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  PFT predicted values by 2022 race-neutral GLI equations, ages 3 to 95

 
Input
 
Sex Female

Male
Age  
Height  
Measured FEV1  
Measured FVC  

 
Results
 
Important: Inputs must be complete to perform calculation.

 
 
Measured FEV1/FVC ratio  
 
Predicted FEV1  
FEV1 percent predicted  
FEV1 Z-score  
FEV1 LLN  
FEV1 ULN  
 
Predicted FVC  
FVC percent predicted  
FVC Z-score  
FVC LLN  
FVC ULN  
 
Predicted FEV1/FVC ratio  
FEV1/FVC percent predicted  
FEV1/FVC ratio Z-score  
FEV1/FVC LLN  
FEV1/FVC ULN  
 
Decimal Precision  
 

 
  Data action

 
     
 
Include literature references: Yes   No
 

 

 
Notes
  • For most accurate calculation, input fractional ages where possible, especially for young individuals.
  • The FEV1/FVC predicted ratio is population based and calculated independently from the FEV1 and FVC. Therefore, there may be minor differences from the predicted value shown here, and the value calculated from simple division of the predicted FEV1 by predicted FVC.
  • The Z-score is the number of standard deviations a value is from the predicted (mean) value. A negative Z-score represents data below the mean and a positive Z-score represents data above the mean.
  • Lower and upper limits of normal pulmonary function tests are calculated using the Z-score equation where Z-score is set to -1.645 for the LLN (5th percentile), and 1.645 for ULN (95th percentile).
  • PFT: pulmonary function test; GLI: Global Lung Function Initiative; FEV1: forced expiratory volume at 1 second; FVC: forced vital capacity; LLN: lower limit of normal; ULN: upper limit of normal.

 
Equations used
 
Measured values
FEV1/FVC ratio = Measured FEV1 / Measured FVC
Predicted values
Female FEV1 = e(-10.901689 + (2.385928 * ln(Height)) - (0.076386 * ln(Age)) + M spline)
Female FVC = e(-12.055901 + (2.621579 * ln(Height)) - (0.035975 * ln(Age)) + M spline)
Female FEV1/FVC = e(0.9189568 - (0.1840671 * ln(Height)) - (0.0461306 * ln(Age)) + M spline)
Male FEV1 = e(-11.399108 + (2.462664 * ln(Height)) - (0.011394 * ln(Age)) + M spline)
Male FVC = e(-12.629131 + (2.727421 * ln(Height)) + (0.009174 * ln(Age)) + M spline)
Male FEV1/FVC = e(1.022608 - (0.218592 * ln(Height)) - (0.027586 * ln(Age)) + M spline)
Percent predicted values
FEV1 percent predicted = 100 * Measured FEV1 / Predicted FEV1
FVC percent predicted = 100 * Measured FVC / Predicted FVC
FEV1/FVC ratio percent predicted = 100 * Measured FEV1/FVC ratio / Predicted FEV1/FVC ratio
Z-score calculation
Z-score = ((Measurement/M)L - 1) / (L * S)
LMS values for female FEV1 Z-score
L = 1.21388
M = Predicted FEV1
S = e(-2.364047 + 0.129402 * ln(Age) + S spline)
LMS values for female FVC Z-score
L = 0.899
M = Predicted FVC
S = e(-2.310148 + 0.120428 * ln(Age) + S spline)
LMS values for female FEV1/FVC ratio Z-score
L = 6.6490 - 0.9920 * ln(Age)
M = Predicted FEV1/FVC ratio
S = e(-3.171582 + 0.144358 * ln(Age) + S spline)
LMS values for male FEV1 Z-score
L = 1.22703
M = Predicted FEV1
S = e(-2.256278 + 0.080729 * ln(Age) + S spline)
LMS values for male FVC Z-score
L = 0.9346
M = Predicted FVC
S = e(-2.195595 + 0.068466 * ln(Age) + S spline)
LMS values for male FEV1/FVC ratio Z-score
L = 3.8243 - 0.3328 * ln(Age)
M = Predicted FEV1/FVC ratio
S = e(-2.882025 + 0.068889 * ln(Age) + S spline)

 

 
Calculation Details and Variables
  • Age-based M and S spline coefficients are listed in the tables below.
  • Linear interpolation is used to obtain M and S spline values between listed ages.

 
References
  1. Bowerman C, Bhakta NR, Brazzale D, et al. A Race-neutral Approach to the Interpretation of Lung Function Measurements. Am J Respir Crit Care Med. 2023; 207:768. PubMed ID: 36383197 PubMed Logo
  2. Quanjer PH, Stanojevic S, Cole TJ, et al. ERS Global Lung Function Initiative. Multi-ethnic reference values for spirometry for the 3-95-yr age range: the global lung function 2012 equations. Eur Respir J. 2012; 40:1324. PubMed ID: 22743675 PubMed Logo

 
Associated Medical Subject Headings [MeSH]
 
         80 and over,   Adolescent,   Adult,   Age Factors,   Aged,   Child,   Ethnicity,   Female,   Forced Expiratory Volume,   Global Health,   Humans,   Lung,   Male,   Middle Aged,   Models,   Nutrition Surveys,   Preschool,   Pulmonary Medicine,   Quality Control,   Reference Values,   Spirometry,   Statistical,   Vital Capacity

 
Associated Logical Observation Identifiers Names and Codes [LOINC]
 
Parameter LOINC's and Suggested Units
Age 21612-7 : yr      21612-7 : yr      21612-7 : years      30525-0 : Years old      30525-0 : yr      30525-0 : years      
Height 8302-2 : cm      8301-4 : cm      3137-7 : cm      91370-7 : cm      3138-5 : cm      8306-3 : cm      
FEV1 20150-9 : L      
FVC 19872-1 : L      
FEV1FVC 19925-7 : ratio      

 
This material contains content from LOINC (http://loinc.org). LOINC is copyright © 1995-2023, Regenstrief Institute, Inc. and the Logical Observation Identifiers Names and Codes (LOINC) Committee and is available at no cost under the license at http://loinc.org/license. LOINC® is a registered United States trademark of Regenstrief Institute, Inc.

