1 /* This is Knut Petras' smolyak.c from SMOLPACK,
2 * modified by Chong Gu to steal the nodes and
3 * weights of the cubature for use in the
4 * R package gss.
5 *
6 * The program implements the delayed Smolyak cubature
7 * as discussed in the references by Knut Petras:
8 *
9 * [1] Asymptotically minimal Smolyak cubature, 2000
10 * [2] Fast Calculation of Coefficients in the Smolyak Algorithm
11 *
12 * Chong Gu, January 27, 2002, at Purdue.
13 */
14
15 # include <math.h>
16 # include <stdio.h>
17 # include <stdlib.h>
18
19 /* replace # include "smolyak.h" by one line -- C. Gu */
20 # define maxdim 40
21 /* replace # include "smolyak.h" by one line -- C. Gu */
22
23 #define uniw 256 /* total # of nodes of quadrature formulae */
24 #define fn 9 /* # of different basic formula */
25 #define gesfn 50 /* # of basic formulae (incl. multiplicities) */
26
27 static double quafo; /* cubature result */
28 static double x[maxdim]; /* function argument */
29 static double xnu[fn][uniw],dnu[fn][uniw]; /* Delta-parameter */
30 static double fsumme, wsum, wprod, summe; /* working var's */
31 static int d, q; /* cubature formula parameter */
32 static int n[fn], ninv[fn], sw[gesfn]; /* working var's */
33 int count, wcount; /* counter of f-calls and coefficient calls */
34
35 static int indeces[maxdim], argind[maxdim]; /* formula and nodal indeces */
36 static int indsum[maxdim][maxdim]; /* parameter for 'divide et conquer' */
37
38 static int anzw[uniw],
39 lookind[fn][uniw],
40 invlook[fn][uniw], maxind; /* tree parameter */
41
42 static int wind[maxdim]; /* Parameter for slow coefficient calculation */
43
44 static double (*f)(int, double x[]); /* integrand (global) */
45 static void formula(int,int); /* sub-formula "between
46 two dimensions" */
47 static double eval(int); /* sub-formula calculator */
48 static double fsum(int); /* sum(f(+-x_nu))
49 (use of symmetry) */
50
51 /* get pt and wt from formula1, eval1, fsum1 -- C. Gu */
52 static double wtt;
53 static void formula1(int, int, double *pt, double *wt);
54 static void eval1(int, double *pt, double *wt);
55 static void fsum1(int, double *pt, double *wt);
56 /* get pt and wt from formula1, eval1, fsum1 -- C. Gu */
57
58 static void init(); /* initialization */
59
60 static double calccoeff(int); /* coefficient calculator */
61 /* static double calccoeff2(int,int); */ /* coefficient calculator (slow) */
62 static double wl(int, int, int); /* 'divide */
63 static double we(int, int, int); /* and */
64 static void sumind(int, int); /* conquer' */
65
66
67 /*************** tree definitions: *************************/
68
69 struct tnode {
70 int empty;
71 double *coeff;
72 int *belegt;
73 struct tnode *left;
74 struct tnode *right;
75 };
76
77 static struct tnode *root;
78
79 static double coeff(); /* tree manager */
80
81 static struct tnode *talloc(void); /* node generator */
82 static void frei(struct tnode *p); /* tree eraser */
83
84
85 /* Start of R interface -- C. Gu */
f_dummy(int dd,double x[])86 double f_dummy(int dd, double x[])
87 {
88 count++;
89 return 1;
90 }
size_smolyak(int * dd,int * qq,int * size)91 void size_smolyak(int *dd, int *qq, int *size)
92 /********************** get size ***************************/
93 {
94 d=*dd;
95 q=*qq;
96 f=f_dummy;
97 init();
98 formula(1,q-d);
99 frei(root);
100 *size = count;
101 }
102
quad_smolyak(int * dd,int * qq,double * pt,double * wt)103 void quad_smolyak(int *dd, int *qq, double *pt, double *wt)
104 /********************** get pt and wt ***************************/
105 {
106 d=*dd;
107 q=*qq;
108 f=f_dummy;
109 init();
110 formula1(1,q-d,pt,wt);
111 frei(root);
112 }
113 /* End of R interface -- C. Gu */
114
115
int_smolyak(int dd,int qq,double (* ff)(int,double xx[]),int size)116 double int_smolyak(int dd, int qq, double(*ff)(int,double xx[]), int size)
117 /********************** main program ***************************/
118 /*** for formula parameter dd<40, qq-dd<48 ******/
119 {
120 /* make parameter global: */
121 d=dd;
122 q=qq;
123 f=ff;
124 /* Initialisation */
125 init();
126
127 /* call of Smolyak algorithm */
128 formula(1,q-d);
129 /* free space */
130 frei(root);
131 /* statistics ( if desired ) */
132 /* if (size) {
133 printf("%i function calls and ", count);
134 printf("%i coefficient calculations \n", wcount);}*/
135
136 return quafo;
137 }
138
formula(int k,int l)139 void formula(int k,int l)
140 /* If k==d: evaluation. */
141 /* Else: */
142 /* determine the required formula */
143 /* l is the index sum that may be distributed */
144 /* to the remaining dimensions */
145 {
146 int i;
147 if (k==d+1)
148 {
149 quafo = quafo + eval(0);
150 }
151 else
152 for (i=0; (i<=l) ; i++)
153 /* Use only non-dummy-formulae */
154 if (sw[i]<fn) {
155 indeces[k] = sw[i];
156 formula(k+1,l-i);
157 };
158 }
159
160 /* get pt and wt from formula1 -- C. Gu */
formula1(int k,int l,double * pt,double * wt)161 void formula1(int k,int l, double *pt, double *wt)
162 {
163 int i;
164 if (k==d+1)
165 {
166 eval1(0,pt,wt);
167 }
168 else
169 for (i=0; (i<=l) ; i++)
170 if (sw[i]<fn) {
171 indeces[k] = sw[i];
172 formula1(k+1,l-i,pt,wt);
173 };
174 }
175 /* get pt and wt from formula1 -- C. Gu */
176
eval(int k)177 double eval(int k)
178 /* Calculates value of a product formula */
179 {
180 int i;
181 double dummy;
182 if (k==0)
183 {summe=0;
184 dummy=eval(1);}
185 else if (k==d+1)
186 /* summation corresponding to one coefficient */
187 /* USUAL if uncommented : */
188 /* summe = summe + calccoeff2(0,q-d) * fsum(0); */
189 /* DAC if uncommented : */
190 /* summe = summe + calccoeff(q-d) * fsum(0); */
191 /* TREE (recommended method): */
192 summe = summe + coeff() * fsum(0);
193 /* all coefficients 1 (speed test) */
194 /* summe = summe + fsum(0); */
195 else
196 /* choice of the nodes */
197 for (i=0; i<=n[indeces[k]]; i++)
198 {
199 argind[k]=i;
200 dummy=eval(k+1);
201 };
202 return summe;
203 }
204
205 /* get pt and wt from eval1 -- C. Gu */
eval1(int k,double * pt,double * wt)206 void eval1(int k, double *pt, double *wt)
207 {
208 int i;
209 if (k==0) eval1(1,pt,wt);
210 else if (k==d+1) {
211 wtt = coeff();
212 fsum1(0,pt,wt);
213 }
214 else
215 for (i=0; i<=n[indeces[k]]; i++)
216 {
217 argind[k]=i;
218 eval1(k+1,pt,wt);
219 };
220 }
221 /* get pt and wt from eval1 -- C. Gu */
222
223
224 /********************** Coefficients ************************/
225 /* Tree-functions: */
226
coeff()227 double coeff ( )
228 /* looks for existing coefficient or calls its
229 calculation */
230 {
231 int i,j;
232 struct tnode *p, *pt;
233 p=root;
234
235 /* Initialisation */
236 for (i=0; i<maxind; i++) anzw[i]=0;
237
238 /* Frequency anzw[ ] of 1-dim nodes */
239 for (i=1; i<=d; i++) anzw[lookind[indeces[i]][argind[i]]]++;
240
241 /* Search in the tree according to anzw[..] */
242 for (j=maxind-1; j>=1; j--){
243
244 /* anzw[j] to the L E F T */
245 if (p->left==NULL){ /* if node not existing, node generation : */
246 p->left = (struct tnode *) calloc(maxdim, sizeof(struct tnode));
247 pt=(p->left+anzw[j]);
248 pt->left=pt->right=NULL;
249 pt->empty = 1;
250 p=pt;}
251 else
252 p=(p->left+anzw[j]);
253
254 /* one to the R I G H T */
255 if (p->right==NULL){ /* if node not existing: */
256 pt=talloc(); /* node generation */
257 pt->empty=1;
258 pt->left=pt->right=NULL;
259 if (j==1){ /* leaf with coefficient */
260 pt->coeff=(double *) calloc(maxdim, sizeof(double));
261 pt->belegt=(int *) calloc(maxdim, sizeof(int));
262 pt->empty=0;
263 };
264 p->right=pt;
265 };
266 p=p->right;
267 }
268
269 if (!*(p->belegt+anzw[0])){ /* evtl. coeff.-calc. necessary */
270 wcount++;
271 *(p->coeff +anzw[0]) = calccoeff(q-d);
272 *(p->belegt+anzw[0]) =1;
273 };
274 return *(p->coeff +anzw[0]);
275 }
276
frei(struct tnode * p)277 void frei(struct tnode *p)
278 /* tree eraser */
279 {
280 if (!(p->empty)) {
281 free (p->coeff); free (p->belegt);};
282 if (!(p->left ==NULL)) frei(p->left);
283 if (!(p->right ==NULL)) frei(p->right);
