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diff --git a/ast/erfa/nut00a.c b/ast/erfa/nut00a.c new file mode 100644 index 0000000..4c4e89a --- /dev/null +++ b/ast/erfa/nut00a.c @@ -0,0 +1,2056 @@ +#include "erfa.h" + +void eraNut00a(double date1, double date2, double *dpsi, double *deps) +/* +** - - - - - - - - - - +** e r a N u t 0 0 a +** - - - - - - - - - - +** +** Nutation, IAU 2000A model (MHB2000 luni-solar and planetary nutation +** with free core nutation omitted). +** +** Given: +** date1,date2 double TT as a 2-part Julian Date (Note 1) +** +** Returned: +** dpsi,deps double nutation, luni-solar + planetary (Note 2) +** +** Notes: +** +** 1) 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 +** +** 2450123.7 0.0 (JD method) +** 2451545.0 -1421.3 (J2000 method) +** 2400000.5 50123.2 (MJD method) +** 2450123.5 0.2 (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. +** +** 2) 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. +** +** 3) The function 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. +** +** 4) 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 function and, if required, must be +** independently computed. With the FCN corrections included, the +** present function 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. +** +** 5) The present function 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 ERFA functions eraBi00 and +** eraPr00. +** +** 6) 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 eraPmat76, to deliver GCRS- +** to-true predictions of sub-mas accuracy at current dates. +** 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 ERFA functions do not generate the "total +** nutations" directly, though they can of course easily be +** generated by calling eraBi00, eraPr00 and the present function +** and adding the results. +** +** 7) 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. +** +** Called: +** eraFal03 mean anomaly of the Moon +** eraFaf03 mean argument of the latitude of the Moon +** eraFaom03 mean longitude of the Moon's ascending node +** eraFame03 mean longitude of Mercury +** eraFave03 mean longitude of Venus +** eraFae03 mean longitude of Earth +** eraFama03 mean longitude of Mars +** eraFaju03 mean longitude of Jupiter +** eraFasa03 mean longitude of Saturn +** eraFaur03 mean longitude of Uranus +** eraFapa03 general accumulated precession in longitude +** +** 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) +** +** Copyright (C) 2013-2016, NumFOCUS Foundation. +** Derived, with permission, from the SOFA library. See notes at end of file. +*/ +{ + int i; + double t, el, elp, f, d, om, arg, dp, de, sarg, carg, + al, af, ad, aom, alme, alve, alea, alma, + alju, alsa, alur, alne, apa, dpsils, depsls, + dpsipl, depspl; + +/* Units of 0.1 microarcsecond to radians */ + const double U2R = ERFA_DAS2R / 1e7; + +/* ------------------------- */ +/* Luni-Solar nutation model */ +/* ------------------------- */ + +/* The units for the sine and cosine coefficients are */ +/* 0.1 microarcsecond and the same per Julian century */ + + static const struct { + int nl,nlp,nf,nd,nom; /* coefficients of l,l',F,D,Om */ + double sp,spt,cp; /* longitude sin, t*sin, cos coefficients */ + double ce,cet,se; /* obliquity cos, t*cos, sin coefficients */ + } xls[] = { + + /* 1- 10 */ + { 0, 0, 0, 0, 1, + -172064161.0, -174666.0, 33386.0, 92052331.0, 9086.0, 15377.0}, + { 0, 0, 2,-2, 2, + -13170906.0, -1675.0, -13696.0, 5730336.0, -3015.0, -4587.0}, + { 0, 0, 2, 0, 2,-2276413.0,-234.0,2796.0,978459.0,-485.0, 1374.0}, + { 0, 0, 0, 0, 2,2074554.0, 207.0, -698.0,-897492.0,470.0, -291.0}, + { 0, 1, 0, 0, 0,1475877.0,-3633.0,11817.0,73871.0,-184.0,-1924.0}, + { 0, 1, 2,-2, 2,-516821.0,1226.0, -524.0,224386.0,-677.0, -174.0}, + { 1, 0, 0, 0, 0, 711159.0, 73.0, -872.0, -6750.0, 0.0, 358.0}, + { 0, 0, 2, 0, 1,-387298.0,-367.0, 380.0, 200728.0, 18.0, 318.0}, + { 1, 0, 2, 0, 2,-301461.0, -36.0, 816.0, 129025.0,-63.0, 367.0}, + { 0,-1, 2,-2, 2, 215829.0,-494.0, 111.0, -95929.0,299.0, 132.0}, + + /* 11-20 */ + { 0, 0, 2,-2, 1, 128227.0, 137.0, 181.0, -68982.0, -9.0, 39.0}, + {-1, 0, 2, 0, 2, 123457.0, 11.0, 19.0, -53311.0, 32.0, -4.0}, + {-1, 0, 0, 2, 0, 156994.0, 10.0, -168.0, -1235.0, 0.0, 82.0}, + { 1, 0, 0, 0, 1, 63110.0, 63.0, 27.0, -33228.0, 0.0, -9.0}, + {-1, 0, 0, 0, 1, -57976.0, -63.0, -189.0, 31429.0, 0.0, -75.0}, + {-1, 0, 2, 2, 2, -59641.0, -11.0, 149.0, 25543.0,-11.0, 66.0}, + { 1, 0, 2, 0, 1, -51613.0, -42.0, 129.0, 26366.0, 0.0, 78.0}, + {-2, 0, 2, 0, 1, 45893.0, 50.0, 31.0, -24236.0,-10.0, 20.0}, + { 0, 0, 0, 2, 0, 63384.0, 11.0, -150.0, -1220.0, 0.0, 29.0}, + { 0, 0, 2, 2, 2, -38571.0, -1.0, 158.0, 16452.0,-11.0, 68.0}, + + /* 21-30 */ + { 0,-2, 2,-2, 2, 32481.0, 0.0, 0.0, -13870.0, 0.0, 0.0}, + {-2, 0, 0, 2, 0, -47722.0, 0.0, -18.0, 477.0, 0.0, -25.0}, + { 2, 0, 2, 0, 2, -31046.0, -1.0, 131.0, 13238.0,-11.0, 59.0}, + { 1, 0, 2,-2, 2, 28593.0, 0.0, -1.0, -12338.0, 10.0, -3.0}, + {-1, 0, 2, 0, 1, 20441.0, 21.0, 10.0, -10758.0, 0.0, -3.0}, + { 2, 0, 0, 0, 0, 29243.0, 0.0, -74.0, -609.0, 0.0, 13.0}, + { 0, 0, 2, 0, 0, 25887.0, 0.0, -66.0, -550.0, 0.0, 11.0}, + { 0, 1, 0, 0, 1, -14053.0, -25.0, 79.0, 8551.0, -2.0, -45.0}, + {-1, 0, 0, 2, 1, 15164.0, 10.0, 11.0, -8001.0, 0.0, -1.0}, + { 0, 2, 2,-2, 2, -15794.0, 72.0, -16.0, 6850.0,-42.0, -5.0}, + + /* 31-40 */ + { 0, 0,-2, 2, 0, 21783.0, 0.0, 13.0, -167.0, 0.0, 13.0}, + { 1, 0, 0,-2, 1, -12873.0, -10.0, -37.0, 6953.0, 0.0, -14.0}, + { 0,-1, 0, 0, 1, -12654.0, 11.0, 63.0, 6415.0, 0.0, 26.0}, + {-1, 0, 2, 2, 1, -10204.0, 0.0, 25.0, 5222.0, 0.0, 15.0}, + { 0, 2, 0, 0, 0, 16707.0, -85.0, -10.0, 168.0, -1.0, 10.0}, + { 1, 0, 2, 2, 2, -7691.0, 0.0, 44.0, 3268.0, 0.0, 19.0}, + {-2, 0, 2, 0, 0, -11024.0, 0.0, -14.0, 104.0, 0.0, 2.0}, + { 0, 1, 2, 0, 2, 7566.0, -21.0, -11.0, -3250.0, 0.0, -5.0}, + { 0, 0, 2, 2, 1, -6637.0, -11.0, 25.0, 3353.0, 0.0, 14.0}, + { 0,-1, 2, 0, 2, -7141.0, 21.0, 8.0, 3070.0, 0.0, 4.0}, + + /* 41-50 */ + { 0, 0, 0, 2, 1, -6302.0, -11.0, 2.0, 3272.0, 0.0, 4.0}, + { 1, 0, 2,-2, 1, 5800.0, 10.0, 2.0, -3045.0, 0.0, -1.0}, + { 2, 0, 2,-2, 2, 6443.0, 0.0, -7.0, -2768.0, 0.0, -4.0}, + {-2, 0, 0, 2, 1, -5774.0, -11.0, -15.0, 3041.0, 0.0, -5.0}, + { 2, 0, 2, 0, 1, -5350.0, 0.0, 21.0, 2695.0, 0.0, 12.0}, + { 0,-1, 2,-2, 1, -4752.0, -11.0, -3.0, 2719.0, 0.0, -3.0}, + { 0, 0, 0,-2, 1, -4940.0, -11.0, -21.0, 2720.0, 0.0, -9.0}, + {-1,-1, 0, 2, 0, 7350.0, 0.0, -8.0, -51.0, 0.0, 4.0}, + { 2, 0, 0,-2, 1, 4065.0, 0.0, 6.0, -2206.0, 0.0, 1.0}, + { 1, 0, 0, 2, 0, 6579.0, 0.0, -24.0, -199.0, 0.0, 2.0}, + + /* 51-60 */ + { 0, 1, 2,-2, 1, 3579.0, 0.0, 5.0, -1900.0, 0.0, 1.0}, + { 1,-1, 0, 0, 0, 4725.0, 0.0, -6.0, -41.0, 0.0, 3.0}, + {-2, 0, 2, 0, 2, -3075.0, 0.0, -2.0, 1313.0, 0.0, -1.0}, + { 3, 0, 2, 0, 2, -2904.0, 0.0, 15.0, 1233.0, 0.0, 7.0}, + { 0,-1, 0, 2, 0, 4348.0, 0.0, -10.0, -81.0, 0.0, 2.0}, + { 1,-1, 2, 0, 2, -2878.0, 0.0, 8.0, 1232.0, 0.0, 4.0}, + { 0, 0, 0, 1, 0, -4230.0, 0.0, 5.0, -20.0, 0.0, -2.0}, + {-1,-1, 2, 2, 2, -2819.0, 0.0, 7.0, 1207.0, 0.0, 3.0}, + {-1, 0, 2, 0, 0, -4056.0, 0.0, 5.0, 40.0, 0.0, -2.0}, + { 0,-1, 2, 2, 2, -2647.0, 0.0, 11.0, 1129.0, 0.0, 5.0}, + + /* 61-70 */ + {-2, 0, 0, 0, 1, -2294.0, 0.0, -10.0, 1266.0, 0.0, -4.0}, + { 1, 1, 2, 0, 2, 2481.0, 0.0, -7.0, -1062.0, 0.0, -3.0}, + { 2, 0, 0, 0, 1, 2179.0, 0.0, -2.0, -1129.0, 0.0, -2.0}, + {-1, 1, 0, 1, 0, 3276.0, 0.0, 1.0, -9.0, 0.0, 0.0}, + { 1, 1, 0, 0, 0, -3389.0, 0.0, 5.0, 35.0, 0.0, -2.0}, + { 1, 0, 2, 0, 0, 3339.0, 0.0, -13.0, -107.0, 0.0, 1.0}, + {-1, 0, 2,-2, 1, -1987.0, 0.0, -6.0, 1073.0, 0.0, -2.0}, + { 1, 0, 0, 0, 2, -1981.0, 0.0, 0.0, 854.0, 0.0, 0.0}, + {-1, 0, 0, 1, 0, 4026.0, 0.0, -353.0, -553.0, 0.0, -139.0}, + { 0, 0, 2, 1, 2, 1660.0, 0.0, -5.0, -710.0, 0.0, -2.0}, + + /* 71-80 */ + {-1, 0, 2, 4, 2, -1521.0, 0.0, 9.0, 647.0, 0.0, 4.0}, + {-1, 1, 0, 1, 1, 1314.0, 0.0, 0.0, -700.0, 0.0, 0.0}, + { 0,-2, 2,-2, 1, -1283.0, 0.0, 0.0, 672.0, 0.0, 0.0}, + { 1, 0, 2, 2, 1, -1331.0, 0.0, 8.0, 663.0, 0.0, 4.0}, + {-2, 0, 2, 2, 2, 1383.0, 0.0, -2.0, -594.0, 0.0, -2.0}, + {-1, 0, 0, 0, 2, 1405.0, 0.0, 4.0, -610.0, 0.0, 2.0}, + { 1, 1, 2,-2, 2, 1290.0, 0.0, 0.0, -556.0, 0.0, 0.0}, + {-2, 0, 2, 4, 2, -1214.0, 0.0, 5.0, 518.0, 0.0, 2.0}, + {-1, 0, 4, 0, 2, 1146.0, 0.0, -3.0, -490.0, 0.0, -1.0}, + { 2, 0, 2,-2, 1, 1019.0, 0.0, -1.0, -527.0, 0.0, -1.0}, + + /* 81-90 */ + { 2, 0, 2, 2, 2, -1100.0, 0.0, 9.0, 465.0, 0.0, 4.0}, + { 1, 0, 0, 2, 1, -970.0, 0.0, 2.0, 496.0, 0.0, 1.0}, + { 3, 0, 0, 0, 0, 1575.0, 0.0, -6.0, -50.0, 0.0, 0.0}, + { 3, 0, 2,-2, 2, 934.0, 0.0, -3.0, -399.0, 0.0, -1.0}, + { 0, 0, 4,-2, 2, 922.0, 0.0, -1.0, -395.0, 0.0, -1.0}, + { 0, 1, 2, 0, 1, 815.0, 0.0, -1.0, -422.0, 0.0, -1.0}, + { 0, 0,-2, 2, 1, 834.0, 0.0, 2.0, -440.0, 0.0, 1.0}, + { 0, 0, 2,-2, 3, 1248.0, 0.0, 0.0, -170.0, 0.0, 1.0}, + {-1, 0, 0, 4, 0, 1338.0, 0.0, -5.0, -39.0, 0.0, 0.0}, + { 2, 0,-2, 0, 1, 716.0, 0.0, -2.0, -389.0, 0.0, -1.0}, + + /* 91-100 */ + {-2, 0, 0, 4, 0, 1282.0, 0.0, -3.0, -23.0, 0.0, 1.0}, + {-1,-1, 0, 2, 1, 742.0, 0.0, 1.0, -391.0, 0.0, 0.0}, + {-1, 0, 0, 1, 1, 1020.0, 0.0, -25.0, -495.0, 0.0, -10.0}, + { 0, 1, 0, 0, 2, 715.0, 0.0, -4.0, -326.0, 0.0, 2.0}, + { 0, 0,-2, 0, 1, -666.0, 0.0, -3.0, 369.0, 0.0, -1.0}, + { 0,-1, 2, 0, 1, -667.0, 0.0, 1.0, 346.0, 0.0, 1.0}, + { 0, 0, 2,-1, 2, -704.0, 0.0, 0.0, 304.0, 0.0, 0.0}, + { 0, 0, 2, 4, 2, -694.0, 0.0, 5.0, 294.0, 0.0, 2.0}, + {-2,-1, 0, 2, 0, -1014.0, 0.0, -1.0, 4.0, 0.0, -1.0}, + { 1, 1, 0,-2, 1, -585.0, 0.0, -2.0, 316.0, 0.0, -1.0}, + + /* 101-110 */ + {-1, 1, 0, 2, 0, -949.0, 0.0, 1.0, 8.0, 0.0, -1.0}, + {-1, 1, 0, 1, 2, -595.0, 0.0, 0.0, 258.0, 0.0, 0.0}, + { 1,-1, 0, 0, 1, 528.0, 0.0, 0.0, -279.0, 0.0, 0.0}, + { 1,-1, 2, 2, 2, -590.0, 0.0, 4.0, 252.0, 0.0, 2.0}, + {-1, 1, 2, 2, 2, 570.0, 0.0, -2.0, -244.0, 0.0, -1.0}, + { 3, 0, 2, 0, 1, -502.0, 0.0, 3.0, 250.0, 0.0, 2.0}, + { 0, 1,-2, 2, 0, -875.0, 0.0, 1.0, 29.0, 0.0, 0.0}, + {-1, 0, 0,-2, 1, -492.0, 0.0, -3.0, 275.0, 0.0, -1.0}, + { 0, 1, 2, 2, 2, 535.0, 0.0, -2.0, -228.0, 0.0, -1.0}, + {-1,-1, 2, 2, 1, -467.0, 0.0, 1.0, 240.0, 0.0, 1.0}, + + /* 111-120 */ + { 0,-1, 0, 0, 2, 591.0, 0.0, 0.0, -253.0, 0.0, 0.0}, + { 1, 0, 2,-4, 1, -453.0, 0.0, -1.0, 244.0, 0.0, -1.0}, + {-1, 0,-2, 2, 0, 766.0, 0.0, 1.0, 9.0, 0.0, 0.0}, + { 0,-1, 2, 2, 1, -446.0, 0.0, 2.0, 225.0, 0.0, 1.0}, + { 2,-1, 2, 0, 2, -488.0, 0.0, 2.0, 207.0, 0.0, 1.0}, + { 0, 0, 0, 2, 2, -468.0, 0.0, 0.0, 201.0, 0.0, 0.0}, + { 1,-1, 2, 0, 1, -421.0, 0.0, 1.0, 216.0, 0.0, 1.0}, + {-1, 1, 2, 0, 2, 463.0, 0.0, 0.0, -200.0, 0.0, 0.0}, + { 0, 1, 0, 2, 0, -673.0, 0.0, 2.0, 14.0, 0.0, 0.0}, + { 0,-1,-2, 2, 0, 658.0, 0.0, 0.0, -2.0, 0.0, 0.0}, + + /* 121-130 */ + { 0, 3, 2,-2, 2, -438.0, 0.0, 0.0, 188.0, 0.0, 0.0}, + { 0, 0, 0, 1, 1, -390.0, 0.0, 0.0, 205.0, 0.0, 0.0}, + {-1, 0, 2, 2, 0, 639.0, -11.0, -2.0, -19.0, 0.0, 0.0}, + { 2, 1, 2, 0, 2, 412.0, 0.0, -2.0, -176.0, 0.0, -1.0}, + { 1, 1, 0, 0, 1, -361.0, 0.0, 0.0, 189.0, 0.0, 0.0}, + { 1, 1, 2, 0, 1, 360.0, 0.0, -1.0, -185.0, 0.0, -1.0}, + { 2, 0, 0, 2, 0, 588.0, 0.0, -3.0, -24.0, 0.0, 0.0}, + { 1, 0,-2, 2, 0, -578.0, 0.0, 1.0, 5.0, 0.0, 0.0}, + {-1, 0, 0, 2, 2, -396.0, 0.0, 0.0, 171.0, 0.0, 0.0}, + { 0, 1, 0, 1, 0, 565.0, 0.0, -1.0, -6.0, 0.0, 0.0}, + + /* 131-140 */ + { 0, 1, 0,-2, 1, -335.0, 0.0, -1.0, 184.0, 0.0, -1.0}, + {-1, 0, 2,-2, 2, 357.0, 0.0, 1.0, -154.0, 0.0, 0.0}, + { 0, 0, 0,-1, 1, 321.0, 0.0, 