 
Associated ICD10-CM Codes
 
   J98.2Interstitial emphysema
   J43.9Emphysema, unspecified
   J98.3Compensatory emphysema
   J42Unspecified chronic bronchitis
   I27.9Pulmonary heart disease, unspecified
   I27.81Cor pulmonale (chronic)

 
Associated ICD9-CM Codes
 
   518.82Other pulmonary insuff
   416.9Chr pulmon heart dis nos
   491.9Chronic bronchitis nos
   518.2Compensatory emphysema
   492.8Emphysema nec
   518.1Interstitial emphysema

 
  Appendix

 
M and S spline coefficients for females 3 to 95 years
 
 FEV1FVCFEV1/FVC ratio
AgeMSMSMS
3-0.2095507780.313300389-0.13635550.26866539-0.0613314020.080526237
3.25-0.2006664340.288280448-0.1303403750.247291282-0.05869480.077631527
3.5-0.192467480.265145552-0.1247856310.227528531-0.056294710.074930735
3.75-0.1848882120.243660411-0.1196434890.20917695-0.0541363530.072381303
4-0.1779132130.223661208-0.1148957270.192097646-0.0522382310.069945704
4.25-0.1715274540.205011666-0.1105261260.17617495-0.0506174990.067589726
4.5-0.1656975330.187599579-0.1065131990.161313729-0.0492826720.065283288
4.75-0.1603655990.171342117-0.1028295020.147444278-0.0482192050.063005418
5-0.1554786340.156163622-0.0994491080.134502704-0.0473774810.060745687
5.25-0.1509847130.141994266-0.0963456930.122430067-0.0466881890.058496974
5.5-0.1467866430.128779429-0.0934728680.111182404-0.046076610.05625979
5.75-0.1427818910.116471401-0.09078170.100721949-0.0454655080.054039438
6-0.1388901270.105023469-0.0882327960.091010919-0.0447843540.051845823
6.25-0.135048490.094390462-0.0857939910.082012215-0.0439712710.049692078
6.5-0.1312080760.084528851-0.0834344780.073690041-0.0429858840.047589678
6.75-0.1273308650.075397095-0.0811261010.066010098-0.0418147840.045544128
7-0.1233872230.066955942-0.0788460870.05893963-0.0404638340.043555518
7.25-0.1193541820.059168418-0.0765760690.052447494-0.0389494620.041618684
7.5-0.1152130760.051999337-0.0743006590.04650368-0.0372950780.039726691
7.75-0.1109377460.045410721-0.0720006310.041073944-0.0355244810.037872312
8-0.1065001680.039364403-0.0696560940.036122984-0.033661710.03604702
8.25-0.1018783250.033825477-0.0672509480.031618633-0.0317247110.034243441
8.5-0.0970552460.028762004-0.0647722930.027531571-0.0297290110.032456688
8.75-0.0920180860.024144699-0.0622098690.023835014-0.0276871480.030682778
9-0.08675850.019945763-0.0595559910.020503561-0.0255863440.028926881
9.25-0.0812831620.016129752-0.0568090520.017504253-0.0234065580.02719917
9.5-0.0756066010.012658692-0.0539708950.014801576-0.021136140.025508116
9.75-0.069742350.009498632-0.0510436090.012363893-0.0187676290.023860817
10-0.0637028990.006619247-0.0480294290.010163041-0.016295740.022262836
10.25-0.0574998010.003993386-0.0449306880.008173904-0.0137227360.020716771
10.5-0.051143750.001596692-0.0417497810.006374035-0.0110597550.019223017
10.75-0.044645293-0.000592797-0.0384893470.004743263-0.0083222450.017780285
11-0.038030844-0.002596684-0.0351575020.003261599-0.0055274630.016386321
11.25-0.031341549-0.004436324-0.0317674290.001909129-0.0026951170.015039025
11.5-0.024614507-0.00613098-0.0283311510.0006679580.0001525070.013735544
11.75-0.017882376-0.00769796-0.024859376-0.0004779210.0029934250.012473357
12-0.011173899-0.009152836-0.021361643-0.0015428410.005806550.011249676
12.25-0.004514363-0.010509632-0.017846457-0.002539650.0085718260.010061673
12.50.002074002-0.011780991-0.014321405-0.0034798670.011269920.008906173
12.750.008571669-0.012978324-0.010793251-0.0043738330.0138831330.00778063
130.014961115-0.014111829-0.007268505-0.005230790.0163968420.00668324
13.250.021224088-0.015189926-0.003756437-0.0060587120.0187990620.005612291
13.50.027343303-0.016219896-0.000266838-0.0068646220.0210799550.004566151
13.750.033303622-0.0172083440.003191571-0.0076548380.0232326150.003543593
140.039091821-0.0181612670.00661104-0.0084350440.0252527610.00254365
14.250.044696388-0.0190841160.009984681-0.0092103540.0271385650.001565448
14.50.050107341-0.0199818460.013306389-0.0099853690.0288894520.000607958
14.750.055316062-0.0208589640.016570757-0.0107642250.030506261-0.000329721
150.060315153-0.021719570.019773006-0.0115506420.031991009-0.00124848
15.250.065098312-0.0225673950.022908924-0.012347960.033346812-0.002149073
15.50.069660283-0.0234058250.025974817-0.0131591620.034577516-0.003032036
15.750.074000208-0.0242374410.02896791-0.0139860620.035687564-0.003897727
