National Bureau of Stamlards d^a-^ii-y

Ubrarv, E-01 Attmin. Bldg.

FEB 1 6 1967

NBS MONOGRAPH 98

Abscissas and Weights for Gaussian Quadrature

For N-2 to 100, and N-125, 150, 175, and 200

U.S. DEPARTMENT OF COMMERCE

NATIONAL BUREAU OF STANDARDS

THE NATIONAL BUREAU OF STANDARDS

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UNITED STATES DEPARTMENT OF COMMERCE • John T. Connor, Secretary

NATIONAL BUREAU OF STANDARDS • A. V. Astin, Director

Abscissas and Weights for Guassian Quadrature

For N=2 to 100, and N=125, 150, 175, 200

Carl H. Love

Institute for Basic Standards

National Bureau of Standards

Boulder Laboratories

Boulder, Colorado

National Bureau of Standards Monograph 98

Issued December 28, 1966

Forjale by the Superintendent of Documents, U.S. Government Printing Of&ce

Washington, D.C. 20402 - Price 55 cents

Library of Congress Catalog Card Number: 66-62096

CONTENTSPage

1 . Introductioij 1

2. Method 3

3. Errors 5

4. Table Errors 8

5. References 9

6. Tables of Gaussian Quadrature 11

ill

ABSCISSAS AND WEIGHTS FOR GAUSSIAN QUADRATUREFOR N = 2 to 100, and N = 125, 150, 175, and 200

Carl H. Love

!

The abscissas and weights for Gaussian Quadrature of order

N = 2 to 100,and N = 125, 150, 175, and 200 are given. The abscissas

are given to twenty-four places and the error is estimated to be no

more than 1 unit in the last place. The weights are given to twenty-

three places and the error is estimated to be no more than 1 unit in

' the last place. Keywords: Integration, Gaussian, Quadrature.

I

1. INTRODUCTION

The advent of high speed digital computers has made the use

' of Gaussian Quadrature formulae of very high order a practical pro-

cedure. It can be programmed with a few instructions and the awkward

,

abscissas are easily handled by the computer. It is a familiar technique

j'l which usually converges rapidly, and since the whole range of inte-

gration can be covered at once instead of making rriany subdivisions,

it will usually be very efficient.

In addition to its use in numerical integration Gaussian

I

Quadrature can be used in the numerical solution of integral equations

land also in the evaluation of functions that can be written as integrals.

'The last four sets of very high order were computed [l] since "exact

lvalues of these quantities are also interesting in view of certain

liunsettled theoretical conjectures that have been made about distributions

liiof the weights and abscissas. " It was reported by Davis and

jjiRabinowitz [2] that there was a "brisk demand" for the sets N = 64,

Il80, and 96 even though they had not been published and there existed

iisome doubt about their accuracy.

1

/

Higher order Gaussian Quadratures were found to be very-

efficient in the calculation of the inductance of rectangular conductors

such as strip transmission lines at various frequencies [3]. It was

found that if the width of the outer conductors were divided into n equal

parts and th'e width of the inner conductors according to a Gaussian

distribution, then the rate of convergence of the inductance function

(with respect to n the number of subdivisions) was greatly improved.

In order to obtain the limiting value of inductance (for an infinite

nixmber of subdivisions) a formula of the form Loo= Lj^ + an"^ was

used for s\afficiently large n. This equation is most easily solved for\

the unknowns Loo, a, and a, if the inductance function Ln is calculated!

for four different n chosen such that Nj/N2 = N3 /N4, Therefore,

specific high order Gaussian Quadratures were needed. I

The only high order Gaussian Quadratures that were found in

the literature were those mentioned in the references. A. H. Stroud

is working on tables for N = 2, 64, 96, 168, 256, 384, and 512 but he,

has not published them at the present time [4].

s

11

It

2. METHOD

The Gaussian Quadrature formula is given byn

F(X) dx ^ Hk F(Xk), (1)

k= 1

j

where the weighing coefficients Hy- are given by

= nPn_, (Xk) P'n (Xk)'

Pjj(X) is Legendre's polynomial of degree n, Pj^' (X) is the first deriv-

ative of Pj^(X), and the Xkig the zeros of Pj^(X) [5].

From the equations

(l-X^) P'^(X) = n X Pj, (X) + nP^_^ (X) =

(n+1) X P^ (X) - (n+l) P^+^

(X), (3)

and with Xk a zero of P^^ (X) in (3), the following relations can be

obtained:

P'n (^k) = n Pn-i (%) = -(^+1) Pn+i (^k) i (4)

jEquation (2) can now be expressed as [6]

rr 2 2(1 -Xk^)^ - (1-X^k) [P'n(Xk) f ~ (n+1)^ [Pn+i (Xk) ]^'

Since P^^ (X) is a symmetric function of X for even n and skew

symmetric for odd n, only the positive roots between 0 and 1 have to

i'be calculated [5]. The weights Hk will be the same for positive andI

(negative X's of the same magnitude.

The roots of the Legendre Polynomials and their corresponding

{weighing factors were computed as follows. Upper and lower bounds

jWere obtained for the kth root of Pj^(X), namely Xj^, k> i^om the fact

that the roots of^(X) separate the roots of P^^ (X):

3

1< Xn, I < Xn_ 1, 1 For k 1

Xn-i, k-i < ^n. k < Xn-i» k For k > 1. (6)

When n is odd, X = 0 is also a root of P^(X).

Setting the lower limit equal to a and the upper limit equal to b,

the method of false position can be used to obtain an initial approxi-

mation c :

In order to calculate P^(X) and Pj^4.j(X) the following recur-

rence relation was used:

After an approximation has been obtained, the root Xj^, ^ can be

obtained much faster by using the Newton-Raphson technique which

converges quadrically{6] :

X , = X - (9)^n+i F'(Xn) ' ^'

where Xj^^^ is the next approximation to the root Xj^. The value of

F (X^) can be obtained from (4).

The last four sets (n = 125, etc) required a little different

approach. The first root, X^^, i , was obtained for all n between 101

and 200. The fact that the roots of Pj^(X) became monotonically

increasingly further apart was then used to locate succeeding roots:

1 - Xj^,1

< 1 - X^, 2 <....< Xj^, - Xj^ +1 . (10)

4

In order to find the X^^, root, the quantity a = Xj^, j- X^, k-2

was found. Then b was set equal to X^, k-i ~ ^ and a equal to b - a.

The polynomials Pn (a) and Pn (b) were examined to see if they were of

opposite sign. If so, the upper and lower bounds were found and the

root was calculated as before. If they had the same sign, then a and b

were both decreased by a and the above process repeated until P^^ (a) and

Pj^ (b) did indeed have opposite signs.

3. ERRORS

The calculations were done with a double precision computer

routine. The routine was accurate to 1.9x10^^ (or 2^'^).

In order to check the accuracy of the abscissas the formula

n

^ X^j^ = was used. The largest error found was 5 units in

1

the 24th decimal place and the next largest was 2 units in the 24th place.

More than half of the checks had zero error in the 24th place. Squaring

a number that has an error in the kth place gives an error in the kth

place that is approximately twice that of the original error. When

checking the tables in references [l], [2], and [5] only one error in the

abscissas was found. This was in reference [5] where an error of 0. 5

units in the 21st place was discovered. The calculations had been

carried out to 7. 6 x 10^^ and the abscissas given to 21 places. The

21st-2 3rd places are 851 but the value given in the table was 8 in the

21st place instead of being rounded up to 9.

In this report the abscissas have been given to 24 places and it

'has been concluded that there is an error of no more than 1 unit in the

last place. It is also concluded that this occurrence will be very rare.

There will be further comments on the abscissas after the weights have

been examined.

239-539 0-66-2

5

The weights were checked by summing them between zero and

one and comparing the results to unity. The largest error found was

1. 48 units in the 23rd place. The previously mentioned references

were checked for errors in the weights and no error larger than 1 unit

in the last place was found through n = 48, In reference [5] a table of

errors obtained by summing the weights in references [l ] and [2] is

given. Even though the error in reference [l] reaches 11 units in the

last place, there is no error in any individual weight of more than 1

unit. It is interesting to note that the errors in [l] are always 1 unit

too small and are caused by not rounding up. It was only when the

first omitted digit was 9 that the rounding was done correctly and then

only half the time.

It was found that the errors in the higher order tables of reference

[5] (up to n = 64) were larger than expected. The sums of some weights

were in error 4 units in the last place, but almost all the error was

concentrated in the first or second weight. For example, the value of

the first weight for n = 64 was found to be 4. 7 units too small in the

last place and the sum of the weights was 4 units too small.

Since the preceding observation questioned the accuracy of the

23rd place of the first two weights of higher n in this report, the follow-

ing analysis was made. It was assumed that the errors would follow

the same behavior pattern in double precision as in single precision.

Starting at n = 50, all the higher orders were calculated in single pre-

cision and the sum of the weights obtained. Single precision was

6. 87 X 10^^ (or 2 ) which is less than eleven significant digits. It was

assumed that there were eleven good digits and the error in the 9th place

was examined. For n up to 100 the largest error in the sum was 3. 0

units in the 9th place and 2.2 units for an individual weight. The largest

error in the last four sets was 3. 9 units in the 9th place of the sum but

only 2. 3 units for any individual term. It was observed that if the error

in the sum was 1 unit or more in the 9th place, it was concentrated in

the first two weights. ^

These resxilts tend to show that the errors do follo^v a similar

pattern and give an error boiind on the weights. It is to be remembered

that in single precision there were less than eleven significant digits

and the error in the 9th place was examined while in double precision

there were more than twenty-five significant digits and the error in

the 23rd place was examined. Hence, the error in the 9th place in

single precision should be greater than the error in the 2 3rd place in

double precision. It was concluded, on the basis of the preceding dis-

cussion and the fact that the largest error in the sum in double pre-

cision was 1. 48 units in the 23rd place, that the individual weights were

accurate to within 1 unit in the 2 3rd place.

The sum of the squares of the abscissas were checked and the

largest error was 4 units in the 10th place. This was a better check

than the double precision because of a "digit" problem. The sum of the

checks reaches a value of approximately fifty for higher n and hence it

is impossible to obtain the sum accurately to more than twenty-three

decimal places. When the single precision was used, the squaring and

summing were done in double precision and hence the error in the 10th

decimal place could be examined. It has been mentioned previously

that squaring tends to double the error and also that there are less than

eleven good digits in single precision while in double precision there

are more than twenty-five good digits. Hence, the error is no more

than 1 unit in the 24th place.

The three values of n given in reference [2] were checked and

were accurate to within 1 unit in the last place. This is better than one

would expect from the above analysis since that author was only cal-

;culating his abscissas to an accuracy of 5. 1 x 10~^^, which is approx-

imately 1 digit less than reference [l]. It is believed the better accuracy

was obtained because of the rapid rate of convergence of the Newton-

!Raphson method and because triple precision was used. The convergence

7

rate was in fact observed to be approximately "squared;" the errors

were approxiraately lO"'^, 10"^, 10"-^^ for successive iterations. Henc

when the error condition was satisfied, the roots were probably more

accurate than expected and therefore the weights were more accurate.

It is believed that the larger error of the first two weights is caused

by the 1 - term in the niimerator of the expression for the weights.

4. TABLE ERRORS

After the final form of the manuscript had been prepared, the

abscissas and weights were punched onto cards from the manuscript.

These values were then subjected to the same nixmerical checks as

before and the errors checked to insure they were the same as before.

The values were also compared against the values that were punched

onto cards during the computation.

8

5. REFERENCES

P. Davis and P. Rabinowitz, Abscissas and Weights for

Gaussian Quadrature of High Order, J. Res. NBS 56, 35-37

(1956).

Philip Davis and Paul Rabinowitz, Abscissas and Weights for

Gaussian Quadrature of High Order: Values for n = 64, 80, 96,

J. Res. NBS 60, 613-614 (1958).

R. L. Brooke, C.A. Hoer, and C. H. Love, Inductance andCharacteristic Impedance of Strip Lines, to be published.

A. H. Stroud, Mathematics of Computation, Vol. 18, p. 164 (1964).

H.J. Gawlik, Zeros of Legendre Polynomials or Orders Z-64and Weight Coefficients of Gaussian Quadrature Formulae,A. R. D. E. Memorandum (B) 77/58. (Dec. 1958).

F. B. Hildebrand, Introduction to Numerical Analysis(McGraw-Hill Book Company, Inc.

, 1956).

9

6. TABLES OF GAUSSIAN QUADRATURE

N 2

ABSCISSAS WEIGHTS

0.57735 02691 89625 76450 9149 1.00000 00000 00000 00000 000

ABSCISSAS WEIGHTS

0.77459 66692 41483 37703 58530.00000 00000 00000 00000 0000

0.55555 55555 55555 55555 5560.88888 88888 88888 88888 889

N s 4

ABSCISSAS WEIGHTS

0.86113 63115 94052 57522 39460.33998 10435 84856 26480 2666

0.34785 48451 37453 85737 3060.65214 51548 62546 14262 694

ABSCISSAS WEIGHTS

0.90617 98459 38663 99279 76270.53846 93101 05683 09103 63140.00000 00000 00000 00000 0000

0.23692 68850 56189 08751 4260.47862 86704 99366 46804 1290.56888 88888 88888 88888 889

11

N B 6

ABSCISSAS WEIGHTS

0.93246 95142 03152 02781 23020.66120 93864 66264 51366 14000.23861 91860 83196 90863 0502

0.17132 44923 79170 34504 0300.36076 15730 48138 60756 9830.46791 39345 72691 04738 987

N B 7

ABSCISSAS WEIGHTS

0.94910 79123 427580.74153 11855 993940.40584 51513 773970.00000 00000 00000

52452 619043986 386516690 660700000 0000

0,12948 49661 68869 69327 0610.27970 53914 89276 66790 1470.38183 00505 05118 94495 0370.41795 91836 73469 38775 510

N s 8

ABSCISSAS WEIGHTS

0.96028 98564 97536 23168 35610.79666 64774 13626 73959 15540.52553 24099 16328 98581 77390.18343 46424 95649 80493 9476

0.10122 85362 90376 25915 2530.22238 10344 53374 47054 4360.31370 66458 77887 28733 7960.36268 37833 78361 98296 515

N s 9

ABSCISSAS WEIGHTS

0.96816 02395 07626 08983 55760.83603 11073 26635 79429 94300.61337 14327 00590 39730 87020.32425 34234 03808 92903 85380.00000 00000 00000 00000 0000

0.08127 43883 61574 41197 1890.18064 81606 94857 40405 8470.26061 06964 02935 46231 8740.31234 70770 40002 84006 8630.33023 93550 01259 76316 453

12

N a 10

ABSCISSAS WEIGHTS

0.97390 65285 17171 72007 79640.86506 33666 88984 51073 20970.67940 95682 99024 40623 43270.43339 53941 29247 19079 92660.14887 43389 81631 21088 4826

0.06667 13443 08688 13759 3570.14945 13491 50580 59314 5780.21908 63625 15982 04399 5540.26926 67193 09996 35509 1230.29552 42247 14752 87017 389

N X 11

ABSCISSAS WEIGHTS

0.978220.887060.730150.519090.269540.00000

86581 4605625997 6809520055 7404961292 0681131559 5234400000 00000

99280 393829907 515832409 341681592 572697233 153200000 0000

0,055660.125580.186290.233190.262800.27292

856710369402109376454544550867

161736490427734919901024677900

66648 27562463 46925142 61047991 85266218 06963071 448

12

ABSCISSAS WEIGHTS

0.981560.904110.769900.587310.367830.12523

063427256326741795421498934Q85

46719704749430*866179818011468

25069 054985667 846668703 689444729 670219375 269291547 2441

0.04717 533630.10693 932590.16007 832850.20316 742670.23349 253650.24914 70458

86511 82719 46295318 43096 02543346 22633 46523065 92174 90638354 80876 08513402 78500 056

