Troubleshooting a transfer matrix program

Comparison of Rotosolve spreadsheet calculated results and analytically-calculated results

I. Simple Beam Cases (calculation option 3)

Beam cases are easy to check since a simple analytical solution is readily available.

The cases in this section are called "simple" because they used the option 3 "simple" for the gyroscopic option, which means that all disk effects are ignored.

The program provides choices for boundary conditions: "hinged", "clamped", "free", which have the same meanings as in normal textbook beam calculations.

The beam was broken into 10 pieces and the lumped-MASS calculation option was set to false (continuos-mass calculation).

In all these cases, the following beam parameters were used:

Length = 1 meter

Diameter = 0.1 meter

Density = 7750 kg/m^3 (more specifically, 7750.37312)

E = 2.31E11 N/m^2 (more specifically, 230974359500)

The thee example simple beam cases were all generated with the inputs shown in the following file: SimpleBeamDemo.xls

A. Free/Free beam,

Geometry:

Free

Free

Results (analytical calculations shown in tab labeled "analytical calculation")

Boundary Conditions: freefree

Frequency

Analytical Calculation

Program Output

1

485.971

485.971

2

1,339.598

1,339.598

3

2,626.148

2,626.148

Mode shapes

Mode shape plot (brg stiffness multiplier =1)

-1.5

-1

-0.5

0

0.5

1

1.5

0

0.5

1

1.5

x = axial distance (meters)

relative amplitude

f1=485.97hz

f2=1339.6hz

f3=2626.15hz

B. Clamped/Free beam (cantilevered)

Geometry as follows:

Free

Results as follows:

Boundary Conditions: clampedfree

Frequency

Analytical Calculation

Program Output

1

76.372

76.372

2

478.612

478.612

3

1,340.128

1,340.128

Mode shapes as follows:

Mode shape plot (brg stiffness multiplier =1)

-1.5

-1

-0.5

0

0.5

1

1.5

0

0.5

1

1.5

x = axial distance (meters)

relative amplitude

f1=76.37hz

f2=478.61hz

f3=1340.13hz

C. Hinged-hinged (Simply-supported) beam

Geometry as follows:

Results as follows:

Boundary Conditions: hinged/hinged

Frequency

Analytical Calculation

Program Output

1

214.378

214.377

2

857.512

857.410

3

1,929.403

1,928.105

Mode shapes as follows:

Mode shape plot (brg stiffness multiplier =1)

-1.5

-1

-0.5

0

0.5

1

1.5

00.511.5

x = axial distance (meters)

relative amplitude

f1=214.38hz

f2=857.41hz

f3=1928.11hz

II. Adding concentrated mass along with distributed mass.

M

M

m

The attached file recreates the well-known scenario where a simply-supported beam with distributed beam mass m and concentrated mass M in the center causes a resonant frequency based on an effective stiffness of 48EI/L^3 and an effective mass of M + 0.5*m.

M_PLUS_Halfm.xls

Again the program calculates the result as expected.

III. Introducing bearings

Most real-world rotors will be modeled as free-free boundary conditions. It is a very simple matter to recreate the simply-supported results above by adding an additional 0-length section on the right, adding bearings to the left of the first and last rotor sections, and setting the bearing stiffness values very high, as was done in the following file: SimplySupportedFromFreeFreeWithBearings.xls

K_bearing=infinity

An examination of the critical speed map and the modeshapes in the above file confirms that the high bearing stiffness causes the bearings to act like rigid supports,

The frequency results match the simply-supported results above, as expected:

Results

Frequency

Analytical Calculation

Program Output

1

214.378

213.906

2

857.512

850.231

3

1,929.403

1,894.069

IV. Varying the bearing stiffness.

The model studied is the same as above, except that we have introduced a variable bearing stiffness as follows:

K_bearing=variable

The above system is solved in the attached file: DemoShaftOnBearings2.xls

The same geometry was also solved in "Turbomachinery Rotordynamics: Phenomena, Modeling, and Analysis" By Dara Childs, page 123, which can be accessed here:

http://books.google.com/books?id=vKPfBxgQQPoC&pg=PA123&dq=%22These+modes+are+commonly+referred+to+as+stick+modes%22&sig=KKcf-5urzLoMB50PNymoxQlBzv8

A visual comparison of the critical speed maps generated by my spreadsheet with those provided by Childs shows good agreement:

My spreadsheet

Childs

Crit Spd Map Rad/sec

1.E+02

1.E+03

1.E+04

1.E+05

0.010.1110100

Brg Stiffness Multiplier (multiple of Kbrg=48EI/L^3)

radians/sec

first nat freq

second nat freq

third nat freq

Looking toward the left of the critical speed map, we suspect that the first two modes increasing linearly on log-log plot with a slope of 0.5 are rigid-rotor modes. We confirm this with a modeshape plot of these first two frequencies (bearing multiplier 0.01):

Mode shape plot (brg stiffness multiplier =0.01)

-1.5

-1

-0.5

0

0.5

1

1.5

00.511.5

x = axial distance (meters)

relative amplitude

f1=21.15hz

f2=36.77hz

With the rigid rotor simplification, we can analytically verify the first two resonant frequencies at a bearing stiffness multiplier of 0.01.

For the first rigid rotor mode at stiffness multiplier 0.01,

Kbrg = 0.01 * 48*E*I/L^3 = 543338. N/m

M = pi * rho * L * (od^2-id^2)/4 = 60.87 kg

F = sqrt(2*Kbrg/M) / (2*pi) = 21.27hz (matches program-calculated 21.15 very well).

For the second rigid rotor mode at stiffness multiplier of 0.01, we calculate the transverse or diametrical mass moment of inertia of the shaft (assuming all mass concentrated on the centerline... consistent with calculation mode 3) as follows:

)

(

4

1

Id

4

4

inner

outer

R

R

L

-

=

p

r

Id = 5.072363139 kg*m^2

The max kinetic energy is KE = 0.5 *Id2 * ((')2

For small angles, ( ~ sin(() = y / (L/2) (where y is transverse displacement at location of the bearing.

(' = y' / (L/2)

Substitute into KE equation:

KE = 0.5 *Id * (y')2 /(L/2)2

We can preserve kinetic energy by rewriting the above as

KE = 0.5 * Meffective * (y')2 = 0.5 * Meffective * v^2

where Meffective = Id / (L/2)2 = 20.28945255 kg

Thus from an energy standpoint, the rotary inertia Id acts like an effective mass Meffective=Id /(L/2)2 at the location of one of the bearings. Since the fundamental frequency can be calculated from energy considerations (KEmax=PEmax), we can calculate the resonant frequency using this effective mass. (This approach of calculating an effective mass based on energy considerations is described in Thompson's "Mechanical Vibrations" section 2.3 or Rao's "Mechanical Vibrations" example 1.6). The relevant spring stiffness includes both bearings in parallel. The frequency is

f = sqrt(2*Kb/Meffective) /(2*pi) = 36.83283813 hz. This matches the program output 36.77409375 very well (2nd mode for bearing multiplier of 0.01).

Looking toward the right side of the critical speed map toward stiffness multiplier of 100, we see a leveling of the first and second modes. We suspect these reprsent the first and second flexible rotor modes.

For the first mode at bearing stiffness multiplier 100, The modeshape plot appears to confirms a flexible rotor/rigid bearing mode.

Mode shape plot (brg stiffness multiplier =100)

-1.2

-1

-0.8

-0.6

-0.4

-0.2

0

0.2

00.20.40.60.811.2

x = axial distance (meters)

relative amplitude

f1=213.61hz

We can check the frequency for this mode (first mode at multiplier =100) using a simply-supported beam calculation, which gives a frequency of 214.21 hz. This is reasonably close to the program-calculated resonant frequency of 213.6hz.

For the second mode at bearing stiffness multiplier 100, The modeshape plot appears to confirm a second flexible rotor/rigid bearing mode.