1.0, -174.0, 0.0, 0.0}, + {-1, 1, 0, 0, 1, -301.0, 0.0, -1.0, 162.0, 0.0, 0.0}, + { 1, 0, 2,-1, 2, -334.0, 0.0, 0.0, 144.0, 0.0, 0.0}, + { 1,-1, 0, 2, 0, 493.0, 0.0, -2.0, -15.0, 0.0, 0.0}, + { 0, 0, 0, 4, 0, 494.0, 0.0, -2.0, -19.0, 0.0, 0.0}, + { 1, 0, 2, 1, 2, 337.0, 0.0, -1.0, -143.0, 0.0, -1.0}, + { 0, 0, 2, 1, 1, 280.0, 0.0, -1.0, -144.0, 0.0, 0.0}, + { 1, 0, 0,-2, 2, 309.0, 0.0, 1.0, -134.0, 0.0, 0.0}, + + /* 141-150 */ + {-1, 0, 2, 4, 1, -263.0, 0.0, 2.0, 131.0, 0.0, 1.0}, + { 1, 0,-2, 0, 1, 253.0, 0.0, 1.0, -138.0, 0.0, 0.0}, + { 1, 1, 2,-2, 1, 245.0, 0.0, 0.0, -128.0, 0.0, 0.0}, + { 0, 0, 2, 2, 0, 416.0, 0.0, -2.0, -17.0, 0.0, 0.0}, + {-1, 0, 2,-1, 1, -229.0, 0.0, 0.0, 128.0, 0.0, 0.0}, + {-2, 0, 2, 2, 1, 231.0, 0.0, 0.0, -120.0, 0.0, 0.0}, + { 4, 0, 2, 0, 2, -259.0, 0.0, 2.0, 109.0, 0.0, 1.0}, + { 2,-1, 0, 0, 0, 375.0, 0.0, -1.0, -8.0, 0.0, 0.0}, + { 2, 1, 2,-2, 2, 252.0, 0.0, 0.0, -108.0, 0.0, 0.0}, + { 0, 1, 2, 1, 2, -245.0, 0.0, 1.0, 104.0, 0.0, 0.0}, + + /* 151-160 */ + { 1, 0, 4,-2, 2, 243.0, 0.0, -1.0, -104.0, 0.0, 0.0}, + {-1,-1, 0, 0, 1, 208.0, 0.0, 1.0, -112.0, 0.0, 0.0}, + { 0, 1, 0, 2, 1, 199.0, 0.0, 0.0, -102.0, 0.0, 0.0}, + {-2, 0, 2, 4, 1, -208.0, 0.0, 1.0, 105.0, 0.0, 0.0}, + { 2, 0, 2, 0, 0, 335.0, 0.0, -2.0, -14.0, 0.0, 0.0}, + { 1, 0, 0, 1, 0, -325.0, 0.0, 1.0, 7.0, 0.0, 0.0}, + {-1, 0, 0, 4, 1, -187.0, 0.0, 0.0, 96.0, 0.0, 0.0}, + {-1, 0, 4, 0, 1, 197.0, 0.0, -1.0, -100.0, 0.0, 0.0}, + { 2, 0, 2, 2, 1, -192.0, 0.0, 2.0, 94.0, 0.0, 1.0}, + { 0, 0, 2,-3, 2, -188.0, 0.0, 0.0, 83.0, 0.0, 0.0}, + + /* 161-170 */ + {-1,-2, 0, 2, 0, 276.0, 0.0, 0.0, -2.0, 0.0, 0.0}, + { 2, 1, 0, 0, 0, -286.0, 0.0, 1.0, 6.0, 0.0, 0.0}, + { 0, 0, 4, 0, 2, 186.0, 0.0, -1.0, -79.0, 0.0, 0.0}, + { 0, 0, 0, 0, 3, -219.0, 0.0, 0.0, 43.0, 0.0, 0.0}, + { 0, 3, 0, 0, 0, 276.0, 0.0, 0.0, 2.0, 0.0, 0.0}, + { 0, 0, 2,-4, 1, -153.0, 0.0, -1.0, 84.0, 0.0, 0.0}, + { 0,-1, 0, 2, 1, -156.0, 0.0, 0.0, 81.0, 0.0, 0.0}, + { 0, 0, 0, 4, 1, -154.0, 0.0, 1.0, 78.0, 0.0, 0.0}, + {-1,-1, 2, 4, 2, -174.0, 0.0, 1.0, 75.0, 0.0, 0.0}, + { 1, 0, 2, 4, 2, -163.0, 0.0, 2.0, 69.0, 0.0, 1.0}, + + /* 171-180 */ + {-2, 2, 0, 2, 0, -228.0, 0.0, 0.0, 1.0, 0.0, 0.0}, + {-2,-1, 2, 0, 1, 91.0, 0.0, -4.0, -54.0, 0.0, -2.0}, + {-2, 0, 0, 2, 2, 175.0, 0.0, 0.0, -75.0, 0.0, 0.0}, + {-1,-1, 2, 0, 2, -159.0, 0.0, 0.0, 69.0, 0.0, 0.0}, + { 0, 0, 4,-2, 1, 141.0, 0.0, 0.0, -72.0, 0.0, 0.0}, + { 3, 0, 2,-2, 1, 147.0, 0.0, 0.0, -75.0, 0.0, 0.0}, + {-2,-1, 0, 2, 1, -132.0, 0.0, 0.0, 69.0, 0.0, 0.0}, + { 1, 0, 0,-1, 1, 159.0, 0.0, -28.0, -54.0, 0.0, 11.0}, + { 0,-2, 0, 2, 0, 213.0, 0.0, 0.0, -4.0, 0.0, 0.0}, + {-2, 0, 0, 4, 1, 123.0, 0.0, 0.0, -64.0, 0.0, 0.0}, + + /* 181-190 */ + {-3, 0, 0, 0, 1, -118.0, 0.0, -1.0, 66.0, 0.0, 0.0}, + { 1, 1, 2, 2, 2, 144.0, 0.0, -1.0, -61.0, 0.0, 0.0}, + { 0, 0, 2, 4, 1, -121.0, 0.0, 1.0, 60.0, 0.0, 0.0}, + { 3, 0, 2, 2, 2, -134.0, 0.0, 1.0, 56.0, 0.0, 1.0}, + {-1, 1, 2,-2, 1, -105.0, 0.0, 0.0, 57.0, 0.0, 0.0}, + { 2, 0, 0,-4, 1, -102.0, 0.0, 0.0, 56.0, 0.0, 0.0}, + { 0, 0, 0,-2, 2, 120.0, 0.0, 0.0, -52.0, 0.0, 0.0}, + { 2, 0, 2,-4, 1, 101.0, 0.0, 0.0, -54.0, 0.0, 0.0}, + {-1, 1, 0, 2, 1, -113.0, 0.0, 0.0, 59.0, 0.0, 0.0}, + { 0, 0, 2,-1, 1, -106.0, 0.0, 0.0, 61.0, 0.0, 0.0}, + + /* 191-200 */ + { 0,-2, 2, 2, 2, -129.0, 0.0, 1.0, 55.0, 0.0, 0.0}, + { 2, 0, 0, 2, 1, -114.0, 0.0, 0.0, 57.0, 0.0, 0.0}, + { 4, 0, 2,-2, 2, 113.0, 0.0, -1.0, -49.0, 0.0, 0.0}, + { 2, 0, 0,-2, 2, -102.0, 0.0, 0.0, 44.0, 0.0, 0.0}, + { 0, 2, 0, 0, 1, -94.0, 0.0, 0.0, 51.0, 0.0, 0.0}, + { 1, 0, 0,-4, 1, -100.0, 0.0, -1.0, 56.0, 0.0, 0.0}, + { 0, 2, 2,-2, 1, 87.0, 0.0, 0.0, -47.0, 0.0, 0.0}, + {-3, 0, 0, 4, 0, 161.0, 0.0, 0.0, -1.0, 0.0, 0.0}, + {-1, 1, 2, 0, 1, 96.0, 0.0, 0.0, -50.0, 0.0, 0.0}, + {-1,-1, 0, 4, 0, 151.0, 0.0, -1.0, -5.0, 0.0, 0.0}, + + /* 201-210 */ + {-1,-2, 2, 2, 2, -104.0, 0.0, 0.0, 44.0, 0.0, 0.0}, + {-2,-1, 2, 4, 2, -110.0, 0.0, 0.0, 48.0, 0.0, 0.0}, + { 1,-1, 2, 2, 1, -100.0, 0.0, 1.0, 50.0, 0.0, 0.0}, + {-2, 1, 0, 2, 0, 92.0, 0.0, -5.0, 12.0, 0.0, -2.0}, + {-2, 1, 2, 0, 1, 82.0, 0.0, 0.0, -45.0, 0.0, 0.0}, + { 2, 1, 0,-2, 1, 82.0, 0.0, 0.0, -45.0, 0.0, 0.0}, + {-3, 0, 2, 0, 1, -78.0, 0.0, 0.0, 41.0, 0.0, 0.0}, + {-2, 0, 2,-2, 1, -77.0, 0.0, 0.0, 43.0, 0.0, 0.0}, + {-1, 1, 0, 2, 2, 2.0, 0.0, 0.0, 54.0, 0.0, 0.0}, + { 0,-1, 2,-1, 2, 94.0, 0.0, 0.0, -40.0, 0.0, 0.0}, + + /* 211-220 */ + {-1, 0, 4,-2, 2, -93.0, 0.0, 0.0, 40.0, 0.0, 0.0}, + { 0,-2, 2, 0, 2, -83.0, 0.0, 10.0, 40.0, 0.0, -2.0}, + {-1, 0, 2, 1, 2, 83.0, 0.0, 0.0, -36.0, 0.0, 0.0}, + { 2, 0, 0, 0, 2, -91.0, 0.0, 0.0, 39.0, 0.0, 0.0}, + { 0, 0, 2, 0, 3, 128.0, 0.0, 0.0, -1.0, 0.0, 0.0}, + {-2, 0, 4, 0, 2, -79.0, 0.0, 0.0, 34.0, 0.0, 0.0}, + {-1, 0,-2, 0, 1, -83.0, 0.0, 0.0, 47.0, 0.0, 0.0}, + {-1, 1, 2, 2, 1, 84.0, 0.0, 0.0, -44.0, 0.0, 0.0}, + { 3, 0, 0, 0, 1, 83.0, 0.0, 0.0, -43.0, 0.0, 0.0}, + {-1, 0, 2, 3, 2, 91.0, 0.0, 0.0, -39.0, 0.0, 0.0}, + + /* 221-230 */ + { 2,-1, 2, 0, 1, -77.0, 0.0, 0.0, 39.0, 0.0, 0.0}, + { 0, 1, 2, 2, 1, 84.0, 0.0, 0.0, -43.0, 0.0, 0.0}, + { 0,-1, 2, 4, 2, -92.0, 0.0, 1.0, 39.0, 0.0, 0.0}, + { 2,-1, 2, 2, 2, -92.0, 0.0, 1.0, 39.0, 0.0, 0.0}, + { 0, 2,-2, 2, 0, -94.0, 0.0, 0.0, 0.0, 0.0, 0.0}, + {-1,-1, 2,-1, 1, 68.0, 0.0, 0.0, -36.0, 0.0, 0.0}, + { 0,-2, 0, 0, 1, -61.0, 0.0, 0.0, 32.0, 0.0, 0.0}, + { 1, 0, 2,-4, 2, 71.0, 0.0, 0.0, -31.0, 0.0, 0.0}, + { 1,-1, 0,-2, 1, 62.0, 0.0, 0.0, -34.0, 0.0, 0.0}, + {-1,-1, 2, 0, 1, -63.0, 0.0, 0.0, 33.0, 0.0, 0.0}, + + /* 231-240 */ + { 1,-1, 2,-2, 2, -73.0, 0.0, 0.0, 32.0, 0.0, 0.0}, + {-2,-1, 0, 4, 0, 115.0, 0.0, 0.0, -2.0, 0.0, 0.0}, + {-1, 0, 0, 3, 0, -103.0, 0.0, 0.0, 2.0, 0.0, 0.0}, + {-2,-1, 2, 2, 2, 63.0, 0.0, 0.0, -28.0, 0.0, 0.0}, + { 0, 2, 2, 0, 2, 74.0, 0.0, 0.0, -32.0, 0.0, 0.0}, + { 1, 1, 0, 2, 0, -103.0, 0.0, -3.0, 3.0, 0.0, -1.0}, + { 2, 0, 2,-1, 2, -69.0, 0.0, 0.0, 30.0, 0.0, 0.0}, + { 1, 0, 2, 1, 1, 57.0, 0.0, 0.0, -29.0, 0.0, 0.0}, + { 4, 0, 0, 0, 0, 94.0, 0.0, 0.0, -4.0, 0.0, 0.0}, + { 2, 1, 2, 0, 1, 64.0, 0.0, 0.0, -33.0, 0.0, 0.0}, + + /* 241-250 */ + { 3,-1, 2, 0, 2, -63.0, 0.0, 0.0, 26.0, 0.0, 0.0}, + {-2, 2, 0, 2, 1, -38.0, 0.0, 0.0, 20.0, 0.0, 0.0}, + { 1, 0, 2,-3, 1, -43.0, 0.0, 0.0, 24.0, 0.0, 0.0}, + { 1, 1, 2,-4, 1, -45.0, 0.0, 0.0, 23.0, 0.0, 0.0}, + {-1,-1, 2,-2, 1, 47.0, 0.0, 0.0, -24.0, 0.0, 0.0}, + { 0,-1, 0,-1, 1, -48.0, 0.0, 0.0, 25.0, 0.0, 0.0}, + { 0,-1, 0,-2, 1, 45.0, 0.0, 0.0, -26.0, 0.0, 0.0}, + {-2, 0, 0, 0, 2, 56.0, 0.0, 0.0, -25.0, 0.0, 0.0}, + {-2, 0,-2, 2, 0, 88.0, 0.0, 0.0, 2.0, 0.0, 0.0}, + {-1, 0,-2, 4, 0, -75.0, 0.0, 0.0, 0.0, 0.0, 0.0}, + + /* 251-260 */ + { 1,-2, 0, 0, 0, 85.0, 0.0, 0.0, 0.0, 0.0, 0.0}, + { 0, 1, 0, 1, 1, 49.0, 0.0, 0.0, -26.0, 0.0, 0.0}, + {-1, 2, 0, 2, 0, -74.0, 0.0, -3.0, -1.0, 0.0, -1.0}, + { 1,-1, 2,-2, 1, -39.0, 0.0, 0.0, 21.0, 0.0, 0.0}, + { 1, 2, 2,-2, 2, 45.0, 0.0, 0.0, -20.0, 0.0, 0.0}, + { 2,-1, 2,-2, 2, 51.0, 0.0, 0.0, -22.0, 0.0, 0.0}, + { 1, 0, 2,-1, 1, -40.0, 0.0, 0.0, 21.0, 0.0, 0.0}, + { 2, 1, 2,-2, 1, 41.0, 0.0, 0.0, -21.0, 0.0, 0.0}, + {-2, 0, 0,-2, 1, -42.0, 0.0, 0.0, 24.0, 0.0, 0.0}, + { 1,-2, 2, 0, 2, -51.0, 0.0, 0.0, 22.0, 0.0, 0.0}, + + /* 261-270 */ + { 0, 1, 2, 1, 1, -42.0, 0.0, 0.0, 22.0, 0.0, 0.0}, + { 1, 0, 4,-2, 1, 39.0, 0.0, 0.0, -21.0, 0.0, 0.0}, + {-2, 0, 4, 2, 2, 46.0, 0.0, 0.0, -18.0, 0.0, 0.0}, + { 1, 1, 2, 1, 2, -53.0, 0.0, 0.0, 22.0, 0.0, 0.0}, + { 1, 0, 0, 4, 0, 82.0, 0.0, 0.0, -4.0, 0.0, 0.0}, + { 1, 0, 2, 2, 0, 81.0, 0.0, -1.0, -4.0, 0.0, 0.0}, + { 2, 0, 2, 1, 2, 47.0, 0.0, 0.0, -19.0, 0.0, 0.0}, + { 3, 1, 2, 0, 2, 53.0, 0.0, 0.0, -23.0, 0.0, 0.0}, + { 4, 0, 2, 0, 1, -45.0, 0.0, 0.0, 22.0, 0.0, 0.0}, + {-2,-1, 2, 0, 0, -44.0, 0.0, 0.0, -2.0, 0.0, 0.0}, + + /* 271-280 */ + { 0, 1,-2, 2, 1, -33.0, 0.0, 0.0, 16.0, 0.0, 0.0}, + { 1, 0,-2, 1, 0, -61.0, 0.0, 0.0, 1.0, 0.0, 0.0}, + { 0,-1,-2, 2, 1, 28.0, 0.0, 0.0, -15.0, 0.0, 0.0}, + { 2,-1, 0,-2, 1, -38.0, 0.0, 0.0, 19.0, 0.0, 0.0}, + {-1, 0, 2,-1, 2, -33.0, 0.0, 0.0, 21.0, 0.0, 0.0}, + { 1, 0, 2,-3, 2, -60.0, 0.0, 0.0, 0.0, 0.0, 0.0}, + { 0, 1, 2,-2, 3, 48.0, 0.0, 0.0, -10.0, 0.0, 0.0}, + { 0, 0, 2,-3, 1, 27.0, 0.0, 0.0, -14.0, 0.0, 0.0}, + {-1, 0,-2, 2, 1, 38.0, 0.0, 0.0, -20.0, 0.0, 0.0}, + { 0, 0, 2,-4, 2, 31.0, 0.0, 0.0, -13.0, 0.0, 0.0}, + + /* 281-290 */ + {-2, 1, 0, 0, 1, -29.0, 0.0, 0.0, 15.0, 0.0, 0.0}, + {-1, 0, 0,-1, 1, 28.0, 0.0, 0.0, -15.0, 0.0, 0.0}, + { 2, 0, 2,-4, 2, -32.0, 0.0, 0.0, 15.0, 0.0, 0.0}, + { 0, 0, 4,-4, 4, 45.0, 0.0, 0.0, -8.0, 0.0, 0.0}, + { 0, 0, 4,-4, 2, -44.0, 0.0, 0.0, 19.0, 0.0, 0.0}, + {-1,-2, 0, 2, 1, 28.0, 0.0, 0.0, -15.0, 0.0, 0.0}, + {-2, 0, 0, 3, 0, -51.0, 0.0, 0.0, 0.0, 0.0, 0.0}, + { 1, 0,-2, 2, 1, -36.0, 0.0, 0.0, 20.0, 0.0, 0.0}, + {-3, 0, 2, 2, 2, 44.0, 0.0, 0.0, -19.0, 0.0, 0.0}, + {-3, 0, 2, 2, 1, 26.0, 0.0, 0.0, -14.0, 0.0, 0.0}, + + /* 291-300 */ + {-2, 0, 2, 2, 0, -60.0, 0.0, 0.0, 2.0, 0.0, 0.0}, + { 2,-1, 0, 0, 1, 35.0, 0.0, 0.0, -18.0, 0.0, 0.0}, + {-2, 1, 2, 2, 2, -27.0, 0.0, 0.0, 11.0, 0.0, 0.0}, + { 1, 1, 0, 1, 0, 47.0, 0.0, 0.0, -1.0, 0.0, 0.0}, + { 0, 1, 4,-2, 2, 36.0, 0.0, 0.0, -15.0, 0.0, 0.0}, + {-1, 1, 0,-2, 1, -36.0, 0.0, 0.0, 20.0, 0.0, 0.0}, + { 0, 0, 0,-4, 1, -35.0, 0.0, 0.0, 19.0, 0.0, 0.0}, + { 1,-1, 0, 2, 1, -37.0, 0.0, 0.0, 19.0, 0.0, 0.0}, + { 1, 1, 0, 2, 1, 32.0, 0.0, 0.0, -16.0, 0.0, 0.0}, + {-1, 2, 2, 2, 2, 35.0, 0.0, 0.0, -14.0, 0.0, 0.0}, + + /* 301-310 */ + { 3, 1, 2,-2, 2, 32.0, 0.0, 0.0, -13.0, 0.0, 0.0}, + { 0,-1, 0, 4, 0, 65.0, 0.0, 0.0, -2.0, 0.0, 0.0}, + { 2,-1, 0, 2, 0, 47.0, 0.0, 0.0, -1.0, 0.0, 0.0}, + { 0, 0, 4, 0, 1, 32.0, 0.0, 0.0, -16.0, 0.0, 0.0}, + { 2, 0, 4,-2, 2, 37.0, 0.0, 0.0, -16.0, 0.0, 0.0}, + {-1,-1, 2, 4, 1, -30.0, 0.0, 0.0, 15.0, 0.0, 0.0}, + { 1, 0, 0, 4, 1, -32.0, 0.0, 0.0, 16.0, 0.0, 0.0}, + { 1,-2, 2, 2, 2, -31.0, 0.0, 0.0, 13.0, 0.0, 0.0}, + { 0, 0, 2, 3, 2, 37.0, 0.0, 0.0, -16.0, 0.0, 0.0}, + {-1, 1, 2, 4, 2, 31.0, 0.0, 0.0, -13.0, 0.0, 0.0}, + + /* 311-320 */ + { 3, 0, 0, 2, 0, 49.0, 0.0, 0.0, -2.0, 0.0, 0.0}, + {-1, 0, 4, 2, 2, 32.0, 0.0, 0.0, -13.0, 0.0, 0.0}, + { 1, 1, 2, 2, 1, 23.0, 0.0, 0.0, -12.0, 0.0, 0.0}, + {-2, 0, 2, 6, 2, -43.0, 0.0, 0.0, 18.0, 0.0, 0.0}, + { 2, 1, 2, 2, 2, 26.0, 0.0, 0.0, -11.0, 0.0, 0.0}, + {-1, 0, 2, 6, 2, -32.0, 0.0, 0.0, 14.0, 0.0, 0.0}, + { 1, 0, 2, 4, 1, -29.0, 0.0, 0.0, 14.0, 0.0, 0.0}, + { 2, 0, 2, 4, 2, -27.0, 0.0, 0.0, 12.0, 0.0, 0.0}, + { 1, 1,-2, 1, 0, 30.0, 0.0, 0.0, 0.0, 0.0, 0.0}, + {-3, 1, 2, 1, 2, -11.0, 0.0, 0.0, 5.0, 0.0, 0.0}, + + /* 321-330 */ + { 2, 0,-2, 0, 2, -21.0, 0.0, 0.0, 10.0, 0.0, 0.0}, + {-1, 0, 0, 1, 2, -34.0, 0.0, 0.0, 15.0, 0.0, 0.0}, + {-4, 0, 2, 2, 1, -10.0, 0.0, 0.0, 6.0, 0.0, 0.0}, + {-1,-1, 0, 1, 0, -36.0, 0.0, 0.0, 0.0, 0.0, 0.0}, + { 0, 0,-2, 2, 2, -9.0, 0.0, 0.0, 4.0, 0.0, 0.0}, + { 1, 0, 0,-1, 2, -12.0, 0.0, 0.0, 5.0, 0.0, 0.0}, + { 0,-1, 2,-2, 3, -21.0, 0.0, 0.0, 5.0, 0.0, 0.0}, + {-2, 1, 2, 0, 0, -29.0, 0.0, 0.0, -1.0, 0.0, 0.0}, + { 0, 0, 2,-2, 4, -15.0, 0.0, 0.0, 3.0, 0.0, 0.0}, + {-2,-2, 0, 2, 0, -20.0, 0.0, 0.0, 0.0, 0.0, 0.0}, + + /* 331-340 */ + {-2, 0,-2, 4, 0, 28.0, 0.0, 0.0, 0.0, 0.0, -2.0}, + { 0,-2,-2, 2, 0, 17.0, 0.0, 0.0, 0.0, 0.0, 0.0}, + { 1, 2, 0,-2, 1, -22.0, 0.0, 0.0, 12.0, 0.0, 0.0}, + { 3, 0, 0,-4, 1, -14.0, 0.0, 0.0, 7.0, 0.0, 0.0}, + {-1, 1, 2,-2, 2, 24.0, 0.0, 0.0, -11.0, 0.0, 0.0}, + { 1,-1, 2,-4, 1, 11.0, 0.0, 0.0, -6.0, 0.0, 0.0}, + { 1, 1, 0,-2, 2, 14.0, 0.0, 0.0, -6.0, 0.0, 0.0}, + {-3, 0, 2, 0, 0, 24.0, 0.0, 0.0, 0.0, 0.0, 0.0}, + {-3, 0, 2, 0, 2, 