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FAST REAL HANKEL TRANSFORM
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C ALGORITHM 588, COLLECTED ALGORITHMS FROM ACM.
C ALGORITHM APPEARED IN ACM-TRANS. MATH. SOFTWARE, VOL.8, NO. 4,
C DEC., 1982, P.369-370, P. 344-468.
SUBROUTINE DHANKL(BMAX,NB,NREL,TOL,NTOL,NORD,FUN1,IJREL,DWORK, DHA 10
* DANS,ARG,NOFUN1,IERR)
C=======================================================================
INTEGER NB,NREL,NTOL,NORD(NREL),IJREL(2,NREL),NOFUN1,IERR
DOUBLE PRECISION BMAX,TOL,DWORK(801,NREL),DANS(NB,NREL),ARG(NB)
C=======================================================================
C PURPOSE
C THE PURPOSE OF SUBPROGRAM DHANKL IS TO PROVIDE IN DOUBLE PRECISION
C A GENERAL ALGORITHM FOR FAST REAL HANKEL TRANSFORMS OF ORDERS
C 0 AND 1 USING RELATED AND LAGGED CONVOLUTIONS.
C
C AUTHOR
C
C ANDERSON, W.L., U.S. GEOLOGICAL SURVEY, DENVER, COLORADO.
C
C REFERENCES
C
C 1. ANDERSON, W.L., IMPROVED DIGITAL FILTERS FOR EVALUATING
C FOURIER AND HANKEL TRANSFORM INTEGRALS. N.T.I.S REPT.
C PB-242-800, SPRINGFIELD, VA., 1975.
C
C 2. ANDERSON, W.L., NUMERICAL INTEGRATION OF RELATED HANKEL
C TRANSFORMS OF ORDERS 0 AND 1 BY ADAPTIVE DIGITAL FILTERING.
C GEOPHYSICS 44 (JULY 1979), 1287-1305.
C
C LANGUAGE
C
C ANS-FORTRAN (X3.9-1966) IS USED, WITH THE EXCEPTION OF THE
C CHARACTERS <,[,&,:,],> APPEARING IN SOME COMMENT STATEMENTS.
C
C ABSTRACT
C
C BY COMBINING BOTH ADAPTIVE LAGGED CONVOLUTION (SEE [1]) AND
C ADAPTIVE RELATED CONVOLUTION (SEE [2]), SUBPROGRAM DHANKL
C MINIMIZES EXTERNAL FUN1 CALLS (NOFUN1 AT EXIT) IN EVALUATING A
C TOTAL OF NB*NREL REAL HANKEL TRANSFORMS OF ORDERS 0 AND (OR) 1,
C WHERE NB IS THE NUMBER OF LAGGED CONVOLUTIONS, AND NREL IS THE
C NUMBER OF RELATED CONVOLUTIONS.
C DIRECT CONVOLUTION METHODS (SEE [1],[2]) DO NOT REQUIRE BESSEL
C FUNCTION EVALUATIONS, AND HENCE ARE GENERALLY AN ORDER OF
C MAGNITUDE FASTER TO COMPUTE THAN MOST DIRECT NUMERICAL
C INTEGRATION METHODS. BY USING PREVIOUSLY SAVED TRANSFORM INPUT
C FUNCTION EVALUATIONS, BOTH LAGGED CONVOLUTION AND RELATED
C CONVOLUTION FURTHER REDUCE SIGNIFICANTLY THE NUMBER OF TRANSFORM
C INPUT FUNCTION EVALUATIONS REQUIRED OVER DIRECT CONVOLUTION.
C LAGGED CONVOLUTION IS SELECTED WHEN NB>1, WHICH DEFINES ARG(NB)
C OVER ANY DESIRED TRANSFORM ARGUMENT RANGE (BMIN,BMAX). RESULTS ARE
C STORED AT THE FILTER SPACING IN ARRAYS ARG(NB) AND DANS(NB,NREL)
C FOR LATER USE IN SPLINE INTERPOLATION, ETC. GIVEN BMAX,NB, THE
C VALUE OF BMIN (NOT GIVEN) CAN BE COMPUTED FROM THE EXPRESSION
C BMIN=BMAX*DEXP(-.1D0*(NB-1)), WHICH MUST BE .GT. 0.0D0 FOR THE
C GIVEN MACHINE EXPONENT RANGE.
C RELATED CONVOLUTION IS SELECTED WHEN NREL>1, AND BY GIVEN
C SIMPLE ALGEBRAIC RELATIONSHIPS BETWEEN FUN1 AND EACH NREL RELATED
C TRANSFORM INPUT FUNCTION, DEFINED AS G**I * FUN1(G)**J, WHERE
C FUN1(G) IS THE FIRST TRANSFORM INPUT FUNCTION, AND ARRAY
C IJREL(2,NREL)= PAIRS OF I,J INTEGERS (NEGATIVE, 0, OR POSITIVE).
C THE ORDER OF ALL RELATED CONVOLUTIONS MUST BE GIVEN IN NORD(NREL),
C AND MUST BE EITHER 0 OR 1, BUT CAN BE IN ANY DESIRED SEQUENCE.
C HIGHER INTEGER ORDERS MAY BE EXPRESSED IN TERMS OF ORDERS 0 AND 1
C BY USING THE RECURRENCE RELATION JN-1(X)+JN+1(X)=2*N*JN(X)/X.
C THE EQUALLY-SPACED J0,J1 FILTER ABSCISSAS ARE GENERATED IN
C DOUBLE-PRECISION (TO CONSERVE STORAGE) AND ARE USED AS ARGUMENTS
C IN THE EXTERNAL DOUBLE PRECISION FUNCTION FUN1.
C BOTH J0 AND J1 FILTER RESPONSE FUNCTIONS (WEIGHTS) WERE
C DESIGNED TO HAVE IDENTICAL ABSCISSA VALUES AS IN [2]. THE J0,J1
C DOUBLE-PRECISION FILTER WEIGHTS USED IN SUBPROGRAM DHANKL WERE
C REDESIGNED FROM [2] IN QUADRUPLE-PRECISION USING A VAX-11/780 IN
C H-FLOATING ARITHMETIC. MUCH OF THE LOGIC USED IN DHANKL FOLLOWS
C THE CODING USED IN [1] AND [2]. THE MAJOR DIFFERENCES ARE IN THE
C DEFINITION OF RELATED INPUT FUNCTIONS (SEE IJREL,DWORK), AND
C FOR HANDLING OSCILLATING FUNCTIONS (SEE NTOL,ITOL).
C
C FOUR GENERAL CASES ARE POSSIBLE USING SUBPROGRAM DHANKL.
C
C CASE 1. SINGLE DIRECT CONVOLUTION AT B=BMAX=BMIN (NB=1,NREL=1).
C CASE 2. RELATED CONVOLUTIONS AT A CONSTANT B=BMAX (NB=1,NREL>1).
C CASE 3. LAGGED CONVOLUTIONS IN (BMIN,BMAX) (NB>1,NREL=1).
C CASE 4. BOTH RELATED AND LAGGED CONVOLUTIONS (NB>1,NREL>1).
C
C MACHINE DEPENDENT REMARKS
C
C THIS SUBPROGRAM WAS IMPLEMENTED AND TESTED ON A 64-BIT DOUBLE-
C WORD MACHINE WITH EXP-RANGE APPROXIMATELY 10**-38 TO 10**+38 AND
C 56-BIT MANTISSA (ABOUT 16-DECIMAL DIGITS). ONLY DOUBLE-PRECISION
C AND INTEGER OPERATIONS ARE USED.
C FOR MACHINES WITH OTHER DOUBLE-WORD SIZES, CHANGES IN THE NUMBER OF
C DIGITS RETAINED IN SOME DATA STATEMENTS MAY BE REQUIRED.
C
C DESCRIPTION OF PARAMETERS
C
C INPUT
C
C BMAX - INITIAL HANKEL TRANSFORM ARGUMENT B=BMAX>0.D0 (ANY CASE),
C USED IN INTEGRAL FROM 0 TO INFINITY OF
C FUN1(G)*JN(G*B)*DG, WHERE JN=BESSEL FUNCTION OF ORDER N,
C N=0 OR 1, AND B>0.0D0. (SEE FUN1 DEFINITION BELOW).
