#############################################################
##                        mmtbx.xtriage                    ##
##                                                         ##
##      P.H. Zwart, R.W. Grosse-Kunstleve & P.D. Adams     ##
##                                                         ##
#############################################################
Date 2005-10-19 Time 21:25:38 PDT -0700


##-------------------------------------------##
## WARNING:                                  ##
## Number of residues unspecified            ##
##-------------------------------------------##


Effective parameters: 
scaling.input {
  basic {
    n_residues = None
    n_bases = None
    n_copies_per_asu = None
    n_terms = None
  }
  analyses {
    verbose = 1
    log = "2bo4.log"
  }
  xray_data {
    file_name = "2bo4.mtz"
    labels = "F,SIGF"
    unit_cell = 261.1499939 151.2899933 153.2400055 90 90.41000366 90
    space_group = "C 1 2 1"
    high_resolution = 0
    low_resolution = 10
  }
}


Symmetry, cell and reflection file content summary

Miller array info: 2bo4.mtz:F,SIGF
Observation type: xray.amplitude
Type of data: double, size=413633
Type of sigmas: double, size=413633
Number of Miller indices: 413633
Anomalous flag: False
Unit cell: (261.15, 151.29, 153.24, 90, 90.41, 90)
Space group: C 1 2 1 (No. 5)
Systematic absences: 0
Centric reflections: 7329
Resolution range: 19.9705 1.95002
Completeness in resolution range: 0.959131
Completeness with d_max=infinity: 0.958156

##----------------------------------------------------##
##                    Basic statistics                ##
##----------------------------------------------------##


Matthews coefficient and Solvent content statistics

Number of residues unknown, asuming 50% solvent content

----------------------------------------------------------------
|              Best guess : 5538  residues in the asu          |
----------------------------------------------------------------


Maximum likelihood isotropic Wilson scaling 
ML estimate of overall B value of 2bo4.mtz:F,SIGF:
28.47 A**(-2)
Estimated -log of scale factor of 2bo4.mtz:F,SIGF:
 0.34


Maximum likelihood anisotropic Wilson scaling 
ML estimate of overall B_cart value of 2bo4.mtz:F,SIGF:
29.12,  0.00,  0.26
       29.51,  0.00
              26.94
Equivalent representation as U_cif: 
 0.37, -0.00,  0.01
        0.37,  0.00
               0.34

ML estimate of  -log of scale factor of 2bo4.mtz:F,SIGF:
 0.34
Correcting for anisotropy in the data

Some basis intensity statistics follow.



Low resolution completeness analyses 

 The following table shows the completeness
 off the data to 5 Angstrom.
unused:         - 19.9707 [   0/439 ] 0.000
bin  1: 19.9707 - 10.3082 [2284/2602] 0.878
bin  2: 10.3082 -  8.3782 [2301/2570] 0.895
bin  3:  8.3782 -  7.3801 [2368/2573] 0.920
bin  4:  7.3801 -  6.7337 [2338/2537] 0.922
bin  5:  6.7337 -  6.2671 [2380/2563] 0.929
bin  6:  6.2671 -  5.9077 [2372/2567] 0.924
bin  7:  5.9077 -  5.6188 [2328/2509] 0.928
bin  8:  5.6188 -  5.3792 [2362/2545] 0.928
bin  9:  5.3792 -  5.1758 [2375/2564] 0.926
bin 10:  5.1758 -  5.0001 [2319/2517] 0.921
unused:  5.0001 -         [   0/0   ]



Mean intensity analyses 
 Analyses of the mean intensity. 
 Inpsired by: Morris et al. (2004). J. Synch. Rad.11, 56-59.
 The following resolution shells are worrisome: 
------------------------------------------------
| d_spacing | z_score | compl. | <Iobs>/<Iexp> |
------------------------------------------------
|    8.451  |   4.60  |   0.92 |     1.284     |
|    6.201  |   5.03  |   0.92 |     1.192     |
|    4.879  |   5.05  |   0.93 |     1.182     |
|    4.662  |   5.20  |   0.93 |     1.192     |
|    4.472  |   6.02  |   0.93 |     1.217     |
|    3.410  |   5.84  |   0.95 |     0.876     |
|    3.194  |   5.66  |   0.96 |     0.887     |
|    3.131  |   5.08  |   0.97 |     0.896     |
|    3.071  |   5.65  |   0.97 |     0.882     |
|    3.015  |   9.48  |   0.97 |     0.810     |
|    2.962  |   6.78  |   0.97 |     0.868     |
|    2.911  |   7.56  |   0.98 |     0.862     |
|    2.863  |   8.31  |   0.98 |     0.858     |
|    2.817  |   8.49  |   0.98 |     0.859     |
|    2.773  |   5.83  |   0.98 |     0.901     |
|    2.548  |   6.65  |   0.98 |     0.881     |
|    2.516  |   4.73  |   0.99 |     0.918     |
|    2.270  |   6.28  |   0.99 |     0.886     |
|    2.247  |   7.11  |   0.98 |     1.136     |
|    2.067  |   9.39  |   0.97 |     1.188     |
|    2.033  |   8.20  |   0.95 |     1.157     |
|    2.016  |   9.21  |   0.93 |     1.178     |
|    2.000  |   5.53  |   0.91 |     1.105     |
|    1.984  |   5.01  |   0.89 |     1.098     |
------------------------------------------------

 Possible reasons for the presence of the reported
 unexpected low or elevated mean intensity in
 a given resolution bin are : 
 - missing overloaded or weak reflections
 - suboptimal data processing
 - satelite (ice) crystals
 - NCS
 - translational pseudo symmetry (detected elsewhere)
 - outliers (detected elsewhere)
 - ice rings (detected elsewhere)
 - other problems
 Note that the presence of abnormalities 
 in a certain region of reciprocal space might
 confuse the data validation algorithm throughout
 a large region of reciprocal space, even though
 the data is acceptable in those areas. 