18.0, 0.0, 0.0, -8.0, 0.0, 0.0}, + {-2, 0, 0, 1, 0, -38.0, 0.0, 0.0, 0.0, 0.0, 0.0}, + + /* 341-350 */ + { 0, 0,-2, 1, 0, -31.0, 0.0, 0.0, 0.0, 0.0, 0.0}, + {-3, 0, 0, 2, 1, -16.0, 0.0, 0.0, 8.0, 0.0, 0.0}, + {-1,-1,-2, 2, 0, 29.0, 0.0, 0.0, 0.0, 0.0, 0.0}, + { 0, 1, 2,-4, 1, -18.0, 0.0, 0.0, 10.0, 0.0, 0.0}, + { 2, 1, 0,-4, 1, -10.0, 0.0, 0.0, 5.0, 0.0, 0.0}, + { 0, 2, 0,-2, 1, -17.0, 0.0, 0.0, 10.0, 0.0, 0.0}, + { 1, 0, 0,-3, 1, 9.0, 0.0, 0.0, -4.0, 0.0, 0.0}, + {-2, 0, 2,-2, 2, 16.0, 0.0, 0.0, -6.0, 0.0, 0.0}, + {-2,-1, 0, 0, 1, 22.0, 0.0, 0.0, -12.0, 0.0, 0.0}, + {-4, 0, 0, 2, 0, 20.0, 0.0, 0.0, 0.0, 0.0, 0.0}, + + /* 351-360 */ + { 1, 1, 0,-4, 1, -13.0, 0.0, 0.0, 6.0, 0.0, 0.0}, + {-1, 0, 2,-4, 1, -17.0, 0.0, 0.0, 9.0, 0.0, 0.0}, + { 0, 0, 4,-4, 1, -14.0, 0.0, 0.0, 8.0, 0.0, 0.0}, + { 0, 3, 2,-2, 2, 0.0, 0.0, 0.0, -7.0, 0.0, 0.0}, + {-3,-1, 0, 4, 0, 14.0, 0.0, 0.0, 0.0, 0.0, 0.0}, + {-3, 0, 0, 4, 1, 19.0, 0.0, 0.0, -10.0, 0.0, 0.0}, + { 1,-1,-2, 2, 0, -34.0, 0.0, 0.0, 0.0, 0.0, 0.0}, + {-1,-1, 0, 2, 2, -20.0, 0.0, 0.0, 8.0, 0.0, 0.0}, + { 1,-2, 0, 0, 1, 9.0, 0.0, 0.0, -5.0, 0.0, 0.0}, + { 1,-1, 0, 0, 2, -18.0, 0.0, 0.0, 7.0, 0.0, 0.0}, + + /* 361-370 */ + { 0, 0, 0, 1, 2, 13.0, 0.0, 0.0, -6.0, 0.0, 0.0}, + {-1,-1, 2, 0, 0, 17.0, 0.0, 0.0, 0.0, 0.0, 0.0}, + { 1,-2, 2,-2, 2, -12.0, 0.0, 0.0, 5.0, 0.0, 0.0}, + { 0,-1, 2,-1, 1, 15.0, 0.0, 0.0, -8.0, 0.0, 0.0}, + {-1, 0, 2, 0, 3, -11.0, 0.0, 0.0, 3.0, 0.0, 0.0}, + { 1, 1, 0, 0, 2, 13.0, 0.0, 0.0, -5.0, 0.0, 0.0}, + {-1, 1, 2, 0, 0, -18.0, 0.0, 0.0, 0.0, 0.0, 0.0}, + { 1, 2, 0, 0, 0, -35.0, 0.0, 0.0, 0.0, 0.0, 0.0}, + {-1, 2, 2, 0, 2, 9.0, 0.0, 0.0, -4.0, 0.0, 0.0}, + {-1, 0, 4,-2, 1, -19.0, 0.0, 0.0, 10.0, 0.0, 0.0}, + + /* 371-380 */ + { 3, 0, 2,-4, 2, -26.0, 0.0, 0.0, 11.0, 0.0, 0.0}, + { 1, 2, 2,-2, 1, 8.0, 0.0, 0.0, -4.0, 0.0, 0.0}, + { 1, 0, 4,-4, 2, -10.0, 0.0, 0.0, 4.0, 0.0, 0.0}, + {-2,-1, 0, 4, 1, 10.0, 0.0, 0.0, -6.0, 0.0, 0.0}, + { 0,-1, 0, 2, 2, -21.0, 0.0, 0.0, 9.0, 0.0, 0.0}, + {-2, 1, 0, 4, 0, -15.0, 0.0, 0.0, 0.0, 0.0, 0.0}, + {-2,-1, 2, 2, 1, 9.0, 0.0, 0.0, -5.0, 0.0, 0.0}, + { 2, 0,-2, 2, 0, -29.0, 0.0, 0.0, 0.0, 0.0, 0.0}, + { 1, 0, 0, 1, 1, -19.0, 0.0, 0.0, 10.0, 0.0, 0.0}, + { 0, 1, 0, 2, 2, 12.0, 0.0, 0.0, -5.0, 0.0, 0.0}, + + /* 381-390 */ + { 1,-1, 2,-1, 2, 22.0, 0.0, 0.0, -9.0, 0.0, 0.0}, + {-2, 0, 4, 0, 1, -10.0, 0.0, 0.0, 5.0, 0.0, 0.0}, + { 2, 1, 0, 0, 1, -20.0, 0.0, 0.0, 11.0, 0.0, 0.0}, + { 0, 1, 2, 0, 0, -20.0, 0.0, 0.0, 0.0, 0.0, 0.0}, + { 0,-1, 4,-2, 2, -17.0, 0.0, 0.0, 7.0, 0.0, 0.0}, + { 0, 0, 4,-2, 4, 15.0, 0.0, 0.0, -3.0, 0.0, 0.0}, + { 0, 2, 2, 0, 1, 8.0, 0.0, 0.0, -4.0, 0.0, 0.0}, + {-3, 0, 0, 6, 0, 14.0, 0.0, 0.0, 0.0, 0.0, 0.0}, + {-1,-1, 0, 4, 1, -12.0, 0.0, 0.0, 6.0, 0.0, 0.0}, + { 1,-2, 0, 2, 0, 25.0, 0.0, 0.0, 0.0, 0.0, 0.0}, + + /* 391-400 */ + {-1, 0, 0, 4, 2, -13.0, 0.0, 0.0, 6.0, 0.0, 0.0}, + {-1,-2, 2, 2, 1, -14.0, 0.0, 0.0, 8.0, 0.0, 0.0}, + {-1, 0, 0,-2, 2, 13.0, 0.0, 0.0, -5.0, 0.0, 0.0}, + { 1, 0,-2,-2, 1, -17.0, 0.0, 0.0, 9.0, 0.0, 0.0}, + { 0, 0,-2,-2, 1, -12.0, 0.0, 0.0, 6.0, 0.0, 0.0}, + {-2, 0,-2, 0, 1, -10.0, 0.0, 0.0, 5.0, 0.0, 0.0}, + { 0, 0, 0, 3, 1, 10.0, 0.0, 0.0, -6.0, 0.0, 0.0}, + { 0, 0, 0, 3, 0, -15.0, 0.0, 0.0, 0.0, 0.0, 0.0}, + {-1, 1, 0, 4, 0, -22.0, 0.0, 0.0, 0.0, 0.0, 0.0}, + {-1,-1, 2, 2, 0, 28.0, 0.0, 0.0, -1.0, 0.0, 0.0}, + + /* 401-410 */ + {-2, 0, 2, 3, 2, 15.0, 0.0, 0.0, -7.0, 0.0, 0.0}, + { 1, 0, 0, 2, 2, 23.0, 0.0, 0.0, -10.0, 0.0, 0.0}, + { 0,-1, 2, 1, 2, 12.0, 0.0, 0.0, -5.0, 0.0, 0.0}, + { 3,-1, 0, 0, 0, 29.0, 0.0, 0.0, -1.0, 0.0, 0.0}, + { 2, 0, 0, 1, 0, -25.0, 0.0, 0.0, 1.0, 0.0, 0.0}, + { 1,-1, 2, 0, 0, 22.0, 0.0, 0.0, 0.0, 0.0, 0.0}, + { 0, 0, 2, 1, 0, -18.0, 0.0, 0.0, 0.0, 0.0, 0.0}, + { 1, 0, 2, 0, 3, 15.0, 0.0, 0.0, 3.0, 0.0, 0.0}, + { 3, 1, 0, 0, 0, -23.0, 0.0, 0.0, 0.0, 0.0, 0.0}, + { 3,-1, 2,-2, 2, 12.0, 0.0, 0.0, -5.0, 0.0, 0.0}, + + /* 411-420 */ + { 2, 0, 2,-1, 1, -8.0, 0.0, 0.0, 4.0, 0.0, 0.0}, + { 1, 1, 2, 0, 0, -19.0, 0.0, 0.0, 0.0, 0.0, 0.0}, + { 0, 0, 4,-1, 2, -10.0, 0.0, 0.0, 4.0, 0.0, 0.0}, + { 1, 2, 2, 0, 2, 21.0, 0.0, 0.0, -9.0, 0.0, 0.0}, + {-2, 0, 0, 6, 0, 23.0, 0.0, 0.0, -1.0, 0.0, 0.0}, + { 0,-1, 0, 4, 1, -16.0, 0.0, 0.0, 8.0, 0.0, 0.0}, + {-2,-1, 2, 4, 1, -19.0, 0.0, 0.0, 9.0, 0.0, 0.0}, + { 0,-2, 2, 2, 1, -22.0, 0.0, 0.0, 10.0, 0.0, 0.0}, + { 0,-1, 2, 2, 0, 27.0, 0.0, 0.0, -1.0, 0.0, 0.0}, + {-1, 0, 2, 3, 1, 16.0, 0.0, 0.0, -8.0, 0.0, 0.0}, + + /* 421-430 */ + {-2, 1, 2, 4, 2, 19.0, 0.0, 0.0, -8.0, 0.0, 0.0}, + { 2, 0, 0, 2, 2, 9.0, 0.0, 0.0, -4.0, 0.0, 0.0}, + { 2,-2, 2, 0, 2, -9.0, 0.0, 0.0, 4.0, 0.0, 0.0}, + {-1, 1, 2, 3, 2, -9.0, 0.0, 0.0, 4.0, 0.0, 0.0}, + { 3, 0, 2,-1, 2, -8.0, 0.0, 0.0, 4.0, 0.0, 0.0}, + { 4, 0, 2,-2, 1, 18.0, 0.0, 0.0, -9.0, 0.0, 0.0}, + {-1, 0, 0, 6, 0, 16.0, 0.0, 0.0, -1.0, 0.0, 0.0}, + {-1,-2, 2, 4, 2, -10.0, 0.0, 0.0, 4.0, 0.0, 0.0}, + {-3, 0, 2, 6, 2, -23.0, 0.0, 0.0, 9.0, 0.0, 0.0}, + {-1, 0, 2, 4, 0, 16.0, 0.0, 0.0, -1.0, 0.0, 0.0}, + + /* 431-440 */ + { 3, 0, 0, 2, 1, -12.0, 0.0, 0.0, 6.0, 0.0, 0.0}, + { 3,-1, 2, 0, 1, -8.0, 0.0, 0.0, 4.0, 0.0, 0.0}, + { 3, 0, 2, 0, 0, 30.0, 0.0, 0.0, -2.0, 0.0, 0.0}, + { 1, 0, 4, 0, 2, 24.0, 0.0, 0.0, -10.0, 0.0, 0.0}, + { 5, 0, 2,-2, 2, 10.0, 0.0, 0.0, -4.0, 0.0, 0.0}, + { 0,-1, 2, 4, 1, -16.0, 0.0, 0.0, 7.0, 0.0, 0.0}, + { 2,-1, 2, 2, 1, -16.0, 0.0, 0.0, 7.0, 0.0, 0.0}, + { 0, 1, 2, 4, 2, 17.0, 0.0, 0.0, -7.0, 0.0, 0.0}, + { 1,-1, 2, 4, 2, -24.0, 0.0, 0.0, 10.0, 0.0, 0.0}, + { 3,-1, 2, 2, 2, -12.0, 0.0, 0.0, 5.0, 0.0, 0.0}, + + /* 441-450 */ + { 3, 0, 2, 2, 1, -24.0, 0.0, 0.0, 11.0, 0.0, 0.0}, + { 5, 0, 2, 0, 2, -23.0, 0.0, 0.0, 9.0, 0.0, 0.0}, + { 0, 0, 2, 6, 2, -13.0, 0.0, 0.0, 5.0, 0.0, 0.0}, + { 4, 0, 2, 2, 2, -15.0, 0.0, 0.0, 7.0, 0.0, 0.0}, + { 0,-1, 1,-1, 1, 0.0, 0.0,-1988.0, 0.0, 0.0,-1679.0}, + {-1, 0, 1, 0, 3, 0.0, 0.0, -63.0, 0.0, 0.0, -27.0}, + { 0,-2, 2,-2, 3, -4.0, 0.0, 0.0, 0.0, 0.0, 0.0}, + { 1, 0,-1, 0, 1, 0.0, 0.0, 5.0, 0.0, 0.0, 4.0}, + { 2,-2, 0,-2, 1, 5.0, 0.0, 0.0, -3.0, 0.0, 0.0}, + {-1, 0, 1, 0, 2, 0.0, 0.0, 364.0, 0.0, 0.0, 176.0}, + + /* 451-460 */ + {-1, 0, 1, 0, 1, 0.0, 0.0,-1044.0, 0.0, 0.0, -891.0}, + {-1,-1, 2,-1, 2, -3.0, 0.0, 0.0, 1.0, 0.0, 0.0}, + {-2, 2, 0, 2, 2, 4.0, 0.0, 0.0, -2.0, 0.0, 0.0}, + {-1, 0, 1, 0, 0, 0.0, 0.0, 330.0, 0.0, 0.0, 0.0}, + {-4, 1, 2, 2, 2, 5.0, 0.0, 0.0, -2.0, 0.0, 0.0}, + {-3, 0, 2, 1, 1, 3.0, 0.0, 0.0, -2.0, 0.0, 0.0}, + {-2,-1, 2, 0, 2, -3.0, 0.0, 0.0, 1.0, 0.0, 0.0}, + { 1, 0,-2, 1, 1, -5.0, 0.0, 0.0, 2.0, 0.0, 0.0}, + { 2,-1,-2, 0, 1, 3.0, 0.0, 0.0, -1.0, 0.0, 0.0}, + {-4, 0, 2, 2, 0, 3.0, 0.0, 0.0, 0.0, 0.0, 0.0}, + + /* 461-470 */ + {-3, 1, 0, 3, 0, 3.0, 0.0, 0.0, 0.0, 0.0, 0.0}, + {-1, 0,-1, 2, 0, 0.0, 0.0, 5.0, 0.0, 0.0, 0.0}, + { 0,-2, 0, 0, 2, 0.0, 0.0, 0.0, 1.0, 0.0, 0.0}, + { 0,-2, 0, 0, 2, 4.0, 0.0, 0.0, -2.0, 0.0, 0.0}, + {-3, 0, 0, 3, 0, 6.0, 0.0, 0.0, 0.0, 0.0, 0.0}, + {-2,-1, 0, 2, 2, 5.0, 0.0, 0.0, -2.0, 0.0, 0.0}, + {-1, 0,-2, 3, 0, -7.0, 0.0, 0.0, 0.0, 0.0, 0.0}, + {-4, 0, 0, 4, 0, -12.0, 0.0, 0.0, 0.0, 0.0, 0.0}, + { 2, 1,-2, 0, 1, 5.0, 0.0, 0.0, -3.0, 0.0, 0.0}, + { 2,-1, 0,-2, 2, 3.0, 0.0, 0.0, -1.0, 0.0, 0.0}, + + /* 471-480 */ + { 0, 0, 1,-1, 0, -5.0, 0.0, 0.0, 0.0, 0.0, 0.0}, + {-1, 2, 0, 1, 0, 3.0, 0.0, 0.0, 0.0, 0.0, 0.0}, + {-2, 1, 2, 0, 2, -7.0, 0.0, 0.0, 3.0, 0.0, 0.0}, + { 1, 1, 0,-1, 1, 7.0, 0.0, 0.0, -4.0, 0.0, 0.0}, + { 1, 0, 1,-2, 1, 0.0, 0.0, -12.0, 0.0, 0.0, -10.0}, + { 0, 2, 0, 0, 2, 4.0, 0.0, 0.0, -2.0, 0.0, 0.0}, + { 1,-1, 2,-3, 1, 3.0, 0.0, 0.0, -2.0, 0.0, 0.0}, + {-1, 1, 2,-1, 1, -3.0, 0.0, 0.0, 2.0, 0.0, 0.0}, + {-2, 0, 4,-2, 2, -7.0, 0.0, 0.0, 3.0, 0.0, 0.0}, + {-2, 0, 4,-2, 1, -4.0, 0.0, 0.0, 2.0, 0.0, 0.0}, + + /* 481-490 */ + {-2,-2, 0, 2, 1, -3.0, 0.0, 0.0, 1.0, 0.0, 0.0}, + {-2, 0,-2, 4, 0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0}, + { 1, 2, 2,-4, 1, -3.0, 0.0, 0.0, 1.0, 0.0, 0.0}, + { 1, 1, 2,-4, 2, 7.0, 0.0, 0.0, -3.0, 0.0, 0.0}, + {-1, 2, 2,-2, 1, -4.0, 0.0, 0.0, 2.0, 0.0, 0.0}, + { 2, 0, 0,-3, 1, 4.0, 0.0, 0.0, -2.0, 0.0, 0.0}, + {-1, 2, 0, 0, 1, -5.0, 0.0, 0.0, 3.0, 0.0, 0.0}, + { 0, 0, 0,-2, 0, 5.0, 0.0, 0.0, 0.0, 0.0, 0.0}, + {-1,-1, 2,-2, 2, -5.0, 0.0, 0.0, 2.0, 0.0, 0.0}, + {-1, 1, 0, 0, 2, 5.0, 0.0, 0.0, -2.0, 0.0, 0.0}, + + /* 491-500 */ + { 0, 0, 0,-1, 2, -8.0, 0.0, 0.0, 3.0, 0.0, 0.0}, + {-2, 1, 0, 1, 0, 9.0, 0.0, 0.0, 0.0, 0.0, 0.0}, + { 1,-2, 0,-2, 1, 6.0, 0.0, 0.0, -3.0, 0.0, 0.0}, + { 1, 0,-2, 0, 2, -5.0, 0.0, 0.0, 2.0, 0.0, 0.0}, + {-3, 1, 0, 2, 0, 3.0, 0.0, 0.0, 0.0, 0.0, 0.0}, + {-1, 1,-2, 2, 0, -7.0, 0.0, 0.0, 0.0, 0.0, 0.0}, + {-1,-1, 0, 0, 2, -3.0, 0.0, 0.0, 1.0, 0.0, 0.0}, + {-3, 0, 0, 2, 0, 5.0, 0.0, 0.0, 0.0, 0.0, 0.0}, + {-3,-1, 0, 2, 0, 3.0, 0.0, 0.0, 0.0, 0.0, 0.0}, + { 2, 0, 2,-6, 1, -3.0, 0.0, 0.0, 2.0, 0.0, 0.0}, + + /* 501-510 */ + { 0, 1, 2,-4, 2, 4.0, 0.0, 0.0, -2.0, 0.0, 0.0}, + { 2, 0, 0,-4, 2, 3.0, 0.0, 0.0, -1.0, 0.0, 0.0}, + {-2, 1, 2,-2, 1, -5.0, 0.0, 0.0, 2.0, 0.0, 0.0}, + { 0,-1, 2,-4, 1, 4.0, 0.0, 0.0, -2.0, 0.0, 0.0}, + { 0, 1, 0,-2, 2, 9.0, 0.0, 0.0, -3.0, 0.0, 0.0}, + {-1, 0, 0,-2, 0, 4.0, 0.0, 0.0, 0.0, 0.0, 0.0}, + { 2, 0,-2,-2, 1, 4.0, 0.0, 0.0, -2.0, 0.0, 0.0}, + {-4, 0, 2, 0, 1, -3.0, 0.0, 0.0, 2.0, 0.0, 0.0}, + {-1,-1, 0,-1, 1, -4.0, 0.0, 0.0, 2.0, 0.0, 0.0}, + { 0, 0,-2, 0, 2, 9.0, 0.0, 0.0, -3.0, 0.0, 0.0}, + + /* 511-520 */ + {-3, 0, 0, 1, 0, -4.0, 0.0, 0.0, 0.0, 0.0, 0.0}, + {-1, 0,-2, 1, 0, -4.0, 0.0, 0.0, 0.0, 0.0, 0.0}, + {-2, 0,-2, 2, 1, 3.0, 0.0, 0.0, -2.0, 0.0, 0.0}, + { 0, 0,-4, 2, 0, 8.0, 0.0, 0.0, 0.0, 0.0, 0.0}, + {-2,-1,-2, 2, 0, 3.0, 0.0, 0.0, 0.0, 0.0, 0.0}, + { 1, 0, 2,-6, 1, -3.0, 0.0, 0.0, 2.0, 0.0, 0.0}, + {-1, 0, 2,-4, 2, 3.0, 0.0, 0.0, -1.0, 0.0, 0.0}, + { 1, 0, 0,-4, 2, 3.0, 0.0, 0.0, -1.0, 0.0, 0.0}, + { 2, 1, 2,-4, 2, -3.0, 0.0, 0.0, 1.0, 0.0, 0.0}, + { 2, 1, 2,-4, 1, 6.0, 0.0, 0.0, -3.0, 0.0, 0.0}, + + /* 521-530 */ + { 0, 1, 4,-4, 4, 3.0, 0.0, 0.0, 0.0, 0.0, 0.0}, + { 0, 1, 4,-4, 2, -3.0, 0.0, 0.0, 1.0, 0.0, 0.0}, + {-1,-1,-2, 4, 0, -7.0, 0.0, 0.0, 0.0, 0.0, 0.0}, + {-1,-3, 0, 2, 0, 9.0, 0.0, 0.0, 0.0, 0.0, 0.0}, + {-1, 0,-2, 4, 1, -3.0, 0.0, 0.0, 2.0, 0.0, 0.0}, + {-2,-1, 0, 3, 0, -3.0, 0.0, 0.0, 0.0, 0.0, 0.0}, + { 0, 0,-2, 3, 0, -4.0, 0.0, 0.0, 0.0, 0.0, 0.0}, + {-2, 0, 0, 3, 1, -5.0, 0.0, 0.0, 3.0, 0.0, 0.0}, + { 0,-1, 0, 1, 0, -13.0, 0.0, 0.0, 0.0, 0.0, 0.0}, + {-3, 0, 2, 2, 0, -7.0, 0.0, 0.0, 0.0, 0.0, 0.0}, + + /* 531-540 */ + { 1, 1,-2, 2, 0, 10.0, 0.0, 0.0, 0.0, 0.0, 0.0}, + {-1, 1, 0, 2, 2, 3.0, 0.0, 0.0, -1.0, 0.0, 0.0}, + { 1,-2, 2,-2, 1, 10.0, 0.0, 13.0, 6.0, 0.0, -5.0}, + { 0, 0, 1, 0, 2, 0.0, 0.0, 30.0, 0.0, 0.0, 14.0}, + { 0, 0, 1, 0, 1, 0.0, 0.0, -162.0, 0.0, 0.0, -138.0}, + { 0, 0, 1, 0, 0, 0.0, 0.0, 75.0, 0.0, 0.0, 0.0}, + {-1, 2, 0, 2, 1, -7.0, 0.0, 0.0, 4.0, 0.0, 0.0}, + { 0, 0, 2, 0, 2, -4.0, 0.0, 0.0, 2.0, 0.0, 0.0}, + {-2, 0, 2, 0, 2, 4.0, 0.0, 0.0, -2.0, 0.0, 0.0}, + { 2, 0, 0,-1, 1, 5.0, 0.0, 0.0, -2.0, 0.0, 0.0}, + + /* 541-550 */ + { 3, 0, 0,-2, 1, 5.0, 0.0, 0.0, -3.0, 0.0, 0.0}, + { 1, 0, 2,-2, 3, -3.0, 0.0, 0.0, 0.0, 0.0, 0.0}, + { 1, 2, 0, 0, 1, -3.0, 0.0, 0.0, 2.0, 0.0, 0.0}, + { 2, 0, 2,-3, 2, -4.0, 0.0, 0.0, 2.0, 0.0, 0.0}, + {-1, 1, 4,-2, 2, -5.0, 0.0, 0.0, 2.0, 0.0, 0.0}, + {-2,-2, 0, 4, 0, 6.0, 0.0, 0.0, 0.0, 0.0, 0.0}, + { 0,-3, 0, 2, 0, 9.0, 0.0, 0.0, 0.0, 0.0, 0.0}, + { 0, 0,-2, 4, 0, 5.0, 0.0, 0.0, 0.0, 0.0, 0.0}, + {-1,-1, 0, 3, 0, -7.0, 0.0, 0.0, 0.0, 0.0, 0.0}, + {-2, 0, 0, 4, 2, -3.0, 0.0, 0.0, 1.0, 0.0, 0.0}, + + /* 551-560 */ + {-1, 0, 0, 3, 