239-539 0-66-3

13

N a 13

ABSCISSAS WEIGHTS

0*984180.917590.801570.642340.448490.230450.00000

30547839928090793394275108315900000

18588229773330940340364465513400000

14947965209127922064852877940600000

2829654842073985791355280000

0.040480.092120.138870.178140.207810.226280.23255

40047149983510259807604753180215532

65315377281978761945368886289730873

87952 00244791 44223846 36073828 00550231 25223841 20991019 459

N s 14

ABSCISSAS WEIGHTS

0.986280.928430.827200.687290.515240.319110.10805

38086488361315029048863632368949487

96812635736976411685581542788907343

33884517339931847014091967604366206

1597639197958020529156726245

0.035110.080150.121510.157200.185530.20S190.21526

94603808718570631671839748463738534

31751597608790358193779372129563157

86303 18320980 56318468 94253456 96081374 17260396 59279019 588

15

ABSCISSAS WEIGHTS

0.987990.937270.848200.724410.570970.394150.201190.00000

2518033924658347731321726134704093900000

2048500705104276017008538775639743400000

4284890430216200474184753369895223000000

95667759064861867227720706280000

0.030750.070360.107150.139570.166260.186160.198430.20257

3241960474922040677992058100001485382419

9611788108671712615416993155622711125561

26835 46312470 92793501 18731444 78193355 32021102 68057645 61227288 062

14

N » 16

ABSCISSAS WEIGHTS

0.989400.944570.865630.755400.617870.458010.281600.09501

0934950230120234408362444677763550725098

9164973232878315500302643572277925837637

9325957607743880338974844386349132344018

61547988046851016672242004615319

0.027150.062250.095150.124620.149590.169150.182600.18945

2459435239851168971259888651933415006104

1175438647824925553316576950024492355068

09485 17889286 28478480 99387205 24873208 15053818 93158886 67649628 540

17

ABSCISSAS WEIGHTS

0.990570.950670.880230.781510.657670.512690.351230.178480.00000

547535521791537400381159205370176344181400000

144176876726985968011669086476538769584700000

335677612290212406927658596788315298558500000

543427172956523003026247718606780000

0.024140.055450.085030.111880.135130.154040.168000.176560.17944

830289529361483384716368457610410212705364703

685477398717179934036852576810564506699256206

931962011218088971094732828808044506463252545

Oil944354479632143997527827

N 18

ABSCISSAS WEIGHTS

0.991560.955820.892600.803700.691680.559770.411750.251880.08477

516843949524664495897043008310116146225650130

209307139797555725236035373947628429150541735

946737551873920115682078753460646035095830124

001611966061241848917872593289732262

0.021610.049710.076420.100940.122550.140640.154680.164270.16914

601354548857302204415206729146467516483723829

264839496954889062871147870650262654583263143

31031 33479645 33305652 91316556 28146018 45265120 47324492 54272298 60559184 066

15

N e 19

ABSCISSAS WEIGHTS

0.992400.960200.903150.822710.720960.600540.464570.316560.160350.00000

68438815215903646565617735304607413409998645600000

43584348301481737142352296168175960636294022500000

40318030859016482497378610234694571831993758600000

901827792661892370969638726701178o960000

0.019460,044810.069040.091490.111560.128750.142600.152760.158960.16105

17882422674542700216664553962567021604208843344498

29726656993764122449473333933673606658599395448783

47703 63160033 28422658 07199946 44699471 60222767 55261177 57566677 88634764 99669597 916

N a 20

ABSCISSAS WEIGHTS

0.99312 85991 85094 92478 61220.96397 19272 77913 79126 76660.91223 44282 51325 90586 77530.83911 69718 22218 82339 45290.74633 19064 6oi50 79261 43050.63605 36807 26515 02545 28370.51086 70019 50827 09800 43640.37370 60887 15419 56067 25480.22778 58511 41645 07808 04960.07652 65211 33497 33375 4640

0.01761 40071 39152 11831 1860.04060 14298 00386 94133 1040.06267 20483 34109 06356 9510.08327 67415 76704 74872 4760.10193 01198 17240 43503 6750.11819 45319 61518 41731 2380.13168 86384 49176 62689 8490.14209 61093 18382 05132 9300.14917 29864 72603 74678 7830.15275 33871 30725 85069 808

16

N a 21

ABSCISSAS WEIGHTS

0.993750.967220.920090.853360.768430.667130.551610.424340.288020.145560.00000

2170668385933413364599634880418835821202131681854100000

2038966306504008331775677974128721907438024016089500000

5002629431828792836490861319308070578357096600909300000

02426622018772515878596790193669079370310000

0.016010.036950.057130,076100.093440.108790.121830.132260.139880.144520.14608

7228237897442540113644234729911416089386739474403911336

5777470852268572837956033671485372833337910738997049690

33332 42249379 99520828 36430201 70586155 32937766 34753419 53746178 10515472 21305906 38342719 199

22

ABSCISSAS WEIGHTS

0.994290.970060.926950.865810.787810.694480.587640.469350.341930.207860.06973

4585404978677212577768059726310403558379562080426692733

8239935428871742030079208866820691186757920848822119722

2920772712000521365316200780055929502640225152854722121

30323951069364264278069088776331814788473842

0.014620.033770.052290.069790.085940.100410.112930.123250.131170.136540.13925

7995249015333516468416062414442296023768350471498318728

9827284814526832452017067428808053910512870624601555631

20068 49915479 33028594 03148809 49672741 44496493 20821839 34042428 55637073 29717135 25799337 541

17

N = 23

ABSCISSAS WEIGHTS

0.994760,972540.932970.876750.804880.718660.619600.509500.390300.264130.133250.00000

933492471210868235828401613631987571477810380568096824200000

975521811526016704411883931950636464600730290703449846600000

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392660249197815711191625509797931489387017430000

0.013410,030980,048030,064230,079280,092910,104890,114990,123040,128900,132460.13365

185948005876717242141411757660209146640290843572212039445721

871415697931084085257671860035645412241106729880820469686106

772084443166857852129549214747410073649453046149976173717535

131069164717289702409164758860164146

24

ABSCISSAS WEIGHTS

0.995180,974720,938270,886410,820000,740120,648090,545420,433790,315040.191110.06405

721998555945520552701985941915365191471335076267968867468928

970217130902732044017390278554369758883926045961637361662605

360174981975852034219219536424569255356513848374383091562608

999783923649315439503828249683767084679386405043

0.012340.028530,044270,059290,073340,086190,097610,107440,115500,121670,125830,12793

122971388674388858496481401615865214270156680047297456381953

999872893317419154361108031953041131596553725278034682846752

19954 68166318 13180616 86078074 63730573 40327591 71988826 98863478 25860135 33439120 44629612 13815697 406

18

N B 25

ABSCISSAS WEIGHTS

0.995550.976660.942970.894990.833440.759250.673560.577660.473000.361170.243860.122860.00000

69697392144571219978262879263063684293022731423058688374692600000

90498595172897478275608343735773468412224571409387209881071000000

09790511493394136885001426305736448967729605283773432043963800000

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0.011390.026350.040930.054900.068030.080140.091020.100530.108510.114850.119450.122240.12317

37985498669156746959833380700382619594909624482591576352442960537

01026150320130675835123563500182963670507426345711357849031026715

28794 79013726 19031265 56219192 59491720 71901801 32364981 15064420 22165311 60964833 93377222 81804168 89645120 390

26

ABSCISSAS WEIGHTS

0.995880.978380.947150.902630.845440.776380.696420.606690.508440.403050.292000.176850.05923

57011544599066678619594275948872604229300714817551483948820300934

45616564706171484307884982067819957176182450523486859565689029313

92900991102501307421018798561926486063237176930648895141839620709

3217058059157666750729673814197957031078283590583719

0,010550.024410.037960.050970.063270.074680.085040.094210.102050.108470.113360.116660.11832

13726785102383258252404634149758943380039161018405181650443414152

17343926319436297147295746565913485559149442528576463198529679262

00715908787639581199835537458823921148464232359065666545820427651

565962030832945708045366841658944466637

19

N a 27

ABSCISSAS WEIGHTS

0.996170.979920.950900.909480.856200.791770.717010.632900.540550.441140.335990.226450.113970.00000

9262834759055782320679080163903473779719156458251739036936542585600000

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5669322285006851043049030227146992914092894908805889973858859669300000

88875873190806452737439748167735030159740319723928950000

0.009790.022680.035290.047440.058980.069740.079600.088420.096080.102500.107570.111250.113470.11422

8996062315705379412535368882374867731585872731637882857248636346108673

5129496180574192061559833662457305743756700281774588533568450896578956

3602662319711020627059911592987712695019507567986718721192671466296904

115603258410030432307432565125216216037505

28

ABSCISSAS WEIGHTS

0.99644 24975 73954 44995 04360.98130 31653 70872 75369 45600.95425 92806 28938 19725 41020.91563 30263 92132 07386 969o0.86569 25225 74395 04894 22550.80564 13709 17179 17144 78660.73561 08780 13631 77202 81450.65665 10940 38864 96121 98980.56972 04718 11401 71930 80030.47587 42249 55118 26103 44120.37625 15160 89078 71022 13570.27206 16276 35178 07767 68260.16456 92821 33380 77128 14720.05507 92898 84034 27042 6517

0.00912 42825 93094 51773 8820.02113 21125 92771 25975 1500.03290 14277 82304 37997 7630.04427 29347 59004 22783 959 i

0.05510 73456 75716 74543 148j

0.06527 29239 66999 59579 3400.07464 62142 34568 77902 3930.06311 34172 26901 21839 0400,09057 17443 93032 84094 2190.09693 06579 97929 91585 0490.10211 29675 78060 76981 4220.10605 57659 22846 41791 0420.10871 11922 58294 13525 3570.11004 70130 16475 19628 238

20

N B 29

ABSCISSAS WEIGHTS

0,996670.982540.957280.921180.874630.818180.752460.678210.596280.507590.413150.314030.211350.106270.00000

944225505255957023297804954876285174537617971295512888116378228618230100000

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586161748772579785097904144498133915151582037642106638993494074502301700000

319209268208375377949572261061859586262807078196637609820000

0.008510.019730.030740.041400.051590.061200.070110.078230.085470.091730.096960.101090.104070.105870.10647

690382085004922206254826930906793328327122573775713834012737331006155093817

787465612202093186820249757079550513576366172392589440859914777299732018314

409657059862264836109239113854278567838252754763346063096612373919414024424

427386441483259211958815534797190182333659651

30

ABSCISSAS WEIGHTS

0.996890.983660.960020.926200.882560.829560.767770.697850.620520.536620.447030.352700.254630.153860.05147

348408123218649004740535757623743210494761829414813769547255692619913618425

746497974768307292749205282768048269331589242420193808930878678890858355317

540272099751221325876815439744194917969386114899261767811347846435469669583

163000336871932431162898797822920478417006101037980537953025

0.007960.018460.028780.038790.048400.057490.065970.073750.080750.086890.092120.096360.099590.101760.10285

819246468347078919252672831562422985974758952978722522287371342052389726528

961661109083323696273059417619821803770529420010823778674644867954840593558

60561 54795914 23036934 97204959 68005290 29406648 17249512 81320626 82421535 47097980 23912871 76325963 94726706 27850459 64384034 129

239-539 0-66-4

21

N « 31

ABSCISSAS WEIGHTS

0.997080.984680.962500.930750.889760.839920.781730.715770.642700.563240.478190.388380.294710.198120.099550.00000

74818590963925069978002990320131484678456722991614378205901680699119935312100000

19477651529294996648482714626716624868532426007149449020823281701355705234100000

07405484006617816495043373400894040283903461826272480449430661661628775203200000

5627246590526946419269056360597144180945059413527904241351750000

0.007470.017310.027000.036430.045490.054100.062170.069620.076390.082390.087570.091890.095290.097740.099220.09972

08315862079019122739370753082447865858320386529917674060113802429333535011205447

79248903108497912385272012491661028354109877661589084779364112319863282667293426

77585 87058246 31642180 06146402 43910290 23285371 16742691 03436616 77661642 63626390 38287612 62047821 53651280 72072509 34730787 48845142 753

32

ABSCISSAS WEIGHTS

0.997260.985610.964760.934900.896320.849360.794480.732180.663040.587710.506890.421350.331860.239280.144470.04830

38618151152255560759115577613737959211874266957572990891276186022736221961576656

49481452688750637739660523256967942402893021540762322293063582127521378279687738

56354335404307768917123969701340696680382009732904390023453664977074544934831623

4981017538120919530736933097742751150746374741209917460351864813

0.007010.016270.025390.034270.042830.050990.058660.065820.072340.078190.083310.087650.091170,093840.095630.09654

86100439472065338629589808059240934222275794138957192422093038786439908720000885

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09660 04167060 51705945 57543310 26968065 68817619 61654714 52884683 76550622 54030647 17475522 22081114 27788471 28756563 91885941 90880056 676

22

N « 33

ABSCISSAS WEIGHTS

0.997420*986450.966820.938690.902310.858000.806160.747230.681730.610240.533380.451850.366330.277600.186430.093630.00000

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61680376837858350532306162019055821672878894599302213248579907430000

0.006600.015320.023910.032300.040400.048140.055470.062300.068590.074270.079310.083640.087240.090080.092120.093350.09376

6227817015554810358615413774280846664825457289854823647787608287619586398666426084461

4758712934017493232831669187113166330317186564395494886670381884460638433166559660209

37805 86567612 79548035 05395328 15659156 34169567 01556128 49448003 16371280 59614934 24773836 39170761 39333760 72857723 97484621 32411616 10099656 730

N a 34

ABSCISSAS WEIGHTS

0.997570.987220.968700.942160.907800.865930.816880.761060.698930.631020.557870.480100.398350.313310.225660.136150.04550

1753778164826252397496777463834227948766911321727055006654519277710813669162357298219

9084106309333440510718324345640093329873162628052869746903275864539463164495918253102

9192448504281760916346380469266645901418907935453164273034199406324745483869758954274

33739750464716760900357215797409300077766460410314958317864144299076

0.006220.014450.022560.030490.038160.045520.052500.059050.065110.070620.075560.079860.083510.086460.088700.090200.09095

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5590848595854943844696387233537267827524540761425560031397719984547035356937064030259

68471 86103541 52097008 40913180 94451632 17727245 38210616 82549319 39641137 85472499 90493127 08384473 88265518 70274978 42586928 70872957 39487361 534

23

N B 35

ABSCISSAS WEIGHTS

0.997700,987930.970430.945340.912850.873210.826740.773810»7l48l0.650220.580540.506320.428130.346600.262350.176050.088370.00000

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0.005880.013650.021320.028820.036110.043100,049760,056040,061870,067220.072040.076300,079960,083000,085380,087100,088140,08843

343340828329799926010115884223937040816236719228524794734571494220593766533444690530467949

204434836111483086946346326170013531237066080690867256055442423242885692099971833027507104

08497 57549226 64058088 34425404 87238053 27221878 23152980 52012857 83318888 70190396 43106466 54605353 86626293 26658837 99312522 59453424 33246297 07429063 821

36

ABSCISSAS WEIGHTS

0,997830,988580.972020,948270.917490.879920.835840.785570.729480.668000.601560.530680.455860.377670.296680.213500.128730.04301

046246476976910298437774598008716696230191715123657658102859394442547149953089236103881964

840850221249697995071565990397924753220693556855213598026245334201968944028168650938473708

836192380794933545200660713198306415128258209062095350716164267202163227050578947866560722

882833955605247458672427882177690261719199450709721827363239322619936969

0.005560.012910.020180.027290,034210,040870,047230,053240,058860,064030,068740,072940,076590.079680,062180,084070,085340,08598

571965947215152862143810757509508344713901442979735323818850841067828972667821896685732756

642458406597735965687030723644902657775945324550153573605653458701207104339796613933870394

04536 12657440 45047153 21077909 44222992 12589547 41197841 66291909 20381730 96848955 63844261 36906135 38767452 87660190 87270951 72293493 34662749 18574749 009

