2087 { 0, 0, 0, 0, 0, 0, 0, 2, 0, -1, 0, 0, 0, 0, } ,
2088 { 0, 0, 0, 0, 0, 0, 0, 2, 0, -1, 0, 0, 0, 2, } ,
2089 { 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, -2, 0, 0, 0, } ,
2090 { 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, -2, 0, 0, 1, } ,
2091 { 0, 0, 0, 0, 0, 0, 0, 3, -2, 0, 0, 0, 0, 0, } ,
2092 { 0, 0, 0, 0, 0, 0, 0, 3, -2, 0, 0, 0, 0, 2, } ,
2093 { 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, -1, 0, 0, 2, } ,
2094 { 0, 0, 0, 0, 0, 0, 0, -6, 15, 0, 0, 0, 0, 2, } ,
2095 { 0, 0, 0, 0, 0, 0, -8, 15, 0, 0, 0, 0, 0, 2, } ,
2096 { 0, 0, 0, 0, 0, 0, -3, 9, -4, 0, 0, 0, 0, 2, } ,
2097 { 0, 0, 0, 0, 0, 0, 0, 2, 0, 2, -5, 0, 0, 2, } ,
2098 { 0, 0, 0, 0, 0, 0, 0, -2, 8, -1, -5, 0, 0, 2, } ,
2099 { 0, 0, 0, 0, 0, 0, 0, 6, -8, 3, 0, 0, 0, 2, } ,
2100 { 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, } ,
2101 { 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, } ,
2102 { 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 1, } ,
2103 { 0, 0, 1, -1, 1, 0, 0, 1, 0, 0, 0, 0, 0, 0, } ,
2104 { 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 1, } ,
2105 { 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 2, } ,
2106 { 0, 0, 0, 0, 0, 0, 0, -6, 16, -4, -5, 0, 0, 2, } ,
2107 { 0, 0, 0, 0, 0, 0, 0, -2, 8, -3, 0, 0, 0, 2, } ,
2108 { 0, 0, 0, 0, 0, 0, 0, -2, 8, -3, 0, 0, 0, 2, } ,
2109 { 0, 0, 0, 0, 0, 0, 0, 6, -8, 1, 5, 0, 0, 2, } ,
2110 { 0, 0, 0, 0, 0, 0, 0, 2, 0, -2, 5, 0, 0, 2, } ,
2111 { 0, 0, 0, 0, 0, 0, 3, -5, 4, 0, 0, 0, 0, 2, } ,
2112 { 0, 0, 0, 0, 0, 0, -8, 11, 0, 0, 0, 0, 0, 2, } ,
2113 { 0, 0, 0, 0, 0, 0, -8, 11, 0, 0, 0, 0, 0, 1, } ,
2114 { 0, 0, 0, 0, 0, 0, -8, 11, 0, 0, 0, 0, 0, 2, } ,
2115 { 0, 0, 0, 0, 0, 0, 0, 11, 0, 0, 0, 0, 0, 2, } ,
2116 { 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 1, 0, 0, 2, } ,
2117 { 0, 0, 0, 0, 0, 0, 3, -3, 0, 2, 0, 0, 0, 2, } ,
2118 { 0, 0, 2, -2, 1, 0, 0, 4, -8, 3, 0, 0, 0, 0, } ,
2119 { 0, 0, 1, -1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, } ,
2120 { 0, 0, 2, -2, 1, 0, 0, -4, 8, -3, 0, 0, 0, 0, } ,
2121 { 0, 0, 0, 0, 0, 0, 0, 1, 2, 0, 0, 0, 0, 2, } ,
2122 { 0, 0, 0, 0, 0, 0, 0, 2, 0, 1, 0, 0, 0, 2, } ,
2123 { 0, 0, 0, 0, 0, 0, -3, 7, 0, 0, 0, 0, 0, 2, } ,
2124 { 0, 0, 0, 0, 0, 0, 0, 0, 4, 0, 0, 0, 0, 2, } ,
2125 { 0, 0, 0, 0, 0, 0, -5, 6, 0, 0, 0, 0, 0, 2, } ,
2126 { 0, 0, 0, 0, 0, 0, -5, 6, 0, 0, 0, 0, 0, 1, } ,
2127 { 0, 0, 0, 0, 0, 0, 5, -6, 0, 0, 0, 0, 0, 0, } ,
2128 { 0, 0, 0, 0, 0, 0, 5, -6, 0, 0, 0, 0, 0, 2, } ,
2129 { 0, 0, 0, 0, 0, 0, 0, 2, 0, 2, 0, 0, 0, 2, } ,
2130 { 0, 0, 0, 0, 0, 0, 0, -1, 6, 0, 0, 0, 0, 2, } ,
2131 { 0, 0, 0, 0, 0, 0, 0, 7, -9, 0, 0, 0, 0, 2, } ,
2132 { 0, 0, 0, 0, 0, 0, 2, -1, 0, 0, 0, 0, 0, 0, } ,
2133 { 0, 0, 0, 0, 0, 0, 2, -1, 0, 0, 0, 0, 0, 2, } ,
2134 { 0, 0, 0, 0, 0, 0, 0, 6, -7, 0, 0, 0, 0, 2, } ,
2135 { 0, 0, 0, 0, 0, 0, 0, 5, -5, 0, 0, 0, 0, 2, } ,
2136 { 0, 0, 0, 0, 0, 0, -1, 4, 0, 0, 0, 0, 0, 1, } ,
2137 { 0, 0, 0, 0, 0, 0, -1, 4, 0, 0, 0, 0, 0, 2, } ,
2138 { 0, 0, 0, 0, 0, 0, -7, 9, 0, 0, 0, 0, 0, 2, } ,
2139 { 0, 0, 0, 0, 0, 0, -7, 9, 0, 0, 0, 0, 0, 1, } ,
2140 { 0, 0, 0, 0, 0, 0, 0, 4, -3, 0, 0, 0, 0, 2, } ,
2141 { 0, 0, 0, 0, 0, 0, 0, 3, -1, 0, 0, 0, 0, 2, } ,
2142 { 0, 0, 0, 0, 0, 0, -4, 4, 0, 0, 0, 0, 0, 1, } ,
2143 { 0, 0, 0, 0, 0, 0, 4, -4, 0, 0, 0, 0, 0, 0, } ,
2144 { 0, 0, 0, 0, 0, 0, 4, -4, 0, 0, 0, 0, 0, 1, } ,
2145 { 0, 0, 0, 0, 0, 0, 4, -4, 0, 0, 0, 0, 0, 2, } ,
2146 { 0, 0, 0, 0, 0, 0, 0, 2, 1, 0, 0, 0, 0, 2, } ,
2147 { 0, 0, 0, 0, 0, 0, 0, -3, 0, 5, 0, 0, 0, 2, } ,
2148 { 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, } ,
2149 { 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 1, } ,
2150 { 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 2, } ,
2151 { 0, 0, 0, 0, 0, 0, -9, 12, 0, 0, 0, 0, 0, 2, } ,
2152 { 0, 0, 0, 0, 0, 0, 0, 3, 0, -4, 0, 0, 0, 0, } ,
2153 { 0, 0, 2, -2, 1, 0, 1, -1, 0, 0, 0, 0, 0, 0, } ,
2154 { 0, 0, 0, 0, 0, 0, 0, 7, -8, 0, 0, 0, 0, 2, } ,
2155 { 0, 0, 0, 0, 0, 0, 0, 3, 0, -3, 0, 0, 0, 0, } ,
2156 { 0, 0, 0, 0, 0, 0, 0, 3, 0, -3, 0, 0, 0, 2, } ,
2157 { 0, 0, 0, 0, 0, 0, -2, 6, 0, 0, 0, 0, 0, 2, } ,
2158 { 0, 0, 0, 0, 0, 0, -6, 7, 0, 0, 0, 0, 0, 1, } ,
2159 { 0, 0, 0, 0, 0, 0, 6, -7, 0, 0, 0, 0, 0, 0, } ,
2160 { 0, 0, 0, 0, 0, 0, 0, 6, -6, 0, 0, 0, 0, 2, } ,
2161 { 0, 0, 0, 0, 0, 0, 0, 3, 0, -2, 0, 0, 0, 0, } ,
2162 { 0, 0, 0, 0, 0, 0, 0, 3, 0, -2, 0, 0, 0, 2, } ,
