SUBROUTINE HRMSYM( NDIM, NF, MINPTS, MAXPTS, FUNSUB, EPSABS, & EPSREL, RESTAR, RESULT, ABSERR, NEVAL, IFAIL, WORK) ****BEGIN PROLOGUE HRMSYM * ****AUTHOR * Alan Genz, * Department of Mathematics * Washington State University * Pullman, WA 99164-3113, USA * Email: alangenz@wsu.edu * * Reference: Genz, A., and Keister, B. (1996), Fully Symmetric * Interpolatory Rules for Multiple Integrals over Infinite * Regions with Gaussian Weight, J. Comp. Appl. Math., 71, 299-309. * ****KEYWORDS automatic multidimensional integrator, * n-dimensional region (-infin, infin)^n * Gaussian weight ****PURPOSE The routine calculates an approximation to a given * vector of definite integrals * * infin infin * I ... I w(X)(F ,F ,...,F ) DX(NDIM)...DX(2)DX(1), * -infin -infin 1 2 NF * * where F = F (X ,X ,...,X ), I = 1,2,...,NF, * I I 1 2 NDIM * * w(X) = EXP(-( X(1)**2 + ... + X(NDIM)**2 )/2)/SQRT(2*PI)**NDIM. * ****DESCRIPTION Computation of integrals over infinite regions with * Gaussian weight. * * ON ENTRY * * NDIM Integer, number of variables, with 1 < NDIM <= 1000. * NF Integer, number of components of the integral. * MINPTS Integer, minimum number of function evaluations. * MAXPTS Integer, maximum number of function evaluations. * FUNSUB Externally declared subroutine for computing * all components of the integrand at the given * evaluation point. * It must have parameters (NDIM,X,NF,FUNVLS) * Input parameters: * NDIM Integer that defines the dimension of the * integral. * X Real array of dimension NDIM * that defines the evaluation point. * NF Integer that defines the number of components of I. * Output parameter: * FUNVLS Real array of dimension NF * that defines NF components of the integrand. * * EPSABS Real, requested absolute accuracy. * EPSREL Real, requested relative accuracy. * RESTAR Integer. * If RESTAR = 0, this is the first attempt to compute * the integral. * If RESTAR = 1, then we restart a previous attempt. * WORK Real array of working storage, must have dimension at * least 2*NF + (NF+1)*NUMSMS. NUMSMS is the number * of NDIM partitions of the integers 0,...,RULE, after * RULE+1 approximations to the integrals have been computed. * The required value for NUMSMS will never exceed 10000. * * ON RETURN * * RESULT Real array of dimension NF. * Approximations to all components of the integral. * ABSERR Real array of dimension NF. * Estimates of absolute accuracies. * NEVAL Integer, number of function evaluations used. * IFAIL Integer. * IFAIL = 0 for normal exit, when * ABSERR(K) <= MAX( EPSABS, ABS(RESULT(K))*EPSREL ) for * all K, 0 < K <= NF, with <= MAXPTS function values. * IFAIL = 1 if MAXPTS was too small to obtain the required * accuracy. In this case values of RESULT are returned * with estimated absolute accuracies ABSERR. * WORK Real array of working storage, that contains information * that might be needed for subsequent calls of HRMSYM. This * array should not be modified. * ****ROUTINES CALLED ****END PROLOGUE HRMSYM * * Global variables. * EXTERNAL FUNSUB INTEGER NDIM, NF, MINPTS, MAXPTS, RESTAR INTEGER NEVAL, IFAIL DOUBLE PRECISION EPSABS, EPSREL DOUBLE PRECISION RESULT(*), ABSERR(*), WORK(*) * * Local variables. * INTEGER I, MAXRUL, RULE, MNRULE, INTCLS, NUMSMS PARAMETER ( MAXRUL = 25 ) SAVE RULE, MNRULE IFAIL = 1 IF ( NDIM .LE. 4 ) THEN * * Call product Gauss-Hermite Rule * CALL HERMIT( NDIM, NF, MINPTS, MAXPTS, FUNSUB, EPSABS, EPSREL, & RESTAR, RESULT, ABSERR, NEVAL, IFAIL, WORK ) ELSE IF ( RESTAR .EQ. 0 ) THEN MNRULE = -1 RULE = 0 DO I = 1, NF WORK(I) = 0 END DO END IF NEVAL = 0 DO WHILE ( NEVAL .LE. MAXPTS .AND. RULE .LE. MAXRUL & .AND. ( IFAIL .GT. 0 .OR. NEVAL .LT. MINPTS ) ) CALL HRMTRL( NDIM, NF, FUNSUB, MNRULE, RULE, RESULT, & INTCLS, WORK(NF+1), WORK(2*NF+1), NUMSMS ) IFAIL = 0 DO I = 1, NF ABSERR(I) = ABS( RESULT(I) - WORK(I) ) WORK(I) = RESULT(I) IF ( ABSERR(I) .GT. MAX(EPSABS,EPSREL*ABS(RESULT(I))) & .OR. RULE .EQ. 0 ) IFAIL = 1 END DO NEVAL = NEVAL + INTCLS RULE = RULE + 1 END DO END IF * ****END HRMSYM * END SUBROUTINE HRMTRL( S, N, F, MINORD, MAXORD, INTVAL, INTCLS, & WORK, FULSMS, NUMSMS ) * MULTIDIMENSIONAL FULLY SYMMETRIC RULE INTEGRATION SUBROUTINE * * THIS SUBROUTINE COMPUTES A SEQUENCE OF FULLY SYMMETRIC RULE * APPROXIMATIONS TO A FULLY SYMMETRIC MULTIPLE INTEGRAL. WRITTEN BY * Alan Genz * Department of Mathematics * Washington State University * Pullman, Washington 99164-3113 USA * Telephone: 509-335-2131 * Electronic Mail: alangenz@wsu.edu * Fax: 509-335-1188 * *************** PARAMETERS FOR HRMTRL ******************************** ******INPUT PARAMETERS * S INTEGER number of variables, with 0 < S <= 1000. * N Integer, number of components of the integral. * F EXTERNALly declared user defined integrand subroutine. * it must have parameters (S,X,N,F), where X is a REAL S-array * and F is a real N-array. * MINORD INTEGER minimum order parameter. On entry MINORD specifies * the current highest order approximation to the integral, * available in the array INTVAL. For the first call * MINORD should be set to -1. Otherwise a previous call is * assumed that computed INTVAL. On exit MINORD is set to MAXORD. * MAXORD INTEGER maximum order parameter, must be greater than MINORD * and not exceed 25. The subroutine computes approximations of * polynomial degree 2*MAXORD+1. *******OUTPUT PARAMETERS * INTVAL REAL array of length N. Upon successful exit * INTVAL(1),..., INTVAL(N) are approximations to the components * of the integral. These are all approximations of polynomial * degree 2*MAXORD+1. * INTCLS INTEGER number of F values needed for INTVAL * WORK REAL working storage array. * FULSMS REAL working storage array with dimension (N+1,*). On exit * FULSMS(I,J) contains the fully symmetric basic rule sum * indexed by the jth s-partition of the integers 0,...,MAXORD, * for the Ith component of the integrand. * FULSMS(N+1,J) contains number of points for the fully * symmetric basic rule sum indexed by the Jth S-partition of * the integers 0,...,MAXORD. * NUMSMS INTEGER number of S-partitions of the integers 0,...,MAXORD. ************************************************************************ EXTERNAL F INTEGER S, N, MAXDIM, MINORD, MAXORD, MAXRDM, NUMSMS PARAMETER ( MAXDIM = 1000, MAXRDM = 25 ) DOUBLE PRECISION