160.078122708-0.0250638810.031886451-0.0148290470.036681939-0.004746278
16.250.082032722-0.0258865840.034729011-0.0156883450.037566018-0.005577625
16.50.085735078-0.0267068640.037494406-0.0165641320.038345273-0.006391723
16.750.089234496-0.027525920.040181666-0.0174565410.039025155-0.007188664
170.092535584-0.0283448450.042790016-0.0183656640.039611046-0.007968582
17.250.09564284-0.0291646360.045318858-0.0192915580.040108339-0.008731663
17.50.098560654-0.0299862040.047767752-0.0202342480.040522416-0.0094781
17.750.101293308-0.0308103780.0501364-0.021193730.040858451-0.010208079
180.103844979-0.0316379110.05242463-0.0221699750.041121214-0.010921835
18.250.106219737-0.0324694920.054632386-0.0231629310.041315187-0.011619668
18.50.108421553-0.0333057440.056759717-0.0241725280.041444392-0.012302024
18.750.11045482-0.0341470930.058806964-0.0251984820.041512563-0.012969396
190.112327738-0.0349928530.060776064-0.0262390750.041523375-0.013622212
19.250.114049843-0.0358419010.062669582-0.027292050.041480594-0.014260787
19.50.115630128-0.0366931910.064489976-0.0283553030.041388018-0.014885384
19.750.11707707-0.0375457530.066239598-0.0294268710.041249279-0.015496245
200.118398662-0.0383986820.067920702-0.0305049270.041067832-0.016093567
20.250.119602445-0.0392511410.069535447-0.0315877690.040846973-0.016677547
20.50.120695538-0.040102350.071085903-0.032673810.040589982-0.017248381
20.750.121684663-0.0409515850.072574055-0.0337615710.04029999-0.017806264
210.122576169-0.0417981730.074001808-0.0348496740.039979943-0.018351395
21.250.123376059-0.0426414910.075370992-0.0359368350.039632607-0.018883953
21.50.124090005-0.0434809590.076683362-0.0370218570.039260496-0.019404038
21.750.124723373-0.0443160390.077940607-0.0381036260.038866043-0.019911739
220.125281242-0.0451462330.07914435-0.0391811040.038451661-0.020407135
22.250.125768417-0.0459710780.080296151-0.0402533240.038019647-0.020890282
22.50.12618943-0.046790090.081397515-0.0413193330.03757198-0.021361156
22.750.126548393-0.047602180.082449915-0.0423776350.037110507-0.021819688
230.126849083-0.0484059210.083454792-0.0434264460.036636994-0.022265797
23.250.127095082-0.0491999770.084413528-0.0444640930.036153054-0.022699429
23.50.12728979-0.0499831040.085327456-0.045489020.035659967-0.023120605
23.750.127436434-0.0507541420.08619786-0.0464997730.035158884-0.023529361
240.127538078-0.0515120110.087025974-0.0474950.034650922-0.023925738
24.250.127597631-0.0522557080.087812991-0.0484734430.034137106-0.024309772
24.50.12761786-0.0529842970.08856006-0.0494339290.033618194-0.02468147
24.750.12760139-0.0536969130.089268287-0.0503753690.033094916-0.025040809
250.12755072-0.0543927480.089938741-0.0512967510.032567993-0.025387753
25.250.127468223-0.0550710560.090572454-0.0521971350.032038124-0.025722253
25.50.127356157-0.0557311440.09117042-0.0530756490.03150591-0.026044201
25.750.127216669-0.0563723720.091733602-0.0539314870.03097194-0.026353481
260.127051801-0.0569941450.092262928-0.05476390.030436775-0.026649986
26.250.126863497-0.0575959180.092759294-0.0555721980.029900922-0.026933591
26.50.126653605-0.0581771850.093223569-0.0563557430.029364778-0.027204135
26.750.126423886-0.0587374820.093656591-0.0571139470.028828721-0.027461456
270.126175989-0.0592763790.094059159-0.0578462690.028293127-0.02770541
27.250.125910729-0.0597933860.094431748-0.0585521840.02775831-0.027935854
27.50.125628046-0.0602879420.094774488-0.0592311770.027224383-0.02815258
27.750.125327849-0.0607595230.095087501-0.0598827760.026691425-0.028355363
280.125010063-0.0612076480.095370919-0.0605065490.026159498-0.028543983
28.250.124674625-0.0616318710.095624883-0.06110210.025628669-0.028718229
28.50.124321487-0.0620317840.095849543-0.0616690690.025098954-0.028877899
28.750.123950611-0.062407010.096045056-0.0622071310.024570364-0.029022808
290.123561972-0.0627572080.096211588-0.0627159910.024042924-0.02915278
29.250.123155555-0.0630820640.096349308-0.0631953850.023516679-0.029267656
29.50.122731356-0.0633812940.096458395-0.0636450740.022991634-0.029367323
29.750.12228938-0.0636546390.09653903-0.064064850.022467786-0.0294517
300.121829639-0.0639018670.0965914-0.0644545260.021945143-0.029520715
30.250.121352156-0.064122770.096615698-0.0648139390.021423732-0.029574291
30.50.120856959-0.0643171620.096612118-0.0651429510.020903543-0.029612323