284 free(p);
285 }
286
talloc(void)287 struct tnode *talloc(void)
288 /* Space for new tree-node */
289 {
290 return (struct tnode *) malloc (sizeof(struct tnode));
291 }
292
293 /******** tree-functions finished ******/
294
295
sumind(int r,int s)296 void sumind(int r, int s)
297 /* Calculation of sums of formula indices at division
298 of dimension r...s */
299 {
300 int q;
301 if (s==r)
302 indsum[r][s] = ninv[indeces[r]];
303 else
304 {
305 q=(r+s)/2;
306 sumind(r,q);
307 sumind(q+1,s);
308 indsum[r][s] = indsum[r][q] + indsum[q+1][s];
309 };
310 }
311
312
calccoeff(int l)313 double calccoeff (int l)
314 {
315 sumind(1,d); /* calculation of parameters of subdivision */
316 return wl(1,d,l); /* start of 'divide and conquer' */
317 }
318
wl(int r,int s,int l)319 double wl(int r,int s, int l)
320 /* sums in dimension s...r with sum of formula numbers <=l */
321 {
322 double sum=0;
323 int i,q, p;
324 if (r==s) /* one-dimensional */
325 {
326 p=lookind[indeces[r]][argind[r]];
327 for (i=ninv[indeces[r]]; i<=l; i++) {
328 if (sw[i]<fn) {
329 if (i==0) sum+= dnu[0][0];
330 else {
331 if (indeces[r]==0) sum+=dnu[sw[i]][0];
332 else {
333 sum+=dnu[sw[i]][invlook[sw[i]][p]];
334 }
335 }
336 }
337 }
338 return sum;
339 }
340 else /* dimension reduction */
341 {
342 q=(r+s)/2;
343 for (i=indsum[r][q]; i<=l-indsum[q+1][s]; i++)
344 sum+=we(r,q,i)*wl(q+1,s,l-i);
345 return sum;
346 };
347 }
348
we(int r,int s,int l)349 double we(int r,int s, int l)
350 /* sums in dimension s...r with sum of formula numbers <=l */
351 {
352 double sum=0;
353 int i,q;
354 if (r==s) { /* one-dimensional */
355 if (sw[l]<fn) {
356 if (sw[l]==0) return dnu[0][0];
357 else
358 if (indeces[r]==0) return dnu[sw[l]][0];
359 else return dnu[sw[l]]
360 [invlook[sw[l]][lookind[indeces[r]][argind[r]]]];}
361 else return 0;
362 }
363 else /* dimension reduction */
364 {
365 q=(r+s)/2;
366 for (i=indsum[r][q]; i<=l-indsum[q+1][s]; i++)
367 sum+=we(r,q,i)*we(q+1,s,l-i);
368 return sum;
369 }
370 }
371
372
373
374
375
376 /********** method USUAL: (slow) ******************************/
377 /*
378
379 double calccoeff2 (int k, int l)
380 {
381 int i;
382 double dummy;
383 if (k==0)
384 {
385 wsum=0;
386 wcount++;
387 dummy=calccoeff2(1,l);}
388 else if (k==d+1)
389 {
390 wprod = 1;
391 for (i=1; i<=d; i++)
392 if (indeces[i]==0)
393 wprod *= dnu[wind[i]][0];
394 else
395 wprod *=
396 dnu[wind[i]][invlook[wind[i]][lookind[indeces[i]][argind[i]]]];
397 wsum+=wprod;
398 }
399 else
400 {
401 i=indeces[k];
402 while (ninv[i]<=l){
403 wind[k]=i;
404 dummy=calccoeff2(k+1, l-ninv[i]);
405 i++;}
406 }
407 return wsum;
408 }
409
410 */
411 /************* coefficients finished **********************/
412
413 /**************************************************************/
414
415 /************ sums of functions values sum(f(+/- x_i)) ********/
416
fsum(int k)417 double fsum (int k)
418 {
419 double dummy;
420 if (k==0)
421 {
422 fsumme = 0;
423 dummy=fsum(1);
424 }
425 else if (k==d+1)
426 {
427 fsumme+=(*f)(d,x);
428 }
429 else
430 if (indeces[k]==0) /* differentiate 'central node', others */
431 {
432 x[k-1]=0.5;
433 dummy=fsum(k+1);
434 }
435 else
436 {
437 x[k-1]= xnu[indeces[k]][2*argind[k]+1];
438 dummy=fsum(k+1);
439 x[k-1] = 1-x[k-1];
440 dummy=fsum(k+1);
441 }
442 return fsumme;
443 }
444
445 /* get pt and wt from fsum1 -- C. Gu */
fsum1(int k,double * pt,double * wt)446 void fsum1 (int k, double *pt, double *wt)
447 {
448 int i;
449 if (k==0) fsum1(1,pt,wt);
450 else if (k==d+1)
451 {
452 for(i=0;i<d;i++) pt[d*count+i]=x[i];
453 wt[count]=wtt;
454 fsumme+=(*f)(d,x);
455 }
456 else
457 if (indeces[k]==0)
458 {
459 x[k-1]=0.5;
460 fsum1(k+1,pt,wt);
461 }
462 else
463 {
464 x[k-1]= xnu[indeces[k]][2*argind[k]+1];
465 fsum1(k+1,pt,wt);
466 x[k-1] = 1-x[k-1];
467 fsum1(k+1,pt,wt);
468 }
469 }
470 /* get pt and wt from fsum1 -- C. Gu */
471
472
473 /**************************************************************/
474
475 /* initialisation */
476
init()477 void init()
478 {
479 int i, j, formfakt, maxform;
480 int nj[fn] ={1,3,7,15,31,63}; /* # nodes of different basic formulae */
481 int freq[fn]={1,2,3, 6,12,24}; /* frequencies of basic formulae */
482
483 /* some parameter calculations */
484 n[0]=0;
485 j=0;
486 ninv[0]=0;
487 for (i=1; i<fn; i++){
488 n[i]=(nj[i]-nj[i-1]-2)/2;
489 j=j+freq[i-1];
490 ninv[i]=j;}
491
492 for (i=0; i<gesfn; i++) sw[i]=fn;
493 for (i=0; i<fn; i++) sw[ninv[i]]=i;
494
495 /* output quantities */
496 wcount=0;
497 count=0;
498 quafo=0;
499
500
501 /* number of the 'largest' used formula */
502 i=q-d;
503 maxform=0;
504 while (i>=ninv[maxform+1]) maxform=maxform+1;
505
506 /* total number of used 1-dim nodes */
507 maxind = (nj[maxform]+1)/2;
508
509 /* table of 1-dim nodal numbers 0..maxind-1 corresponding
510 to a combination formula number/nodal number
511 and inverse formula */
512 lookind[0][0] = 0;
513 for (i=1; i<=maxform; i++) {
514 formfakt=pow(2, maxform-i);
515 for (j=0; j<(nj[i]+1)/4; j++) lookind[i][j] = formfakt*(2*j+1);
516 /* in a linear ordering of all used nodes, the (2j+1)-th
517 node of the i-th basic formula is lookind[i][j]-th node */
518 for (j=0; j<(nj[i]+1)/2; j++) invlook[i][formfakt*j] = j;
519 /* the lookind[i][2^(maxform-i)]-th node in a linear
520 ordering of all used nodes is the j-th node of the
521 i-th basic formula. Note that maxrorm is the number
522 of used different basic formulae */
523 };
524
525
526 /* root of the coefficient TREE */
527 root=talloc();
528 root->empty=1;
529 root->left=root->right=NULL;
530
531 /* one dimensional formulae (Deltas) */
532
533
534 xnu[0][0] = 0.5;
535 dnu[0][0] = 1.0;
536 xnu[1][0] = 5.000000000000000E-001;
537 xnu[1][1] = 8.8729833462074168851793E-001;
538 dnu[1][0] = -5.5555555555555555555556E-001;
539 dnu[1][1] = 2.7777777777777777777778E-001;
540 xnu[2][0] = 5.0000000000000000000000E-001;
541 xnu[2][1] = 7.1712187467340127900104E-001;
542 xnu[2][2] = 8.8729833462074168851793E-001;
543 xnu[2][3] = 9.8024563435401014171175E-001;
544 dnu[2][0] = -2.1898617511520737327189E-001;
545 dnu[2][1] = 2.0069870738798111145253E-001;
546 dnu[2][2] = -1.4353373284361105741349E-001;
547 dnu[2][3] = 5.2328113013233632596912E-002;
548 xnu[3][0] = 5.0000000000000000000000E-001;
549 xnu[3][1] = 6.1169334321448344081410E-001;
550 xnu[3][2] = 7.1712187467340127900104E-001;
551 xnu[3][3] = 8.1055147336861320147034E-001;
552 xnu[3][4] = 8.8729833462074168851793E-001;
553 xnu[3][5] = 9.4422961643612849944521E-001;
554 xnu[3][6] = 9.8024563435401014171175E-001;
555 xnu[3][7] = 9.9691598160637751110426E-001;
556 dnu[3][0] = -1.1270301943013372747934E-001;
557 dnu[3][1] = 1.0957842920079374820185E-001;
558 dnu[3][2] = -1.0038444269948660093556E-001;
559 dnu[3][3] = 8.5755954568195690393677E-002;
560 dnu[3][4] = -6.7036417312274610184300E-002;
561 dnu[3][5] = 4.6463597657562268842947E-002;
562 dnu[3][6] = -2.6526471514693762748452E-002;
563 dnu[3][7] = 8.5008598149701301695137E-003;
564 xnu[4][0] = 5.0000000000000000000000E-001;
565 xnu[4][1] = 5.5624447156659331287292E-001;
566 xnu[4][2] = 6.1169334321448344081410E-001;
567 xnu[4][3] = 6.6556769662898841654632E-001;
568 xnu[4][4] = 7.1712187467340127900104E-001;
569 xnu[4][5] = 7.6565987182218781198605E-001;
570 xnu[4][6] = 8.1055147336861320147034E-001;
571 xnu[4][7] = 8.5124810324576353930490E-001;
572 xnu[4][8] = 8.8729833462074168851793E-001;
573 xnu[4][9] = 9.1836296908443436775138E-001;
574 xnu[4][10] = 9.4422961643612849944521E-001;
575 xnu[4][11] = 9.6482742871487002833506E-001;
576 xnu[4][12] = 9.8024563435401014171175E-001;
577 xnu[4][13] = 9.9076557477687005343368E-001;
578 xnu[4][14] = 9.9691598160637751110426E-001;
579 xnu[4][15] = 9.9954906248383379883111E-001;
580 dnu[4][0] = -5.6377621538718997889636E-002;
581 dnu[4][1] = 5.5978436510476728440072E-002;
582 dnu[4][2] = -5.4789218672831429083502E-002;
583 dnu[4][3] = 5.2834946790117404871908E-002;
584 dnu[4][4] = -5.0157125382596721131319E-002;