24

N a 37

ABSCISSAS WEIGHTS

0.997940.989180.973490.950970.921780.886120.844250.796450.743070.664480.621090.553340.481710.406700.328830.248660.166750.083670.00000

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0803409988908576814461507456304670485523815350987193093284725568867230480000

0.005270.012230.019120.025880.032460.038800.044880.050640.056050.061060.065640.069770.073400.076520.079100.081130.082590.083470.08376

30572878019044460369163989602553646629761987945165872282451567772620758861866245527224573683609

79497003078908390558475210193462437548249827423225727515570048488705293752908465364372586293138

93935 17255652 63096604 35093352 27648106 72354448 89616665 74160160 38891780 85498613 09924948 40234488 50817272 46323788 58938076 72103050 98825089 12378725 22590479 702

38

ABSCISSAS WEIGHTS

0.998040.989730.974840.953460.925740.891850.852030.806540.755680.699790.639250.574450.505830.433840.358970.281700.202570.122080.04078

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2847442608860542511049379650156677382826034529280534325667180114397896123316

0.005000.011610.018150.024570.030830.036890.042700.048220.053430.058280.062740.066780.070380.073510.076150.078280.079900.080980.08152

28807344476577797397950054081531585806182019903991093333937925070269253663578446103322493750292

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34567 59067417 76723689 88837589 52005465 87373816 49443423 58868337 43531997 37620602 23105405 29741193 50595473 92845714 52139606 59994807 53882158 60310062 32778669 922

25

N = 39

ABSCISSAS WEIGHTS

0,998140.990250.976090.955770.929400.897160.859250.815900.767400.714040.656170.594150.528370.459260.387240.312770.236320.158380.079440.00000

7383015368870935212391484711922937962974124294435832134345497268605123016391559255124533993804600000

6643254685334712465286738929929990630143310639453432010572776043709136715614818561835978370875500000

9060098363053842771122969887841539110435499836791391073988694738904866455859225376733799924775800000

54729775485008927817829137983233227238674426289063443247388259976006270119170000

0.004750.011030.017250.023360.029330.035110.040670,045970.050980.055670.060000.063960.067510.070640.073320.075530.077270.078520.079270.07952

2944647889622909384849559511143276843011466522690387360538817630930059175346937345525361326222576221

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078268081471216107906418402739494671302Oil115478851506016742

N a 40

ABSCISSAS WEIGHTS

0.998230.990720.977250.957910.932810.902090.865950.824610.778300.727310.671950.612550.549460.483070.413770.341990.268150.192690.116080.03877

7709762386994996819228082880699503222308565148255166846388967125058016920434090821850758074070624175

1055999457837741379178676688741225933311265198992714179679809512886178716052575807253013717525506050

2003400645262666558053336296725038266319387691032854837237952020771290001524730068114099712084882193

96233054337045410852825307826320497209969354261359318567488074931184551734513193

0.004520.010490.016420.022240.027930.033460.038780.043870.048690.053220.057430.061300.064800.067910.070610.072880.074720.076110.077030.07750

1277082845105835849170069019522167909081580767846997690624244013420458164736582331690036199818159479

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847474286150849268997167143500662654455569548051019156831372

26

N a 41

ABSCISSAS WEIGHTS

0 •998320.991160.978330.959900.935970.906680.872200.832720.788470.739700.686700.629760.569220.505410.438710.369500.298170.225130.150810.075620.00000

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0,004300.009990.015640,021200,026630,031910.037010,041900.046550,050930,055020,058790,062230,065310,068020,070330,072250,073750,074820,075470,07569

614039938749384106335899282117771675195126483345422519264209354254196407367766061696818820962318747055356

581647390507818687790711031699035079590969014946174257849871809665352760876208176102327223762219271547298

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400850083570755707526934076117015119157616553166635928131725878

ABSCISSAS42

WEIGHTS

0.998390.991570.979340.961750.938920.910950.878020.840280.797960.751270.700490.645880.587740.526390.462170.395420.326510.255820.183730.110640.03694

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599866220324436786952959592406907105735135777814076295663693826223558056243970332992447142617520813442342

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27

N B 43

ABSCISSAS WEIGHTS

0.998470.991950.980270.963480.941670.914940.883450.847350.806830.762110.713410.660990.605130.546110.484250.419860.353280.284860.214950.143920.072150.00000

2332295575822096613019!3687907237652371625964117471423527313742596631661176713760261281998062448980952990800000

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0.003910.009100.014240.019310.024290.029130.033820.038340.042650.046750.050600.054180.057490.060490.063180.065540.067550.069220.070520.071460.072020.07221

94902399668756499014045664413264920222218057114947119277080304619411522380412421840223344173877373427501957516

53844374013157623683138386149886860941329798254346843901888156910499914939626322293659365665085525147142193798

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ABSCISSAS44

WEIGHTS

0.99854 02006 36774 22493 60570.99231 63921 38515 80848 33380.98115 18330 77913 96666 2749Oo96509 96504 22493 13939 43980.94423 95091 18194 09920 32550.91867 52599 84175 77432 30010.88853 42382 86043 20233 83680.85396 65950 04710 37872 83020.81514 45396 45135 01048 74380.77226 14792 48755 89901 77590.72553 10536 60717 00260 69650.67518 60706 66122 36533 36990.62147 73459 03575 84780 24250.56467 24531 85470 76842 46370.50505 43913 88202 31798 27980.44292 01745 25411 48383 48270.37857 93S20 14707 13251 17650.31235 24665 02785 81223 65450.24456 94569 28201 25150 73030.17556 80147 75516 78574 65080.10569 19017 08653 24711 73060.03528 92369 64135 35905 8197

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28

N s 45

ABSCISSAS WEIGHTS

0*99860 36451 81936 63815 65480*99264 99984 47203 74174 86170.98196 87150 34540 56823 93190.96660 83103 96894 60473 64250.94664 16909 95629 06178 47210.92216 39367 19000 38809 74670.89329 16717 53241 73846 46490.86016 24759 60664 22533 9o790.82293 42205 02086 33703 57750.78178 43125 93906 29131 23630.73690 88489 45490 35262 37390.68852 16807 71200 52523 20200.63685 33944 53223 35927 12240.S8215 02125 69353 18668 09670.52467 28204 62916 06709 11340.46469 51239 19635 09857 96020.40250 29438 58541 91407 79750.33839 26542 50602 16164 34040.27266 97697 52377 56060 87650.20564 74897 83263 74571 97870.13764 52059 83253 02875 65900.06898 69801 63144 17249 04150.00000 00000 00000 00000 0000

ABSCISSAS

0.00358 26631 55283 55893 1140.00832 31892 96218 24164 5740,01303 11049 91582 78432 0630.01767 75352 57937 59061 7090.02223 98475 50578 73239 3950.02669 62139 67577 66480 5670.03102 53749 34515 46716 2510.03520 66922 01609 01624 7700.03922 02367 29302 44756 4190.04304 68807 09164 97115 1690.04666 83877 18373 36526 7770.05006 74992 37952 02979 9130.05322 80167 31268 95194 5900.05613 48787 59786 47664 3920.05877 42327 18841 73857 4360.06113 35008 31066 52250 1890.06320 14400 73819 93774 9960.06496 81957 50723 43085 3830.06642 53484 49842 52808 2910.06756 59541 63607 53627 0910.06838 45773 78669 67453 1690.06887 73169 77661 32288 2000.06904 18248 29232 02011 080

46 WEIGHTS

0.998660.992960.982730.968020.948890.925430.897750.865970.830240.790730.747600.701060.651330.598620.543190.485270.425140.363070.299340.234250.168090.101160.03377

30*2123489366981391823634379882711553948683700057053596951204846282897033023918333132287705822729222117942475321900

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29

239-5J9 0-66-5

N a 47

ABSCISSAS

0.99871 87285 84212 10918 39480.99325 52109 87768 63469 21900.98345 10030 71623 70876 49010.96934 67873 26564 49714 57440.95100 39692 57708 44258 98030.92850 26930 12360 64819 71850.90194 13294 38525 35686 7l7l0.87143 60157 96896 31694 09860.83712 01398 99902 12127 75990.79914 37541 67741 94291 55620.75767 29184 45438 63357 39970.71288 89734 09064 30166 18790.66498 77473 90332 72913 67030.61417 86999 56373 60859 54630.56068 40059 34664 19448 30580.50473 75838 63577 91977 42890.44658 40731 04855 70272 51820.38647 77640 84667 13958 33020.32468 14863 37735 90221 07610.26146 54592 14974 57030 69830.19710 61102 79111 80796 14910.13188 48665 54514 89705 38240.06608 69239 16355 67516 04740.00000 00000 00000 00000 0000

ABSCISSAS

0.99877 10072 52426 11860 05420.99353 01722 66350 75754 79290.98412 45837 22826 85774 45840.97059 15925 46247 25046 14120.95298 77031 60430 86072 29610.93138 66907 06554 33311 41740.90587 91367 15569 67282 20750.87657 20202 74247 88590 56940.84358 82616 24393 53071 10900.80706 62040 29442 62708 25530.76715 90325 15740 33925 38550.72403 41309 23814 65467 44820.67787 23796 32663 90521 18510.62886 73967 76513 62399 51650.57722 47260 83972 70381 78090.52316 09747 22233 03367 82260.46690 29047 50958 40454 49290.40868 64819 90716 72991 62260.34875 58862 92160 73815 98180.28736 24873 55455 57673 58870.22476 37903 94689 06122 48660.16122 23560 68891 71805 64370.09700 46992 09462 69893 00540.03238 01709 62869 36203 3322

WEIGHTS

0.00328 74538 42528 01488 3250.00763 86162 95848 83361 4100.01196 28484 64312 32096 394 '

0.01623 53331 46433 05967 0720.02043 693B1 47668 42764 204

|

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WEIGHTS

0.00315 33460 52305 83863 2680.00732 75539 01276 26210 2390.01147 72345 79234 53948 9590.01557 93157 22943 84872 8180.01961 61604 57355 52781 4460.02357 07608 39324 37914 0520.02742 65097 08356 94820 0070.03116 72278 32798 08890 2070.03477 72225 64770 43889 2550.03824 13510 65830 70631 7220.04154 50829 43464 74921 4060.04467 45608 56694 28041 9450.04761 66584 92490 47482 5910.05035 90355 53854 47495 7810.05289 01894 85193 66709 5510.05519 95036 99984 16286 8200.05727 72921 00403 21570 5150.05911 48396 98395 63574 6470.06070 44391 65893 88005 2970.06203 94231 59892 66390 4200.06311 41922 86254 02565 7130.06392 42385 84648 18662 3910.06446 61644 35950 08220 6500.06473 76968 12683 92250 302

30

ABSCISSAS49

WEIGHTS

0.998820.993780.984750.971760.954850.934100.909580.881400.849680.814530.776100.734550.690040.642750.592870.540610.486170.429770.371640.312010.251130.189240.126580.063420.00000

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ABSCISSAS N 30 WEIGHTS

0.998860.994030.985350.972866.956610.936650.913070.885960.853420.821580.784550.744490.701550.655890.607700.557150.504450.449800.393410.335500.276280.216000.154890.093170.03109

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31

N a 51ABSCISSAS WEIGHTS

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ABSCISSAS

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52

0.002790.006500.010180.013830.017420.020950.024410.027770.031030.034170.037190.040070.042800.045370.047770.049990.052030.053870.055520.056950.058180.059190.059980.060540.060880.06099

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WEIGHTS

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32

N s 53

ABSCISSAS WEIGHTS

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33

N s 54

ABSCISSAS WEIGHTS

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34

N 55

ABSCISSAS WEIGHTS

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35

N « 56

ABSCISSAS

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36

N a 57

ABSCISSAS

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239-539 0-66-6

37

N « 58

ABSCISSAS

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38

N « 59

ABSCISSAS WEIGHTS

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N B 60

ABSCISSAS

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40

N a 61

ABSCISSAS WEIGHTS

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0,W 1,941 1

0

89866 8l 161 14747 7544 0.01726 62929 87613 74359 4430<,92262 25813 82955 26125 7552 0.01969 84777 461 01 18133 0520<,90172 91624 74001 17064 2040 0 .02207 92731 48319 04400 2460

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w <,87848 3?372 14861 03247 8948 0 . 02440 24671 87544 20291 5340*,85294 54508 47663 44556 4847 0.02666 19985 24150 88966 281Oi,82516 24281 08659 95066 4262 0.02885 19720 68183 40150 434W i 6599P 6491 5 0 . 01096 66741 68397 39482•J 7~O fc» 470Oi,76327 60111 7211

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19714 5915 0 .03300 05887v vj rj C. 75907 41 063 2720

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N B 62

ABSCISSAS

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N « 63

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N s 64

ABSCISSAS

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N > 65

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N « 66

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882076911274553132899518537096339094943701595938467304021946611345705362586799571858359260169404583206423513578429666835949755488910001222999934760725997115912857053

281721681763055358984861246726320429083610052098708227309543923762594287389579344948257519307696512297556129420045413651471493646223

0.001670.003900.006120.008320.010510.012670.014810.016910.018970.020990.022970.024890.026760.028570.030310.031990.033600.035130.036580.037950.039240.040430.041540.042560.043480.044300.045030.045650.046170.046590.046910.047120.04722

765371625601920538872065953039026502181463617819903181769025506873511781962522890867815301380024437603838876946920323637283396276908553495227175063586156742098274812

440074174418447659908770581261027337224522771918643532614757542508293118868640468611265472881396594166828389541324170055566674315305441252739791539584876208764462998

23859 93324825 92393636 55790141 67375465 73868187 64596017 36421718 03532593 48762577 73365591 81037263 77300190 87987118 28251919 36488727 12823267 03555590 06409441 36962094 91333018 78197912 58788131 77371631 89147864 75816190 46050021 51905612 04497547 16710362 58282774 62573218 54555484 563

46

N e 67

ABSCISSAS

0.99936 54355 52976 79797 04160.99665 80272 06113 73536 43710.99179 33470 82309 60946 16980.98478 08477 55951 11344 25930.97563 55839 22908 05239 42540.96437 73304 27712 61169 56470.95103 04595 40145 37321 23480.93562 38732 70750 87686 66530.91819 09368 12738 58124 72470.89876 94049 61320 37581 84890.87740 13398 31658 72040 02980.85413 30195 37050 65079 07430.82901 48378 53301 19768 90740.80210 11^50 21694 43441 72540.77345 03798 99980 32754 15490.74312 44437 04366 20669 59620.71118 90656 10040 32785 48360.67771 34104 98280 82878 05250.64276 99791 56615 35427 81340.60643 44512 55557 38620 02980.56878 55214 41471 02125 75720.52990 47289 00236 01616 98010.48987 62807 60646 62609 55930.44878 68697 19890 88399 51330.40672 54862 86013 91598 52990.36378 32260 43954 17082 60450.32005 30^23 62536 33106 68750.27562 97949 69689 58771 55550.23060 95448 32115 73792 52300.18508 98457 83640 16881 62320.13916 92833 53523 71356 38910.09294 73112 52079 87663 17210.04652 40359 7601^ 21956 46390.00000 00000 00000 00000 0000

WEIGHTS

0.00162 83250 35240 01286 6460.00378 70083 01825 50844 5960.00594 06931 77582 23521 6510.00808 17902 99023 13621 5350.01020 54400 34102 44098 6660.01230 70038 49288 15052 1950.01438 19198 27200 55093 0980.01642 56906 22530 87920 4730.01843 38884 56804 57387 2170.02040 21633 71343 54044 9260.02232 62521 96452 07692 2800.02420 19876 09673 16472 0690.02602 53070 86213 23880 3710.02779 22616 62436 76998 7200.02949 90244 70945 66969 5850.03114 18990 19472 82393 7430.03271 73271 91531 20542 7120.03422 18969 49536 64673 9840.03565 23497 22745 00666 1330.03700 55874 63492 58202 3140.03827 86793 56179 48064 7640.03946 88681 64308 88264 2890.04057 35762 01744 52522 7250.04159 04109 15199 24309 8550.04251 71700 65830 49147 1550.04335 18464 98699 51735 9160.04409 26324 89751 01830 7830.04473 79236 60889 82547 2140.04528 63224 54669 53156 8050.04573 66411 61063 69093 6890.04608 79044 89761 57619 7220.04633 93516 82415 62110 8450.04649 04381 60264 62820 8310.04654 08367 03563 50824 990