X(MAXDIM), FULWGT, WEIGHT, & INTVAL(N), FULSMS(N+1,*), WORK(*) INTEGER D, I, L, MODOFM, M(MAXDIM), K(MAXDIM), INTCLS, PRTCNT D = MINORD + 1 INTCLS = 0 IF ( D .EQ. 0 ) THEN DO I = 1,N INTVAL(I) = 0 END DO END IF * **** Begin loop for each D * for each D find all distinct partitions M with |M| <= D * DO WHILE( D .LE. MIN ( MAXORD, MAXRDM ) ) PRTCNT = 0 CALL NXPART( PRTCNT, S, M, MODOFM ) DO WHILE( MODOFM .LE. D ) * **** Calculate updated weight for partition M alnd **** fully symmetric sums ( when necessary ) * FULWGT = WEIGHT( S, X, M, K, MODOFM, D ) IF ( D .EQ. MODOFM ) THEN DO I = 1,N FULSMS(I,PRTCNT) = 0 END DO FULSMS(N+1,PRTCNT) = 0 END IF IF ( FULSMS(N+1,PRTCNT) .EQ. 0 .AND. FULWGT .NE. 0 ) THEN CALL FULSMH( S, M, N, F, FULSMS(1,PRTCNT), X, WORK ) & INTCLS = INTCLS + FULSMS(N+1,PRTCNT) END IF DO I = 1,N INTVAL(I) = INTVAL(I) + FULWGT*FULSMS(I,PRTCNT) END DO CALL NXPART( PRTCNT, S, M, MODOFM ) END DO * **** End loop for each D * D = D + 1 END DO MINORD = MAXORD NUMSMS = PRTCNT - 1 END * SUBROUTINE FULSMH( S, M, N, F, FULSMS, X, FUNVAL ) * **** To compute fully symmetric basic rule sums * INTEGER S, M(*), SUMCLS, IX, LX, I,L, MI, ML, IL, N, MX DOUBLE PRECISION X(*), INTWGT, FULSMS(*), FUNVAL(*) * * Generators for 1 + 2 + 6 + 10 + 16 = 35 point * degree 51 rule, with degree 1, 5, 15 and 29 imbedded rules. * PARAMETER ( MX = 17 ) DOUBLE PRECISION G(0:MX) SAVE G DATA G( 0),G( 1)/0D0 , 0.17320508075688773D1/ DATA G( 2),G( 3)/0.41849560176727319D1, 0.74109534999454084D0/ DATA G( 4),G( 5)/0.28612795760570581D1, 0.63633944943363700D1/ DATA G( 6),G( 7)/0.12304236340273060D1, 0.51870160399136561D1/ DATA G( 8),G( 9)/0.25960831150492022D1, 0.32053337944991945D1/ DATA G(10),G(11)/0.90169397898903025D1, 0.24899229757996061D0/ DATA G(12),G(13)/0.79807717985905609D1, 0.22336260616769417D1/ DATA G(14),G(15)/0.71221067008046167D1, 0.36353185190372782D1/ DATA G(16),G(17)/0.56981777684881096D1, 0.47364330859522971D1/ INTWGT = 1 DO I = 1, S IF ( M(I) .NE. 0 ) INTWGT = INTWGT/2 END DO SUMCLS = 0 DO I = 1,N FULSMS(I) = 0 END DO * ******** Compute centrally symmetric sum for permutation M * 10 DO I = 1, S X(I) = -G(M(I)) END DO 20 SUMCLS = SUMCLS + 1 CALL F( S, X, N, FUNVAL ) DO I = 1,N FULSMS(I) = FULSMS(I) + INTWGT*FUNVAL(I) END DO DO I = 1, S X(I) = -X(I) IF ( X(I) .GT. 0 ) GO TO 20 END DO * ******** END Integration loop for M * * ******** Find next distinct permutation of M and loop back * to compute next centrally symmetric sum * DO I = 2, S IF ( M(I-1) .GT. M(I) ) THEN MI = M(I) IX = I - 1 IF ( I .GT. 2 ) THEN DO L = 1, IX/2 ML = M(L) IL = I - L M(L) = M(IL) M(IL) = ML IF ( ML .LE. MI ) IX = IX - 1 IF ( M(L) .GT. MI ) LX = L END DO IF ( M(IX) .LE. MI ) IX = LX END IF M(I) = M(IX) M(IX) = MI GO TO 10 END IF END DO * **** END Loop for permutations of M and associated sums * * **** Restore original order to M. * DO I = 1, S/2 MI = M(I) M(I) = M(S-I+1) M(S-I+1) = MI END DO FULSMS(N+1) = SUMCLS END * DOUBLE PRECISION FUNCTION WEIGHT( S, INTRPS, M,K, MODOFM, D ) * **** Subroutine to update weight for partition m * INTEGER S, M(S), K(S), I, L, D, MAXRDM, NZRMAX, MODOFM PARAMETER ( MAXRDM = 25 ) DOUBLE PRECISION INTRPS(S), MOMPRD(0:MAXRDM,0:MAXRDM), MOMNKN, & INTMPA, INTMPB SAVE MOMPRD * * Modified moments and generators for 1 + 2 + 6 + 10 + 16 = 35 point * degree 51 rule, with degree 1, 5 and 19 imbedded rules. * PARAMETER ( NZRMAX = 17 ) DOUBLE PRECISION A(0:NZRMAX), G(0:NZRMAX) DATA A / 2*1D0, 0D0, 6D0, & -0.48378475125832451D2, 3*0D0, 34020D0, & -0.98606453173677489D6, 5*0D0, 0.12912054173706603D13, & -0.11268664521456168D15, 0.29248520348796280D16 / DATA G( 0),G( 1)/0D0 , 0.17320508075688773D1/ DATA G( 2),G( 3)/0.41849560176727319D1, 0.74109534999454084D0/ DATA G( 4),G( 5)/0.28612795760570581D1, 0.63633944943363700D1/ DATA G( 6),G( 7)/0.12304236340273060D1, 0.51870160399136561D1/ DATA G( 8),G( 9)/0.25960831150492022D1, 0.32053337944991945D1/ DATA G(10),G(11)/0.90169397898903025D1, 0.24899229757996061D0/ DATA G(12),G(13)/0.79807717985905609D1, 0.22336260616769417D1/ DATA G(14),G(15)/0.71221067008046167D1, 0.36353185190372782D1/ DATA G(16),G(17)/0.56981777684881096D1, 0.47364330859522971D1/ DATA MOMPRD(0,0) / 0D0 / IF ( MOMPRD(0,0) .EQ. 0 ) THEN * **** Calculate moments * DO L = 0, MAXRDM DO I = 0, MAXRDM MOMPRD(L,I) = 0 END DO END DO MOMPRD(0,0) = A(0) DO L = 0, NZRMAX MOMNKN = 1 DO I = 1, NZRMAX IF ( I .LE. L ) THEN MOMNKN = MOMNKN*( G(L)**2 - G(I-1)**2 ) ELSE MOMNKN = MOMNKN*( G(L)**2 - G(I)**2 ) END IF IF ( I .GE. L ) MOMPRD(L,I) = A(I)/MOMNKN END DO END DO END IF * * Determine Updated Weight Contribution * DO I = 2,S INTRPS(I) = 0 K(I) = M(I) END DO K(1) = D - MODOFM + M(1) 10 INTRPS(1) = MOMPRD( M(1), K(1) ) DO I = 2, S INTRPS(I) = INTRPS(I) + MOMPRD( M(I), K(I) )*INTRPS(I-1) INTRPS(I-1) = 0 K(1) = K(1) - 1 K(I) = K(I) + 1 IF ( K(1) .GE. M(1) ) GO TO 10 K(1) = K(1) + K(I) - M(I) K(I) = M(I) END DO WEIGHT = INTRPS(S) END SUBROUTINE NXPART( PRTCNT, S, M, MODOFM ) * **** SUBROUTINE TO COMPUTE THE NEXT S PARTITION * INTEGER S, M(S), PRTCNT, MODOFM, I, MSUM, L IF ( PRTCNT .EQ. 0 ) THEN DO I = 1, S M(I) = 0 END DO PRTCNT = 1 MODOFM = 0 ELSE PRTCNT = PRTCNT + 1 MSUM = M(1) DO I = 2, S MSUM = MSUM + M(I) IF ( M(1) .LE. M(I) + 1 ) THEN M(I) = 0 ELSE M(1) = MSUM - (I-1)*(M(I)+1) DO L = 2, I M(L) = M(I) + 1 END DO RETURN END IF END DO M(1) = MSUM + 1 MODOFM = M(1) END IF END * SUBROUTINE MLTRUL( NDIM, NUMFUN, FUNSUB, NP, POINT, WEIGHT, & INTVAL, FUNS, X, IC ) * * Computes product integration rule * EXTERNAL FUNSUB INTEGER NDIM, NP, NUMFUN, ICI, I DOUBLE PRECISION POINT(*), WEIGHT(*), INTVAL(*) DOUBLE PRECISION WTPROD, X(*), FUNS(*), IC(*) DO I = 1, NDIM IC(I) = 1 END DO DO I = 1, NUMFUN INTVAL(I) = 0 END DO 10 WTPROD = 1 DO I = 1, NDIM ICI = IC(I) X(I) = POINT(ICI) WTPROD = WTPROD*WEIGHT(ICI) END DO CALL FUNSUB( NDIM, X, NUMFUN, FUNS ) DO I = 1, NUMFUN INTVAL(I) = INTVAL(I) + WTPROD*FUNS(I) END DO DO I = 1, NDIM IC(I) = IC(I) + 1 IF ( IC(I) .LE. NP ) GO TO 10 IC(I) = 1 END DO END * SUBROUTINE HERMIT( NDIM, NUMFUN, MINPTS, MAXPTS, FUNSUB, & EPSABS, EPSREL, RESTAR, RESULT, ABSERR, NEVAL, IFAIL, WORK ) ****BEGIN PROLOGUE HERMIT ****CATEGORY NO. H2B1A1 ****AUTHOR * * Alan Genz * Department of Mathematics * Washington State University * Pullman, Washington 99164-3113 USA * Telephone: 509-335-2131 * Electronic Mail: alangenz@wsu.edu * Fax: 509-335-1188 * ****KEYWORDS automatic multidimensional integrator, Gaussian weight * n-dimensional region (-infin, infin)^n ****PURPOSE The routine calculates an approximation to a vector of * definite integrals using Gauss-Hermite product rules. * * infin infin * I ... I w(X) (F ,F ,...,F ) DX(NDIM)...DX(2)DX(1), * -infin -infin 1 2 NUMFUN * * where F = F (X ,X ,...,X ), I = 1,2,...,NUMFUN, * I I 1 2 NDIM * * w(X) = EXP(-( X(1)**2 + ... + X(NDIM)**2 )/2)/SQRT(2*PI)**NDIM. * ****DESCRIPTION Computation of integrals over infinite regions with * Gaussian weight using Gauss-Hermite product rules. * * ON ENTRY * * NDIM Integer, number of variables. * NUMFUN Integer, number of components of the integral. * MINPTS Integer, minimum number of function evaluations. * MAXPTS Integer, maximum number of function evaluations. * FUNSUB Externally declared subroutine for computing components of * the integrand at the given evaluation point. * It must have parameters (NDIM,X,NUMFUN,FUNVLS) * Input parameters: * NDIM Integer, number of dimensions for the integral. * X Real NDIM-array for the evaluation point. * NUMFUN Integer, number of components of I. * Output parameter: * FUNVLS Real NUMFUN-array for integrand components. * * EPSABS Real, requested absolute accuracy. * EPSREL Real, requested relative accuracy. * RESTAR Integer. * If RESTAR = 0, this is the first attempt to compute * the integral. * If RESTAR = 1, then we restart a previous attempt. * WORK Real array of working storage, must have dimensions at * least 2*NUMFUN+2*NDIM * * ON RETURN * * RESULT Real NUMFUN-array of approximations to all components * of the integral. * ABSERR Real NUMFUN-array of estimates of absolute accuracies. * NEVAL Integer, number of function evaluations used. * IFAIL Integer. * IFAIL = 0 for normal exit, when * ABSERR(K) <= MAX( EPSABS, ABS(RESULT(K))*EPSREL ) for * all K, 0 < K <= NUMFUN, with <= MAXPTS function values. * IFAIL = 1 if MAXPTS was too small to obtain the required * accuracy. In this case values of RESULT are returned * with estimated absolute accuracies ABSERR. * ****ROUTINES CALLED MLTRUL ****END PROLOGUE HERMIT * * Global variables. * EXTERNAL FUNSUB INTEGER NDIM, NUMFUN, MINPTS, MAXPTS, RESTAR INTEGER NEVAL, IFAIL DOUBLE PRECISION EPSABS, EPSREL DOUBLE PRECISION RESULT(*), ABSERR(*), WORK(*) * * Local variables. * INTEGER I, K, MAXRUL, RULE PARAMETER ( MAXRUL = 50 ) DOUBLE PRECISION POINT(MAXRUL), WEIGHT(MAXRUL) SAVE RULE DOUBLE PRECISION W(25,50), T(25,50) SAVE W, T IF ( RESTAR .EQ. 0 ) RULE = 1 NEVAL = 0 10 IF ( NEVAL + RULE**NDIM .LE. MAXPTS .AND. RULE .LT. MAXRUL ) THEN DO I = 1, RULE/2 POINT( I) = -T(I,RULE) WEIGHT(I) = W(I,RULE) POINT( RULE-I+1) = T(I,RULE) WEIGHT(RULE-I+1) = W(I,RULE) END DO IF ( MOD( RULE, 2 ) .EQ. 1 ) THEN POINT( RULE/2 + 1 ) = 0 WEIGHT( RULE/2 + 1 ) = W( RULE/2 + 1, RULE ) END IF CALL MLTRUL( NDIM, NUMFUN, FUNSUB, RULE, POINT, WEIGHT, & RESULT, WORK, WORK(NUMFUN+1), WORK(NUMFUN+NDIM+1) ) NEVAL = NEVAL + RULE**NDIM IFAIL = 0 DO I = 1,NUMFUN IF ( RULE .GT. 1 ) THEN ABSERR(I) = ABS( RESULT(I) - WORK(2*NDIM+NUMFUN+I) ) ELSE ABSERR(I) = ABS( RESULT(I) ) ENDIF WORK(2*NDIM+NUMFUN+I) = RESULT(I) IF ( ABSERR(I) .GE. MAX( EPSABS, EPSREL*ABS(RESULT(I)) ) & .OR. RULE .EQ. 1 ) IFAIL = 1 END DO RULE = RULE + 1 IF ( IFAIL .GT. 0 .OR. NEVAL .LT. MINPTS ) GO TO 10 END IF * * Gauss Hermite Weights and Points, N = 1,50 * DATA W(1, 1), T(1, 1) / 1D0, 0D0 / DATA ( W(I, 2), T(I, 2), I = 1, 1) / & 0.5000000000000001D+00, 0.1000000000000000D+01/ DATA ( W(I, 3), T(I, 3), I = 1, 2) / & 0.1666666666666667D+00, 0.1732050807568877D+01, & 0.6666666666666664D+00, 0.1107367643833737D-15/ DATA ( W(I, 4), T(I, 4), I = 1, 2) / & 0.4587585476806855D-01, 0.2334414218338977D+01, & 0.4541241452319317D+00, 0.7419637843027258D+00/ DATA ( W(I, 5), T(I, 5), I = 1, 3) / & 0.1125741132772071D-01, 0.2856970013872805D+01, & 0.2220759220056126D+00, 0.1355626179974265D+01, & 0.5333333333333342D+00, 0.9386691848789097D-16/ DATA ( W(I, 6), T(I, 6), I = 1, 3) / & 0.2555784402056243D-02, 0.3324257433552119D+01, & 0.8861574604191447D-01, 0.1889175877753710D+01, & 0.4088284695560291D+00, 0.6167065901925933D+00/ DATA ( W(I, 7), T(I, 7), I = 1, 4) / & 0.5482688559722184D-03, 0.3750439717725742D+01, & 0.3075712396758645D-01, 0.2366759410734542D+01, & 0.2401231786050126D+00, 0.1154405394739968D+01, & 0.4571428571428575D+00, 0.2669848554723344D-16/ DATA ( W(I, 8), T(I, 8), I = 1, 4) / & 0.1126145383753679D-03, 0.4144547186125893D+01, & 0.9635220120788268D-02, 0.2802485861287542D+01, & 0.1172399076617590D+00, 0.1636519042435109D+01, & 0.3730122576790775D+00, 0.5390798113513754D+00/ DATA ( W(I, 9), T(I, 9), I = 1, 5) / & 0.2234584400774664D-04, 0.4512745863399781D+01, & 0.2789141321231769D-02, 0.3205429002856470D+01, & 0.4991640676521780D-01, 0.2076847978677829D+01, & 0.2440975028949394D+00, 0.1023255663789133D+01, & 0.4063492063492066D+00, 0.0000000000000000D+00/ DATA ( W(I,10), T(I,10), I = 1, 5) / & 0.4310652630718282D-05, 0.4859462828332311D+01, & 0.7580709343122187D-03, 0.3581823483551927D+01, & 0.1911158050077027D-01, 0.2484325841638954D+01, & 0.1354837029802680D+00, 0.1465989094391158D+01, & 0.3446423349320194D+00, 0.4849357075154977D+00/ DATA ( W(I,11), T(I,11), I = 1, 6) / & 0.8121849790214922D-06, 0.5188001224374871D+01, & 0.1956719302712241D-03, 0.3936166607129977D+01, & 0.6720285235537304D-02, 0.2865123160643646D+01, & 0.6613874607105794D-01, 0.1876035020154847D+01, & 0.2422402998739701D+00, 0.9288689973810635D+00, & 0.3694083694083690D+00, 0.0000000000000000D+00/ DATA ( W(I,12), T(I,12), I = 1, 6) / & 0.1499927167637166D-06, 0.5500901704467746D+01, & 0.4837184922590630D-04, 0.4271825847932281D+01, & 0.2203380687533207D-02, 0.3223709828770096D+01, & 0.2911668791236414D-01, 0.2259464451000800D+01, & 0.1469670480453302D+00, 0.1340375197151617D+01, & 0.3216643615128298D+00, 0.4444030019441390D+00/ DATA ( W(I,13), T(I,13), I = 1, 7) / & 0.2722627642805887D-07, 0.5800167252386502D+01, & 0.1152659652733391D-04, 0.4591398448936520D+01, & 0.6812363504429268D-03, 0.3563444380281636D+01, & 0.1177056050599653D-01, 0.2620689973432215D+01, & 0.7916895586044999D-01, 0.1725418379588239D+01, & 0.2378715229641365D+00, 0.8566794935194499D+00, & 0.3409923409923412D+00, 0.2011511664336819D-15/ DATA ( W(I,14), T(I,14), I = 1, 7) / & 0.4868161257748367D-08, 0.6087409546901291D+01, & 0.2660991344067620D-05, 0.4896936397345567D+01, & 0.2003395537607445D-03, 0.3886924575059772D+01, & 0.4428919106947401D-02, 0.2963036579838668D+01, & 0.3865010882425336D-01, 0.2088344745701943D+01, & 0.1540833398425136D+00, 0.1242688955485464D+01, & 0.3026346268130198D+00, 0.4125904579546022D+00/ DATA ( W(I,15), T(I,15), I = 1, 8) / & 0.8589649899633300D-09, 0.6363947888829836D+01, & 0.5975419597920602D-06, 0.5190093591304780D+01, & 0.5642146405189029D-04, 0.4196207711269018D+01, & 0.1567357503549958D-02, 0.3289082424398766D+01, & 0.1736577449213763D-01, 0.2432436827009758D+01, & 0.8941779539984458D-01, 0.1606710069028730D+01, & 0.2324622936097322D+00, 0.7991290683245483D+00, & 0.3182595182595181D+00, 0.0000000000000000D+00/ DATA ( W(I,16), T(I,16), I = 1, 8) / & 0.1497814723161838D-09, 0.6630878198393126D+01, & 0.1309473216286842D-06, 0.5472225705949343D+01, & 0.1530003216248727D-04, 0.4492955302520013D+01, & 0.5259849265739089D-03, 0.3600873624171548D+01, & 0.7266937601184742D-02, 0.2760245047630703D+01, & 0.4728475235401395D-01, 0.1951980345716333D+01, & 0.1583383727509496D+00, 0.1163829100554964D+01, & 0.2865685212380120D+00, 0.3867606045005573D+00/ DATA ( W(I,17), T(I,17), I = 1, 9) / & 0.2584314919374932D-10, 0.6889122439895331D+01, & 0.2808016117930569D-07, 0.5744460078659410D+01, & 0.4012679447979839D-05, 0.4778531589629983D+01, & 0.1684914315513387D-03, 0.3900065717198010D+01, & 0.2858946062284621D-02, 0.3073797175328194D+01, & 0.2308665702571097D-01, 0.2281019440252989D+01, & 0.9740637116272111D-01, 0.1509883307796740D+01, & 0.2267063084689769D+00, 0.7518426007038956D+00, & 0.2995383701266057D+00, 0.0000000000000000D+00/ DATA ( W(I,18), T(I,18), I = 1, 9) / & 0.4416588769358736D-11, 0.7139464849146476D+01, & 0.5905488478836554D-08, 0.6007745911359599D+01, & 0.1021552397636983D-05, 0.5054072685442739D+01, & 0.5179896144116204D-04, 0.4188020231629400D+01, & 0.1065484796291652D-02, 0.3374736535778089D+01, & 0.1051651775194131D-01, 0.2595833688911239D+01, & 0.5489663248022256D-01, 0.1839779921508646D+01, & 0.1606853038935128D+00, 0.1098395518091501D+01, & 0.2727832346542882D+00, 0.3652457555076979D+00/ DATA ( W(I,19), T(I,19), I = 1,10) / & 0.7482830054057162D-12, 0.7382579024030434D+01, & 0.1220370848447449D-08, 0.6262891156513252D+01, & 0.2532220032092866D-06, 0.5320536377336039D+01, & 0.1535114595466674D-04, 0.4465872626831029D+01, & 0.3785021094142701D-03, 0.3664416547450636D+01, & 0.4507235420342067D-02, 0.2898051276515753D+01, & 0.2866669103011841D-01, 0.2155502761316934D+01, & 0.1036036572761442D+00, 0.1428876676078373D+01, & 0.2209417121991433D+00, 0.7120850440423796D+00, & 0.2837731927515210D+00, 0.4118522463420039D-15/ DATA ( W(I,20), T(I,20), I = 1,10) / & 0.1257800672437914D-12, 0.7619048541679760D+01, & 0.2482062362315163D-09, 0.6510590157013660D+01, & 0.6127490259983006D-07, 0.5578738805893195D+01, & 0.4402121090230841D-05, 0.4734581334046057D+01, & 0.1288262799619300D-03, 0.3943967350657311D+01, & 0.1830103131080496D-02, 0.3189014816553389D+01, & 0.1399783744710099D-01, 0.2458663611172367D+01, & 0.6150637206397690D-01, 0.1745247320814126D+01, & 0.1617393339840001D+00, 0.1042945348802752D+01, & 0.2607930634495551D+00, 0.3469641570813557D+00/ DATA ( W(I,21), T(I,21), I = 1,11) / & 0.2098991219565665D-13, 0.7849382895113822D+01, & 0.4975368604121770D-10, 0.6751444718717456D+01, & 0.1450661284493093D-07, 0.5829382007304472D+01, & 0.1225354836148259D-05, 0.4994963944782024D+01, & 0.4219234742551696D-04, 0.4214343981688420D+01, & 0.7080477954815349D-03, 0.3469846690475375D+01, & 0.6439697051408779D-02, 0.2750592981052372D+01, & 0.3395272978654278D-01, 0.2049102468257161D+01, & 0.1083922856264195D+00, 0.1359765823211230D+01, & 0.2153337156950595D+00, 0.6780456924406435D+00, & 0.2702601835728773D+00, 0.0000000000000000D+00/ DATA ( W(I,22), T(I,22), I = 1,11) / & 0.3479460647877136D-14, 0.8074029984021710D+01, & 0.9841378982346056D-11, 0.6985980424018808D+01, & 0.3366514159458310D-08, 0.6073074951122888D+01, & 0.3319853749814059D-06, 0.5247724433714421D+01, & 0.1334597712680954D-04, 0.4476361977310866D+01, & 0.2622833032559635D-03, 0.3741496350266517D+01, & 0.2808761047577212D-02, 0.3032404227831676D+01, & 0.1756907288080571D-01, 0.2341759996287707D+01, & 0.6719631142889003D-01, 0.1664124839117906D+01, & 0.1619062934136754D+00, 0.9951624222712152D+00, & 0.2502435965869353D+00, 0.3311793157152742D+00/ DATA ( W(I,23), T(I,23), I = 1,12) / & 0.5732383167802038D-15, 0.8293386027417354D+01, & 0.1922935311567786D-11, 0.7214659435051866D+01, & 0.7670888862399855D-09, 0.6310349854448401D+01, & 0.8775062483861979D-07, 0.5493473986471793D+01, & 0.4089977244992140D-05, 0.4730724197451473D+01, & 0.9340818609031275D-04, 0.4004775321733304D+01, & 0.1167628637497855D-02, 0.3305040021752963D+01, & 0.8579678391465647D-02, 0.2624323634059181D+01, & 0.3886718370348111D-01, 0.1957327552933424D+01, & 0.1120733826026210D+00, 0.1299876468303978D+01, & 0.2099596695775429D+00, 0.6484711535344957D+00, & 0.2585097408088385D+00, 0.0000000000000000D+00/ DATA ( W(I,24), T(I,24), I = 1,12) / & 0.9390193689041782D-16, 0.8507803519195264D+01, & 0.3714974152762395D-12, 0.7437890666021664D+01, & 0.1718664927964866D-09, 0.6541675005098631D+01, & 0.2267461673480609D-07, 0.5732747175251204D+01, & 0.1217659745442582D-05, 0.4978041374639117D+01, & 0.3209500565274598D-04, 0.4260383605019904D+01, & 0.4647187187793975D-03, 0.3569306764073560D+01, & 0.3976608929181313D-02, 0.2897728643223314D+01, & 0.2112634440896754D-01, 0.2240467851691752D+01, & 0.7206936401717838D-01, 0.1593480429816420D+01, & 0.1614595128670001D+00, 0.9534219229321088D+00, & 0.2408701155466405D+00, 0.3173700966294525D+00/ DATA ( W(I,25), T(I,25), I = 1,13) / & 0.1530038997998690D-16, 0.8717597678399592D+01, & 0.7102103037003980D-13, 0.7656037955393078D+01, & 0.3791150000477161D-10, 0.6767464963809719D+01, & 0.5738023868899356D-08, 0.5966014690606704D+01, & 0.3530152560245470D-06, 0.5218848093644280D+01, & 0.1067219490520254D-04, 0.4508929922967284D+01, & 0.1777669069265268D-03, 0.3825900569972490D+01, & 0.1757850405263803D-02, 0.3162775679388193D+01, & 0.1085675599146230D-01, 0.2514473303952205D+01, & 0.4337997016764489D-01, 0.1877058369947839D+01, & 