2163 { 0, 0, 0, 0, 0, 0, 0, 5, -4, 0, 0, 0, 0, 2, } ,
2164 { 0, 0, 0, 0, 0, 0, 3, -2, 0, 0, 0, 0, 0, 0, } ,
2165 { 0, 0, 0, 0, 0, 0, 3, -2, 0, 0, 0, 0, 0, 2, } ,
2166 { 0, 0, 0, 0, 0, 0, 0, 3, 0, -1, 0, 0, 0, 2, } ,
2167 { 0, 0, 0, 0, 0, 0, 0, 3, 0, -1, 0, 0, 0, 2, } ,
2168 { 0, 0, 0, 0, 0, 0, 0, 3, 0, 0, -2, 0, 0, 2, } ,
2169 { 0, 0, 0, 0, 0, 0, 0, 4, -2, 0, 0, 0, 0, 2, } ,
2170 { 0, 0, 0, 0, 0, 0, 0, 3, 0, 0, -1, 0, 0, 2, } ,
2171 { 0, 0, 2, -2, 1, 0, 0, 1, 0, -1, 0, 0, 0, 0, } ,
2172 { 0, 0, 0, 0, 0, 0, -8, 16, 0, 0, 0, 0, 0, 2, } ,
2173 { 0, 0, 0, 0, 0, 0, 0, 3, 0, 2, -5, 0, 0, 2, } ,
2174 { 0, 0, 0, 0, 0, 0, 0, 7, -8, 3, 0, 0, 0, 2, } ,
2175 { 0, 0, 0, 0, 0, 0, 0, -5, 16, -4, -5, 0, 0, 2, } ,
2176 { 0, 0, 0, 0, 0, 0, 0, 3, 0, 0, 0, 0, 0, 2, } ,
2177 { 0, 0, 0, 0, 0, 0, 0, -1, 8, -3, 0, 0, 0, 2, } ,
2178 { 0, 0, 0, 0, 0, 0, -8, 10, 0, 0, 0, 0, 0, 2, } ,
2179 { 0, 0, 0, 0, 0, 0, -8, 10, 0, 0, 0, 0, 0, 1, } ,
2180 { 0, 0, 0, 0, 0, 0, -8, 10, 0, 0, 0, 0, 0, 2, } ,
2181 { 0, 0, 0, 0, 0, 0, 0, 2, 2, 0, 0, 0, 0, 2, } ,
2182 { 0, 0, 0, 0, 0, 0, 0, 3, 0, 1, 0, 0, 0, 2, } ,
2183 { 0, 0, 0, 0, 0, 0, -3, 8, 0, 0, 0, 0, 0, 2, } ,
2184 { 0, 0, 0, 0, 0, 0, -5, 5, 0, 0, 0, 0, 0, 1, } ,
2185 { 0, 0, 0, 0, 0, 0, 5, -5, 0, 0, 0, 0, 0, 0, } ,
2186 { 0, 0, 0, 0, 0, 0, 5, -5, 0, 0, 0, 0, 0, 1, } ,
2187 { 0, 0, 0, 0, 0, 0, 5, -5, 0, 0, 0, 0, 0, 2, } ,
2188 { 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, } ,
2189 { 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 1, } ,
2190 { 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 2, } ,
2191 { 0, 0, 0, 0, 0, 0, 0, 7, -7, 0, 0, 0, 0, 2, } ,
2192 { 0, 0, 0, 0, 0, 0, 0, 7, -7, 0, 0, 0, 0, 2, } ,
2193 { 0, 0, 0, 0, 0, 0, 0, 6, -5, 0, 0, 0, 0, 2, } ,
2194 { 0, 0, 0, 0, 0, 0, 7, -8, 0, 0, 0, 0, 0, 0, } ,
2195 { 0, 0, 0, 0, 0, 0, 0, 5, -3, 0, 0, 0, 0, 2, } ,
2196 { 0, 0, 0, 0, 0, 0, 4, -3, 0, 0, 0, 0, 0, 2, } ,
2197 { 0, 0, 0, 0, 0, 0, 1, 2, 0, 0, 0, 0, 0, 2, } ,
2198 { 0, 0, 0, 0, 0, 0, -9, 11, 0, 0, 0, 0, 0, 2, } ,
2199 { 0, 0, 0, 0, 0, 0, -9, 11, 0, 0, 0, 0, 0, 1, } ,
2200 { 0, 0, 0, 0, 0, 0, 0, 4, 0, -4, 0, 0, 0, 2, } ,
2201 { 0, 0, 0, 0, 0, 0, 0, 4, 0, -3, 0, 0, 0, 2, } ,
2202 { 0, 0, 0, 0, 0, 0, -6, 6, 0, 0, 0, 0, 0, 1, } ,
2203 { 0, 0, 0, 0, 0, 0, 6, -6, 0, 0, 0, 0, 0, 0, } ,
2204 { 0, 0, 0, 0, 0, 0, 6, -6, 0, 0, 0, 0, 0, 1, } ,
2205 { 0, 0, 0, 0, 0, 0, 0, 4, 0, -2, 0, 0, 0, 2, } ,
2206 { 0, 0, 0, 0, 0, 0, 0, 6, -4, 0, 0, 0, 0, 2, } ,
2207 { 0, 0, 0, 0, 0, 0, 3, -1, 0, 0, 0, 0, 0, 0, } ,
2208 { 0, 0, 0, 0, 0, 0, 3, -1, 0, 0, 0, 0, 0, 1, } ,
2209 { 0, 0, 0, 0, 0, 0, 3, -1, 0, 0, 0, 0, 0, 2, } ,
2210 { 0, 0, 0, 0, 0, 0, 0, 4, 0, -1, 0, 0, 0, 2, } ,
2211 { 0, 0, 0, 0, 0, 0, 0, 4, 0, 0, -2, 0, 0, 2, } ,
2212 { 0, 0, 0, 0, 0, 0, 0, 5, -2, 0, 0, 0, 0, 2, } ,
2213 { 0, 0, 0, 0, 0, 0, 0, 4, 0, 0, 0, 0, 0, 0, } ,
2214 { 0, 0, 0, 0, 0, 0, 8, -9, 0, 0, 0, 0, 0, 0, } ,
2215 { 0, 0, 0, 0, 0, 0, 5, -4, 0, 0, 0, 0, 0, 2, } ,
2216 { 0, 0, 0, 0, 0, 0, 2, 1, 0, 0, 0, 0, 0, 2, } ,
2217 { 0, 0, 0, 0, 0, 0, 2, 1, 0, 0, 0, 0, 0, 1, } ,
2218 { 0, 0, 0, 0, 0, 0, 2, 1, 0, 0, 0, 0, 0, 1, } ,
2219 { 0, 0, 0, 0, 0, 0, -7, 7, 0, 0, 0, 0, 0, 1, } ,
2220 { 0, 0, 0, 0, 0, 0, 7, -7, 0, 0, 0, 0, 0, 0, } ,
2221 { 0, 0, 0, 0, 0, 0, 4, -2, 0, 0, 0, 0, 0, 1, } ,
2222 { 0, 0, 0, 0, 0, 0, 4, -2, 0, 0, 0, 0, 0, 2, } ,
2223 { 0, 0, 0, 0, 0, 0, 4, -2, 0, 0, 0, 0, 0, 0, } ,
2224 { 0, 0, 0, 0, 0, 0, 4, -2, 0, 0, 0, 0, 0, 0, } ,
2225 { 0, 0, 0, 0, 0, 0, 0, 5, 0, -4, 0, 0, 0, 2, } ,
2226 { 0, 0, 0, 0, 0, 0, 0, 5, 0, -3, 0, 0, 0, 2, } ,
2227 { 0, 0, 0, 0, 0, 0, 0, 5, 0, -2, 0, 0, 0, 2, } ,
2228 { 0, 0, 0, 0, 0, 0, 3, 0, 0, 0, 0, 0, 0, 2, } ,
2229 { 0, 0, 0, 0, 0, 0, -8, 8, 0, 0, 0, 0, 0, 1, } ,
2230 { 0, 0, 0, 0, 0, 0, 8, -8, 0, 0, 0, 0, 0, 0, } ,
2231 { 0, 0, 0, 0, 0, 0, 5, -3, 0, 0, 0, 0, 0, 1, } ,
2232 { 0, 0, 0, 0, 0, 0, 5, -3, 0, 0, 0, 0, 0, 2, } ,
2233 { 0, 0, 0, 0, 0, 0, -9, 9, 0, 0, 0, 0, 0, 1, } ,
2234 { 0, 0, 0, 0, 0, 0, -9, 9, 0, 0, 0, 0, 0, 1, } ,
2235 { 0, 0, 0, 0, 0, 0, -9, 9, 0, 0, 0, 0, 0, 1, } ,
2236 { 0, 0, 0, 0, 0, 0, 9, -9, 0, 0, 0, 0, 0, 0, } ,
2237 { 0, 0, 0, 0, 0, 0, 6, -4, 0, 0, 0, 0, 0, 1, } ,
2238 { 0, 0, 0, 0, 0, 0, 0, 6, 0, 0, 0, 0, 0, 2, } ,
2239 { 0, 0, 0, 0, 0, 0, 0, 6, 0, 0, 0, 0, 0, 0, } ,
2240 { 0, 0, 0, 0, 0, 0, 0, 6, 0, 0, 0, 0, 0, 0, } ,
2241 { 0, 0, 0, 0, 0, 0, 0, 6, 0, 0, 0, 0, 0, 1, } ,
2242 { 0, 0, 0, 0, 0, 0, 0, 6, 0, 0, 0, 0, 0, 2, } ,