Mode shape for f= 842.86 hz and Kbrg

multiplier = 100

-25

-20

-15

-10

-5

0

5

10

15

20

25

0

0.2

0.4

0.6

0.8

1

1.2

x = axial distance (meters)

y = transverse displacement (no units)

The theoretical modeshape of this second flexible rotor mode is sin(2(*x/L). Examining the area between x=0 and x=L/2, we find it has the same modeshape as the first flexible-rotor/rigid-bearing modeshape of a beam of length L/2. We can use this information to analytically confirm our frequency based on a simply supported beam of length L/2. The analytical solution of the half-length simply-supported beam gives 856.8hz, while the program predicts the second mode at bearing stiffness multiplier of 100 to be 842.4 hz. The small difference can be reconciled by noting that the mode shape does not come completely to 0, so there is some flexibility still present in the bearings (even at bearing stiffness multiplier of 100) which reduces the resonant frequency.

V. Adding tilting disk effects (like bump test scenario) Calculation option 2

If we bump test a rotor with a large disk (especially overhung), the disk inertia causes the natural frequency to lower by virtue of the fact that a moment must be exerted to tilt the disk back and forth. This effect is called "rotary inertia" in beam theory, even though it is not the way we would normally use the word "rotary".

The "simply-supported" beam scenario above (1 meter beam, 0.1 m diameter, etc) was run again using option 2 to add the effects of rotary inertia. The results are shown in this file SimplySupportedWithRotaryInertaVsRaoGood.xls

As shown in the "Analytical check" tab, Rao's "Mechanical Vibrations" provides a formula for calculating the natural frequencies for this geometry (simply-supported uniform beam) including the effects of rotary inertia. The first three resonant frequencies are shown below using simple analytical calc, adding rotary inertia, and comparing to program output:

Analytical, no rotary inertia (simple calculation)

Analytical, with rotary inertia

Program output (with rotary inertia=option 2)

f1

214.3781239

213.7199712

213.7202468

f2

857.5124957

847.1251912

847.1172571

f3

1929.403115

1877.977813

1877.775498

The rotary inertia does not play a very important role in the first mode for this geometry, but increases in importance as the higher order modeshapes introduce more nodes and more tilting. The program matches the analytical calculation very well, even at the higher mode numbers. When I increased the number of elements from 10 to 200 while keeping the total length the same, the program results matched even better (program computed f3=1877.977).

In general, we suspect rotary inertia will play in important role when there are large disks and lots of bending/tilting at the location of the disks.

VI. Gryoscopic Effects calculation option 1

While the disk-tilting effects of option 2 tend to lower critical speed, the gryoscopic effects tend to increase critical speed. Option 1 includes both effects. This results in higher critical speeds than the simple mode (no disk effects) since the increase caused by gyroscopic effects is larger than the decrease caused by the disk tilt effects.

Rigid-rotor gyroscopically-stiffened whirl

"Formulas For Stress, Strain, And Structural Matrices", 2nd ed. by Walter D. Pilkey Table 17-1 gives the following solution for the resonant frequencies of a rigid rotor with a center disk having significant polar and transverse inertia.

This was simulated in the following file RigidRotorGyroDemoWorks1.xls

The mode shapes are as follows:

Mode shape plot (brg stiffness multiplier =1)

-1.5

-1

-0.5

0

0.5

1

1.5

0

0.2

0.4

0.6

0.8

x = axial distance (meters)

relative amplitude

f1=11.77hz

f2=241.85hz

Pilkey's wc1 corresponds to the first mode f1 at 11.77hz where the rigid rotor moves parallel to it's axis with a very simple solution w=sqrt(Ktotal./M).

Pilkey's wc3 corresponds to f2 and represents the forward-rotating gryoscopically-stiffened mode whose 3-d modeshape would resemble two cones with their points meeting at the center of the rotor. Note that for problems involving gryoscopic stiffening, the whirl speed changes as a function of machine speed. Therefore the analytical solution for the critical speed wc3 requires solving an implicit relationship to find the speed where the whirling frequency is equal to the machine speed (as is typical of most problems that include gyroscopic stiffening).

The parameters used for the simulation are defined in the file. The analytical calculations are shown in the analytical tab. The program results match the analytical predications reasonably well:

Analytical

Program

f1

11.7775

11.77269

f2

244.7908

241.8507

VII. Overhung rotor solved/checked for all three calculation modes

This is intended to model the an overhung rotor described in the thread "Gyroscopic effect", at

http://maintenanceforums.com/eve/forums/a/tpc/f/3751089011/m/9291040423/p/1

(except that the smaller disk and shaft stub on the left is omitted for simplicity of the analytical solution).

The rotosolve spreadsheet solution is here: OverhungRotor.xls

The geometry looks as follows:

Rotor Geometry (rotor in horizontal position with only upper half showing)

-0.2

-0.1

0

0.1

0.2

0.3

0.4

0.5

-0.200.20.40.60.81

x = axial distance (meters)

y = profile

od profile

id profile

attached disk od profile

attached disk id profile

Bearing 1

Bearing 2

A complete analytical solution of this geometry (mode 3= simple/point mass, mode 2 = bump test, and mode 1 = critspd) is provided in the following file: FindAlphaR1a.pdf

Critical Speed (like calc option 1)

Bump test frequency (like calc option 2)

My rotosolve spreadsheet was run on the same model, and the results are compared below:

Analytical Solution (hz)

Program output (hz)

Mode 1 = simple / point mass neglects all disk effects

47.2

47.8

Mode 2 = bump test includes disk effects but neglects gyro

~ 35 hz

36.12

Mode 3 = Critical speed includes gryo and disk effects

~59.5

60.44

The mode shapes for the three calculation modes are as follows:

Calc Mode 1 (crit speed)

Calc Mode 2 (bump test)

Calc Mode 3 (simple)

Mode shape plot (brg stiffness multiplier =1)

-0.2

0

0.2

0.4

0.6

0.8

1

1.2

00.20.40.60.8

x = axial distance (meters)

relative amplitude

f1=60.44hz

Mode shape plot (brg stiffness multiplier =1)

-0.4

-0.2

0

0.2

0.4

0.6

0.8

1

1.2

00.20.40.60.8

x = axial distance (meters)

relative amplitude

f1=36.12hz

Mode shape plot (brg stiffness multiplier =1)

-0.2

0

0.2

0.4

0.6

0.8

1

1.2

00.20.40.60.8

x = axial distance (meters)

relative amplitude

f1=47.82hz

This geometry was checked with the Critspd program, and similar results were obtained.

_1260715176.ppt

K_bearing=variable

_1278084296.xlsChart1

-1-1-1

-0.5371643859-0.2274294260.0519642229

-0.09772682630.39724916670.6428633084

0.27200427410.66201187450.3969312004

0.52024744110.4830290696-0.3278434515

0.60782222940.0000002908-0.7111906071

0.5202476282-0.4830286686-0.3278437995

0.2720046176-0.66201191630.3969308918

-0.0977263783-0.39724967840.6428634009

-0.53716389030.22742863450.0519646904

-0.99999949650.9999991536-0.9999994428

f1=485.97hz

f2=1339.6hz

f3=2626.15hz

x = axial distance (meters)

relative amplitude

Mode shape plot (brg stiffness multiplier =1)

Instructions

Approach

Break your rotor shaft into pieces.

Number the pieces from left (1) to right (n). (these will be entered in rows from top to bottom in RotorSections tab)

For each piece you can specify the length, i.d., o.d. density, young's modulus

For each piece, you can also specify an "attached disk" with associated rho, id, od (same length as shaft piece). It has mass and MOI, but does not contribute to stiffness

If you need a bearing on the extreme right of your rotor, you'll need to add a zero-length piece on the right so you can put that bearing on the left of it.

(see example of simply-supported beam)

How many pieces should your break it into?

For most purposes, breaking the rotor into pieces whose length is the diameter of the shaft is more than enough.