585 dnu[4][5] = 4.6813554990632236808329E-002;
586 dnu[4][6] = -4.2877994543200514816583E-002;
587 dnu[4][7] = 3.8439810249501765521353E-002;
588 dnu[4][8] = -3.3603750473896758409784E-002;
589 dnu[4][9] = 2.8489754747061678706099E-002;
590 dnu[4][10] = -2.3232151026683275572245E-002;
591 dnu[4][11] = 1.7978551653564661048389E-002;
592 dnu[4][12] = -1.2897842450451543066137E-002;
593 dnu[4][13] = 8.2230249271939054668942E-003;
594 dnu[4][14] = -4.2835769453095770463562E-003;
595 dnu[4][15] = 1.2723903957809372077014E-003;
596 xnu[5][0] = 5.0000000000000000000000E-001;
597 xnu[5][1] = 5.2817215652329639498598E-001;
598 xnu[5][2] = 5.5624447156659331287292E-001;
599 xnu[5][3] = 5.8411762577610373249116E-001;
600 xnu[5][4] = 6.1169334321448344081410E-001;
601 xnu[5][5] = 6.3887491101091215753268E-001;
602 xnu[5][6] = 6.6556769662898841654632E-001;
603 xnu[5][7] = 6.9167966209936517345824E-001;
604 xnu[5][8] = 7.1712187467340127900104E-001;
605 xnu[5][9] = 7.4180901347292051378108E-001;
606 xnu[5][10] = 7.6565987182218781198605E-001;
607 xnu[5][11] = 7.8859785502602290742185E-001;
608 xnu[5][12] = 8.1055147336861320147034E-001;
609 xnu[5][13] = 8.3145483001239029773051E-001;
610 xnu[5][14] = 8.5124810324576353930490E-001;
611 xnu[5][15] = 8.6987802217634737933861E-001;
612 xnu[5][16] = 8.8729833462074168851793E-001;
613 xnu[5][17] = 9.0347026597510880592815E-001;
614 xnu[5][18] = 9.1836296908443436775138E-001;
615 xnu[5][19] = 9.3195396909684523857321E-001;
616 xnu[5][20] = 9.4422961643612849944521E-001;
617 xnu[5][21] = 9.5518557847850214624890E-001;
618 xnu[5][22] = 9.6482742871487002833506E-001;
619 xnu[5][23] = 9.7317142918670145257425E-001;
620 xnu[5][24] = 9.8024563435401014171175E-001;
621 xnu[5][25] = 9.8609143737429089828903E-001;
622 xnu[5][26] = 9.9076557477687005343368E-001;
623 xnu[5][27] = 9.9434237877371473996926E-001;
624 xnu[5][28] = 9.9691598160637751110426E-001;
625 xnu[5][29] = 9.9860312968611097953823E-001;
626 xnu[5][30] = 9.9954906248383379883111E-001;
627 xnu[5][31] = 9.9993644406017880596898E-001;
628 dnu[5][0] = -2.8188814180191987109744E-002;
629 dnu[5][1] = 2.8138849915627150636298E-002;
630 dnu[5][2] = -2.7989218255238568736295E-002;
631 dnu[5][3] = 2.7740702178279681993919E-002;
632 dnu[5][4] = -2.7394605263980886602235E-002;
633 dnu[5][5] = 2.6952749667633031963438E-002;
634 dnu[5][6] = -2.6417473395059144940870E-002;
635 dnu[5][7] = 2.5791626976024229388405E-002;
636 dnu[5][8] = -2.5078569652948020678807E-002;
637 dnu[5][9] = 2.4282165203336599357974E-002;
638 dnu[5][10] = -2.3406777495318230607005E-002;
639 dnu[5][11] = 2.2457265826816098707127E-002;
640 dnu[5][12] = -2.1438980012491308330637E-002;
641 dnu[5][13] = 2.0357755058472159466947E-002;
642 dnu[5][14] = -1.9219905124773999502032E-002;
643 dnu[5][15] = 1.8032216390391286320054E-002;
644 dnu[5][16] = -1.6801938573891486499334E-002;
645 dnu[5][17] = 1.5536775555843982439942E-002;
646 dnu[5][18] = -1.4244877374144904399846E-002;
647 dnu[5][19] = 1.2934839663607373455379E-002;
648 dnu[5][20] = -1.1615723310923858549074E-002;
649 dnu[5][21] = 1.0297116957956355574594E-002;
650 dnu[5][22] = -8.9892758695005258819409E-003;
651 dnu[5][23] = 7.7033752332797489010654E-003;
652 dnu[5][24] = -6.4518989979126939693347E-003;
653 dnu[5][25] = 5.2491234548106609491364E-003;
654 dnu[5][26] = -4.1115209485759406322653E-003;
655 dnu[5][27] = 3.0577534110586231698391E-003;
656 dnu[5][28] = -2.1084676488811257036154E-003;
657 dnu[5][29] = 1.2895248973428441362139E-003;
658 dnu[5][30] = -6.3981211766590320201509E-004;
659 dnu[5][31] = 1.8161074092276532984679E-004;
660 xnu[6][0] = 5.0000000000000000000000E-001;
661 xnu[6][1] = 5.1409232447487284716970E-001;
662 xnu[6][2] = 5.2817215652329639498598E-001;
663 xnu[6][3] = 5.4222702004185544185509E-001;
664 xnu[6][4] = 5.5624447156659331287292E-001;
665 xnu[6][5] = 5.7021211657628008729691E-001;
666 xnu[6][6] = 5.8411762577610373249116E-001;
667 xnu[6][7] = 5.9794875135555007695773E-001;
668 xnu[6][8] = 6.1169334321448344081410E-001;
669 xnu[6][9] = 6.2533936515174158830648E-001;
670 xnu[6][10] = 6.3887491101091215753268E-001;
671 xnu[6][11] = 6.5228822077835702166766E-001;
672 xnu[6][12] = 6.6556769662898841654632E-001;
673 xnu[6][13] = 6.7870191891576607618811E-001;
674 xnu[6][14] = 6.9167966209936517345824E-001;
675 xnu[6][15] = 7.0448991061494433620452E-001;
676 xnu[6][16] = 7.1712187467340127900104E-001;
677 xnu[6][17] = 7.2956500599491616643675E-001;
678 xnu[6][18] = 7.4180901347292051378108E-001;
679 xnu[6][19] = 7.5384387876685830107739E-001;
680 xnu[6][20] = 7.6565987182218781198605E-001;
681 xnu[6][21] = 7.7724756631596627443319E-001;
682 xnu[6][22] = 7.8859785502602290742185E-001;
683 xnu[6][23] = 7.9970196512112144648713E-001;
684 xnu[6][24] = 8.1055147336861320147034E-001;
685 xnu[6][25] = 8.2113832125487975688706E-001;
686 xnu[6][26] = 8.3145483001239029773051E-001;
687 xnu[6][27] = 8.4149371554553961404354E-001;
688 xnu[6][28] = 8.5124810324576353930490E-001;
689 xnu[6][29] = 8.6071154268504945774249E-001;
690 xnu[6][30] = 8.6987802217634737933861E-001;
691 xnu[6][31] = 8.7874198319025681896313E-001;
692 xnu[6][32] = 8.8729833462074168851793E-001;
693 xnu[6][33] = 8.9554246689992418071732E-001;
694 xnu[6][34] = 9.0347026597510880592815E-001;
695 xnu[6][35] = 9.1107812718249020368626E-001;
696 xnu[6][36] = 9.1836296908443436775138E-001;
697 xnu[6][37] = 9.2532224738417513987891E-001;
698 xnu[6][38] = 9.3195396909684523857321E-001;
699 xnu[6][39] = 9.3825670724235263487081E-001;
700 xnu[6][40] = 9.4422961643612849944521E-001;
701 xnu[6][41] = 9.4987244988847001831932E-001;
702 xnu[6][42] = 9.5518557847850214624890E-001;
703 xnu[6][43] = 9.6017001273500621036491E-001;
704 xnu[6][44] = 9.6482742871487002833506E-001;
705 xnu[6][45] = 9.6916019888979644182741E-001;
706 xnu[6][46] = 9.7317142918670145257425E-001;
707 xnu[6][47] = 9.7686500321288056820737E-001;
708 xnu[6][48] = 9.8024563435401014171175E-001;
709 xnu[6][49] = 9.8331892577920828354614E-001;
710 xnu[6][50] = 9.8609143737429089828903E-001;
711 xnu[6][51] = 9.8857075731985285707820E-001;
712 xnu[6][52] = 9.9076557477687005343368E-001;
713 xnu[6][53] = 9.9268574979926018555688E-001;
714 xnu[6][54] = 9.9434237877371473996926E-001;
715 xnu[6][55] = 9.9574786058905306619925E-001;
716 xnu[6][56] = 9.9691598160637751110426E-001;
717 xnu[6][57] = 9.9786205234920359425472E-001;
718 xnu[6][58] = 9.9860312968611097953823E-001;
719 xnu[6][59] = 9.9915831765920369626532E-001;
720 xnu[6][60] = 9.9954906248383379883111E-001;
721 xnu[6][61] = 9.9979939983595534162598E-001;
722 xnu[6][62] = 9.9993644406017880596898E-001;
723 xnu[6][63] = 9.9999121517744579929001E-001;
724 dnu[6][0] = -1.4094407090096179346916E-002;
725 dnu[6][1] = 1.4088159516508301065327E-002;
726 dnu[6][2] = -1.4069424957813575318149E-002;
727 dnu[6][3] = 1.4038227896908623303424E-002;
728 dnu[6][4] = -1.3994609127619079851888E-002;
729 dnu[6][5] = 1.3938625738306850804262E-002;
730 dnu[6][6] = -1.3870351089139840996960E-002;
731 dnu[6][7] = 1.3789874783240936517434E-002;
732 dnu[6][8] = -1.3697302631990716258054E-002;
733 dnu[6][9] = 1.3592756614812395909604E-002;
734 dnu[6][10] = -1.3476374833816515981719E-002;
735 dnu[6][11] = 1.3348311463725179953077E-002;
736 dnu[6][12] = -1.3208736697529129965519E-002;
737 dnu[6][13] = 1.3057836688353048840249E-002;
738 dnu[6][14] = -1.2895813488012114694202E-002;
739 dnu[6][15] = 1.2722884982732382906287E-002;
740 dnu[6][16] = -1.2539284826474884353420E-002;
741 dnu[6][17] = 1.2345262372243838454530E-002;
742 dnu[6][18] = -1.2141082601668299678987E-002;
743 dnu[6][19] = 1.1927026053019270040223E-002;
744 dnu[6][20] = -1.1703388747657003100662E-002;
745 dnu[6][21] = 1.1470482114693874380400E-002;
746 dnu[6][22] = -1.1228632913408049353564E-002;
747 dnu[6][23] = 1.0978183152658912469630E-002;
748 dnu[6][24] = -1.0719490006251933623228E-002;
749 dnu[6][25] = 1.0452925722906011926111E-002;
750 dnu[6][26] = -1.0178877529236079733474E-002;