1, -4.0, 0.0, 0.0, 2.0, 0.0, 0.0}, + { 2,-2, 0, 0, 0, 7.0, 0.0, 0.0, 0.0, 0.0, 0.0}, + { 1,-1, 0, 1, 0, -4.0, 0.0, 0.0, 0.0, 0.0, 0.0}, + {-1, 0, 0, 2, 0, 4.0, 0.0, 0.0, 0.0, 0.0, 0.0}, + { 0,-2, 2, 0, 1, -6.0, 0.0, -3.0, 3.0, 0.0, 1.0}, + {-1, 0, 1, 2, 1, 0.0, 0.0, -3.0, 0.0, 0.0, -2.0}, + {-1, 1, 0, 3, 0, 11.0, 0.0, 0.0, 0.0, 0.0, 0.0}, + {-1,-1, 2, 1, 2, 3.0, 0.0, 0.0, -1.0, 0.0, 0.0}, + { 0,-1, 2, 0, 0, 11.0, 0.0, 0.0, 0.0, 0.0, 0.0}, + {-2, 1, 2, 2, 1, -3.0, 0.0, 0.0, 2.0, 0.0, 0.0}, + + /* 561-570 */ + { 2,-2, 2,-2, 2, -1.0, 0.0, 3.0, 3.0, 0.0, -1.0}, + { 1, 1, 0, 1, 1, 4.0, 0.0, 0.0, -2.0, 0.0, 0.0}, + { 1, 0, 1, 0, 1, 0.0, 0.0, -13.0, 0.0, 0.0, -11.0}, + { 1, 0, 1, 0, 0, 3.0, 0.0, 6.0, 0.0, 0.0, 0.0}, + { 0, 2, 0, 2, 0, -7.0, 0.0, 0.0, 0.0, 0.0, 0.0}, + { 2,-1, 2,-2, 1, 5.0, 0.0, 0.0, -3.0, 0.0, 0.0}, + { 0,-1, 4,-2, 1, -3.0, 0.0, 0.0, 1.0, 0.0, 0.0}, + { 0, 0, 4,-2, 3, 3.0, 0.0, 0.0, 0.0, 0.0, 0.0}, + { 0, 1, 4,-2, 1, 5.0, 0.0, 0.0, -3.0, 0.0, 0.0}, + { 4, 0, 2,-4, 2, -7.0, 0.0, 0.0, 3.0, 0.0, 0.0}, + + /* 571-580 */ + { 2, 2, 2,-2, 2, 8.0, 0.0, 0.0, -3.0, 0.0, 0.0}, + { 2, 0, 4,-4, 2, -4.0, 0.0, 0.0, 2.0, 0.0, 0.0}, + {-1,-2, 0, 4, 0, 11.0, 0.0, 0.0, 0.0, 0.0, 0.0}, + {-1,-3, 2, 2, 2, -3.0, 0.0, 0.0, 1.0, 0.0, 0.0}, + {-3, 0, 2, 4, 2, 3.0, 0.0, 0.0, -1.0, 0.0, 0.0}, + {-3, 0, 2,-2, 1, -4.0, 0.0, 0.0, 2.0, 0.0, 0.0}, + {-1,-1, 0,-2, 1, 8.0, 0.0, 0.0, -4.0, 0.0, 0.0}, + {-3, 0, 0, 0, 2, 3.0, 0.0, 0.0, -1.0, 0.0, 0.0}, + {-3, 0,-2, 2, 0, 11.0, 0.0, 0.0, 0.0, 0.0, 0.0}, + { 0, 1, 0,-4, 1, -6.0, 0.0, 0.0, 3.0, 0.0, 0.0}, + + /* 581-590 */ + {-2, 1, 0,-2, 1, -4.0, 0.0, 0.0, 2.0, 0.0, 0.0}, + {-4, 0, 0, 0, 1, -8.0, 0.0, 0.0, 4.0, 0.0, 0.0}, + {-1, 0, 0,-4, 1, -7.0, 0.0, 0.0, 3.0, 0.0, 0.0}, + {-3, 0, 0,-2, 1, -4.0, 0.0, 0.0, 2.0, 0.0, 0.0}, + { 0, 0, 0, 3, 2, 3.0, 0.0, 0.0, -1.0, 0.0, 0.0}, + {-1, 1, 0, 4, 1, 6.0, 0.0, 0.0, -3.0, 0.0, 0.0}, + { 1,-2, 2, 0, 1, -6.0, 0.0, 0.0, 3.0, 0.0, 0.0}, + { 0, 1, 0, 3, 0, 6.0, 0.0, 0.0, 0.0, 0.0, 0.0}, + {-1, 0, 2, 2, 3, 6.0, 0.0, 0.0, -1.0, 0.0, 0.0}, + { 0, 0, 2, 2, 2, 5.0, 0.0, 0.0, -2.0, 0.0, 0.0}, + + /* 591-600 */ + {-2, 0, 2, 2, 2, -5.0, 0.0, 0.0, 2.0, 0.0, 0.0}, + {-1, 1, 2, 2, 0, -4.0, 0.0, 0.0, 0.0, 0.0, 0.0}, + { 3, 0, 0, 0, 2, -4.0, 0.0, 0.0, 2.0, 0.0, 0.0}, + { 2, 1, 0, 1, 0, 4.0, 0.0, 0.0, 0.0, 0.0, 0.0}, + { 2,-1, 2,-1, 2, 6.0, 0.0, 0.0, -3.0, 0.0, 0.0}, + { 0, 0, 2, 0, 1, -4.0, 0.0, 0.0, 2.0, 0.0, 0.0}, + { 0, 0, 3, 0, 3, 0.0, 0.0, -26.0, 0.0, 0.0, -11.0}, + { 0, 0, 3, 0, 2, 0.0, 0.0, -10.0, 0.0, 0.0, -5.0}, + {-1, 2, 2, 2, 1, 5.0, 0.0, 0.0, -3.0, 0.0, 0.0}, + {-1, 0, 4, 0, 0, -13.0, 0.0, 0.0, 0.0, 0.0, 0.0}, + + /* 601-610 */ + { 1, 2, 2, 0, 1, 3.0, 0.0, 0.0, -2.0, 0.0, 0.0}, + { 3, 1, 2,-2, 1, 4.0, 0.0, 0.0, -2.0, 0.0, 0.0}, + { 1, 1, 4,-2, 2, 7.0, 0.0, 0.0, -3.0, 0.0, 0.0}, + {-2,-1, 0, 6, 0, 4.0, 0.0, 0.0, 0.0, 0.0, 0.0}, + { 0,-2, 0, 4, 0, 5.0, 0.0, 0.0, 0.0, 0.0, 0.0}, + {-2, 0, 0, 6, 1, -3.0, 0.0, 0.0, 2.0, 0.0, 0.0}, + {-2,-2, 2, 4, 2, -6.0, 0.0, 0.0, 2.0, 0.0, 0.0}, + { 0,-3, 2, 2, 2, -5.0, 0.0, 0.0, 2.0, 0.0, 0.0}, + { 0, 0, 0, 4, 2, -7.0, 0.0, 0.0, 3.0, 0.0, 0.0}, + {-1,-1, 2, 3, 2, 5.0, 0.0, 0.0, -2.0, 0.0, 0.0}, + + /* 611-620 */ + {-2, 0, 2, 4, 0, 13.0, 0.0, 0.0, 0.0, 0.0, 0.0}, + { 2,-1, 0, 2, 1, -4.0, 0.0, 0.0, 2.0, 0.0, 0.0}, + { 1, 0, 0, 3, 0, -3.0, 0.0, 0.0, 0.0, 0.0, 0.0}, + { 0, 1, 0, 4, 1, 5.0, 0.0, 0.0, -2.0, 0.0, 0.0}, + { 0, 1, 0, 4, 0, -11.0, 0.0, 0.0, 0.0, 0.0, 0.0}, + { 1,-1, 2, 1, 2, 5.0, 0.0, 0.0, -2.0, 0.0, 0.0}, + { 0, 0, 2, 2, 3, 4.0, 0.0, 0.0, 0.0, 0.0, 0.0}, + { 1, 0, 2, 2, 2, 4.0, 0.0, 0.0, -2.0, 0.0, 0.0}, + {-1, 0, 2, 2, 2, -4.0, 0.0, 0.0, 2.0, 0.0, 0.0}, + {-2, 0, 4, 2, 1, 6.0, 0.0, 0.0, -3.0, 0.0, 0.0}, + + /* 621-630 */ + { 2, 1, 0, 2, 1, 3.0, 0.0, 0.0, -2.0, 0.0, 0.0}, + { 2, 1, 0, 2, 0, -12.0, 0.0, 0.0, 0.0, 0.0, 0.0}, + { 2,-1, 2, 0, 0, 4.0, 0.0, 0.0, 0.0, 0.0, 0.0}, + { 1, 0, 2, 1, 0, -3.0, 0.0, 0.0, 0.0, 0.0, 0.0}, + { 0, 1, 2, 2, 0, -4.0, 0.0, 0.0, 0.0, 0.0, 0.0}, + { 2, 0, 2, 0, 3, 3.0, 0.0, 0.0, 0.0, 0.0, 0.0}, + { 3, 0, 2, 0, 2, 3.0, 0.0, 0.0, -1.0, 0.0, 0.0}, + { 1, 0, 2, 0, 2, -3.0, 0.0, 0.0, 1.0, 0.0, 0.0}, + { 1, 0, 3, 0, 3, 0.0, 0.0, -5.0, 0.0, 0.0, -2.0}, + { 1, 1, 2, 1, 1, -7.0, 0.0, 0.0, 4.0, 0.0, 0.0}, + + /* 631-640 */ + { 0, 2, 2, 2, 2, 6.0, 0.0, 0.0, -3.0, 0.0, 0.0}, + { 2, 1, 2, 0, 0, -3.0, 0.0, 0.0, 0.0, 0.0, 0.0}, + { 2, 0, 4,-2, 1, 5.0, 0.0, 0.0, -3.0, 0.0, 0.0}, + { 4, 1, 2,-2, 2, 3.0, 0.0, 0.0, -1.0, 0.0, 0.0}, + {-1,-1, 0, 6, 0, 3.0, 0.0, 0.0, 0.0, 0.0, 0.0}, + {-3,-1, 2, 6, 2, -3.0, 0.0, 0.0, 1.0, 0.0, 0.0}, + {-1, 0, 0, 6, 1, -5.0, 0.0, 0.0, 3.0, 0.0, 0.0}, + {-3, 0, 2, 6, 1, -3.0, 0.0, 0.0, 2.0, 0.0, 0.0}, + { 1,-1, 0, 4, 1, -3.0, 0.0, 0.0, 2.0, 0.0, 0.0}, + { 1,-1, 0, 4, 0, 12.0, 0.0, 0.0, 0.0, 0.0, 0.0}, + + /* 641-650 */ + {-2, 0, 2, 5, 2, 3.0, 0.0, 0.0, -1.0, 0.0, 0.0}, + { 1,-2, 2, 2, 1, -4.0, 0.0, 0.0, 2.0, 0.0, 0.0}, + { 3,-1, 0, 2, 0, 4.0, 0.0, 0.0, 0.0, 0.0, 0.0}, + { 1,-1, 2, 2, 0, 6.0, 0.0, 0.0, 0.0, 0.0, 0.0}, + { 0, 0, 2, 3, 1, 5.0, 0.0, 0.0, -3.0, 0.0, 0.0}, + {-1, 1, 2, 4, 1, 4.0, 0.0, 0.0, -2.0, 0.0, 0.0}, + { 0, 1, 2, 3, 2, -6.0, 0.0, 0.0, 3.0, 0.0, 0.0}, + {-1, 0, 4, 2, 1, 4.0, 0.0, 0.0, -2.0, 0.0, 0.0}, + { 2, 0, 2, 1, 1, 6.0, 0.0, 0.0, -3.0, 0.0, 0.0}, + { 5, 0, 0, 0, 0, 6.0, 0.0, 0.0, 0.0, 0.0, 0.0}, + + /* 651-660 */ + { 2, 1, 2, 1, 2, -6.0, 0.0, 0.0, 3.0, 0.0, 0.0}, + { 1, 0, 4, 0, 1, 3.0, 0.0, 0.0, -2.0, 0.0, 0.0}, + { 3, 1, 2, 0, 1, 7.0, 0.0, 0.0, -4.0, 0.0, 0.0}, + { 3, 0, 4,-2, 2, 4.0, 0.0, 0.0, -2.0, 0.0, 0.0}, + {-2,-1, 2, 6, 2, -5.0, 0.0, 0.0, 2.0, 0.0, 0.0}, + { 0, 0, 0, 6, 0, 5.0, 0.0, 0.0, 0.0, 0.0, 0.0}, + { 0,-2, 2, 4, 2, -6.0, 0.0, 0.0, 3.0, 0.0, 0.0}, + {-2, 0, 2, 6, 1, -6.0, 0.0, 0.0, 3.0, 0.0, 0.0}, + { 2, 0, 0, 4, 1, -4.0, 0.0, 0.0, 2.0, 0.0, 0.0}, + { 2, 0, 0, 4, 0, 10.0, 0.0, 0.0, 0.0, 0.0, 0.0}, + + /* 661-670 */ + { 2,-2, 2, 2, 2, -4.0, 0.0, 0.0, 2.0, 0.0, 0.0}, + { 0, 0, 2, 4, 0, 7.0, 0.0, 0.0, 0.0, 0.0, 0.0}, + { 1, 0, 2, 3, 2, 7.0, 0.0, 0.0, -3.0, 0.0, 0.0}, + { 4, 0, 0, 2, 0, 4.0, 0.0, 0.0, 0.0, 0.0, 0.0}, + { 2, 0, 2, 2, 0, 11.0, 0.0, 0.0, 0.0, 0.0, 0.0}, + { 0, 0, 4, 2, 2, 5.0, 0.0, 0.0, -2.0, 0.0, 0.0}, + { 4,-1, 2, 0, 2, -6.0, 0.0, 0.0, 2.0, 0.0, 0.0}, + { 3, 0, 2, 1, 2, 4.0, 0.0, 0.0, -2.0, 0.0, 0.0}, + { 2, 1, 2, 2, 1, 3.0, 0.0, 0.0, -2.0, 0.0, 0.0}, + { 4, 1, 2, 0, 2, 5.0, 0.0, 0.0, -2.0, 0.0, 0.0}, + + /* 671-678 */ + {-1,-1, 2, 6, 2, -4.0, 0.0, 0.0, 2.0, 0.0, 0.0}, + {-1, 0, 2, 6, 1, -4.0, 0.0, 0.0, 2.0, 0.0, 0.0}, + { 1,-1, 2, 4, 1, -3.0, 0.0, 0.0, 2.0, 0.0, 0.0}, + { 1, 1, 2, 4, 2, 4.0, 0.0, 0.0, -2.0, 0.0, 0.0}, + { 3, 1, 2, 2, 2, 3.0, 0.0, 0.0, -1.0, 0.0, 0.0}, + { 5, 0, 2, 0, 1, -3.0, 0.0, 0.0, 1.0, 0.0, 0.0}, + { 2,-1, 2, 4, 2, -3.0, 0.0, 0.0, 1.0, 0.0, 0.0}, + { 2, 0, 2, 4, 1, -3.0, 0.0, 0.0, 2.0, 0.0, 0.0} + }; + +/* Number of terms in the luni-solar nutation model */ + const int NLS = (int) (sizeof xls / sizeof xls[0]); + +/* ------------------------ */ +/* Planetary nutation model */ +/* ------------------------ */ + +/* The units for the sine and cosine coefficients are */ +/* 0.1 microarcsecond */ + + static const struct { + int nl, /* coefficients of l, F, D and Omega */ + nf, + nd, + nom, + nme, /* coefficients of planetary longitudes */ + nve, + nea, + nma, + nju, + nsa, + nur, + nne, + npa; /* coefficient of general precession */ + int sp,cp; /* longitude sin, cos coefficients */ + int se,ce; /* obliquity sin, cos coefficients */ + } xpl[] = { + + /* 1-10 */ + { 0, 0, 0, 0, 0, 0, 8,-16, 4, 5, 0, 0, 0, 1440, 0, 0, 0}, + { 0, 0, 0, 0, 0, 0, -8, 16,-4,-5, 0, 0, 2, 56,-117, -42, -40}, + { 0, 0, 0, 0, 0, 0, 8,-16, 4, 5, 0, 0, 2, 125, -43, 0, -54}, + { 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,-1, 2, 2, 0, 5, 0, 0}, + { 0, 0, 0, 0, 0, 0, -4, 8,-1,-5, 0, 0, 2, 3, -7, -3, 0}, + { 0, 0, 0, 0, 0, 0, 4, -8, 3, 0, 0, 0, 1, 3, 0, 0, -2}, + { 0, 1,-1, 1, 0, 0, 3, -8, 3, 0, 0, 0, 0, -114, 0, 0, 61}, + {-1, 0, 0, 0, 0, 10, -3, 0, 0, 0, 0, 0, 0, -219, 89, 0, 0}, + { 0, 0, 0, 0, 0, 0, 0, 0,-2, 6,-3, 0, 2, -3, 0, 0, 0}, + { 0, 0, 0, 0, 0, 0, 4, -8, 3, 0, 0, 0, 0, -462,1604, 0, 0}, + + /* 11-20 */ + { 0, 1,-1, 1, 0, 0, -5, 8,-3, 0, 0, 0, 0, 99, 0, 0, -53}, + { 0, 0, 0, 0, 0, 0, -4, 8,-3, 0, 0, 0, 1, -3, 0, 0, 2}, + { 0, 0, 0, 0, 0, 0, 4, -8, 1, 5, 0, 0, 2, 0, 6, 2, 0}, + { 0, 0, 0, 0, 0, -5, 6, 4, 0, 0, 0, 0, 2, 3, 0, 0, 0}, + { 0, 0, 0, 0, 0, 0, 0, 0, 2,-5, 0, 0, 2, -12, 0, 0, 0}, + { 0, 0, 0, 0, 0, 0, 0, 0, 2,-5, 0, 0, 1, 14,-218, 117, 8}, + { 0, 1,-1, 1, 0, 0, -1, 0, 2,-5, 0, 0, 0, 31,-481, -257, -17}, + { 0, 0, 0, 0, 0, 0, 0, 0, 2,-5, 0, 0, 0, -491, 128, 0, 0}, + { 0, 1,-1, 1, 0, 0, -1, 0,-2, 5, 0, 0, 0,-3084,5123, 2735,1647}, + { 0, 0, 0, 0, 0, 0, 0, 0,-2, 5, 0, 0, 1,-1444,2409,-1286,-771}, + + /* 21-30 */ + { 0, 0, 0, 0, 0, 0, 0, 0,-2, 5, 0, 0, 2, 11, -24, -11, -9}, + { 2,-1,-1, 0, 0, 0, 3, -7, 0, 0, 0, 0, 0, 26, -9, 0, 0}, + { 1, 0,-2, 0, 0, 19,-21, 3, 0, 0, 0, 0, 0, 103, -60, 0, 0}, + { 0, 1,-1, 1, 0, 2, -4, 0,-3, 0, 0, 0, 0, 0, -13, -7, 0}, + { 1, 0,-1, 1, 0, 0, -1, 0, 2, 0, 0, 0, 0, -26, -29, -16, 14}, + { 0, 1,-1, 1, 0, 0, -1, 0,-4,10, 0, 0, 0, 9, -27, -14, -5}, + {-2, 0, 2, 1, 0, 0, 2, 0, 0,-5, 0, 0, 0, 12, 0, 0, -6}, + { 0, 0, 0, 0, 0, 3, -7, 4, 0, 0, 0, 0, 0, -7, 0, 0, 0}, + { 0,-1, 1, 0, 0, 0, 1, 0, 1,-1, 0, 0, 0, 0, 24, 0, 0}, + {-2, 0, 2, 1, 0, 0, 2, 0,-2, 0, 0, 0, 0, 284, 0, 0,-151}, + + /* 31-40 */ + {-1, 0, 0, 0, 0, 18,-16, 0, 0, 0, 0, 0, 0, 226, 101, 0, 0}, + {-2, 1, 1, 2, 0, 0, 1, 0,-2, 0, 0, 0, 0, 0, -8, -2, 0}, + {-1, 1,-1, 1, 0, 18,-17, 0, 0, 0, 0, 0, 0, 0, -6, -3, 0}, + {-1, 0, 1, 1, 0, 0, 2, -2, 0, 0, 0, 0, 0, 5, 0, 0, -3}, + { 0, 0, 0, 0, 0, -8, 13, 0, 0, 0, 0, 0, 2, -41, 175, 76, 17}, + { 0, 2,-2, 2, 0, -8, 11, 0, 0, 0, 0, 0, 0, 0, 15, 6, 0}, + { 0, 0, 0, 0, 0, -8, 13, 0, 0, 0, 0, 0, 1, 425, 212, -133, 269}, + { 0, 1,-1, 1, 0, -8, 12, 0, 0, 0, 0, 0, 0, 1200, 598, 319,-641}, + { 0, 0, 0, 0, 0, 8,-13, 0, 0, 0, 0, 0, 0, 235, 334, 0, 0}, + { 0, 1,-1, 1, 0, 8,-14, 0, 0, 0, 0, 0, 0, 11, -12, -7, -6}, + + /* 41-50 */ + { 0, 0, 0, 0, 0, 8,-13, 0, 0, 0, 0, 0, 1, 5, -6, 3, 3}, + {-2, 0, 2, 1, 0, 0, 2, 0,-4, 5, 0, 0, 0, -5, 0, 0, 3}, + {-2, 0, 2, 2, 0, 3, -3, 0, 0, 0, 0, 0, 0, 6, 0, 0, -3}, + {-2, 0, 2, 0, 0, 0, 2, 0,-3, 1, 0, 0, 0, 15, 0, 0, 0}, + { 0, 0, 0, 1, 0, 3, -5, 0, 2, 0, 0, 0, 0, 13, 0, 0, -7}, + {-2, 0, 2, 0, 0, 0, 2, 0,-4, 3, 0, 0, 0, -6, -9, 0, 0}, + { 0,-1, 1, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 266, -78, 0, 0}, + { 0, 0, 0, 1, 0, 0, -1, 2, 0, 0, 0, 0, 0, -460,-435, -232, 246}, + { 0, 1,-1, 2, 0, 0, -2, 2, 0, 0, 0, 0, 0, 0, 15, 7, 0}, + {-1, 1, 0, 1, 0, 3, -5, 0, 0, 0, 0, 0, 0, -3, 0, 0, 2}, + + /* 51-60 */ + {-1, 0, 1, 0, 0, 3, -4, 0, 0, 0, 0, 0, 0, 0, 131, 0, 0}, + {-2, 0, 2, 0, 0, 0, 2, 0,-2,-2, 0, 0, 0, 4, 0, 0, 0}, + {-2, 2, 0, 2, 0, 0, -5, 9, 0, 0, 0, 0, 0, 0, 3, 0, 0}, + { 0, 1,-1, 1, 0, 0, -1, 0, 0, 0,-1, 0, 0, 0, 4, 2, 0}, + { 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 3, 0, 0}, + { 0, 1,-1, 1, 0, 0, -1, 0, 0, 0, 0, 2, 0, -17, -19, -10, 9}, + { 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 1, -9, -11, 6, -5}, + { 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 2, -6, 0, 0, 3}, + {-1, 0, 1, 0, 0, 0, 3, -4, 0, 0, 0, 0, 0, -16, 8, 0, 0}, + { 0,-1, 1, 0, 0, 0, 1, 0, 0, 2, 0, 0, 0, 0, 3, 0, 0}, + + /* 61-70 */ + { 0, 1,-1, 2, 0, 0, -1, 0, 0, 2, 0, 0, 0, 11, 24, 11, -5}, + { 0, 0, 0, 1, 0, 0, -9, 17, 0, 0, 0, 0, 0, -3, -4, -2, 1}, + { 0, 0, 0, 2, 0, -3, 