Possible outliers 
  Inspired by: Read, Acta Cryst. (1999). D55, 1759-1764

 Acentric reflections:

-----------------------------------------------------------------
| d_space |      H     K     L |  |E|  | p(wilson) | p(extreme) |
-----------------------------------------------------------------
|   2.065 |    -98,   44,   15 |  4.06 |  6.95e-08 |   2.77e-02 |
|   2.070 |    -83,   15,   54 |  4.05 |  7.34e-08 |   2.93e-02 |
|   2.068 |    -61,   25,   60 |  4.35 |  6.29e-09 |   2.54e-03 |
|   2.017 |    -46,   50,   50 |  3.93 |  2.01e-07 |   7.82e-02 |
|   2.084 |    -13,   13,   72 |  4.08 |  5.66e-08 |   2.27e-02 |
|   2.069 |     -9,   69,   24 |  4.04 |  8.30e-08 |   3.30e-02 |
|   1.955 |     -9,   77,    6 |  5.95 |  4.44e-16 |   1.80e-10 |
|   2.093 |     -5,    5,   73 |  4.10 |  4.98e-08 |   1.99e-02 |
|   2.073 |     -3,   71,   17 |  4.40 |  3.89e-09 |   1.57e-03 |
|   1.954 |      6,   56,   54 |  4.53 |  1.20e-09 |   4.86e-04 |
|   1.968 |     30,   26,   71 |  4.04 |  7.97e-08 |   3.17e-02 |
|   3.434 |     30,   32,   25 |  4.42 |  3.24e-09 |   1.31e-03 |
|   2.251 |     36,   56,   31 |  4.45 |  2.51e-09 |   1.01e-03 |
|   2.249 |     61,   57,    5 |  5.02 |  1.18e-11 |   4.79e-06 |
|   2.245 |     95,   19,   34 |  4.05 |  7.50e-08 |   2.99e-02 |
-----------------------------------------------------------------

 p(wilson)  : 1-(1-exp[-|E|^2]) 
 p(extreme) : 1-(1-exp[-|E|^2])^(n_acentrics)
 p(wilson) is the probability that an E-value of the specified
 value would be observed when it would selected at random from
 the given data set.
 p(extreme) is the probability that the largest |E| value is 
 larger or equal than the observed largest |E| value.

 Both measures can be used for outlier detection. p(extreme)
 takes into account the size of the dataset.


 Centric reflections:

-----------------------------------------------------------------
| d_space |      H     K     L |  |E|  | p(wilson) | p(extreme) |
-----------------------------------------------------------------
|   2.250 |   -116,    0,    3 |  5.22 |  1.83e-07 |   1.31e-03 |
|   2.248 |   -116,    0,    4 |  9.74 |  0.00e+00 |   0.00e+00 |
|   1.965 |      0,    0,   78 |  4.45 |  8.50e-06 |   5.92e-02 |
|   2.091 |     10,    0,   73 |  4.35 |  1.34e-05 |   9.18e-02 |
|   2.063 |     96,    0,   48 |  6.26 |  3.96e-10 |   2.84e-06 |
-----------------------------------------------------------------

 p(wilson)  : 1-(erf[|E|/sqrt(2)]) 
 p(extreme) : 1-(erf[|E|/sqrt(2)])^(n_acentrics)
 p(wilson) is the probability that an E-value of the specified
 value would be observed when it would selected at random from
 the given data set.
 p(extreme) is the probability that the largest |E| value is 
 larger or equal than the observed largest |E| value.

 Both measures can be used for outlier detection. p(extreme)
 takes into account the size of the dataset.

Ice ring related problems

 The following statistics were obtained from ice-ring 
 insensitive resolution ranges 
  mean bin z_score      : 4.23
      ( rms deviation   : 2.33 )
  mean bin completeness : 0.95
     ( rms deviation   : 0.06 )

 The following table shows the z-scores 
 and completeness in ice-ring sensitive areas.
 Large z-scores and high completeness in these 
 resolution ranges might be a reason to re-assess
 your data processsing if ice rings were present.

------------------------------------------------
| d_spacing | z_score | compl. | Rel. Ice int. |
------------------------------------------------
|    3.897  |   3.88  |   0.94 |     1.000     |
|    3.669  |   0.12  |   0.95 |     0.750     |
|    3.441  |   5.84  |   0.95 |     0.530     |
|    2.671  |   4.15  |   0.98 |     0.170     |
|    2.249  |   7.11  |   0.98 |     0.390     |
|    2.072  |   9.39  |   0.97 |     0.300     |
------------------------------------------------

 Abnormalities in mean intensity or completeness at
 resolution ranges with a relative ice ring intensity
 lower than 0.10 will be ignored.

 No ice ring related problems detected.
 If ice rings were present, the data does not look
 worse at ice ring related d_spacings as compared
 to the rest of the data set 




Basic analyses completed

##----------------------------------------------------##
##                   Twinning Analyses                ##
##----------------------------------------------------##



Using data between 10.00 to 0.00 Angstrom.

Determining possible twin laws.

The following twin laws have been found:

---------------------------------------
| Type | Twin law                     |
---------------------------------------
|  PM  | -1/2*h-3/2*k,-1/2*h+1/2*k,-l |
|  PM  | 1/2*h-3/2*k,1/2*h+1/2*k,l    |
|  PM  | 1/2*h-3/2*k,-1/2*h-1/2*k,-l  |
|  PM  | -1/2*h-3/2*k,1/2*h-1/2*k,l   |
|  PM  | h,-k,-l                      |
---------------------------------------
M:  Merohedral twin law
PM: Pseudomerohedral twin law

  0 merohedral twin operators found
  5 pseudo-merohedral twin operators found
In total,   5 twin operator were found


Number of centrics  : 7130
Number of acentrics : 403971

 Largest patterson peak with length larger then 15 Angstrom 

 Frac. coord.        :   0.027    0.076   -0.104
 Distance to origin  :  20.963
 Height (origin=100) :   3.125
 p_value(height)     :   1.000e-00

   The reported p_value has the following meaning: 
     The probability that a peak of the specified height 
     or larger is found in a Patterson function of a 
     macro molecule that does not have any translational
     pseudo symmetry is equal to  1.000e-00 
     p_values smaller then 0.05 might indicate 
     weak translation pseudo symmetry, or the self vector of 
     a large anomalous scatterer such as Hg, whereas values 
     smaller than 1e-3 are a very strong indication for 
     the presence of translational pseudo symmetry.



Wilson ratio and moments 

Acentric reflections 
   <I^2>/<I>^2    :2.101   (untwinned: 2.000; perfect twin 1.500)
   <F>^2/<F^2>    :0.791   (untwinned: 0.785; perfect twin 0.885)
   <|E^2 - 1|>    :0.741   (untwinned: 0.736; perfect twin 0.541)


Centric reflections 
   <I^2>/<I>^2    :4.682   (untwinned: 3.000; perfect twin 2.000)
   <F>^2/<F^2>    :0.619   (untwinned: 0.637; perfect twin 0.785)
   <|E^2 - 1|>    :1.014   (untwinned: 0.968; perfect twin 0.736)