47

N s 68

ABSC

0.99938 382550.99675 483660.99203 08tt77

0.98522 086140.97633 895040.96540 380250.95243 840440.93747 001830.92053 012080.90165 433590.88088 235900.85825 787350.83382 845900.80764 549060.77976 403160.75024 271690.71914 363020.68653 217350.65247 692910.61704 951560.58032 443760.54237 892820.50329 278770.46314 821460.42202 963360.38002 351790.33721 820670.29370 372050.24957 157080.20491 456830.15982 662720.11440 256830.06873 791900.02292 87128

SSAS

29704 34716 393476664 29253 617442443 57464 784540244 63889 449500356 95694 261282199 80323 195579602 04932 335912800 88646 562147918 16646 055220107 83021 570917455 91769 726482659 84549 496241670 94582 071189708 66523 362618897 65874 495102916 51976 757876472 99262 307366012 94478 435644676 96420 055599883 42271 694716350 74017 513591003 38581 449109084 87263 513522939 03917 277286313 5T914 693907674 47749 796495880 76272 748580638 73997 842398416 73451 157541939 29584 253077978 96099 522143910 68443 057838377 15221 139025422 34971 3996

WEIGHTS

0.00158 11402 56372 91293 9100.00367 73665 95011 73063 3570.00576 89699 18729 95202 1470.00784 87113 93177 16741 5050.00991 20012 51585 93720 9130.01195 44623 19769 44210 3220.01397 17891 74457 65581 5960.01595 97359 09613 80007 2130.01791 41204 57923 15248 9410.01983 08320 87955 49829 1030.02170 58396 10378 07980 1470.02353 51996 85876 33336 1290.02531 50650 45176 39832 3900.02704 16925 45903 96155 7980.02871 14510 27484 99071 0800.03032 08289 38553 98034 1580.03186 64417 16821 06493 9350.03334 50389 03980 68790 3140.03475 35109 79751 51316 6790.03608 88959 00179 87071 4980.03734 83853 26186 66771 6080.03852 93305 29106 71449 3250.03962 92479 60712 30802 5410.04064 58244 75954 07614 0880.04157 69221 97402 91648 4580.04242 05830 11142 49930 0610.04317 50326 84644 22322 5840.04383 86845 97956 05201 0600.04441 01430 80352 75590 9350.04488 82063 45426 66782 6350.04527 18690 18443 77786 9410.04556 03242 50648 28598 0710.04575 29654 16067 95051 9010.04584 93873 87250 97468 656

48

N = 69

ABSCISSAS WEIGHTS

0.999400.996840.992250.985640.977010.966380.953780.939230.922770.904410.884210.862210.838440.812960.785820.757070.726780.695000.661800.627250.591420.554380.516200.476980.436770.395680.353780.311150.267890.224080.179820.135180.090280.045180.00000

1427575004826672080023316662166647881470083918364982169166243659427645103343915201385159183196827758091340812181425088939191651789280427671568615875362845295690010836210600000

4324485195168532263722094428600518141608804448582747252727448050^00295467595583796008829284107869849845551513256933790450584497244620664728153503339994064385682928281510100000

7882010045118705932326338566858975347296997181400643666083852132661385760338515908865460922440240176825560145370917710344208644735317961865842858013281643599215742567235300000

80619497043471399466580039406836881865252819717216176460536947237160974442267458931079731821144198771756012759051599146497138472212016320000

0.001530.003570.005600.007620.009630.011610.013570.015510.017410.019280.021110.022890.024630.026320.027950.029530.031040.032490.033880.035200.036440.037610.038710.039720.040660.041510.042270.042950.043540.044050.044460.044780.045010.045150.04520

5976924167457995555910061679668860631865582122877105396507472836702754394330502967335953745946631288839309195331437800341701023291815007599092880200844733166188700815430216023

5279239397278703120150415106714907543406319692884939871907408454216869121875790617890096463083221683507001164020492017615406185654112800230582926659092204778312403993614577079

08407 51337260 97059482 85351061 14657558 86696554 87467099 98116473 97782913 20740278 92489462 78978565 55245536 43448379 17670599 08671177 98153903 26911124 47328949 78148614 77551405 66490650 81651393 27464120 64660053 75350208 28751285 15821387 84274103 35828438 09913809 62355754 21480219 87246051 65295424 229

49

N c 70

ABSCISSAS

0.99941 82859 73575 84205 67430.99693 62519 61680 15660 98130.99247 60552 11689 98109 89420.98604 55580 70398 65992 71010.97765 74059 57592 40039 39080.96732 82236 64986 43838 86180.95507 85091 14292 84264 03270.94093 25790 03815 35552 28160.92491 85168 97934 44027 22660.90706 81162 60922 84943 63530.88741 68168 63348 17112 43740.86600 36342 13858 62938 00350.84287 10819 98980 24231 85940.81806 50876 25441 18902 72320.79163 49010 07892 75810 76760.76363 29967 71899 56892 50950.73411 49700 60942 64130 76520.70313 94261 51528 59706 29470.67076 78640 94077 40564 62810.63706 45546 09778 09627 88600.60209 64124 85355 48733 67670.56593 28637 18808 28637 29590.52864 57076 79711 12726 50810.49030 89745 57636 58926 97780.45099 87783 81647 86573 16400.41079 31659 02630 58937 12630.36977 19616 38461 89583 94050.32801 66093 89643 25784 61320.28561 00105 40037 86169 16650.24263 63594 63740 64578 35790.19918 09763 64857 66415 14040.15533 01378 82070 24730 90060.11117 09057 94298 69373 57520.06679 09541 67551 32400 37190.02227 83952 86140 30969 3493

WEIGHTS

0.00149 27212 88844 51573 1040.00347 18948 93078 14325 5000.00544 71118 74217 21831 2820.00741 17693 63190 21036 2110.00936 17627 69699 02681 1500.01129 31846 49931 53764 9630.01320 21908 14676 74762 5070.01508 49878 65443 12768 2300.01693 78363 76302 93253 1840.01875 70570 93133 42341 5450.02053 90378 24326 45338 4490.02228 02404 52256 59583 3890.02397 72078 89100 29227 8690.02562 65709 08468 48279 8990.02722 50548 18664 41715 9110.02876 94859 55808 28066 1310.03025 67979 80154 23781 6540.03168 40379 61308 48173 4650.03304 83722 39372 42047 0870.03434 70920 49906 53756 8550.03557 76189 01292 38053 2770.03673 75096 93672 69534 8040.03782 44615 69222 81719 7270.03883 63164 84073 40397 9000.03977 10654 92776 56747 7850.04062 68527 36789 61635 1230.04140 19791 29045 20863 8230.04209 49057 27284 40602 0980.04270 42567 89449 77776 9970.04322 88225 05068 69978 9400.04366 75613 97201 44025 2550.04401 96023 90183 45875 7360.04428 42465 39055 40677 5800.04446 09684 17246 37082 3560,04454 94171 59754 66720 217

50

N 71

ABSCISSAS WEIGHTS

u <t Tf J i >f f JO ^C 1 OO 1 A6 A1 oou A A A 1 ACU • U U i *r9 1 9A791 cO f 3 9 A A90 9Q79AJ7 1 CO ARAnV 1

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ccce A9999* 0A7 9 A70 f 30 A7ROA0 ' 900 C 1 9913A0 (

AAQ 7 A A A 170641 1 OA A1 BOO A A A C9Q0 •00327 A 1 Q 9 O A A A 9S4*029 H920 J 9AO208

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9o7^9 08201 9 AOJOO09 *5 1 A 9 A A A T 9 A0 (00720 A Q 9 e o00352 Q 1 Q 9 181o31 A 0 9 9 n49330 79A7340 < 97<90

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13601 f V2o rAI19A A A AQ 1 A0 •007X0 9A9A A36264 A 1 QQ96 1992 AaRBR00909 19 9132

0 1

OSLO'S "a 9C^'3(«co3e9 9AC&QJ'v90B a9 AR0309 A A 1 AOQ0 • 0 1 O^O 9fi A A 1cooo 1 9*27o ce 1 7 A991 f U A9702 f

A0« 7 A A 1 A £. 1 aC9#1 09c A7AOOo f *oo AT AA* f 04 A A 1 9B

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0«0l2o4 A OOOA A 0 A Q 7OOOO7 D A A A7oOoO fA A 90*2

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7*3 '^OQ 99971 1 C«0 1 9 A9QA*J70 A A 1 AA70^0 i**o f4 1 RS 9* 1 993 94|!| 1 1j*oi 1

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Q AA79'OO r 2 A7AA90 1 *D2 37099 aRQ097A0 )

Q A Q7AAQT f OO 7 AAC 9A J9^*«> 1 DJ9 A A 1 A9C0 • 0 10C9 99 1 A 7cc 1 0 rAA A7fi0*0 f 0 A7 ARft0 f 09

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99923 Jft .. AQft4A ^11 ^73 1 i O f

1 9 ft ftlQQQ ft 1 ft9Q 999CAJC J Z3 U 111 98III 74Q17 7ft 9 A 9CQ («&9 a7903v '

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1 03AU 4 f IZ "lo f J OAAOA 1 aA7

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A099907223 9R9A')29cOJ 1 791 r 2

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t f Ot»7J •aQ77BJ7 f 1 3 AA7A A0*r f 4U Rl9 i 09 ft n9Aft9V • Ucoo

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7 1 c399 r1 OCA Alo94* 97AOV3 f 0" f

AAAC*o09 A A 9 AAQ0 • 03UO7 79AQ A1 c*oO ARAQ A79U70 79 1 AQ

f 2 1 07 AA 100 1A0 i

0 O 7A 1oo r 4 J9A A A A29644 976Zo A C7Q49 f O A A 99990 • 03223 Occe A79950 99AA 923**3 9209* 191

A "aafloA390t4 70787 C A 9Q Au42oO 1 A A A1404 A A ^ 9C 10 •03391 96322 AO A C A09*9* A <S A 0 903083 A A 144

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A 57705 63Z63 A A IM 1 A90519 81048 9 YAA5799 A A IT O O0 • 03586 9 9 9 ^33337 « e A A156*8 A V A *V 791077 797

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0<c A ^ « e»50315 53182 68290 07083 3606 A A 4 YAW0*03797 01 1 1 0 34831 1 e A ^ 115621 442

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f 579 A A ^ OA A0 •03890 A c ^ <4 e49335 02262 A A 7 A 0 ^ y. A240

1*2537 12849 42369 99986 3252 A A <^ O7 A0 ^03976 38597 66857 58167 A ^ A

0<i38520 96 '80 38527 29598 9720 0^04054 64310 97246 89643 493A0 1

AR 1 90 90aa7 A9A7 1Oc* f 1AA&O0*00 A A A 1 9R0 •0*129 A79AO0 f 3o9 1 OAAA

i 7000 A 9A9402*2* oil9110..30273 47475 76191 37643 4942 0^04187 54177 34733 00618 9540,,26058 06227 97318 66202 3927 0^04241 92677 39624 59303 534Oi.21792 35073 82453 33553 4383 0^04288 12371 57580 43502 0610..17484 57410 28584 86316 9688 0^04326 04342 63241 26659 8860..13143 04754 02266 08701 2910 0.04355 61271 04108 53337 1130..08776 15136 34500 68236 1807 0.04376 77449 13402 14497 2310 .04392 31485 58135 32933 2217 0^04389 48792 11788 58632 1250..00000 00000 00000 00000 0000 0^04393 72845 95852 36575 823

51

N s 72

ABSCISSAS

0.99944 99344 52962 64218 18540.99710 28716 42729 07846 59670.99288 49510 16801 90822 81040.98680 31523 75830 46580 80740.97886 87785 57233 77179 61870.96909 66979 98780 42592 21710.95750 52^75 77698 22566 42040.94411 61852 72537 96500 71810.92895 46458 80918 01057 22240.91204 90926 88671 46992 30300.89343 12635 88091 25619 58970.87313 61112 98778 90528 17080.85120 17376 54437 85111 19500.82766 93220 22754 31461 65600.80258 30439 69291 85202 70030.77599 00002 99982 56214 21970.74794 01166 32832 39067 08060.71848 60536 62234 96136 24620.68768 31082 90467 80749 14090.65558 91098 11201 05614 88970.62226 43113 39468 19100 77240.58777 12766 91655 59920 37730.55217 47629 27714 39740 02580.51554 15987 76003 52386 01590.47794 05591 68940 45718 37510.43944 22361 24960 73208 38760.40011 89062 19161 61270 27080.36004 43948 91419 23754 00740.31929 39378 46712 17133 29830.27794 40398 07847 60698 01110.23607 23308 85759 92505 78050.19375 74208 37026 05980 31330.15107 87514 82210 03032 67070.10811 64475 62102 81480 96330.06495 11663 11857 11407 46760.02166 39460 35424 04467 0326

WEIGHTS

0.00141 15163 93973 43413 5720.00328 31697 74667 49580 1900.00515 14360 18790 88690 8250o00701 02723 21861 86329 6080.00885 59960 73706 15338 3960.01068 51081 65351 89715 8960.01249 41656 19873 75776 7780.01427 97690 54554 19326 6560.01603 35649 50285 15521 8160.01776 72507 89200 65359 4360.01946 25808 63294 27804 3020.02112 13722 16440 55350 9820.02274 05105 55035 75445 5930.02431 69560 64419 16432 6350.02584 77491 00655 89028 3900.02733 00157 38950 93443 3800.02876 09731 64701 76109 5120.03013 79348 95375 47929 2980.03145 83158 22561 81397 7780.03271 96370 64293 84670 4310.03391 95306 18286 05949 7200.03505 57438 07217 87043 4140.03612 61435 07637 99298 5630.03712 87201 54502 89946 0560.03806 15915 13802 16363 4380.03892 30062 16169 66379 9960.03971 13470 44834 90178 2400.04042 51339 71733 97004 3330.04106 30269 36075 06110 1940.04162 38283 60138 59820 7610.04210 64853 97586 46414 6590.04251 00919 10057 72007 7800.04283 38901 68338 81366 6840.04307 72722 74913 69974 5250.04323 97813 05222 61748 5270.04332 11121 65486 53707 639

52

N a 73

ABSCISSAS WEIGHTS

0.999460.997180.993070.987150.979430.969920.958640.945610.930850.914390.896260.876490.855120.832190.807740.781810.754450.725720.695660.664330.631790.598090.563300.527480.490700.453020.414520.375250.335300.294740.253640.212080.170130.127870.085370.042720.00000

479881130770155903667892076590570062621622273147910444822*34298451702702855339748398152561645726908638390669367025963849619937657815664832309588283551871555744653640420319458987S5000000

4588171611889452493256483549859797*894838122476256466912065194299249090273521644833238155923262521965011898270900169287065251399459257519251530225383611301037306070079614495963841300000

17099267251515511478624569127422041571935599041474221044998248450743759248075133480238185071722336884565197600512739368098770395197638850290456117682539355526527585030175300999911800000

6471356152041028270570083851166846981684893859437991578870614091844531360220237610410399624304410222199191215739574158555805724456464679535756910000

0.001370.003190.005010.006820.008610.010390.012160.013900.015610.017300.018950.020570.022150.023690.025190.026640.028050.029400.030700.031940.033130.034250.035310.036310.037240.038100.036890.039610.040260.040840.041340.041760.042110.042390.042580.042700.04274

33764452432538516313831049260912209096875325411587538904994470163856486824190572261154923135218603540194338355490641468817022390766509980613724382871538929939298594208589568982730817683