751 dnu[6][27] = 9.8977475240487497440139E-003;
752 dnu[6][28] = -9.6099525623638830096600E-003;
753 dnu[6][29] = 9.3159241280693950931570E-003;
754 dnu[6][30] = -9.0161081951956431600270E-003;
755 dnu[6][31] = 8.7109650797320868735761E-003;
756 dnu[6][32] = -8.4009692870519326354323E-003;
757 dnu[6][33] = 8.0866093647888599709740E-003;
758 dnu[6][34] = -7.7683877779219912199780E-003;
759 dnu[6][35] = 7.4468208324075910174052E-003;
760 dnu[6][36] = -7.1224386864583871530823E-003;
761 dnu[6][37] = 6.7957855048827733947865E-003;
762 dnu[6][38] = -6.4674198318036867280122E-003;
763 dnu[6][39] = 6.1379152800413850434832E-003;
764 dnu[6][40] = -5.8078616599775673581358E-003;
765 dnu[6][41] = 5.4778666939189508240164E-003;
766 dnu[6][42] = -5.1485584789781778127510E-003;
767 dnu[6][43] = 4.8205888648512683476492E-003;
768 dnu[6][44] = -4.4946378920320673048077E-003;
769 dnu[6][45] = 4.1714193769840788527921E-003;
770 dnu[6][46] = -3.8516876166398779769824E-003;
771 dnu[6][47] = 3.5362449977167777340232E-003;
772 dnu[6][48] = -3.2259500250877643515858E-003;
773 dnu[6][49] = 2.9217249379178197537798E-003;
774 dnu[6][50] = -2.6245617274062313865695E-003;
775 dnu[6][51] = 2.3355251860571608737027E-003;
776 dnu[6][52] = -2.0557519892906183110438E-003;
777 dnu[6][53] = 1.7864463917586498246922E-003;
778 dnu[6][54] = -1.5288767059708576017734E-003;
779 dnu[6][55] = 1.2843824718970101865639E-003;
780 dnu[6][56] = -1.0544075979161109798758E-003;
781 dnu[6][57] = 8.4057143271073495315687E-004;
782 dnu[6][58] = -6.4476285603763544016464E-004;
783 dnu[6][59] = 4.6918492427119075039702E-004;
784 dnu[6][60] = -3.1627461843371723357680E-004;
785 dnu[6][61] = 1.8887332316349233013718E-004;
786 dnu[6][62] = -9.1240958700071150936623E-005;
787 dnu[6][63] = 2.5268047603931258812333E-005;
788 xnu[7][0] = 5.0000000000000000000000E-001;
789 xnu[7][1] = 5.0704694320539123130709E-001;
790 xnu[7][2] = 5.1409232447487284716970E-001;
791 xnu[7][3] = 5.2113458238268180160620E-001;
792 xnu[7][4] = 5.2817215652329639498598E-001;
793 xnu[7][5] = 5.3520348802142758953165E-001;
794 xnu[7][6] = 5.4222702004185544185509E-001;
795 xnu[7][7] = 5.4924119829905960104514E-001;
796 xnu[7][8] = 5.5624447156659331287292E-001;
797 xnu[7][9] = 5.6323529218615098342533E-001;
798 xnu[7][10] = 5.7021211657628008729691E-001;
799 xnu[7][11] = 5.7717340574068905434622E-001;
800 xnu[7][12] = 5.8411762577610373249116E-001;
801 xnu[7][13] = 5.9104324837962609912320E-001;
802 xnu[7][14] = 5.9794875135555007695773E-001;
803 xnu[7][15] = 6.0483261912159059738317E-001;
804 xnu[7][16] = 6.1169334321448344081410E-001;
805 xnu[7][17] = 6.1852942279491486360633E-001;
806 xnu[7][18] = 6.2533936515174158830648E-001;
807 xnu[7][19] = 6.3212168620546338097247E-001;
808 xnu[7][20] = 6.3887491101091215753268E-001;
809 xnu[7][21] = 6.4559757425912334098185E-001;
810 xnu[7][22] = 6.5228822077835702166766E-001;
811 xnu[7][23] = 6.5894540603423834159087E-001;
812 xnu[7][24] = 6.6556769662898841654632E-001;
813 xnu[7][25] = 6.7215367079971901138831E-001;
814 xnu[7][26] = 6.7870191891576607618811E-001;
815 xnu[7][27] = 6.8521104397503911506877E-001;
816 xnu[7][28] = 6.9167966209936517345824E-001;
817 xnu[7][29] = 6.9810640302880796959126E-001;
818 xnu[7][30] = 7.0448991061494433620452E-001;
819 xnu[7][31] = 7.1082884331308165002815E-001;
820 xnu[7][32] = 7.1712187467340127900104E-001;
821 xnu[7][33] = 7.2336769383101423687111E-001;
822 xnu[7][34] = 7.2956500599491616643675E-001;
823 xnu[7][35] = 7.3571253293582943846704E-001;
824 xnu[7][36] = 7.4180901347292051378108E-001;
825 xnu[7][37] = 7.4785320395938073008506E-001;
826 xnu[7][38] = 7.5384387876685830107739E-001;
827 xnu[7][39] = 7.5977983076872851099646E-001;
828 xnu[7][40] = 7.6565987182218781198605E-001;
829 xnu[7][41] = 7.7148283324915574524615E-001;
830 xnu[7][42] = 7.7724756631596627443319E-001;
831 xnu[7][43] = 7.8295294271182721131149E-001;
832 xnu[7][44] = 7.8859785502602290742185E-001;
833 xnu[7][45] = 7.9418121722383127071718E-001;
834 xnu[7][46] = 7.9970196512112144648713E-001;
835 xnu[7][47] = 8.0515905685759320007779E-001;
836 xnu[7][48] = 8.1055147336861320147034E-001;
837 xnu[7][49] = 8.1587821885559711520679E-001;
838 xnu[7][50] = 8.2113832125487975688706E-001;
839 xnu[7][51] = 8.2633083270500874805039E-001;
840 xnu[7][52] = 8.3145483001239029773051E-001;
841 xnu[7][53] = 8.3650941511520923959944E-001;
842 xnu[7][54] = 8.4149371554553961404354E-001;
843 xnu[7][55] = 8.4640688488955735144733E-001;
844 xnu[7][56] = 8.5124810324576353930490E-001;
845 xnu[7][57] = 8.5601657768112601729334E-001;
846 xnu[7][58] = 8.6071154268504945774249E-001;
847 xnu[7][59] = 8.6533226062109063066465E-001;
848 xnu[7][60] = 8.6987802217634737933861E-001;
849 xnu[7][61] = 8.7434814680846830141141E-001;
850 xnu[7][62] = 8.7874198319025681896313E-001;
851 xnu[7][63] = 8.8305890965188004535834E-001;
852 xnu[7][64] = 8.8729833462074168851793E-001;
853 xnu[7][65] = 8.9145969705914150819259E-001;
854 xnu[7][66] = 8.9554246689992418071732E-001;
855 xnu[7][67] = 8.9954614548042070089990E-001;
856 xnu[7][68] = 9.0347026597510880592815E-001;
857 xnu[7][69] = 9.0731439382756870671791E-001;
858 xnu[7][70] = 9.1107812718249020368626E-001;
859 xnu[7][71] = 9.1476109731870070008905E-001;
860 xnu[7][72] = 9.1836296908443436775138E-001;
861 xnu[7][73] = 9.2188344133635430051916E-001;
862 xnu[7][74] = 9.2532224738417513987891E-001;
863 xnu[7][75] = 9.2867915544311607826256E-001;
864 xnu[7][76] = 9.3195396909684523857321E-001;
865 xnu[7][77] = 9.3514652777405695292558E-001;
866 xnu[7][78] = 9.3825670724235263487081E-001;
867 xnu[7][79] = 9.4128442012367095342085E-001;
868 xnu[7][80] = 9.4422961643612849944521E-001;
869 xnu[7][81] = 9.4709228416777951142968E-001;
870 xnu[7][82] = 9.4987244988847001831932E-001;
871 xnu[7][83] = 9.5257017940663079759465E-001;
872 xnu[7][84] = 9.5518557847850214624890E-001;
873 xnu[7][85] = 9.5771879357788252032198E-001;
874 xnu[7][86] = 9.6017001273500621036491E-001;
875 xnu[7][87] = 9.6253946645353782618207E-001;
876 xnu[7][88] = 9.6482742871487002833506E-001;
877 xnu[7][89] = 9.6703421807886289399974E-001;
878 xnu[7][90] = 9.6916019888979644182741E-001;
879 xnu[7][91] = 9.7120578259554152990628E-001;
880 xnu[7][92] = 9.7317142918670145257425E-001;
881 xnu[7][93] = 9.7505764876064743827892E-001;
882 xnu[7][94] = 9.7686500321288056820737E-001;
883 xnu[7][95] = 9.7859410805493048136810E-001;
884 xnu[7][96] = 9.8024563435401014171175E-001;
885 xnu[7][97] = 9.8182031078490606626049E-001;
886 xnu[7][98] = 9.8331892577920828354614E-001;
887 xnu[7][99] = 9.8474232975122961588545E-001;
888 xnu[7][100] = 9.8609143737429089828903E-001;
889 xnu[7][101] = 9.8736722987620133388036E-001;
890 xnu[7][102] = 9.8857075731985285707820E-001;
891 xnu[7][103] = 9.8970314083543134190307E-001;
892 xnu[7][104] = 9.9076557477687005343368E-001;
893 xnu[7][105] = 9.9175932878931636438083E-001;
894 xnu[7][106] = 9.9268574979926018555688E-001;
895 xnu[7][107] = 9.9354626397701703359495E-001;
896 xnu[7][108] = 9.9434237877371473996926E-001;
897 xnu[7][109] = 9.9507568520038507959027E-001;
898 xnu[7][110] = 9.9574786058905306619925E-001;
899 xnu[7][111] = 9.9636067214139430766410E-001;
900 xnu[7][112] = 9.9691598160637751110426E-001;
901 xnu[7][113] = 9.9741575140031050025957E-001;
902 xnu[7][114] = 9.9786205234920359425472E-001;
903 xnu[7][115] = 9.9825707295744513692434E-001;
904 xnu[7][116] = 9.9860312968611097953823E-001;
905 xnu[7][117] = 9.9890267724797863728092E-001;
906 xnu[7][118] = 9.9915831765920369626532E-001;
907 xnu[7][119] = 9.9937280723404755735176E-001;
908 xnu[7][120] = 9.9954906248383379883111E-001;
909 xnu[7][121] = 9.9969016901251179096404E-001;
910 xnu[7][122] = 9.9979939983595534162598E-001;
911 xnu[7][123] = 9.9988024546221602366522E-001;
912 xnu[7][124] = 9.9993644406017880596898E-001;
913 xnu[7][125] = 9.9997199810352718788193E-001;
914 xnu[7][126] = 9.9999121517744579929001E-001;
915 xnu[7][127] = 9.9999879818987423231012E-001;