C NB - NUMBER OF LAGGED CONVOLUTIONS DESIRED (NB.GE.1). USE
C NB=1 IF B=BMIN=BMAX (I.E., CASE 1 OR 2). USE
C NB>1 IF B IS LAGGED IN (BMIN,BMAX), WHERE
C BMIN=BMAX*DEXP(-.1D0*(NB-1)) DOES NOT UNDERFLOW THE DEXP
C RANGE. THE B-LAGGED SPACING IS .1D0 IN LOG-SPACE. FOR
C CONVENIENCE IN SPLINE INTERPOLATION LATER, EACH B IN
C (BMIN,BMAX) IS RETURNED IN ARRAY ARG(I),I=1,NB, WHERE
C ARG(I+1)/ARG(I)=DEXP(.1D0) FOR ALL I. IF BMAX>BMIN>0 IS
C GIVEN, THEN AN EFFECTIVE VALUE OF NB IS DETERMINED AS
C NB=DINT(10.*DLOG(BMAX/BMIN))+I, WHERE I>1 IS RECOMMENDED,
C PARTICULARLY IF USING SUBSEQUENT SPLINE INTERPOLATION FOR
C A DIFFERENT B-SPACING THAN USED IN THE SAMPLED FILTERS. IF
C SPLINE INTERPOLATION IS TO BE USED LATER, IT IS GENERALLY
C BEST TO USE DLOG(ARG(I)) INSTEAD OF ARG(I) -VS- DANS(I,J),
C FOR I=1,NB, AND FOR ANY GIVEN J BETWEEN 1 AND NREL. NOTE
C NB IS USED AS AN ADJUSTABLE DIMENSION IN DANS(NB,NREL).
C NREL - NUMBER OF RELATED CONVOLUTIONS DESIRED (NREL.GE.1). USE
C NREL=1 IF ONLY A SINGLE HANKEL TRANSFORM IS USED.
C NREL>1 REQUIRES ARRAY IJREL(2,NREL) (SEE BELOW).
C NOTE NREL IS USED AS ADJUSTABLE DIMENSIONS IN ARRAYS
C DANS(NB,NREL),DWORK(801,NREL),NORD(NREL),IJREL(2,NREL).
C TOL - REQUESTED TRUNCATION TOLERANCE AT BOTH FILTER TAILS
C FOR ADAPTIVE CONVOLUTION FOR ALL NB*NREL TRANSFORMS. THE
C TRUNCATION CRITERION IS ESTABLISHED DURING CONVOLUTION IN
C A FIXED ABSCISSA RANGE (USING WEIGHTS 299-339) OF EITHER
C ORDER FILTER AS THE MAXIMUM ABSOLUTE CONVOLVED PRODUCT
C TIMES TOL. THE CONVOLUTION SUMMATION IS TERMINATED
C ON EITHER SIDE OF THE FIXED RANGE WHENEVER THE ABSOLUTE
C PRODUCT .LE. THE TRUNCATION CRITERION. IN GENERAL, A
C DECREASING TOLERANCE WILL PRODUCE HIGHER ACCURACY SINCE
C MORE FILTER WEIGHTS ARE USED (UNLESS EXPONENT UNDERFLOW
C OCCURS IN THE TRANSFORM INPUT FUNCTION EVALUATION).
C ONE MAY SET TOL=0.D0 TO OBTAIN MAXIMUM ACCURACY FOR ALL
C NB*NREL REAL HANKEL TRANSFORMS IN DANS(NB,NREL).
C HOWEVER, THE ACTUAL RELATIVE ERRORS CANNOT BE EXPECTED TO
C BE SMALLER THAN ABOUT .1D-13 REGARDLESS OF THE TOLERANCE
C VALUE USED, SINCE DOUBLE-PRECISION FILTER WEIGHTS AND
C DOUBLE-PRECISION FUNCTIONS ARE USED. IN ANY EVENT,
C ONE SHOULD ALWAYS CHOOSE TOL<<DESIRED RELATIVE ERROR.
C ** ACCURACY WARNING ** SOME HIGHLY OSCILLATORY FUNCTIONS
C FUN1(G) AND (OR) LIMITING CASES OF B NEAR MACHINE-ZERO
C (OR INFINITY) SHOULD BE AVOIDED, OTHERWISE UNSATISFACTORY
C RESULTS (E.G., RELATIVE & ABSOLUTE ERRORS>>TOL) MAY OCCUR.
C NTOL - NUMBER OF CONSECUTIVE TIMES THE TRUNCATION CRITERION (TOL)
C IS TO BE MET AT EITHER FILTER TAIL BEFORE FILTER
C TRUNCATION OCCURS. NTOL=1 SHOULD BE USED FOR INPUT
C FUNCTIONS THAT DO NOT HAVE MANY ZEROS IN (0,INFINITY). FOR
C OSCILLATORY FUNCTIONS WITH MANY ZEROS, NTOL>1 MAY BE USED
C TO INSURE A PREMATURE CUTOFF DOES NOT OCCUR FOR TRUNCATION
C (SEE USE OF ITOL,NTOL,TOL IN THE CODE BELOW).
C NORD - INTEGER ARRAY NORD(NREL) GIVING THE NREL ORDERS (0 OR 1)
C OF EACH RELATED HANKEL TRANSFORM. IF ANY NORD(I),I=1,NREL,
C IS NOT 0 OR 1, THEN ORDER 1 WILL BE ASSUMED.
C FUN1 - NAME OF AN EXTERNAL DOUBLE PRECISION FUNCTION OF A REAL
C ARGUMENT DEFINING THE 1ST TRANSFORM INPUT FUNCTION OF THE
C SET OF RELATED TRANSFORMS TO BE EVALUATED. AN EXTERNAL
C FUN1 STATEMENT MUST APPEAR IN THE CALLING PROGRAM. THE
C DOUBLE PRECISION FUNCTION FUN1(G) MUST BE CODED BY THE
C USER AND MUST BE A CONTINUOUS DECREASING REAL FUNCTION
C FOR ALL REAL G>0.0D0. THE VALUE OF G MUST BE UNCHANGED
C UPON RETURN FROM FUN1. A MULTIPLE-POLE OF FUN1(G) AT G=0.0
C CAN EXIST, PROVIDED THE HANKEL TRANSFORM CONVERGES (NOTE
C FUN1(0D0) IS NOT USED). GENERALLY, FUN1(G)
C IS DEFINED ANALYTICALLY FOR ALL G>0.D0. HOWEVER,
C DISCRETELY DEFINED FUNCTIONS MAY BE USED IF FUN1(G)
C RETURNS A SMOOTH INTERPOLATION VALUE (E.G., VIA CUBIC
C SPLINES) WHICH SATISFIES THE CONTINUITY CONDITION FOR ALL
C G>0, AND PROVIDED THE PROPER LIMITING VALUE OF FUN1(G) IS
C GIVEN AS G TENDS TO INFINITY. PARAMETERS OTHER
C THAN G NEEDED IN FUN1(G) MAY BE INCLUDED BY USING LABELED
C COMMON IN FUN1 AND IN THE USERS CALLING PROGRAM. IF
C FUN1(G) IS AN OSCILLATING FUNCTION, THEN THE HIGHEST
C FREQUENCY COMPONENT (IN LOG-SPACE) SHOULD NOT EXCEED THE
C FILTER NYQUIST FREQUENCY, 1/(2*0.1D0). IN GENERAL,
C SUBPROGRAM DHANKL PERFORMS BEST WHEN USING SMOOTH, WELL-
C BEHAVED FUNCTIONS FUN1(G), THAT ARE CHARACTERIZED AS
C MONOTONICALLY DECREASING FUNCTIONS WITH RELATIVELY FEW
C ZEROS FOR G>0. (SEE THE ACCURACY WARNING UNDER TOL, AND
C ERROR CONDITION (4).)