62759772897160649174795329500029281883143359162489486702036117040642183753898727905728011640433619768504345302247280069786349557394769642706075600293849525486925425592231260186485713923

61922034521902679236247615322011272650664229908300021681691607205974623128148295060325601050493706486406721541287507846977315800597395214331033368615449452853756362659440387022220756241

399208381221391130776752553561974602677661333223380546813650707413906035689551048651494936688410895537576660145

53

N » 74

ABSCISSAS WEIGHTS

0.99947 90687 80329 52427 10440.99725 62617 11016 39083 80640.99326 14098 04644 97271 38850.98750 07266 16238 55960 71240.97998 43454 31300 33609 88040.97072 56040 42518 72681 93550.95974 09554 59528 91269 99170.94704 99264 28385 00827 26280.93267 50794 62054 56608 56010.91664 19716 42906 46067 71480.89897 91087 61895 79558 37150.87971 78944 52083 80922 87630.85889 25742 65983 57679 64870.83654 01747 42815 73916 83480.81270 04375 51974 37387 52550.78741 57488 19575 51781 99870.76073 10637 58994 47596 86230.73269 38267 36880 27776 24640.70335 38869 15441 85906 03200.67276 34096 20247 60271 85060.64097 67835 90692 38859 53420.60805 05242 77779 82552 51630.57404 31733 60994 15250 18930.53901 51946 62817 08324 07270.50302 88666 45885 16591 40730.46614 81716 83881 18342 20600.42843 86823 03003 27937 58290.38996 74445 96250 75057 10720.35080 28590 17798 04749 25350.31101 45587 69390 63704 97580.27067 32859 94980 40553 76720.22985 07660 03717 03101 81700.18861 95797 44918 57831 07210.14705 30347 61753 41172 885l0.10522 50348 53070 97186 39890.06320 99486 75116 29189 57270.02108 24775 16748 30444 7535

0.00133 67616 50069 88355 0330,00310 94201 49896 75467 8670.00487 91797 58594 14458 4290,00664 04929 09114 35763 4760.00839 00454 33971 39706 4090,01012 46945 38287 30542 1120.01184 13475 47499 66732 3170,01353 69494 11787 49434 1050.01520 84842 43401 23480 8870.01685 29795 82024 85358 4850.01846 75113 08979 87978 2850.02004 92087 02794 94425 273

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0.02310 29147 74915 82303 0930,02456 94939 95942 76724 565

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0,02599 23896 00723 78786 677 '

0,02736 90717 19679 35230 2440,02869 70926 53269 87534 2100,02997 40912 22461 18733 9960,03119 77969 65915 42603 3370,03236 60341 76216 99952 5280,03347 67257 67828 76626 3720,03452 78969 69826 46100 3330.03551 76788 36800 95992 5850.03644 43115 71658 56448 1810.03730 61476 54394 15573 3710.03810 16547 71263 24889 6350.03882 94185 39137 70775 8080.03948 81450 20196 46832 3630.04007 66630 22476 96675 9150.04059 39261 82194 72805 8080.04103 90148 24127 26684 7420.04141 11375 96753 51082 0070.04170 96328 79240 75437 8710.04193 39699 57777 02146 9960,04208 37499 69156 97247 4900,04215 87066 09943 42212 223

54

II

N « 75

ABSCISSAS WEIGHTS

0.999490.997320.993430.987820.980500.971490.960790.948430.934420.918800.901590.882810.862510.840720.817470.792800.76677Oa739400.710750.680880.649820.617640.584400.550140.514920.478820.441890.404190.365790«326760.287160.247070.206550.165670.124500.083120.041590.00000

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55

N s 76

ABSCISSAS

0.99950 59^83 62153 07810 62020.99739 77863 55355 43669 14340*99360 87727 23526 98461 61910.98814 44533 59837 43849 86450.98101 39389 75655 89525 18380.97222 92285 20376 90447 80800.96180 51267 58767 82716 80320.94975 92077 10896 38508 48950.93611 17819 34810 79626 32230.92088 58612 52150 11849 15810.90410 71195 45566 82854 44260.88580 38492 92082 78721 49100.86600 69137 71981 95522 78680.84474 96949 83342 39401 08900.82206 80373 28974 61347 77710.79800 01871 61200 16975 28100.77258 67282 8l809 76129 76740.74587 05135 03610 44314 86390.71789 65923 87703 63937 30060.68871 21352 77640 59699 65250.65836 63537 58142 63027 52330.62691 04176 72266 55914 54520.59439 73688 36792 91815 15060.56088 20316 01237 47899 91620.52642 09204 01242 59095 53070.49107 21444 62193 86486 17450.45489 53098 13726 33943 38410.41795 14187 80327 29879 56600.38030 27671 17504 44346 75050.34201 28389 66962 02393 12010.30314 61998 07907 77809 94150.26376 83875 84994 27647 94060.22394 58021 96474 13376 26380.18374 55935 28914 47741 92450.14323 55482 27267 52144 55080.10248 39753 91227 01830 005l0.06155 95913 90611 20842 86680.02053 14039 93998 63550 1747

WEIGHTS

0.00126 77916 34085 35966 3280.00294 91029 53642 47490 0390.00462 79352 28037 42132 6130.00629 91804 97328 44586 6570.00795 98474 77239 73462 1120.00960 71054 14713 75408 2400.01123 81685 69667 68723 9670.01285 02838 47510 14494 4920.01444 07317 48276 67993 9890.01600 68299 12248 57088 8510.01754 59372 91474 23095 4200.01905 54584 67190 58280 6800.02053 28479 67908 02109 2970.02197 56145 34416 24916 8010.02338 13253 07011 18662 248

,

0.02474 76099 20659 67164 3260.02607 21644 97985 98352 4270.02735 27555 31827 52167 4150.02858 72236 50054 00377 3980.02977 34872 55905 04095 6710.03090 95460 37491 59538 9940.03199 34843 40421 60006 8540.03302 34743 97791 74100 6540.03399 77794 12056 38084 6740.03491 47564 83550 76744 4130.03577 28593 80713 94752 7780.03657 06411 47329 61700 7240.03730 67565 42381 60982 7570.03797 99643 08405 28319 5240.03858 91292 64506 73834 2920.03913 32242 20518 44076 7510.03961 13317 09062 05842 3l50.04002 26455 32596 82611 6460,04036 64721 22844 02315 4100.04064 22317 10294 73877 7460,04084 94593 01828 49228 0390.04098 78054 64793 95154 1310904105 70369 16229 42259 326

N a 77

ABSCISSAS WEIGHTS

Ot999510.997460.993770.988440.981490.972930.962770.951030.937730.922880.906520.888670.869360.848620.826490.803000.778190.752100.724770.696260.666600.635840.604040.571250.537520.502910.467470.431260.394340.356780.318630.279950.240820.201290.161430.121300.080980.040520.00000

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417728324927184926859736017508624918625512291059264200151870140396357284532488264346876167368103713104035527033525205

57

N o 78

ABSCISSAS

0.99953 07999 92423 759510.99752 86383 7872^ 361500.99392 99616 94488 743180.98873 97320 93717 434380.98196 61630 99550 497780.97362 00785 06236 442050.96371 48359 86755 901550.95226 62946 89863 363710.93929 27869 14946 593070.92481 50877 80063 776360.90885 63815 73188 258200.89144 22244 58818 578800.87260 05034 72724 504930.85236 13918 22557 703280.83075 73005 45911 272730.80782 28265 94201 686760.78359 46974 21142 787070.75811 17121 62315 315070.73141 46794 98830 397490.70354 63523 03923 772120.67455 13591 76750 790320.64447 61329 72792 854590.61336 88364 45184 776790.58127 92851 15951 755220.54825 88675 00612 608740.51436 04628 13864 058020.47963 83562 88107 239680.44414 81522 40408 603060.40794 66850 27098 391640.37109 19280 28596 274320.33364 29008 10210 560780.29565 95746 07580 145220.25720 27762 88112 442980.21833 40909 42211 978810.17911 57632 60289 151560.13961 05978 53483 594900.09988 18586 77728 410520.05999 31677 22217 693630.02000 84031 24517 92295

8690 0.001202298 0.002802190 0.004394564 0.005984518 0.00756991

1

0.009129840 0.010677212 0.012210647 0.013720328 0.015227326 0.016698555 0.018131392 0.019546002 0.020927268 0.022278652 0.023581318 0.024860401 0.026098445 0.027280565 0.028433894 0.029543098 0,030599409 0.031601530 0.032566769 0.033461891 0.034315151 0.035117264 0.035856849 0.036535727 0.037162719 0.037722958 0.038238523 0.038673689 0.039052423 0^039379276 0.039628495 0.039815875 0.039942067 0.04001

WEIGHTS

40245 66067 35328 0330B688 11838 63041 16155960 39460 34674 27434899 44440 40798 96518431 89439 71882 69880992 27255 08727 69497421 57481 11335 35242845 49789 88639 76892679 20144 14839 37322656 80178 45169 33208866 89343 89186 62127789 54982 32864 44156333 43399 92337 79271872 51877 72678 53852282 19113 88676 30575974 61457 47209 64521933 26222 45076 14469746 55108 83502 98399640 51624 36486 45692510 46897 51626 23929951 58606 94641 16294288 38013 04528 94368603 00304 79773 88836762 33689 04440 80683443 82858 97797 29894160 02689 09029 02955281 78217 18947 48854060 07191 69544 50178646 41684 70064 81918111 85498 38685 06762464 44324 24786 42902665 25850 98764 96230642 87257 67400 39039306 27773 41314 73122556 24233 12193 72275295 07810 54295 63993434 80364 08922 50373903 69088 02487 93014651 18420 48298 878

58

N 79

ABSCISSAS

0.» 99954 25284 79569 84432 41520..99759 03943 36941 43517 68540.99408 15547 85542 62241 11550..98902 07076 87784 33787 47580<.98241 56592 51278 93009 85810..97427 66995 97807 11817 88340..96461 65291 14864 78610 74500«.95345 02278 89269 13596 32760..94079 52293 06577 25030 00170..92667 12918 80903 87366 45230..91110 04680 34580 80024 50060..89410 70695 04235 10131 04300..87571 76293 03529 47665 95180<.85596 08602 55219 37647 3271Oi.83486 76101 37777 88206 73140..81247 08135 07806 77376 48080*.78880 54402 69197 76556 5029Oi.76390 84410 67170 10845 83260..73781 86895 91278 20952 53220,.71057 69218 76824 16375 8205Oi.68222 56726 99071 05927 7620Oi.65280 92091 59343 99852 4893Oi.62237 34615 66577 23888 2910Oi.59096 59517 22139 98285 3282Oi.55863 57187 19858 90665 5853Oi.52543 32423 77054 54789 62680,.49141 03644 16119 82109 5861Oi.45662 02075 19689 13114 8710Oi.2111 70923 85771 92873 2146Oi.38495 64529 12350 88392 2247Oi.34819 47496 43867 86723 9137Oi.31088 93816 14736 43720 8875Oi.27309 85967 27523 54374 2536Oi.23488 14008 05731 91587 7249Oi.19629 74654 63184 64165 9194Oi.15740 70349 33861 60502 82260..11827 08320 07660 88116 69120<,07894 99632 18954 40544 80850 .03950 58234 35974 06405 89950..00000 00000 00000 00000 0000

WEIGHTS

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59

N 3 eo

ABSCISSAS

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60

N a 81

ABSCISSAS

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WEIGHTS

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61

N 82

ABSCISSAS

0.99957 51915 01652 64887 41290.99776 23858 26385 86256 23580.99450 37683 78075 62893 40000.98980 33388 39908 94993 26250.98366 78235 22007 60336 78880.97610 60970 94498 82869 14200.96712 91162 52590 69599 60770.95674 98938 61610 90312 17990.94498 34774 38960 48918 22460.93184 69264 54622 88785 47330.91735 92872 53280 10714 57620.90154 15652 88841 25819 62850.88441 66945 96724 70822 79910.86600 95045 04765 44857 06840.84634 66836 12913 70179 5724Og82545 67410 85767 65602 86350.80336 99653 10108 29930 18830.78011 83799 75358 24519 39670.75573 56976 39560 41729 75540.73025 72708 47596 24505 16930.70372 00^08 72166 67849 38360.67616 24841 51647 02456 59510.64762 45565 02346 59856 63110.61814 76351 85978 68204 10300.58777 44589 16284 86715 37090.55654 90658 91763 81234 73220.52451 67299 44327 76797 50800.49172 38948 96449 32246 34590.45821 81072 21963 19782 28630.42404 79471 08150 72216 35590.38926 29580 19054 81592 10470.35391 35748 62147 93640 53950.31805 10508 62501 50501 00840.28172 73832 50480 10236 82640.24499 52378 70704 53783 91770.20790 78728 21592 35096 62290.17051 90612 36190 15976 70990.13288 30133 16257 52576 48140.09505 42977 32644 87395 28870.05708 77625 05926 93190 29600.01903 84554 82006 81376 1455

WEIGHTS

0.00109 01185 95275 83086 6110.00253 60546 96856 10610 9820.00398 04579 37856 07461 9030.00541 92762 32446 76509 0710.00685 02745 34183 52618 4330.00827 13518 18383 68560 4430.00968 04407 04371 07373 6970.01107 54957 81759 89632 0220.01245 44934 01142 10467 9730.01381 54337 14126 45938 7730.01515 63432 70762 56178 8470.01647 52777 63983 70889 1010.01777 03247 98498 40714 6980.01903 96066 40178 92507 3040.02028 12829 26912 15890 1570.02149 35533 30774 84404 3490.02267 46601 64914 10310 2440.02382 28909 30047 82634 2230.02493 65807 96240 75515 5770.02601 41150 16017 02375 3870.02705 39312 65124 77151 9790.02805 45219 07454 23047 1710.02901 44361 80764 40396 1450.02993 22823 00012 72463 5090.03080 67294 75215 62981 3670.03163 65098 40900 24553 7620.03242 04202 94340 60507 7840.03315 73242 39907 21132 7760.03384 61532 36996 85874 4640.03448 59085 49150 70550 7380.03507 56625 92112 69038 4780.03561 45602 78727 47268 0500.03610 18202 58727 0230? 5700.03653 67360 51607 65284 2200.03691 86770 70954 45699 8530.03724 70895 38727 66418 7840.03752 14972 88185 02087 1570.03774 15024 54275 86967 1540.03790 67860 50505 78477 9460.03801 71084 31435 26990 5300.03807 23096 40141 87120 770

4

N > 83

ABSCISSAS WEIGHTS

0.999580.997810.994630.990040.984050.976670.967900.957770.946280.933450.919290.903840.887U0.869120.849910.829460.807890.785150.761300.736380.710410.683430.655490.626620.596860.566260.534860.502700.469830.436290.402140.367410.332170.296460,260320.223820.187000.149920.112630.075170.037610.00000

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0.001060.002470.003830.005290.006680.008070.009450.010810.012160.013490.014800.016090.017360.018600.019820.021010.022170.023290.024390.025450.026470.027460.028410.029320.030180.031000.031780.032520.033210.033850.034440.034990.035480.035930.036320.036660.036950.037190.037380.037510.037590.03762

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638333200524136359824036303070085544017167931401199016743082511893375804410307355129117-