NZ test (0<=z<1) to detect twinning and possible translational NCS


-----------------------------------------------
|  Z  | Nac_obs | Nac_theo | Nc_obs | Nc_theo |
-----------------------------------------------
| 0.0 |   0.000 |    0.000 |  0.000 |   0.000 |
| 0.1 |   0.066 |    0.095 |  0.256 |   0.248 |
| 0.2 |   0.159 |    0.181 |  0.377 |   0.345 |
| 0.3 |   0.251 |    0.259 |  0.454 |   0.419 |
| 0.4 |   0.336 |    0.330 |  0.510 |   0.474 |
| 0.5 |   0.412 |    0.394 |  0.554 |   0.520 |
| 0.6 |   0.476 |    0.451 |  0.587 |   0.561 |
| 0.7 |   0.532 |    0.503 |  0.617 |   0.597 |
| 0.8 |   0.580 |    0.551 |  0.645 |   0.629 |
| 0.9 |   0.621 |    0.593 |  0.672 |   0.657 |
| 1.0 |   0.657 |    0.632 |  0.697 |   0.683 |
-----------------------------------------------
| Maximum deviation acentric      :  0.029    |
| Maximum deviation centric       :  0.036    |
|                                             |
| <NZ(obs)-NZ(twinned)>_acentric  : +0.009    |
| <NZ(obs)-NZ(twinned)>_centric   : +0.021    |
-----------------------------------------------


 L test for acentric data

 using difference vectors (dh,dk,dl) of the form: 
(2hp,2kp,2lp)
  where hp, kp, and lp are random signed integers such that 
  2 <= |dh| + |dk| + |dl| <= 8 

  Mean |L|   :0.471  (untwinned: 0.500; perfect twin: 0.375)
  Mean  L^2  :0.301  (untwinned: 0.333; perfect twin: 0.200)

  The distribution of |L| values indicates a twin fraction of
  0.03. Note that this estimate is not as reliable as obtained
  via a britton plot or H-test if twin laws are available. 



---------------------------------------------
 Analysing possible twin law :  -1/2*h-3/2*k,-1/2*h+1/2*k,-l
---------------------------------------------


Results of the H-test on a-centric data: 

 (Only 50.0% of the strongest twin pairs were used)

mean |H| : 0.501   (0.50: untwinned; 0.0: 50% twinned)
mean H^2 : 0.331   (0.33: untwinned; 0.0: 50% twinned)
Estimation of twin fraction via mean |H|: -0.001
Estimation of twin fraction via cum. dist. of H: 0.003



Britton analyses

  Extrapolation performed on  0.00 < alpha < 0.495 
  Estimated twin fraction: 0.024
  Correlation: 0.9987

---------------------------------------------
 Analysing possible twin law :  1/2*h-3/2*k,1/2*h+1/2*k,l
---------------------------------------------


Results of the H-test on a-centric data: 

 (Only 50.0% of the strongest twin pairs were used)

mean |H| : 0.503   (0.50: untwinned; 0.0: 50% twinned)
mean H^2 : 0.335   (0.33: untwinned; 0.0: 50% twinned)
Estimation of twin fraction via mean |H|: -0.003
Estimation of twin fraction via cum. dist. of H: 0.001



Britton analyses

  Extrapolation performed on  0.00 < alpha < 0.495 
  Estimated twin fraction: 0.021
  Correlation: 0.9992

---------------------------------------------
 Analysing possible twin law :  1/2*h-3/2*k,-1/2*h-1/2*k,-l
---------------------------------------------


Results of the H-test on a-centric data: 

 (Only 50.0% of the strongest twin pairs were used)

mean |H| : 0.224   (0.50: untwinned; 0.0: 50% twinned)
mean H^2 : 0.084   (0.33: untwinned; 0.0: 50% twinned)
Estimation of twin fraction via mean |H|: 0.276
Estimation of twin fraction via cum. dist. of H: 0.268



Britton analyses

  Extrapolation performed on  0.33 < alpha < 0.495 
  Estimated twin fraction: 0.256
  Correlation: 0.9951

---------------------------------------------
 Analysing possible twin law :  -1/2*h-3/2*k,1/2*h-1/2*k,l
---------------------------------------------


Results of the H-test on a-centric data: 

 (Only 50.0% of the strongest twin pairs were used)

mean |H| : 0.199   (0.50: untwinned; 0.0: 50% twinned)
mean H^2 : 0.068   (0.33: untwinned; 0.0: 50% twinned)
Estimation of twin fraction via mean |H|: 0.301
Estimation of twin fraction via cum. dist. of H: 0.297



Britton analyses

  Extrapolation performed on  0.36 < alpha < 0.495 
  Estimated twin fraction: 0.287
  Correlation: 0.9953

---------------------------------------------
 Analysing possible twin law :  h,-k,-l
---------------------------------------------


Results of the H-test on a-centric data: 

 (Only 50.0% of the strongest twin pairs were used)

mean |H| : 0.502   (0.50: untwinned; 0.0: 50% twinned)
mean H^2 : 0.335   (0.33: untwinned; 0.0: 50% twinned)
Estimation of twin fraction via mean |H|: -0.002
Estimation of twin fraction via cum. dist. of H: 0.001



Britton analyses

  Extrapolation performed on  0.00 < alpha < 0.495 
  Estimated twin fraction: 0.022
  Correlation: 0.9991

------------------------------------------------------------------
Twin analyses summary 

 Twinning tests independent of twin laws 

 Ratio of moments of intensity 
   Intensity ratio                          : 2.101  
   Amplitude ratio                          : 0.791 
     Mahalanobis distance I and F ratio     : 2.383 

 L-test 
   mean |L|                                 : 0.471 
   mean L^2                                 : 0.301 
     Mahalanobis distance of L-test moments : 2.602 

 Detection of translational pseudo symmtery
   Patterson peak height                    : 3.125 (p_value: 1.000e-00)

 Twin law dependent tests 

   Twin law : -1/2*h-3/2*k,-1/2*h+1/2*k,-l
     estimated twin fraction 
       - via Britton analyses : 0.02
       - via H-test           : 0.00

   Twin law : 1/2*h-3/2*k,1/2*h+1/2*k,l
     estimated twin fraction 
       - via Britton analyses : 0.02
       - via H-test           : 0.00

   Twin law : 1/2*h-3/2*k,-1/2*h-1/2*k,-l
     estimated twin fraction 
       - via Britton analyses : 0.26
       - via H-test           : 0.27

   Twin law : -1/2*h-3/2*k,1/2*h-1/2*k,l
     estimated twin fraction 
       - via Britton analyses : 0.29
       - via H-test           : 0.30

   Twin law : h,-k,-l
     estimated twin fraction 
       - via Britton analyses : 0.02
       - via H-test           : 0.00

 Mahalanobis distance: multidimensional equivalent of Z-score.
   Values of the Mahalanobis distance larger then 4 should be 
   seen as an indication that the data does not behave as 
   expected.