C IJREL - INTEGER ARRAY IJREL(2,NREL) USED WHEN NREL>1 TO DEFINE
C THE PAIR OF I,J INTEGER EXPONENTS FOR EACH RELATED INPUT
C FUNCTION. THE RELATED INPUT FUNCTIONS ARE ASSUMED
C TO BE SIMPLY RELATED IN TERMS OF FUN1 VIA THE INTEGER
C ARRAY IJREL(2,K),K=2,NREL. THAT IS, WE ASSUME THE K-TH
C RELATED INPUT FUNCTION IS GIVEN (SEE STATEMENT 160) AS
C FUNK(G)=G**IJREL(1,K) * FUN1(G)**IJREL(2,K), WHERE
C THE INTEGER EXPONENTS MAY BE POSITIVE, ZERO, OR NEGATIVE.
C IN THIS WAY, ONLY FUN1 NEED BE DECLARED AN EXTERNAL
C FUNCTION. MORE COMPLICATED CODE COULD BE USED
C FOR THE RELATED FUNCTIONS, PROVIDED THE MEANING OF IJREL
C IS REDEFINED AND STATEMENT 160 IS CHANGED (ALSO, SEE
C ERROR CONDITION (3) BELOW). WHEN NREL=1, ARRAY
C IJREL IS A DUMMY NAME (I.E., NOT REFERENCED).
C IF NREL>1, THEN THE STATEMENT AT LABEL 160
C IS DEFINED ONLY FOR K=J=2,...,NREL. THAT IS,
C IJREL(1,1),IJREL(2,1) ARE NOT USED IN THIS VERSION.
C DWORK - WORK ARRAY DWORK(801,NREL), WHICH IS USED TO
C HOLD VARIOUS COMPUTED FUNCTIONAL VALUES DURING RELATED AND
C LAGGED CONVOLUTIONS. A STORAGE ROLL FEATURE USING
C DWORK(801,NREL) AND INTERNAL ARRAY KEY(801) ALLOWS FOR
C ANY B RANGE (BMIN,BMAX) TO BE USED DURING CONVOLUTION.
C
C OUTPUT
C
C DANS - THE ARRAY DANS(NB,NREL) IS RETURNED GIVING THE
C NB*NREL REAL HANKEL TRANSFORMS, WITH CORRESPONDING
C B ARGUMENTS GIVEN IN ARRAY ARG(NB).
C ARG - THE ARRAY ARG(NB) IS RETURNED GIVING THE RESULTING
C B ARGUMENTS IN (BMIN,BMAX), WHERE ARG(I+1)/ARG(I)=EXP(.1),
C I=1,NB-1 (THIS ARRAY COULD BE ELIMINATED TO SAVE STORAGE
C AND REGENERATED AFTER THE CALL DHANKL, IF DESIRED).
C NOFUN1 - NUMBER OF DIRECT FUN1 EVALUATIONS USED FOR ALL NB*NREL
C REAL HANKEL TRANSFORMS. NOFUN1 IS USUALLY NOT MORE
C THAN THE NUMBER OF WEIGHTS NEEDED FOR A SINGLE DIRECT
C CONVOLUTION, FOR ANY NB AND NREL.
C IERR - ERROR RETURN CODE. THE FOLLOWING CODES ARE POSSIBLE --
C = 0, NO ERROR IN INPUT PARAMETERS. DANS,ARG COMPUTED.
C = 1, IMPROPER INPUT PARAMETERS (I.E., NB<1,NREL<1,BMAX<=0,
C OR BMAX*DEXP(-.1D0*(NB-1))<=0.D0). DANS,ARG NOT COMPUTED.
C
C
C ERROR CONDITIONS
C
C (1) IMPROPER INPUT PARAMETERS GIVEN (SEE IERR=1 ABOVE).
C (2) UNDERFLOW CONDITIONS ARE POSSIBLE DURING CONVOLUTION, DUE TO
C THE BEHAVIOR OF FUN1, VALUE OF B IN (BMIN,BMAX), TOL, AND
C NTOL. EXPONENT AND (OR) ARITHMETIC UNDERFLOW TRAPS MUST RETURN
C A VALUE OF 0.D0 FOR THE COMPUTER SYSTEM BEING USED. NOTE THAT
C UNDERFLOW MAY ALSO OCCUR IN THE USERS EXTERNAL FUNCTION
C FUN1(G) FOR ANY VALUE OF G AS SET BY SUBPROGRAM DHANKL.
C (3) AN UNRECOVERABLE OVERFLOW CONDITION CAN OCCUR IN EXECUTING
C STATEMENT 160, DEPENDING ON THE VALUE OF B IN (BMIN,BMAX),
C TOL, OR THE INTEGER EXPONENTS USED IN IJREL(2,NREL),NREL>1.
C IN GENERAL, EXTREMELY SMALL OR LARGE VALUES OF B SHOULD BE
C AVOIDED (SEE ACCURACY WARNING UNDER TOL ABOVE). ALSO, IN MANY
C CASES, EXPONENT OVERFLOW CAN BE AVOIDED BY PROPER CHOICE OF
C FUN1 AND THE RELATED INPUT FUNCTION ORDERING DEFINED BY
C THE IJREL SIGNED INTEGER EXPONENTS.
C (4) UNDETECTED ERRORS ARE POSSIBLE IF FUN1 IS IMPROPERLY CODED, OR
C DOES NOT YIELD DOUBLE-PRECISION ACCURACY, OR IS NOT
C A CONTINUOUS DECREASING REAL FUNCTION FOR ALL G>0.D0.
C
C USAGE
C
C SUBPROGRAM DHANKL IS CALLED AS FOLLOWS (USE NUMERICAL VALUES FOR
C <EXPRESSION>, EXCLUDING < AND >, IN DECLARATIONS) --
C
C DOUBLE PRECISION BMAX,TOL,DWORK(801,<NREL>),DANS(<NB>,<NREL>),
C 1 ARG(<NB>)
C DIMENSION NORD(<NREL>),IJREL(2,<NREL>)
C EXTERNAL DFUN1
CC-----READ/LOAD INPUT PARAMETERS FOR DHANKL AS REQUIRED
C ...
C CALL DHANKL(BMAX,NB,NREL,TOL,NTOL,NORD,DFUN1,IJREL,DWORK,
C * DANS,ARG,NOFUN1,IERR)
C IF(IERR.EQ.1) STOP
C ...
C END
C DOUBLE PRECISION FUNCTION DFUN1(G)
C DOUBLE PRECISION G
CC-----INSERT USER SUPPLIED CODE FOR EVALUATION OF DFUN1(G),G>0.0D0
C END
C
C=======================================================================
DOUBLE PRECISION ABSCIS,C,CMAX,DSUM,E,ER,FUN1,G,Y,Y1,WT0,WT1
DIMENSION KEY(801),WT0(801),WT1(801)
C-----WE DEFINE C,CMAX FOR USE IN THE TRUNCATION CRITERION TESTS,
C WHERE C IS ANY CONVOLUTION PRODUCT AND CMAX IS THE MAXIMUM
C CONVOLVED PRODUCT IN THE FIXED ABSCISSA RANGE (SEE PARAMETER TOL).