0.1148809243039517D+00, 0.1247311975616789D+01, & 0.2048510256503405D+00, 0.6224622791860757D+00, & 0.2481693511764858D+00, 0.0000000000000000D+00/ DATA ( W(I,26), T(I,26), I = 1,13) / & 0.2480694260393664D-17, 0.8923051727828243D+01, & 0.1344547649663596D-13, 0.7869426697637738D+01, & 0.8242809443163844D-11, 0.6988088770623415D+01, & 0.1424293237988014D-08, 0.6193693483796317D+01, & 0.9986755573314568D-07, 0.5453615383857833D+01, & 0.3443413612308114D-05, 0.4750947483085378D+01, & 0.6557558694333818D-04, 0.4075427214412228D+01, & 0.7442025763604303D-03, 0.3420156373999979D+01, & 0.5302198015682246D-02, 0.2780138499509748D+01, & 0.2459766565712125D-01, 0.2151530090121648D+01, & 0.7622953220630281D-01, 0.1531215708695402D+01, & 0.1605865456137948D+00, 0.9165450413386282D+00, & 0.2324707356300776D+00, 0.3051559707592978D+00/ DATA ( W(I,27), T(I,27), I = 1,14) / & 0.4003364766550257D-18, 0.9124421250672931D+01, & 0.2522363250873417D-14, 0.8078349274534165D+01, & 0.1768236511219616D-11, 0.7203876611910644D+01, & 0.3472604702845840D-09, 0.6416154934562174D+01, & 0.2761933918447925D-07, 0.5682760761629052D+01, & 0.1080581533683832D-05, 0.4986906410679802D+01, & 0.2339557671566820D-04, 0.4318417671936682D+01, & 0.3028398259361645D-03, 0.3670472986492407D+01, & 0.2471872445961970D-02, 0.3038150251871036D+01, & 0.1321102584046355D-01, 0.2417683983162542D+01, & 0.4748957556274264D-01, 0.1806045213138672D+01, & 0.1169962651750102D+00, 0.1200683354549981D+01, & 0.2000149701605136D+00, 0.5993548807899852D+00, & 0.2389778937255043D+00, 0.0000000000000000D+00/ DATA ( W(I,28), T(I,28), I = 1,14) / & 0.6432547438801930D-19, 0.9321937814408766D+01, & 0.4691765569500354D-15, 0.8283069540861421D+01, & 0.3745901035176660D-12, 0.7415125286176065D+01, & 0.8326609843882241D-10, 0.6633731493950435D+01, & 0.7479362584613589D-08, 0.5906656325824994D+01, & 0.3304864449926482D-06, 0.5217223673447450D+01, & 0.8093584057145153D-05, 0.4555340384596974D+01, & 0.1188285381401779D-03, 0.3914253725963635D+01, & 0.1104305927857598D-02, 0.3289106970171833D+01, & 0.6752459709030160D-02, 0.2676201879526944D+01, & 0.2793578476788097D-01, 0.2072582674144621D+01, & 0.7977336601159966D-01, 0.1475781736957922D+01, & 0.1594181936613094D+00, 0.8836525629929802D+00, & 0.2248886297506769D+00, 0.2942517144887133D+00/ DATA ( W(I,29), T(I,29), I = 1,15) / & 0.1029341808721942D-19, 0.9515812006947357D+01, & 0.8657491667957282D-16, 0.8483826557846555D+01, & 0.7842840425658472D-13, 0.7622102722480985D+01, & 0.1965709944734762D-10, 0.6846722135707994D+01, & 0.1986123546067053D-08, 0.6125635348243716D+01, & 0.9868968543560684D-07, 0.5442271089178505D+01, & 0.2721127828058099D-05, 0.4786611062352805D+01, & 0.4508394026980976D-04, 0.4151964855100983D+01, & 0.4743663738893483D-03, 0.3533533770990993D+01, & 0.3297972210833669D-02, 0.2927678154322886D+01, & 0.1559400577786720D-01, 0.2331504884065565D+01, & 0.5121083528871912D-01, 0.1742616232610662D+01, & 0.1185603192669036D+00, 0.1158946149400189D+01, & 0.1954459569679010D+00, 0.5786461780331649D+00, & 0.2307372767004873D+00, 0.0000000000000000D+00/ DATA ( W(I,30), T(I,30), I = 1,15) / & 0.1640807008117853D-20, 0.9706235997359524D+01, & 0.1585560944966296D-16, 0.8680837722732207D+01, & 0.1624080129972436D-13, 0.7825051744352813D+01, & 0.4573425871326147D-11, 0.7055396866960296D+01, & 0.5178459467189710D-09, 0.6339997686869597D+01, & 0.2882175154047618D-07, 0.5662381850082873D+01, & 0.8909088868621158D-06, 0.5012600596486518D+01, & 0.1657998163067346D-04, 0.4384020365898051D+01, & 0.1965129439848249D-03, 0.3771894423159236D+01, & 0.1544707339866097D-02, 0.3172634639420402D+01, & 0.8295747557723240D-02, 0.2583402100229274D+01, & 0.3111177018350134D-01, 0.2001858612956431D+01, & 0.8278683671562172D-01, 0.1426005658374115D+01, & 0.1580469532090208D+00, 0.8540733517109733D+00, & 0.2179999718155776D+00, 0.2844387607362094D+00/ DATA ( W(I,31), T(I,31), I = 1,16) / & 0.2605973854893011D-21, 0.9893385708986649D+01, & 0.2883352367857899D-17, 0.8874301409488794D+01, & 0.3328468324148409D-14, 0.8024193227361653D+01, & 0.1049603362311349D-11, 0.7260000488890867D+01, & 0.1327251483589731D-09, 0.6550014268765684D+01, & 0.8243931619119761D-08, 0.5877855885986261D+01, & 0.2845610088162858D-06, 0.5233641511712708D+01, & 0.5923202317686233D-05, 0.4610789797323995D+01, & 0.7871624069602249D-04, 0.4004600901491224D+01, & 0.6960312713792868D-03, 0.3411532415843158D+01, & 0.4221717767270697D-02, 0.2828792768157509D+01, & 0.1796787584344161D-01, 0.2254095000754410D+01, & 0.5456725889447496D-01, 0.1685497905069052D+01, & 0.1196831096958545D+00, 0.1121297374047009D+01, & 0.1911320047746435D+00, 0.5599475878410030D+00, & 0.2232941387424060D+00, 0.9191380905810332D-16/ DATA ( W(I,32), T(I,32), I = 1,16) / & 0.4124607489018384D-22, 0.1007742267422945D+02, & 0.5208449591960853D-18, 0.9064399210702408D+01, & 0.6755290223670036D-15, 0.8219728765382246D+01, & 0.2378064855777808D-12, 0.7460755754121516D+01, & 0.3347501239801238D-10, 0.6755930830540704D+01, & 0.2312518412074224D-08, 0.6088964309076983D+01, & 0.8881290713105934D-07, 0.5450033273623426D+01, & 0.2059622103953437D-05, 0.4832604613244488D+01, & 0.3055980306089618D-04, 0.4232021109995410D+01, & 0.3025570258170642D-03, 0.3644781249880835D+01, & 0.2062051051307883D-02, 0.3068135169013122D+01, & 0.9903461702320572D-02, 0.2499840415187396D+01, & 0.3410984772609194D-01, 0.1938004905925718D+01, & 0.8534480827208071D-01, 0.1380980199272144D+01, & 0.1565389937575984D+00, 0.8272849037797656D+00, & 0.2117055698804795D+00, 0.2755464192302757D+00/ DATA ( W(I,33), T(I,33), I = 1,17) / & 0.6506889970402893D-23, 0.1025849562613868D+02, & 0.9349155921250728D-19, 0.9251297851734609D+01, & 0.1358447599822066D-15, 0.8411842935668213D+01, & 0.5323023871225154D-13, 0.7657866034784416D+01, & 0.8316046910555386D-11, 0.6957971061087896D+01, & 0.6369261724538402D-09, 0.6295953125159368D+01, & 0.2712480030928315D-07, 0.5662046690089215D+01, & 0.6982937054010693D-06, 0.5049763451908822D+01, & 0.1152282979948381D-04, 0.4454485185983318D+01, & 0.1271924628565943D-03, 0.3872747224621657D+01, & 0.9695342064240463D-03, 0.3301836743259241D+01, & 0.5227605765843533D-02, 0.2739550282026145D+01, & 0.2030404475704196D-01, 0.2184038256077331D+01, & 0.5758631173578715D-01, 0.1633699795932273D+01, & 