2243 { 0, 0, 0, 0, 0, 0, 0, 6, 0, 0, 0, 0, 0, 0, } ,
2244 { 0, 0, 0, 0, 0, 0, 0, 6, 0, 0, 0, 0, 0, 1, } ,
2245 { 0, 0, 0, 0, 0, 0, 0, 6, 0, 0, 0, 0, 0, 2, } ,
2246 { 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, } ,
2247 { 1, 0, 0, -2, 0, 0, 0, 2, 0, -2, 0, 0, 0, 0, } ,
2248 { 1, 0, 0, -2, 0, 0, 2, -2, 0, 0, 0, 0, 0, 0, } ,
2249 { 1, 0, 0, -2, 0, 0, 0, 1, 0, -1, 0, 0, 0, 0, } ,
2250 { 1, 0, 0, -2, 0, 0, 1, -1, 0, 0, 0, 0, 0, 0, } ,
2251 { -1, 0, 0, 0, 0, 0, 3, -3, 0, 0, 0, 0, 0, 0, } ,
2252 { -1, 0, 0, 0, 0, 0, 0, 2, 0, -2, 0, 0, 0, 0, } ,
2253 { -1, 0, 0, 2, 0, 0, 0, 4, -8, 3, 0, 0, 0, 0, } ,
2254 { 1, 0, 0, -2, 0, 0, 0, 4, -8, 3, 0, 0, 0, 0, } ,
2255 { -2, 0, 0, 2, 0, 0, 0, 4, -8, 3, 0, 0, 0, 0, } ,
2256 { -1, 0, 0, 0, 0, 0, 0, 2, 0, -3, 0, 0, 0, 0, } ,
2257 { -1, 0, 0, 0, 0, 0, 0, 1, 0, -1, 0, 0, 0, 0, } ,
2258 { -1, 0, 0, 0, 0, 0, 1, -1, 0, 0, 0, 0, 0, 0, } ,
2259 { -1, 0, 0, 2, 0, 0, 2, -2, 0, 0, 0, 0, 0, 0, } ,
2260 { 1, 0, -1, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, } ,
2261 { -1, 0, 0, 2, 0, 0, 0, 2, 0, -3, 0, 0, 0, 0, } ,
2262 { -2, 0, 0, 0, 0, 0, 0, 2, 0, -3, 0, 0, 0, 0, } ,
2263 { 1, 0, 0, 0, 0, 0, 0, 4, -8, 3, 0, 0, 0, 0, } ,
2264 { -1, 0, 1, -1, 1, 0, 0, -1, 0, 0, 0, 0, 0, 0, } ,
2265 { 1, 0, 1, -1, 1, 0, 0, -1, 0, 0, 0, 0, 0, 0, } ,
2266 { -1, 0, 0, 0, 0, 0, 0, 4, -8, 3, 0, 0, 0, 0, } ,
2267 { -1, 0, 0, 2, 1, 0, 0, 2, 0, -2, 0, 0, 0, 0, } ,
2268 { 0, 0, 0, 0, 0, 0, 0, 2, 0, -2, 0, 0, 0, 0, } ,
2269 { -1, 0, 0, 2, 0, 0, 0, 2, 0, -2, 0, 0, 0, 0, } ,
2270 { -1, 0, 0, 2, 0, 0, 3, -3, 0, 0, 0, 0, 0, 0, } ,
2271 { 1, 0, 0, -2, 1, 0, 0, -2, 0, 2, 0, 0, 0, 0, } ,
2272 { 1, 0, 2, -2, 2, 0, -3, 3, 0, 0, 0, 0, 0, 0, } ,
2273 { 1, 0, 2, -2, 2, 0, 0, -2, 0, 2, 0, 0, 0, 0, } ,
2274 { 1, 0, 0, 0, 0, 0, 1, -1, 0, 0, 0, 0, 0, 0, } ,
2275 { 1, 0, 0, 0, 0, 0, 0, 1, 0, -1, 0, 0, 0, 0, } ,
2276 { 0, 0, 0, -2, 0, 0, 2, -2, 0, 0, 0, 0, 0, 0, } ,
2277 { 0, 0, 0, -2, 0, 0, 0, 1, 0, -1, 0, 0, 0, 0, } ,
2278 { 0, 0, 2, 0, 2, 0, -2, 2, 0, 0, 0, 0, 0, 0, } ,
2279 { 0, 0, 2, 0, 2, 0, 0, -1, 0, 1, 0, 0, 0, 0, } ,
2280 { 0, 0, 2, 0, 2, 0, -1, 1, 0, 0, 0, 0, 0, 0, } ,
2281 { 0, 0, 2, 0, 2, 0, -2, 3, 0, 0, 0, 0, 0, 0, } ,
2282 { 0, 0, 0, 2, 0, 0, 0, 2, 0, -2, 0, 0, 0, 0, } ,
2283 { 0, 0, 1, 1, 2, 0, 0, 1, 0, 0, 0, 0, 0, 0, } ,
2284 { 1, 0, 2, 0, 2, 0, 0, 1, 0, 0, 0, 0, 0, 0, } ,
2285 { -1, 0, 2, 0, 2, 0, 10, -3, 0, 0, 0, 0, 0, 0, } ,
2286 { 0, 0, 1, 1, 1, 0, 0, 1, 0, 0, 0, 0, 0, 0, } ,
2287 { 1, 0, 2, 0, 2, 0, 0, 1, 0, 0, 0, 0, 0, 0, } ,
2288 { 0, 0, 2, 0, 2, 0, 0, 4, -8, 3, 0, 0, 0, 0, } ,
2289 { 0, 0, 2, 0, 2, 0, 0, -4, 8, -3, 0, 0, 0, 0, } ,
2290 { -1, 0, 2, 0, 2, 0, 0, -4, 8, -3, 0, 0, 0, 0, } ,
2291 { 2, 0, 2, -2, 2, 0, 0, -2, 0, 3, 0, 0, 0, 0, } ,
2292 { 1, 0, 2, 0, 1, 0, 0, -2, 0, 3, 0, 0, 0, 0, } ,
2293 { 0, 0, 1, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, } ,
2294 { -1, 0, 2, 0, 1, 0, 0, 1, 0, 0, 0, 0, 0, 0, } ,
2295 { -2, 0, 2, 2, 2, 0, 0, 2, 0, -2, 0, 0, 0, 0, } ,
2296 { 0, 0, 2, 0, 2, 0, 2, -3, 0, 0, 0, 0, 0, 0, } ,
2297 { 0, 0, 2, 0, 2, 0, 1, -1, 0, 0, 0, 0, 0, 0, } ,
2298 { 0, 0, 2, 0, 2, 0, 0, 1, 0, -1, 0, 0, 0, 0, } ,
2299 { 0, 0, 2, 0, 2, 0, 2, -2, 0, 0, 0, 0, 0, 0, } ,
2300 { -1, 0, 2, 2, 2, 0, 0, -1, 0, 1, 0, 0, 0, 0, } ,
2301 { 1, 0, 2, 0, 2, 0, -1, 1, 0, 0, 0, 0, 0, 0, } ,
2302 { -1, 0, 2, 2, 2, 0, 0, 2, 0, -3, 0, 0, 0, 0, } ,
2303 { 2, 0, 2, 0, 2, 0, 0, 2, 0, -3, 0, 0, 0, 0, } ,
2304 { 1, 0, 2, 0, 2, 0, 0, -4, 8, -3, 0, 0, 0, 0, } ,
2305 { 1, 0, 2, 0, 2, 0, 0, 4, -8, 3, 0, 0, 0, 0, } ,
2306 { 1, 0, 1, 1, 1, 0, 0, 1, 0, 0, 0, 0, 0, 0, } ,
2307 { 0, 0, 2, 0, 2, 0, 0, 1, 0, 0, 0, 0, 0, 0, } ,
2308 { 2, 0, 2, 0, 1, 0, 0, 1, 0, 0, 0, 0, 0, 0, } ,
2309 { -1, 0, 2, 2, 2, 0, 0, 2, 0, -2, 0, 0, 0, 0, } ,
2310 { -1, 0, 2, 2, 2, 0, 3, -3, 0, 0, 0, 0, 0, 0, } ,
2311 { 1, 0, 2, 0, 2, 0, 1, -1, 0, 0, 0, 0, 0, 0, } ,
2312 { 0, 0, 2, 2, 2, 0, 0, 2, 0, -2, 0, 0, 0, 0, } ,
2313 } ;
2314
2315 /*
2316 * Longitude and obliquity coefficients
2317 */
2318
2319 static const int ICPL[ NPL ][4] = {
2320
2321 /*
2322 * Planetary nutation coefficients, unit 1e-7 arcsec
2323 * longitude (sin, cos), obliquity (sin, cos)
2324 */
2325
2326 { 1440, 0, 0, 0, } ,
2327 { 56, -117, -42, -40, } ,
2328 { 125, -43, 0, -54, } ,
2329 { 0, 5, 0, 0, } ,
2330 { 3, -7, -3, 0, } ,
2331 { 3, 0, 0, -2, } ,
2332 { -114, 0, 0, 61, } ,
2333 { -219, 89, 0, 0, } ,