30.750.120344086-0.0644848770.096580859-0.0654414410.020384574-0.029634695
310.119813578-0.0646257720.096522124-0.0657093090.019866836-0.029641288
31.250.119265485-0.0647397190.096436118-0.0659464740.019350344-0.029631988
31.50.118699862-0.0648266120.096323047-0.0661528730.018835079-0.029606697
31.750.118116769-0.0648863580.096183123-0.0663284560.01832102-0.02956533
320.117516272-0.0649188830.096016555-0.0664731930.017808159-0.029507811
32.250.11689844-0.0649241270.095823558-0.0665870650.017296508-0.029434052
32.50.116263337-0.064902050.09560434-0.0666700750.016786103-0.029343937
32.750.115610789-0.0648527720.095358993-0.0667223740.016276995-0.029237351
330.114940426-0.0647765510.095087507-0.0667442440.015769248-0.029114184
33.250.11425189-0.0646736480.094789882-0.0667359710.015262907-0.028974329
33.50.113544848-0.0645443230.094466124-0.0666978390.014757941-0.02881769
33.750.112818987-0.0643888360.094116253-0.0666301320.01425432-0.028644174
340.112074018-0.0642074460.093740296-0.0665331340.01375205-0.028453694
34.250.111309671-0.0640004080.09333829-0.0664071240.013251166-0.028246166
34.50.110525694-0.0637679770.092910278-0.0662523840.012751779-0.028021478
34.750.109721855-0.0635104080.092456314-0.0660691920.012254028-0.027779521
350.108897938-0.0632279520.091976457-0.0658578250.01175805-0.027520198
35.250.108053744-0.0629208580.091470772-0.0656185580.01126399-0.027243418
35.50.10718909-0.0625893760.090939334-0.0653516650.010772024-0.026949102
35.750.106303807-0.0622337530.09038222-0.0650574190.010282322-0.026637179
360.105397742-0.0618542310.089799516-0.0647360880.009795055-0.026307581
36.250.104470754-0.0614510550.089191311-0.0643879410.009310404-0.025960248
36.50.103522716-0.0610244660.0885577-0.0640132450.008828527-0.025595139
36.750.102553512-0.0605747010.087898782-0.0636122630.008349571-0.025212224
370.10156304-0.0601019980.087214661-0.0631852570.007873685-0.024811479
37.250.100551206-0.0596065910.086505445-0.0627324880.007401022-0.024392889
37.50.09951793-0.0590887130.085771246-0.0622542130.006931769-0.023956434
37.750.09846314-0.0585485950.085012178-0.0617506890.006466103-0.023502104
380.097386774-0.0579864650.084228359-0.0612221680.006004177-0.02302989
38.250.096288781-0.0574025490.083419913-0.0606689020.005546138-0.022539783
38.50.095169115-0.0567970720.082586962-0.0600911390.005092181-0.022031774
38.750.094027742-0.0561702550.081729634-0.0594891280.004642508-0.021505862
390.092864634-0.055522320.080848058-0.0588631120.004197303-0.020962052
39.250.091679801-0.0548535620.079942413-0.0582134290.003756737-0.020400368
39.50.090473337-0.0541644810.079013007-0.057540660.003320988-0.019820854
39.750.08924535-0.0534555990.078060162-0.0568454110.002890241-0.019223559
400.087995951-0.0527274220.077084193-0.0561282720.002464665-0.018608539
40.250.086725254-0.0519804420.076085413-0.0553898160.002044417-0.017975858
40.50.085433373-0.0512151420.075064129-0.0546306040.001629632-0.01732559
40.750.084120424-0.0504319880.074020641-0.0538511780.001220432-0.016657815
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90.75-0.3307533070.168575126-0.261965130.172989923-0.036096540.229259442
91-0.332622940.169467478-0.2634301650.173919703-0.03622460.2303464
91.25-0.3344876780.170357413-0.2648912950.174846986-0.0363523130.231430384
91.5-0.336347540.171244943-0.2663485380.175771783-0.036479680.23251141
91.75-0.3382025460.17213008-0.2678019120.176694106-0.0366067030.233589493
92-0.3400527140.173012837-0.2692514330.177613968-0.0367333830.234664648
92.25-0.3418980620.173893224-0.2706971180.178531378-0.0368597210.23573689
92.5-0.3437386060.174771254-0.2721389840.17944635-0.036985720.236806235
92.75-0.3455743620.175646938-0.2735770460.180358892-0.0371113810.237872698
93-0.3474053450.176520288-0.2750113180.181269017-0.0372367050.238936294
93.25-0.3492315720.177391314-0.2764418190.182176735-0.0373616940.239997039
93.5-0.3510530690.178260029-0.2778685670.183082059-0.037486350.241054946
93.75-0.3528698620.179126446-0.2792915820.183985002-0.0376106730.242110032
94-0.3546819760.179990577-0.2807108860.184885577-0.0377346670.24316231
94.25-0.3564894320.180852434-0.2821264960.185783796-0.0378583320.244211795
94.5-0.358292220.181712024-0.2835384140.186679663-0.0379816690.245258502
94.75-0.3600903250.182569354-0.284946640.187573182-0.0381046810.246302444
95-0.3618837310.18342443-0.2863511750.188464355-0.0382273690.247343636