5, 0, 0, 0, 0, 0, 0, 3, 0, 0, -1}, + { 0, 1,-1, 1, 0, 0, -1, 0,-1, 2, 0, 0, 0, 0, -8, -4, 0}, + { 0, 0, 0, 0, 0, 0, 0, 0, 1,-2, 0, 0, 0, 0, 3, 0, 0}, + { 1, 0,-2, 0, 0, 17,-16, 0,-2, 0, 0, 0, 0, 0, 5, 0, 0}, + { 0, 1,-1, 1, 0, 0, -1, 0, 1,-3, 0, 0, 0, 0, 3, 2, 0}, + {-2, 0, 2, 1, 0, 0, 5, -6, 0, 0, 0, 0, 0, -6, 4, 2, 3}, + { 0,-2, 2, 0, 0, 0, 9,-13, 0, 0, 0, 0, 0, -3, -5, 0, 0}, + { 0, 1,-1, 2, 0, 0, -1, 0, 0, 1, 0, 0, 0, -5, 0, 0, 2}, + + /* 71-80 */ + { 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 4, 24, 13, -2}, + { 0,-1, 1, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, -42, 20, 0, 0}, + { 0,-2, 2, 0, 0, 5, -6, 0, 0, 0, 0, 0, 0, -10, 233, 0, 0}, + { 0,-1, 1, 1, 0, 5, -7, 0, 0, 0, 0, 0, 0, -3, 0, 0, 1}, + {-2, 0, 2, 0, 0, 6, -8, 0, 0, 0, 0, 0, 0, 78, -18, 0, 0}, + { 2, 1,-3, 1, 0, -6, 7, 0, 0, 0, 0, 0, 0, 0, 3, 1, 0}, + { 0, 0, 0, 2, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, -3, -1, 0}, + { 0,-1, 1, 1, 0, 0, 1, 0, 1, 0, 0, 0, 0, 0, -4, -2, 1}, + { 0, 1,-1, 1, 0, 0, -1, 0, 0, 0, 2, 0, 0, 0, -8, -4, -1}, + { 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 1, 0, -5, 3, 0}, + + /* 81-90 */ + { 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 2, -7, 0, 0, 3}, + { 0, 0, 0, 0, 0, 0, -8, 15, 0, 0, 0, 0, 2, -14, 8, 3, 6}, + { 0, 0, 0, 0, 0, 0, -8, 15, 0, 0, 0, 0, 1, 0, 8, -4, 0}, + { 0, 1,-1, 1, 0, 0, -9, 15, 0, 0, 0, 0, 0, 0, 19, 10, 0}, + { 0, 0, 0, 0, 0, 0, 8,-15, 0, 0, 0, 0, 0, 45, -22, 0, 0}, + { 1,-1,-1, 0, 0, 0, 8,-15, 0, 0, 0, 0, 0, -3, 0, 0, 0}, + { 2, 0,-2, 0, 0, 2, -5, 0, 0, 0, 0, 0, 0, 0, -3, 0, 0}, + {-2, 0, 2, 0, 0, 0, 2, 0,-5, 5, 0, 0, 0, 0, 3, 0, 0}, + { 2, 0,-2, 1, 0, 0, -6, 8, 0, 0, 0, 0, 0, 3, 5, 3, -2}, + { 2, 0,-2, 1, 0, 0, -2, 0, 3, 0, 0, 0, 0, 89, -16, -9, -48}, + + /* 91-100 */ + {-2, 1, 1, 0, 0, 0, 1, 0,-3, 0, 0, 0, 0, 0, 3, 0, 0}, + {-2, 1, 1, 1, 0, 0, 1, 0,-3, 0, 0, 0, 0, -3, 7, 4, 2}, + {-2, 0, 2, 0, 0, 0, 2, 0,-3, 0, 0, 0, 0, -349, -62, 0, 0}, + {-2, 0, 2, 0, 0, 0, 6, -8, 0, 0, 0, 0, 0, -15, 22, 0, 0}, + {-2, 0, 2, 0, 0, 0, 2, 0,-1,-5, 0, 0, 0, -3, 0, 0, 0}, + {-1, 0, 1, 0, 0, 0, 1, 0,-1, 0, 0, 0, 0, -53, 0, 0, 0}, + {-1, 1, 1, 1, 0,-20, 20, 0, 0, 0, 0, 0, 0, 5, 0, 0, -3}, + { 1, 0,-2, 0, 0, 20,-21, 0, 0, 0, 0, 0, 0, 0, -8, 0, 0}, + { 0, 0, 0, 1, 0, 0, 8,-15, 0, 0, 0, 0, 0, 15, -7, -4, -8}, + { 0, 2,-2, 1, 0, 0,-10, 15, 0, 0, 0, 0, 0, -3, 0, 0, 1}, + + /* 101-110 */ + { 0,-1, 1, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, -21, -78, 0, 0}, + { 0, 0, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 20, -70, -37, -11}, + { 0, 1,-1, 2, 0, 0, -1, 0, 1, 0, 0, 0, 0, 0, 6, 3, 0}, + { 0, 1,-1, 1, 0, 0, -1, 0,-2, 4, 0, 0, 0, 5, 3, 2, -2}, + { 2, 0,-2, 1, 0, -6, 8, 0, 0, 0, 0, 0, 0, -17, -4, -2, 9}, + { 0,-2, 2, 1, 0, 5, -6, 0, 0, 0, 0, 0, 0, 0, 6, 3, 0}, + { 0, 0, 0, 0, 0, 0, 0, 0, 0,-1, 0, 0, 1, 32, 15, -8, 17}, + { 0, 1,-1, 1, 0, 0, -1, 0, 0,-1, 0, 0, 0, 174, 84, 45, -93}, + { 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 11, 56, 0, 0}, + { 0, 1,-1, 1, 0, 0, -1, 0, 0, 1, 0, 0, 0, -66, -12, -6, 35}, + + /* 111-120 */ + { 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 1, 47, 8, 4, -25}, + { 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 2, 0, 8, 4, 0}, + { 0, 2,-2, 1, 0, 0, -9, 13, 0, 0, 0, 0, 0, 10, -22, -12, -5}, + { 0, 0, 0, 1, 0, 0, 7,-13, 0, 0, 0, 0, 0, -3, 0, 0, 2}, + {-2, 0, 2, 0, 0, 0, 5, -6, 0, 0, 0, 0, 0, -24, 12, 0, 0}, + { 0, 0, 0, 0, 0, 0, 9,-17, 0, 0, 0, 0, 0, 5, -6, 0, 0}, + { 0, 0, 0, 0, 0, 0, -9, 17, 0, 0, 0, 0, 2, 3, 0, 0, -2}, + { 1, 0,-1, 1, 0, 0, -3, 4, 0, 0, 0, 0, 0, 4, 3, 1, -2}, + { 1, 0,-1, 1, 0, -3, 4, 0, 0, 0, 0, 0, 0, 0, 29, 15, 0}, + { 0, 0, 0, 2, 0, 0, -1, 2, 0, 0, 0, 0, 0, -5, -4, -2, 2}, + + /* 121-130 */ + { 0,-1, 1, 1, 0, 0, 0, 2, 0, 0, 0, 0, 0, 8, -3, -1, -5}, + { 0,-2, 2, 0, 1, 0, -2, 0, 0, 0, 0, 0, 0, 0, -3, 0, 0}, + { 0, 0, 0, 0, 0, 3, -5, 0, 2, 0, 0, 0, 0, 10, 0, 0, 0}, + {-2, 0, 2, 1, 0, 0, 2, 0,-3, 1, 0, 0, 0, 3, 0, 0, -2}, + {-2, 0, 2, 1, 0, 3, -3, 0, 0, 0, 0, 0, 0, -5, 0, 0, 3}, + { 0, 0, 0, 1, 0, 8,-13, 0, 0, 0, 0, 0, 0, 46, 66, 35, -25}, + { 0,-1, 1, 0, 0, 8,-12, 0, 0, 0, 0, 0, 0, -14, 7, 0, 0}, + { 0, 2,-2, 1, 0, -8, 11, 0, 0, 0, 0, 0, 0, 0, 3, 2, 0}, + {-1, 0, 1, 0, 0, 0, 2, -2, 0, 0, 0, 0, 0, -5, 0, 0, 0}, + {-1, 0, 0, 1, 0, 18,-16, 0, 0, 0, 0, 0, 0, -68, -34, -18, 36}, + + /* 131-140 */ + { 0, 1,-1, 1, 0, 0, -1, 0,-1, 1, 0, 0, 0, 0, 14, 7, 0}, + { 0, 0, 0, 1, 0, 3, -7, 4, 0, 0, 0, 0, 0, 10, -6, -3, -5}, + {-2, 1, 1, 1, 0, 0, -3, 7, 0, 0, 0, 0, 0, -5, -4, -2, 3}, + { 0, 1,-1, 2, 0, 0, -1, 0,-2, 5, 0, 0, 0, -3, 5, 2, 1}, + { 0, 0, 0, 1, 0, 0, 0, 0,-2, 5, 0, 0, 0, 76, 17, 9, -41}, + { 0, 0, 0, 1, 0, 0, -4, 8,-3, 0, 0, 0, 0, 84, 298, 159, -45}, + { 1, 0, 0, 1, 0,-10, 3, 0, 0, 0, 0, 0, 0, 3, 0, 0, -1}, + { 0, 2,-2, 1, 0, 0, -2, 0, 0, 0, 0, 0, 0, -3, 0, 0, 2}, + {-1, 0, 0, 1, 0, 10, -3, 0, 0, 0, 0, 0, 0, -3, 0, 0, 1}, + { 0, 0, 0, 1, 0, 0, 4, -8, 3, 0, 0, 0, 0, -82, 292, 156, 44}, + + /* 141-150 */ + { 0, 0, 0, 1, 0, 0, 0, 0, 2,-5, 0, 0, 0, -73, 17, 9, 39}, + { 0,-1, 1, 0, 0, 0, 1, 0, 2,-5, 0, 0, 0, -9, -16, 0, 0}, + { 2,-1,-1, 1, 0, 0, 3, -7, 0, 0, 0, 0, 0, 3, 0, -1, -2}, + {-2, 0, 2, 0, 0, 0, 2, 0, 0,-5, 0, 0, 0, -3, 0, 0, 0}, + { 0, 0, 0, 1, 0, -3, 7, -4, 0, 0, 0, 0, 0, -9, -5, -3, 5}, + {-2, 0, 2, 0, 0, 0, 2, 0,-2, 0, 0, 0, 0, -439, 0, 0, 0}, + { 1, 0, 0, 1, 0,-18, 16, 0, 0, 0, 0, 0, 0, 57, -28, -15, -30}, + {-2, 1, 1, 1, 0, 0, 1, 0,-2, 0, 0, 0, 0, 0, -6, -3, 0}, + { 0, 1,-1, 2, 0, -8, 12, 0, 0, 0, 0, 0, 0, -4, 0, 0, 2}, + { 0, 0, 0, 1, 0, -8, 13, 0, 0, 0, 0, 0, 0, -40, 57, 30, 21}, + + /* 151-160 */ + { 0, 0, 0, 0, 0, 0, 1, -2, 0, 0, 0, 0, 1, 23, 7, 3, -13}, + { 0, 1,-1, 1, 0, 0, 0, -2, 0, 0, 0, 0, 0, 273, 80, 43,-146}, + { 0, 0, 0, 0, 0, 0, 1, -2, 0, 0, 0, 0, 0, -449, 430, 0, 0}, + { 0, 1,-1, 1, 0, 0, -2, 2, 0, 0, 0, 0, 0, -8, -47, -25, 4}, + { 0, 0, 0, 0, 0, 0, -1, 2, 0, 0, 0, 0, 1, 6, 47, 25, -3}, + {-1, 0, 1, 1, 0, 3, -4, 0, 0, 0, 0, 0, 0, 0, 23, 13, 0}, + {-1, 0, 1, 1, 0, 0, 3, -4, 0, 0, 0, 0, 0, -3, 0, 0, 2}, + { 0, 1,-1, 1, 0, 0, -1, 0, 0,-2, 0, 0, 0, 3, -4, -2, -2}, + { 0, 1,-1, 1, 0, 0, -1, 0, 0, 2, 0, 0, 0, -48,-110, -59, 26}, + { 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 1, 51, 114, 61, -27}, + + /* 161-170 */ + { 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 2, -133, 0, 0, 57}, + { 0, 1,-1, 0, 0, 3, -6, 0, 0, 0, 0, 0, 0, 0, 4, 0, 0}, + { 0, 0, 0, 1, 0, -3, 5, 0, 0, 0, 0, 0, 0, -21, -6, -3, 11}, + { 0, 1,-1, 2, 0, -3, 4, 0, 0, 0, 0, 0, 0, 0, -3, -1, 0}, + { 0, 0, 0, 1, 0, 0, -2, 4, 0, 0, 0, 0, 0, -11, -21, -11, 6}, + { 0, 2,-2, 1, 0, -5, 6, 0, 0, 0, 0, 0, 0, -18,-436, -233, 9}, + { 0,-1, 1, 0, 0, 5, -7, 0, 0, 0, 0, 0, 0, 35, -7, 0, 0}, + { 0, 0, 0, 1, 0, 5, -8, 0, 0, 0, 0, 0, 0, 0, 5, 3, 0}, + {-2, 0, 2, 1, 0, 6, -8, 0, 0, 0, 0, 0, 0, 11, -3, -1, -6}, + { 0, 0, 0, 1, 0, 0, -8, 15, 0, 0, 0, 0, 0, -5, -3, -1, 3}, + + /* 171-180 */ + {-2, 0, 2, 1, 0, 0, 2, 0,-3, 0, 0, 0, 0, -53, -9, -5, 28}, + {-2, 0, 2, 1, 0, 0, 6, -8, 0, 0, 0, 0, 0, 0, 3, 2, 1}, + { 1, 0,-1, 1, 0, 0, -1, 0, 1, 0, 0, 0, 0, 4, 0, 0, -2}, + { 0, 0, 0, 0, 0, 0, 0, 0, 3,-5, 0, 0, 0, 0, -4, 0, 0}, + { 0, 1,-1, 1, 0, 0, -1, 0,-1, 0, 0, 0, 0, -50, 194, 103, 27}, + { 0, 0, 0, 0, 0, 0, 0, 0,-1, 0, 0, 0, 1, -13, 52, 28, 7}, + { 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, -91, 248, 0, 0}, + { 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 1, 6, 49, 26, -3}, + { 0, 1,-1, 1, 0, 0, -1, 0, 1, 0, 0, 0, 0, -6, -47, -25, 3}, + { 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 1, 0, 5, 3, 0}, + + /* 181-190 */ + { 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 2, 52, 23, 10, -23}, + { 0, 1,-1, 2, 0, 0, -1, 0, 0,-1, 0, 0, 0, -3, 0, 0, 1}, + { 0, 0, 0, 1, 0, 0, 0, 0, 0,-1, 0, 0, 0, 0, 5, 3, 0}, + { 0,-1, 1, 0, 0, 0, 1, 0, 0,-1, 0, 0, 0, -4, 0, 0, 0}, + { 0, 0, 0, 0, 0, 0, -7, 13, 0, 0, 0, 0, 2, -4, 8, 3, 2}, + { 0, 0, 0, 0, 0, 0, 7,-13, 0, 0, 0, 0, 0, 10, 0, 0, 0}, + { 2, 0,-2, 1, 0, 0, -5, 6, 0, 0, 0, 0, 0, 3, 0, 0, -2}, + { 0, 2,-2, 1, 0, 0, -8, 11, 0, 0, 0, 0, 0, 0, 8, 4, 0}, + { 0, 2,-2, 1,-1, 0, 2, 0, 0, 0, 0, 0, 0, 0, 8, 4, 1}, + {-2, 0, 2, 0, 0, 0, 4, -4, 0, 0, 0, 0, 0, -4, 0, 0, 0}, + + /* 191-200 */ + { 0, 0, 0, 0, 0, 0, 0, 0, 2,-2, 0, 0, 0, -4, 0, 0, 0}, + { 0, 1,-1, 1, 0, 0, -1, 0, 0, 3, 0, 0, 0, -8, 4, 2, 4}, + { 0, 0, 0, 0, 0, 0, 0, 0, 0, 3, 0, 0, 1, 8, -4, -2, -4}, + { 0, 0, 0, 0, 0, 0, 0, 0, 0, 3, 0, 0, 2, 0, 15, 7, 0}, + {-2, 0, 2, 0, 0, 3, -3, 0, 0, 0, 0, 0, 0, -138, 0, 0, 0}, + { 0, 0, 0, 2, 0, 0, -4, 8,-3, 0, 0, 0, 0, 0, -7, -3, 0}, + { 0, 0, 0, 2, 0, 0, 4, -8, 3, 0, 0, 0, 0, 0, -7, -3, 0}, + { 2, 0,-2, 1, 0, 0, -2, 0, 2, 0, 0, 0, 0, 54, 0, 0, -29}, + { 0, 1,-1, 2, 0, 0, -1, 0, 2, 0, 0, 0, 0, 0, 10, 4, 0}, + { 0, 1,-1, 2, 0, 0, 0, -2, 0, 0, 0, 0, 0, -7, 0, 0, 3}, + + /* 201-210 */ + { 0, 0, 0, 1, 0, 0, 1, -2, 0, 0, 0, 0, 0, -37, 35, 19, 20}, + { 0,-1, 1, 0, 0, 0, 2, -2, 0, 0, 0, 0, 0, 0, 4, 0, 0}, + { 0,-1, 1, 0, 0, 0, 1, 0, 0,-2, 0, 0, 0, -4, 9, 0, 0}, + { 0, 2,-2, 1, 0, 0, -2, 0, 0, 2, 0, 0, 0, 8, 0, 0, -4}, + { 0, 1,-1, 1, 0, 3, -6, 0, 0, 0, 0, 0, 0, -9, -14, -8, 5}, + { 0, 0, 0, 0, 0, 3, -5, 0, 0, 0, 0, 0, 1, -3, -9, -5, 3}, + { 0, 0, 0, 0, 0, 3, -5, 0, 0, 0, 0, 0, 0, -145, 47, 0, 0}, + { 0, 1,-1, 1, 0, -3, 4, 0, 0, 0, 0, 0, 0, -10, 40, 21, 5}, + { 0, 0, 0, 0, 0, -3, 5, 0, 0, 0, 0, 0, 1, 11, -49, -26, -7}, + { 0, 0, 0, 0, 0, -3, 5, 0, 0, 0, 0, 0, 2,-2150, 0, 0, 932}, + + /* 211-220 */ + { 0, 2,-2, 2, 0, -3, 3, 0, 0, 0, 0, 0, 0, -12, 0, 0, 5}, + { 0, 0, 0, 0, 0, -3, 5, 0, 0, 0, 0, 0, 2, 85, 0, 0, -37}, + { 0, 0, 0, 0, 0, 0, 2, -4, 0, 0, 0, 0, 1, 4, 0, 0, -2}, + { 0, 1,-1, 1, 0, 0, 1, -4, 0, 0, 0, 0, 0, 3, 0, 0, -2}, + { 0, 0, 0, 0, 0, 0, 2, -4, 0, 0, 0, 0, 0, -86, 153, 0, 0}, + { 0, 0, 0, 0, 0, 0, -2, 4, 0, 0, 0, 0, 1, -6, 9, 5, 3}, + { 0, 1,-1, 1, 0, 0, -3, 4, 0, 0, 0, 0, 0, 9, -13, -7, -5}, + { 0, 0, 0, 0, 0, 0, -2, 4, 0, 0, 0, 0, 1, -8, 12, 6, 4}, + { 0, 0, 0, 0, 0, 0, -2, 4, 0, 0, 0, 0, 2, -51, 0, 0, 22}, + { 0, 0, 0, 0, 0, -5, 8, 0, 0, 0, 0, 0, 2, -11,-268, -116, 5}, + + /* 221-230 */ + { 0, 2,-2, 2, 0, -5, 6, 0, 0, 0, 0, 0, 0, 0, 12, 5, 0}, + { 0, 0, 0, 0, 0, -5, 8, 0, 0, 0, 0, 0, 2, 0, 7, 3, 0}, + { 0, 0, 0, 0, 0, -5, 8, 0, 0, 0, 0, 0, 1, 31, 6, 3, -17}, + { 0, 1,-1, 1, 0, -5, 7, 0, 0, 0, 0, 0, 0, 140, 27, 14, -75}, + { 0, 0, 0, 0, 0, -5, 8, 0, 0, 0, 0, 0, 1, 57, 11, 6, -30}, + { 0, 0, 0, 0, 0, 5, -8, 0, 0, 0, 0, 0, 0, -14, -39, 0, 0}, + { 0, 1,-1, 2, 0, 0, -1, 0,-1, 0, 0, 0, 0, 0, -6, -2, 0}, + { 0, 0, 0, 1, 0, 0, 0, 0,-1, 0, 0, 0, 0, 4, 15, 8, -2}, + { 0,-1, 1, 0, 0, 0, 1, 0,-1, 0, 0, 0, 0, 0, 4, 0, 0}, + { 0, 2,-2, 1, 0, 0, -2, 0, 1, 0, 0, 0, 0, -3, 0, 0, 1}, + + /* 231-240 */ + { 0, 0, 0, 0, 0, 0, -6, 11, 0, 0, 0, 0, 2, 0, 11, 5, 0}, + { 0, 0, 0, 0, 0, 0, 6,-11, 0, 0, 0, 0, 0, 9, 6, 0, 0}, + { 0, 0, 0, 0,-1, 0, 4, 0, 0, 0, 0, 0, 2, -4, 10, 4, 2}, + { 0, 0, 0, 0, 1, 0, -4, 0, 0, 0, 0, 0, 0, 5, 3, 0, 0}, + { 2, 0,-2, 1, 0, -3, 3, 0, 0, 0, 0, 0, 0, 16, 0, 0, -9}, + {-2, 0, 2, 0, 0, 0, 2, 0, 0,-2, 0, 0, 0, -3, 0, 0, 0}, + { 0, 2,-2, 1, 0, 0, -7, 9, 0, 0, 0, 0, 0, 0, 3, 2, -1}, + { 0, 0, 0, 0, 0, 0, 0, 0, 4,-5, 0, 0, 2, 7, 0, 0, -3}, + { 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, -25, 22, 0, 0}, + { 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 1, 42, 223, 119, -22}, + + /* 241-250 */ + { 0, 1,-1, 1, 0, 0, -1, 0, 2, 0, 0, 0, 0, -27,-143, -77, 14}, + { 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 1, 9, 49, 26, -5}, + { 