916 dnu[7][0] = -7.0472035450480896734578E-003;
917 dnu[7][1] = 7.0464225345802041774796E-003;
918 dnu[7][2] = -7.0440797582541505326634E-003;
919 dnu[7][3] = 7.0401759812768306624229E-003;
920 dnu[7][4] = -7.0347124789067876590744E-003;
921 dnu[7][5] = 7.0276910363249821385840E-003;
922 dnu[7][6] = -7.0191139484543116517120E-003;
923 dnu[7][7] = 7.0089840197283044049361E-003;
924 dnu[7][8] = -6.9973045638095399259442E-003;
925 dnu[7][9] = 6.9840794032584692578639E-003;
926 dnu[7][10] = -6.9693128691534254021309E-003;
927 dnu[7][11] = 6.9530098006627306317656E-003;
928 dnu[7][12] = -6.9351755445699204984798E-003;
929 dnu[7][13] = 6.9158159547532143382480E-003;
930 dnu[7][14] = -6.8949373916204682587172E-003;
931 dnu[7][15] = 6.8725467215009483161260E-003;
932 dnu[7][16] = -6.8486513159953581290272E-003;
933 dnu[7][17] = 6.8232590512856457141999E-003;
934 dnu[7][18] = -6.7963783074061979548022E-003;
935 dnu[7][19] = 6.7680179674781068068327E-003;
936 dnu[7][20] = -6.7381874169082579908596E-003;
937 dnu[7][21] = 6.7068965425550492564832E-003;
938 dnu[7][22] = -6.6741557318625899765387E-003;
939 dnu[7][23] = 6.6399758719652653251888E-003;
940 dnu[7][24] = -6.6043683487645649827596E-003;
941 dnu[7][25] = 6.5673450459800764181907E-003;
942 dnu[7][26] = -6.5289183441765244201247E-003;
943 dnu[7][27] = 6.4891011197686996429211E-003;
944 dnu[7][28] = -6.4479067440060573471011E-003;
945 dnu[7][29] = 6.4053490819386809834209E-003;
946 dnu[7][30] = -6.3614424913661914531436E-003;
947 dnu[7][31] = 6.3162018217710393822703E-003;
948 dnu[7][32] = -6.2696424132374421767099E-003;
949 dnu[7][33] = 6.2217800953570176315748E-003;
950 dnu[7][34] = -6.1726311861219192272652E-003;
951 dnu[7][35] = 6.1222124908059929493146E-003;
952 dnu[7][36] = -6.0705413008341498394934E-003;
953 dnu[7][37] = 6.0176353926397813152249E-003;
954 dnu[7][38] = -5.9635130265096350201115E-003;
955 dnu[7][39] = 5.9081929454151178816124E-003;
956 dnu[7][40] = -5.8516943738285015503310E-003;
957 dnu[7][41] = 5.7940370165219762842120E-003;
958 dnu[7][42] = -5.7352410573469371902001E-003;
959 dnu[7][43] = 5.6753271579902983008672E-003;
960 dnu[7][44] = -5.6143164567040246767818E-003;
961 dnu[7][45] = 5.5522305670034632684997E-003;
962 dnu[7][46] = -5.4890915763294562348151E-003;
963 dnu[7][47] = 5.4249220446686570495123E-003;
964 dnu[7][48] = -5.3597450031259668116140E-003;
965 dnu[7][49] = 5.2935839524425989654714E-003;
966 dnu[7][50] = -5.2264628614530059630555E-003;
967 dnu[7][51] = 5.1584061654738108409604E-003;
968 dnu[7][52] = -5.0894387646180398667368E-003;
969 dnu[7][53] = 5.0195860220284203990905E-003;
970 dnu[7][54] = -4.9488737620243748720069E-003;
971 dnu[7][55] = 4.8773282681587057305415E-003;
972 dnu[7][56] = -4.8049762811819415048301E-003;
973 dnu[7][57] = 4.7318449969150326471362E-003;
974 dnu[7][58] = -4.6579620640346975465785E-003;
975 dnu[7][59] = 4.5833555817803942033526E-003;
976 dnu[7][60] = -4.5080540975978215800133E-003;
977 dnu[7][61] = 4.4320866047412471320571E-003;
978 dnu[7][62] = -4.3554825398660434367881E-003;
979 dnu[7][63] = 4.2782717806538448095865E-003;
980 dnu[7][64] = -4.2004846435259663177174E-003;
981 dnu[7][65] = 4.1221518815164340152753E-003;
982 dnu[7][66] = -4.0433046823944299854870E-003;
983 dnu[7][67] = 3.9639746671474245551263E-003;
984 dnu[7][68] = -3.8841938889609956099821E-003;
985 dnu[7][69] = 3.8039948328595282916087E-003;
986 dnu[7][70] = -3.7234104162037955087026E-003;
987 dnu[7][71] = 3.6424739902769035319399E-003;
988 dnu[7][72] = -3.5612193432291935765854E-003;
989 dnu[7][73] = 3.4796807046952114697225E-003;
990 dnu[7][74] = -3.3978927524413866973932E-003;
991 dnu[7][75] = 3.3158906214509439470610E-003;
992 dnu[7][76] = -3.2337099159018433636835E-003;
993 dnu[7][77] = 3.1513867245428793585820E-003;
994 dnu[7][78] = -3.0689576400206925217416E-003;
995 dnu[7][79] = 2.9864597827540829024736E-003;
996 dnu[7][80] = -2.9039308299887836817462E-003;
997 dnu[7][81] = 2.8214090506922220792273E-003;
998 dnu[7][82] = -2.7389333469594754120082E-003;
999 dnu[7][83] = 2.6565433025935282831440E-003;
1000 dnu[7][84] = -2.5742792394890888809216E-003;
1001 dnu[7][85] = 2.4921822823827693006000E-003;
1002 dnu[7][86] = -2.4102944324256341738246E-003;
1003 dnu[7][87] = 2.3286586498784273886390E-003;
1004 dnu[7][88] = -2.2473189460160339308202E-003;
1005 dnu[7][89] = 2.1663204840464914272688E-003;
1006 dnu[7][90] = -2.0857096884920394263960E-003;
1007 dnu[7][91] = 2.0055343620375116994450E-003;
1008 dnu[7][92] = -1.9258438083199354620415E-003;
1009 dnu[7][93] = 1.8466889585128254091286E-003;
1010 dnu[7][94] = -1.7681224988583888670116E-003;
1011 dnu[7][95] = 1.6901989955434601911750E-003;
1012 dnu[7][96] = -1.6129750125439342307013E-003;
1013 dnu[7][97] = 1.5365092173512891617039E-003;
1014 dnu[7][98] = -1.4608624689589098768899E-003;
1015 dnu[7][99] = 1.3860978822967254969976E-003;
1016 dnu[7][100] = -1.3122808637022147812835E-003;
1017 dnu[7][101] = 1.2394791133287839653391E-003;
1018 dnu[7][102] = -1.1677625930285804368514E-003;
1019 dnu[7][103] = 1.0972034626819194194015E-003;
1020 dnu[7][104] = -1.0278759946636732617923E-003;
1021 dnu[7][105] = 9.5985648550693620626136E-004;
1022 dnu[7][106] = -8.9322319587932491235173E-004;
1023 dnu[7][107] = 8.2805636407722630260841E-004;
1024 dnu[7][108] = -7.6443835254388278387516E-004;
1025 dnu[7][109] = 7.0245399782757232135761E-004;
1026 dnu[7][110] = -6.4219123594850509816130E-004;
1027 dnu[7][111] = 5.8374205871497970384667E-004;
1028 dnu[7][112] = -5.2720381143165805354149E-004;
1029 dnu[7][113] = 4.7268075842926269123151E-004;
1030 dnu[7][114] = -4.2028571635537372133344E-004;
1031 dnu[7][115] = 3.7014140212225166523158E-004;
1032 dnu[7][116] = -3.2238102065234630638566E-004;
1033 dnu[7][117] = 2.7714765746518735745887E-004;
1034 dnu[7][118] = -2.3459246214726554551974E-004;
1035 dnu[7][119] = 1.9487264223664114660778E-004;
1036 dnu[7][120] = -1.5815182927018453366651E-004;
1037 dnu[7][121] = 1.2460620024149864701227E-004;
1038 dnu[7][122] = -9.4436690910239873306717E-005;
1039 dnu[7][123] = 6.7877455474614359864921E-005;
1040 dnu[7][124] = -4.5183414893318604279565E-005;
1041 dnu[7][125] = 2.6637646834890306562676E-005;
1042 dnu[7][126] = -1.2689112411790928068031E-005;
1043 dnu[7][127] = 3.4689682162054133584769E-006;
1044 xnu[8][0] = 5.0000000000000000000000E-001;
1045 xnu[8][1] = 5.0352356922966837324257E-001;
1046 xnu[8][2] = 5.0704694320539123130709E-001;
1047 xnu[8][3] = 5.1056992668916554416748E-001;
1048 xnu[8][4] = 5.1409232447487284716970E-001;
1049 xnu[8][5] = 5.1761394140422051163016E-001;
1050 xnu[8][6] = 5.2113458238268180160620E-001;
1051 xnu[8][7] = 5.2465405239543431335782E-001;
1052 xnu[8][8] = 5.2817215652329639498598E-001;
1053 xnu[8][9] = 5.3168869995866114493983E-001;
1054 xnu[8][10] = 5.3520348802142758953165E-001;
1055 xnu[8][11] = 5.3871632617492864128376E-001;
1056 xnu[8][12] = 5.4222702004185544185509E-001;
1057 xnu[8][13] = 5.4573537542017769545473E-001;
1058 xnu[8][14] = 5.4924119829905960104514E-001;
1059 xnu[8][15] = 5.5274429487477099426633E-001;
1060 xnu[8][16] = 5.5624447156659331287292E-001;
1061 xnu[8][17] = 5.5974153503272000256669E-001;
1062 xnu[8][18] = 5.6323529218615098342533E-001;
1063 xnu[8][19] = 5.6672555021058080067206E-001;
1064 xnu[8][20] = 5.7021211657628008729691E-001;
1065 xnu[8][21] = 5.7369479905596997002704E-001;
1066 xnu[8][22] = 5.7717340574068905434622E-001;
1067 xnu[8][23] = 5.8064774505565262868030E-001;
1068 xnu[8][24] = 5.8411762577610373249116E-001;
1069 xnu[8][25] = 5.8758285704315573785372E-001;
1070 xnu[8][26] = 5.9104324837962609912320E-001;
1071 xnu[8][27] = 5.9449860970586093052960E-001;
1072 xnu[8][28] = 5.9794875135555007695773E-001;
1073 xnu[8][29] = 6.0139348409153234877826E-001;
1074 xnu[8][30] = 6.0483261912159059738317E-001;
1075 xnu[8][31] = 6.0826596811423631404069E-001;
1076 xnu[8][32] = 6.1169334321448344081410E-001;
1077 xnu[8][33] = 6.1511455705961108857785E-001;
