Full Frame Images

Understanding Full Frame Images

Learning goals

In this tutorial we will learn the following, - What a TESS Full Frame Image (FFI) is. - How to obtain an FFI from the MAST archive via Lightkurve. - How to cut out data around an object of interest in an FFI. - How to plot the cut FFI data. - How to access the metadata, and understand the files properties and units.

We will also show the user where they can find more details about TESS FFIs.

What is a Full Frame Image?

The TESS telescope observes stars for long periods of time, just under a month per sector. Each sector is covered by 4 cameras.

A single FFI is the full set of all science and collateral pixels across all CCDs of a given camera. FFIs were taken every 30 minutes during science operations in the primary mission, and every 10 min in the extended.

FFI data is provided in three types: uncalibrated, calibrated, and uncertainty.

Uncalibrated FFI data is provided in one file with two Header/Data Units (HDUs): a primary header and the CCD image header and data.

The calibrated image and its uncertainty are provided in a separate file with several HDUs: a primary header, the CCD calibrated image header and data, the CCD uncertainty image header and data, and the cosmic ray corrections binary table header and data.

Cosmic Ray Mitigated (CRM) FFIs are the same as FFIs except they will are collected with the on-board cosmic ray mitigation enabled.

Sometimes an object of interest isn’t in a TPF (see the TPF tutorial) but is in an FFI and as such the user may wish to create a cut out of the object in this FFI and work with this object only.

In this tutorial we’ll cover the basics of working with FFIs.

Imports

This tutorial requires that you import Lightkurve only.

%matplotlib inline
import lightkurve as lk

Defining terms

  • Target Pixel File (TPF): A file containing the original CCD pixel observations from which light curves are extracted.
  • Full Frame Image (FFI): A file containing the full set of all science and collateral pixels across all CCDs of a given camera.
  • Cadence: The rate at which TESS photometric observations are stored.
  • Sector: One of TESS’s 27 (to date) observing periods, approximately ~27 days in duration.

Downloading data

The TESS FFIs are stored on the Mikulksi Archive for Space Telescopes (MAST) archive.

First, let’s create a TPF for an object of interest, let’s choose Gaia object DR25290850609994130560. This object was observed in the TESS FFI data only. We’ll use the search_tesscut function to download a cut out of the target in a chosen sector. You can determine which sectors the target was observed in using the MAST TESS portal.

search_result = lk.search_tesscut('Gaia DR25290850609994130560')
print(search_result)
SearchResult containing 5 data products.

 #   observation   author         target_name         productFilename distance
--- -------------- ------ --------------------------- --------------- --------
  0  TESS Sector 4   MAST Gaia DR25290850609994130560         TESSCut      0.0
  1  TESS Sector 7   MAST Gaia DR25290850609994130560         TESSCut      0.0
  2  TESS Sector 8   MAST Gaia DR25290850609994130560         TESSCut      0.0
  3  TESS Sector 9   MAST Gaia DR25290850609994130560         TESSCut      0.0
  4 TESS Sector 10   MAST Gaia DR25290850609994130560         TESSCut      0.0

We can see that this object is detected in Sectors 4, 7, 8, 9, and 10. You can download data from just one sector and specify the cutout_size in number of TESS pixels on a side as an argument to .download(). The default is a meager 5 × 5 square. Let’s go with 10 pixels square.

search_result_s4 = lk.search_tesscut('Gaia DR25290850609994130560', sector=4)
tpfs_s4 = search_result_s4.download(cutout_size=10)
print(tpfs_s4)
TessTargetPixelFile(TICID: Gaia DR25290850609994130560)

The above code has created a variable named tpfs_s4 which is a Python object of type TessTargetPixelFile This can then be treated and examined the same way as in the previous Target Pixel File tutorial, for example lets plot the object.

%matplotlib inline
tpfs_s4.plot();