 Interpretation of results: 

 No significant pseudotranslation is detected 
 The data does not appear to be twinned

 The data does not appear to be twinned as judged from the 
 L-test. 
 The estimated twin fractions via the britton test do however
 indicate a symmetry relation between possible twin related
 intensities. As the data does not apear to be twinned, one
 can interpret this as origination from a 2-fold NCS axis
 parallel to the putative twin axis. It might be usefull to 
 refine a putative twin fraction during refinement.
------------------------------------------------------------------


$TABLE: Intensity plots:
$GRAPHS
:Intensity plots 
:A:1,2,3,4:
$$
1/resol^2   <I>_smooth_approximation   <I>_via_binning   <I>_expected   $$ 
$$
0.010002   3500327.445452   3078188.035531   2275426.619066
0.014002   2239040.609393   2300965.380444   1792649.975363
0.018002   1265318.832859   1312512.803616   1316350.324490
0.022002   1139632.448239   1266832.903012   1127684.113010
0.026002   1310333.509474   1343253.834783   1127024.769271
0.030002   1405730.509093   1451266.618095   1240186.883649
0.034002   1626905.621607   1632606.287769   1506435.265638
0.038002   2070856.439763   2094495.283404   1930321.290921
0.042002   2698578.912211   2848207.501519   2410486.847101
0.046002   3334916.661369   3342436.875925   2804857.707861
0.050002   3628139.182147   3682041.030598   3025858.653245
0.054002   3492074.347193   3386019.539470   3077396.440645
0.058002   3232370.547306   3284103.858814   3025829.263753
0.062002   3108430.160392   3095726.091464   2945655.981749
0.066002   3081637.135305   3158049.510571   2880327.652479
0.070002   3012674.431102   2852661.570768   2833751.703059
0.074002   2865622.456716   2800836.071595   2785129.312791
0.078002   2675583.597522   2718372.627710   2710620.946465
0.082002   2464949.302403   2492382.357816   2598538.566499
0.086002   2252630.679568   2149963.902607   2453194.749273
0.090002   2073975.527981   2110596.234709   2289812.297717
0.094002   1941883.936450   1942139.717027   2126087.582772
0.098002   1820034.185879   1752956.345874   1975370.191109
0.102002   1669054.315153   1651873.711808   1843835.023794
0.106002   1503112.941776   1527952.858498   1731407.378086
0.110002   1373353.845240   1323997.218493   1634691.576087
0.114002   1302826.711170   1344622.847067   1549954.843653
0.118002   1264012.537353   1271847.550928   1474910.244439
0.122002   1223498.552735   1208344.870948   1409005.143484
0.126002   1185216.061903   1162386.244278   1352661.538107
0.130002   1174014.617212   1176346.117322   1306210.417516
0.134002   1189165.813044   1226465.131491   1269148.545049
0.138002   1195842.594758   1174034.945911   1240005.990746
0.142002   1165671.459189   1118105.861478   1216755.890503
0.146002   1110824.360395   1106411.494247   1197472.013273
0.150002   1068565.499290   1099780.502328   1180896.091420
0.154002   1059710.086936   1027362.827043   1166682.250750
0.158002   1072910.754436   1060575.207057   1155260.576594
0.162002   1086590.952384   1073892.388734   1147422.230627
0.166002   1093954.139774   1074979.803469   1143817.940079
0.170002   1102765.146065   1104809.146971   1144563.053862
0.174002   1119280.340302   1094574.083319   1149073.822342
0.178002   1138914.490348   1138699.103183   1156159.416780
0.182002   1149397.991074   1148624.321503   1164303.191372
0.186002   1141685.159020   1180176.712757   1172013.876018
0.190002   1124659.852496   1084458.476348   1178123.270776
0.194002   1126824.391500   1046766.316288   1181944.131147
0.198002   1163132.677760   1344584.403698   1183260.974964
0.202002   1196186.406493   1106079.355221   1182184.801431
0.206002   1169708.271360   1098471.908552   1178941.810006
0.210002   1103576.764241   1120491.677801   1173676.926106
0.214002   1089533.154776   1122615.189199   1166336.374691
0.218002   1132485.639085   1091425.096364   1156658.958838
0.222002   1111251.455686   1108302.140402   1144266.391954
0.226002   1029479.086940   1082445.746483   1128811.726731
0.230002   1088776.608086   1068247.522863   1110130.131708
0.234002   1260763.089393   1292827.691710   1088340.429978
0.238002   1243059.302562   1141027.863414   1063865.472261
0.242002   1152261.252174   1200043.399453   1037367.002323
0.246002   1216102.371976   1188885.982293   1009617.206734
0.250002   1105545.982121   1084762.728348   981346.941162
0.254002   1057196.611475   1046838.663134   953115.306931
0.258002   1011993.490339   997898.150431   925236.574774
0.262978   977961.715863   906757.185909   891139.030385
$$


$TABLE: Z scores and completeness:
$GRAPHS
:Data sanity and completeness check 
:A:1,2,3:
$$
1/resol^2   Z_score   Completeness   $$ 
$$
0.010002   4.188557   0.875447
0.014002   4.595238   0.915615
0.018002   0.059357   0.922404
0.022002   3.330626   0.924594
0.026002   5.026205   0.923696
0.030002   4.324532   0.928996
0.034002   2.347112   0.924022
0.038002   2.484663   0.925413
0.042002   5.045072   0.927438
0.046002   5.198705   0.928710
0.050002   6.015019   0.929466
0.054002   3.108520   0.928571
0.058002   2.984499   0.940060
0.062002   1.993209   0.941432
0.066002   3.882428   0.944005
0.070002   0.278620   0.947935
0.074002   0.232483   0.947549
0.078002   0.118535   0.948008
0.082002   1.780183   0.948263
0.086002   5.842307   0.947453
0.090002   3.819451   0.952464
0.094002   4.337584   0.959485
0.098002   5.655840   0.964848
0.102002   5.077161   0.965545
0.106002   5.652561   0.965738
0.110002   9.477739   0.965884
0.114002   6.776149   0.971739
0.118002   7.560766   0.975584
0.122002   8.312906   0.976765
0.126002   8.492929   0.978621
0.130002   5.832167   0.979029
0.134002   1.839857   0.982247
0.138002   2.793794   0.981953
0.142002   4.148490   0.980823
0.146002   3.864986   0.982813
0.150002   3.585612   0.987147
0.154002   6.652884   0.984764
0.158002   4.731303   0.986870
0.162002   3.788837   0.988024
0.166002   3.565684   0.988371
0.170002   1.986020   0.989310
0.174002   2.609992   0.989258
0.178002   0.786900   0.990878
0.182002   0.684806   0.989571
0.186002   0.350287   0.993612
0.190002   4.170793   0.991800
0.194002   6.280068   0.988273
0.198002   7.111886   0.977583
0.202002   3.731791   0.989907
0.206002   4.022817   0.993661
0.210002   2.638783   0.995452
0.214002   2.131279   0.995244
0.218002   3.140879   0.993740
0.222002   1.693967   0.994240
0.226002   2.187618   0.994921
0.230002   2.010325   0.992214
0.234002   9.392267   0.965751
0.238002   3.836070   0.970550
0.242002   8.195021   0.950258
0.246002   9.207475   0.929515
0.250002   5.525373   0.908347
0.254002   5.011833   0.893771
0.258002   3.826624   0.871282
0.262978   0.734879   0.617024
$$