2334 { -3, 0, 0, 0, } ,
2335 { -462, 1604, 0, 0, } ,
2336 { 99, 0, 0, -53, } ,
2337 { -3, 0, 0, 2, } ,
2338 { 0, 6, 2, 0, } ,
2339 { 3, 0, 0, 0, } ,
2340 { -12, 0, 0, 0, } ,
2341 { 14, -218, 117, 8, } ,
2342 { 31, -481, -257, -17, } ,
2343 { -491, 128, 0, 0, } ,
2344 { -3084, 5123, 2735, 1647, } ,
2345 { -1444, 2409, -1286, -771, } ,
2346 { 11, -24, -11, -9, } ,
2347 { 26, -9, 0, 0, } ,
2348 { 103, -60, 0, 0, } ,
2349 { 0, -13, -7, 0, } ,
2350 { -26, -29, -16, 14, } ,
2351 { 9, -27, -14, -5, } ,
2352 { 12, 0, 0, -6, } ,
2353 { -7, 0, 0, 0, } ,
2354 { 0, 24, 0, 0, } ,
2355 { 284, 0, 0, -151, } ,
2356 { 226, 101, 0, 0, } ,
2357 { 0, -8, -2, 0, } ,
2358 { 0, -6, -3, 0, } ,
2359 { 5, 0, 0, -3, } ,
2360 { -41, 175, 76, 17, } ,
2361 { 0, 15, 6, 0, } ,
2362 { 425, 212, -133, 269, } ,
2363 { 1200, 598, 319, -641, } ,
2364 { 235, 334, 0, 0, } ,
2365 { 11, -12, -7, -6, } ,
2366 { 5, -6, 3, 3, } ,
2367 { -5, 0, 0, 3, } ,
2368 { 6, 0, 0, -3, } ,
2369 { 15, 0, 0, 0, } ,
2370 { 13, 0, 0, -7, } ,
2371 { -6, -9, 0, 0, } ,
2372 { 266, -78, 0, 0, } ,
2373 { -460, -435, -232, 246, } ,
2374 { 0, 15, 7, 0, } ,
2375 { -3, 0, 0, 2, } ,
2376 { 0, 131, 0, 0, } ,
2377 { 4, 0, 0, 0, } ,
2378 { 0, 3, 0, 0, } ,
2379 { 0, 4, 2, 0, } ,
2380 { 0, 3, 0, 0, } ,
2381 { -17, -19, -10, 9, } ,
2382 { -9, -11, 6, -5, } ,
2383 { -6, 0, 0, 3, } ,
2384 { -16, 8, 0, 0, } ,
2385 { 0, 3, 0, 0, } ,
2386 { 11, 24, 11, -5, } ,
2387 { -3, -4, -2, 1, } ,
2388 { 3, 0, 0, -1, } ,
2389 { 0, -8, -4, 0, } ,
2390 { 0, 3, 0, 0, } ,
2391 { 0, 5, 0, 0, } ,
2392 { 0, 3, 2, 0, } ,
2393 { -6, 4, 2, 3, } ,
2394 { -3, -5, 0, 0, } ,
2395 { -5, 0, 0, 2, } ,
2396 { 4, 24, 13, -2, } ,
2397 { -42, 20, 0, 0, } ,
2398 { -10, 233, 0, 0, } ,
2399 { -3, 0, 0, 1, } ,
2400 { 78, -18, 0, 0, } ,
2401 { 0, 3, 1, 0, } ,
2402 { 0, -3, -1, 0, } ,
2403 { 0, -4, -2, 1, } ,
2404 { 0, -8, -4, -1, } ,
2405 { 0, -5, 3, 0, } ,
2406 { -7, 0, 0, 3, } ,
2407 { -14, 8, 3, 6, } ,
2408 { 0, 8, -4, 0, } ,
2409 { 0, 19, 10, 0, } ,
2410 { 45, -22, 0, 0, } ,
2411 { -3, 0, 0, 0, } ,
2412 { 0, -3, 0, 0, } ,
2413 { 0, 3, 0, 0, } ,
2414 { 3, 5, 3, -2, } ,
2415 { 89, -16, -9, -48, } ,
2416 { 0, 3, 0, 0, } ,
2417 { -3, 7, 4, 2, } ,
2418 { -349, -62, 0, 0, } ,
2419 { -15, 22, 0, 0, } ,
2420 { -3, 0, 0, 0, } ,
2421 { -53, 0, 0, 0, } ,
2422 { 5, 0, 0, -3, } ,
2423 { 0, -8, 0, 0, } ,
2424 { 15, -7, -4, -8, } ,
2425 { -3, 0, 0, 1, } ,
2426 { -21, -78, 0, 0, } ,
2427 { 20, -70, -37, -11, } ,
2428 { 0, 6, 3, 0, } ,
2429 { 5, 3, 2, -2, } ,
2430 { -17, -4, -2, 9, } ,
2431 { 0, 6, 3, 0, } ,
2432 { 32, 15, -8, 17, } ,
2433 { 174, 84, 45, -93, } ,
2434 { 11, 56, 0, 0, } ,
2435 { -66, -12, -6, 35, } ,
2436 { 47, 8, 4, -25, } ,
2437 { 0, 8, 4, 0, } ,
2438 { 10, -22, -12, -5, } ,
2439 { -3, 0, 0, 2, } ,
2440 { -24, 12, 0, 0, } ,
2441 { 5, -6, 0, 0, } ,
2442 { 3, 0, 0, -2, } ,
2443 { 4, 3, 1, -2, } ,
2444 { 0, 29, 15, 0, } ,
2445 { -5, -4, -2, 2, } ,
2446 { 8, -3, -1, -5, } ,
2447 { 0, -3, 0, 0, } ,
2448 { 10, 0, 0, 0, } ,
2449 { 3, 0, 0, -2, } ,
2450 { -5, 0, 0, 3, } ,
2451 { 46, 66, 35, -25, } ,
2452 { -14, 7, 0, 0, } ,
2453 { 0, 3, 2, 0, } ,
2454 { -5, 0, 0, 0, } ,
2455 { -68, -34, -18, 36, } ,
2456 { 0, 14, 7, 0, } ,
2457 { 10, -6, -3, -5, } ,
2458 { -5, -4, -2, 3, } ,
2459 { -3, 5, 2, 1, } ,
2460 { 76, 17, 9, -41, } ,
2461 { 84, 298, 159, -45, } ,
2462 { 3, 0, 0, -1, } ,
2463 { -3, 0, 0, 2, } ,
2464 { -3, 0, 0, 1, } ,
2465 { -82, 292, 156, 44, } ,
2466 { -73, 17, 9, 39, } ,
2467 { -9, -16, 0, 0, } ,
2468 { 3, 0, -1, -2, } ,
2469 { -3, 0, 0, 0, } ,
2470 { -9, -5, -3, 5, } ,
2471 { -439, 0, 0, 0, } ,
2472 { 57, -28, -15, -30, } ,
2473 { 0, -6, -3, 0, } ,
2474 { -4, 0, 0, 2, } ,
2475 { -40, 57, 30, 21, } ,
2476 { 23, 7, 3, -13, } ,
2477 { 273, 80, 43, -146, } ,
2478 { -449, 430, 0, 0, } ,
2479 { -8, -47, -25, 4, } ,
2480 { 6, 47, 25, -3, } ,
2481 { 0, 23, 13, 0, } ,
2482 { -3, 0, 0, 2, } ,
2483 { 3, -4, -2, -2, } ,
2484 { -48, -110, -59, 26, } ,
2485 { 51, 114, 61, -27, } ,
2486 { -133, 0, 0, 57, } ,
2487 { 0, 4, 0, 0, } ,
2488 { -21, -6, -3, 11, } ,
2489 { 0, -3, -1, 0, } ,
2490 { -11, -21, -11, 6, } ,
2491 { -18, -436, -233, 9, } ,
2492 { 35, -7, 0, 0, } ,
2493 { 0, 5, 3, 0, } ,
2494 { 11, -3, -1, -6, } ,
2495 { -5, -3, -1, 3, } ,
2496 { -53, -9, -5, 28, } ,
2497 { 0, 3, 2, 1, } ,
2498 { 4, 0, 0, -2, } ,
2499 { 0, -4, 0, 0, } ,
2500 { -50, 194, 103, 27, } ,