1078 xnu[8][34] = 6.1852942279491486360633E-001;
1079 xnu[8][35] = 6.2193775408944651079646E-001;
1080 xnu[8][36] = 6.2533936515174158830648E-001;
1081 xnu[8][37] = 6.2873407074553489524063E-001;
1082 xnu[8][38] = 6.3212168620546338097247E-001;
1083 xnu[8][39] = 6.3550202745275627176810E-001;
1084 xnu[8][40] = 6.3887491101091215753268E-001;
1085 xnu[8][41] = 6.4224015402136278874800E-001;
1086 xnu[8][42] = 6.4559757425912334098185E-001;
1087 xnu[8][43] = 6.4894699014842891171828E-001;
1088 xnu[8][44] = 6.5228822077835702166766E-001;
1089 xnu[8][45] = 6.5562108591843590015010E-001;
1090 xnu[8][46] = 6.5894540603423834159087E-001;
1091 xnu[8][47] = 6.6226100230296092760332E-001;
1092 xnu[8][48] = 6.6556769662898841654632E-001;
1093 xnu[8][49] = 6.6886531165944310981029E-001;
1094 xnu[8][50] = 6.7215367079971901138831E-001;
1095 xnu[8][51] = 6.7543259822900060450540E-001;
1096 xnu[8][52] = 6.7870191891576607618811E-001;
1097 xnu[8][53] = 6.8196145863327482763471E-001;
1098 xnu[8][54] = 6.8521104397503911506877E-001;
1099 xnu[8][55] = 6.8845050237027967240092E-001;
1100 xnu[8][56] = 6.9167966209936517345824E-001;
1101 xnu[8][57] = 6.9489835230923539773967E-001;
1102 xnu[8][58] = 6.9810640302880796959126E-001;
1103 xnu[8][59] = 7.0130364518436854633556E-001;
1104 xnu[8][60] = 7.0448991061494433620452E-001;
1105 xnu[8][61] = 7.0766503208766083188217E-001;
1106 xnu[8][62] = 7.1082884331308165002815E-001;
1107 xnu[8][63] = 7.1398117896053137129164E-001;
1108 xnu[8][64] = 7.1712187467340127900104E-001;
1109 xnu[8][65] = 7.2025076708443789789144E-001;
1110 xnu[8][66] = 7.2336769383101423687111E-001;
1111 xnu[8][67] = 7.2647249357038364189194E-001;
1112 xnu[8][68] = 7.2956500599491616643675E-001;
1113 xnu[8][69] = 7.3264507184731736792908E-001;
1114 xnu[8][70] = 7.3571253293582943846704E-001;
1115 xnu[8][71] = 7.3876723214941457764179E-001;
1116 xnu[8][72] = 7.4180901347292051378108E-001;
1117 xnu[8][73] = 7.4483772200222807771818E-001;
1118 xnu[8][74] = 7.4785320395938073008506E-001;
1119 xnu[8][75] = 7.5085530670769593912527E-001;
1120 xnu[8][76] = 7.5384387876685830107739E-001;
1121 xnu[8][77] = 7.5681876982799428925371E-001;
1122 xnu[8][78] = 7.5977983076872851099646E-001;
1123 xnu[8][79] = 7.6272691366822134369754E-001;
1124 xnu[8][80] = 7.6565987182218781198605E-001;
1125 xnu[8][81] = 7.6857855975789755799089E-001;
1126 xnu[8][82] = 7.7148283324915574524615E-001;
1127 xnu[8][83] = 7.7437254933126472430380E-001;
1128 xnu[8][84] = 7.7724756631596627443319E-001;
1129 xnu[8][85] = 7.8010774380636422090881E-001;
1130 xnu[8][86] = 7.8295294271182721131149E-001;
1131 xnu[8][87] = 7.8578302526287141699609E-001;
1132 xnu[8][88] = 7.8859785502602290742185E-001;
1133 xnu[8][89] = 7.9139729691865942541974E-001;
1134 xnu[8][90] = 7.9418121722383127071718E-001;
1135 xnu[8][91] = 7.9694948360506097719637E-001;
1136 xnu[8][92] = 7.9970196512112144648713E-001;
1137 xnu[8][93] = 8.0243853224079217665963E-001;
1138 xnu[8][94] = 8.0515905685759320007779E-001;
1139 xnu[8][95] = 8.0786341230449631900687E-001;
1140 xnu[8][96] = 8.1055147336861320147034E-001;
1141 xnu[8][97] = 8.1322311630585987327081E-001;
1142 xnu[8][98] = 8.1587821885559711520679E-001;
1143 xnu[8][99] = 8.1851666025524624753565E-001;
1144 xnu[8][100] = 8.2113832125487975688706E-001;
1145 xnu[8][101] = 8.2374308413178619439088E-001;
1146 xnu[8][102] = 8.2633083270500874805039E-001;
1147 xnu[8][103] = 8.2890145234985686771097E-001;
1148 xnu[8][104] = 8.3145483001239029773051E-001;
1149 xnu[8][105] = 8.3399085422387485108267E-001;
1150 xnu[8][106] = 8.3650941511520923959944E-001;
1151 xnu[8][107] = 8.3901040443132225891910E-001;
1152 xnu[8][108] = 8.4149371554553961404354E-001;
1153 xnu[8][109] = 8.4395924347391966287784E-001;
1154 xnu[8][110] = 8.4640688488955735144733E-001;
1155 xnu[8][111] = 8.4883653813685561645313E-001;
1156 xnu[8][112] = 8.5124810324576353930490E-001;
1157 xnu[8][113] = 8.5364148194598055170579E-001;
1158 xnu[8][114] = 8.5601657768112601729334E-001;
1159 xnu[8][115] = 8.5837329562287354788348E-001;
1160 xnu[8][116] = 8.6071154268504945774249E-001;
1161 xnu[8][117] = 8.6303122753769481634259E-001;
1162 xnu[8][118] = 8.6533226062109063066465E-001;
1163 xnu[8][119] = 8.6761455415974577383172E-001;
1164 xnu[8][120] = 8.6987802217634737933861E-001;
1165 xnu[8][121] = 8.7212258050567354115472E-001;
1166 xnu[8][122] = 8.7434814680846830141141E-001;
1167 xnu[8][123] = 8.7655464058527907126126E-001;
1168 xnu[8][124] = 8.7874198319025681896313E-001;
1169 xnu[8][125] = 8.8091009784491957458672E-001;
1170 xnu[8][126] = 8.8305890965188004535834E-001;
1171 xnu[8][127] = 8.8518834560853841213875E-001;
1172 xnu[8][128] = 8.8729833462074168851793E-001;
1173 xnu[8][129] = 8.8938880751641137235105E-001;
1174 xnu[8][130] = 8.9145969705914150819259E-001;
1175 xnu[8][131] = 8.9351093796176971108496E-001;
1176 xnu[8][132] = 8.9554246689992418071732E-001;
1177 xnu[8][133] = 8.9755422252555026338988E-001;
1178 xnu[8][134] = 8.9954614548042070089990E-001;
1179 xnu[8][135] = 9.0151817840963434389085E-001;
1180 xnu[8][136] = 9.0347026597510880592815E-001;
1181 xnu[8][137] = 9.0540235486907329718058E-001;
1182 xnu[8][138] = 9.0731439382756870671791E-001;
1183 xnu[8][139] = 9.0920633364396290369770E-001;
1184 xnu[8][140] = 9.1107812718249020368626E-001;
1185 xnu[8][141] = 9.1292972939182500054383E-001;
1186 xnu[8][142] = 9.1476109731870070008905E-001;
1187 xnu[8][143] = 9.1657219012158631236397E-001;
1188 xnu[8][144] = 9.1836296908443436775138E-001;
1189 xnu[8][145] = 9.2013339763051522117512E-001;
1190 xnu[8][146] = 9.2188344133635430051916E-001;
1191 xnu[8][147] = 9.2361306794579044219027E-001;
1192 xnu[8][148] = 9.2532224738417513987891E-001;
1193 xnu[8][149] = 9.2701095177273431290670E-001;
1194 xnu[8][150] = 9.2867915544311607826256E-001;
1195 xnu[8][151] = 9.3032683495214998490117E-001;
1196 xnu[8][152] = 9.3195396909684523857321E-001;
1197 xnu[8][153] = 9.3356053892965760780721E-001;
1198 xnu[8][154] = 9.3514652777405695292558E-001;
1199 xnu[8][155] = 9.3671192124042965509622E-001;
1200 xnu[8][156] = 9.3825670724235263487081E-001;
1201 xnu[8][157] = 9.3978087601327813128378E-001;
1202 xnu[8][158] = 9.4128442012367095342085E-001;
1203 xnu[8][159] = 9.4276733449864250446303E-001;
1204 xnu[8][160] = 9.4422961643612849944521E-001;
1205 xnu[8][161] = 9.4567126562565993583304E-001;
1206 xnu[8][162] = 9.4709228416777951142968E-001;
1207 xnu[8][163] = 9.4849267659415829518778E-001;
1208 xnu[8][164] = 9.4987244988847001831932E-001;
1209 xnu[8][165] = 9.5123161350808283752414E-001;
1210 xnu[8][166] = 9.5257017940663079759465E-001;
1211 xnu[8][167] = 9.5388816205752945181220E-001;
1212 xnu[8][168] = 9.5518557847850214624890E-001;
1213 xnu[8][169] = 9.5646244825718529503981E-001;
1214 xnu[8][170] = 9.5771879357788252032198E-001;
1215 xnu[8][171] = 9.5895463924953875081824E-001;
1216 xnu[8][172] = 9.6017001273500621036491E-001;
1217 xnu[8][173] = 9.6136494418167462076137E-001;
1218 xnu[8][174] = 9.6253946645353782618207E-001;
1219 xnu[8][175] = 9.6369361516476834842161E-001;
1220 xnu[8][176] = 9.6482742871487002833506E-001;
1221 xnu[8][177] = 9.6594094832547681967268E-001;
1222 xnu[8][178] = 9.6703421807886289399974E-001;
1223 xnu[8][179] = 9.6810728495822540331247E-001;
1224 xnu[8][180] = 9.6916019888979644182741E-001;
1225 xnu[8][181] = 9.7019301278683486068516E-001;
1226 xnu[8][182] = 9.7120578259554152990628E-001;
1227 xnu[8][183] = 9.7219856734293332429533E-001;
1228 xnu[8][184] = 9.7317142918670145257425E-001;
1229 xnu[8][185] = 9.7412443346706867853133E-001;
1230 xnu[8][186] = 9.7505764876064743827892E-001;
1231 xnu[8][187] = 9.7597114693628679474913E-001;
1232 xnu[8][188] = 9.7686500321288056820737E-001;
1233 xnu[8][189] = 9.7773929621909184878677E-001;
1234 xnu[8][190] = 9.7859410805493048136810E-001;
1235 xnu[8][191] = 9.7942952435510011067792E-001;
1236 xnu[8][192] = 9.8024563435401014171175E-001;
1237 xnu[8][193] = 9.8104253095232573787034E-001;
1238 xnu[8][194] = 9.8182031078490606626049E-001;