931252152584733990390976400092506197575

63

N 84

ABSCISSAS

0,99959 50612 26923 24220 47470.99786 70164 21711 96156 14190.99476 06382 61284 64119 58370.99027 95289 65356 68733 42160.98442 97971 27581 65151 90750,97721 95073 58315 78265 43010.96865 86181 73621 89769 06280.95875 89587 29693 47201 99490.94753 42099 47443 12281 12760.93499 98847 63558 81775 24010.92117 33063 63051 21772 72070.90607 35840 94008 42133 99760.88972 15869 88315 46080 39390.87213 99148 83579 03202 98110.85335 28671 68918 66159 87410.83338 64091 90021 42884 60530.81226 81363 56123 03902 29380.79002 72359 96596 86796 77380.76669 44470 18836 28266 69000.74230 20174 22609 92077 35220.71688 36597 29274 82382 28820.69047 45043 87248 47122 03070.66311 10512 18014 63433 61990.63483 11189 69691 48364 40140.60567 37930 47833 38968 42690.57567 93714 95674 15604 19160.54488 93092 98449 68891 26470.51334 61610 88761 40004 61040,48109 35223 32156 17605 43090.44817 59690 74202 33115 85000.41463 89963 32331 21933 99900.38052 89552 17588 70053 88010.34589 29888 73197 05903 31300.31077 89673 18463 97262 79710.27523 54212 88088 56049 93540.23931 14751 58303 36570 92930.20305 67790 52553 47812 88090.16652 14402 20548 15896 64450.12975 59537 85524 74180 0538Oc0928l 11329 55437 88274 62500.05573 80387 94528 21699 92730.01858 79096 52332 13328 6830

WEIGHTS

0.00103 91335 16451 97188 9190,00241 75112 65443 12285 5230,00379 45916 50452 34969 6390,00516 66051 82746 80832 9880,00653 15136 87713 65460 1120,00788 74057 52648 14638 2110.00923 24007 84190 24701 4380,01056 46376 23008 24526 4850,01188 22740 89801 22349 5050,01318 34886 79182 34598 6800,01446 64827 89161 18624 2270,01572 94830 95583 59820 1600.01697 07439 55211 61134 3080.01818 85497 96056 54992 7600.01938 12174 77318 80864 7810.02054 70986 09756 27861 1520.02168 45818 30644 82298 9240.02279 20950 28942 12933 8890,02386 81075 16958 23938 4720.02491 11321 45206 42888 4390.02591 97273 57334 64772 5160.02689 24991 82197 63751 5820.02782 81031 60258 40603 5770.02872 52462 01621 80221 2660.02958 26883 73110 84528 9610.03039 92446 11902 46977 3110.03117 37863 63345 66129 1970,03190 52431 40692 72748 4020.03259 26040 04584 25718 3610.03323 49189 60240 44407 4720.03383 13002 70425 98480 3720.03438 09236 82372 70062 1340,03488 30295 66963 30845 6420.03533 69239 68601 27616 0390,03574 19795 64315 30727 7890.03609 76365 30772 56670 1750.03640 34033 18002 12248 8630.03665 88573 28759 07563 6580,03686 36455 02590 30771 8450.03701 74848 03794 52058 5240,03712 01626 12602 09427 3730,03717 15370 19034 06760 328

64

N = 85

ABSCISSA3 WEIGHTS

0.999600.997910.994880.990500.984790.977740.969380.959710.948740.936490.922980.908220.892230.875040.856670.837150.816490.794730.771900.748020.723140.697280.670480.642770.614200.584790.554600.523660.492010.459700.426760.393250.359210.324690.289730.254370,218670.182680.146440.110000.073420.036730.00000

44773660112374252177095767288437U9151593756252381249603771589878972379183821673503485672534544920305147448798331046620122115365895655539606534402529791387962949238039176027565511473522398894010763401016604878200000

57478981169561616415855801224323678571885457B16430960903909191355690970995637082747915911690293774342860142249586623251490136373888626970567228518708843009200598043852247951738245384059371129051011577432910124900000

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0.001010.002360.003700.005040.006380.007700.009010.010320.011610.012880.014130.015370.016590.017780.018950.020090.021210.022300.023350.024380.025370.026330.027260.028140.028990.029800.030570.031300.031980,032630.033220.033780.034290.034750.035160.035530.035850,036120,036340,036520,036640.036710.03674

49719133176500168384039855355999154230020751235288891455213507568390343042665962302030807984904464017871668443026346882555046498414228421988791270444589267255140571323005711574457038284479897002501394397598344731454

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74369 53702089 67731670 68744272 54551509 86975707 99063127 89724589 38289800 96208429 05183293 05662687 44167007 52117090 77484044 68142174 17937967 24237418 94689189 77068314 24208847 73735982 17316478 57707584 63815208 98788737 56199572 39287044 84067445 97717818 90476976 25353033 13184670 82263752 92578824 98169908 19981255 69246037 47520376 67688485 74870248 64161622 21510660 021

65

N 86

ABSCISSAS

0,99961 35688 41325 85701 73520.99796 44770 35243 94478 51980.99499 99174 85337 89622 40280.99072 31407 45518 70521 99460.98513 97067 32502 41361 11350.97825 69602 53684 71662 24820.97008 39726 85740 13135 85670.96063 15209 42898 44862 94150.94991 20708 52210 25571 20080.93793 97599 09892 61443 30430.92473 03783 22861 94977 70460.91030 13480 46165 83021 05530.89467 16997 39446 33437 90390.87786 20476 33365 93733 99160.85989 45623 22684 95530 02090.84079 29415 14433 05169 97110.82058 23787 66160 22153 70500.79928 95302 53661 78813 62530.77694 24796 11023 37105 44700.75357 07008 88808 90349 79410.72920 50196 78928 32289 87180.70387 75724 57267 69479 64270.67762 17641 97588 51065 59520.65047 22243 12526 23285 09950.62246 47609 79750 81191 32540.59363 63139 13498 03367 20880.56402 49056 43741 32901 51050.53366 95913 67248 68330 38490.50261 04074 36657 27450 19130.47088 83185 55497 78357 79450.43854 51637 48809 09401 17830.40562 36011 80600 39615 11740.37216 70518 90939 61032 41350.33821 96425 26872 66641 19640.30382 61471 42705 73506 27720.26903 19281 46410 30510 04100.23388 28764 70037 46374 0116Ool9842 53510 43051 40281 45320.16270 61176 48411 71433 75320.12677 22872 420*8 25298 61990.09067 12538 17080 16703 13770.05445 06318 94731 20602 99350.01815 81937 24385 81593 3443

WEIGHTS

0.00099 16432 66620 36352 5570.00230 70874 88809 90292 5970.00362 14392 49610 90143 7560.00493 11840 96960 10369 6420.00623 44591 39140 12346 3890.00752 95216 12194 56260 6850.00881 46571 01954 81570 3780.01008 81684 60386 10565 4670.01134 83751 56177 70397 7170.01259 36146 78069 69781 04l0.01382 22444 52766 67086 6650.01503 26439 05081 37868 4950.01622 32165 49729 02258 8080.01739 23920 75690 54238 6720.01853 86284 06709 85920 6310.01966 04137 29562 17980 7400.02075 62684 84909 14279 0580.02182 47473 16927 62780 0680.02286 44409 78548 00644 5770.02387 39781 89479 00497 3220.02485 20274 44399 83591 8330.02579 72987 68839 53540 7770.02670 85454 20372 20957 5310.02758 45655 32851 24838 7380.02842 ^2037 01493 49475 7310.02922 63525 06709 94458 3660.02998 99539 74664 93249 1340.03071 40009 72632 05318 3040.03139 75385 37302 86555 8530.03203 96651 34294 01611 0230.03263 95338 47189 92195 6100.03319 63534 94551 59712 0090.03370 93896 73417 55486 4970.03417 79657 27919 90463 4240.03460 U636 41737 69225 9930.03497 93248 53210 09937 1410.03531 10509 92034 20508 0580.03559 62045 36575 49559 0690.03583 44093 90924 05578 9780.03602 53513 80935 25771 0090.03616 87786 68600 63758 2750.03626 45020 84202 38743 1490.03631 23953 75813 33828 232

66

N 87

ABSCISSAS WEIGHTS

0*999620*998010*995110.990930*985470*978740*970760*961520*951040.939330*926410.912300*897020*880580*863000*844310*824530*803690*781810*758930*735070*710260*684530.657920.630470.602200.573150.543370*512890.481740.449970*417630.384740.351360.317530.283290*248680*213750*178550*143120*107500*071740*035890*00000

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67

N 88

ABSCISSAS

0.99963 08360 56270 65578 13230.99805 54080 53249 67760 60020.99522 31758 87988 87078 11010.99113 70781 54015 55511 16120.98580 21860 87763 55228 39360.97922 52031 54296 70377 68920.97141 44101 41322 27648 03680.96237 96460 63770 68298 98880.95213 22934 63802 11252 20330.94068 52633 02643 54526 20050.92805 29783 94692 05558 05040.91425 13551 04527 19133 99780.89929 77832 30057 05484 46730.88321 11040 59450 58162 37220.86601 15866 13781 33402 29130.84772 09020 98209 08719 70150.82836 20965 90456 24485 08380.80795 95619 99236 49182 45330.78653 90053 28287 15747 99790.76412 74162 84206 84196 75970.74075 30332 68607 77358 17680.71644 53077 97250 48565 99420.69123 48673 90880 43802 03430.66515 34769 84453 17222 19940.63823 39989 03326 45028 35410.61051 03514 56818 98623 95870.58201 74662 01287 35758 07580.55279 12439 26555 47279 7l760.52286 85094 21143 75372 7o450.49228 69650 73286 72288 58880.46108 51433 66196 51061 27510.42930 23583 27424 37021 10250.39697 86559 93491 05024 59840.36415 47639 52198 28781 53010.33087 20400 26196 27510 91260.29717 24201 62464 30558 75420.26309 83655 93362 60022 8498Oc22869 28093 35831 31389 64010.19399 91020 96146 78857 79600.15906 09576 48394 21594 409l0.12392 23977 55479 06164 76220.08862 76967 02076 05880 46140.05322 13255 09403 57652 19640.01774 78959 02112 09828 8902

WEIGHTS

0.00094 73355 98161 92726 6770.00220 40585 63143 69662 8540.00345 98676 67862 79642 3970.00471 14792 79598 66174 3020.00595 71869 96138 04658 3130.00719 53984 59796 37205 9760.00842 45474 92702 47301 5100.00964 30833 22053 20440 0770.01084 94697 75429 27125 9400.01204 21864 39581 21230 9740.01321 97303 13627 91170 8180.01438 06176 01299 94423 5930.01552 33855 36933 55384 0170.01664 65942 08217 65604 5110.01774 88283 60324 07455 6500.01882 86991 73755 45139 4710.01988 48460 11274 11324 3600.02091 59381 30576 62423 225Oa02192 06763 59989 85359 5630.02289 77947 34781 14232 7250.02384 60620 91859 66126 3580.02476 42836 20768 73302 5320.02565 13023 68961 94788 4780,02650 60006 99434 73772 1410.02732 73016 98855 33083 5620.02811 41705 34408 61349 1580.02886 56157 57635 42924 6480.02958 06905 53619 34911 3350.03025 84939 33943 52533 5140.03089 81718 71912 19763 3700.03149 89183 78604 89232 0040.03205 99765 18406 38806 9270.03258 06393 62732 10868 6240.03306 02508 80746 70014 5280.03349 82067 65953 09252 8070.03389 39551 97610 25923 9890.03424 69975 36020 07873 7370.03455 68889 50807 08413 4870.03482 32389 81399 35499 3130.03504 57120 29004 26139 6590.03522 40277 79459 10853 2880.03535 79615 56423 84379 3670.03544 73446 04470 76970 6140.03549 20643 01714 54529 607

68

N 89

ABSCISSAS

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N a 93

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N B 94

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N « 95

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75

N a 96

ABSCISSAS WEIGHTS

0.999680.998360,995980.992540.988050.982510.975930.968320.959680.950030.939370.927710.915070.901460.886890.871380.854950.837620.819400.800300.780360.759600.738030.715670.692560.668710.644160.618920.593030.566510.539380.511690.483450.454700.425470.395790.365690.335200.304360.273190.241740.210030.178090.145970.113690.081290.048810.01627

950384375818429390034126372635917456828482914271770339724567142310635345174850599033435112031078744190438234110643768123453668310034037584012364704185810834177179739942218988476498686148522849443881253156113104688233714658501749542985167448

8323063181872092376229623630H851366326448742844375275522308208981585202420092963460128187379313914067433766474440048967421714391684967254687757261397243575466720596677430730028908723139262554496910496384060567676185489610665644253604949602

766826777229065624577994867744466452121753930635752169369096074203413141605502874554612149675538172221760498701328562622561341539510679570380806816840436226735835976008635453660328635034226135302141480123220360602759419892091558997311196957

7690414903991892076370462601365900686099185746905885923368783775278743039000879636042970116651444246255784126369355642506803551084065676481950000896632639307272793228*7940391071208447119589135

0.000790.001850.002910.003960.005010.006050.007090.008120.009140.010160.011160.012150.013120.014090.015030.015970.016880.017780.018660.019510.020350.021170.021960.022730.023480.024200.024900.025570.026210,026820.027410,027970,028490,028990,029460,029890.030290,030670.031010.031310.031580.031820.032030.032200,032340,032440,032510.03255

67920396070731845543420278545564707687698671207705210201604682295094178721005629547982502306796908116797129398664447069633990484i706332003602340768667296270007674110461411089963441991541376103325642559330787588445626204738225716376118706144

655528894617934384444292704235911532569830783350089983871088669617231426994025626424516045274114014554333921913874458329859269236422483053493567225591260291684865085505555816736328208272366986313968617072794411319929403068575140641386892363

01242 94392173 23494640 84168667 37351769 24796168 33286526 91475921 73838663 25841575 75949859 12131963 51857263 70686091 58693800 58829138 06217245 04826083 76146738 51602241 00932459 52529898 76734919 47637400 13521984 22469128 22761028 83836149 88041391 34676219 80624282 34233443 98238564 56023654 26890597 04438598 43959379 40914901 42383742 32535581 27816855 80200653 47566321 81425066 86792842 87726936 40183598 72116624 196

76

N « 97

ABSCISSAS

0.99969 58399 95246 72491 19680.99839 77458 60566 43673 32440.99606 37894 77488 41302 43120.99269 58747 78551 60925 8l500.98829 74345 01838 78731 78940.98287 30196 13528 35103 59240.97642 82563 08619 76492 42450.96896 98330 34950 92210 01100.96050 54916 52787 24615 74860.95104 40187 66639 19521 09080.94059 52363 58027 98437 16850.92916 99914 81619 14082 22600.91678 01449 53188 88804 97960.90343 85590 10121 61641 49130.88915 90839 44300 36203 90290.87395 65437 15414 21535 92030.85784 67205 56790 30126 05580.84084 63385 88286 76745 75150.82297 30^64 52484 44175 04200.80424 53989 9i770 56547 88880.78468 28379 85085 72883 04140.76430 56719 64182 05690 20060.74313 50551 30253 93804 30620.72119 29653 92770 52494 62370.69850 21815 53271 11663 67790.67508 62596 57784 96582 45650.65096 95085 42408 25510 96240.62617 69645 97413 85451 29890.60073 43657 76084 20837 69190.57466 81248 75244 10432 73780.54800 53021 15227 73465 59860.52077 35770 47742 83654 72200.49300 12198 20793 19724 53210.46471 70618 30488 81340 72760.43595 04657 9o209 87643 83860.40673 12952 48l95 90288 42060.37708 98835 85204 14430 09730.34705 70025 24421 32148 19130.31666 38301 86319 18806 11980.28594 19187 21616 92317 37700.25492 31615 55951 39902 50670.22363 97602 80259 51755 51850.19212 41912 21244 64623 57200.16040 91717 26631 32738 27810.12852 76262 00208 54546 96830.09651 26519 21921 60690 16570.06439 74846 88495 84802 18850.03221 54643 10261 70891 10520.00000 00000 00000 00000 0000