(that algorithm uses distributed stiffness and mass)

(the algorithm uses lumped polar inertia model)

(the modeshape plot examines position of boundary of each piece, not within a piece

Example - a 1-section model will accurately determine all frequencies of a uniform rotor, but will generate a mode-shape of a straight-line plot connecting the ends

Input

Rotor Sections sheet

enter the rotor data (in mks units). Start at top of RotorSections sheet corresponds to left side of rotor.

a button is provided four your convenience to transfer default values from main tab if desired (E and rho for all sections, Kbrg for sections with bearing, and rho_disk for sections with attached disks)

If you want to change parameters like rho or E between sections, you can't use the button

a button is provided to generate a crude plot of your rotor geometry - this helps you double-check that the program interprets your data (bearings, etc) in the same position that you intended

The triangles represent bearings with specified stiffness, not hinged boundary conditions (boundary conditions are not shown on the plot)

You can customize the spreadsheet to add extra columns for your own info if desired

if you want to add into the rotorsections tab a column calculating the the x (axial) coordinate of LHS of each section, type =+SUM(B2:$B$2) in cell M3 and copy it down column M

You may find it handy to add a column off to the right calculating the mass of your shaft sections and attached disks. Of course M=rho*L*pi*()*(OD^2-id^2)/4

* Don't add anything below your data in columns A, B, or H. - this will confuse the formula for number of sections (formula in Main:C2)

Main sheet

Enter the green parameters

Verify the number of sections is right (it should be filled in by formula)

Enter frequency sweep parameters: fstart, fstop, nfsteps. freqtol

fstop=1 (very low) is recommended so program identifies low frequencies. Critical speed map and modeshape labeling (f1=, f2= etc) assume no low frequencies are missed

Identify your option for gyroscopic parameters, 1 2 or 3:

1-Critical Speed calc - include both rotating disk effect and tilting disk effect

2 -Bump test calc - Includes only tilting disk effect

3 -Simple calc - neglects both disk effects. i.e neglects polar and diametral MOI, as if all mass is concentrated at the centerline of the shaft

Identify whether you want to use a bearing stiffness multipliers (true or false)

Enter bearing stiffness multipliers in the specified format, for example '{0.1, 0.2, 0.5, 1, 2, 5, 10}

For each bearing stiffness multiplier, critical speeds will be found and recorded

Select lumped-mass model (true or false)

In general select FALSE. Select true if you get a numerical error

THIS DOES NOT AFFECT HOW YOU INPUT YOUR DATA INTO THE PROGRAM (mass is always entered as continuous vis the rho and rhodisk parameters)

Both models treat gyroscopic properties as lumped (calculated based on input rho, od, length)

Both models treat stiffness as distributed

For rotors without significant gyroscopic effects (no large-diameter disks), the continuous-mass option can give accurate frequency with very few sections

However if you want an accurate mode-shape, you still need to break up into more sections since mode shape is only calculated at boundary betw sections

For some extreme input parameters (for example very high rho combined with low E and I), the continuous model generates numerical error messages due to use of cosh and sinh functions (try cosh(800) in excel

lumped mass model seems to run a little faster

The distributed-mass option will generate an error if you use density=0, the lumped-mass operation will not

Run Critical Speed analysis

Main Sheet - press the grey button labeled "run"

Note that previous results in outsheet tab will be deleted and overwritten. Previous modeshape plots will remain but don't update with the new paramters

View results

outsheet

outsheet will contain a row for each bearing stiffness multiplier, with the critical frequencies listed to the right of the multiplier

Generate Modeshape plots

outsheet tab

You should have a "fresh" set of calculated frequencies (i.e. you you should not have changed input parameters since the frequencies were generated)

Combining old frequencies with new input data will give you garbage

If you have changed input parameters, push the "run" button in "main" tab again to generate fresh set of frequencies

Put your cursor in a cell which contains a frequency of interest.

Press the grey button for modeshape

The program will create a new sheet with a modeshape plot for that critical frequency and bearing stiffness multiplier

Repeat as many as desired. - each one creates a new sheet

Generate Critical Speed Map

outsheet tab

Press the critical speed map tab

New rotor?

If you want to go back and change your rotor definition in "main" and "rotor sections" tabs, be careful - your modeshape plots will not update.

Recommend either: 1 - delete all modeshape sheets or 2 - save old results and start again using a new file

If you get an error message

There are two types

Error Messages from my program - just a message with an "ok" button at the bottom. Read the message

Usually I am telling you there is a problem with your input

Often an excel message will come just after my message. Pay attention to both error messages.

Error Messages from excel - usually has choices "end" or "debug" at the bottom.

"End" will terminate the program

"debug will put you in editor mode and allow you to see what step of the program is causing problems, as well as examine variables in the "locals" window

To terminate the program (necessary before continuing), select "reset" from the "run" menu

To return to excel select "close and return to excel" from the "file" menu

If you got an earlier message from me that you didn't pay attention to, run the program again and read it carefully.

If you are using lumped-mass calc=false, try switching to true

Other misc and minor glitches

When you rerun the program with a new scenario, the old modeshape sheets will be unchanged. Don't be fooled thinking they show the new scenario

Either delete them, rename them so you know what they are, or start a new file

If you change the input model parameters between generating the frequencies and generating modeshapes, modeshape will not be valide/

Modeshape module uses both the frequency and the model as an input - combining a frequency with a model that didn't generate the frequency gives garbage

Blanks on the rotorsections sheet are interpretted as zero's

All inputs are to be mks

* If you press a grey buttons and nothing happens, it's likely that the vba program is hung up in debug mode. This can happen if you get an error message, press debug (vs end), and don't reset

Go to vba window and select "reset" from the run menu. OR - exit and re-enter excel.

Model And Assumpions

Uses the Myklestad / Prohl transfer matrix approach

Two types of matrices: field matrix represents a (distributed) length of shaft/disk, point matrix represents the lumped parameters concentrated at the point between adjacent lengths

The field matrix includes the distributed stiffness and (depending on program option) distributed mass

The distributed mass field matrix is the same as given by Harris' Shock and Vib Handbook Chapter 7

The lumped mass field matrix is similar to Thompson's "Theory of Vibrations" chapter 7

The point matrix includes lumped polar/transverse inertia and also includes effects of bearing force, and (depending on program options) lumped mass

Similar matrices in many references

the MOI properties related to gryoscopic/bump-test/point-mass option are based on "Dynamics Of Rotating Systems" page 146.

Assumed isotropic (i.e. horizontal and veritcal direction stiffnesses are the same on horizontal rotor)

Assume H and V vibrations are uncoupled (except gryoscopic effects which are modeled)

Assumed linearity of all aspects

Neglect damping (undamped analysis)

The support on which the bearing springs are mounted is assumed to be massive and does not move.

The bearing spring may represent series combination of bearing stiffness and support stiffness provided the bearing housing has negligible mass

fluid effects are not modeled (of course)

bearing stiffness assumed constant at the value specified times the bearing stiffness multiplier of interest (in reality stiffness may change with speed)

The model is based on Euler Bernoulli beam model which neglects shear deformation. Shear deformation is negligible for all but the shortest/fattest rotors

The effects of rotary inertia (for example Timoshenko beam) is included in calculation options 1 and 2, but it is lumped (vs distributed)

Any attached disks are assumed to be rigid and ridigly attached to the shaft. Whatever the angle of the shaft, the entire disk takes the same angle

Accuracy

Every trial case that I have checked matches other calculations (based on similar assumptions/models) to within a few percent with one exception:

IF the rotor is very stiff in the middle (including bearing stiffness, high E, high radius), and has a very flexible attachment on the end (smaller E and smaller od)

THEN the program generates many extra frequencies that don't seem to belong.