Great we now see our object of interest and the surrounding region. As indicated in the previous Target Pixel File tutorial, we can examine the header of this file via,

tpfs_s4.hdu[1].header
XTENSION= 'BINTABLE'           / binary table extension
BITPIX  =                    8 / array data type
NAXIS   =                    2 / number of array dimensions
NAXIS1  =                 2066 / length of dimension 1
NAXIS2  =                 1060 / length of dimension 2
PCOUNT  =                    0 / number of group parameters
GCOUNT  =                    1 / number of groups
TFIELDS =                   12 / number of table fields
TTYPE1  = 'TIME    '           / column name
TFORM1  = 'D       '           / column format
TUNIT1  = 'BJD - 2457000, days' / unit
TDISP1  = 'D14.7   '           / display format
TTYPE2  = 'TIMECORR'           / column name
TFORM2  = 'E       '           / column format
TUNIT2  = 'd       '           / unit
TDISP2  = 'E14.7   '           / display format
TTYPE3  = 'CADENCENO'          / column name
TFORM3  = 'J       '           / column format
TDISP3  = 'I10     '           / display format
TTYPE4  = 'RAW_CNTS'           / column name
TFORM4  = '100J    '           / column format
TUNIT4  = 'count   '           / unit
TNULL4  =                   -1 / null value
TDISP4  = 'I8      '           / display format
TDIM4   = '(10, 10)'           / multi-dimensional array spec
WCAX4   =                    2 / number of WCS axes
1CTYP4  = 'RA---TAN'           / right ascension coordinate type
2CTYP4  = 'DEC--TAN'           / declination coordinate type
1CRPX4  =      5.4970243878873 / [pixel] reference pixel along image axis 1
2CRPX4  =      5.5084913439498 / [pixel] reference pixel along image axis 2
1CRVL4  =      120.49774824319 / [deg] right ascension at reference pixel
2CRVL4  =      -60.35838348711 / [deg] declination at reference pixel
1CUNI4  = 'deg     '           / physical unit in column dimension
2CUNI4  = 'deg     '           / physical unit in row dimension
1CDLT4  =                  1.0 / [deg] pixel scale in RA dimension
2CDLT4  =                  1.0 / [deg] pixel scale in DEC dimension
11PC4   =  0.00082008272000062 / Coordinate transformation matrix element
12PC4   =  -0.0052652158454813 / Coordinate transformation matrix element
21PC4   =   0.0052951771787336 / Coordinate transformation matrix element
22PC4   =   0.0012306942427273 / Coordinate transformation matrix element
WCSN4P  = 'PHYSICAL'           / table column WCS name
WCAX4P  =                    2 / table column physical WCS dimensions
1CTY4P  = 'RAWX    '           / table column physical WCS axis 1 type, CCD col
2CTY4P  = 'RAWY    '           / table column physical WCS axis 2 type, CCD row
1CUN4P  = 'PIXEL   '           / table column physical WCS axis 1 unit
2CUN4P  = 'PIXEL   '           / table column physical WCS axis 2 unit
1CRV4P  =                 1948 / table column physical WCS ax 1 ref value
2CRV4P  =                  380 / table column physical WCS ax 2 ref value
1CDL4P  =                  1.0 / table column physical WCS a1 step
2CDL4P  =                  1.0 / table column physical WCS a2 step
1CRP4P  =                    1 / table column physical WCS a1 reference
2CRP4P  =                    1 / table column physical WCS a2 reference
TTYPE5  = 'FLUX    '           / column name
TFORM5  = '100E    '           / column format
TUNIT5  = 'e-/s    '           / unit
TDISP5  = 'E14.7   '           / display format
TDIM5   = '(10, 10)'           / multi-dimensional array spec
WCAX5   =                    2 / number of WCS axes
1CTYP5  = 'RA---TAN'           / right ascension coordinate type
2CTYP5  = 'DEC--TAN'           / declination coordinate type
1CRPX5  =      5.4970243878873 / [pixel] reference pixel along image axis 1
2CRPX5  =      5.5084913439498 / [pixel] reference pixel along image axis 2
1CRVL5  =      120.49774824319 / [deg] right ascension at reference pixel
2CRVL5  =      -60.35838348711 / [deg] declination at reference pixel
1CUNI5  = 'deg     '           / physical unit in column dimension
2CUNI5  = 'deg     '           / physical unit in row dimension
1CDLT5  =                  1.0 / [deg] pixel scale in RA dimension
2CDLT5  =                  1.0 / [deg] pixel scale in DEC dimension
11PC5   =  0.00082008272000062 / Coordinate transformation matrix element
12PC5   =  -0.0052652158454813 / Coordinate transformation matrix element