C-----ABSCIS=BASE CONSTANT FOR FILTER ABSCISSA GENERATION
DATA ABSCIS/0.7059431685223780D0/
C-----E=DEXP(.1D0), ER=1.0D0/E (ALSO USED IN ABSCISSA GENERATION)
DATA E/1.10517091807564762 D0/,ER/.904837418035959573 D0/
C-----WT0(I)=J0 HANKEL TRANSFORM FILTER WEIGHTS FOR I=1,801
DATA
*WT0( 1)/ 2.103562053838982D-29/,WT0( 2)/-1.264469361608894D-14/,
*WT0( 3)/ 4.615731256788567D-14/,WT0( 4)/-2.798703374257668D-14/,
*WT0( 5)/ 5.465764965410841D-14/,WT0( 6)/-2.652933109928729D-14/,
*WT0( 7)/ 5.674913434067321D-14/,WT0( 8)/-2.157276828977208D-14/,
*WT0( 9)/ 5.831846086773976D-14/,WT0( 10)/-1.546589284868783D-14/,
*WT0( 11)/ 6.057302455652974D-14/,WT0( 12)/-8.502531259083065D-15/,
*WT0( 13)/ 6.388018061147645D-14/,WT0( 14)/-5.659657635010288D-16/,
*WT0( 15)/ 6.848500604791407D-14/,WT0( 16)/ 8.572897732168277D-15/,
*WT0( 17)/ 7.465068154681814D-14/,WT0( 18)/ 1.920837293261338D-14/,
*WT0( 19)/ 8.269345428975771D-14/,WT0( 20)/ 3.170116562922900D-14/,
*WT0( 21)/ 9.300004039695208D-14/,WT0( 22)/ 4.649069639417992D-14/,
*WT0( 23)/ 1.060441944490564D-13/,WT0( 24)/ 6.411216589597457D-14/,
*WT0( 25)/ 1.224060834001701D-13/,WT0( 26)/ 8.521776751507022D-14/,
*WT0( 27)/ 1.427957940487172D-13/,WT0( 28)/ 1.106026606968463D-13/,
*WT0( 29)/ 1.680820203098405D-13/,WT0( 30)/ 1.412367028159546D-13/,
*WT0( 31)/ 1.993271011776308D-13/,WT0( 32)/ 1.783032042964119D-13/,
*WT0( 33)/ 2.378298196799422D-13/,WT0( 34)/ 2.232462602765097D-13/,
*WT0( 35)/ 2.851776817107034D-13/,WT0( 36)/ 2.778285575785995D-13/,
*WT0( 37)/ 3.433107735233557D-13/,WT0( 38)/ 3.442019764139949D-13/
DATA
*WT0( 39)/ 4.145997612327839D-13/,WT0( 40)/ 4.249938198224969D-13/,
*WT0( 41)/ 5.019411631949951D-13/,WT0( 42)/ 5.234121310773422D-13/,
*WT0( 43)/ 6.088737193247560D-13/,WT0( 44)/ 6.433743253810275D-13/,
*WT0( 45)/ 7.397205280796933D-13/,WT0( 46)/ 7.896642978865920D-13/,
*WT0( 47)/ 8.997626559623209D-13/,WT0( 48)/ 9.681243129571424D-13/,
*WT0( 49)/ 1.095451187471558D-12/,WT0( 50)/ 1.185889375491455D-12/,
*WT0( 51)/ 1.334666226164323D-12/,WT0( 52)/ 1.451673490118585D-12/,
*WT0( 53)/ 1.627033241780647D-12/,WT0( 54)/ 1.776119296526221D-12/,
*WT0( 55)/ 1.984309459865773D-12/,WT0( 56)/ 2.172225112712636D-12/,
*WT0( 57)/ 2.420855801356264D-12/,WT0( 58)/ 2.655866524621122D-12/,
*WT0( 59)/ 2.954213313000758D-12/,WT0( 60)/ 3.246433455110429D-12/,
*WT0( 61)/ 3.605807223054322D-12/,WT0( 62)/ 3.967608279821300D-12/,
*WT0( 63)/ 4.401806878720721D-12/,WT0( 64)/ 4.848316218220904D-12/,
*WT0( 65)/ 5.374176077884770D-12/,WT0( 66)/ 5.923886142128417D-12/,
*WT0( 67)/ 6.561955948855011D-12/,WT0( 68)/ 7.237468388830243D-12/,
*WT0( 69)/ 8.012831864792648D-12/,WT0( 70)/ 8.841766480402105D-12/,
*WT0( 71)/ 9.785047278800097D-12/,WT0( 72)/ 1.080115224902499D-11/,
*WT0( 73)/ 1.194974128877562D-11/,WT0( 74)/ 1.319424925552153D-11/,
*WT0( 75)/ 1.459380374689331D-11/,WT0( 76)/ 1.611708818260074D-11/
DATA
*WT0( 77)/ 1.782336249944076D-11/,WT0( 78)/ 1.968696083966218D-11/,
*WT0( 79)/ 2.176804271234846D-11/,WT0( 80)/ 2.404712745375440D-11/,
*WT0( 81)/ 2.658616922424555D-11/,WT0( 82)/ 2.937256616666064D-11/,
*WT0( 83)/ 3.247112071587450D-11/,WT0( 84)/ 3.587699548548411D-11/,
*WT0( 85)/ 3.965909071112399D-11/,WT0( 86)/ 4.382145152220635D-11/,
*WT0( 87)/ 4.843856688602439D-11/,WT0( 88)/ 5.352476425684008D-11/,
*WT0( 89)/ 5.916190912377549D-11/,WT0( 90)/ 6.537635327328955D-11/,
*WT0( 91)/ 7.225949098391667D-11/,WT0( 92)/ 7.985185650562155D-11/,
*WT0( 93)/ 8.825697213255412D-11/,WT0( 94)/ 9.753221923111176D-11/,
*WT0( 95)/ 1.077963949370144D-10/,WT0( 96)/ 1.191270094182892D-10/,
*WT0( 97)/ 1.316619519054340D-10/,WT0( 98)/ 1.455028951566729D-10/,
*WT0( 99)/ 1.608114581091983D-10/,WT0(100)/ 1.777184270673645D-10/,
*WT0(101)/ 1.964147916871289D-10/,WT0(102)/ 2.170665216346822D-10/,
*WT0(103)/ 2.399008451839042D-10/,WT0(104)/ 2.651263504640323D-10/,
*WT0(105)/ 2.930148720448538D-10/,WT0(106)/ 3.238267179640594D-10/,
*WT0(107)/ 3.578885297833856D-10/,WT0(108)/ 3.955234710219298D-10/,
*WT0(109)/ 4.371254308993604D-10/,WT0(110)/ 4.830940473937580D-10/,
*WT0(111)/ 5.339056350072159D-10/,WT0(112)/ 5.900529573690070D-10/,
*WT0(113)/ 6.521132758098962D-10/,WT0(114)/ 7.206928333934838D-10/
DATA
*WT0(115)/ 7.964924450372341D-10/,WT0(116)/ 8.802567084675067D-10/,
*WT0(117)/ 9.728375895186283D-10/,WT0(118)/ 1.075148437456224D-09/,
*WT0(119)/ 1.188226062693121D-09/,WT0(120)/ 1.313189706258061D-09/,
*WT0(121)/ 1.451302163665563D-09/,WT0(122)/ 1.603933943511600D-09/,
*WT0(123)/ 1.772624063293560D-09/,WT0(124)/ 1.959049733219870D-09/,
*WT0(125)/ 2.165087540667258D-09/,WT0(126)/ 2.392789115986871D-09/,
*WT0(127)/ 2.644443536014764D-09/,WT0(128)/ 2.922559573439235D-09/,
*WT0(129)/ 3.229930291248597D-09/,WT0(130)/ 3.569622651576204D-09/,
*WT0(131)/ 3.945045448172924D-09/,WT0(132)/ 4.359947261255963D-09/,
*WT0(133)/ 4.818489091363688D-09/,WT0(134)/ 5.325251901762953D-09/,
*WT0(135)/ 5.885315583343685D-09/,WT0(136)/ 6.504277635547376D-09/,
*WT0(137)/ 7.188340419242570D-09/,WT0(138)/ 7.944342903082902D-09/,
*WT0(139)/ 8.779858562959109D-09/,WT0(140)/ 9.703242578022093D-09/,
*WT0(141)/ 1.072374322768940D-08/,WT0(142)/ 1.185156747840095D-08/,
*WT0(143)/ 1.309800933225301D-08/,WT0(144)/ 1.447553742402158D-08/,
*WT0(145)/ 1.599794451372024D-08/,WT0(146)/ 1.768046154055318D-08/,