You can recognize this situation by

Many more resonant frequencies than expected

Mode shapes that show wild wiggles at the ends with very little movement along the length of the rotor

Main

Variable DescriptionSymbolValueUnits

n_10unitlessEnglish Value **UnitsTo match Irvine

DefaultDensity rho *rho_def7750.37312kg/m^30.28lbm/inch^3**0.278

Default Young's Modulus E *e_def230974359500n/m^23.35E+07psi**2.98E+07

Default Bearing Stiffness *kb_def1.78E+07n/m1.00E+05lbf/inch**

fstart1hz

upper bound for frequency sweepfstop5000hz

Number of steps for frequency sweepnfsteps1000unitless

4.999hz

freqtol0.001hz

inclgyro31,2,3(1=critspeed; 2=bumptest,3=simple)

Sweep bearing stiffness using multipliers?sweepbrgTrue or false

brgmultipliertext{0.01,0.02,0.05,0.1,0.2, 0.5, 1, 2, 5, 10,20,50,100}unitlessNot programmed yet:

leftbcfreefree, hinged, or clamped

rightbcfreefree, hinged, or clamped

Use lumped mass calc? (usually false)lumpedmasscalcTrue or false

* - the three "default" parameters identified (rho_def,e_def,kb_def) above accomplish nothing unless you copy them into the rotorsections sheet (using FILL IN DEFAULTS button in RotorSections sheet)

** - the three blue parameters in English units do nothing unless you copy them to the green cells using the button provided in this sheet

output1

radian freqfreqobjective functionrootsobjective fn at root

6.28318530721481239.226694412485.97104058849505398668.21875

37.69282865785.999623160304.7023991339.5978884888-2658840315136

69.102472008410.9987036438895.131642626.1477780151156038325338112

100.51211535915.99731474314213.25424341.15627020264.35904498683085E15THIS SHEET IS EXTRA INFO THAT IS NOT OF MUCH INTEREST (BUT DON'T DELETE IT, THE PROGRAM WRITES TO IT)

131.921758709520.99693313083728.3624905.88461053470.0018826872THIS SHEET HOUSES THE OBJECTIVE FUNCTION VS FREQUENCY FOR THE LAST KMULT CALCULATED

163.331402060125.995218997769149.24351.64672540282.6026291847THE ROOTS FALL WHERE THE OBJECTIVE FUNCTION CROSSES 0

194.741045410730.994441941397923.68782.6760546875-6.06095443234122E30If you want, you can examine the behavior of the objective funciton to decide if your sweep is fine enough

226.150688761335.993802397242990.75888.37347656255.31819040876999E30

257.560332111940.9921347304148654.14110.61683593752.34218255432794E31

288.969975462545.9912130105097536.53114.9094140625-2.099546306628E31

320.379618813150.993210539200593.58120.4507421875-2.45607303794219E30

351.789262163755.9894654407319108.42130.28464843752.02031814411374E31

383.198905514360.9886533311554437.61134.57722656253.02849651210775E31

414.608548864965.9878924368868025.8160.17660156251.53306494465101E31

446.018192215470.98611909899120838.9162.7521484375-8.47741338902628E31booleanlistbclistgyrolist