1239 xnu[8][195] = 9.8257907428995783298937E-001;
1240 xnu[8][196] = 9.8331892577920828354614E-001;
1241 xnu[8][197] = 9.8403997350887997398176E-001;
1242 xnu[8][198] = 9.8474232975122961588545E-001;
1243 xnu[8][199] = 9.8542611086639622162798E-001;
1244 xnu[8][200] = 9.8609143737429089828903E-001;
1245 xnu[8][201] = 9.8673843402625346338665E-001;
1246 xnu[8][202] = 9.8736722987620133388036E-001;
1247 xnu[8][203] = 9.8797795835100587656440E-001;
1248 xnu[8][204] = 9.8857075731985285707820E-001;
1249 xnu[8][205] = 9.8914576916237926976304E-001;
1250 xnu[8][206] = 9.8970314083543134190307E-001;
1251 xnu[8][207] = 9.9024302393836066970799E-001;
1252 xnu[8][208] = 9.9076557477687005343368E-001;
1253 xnu[8][209] = 9.9127095442554030212529E-001;
1254 xnu[8][210] = 9.9175932878931636438083E-001;
1255 xnu[8][211] = 9.9223086866440726729820E-001;
1256 xnu[8][212] = 9.9268574979926018555688E-001;
1257 xnu[8][213] = 9.9312415295650377634075E-001;
1258 xnu[8][214] = 9.9354626397701703359495E-001;
1259 xnu[8][215] = 9.9395227384756214023332E-001;
1260 xnu[8][216] = 9.9434237877371473996926E-001;
1261 xnu[8][217] = 9.9471678026012041935822E-001;
1262 xnu[8][218] = 9.9507568520038507959027E-001;
1263 xnu[8][219] = 9.9541930597914712183853E-001;
1264 xnu[8][220] = 9.9574786058905306619925E-001;
1265 xnu[8][221] = 9.9606157276543155884129E-001;
1266 xnu[8][222] = 9.9636067214139430766410E-001;
1267 xnu[8][223] = 9.9664539442584248310532E-001;
1268 xnu[8][224] = 9.9691598160637751110426E-001;
1269 xnu[8][225] = 9.9717268217836170296553E-001;
1270 xnu[8][226] = 9.9741575140031050025957E-001;
1271 xnu[8][227] = 9.9764545157440515113072E-001;
1272 xnu[8][228] = 9.9786205234920359425472E-001;
1273 xnu[8][229] = 9.9806583103965751889305E-001;
1274 xnu[8][230] = 9.9825707295744513692434E-001;
1275 xnu[8][231] = 9.9843607174263008064974E-001;
1276 xnu[8][232] = 9.9860312968611097953823E-001;
1277 xnu[8][233] = 9.9875855803173619998262E-001;
1278 xnu[8][234] = 9.9890267724797863728092E-001;
1279 xnu[8][235] = 9.9903581726246516165093E-001;
1280 xnu[8][236] = 9.9915831765920369626532E-001;
1281 xnu[8][237] = 9.9927052784858395301327E-001;
1282 xnu[8][238] = 9.9937280723404755735176E-001;
1283 xnu[8][239] = 9.9946552541540528111790E-001;
1284 xnu[8][240] = 9.9954906248383379883111E-001;
1285 xnu[8][241] = 9.9962380947167123679948E-001;
1286 xnu[8][242] = 9.9969016901251179096404E-001;
1287 xnu[8][243] = 9.9974855623359359526763E-001;
1288 xnu[8][244] = 9.9979939983595534162598E-001;
1289 xnu[8][245] = 9.9984314322415886588808E-001;
1290 xnu[8][246] = 9.9988024546221602366522E-001;
1291 xnu[8][247] = 9.9991118183989386959794E-001;
1292 xnu[8][248] = 9.9993644406017880596898E-001;
1293 xnu[8][249] = 9.9995654057233914140003E-001;
1294 xnu[8][250] = 9.9997199810352718788193E-001;
1295 xnu[8][251] = 9.9998336504924313844142E-001;
1296 xnu[8][252] = 9.9999121517744579929001E-001;
1297 xnu[8][253] = 9.9999614906812879401388E-001;
1298 xnu[8][254] = 9.9999879818987423231012E-001;
1299 xnu[8][255] = 9.9999983647836719219063E-001;
1300 dnu[8][0] = -3.5236017725240448367289E-003;
1301 dnu[8][1] = 3.5235041442227400686498E-003;
1302 dnu[8][2] = -3.5232112672901020887398E-003;
1303 dnu[8][3] = 3.5227231656397573838983E-003;
1304 dnu[8][4] = -3.5220398791270752663317E-003;
1305 dnu[8][5] = 3.5211614635481560479832E-003;
1306 dnu[8][6] = -3.5200879906384153312115E-003;
1307 dnu[8][7] = 3.5188195480707652615937E-003;
1308 dnu[8][8] = -3.5173562394533938295372E-003;
1309 dnu[8][9] = 3.5156981843271435475412E-003;
1310 dnu[8][10] = -3.5138455181624910692920E-003;
1311 dnu[8][11] = 3.5117983923561295551537E-003;
1312 dnu[8][12] = -3.5095569742271558258560E-003;
1313 dnu[8][13] = 3.5071214470128645821259E-003;
1314 dnu[8][14] = -3.5044920098641522024681E-003;
1315 dnu[8][15] = 3.5016688778405328640984E-003;
1316 dnu[8][16] = -3.4986522819047699629721E-003;
1317 dnu[8][17] = 3.4954424689171260377234E-003;
1318 dnu[8][18] = -3.4920397016292346289319E-003;
1319 dnu[8][19] = 3.4884442586775977292236E-003;
1320 dnu[8][20] = -3.4846564345767127010655E-003;
1321 dnu[8][21] = 3.4806765397118327574657E-003;
1322 dnu[8][22] = -3.4765049003313653158828E-003;
1323 dnu[8][23] = 3.4721418585389127471901E-003;
1324 dnu[8][24] = -3.4675877722849602492399E-003;
1325 dnu[8][25] = 3.4628430153582157781065E-003;
1326 dnu[8][26] = -3.4579079773766071691240E-003;
1327 dnu[8][27] = 3.4527830637779417740149E-003;
1328 dnu[8][28] = -3.4474686958102341293586E-003;
1329 dnu[8][29] = 3.4419653105217073549737E-003;
1330 dnu[8][30] = -3.4362733607504741580630E-003;
1331 dnu[8][31] = 3.4303933151139034897570E-003;
1332 dnu[8][32] = -3.4243256579976790645136E-003;
1333 dnu[8][33] = 3.4180708895445561092032E-003;
1334 dnu[8][34] = -3.4116295256428228571000E-003;
1335 dnu[8][35] = 3.4050020979144734418687E-003;
1336 dnu[8][36] = -3.3981891537030989774011E-003;
1337 dnu[8][37] = 3.3911912560615037304123E-003;
1338 dnu[8][38] = -3.3840089837390534034163E-003;
1339 dnu[8][39] = 3.3766429311687626453919E-003;
1340 dnu[8][40] = -3.3690937084541289954298E-003;
1341 dnu[8][41] = 3.3613619413557205401809E-003;
1342 dnu[8][42] = -3.3534482712775246282416E-003;
1343 dnu[8][43] = 3.3453533552530650329179E-003;
1344 dnu[8][44] = -3.3370778659312949882693E-003;
1345 dnu[8][45] = 3.3286224915622735410861E-003;
1346 dnu[8][46] = -3.3199879359826326625944E-003;
1347 dnu[8][47] = 3.3111749186008425472876E-003;
1348 dnu[8][48] = -3.3021841743822824913798E-003;
1349 dnu[8][49] = 3.2930164538341246889724E-003;
1350 dnu[8][50] = -3.2836725229900382090953E-003;
1351 dnu[8][51] = 3.2741531633947203202702E-003;
1352 dnu[8][52] = -3.2644591720882622100624E-003;
1353 dnu[8][53] = 3.2545913615903560041347E-003;
1354 dnu[8][54] = -3.2445505598843498214605E-003;
1355 dnu[8][55] = 3.2343376104011574084413E-003;
1356 dnu[8][56] = -3.2239533720030286735506E-003;
1357 dnu[8][57] = 3.2133987189671871946092E-003;
1358 dnu[8][58] = -3.2026745409693404917104E-003;
1359 dnu[8][59] = 3.1917817430670685489766E-003;
1360 dnu[8][60] = -3.1807212456830957265718E-003;
1361 dnu[8][61] = 3.1694939845884508295582E-003;
1362 dnu[8][62] = -3.1581009108855196911351E-003;
1363 dnu[8][63] = 3.1465429909909941834386E-003;
1364 dnu[8][64] = -3.1348212066187210883550E-003;
1365 dnu[8][65] = 3.1229365547624537427064E-003;
1366 dnu[8][66] = -3.1108900476785088157874E-003;
1367 dnu[8][67] = 3.0986827128683299817099E-003;
1368 dnu[8][68] = -3.0863155930609596136326E-003;
1369 dnu[8][69] = 3.0737897461954189510710E-003;
1370 dnu[8][70] = -3.0611062454029964746573E-003;
1371 dnu[8][71] = 3.0482661789894434646161E-003;
1372 dnu[8][72] = -3.0352706504170749197467E-003;
1373 dnu[8][73] = 3.0221207782867731729442E-003;
1374 dnu[8][74] = -3.0088176963198906576125E-003;
1375 dnu[8][75] = 2.9953625533400473573579E-003;
1376 dnu[8][76] = -2.9817565132548175100558E-003;
1377 dnu[8][77] = 2.9680007550372991380706E-003;
1378 dnu[8][78] = -2.9540964727075589408062E-003;
1379 dnu[8][79] = 2.9400448753139440160228E-003;
1380 dnu[8][80] = -2.9258471869142507751655E-003;
1381 dnu[8][81] = 2.9115046465567402885106E-003;
1382 dnu[8][82] = -2.8970185082609881421060E-003;
1383 dnu[8][83] = 2.8823900409985557147716E-003;
1384 dnu[8][84] = -2.8676205286734685951001E-003;
1385 dnu[8][85] = 2.8527112701024866615598E-003;
1386 dnu[8][86] = -2.8376635789951491504336E-003;
1387 dnu[8][87] = 2.8224787839335768444255E-003;
1388 dnu[8][88] = -2.8071582283520123383909E-003;
1389 dnu[8][89] = 2.7917032705160781880498E-003;
1390 dnu[8][90] = -2.7761152835017316342499E-003;
1391 dnu[8][91] = 2.7603956551738935322869E-003;
1392 dnu[8][92] = -2.7445457881647281174076E-003;
1393 dnu[8][93] = 2.7285670998515493199771E-003;
1394 dnu[8][94] = -2.7124610223343285247561E-003;
1395 dnu[8][95] = 2.6962290024127779680319E-003;
1396 dnu[8][96] = -2.6798725015629834058070E-003;
1397 dnu[8][97] = 2.6633929959135592898706E-003;
1398 dnu[8][98] = -2.6467919762212994827357E-003;