21PC5   =   0.0052951771787336 / Coordinate transformation matrix element
22PC5   =   0.0012306942427273 / Coordinate transformation matrix element
WCSN5P  = 'PHYSICAL'           / table column WCS name
WCAX5P  =                    2 / table column physical WCS dimensions
1CTY5P  = 'RAWX    '           / table column physical WCS axis 1 type, CCD col
2CTY5P  = 'RAWY    '           / table column physical WCS axis 2 type, CCD row
1CUN5P  = 'PIXEL   '           / table column physical WCS axis 1 unit
2CUN5P  = 'PIXEL   '           / table column physical WCS axis 2 unit
1CRV5P  =                 1948 / table column physical WCS ax 1 ref value
2CRV5P  =                  380 / table column physical WCS ax 2 ref value
1CDL5P  =                  1.0 / table column physical WCS a1 step
2CDL5P  =                  1.0 / table column physical WCS a2 step
1CRP5P  =                    1 / table column physical WCS a1 reference
2CRP5P  =                    1 / table column physical WCS a2 reference
TTYPE6  = 'FLUX_ERR'           / column name
TFORM6  = '100E    '           / column format
TUNIT6  = 'e-/s    '           / unit
TDISP6  = 'E14.7   '           / display format
TDIM6   = '(10, 10)'           / multi-dimensional array spec
WCAX6   =                    2 / number of WCS axes
1CTYP6  = 'RA---TAN'           / right ascension coordinate type
2CTYP6  = 'DEC--TAN'           / declination coordinate type
1CRPX6  =      5.4970243878873 / [pixel] reference pixel along image axis 1
2CRPX6  =      5.5084913439498 / [pixel] reference pixel along image axis 2
1CRVL6  =      120.49774824319 / [deg] right ascension at reference pixel
2CRVL6  =      -60.35838348711 / [deg] declination at reference pixel
1CUNI6  = 'deg     '           / physical unit in column dimension
2CUNI6  = 'deg     '           / physical unit in row dimension
1CDLT6  =                  1.0 / [deg] pixel scale in RA dimension
2CDLT6  =                  1.0 / [deg] pixel scale in DEC dimension
11PC6   =  0.00082008272000062 / Coordinate transformation matrix element
12PC6   =  -0.0052652158454813 / Coordinate transformation matrix element
21PC6   =   0.0052951771787336 / Coordinate transformation matrix element
22PC6   =   0.0012306942427273 / Coordinate transformation matrix element
WCSN6P  = 'PHYSICAL'           / table column WCS name
WCAX6P  =                    2 / table column physical WCS dimensions
1CTY6P  = 'RAWX    '           / table column physical WCS axis 1 type, CCD col
2CTY6P  = 'RAWY    '           / table column physical WCS axis 2 type, CCD row
1CUN6P  = 'PIXEL   '           / table column physical WCS axis 1 unit
2CUN6P  = 'PIXEL   '           / table column physical WCS axis 2 unit
1CRV6P  =                 1948 / table column physical WCS ax 1 ref value
2CRV6P  =                  380 / table column physical WCS ax 2 ref value
1CDL6P  =                  1.0 / table column physical WCS a1 step
2CDL6P  =                  1.0 / table column physical WCS a2 step
1CRP6P  =                    1 / table column physical WCS a1 reference
2CRP6P  =                    1 / table column physical WCS a2 reference
TTYPE7  = 'FLUX_BKG'           / column name
TFORM7  = '100E    '           / column format
TUNIT7  = 'e-/s    '           / unit
TDISP7  = 'E14.7   '           / display format
TDIM7   = '(10, 10)'           / multi-dimensional array spec
WCAX7   =                    2 / number of WCS axes
1CTYP7  = 'RA---TAN'           / right ascension coordinate type
2CTYP7  = 'DEC--TAN'           / declination coordinate type
1CRPX7  =      5.4970243878873 / [pixel] reference pixel along image axis 1
2CRPX7  =      5.5084913439498 / [pixel] reference pixel along image axis 2
1CRVL7  =      120.49774824319 / [deg] right ascension at reference pixel
2CRVL7  =      -60.35838348711 / [deg] declination at reference pixel
1CUNI7  = 'deg     '           / physical unit in column dimension
2CUNI7  = 'deg     '           / physical unit in row dimension
1CDLT7  =                  1.0 / [deg] pixel scale in RA dimension
2CDLT7  =                  1.0 / [deg] pixel scale in DEC dimension
11PC7   =  0.00082008272000062 / Coordinate transformation matrix element
12PC7   =  -0.0052652158454813 / Coordinate transformation matrix element
21PC7   =   0.0052951771787336 / Coordinate transformation matrix element
22PC7   =   0.0012306942427273 / Coordinate transformation matrix element