477.42783556675.98515577087847869.8171.4153515625-5.22113590969002E31free1

508.837478916680.98420017624109738.7179.14199218758.31103424774633E31clamped2

540.247122267285.98325327313789624.7187.1808203125-1.90147590034234E32hinged3

571.656765617890.98231605668729822.8204.0389453125-9.71337272424881E31

603.066408968495.98138955472128099.1206.14621093751.78580278307152E32

634.476052319100.9847482320639717.2215.51183593755.15141512667747E32

665.8856956696105.97957294143656503.4223.94089843758.14465510646637E31

697.2953390202110.97868500700259616.7229.7163671875-3.21824796132942E32

728.7049823708115.97781213054367758.9233.69675781257.24145405380376E31

760.1146257214120.97695543028627402.3238.22347656256.0197557878338E32

791.5242690719125.975111602637616213243.29652343751.7556960813161E32

822.9339124225130.974129503500955196276.31035156251.28064401888057E33

854.3435557731135.973149356236949169281.14925781251.17796432026208E33

885.7531991237140.972171269837398977290.35878906252.25007981540511E32

917.1628424743145.971195351024252386296.21230468756.42065029015598E32

948.5724858249150.97221703588783805320.56292968752.66840451348042E32

979.9821291755155.969250427714015920330.08464843751.61118391289008E33

1011.3917725261160.968281619281118885345.3037890625-2.16768252639027E32

1042.8014158767165.967315369160545011348.34761718754.60664228122939E33

1074.2110592273170.966351762488678815380.2687890625-2.14106186378548E33

1105.6207025778175.965390877930803823395.64402343751.51611011787296E33

1137.0303459285180.964432786931208781417.5751953125-7.2433555297041E33

1168.439989279185.963477552951276754433.10652343753.66604553586004E33

1199.8496326296190.962525230696421007446.53058593758.92426022560673E32

1231.2592759802195.961575865332751670451.8377734375-8.4780472143264E33

1262.6689193308200.96629491694376855462.3741015625-2.73812529649298E33

1294.0785626814205.959686133482261054471.3494921875-3.69900445146597E33

1325.488206032210.958745802455582606481.26144531256.18106432671285E33

1356.8978493826215.957808497616550232489.3002734375-2.5910778268665E33

1388.3074927332220.956874204389656831494.37332031256.03908745948728E33

1419.7171360838225.955942893796365871496.24644531251.54856197323881E34

1451.1267794344230.9541.01452162624319E15521.92386718754.21874119755955E33

1482.5364227849235.9531.08902760556306E15526.91886718756.43966504915941E32

1513.9460661355240.9521.16633456443402E15537.14300781254.76129565445723E33

1545.3557094861245.9511.24634760350499E15544.3233203125-5.20243806333665E33

1576.7653528367250.951.32895326132782E15545.72816406251.84924869561294E34

1608.1749961873255.9491.41401868346645E15564.14722656251.83910749081112E34

1639.5846395379260.9481.50139079445761E15573.04457031254.91848432888553E33

1670.9942828885265.9471.59089547374074E15576.16644531258.67073010556109E33

1702.4039262391270.9461.68233673668841E15582.80042968751.69763768382564E34

1733.8135695897275.9451.77549592188092E15586.78082031252.08604582773557E34

1765.2232129403280.9441.87013088578023E15598.25371093753.12856168136327E34

1796.6328562908285.9431.96597520597034E15608.3998046875-7.71745685418946E33

1828.0424996414290.9422.06273739414158E15614.56550781255.22272047294031E33

1859.452142992295.9412.16010012000663E15617.60933593755.87784230313825E34

1890.8617863426300.942.25771944734585E15635.01378906253.90030736678222E34

1922.2714296932305.9392.35522408338829E15636.57472656251.71994833438966E34

1953.6810730438310.9382.45221464274343E15669.97878906253.00281074182063E34

1985.0907163944315.9372.54826292710633E15678.0176171875-3.57984529504452E33

2016.500359745320.9362.64291122196644E15691.1294921875-4.7744792206996E34

2047.9100030956325.9352.73567161155637E15709.2363671875-2.53732944141682E34

2079.3196464462330.9342.82602531328356E15712.7484765625-1.34472375672211E34

2110.7292897968335.9332.91342203289262E15718.44589843753.54130871679758E34

2142.1389331474340.9322.99727934161113E15724.4555078125-2.4338891524382E34

2173.5485764979345.9313.07698207653575E15725.8603515625-6.02387565228455E33

2204.9582198485350.933.15188176551844E15733.9772265625-1.56174553948118E34

2236.3678631991355.9293.2212960778165E15741.5477734375-6.51876644661365E34

2267.7775065497360.9283.28450830177039E15746.07449218752.79288780242284E34

2299.1871499003365.9273.34076685077698E15754.26941406254.04431247496814E34

2330.5967932509370.9263.38928479882495E15790.1709765625-6.46400394068379E34

2362.0064366015375.9253.42923944685902E15791.49777343757.33006283075971E34

2393.4160799521380.9243.45977192124129E15797.66347656252.28379932137118E34

2424.8257233027385.9233.47998680557355E15803.04871093753.00990958518191E34

2456.2353666533390.9223.48895180714485E15807.02910156256.03401685708637E34

2487.6450100039395.9213.48569745926556E15813.19480468751.51469034920071E35

2519.0546533544400.923.46921686074342E15818.26785156251.53618970338058E35

2550.464296705405.9193.43846545375777E15822.79457031251.06685474515208E34

2581.8739400556410.9183.39236084137706E15835.04792968752.24729098408461E34

2613.2835834062415.9173.32978264596632E15836.5308203125-4.88806071448005E34

2644.6932267568420.9163.2495724097177E15860.10097656253.89016616198039E34

2676.1028701074425.9153.1505335385367E15873.21285156256.82705907258915E34

2707.512513458430.9143.03143129050466E15877.3493359375-8.92426022560673E32

2738.9221568086435.9132.89099281013142E15896.1586328125-5.50464596643106E34

2770.3318001592440.9122.72790720960364E15904.50964843758.04806013072898E34

2801.7414435097445.9112.54082569822142E15905.60230468758.34012682902157E34

2833.1510868603450.912.32836176121044E15920.0409765625-2.78274659762101E34

2864.5607302109455.9092.08909138907877E15921.99214843757.49232210758893E34

2895.9703735615460.9081.82155335868158E15929.5626953125-2.68133454960275E34

2927.3800169121465.9071.52424956714126E15930.10902343758.98510745441769E34

2958.7896602627470.9061.19564541975495E15951.8841015625-1.9795631773164E34

2990.1993036133475.905834170273012947956.02058593751.932913635228E35

3021.6089469639480.904438217933829785969.21050781251.28996125079225E35

3053.0185903145485.9036147216079088.19980.76144531251.26562235926786E34

3084.4282336651490.902-463717444496829992.15628906254.8677783048764E32

3115.8378770157495.901-973085315946528956.1766796875-1.47798126620721E63

3147.2475203662500.9-1.52369863530017E15993.6391796875-8.67746543899855E61

3178.6571637168505.899-2.11733181227703E15

3210.0668070674510.898-2.75579057050448E15

3241.476450418515.897-3.44091102527561E15

3272.8860937686520.896-4.17455869688708E15

3304.2957371192525.895-4.95862745861824E15

3335.7053804698530.894-5.79503841844178E15

3367.1150238204535.893-6.68573873357559E15

3398.524667171540.892-7.63270035700955E15

3429.9343105216545.891-8.63791871516574E15

3461.3439538722550.89-9.70341131587618E15

3492.7535972228555.889-1.08312162858914E16

3524.1632405733560.888-1.20233908371573E16

3555.5728839239565.887-1.3282009661122E16

3586.9825272745570.886-1.46091632503668E16

3618.3921706251575.885-1.60069561468957E16

3649.8018139757580.884-1.74775051164179E16

3681.2114573263585.883-1.902293724802E16

3712.6211006769590.882-2.06453879786442E16

3744.0307440275595.881-2.2346999041808E16

3775.4403873781600.88-2.41299163400524E16

3806.8500307287605.879-2.5996287740641E16

3838.2596740793610.878-2.79482607940347E16

3869.6693174298615.877-2.9987980374749E16

3901.0789607804620.876-3.21175862441947E16

3932.488604131625.875-3.4339210535165E16

3963.8982474816630.874-3.66549751576544E16

3995.3078908322635.873-3.90669891257477E16

4026.7175341828640.872-4.15773458053268E16

4058.1271775334645.871-4.41881200824291E16

4089.536820884650.87-4.69013654520796E16

4120.9464642346655.869-4.97191110274945E16

4152.3561075852660.868-5.26433584695734E16

4183.7657509357665.867-5.56760788366526E16

4215.1753942863670.866-5.88192093545558E16

4246.5850376369675.865-6.20746501069343E16

4277.9946809875680.864-6.5444260646062E16

4309.4043243381685.863-6.89298565241694E16

4340.8139676887690.862-7.25332057455533E16

4372.2236110393695.861-7.62560251396303E16

4403.6332543899700.86-8.00999766552829E16

4435.0428977405705.859-8.40666635767674E16

4466.4525410911710.858-8.81576266615524E16

4497.8621844417715.857-9.23743402005501E16

4529.2718277922720.856-9.67182080011506E16

4560.6814711428725.855-1.01190559293645E17

4592.0911144934730.854-1.0579264456147E17

4623.500757844735.853-1.10525631296065E17