2501 { -13, 52, 28, 7, } ,
2502 { -91, 248, 0, 0, } ,
2503 { 6, 49, 26, -3, } ,
2504 { -6, -47, -25, 3, } ,
2505 { 0, 5, 3, 0, } ,
2506 { 52, 23, 10, -23, } ,
2507 { -3, 0, 0, 1, } ,
2508 { 0, 5, 3, 0, } ,
2509 { -4, 0, 0, 0, } ,
2510 { -4, 8, 3, 2, } ,
2511 { 10, 0, 0, 0, } ,
2512 { 3, 0, 0, -2, } ,
2513 { 0, 8, 4, 0, } ,
2514 { 0, 8, 4, 1, } ,
2515 { -4, 0, 0, 0, } ,
2516 { -4, 0, 0, 0, } ,
2517 { -8, 4, 2, 4, } ,
2518 { 8, -4, -2, -4, } ,
2519 { 0, 15, 7, 0, } ,
2520 { -138, 0, 0, 0, } ,
2521 { 0, -7, -3, 0, } ,
2522 { 0, -7, -3, 0, } ,
2523 { 54, 0, 0, -29, } ,
2524 { 0, 10, 4, 0, } ,
2525 { -7, 0, 0, 3, } ,
2526 { -37, 35, 19, 20, } ,
2527 { 0, 4, 0, 0, } ,
2528 { -4, 9, 0, 0, } ,
2529 { 8, 0, 0, -4, } ,
2530 { -9, -14, -8, 5, } ,
2531 { -3, -9, -5, 3, } ,
2532 { -145, 47, 0, 0, } ,
2533 { -10, 40, 21, 5, } ,
2534 { 11, -49, -26, -7, } ,
2535 { -2150, 0, 0, 932, } ,
2536 { -12, 0, 0, 5, } ,
2537 { 85, 0, 0, -37, } ,
2538 { 4, 0, 0, -2, } ,
2539 { 3, 0, 0, -2, } ,
2540 { -86, 153, 0, 0, } ,
2541 { -6, 9, 5, 3, } ,
2542 { 9, -13, -7, -5, } ,
2543 { -8, 12, 6, 4, } ,
2544 { -51, 0, 0, 22, } ,
2545 { -11, -268, -116, 5, } ,
2546 { 0, 12, 5, 0, } ,
2547 { 0, 7, 3, 0, } ,
2548 { 31, 6, 3, -17, } ,
2549 { 140, 27, 14, -75, } ,
2550 { 57, 11, 6, -30, } ,
2551 { -14, -39, 0, 0, } ,
2552 { 0, -6, -2, 0, } ,
2553 { 4, 15, 8, -2, } ,
2554 { 0, 4, 0, 0, } ,
2555 { -3, 0, 0, 1, } ,
2556 { 0, 11, 5, 0, } ,
2557 { 9, 6, 0, 0, } ,
2558 { -4, 10, 4, 2, } ,
2559 { 5, 3, 0, 0, } ,
2560 { 16, 0, 0, -9, } ,
2561 { -3, 0, 0, 0, } ,
2562 { 0, 3, 2, -1, } ,
2563 { 7, 0, 0, -3, } ,
2564 { -25, 22, 0, 0, } ,
2565 { 42, 223, 119, -22, } ,
2566 { -27, -143, -77, 14, } ,
2567 { 9, 49, 26, -5, } ,
2568 { -1166, 0, 0, 505, } ,
2569 { -5, 0, 0, 2, } ,
2570 { -6, 0, 0, 3, } ,
2571 { -8, 0, 1, 4, } ,
2572 { 0, -4, 0, 0, } ,
2573 { 117, 0, 0, -63, } ,
2574 { -4, 8, 4, 2, } ,
2575 { 3, 0, 0, -2, } ,
2576 { -5, 0, 0, 2, } ,
2577 { 0, 31, 0, 0, } ,
2578 { -5, 0, 1, 3, } ,
2579 { 4, 0, 0, -2, } ,
2580 { -4, 0, 0, 2, } ,
2581 { -24, -13, -6, 10, } ,
2582 { 3, 0, 0, 0, } ,
2583 { 0, -32, -17, 0, } ,
2584 { 8, 12, 5, -3, } ,
2585 { 3, 0, 0, -1, } ,
2586 { 7, 13, 0, 0, } ,
2587 { -3, 16, 0, 0, } ,
2588 { 50, 0, 0, -27, } ,
2589 { 0, -5, -3, 0, } ,
2590 { 13, 0, 0, 0, } ,
2591 { 0, 5, 3, 1, } ,
2592 { 24, 5, 2, -11, } ,
2593 { 5, -11, -5, -2, } ,
2594 { 30, -3, -2, -16, } ,
2595 { 18, 0, 0, -9, } ,
2596 { 8, 614, 0, 0, } ,
2597 { 3, -3, -1, -2, } ,
2598 { 6, 17, 9, -3, } ,
2599 { -3, -9, -5, 2, } ,
2600 { 0, 6, 3, -1, } ,
2601 { -127, 21, 9, 55, } ,
2602 { 3, 5, 0, 0, } ,
2603 { -6, -10, -4, 3, } ,
2604 { 5, 0, 0, 0, } ,
2605 { 16, 9, 4, -7, } ,
2606 { 3, 0, 0, -2, } ,
2607 { 0, 22, 0, 0, } ,
2608 { 0, 19, 10, 0, } ,
2609 { 7, 0, 0, -4, } ,
2610 { 0, -5, -2, 0, } ,
2611 { 0, 3, 1, 0, } ,
2612 { -9, 3, 1, 4, } ,
2613 { 17, 0, 0, -7, } ,
2614 { 0, -3, -2, -1, } ,
2615 { -20, 34, 0, 0, } ,
2616 { -10, 0, 1, 5, } ,
2617 { -4, 0, 0, 2, } ,
2618 { 22, -87, 0, 0, } ,
2619 { -4, 0, 0, 2, } ,
2620 { -3, -6, -2, 1, } ,
2621 { -16, -3, -1, 7, } ,
2622 { 0, -3, -2, 0, } ,
2623 { 4, 0, 0, 0, } ,
2624 { -68, 39, 0, 0, } ,
2625 { 27, 0, 0, -14, } ,
2626 { 0, -4, 0, 0, } ,
2627 { -25, 0, 0, 0, } ,
2628 { -12, -3, -2, 6, } ,
2629 { 3, 0, 0, -1, } ,
2630 { 3, 66, 29, -1, } ,
2631 { 490, 0, 0, -213, } ,
2632 { -22, 93, 49, 12, } ,
2633 { -7, 28, 15, 4, } ,
2634 { -3, 13, 7, 2, } ,
2635 { -46, 14, 0, 0, } ,
2636 { -5, 0, 0, 0, } ,
2637 { 2, 1, 0, 0, } ,
2638 { 0, -3, 0, 0, } ,
2639 { -28, 0, 0, 15, } ,
2640 { 5, 0, 0, -2, } ,
2641 { 0, 3, 0, 0, } ,
2642 { -11, 0, 0, 5, } ,
2643 { 0, 3, 1, 0, } ,
2644 { -3, 0, 0, 1, } ,
2645 { 25, 106, 57, -13, } ,
2646 { 5, 21, 11, -3, } ,
2647 { 1485, 0, 0, 0, } ,
2648 { -7, -32, -17, 4, } ,
2649 { 0, 5, 3, 0, } ,
2650 { -6, -3, -2, 3, } ,
2651 { 30, -6, -2, -13, } ,
2652 { -4, 4, 0, 0, } ,
2653 { -19, 0, 0, 10, } ,
2654 { 0, 4, 2, -1, } ,
2655 { 0, 3, 0, 0, } ,
2656 { 4, 0, 0, -2, } ,
2657 { 0, -3, -1, 0, } ,
2658 { -3, 0, 0, 0, } ,
2659 { 5, 3, 1, -2, } ,
2660 { 0, 11, 0, 0, } ,
2661 { 118, 0, 0, -52, } ,
2662 { 0, -5, -3, 0, } ,
2663 { -28, 36, 0, 0, } ,
2664 { 5, -5, 0, 0, } ,
2665 { 14, -59, -31, -8, } ,
2666 { 0, 9, 5, 1, } ,
2667 { -458, 0, 0, 198, } ,
2668 { 0, -45, -20, 0, } ,
2669 { 9, 0, 0, -5, } ,
2670 { 0, -3, 0, 0, } ,
2671 { 0, -4, -2, -1, } ,
2672 { 11, 0, 0, -6, } ,