WEIGHTS

0.00078 05332 21942 56124 5720,00181 61463 98210 03960 9510.00285 14092 43213 05577 1420.00388 38453 29489 29442 1730.00491 22762 62166 02813 0840.00593 56156 30788 22295 4180.00695 27960 96469 40552 6470.00796 27599 97865 49559 5600.00896 44581 76697 99943 2570.00995 68504 27084 04494 8240.01093 89063 59195 94895 3970.01190 96063 85330 75683 2740.01286 79427 42493 38667 5710.01381 29205 21853 04327 1150.01474 35586 93236 95017 6360.01565 88911 19156 92052 0210.01655 79675 55342 45662 9030.01743 98546 35807 80463 9410.01830 36368 40964 14082 2290.01914 84174 47528 12933 5260.01997 33194 59108 04688 8190.02077 74865 16426 56849 7990.02156 00837 86191 71827 8430.02232 02988 27667 13237 8620.02305 73424 36025 99579 6400.02377 04494 61603 06882 1040.02445 88796 04187 84729 0600.02512 19181 81530 04673 5650.02575 88768 71256 78489 5350.02636 90944 25429 34975 7080.02695 19373 56996 44067 3630.02750 68005 97430 34256 0100.02803 31081 24862 67752 6810.02853 03135 62067 18751 8240.02899 79007 43668 43187 2050.02943 53842 51987 32086 4240.02984 23099 20967 02903 4580.03021 82553 07656 01453 4520.03056 28301 30758 58386 1350.03087 56766 75797 65382 4330.03115 64701 66469 04145 7750.03140 49191 01801 72362 4580,03162 07655 58774 01604 2950.03180 37854 60071 49044 4950,03195 37888 06708 64194 5280.03207 06198 75272 79934 9280.03215 41573 79585 50153 5780.03220 43145 96613 50533 4760.03222 10394 56498 70632 617

77

N s 98

ABSCISSAS WEIGHTS

0.999700.998430.996140.992840.988530.983210.976900.969590.961290.952020.941780.930580.918430.905350.891350.876440.860640.843970.826440.808060.788870.768870.748090.726550.704270.681270.657580.633220.608220.582600.556390.529610.502290.474460.446150.417380.388190.358610.328660.298370.267780.236920.205820.174510.143030.111390.079650.047820.01594

19841010503254932515338898036225950348718146050089350804060380573785356753589987975265085619587820582516044144424243136830084651977o6l887309630335210515134187553536242825242156750765298144971603474548980779774887458835540451470622036402648462894

25490472309685936906891589372263886007940289186401627113930773568598394889106844245519077044047195340802245517525924365827177186468901471969542797412353040877942913675028065259505410383590718366853387773917219215053155763794206553280056254978309

90363453772960673013168379912808249472310577150130821090421211719135950664310511753154672885510351292667079711450644809142365320799051686188533519596558645876248598284412448593341886372965241588157715413731509977030567878751661799988213229639928

7295869329801880217353389069986404188772879644957214333319572915900759567785490709676596056725706977603903051957441732967398843634627023705714710304841776098828274722287665496760308208293427687564

0.000760.001770.002790.003800.004810.005810.006810.007800.008780.009750.010720.011670.012610.013540.014450.015350,016230.017100.017950.018780.019600.020390.021160.021910.022640.023340.024020.024680.025310.025920.026500.027050.027570.028070.028540.028980.029390.029770.030120.030440,030720.030980.031210.031400.031560.031690,031790,031850,03188

476699477038811557403422363825342943547357284897342292047045524202947868783610389709667971648417906502185259394226843322214716931379679456416052117895116033575084719531703604928593263352510521041105869049557840lOOlO447125998054171259677438198753

82274410143572285352985864643979165791006739202174832247713878921810293830423497704530308948770349046772692291327741217850618413490374512460020264616211123823966412250636695279568835806828293992113493748939040919226790467910820349625285812452876

31345528741308735956770916391121599754892632009683317121242895285465144019775576695659002662812686563307791457856916504143311274714988099618097344489163935128273939013875885703420449216476268988425839669929346326441561510529025160630190107146727

803169063552848276877098270535024743778365757850273235244149324948128902126268324198315847249768010325349745776618853491001104684749145907832310795

78

N a 99

ABSCISSAS

0.99970 79^39 52169 35586 3584I0.99846 14938 35841 33897 2881

i 0.99622 03386 73088 60856 28950.99298 62141 33112 27732 96340.98876 22829 89873 61251 03^20.98355 27411 56280 01296 55620.97736 27767 50705 94456 97940.97019 85580 74290 21548 0730

i

0.96206 72256 40901 94273 907l!' 0.95297 68844 53373 50257 56680.94293 65956 88479 41029 46600.93195 63675 61496 96436 16500.92004 71453 00500 21871 51300.90722 08002 10573 56823 7880

I 0.89349 01178 26414 21500 22450.87886 87851 59513 85027 00770.86337 13770 49917 04443 48980.84701 33416 34774 14729 91400.82981 09849 47430 56502 90500.81178 14546 61989 13468 30120.79294 27229 99308 89390 85000.77331 35688 11336 14519 84370.75291 35588 61538 11825 45080.73176 30283 20043 52218 08190.70988 30604 92896 85820 65030.68729 54658 05609 09750 06260.66402 27600 61938 45755 83420.64008 81419 99562 52510 28200.61551 54701 65007 17705 07070.59032 92391 30878 56421 66500.56455 45550 79lOl 55074 30^40.53821 71107 74501 03254 48690.51134 31599 53671 01421 91370.48395 94911 54659 70017 72570.45609 34010 13556 63729 29610.42777 26670 54599 62175 51680.39902 55200 00924 15237 93180.36988 06156 33556 19372 86670.34036 70062 26699 44304 13910.31051 41115 87790 73632 39910.28035 16897 31191 26717 76650.24990 98072 14746 53935 88340.21921 88091 68784 07038 94440.18830 92890 47424 47642 16350.15721 20581 32358 39438 37990.12595 81148 19488 46171 82410.09457 86137 19052 03187 64390.06310 48346 00026 24020 65080.03156 81512 09772 26520 34580.00000 00000 00000 00000 0000

WEIGHTS

0.00074 94736 46737 40536 3380.00174 39069 58219 24493 8640.00273 80758 73626 87809 1320.00372 96434 87243 03474 9200.00471 75190 37520 83007 9690.00570 06997 73395 92687 5150.00667 82008 60575 09816 5180.00764 90462 79335 25793 5390.00861 22676 15478 88899 1730.00956 69044 11326 13635 6900.01051 20049 15524 74540 5750.01144 66269 51498 25376 1130.01236 98388 22175 16210 3430.01328 07202 22657 28347 9950.01417 83631 49579 44606 6140.01506 18728 01990 23331 2950.01593 03684 70960 84971 1040.01678 29844 16138 70708 9500.01761 88707 27924 38050 6760.01843 71941 74178 49927 0990.01923 71390 30487 18479 8670.02001 79078 93086 56620 7950.02077 87224 73594 21120 7430.02151 88243 74730 22381 8250.02223 74758 46239 37158 4360.02293 39605 20251 05528 4080.02360 75841 25337 89404 6620.02425 76751 78557 07823 1640.02488 35856 54781 94644 5990.02548 46916 32654 75465 0580.02606 03939 16515 48254 0930.02661 01186 33685 85130 1790.02713 33178 06512 55092 6390.02762 94698 98599 01232 2080.02809 80803 34680 91126 5930.02853 86819 93626 94972 6640.02895 08356 74073 31040 3740.02933 41305 32227 50347 6430.02968 81844 91405 09844 8020.03001 26446 22891 03447 1900.03030 71874 97745 80397 9610.03057 15195 09205 77999 2180.03080 53771 65356 27949 9180.03100 85273 51785 59535 8330.03118 07675 63958 15837 0330.03132 19261 09075 18012 8170.03143 18622 77221 54616 1520.03151 04664 81628 34771 3240.03155 76603 67911 22885 8090.03157 33968 92175 65305 137

79

N a 100

ABSCISSAS WEIGHTS

0.999710,998490.996290.993120.988960.983870.977800.970780.962810.953900.944050.933280.921600.909020.895560.881210.866010.849960.833080.815380.796890.777620.757590.736820.715330.693140.670280.646760.622600.597840.572500.546590.520150.493210.465780.437890.409580.380870.351780.322360.292610.262580.232300.201780.171080.140200.109180.078060.046870.01562

372671950651347493704395275407935845775736542078295870185350929819570916^498679346884452783879892383789237909681185808988117591993301561908588602747021932670120801980789216497740215291629816852630343971880812032481898640008053137292035858281682489844

7344139595331253744342991060578691863706558152549136255430794533382529707268501897164795918840039176903144949519707020207305655801031411412903707471782138165094817630819073358720317830124629724210052938471715034497395735386033611380061134362159121543

2336781840149184596574800015492885533193527297428497796545929526669046986694155762341284298235425439476384756217603705514464596594015802798377160721261913116746056649335604224513105425295676720971517296473479169696499723274889732011500636696316108287

82280163613220104419610037810898365993372775433469517127852133170740336329163989957375525668242899676648258726304191480768707994681693099217897868683363234424777556892995106049753275153426481749242217

0.000730.001700.002680.003650.004620.005580.006540.007490.008440.009380.010300.011220.012130.013020.013900.014770.015620.016460.017290.018090.018880.019650.020400.021130.021840.022530.023190.023840.024460.025050.025620.026170.026690.027190.027660.028100.028510.028900.029260.029590.029890.030160.030400.030610.030790.030950.031070.031160.031220.03125

4634493926392535961244500842806948490732387140419678025511401457659478771075884596210808610460559407373963087432326344213002412202742310960212027754449402962192745912613411982275566854330896108410488009795226514079561865837900478823374383564884254234

9050553518715530132663422038655084555464696685369474868231856297992971037182744177546761456832322128133749443546209125271624756336852546596807957815791020839545835704657620792591012239501125106385991293332051692645483980311525049027566962095484953863

6717310523482413751811935515153227671157971404579596958977114974054228772683017600272212645824311666904553058643276641543863127270121622059605271589701160767634962668801338829173310979920313276626425183091144918200144849590429882351658906783577335694

041953944234110721415883262142578722774556795888394310934439294538684267395180249256998376564231038649420765094488012175684907651646771406781382238764

80

N = 125

ABSCISSAS WEIGHTS

0,999810.999030.997620.995580.992930.989650.985750.981230.976090.970350.964000.957040.949480.941330.932590.923270.913360.90289.0.891850.880240.868090.855400.842160.826400.814120.799340.784040.768260.752000.735270.718070.70043

6416228347362689362212773102850668126387977105280627671621079970487808774952353584362220320219194026702290694583730834989246900115991058524757428175497046523919

977685297610961521626660238750124879985906108754752800^394971646048915349707550339248995744478164092117675196987169730652309605804384188015528893249536588136226

5171543860577587966051123625241969288211914874800957128133386177148940739518197284934637572938713430844505801379814721925286888308132263300183622851260582163272

78462660032453753627868173961399923360895791699463216317073599737365657188063205290898873371053633118374068768089546259487209048

0.000470.001090.001720.002340,002960.003590.004200.004820.005430.006040.006650.007250.007850.008440.009030.009610.010190.010760.011320.011870.012420.012960.013490.014020.014530.015040.015530.016020.016500.016960.017420.01786

1120663927190426417294762067939634359524924709133652299715624535269926415715660811394023222582778385565175678975819102735687212390736603757301081611991500959655

4849305586078885367301558228247012685939750796094095985508373064401337191536059951515945439456881841325808684563538723772268828903126020099721709937331445842635

5239699382471247895705289512646988844388588903391013677616697368562273902854585340621733860393421408314183100595218324996213124281576943035417155051138184733843

828805522483679179917068489110076134249968052333795756524760692404545465986067975853201511658785

81

N = 125 (cont.)

ABSCISSAS WEIGHTS

0*682340.663830.644910.625570.605850.585750.565280.544450.523290.501800.479990.457880.435490.412820.389890.366720.343320.319700.295890.271890.247710.223390.198920.174330.149630.124830.099960.075020.050040.025020.00000

88471774330679595154636393583537705975134574315015400045735705602250685779447436391867967116870000157950106788343121538404097552272413966688391209797800000

56440551056885774432574002224048509979627756963449908751552551286899700836268246145747811087552973133662485847858928669440734476165575827269721195771200000

26365498676567169318715182688100560822210024021704401764814259222819094675548176758927533187105692149837775541220774465565557589930050424075881877652000000

7758751700166098428936936581304897082508694208331400651387303721524498408333263983769295984608638767316349877811897469240000

0.018290.018720.019130.019520.019910.020280.020640.020990.021330.021650.021960.022250.022530.022790.023050.023280.023510.023710.023910.024080.024250.024390.024530.024640.024750.024830.024900.024960.025000.025020.02503

92353103891111991973504588415590725679081352625482017634044239677977151288983625084368592814799938422194198076213229085005927659177028118578104644569424121

77161315920424843829104123175554786921986405634313421722819555085230647978324679077292253093653582104158327279208520785705808100913382841632772698518425886

51444100167292742731728284318800606664482291002346231463974103519654408989792577625448037599560174602460986773828739321906387892334272946272747155519614839

763604686844993826366400278679 I

219654863285634175364712054918897374504702462915123352923896339

82

N > 150

ABSCISSAS WEIGHTS

0.99987 23404 45733 35275 14820.99932 74305 06594 70647 2643

i

0.99834 73449 34083 36809 3970! 0.99693 22929 77599 62985 6897! 0.99508 28645 25528 95395 31240.99279 98590 43437 25051 69780.99008 42691 66019 18857 22840.98693 72772 71279 43853 67120.98336 02541 69752 91657 6011

i 0.97935 47582 42589 39415 18380.97492 25346 59594 27827 63300.97006 55145 73837 32683 90250.96478 58142 58695 60966 98870.95908 57341 74690 40401 01910.95296 77579 61097 10802 79490.94643 45513 50314 77969 41630.93948 89610 04283 67786 65930.93213 40132 72852 69823 53620.92437 29128 74313 50040 47540.91620 90414 98495 20869 35330.90764 59563 32923 54182 62880.89868 73885 12623 91873 61130.88933 72414 94205 48655 05720.87959 95893 54910 23699 01080.86947 86750 17352 69039 92540.85897 89084 00713 35419 33070.84810 48644 99184 60232 17800.83686 12813 88501 51727 60020.82525 30581 61423 01987 05090.81328 52527 93060 54143 13590.80096 30799 36982 72164 86110.78829 19086 53055 23492 68740.77527 72600 68004 91269 77960.76192 48049 69726 86962 58880.74824 03613 36382 37406 08080.73422 98918 01363 73423 37490.71989 95010 55230 50231 10640.70525 54331 85748 82534 6680.

0.00032 76086 70553 76841 5150.00076 24720 93212 11815 4170.00119 76474 86469 62461 8330.00163 23569 98610 50907 3680.00206 63664 92413 81981 0410.00249 94789 88894 45186 4730.00293 15036 83655 86293 3260.00336 22516 23677 83131 7650.00379 15348 36345 10472 4770.00421 91661 42991 91132 7210.00464 49591 49796 54539 5350.00506 87282 93945 58836 9590.00549 02889 09448 68736 6820.00590 94573 00590 10763 9320.00632 60508 18470 39583 7400.00673 98879 38743 10962 3350.00715 07883 39685 55146 3260.00755 85729 80178 16402 7960.00796 30641 77363 30978 3940.00836 40856 83847 51862 1750.00876 14627 64358 01457 4470.00915 50222 71788 79700 5210.00954 45927 22584 91211 6700.00993 00043 71421 15578 9210.01031 10892 85135 96814 3640.01068 76814 15884 09534 6670.01105 96166 73473 44354 9770.01142 67329 96852 84002 8980.01178 88704 24718 37739 5090.01214 58711 65206 78127 3100.01249 75796 64644 88890 0810.01284 38426 75324 90325 5770.01318 45093 22275 62384 9640.01351 94311 69000 36951 5390.01384 84622 82152 81194 4050.01417 14592 95122 43883 4700.01448 82814 70501 86711 1550.01479 87907 61408 73286 186

83

N = 150 (cont.