4654.9104011946740.852-1.15390599676827E17

4686.3200445452745.851-1.20388538177026E17

4717.7296878958750.85-1.25520339096325E17

4749.1393312464755.849-1.30786794020784E17

4780.548974597760.848-1.3618858921123E17

4811.9586179476765.847-1.41726300920821E17

4843.3682612982770.846-1.47400390642934E17

4874.7779046487775.845-1.53211200290231E17

4906.1875479993780.844-1.5915894730608E17

4937.5971913499785.843-1.65243719709464E17

4969.0068347005790.842-1.7146547107453E17

5000.4164780511795.841-1.77824015446081E17

5031.8261214017800.84-1.84319022192186E17

5063.2357647523805.839-1.90950010795422E17

5094.6454081029810.838-1.97716345584032E17

5126.0550514535815.837-2.04617230404556E17

5157.4646948041820.836-2.11651703237377E17

5188.8743381547825.835-2.18818630756791E17

5220.2839815052830.834-2.261167028373E17

5251.6936248558835.833-2.33544427007752E17

5283.1032682064840.832-2.41100122855011E17

5314.512911557845.831-2.48781916379169E17

5345.9225549076850.83-2.56587734302018E17

5377.3321982582855.829-2.64515298330694E17

5408.7418416088860.828-2.72562119378572E17

5440.1514849594865.827-2.80725491745379E17

5471.56112831870.826-2.89002487258725E17

5502.9707716606875.825-2.97389949378972E17

5534.3804150112880.824-3.05884487270106E17

5565.7900583617885.823-3.14482469838352E17

5597.1997017123890.822-3.23180019741306E17

5628.6093450629895.821-3.31973007369708E17

5660.0189884135900.82-3.4085704480458E17

5691.4286317641905.819-3.49827479751863E17

5722.8382751147910.818-3.58879389457594E17

5754.2479184653915.817-3.68007574605757E17

5785.6575618159920.816-3.7720655320211E17

5817.0672051665925.815-3.8647055444596E17

5848.476848517930.814-3.95793512593558E17

5879.8864918676935.813-4.05169060815325E17

5911.2961352182940.812-4.14590525050267E17

5942.7057785688945.811-4.24050917860149E17

5974.1154219194950.81-4.33542932286929E17

6005.52506527955.809-4.43058935716274E17

6036.9347086206960.808-4.52590963750567E17

6068.3443519712965.807-4.62130714094178E17

6099.7539953218970.806-4.71669540454948E17

6131.1636386724975.805-4.81198446464515E17

6162.573282023980.804-4.90708079621721E17

6193.9829253735985.803-5.00188725261277E17

6225.3925687241990.802-5.09630300553162E17

6256.8022120747995.801-5.19022348534112E17

6288.21185542531000.8-5.28354032176488E17

6319.62149877591005.799-5.37614128497549E17

6351.03114212651010.798-5.46791022712809E17

6382.44078547711015.797-5.55872702437555E17

6413.85042882771020.796-5.64846751940194E17

6445.26007217831025.795-5.73700346451523E17

6476.66971552891030.794-5.82420246533567E17

6508.07935887951035.793-5.90992792512529E17

6539.489002231040.792-5.99403898979037E17

6570.89864558061045.791-6.07639049361267E17

6602.30828893121050.79-6.15683290573312E17

6633.71793228181055.789-6.23521227744768E17

6665.12757563241060.788-6.31137019034302E17

6696.5372189831065.787-6.38514370533073E17

6727.94686233361070.786-6.45636531260502E17

6759.35650568421075.785-6.52486288259266E17

6790.76614903481080.784-6.59045961791525E17

6822.17579238541085.783-6.65297400642187E17

6853.5854357361090.782-6.712219775345E17

6884.99507908651095.781-6.76800584660592E17

6916.40472243711100.78-6.82013629333681E17

6947.81436578771105.779-6.86841029765452E17

6979.22400913831110.778-6.91262210973076E17

7010.63365248891115.777-6.95256100823008E17

7042.04329583951120.776-6.98801126212905E17

7073.45293919011125.775-7.01875209399062E17

7104.86258254071130.774-7.04455764474293E17

7136.27222589131135.773-7.06519693999628E17

7167.68186924191140.772-7.08043385795993E17

7199.09151259251145.771-7.09002709901268E17

7230.5011559431150.77-7.09373015696691E17

7261.91079929361155.769-7.09129129208881E17

7293.32044264421160.768-7.08245350591017E17

7324.73008599481165.767-7.06695451791285E17

7356.13972934541170.766-7.04452674410531E17

7387.5493726961175.765-7.01489727756136E17

7418.95901604661180.764-6.97778787097674E17

7450.36865939721185.763-6.93291492128895E17

7481.77830274781190.762-6.87998945642206E17

7513.18794609841195.761-6.81871712419035E17

7544.5975894491200.76-6.74879818344134E17

7576.00723279951205.759-6.66992749749657E17

7607.41687615011210.758-6.58179452989986E17

7638.82651950071215.757-6.484083342568E17

7670.23616285131220.756-6.37647259639786E17

7701.64580620191225.755-6.25863555438051E17

7733.05544955251230.754-6.13024008725213E17

7764.46509290311235.753-5.99094868177277E17

7795.87473625371240.752-5.84041845169212E17

7827.28437960431245.751-5.67830115139234E17

7858.69402295491250.75-5.50424319239655E17

7890.10366630551255.749-5.31788566260375E17

7921.5133096561260.748-5.11886434853555E17

7952.92295300661265.747-4.90680976046313E17

7984.33259635721270.746-4.68134716055484E17

8015.74223970781275.745-4.44209659411808E17

8047.15188305841280.744-4.18867292393412E17

8078.5615264091285.743-3.92068586776378E17

8109.97116975961290.742-3.63774003917184E17

8141.38081311021295.741-3.3394349915111E17

8172.79045646081300.74-3.02536526538152E17

8204.20009981141305.739-2.69512043942569E17

8235.60974316191310.738-2.34828518461199E17

8267.01938651251315.737-1.98443932205543E17

8298.42902986311320.736-1.60315788435769E17

8329.83867321371325.735-1.20401118070759E17

8361.24831656431330.734-7.86564865493754E16

8392.65795991491335.733-3.50380010819808E16

8424.06760326551340.7321.04986817232882E16

8455.47724661611345.7315.79983478491118E16

8486.88688996671350.731.07506217461502E17

8518.29653331731355.7291.59067936114468E17

8549.70617666791360.7282.12729565540264E17

8581.11582001851365.7272.6853757403749E17

8612.5254633691370.7263.26538826442734E17

8643.93510671961375.7253.86780573687905E17

8675.34475007021380.7244.4931044192277E17

8706.75439342081385.7235.14176421220566E17

8738.16403677141390.7225.81426853833552E17

8769.5736801221395.7216.5111042201612E17

8800.98332347261400.727.2327613540266E17

8832.39296682321405.7197.9797331792732E17

8863.80261017381410.7188.75251594288373E17

8895.21225352441415.7179.55160875955912E17

8926.62189687491420.7161.03775134670605E18

8958.03154022551425.7151.12307344768261E18

8989.44118357611430.7141.21117786198673E18

9020.85082692671435.7131.30211549877614E18

9052.26047027731440.7121.39593747688122E18

9083.67011362791445.7111.49269510793519E18

9115.07975697851450.711.59243987899066E18

9146.48940032911455.7091.69522343463945E18

9177.89904367971460.7081.8010975586484E18

9209.30868703031465.7071.9101141550378E18

9240.71833038091470.7062.02232522869649E18

9272.12797373141475.7052.13778286542298E18

9303.5376170821480.7042.25653921149069E18

9334.94726043261485.7032.37864645263864E18

9366.35690378321490.7022.50415679257749E18

9397.76654713381495.7012.63312243089259E18

9429.17619048441500.72.76559554048156E18

9460.5858338351505.6992.90162824437244E18

9491.99547718561510.6983.04127259203699E18

9523.40512053621515.6973.1845805351472E18

9554.81476388681520.6963.33160390274004E18

9586.22440723741525.6953.48239437585811E18

9617.63405058791530.6943.63700346160262E18

9649.04369393851535.6933.79548246662842E18

9680.45333728911540.6923.95788247005366E18

9711.86298063971545.6914.12425429580425E18

9743.27262399031550.694.29464848437201E18

9774.68226734091555.6894.4691152640062E18

9806.09191069151560.6884.64770452127986E18

9837.50155404211565.6874.83046577111721E18

9868.91119739271570.6865.01744812620377E18

9900.32084074331575.6855.20870026578551E18

9931.73048409391580.6845.40427040391557E18

9963.14012744441585.6835.6042062570517E18

9994.5497707951590.6825.80855501109508E18

10025.95941414561595.6816.01736328780046E18

10057.36905749621600.686.23067711058836E18

10088.77870084681605.6796.44854186972258E18

10120.18834419741610.6786.67100228695435E18

10151.5979875481615.6776.89810237944085E18

10183.00763089861620.6767.12988542316796E18

10214.41727424921625.6757.3663939156555E18

10245.82691759981630.6747.60766953812385E18

10277.23656095031635.6737.85375311700942E18

10308.64620430091640.6728.10468458483838E18

10340.05584765151645.6718.36050294055737E18

10371.46549100211650.678.62124620913956E18

10402.87513435271655.6698.88695140066404E18

10434.28477770331660.6689.15765446871858E18

10465.69442105391665.6679.43339026822683E18

10497.10406440451670.6669.71419251255163E18

10528.51370775511675.6651.00000937301614E19

10559.92335110571680.6641.02911252204713E19

10591.33299445631685.6631.05873170092091E19

10622.74263780681690.6621.08886978030859E19

10654.15228115741695.6611.1195294943886E19