$TABLE: <I/sigma_I>:
$GRAPHS
:Signal to noise 
:N:1,2:
$$
1/resol^2   <I/sigma_I>;_Signal_to_noise   $$ 
$$
0.004507   33.388088
0.008507   34.158186
0.012507   34.231265
0.016507   32.418644
0.020507   31.108267
0.024507   30.442820
0.028507   30.331843
0.032507   30.290925
0.036507   30.214452
0.040507   30.985533
0.044507   30.999686
0.048507   30.613308
0.052507   29.860382
0.056507   26.088085
0.060507   21.874889
0.064507   21.424101
0.068507   21.201449
0.072507   20.459405
0.076507   20.116158
0.080507   19.522220
0.084507   18.423189
0.088507   17.703380
0.092507   15.924942
0.096507   15.323002
0.100507   14.426485
0.104507   13.989084
0.108507   12.803018
0.112507   12.406962
0.116507   11.991362
0.120507   10.703743
0.124507   10.221791
0.128507   9.906803
0.132507   9.604026
0.136507   9.337904
0.140507   8.723794
0.144507   8.230520
0.148507   8.015867
0.152507   7.486550
0.156507   7.089040
0.160507   7.083022
0.164507   6.534994
0.168507   6.216686
0.172507   6.030790
0.176507   5.734215
0.180507   5.544864
0.184507   5.438094
0.188507   4.945599
0.192507   4.508817
0.196507   4.518907
0.200507   4.265858
0.204507   3.922343
0.208507   3.668871
0.212507   3.606012
0.216507   3.302531
0.220507   3.201576
0.224507   2.977875
0.228507   2.719952
0.232507   2.694281
0.236507   2.541417
0.240507   2.353145
0.244507   2.310364
0.248507   2.114055
0.252507   1.982277
0.256507   1.826211
0.260507   1.679987
0.264507   1.380469
$$


$TABLE: NZ test:
$GRAPHS
:NZ test, acentric and centric data 
:A:1,2,3,4,5:
$$
z   Acentric_observed   Acentric_untwinned   Centric_observed   Centric_untwinned   $$ 
$$
0.000000   0.000000   0.000000   0.000000   0.000000
0.100000   0.066465   0.095200   0.256101   0.248100
0.200000   0.158784   0.181300   0.376718   0.345300
0.300000   0.250761   0.259200   0.454418   0.418700
0.400000   0.336487   0.329700   0.509537   0.473800
0.500000   0.411713   0.393500   0.553576   0.520500
0.600000   0.476485   0.451200   0.586957   0.561400
0.700000   0.531979   0.503400   0.617391   0.597200
0.800000   0.579542   0.550700   0.644881   0.628900
0.900000   0.620569   0.593400   0.672230   0.657200
1.000000   0.657159   0.632100   0.697335   0.683300
$$


$TABLE: L test,acentric data:
$GRAPHS
:L test, acentric data 
:A:1,2,3,4:
$$
|l|   Observed   Acentric_theory   Acentric_theory,_perfect_twin   $$ 
$$
0.000000   0.000933   0.000000   0.000000
0.020000   0.023170   0.020000   0.029996
0.040000   0.045117   0.040000   0.059968
0.060000   0.067161   0.060000   0.089892
0.080000   0.089427   0.080000   0.119744
0.100000   0.111423   0.100000   0.149500
0.120000   0.133252   0.120000   0.179136
0.140000   0.154927   0.140000   0.208628
0.160000   0.176918   0.160000   0.237952
0.180000   0.198922   0.180000   0.267084
0.200000   0.220801   0.200000   0.296000
0.220000   0.242824   0.220000   0.324676
0.240000   0.264202   0.240000   0.353088
0.260000   0.285748   0.260000   0.381212
0.280000   0.307048   0.280000   0.409024
0.300000   0.328570   0.300000   0.436500
0.320000   0.349922   0.320000   0.463616
0.340000   0.370735   0.340000   0.490348
0.360000   0.392061   0.360000   0.516672
0.380000   0.412805   0.380000   0.542564
0.400000   0.433439   0.400000   0.568000
0.420000   0.454270   0.420000   0.592956
0.440000   0.474994   0.440000   0.617408
0.460000   0.495644   0.460000   0.641332
0.480000   0.516113   0.480000   0.664704
0.500000   0.536658   0.500000   0.687500
0.520000   0.557125   0.520000   0.709696
0.540000   0.577573   0.540000   0.731268
0.560000   0.597770   0.560000   0.752192
0.580000   0.617718   0.580000   0.772444
0.600000   0.637960   0.600000   0.792000
0.620000   0.658206   0.620000   0.810836
0.640000   0.678078   0.640000   0.828928
0.660000   0.698066   0.660000   0.846252
0.680000   0.718003   0.680000   0.862784
0.700000   0.738088   0.700000   0.878500
0.720000   0.758520   0.720000   0.893376
0.740000   0.778853   0.740000   0.907388
0.760000   0.798985   0.760000   0.920512
0.780000   0.818815   0.780000   0.932724
0.800000   0.838480   0.800000   0.944000
0.820000   0.858066   0.820000   0.954316
0.840000   0.877441   0.840000   0.963648
0.860000   0.896600   0.860000   0.971972
0.880000   0.915666   0.880000   0.979264
0.900000   0.934233   0.900000   0.985500
0.920000   0.951761   0.920000   0.990656
0.940000   0.967936   0.940000   0.994708
0.960000   0.982661   0.960000   0.997632
0.980000   0.994135   0.980000   0.999404
$$