WCSN7P  = 'PHYSICAL'           / table column WCS name
WCAX7P  =                    2 / table column physical WCS dimensions
1CTY7P  = 'RAWX    '           / table column physical WCS axis 1 type, CCD col
2CTY7P  = 'RAWY    '           / table column physical WCS axis 2 type, CCD row
1CUN7P  = 'PIXEL   '           / table column physical WCS axis 1 unit
2CUN7P  = 'PIXEL   '           / table column physical WCS axis 2 unit
1CRV7P  =                 1948 / table column physical WCS ax 1 ref value
2CRV7P  =                  380 / table column physical WCS ax 2 ref value
1CDL7P  =                  1.0 / table column physical WCS a1 step
2CDL7P  =                  1.0 / table column physical WCS a2 step
1CRP7P  =                    1 / table column physical WCS a1 reference
2CRP7P  =                    1 / table column physical WCS a2 reference
TTYPE8  = 'FLUX_BKG_ERR'       / column name
TFORM8  = '100E    '           / column format
TUNIT8  = 'e-/s    '           / unit
TDISP8  = 'E14.7   '           / display format
TDIM8   = '(10, 10)'           / multi-dimensional array spec
WCAX8   =                    2 / number of WCS axes
1CTYP8  = 'RA---TAN'           / right ascension coordinate type
2CTYP8  = 'DEC--TAN'           / declination coordinate type
1CRPX8  =      5.4970243878873 / [pixel] reference pixel along image axis 1
2CRPX8  =      5.5084913439498 / [pixel] reference pixel along image axis 2
1CRVL8  =      120.49774824319 / [deg] right ascension at reference pixel
2CRVL8  =      -60.35838348711 / [deg] declination at reference pixel
1CUNI8  = 'deg     '           / physical unit in column dimension
2CUNI8  = 'deg     '           / physical unit in row dimension
1CDLT8  =                  1.0 / [deg] pixel scale in RA dimension
2CDLT8  =                  1.0 / [deg] pixel scale in DEC dimension
11PC8   =  0.00082008272000062 / Coordinate transformation matrix element
12PC8   =  -0.0052652158454813 / Coordinate transformation matrix element
21PC8   =   0.0052951771787336 / Coordinate transformation matrix element
22PC8   =   0.0012306942427273 / Coordinate transformation matrix element
WCSN8P  = 'PHYSICAL'           / table column WCS name
WCAX8P  =                    2 / table column physical WCS dimensions
1CTY8P  = 'RAWX    '           / table column physical WCS axis 1 type, CCD col
2CTY8P  = 'RAWY    '           / table column physical WCS axis 2 type, CCD row
1CUN8P  = 'PIXEL   '           / table column physical WCS axis 1 unit
2CUN8P  = 'PIXEL   '           / table column physical WCS axis 2 unit
1CRV8P  =                 1948 / table column physical WCS ax 1 ref value
2CRV8P  =                  380 / table column physical WCS ax 2 ref value
1CDL8P  =                  1.0 / table column physical WCS a1 step
2CDL8P  =                  1.0 / table column physical WCS a2 step
1CRP8P  =                    1 / table column physical WCS a1 reference
2CRP8P  =                    1 / table column physical WCS a2 reference
TTYPE9  = 'QUALITY '           / column name
TFORM9  = 'J       '           / column format
TDISP9  = 'B16.16  '           / display format
TTYPE10 = 'POS_CORR1'          / column name
TFORM10 = 'E       '           / column format
TUNIT10 = 'pixel   '           / unit
TDISP10 = 'E14.7   '           / display format
TTYPE11 = 'POS_CORR2'          / column name
TFORM11 = 'E       '           / column format
TUNIT11 = 'pixel   '           / unit
TDISP11 = 'E14.7   '           / display format
TTYPE12 = 'FFI_FILE'           / column name
TFORM12 = '38A     '           / column format
TUNIT12 = 'pixel   '           / unit
EXTNAME = 'PIXELS  '
INHERIT =                    T
BACKAPP =                  0.0 / background is subtracted
CDPP0_5 = '' / RMS CDPP on 0.5-hr time scales
CDPP1_0 = '' / RMS CDPP on 1.0-hr time scales
CDPP2_0 = '' / RMS CDPP on 2.0-hr time scales
CROWDSAP= '' / Ratio of target flux to total flux in op. ap.
DEADAPP =                  1.0 / deadtime applied
DEADC   =   0.7919999957084656 / deadtime correction
EXPOSURE=  0.01649999618530273 / [d] time on source
FLFRCSAP= '' / Frac. of target flux w/in the op. aperture
FRAMETIM=                  2.0 / [s] frame time [INT_TIME + READTIME]
FXDOFF  =              3355400 / compression fixed offset
GAINA   =    5.239999771118164 / [electrons/count] CCD output A gain
GAINB   =    5.119999885559082 / [electrons/count] CCD output B gain
GAINC   =    5.159999847412109 / [electrons/count] CCD output C gain