10685.5619245081700.661.15071343619359E19

10716.97156785861705.6591.18242405288935E19

10748.38121120921710.6581.21466364100412E19

10779.79085455981715.6571.24743434158441E19

10811.20049791041720.6561.28073813529678E19

10842.6101412611725.6551.31457683746665E19

10874.01978461161730.6541.34895209305735E19

10905.42942796221735.6531.38386537157961E19

10936.83907131281740.6521.41931796195894E19

10968.24871466331745.6511.45531096732543E19

10999.65835801391750.651.4918452997503E19

11031.06800136451755.6491.52892167492609E19

11062.47764471511760.6481.56654060678096E19

11093.88728806571765.6471.60470240203946E19

11125.29693141631770.6461.6434071547205E19

11156.70657476691775.6451.68265474057984E19

11188.11621811751780.6441.72244481149849E19

11219.52586146811785.6431.76277678980169E19

11250.93550481871790.6421.80364986253594E19

11282.34514816921795.6411.84506297567751E19

11313.75479151981800.641.88701482829281E19

11345.16443487041805.6391.92950386663698E19

11376.5740782211810.6381.97252827820348E19

11407.98372157161815.6372.01608598571957E19

11439.39336492221820.6362.06017464108164E19

11470.80300827281825.6352.10479161923758E19

11502.21265162341830.6342.14993401203037E19

11533.6222949741835.6332.19559862196557E19

11565.03193832461840.6322.24178195595786E19

11596.44158167521845.6312.28848021899981E19

11627.85122502571850.632.33568930778998E19

11659.26086837631855.6292.38340480432834E19

11690.67051172691860.6282.4316219694299E19

11722.08015507751865.6272.48033573622821E19

11753.48979842811870.6262.52954070359526E19

11784.89944177871875.6252.57923112956225E19

11816.30908512931880.6242.62940092463257E19

11847.71872847991885.6232.68004364512308E19

11879.12837183051890.6222.73115248638747E19

11910.53801518111895.6212.78272027607785E19

11941.94765853171900.622.83473946727876E19

11973.35730188221905.6192.88720213168167E19

12004.76694523281910.6182.94009995266746E19

12036.17658858341915.6172.99342421837015E19

12067.5862319341920.6163.0471658146951E19

12098.99587528461925.6153.10131521832699E19

12130.40551863521930.6143.15586248965406E19

12161.81516198581935.6133.21079726572136E19

12193.22480533641940.6123.26610875309767E19

12224.6344486871945.6113.3217857207362E19

12256.04409203761950.613.37781649281424E19

12287.45373538821955.6093.43418894151387E19

12318.86337873871960.6083.49089047981548E19

12350.27302208931965.6073.54790805422489E19

12381.68266543991970.6063.60522813751722E19

12413.09230879051975.6053.66283672139343E19

12444.50195214111980.6043.72071930922481E19

12475.91159549171985.6033.77886090866011E19

12507.32123884231990.6023.8372460242707E19

12538.73088219291995.6013.89585865017843E19

12570.14052554352000.63.95468226269382E19

12601.55016889412005.5994.01369981284034E19

12632.95981224462010.5984.07289371900748E19

12664.36945559522015.5974.13224585945448E19

12695.77909894582020.5964.19173756493642E19

12727.18874229642025.5954.25134961121638E19

12758.5983856472030.5944.31106221160331E19

12790.00802899762035.5934.37085500953571E19

12821.41767234822040.5924.43070707109571E19

12852.82731569882045.5914.49059687757703E19

12884.23695904942050.594.55050231797706E19

12915.64660242055.5894.61040068160185E19

12947.05624575062060.5884.67026865059688E19

12978.46588910112065.5874.73008229250525E19

13009.87553245172070.5864.78981705282608E19

13041.28517580232075.5854.84944774761757E19

13072.69481915292080.5844.90894855609871E19

13104.10446250352085.5834.96829301321663E19

13135.51410585412090.5825.0274540023304E19

13166.92374920472095.5815.08640374779327E19

13198.33339255532100.585.1451138077196E19

13229.74303590592105.5795.20355506656814E19

13261.15267925652110.5785.2616977279431E19

13292.56232260712115.5775.31951130729414E19

13323.97196595762120.5765.37696462475031E19

13355.38160930822125.5755.43402579788712E19

13386.79125265882130.5745.49066223460329E19

13418.20089600942135.5735.54684062596286E19

13449.610539362140.5725.60252693921115E19

13481.02018271062145.5715.6576864106533E19

13512.42982606122150.575.7122835387442E19

13543.83946941182155.5695.76628207706972E19

13575.24911276242160.5685.81964502758928E19

13606.6587561132165.5675.87233463365725E19

13638.06839946362170.5665.92431237336657E19

13669.47804281412175.5655.97553895275305E19

13700.88768616472180.5646.02597429921573E19

13732.29732951532185.5636.07557755481285E19

13763.70697286592190.5626.12430706987867E19

13795.11661621652195.5616.17212039642804E19

13826.52625956712200.566.21897428188103E19

13857.93590291772205.5596.26482466268755E19

13889.34554626832210.5586.30962665814054E19

13920.75518961892215.5576.35333456416479E19

13952.16483296952220.5566.3959018473303E19

13983.574476322225.5556.43728113879808E19

14014.98411967062230.5546.47742422848961E19

14046.39376302122235.5536.51628205926015E19

14077.80340637182240.5526.5538047211626E19

14109.21304972242245.5516.58994144592303E19

14140.6226930732250.556.62464060138643E19

14172.03233642362255.5496.65784968611687E19

14203.44197977422260.5486.6895153241164E19

14234.85162312482265.5476.71958325974781E19

14266.26126647542270.5466.74799835243978E19

14297.6709098262275.5456.77470457197453E19

14329.08055317652280.5446.7996449935759E19

14360.49019652712285.5436.82276179318652E19

14391.89983987772290.5426.84399624292872E19

14423.30948322832295.5416.86328870667074E19

14454.71912657892300.546.88057863569476E19

14486.12876992952305.5396.89580456459028E19

14517.53841328012310.5386.90890410712805E19

14548.94805663072315.5376.91981395250224E19

14580.35769998132320.5366.92846986153649E19

14611.76734333192325.5356.93480666308588E19

14643.17698668252330.5346.93875825065789E19

14674.5866300332335.5336.9402575791041E19

14705.99627338362340.5326.93923666159065E19

14737.40591673422345.5316.93562656659902E19

14768.81556008482350.536.92935741523738E19

14800.22520343542355.5296.92035837851982E19

14831.6348467862360.5286.90855767516209E19

14863.04449013662365.5276.89388256915704E19

14894.45413348722370.5266.87625936774581E19

14925.86377683782375.5256.85561341977933E19

14957.27342018842380.5246.83186911377282E19

14988.6830635392385.5236.80494987667676E19

15020.09270688952390.5226.77477817241554E19

15051.50235024012395.5216.74127550103704E19

15082.91199359072400.526.70436239763714E19

15114.32163694132405.5196.66395843200882E19

15145.73128029192410.5186.61998220775668E19

15177.14092364252415.5176.57235136275153E19

15208.55056699312420.5166.52098256856981E19

15239.96021034372425.5156.46579153103956E19

15271.36985369432430.5146.40669299066369E19

15302.77949704492435.5136.3436007233419E19

15334.18914039552440.5126.27642754134662E19

15365.5987837462445.5116.20508529459302E19

15397.00842709662450.516.12948487191259E19

15428.41807044722455.5096.04953620293031E19

15459.82771379782460.5085.96514826017522E19

15491.23735714842465.5075.87622906076432E19

15522.6470004992470.5065.78268566964601E19

15554.05664384962475.5055.68442420170004E19

15585.46628720022480.5045.58134982535769E19

15616.87593055082485.5035.47336676525796E19

15648.28557390142490.5025.36037830665509E19

15679.69521725192495.5015.24228679860229E19

15711.10486060252500.55.11899365868489E19

15742.51450395312505.4994.99039937685478E19

15773.92414730372510.4984.85640352105021E19

15805.33379065432515.4974.71690474163888E19

15836.74343400492520.4964.57180077690543E19

15868.15307735552525.4954.42098845900664E19

15899.56272070612530.4944.26436371980844E19

15930.97236405672535.4934.10182159735212E19

15962.38200740732540.4923.93325624246461E19

15993.79165075792545.4913.75856092582104E19

16025.20129410842550.493.57762804489978E19

16056.6109374592555.4893.39034913261303E19

16088.02058080962560.4883.19661486403305E19

16119.43022416022565.4872.99631506609825E19

16150.83986751082570.4862.78933872531957E19

16182.24951086142575.4852.57557399728947E19

16213.6591542122580.4842.35490821642605E19

16245.06879756262585.4832.127227905157E19

16276.47844091322590.4821.89241878461486E19

16307.88808426382595.4811.65036578463642E19

16339.29772761442600.481.40095305587103E19

16370.70737096492605.4791.14406397942314E19

16402.11701431552610.4788.79581180354914E18

16433.52665766612615.4776.07386537901765E18

16464.93630101672620.4763.27361200190888E18

16496.34594436732625.4753.93855949736247E17

16527.75558771792630.474-2.56660555310825E18

16559.16523106852635.473-5.60898220940408E18

16590.57487441912640.472-8.73449050150692E18