 
M and S spline coefficients for males 3 to 95 years
 
 FEV1FVCFEV1/FVC ratio
AgeMSMSMS
3-0.1197755940.184307362-0.0569425650.149455893-0.0349395380.01755124
3.25-0.1139554540.171160981-0.0542627730.138593778-0.0339256170.0221529
3.5-0.1084033080.158994969-0.0517467030.12854384-0.0330647070.026377944
3.75-0.1030896760.147679297-0.0493937720.119199604-0.0323747790.030225016
4-0.0980349020.137110566-0.0472176130.110476538-0.0318653470.033665118
4.25-0.0934008370.127211229-0.0452841070.102312293-0.031538990.03665079
4.5-0.0893237420.117916644-0.0436467060.094654776-0.0313799080.039135686
4.75-0.0858706330.109172031-0.0423340310.087459385-0.0313720240.041108046
5-0.083017780.100933825-0.04135020.080690062-0.0314923210.042596322
5.25-0.0807253620.093163853-0.040690620.074315006-0.0316874960.043662055
5.5-0.0789541470.085827647-0.0403463540.068305417-0.0318923790.044381505
5.75-0.0776255960.078894526-0.0402870430.062635308-0.0320509650.044814446
6-0.0766296830.072337153-0.0404653970.057281204-0.0321173660.04501273
6.25-0.0758756120.066130609-0.040841180.05222175-0.0320665480.04502296
6.5-0.0752902080.060252124-0.0413809210.047437478-0.0318939440.044882986
6.75-0.0748328880.054680771-0.0420550960.042910563-0.0315986290.044626511
7-0.0745142020.049397165-0.0428353530.038624578-0.0311757460.044271869
7.25-0.0743478060.044383519-0.0436975190.03456448-0.030628990.043819595
7.5-0.0743435020.039623524-0.0446213960.030716481-0.0299746710.043257301
7.75-0.0745080430.035102191-0.0455900690.027067926-0.0292351740.042569823
8-0.0748233240.030805517-0.0465805450.023607021-0.0284357290.041741105
8.25-0.07519160.026719872-0.0475416280.020322364-0.0275999740.040752118
8.5-0.075512830.022832583-0.0484237140.017203371-0.0267460360.039582986
8.75-0.075703890.019132025-0.0491858940.014240327-0.0258822230.038233467
9-0.0756958290.015607502-0.049794530.011424295-0.0249789450.036751685
9.25-0.0754316150.012249159-0.050222080.008747034-0.0239897890.03520758
9.5-0.0748604140.009047749-0.0504446750.006200837-0.0228753580.033668013
9.75-0.0739168450.005993827-0.0504340670.003777988-0.0216090780.032185617
10-0.0725378050.003078378-0.0501637990.001471157-0.0201739250.030798272
10.25-0.0706710540.00029313-0.049612291-0.000726394-0.018560.029531439
10.5-0.068273636-0.002369527-0.04876212-0.002820878-0.0167647090.028398948
10.75-0.065310536-0.004916603-0.047599405-0.004818033-0.0147906510.027407663
11-0.061753529-0.00735457-0.046113283-0.006723165-0.0126454590.026562318
11.25-0.057581415-0.009689409-0.044295848-0.008541194-0.0103421140.025863005
11.5-0.052812865-0.011926584-0.042152399-0.010276713-0.0078995620.025303362
11.75-0.047505135-0.014071079-0.039700947-0.011934022-0.0053412560.024874178
12-0.041712276-0.01612753-0.036958928-0.013517123-0.002691770.024563815
12.25-0.035483352-0.018100261-0.033942579-0.0150297432.39E-050.024359257
12.5-0.028862958-0.019993309-0.030667035-0.0164753620.0027799720.024243716
12.75-0.021891672-0.021810449-0.027146425-0.0178572280.0055508510.02419839
13-0.01460646-0.023555217-0.02339395-0.0191783810.0083119220.024204644
13.25-0.007041031-0.025230925-0.019421961-0.0204416680.0110408790.024245236
13.50.000772006-0.026840657-0.015243034-0.0216497540.0137177830.024304884
13.750.008773402-0.0283869-0.010885127-0.0228050960.0163251510.02437092
140.016886095-0.029871683-0.006386638-0.0239099710.0188472920.024432178
14.250.025040024-0.031296943-0.001782701-0.0249665210.02126960.024476893
14.50.033172115-0.0326645380.002894871-0.0259767690.0235791360.024493244
14.750.041225603-0.033976250.007617271-0.0269426230.0257657070.024471153
150.049149418-0.0352337930.012358413-0.0278658890.0278215110.0244019
15.250.056897642-0.0364388090.017094676-0.0287482730.0297409640.024278415
15.50.064429016-0.0375928790.021804675-0.0295913920.0315203660.02409507
15.750.071706506-0.0386975190.026469057-0.0303967770.0331581490.023847746
160.078696905-0.0397541880.031070313-0.0311658810.0346541660.023533943
16.250.085373739-0.0407642160.035592604-0.0319000130.0360095090.023152924
16.50.091728764-0.0417285370.040021563-0.0326000910.0372274980.022705226
16.750.09775948-0.0426479680.044344203-0.0332669080.0383128720.022191606
170.10346408-0.0435233230.048548818-0.0339012360.0392708830.021612804
17.250.108841384-0.0443554070.052624865-0.0345038270.0401068270.020969752
17.50.113890765-0.0451450170.056562868-0.0350754140.0408263210.020263937
17.750.118612098-0.0458929450.060354319-0.0356167110.0414353240.019497286
180.123005703-0.0465999670.063991603-0.0361284140.0419397180.018671858
18.250.127072297-0.0472668530.067467915-0.0366111980.0423453540.017789909
18.50.130812954-0.047894360.070777195-0.0370657240.0426586410.016854992
18.750.134229065-0.0484832340.073914063-0.0374926320.0428860160.015870864
190.137322301-0.0490342070.076873763-0.0378925470.0430337260.014840877
19.250.140094604-0.0495480030.079652118-0.0382660770.0431076970.013768374
19.50.142553-0.0500253710.082248345-0.0386137790.0431133680.012657416
19.750.144715578-0.0504671480.084668541-0.0389361250.0430557350.011512017
200.146600993-0.050874160.086919473-0.0392335670.0429394120.010335984
20.250.148226832-0.051247210.089007595-0.0395065510.0427688470.00913302
20.50.149609679-0.0515870760.090939061-0.0397555170.0425485860.007906602
20.750.150765184-0.0518945170.092719741-0.0399808940.0422830770.006660033
210.151708117-0.0521702680.094355241-0.0401831090.0419766430.005396413
21.250.152452425-0.0524150440.095850915-0.0403625780.0416333640.004118707
21.50.153011281-0.0526295410.097211879-0.0405197110.0412568780.00282972
21.750.153397135-0.0528144340.098443024-0.0406549110.0408505330.001531999