1399 dnu[8][99] = 2.6300709478462965560248E-003;
1400 dnu[8][100] = -2.6132314307265029815277E-003;
1401 dnu[8][101] = 2.5962749593517080743133E-003;
1402 dnu[8][102] = -2.5792030827369054204802E-003;
1403 dnu[8][103] = 2.5620173643950267591546E-003;
1404 dnu[8][104] = -2.5447193823090199333684E-003;
1405 dnu[8][105] = 2.5273107289032506252914E-003;
1406 dnu[8][106] = -2.5097930110142101995453E-003;
1407 dnu[8][107] = 2.4921678498605151495699E-003;
1408 dnu[8][108] = -2.4744368810121874360035E-003;
1409 dnu[8][109] = 2.4566017543592094868339E-003;
1410 dnu[8][110] = -2.4386641340793528652707E-003;
1411 dnu[8][111] = 2.4206256986052856760690E-003;
1412 dnu[8][112] = -2.4024881405909707524150E-003;
1413 dnu[8][113] = 2.3842531668773746263160E-003;
1414 dnu[8][114] = -2.3659224984575163235681E-003;
1415 dnu[8][115] = 2.3474978704408952326600E-003;
1416 dnu[8][116] = -2.3289810320173487732893E-003;
1417 dnu[8][117] = 2.3103737464204034374082E-003;
1418 dnu[8][118] = -2.2916777908901971016763E-003;
1419 dnu[8][119] = 2.2728949566360664274378E-003;
1420 dnu[8][120] = -2.2540270487989107900066E-003;
1421 dnu[8][121] = 2.2350758864134636345022E-003;
1422 dnu[8][122] = -2.2160433023706235660286E-003;
1423 dnu[8][123] = 2.1969311433800209763024E-003;
1424 dnu[8][124] = -2.1777412699330217183940E-003;
1425 dnu[8][125] = 2.1584755562663973996390E-003;
1426 dnu[8][126] = -2.1391358903269224047932E-003;
1427 dnu[8][127] = 2.1197241737371909221716E-003;
1428 dnu[8][128] = -2.1002423217629831588587E-003;
1429 dnu[8][129] = 2.0806922632825487288194E-003;
1430 dnu[8][130] = -2.0610759407582170076376E-003;
1431 dnu[8][131] = 2.0413953102107891917508E-003;
1432 dnu[8][132] = -2.0216523411972149927435E-003;
1433 dnu[8][133] = 2.0018490167921084428078E-003;
1434 dnu[8][134] = -1.9819873335737122775631E-003;
1435 dnu[8][135] = 1.9620693016149788733009E-003;
1436 dnu[8][136] = -1.9420969444804978049911E-003;
1437 dnu[8][137] = 1.9220722992300657945837E-003;
1438 dnu[8][138] = -1.9019974164297641458043E-003;
1439 dnu[8][139] = 1.8818743601714816912025E-003;
1440 dnu[8][140] = -1.8617052081018977543513E-003;
1441 dnu[8][141] = 1.8414920514620195598335E-003;
1442 dnu[8][142] = -1.8212369951384517659700E-003;
1443 dnu[8][143] = 1.8009421577276621593433E-003;
1444 dnu[8][144] = -1.7806096716145967882927E-003;
1445 dnu[8][145] = 1.7602416830670896134102E-003;
1446 dnu[8][146] = -1.7398403523476057348613E-003;
1447 dnu[8][147] = 1.7194078538439529593811E-003;
1448 dnu[8][148] = -1.6989463762206933486966E-003;
1449 dnu[8][149] = 1.6784581225930838067080E-003;
1450 dnu[8][150] = -1.6579453107254719735305E-003;
1451 dnu[8][151] = 1.6374101732561698478224E-003;
1452 dnu[8][152] = -1.6168549579509216818417E-003;
1453 dnu[8][153] = 1.5962819279871736839512E-003;
1454 dnu[8][154] = -1.5756933622714396792910E-003;
1455 dnu[8][155] = 1.5550915557921377307891E-003;
1456 dnu[8][156] = -1.5344788200103462608708E-003;
1457 dnu[8][157] = 1.5138574832909927223987E-003;
1458 dnu[8][158] = -1.4932298913770414512368E-003;
1459 dnu[8][159] = 1.4725984079092879114196E-003;
1460 dnu[8][160] = -1.4519654149943918408731E-003;
1461 dnu[8][161] = 1.4313333138237893412643E-003;
1462 dnu[8][162] = -1.4107045253461110396137E-003;
1463 dnu[8][163] = 1.3900814909956971752233E-003;
1464 dnu[8][164] = -1.3694666734797377060041E-003;
1465 dnu[8][165] = 1.3488625576264729333326E-003;
1466 dnu[8][166] = -1.3282716512967641415720E-003;
1467 dnu[8][167] = 1.3076964863611805461264E-003;
1468 dnu[8][168] = -1.2871396197445444404608E-003;
1469 dnu[8][169] = 1.2666036345396266287484E-003;
1470 dnu[8][170] = -1.2460911411913846503000E-003;
1471 dnu[8][171] = 1.2256047787527824196154E-003;
1472 dnu[8][172] = -1.2051472162128170869123E-003;
1473 dnu[8][173] = 1.1847211538969024757289E-003;
1474 dnu[8][174] = -1.1643293249392136943195E-003;
1475 dnu[8][175] = 1.1439744968259798618913E-003;
1476 dnu[8][176] = -1.1236594730080169654101E-003;
1477 dnu[8][177] = 1.1033870945800166459678E-003;
1478 dnu[8][178] = -1.0831602420232457136344E-003;
1479 dnu[8][179] = 1.0629818370073626652228E-003;
1480 dnu[8][180] = -1.0428548442460197131980E-003;
1481 dnu[8][181] = 1.0227822733997914672317E-003;
1482 dnu[8][182] = -1.0027671810187558497225E-003;
1483 dnu[8][183] = 9.8281267251575273865993E-004;
1484 dnu[8][184] = -9.6292190415996773102075E-004;
1485 dnu[8][185] = 9.4309808507904237696790E-004;
1486 dnu[8][186] = -9.2334447925641270456432E-004;
1487 dnu[8][187] = 9.0366440750904465039505E-004;
1488 dnu[8][188] = -8.8406124942919443350579E-004;
1489 dnu[8][189] = 8.6453844527230803583806E-004;
1490 dnu[8][190] = -8.4509949777173009558748E-004;
1491 dnu[8][191] = 8.2574797385957285327574E-004;
1492 dnu[8][192] = -8.0648750627196711535064E-004;
1493 dnu[8][193] = 7.8732179501606083094277E-004;
1494 dnu[8][194] = -7.6825460867564458085196E-004;
1495 dnu[8][195] = 7.4928978553228318107157E-004;
1496 dnu[8][196] = -7.3043123447945493844494E-004;
1497 dnu[8][197] = 7.1168293570860259950151E-004;
1498 dnu[8][198] = -6.9304894114836274849880E-004;
1499 dnu[8][199] = 6.7453337464176556563600E-004;
1500 dnu[8][200] = -6.5614043185110739064173E-004;
1501 dnu[8][201] = 6.3787437988673473672259E-004;
1502 dnu[8][202] = -6.1973955666439198266955E-004;
1503 dnu[8][203] = 6.0174037000632982440356E-004;
1504 dnu[8][204] = -5.8388129651429021842567E-004;
1505 dnu[8][205] = 5.6616688025798832458331E-004;
1506 dnu[8][206] = -5.4860173134095970970073E-004;
1507 dnu[8][207] = 5.3119052442670035687534E-004;
1508 dnu[8][208] = -5.1393799733183663089639E-004;
1509 dnu[8][209] = 4.9684894981938042897235E-004;
1510 dnu[8][210] = -4.7992824275346810313068E-004;
1511 dnu[8][211] = 4.6318079780655564168411E-004;
1512 dnu[8][212] = -4.4661159793966245617026E-004;
1513 dnu[8][213] = 4.3022568890426392406400E-004;
1514 dnu[8][214] = -4.1402818203861315130421E-004;
1515 dnu[8][215] = 3.9802425864877543575304E-004;
1516 dnu[8][216] = -3.8221917627194139209526E-004;
1517 dnu[8][217] = 3.6661827711238395602767E-004;
1518 dnu[8][218] = -3.5122699891378616067880E-004;
1519 dnu[8][219] = 3.3605088848005409732297E-004;
1520 dnu[8][220] = -3.2109561797425254420128E-004;
1521 dnu[8][221] = 3.0636700400611260464706E-004;
1522 dnu[8][222] = -2.9187102935748985192333E-004;
1523 dnu[8][223] = 2.7761386698865378985736E-004;
1524 dnu[8][224] = -2.6360190571582919306239E-004;
1525 dnu[8][225] = 2.4984177665640024225928E-004;
1526 dnu[8][226] = -2.3634037921463134561575E-004;
1527 dnu[8][227] = 2.2310490505070162374404E-004;
1528 dnu[8][228] = -2.1014285817768061591171E-004;
1529 dnu[8][229] = 1.9746206912343685221695E-004;
1530 dnu[8][230] = -1.8507070106112583261579E-004;
1531 dnu[8][231] = 1.7297724606495193567507E-004;
1532 dnu[8][232] = -1.6119051032643119483180E-004;
1533 dnu[8][233] = 1.4971958842545586543710E-004;
1534 dnu[8][234] = -1.3857382873259367872945E-004;
1535 dnu[8][235] = 1.2776279479761843100676E-004;
1536 dnu[8][236] = -1.1729623106196260243797E-004;
1537 dnu[8][237] = 1.0718404501710846857448E-004;
1538 dnu[8][238] = -9.7436321118320573341744E-005;
1539 dnu[8][239] = 8.8063382772541597737195E-005;
1540 dnu[8][240] = -7.9075915205566116981157E-005;
1541 dnu[8][241] = 7.0485151102052395706581E-005;
1542 dnu[8][242] = -6.2303100120749462771247E-005;
1543 dnu[8][243] = 5.4542772822870761025480E-005;
1544 dnu[8][244] = -4.7218316126617180477170E-005;
1545 dnu[8][245] = 4.0344961400701764692553E-005;
1546 dnu[8][246] = -3.3938727737915739053586E-005;
1547 dnu[8][247] = 2.8015975392808212607024E-005;
1548 dnu[8][248] = -2.2593183623060767475330E-005;
1549 dnu[8][249] = 1.7687568602759479431384E-005;
1550 dnu[8][250] = -1.3318826217940261494781E-005;
1551 dnu[8][251] = 9.5106840952937908339661E-006;
1552 dnu[8][252] = -6.2892960976606935680311E-006;
1553 dnu[8][253] = 3.6831203455116083442839E-006;
1554 dnu[8][254] = -1.7416856803596676839876E-006;
1555 dnu[8][255] = 4.7285796697500352441360E-007;
1556 }
1557