0.1204510521056565D+00, 0.1087107916669903D+01, & 0.1870581852279859D+00, 0.5429533766656418D+00, & 0.2165276496896071D+00, 0.0000000000000000D+00/ DATA ( W(I,34), T(I,34), I = 1,17) / & 0.1023327129805438D-23, 0.1043674187100505D+02, & 0.1668144375578546D-19, 0.9435150833760799D+01, & 0.2708054709262291D-16, 0.8600705233983431D+01, & 0.1177937790622538D-13, 0.7851517590699072D+01, & 0.2036657679770825D-11, 0.7156339259134842D+01, & 0.1724305566745258D-09, 0.6499046353927969D+01, & 0.8117409040122166D-08, 0.5869927588596779D+01, & 0.2312034264322868D-06, 0.5262536481734633D+01, & 0.4227725748387717D-05, 0.4672290691400979D+01, & 0.5182712643366873D-04, 0.4095758971954162D+01, & 0.4399649667746255D-03, 0.3530261634074169D+01, & 0.2650824238310194D-02, 0.2973629650303989D+01, & 0.1155073894677711D-01, 0.2424050509756231D+01, & 0.3692346295804431D-01, 0.1879964366420186D+01, & 0.8751168135862399D-01, 0.1339990625522619D+01, & 0.1549420965148600D+00, 0.8028734607837125D+00, & 0.2059249366691133D+00, 0.2674391839515571D+00/ DATA ( W(I,35), T(I,35), I = 1,18) / & 0.1604619191790137D-24, 0.1061228847764259D+02, & 0.2959542628709020D-20, 0.9616099851106188D+01, & 0.5354094198066113D-17, 0.8786471736571588D+01, & 0.2578597004420350D-14, 0.8041881508402966D+01, & 0.4921158318497817D-12, 0.7351222593955577D+01, & 0.4592895709255784D-10, 0.6698448669188526D+01, & 0.2383123333705684D-08, 0.6073899909835108D+01, & 0.7486460178518943D-07, 0.5471169042499284D+01, & 0.1511924078161164D-05, 0.4885706922446520D+01, & 0.2050985370117561D-04, 0.4314112806712937D+01, & 0.1931447146139865D-03, 0.3753736849678044D+01, & 0.1294831077498348D-02, 0.3202440651527510D+01, & 0.6300195959720374D-02, 0.2658444295466304D+01, & 0.2258156121393648D-01, 0.2120223604836576D+01, & 0.6029658086774051D-01, 0.1586437891088980D+01, & 0.1209324521970301D+00, 0.1055876792225099D+01, & 0.1832085621911518D+00, 0.5274192342262778D+00, & 0.2103411454127607D+00, 0.2220535009031490D-16/ DATA ( W(I,36), T(I,36), I = 1,18) / & 0.2509037634634927D-25, 0.1078525331238753D+02, & 0.5222366200862934D-21, 0.9794276019583023D+01, & 0.1050294193474738D-17, 0.8969286534562617D+01, & 0.5587113978649920D-15, 0.8229115367471579D+01, & 0.1174029255105150D-12, 0.7542793039211395D+01, & 0.1204744586548017D-10, 0.6894347646173911D+01, & 0.6871083387212228D-09, 0.6274168326809511D+01, & 0.2373822777365743D-07, 0.5675884710106672D+01, & 0.5278315192800947D-06, 0.5094978513857614D+01, & 0.7896978086723001D-05, 0.4528076990600175D+01, & 0.8220025562410442D-04, 0.3972557341929988D+01, & 0.6107548335511020D-03, 0.3426308595129129D+01, & 0.3304134538435289D-02, 0.2887579695004719D+01, & 0.1321657401560215D-01, 0.2354877715992540D+01, & 0.3955236976655980D-01, 0.1826896577986744D+01, & 0.8934249750438648D-01, 0.1302464954480165D+01, & 0.1532910133997116D+00, 0.7805064920524665D+00, & 0.2005920064390222D+00, 0.2600079252490002D+00/ DATA ( W(I,37), T(I,37), I = 1,19) / & 0.3912701900272739D-26, 0.1095574594356165D+02, & 0.9167997950194993D-22, 0.9969800945691102D+01, & 0.2045033189096993D-18, 0.9149282977696753D+01, & 0.1198838092763842D-15, 0.8413364679488879D+01, & 0.2767202859289950D-13, 0.7731209035776908D+01, & 0.3114550633754001D-11, 0.7086915685017345D+01, & 0.1947529536776704D-09, 0.6470920475390299D+01, & 0.7379429831202629D-08, 0.5876887892594201D+01, & 0.1801392729842884D-06, 0.5300328473991422D+01, & 0.2963204697508371D-05, 0.4737895299703953D+01, & 0.3397941877127311D-04, 0.4186990225627911D+01, & 0.2788064134714879D-03, 0.3645526993515297D+01, & 0.1670452623119233D-02, 0.3111780274991816D+01, & 0.7424836460756516D-02, 0.2584284718210775D+01, & 0.2478561700046269D-01, 0.2061764482625703D+01, & 0.6272612686101582D-01, 0.1543082026656558D+01, & 0.1211816464812620D+00, 0.1027199336691835D+01, & 0.1795672590244481D+00, 0.5131472568284307D+00, & 0.2046562495907946D+00, 0.0000000000000000D+00/ DATA ( W(I,38), T(I,38), I = 1,19) / & 0.6086019568424894D-27, 0.1112386843494987D+02, & 0.1601586834974089D-22, 0.1014278766112967D+02, & 0.3953752210235847D-19, 0.9326584757395571D+01, & 0.2548653789376282D-16, 0.8594764136386107D+01, & 0.6447906524854284D-14, 0.7916616928480361D+01, & 0.7941720700519787D-12, 0.7276311665555140D+01, & 0.5431469647397207D-10, 0.6664328864414711D+01, & 0.2251484789660455D-08, 0.6074366042059564D+01, & 0.6017570329946914D-07, 0.5501960756811018D+01, & 0.1085199304765951D-05, 0.4943790029802265D+01, & 0.1366659848918500D-04, 0.4397278309932714D+01, & 0.1234207566124386D-03, 0.3860361738163258D+01, & 0.8159914125966156D-03, 0.3331338060544006D+01, & 0.4014342501780207D-02, 0.2808766413901917D+01, & 0.1488362222069118D-01, 0.2291397563624214D+01, & 0.4200051997416258D-01, 0.1778123425136563D+01, & 0.9088415555258827D-01, 0.1267939114780749D+01, & 0.1516111462601078D+00, 0.7599132481367392D+00, & 0.1956519870413640D+00, 0.2531636353359348D+00/ DATA ( W(I,39), T(I,39), I = 1,20) / & 0.9443344575063092D-28, 0.1128971604447632D+02, & 0.2784787505225604D-23, 0.1031334144275699D+02, & 0.7592450542206611D-20, 0.9501306853782864D+01, & 0.5370701458462819D-17, 0.8773438698067656D+01, & 0.1486129587733307D-14, 0.8099152213152410D+01, & 0.1998726680623669D-12, 0.7462682377866057D+01, & 0.1491720010448932D-10, 0.6854552519790964D+01, & 0.6748646364787737D-09, 0.6268491549685291D+01, & 0.1969872920599359D-07, 0.5700062454271859D+01, & 0.3884118283713278D-06, 0.5145964544094186D+01, & 0.5356584901373566D-05, 0.4603643074288992D+01, & 0.5307742112417270D-04, 0.4071054595947238D+01, & 0.3859381697690359D-03, 0.3546517669768644D+01, & 0.2093837438880663D-02, 0.3028613314092798D+01, & 0.8588083029362219D-02, 0.2516115854339318D+01, & 0.2690624148395815D-01, 0.2007943065265498D+01, & 0.6490157458316884D-01, 0.1503118900228415D+01, & 0.1212421280631244D+00, 0.1000744572356018D+01, & 0.1761190277014499D+00, 0.4999751896072681D+00, & 0.1994086534474408D+00, 0.1536204102353874D-15/ DATA ( W(I,40), T(I,40), I = 1,20) / & 0.1461839873869467D-28, 0.1145337784154873D+02, & 0.4820467940200524D-24, 0.1048156053467427D+02, & 0.1448609431551587D-20, 0.9673556366934033D+01, & 0.1122275206827074D-17, 0.8949504543855559D+01, & 0.3389853443248306D-15, 0.8278940623659475D+01, & 0.4968088529197761D-13, 0.7646163764541459D+01, & 0.4037638581695192D-11, 