220.153621752-0.0529703810.099549029-0.0407685730.0404174610.000227949
22.250.15369626-0.0530980190.100534369-0.0408610850.039960552-0.00107999
22.50.153631182-0.053197970.101403331-0.0409328280.039482359-0.002389467
22.750.153436475-0.0532708380.102160019-0.0409841760.0389853-0.00369825
230.153121563-0.0533172120.102808364-0.0410154950.038471711-0.005004279
23.250.152695354-0.0533376870.103352414-0.0410271680.037943744-0.006305684
23.50.152166213-0.053332990.103797587-0.04101970.037403189-0.007600732
23.750.151542039-0.0533038680.10414958-0.0409936260.03685169-0.008887798
240.150830316-0.0532510420.104413805-0.040949460.036290841-0.010165307
24.250.150038139-0.0531752070.10459541-0.0408877010.035722131-0.011431734
24.50.149172229-0.0530770330.104699293-0.0408088290.035146854-0.012685512
24.750.148238961-0.0529571650.104730112-0.0407133070.034566225-0.013925127
250.147244378-0.0528162260.104692301-0.0406015840.033981428-0.01514917
25.250.146194214-0.0526548180.10459008-0.0404740930.033393577-0.01635626
25.50.145093904-0.0524735190.104427469-0.0403312530.032803597-0.017544681
25.750.143948606-0.0522728910.104208294-0.0401734690.032212316-0.018712685
260.142763215-0.0520534730.103936201-0.0400011330.031620531-0.019858591
26.250.141542372-0.0518157880.103614664-0.0398146240.031029015-0.020980785
26.50.140290484-0.0515603410.103246992-0.0396143090.030438422-0.022077715
26.750.139011733-0.051287620.102836341-0.0394005430.029849329-0.023147909
270.137710088-0.0509980970.102385718-0.039173670.029262244-0.024189964
27.250.136389316-0.0506922270.101897992-0.0389340230.028677634-0.025202541
27.50.135052993-0.0503704530.101375896-0.0386819250.028095899-0.026184314
27.750.13370446-0.0500332010.10082202-0.0384176910.027517402-0.027133962
280.132345912-0.0496809140.100238459-0.0381416560.026942503-0.028050214
28.250.130978568-0.0493140380.099626887-0.037854170.026371535-0.028931923
28.50.129603563-0.0489330080.098988891-0.0375555750.025804734-0.029778186
28.750.128221973-0.0485382430.098325994-0.0372461980.025242287-0.030588207
290.126834828-0.0481301480.097639652-0.0369263580.0246844-0.031361205
29.250.125443106-0.0477091140.096931261-0.0365963610.024131279-0.032096402
29.50.124047741-0.047275520.096202159-0.0362565050.023583073-0.032793049
29.750.122649622-0.0468297330.095453625-0.0359070770.023039887-0.033450455
300.121249596-0.0463721070.094686887-0.0355483540.022501808-0.034067995
30.250.11984847-0.0459029840.09390312-0.0351806070.021968905-0.034645147
30.50.118447015-0.0454226970.093103452-0.0348040940.021441167-0.035181631
30.750.117045962-0.0449315680.092288964-0.0344190690.020918542-0.035677253
310.11564601-0.0444299060.091460691-0.0340257740.020400952-0.036131842
31.250.114247825-0.0439180140.090619626-0.0336244470.019888292-0.036545282
31.50.11285204-0.0433961840.089766723-0.0332153170.019380366-0.036917567
31.750.11145926-0.0428646980.088902894-0.0327986050.018876933-0.037248713
320.110070059-0.042323830.088029015-0.0323745260.018377747-0.037538767
32.250.108684985-0.0417738470.087145926-0.031943290.017882577-0.037787807
32.50.107304559-0.0412150050.086254434-0.0315050960.0173912-0.037996034
32.750.105929279-0.0406475540.085355312-0.0310601430.016903399-0.038163668
330.104559617-0.0400717370.084449302-0.0306086190.016418939-0.038290925
33.250.103195985-0.0394877890.083537089-0.030150710.015937573-0.038377998
33.50.101838102-0.0388959430.08261885-0.0296866110.015458996-0.038425025
33.750.100485103-0.038296430.081694336-0.0292165210.014982889-0.038432125
340.099136143-0.0376894710.080763297-0.0287406370.014508933-0.038399416
34.250.097790409-0.0370752850.079825496-0.0282591480.014036849-0.038327004
34.50.096447126-0.0364540810.078880711-0.0277722370.013566473-0.038214999
34.750.095105549-0.0358260640.07792873-0.0272800820.01309769-0.038063486
350.093764967-0.0351914320.076969355-0.0267828550.012630404-0.037872532
35.250.092424697-0.0345503770.076002399-0.0262807220.012164561-0.037642211
35.50.091084086-0.0339030860.075027684-0.0257738450.011700136-0.037372631
35.750.089742509-0.0332497390.074045046-0.0252623810.011237103-0.037063915
360.088399368-0.0325905140.073054326-0.0247464820.010775431-0.036716206
36.250.087054089-0.0319255810.072055379-0.0242262960.010315107-0.036329688
36.50.085706124-0.0312551060.071048067-0.0237019650.009856156-0.035904622
36.750.084354948-0.0305792510.070032261-0.0231736280.00939863-0.035441292
370.083000059-0.0298981730.069007839-0.0226414190.008942585-0.034939952
37.250.081640976-0.0292120230.067974689-0.0221054710.008488068-0.034400872
37.50.080277239-0.0285209510.066932706-0.0215659080.008035079-0.033824379
37.750.078908408-0.0278251010.06588179-0.0210228540.007583618-0.033210809
380.077534064-0.0271246120.064821851-0.0204764290.007133684-0.032560508
38.250.076153802-0.026419620.063752803-0.0199267480.006685275-0.031873847
38.50.07476724-0.0257102590.062674569-0.0193739240.006238411-0.031151208
38.750.07337401-0.0249966570.061587075-0.0188180670.005793124-0.030392952
390.07197376-0.024278940.060490255-0.0182592820.005349458-0.029599422
39.250.070566155-0.0235572290.059384048-0.0176976720.004907443-0.02877097
39.50.069150874-0.0228316430.058268397-0.0171333380.004467099-0.027908004
39.750.067727613-0.0221022980.057143252-0.0165663780.004028433-0.027010938
400.06629601-0.0213693160.056008528-0.0159968910.003591451-0.026080176
40.250.064855563-0.020632840.054864057-0.0154249920.003156162-0.025116118
40.50.063405765-0.0198930120.053709668-0.0148507940.002722596-0.024119172
40.750.061946131-0.019149970.052545197-0.0142744060.002290793-0.023089744