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 2,-1166, 0, 0, 505}, + { 0, 2,-2, 2, 0, 0, -2, 0, 2, 0, 0, 0, 0, -5, 0, 0, 2}, + { 0, 0, 0, 0, 0, 0, 0, 0, 0, 5, 0, 0, 2, -6, 0, 0, 3}, + { 0, 0, 0, 1, 0, 3, -5, 0, 0, 0, 0, 0, 0, -8, 0, 1, 4}, + { 0,-1, 1, 0, 0, 3, -4, 0, 0, 0, 0, 0, 0, 0, -4, 0, 0}, + { 0, 2,-2, 1, 0, -3, 3, 0, 0, 0, 0, 0, 0, 117, 0, 0, -63}, + { 0, 0, 0, 1, 0, 0, 2, -4, 0, 0, 0, 0, 0, -4, 8, 4, 2}, + { 0, 2,-2, 1, 0, 0, -4, 4, 0, 0, 0, 0, 0, 3, 0, 0, -2}, + + /* 251-260 */ + { 0, 1,-1, 2, 0, -5, 7, 0, 0, 0, 0, 0, 0, -5, 0, 0, 2}, + { 0, 0, 0, 0, 0, 0, 3, -6, 0, 0, 0, 0, 0, 0, 31, 0, 0}, + { 0, 0, 0, 0, 0, 0, -3, 6, 0, 0, 0, 0, 1, -5, 0, 1, 3}, + { 0, 1,-1, 1, 0, 0, -4, 6, 0, 0, 0, 0, 0, 4, 0, 0, -2}, + { 0, 0, 0, 0, 0, 0, -3, 6, 0, 0, 0, 0, 1, -4, 0, 0, 2}, + { 0, 0, 0, 0, 0, 0, -3, 6, 0, 0, 0, 0, 2, -24, -13, -6, 10}, + { 0,-1, 1, 0, 0, 2, -2, 0, 0, 0, 0, 0, 0, 3, 0, 0, 0}, + { 0, 0, 0, 1, 0, 2, -3, 0, 0, 0, 0, 0, 0, 0, -32, -17, 0}, + { 0, 0, 0, 0, 0, 0, -5, 9, 0, 0, 0, 0, 2, 8, 12, 5, -3}, + { 0, 0, 0, 0, 0, 0, -5, 9, 0, 0, 0, 0, 1, 3, 0, 0, -1}, + + /* 261-270 */ + { 0, 0, 0, 0, 0, 0, 5, -9, 0, 0, 0, 0, 0, 7, 13, 0, 0}, + { 0,-1, 1, 0, 0, 0, 1, 0,-2, 0, 0, 0, 0, -3, 16, 0, 0}, + { 0, 2,-2, 1, 0, 0, -2, 0, 2, 0, 0, 0, 0, 50, 0, 0, -27}, + {-2, 1, 1, 1, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, -5, -3, 0}, + { 0,-2, 2, 0, 0, 3, -3, 0, 0, 0, 0, 0, 0, 13, 0, 0, 0}, + { 0, 0, 0, 0, 0, -6, 10, 0, 0, 0, 0, 0, 1, 0, 5, 3, 1}, + { 0, 0, 0, 0, 0, -6, 10, 0, 0, 0, 0, 0, 2, 24, 5, 2, -11}, + { 0, 0, 0, 0, 0, -2, 3, 0, 0, 0, 0, 0, 2, 5, -11, -5, -2}, + { 0, 0, 0, 0, 0, -2, 3, 0, 0, 0, 0, 0, 1, 30, -3, -2, -16}, + { 0, 1,-1, 1, 0, -2, 2, 0, 0, 0, 0, 0, 0, 18, 0, 0, -9}, + + /* 271-280 */ + { 0, 0, 0, 0, 0, 2, -3, 0, 0, 0, 0, 0, 0, 8, 614, 0, 0}, + { 0, 0, 0, 0, 0, 2, -3, 0, 0, 0, 0, 0, 1, 3, -3, -1, -2}, + { 0, 0, 0, 0, 0, 0, 0, 0, 3, 0, 0, 0, 1, 6, 17, 9, -3}, + { 0, 1,-1, 1, 0, 0, -1, 0, 3, 0, 0, 0, 0, -3, -9, -5, 2}, + { 0, 0, 0, 0, 0, 0, 0, 0, 3, 0, 0, 0, 1, 0, 6, 3, -1}, + { 0, 0, 0, 0, 0, 0, 0, 0, 3, 0, 0, 0, 2, -127, 21, 9, 55}, + { 0, 0, 0, 0, 0, 0, 4, -8, 0, 0, 0, 0, 0, 3, 5, 0, 0}, + { 0, 0, 0, 0, 0, 0, -4, 8, 0, 0, 0, 0, 2, -6, -10, -4, 3}, + { 0,-2, 2, 0, 0, 0, 2, 0,-2, 0, 0, 0, 0, 5, 0, 0, 0}, + { 0, 0, 0, 0, 0, 0, -4, 7, 0, 0, 0, 0, 2, 16, 9, 4, -7}, + + /* 281-290 */ + { 0, 0, 0, 0, 0, 0, -4, 7, 0, 0, 0, 0, 1, 3, 0, 0, -2}, + { 0, 0, 0, 0, 0, 0, 4, -7, 0, 0, 0, 0, 0, 0, 22, 0, 0}, + { 0, 0, 0, 1, 0, -2, 3, 0, 0, 0, 0, 0, 0, 0, 19, 10, 0}, + { 0, 2,-2, 1, 0, 0, -2, 0, 3, 0, 0, 0, 0, 7, 0, 0, -4}, + { 0, 0, 0, 0, 0, 0, -5, 10, 0, 0, 0, 0, 2, 0, -5, -2, 0}, + { 0, 0, 0, 1, 0, -1, 2, 0, 0, 0, 0, 0, 0, 0, 3, 1, 0}, + { 0, 0, 0, 0, 0, 0, 0, 0, 4, 0, 0, 0, 2, -9, 3, 1, 4}, + { 0, 0, 0, 0, 0, 0, -3, 5, 0, 0, 0, 0, 2, 17, 0, 0, -7}, + { 0, 0, 0, 0, 0, 0, -3, 5, 0, 0, 0, 0, 1, 0, -3, -2, -1}, + { 0, 0, 0, 0, 0, 0, 3, -5, 0, 0, 0, 0, 0, -20, 34, 0, 0}, + + /* 291-300 */ + { 0, 0, 0, 0, 0, 1, -2, 0, 0, 0, 0, 0, 1, -10, 0, 1, 5}, + { 0, 1,-1, 1, 0, 1, -3, 0, 0, 0, 0, 0, 0, -4, 0, 0, 2}, + { 0, 0, 0, 0, 0, 1, -2, 0, 0, 0, 0, 0, 0, 22, -87, 0, 0}, + { 0, 0, 0, 0, 0, -1, 2, 0, 0, 0, 0, 0, 1, -4, 0, 0, 2}, + { 0, 0, 0, 0, 0, -1, 2, 0, 0, 0, 0, 0, 2, -3, -6, -2, 1}, + { 0, 0, 0, 0, 0, -7, 11, 0, 0, 0, 0, 0, 2, -16, -3, -1, 7}, + { 0, 0, 0, 0, 0, -7, 11, 0, 0, 0, 0, 0, 1, 0, -3, -2, 0}, + { 0,-2, 2, 0, 0, 4, -4, 0, 0, 0, 0, 0, 0, 4, 0, 0, 0}, + { 0, 0, 0, 0, 0, 0, 2, -3, 0, 0, 0, 0, 0, -68, 39, 0, 0}, + { 0, 2,-2, 1, 0, -4, 4, 0, 0, 0, 0, 0, 0, 27, 0, 0, -14}, + + /* 301-310 */ + { 0,-1, 1, 0, 0, 4, -5, 0, 0, 0, 0, 0, 0, 0, -4, 0, 0}, + { 0, 0, 0, 0, 0, 0, 1, -1, 0, 0, 0, 0, 0, -25, 0, 0, 0}, + { 0, 0, 0, 0, 0, -4, 7, 0, 0, 0, 0, 0, 1, -12, -3, -2, 6}, + { 0, 1,-1, 1, 0, -4, 6, 0, 0, 0, 0, 0, 0, 3, 0, 0, -1}, + { 0, 0, 0, 0, 0, -4, 7, 0, 0, 0, 0, 0, 2, 3, 66, 29, -1}, + { 0, 0, 0, 0, 0, -4, 6, 0, 0, 0, 0, 0, 2, 490, 0, 0,-213}, + { 0, 0, 0, 0, 0, -4, 6, 0, 0, 0, 0, 0, 1, -22, 93, 49, 12}, + { 0, 1,-1, 1, 0, -4, 5, 0, 0, 0, 0, 0, 0, -7, 28, 15, 4}, + { 0, 0, 0, 0, 0, -4, 6, 0, 0, 0, 0, 0, 1, -3, 13, 7, 2}, + { 0, 0, 0, 0, 0, 4, -6, 0, 0, 0, 0, 0, 0, -46, 14, 0, 0}, + + /* 311-320 */ + {-2, 0, 2, 0, 0, 2, -2, 0, 0, 0, 0, 0, 0, -5, 0, 0, 0}, + { 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 2, 1, 0, 0}, + { 0,-1, 1, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, -3, 0, 0}, + { 0, 0, 0, 1, 0, 1, -1, 0, 0, 0, 0, 0, 0, -28, 0, 0, 15}, + { 0, 0, 0, 0, 0, 0, -1, 0, 5, 0, 0, 0, 2, 5, 0, 0, -2}, + { 0, 0, 0, 0, 0, 0, 1, -3, 0, 0, 0, 0, 0, 0, 3, 0, 0}, + { 0, 0, 0, 0, 0, 0, -1, 3, 0, 0, 0, 0, 2, -11, 0, 0, 5}, + { 0, 0, 0, 0, 0, 0, -7, 12, 0, 0, 0, 0, 2, 0, 3, 1, 0}, + { 0, 0, 0, 0, 0, -1, 1, 0, 0, 0, 0, 0, 2, -3, 0, 0, 1}, + { 0, 0, 0, 0, 0, -1, 1, 0, 0, 0, 0, 0, 1, 25, 106, 57, -13}, + + /* 321-330 */ + { 0, 1,-1, 1, 0, -1, 0, 0, 0, 0, 0, 0, 0, 5, 21, 11, -3}, + { 0, 0, 0, 0, 0, 1, -1, 0, 0, 0, 0, 0, 0, 1485, 0, 0, 0}, + { 0, 0, 0, 0, 0, 1, -1, 0, 0, 0, 0, 0, 1, -7, -32, -17, 4}, + { 0, 1,-1, 1, 0, 1, -2, 0, 0, 0, 0, 0, 0, 0, 5, 3, 0}, + { 0, 0, 0, 0, 0, 0, -2, 5, 0, 0, 0, 0, 2, -6, -3, -2, 3}, + { 0, 0, 0, 0, 0, 0, -1, 0, 4, 0, 0, 0, 2, 30, -6, -2, -13}, + { 0, 0, 0, 0, 0, 0, 1, 0,-4, 0, 0, 0, 0, -4, 4, 0, 0}, + { 0, 0, 0, 1, 0, -1, 1, 0, 0, 0, 0, 0, 0, -19, 0, 0, 10}, + { 0, 0, 0, 0, 0, 0, -6, 10, 0, 0, 0, 0, 2, 0, 4, 2, -1}, + { 0, 0, 0, 0, 0, 0, -6, 10, 0, 0, 0, 0, 0, 0, 3, 0, 0}, + + /* 331-340 */ + { 0, 2,-2, 1, 0, 0, -3, 0, 3, 0, 0, 0, 0, 4, 0, 0, -2}, + { 0, 0, 0, 0, 0, 0, -3, 7, 0, 0, 0, 0, 2, 0, -3, -1, 0}, + {-2, 0, 2, 0, 0, 4, -4, 0, 0, 0, 0, 0, 0, -3, 0, 0, 0}, + { 0, 0, 0, 0, 0, 0, -5, 8, 0, 0, 0, 0, 2, 5, 3, 1, -2}, + { 0, 0, 0, 0, 0, 0, 5, -8, 0, 0, 0, 0, 0, 0, 11, 0, 0}, + { 0, 0, 0, 0, 0, 0, -1, 0, 3, 0, 0, 0, 2, 118, 0, 0, -52}, + { 0, 0, 0, 0, 0, 0, -1, 0, 3, 0, 0, 0, 1, 0, -5, -3, 0}, + { 0, 0, 0, 0, 0, 0, 1, 0,-3, 0, 0, 0, 0, -28, 36, 0, 0}, + { 0, 0, 0, 0, 0, 2, -4, 0, 0, 0, 0, 0, 0, 5, -5, 0, 0}, + { 0, 0, 0, 0, 0, -2, 4, 0, 0, 0, 0, 0, 1, 14, -59, -31, -8}, + + /* 341-350 */ + { 0, 1,-1, 1, 0, -2, 3, 0, 0, 0, 0, 0, 0, 0, 9, 5, 1}, + { 0, 0, 0, 0, 0, -2, 4, 0, 0, 0, 0, 0, 2, -458, 0, 0, 198}, + { 0, 0, 0, 0, 0, -6, 9, 0, 0, 0, 0, 0, 2, 0, -45, -20, 0}, + { 0, 0, 0, 0, 0, -6, 9, 0, 0, 0, 0, 0, 1, 9, 0, 0, -5}, + { 0, 0, 0, 0, 0, 6, -9, 0, 0, 0, 0, 0, 0, 0, -3, 0, 0}, + { 0, 0, 0, 1, 0, 0, 1, 0,-2, 0, 0, 0, 0, 0, -4, -2, -1}, + { 0, 2,-2, 1, 0, -2, 2, 0, 0, 0, 0, 0, 0, 11, 0, 0, -6}, + { 0, 0, 0, 0, 0, 0, -4, 6, 0, 0, 0, 0, 2, 6, 0, 0, -2}, + { 0, 0, 0, 0, 0, 0, 4, -6, 0, 0, 0, 0, 0, -16, 23, 0, 0}, + { 0, 0, 0, 1, 0, 3, -4, 0, 0, 0, 0, 0, 0, 0, -4, -2, 0}, + + /* 351-360 */ + { 0, 0, 0, 0, 0, 0, -1, 0, 2, 0, 0, 0, 2, -5, 0, 0, 2}, + { 0, 0, 0, 0, 0, 0, 1, 0,-2, 0, 0, 0, 0, -166, 269, 0, 0}, + { 0, 0, 0, 1, 0, 0, 1, 0,-1, 0, 0, 0, 0, 15, 0, 0, -8}, + { 0, 0, 0, 0, 0, -5, 9, 0, 0, 0, 0, 0, 2, 10, 0, 0, -4}, + { 0, 0, 0, 0, 0, 0, 3, -4, 0, 0, 0, 0, 0, -78, 45, 0, 0}, + { 0, 0, 0, 0, 0, -3, 4, 0, 0, 0, 0, 0, 2, 0, -5, -2, 0}, + { 0, 0, 0, 0, 0, -3, 4, 0, 0, 0, 0, 0, 1, 7, 0, 0, -4}, + { 0, 0, 0, 0, 0, 3, -4, 0, 0, 0, 0, 0, 0, -5, 328, 0, 0}, + { 0, 0, 0, 0, 0, 3, -4, 0, 0, 0, 0, 0, 1, 3, 0, 0, -2}, + { 0, 0, 0, 1, 0, 0, 2, -2, 0, 0, 0, 0, 0, 5, 0, 0, -2}, + + /* 361-370 */ + { 0, 0, 0, 1, 0, 0, -1, 0, 2, 0, 0, 0, 0, 0, 3, 1, 0}, + { 0, 0, 0, 0, 0, 0, 1, 0, 0,-3, 0, 0, 0, -3, 0, 0, 0}, + { 0, 0, 0, 0, 0, 0, 1, 0, 1,-5, 0, 0, 0, -3, 0, 0, 0}, + { 0, 0, 0, 0, 0, 0, -1, 0, 1, 0, 0, 0, 1, 0, -4, -2, 0}, + { 0, 0, 0, 0, 0, 0, 1, 0,-1, 0, 0, 0, 0,-1223, -26, 0, 0}, + { 0, 0, 0, 0, 0, 0, 1, 0,-1, 0, 0, 0, 1, 0, 7, 3, 0}, + { 0, 0, 0, 0, 0, 0, 1, 0,-3, 5, 0, 0, 0, 3, 0, 0, 0}, + { 0, 0, 0, 1, 0, -3, 4, 0, 0, 0, 0, 0, 0, 0, 3, 2, 0}, + { 0, 0, 0, 0, 0, 0, 1, 0, 0,-2, 0, 0, 0, -6, 20, 0, 0}, + { 0, 0, 0, 0, 0, 0, 2, -2, 0, 0, 0, 0, 0, -368, 0, 0, 0}, + + /* 371-380 */ + { 0, 0, 0, 0, 0, 0, 1, 0, 0,-1, 0, 0, 0, -75, 0, 0, 0}, + { 0, 0, 0, 1, 0, 0, -1, 0, 1, 0, 0, 0, 0, 11, 0, 0, -6}, + { 0, 0, 0, 1, 0, 0, -2, 2, 0, 0, 0, 0, 0, 3, 0, 0, -2}, + { 0, 0, 0, 0, 0, -8, 14, 0, 0, 0, 0, 0, 2, -3, 0, 0, 1}, + { 0, 0, 0, 0, 0, 0, 1, 0, 2,-5, 0, 0, 0, -13, -30, 0, 0}, + { 0, 0, 0, 0, 0, 0, 5, -8, 3, 0, 0, 0, 0, 21, 3, 0, 0}, + { 0, 0, 0, 0, 0, 0, 5, -8, 3, 0, 0, 0, 2, -3, 0, 0, 1}, + { 0, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, 1, -4, 0, 0, 2}, + { 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 8, -27, 0, 0}, + { 0, 0, 0, 0, 0, 0, 3, -8, 3, 0, 0, 0, 0, -19, -11, 0, 0}, + + /* 381-390 */ + { 0, 0, 0, 0, 0, 0, -3, 8,-3, 0, 0, 0, 2, -4, 0, 0, 2}, + { 0, 0, 0, 0, 0, 0, 1, 0,-2, 5, 0, 0, 2, 0, 5, 2, 0}, + { 0, 0, 0, 0, 0, -8, 12, 0, 0, 0, 0, 0, 2, -6, 0, 0, 2}, + { 0, 0, 0, 0, 0, -8, 12, 0, 0, 0, 0, 0, 0, -8, 0, 0, 0}, + { 0, 0, 0, 0, 0, 0, 1, 0, 1,-2, 0, 0, 0, -1, 0, 0, 0}, + { 0, 0, 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 2, -14, 0, 0, 6}, + { 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 6, 0, 0, 0}, + { 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 2, -74, 0, 0, 32}, + { 0, 0, 0, 0, 0, 0, 1, 0, 0, 2, 0, 0, 2, 0, -3, -1, 0}, + { 0, 2,-2, 1, 0, -5, 5, 0, 0, 0, 0, 0, 0, 4, 0, 0, -2}, + + /* 391-400 */ + { 0, 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 8, 11, 0, 0}, + { 0, 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 1, 0, 3, 2, 0}, + { 0, 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 2, -262, 0, 0, 114}, + { 0, 0, 0, 0, 0, 3, -6, 0, 0, 0, 0, 0, 0, 0, -4, 0, 0}, + { 0, 0, 0, 0, 0, -3, 6, 0, 0, 0, 0, 0, 1, -7, 0, 0, 4}, + { 0, 0, 0, 0, 0, -3, 6, 0, 0, 0, 0, 0, 2, 0, -27, -12, 0}, + { 0, 0, 0, 0, 0, 0, -1, 4, 0, 0, 0, 0, 2, -19, -8, -4, 8}, + { 0, 0, 0, 0, 0, -5, 7, 0, 0, 0, 0, 0, 2, 202, 0, 0, -87}, + { 0, 0, 0, 0, 0, -5, 7, 0, 0, 0, 0, 0, 1, -8, 35, 19, 5}, + { 0, 1,-1, 1, 0, -5, 6, 0, 0, 0, 0, 0, 0, 0, 4, 2, 0}, + + /* 401-410 */ + { 0, 0, 0, 0, 0, 5, -7, 0, 0, 0, 0, 0, 0, 16, -5, 0, 0}, + { 0, 2,-2, 1, 0, 0, -1, 0, 1, 0, 0, 0, 0, 5, 0, 0, -3}, + { 0, 0, 0, 0, 0, 0, -1, 0, 1, 0, 0, 0, 0, 0, -3, 0, 0}, + { 0, 0, 0, 0,-1, 0, 3, 0, 0, 0, 0, 0, 2, 1, 0, 0, 0}, + { 0, 0, 0, 0, 0, 0, 1, 0, 2, 0, 0, 0, 2, -35, -48, -21, 15}, + { 0, 0, 0, 0, 0, 0, -2, 6, 0, 0, 0, 0, 2, -3, -5, -2, 1}, + { 0, 0, 0, 1, 0, 2, -2, 0, 0, 0, 0, 0, 0, 6, 0, 0, -3}, + { 0, 0, 0, 0, 0, 0, -6, 9, 0, 0, 0, 0, 2, 3, 0, 0, -1}, + { 0, 0, 0, 0, 0, 0, 6, -9, 0, 0, 0, 0, 0, 0, -5, 0, 0}, + { 0, 0, 0, 0, 0, -2, 2, 0, 0, 0, 0, 0, 1, 12, 55, 29, -6}, + + /* 411-420 */ + { 0, 1,-1, 1, 0, -2, 1, 0, 0, 0, 0, 0, 0, 0, 5, 3, 0}, + { 0, 0, 0, 0, 0, 2, -2, 0, 0, 0, 0, 0, 0, -598, 0, 0, 0}, + { 0, 0, 0, 0, 0, 2, -2, 0, 0, 0, 0, 0, 1, -3, -13, -7, 1}, + { 0, 0, 0, 0, 0, 0, 1, 0, 3, 0, 0, 0, 2, -5, -7, -3, 2}, + { 0, 0, 0, 0, 0, 0, -5, 7, 0, 0, 0, 0, 2, 3, 0, 0, -1}, + { 0, 0, 0, 0, 0, 0, 5, -7, 0, 0, 0, 0, 0, 5, -7, 0, 0}, + { 0, 0, 0, 1, 0, -2, 2, 0, 0, 0, 0, 0, 0, 4, 0, 0, -2}, + { 0, 0, 0, 0, 0, 0, 4, -5, 0, 0, 0, 0, 0, 16, -6, 0, 0}, + { 0, 0, 0, 0, 0, 1, -3, 0, 0, 0, 0, 0, 0, 8, -3, 0, 0}, + { 0, 0, 0, 0, 0, -1, 3, 0, 0, 0, 0, 0, 1, 8, -31, -16, -4}, + + /* 421-430 */ + { 0, 1,-1, 1, 0, -1, 2, 0, 0, 0, 0, 0, 0, 0, 3, 1, 0}, + { 0, 0, 0, 0, 0, -1, 3, 0, 0, 0, 0, 0, 2, 113, 0, 0, -49}, + { 0, 0, 0, 0, 0, -7, 10, 0, 0, 0, 0, 0, 2, 0, -24, -10, 0}, + { 0, 0, 0, 0, 0, -7, 10, 0, 0, 0, 0, 0, 1, 4, 0, 0, -2}, + { 0, 0, 0, 0, 0, 0, 3, -3, 0, 0, 0, 0, 0, 27, 0, 0, 0}, + { 0, 0, 0, 0, 