GAIND   =    5.159999847412109 / [electrons/count] CCD output D gain
INT_TIME=    1.980000019073486 / [s] photon accumulation time per frame
LIVETIME=  0.01649999618530273 / [d] TELAPSE multiplied by DEADC
MEANBLCA=                 6689 / [count] FSW mean black level CCD output A
MEANBLCB=                 6826 / [count] FSW mean black level CCD output B
MEANBLCC=                 6751 / [count] FSW mean black level CCD output C
MEANBLCD=                 6503 / [count] FSW mean black level CCD output D
NREADOUT=                  720 / number of read per cadence
NUM_FRM =                  900 / number of frames per time stamp
READNOIA=    10.27040004730225 / [electrons] read noise CCD output A
READNOIB=    7.424000263214111 / [electrons] read noise CCD output B
READNOIC=    7.327199459075928 / [electrons] read noise CCD output C
READNOID=    9.391200065612793 / [electrons] read noise CCD output D
READTIME=  0.01999999955296516 / [s] readout time per frame
TIERRELA= 1.16000001071370E-05 / [d] relative time error
TIMEDEL =  0.02083333395421505 / [d] time resolution of data
TIMEPIXR=                  0.5 / bin time beginning=0 middle=0.5 end=1
TMOFST11= '' / (s) readout delay for camera 1 and ccd 1
VIGNAPP =                  1.0 / vignetting or collimator correction applied
WCS_FFI = 'tess2018307065940-s0004-4-4-0124-s_ffic.fits' / FFI used for cutout W
EXTVER  =                    1 / extension version number (not format version)
SIMDATA =                    F / file is based on simulated data
ORIGIN  = 'STScI/MAST'         / institution responsible for creating this file
DATE    = '2019-01-24'         / file creation date.
TSTART  =    1410.917241951712 / observation start time in TJD
TSTOP   =    1436.833902272608 / observation stop time in TJD
DATE-OBS= '2018-10-19T09:59:40.521Z' / TSTART as UTC calendar date
DATE-END= '2018-11-14T07:59:39.972Z' / TSTOP as UTC calendar date
CREATOR = 'astrocut'           / software used to produce this file
PROCVER = '0.7     '           / software version
FILEVER = '1.0     '           / file format version
TIMVERSN= 'OGIP/93-003'        / OGIP memo number for file format
TELESCOP= 'TESS    '           / telescope
INSTRUME= 'TESS Photometer'    / detector type
DATA_REL=                    5 / data release version number
ASTATE  =                    T / archive state F indicates single orbit processi
SCCONFIG=                  124 / spacecraft configuration ID
RADESYS = 'ICRS    '           / reference frame of celestial coordinates
EQUINOX =               2000.0 / equinox of celestial coordinate system
CRMITEN =                    T / spacecraft cosmic ray mitigation enabled
CRBLKSZ =                   10 / [exposures] s/c cosmic ray mitigation block siz
CRSPOC  =                    F / SPOC cosmic ray cleaning enabled
SECTOR  =                    4 / Observing sector
CAMERA  =                    4 / Camera number
CCD     =                    4 / CCD chip number
RA_OBJ  =      120.49008353007 / [deg] right ascension
DEC_OBJ =    -60.3546627100264 / [deg] declination
TIMEREF = 'SOLARSYSTEM'        / barycentric correction applied to times
TASSIGN = 'SPACECRAFT'         / where time is assigned
TIMESYS = 'TDB     '           / time system is Barycentric Dynamical Time (TDB)
BJDREFI =              2457000 / integer part of BTJD reference date
BJDREFF =                  0.0 / fraction of the day in BTJD reference date
TIMEUNIT= 'd       '           / time unit for TIME, TSTART and TSTOP
TELAPSE =    25.91666032089597 / [d] TSTOP - TSTART
OBJECT  = '' / string version of target id
TCID    =                    0 / unique tess target identifier
PXTABLE =                    0 / pixel table id
PMRA    =                  0.0 / [mas/yr] RA proper motion
PMDEC   =                  0.0 / [mas/yr] Dec proper motion
PMTOTAL =                  0.0 / [mas/yr] total proper motion
TESSMAG =                  0.0 / [mag] TESS magnitude
TEFF    =                  0.0 / [K] Effective temperature
LOGG    =                  0.0 / [cm/s2] log10 surface gravity
MH      =                  0.0 / [log10([M/H])] metallicity
RADIUS  =                  0.0 / [solar radii] stellar radius
TICVER  =                    0 / TICVER
TICID   = '' / unique tess target identifier
CHECKSUM= 'f752h751f751f751'   / HDU checksum updated 2020-08-26T14:10:38
DATASUM = '3805688324'         / data unit checksum updated 2020-08-26T14:10:38