410.060476196-0.0184038480.05137049-0.0136959330.001860799-0.022028226
41.250.058995517-0.0176547760.050185402-0.0131154790.001432648-0.020935001
41.50.057503667-0.0169028810.048989794-0.0125331430.001006361-0.019810437
41.750.056000239-0.0161482850.047783539-0.0119490230.000581943-0.018654887
420.054484844-0.0153911070.046566513-0.0113632110.000159386-0.017468703
42.250.052957109-0.0146314640.045338602-0.010775799-0.000261316-0.016252268
42.50.051416678-0.0138694680.044099697-0.010186877-0.000680136-0.015006035
42.750.04986321-0.0131052280.042849698-0.009596528-0.001097037-0.013730463
430.048296381-0.012338850.041588509-0.009004838-0.001511981-0.01242601
43.250.04671588-0.0115704380.040316042-0.008411887-0.001924938-0.011093151
43.50.045121411-0.0108000910.039032214-0.007817752-0.002335884-0.009732389
43.750.043512691-0.0100279080.037736948-0.007222512-0.002744805-0.008344222
440.04188945-0.0092539830.036430171-0.006626239-0.003151699-0.006929132
44.250.040251431-0.0084784070.035111819-0.006029005-0.00355657-0.005487604
44.50.03859839-0.0077012710.033781829-0.005430881-0.003959413-0.00402015
44.750.036930093-0.0069226620.032440144-0.004831934-0.004360223-0.002527274
450.035246319-0.0061426630.031086714-0.004232229-0.004759005-0.001009467
45.250.033546857-0.0053613580.029721489-0.003631832-0.0051557840.000532769
45.50.031831507-0.0045788250.028344428-0.003030803-0.0055506170.002098882
45.750.030100079-0.0037951430.026955491-0.002429203-0.0059435720.003688313
460.028352392-0.0030103870.025554642-0.00182709-0.0063347220.005300503
46.250.026588275-0.0022246310.024141852-0.001224522-0.0067241520.006934894
46.50.024807568-0.0014379460.022717092-0.000621554-0.0071119540.008590905
46.750.023010116-0.0006504010.021280337-1.82E-05-0.007498220.010267956
470.0211957750.0001379350.0198315680.000585371-0.0078830470.011965483
47.250.0193644090.0009269980.0183707670.001189225-0.0082665250.013682929
47.50.017515890.0017167240.0168979190.001793275-0.0086487260.015419752
47.750.0156501060.0025070490.0154130210.002397471-0.0090297120.017175427
480.013767150.0032978980.0139162230.003001762-0.009409540.01894945
48.250.0118672820.0040891860.0124078040.003606091-0.0097882540.020741347
48.50.0099507680.0048808290.0108880410.004210404-0.0101658480.022550727
48.750.0080178650.0056727450.0093572070.004814648-0.0105423050.024377222
490.0060688280.0064648560.0078155660.005418772-0.0109176160.026220461
49.250.0041039070.0072570850.0062633780.006022726-0.0112917690.028080074
49.50.0021233470.0080493570.0047008980.00662646-0.0116647390.029955659
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60.75-0.0997528580.042868261-0.0729558210.033001541-0.0273472080.124718233
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61.5-0.107142660.045087224-0.0784165040.034676619-0.0283176590.131369604
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62.75-0.1195080270.048748535-0.087521230.03744007-0.0299166660.142451781
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66.75-0.1591036550.060137139-0.1164562290.046035257-0.0348968650.177601671
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67.5-0.1664762760.062214683-0.1218142750.047603573-0.0358099590.184099415
67.75-0.1689273650.06290304-0.1235938960.048123255-0.0361129230.18625707
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68.25-0.1738187520.064273483-0.1271428860.049157967-0.0367166430.190559412
68.5-0.176258690.064955558-0.1289120460.049672992-0.0370173570.192703925
68.75-0.1786945830.065635532-0.130677530.050186462-0.0373172760.194843891
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69.25-0.1835538950.066989202-0.1341973170.051208751-0.0379146390.199109876
69.5-0.1859771650.067662911-0.1359515570.051717581-0.0382120440.201235755
69.75-0.1883960790.068334547-0.1377019860.052224872-0.0385085740.203356801
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70.25-0.1932205650.069671622-0.1411912990.05323486-0.0390989360.207584138
70.5-0.1956260.070337076-0.1429301260.053737566-0.039392730.209690323
70.75-0.198026810.071000484-0.1446650310.054238752-0.0396855680.21179146
71-0.2004229310.071661853-0.1463959870.054738424-0.039977430.213887511
71.25-0.2028143010.07232119-0.148122970.055236586-0.0402682980.215978436
71.5-0.205200860.072978501-0.1498459550.055733243-0.0405581560.218064202
71.75-0.207582550.073633794-0.1515649190.056228399-0.040846990.220144778
72-0.2099593130.074287076-0.1532798380.05672206-0.041134790.22222013
72.25-0.2123310930.074938354-0.1549906910.057214229-0.0414215450.224290225
72.5-0.2146978370.075587635-0.1566974570.057704912-0.041707250.226355034
72.75-0.2170594920.076234926-0.1584001140.058194114-0.0419918990.228414528
73-0.2194160060.076880233-0.1600986420.058681838-0.042275490.230468683
73.25-0.221767330.077523564-0.1617930240.05916809-0.0425580190.232517471
73.5-0.2241134140.078164926-0.1634832380.059652875-0.0428394820.234560872
73.75-0.2264542130.078804326-0.1651692690.060136197-0.0431198760.236598867
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74.25-0.2311197670.080077267-0.1685287090.061098472-0.0436774460.240658567
74.5-0.2334444350.080710822-0.1702020860.061577434-0.0439546220.242680246
74.75-0.235763640.081342442-0.1718712120.062054952-0.0442307270.244696464
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75.25-0.2403854990.082599908-0.1751966560.063005677-0.0447797280.248712479
75.5-0.2426880730.083225766-0.1768529450.063478893-0.0450526280.250712261
75.75-0.2449850270.083849718-0.1785049280.063950683-0.0453244630.25270655
76-0.2472763240.08447177-0.1801525920.064421054-0.0455952320.254695343