0.7041738406453829D+01, & 0.1989118526027766D-09, 0.6459423377583766D+01, & 0.6325897188548972D-08, 0.5894805675372016D+01, & 0.1360342421574886D-06, 0.5344605445720084D+01, & 0.2048897436081474D-05, 0.4806287192093873D+01, & 0.2221177143247582D-04, 0.4277826156362752D+01, & 0.1770729287992397D-03, 0.3757559776168985D+01, & 0.1055879016901825D-02, 0.3244088732999869D+01, & 0.4773544881823334D-02, 0.2736208340465433D+01, & 0.1653784414256937D-01, 0.2232859218634873D+01, & 0.4427455520227679D-01, 0.1733090590631720D+01, & 0.9217657917006089D-01, 0.1236032004799159D+01, & 0.1499211117635710D+00, 0.7408707252859313D+00, & 0.1910590096619904D+00, 0.2468328960227240D+00/ DATA ( W(I,41), T(I,41), I = 1,21) / & 0.2257863956583089D-29, 0.1161493725433746D+02, & 0.8308558938782992D-25, 0.1064753678631932D+02, & 0.2746891228522292D-21, 0.9843433249157988D+01, & 0.2326384145587187D-18, 0.9123069907984480D+01, & 0.7655982291966812D-16, 0.8456099083269388D+01, & 0.1220334874202772D-13, 0.7826882004053867D+01, & 0.1077818394935909D-11, 0.7226022663732790D+01, & 0.5769853428092003D-10, 0.6647308470747191D+01, & 0.1994794756757339D-08, 0.6086349164878472D+01, & 0.4667347708107243D-07, 0.5539884440458126D+01, & 0.7658186077982435D-06, 0.5005396683404125D+01, & 0.9058608622433030D-05, 0.4480878331594004D+01, & 0.7894719319504627D-04, 0.3964684028033266D+01, & 0.5158014443431912D-03, 0.3455432217780992D+01, & 0.2561642428649777D-02, 0.2951937016381193D+01, & 0.9777902738208298D-02, 0.2453159345907049D+01, & 0.2893721174793441D-01, 0.1958170711977291D+01, & 0.6684765935446599D-01, 0.1466125457295967D+01, & 0.1211489170115104D+00, 0.9762387671800500D+00, & 0.1728495310506020D+00, 0.4877685693194347D+00, & 0.1945450277536008D+00, 0.2585532684499631D-15/ DATA ( W(I,42), T(I,42), I = 1,21) / & 0.3479841758734498D-30, 0.1177447255645880D+02, & 0.1426197845863333D-25, 0.1081135621818894D+02, & 0.5178070329449428D-22, 0.1001103095231325D+02, & 0.4785541849652557D-19, 0.9294235815925036D+01, & 0.1712817711028008D-16, 0.8630736540442662D+01, & 0.2963878417982294D-14, 0.8004954459331870D+01, & 0.2839400066530831D-12, 0.7407531683161432D+01, & 0.1648408975918176D-10, 0.6832282984221202D+01, & 0.6182418956905496D-09, 0.6274839704458262D+01, & 0.1570405641380752D-07, 0.5731959941924930D+01, & 0.2800444926136691D-06, 0.5201142761234950D+01, & 0.3605310211304410D-05, 0.4680396489703305D+01, & 0.3425737772910867D-04, 0.4168091525525806D+01, & 0.2445266890869028D-03, 0.3662862441045986D+01, & 0.1329885905572134D-02, 0.3163540283549010D+01, & 0.5573924561218487D-02, 0.2669104116603810D+01, & 0.1816809011555160D-01, 0.2178645208762502D+01, & 0.4638274179115778D-01, 0.1691339732834912D+01, & 0.9325376860459540D-01, 0.1206427277827926D+01, & 0.1482345543992958D+00, 0.7231933449391704D+00, & 0.1867743488620199D+00, 0.2409545348665914D+00/ DATA ( W(I,43), T(I,43), I = 1,22) / & 0.5352075224079761D-31, 0.1193205730105631D+02, & 0.2438509785586889D-26, 0.1097309952495776D+02, & 0.9705961174387400D-23, 0.1017643700187913D+02, & 0.9772188868027905D-20, 0.9463096735522324D+01, & 0.3797453851791020D-17, 0.8802954705722227D+01, & 0.7121219095950012D-15, 0.8180490511448660D+01, & 0.7386428797509359D-13, 0.7586383052570858D+01, & 0.4641647576106650D-11, 0.7014473354182730D+01, & 0.1884798249393598D-09, 0.6460413330895460D+01, & 0.5186705460818634D-08, 0.5920978461471519D+01, & 0.1003006675541783D-06, 0.5393683423125381D+01, & 0.1402088827949991D-05, 0.4876551284706595D+01, & 0.1448871182961238D-04, 0.4367966934806672D+01, & 0.1126824016383807D-03, 0.3866579655692208D+01, & 0.6691683916969021D-03, 0.3371235817148052D+01, & 0.3070012395787847D-02, 0.2880930777450376D+01, & 0.1098373316809114D-01, 0.2394773428842528D+01, & 0.3087516724563331D-01, 0.1911959274951712D+01, & 0.6858704943109335D-01, 0.1431749364451692D+01, & 0.1209303683096624D+00, 0.9534532756297385D+00, & 0.1697454597838771D+00, 0.4764148861084949D+00, & 0.1900207247825863D+00, 0.0000000000000000D+00/ DATA ( W(I,44), T(I,44), I = 1,22) / & 0.8215250893174055D-32, 0.1208776070905845D+02, & 0.4153634860809548D-27, 0.1113284252424393D+02, & 0.1809481070701256D-23, 0.1033973350764328D+02, & 0.1981515599992759D-20, 0.9629741154666469D+01, & 0.8346676981526894D-18, 0.8972848703628870D+01, & 0.1693427110357361D-15, 0.8353592294951005D+01, & 0.1898518041004563D-13, 0.7762686386163553D+01, & 0.1289064815963923D-11, 0.7193997236488432D+01, & 0.5656565204102218D-10, 0.6643196399727595D+01, & 0.1683045805404500D-08, 0.6107075817029749D+01, & 0.3522080139402352D-07, 0.5583164829645622D+01, & 0.5334152162808288D-06, 0.5069500234589782D+01, & 0.5980506497871435D-05, 0.4564480302199131D+01, & 0.5055024343502252D-04, 0.4066767790495557D+01, & 0.3269029726329101D-03, 0.3575222999425195D+01, & 0.1636879726834301D-02, 0.3088855994142003D+01, & 0.6407990218344719D-02, 0.2606791462987426D+01, & 0.1976568083382755D-01, 0.2128242119185467D+01, & 0.4833422729538417D-01, 0.1652487989479395D+01, & 0.9414471679496565D-01, 0.1178859803328855D+01, & 0.1465614441714095D+00, 0.7067252381063451D+00, & 0.1827650568597313D+00, 0.2354771181719222D+00/ DATA ( W(I,45), T(I,45), I = 1,23) / & 0.1258601266761721D-32, 0.1224164801738294D+02, & 0.7049452438028993D-28, 0.1129065655801674D+02, & 0.3355898215846036D-24, 0.1050099761933589D+02, & 0.3990921764567262D-21, 0.9794252095357150D+01, & 0.1819415421781025D-18, 0.9140507651218687D+01, & 0.3987388394988911D-16, 0.8524355348620958D+01, & 0.4823870286948576D-14, 0.7936544056928108D+01, & 0.3532976789571211D-12, 0.7370964332170609D+01, & 0.1672373578472200D-10, 0.6823306517591415D+01, & 0.5370107061670978D-09, 0.6290378188903940D+01, & 0.1213731971819947D-07, 0.5769722503692224D+01, & 0.1987368663904533D-06, 0.5259389088450044D+01, & 0.2412167676023244D-05, 0.4757788618871960D+01, & 0.2210680714129846D-04, 0.4263596248773437D+01, & 0.1552889103199588D-03, 0.3775684997351202D+01, & 0.8463565255385183D-03, 0.3293078264001083D+01, & 0.3614802525284821D-02, 0.2814914962782011D+01, & 0.1219644981036976D-01, 0.2340423205074869D+01, & 0.3271890357088906D-01, 0.1868899890086888D+01, & 0.7014033220973423D-01, 0.1399694432579061D+01, & 0.1206095596750258D+00, 0.9321954002025563D+00, & 0.1667945553649214D+00, 0.4658191781783683D+00, & 0.1857980420096402D+00, 