2673 { 6, 0, 0, -2, } ,
2674 { -16, 23, 0, 0, } ,
2675 { 0, -4, -2, 0, } ,
2676 { -5, 0, 0, 2, } ,
2677 { -166, 269, 0, 0, } ,
2678 { 15, 0, 0, -8, } ,
2679 { 10, 0, 0, -4, } ,
2680 { -78, 45, 0, 0, } ,
2681 { 0, -5, -2, 0, } ,
2682 { 7, 0, 0, -4, } ,
2683 { -5, 328, 0, 0, } ,
2684 { 3, 0, 0, -2, } ,
2685 { 5, 0, 0, -2, } ,
2686 { 0, 3, 1, 0, } ,
2687 { -3, 0, 0, 0, } ,
2688 { -3, 0, 0, 0, } ,
2689 { 0, -4, -2, 0, } ,
2690 { -1223, -26, 0, 0, } ,
2691 { 0, 7, 3, 0, } ,
2692 { 3, 0, 0, 0, } ,
2693 { 0, 3, 2, 0, } ,
2694 { -6, 20, 0, 0, } ,
2695 { -368, 0, 0, 0, } ,
2696 { -75, 0, 0, 0, } ,
2697 { 11, 0, 0, -6, } ,
2698 { 3, 0, 0, -2, } ,
2699 { -3, 0, 0, 1, } ,
2700 { -13, -30, 0, 0, } ,
2701 { 21, 3, 0, 0, } ,
2702 { -3, 0, 0, 1, } ,
2703 { -4, 0, 0, 2, } ,
2704 { 8, -27, 0, 0, } ,
2705 { -19, -11, 0, 0, } ,
2706 { -4, 0, 0, 2, } ,
2707 { 0, 5, 2, 0, } ,
2708 { -6, 0, 0, 2, } ,
2709 { -8, 0, 0, 0, } ,
2710 { -1, 0, 0, 0, } ,
2711 { -14, 0, 0, 6, } ,
2712 { 6, 0, 0, 0, } ,
2713 { -74, 0, 0, 32, } ,
2714 { 0, -3, -1, 0, } ,
2715 { 4, 0, 0, -2, } ,
2716 { 8, 11, 0, 0, } ,
2717 { 0, 3, 2, 0, } ,
2718 { -262, 0, 0, 114, } ,
2719 { 0, -4, 0, 0, } ,
2720 { -7, 0, 0, 4, } ,
2721 { 0, -27, -12, 0, } ,
2722 { -19, -8, -4, 8, } ,
2723 { 202, 0, 0, -87, } ,
2724 { -8, 35, 19, 5, } ,
2725 { 0, 4, 2, 0, } ,
2726 { 16, -5, 0, 0, } ,
2727 { 5, 0, 0, -3, } ,
2728 { 0, -3, 0, 0, } ,
2729 { 1, 0, 0, 0, } ,
2730 { -35, -48, -21, 15, } ,
2731 { -3, -5, -2, 1, } ,
2732 { 6, 0, 0, -3, } ,
2733 { 3, 0, 0, -1, } ,
2734 { 0, -5, 0, 0, } ,
2735 { 12, 55, 29, -6, } ,
2736 { 0, 5, 3, 0, } ,
2737 { -598, 0, 0, 0, } ,
2738 { -3, -13, -7, 1, } ,
2739 { -5, -7, -3, 2, } ,
2740 { 3, 0, 0, -1, } ,
2741 { 5, -7, 0, 0, } ,
2742 { 4, 0, 0, -2, } ,
2743 { 16, -6, 0, 0, } ,
2744 { 8, -3, 0, 0, } ,
2745 { 8, -31, -16, -4, } ,
2746 { 0, 3, 1, 0, } ,
2747 { 113, 0, 0, -49, } ,
2748 { 0, -24, -10, 0, } ,
2749 { 4, 0, 0, -2, } ,
2750 { 27, 0, 0, 0, } ,
2751 { -3, 0, 0, 1, } ,
2752 { 0, -4, -2, 0, } ,
2753 { 5, 0, 0, -2, } ,
2754 { 0, -3, 0, 0, } ,
2755 { -13, 0, 0, 6, } ,
2756 { 5, 0, 0, -2, } ,
2757 { -18, -10, -4, 8, } ,
2758 { -4, -28, 0, 0, } ,
2759 { -5, 6, 3, 2, } ,
2760 { -3, 0, 0, 1, } ,
2761 { -5, -9, -4, 2, } ,
2762 { 17, 0, 0, -7, } ,
2763 { 11, 4, 0, 0, } ,
2764 { 0, -6, -2, 0, } ,
2765 { 83, 15, 0, 0, } ,
2766 { -4, 0, 0, 2, } ,
2767 { 0, -114, -49, 0, } ,
2768 { 117, 0, 0, -51, } ,
2769 { -5, 19, 10, 2, } ,
2770 { -3, 0, 0, 0, } ,
2771 { -3, 0, 0, 2, } ,
2772 { 0, -3, -1, 0, } ,
2773 { 3, 0, 0, 0, } ,
2774 { 0, -6, -2, 0, } ,
2775 { 393, 3, 0, 0, } ,
2776 { -4, 21, 11, 2, } ,
2777 { -6, 0, -1, 3, } ,
2778 { -3, 8, 4, 1, } ,
2779 { 8, 0, 0, 0, } ,
2780 { 18, -29, -13, -8, } ,
2781 { 8, 34, 18, -4, } ,
2782 { 89, 0, 0, 0, } ,
2783 { 3, 12, 6, -1, } ,
2784 { 54, -15, -7, -24, } ,
2785 { 0, 3, 0, 0, } ,
2786 { 3, 0, 0, -1, } ,
2787 { 0, 35, 0, 0, } ,
2788 { -154, -30, -13, 67, } ,
2789 { 15, 0, 0, 0, } ,
2790 { 0, 4, 2, 0, } ,
2791 { 0, 9, 0, 0, } ,
2792 { 80, -71, -31, -35, } ,
2793 { 0, -20, -9, 0, } ,
2794 { 11, 5, 2, -5, } ,
2795 { 61, -96, -42, -27, } ,
2796 { 14, 9, 4, -6, } ,
2797 { -11, -6, -3, 5, } ,
2798 { 0, -3, -1, 0, } ,
2799 { 123, -415, -180, -53, } ,
2800 { 0, 0, 0, -35, } ,
2801 { -5, 0, 0, 0, } ,
2802 { 7, -32, -17, -4, } ,
2803 { 0, -9, -5, 0, } ,
2804 { 0, -4, 2, 0, } ,
2805 { -89, 0, 0, 38, } ,
2806 { 0, -86, -19, -6, } ,
2807 { 0, 0, -19, 6, } ,
2808 { -123, -416, -180, 53, } ,
2809 { 0, -3, -1, 0, } ,
2810 { 12, -6, -3, -5, } ,
2811 { -13, 9, 4, 6, } ,
2812 { 0, -15, -7, 0, } ,
2813 { 3, 0, 0, -1, } ,
2814 { -62, -97, -42, 27, } ,
2815 { -11, 5, 2, 5, } ,
2816 { 0, -19, -8, 0, } ,
2817 { -3, 0, 0, 1, } ,
2818 { 0, 4, 2, 0, } ,
2819 { 0, 3, 0, 0, } ,
2820 { 0, 4, 2, 0, } ,
2821 { -85, -70, -31, 37, } ,
2822 { 163, -12, -5, -72, } ,
2823 { -63, -16, -7, 28, } ,
2824 { -21, -32, -14, 9, } ,
2825 { 0, -3, -1, 0, } ,
2826 { 3, 0, 0, -2, } ,
2827 { 0, 8, 0, 0, } ,
2828 { 3, 10, 4, -1, } ,
2829 { 3, 0, 0, -1, } ,
2830 { 0, -7, -3, 0, } ,
2831 { 0, -4, -2, 0, } ,
2832 { 6, 19, 0, 0, } ,
2833 { 5, -173, -75, -2, } ,
2834 { 0, -7, -3, 0, } ,
2835 { 7, -12, -5, -3, } ,
2836 { -3, 0, 0, 2, } ,
2837 { 3, -4, -2, -1, } ,
2838 { 74, 0, 0, -32, } ,
2839 { -3, 12, 6, 2, } ,
2840 { 26, -14, -6, -11, } ,
2841 { 19, 0, 0, -8, } ,
2842 { 6, 24, 13, -3, } ,
2843 { 83, 0, 0, 0, } ,
2844 { 0, -10, -5, 0, } ,