*WT0(147)/ 1.953993335487118D-08/,WT0(148)/ 2.159496468450500D-08/,
*WT0(149)/ 2.386612830616206D-08/,WT0(150)/ 2.637614961034523D-08/,
*WT0(151)/ 2.915015476269831D-08/,WT0(152)/ 3.221590205565798D-08/
DATA
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*WT0(155)/ 4.348692045365787D-08/,WT0(156)/ 4.806047869438007D-08/,
*WT0(157)/ 5.311504443749314D-08/,WT0(158)/ 5.870120138001748D-08/,
*WT0(159)/ 6.487486163571268D-08/,WT0(160)/ 7.169780940885934D-08/,
*WT0(161)/ 7.923833480505012D-08/,WT0(162)/ 8.757190229426675D-08/,
*WT0(163)/ 9.678192055835553D-08/,WT0(164)/ 1.069605631204864D-07/,
*WT0(165)/ 1.182097045925483D-07/,WT0(166)/ 1.306419269237675D-07/,
*WT0(167)/ 1.443816591198488D-07/,WT0(168)/ 1.595664099835792D-07/,
*WT0(169)/ 1.763481565722233D-07/,WT0(170)/ 1.948948533650376D-07/,
*WT0(171)/ 2.153921247351847D-07/,WT0(172)/ 2.380451115468297D-07/,
*WT0(173)/ 2.630805351444854D-07/,WT0(174)/ 2.907489558998551D-07/,
*WT0(175)/ 3.213272911558462D-07/,WT0(176)/ 3.551215767529809D-07/,
*WT0(177)/ 3.924700396067688D-07/,WT0(178)/ 4.337464734078393D-07/,
*WT0(179)/ 4.793639887921159D-07/,WT0(180)/ 5.297791390370199D-07/,
*WT0(181)/ 5.854964979982190D-07/,WT0(182)/ 6.470737017046583D-07/,
*WT0(183)/ 7.151270374758372D-07/,WT0(184)/ 7.903376040582035D-07/,
*WT0(185)/ 8.734581359370587D-07/,WT0(186)/ 9.653205295304359D-07/,
*WT0(187)/ 1.066844176299330D-06/,WT0(188)/ 1.179045157323447D-06/,
*WT0(189)/ 1.303046419382764D-06/,WT0(190)/ 1.440089007182073D-06/
DATA
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*WT0(193)/ 1.943916830388476D-06/,WT0(194)/ 2.148360347694608D-06/,
*WT0(195)/ 2.374305378111399D-06/,WT0(196)/ 2.624013254094558D-06/,
*WT0(197)/ 2.899983137292810D-06/,WT0(198)/ 3.204977025773239D-06/,
*WT0(199)/ 3.542047402097807D-06/,WT0(200)/ 3.914567778667102D-06/,
*WT0(201)/ 4.326266465748067D-06/,WT0(202)/ 4.781263881007758D-06/,
*WT0(203)/ 5.284113792545945D-06/,WT0(204)/ 5.839848890150422D-06/,
*WT0(205)/ 6.454031158395685D-06/,WT0(206)/ 7.132807538712648D-06/,
*WT0(207)/ 7.882971454044484D-06/,WT0(208)/ 8.712030795792633D-06/,
*WT0(209)/ 9.628283069078871D-06/,WT0(210)/ 1.064089843325841D-05/,
*WT0(211)/ 1.176001148348469D-05/,WT0(212)/ 1.299682267761921D-05/,
*WT0(213)/ 1.436371043746991D-05/,WT0(214)/ 1.587435503282041D-05/,
*WT0(215)/ 1.754387550120777D-05/,WT0(216)/ 1.938898096105121D-05/,
*WT0(217)/ 2.142813784487508D-05/,WT0(218)/ 2.368175471430264D-05/,
*WT0(219)/ 2.617238651818130D-05/,WT0(220)/ 2.892496032668667D-05/,
*WT0(221)/ 3.196702481167932D-05/,WT0(222)/ 3.532902595927333D-05/,
*WT0(223)/ 3.904461178455365D-05/,WT0(224)/ 4.315096908756330D-05/,
*WT0(225)/ 4.768919563102351D-05/,WT0(226)/ 5.270471145419851D-05/,
*WT0(227)/ 5.824771344935570D-05/,WT0(228)/ 6.437367773954276D-05/
DATA
*WT0(229)/ 7.114391489568718D-05/,WT0(230)/ 7.862618353777022D-05/,
*WT0(231)/ 8.689536847209423D-05/,WT0(232)/ 9.603423013681158D-05/,
*WT0(233)/ 1.061342328695059D-04/,WT0(234)/ 1.172964602657162D-04/,
*WT0(235)/ 1.296326268075215D-04/,WT0(236)/ 1.432661958546299D-04/,
*WT0(237)/ 1.583336152150400D-04/,WT0(238)/ 1.749856826064412D-04/,
*WT0(239)/ 1.933890547221590D-04/,WT0(240)/ 2.137279149064782D-04/,
*WT0(241)/ 2.362058162174614D-04/,WT0(242)/ 2.610477181410775D-04/,
*WT0(243)/ 2.885022375064333D-04/,WT0(244)/ 3.188441357870562D-04/,
*WT0(245)/ 3.523770680013592D-04/,WT0(246)/ 3.894366200728159D-04/,
*WT0(247)/ 4.303936656695837D-04/,WT0(248)/ 4.756580748770003D-04/,
*WT0(249)/ 5.256828130316798D-04/,WT0(250)/ 5.809684683619367D-04/,
*WT0(251)/ 6.420682561143772D-04/,WT0(252)/ 7.095935446942389D-04/,
*WT0(253)/ 7.842199637491256D-04/,WT0(254)/ 8.666941465924691D-04/,
*WT0(255)/ 9.578411834759010D-04/,WT0(256)/ 1.058572843543458D-03/,
*WT0(257)/ 1.169896665384001D-03/,WT0(258)/ 1.292925974983324D-03/,
*WT0(259)/ 1.428890965739396D-03/,WT0(260)/ 1.579150889627630D-03/,
*WT0(261)/ 1.745207548623177D-03/,WT0(262)/ 1.928720102656342D-03/,
*WT0(263)/ 2.131521473093367D-03/,WT0(264)/ 2.355636277673631D-03/,
*WT0(265)/ 2.603300731229735D-03/,WT0(266)/ 2.876984272542283D-03/
DATA
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*WT0(269)/ 3.882861625673649D-03/,WT0(270)/ 4.290867254031690D-03/,
*WT0(271)/ 4.741657973486860D-03/,WT0(272)/ 5.239689338467119D-03/,
*WT0(273)/ 5.789870985188969D-03/,WT0(274)/ 6.397607072000340D-03/,
*WT0(275)/ 7.068843783102744D-03/,WT0(276)/ 7.810112796625723D-03/,
*WT0(277)/ 8.628584975720666D-03/,WT0(278)/ 9.532112534855741D-03/,
*WT0(279)/ 1.052928697105230D-02/,WT0(280)/ 1.162947042684567D-02/,
*WT0(281)/ 1.284285301027502D-02/,WT0(282)/ 1.418045400408490D-02/,
*WT0(283)/ 1.565416842684913D-02/,WT0(284)/ 1.727670025860997D-02/,
*WT0(285)/ 1.906157878467033D-02/,WT0(286)/ 2.102295173845023D-02/,
*WT0(287)/ 2.317553622087861D-02/,WT0(288)/ 2.553413681316817D-02/,
*WT0(289)/ 2.811347056705691D-02/,WT0(290)/ 3.092716134472897D-02/,
*WT0(291)/ 3.398734108220733D-02/,WT0(292)/ 3.730266904318316D-02/,
*WT0(293)/ 4.087756584601726D-02/,WT0(294)/ 4.470845458227711D-02/,
*WT0(295)/ 4.878245655564208D-02/,WT0(296)/ 5.307046388837388D-02/,
*WT0(297)/ 5.752521479656082D-02/,WT0(298)/ 6.206888924914453D-02/,
*WT0(299)/ 6.659098690582325D-02/,WT0(300)/ 7.092687097703928D-02/,