0.0000000000000000D+00/ DATA ( W(I,46), T(I,46), I = 1,23) / & 0.1924664627046275D-33, 0.1239378079201923D+02, & 0.1192246272132870D-28, 0.1144660885260523D+02, & 0.6192859698073460D-25, 0.1066030193428052D+02, & 0.7986127260533585D-22, 0.9956707572498630D+01, & 0.3934545090204791D-19, 0.9306015173119082D+01, & 0.9300353507700858D-17, 0.8692869193236842D+01, & 0.1212244415430154D-14, 0.8108051845054231D+01, & 0.9561363845435019D-13, 0.7545477116064648D+01, & 0.4874112963243041D-11, 0.7000853362533224D+01, & 0.1686106290702903D-09, 0.6471003045526279D+01, & 0.4108222480852658D-08, 0.5953482378238384D+01, & 0.7258481863429432D-07, 0.5446353016216582D+01, & 0.9517578349775918D-06, 0.4948037176754664D+01, & 0.9436598821520223D-05, 0.4457221460031489D+01, & 0.7183252612530643D-04, 0.3972790546235975D+01, & 0.4250585899081316D-03, 0.3493779976317873D+01, & 0.1975260370663049D-02, 0.3019341533379349D+01, & 0.7268729480993403D-02, 0.2548717171165183D+01, & 0.2132401414735712D-01, 0.2081218863808104D+01, & 0.5013852830109192D-01, 0.1616212619554741D+01, & 0.9487419222577377D-01, 0.1153105444663487D+01, & 0.1449090160374568D+00, 0.6913343908693306D+00, & 0.1790029030973513D+00, 0.2303570440689780D+00/ DATA ( W(I,47), T(I,47), I = 1,24) / & 0.2937991918931770D-34, 0.1254421721021957D+02, & 0.2009633017503842D-29, 0.1160076284239976D+02, & 0.1137324853690828D-25, 0.1081771486308368D+02, & 0.1588168143815981D-22, 0.1011718100450289D+02, & 0.8443830093861547D-20, 0.9469449861345275D+01, & 0.2149644881290608D-17, 0.8859217846077781D+01, & 0.3014376026444397D-15, 0.8277299513807538D+01, & 0.2556494006562142D-13, 0.7717631482085797D+01, & 0.1401228890589135D-11, 0.7175939408289193D+01, & 0.5213279817493255D-10, 0.6649059958212412D+01, & 0.1366926136038253D-08, 0.6134561715294918D+01, & 0.2601160240819878D-07, 0.5630517648304252D+01, & 0.3677447240564392D-06, 0.5135360748767347D+01, & 0.3936411635330397D-05, 0.4647788224870149D+01, & 0.3239911617951789D-04, 0.4166695488690111D+01, & 0.2076565749155176D-03, 0.3691129181403769D+01, & 0.1047278482271871D-02, 0.3220252777152719D+01, & 0.4191754574650512D-02, 0.2753320728634848D+01, & 0.1340827900837288D-01, 0.2289658541588672D+01, & 0.3446881631958411D-01, 0.1828647032406020D+01, & 0.7152609366400937D-01, 0.1369709566513547D+01, & 0.1202053639683183D+00, 0.9123014234783601D+00, & 0.1639855806134269D+00, 0.4559006613049348D+00, & 0.1818448921796476D+00, 0.0000000000000000D+00/ DATA ( W(I,48), T(I,48), I = 1,24) / & 0.4477155473876067D-35, 0.1269301231543958D+02, & 0.3376456143135106D-30, 0.1175317846161662D+02, & 0.2079058971418782D-26, 0.1097330095851353D+02, & 0.3139476644799137D-23, 0.1027574158173351D+02, & 0.1798854916237414D-20, 0.9630885686949055D+01, & 0.4925465109698832D-18, 0.9023480280417658D+01, & 0.7419993598065164D-16, 0.8444371322523445D+01, & 0.6756677274657091D-14, 0.7887517316500372D+01, & 0.3975805958471478D-12, 0.7348660565908911D+01, & 0.1588360981246298D-10, 0.6824651320745980D+01, & 0.4474287153436318D-09, 0.6313069914905501D+01, & 0.9154055746313672D-08, 0.5811999987702533D+01, & 0.1392791689559962D-06, 0.5319884620419087D+01, & 0.1606393695542611D-05, 0.4835430885878957D+01, & 0.1426609232424675D-04, 0.4357544108790293D+01, & 0.9881804917611217D-04, 0.3885281117248394D+01, & 0.5395865846271863D-03, 0.3417816048684776D+01, & 0.2343082111760394D-02, 0.2954414688880120D+01, & 0.8149696855351926D-02, 0.2494414743040025D+01, & 0.2283821210009132D-01, 0.2037210303259033D+01, & 0.5180518354956036D-01, 0.1582239319674964D+01, & 0.9546340056142952D-01, 0.1128973231509649D+01, & 0.1432824569931762D+00, 0.6769081422063483D+00, & 0.1754635418118663D+00, 0.2255570729801638D+00/ DATA ( W(I,49), T(I,49), I = 1,25) / & 0.6811389123116583D-36, 0.1284021824817448D+02, & 0.5655218285268972D-31, 0.1190391240788757D+02, & 0.3783656387961836D-27, 0.1112712121198839D+02, & 0.6170433961110509D-24, 0.1043245459795100D+02, & 0.3805275010242669D-21, 0.9790392369513130D+01, & 0.1119149962220974D-18, 0.9185730837014976D+01, & 0.1808768646225968D-16, 0.8609346484896321D+01, & 0.1765991900170034D-14, 0.8055219008757504D+01, & 0.1113983833798787D-12, 0.7519106753949869D+01, & 0.4771647040124784D-11, 0.6997872987021261D+01, & 0.1441769692730330D-09, 0.6489109229832087D+01, & 0.3166143293671931D-08, 0.5990909213118121D+01, & 0.5175289227690812D-07, 0.5501725495034997D+01, & 0.6419581525894787D-06, 0.5020274351287227D+01, & 0.6139401305210235D-05, 0.4545470293840825D+01, & 0.4586356164456607D-04, 0.4076379533242183D+01, & 0.2705406889774859D-03, 0.3612185969516418D+01, & 0.1271499268760875D-02, 0.3152165704938866D+01, & 0.4796631268346652D-02, 0.2695667488564915D+01, & 0.1461268197482865D-01, 0.2242097365824569D+01, & 0.3612646737149015D-01, 0.1790906348772901D+01, & 0.7276104720165333D-01, 0.1341580271678923D+01, & 0.1197332834080540D+00, 0.8936312256129486D+00, & 0.1613082628631473D+00, 0.4465901175404579D+00, & 0.1781337719310835D+00, 0.0000000000000000D+00/ DATA ( W(I,50), T(I,50), I = 1,25) / & 0.1034607500576990D-36, 0.1298588445541555D+02, & 0.9443414659584510D-32, 0.1205301838092448D+02, & 0.6856280758924735D-28, 0.1127923332148262D+02, & 0.1206044550761014D-24, 0.1058738174919177D+02, & 0.7995094477915292D-22, 0.9948035709637500D+01, & 0.2522482807168144D-19, 0.9346039593575728D+01, & 0.4368171816201588D-17, 0.8772299579514598D+01, & 0.4566698246800344D-15, 0.8220815907982127D+01, & 0.3083828687005300D-13, 0.7687362406712500D+01, & 0.1414228936126661D-11, 0.7168814837853899D+01, & 0.4576636712310442D-10, 0.6662775399018720D+01, & 0.1077060789389039D-08, 0.6167347388659921D+01, & 0.1888225976835208D-07, 0.5680992291033284D+01, & 0.2514609880838772D-06, 0.5202434993399912D+01, & 0.2584937658949391D-05, 0.4730598550228594D+01, & 0.2078485175734569D-04, 0.4264557843038109D+01, & 0.1321726328668984D-03, 0.3803505741742012D+01, & 0.6708280619787080D-03, 0.3346727774732429D+01, & 0.2738160896935348D-02, 0.2893582727707738D+01, & 0.9045054154849623D-02, 0.2443487452654017D+01, & 0.2430481286424306D-01, 0.1995904709795124D+01, & 0.5334352453170102D-01, 0.1550333214338771D+01, & 0.9593054035810168D-01, 0.1106299289397183D+01, & 0.1416854132499443D+00, 0.6633496795082918D+00, & 0.1721258519924433D+00, 0.2210451816445435D+00/ * * ****END HERMIT * END