We can also examine specific things like the flux or time via,

tpfs_s4.flux
[[[129.99297, 128.63951, 132.87094, …, 139.99612, 137.95688, 142.58392], [138.64349, 153.85022, 161.18605, …, 132.13853, 131.88116, 136.26653], [147.42535, 185.44145, 202.03874, …, 131.27419, 129.55354, 132.28387], …, [148.45624, 168.75594, 169.70703, …, 193.291, 262.43341, 225.49281], [143.34943, 148.85297, 140.99071, …, 632.60272, 1230.0093, 481.08664], [138.4722, 136.3645, 133.1722, …, 582.95276, 1186.0709, 478.35709]], 
[[129.82346, 128.34328, 132.64188, …, 139.19876, 137.08186, 142.32404], [139.79184, 152.97951, 161.24356, …, 132.91368, 131.2858, 136.80386], [147.51363, 185.70856, 202.45325, …, 131.01465, 129.47301, 132.81329], …, [147.99286, 167.25301, 168.89616, …, 194.54517, 264.9231, 225.16179], [143.70619, 149.3633, 140.49521, …, 632.60107, 1227.5686, 482.08145], [138.03108, 136.32384, 133.2, …, 582.40741, 1182.1221, 479.85046]], 
[[129.21542, 129.74716, 132.78502, …, 138.40413, 137.88484, 143.00275], [139.7187, 155.0994, 160.00632, …, 132.12894, 131.79468, 136.66957], [147.73445, 183.78162, 200.47708, …, 130.74011, 129.2097, 132.41162], …, [147.66319, 166.57088, 168.81226, …, 215.93103, 281.56219, 224.84123], [142.83057, 148.42052, 140.91992, …, 642.88855, 1205.141, 467.6749], [137.69144, 135.93571, 133.34496, …, 573.22418, 1151.689, 483.14612]], 
…, 
[[792.39258, 789.263, 795.30682, …, 809.82086, 811.76941, 815.80994], [803.67145, 809.58545, 835.54602, …, 800.33563, 802.27563, 808.07153], [803.70325, 832.35767, 866.13525, …, 802.09814, 800.79468, 804.69025], …, [799.46198, 814.78491, 819.1286, …, 869.16278, 1009.9353, 943.88312], [794.48761, 799.0069, 792.25012, …, 1211.3436, 2031.7046, 1349.0428], [790.42419, 785.95496, 787.04718, …, 1130.4243, 1644.5442, 1246.1456]], 
[[813.54431, 809.97974, 817.47009, …, 830.65527, 830.61475, 836.75928], [826.25146, 831.77899, 856.91522, …, 821.61914, 823.5957, 828.23602], [825.62567, 854.96924, 889.86981, …, 822.89606, 820.79828, 824.80457], …, [821.97601, 836.54681, 844.15063, …, 892.07336, 1033.9146, 965.64771], [816.31024, 823.79694, 816.89545, …, 1233.7531, 2053.4348, 1371.8173], [813.43365, 809.15466, 809.1488, …, 1154.3142, 1664.0698, 1269.6807]], 
[[843.42645, 838.84576, 847.90161, …, 861.24701, 861.25537, 867.8017], [855.00861, 862.23065, 888.0213, …, 849.95538, 852.78198, 859.7309], [856.35095, 883.28583, 919.44934, …, 852.11145, 851.24445, 854.23767], …, [849.98053, 867.28394, 872.92499, …, 923.02142, 1061.4458, 994.54596], [847.56006, 852.9693, 846.55609, …, 1264.6205, 2082.7625, 1403.7192], [843.9043, 838.604, 839.48645, …, 1181.7628, 1696.9923, 1301.2625]]] (e − )/(s)