)

ABSCISSAS WEIGHTS

0.690300»675050.659500.643670.627550.611170.594510.577600.560430.543030.525380.507510.489410.471100.452590.433880.414980.395900.376640.357220.337650.317930.298070.278080.257970.237750.217420.197000.176500.155910.135260.114550.093790.072990.052160.031300.01043

40689192305641119971789000341364913359659026202595488180581551469646272506313447113080099965660891845617751925623567399773947498298975682295164228149067186634936065149118195296265769378

57192300932264415008977726585559158513148786175254220803391763275160661609929086476703902556552172504633990725029079695778203482458697113234258562665127144406956172233735078929379704259

78971106424603028768644631726794987224046509169418277826031824702232277018512069573037038516766087769873892502142334100042770094492103919350695975722448995575518479681533482901524577212

6286060041711221246946522829917511120621936111512037901779862040015924428577138455934171738497355999460073813245583241298547086825621613579268496904

0.015100.015400.015690.015970.016250.016520.016780.017030.017280.017520.017760.017980.018200.018410.018610.018800.018990.019160.019330.019490,019640.019790.019920.020050.020160.020270.020370.020460.020540.020610.020680.020730.020780.020810.020840.020860.02087

28518033231102450356200811899245913997007923983451112886173633813265743910770535200168674469950689008289811283534340876576730568194856351529653238959124018683262227985680583684022731176

71635146007107445661219971666231758061546535870001629121476568271809076615333222252715607045116511710422535848079343982333780988287292343459661008191932850754409289105398787623129638995

39749 26923040 76775810 02750845 63492754 08930434 24320688 51551073 72768813 20162252 15781922 01649765 17467437 64197828 55057987 93326511 15734063 20772111 11322040 13774630 26878335 13523906 20042611 18265577 12862614 76250221 19430281 68493266 81292417 63868496 70378125 18752494 25687299 53239069 42277608 39219022 77538706 698

84

N a 175

ABSCISSAS

1 0 ,99990 61195 95989 27465 4676

jOi.99950 53827 83533 27416 4235

\

0 1 99878 45612 90139 83173 73841

0..99774 37259 28077 21777 6278!0<.99638 31905 91991 62286 4822

!

o«.99470 33865 52412 01867 032410..99270 48505 07961 47319 5406

i

o«.99038 82222 12319 48439 66350.,98775 42436 84231 06833 4410Oi,98480 37587 75176 51208 73330.,98153 77128 23295 59655 87820.,97795 71523 17404 80382 36630.,97406 32245 45859 38385 58940.,96985 71772 20802 56339 98150.,96534 03580 73931 90088 17730.,96051 42144 22109 08592 07020<,95538 02927 02081 48354 59220.,94994 02379 74019 69768 03820.,94419 57933 93791 92150 15820.,93814 87996 54011 10839 10970<.93180 11943 93957 03861 78450..92515 50115 78516 32642 9847Oi,91821 23808 46311 07431 9495Oi,91097 55268 27207 21067 5093Oi.90344 67684 29409 69248 1723Oi,89562 85180 96365 43090 0977Oi,88752 32810 33706 96599 8693Oi,87913 36544 06481 13105 6420Oi,87046 23265 06917 53279 2547Oi.86151 20758 93001 82736 2900Oi,85228 57704 98128 61299 9953Oi.84278 63667 12118 36284 04710,,83301 69084 33892 23236 4186Oi.82298 05260 96107 82415 0332Oi.81268 04356 62068 09668 9477Oi.80211 99375 95224 57511 45590.,79130 24158 01604 86674 48620.,78023 13365 45503 20708 80550..76891 02473 38781 36424 63110.,75734 27758 04135 71201 46800,,74553 26285 12694 64393 04030.,73348 35897 96318 74110 3344Oi.72119 95205 34984 22438 4111Oi,70868 43569 19638 21457 7920

WEIGHTS

0.00024 09236 63646 21375 0600.00056 07495 09521 13521 5040.00088 08694 02273 51893 7920.00120 07481 88985 39122 1630.00152 02504 82564 86908 7930.00183 92681 17081 74307 3280.00215 76973 34923 37046 2930.00247 54355 79836 61442 3150.00279 23808 28802 01232 4820.00310 84314 27400 66650 1720.00342 34860 55725 47927 1300.00373 74437 35075 83393 5420.00405 02038 49257 47229 0540.00436 16661 71668 30706 2380.00467 17308 94842 05588 3940.00498 02986 61071 45847 8890.00528 72705 93493 11454 2410.00559 25483 27336 29231 3340.00589 60340 41182 12343 6540.00619 76304 88148 13035 4910.00649 72410 26947 26130 7630.00679 47696 52788 45739 4450.00709 01210 28095 45238 3660.00738 32005 13025 94231 2860.00767 39141 95776 42169 3750.00796 21689 22659 88229 9580.00824 78723 27944 75226 9720.00853 09328 63444 21666 7070.00881 12598 27845 57477 1500.00908 87633 95769 65225 9970.00936 33546 46550 55605 1520.00963 49455 92726 27107 9250.00990 34492 08230 77321 2230.01016 87794 56278 48454 3000.01043 08513 16932 03491 1610.01068 95808 14344 42243 2870.01094 48850 43666 78958 0270.01119 66821 97613 15247 6340.01144 48915 92673 54106 2860.01168 94336 94967 12786 6820.01193 02301 45727 04387 9590.01216 72037 86408 70213 2070.01240 02786 83413 57322 0070.01262 93801 52420 48254 392

85

N = 175 (cont.

)

ABSCISSAS WEIGHTS

0*695940.682970.669790.656390.642760.628960.614950.600730*586330.571730*556960*542000.526870.511570*496110*480490*464720*448790.432720.416520.400180*383710.367120.350410.333590*316660*299630*282510*265290.247990.230610.213160.195630.178050.160410.142710.124970.107190.089380.071540.053670.035790.017890*00000

2109168603276484047350010998683431598262372569745725630691247586394325735306302312860735889623232278336565272542253554034571467086737622030761598527994934806936814912916306298694297525180607424681791464118383279784100000

909225416771076285038A768939360849360882243435351905300403750597400283190348475259176393543793748171941366674046011102253240764754115349099786884900653088802798777971432058091365484740841954036312252166299482479291200000

19106 8237 0*01285 44347 82316 62652 80377732 8807 0.01307 53704 58720 63468 03258925 0800 0.01329 21163 87090 13609 75435682 2208 0.01350 46031 15406 42295 55586927 5997 0.01371 27625 56428 93965 33549617 3556 0.01391 65280 09512 46460 71109982 0574 0.01411 58341 81979 99219 90607575 1178 0.01431 06172 10044 46505 68603561 5485 0.01450 08146 79272 65164 22327854 8661 0.01468 63656 44584 61103 11268090 4151 0.01486 72106 49782 33573 48096805 5998 0.01504 32917 46601 31440 17151381 2352 0.01521 45525 13278 90921 25884087 4692 0.01538 09380 72633 59769 05486781 0461 0*01554 23951 09649 28544 95866231 2544 0.01569 88718 88559 05504 98201527 7415 0.01585 03182 69422 87656 95754367 3524 0.01599 66857 24193 96769 15926057 1657 0.01613 79273 52268 65498 42061639 9339 0.01627 39978 95514 75358 56491484 3440 0.01640 48537 52773 64962 Oil73829 2927 0.01653 04529 93831 43833 36757977 4351 0.01665 07553 72854 64108 37826952 6860 0.01676 57223 41286 19589 43300328 6508 0.01687 53170 60197 58924 35582465 1243 0.01697 95044 12093 17102 98328428 3483 0.01707 82510 12162 87020 58869293 7732 0.01717 15252 18979 70532 69890219 3478 0.01725 92971 44638 66216 94588520 2680 0.01734 15386 64333 68958 34754865 7431 0.01741 82234 25369 74479 20218553 5351 0.01748 93268 55607 00037 92077503 4025 0.01755 48261 71334 50716 66095056 5631 0.01761 47003 84570 78999 88388791 1450 0.01766 89303 09789 03708 98061285 4390 0.01771 74985 70064 72796 12629009 6319 0.01776 03896 02643 73007 50093236 5068 0.01779 75896 63929 07996 11965972 2308 0.01782 90868 33884 85091 81314365 6238 0.01785 48710 19855 69614 29718810 0313 0.01787 49339 59800 84338 96352963 8891 0.01788 92692 24941 50487 86388148 0753 0.01789 78722 21820 85414 43800000 0000 0.01790 07401 93775 90973 759

86

I

ABSCISSAS

N B 200

WEIGHTS

0<•99992 80712i 0<.99962 103120 •99906 87218o!•99827 115590<•99722 85142V 1•99594 104920<•99440 907570«•99263 296940«•99061 31660o!•98835 01613•98584 45109

0<•98309 68298Oi•98010 779260<•97687 813310<.97340 86442Oi•96970 01776Oi•96575 36439Oi•96157 00118Oi•95715 03086Oi•95249 56192Oi•94760 70865Oi•94248 59105Oi•93713 33486Oi•93155 07149Oi•92573 93798Oi•91970 077020 1•91343 63686Oiw <1 ^ V V/ y ^ 77128Oi•9Q0?3 63959Oi• w y JJ U 40656~ U V Ww0 .•88615 242380 ,87878 3?2630(.871 19 828220<•86339 94537o<•85538 865550«•84716 78542Oi.83873 9o6820 ,83010 436660<•82126 586950<>81222 574670(i60298 621750 i79354 955050 .78391 806230 »77409 411740 .76408 012790 .75387 855210 .74349 189450 .73292 270530 .72217 357910 .71124 71550

85069 97704 926380936 39632 813673152 18081 735348910 70943 080883379 77581 966661011 20189 715265701 45178 917717189 75969 601430673 61374 224260761 29958 681121786 47742 562426095 75204 468520924 03187 807416566 22201 457902830 58499 885352437 50713 293610744 83267 357571510 67328 737738566 20927 155173355 07681 522428342 32609 569866323 14496 651465678 58756 135811637 00559 978273608 16650 787568663 47198 527211241 00162 739449158 72422 810686023 39573 821890126 54916 752989922 67127 072056188 21202 538470963 52277 224683383 19128 783852503 55247 925277239 41194 003113525 23289 930778819 20943 689544071 78298 612013283 25682 050490778 22542 449236327 56289 474608251 70697 838794641 93296 013132839 23412 581017313 31260 111696087 03555 413255854 52656 209l95943 83984 026791277 90544 9336

0,00018 45900 97471 29744 3980.00042 96466 30451 05707 2830.00067 49606 34479 37275 0300.00092 01404 59341 77191 4690.00116 51007 14755 86853 6850.00140 97768 27453 56002 2160.00165 41075 52313 02417 7360.00189 80325 04938 62859 6110.00214 1491^ 39440 58844 6170.00238 44251 12004 89258 7820.00262 67732 44516 51482 7250.00286 84765 19468 31566 8600.00310 94755 86103 05615 9970.00334 97112 71035 83940 0080.00358 91245 90811 42181 5850.00382 76567 65344 74925 2020.00406 52492 31775 55080 6690.00430 18436 58513 21359 1390.00453 73819 59358 51540 4390.00477 18063 07641 27199 0550.00500 50591 50339 15267 3470.00523 70832 22156 56423 3340.00546 78215 59549 88537 5150.00569 72175 14689 46658 3680.00592 52147 69351 19677 3920.00615 17573 48731 85737 0800.00637 67896 35183 35247 1290.00660 02563 81861 44969 7450.00682 21027 26285 01981 4720.00704 22742 03801 99924 3280.00726 07167 60958 46271 7260.00747 73767 68767 31045 0620.00769 22010 35873 16183 1360.00790 51368 21610 11629 0040.00811 61318 48949 09820 3060.00832 51343 17331 55078 8210.00853 20929 15386 28674 4050,00873 69568 33526 34274 8290.00893 96757 76422 72212 1140,00914 01999 75351 94583 5060,00933 84802 00414 36719 8500.00953 44677 72620 24036 6420.00972 81145 75840 56761 7580.00991 93730 68619 78528 7540.01010 81962 95847 38349 6980.01029 45379 00285 59046 6350.01047 83521 33950 28832 9370.01065 95938 69342 36399 8680.01083 82186 10526 73582 9840.01101 41825 04056 33459 768

87

N = 200 (cont.

)

ABSCISSAS WEIGHTS

0.70014 61155 44490 13595 43550.68887 31859 27353 74870 95340.67743 11338 11686 48238 81940.66582 27682 89894 97096 41640.65405 09392 85325 58247 78270.64211 85368 52591 03298 8l840.63002 84904 68044 54752 76490.61778 37683 10575 75905 07520.60538 73765 32904 91272 05020.59284 23585 23554 27583 38500.58015 17941 59677 94268 60540.56731 87990 50933 46815 75730.55434 65237 74580 96323 086o0.54123 81531 01997 43947 24630.52799 69052 16796 29722 31880.51462 60309 24743 91331 10700.50112 88128 55667 29803 50940.48750 85646 57548 75746 95750.47376 86301 83005 41532 87030.45991 23826 66353 31823 85110.44594 32239 05457 66883 15690.43186 45834 06572 50216 19930.41767 99175 62374 84210 09720.40339 27087 93400 04519 39280.38900 64646 95086 65953 01930.37452 47171 76640 69509 72820.35995 10215 93930 71947 97480.34528 89558 76626 65824 51240.33054 21196 49796 59257 68870.31571 41333 50177 20732 02710.30080 86373 37334 85026 70210.28582 92909 99935 41789 92060.27077 97718 57342 48363 19650.25566 37746 56764 23154 60440.24048 50104 66170 85140 16190.22524 72057 63205 08910 70330.20995 41015 20309 63052 48570.19460 94522 86295 92529 16950.17921 70252 64579 93097 93830.16378 05993 88311 07621 93090.14830 39643 92621 50414 75960.13279 09198 84223 36451 96870.11724 52744 08582 57391 48630.10167 08445 14898 05844 46080.08607 14538 19116 03214 74950.07045 09320 65209 34666 51280.05481 31141 84952 37373 01870.03916 18393 56422 25135 43270.02350 09500 61457 63728 97830.00783 42911 42306 36927 7408

0.01118 74423 49738 35565 6490.01135 79556 11240 13811 0680.01152 56804 26532 06637 9260.01169 05756 18164 92969 7320.01185 26007 03379 21585 7320.01201 17159 04043 85685 0050.01216 78821 56421 98601 2820,01232 10611 20761 30882 5130.01247 12151 90706 73260 1960.01261 83075 02532 94401 3320,01276 23019 44194 66759 7180.01290 31631 64192 38322 1890.01304 08565 80251 32578 3920.01317 53483 87811 63628 6330.01330 66055 68327 57982 3780.01343 45958 97373 79288 8230.01355 92879 52556 56979 6650.01368 06511 21228 24591 5930,01379 86556 08002 78370 8730,01391 32724 42070 71643 7310.01402 44734 84311 65362 6670.01413 22314 34202 60209 3290.01423 65198 36520 40647 8390.01433 73130 87836 66377 3120.01443 45864 42803 51727 5090.01452 83160 20228 78675 8480.01461 84788 08938 94336 1620.01470 50526 73428 48978 3280.01478 80163 59294 35881 9090.01486 73494 98453 99605 0720.01494 30326 14145 84560 8010.01501 50471 25711 01134 7160.01508 33753 53154 91951 1510.01514 80005 21487 86295 327 i

0.01520 89067 64843 36128 127 •

0.01526 60791 30373 32584 7910.01531 95035 81919 07328 4740.01536 91670 03457 28632 7280.01541 50572 02320 07592 1750.01545 71629 12188 35406 6270.01549 54737 95857 78249 3260.01552 99804 47776 6l8l3 3590.01556 06743 96354 83230 4520,01558 75481 06043 93671 7110.01561 05949 79187 00569 1810.01562 98093 57638 44038 9580.01564 51865 24153 07739 5620.01565 67227 03544 30062 0300,01566 44150 63610 87219 3260.01566 82617 15832 25480 757

U.S. GOVERNMENT PRINTFNG OFFICE I M< O—239-S»

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i

U.S. DEPARTMENT OF COMMERCE postage and fees paid

WASHINGTON, D.C. 20230 u.s. department of coMMERCi

OFFICIAL BUSINESS