$TABLE: Britton plot for twin law -1/2*h-3/2*k,-1/2*h+1/2*k,-l:
$GRAPHS
:percentage negatives 
:A:1,2,3:
$$
alpha   percentage_negatives   fit   $$ 
$$
0.000000   0.000000   0.000000
0.009901   0.002394   0.000000
0.019802   0.007584   0.000000
0.029703   0.014300   0.005547
0.039604   0.021738   0.015657
0.049505   0.029653   0.025768
0.059406   0.038127   0.035878
0.069307   0.046886   0.045989
0.079208   0.056114   0.056099
0.089109   0.065146   0.066209
0.099010   0.074366   0.076320
0.108911   0.083797   0.086430
0.118812   0.093259   0.096541
0.128713   0.102513   0.106651
0.138614   0.111808   0.116762
0.148515   0.121435   0.126872
0.158416   0.131306   0.136982
0.168317   0.141258   0.147093
0.178218   0.151239   0.157203
0.188119   0.161024   0.167314
0.198020   0.170830   0.177424
0.207921   0.180719   0.187535
0.217822   0.190632   0.197645
0.227723   0.200589   0.207755
0.237624   0.210903   0.217866
0.247525   0.220902   0.227976
0.257426   0.231016   0.238087
0.267327   0.241056   0.248197
0.277228   0.251420   0.258308
0.287129   0.261697   0.268418
0.297030   0.272277   0.278529
0.306931   0.282925   0.288639
0.316832   0.293661   0.298749
0.326733   0.304381   0.308860
0.336634   0.315365   0.318970
0.346535   0.325971   0.329081
0.356436   0.336871   0.339191
0.366337   0.348022   0.349302
0.376238   0.359112   0.359412
0.386139   0.370117   0.369522
0.396040   0.381452   0.379633
0.405941   0.392615   0.389743
0.415842   0.403966   0.399854
0.425743   0.415247   0.409964
0.435644   0.426681   0.420075
0.445545   0.437938   0.430185
0.455446   0.449425   0.440295
0.465347   0.460830   0.450406
0.475248   0.472036   0.460516
0.485149   0.483452   0.470627
$$


$TABLE: H test for possible twin law -1/2*h-3/2*k,-1/2*h+1/2*k,-l:
$GRAPHS
:H test for Acentric data 
:A:1,2,3:
$$
H   Observed_S(H)   Fitted_S(H)   $$ 
$$
0.000000   0.004877   0.000000
0.020000   0.024114   0.020121
0.040000   0.043242   0.040241
0.060000   0.062687   0.060362
0.080000   0.081908   0.080482
0.100000   0.101437   0.100603
0.120000   0.120507   0.120724
0.140000   0.140281   0.140844
0.160000   0.159481   0.160965
0.180000   0.178526   0.181085
0.200000   0.197575   0.201206
0.220000   0.216994   0.221327
0.240000   0.236059   0.241447
0.260000   0.255270   0.261568
0.280000   0.273971   0.281688
0.300000   0.293453   0.301809
0.320000   0.311616   0.321930
0.340000   0.330900   0.342050
0.360000   0.350262   0.362171
0.380000   0.370098   0.382291
0.400000   0.389096   0.402412
0.420000   0.408697   0.422533
0.440000   0.428164   0.442653
0.460000   0.447718   0.462774
0.480000   0.467169   0.482894
0.500000   0.486552   0.503015
0.520000   0.506701   0.523136
0.540000   0.527214   0.543256
0.560000   0.548030   0.563377
0.580000   0.568627   0.583497
0.600000   0.589198   0.603618
0.620000   0.610623   0.623739
0.640000   0.631564   0.643859
0.660000   0.653312   0.663980
0.680000   0.675712   0.684101
0.700000   0.697961   0.704221
0.720000   0.719933   0.724342
0.740000   0.741843   0.744462
0.760000   0.763373   0.764583
0.780000   0.785840   0.784704
0.800000   0.808589   0.804824
0.820000   0.831108   0.824945
0.840000   0.853790   0.845065
0.860000   0.876262   0.865186
0.880000   0.898646   0.885307
0.900000   0.920989   0.905427
0.920000   0.941580   0.925548
0.940000   0.960979   0.945668
0.960000   0.978965   0.965789
0.980000   0.993294   0.985910
$$


$TABLE: Britton plot for twin law 1/2*h-3/2*k,1/2*h+1/2*k,l:
$GRAPHS
:percentage negatives 
:A:1,2,3:
$$
alpha   percentage_negatives   fit   $$ 
$$
0.000000   0.000000   0.000000
0.009901   0.002374   0.000000
0.019802   0.007637   0.000000
0.029703   0.014106   0.008408
0.039604   0.021692   0.018379
0.049505   0.029905   0.028350
0.059406   0.038866   0.038321
0.069307   0.047749   0.048292
0.079208   0.057006   0.058262
0.089109   0.066450   0.068233
0.099010   0.075909   0.078204
0.108911   0.085767   0.088175
0.118812   0.095556   0.098146
0.128713   0.105164   0.108117
0.138614   0.114911   0.118088
0.148515   0.124651   0.128059
0.158416   0.134478   0.138030
0.168317   0.144086   0.148000
0.178218   0.153998   0.157971
0.188119   0.163714   0.167942
0.198020   0.173567   0.177913
0.207921   0.183371   0.187884
0.217822   0.193347   0.197855
0.227723   0.203228   0.207826
0.237624   0.212995   0.217797
0.247525   0.222889   0.227767
0.257426   0.232814   0.237738
0.267327   0.242877   0.247709
0.277228   0.252833   0.257680
0.287129   0.262911   0.267651
0.297030   0.273098   0.277622
0.306931   0.283264   0.287593
0.316832   0.293672   0.297564
0.326733   0.304092   0.307534
0.336634   0.314418   0.317505
0.346535   0.324728   0.327476
0.356436   0.335452   0.337447
0.366337   0.345954   0.347418
0.376238   0.356509   0.357389
0.386139   0.367392   0.367360
0.396040   0.378092   0.377331
0.405941   0.389186   0.387301
0.415842   0.400057   0.397272
0.425743   0.411022   0.407243
0.435644   0.422049   0.417214
0.445545   0.432775   0.427185
0.455446   0.443977   0.437156
0.465347   0.455055   0.447127
0.475248   0.466278   0.457098
0.485149   0.477176   0.467068
$$


$TABLE: H test for possible twin law 1/2*h-3/2*k,1/2*h+1/2*k,l:
$GRAPHS
:H test for Acentric data 
:A:1,2,3:
$$
H   Observed_S(H)   Fitted_S(H)   $$ 
$$
0.000000   0.005278   0.000000
0.020000   0.024999   0.020040
0.040000   0.044262   0.040080
0.060000   0.063562   0.060120
0.080000   0.082655   0.080160
0.100000   0.101883   0.100200
0.120000   0.120868   0.120240
0.140000   0.139993   0.140280
0.160000   0.159138   0.160320
0.180000   0.178463   0.180360
0.200000   0.197007   0.200400
0.220000   0.216028   0.220440
0.240000   0.235040   0.240480
0.260000   0.254298   0.260521
0.280000   0.273243   0.280561
0.300000   0.292465   0.300601
0.320000   0.311307   0.320641
0.340000   0.329871   0.340681
0.360000   0.349355   0.360721
0.380000   0.368644   0.380761
0.400000   0.387466   0.400801
0.420000   0.406832   0.420841
0.440000   0.425632   0.440881
0.460000   0.445322   0.460921
0.480000   0.464940   0.480961
0.500000   0.484543   0.501001
0.520000   0.504109   0.521041
0.540000   0.523676   0.541081
0.560000   0.543993   0.561121
0.580000   0.563724   0.581161
0.600000   0.584482   0.601201
0.620000   0.605483   0.621241
0.640000   0.625975   0.641281
0.660000   0.647350   0.661321
0.680000   0.669081   0.681361
0.700000   0.690693   0.701401
0.720000   0.712330   0.721441
0.740000   0.734621   0.741481
0.760000   0.756382   0.761522
0.780000   0.778894   0.781562
0.800000   0.802341   0.801602
0.820000   0.825063   0.821642
0.840000   0.847615   0.841682
0.860000   0.870996   0.861722
0.880000   0.893666   0.881762
0.900000   0.916754   0.901802
0.920000   0.938546   0.921842
0.940000   0.959063   0.941882
0.960000   0.977545   0.961922
0.980000   0.993108   0.981962
$$