0, -4, 8, 0, 0, 0, 0, 0, 2, -3, 0, 0, 1}, + { 0, 0, 0, 0, 0, -4, 5, 0, 0, 0, 0, 0, 2, 0, -4, -2, 0}, + { 0, 0, 0, 0, 0, -4, 5, 0, 0, 0, 0, 0, 1, 5, 0, 0, -2}, + { 0, 0, 0, 0, 0, 4, -5, 0, 0, 0, 0, 0, 0, 0, -3, 0, 0}, + { 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 2, -13, 0, 0, 6}, + + /* 431-440 */ + { 0, 0, 0, 0, 0, 0, -2, 0, 5, 0, 0, 0, 2, 5, 0, 0, -2}, + { 0, 0, 0, 0, 0, 0, 0, 3, 0, 0, 0, 0, 2, -18, -10, -4, 8}, + { 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, -4, -28, 0, 0}, + { 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 2, -5, 6, 3, 2}, + { 0, 0, 0, 0, 0, -9, 13, 0, 0, 0, 0, 0, 2, -3, 0, 0, 1}, + { 0, 0, 0, 0, 0, 0, -1, 5, 0, 0, 0, 0, 2, -5, -9, -4, 2}, + { 0, 0, 0, 0, 0, 0, -2, 0, 4, 0, 0, 0, 2, 17, 0, 0, -7}, + { 0, 0, 0, 0, 0, 0, 2, 0,-4, 0, 0, 0, 0, 11, 4, 0, 0}, + { 0, 0, 0, 0, 0, 0, -2, 7, 0, 0, 0, 0, 2, 0, -6, -2, 0}, + { 0, 0, 0, 0, 0, 0, 2, 0,-3, 0, 0, 0, 0, 83, 15, 0, 0}, + + /* 441-450 */ + { 0, 0, 0, 0, 0, -2, 5, 0, 0, 0, 0, 0, 1, -4, 0, 0, 2}, + { 0, 0, 0, 0, 0, -2, 5, 0, 0, 0, 0, 0, 2, 0,-114, -49, 0}, + { 0, 0, 0, 0, 0, -6, 8, 0, 0, 0, 0, 0, 2, 117, 0, 0, -51}, + { 0, 0, 0, 0, 0, -6, 8, 0, 0, 0, 0, 0, 1, -5, 19, 10, 2}, + { 0, 0, 0, 0, 0, 6, -8, 0, 0, 0, 0, 0, 0, -3, 0, 0, 0}, + { 0, 0, 0, 1, 0, 0, 2, 0,-2, 0, 0, 0, 0, -3, 0, 0, 2}, + { 0, 0, 0, 0, 0, 0, -3, 9, 0, 0, 0, 0, 2, 0, -3, -1, 0}, + { 0, 0, 0, 0, 0, 0, 5, -6, 0, 0, 0, 0, 0, 3, 0, 0, 0}, + { 0, 0, 0, 0, 0, 0, 5, -6, 0, 0, 0, 0, 2, 0, -6, -2, 0}, + { 0, 0, 0, 0, 0, 0, 2, 0,-2, 0, 0, 0, 0, 393, 3, 0, 0}, + + /* 451-460 */ + { 0, 0, 0, 0, 0, 0, 2, 0,-2, 0, 0, 0, 1, -4, 21, 11, 2}, + { 0, 0, 0, 0, 0, 0, 2, 0,-2, 0, 0, 0, 2, -6, 0, -1, 3}, + { 0, 0, 0, 0, 0, -5, 10, 0, 0, 0, 0, 0, 2, -3, 8, 4, 1}, + { 0, 0, 0, 0, 0, 0, 4, -4, 0, 0, 0, 0, 0, 8, 0, 0, 0}, + { 0, 0, 0, 0, 0, 0, 4, -4, 0, 0, 0, 0, 2, 18, -29, -13, -8}, + { 0, 0, 0, 0, 0, -3, 3, 0, 0, 0, 0, 0, 1, 8, 34, 18, -4}, + { 0, 0, 0, 0, 0, 3, -3, 0, 0, 0, 0, 0, 0, 89, 0, 0, 0}, + { 0, 0, 0, 0, 0, 3, -3, 0, 0, 0, 0, 0, 1, 3, 12, 6, -1}, + { 0, 0, 0, 0, 0, 3, -3, 0, 0, 0, 0, 0, 2, 54, -15, -7, -24}, + { 0, 0, 0, 0, 0, 0, 2, 0, 0,-3, 0, 0, 0, 0, 3, 0, 0}, + + /* 461-470 */ + { 0, 0, 0, 0, 0, 0, -5, 13, 0, 0, 0, 0, 2, 3, 0, 0, -1}, + { 0, 0, 0, 0, 0, 0, 2, 0,-1, 0, 0, 0, 0, 0, 35, 0, 0}, + { 0, 0, 0, 0, 0, 0, 2, 0,-1, 0, 0, 0, 2, -154, -30, -13, 67}, + { 0, 0, 0, 0, 0, 0, 2, 0, 0,-2, 0, 0, 0, 15, 0, 0, 0}, + { 0, 0, 0, 0, 0, 0, 2, 0, 0,-2, 0, 0, 1, 0, 4, 2, 0}, + { 0, 0, 0, 0, 0, 0, 3, -2, 0, 0, 0, 0, 0, 0, 9, 0, 0}, + { 0, 0, 0, 0, 0, 0, 3, -2, 0, 0, 0, 0, 2, 80, -71, -31, -35}, + { 0, 0, 0, 0, 0, 0, 2, 0, 0,-1, 0, 0, 2, 0, -20, -9, 0}, + { 0, 0, 0, 0, 0, 0, -6, 15, 0, 0, 0, 0, 2, 11, 5, 2, -5}, + { 0, 0, 0, 0, 0, -8, 15, 0, 0, 0, 0, 0, 2, 61, -96, -42, -27}, + + /* 471-480 */ + { 0, 0, 0, 0, 0, -3, 9, -4, 0, 0, 0, 0, 2, 14, 9, 4, -6}, + { 0, 0, 0, 0, 0, 0, 2, 0, 2,-5, 0, 0, 2, -11, -6, -3, 5}, + { 0, 0, 0, 0, 0, 0, -2, 8,-1,-5, 0, 0, 2, 0, -3, -1, 0}, + { 0, 0, 0, 0, 0, 0, 6, -8, 3, 0, 0, 0, 2, 123,-415, -180, -53}, + { 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, -35}, + { 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, -5, 0, 0, 0}, + { 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 1, 7, -32, -17, -4}, + { 0, 1,-1, 1, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, -9, -5, 0}, + { 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 1, 0, -4, 2, 0}, + { 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 2, -89, 0, 0, 38}, + + /* 481-490 */ + { 0, 0, 0, 0, 0, 0, -6, 16,-4,-5, 0, 0, 2, 0, -86, -19, -6}, + { 0, 0, 0, 0, 0, 0, -2, 8,-3, 0, 0, 0, 2, 0, 0, -19, 6}, + { 0, 0, 0, 0, 0, 0, -2, 8,-3, 0, 0, 0, 2, -123,-416, -180, 53}, + { 0, 0, 0, 0, 0, 0, 6, -8, 1, 5, 0, 0, 2, 0, -3, -1, 0}, + { 0, 0, 0, 0, 0, 0, 2, 0,-2, 5, 0, 0, 2, 12, -6, -3, -5}, + { 0, 0, 0, 0, 0, 3, -5, 4, 0, 0, 0, 0, 2, -13, 9, 4, 6}, + { 0, 0, 0, 0, 0, -8, 11, 0, 0, 0, 0, 0, 2, 0, -15, -7, 0}, + { 0, 0, 0, 0, 0, -8, 11, 0, 0, 0, 0, 0, 1, 3, 0, 0, -1}, + { 0, 0, 0, 0, 0, -8, 11, 0, 0, 0, 0, 0, 2, -62, -97, -42, 27}, + { 0, 0, 0, 0, 0, 0, 11, 0, 0, 0, 0, 0, 2, -11, 5, 2, 5}, + + /* 491-500 */ + { 0, 0, 0, 0, 0, 0, 2, 0, 0, 1, 0, 0, 2, 0, -19, -8, 0}, + { 0, 0, 0, 0, 0, 3, -3, 0, 2, 0, 0, 0, 2, -3, 0, 0, 1}, + { 0, 2,-2, 1, 0, 0, 4, -8, 3, 0, 0, 0, 0, 0, 4, 2, 0}, + { 0, 1,-1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 3, 0, 0}, + { 0, 2,-2, 1, 0, 0, -4, 8,-3, 0, 0, 0, 0, 0, 4, 2, 0}, + { 0, 0, 0, 0, 0, 0, 1, 2, 0, 0, 0, 0, 2, -85, -70, -31, 37}, + { 0, 0, 0, 0, 0, 0, 2, 0, 1, 0, 0, 0, 2, 163, -12, -5, -72}, + { 0, 0, 0, 0, 0, -3, 7, 0, 0, 0, 0, 0, 2, -63, -16, -7, 28}, + { 0, 0, 0, 0, 0, 0, 0, 4, 0, 0, 0, 0, 2, -21, -32, -14, 9}, + { 0, 0, 0, 0, 0, -5, 6, 0, 0, 0, 0, 0, 2, 0, -3, -1, 0}, + + /* 501-510 */ + { 0, 0, 0, 0, 0, -5, 6, 0, 0, 0, 0, 0, 1, 3, 0, 0, -2}, + { 0, 0, 0, 0, 0, 5, -6, 0, 0, 0, 0, 0, 0, 0, 8, 0, 0}, + { 0, 0, 0, 0, 0, 5, -6, 0, 0, 0, 0, 0, 2, 3, 10, 4, -1}, + { 0, 0, 0, 0, 0, 0, 2, 0, 2, 0, 0, 0, 2, 3, 0, 0, -1}, + { 0, 0, 0, 0, 0, 0, -1, 6, 0, 0, 0, 0, 2, 0, -7, -3, 0}, + { 0, 0, 0, 0, 0, 0, 7, -9, 0, 0, 0, 0, 2, 0, -4, -2, 0}, + { 0, 0, 0, 0, 0, 2, -1, 0, 0, 0, 0, 0, 0, 6, 19, 0, 0}, + { 0, 0, 0, 0, 0, 2, -1, 0, 0, 0, 0, 0, 2, 5,-173, -75, -2}, + { 0, 0, 0, 0, 0, 0, 6, -7, 0, 0, 0, 0, 2, 0, -7, -3, 0}, + { 0, 0, 0, 0, 0, 0, 5, -5, 0, 0, 0, 0, 2, 7, -12, -5, -3}, + + /* 511-520 */ + { 0, 0, 0, 0, 0, -1, 4, 0, 0, 0, 0, 0, 1, -3, 0, 0, 2}, + { 0, 0, 0, 0, 0, -1, 4, 0, 0, 0, 0, 0, 2, 3, -4, -2, -1}, + { 0, 0, 0, 0, 0, -7, 9, 0, 0, 0, 0, 0, 2, 74, 0, 0, -32}, + { 0, 0, 0, 0, 0, -7, 9, 0, 0, 0, 0, 0, 1, -3, 12, 6, 2}, + { 0, 0, 0, 0, 0, 0, 4, -3, 0, 0, 0, 0, 2, 26, -14, -6, -11}, + { 0, 0, 0, 0, 0, 0, 3, -1, 0, 0, 0, 0, 2, 19, 0, 0, -8}, + { 0, 0, 0, 0, 0, -4, 4, 0, 0, 0, 0, 0, 1, 6, 24, 13, -3}, + { 0, 0, 0, 0, 0, 4, -4, 0, 0, 0, 0, 0, 0, 83, 0, 0, 0}, + { 0, 0, 0, 0, 0, 4, -4, 0, 0, 0, 0, 0, 1, 0, -10, -5, 0}, + { 0, 0, 0, 0, 0, 4, -4, 0, 0, 0, 0, 0, 2, 11, -3, -1, -5}, + + /* 521-530 */ + { 0, 0, 0, 0, 0, 0, 2, 1, 0, 0, 0, 0, 2, 3, 0, 1, -1}, + { 0, 0, 0, 0, 0, 0, -3, 0, 5, 0, 0, 0, 2, 3, 0, 0, -1}, + { 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, -4, 0, 0, 0}, + { 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 1, 5, -23, -12, -3}, + { 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 2, -339, 0, 0, 147}, + { 0, 0, 0, 0, 0, -9, 12, 0, 0, 0, 0, 0, 2, 0, -10, -5, 0}, + { 0, 0, 0, 0, 0, 0, 3, 0,-4, 0, 0, 0, 0, 5, 0, 0, 0}, + { 0, 2,-2, 1, 0, 1, -1, 0, 0, 0, 0, 0, 0, 3, 0, 0, -1}, + { 0, 0, 0, 0, 0, 0, 7, -8, 0, 0, 0, 0, 2, 0, -4, -2, 0}, + { 0, 0, 0, 0, 0, 0, 3, 0,-3, 0, 0, 0, 0, 18, -3, 0, 0}, + + /* 531-540 */ + { 0, 0, 0, 0, 0, 0, 3, 0,-3, 0, 0, 0, 2, 9, -11, -5, -4}, + { 0, 0, 0, 0, 0, -2, 6, 0, 0, 0, 0, 0, 2, -8, 0, 0, 4}, + { 0, 0, 0, 0, 0, -6, 7, 0, 0, 0, 0, 0, 1, 3, 0, 0, -1}, + { 0, 0, 0, 0, 0, 6, -7, 0, 0, 0, 0, 0, 0, 0, 9, 0, 0}, + { 0, 0, 0, 0, 0, 0, 6, -6, 0, 0, 0, 0, 2, 6, -9, -4, -2}, + { 0, 0, 0, 0, 0, 0, 3, 0,-2, 0, 0, 0, 0, -4, -12, 0, 0}, + { 0, 0, 0, 0, 0, 0, 3, 0,-2, 0, 0, 0, 2, 67, -91, -39, -29}, + { 0, 0, 0, 0, 0, 0, 5, -4, 0, 0, 0, 0, 2, 30, -18, -8, -13}, + { 0, 0, 0, 0, 0, 3, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0}, + { 0, 0, 0, 0, 0, 3, -2, 0, 0, 0, 0, 0, 2, 0,-114, -50, 0}, + + /* 541-550 */ + { 0, 0, 0, 0, 0, 0, 3, 0,-1, 0, 0, 0, 2, 0, 0, 0, 23}, + { 0, 0, 0, 0, 0, 0, 3, 0,-1, 0, 0, 0, 2, 517, 16, 7,-224}, + { 0, 0, 0, 0, 0, 0, 3, 0, 0,-2, 0, 0, 2, 0, -7, -3, 0}, + { 0, 0, 0, 0, 0, 0, 4, -2, 0, 0, 0, 0, 2, 143, -3, -1, -62}, + { 0, 0, 0, 0, 0, 0, 3, 0, 0,-1, 0, 0, 2, 29, 0, 0, -13}, + { 0, 2,-2, 1, 0, 0, 1, 0,-1, 0, 0, 0, 0, -4, 0, 0, 2}, + { 0, 0, 0, 0, 0, -8, 16, 0, 0, 0, 0, 0, 2, -6, 0, 0, 3}, + { 0, 0, 0, 0, 0, 0, 3, 0, 2,-5, 0, 0, 2, 5, 12, 5, -2}, + { 0, 0, 0, 0, 0, 0, 7, -8, 3, 0, 0, 0, 2, -25, 0, 0, 11}, + { 0, 0, 0, 0, 0, 0, -5, 16,-4,-5, 0, 0, 2, -3, 0, 0, 1}, + + /* 551-560 */ + { 0, 0, 0, 0, 0, 0, 3, 0, 0, 0, 0, 0, 2, 0, 4, 2, 0}, + { 0, 0, 0, 0, 0, 0, -1, 8,-3, 0, 0, 0, 2, -22, 12, 5, 10}, + { 0, 0, 0, 0, 0, -8, 10, 0, 0, 0, 0, 0, 2, 50, 0, 0, -22}, + { 0, 0, 0, 0, 0, -8, 10, 0, 0, 0, 0, 0, 1, 0, 7, 4, 0}, + { 0, 0, 0, 0, 0, -8, 10, 0, 0, 0, 0, 0, 2, 0, 3, 1, 0}, + { 0, 0, 0, 0, 0, 0, 2, 2, 0, 0, 0, 0, 2, -4, 4, 2, 2}, + { 0, 0, 0, 0, 0, 0, 3, 0, 1, 0, 0, 0, 2, -5, -11, -5, 2}, + { 0, 0, 0, 0, 0, -3, 8, 0, 0, 0, 0, 0, 2, 0, 4, 2, 0}, + { 0, 0, 0, 0, 0, -5, 5, 0, 0, 0, 0, 0, 1, 4, 17, 9, -2}, + { 0, 0, 0, 0, 0, 5, -5, 0, 0, 0, 0, 0, 0, 59, 0, 0, 0}, + + /* 561-570 */ + { 0, 0, 0, 0, 0, 5, -5, 0, 0, 0, 0, 0, 1, 0, -4, -2, 0}, + { 0, 0, 0, 0, 0, 5, -5, 0, 0, 0, 0, 0, 2, -8, 0, 0, 4}, + { 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, -3, 0, 0, 0}, + { 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 1, 4, -15, -8, -2}, + { 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 2, 370, -8, 0,-160}, + { 0, 0, 0, 0, 0, 0, 7, -7, 0, 0, 0, 0, 2, 0, 0, -3, 0}, + { 0, 0, 0, 0, 0, 0, 7, -7, 0, 0, 0, 0, 2, 0, 3, 1, 0}, + { 0, 0, 0, 0, 0, 0, 6, -5, 0, 0, 0, 0, 2, -6, 3, 1, 3}, + { 0, 0, 0, 0, 0, 7, -8, 0, 0, 0, 0, 0, 0, 0, 6, 0, 0}, + { 0, 0, 0, 0, 0, 0, 5, -3, 0, 0, 0, 0, 2, -10, 0, 0, 4}, + + /* 571-580 */ + { 0, 0, 0, 0, 0, 4, -3, 0, 0, 0, 0, 0, 2, 0, 9, 4, 0}, + { 0, 0, 0, 0, 0, 1, 2, 0, 0, 0, 0, 0, 2, 4, 17, 7, -2}, + { 0, 0, 0, 0, 0, -9, 11, 0, 0, 0, 0, 0, 2, 34, 0, 0, -15}, + { 0, 0, 0, 0, 0, -9, 11, 0, 0, 0, 0, 0, 1, 0, 5, 3, 0}, + { 0, 0, 0, 0, 0, 0, 4, 0,-4, 0, 0, 0, 2, -5, 0, 0, 2}, + { 0, 0, 0, 0, 0, 0, 4, 0,-3, 0, 0, 0, 2, -37, -7, -3, 16}, + { 0, 0, 0, 0, 0, -6, 6, 0, 0, 0, 0, 0, 1, 3, 13, 7, -2}, + { 0, 0, 0, 0, 0, 6, -6, 0, 0, 0, 0, 0, 0, 40, 0, 0, 0}, + { 0, 0, 0, 0, 0, 6, -6, 0, 0, 0, 0, 0, 1, 0, -3, -2, 0}, + { 0, 0, 0, 0, 0, 0, 4, 0,-2, 0, 0, 0, 2, -184, -3, -1, 80}, + + /* 581-590 */ + { 0, 0, 0, 0, 0, 0, 6, -4, 0, 0, 0, 0, 2, -3, 0, 0, 1}, + { 0, 0, 0, 0, 0, 3, -1, 0, 0, 0, 0, 0, 0, -3, 0, 0, 0}, + { 0, 0, 0, 0, 0, 3, -1, 0, 0, 0, 0, 0, 1, 0, -10, -6, -1}, + { 0, 0, 0, 0, 0, 3, -1, 0, 0, 0, 0, 0, 2, 31, -6, 0, -13}, + { 0, 0, 0, 0, 0, 0, 4, 0,-1, 0, 0, 0, 2, -3, -32, -14, 1}, + { 0, 0, 0, 0, 0, 0, 4, 0, 0,-2, 0, 0, 2, -7, 0, 0, 3}, + { 0, 0, 0, 0, 0, 0, 5, -2, 0, 0, 0, 0, 2, 0, -8, -4, 0}, + { 0, 0, 0, 0, 0, 0, 4, 0, 0, 0, 0, 0, 0, 3, -4, 0, 0}, + { 0, 0, 0, 0, 0, 8, -9, 0, 0, 0, 0, 0, 0, 0, 4, 0, 0}, + { 0, 0, 0, 0, 0, 5, -4, 0, 0, 0, 0, 0, 2, 0, 3, 1, 0}, + + /* 591-600 */ + { 0, 0, 0, 0, 0, 2, 1, 0, 0, 0, 0, 0, 2, 19, -23, -10, 2}, + { 0, 0, 0, 0, 0, 2, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, -10}, + { 0, 0, 0, 0, 0, 2, 1, 0, 0, 0, 0, 0, 1, 0, 3, 2, 0}, + { 0, 0, 0, 0, 0, -7, 7, 0, 0, 0, 0, 0, 1, 0, 9, 5, -1}, + { 0, 0, 0, 0, 0, 7, -7, 0, 0, 0, 0, 0, 0, 28, 0, 0, 0}, + { 0, 0, 0, 0, 0, 4, -2, 0, 0, 0, 0, 0, 1, 0, -7, -4, 0}, + { 0, 0, 0, 0, 0, 4, -2, 0, 0, 0, 0, 0, 2, 8, -4, 0, -4}, + { 0, 0, 0, 0, 0, 4, -2, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0}, + { 0, 0, 0, 0, 0, 4, -2, 0, 0, 0, 0, 0, 0, 0, 3, 0, 0}, + { 0, 0, 0, 0, 0, 0, 5, 0,-4, 0, 0, 0, 2, -3, 0, 0, 1}, + + /* 601-610 */ + { 0, 0, 0, 0, 0, 0, 5, 0,-3, 0, 0, 0, 2, -9, 0, 1, 4}, + { 0, 0, 0, 0, 0, 0, 5, 0,-2, 0, 0, 0, 2, 3, 12, 5, -1}, + { 0, 0, 0, 0, 0, 3, 0, 0, 0, 0, 0, 0, 2, 17, -3, -1, 0}, + { 0, 0, 0, 0, 0, -8, 8, 0, 0, 0, 0, 0, 1, 0, 7, 4, 0}, + { 0, 0, 0, 0, 0, 8, -8, 0, 0, 0, 0, 0, 0, 19, 0, 0, 0}, + { 0, 0, 0, 0, 0, 5, -3, 0, 0, 0, 0, 0, 1, 