76.25-0.2495619280.085091929-0.1817959240.06489001-0.045864940.256678632
76.5-0.2518418040.085710202-0.1834349130.065357555-0.0461335910.258656407
76.75-0.254115920.086326595-0.1850695470.065823694-0.0464011950.260628661
77-0.2563842430.086941116-0.1866998170.066288432-0.0466677580.262595384
77.25-0.2586467410.08755377-0.1883257110.066751774-0.046933290.26455657
77.5-0.2609033840.088164566-0.1899472190.067213724-0.0471977990.266512217
77.75-0.2631541410.08877351-0.1915643330.067674287-0.0474612950.268462322
78-0.2653989860.089380608-0.1931770440.068133468-0.0477237860.270406884
78.25-0.2676378880.089985868-0.1947853420.068591271-0.0479852810.272345905
78.5-0.2698708220.090589295-0.196389220.069047702-0.0482457870.274279389
78.75-0.2720977620.091190897-0.197988670.069502764-0.0485053130.276207344
79-0.2743186820.091790681-0.1995836860.069956463-0.0487638670.278129776
79.25-0.2765335570.092388653-0.2011742590.070408804-0.0490214580.280046689
79.5-0.2787423650.092984819-0.2027603840.07085979-0.0492780960.281958087
79.75-0.2809450830.093579187-0.2043420550.071309426-0.0495337940.283863971
80-0.2831416880.094171762-0.2059192650.071757718-0.0497885630.285764342
80.25-0.2853321590.094762552-0.207492010.07220467-0.0500424130.287659206
80.5-0.2875164760.095351563-0.2090602840.072650286-0.0502953550.289548573
80.75-0.2896946180.095938802-0.2106240830.073094571-0.05054740.291432459
81-0.2918665680.096524275-0.2121834020.07353753-0.0507985580.29331088
81.25-0.2940323050.097107989-0.2137382380.073979168-0.0510488370.295183855
81.5-0.2961918140.09768995-0.2152885870.074419488-0.0512982460.297051402
81.75-0.2983450760.098270165-0.2168344450.074858496-0.0515467930.298913541
82-0.3004920750.098848639-0.218375810.075296195-0.0517944870.300770291
82.25-0.3026327990.099425381-0.2199126790.075732592-0.0520413360.302621674
82.5-0.3047672580.100000397-0.2214450660.076167691-0.0522873450.304467707
82.75-0.3068954870.100573699-0.2229729940.076601501-0.0525325240.306308409
83-0.3090175180.101145296-0.2244964860.077034028-0.0527768790.308143798
83.25-0.3111333850.101715197-0.2260155660.07746528-0.0530204180.309973891
83.5-0.3132431190.102283413-0.2275302560.077895263-0.0532631480.311798707
83.75-0.3153467520.102849953-0.2290405790.078323986-0.0535050770.313618262
84-0.3174443170.103414826-0.2305465590.078751454-0.0537462130.315432574
84.25-0.3195358460.103978043-0.2320482170.079177675-0.0539865640.31724166
84.5-0.321621370.104539612-0.2335455760.079602656-0.0542261380.319045536
84.75-0.3237009190.105099542-0.2350386580.080026404-0.0544649440.320844219
85-0.3257745250.105657843-0.2365274850.080448924-0.0547029920.322637725
85.25-0.327842220.106214524-0.2380120790.080870225-0.0549402880.324426071
85.5-0.3299040320.106769595-0.2394924620.081290313-0.0551768420.326209278
85.75-0.3319599930.107323063-0.2409686550.081709194-0.055412660.327987368
86-0.3340101320.107874938-0.2424406790.082126875-0.055647750.329760361
86.25-0.336054480.108425229-0.2439085560.082543362-0.055882120.33152828
86.5-0.3380930660.108973944-0.2453723070.082958662-0.0561157760.333291143
86.75-0.3401259190.109521092-0.2468319520.083372781-0.0563487260.335048971
87-0.3421530680.110066682-0.2482875120.083785727-0.0565809780.336801784
87.25-0.3441745430.110610723-0.2497390080.084197504-0.0568125390.338549603
87.5-0.3461903710.111153222-0.251186460.084608119-0.0570434140.340292453
87.75-0.3482005820.111694188-0.2526298890.085017578-0.057273610.342030359
88-0.3502052040.11223363-0.2540693140.085425888-0.0575031320.343763346
88.25-0.3522042650.112771555-0.2555047550.085833055-0.0577319870.345491441
88.5-0.3541977930.113307973-0.2569362330.086239085-0.057960180.34721467
88.75-0.3561858150.113842891-0.2583637670.086643983-0.0581877150.348933058
89-0.3581683580.114376316-0.2597873760.087047756-0.0584145970.35064663
89.25-0.3601454510.114908258-0.261207080.087450409-0.0586408320.352355414
89.5-0.362117120.115438724-0.2626228980.087851949-0.0588664240.354059434
89.75-0.3640833910.115967722-0.2640348490.088252381-0.0590913760.355758716
90-0.3660442930.116495259-0.2654429530.088651712-0.0593156920.357453286
90.25-0.3679998520.117021345-0.2668472280.089049946-0.0595393770.359143169
90.5-0.3699500930.117545985-0.2682476930.08944709-0.0597624350.36082839
90.75-0.3718950410.118069188-0.2696443660.089843148-0.0599848690.362508972
91-0.3738347210.118590961-0.2710372620.090238127-0.0602066850.364184941
91.25-0.3757691580.119111312-0.2724264010.090632032-0.0604278850.365856321
91.5-0.3776983810.119630248-0.2738118030.091024869-0.0606484750.367523134
91.75-0.379622420.120147777-0.2751934910.091416643-0.0608684570.369185406
92-0.3815413040.120663908-0.2765714860.091807362-0.0610878380.370843159
92.25-0.383455060.121178647-0.2779458090.09219703-0.0613066190.372496417
92.5-0.3853637120.121692002-0.2793164730.092585653-0.0615248060.374145204
92.75-0.3872672780.12220398-0.2806834940.092973235-0.0617424010.375789544
93-0.3891657810.122714586-0.2820468860.093359781-0.0619594090.37742946
93.25-0.391059240.123223828-0.2834066610.093745296-0.0621758310.379064976
93.5-0.3929476750.123731712-0.2847628340.094129784-0.0623916730.380696114
93.75-0.3948311070.124238244-0.2861154190.094513251-0.0626069370.382322899
94-0.3967095550.124743431-0.2874644280.0948957-0.0628216260.383945353
94.25-0.398583040.12524728-0.2888098760.095277137-0.0630357440.385563499
94.5-0.4004515810.125749796-0.2901517760.095657566-0.0632492940.387177359
94.75-0.4023151980.126250986-0.2914901410.096036991-0.0634622790.388786956
95-0.404173910.126750856-0.2928249840.096415417-0.0636747030.390392312

 

 

 
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