*WT0(301)/ 7.485762155329997D-02/,WT0(302)/ 7.807466421172765D-02/,
*WT0(303)/ 8.018887211338042D-02/,WT0(304)/ 8.067640670918657D-02/
DATA
*WT0(305)/ 7.891767306422777D-02/,WT0(306)/ 7.412406301630496D-02/,
*WT0(307)/ 6.545864753141331D-02/,WT0(308)/ 5.195771725733346D-02/,
*WT0(309)/ 3.284797274184859D-02/,WT0(310)/ 7.497076325831270D-03/,
*WT0(311)/-2.386612869894549D-02/,WT0(312)/-6.017494378476118D-02/,
*WT0(313)/-9.817899798850670D-02/,WT0(314)/-1.328147797272611D-01/,
*WT0(315)/-1.554628569772562D-01/,WT0(316)/-1.563982157987450D-01/,
*WT0(317)/-1.243049866529050D-01/,WT0(318)/-5.486815986343697D-02/,
*WT0(319)/ 4.686255899170307D-02/,WT0(320)/ 1.511218295806206D-01/,
*WT0(321)/ 2.119315534410599D-01/,WT0(322)/ 1.695134135887796D-01/,
*WT0(323)/ 1.386197420331480D-02/,WT0(324)/-1.869350451838135D-01/,
*WT0(325)/-2.455889606925336D-01/,WT0(326)/-5.309269401899814D-02/,
*WT0(327)/ 2.519998415798595D-01/,WT0(328)/ 1.968224876057428D-01/,
*WT0(329)/-2.014333618969160D-01/,WT0(330)/-2.458450827258603D-01/,
*WT0(331)/ 3.433559314076636D-01/,WT0(332)/-4.770066510626292D-02/,
*WT0(333)/-2.096628473507452D-01/,WT0(334)/ 2.509085123794248D-01/,
*WT0(335)/-1.676412661335192D-01/,WT0(336)/ 7.495199786896762D-02/,
*WT0(337)/-1.695135102751146D-02/,WT0(338)/-8.828524201374996D-03/,
*WT0(339)/ 1.616787356183550D-02/,WT0(340)/-1.556411755992529D-02/,
*WT0(341)/ 1.251311125216370D-02/,WT0(342)/-9.299315246978098D-03/
DATA
*WT0(343)/ 6.650525996779493D-03/,WT0(344)/-4.667707408671884D-03/,
*WT0(345)/ 3.248885545556855D-03/,WT0(346)/-2.255529108544675D-03/,
*WT0(347)/ 1.566875211100915D-03/,WT0(348)/-1.091132486368091D-03/,
*WT0(349)/ 7.625383049040949D-04/,WT0(350)/-5.352540577820408D-04/,
*WT0(351)/ 3.777104567214670D-04/,WT0(352)/-2.682528211535297D-04/,
*WT0(353)/ 1.920265274996755D-04/,WT0(354)/-1.388213723208944D-04/,
*WT0(355)/ 1.015998917810005D-04/,WT0(356)/-7.549725062631259D-05/,
*WT0(357)/ 5.714172920052936D-05/,WT0(358)/-4.419160967680634D-05/,
*WT0(359)/ 3.501776199578583D-05/,WT0(360)/-2.848496954139990D-05/,
*WT0(361)/ 2.380104817324115D-05/,WT0(362)/-2.041274924032166D-05/,
*WT0(363)/ 1.793363489791860D-05/,WT0(364)/-1.609367780777977D-05/,
*WT0(365)/ 1.470394692017765D-05/,WT0(366)/-1.363208540087839D-05/,
*WT0(367)/ 1.278540851480116D-05/,WT0(368)/-1.209910323276592D-05/,
*WT0(369)/ 1.152780746372085D-05/,WT0(370)/-1.103964249967709D-05/,
*WT0(371)/ 1.061214724478712D-05/,WT0(372)/-1.022954672255804D-05/,
*WT0(373)/ 9.880801917269063D-06/,WT0(374)/-9.558136268373164D-06/,
*WT0(375)/ 9.255989462874843D-06/,WT0(376)/-8.970368039834961D-06/,
*WT0(377)/ 8.698439226217636D-06/,WT0(378)/-8.438199899378174D-06/,
*WT0(379)/ 8.188185039708096D-06/,WT0(380)/-7.947275976752668D-06/
DATA
*WT0(381)/ 7.714620489277084D-06/,WT0(382)/-7.489590334670121D-06/,
*WT0(383)/ 7.271712845563131D-06/,WT0(384)/-7.060595202720040D-06/,
*WT0(385)/ 6.855890958634290D-06/,WT0(386)/-6.657307826365352D-06/,
*WT0(387)/ 6.464610635947412D-06/,WT0(388)/-6.277596705248834D-06/,
*WT0(389)/ 6.096069004564178D-06/,WT0(390)/-5.919835014912806D-06/,
*WT0(391)/ 5.748721389173238D-06/,WT0(392)/-5.582576428368341D-06/,
*WT0(393)/ 5.421255729073172D-06/,WT0(394)/-5.264611483233620D-06/,
*WT0(395)/ 5.112497827757443D-06/,WT0(396)/-4.964780650195476D-06/,
*WT0(397)/ 4.821336526159266D-06/,WT0(398)/-4.682043530422997D-06/,
*WT0(399)/ 4.546777587820041D-06/,WT0(400)/-4.415418000076004D-06/,
*WT0(401)/ 4.287852503112911D-06/,WT0(402)/-4.163974668109847D-06/,
*WT0(403)/ 4.043678407829827D-06/,WT0(404)/-3.926857526517075D-06/,
*WT0(405)/ 3.813409851360361D-06/,WT0(406)/-3.703239239834851D-06/,
*WT0(407)/ 3.596252927182967D-06/,WT0(408)/-3.492358600906126D-06/,
*WT0(409)/ 3.391465179914198D-06/,WT0(410)/-3.293485431241940D-06/,
*WT0(411)/ 3.198336356446399D-06/,WT0(412)/-3.105937110348406D-06/,
*WT0(413)/ 3.016207679069661D-06/,WT0(414)/-2.929069911562291D-06/,
*WT0(415)/ 2.844448954094881D-06/,WT0(416)/-2.762272935820411D-06/,
*WT0(417)/ 2.682471568415877D-06/,WT0(418)/-2.604975709140556D-06/
DATA
*WT0(419)/ 2.529718233664062D-06/,WT0(420)/-2.456634690985054D-06/,
*WT0(421)/ 2.385662793855871D-06/,WT0(422)/-2.316741584624232D-06/,
*WT0(423)/ 2.249811415880699D-06/,WT0(424)/-2.184814552602377D-06/,
*WT0(425)/ 2.121695378987067D-06/,WT0(426)/-2.060399926949900D-06/,
*WT0(427)/ 2.000875435893980D-06/,WT0(428)/-1.943070483347481D-06/,
*WT0(429)/ 1.886935339579619D-06/,WT0(430)/-1.832421953831803D-06/,
*WT0(431)/ 1.779483599068986D-06/,WT0(432)/-1.728074671861562D-06/,
*WT0(433)/ 1.678150840818710D-06/,WT0(434)/-1.629669220867866D-06/,
*WT0(435)/ 1.582588274939725D-06/,WT0(436)/-1.536867577717458D-06/,
*WT0(437)/ 1.492467744182388D-06/,WT0(438)/-1.449350544031671D-06/,
*WT0(439)/ 1.407478963215944D-06/,WT0(440)/-1.366817091697906D-06/,
*WT0(441)/ 1.327329980403758D-06/,WT0(442)/-1.288983628354532D-06/,
*WT0(443)/ 1.251745052743577D-06/,WT0(444)/-1.215582289623042D-06/,
*WT0(445)/ 1.180464297731392D-06/,WT0(446)/-1.146360878232118D-06/,
*WT0(447)/ 1.113242681755176D-06/,WT0(448)/-1.081081241360643D-06/,
*WT0(449)/ 1.049848946307979D-06/,WT0(450)/-1.019518969919736D-06/,
*WT0(451)/ 9.900652269648073D-07/,WT0(452)/-9.614623823829486D-07/,
*WT0(453)/ 9.336858590396268D-07/,WT0(454)/-9.067118039187765D-07/,