$TABLE: Britton plot for twin law 1/2*h-3/2*k,-1/2*h-1/2*k,-l:
$GRAPHS
:percentage negatives 
:A:1,2,3:
$$
alpha   percentage_negatives   fit   $$ 
$$
0.000000   0.000000   0.000000
0.009901   0.000021   0.000000
0.019802   0.000089   0.000000
0.029703   0.000225   0.000000
0.039604   0.000482   0.000000
0.049505   0.000909   0.000000
0.059406   0.001499   0.000000
0.069307   0.002214   0.000000
0.079208   0.003236   0.000000
0.089109   0.004501   0.000000
0.099010   0.005942   0.000000
0.108911   0.007648   0.000000
0.118812   0.009715   0.000000
0.128713   0.012212   0.000000
0.138614   0.015047   0.000000
0.148515   0.018123   0.000000
0.158416   0.021618   0.000000
0.168317   0.025438   0.000000
0.178218   0.029756   0.000000
0.188119   0.034378   0.000000
0.198020   0.039471   0.000000
0.207921   0.045219   0.000000
0.217822   0.051211   0.000000
0.227723   0.057541   0.000000
0.237624   0.064770   0.000000
0.247525   0.072305   0.000000
0.257426   0.080435   0.001989
0.267327   0.089367   0.021309
0.277228   0.098765   0.040629
0.287129   0.108422   0.059949
0.297030   0.118696   0.079269
0.306931   0.129972   0.098589
0.316832   0.141948   0.117909
0.326733   0.153990   0.137229
0.336634   0.167300   0.156549
0.346535   0.181189   0.175869
0.356436   0.195856   0.195189
0.366337   0.211233   0.214508
0.376238   0.227422   0.233828
0.386139   0.244326   0.253148
0.396040   0.262242   0.272468
0.405941   0.281421   0.291788
0.415842   0.301095   0.311108
0.425743   0.321693   0.330428
0.435644   0.343243   0.349748
0.445545   0.365967   0.369068
0.455446   0.389191   0.388388
0.465347   0.413243   0.407708
0.475248   0.438005   0.427027
0.485149   0.462984   0.446347
$$


$TABLE: H test for possible twin law 1/2*h-3/2*k,-1/2*h-1/2*k,-l:
$GRAPHS
:H test for Acentric data 
:A:1,2,3:
$$
H   Observed_S(H)   Fitted_S(H)   $$ 
$$
0.000000   0.008306   0.000000
0.020000   0.072187   0.043054
0.040000   0.135356   0.086108
0.060000   0.194873   0.129161
0.080000   0.254495   0.172215
0.100000   0.309924   0.215269
0.120000   0.363163   0.258323
0.140000   0.413447   0.301376
0.160000   0.461310   0.344430
0.180000   0.505065   0.387484
0.200000   0.546702   0.430538
0.220000   0.585070   0.473591
0.240000   0.621064   0.516645
0.260000   0.654679   0.559699
0.280000   0.684778   0.602753
0.300000   0.713672   0.645806
0.320000   0.738908   0.688860
0.340000   0.763138   0.731914
0.360000   0.786032   0.774968
0.380000   0.806851   0.818022
0.400000   0.826915   0.861075
0.420000   0.843725   0.904129
0.440000   0.859985   0.947183
0.460000   0.874788   0.990237
0.480000   0.888214   1.000000
0.500000   0.901607   1.000000
0.520000   0.913303   1.000000
0.540000   0.924695   1.000000
0.560000   0.934012   1.000000
0.580000   0.942406   1.000000
0.600000   0.950843   1.000000
0.620000   0.958457   1.000000
0.640000   0.965216   1.000000
0.660000   0.971174   1.000000
0.680000   0.976393   1.000000
0.700000   0.980790   1.000000
0.720000   0.985019   1.000000
0.740000   0.988535   1.000000
0.760000   0.991453   1.000000
0.780000   0.993780   1.000000
0.800000   0.995410   1.000000
0.820000   0.996662   1.000000
0.840000   0.997584   1.000000
0.860000   0.998459   1.000000
0.880000   0.998983   1.000000
0.900000   0.999324   1.000000
0.920000   0.999623   1.000000
0.940000   0.999806   1.000000
0.960000   0.999900   1.000000
0.980000   0.999995   1.000000
$$


$TABLE: Britton plot for twin law -1/2*h-3/2*k,1/2*h-1/2*k,l:
$GRAPHS
:percentage negatives 
:A:1,2,3:
$$
alpha   percentage_negatives   fit   $$ 
$$
0.000000   0.000000   0.000000
0.009901   0.000013   0.000000
0.019802   0.000033   0.000000
0.029703   0.000123   0.000000
0.039604   0.000241   0.000000
0.049505   0.000475   0.000000
0.059406   0.000809   0.000000
0.069307   0.001335   0.000000
0.079208   0.001982   0.000000
0.089109   0.002896   0.000000
0.099010   0.003885   0.000000
0.108911   0.005189   0.000000
0.118812   0.006557   0.000000
0.128713   0.008303   0.000000
0.138614   0.010260   0.000000
0.148515   0.012483   0.000000
0.158416   0.015020   0.000000
0.168317   0.017998   0.000000
0.178218   0.021328   0.000000
0.188119   0.025079   0.000000
0.198020   0.028972   0.000000
0.207921   0.033285   0.000000
0.217822   0.038256   0.000000
0.227723   0.043560   0.000000
0.237624   0.049376   0.000000
0.247525   0.055661   0.000000
0.257426   0.062439   0.000000
0.267327   0.069764   0.000000
0.277228   0.077626   0.000000
0.287129   0.085839   0.000867
0.297030   0.095090   0.022384
0.306931   0.104993   0.043901
0.316832   0.115712   0.065418
0.326733   0.127348   0.086935
0.336634   0.139277   0.108452
0.346535   0.152340   0.129969
0.356436   0.166140   0.151486
0.366337   0.180986   0.173003
0.376238   0.197030   0.194520
0.386139   0.213588   0.216037
0.396040   0.231743   0.237554
0.405941   0.250729   0.259071
0.415842   0.271487   0.280588
0.425743   0.292921   0.302105
0.435644   0.315700   0.323622
0.445545   0.339524   0.345139
0.455446   0.364590   0.366656
0.465347   0.390915   0.388173
0.475248   0.417840   0.409690
0.485149   0.445659   0.431207
$$