0, -5, -3, 0}, + { 0, 0, 0, 0, 0, 5, -3, 0, 0, 0, 0, 0, 2, 14, -3, 0, -1}, + { 0, 0, 0, 0, 0, -9, 9, 0, 0, 0, 0, 0, 1, 0, 0, -1, 0}, + { 0, 0, 0, 0, 0, -9, 9, 0, 0, 0, 0, 0, 1, 0, 0, 0, -5}, + { 0, 0, 0, 0, 0, -9, 9, 0, 0, 0, 0, 0, 1, 0, 5, 3, 0}, + + /* 611-620 */ + { 0, 0, 0, 0, 0, 9, -9, 0, 0, 0, 0, 0, 0, 13, 0, 0, 0}, + { 0, 0, 0, 0, 0, 6, -4, 0, 0, 0, 0, 0, 1, 0, -3, -2, 0}, + { 0, 0, 0, 0, 0, 0, 6, 0, 0, 0, 0, 0, 2, 2, 9, 4, 3}, + { 0, 0, 0, 0, 0, 0, 6, 0, 0, 0, 0, 0, 0, 0, 0, 0, -4}, + { 0, 0, 0, 0, 0, 0, 6, 0, 0, 0, 0, 0, 0, 8, 0, 0, 0}, + { 0, 0, 0, 0, 0, 0, 6, 0, 0, 0, 0, 0, 1, 0, 4, 2, 0}, + { 0, 0, 0, 0, 0, 0, 6, 0, 0, 0, 0, 0, 2, 6, 0, 0, -3}, + { 0, 0, 0, 0, 0, 0, 6, 0, 0, 0, 0, 0, 0, 6, 0, 0, 0}, + { 0, 0, 0, 0, 0, 0, 6, 0, 0, 0, 0, 0, 1, 0, 3, 1, 0}, + { 0, 0, 0, 0, 0, 0, 6, 0, 0, 0, 0, 0, 2, 5, 0, 0, -2}, + + /* 621-630 */ + { 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 3, 0, 0, -1}, + { 1, 0,-2, 0, 0, 0, 2, 0,-2, 0, 0, 0, 0, -3, 0, 0, 0}, + { 1, 0,-2, 0, 0, 2, -2, 0, 0, 0, 0, 0, 0, 6, 0, 0, 0}, + { 1, 0,-2, 0, 0, 0, 1, 0,-1, 0, 0, 0, 0, 7, 0, 0, 0}, + { 1, 0,-2, 0, 0, 1, -1, 0, 0, 0, 0, 0, 0, -4, 0, 0, 0}, + {-1, 0, 0, 0, 0, 3, -3, 0, 0, 0, 0, 0, 0, 4, 0, 0, 0}, + {-1, 0, 0, 0, 0, 0, 2, 0,-2, 0, 0, 0, 0, 6, 0, 0, 0}, + {-1, 0, 2, 0, 0, 0, 4, -8, 3, 0, 0, 0, 0, 0, -4, 0, 0}, + { 1, 0,-2, 0, 0, 0, 4, -8, 3, 0, 0, 0, 0, 0, -4, 0, 0}, + {-2, 0, 2, 0, 0, 0, 4, -8, 3, 0, 0, 0, 0, 5, 0, 0, 0}, + + /* 631-640 */ + {-1, 0, 0, 0, 0, 0, 2, 0,-3, 0, 0, 0, 0, -3, 0, 0, 0}, + {-1, 0, 0, 0, 0, 0, 1, 0,-1, 0, 0, 0, 0, 4, 0, 0, 0}, + {-1, 0, 0, 0, 0, 1, -1, 0, 0, 0, 0, 0, 0, -5, 0, 0, 0}, + {-1, 0, 2, 0, 0, 2, -2, 0, 0, 0, 0, 0, 0, 4, 0, 0, 0}, + { 1,-1, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 3, 0, 0}, + {-1, 0, 2, 0, 0, 0, 2, 0,-3, 0, 0, 0, 0, 13, 0, 0, 0}, + {-2, 0, 0, 0, 0, 0, 2, 0,-3, 0, 0, 0, 0, 21, 11, 0, 0}, + { 1, 0, 0, 0, 0, 0, 4, -8, 3, 0, 0, 0, 0, 0, -5, 0, 0}, + {-1, 1,-1, 1, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, -5, -2, 0}, + { 1, 1,-1, 1, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, 5, 3, 0}, + + /* 641-650 */ + {-1, 0, 0, 0, 0, 0, 4, -8, 3, 0, 0, 0, 0, 0, -5, 0, 0}, + {-1, 0, 2, 1, 0, 0, 2, 0,-2, 0, 0, 0, 0, -3, 0, 0, 2}, + { 0, 0, 0, 0, 0, 0, 2, 0,-2, 0, 0, 0, 0, 20, 10, 0, 0}, + {-1, 0, 2, 0, 0, 0, 2, 0,-2, 0, 0, 0, 0, -34, 0, 0, 0}, + {-1, 0, 2, 0, 0, 3, -3, 0, 0, 0, 0, 0, 0, -19, 0, 0, 0}, + { 1, 0,-2, 1, 0, 0, -2, 0, 2, 0, 0, 0, 0, 3, 0, 0, -2}, + { 1, 2,-2, 2, 0, -3, 3, 0, 0, 0, 0, 0, 0, -3, 0, 0, 1}, + { 1, 2,-2, 2, 0, 0, -2, 0, 2, 0, 0, 0, 0, -6, 0, 0, 3}, + { 1, 0, 0, 0, 0, 1, -1, 0, 0, 0, 0, 0, 0, -4, 0, 0, 0}, + { 1, 0, 0, 0, 0, 0, 1, 0,-1, 0, 0, 0, 0, 3, 0, 0, 0}, + + /* 651-660 */ + { 0, 0,-2, 0, 0, 2, -2, 0, 0, 0, 0, 0, 0, 3, 0, 0, 0}, + { 0, 0,-2, 0, 0, 0, 1, 0,-1, 0, 0, 0, 0, 4, 0, 0, 0}, + { 0, 2, 0, 2, 0, -2, 2, 0, 0, 0, 0, 0, 0, 3, 0, 0, -1}, + { 0, 2, 0, 2, 0, 0, -1, 0, 1, 0, 0, 0, 0, 6, 0, 0, -3}, + { 0, 2, 0, 2, 0, -1, 1, 0, 0, 0, 0, 0, 0, -8, 0, 0, 3}, + { 0, 2, 0, 2, 0, -2, 3, 0, 0, 0, 0, 0, 0, 0, 3, 1, 0}, + { 0, 0, 2, 0, 0, 0, 2, 0,-2, 0, 0, 0, 0, -3, 0, 0, 0}, + { 0, 1, 1, 2, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, -3, -2, 0}, + { 1, 2, 0, 2, 0, 0, 1, 0, 0, 0, 0, 0, 0, 126, -63, -27, -55}, + {-1, 2, 0, 2, 0, 10, -3, 0, 0, 0, 0, 0, 0, -5, 0, 1, 2}, + + /* 661-670 */ + { 0, 1, 1, 1, 0, 0, 1, 0, 0, 0, 0, 0, 0, -3, 28, 15, 2}, + { 1, 2, 0, 2, 0, 0, 1, 0, 0, 0, 0, 0, 0, 5, 0, 1, -2}, + { 0, 2, 0, 2, 0, 0, 4, -8, 3, 0, 0, 0, 0, 0, 9, 4, 1}, + { 0, 2, 0, 2, 0, 0, -4, 8,-3, 0, 0, 0, 0, 0, 9, 4, -1}, + {-1, 2, 0, 2, 0, 0, -4, 8,-3, 0, 0, 0, 0, -126, -63, -27, 55}, + { 2, 2,-2, 2, 0, 0, -2, 0, 3, 0, 0, 0, 0, 3, 0, 0, -1}, + { 1, 2, 0, 1, 0, 0, -2, 0, 3, 0, 0, 0, 0, 21, -11, -6, -11}, + { 0, 1, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, -4, 0, 0}, + {-1, 2, 0, 1, 0, 0, 1, 0, 0, 0, 0, 0, 0, -21, -11, -6, 11}, + {-2, 2, 2, 2, 0, 0, 2, 0,-2, 0, 0, 0, 0, -3, 0, 0, 1}, + + /* 671-680 */ + { 0, 2, 0, 2, 0, 2, -3, 0, 0, 0, 0, 0, 0, 0, 3, 1, 0}, + { 0, 2, 0, 2, 0, 1, -1, 0, 0, 0, 0, 0, 0, 8, 0, 0, -4}, + { 0, 2, 0, 2, 0, 0, 1, 0,-1, 0, 0, 0, 0, -6, 0, 0, 3}, + { 0, 2, 0, 2, 0, 2, -2, 0, 0, 0, 0, 0, 0, -3, 0, 0, 1}, + {-1, 2, 2, 2, 0, 0, -1, 0, 1, 0, 0, 0, 0, 3, 0, 0, -1}, + { 1, 2, 0, 2, 0, -1, 1, 0, 0, 0, 0, 0, 0, -3, 0, 0, 1}, + {-1, 2, 2, 2, 0, 0, 2, 0,-3, 0, 0, 0, 0, -5, 0, 0, 2}, + { 2, 2, 0, 2, 0, 0, 2, 0,-3, 0, 0, 0, 0, 24, -12, -5, -11}, + { 1, 2, 0, 2, 0, 0, -4, 8,-3, 0, 0, 0, 0, 0, 3, 1, 0}, + { 1, 2, 0, 2, 0, 0, 4, -8, 3, 0, 0, 0, 0, 0, 3, 1, 0}, + + /* 681-687 */ + { 1, 1, 1, 1, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 3, 2, 0}, + { 0, 2, 0, 2, 0, 0, 1, 0, 0, 0, 0, 0, 0, -24, -12, -5, 10}, + { 2, 2, 0, 1, 0, 0, 1, 0, 0, 0, 0, 0, 0, 4, 0, -1, -2}, + {-1, 2, 2, 2, 0, 0, 2, 0,-2, 0, 0, 0, 0, 13, 0, 0, -6}, + {-1, 2, 2, 2, 0, 3, -3, 0, 0, 0, 0, 0, 0, 7, 0, 0, -3}, + { 1, 2, 0, 2, 0, 1, -1, 0, 0, 0, 0, 0, 0, 3, 0, 0, -1}, + { 0, 2, 2, 2, 0, 0, 2, 0,-2, 0, 0, 0, 0, 3, 0, 0, -1} + }; + +/* Number of terms in the planetary nutation model */ + const int NPL = (int) (sizeof xpl / sizeof xpl[0]); + +/*--------------------------------------------------------------------*/ + +/* Interval between fundamental date J2000.0 and given date (JC). */ + t = ((date1 - ERFA_DJ00) + date2) / ERFA_DJC; + +/* ------------------- */ +/* LUNI-SOLAR NUTATION */ +/* ------------------- */ + +/* Fundamental (Delaunay) arguments */ + +/* Mean anomaly of the Moon (IERS 2003). */ + el = eraFal03(t); + +/* Mean anomaly of the Sun (MHB2000). */ + elp = fmod(1287104.79305 + + t * (129596581.0481 + + t * (-0.5532 + + t * (0.000136 + + t * (-0.00001149)))), ERFA_TURNAS) * ERFA_DAS2R; + +/* Mean longitude of the Moon minus that of the ascending node */ +/* (IERS 2003. */ + f = eraFaf03(t); + +/* Mean elongation of the Moon from the Sun (MHB2000). */ + d = fmod(1072260.70369 + + t * (1602961601.2090 + + t * (-6.3706 + + t * (0.006593 + + t * (-0.00003169)))), ERFA_TURNAS) * ERFA_DAS2R; + +/* Mean longitude of the ascending node of the Moon (IERS 2003). */ + om = eraFaom03(t); + +/* Initialize the nutation values. */ + dp = 0.0; + de = 0.0; + +/* Summation of luni-solar nutation series (in reverse order). */ + for (i = NLS-1; i >= 0; i--) { + + /* Argument and functions. */ + arg = fmod((double)xls[i].nl * el + + (double)xls[i].nlp * elp + + (double)xls[i].nf * f + + (double)xls[i].nd * d + + (double)xls[i].nom * om, ERFA_D2PI); + sarg = sin(arg); + carg = cos(arg); + + /* Term. */ + dp += (xls[i].sp + xls[i].spt * t) * sarg + xls[i].cp * carg; + de += (xls[i].ce + xls[i].cet * t) * carg + xls[i].se * sarg; + } + +/* 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 functions, 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 = fmod(2.35555598 + 8328.6914269554 * t, ERFA_D2PI); + +/* Mean longitude of the Moon minus that of the ascending node */ +/*(MHB2000). */ + af = fmod(1.627905234 + 8433.466158131 * t, ERFA_D2PI); + +/* Mean elongation of the Moon from the Sun (MHB2000). */ + ad = fmod(5.198466741 + 7771.3771468121 * t, ERFA_D2PI); + +/* Mean longitude of the ascending node of the Moon (MHB2000). */ + aom = fmod(2.18243920 - 33.757045 * t, ERFA_D2PI); + +/* General accumulated precession in longitude (IERS 2003). */ + apa = eraFapa03(t); + +/* Planetary longitudes, Mercury through Uranus (IERS 2003). */ + alme = eraFame03(t); + alve = eraFave03(t); + alea = eraFae03(t); + alma = eraFama03(t); + alju = eraFaju03(t); + alsa = eraFasa03(t); + alur = eraFaur03(t); + +/* Neptune longitude (MHB2000). */ + alne = fmod(5.321159000 + 3.8127774000 * t, ERFA_D2PI); + +/* Initialize the nutation values. */ + dp = 0.0; + de = 0.0; + +/* Summation of planetary nutation series (in reverse order). */ + for (i = NPL-1; i >= 0; i--) { + + /* Argument and functions. */ + arg = fmod((double)xpl[i].nl * al + + (double)xpl[i].nf * af + + (double)xpl[i].nd * ad + + (double)xpl[i].nom * aom + + (double)xpl[i].nme * alme + + (double)xpl[i].nve * alve + + (double)xpl[i].nea * alea + + (double)xpl[i].nma * alma + + (double)xpl[i].nju * alju + + (double)xpl[i].nsa * alsa + + (double)xpl[i].nur * alur + + (double)xpl[i].nne * alne + + (double)xpl[i].npa * apa, ERFA_D2PI); + sarg = sin(arg); + carg = cos(arg); + + /* Term. */ + dp += (double)xpl[i].sp * sarg + (double)xpl[i].cp * carg; + de += (double)xpl[i].se * sarg + (double)xpl[i].ce * carg; + + } + +/* 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; + + return; + +} +/*---------------------------------------------------------------------- +** +** +** Copyright (C) 2013-2016, NumFOCUS Foundation. +** All rights reserved. +** +** This library is derived, with permission, from the International +** Astronomical Union's "Standards of Fundamental Astronomy" library, +** available from http://www.iausofa.org. +** +** The ERFA version is intended to retain identical functionality to +** the SOFA library, but made distinct through different function and +** file names, as set out in the SOFA license conditions. The SOFA +** original has a role as a reference standard for the IAU and IERS, +** and consequently redistribution is permitted only in its unaltered +** state. The ERFA version is not subject to this restriction and +** therefore can be included in distributions which do not support the +** concept of "read only" software. +** +** Although the intent is to replicate the SOFA API (other than +** replacement of prefix names) and results (with the exception of +** bugs; any that are discovered will be fixed), SOFA is not +** responsible for any errors found in this version of the library. +** +** If you wish to acknowledge the SOFA heritage, please acknowledge +** that you are using a library derived from SOFA, rather than SOFA +** itself. +** +** +** TERMS AND CONDITIONS +** +** Redistribution and use in source and binary forms, with or without +** modification, are permitted provided that the following conditions +** are met: +** +** 1 Redistributions of source code must retain the above copyright +** notice, this list of conditions and the following disclaimer. +** +** 2 Redistributions in binary form must reproduce the above copyright +** notice, this list of conditions and the following disclaimer in +** the documentation and/or other materials provided with the +** distribution. +** +** 3 Neither the name of the Standards Of Fundamental Astronomy Board, +** the International Astronomical Union nor the names of its +** contributors may be used to endorse or promote products derived +** from this software without specific prior written permission. +** +** THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS +** "AS IS" AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT +** LIMITED TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS +** FOR A PARTICULAR PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL THE +** COPYRIGHT HOLDER OR CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT, +** INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, +** BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; +** LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER +** CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT +** LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN +** ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE +** POSSIBILITY OF SUCH DAMAGE. +** +*/ |