*WT0(455)/ 8.805170379415897D-07/,WT0(456)/-8.550790335506564D-07/
DATA
*WT0(457)/ 8.303759185665738D-07/,WT0(458)/-8.063864695073603D-07/,
*WT0(459)/ 7.830900795968434D-07/,WT0(460)/-7.604667251660013D-07/,
*WT0(461)/ 7.384969528074763D-07/,WT0(462)/-7.171618775580271D-07/,
*WT0(463)/ 6.964431695613518D-07/,WT0(464)/-6.763230273695452D-07/,
*WT0(465)/ 6.567841555251206D-07/,WT0(466)/-6.378097555683096D-07/,
*WT0(467)/ 6.193835199757372D-07/,WT0(468)/-6.014896169720738D-07/,
*WT0(469)/ 5.841126695566173D-07/,WT0(470)/-5.672377400509635D-07/,
*WT0(471)/ 5.508503223216395D-07/,WT0(472)/-5.349363333399711D-07/,
*WT0(473)/ 5.194820986824491D-07/,WT0(474)/-5.044743364413132D-07/,
*WT0(475)/ 4.899001458890472D-07/,WT0(476)/-4.757469999761242D-07/,
*WT0(477)/ 4.620027360551677D-07/,WT0(478)/-4.486555431391317D-07/,
*WT0(479)/ 4.356939495368206D-07/,WT0(480)/-4.231068139067277D-07/,
*WT0(481)/ 4.108833178901058D-07/,WT0(482)/-3.990129570237777D-07/,
*WT0(483)/ 3.874855299952715D-07/,WT0(484)/-3.762911289578004D-07/,
*WT0(485)/ 3.654201320223786D-07/,WT0(486)/-3.548631961765860D-07/,
*WT0(487)/ 3.446112489455190D-07/,WT0(488)/-3.346554794873414D-07/,
*WT0(489)/ 3.249873307934947D-07/,WT0(490)/-3.155984931421240D-07/,
*WT0(491)/ 3.064808974928670D-07/,WT0(492)/-2.976267081233949D-07/,
*WT0(493)/ 2.890283152696976D-07/,WT0(494)/-2.806783286653362D-07/
DATA
*WT0(495)/ 2.725695717362821D-07/,WT0(496)/-2.646950756050221D-07/,
*WT0(497)/ 2.570480727284082D-07/,WT0(498)/-2.496219907786807D-07/,
*WT0(499)/ 2.424104471687142D-07/,WT0(500)/-2.354072438896643D-07/,
*WT0(501)/ 2.286063621819694D-07/,WT0(502)/-2.220019570969968D-07/,
*WT0(503)/ 2.155883523600859D-07/,WT0(504)/-2.093600356601861D-07/,
*WT0(505)/ 2.033116540781646D-07/,WT0(506)/-1.974380094205501D-07/,
*WT0(507)/ 1.917340535876188D-07/,WT0(508)/-1.861948842172547D-07/,
*WT0(509)/ 1.808157405985162D-07/,WT0(510)/-1.755919996494557D-07/,
*WT0(511)/ 1.705191718700136D-07/,WT0(512)/-1.655928973946416D-07/,
*WT0(513)/ 1.608089422670497D-07/,WT0(514)/-1.561631948835526D-07/,
*WT0(515)/ 1.516516624771349D-07/,WT0(516)/-1.472704676262496D-07/,
*WT0(517)/ 1.430158448819191D-07/,WT0(518)/-1.388841375627619D-07/,
*WT0(519)/ 1.348717946589134D-07/,WT0(520)/-1.309753677747614D-07/,
*WT0(521)/ 1.271915081246862D-07/,WT0(522)/-1.235169636417206D-07/,
*WT0(523)/ 1.199485762099940D-07/,WT0(524)/-1.164832789732080D-07/,
*WT0(525)/ 1.131180936862105D-07/,WT0(526)/-1.098501281312535D-07/,
*WT0(527)/ 1.066765736321394D-07/,WT0(528)/-1.035947026599537D-07/,
*WT0(529)/ 1.006018664975167D-07/,WT0(530)/-9.769549295058651D-08/,
*WT0(531)/ 9.487308412474974D-08/,WT0(532)/-9.213221428331440D-08/
DATA
*WT0(533)/ 8.947052777472484D-08/,WT0(534)/-8.688573700943115D-08/,
*WT0(535)/ 8.437562048443172D-08/,WT0(536)/-8.193802086874367D-08/,
*WT0(537)/ 7.957084315467929D-08/,WT0(538)/-7.727205286392824D-08/,
*WT0(539)/ 7.503967429747869D-08/,WT0(540)/-7.287178883148888D-08/,
*WT0(541)/ 7.076653326692979D-08/,WT0(542)/-6.872209823264986D-08/,
*WT0(543)/ 6.673672663335082D-08/,WT0(544)/-6.480871213716780D-08/,
*WT0(545)/ 6.293639770567428D-08/,WT0(546)/-6.111817417008917D-08/,
*WT0(547)/ 5.935247885127626D-08/,WT0(548)/-5.763779421770836D-08/,
*WT0(549)/ 5.597264657919956D-08/,WT0(550)/-5.435560481863042D-08/,
*WT0(551)/ 5.278527916288309D-08/,WT0(552)/-5.126031999018991D-08/,
*WT0(553)/ 4.977941667022704D-08/,WT0(554)/-4.834129643623350D-08/,
*WT0(555)/ 4.694472329047102D-08/,WT0(556)/-4.558849694284832D-08/,
*WT0(557)/ 4.427145178025873D-08/,WT0(558)/-4.299245586445184D-08/,
*WT0(559)/ 4.175040995827635D-08/,WT0(560)/-4.054424658081963D-08/,
*WT0(561)/ 3.937292909065092D-08/,WT0(562)/-3.823545079527342D-08/,
*WT0(563)/ 3.713083408552377D-08/,WT0(564)/-3.605812959486601D-08/,
*WT0(565)/ 3.501641538356351D-08/,WT0(566)/-3.400479614676831D-08/,
*WT0(567)/ 3.302240244515663D-08/,WT0(568)/-3.206838995736202D-08/,
*WT0(569)/ 3.114193875409117D-08/,WT0(570)/-3.024225259359901D-08/
DATA
*WT0(571)/ 2.936855823761587D-08/,WT0(572)/-2.852010478676213D-08/,
*WT0(573)/ 2.769616303496246D-08/,WT0(574)/-2.689602484264953D-08/,
*WT0(575)/ 2.611900252829978D-08/,WT0(576)/-2.536442827753140D-08/,
*WT0(577)/ 2.463165356908288D-08/,WT0(578)/-2.392004861730570D-08/,
*WT0(579)/ 2.322900183088905D-08/,WT0(580)/-2.255791928733344D-08/,
*WT0(581)/ 2.190622422255186D-08/,WT0(582)/-2.127335653510145D-08/,
*WT0(583)/ 2.065877230473273D-08/,WT0(584)/-2.006194332493974D-08/,
*WT0(585)/ 1.948235664905881D-08/,WT0(586)/-1.891951414942437D-08/,
*WT0(587)/ 1.837293208920017D-08/,WT0(588)/-1.784214070660012D-08/,
*WT0(589)/ 1.732668381117887D-08/,WT0(590)/-1.682611839179446D-08/,
*WT0(591)/ 1.634001423585344D-08/,WT0(592)/-1.586795355952947D-08/,
*WT0(593)/ 1.540953064868929D-08/,WT0(594)/-1.496435151022419D-08/,
*WT0(595)/ 1.453203353344868D-08/,WT0(596)/-1.411220516125227D-08/,
*WT0(597)/ 1.370450557074419D-08/,WT0(598)/-1.330858436314438D-08/,
*WT0(599)/ 1.292410126264865D-08/,WT0(600)/-1.255072582398340D-08/,
*WT0(601)/ 1.218813714839246D-08/,WT0(602)/-1.183602360782992D-08/,
*WT0(603)/ 1.149408257713515D-08/,WT0(604)/-1.116202017395058D-08/,
*WT0(605)/ 1.083955100614394D-08/,WT0(606)/-1.052639792651900D-08/,
*WT0(607)/ 1.022229179461678D-08/,WT0(608)/-9.926971245406734D-09/