$TABLE: H test for possible twin law -1/2*h-3/2*k,1/2*h-1/2*k,l:
$GRAPHS
:H test for Acentric data 
:A:1,2,3:
$$
H   Observed_S(H)   Fitted_S(H)   $$ 
$$
0.000000   0.008180   0.000000
0.020000   0.081184   0.049189
0.040000   0.152782   0.098378
0.060000   0.221868   0.147568
0.080000   0.286872   0.196757
0.100000   0.349437   0.245946
0.120000   0.407318   0.295135
0.140000   0.461559   0.344324
0.160000   0.512380   0.393514
0.180000   0.560244   0.442703
0.200000   0.602459   0.491892
0.220000   0.641659   0.541081
0.240000   0.676649   0.590270
0.260000   0.709380   0.639459
0.280000   0.739609   0.688649
0.300000   0.766286   0.737838
0.320000   0.790677   0.787027
0.340000   0.813127   0.836216
0.360000   0.833482   0.885405
0.380000   0.851296   0.934595
0.400000   0.867805   0.983784
0.420000   0.883025   1.000000
0.440000   0.897002   1.000000
0.460000   0.909275   1.000000
0.480000   0.920618   1.000000
0.500000   0.930647   1.000000
0.520000   0.940496   1.000000
0.540000   0.948917   1.000000
0.560000   0.956296   1.000000
0.580000   0.963177   1.000000
0.600000   0.969046   1.000000
0.620000   0.974217   1.000000
0.640000   0.978813   1.000000
0.660000   0.982628   1.000000
0.680000   0.986228   1.000000
0.700000   0.989175   1.000000
0.720000   0.991435   1.000000
0.740000   0.993669   1.000000
0.760000   0.995204   1.000000
0.780000   0.996565   1.000000
0.800000   0.997653   1.000000
0.820000   0.998321   1.000000
0.840000   0.998793   1.000000
0.860000   0.999168   1.000000
0.880000   0.999497   1.000000
0.900000   0.999646   1.000000
0.920000   0.999795   1.000000
0.940000   0.999872   1.000000
0.960000   0.999985   1.000000
0.980000   0.999995   1.000000
$$


$TABLE: Britton plot for twin law h,-k,-l:
$GRAPHS
:percentage negatives 
:A:1,2,3:
$$
alpha   percentage_negatives   fit   $$ 
$$
0.000000   0.000000   0.000000
0.009901   0.002432   0.000000
0.019802   0.007676   0.000000
0.029703   0.014336   0.007983
0.039604   0.021861   0.017939
0.049505   0.029990   0.027894
0.059406   0.038667   0.037849
0.069307   0.047748   0.047804
0.079208   0.056852   0.057759
0.089109   0.066276   0.067715
0.099010   0.075864   0.077670
0.108911   0.085202   0.087625
0.118812   0.094592   0.097580
0.128713   0.104122   0.107535
0.138614   0.113763   0.117491
0.148515   0.123413   0.127446
0.158416   0.133075   0.137401
0.168317   0.143029   0.147356
0.178218   0.152550   0.157311
0.188119   0.162461   0.167267
0.198020   0.171941   0.177222
0.207921   0.181785   0.187177
0.217822   0.191857   0.197132
0.227723   0.201655   0.207087
0.237624   0.211612   0.217043
0.247525   0.221632   0.226998
0.257426   0.231799   0.236953
0.267327   0.241566   0.246908
0.277228   0.251696   0.256863
0.287129   0.262139   0.266819
0.297030   0.272370   0.276774
0.306931   0.282864   0.286729
0.316832   0.292994   0.296684
0.326733   0.303857   0.306639
0.336634   0.314305   0.316595
0.346535   0.324464   0.326550
0.356436   0.334950   0.336505
0.366337   0.345239   0.346460
0.376238   0.356056   0.356416
0.386139   0.366658   0.366371
0.396040   0.377617   0.376326
0.405941   0.388370   0.386281
0.415842   0.399299   0.396236
0.425743   0.410349   0.406192
0.435644   0.421316   0.416147
0.445545   0.432082   0.426102
0.455446   0.442594   0.436057
0.465347   0.453669   0.446012
0.475248   0.464552   0.455968
0.485149   0.475816   0.465923
$$


$TABLE: H test for possible twin law h,-k,-l:
$GRAPHS
:H test for Acentric data 
:A:1,2,3:
$$
H   Observed_S(H)   Fitted_S(H)   $$ 
$$
0.000000   0.014405   0.000000
0.020000   0.033346   0.020040
0.040000   0.051979   0.040080
0.060000   0.070684   0.060120
0.080000   0.089522   0.080160
0.100000   0.107234   0.100200
0.120000   0.125161   0.120240
0.140000   0.142802   0.140280
0.160000   0.161681   0.160320
0.180000   0.180724   0.180360
0.200000   0.199654   0.200400
0.220000   0.218502   0.220440
0.240000   0.236859   0.240480
0.260000   0.255738   0.260521
0.280000   0.273696   0.280561
0.300000   0.292053   0.300601
0.320000   0.310871   0.320641
0.340000   0.329545   0.340681
0.360000   0.348721   0.360721
0.380000   0.367396   0.380761
0.400000   0.386541   0.400801
0.420000   0.405901   0.420841
0.440000   0.425149   0.440881
0.460000   0.444223   0.460921
0.480000   0.463378   0.480961
0.500000   0.483046   0.501001
0.520000   0.503174   0.521041
0.540000   0.522155   0.541081
0.560000   0.542099   0.561121
0.580000   0.563139   0.581161
0.600000   0.584403   0.601201
0.620000   0.604531   0.621241
0.640000   0.625991   0.641281
0.660000   0.647921   0.661321
0.680000   0.669861   0.681361
0.700000   0.691637   0.701401
0.720000   0.712953   0.721441
0.740000   0.735549   0.741481
0.760000   0.757868   0.761522
0.780000   0.779921   0.781562
0.800000   0.802332   0.801602
0.820000   0.825685   0.821642
0.840000   0.849448   0.841682
0.860000   0.872156   0.861722
0.880000   0.895438   0.881762
0.900000   0.917706   0.901802
0.920000   0.938848   0.921842
0.940000   0.959334   0.941882
0.960000   0.977937   0.961922
0.980000   0.992936   0.981962
$$