2845 { 11, -3, -1, -5, } ,
2846 { 3, 0, 1, -1, } ,
2847 { 3, 0, 0, -1, } ,
2848 { -4, 0, 0, 0, } ,
2849 { 5, -23, -12, -3, } ,
2850 { -339, 0, 0, 147, } ,
2851 { 0, -10, -5, 0, } ,
2852 { 5, 0, 0, 0, } ,
2853 { 3, 0, 0, -1, } ,
2854 { 0, -4, -2, 0, } ,
2855 { 18, -3, 0, 0, } ,
2856 { 9, -11, -5, -4, } ,
2857 { -8, 0, 0, 4, } ,
2858 { 3, 0, 0, -1, } ,
2859 { 0, 9, 0, 0, } ,
2860 { 6, -9, -4, -2, } ,
2861 { -4, -12, 0, 0, } ,
2862 { 67, -91, -39, -29, } ,
2863 { 30, -18, -8, -13, } ,
2864 { 0, 0, 0, 0, } ,
2865 { 0, -114, -50, 0, } ,
2866 { 0, 0, 0, 23, } ,
2867 { 517, 16, 7, -224, } ,
2868 { 0, -7, -3, 0, } ,
2869 { 143, -3, -1, -62, } ,
2870 { 29, 0, 0, -13, } ,
2871 { -4, 0, 0, 2, } ,
2872 { -6, 0, 0, 3, } ,
2873 { 5, 12, 5, -2, } ,
2874 { -25, 0, 0, 11, } ,
2875 { -3, 0, 0, 1, } ,
2876 { 0, 4, 2, 0, } ,
2877 { -22, 12, 5, 10, } ,
2878 { 50, 0, 0, -22, } ,
2879 { 0, 7, 4, 0, } ,
2880 { 0, 3, 1, 0, } ,
2881 { -4, 4, 2, 2, } ,
2882 { -5, -11, -5, 2, } ,
2883 { 0, 4, 2, 0, } ,
2884 { 4, 17, 9, -2, } ,
2885 { 59, 0, 0, 0, } ,
2886 { 0, -4, -2, 0, } ,
2887 { -8, 0, 0, 4, } ,
2888 { -3, 0, 0, 0, } ,
2889 { 4, -15, -8, -2, } ,
2890 { 370, -8, 0, -160, } ,
2891 { 0, 0, -3, 0, } ,
2892 { 0, 3, 1, 0, } ,
2893 { -6, 3, 1, 3, } ,
2894 { 0, 6, 0, 0, } ,
2895 { -10, 0, 0, 4, } ,
2896 { 0, 9, 4, 0, } ,
2897 { 4, 17, 7, -2, } ,
2898 { 34, 0, 0, -15, } ,
2899 { 0, 5, 3, 0, } ,
2900 { -5, 0, 0, 2, } ,
2901 { -37, -7, -3, 16, } ,
2902 { 3, 13, 7, -2, } ,
2903 { 40, 0, 0, 0, } ,
2904 { 0, -3, -2, 0, } ,
2905 { -184, -3, -1, 80, } ,
2906 { -3, 0, 0, 1, } ,
2907 { -3, 0, 0, 0, } ,
2908 { 0, -10, -6, -1, } ,
2909 { 31, -6, 0, -13, } ,
2910 { -3, -32, -14, 1, } ,
2911 { -7, 0, 0, 3, } ,
2912 { 0, -8, -4, 0, } ,
2913 { 3, -4, 0, 0, } ,
2914 { 0, 4, 0, 0, } ,
2915 { 0, 3, 1, 0, } ,
2916 { 19, -23, -10, 2, } ,
2917 { 0, 0, 0, -10, } ,
2918 { 0, 3, 2, 0, } ,
2919 { 0, 9, 5, -1, } ,
2920 { 28, 0, 0, 0, } ,
2921 { 0, -7, -4, 0, } ,
2922 { 8, -4, 0, -4, } ,
2923 { 0, 0, -2, 0, } ,
2924 { 0, 3, 0, 0, } ,
2925 { -3, 0, 0, 1, } ,
2926 { -9, 0, 1, 4, } ,
2927 { 3, 12, 5, -1, } ,
2928 { 17, -3, -1, 0, } ,
2929 { 0, 7, 4, 0, } ,
2930 { 19, 0, 0, 0, } ,
2931 { 0, -5, -3, 0, } ,
2932 { 14, -3, 0, -1, } ,
2933 { 0, 0, -1, 0, } ,
2934 { 0, 0, 0, -5, } ,
2935 { 0, 5, 3, 0, } ,
2936 { 13, 0, 0, 0, } ,
2937 { 0, -3, -2, 0, } ,
2938 { 2, 9, 4, 3, } ,
2939 { 0, 0, 0, -4, } ,
2940 { 8, 0, 0, 0, } ,
2941 { 0, 4, 2, 0, } ,
2942 { 6, 0, 0, -3, } ,
2943 { 6, 0, 0, 0, } ,
2944 { 0, 3, 1, 0, } ,
2945 { 5, 0, 0, -2, } ,
2946 { 3, 0, 0, -1, } ,
2947 { -3, 0, 0, 0, } ,
2948 { 6, 0, 0, 0, } ,
2949 { 7, 0, 0, 0, } ,
2950 { -4, 0, 0, 0, } ,
2951 { 4, 0, 0, 0, } ,
2952 { 6, 0, 0, 0, } ,
2953 { 0, -4, 0, 0, } ,
2954 { 0, -4, 0, 0, } ,
2955 { 5, 0, 0, 0, } ,
2956 { -3, 0, 0, 0, } ,
2957 { 4, 0, 0, 0, } ,
2958 { -5, 0, 0, 0, } ,
2959 { 4, 0, 0, 0, } ,
2960 { 0, 3, 0, 0, } ,
2961 { 13, 0, 0, 0, } ,
2962 { 21, 11, 0, 0, } ,
2963 { 0, -5, 0, 0, } ,
2964 { 0, -5, -2, 0, } ,
2965 { 0, 5, 3, 0, } ,
2966 { 0, -5, 0, 0, } ,
2967 { -3, 0, 0, 2, } ,
2968 { 20, 10, 0, 0, } ,
2969 { -34, 0, 0, 0, } ,
2970 { -19, 0, 0, 0, } ,
2971 { 3, 0, 0, -2, } ,
2972 { -3, 0, 0, 1, } ,
2973 { -6, 0, 0, 3, } ,
2974 { -4, 0, 0, 0, } ,
2975 { 3, 0, 0, 0, } ,
2976 { 3, 0, 0, 0, } ,
2977 { 4, 0, 0, 0, } ,
2978 { 3, 0, 0, -1, } ,
2979 { 6, 0, 0, -3, } ,
2980 { -8, 0, 0, 3, } ,
2981 { 0, 3, 1, 0, } ,
2982 { -3, 0, 0, 0, } ,
2983 { 0, -3, -2, 0, } ,
2984 { 126, -63, -27, -55, } ,
2985 { -5, 0, 1, 2, } ,
2986 { -3, 28, 15, 2, } ,
2987 { 5, 0, 1, -2, } ,
2988 { 0, 9, 4, 1, } ,
2989 { 0, 9, 4, -1, } ,
2990 { -126, -63, -27, 55, } ,
2991 { 3, 0, 0, -1, } ,
2992 { 21, -11, -6, -11, } ,
2993 { 0, -4, 0, 0, } ,
2994 { -21, -11, -6, 11, } ,
2995 { -3, 0, 0, 1, } ,
2996 { 0, 3, 1, 0, } ,
2997 { 8, 0, 0, -4, } ,
2998 { -6, 0, 0, 3, } ,
2999 { -3, 0, 0, 1, } ,
3000 { 3, 0, 0, -1, } ,
3001 { -3, 0, 0, 1, } ,
3002 { -5, 0, 0, 2, } ,
3003 { 24, -12, -5, -11, } ,
3004 { 0, 3, 1, 0, } ,
3005 { 0, 3, 1, 0, } ,
3006 { 0, 3, 2, 0, } ,
3007 { -24, -12, -5, 10, } ,
3008 { 4, 0, -1, -2, } ,
3009 { 13, 0, 0, -6, } ,
3010 { 7, 0, 0, -3, } ,
3011 { 3, 0, 0, -1, } ,
3012 { 3, 0, 0, -1, } ,
3013
3014 } ;
3015
3016 /*
3017 * - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
3018 */
3019
3020 /*
3021 * Interval between fundamental date J2000.0 and given date (JC).