DATA
*WT0(609)/ 9.640182464660921D-09/,WT0(610)/-9.361678970810806D-09/,
*WT0(611)/ 9.091221403102823D-09/,WT0(612)/-8.828577315878212D-09/,
*WT0(613)/ 8.573520978800615D-09/,WT0(614)/-8.325833182853652D-09/,
*WT0(615)/ 8.085301051938885D-09/,WT0(616)/-7.851717859915976D-09/,
*WT0(617)/ 7.624882852931747D-09/,WT0(618)/-7.404601076884107D-09/,
*WT0(619)/ 7.190683209868762D-09/,WT0(620)/-6.982945399464102D-09/,
*WT0(621)/ 6.781209104717332D-09/,WT0(622)/-6.585300942697731D-09/,
*WT0(623)/ 6.395052539483568D-09/,WT0(624)/-6.210300385452473D-09/,
*WT0(625)/ 6.030885694751333D-09/,WT0(626)/-5.856654268826800D-09/,
*WT0(627)/ 5.687456363899640D-09/,WT0(628)/-5.523146562267662D-09/,
*WT0(629)/ 5.363583647325650D-09/,WT0(630)/-5.208630482195534D-09/,
*WT0(631)/ 5.058153891863612D-09/,WT0(632)/-4.912024548723426D-09/,
*WT0(633)/ 4.770116861425010D-09/,WT0(634)/-4.632308866934630D-09/,
*WT0(635)/ 4.498482125712853D-09/,WT0(636)/-4.368521619921419D-09/,
*WT0(637)/ 4.242315654571151D-09/,WT0(638)/-4.119755761525383D-09/,
*WT0(639)/ 4.000736606276379D-09/,WT0(640)/-3.885155897415073D-09/,
*WT0(641)/ 3.772914298716528D-09/,WT0(642)/-3.663915343765296D-09/,
*WT0(643)/ 3.558065353046999D-09/,WT0(644)/-3.455273353434971D-09/,
*WT0(645)/ 3.355451000003056D-09/,WT0(646)/-3.258512500097394D-09/
DATA
*WT0(647)/ 3.164374539601736D-09/,WT0(648)/-3.072956211332787D-09/,
*WT0(649)/ 2.984178945504153D-09/,WT0(650)/-2.897966442199276D-09/,
*WT0(651)/ 2.814244605795313D-09/,WT0(652)/-2.732941481281439D-09/,
*WT0(653)/ 2.653987192416816D-09/,WT0(654)/-2.577313881675167D-09/,
*WT0(655)/ 2.502855651924429D-09/,WT0(656)/-2.430548509791296D-09/,
*WT0(657)/ 2.360330310661908D-09/,WT0(658)/-2.292140705271406D-09/,
*WT0(659)/ 2.225921087836540D-09/,WT0(660)/-2.161614545686758D-09/,
*WT0(661)/ 2.099165810350450D-09/,WT0(662)/-2.038521210054267D-09/,
*WT0(663)/ 1.979628623594711D-09/,WT0(664)/-1.922437435542387D-09/,
*WT0(665)/ 1.866898492740427D-09/,WT0(666)/-1.812964062059653D-09/,
*WT0(667)/ 1.760587789374176D-09/,WT0(668)/-1.709724659722168D-09/,
*WT0(669)/ 1.660330958617607D-09/,WT0(670)/-1.612364234479730D-09/,
*WT0(671)/ 1.565783262147887D-09/,WT0(672)/-1.520548007450427D-09/,
*WT0(673)/ 1.476619592797189D-09/,WT0(674)/-1.433960263766035D-09/,
*WT0(675)/ 1.392533356654690D-09/,WT0(676)/-1.352303266970005D-09/,
*WT0(677)/ 1.313235418827548D-09/,WT0(678)/-1.275296235235242D-09/,
*WT0(679)/ 1.238453109235514D-09/,WT0(680)/-1.202674375881138D-09/,
*WT0(681)/ 1.167929285020692D-09/,WT0(682)/-1.134187974870230D-09/,
*WT0(683)/ 1.101421446348478D-09/,WT0(684)/-1.069601538153474D-09/
DATA
*WT0(685)/ 1.038700902559248D-09/,WT0(686)/-1.008692981911727D-09/,
*WT0(687)/ 9.795519858036667D-10/,WT0(688)/-9.512528689090021D-10/,
*WT0(689)/ 9.237713094575600D-10/,WT0(690)/-8.970836883316330D-10/,
*WT0(691)/ 8.711670687664494D-10/,WT0(692)/-8.459991766370928D-10/,
*WT0(693)/ 8.215583813149323D-10/,WT0(694)/-7.978236770771082D-10/,
*WT0(695)/ 7.747746650530930D-10/,WT0(696)/-7.523915356928136D-10/,
*WT0(697)/ 7.306550517412669D-10/,WT0(698)/-7.095465317049981D-10/,
*WT0(699)/ 6.890478337962292D-10/,WT0(700)/-6.691413403408390D-10/,
*WT0(701)/ 6.498099426367938D-10/,WT0(702)/-6.310370262500165D-10/,
*WT0(703)/ 6.128064567350563D-10/,WT0(704)/-5.951025657682865D-10/,
*WT0(705)/ 5.779101376817111D-10/,WT0(706)/-5.612143963858077D-10/,
*WT0(707)/ 5.450009926701687D-10/,WT0(708)/-5.292559918710250D-10/,
*WT0(709)/ 5.139658618950525D-10/,WT0(710)/-4.991174615891697D-10/,
*WT0(711)/ 4.846980294463296D-10/,WT0(712)/-4.706951726376001D-10/,
*WT0(713)/ 4.570968563611062D-10/,WT0(714)/-4.438913934986793D-10/,
*WT0(715)/ 4.310674345713248D-10/,WT0(716)/-4.186139579848742D-10/,
*WT0(717)/ 4.065202605574395D-10/,WT0(718)/-3.947759483205284D-10/,
*WT0(719)/ 3.833709275859127D-10/,WT0(720)/-3.722953962705749D-10/,
*WT0(721)/ 3.615398354722752D-10/,WT0(722)/-3.510950012884991D-10/
DATA
*WT0(723)/ 3.409519168717552D-10/,WT0(724)/-3.311018647143929D-10/,
*WT0(725)/ 3.215363791563124D-10/,WT0(726)/-3.122472391091240D-10/,
*WT0(727)/ 3.032264609905071D-10/,WT0(728)/-2.944662918626933D-10/,
*WT0(729)/ 2.859592027691788D-10/,WT0(730)/-2.776978822639370D-10/,
*WT0(731)/ 2.696752301275724D-10/,WT0(732)/-2.618843512650130D-10/,
*WT0(733)/ 2.543185497794985D-10/,WT0(734)/-2.469713232177689D-10/,
*WT0(735)/ 2.398363569815098D-10/,WT0(736)/-2.329075189002498D-10/,
*WT0(737)/ 2.261788539610461D-10/,WT0(738)/-2.196445791904288D-10/,
*WT0(739)/ 2.132990786842053D-10/,WT0(740)/-2.071368987808525D-10/,
*WT0(741)/ 2.011527433743496D-10/,WT0(742)/-1.953414693624216D-10/,
*WT0(743)/ 1.896980822262837D-10/,WT0(744)/-1.842177317380848D-10/,
*WT0(745)/ 1.788957077923634D-10/,WT0(746)/-1.737274363579317D-10/,
*WT0(747)/ 1.687084755467094D-10/,WT0(748)/-1.638345117961281D-10/,
*WT0(749)/ 1.591013561618254D-10/,WT0(750)/-1.545049407174433D-10/,
*WT0(751)/ 1.500413150584345D-10/,WT0(752)/-1.457066429068751D-10/,
*WT0(753)/ 1.414971988143619D-10/,WT0(754)/-1.374093649601637D-10/,
*WT0(755)/ 1.334396280418735D-10/,WT0(756)/-1.295845762558885D-10/,
*WT0(757)/ 1.258408963651246D-10/,WT0(758)/-1.222053708514437D-10/,
*WT0(759)/ 1.186748751503467D-10/,WT0(760)/-1.152463749655566D-10/
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