3022 */
3023
3024 t = ( ( date1 - GAL_J2000 ) + date2 ) / GAL_DJC ;
3025
3026 /*
3027 * -------------------
3028 * LUNI-SOLAR NUTATION
3029 * -------------------
3030 */
3031
3032 /*
3033 * Fundamental (Delaunay) arguments
3034 */
3035
3036 /*
3037 * Mean anomaly of the Moon (IERS 2003).
3038 */
3039
3040 el = gal_fal03 ( t ) ;
3041
3042 /*
3043 * Mean anomaly of the Sun (MHB2000).
3044 */
3045
3046 elp = fmod ( 1287104.79305 +
3047 t * ( 129596581.0481 +
3048 t * ( - 0.5532 +
3049 t * ( 0.000136 +
3050 t * ( - 0.00001149 )))), GAL_TURNAS ) * GAL_AS2R ;
3051
3052 /*
3053 * Mean longitude of the Moon minus that of the ascending node
3054 * (IERS 2003.
3055 */
3056
3057 f = gal_faf03 ( t ) ;
3058
3059 /*
3060 * Mean elongation of the Moon from the Sun (MHB2000).
3061 */
3062
3063 d = fmod ( 1072260.70369 +
3064 t * ( 1602961601.2090 +
3065 t * ( - 6.3706 +
3066 t * ( 0.006593 +
3067 t * ( - 0.00003169 )))), GAL_TURNAS ) * GAL_AS2R ;
3068
3069 /*
3070 * Mean longitude of the ascending node of the Moon (IERS 2003).
3071 */
3072
3073 om = gal_faom03 ( t ) ;
3074
3075 /*
3076 * Initialize the nutation values.
3077 */
3078
3079 dp = 0.0 ;
3080 de = 0.0 ;
3081
3082 /*
3083 * Summation of luni-solar nutation series (in reverse order).
3084 */
3085
3086 for ( i = NLS - 1 ; i >= 0; i-- ) {
3087
3088 /*
3089 * Argument and functions.
3090 */
3091
3092 arg = fmod ( ( double ) NALS[i][0] * el +
3093 ( double ) NALS[i][1] * elp +
3094 ( double ) NALS[i][2] * f +
3095 ( double ) NALS[i][3] * d +
3096 ( double ) NALS[i][4] * om, GAL_2PI ) ;
3097
3098 sarg = sin ( arg ) ;
3099 carg = cos ( arg ) ;
3100
3101 /*
3102 * Term.
3103 */
3104
3105 dp += ( CLS[i][0] + CLS[i][1] * t ) * sarg
3106 + CLS[i][2] * carg ;
3107
3108 de += ( CLS[i][3] + CLS[i][4] * t ) * carg
3109 + CLS[i][5] * sarg ;
3110
3111 }
3112
3113 /*
3114 * Convert from 0.1 microarcsec units to radians.
3115 */
3116
3117 dpsils = dp * GAL_U2R ;
3118 depsls = de * GAL_U2R ;
3119
3120 /*
3121 * ------------------
3122 * PLANETARY NUTATION
3123 * ------------------
3124 */
3125
3126 /*
3127 * n.b. The MHB2000 code computes the luni-solar and planetary nutation
3128 * in different routines, using slightly different Delaunay
3129 * arguments in the two cases. This behaviour is faithfully
3130 * reproduced here. Use of the IERS 2003 expressions for both
3131 * cases leads to negligible changes, well below
3132 * 0.1 microarcsecond.
3133 */
3134
3135 /*
3136 * Mean anomaly of the Moon (MHB2000).
3137 */
3138
3139 al = fmod ( 2.35555598 + 8328.6914269554 * t, GAL_2PI ) ;
3140
3141 /*
3142 * Mean anomaly of the Sun (MHB2000).
3143 */
3144
3145 alsu = fmod ( 6.24006013 + 628.301955 * t, GAL_2PI ) ;
3146
3147 /*
3148 * Mean longitude of the Moon minus that of the ascending node
3149 * (MHB2000).
3150 */
3151
3152 af = fmod ( 1.627905234 + 8433.466158131 * t, GAL_2PI ) ;
3153
3154 /*
3155 * Mean elongation of the Moon from the Sun (MHB2000).
3156 */
3157
3158 ad = fmod ( 5.198466741 + 7771.3771468121 * t, GAL_2PI ) ;
3159
3160 /*
3161 * Mean longitude of the ascending node of the Moon (MHB2000).
3162 */
3163
3164 aom = fmod ( 2.18243920 - 33.757045 * t, GAL_2PI ) ;
3165
3166 /*
3167 * General accumulated precession in longitude (IERS 2003).
3168 */
3169
3170 apa = gal_fapa03 ( t ) ;
3171
3172 /*
3173 * Planetary longitudes, Mercury through Uranus (IERS 2003).
3174 */
3175
3176 alme = gal_fame03 ( t ) ;
3177 alve = gal_fave03 ( t ) ;
3178 alea = gal_fae03 ( t ) ;
3179 alma = gal_fama03 ( t ) ;
3180 alju = gal_faju03 ( t ) ;
3181 alsa = gal_fasa03 ( t ) ;
3182 alur = gal_faur03 ( t ) ;
3183
3184 /*
3185 * Neptune longitude (MHB2000).
3186 */
3187
3188 alne = fmod ( 5.321159000 + 3.8127774000 * t, GAL_2PI ) ;
3189
3190 /*
3191 * Initialize the nutation values.
3192 */
3193
3194 dp = 0.0 ;
3195 de = 0.0 ;
3196
3197 /*
3198 * Summation of planetary nutation series (in reverse order).
3199 */
3200
3201 for ( i = NPL - 1; i >= 0 ; i-- ) {
3202
3203 /*
3204 * Argument and functions.
3205 */
3206
3207 arg = fmod( ( double ) NAPL[i][0] * al +
3208 ( double ) NAPL[i][1] * alsu +
3209 ( double ) NAPL[i][2] * af +
3210 ( double ) NAPL[i][3] * ad +
3211 ( double ) NAPL[i][4] * aom +
3212 ( double ) NAPL[i][5] * alme +
3213 ( double ) NAPL[i][6] * alve +
3214 ( double ) NAPL[i][7] * alea +
3215 ( double ) NAPL[i][8] * alma +
3216 ( double ) NAPL[i][9] * alju +
3217 ( double ) NAPL[i][10] * alsa +
3218 ( double ) NAPL[i][11] * alur +
3219 ( double ) NAPL[i][12] * alne +
3220 ( double ) NAPL[i][13] * apa, GAL_2PI ) ;
3221
3222 sarg = sin ( arg ) ;
3223 carg = cos ( arg ) ;
3224
3225 /*
3226 * Term.
3227 */
3228
3229 dp += ( double ) ICPL[i][0] * sarg + ( double ) ICPL[i][1] * carg ;
3230 de += ( double ) ICPL[i][2] * sarg + ( double ) ICPL[i][3] * carg ;
3231
3232 }
3233
3234 /*
3235 * Convert from 0.1 microarcsec units to radians.
3236 */
3237
3238 dpsipl = dp * GAL_U2R ;
3239 depspl = de * GAL_U2R ;
3240
3241 /*
3242 * -------
3243 * RESULTS
3244 * -------
3245 */
3246
3247 /*
3248 * Add luni-solar and planetary components.
3249 */
3250
3251 *dpsi = dpsils + dpsipl ;
3252 *deps = depsls + depspl ;
3253
3254 /*
3255 * Finished.
3256 */
3257
3258 }
3259
3260 /*
3261 * gal - General Astrodynamics Library
3262 * Copyright (C) 2008 Paul C. L. Willmott
3263 *
3264 * This program is free software; you can redistribute it and/or modify
3265 * it under the terms of the GNU General Public License as published by
3266 * the Free Software Foundation; either version 2 of the License, or
3267 * (at your option) any later version.
3268 *
3269 * This program is distributed in the hope that it will be useful,
3270 * but WITHOUT ANY WARRANTY; without even the implied warranty of
3271 * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
3272 * GNU General Public License for more details.
3273 *
3274 * You should have received a copy of the GNU General Public License along
3275 * with this program; if not, write to the Free Software Foundation, Inc.,
3276 * 51 Franklin Street, Fifth Floor, Boston, MA 02110-1301 USA.
3277 *
3278 * Contact:
3279 *
3280 * Paul Willmott
3281 * vp9mu@amsat.org
3282 */
3283