16621.98451776972645.471-1.19443535513791E19

16653.39416112032650.47-1.52398009576309E19

16684.80380447092655.469-1.86220686654266E19

16716.21344782142660.468-2.20923987744999E19

16747.6230911722665.467-2.5652039410376E19

16779.03273452262670.466-2.93022445309374E19

16810.44237787322675.465-3.30442737672766E19

16841.85202122382680.464-3.68793922505042E19

16873.26166457442685.463-4.08088704141225E19

16904.6713079252690.462-4.48339838268007E19

16936.08095127562695.461-4.89560129929845E19

16967.49059462622700.46-5.31762431540079E19

16998.90023797682705.459-5.74959640999457E19

17030.30988132742710.458-6.19164699581638E19

17061.71952467792715.457-6.64390589838E19

17093.12916802852720.456-7.10650333398408E19

17124.53881137912725.455-7.57956988930511E19

17155.94845472972730.454-8.06323649848132E19

17187.35809808032735.453-8.55763441843081E19

17218.76774143092740.452-9.06289520787482E19

17250.17738478152745.451-9.57915070230597E19

17281.58702813212750.45-1.01065329898893E20

17312.99667148272755.449-1.06451743854356E20

17344.40631483332760.448-1.11952074069203E20

17375.81595818382765.447-1.17567647475232E20

17407.22560153442770.446-1.23299792499959E20

17438.6352448852775.445-1.29149838801128E20

17470.04488823562780.444-1.35119116975346E20

17501.45453158622785.443-1.41208958302382E20

17532.86417493682790.442-1.474206944244E20

17564.27381828742795.441-1.53755657077535E20

17595.6834616382800.44-1.60215177800581E20

17627.09310498862805.439-1.66800587597618E20

17658.50274833922810.438-1.73513216669404E20

17689.91239168982815.437-1.80354394074909E20

17721.32203504032820.436-1.87325447400973E20

17752.73167839092825.435-1.9442770247118E20

17784.14132174152830.434-2.01662482988204E20

17815.55096509212835.433-2.09031110199534E20

17846.96060844272840.432-2.16534902550203E20

17878.37025179332845.431-2.24175175348388E20

17909.77989514392850.43-2.31953240408468E20

17941.18953849452855.429-2.39870405656437E20

17972.59918184512860.428-2.47927974828493E20

18004.00882519572865.427-2.56127247010567E20

18035.41846854632870.426-2.64469516355355E20

18066.82811189682875.425-2.72956071612295E20

18098.23775524742880.424-2.81588195788743E20

18129.6473985982885.423-2.90367165742072E20

18161.05704194862890.422-2.99294251742467E20

18192.46668529922895.421-3.08370717136337E20

18223.87632864982900.42-3.17597817836159E20

18255.28597200042905.419-3.26976801979708E20

18286.6956153512910.418-3.36508909453195E20

18318.10525870162915.417-3.46195371482036E20

18349.51490205222920.416-3.56037410159289E20

18380.92454540282925.415-3.66036238042753E20

18412.33418875332930.414-3.7619305765335E20

18443.74383210392935.413-3.86509061049457E20

18475.15347545452940.412-3.96985429341287E20

18506.56311880512945.411-4.07623332225288E20

18537.97276215572950.41-4.18423927509778E20

18569.38240550632955.409-4.29388360600416E20

18600.79204885692960.408-4.40517764043747E20

18632.20169220752965.407-4.51813257013197E20

18663.61133555812970.406-4.63275944786482E20

18695.02097890872975.405-4.74906918254862E20

18726.43062225922980.404-4.86707253404278E20

18757.84026560982985.403-4.98678010766302E20

18789.24990896042990.402-5.10820234898908E20

18820.6595523112995.401-5.23134953873994E20

18852.06919566163000.4-5.3562317866748E20

18883.47883901223005.399-5.48285902670411E20

18914.88848236283010.398-5.61124101087964E20

18946.29812571343015.397-5.74138730395428E20

18977.7077690643020.396-5.87330727767097E20

19009.11741241463025.395-6.00701010467218E20

19040.52705576523030.394-6.14250475287269E20

19071.93669911573035.393-6.27979997953999E20

19103.34634246633040.392-6.41890432519365E20

19134.75598581693045.391-6.55982610763412E20

19166.16562916753050.39-6.70257341571141E20

19197.57527251813055.389-6.84715410288313E20

19228.98491586873060.388-6.99357578172001E20

19260.39455921933065.387-7.1418458164463E20

19291.80420256993070.386-7.29197131757185E20

19323.21384592053075.385-7.44395913483199E20

19354.62348927113080.384-7.59781585040741E20

19386.03313262173085.383-7.7535477732783E20

19417.44277597223090.382-7.91116093157393E20

19448.85241932283095.381-8.07066106594018E20

19480.26206267343100.38-8.23205362335199E20

19511.6717060243105.379-8.39534374953559E20

19543.08134937463110.378-8.56053628244316E20

19574.49099272523115.377-8.7276357448845E20

19605.90063607583120.376-8.89664633752785E20

19637.31027942643125.375-9.06757193187459E20

19668.7199227773130.374-9.24041606334647E20

19700.12956612763135.373-9.41518192276815E20

19731.53920947823140.372-9.59187235060794E20

19762.94885282873145.371-9.77048982839699E20

19794.35849617933150.37-9.95103647141353E20

19825.76813952993155.369-1.01335140211655E21

19857.17778288053160.368-1.03179238384795E21

19888.58742623113165.367-1.05042668945727E21

19919.99706958173170.366-1.06925437641914E21

19951.40671293233175.365-1.08827546170271E21

19982.81635628293180.364-1.10748992107005E21

20014.22599963353185.363-1.12689768820777E21

20045.63564298413190.362-1.14649865392833E21

20077.04528633473195.361-1.16629266539264E21

20108.45492968523200.36-1.18627952532446E21

20139.86457303583205.359-1.20645899102878E21

20171.27421638643210.358-1.22683077374904E21

20202.6838597373215.357-1.24739453777438E21

20234.09350308763220.356-1.2681498995082E21

20265.50314643823225.355-1.28909642668265E21

20296.91278978883230.354-1.31023363756529E21

20328.32243313943235.353-1.33156100000772E21

20359.732076493240.352-1.35307793062229E21

20391.14171984063245.351-1.37478379380974E21

20422.55136319113250.35-1.39667790108027E21

20453.96100654173255.349-1.41875950992631E21

20485.37064989233260.348-1.44102782312887E21

20516.78029324293265.347-1.46348198774988E21

20548.18993659353270.346-1.48612109426696E21

20579.59957994413275.345-1.50894417558184E21

20611.00922329473280.344-1.53195020629363E21

20642.41886664533285.343-1.55513810147976E21

20673.82850999593290.342-1.57850671612333E21

20705.23815334653295.341-1.60205484384643E21

20736.64779669713300.34-1.62578121620305E21

20768.05744004763305.339-1.64968450156591E21

20799.46708339823310.338-1.67376330437204E21

20830.87672674883315.337-1.6980161639102E21

20862.28637009943320.336-1.72244155355374E21

20893.696013453325.335-1.74703787982026E21

20925.10565680063330.334-1.77180348108303E21

20956.51530015123335.333-1.79673662713137E21

20987.92494350183340.332-1.82183551760393E21

21019.33458685243345.331-1.84709828136898E21

21050.7442302033350.33-1.87252297548717E21

21082.15387355363355.329-1.89810758403442E21

21113.56351690413360.328-1.92385001731741E21

21144.97316025473365.327-1.94974811080734E21

21176.38280360533370.326-1.97579962391932E21

21207.79244695593375.325-2.00200223929125E21

21239.20209030653380.324-2.02835356151312E21

21270.61173365713385.323-2.05485111645281E21

21302.02137700773390.322-2.08149234973013E21

21333.43102035833395.321-2.10827462604695E21

21364.84066370893400.32-2.13519522794952E21

21396.25030705953405.319-2.16225135513717E21

21427.65995041013410.318-2.18944012279954E21

21459.06959376063415.317-2.21675856104999E21

21490.47923711123420.316-2.24420361396739E21

21521.88888046183425.315-2.27177213784411E21

21553.29852381243430.314-2.29946090097066E21

21584.7081671633435.313-2.32726658199031E21

21616.11781051363440.312-2.35518576902786E21

21647.52745386423445.311-2.38321495866355E21

21678.93709721483450.31-2.41135055482783E21

21710.34674056543455.309-2.43958886753312E21

21741.7563839163460.308-2.46792611200336E21

21773.16602726653465.307-2.49635840763391E21

21804.57567061713470.306-2.52488177675311E21

21835.98531396773475.305-2.55349214365681E21

21867.39495731833480.304-2.58218533309151E21

21898.80460066893485.303-2.61095707003104E21

21930.21424401953490.302-2.63980297761967E21

21961.62388737013495.301-2.66871857670544E21

21993.03353072073500.3-2.69769928443269E21

22024.44317407133505.299-2.72674041355081E21

22055.85281742193510.298-2.75583717053936E21

22087.26246077253515.297-2.78498465526302E21

22118.6721041233520.296-2.81417785947576E21

22150.08174747363525.295-2.84341166571602E21

22181.49139082423530.294-2.87268084654176E21

22212.90103417483535.293-2.90198006298818E21

22244.31067752543540.292-2.93130386351487E21

22275.7203208763545.291-2.96064668319417E21

22307.12996422663550.29-2.99000284227776E21

22338.53960757723555.289-3.01936654538179E21

22369.94925092783560.288-3.04873187993855E21

22401.35889427843565.287-3.07809281561966E21

22432.7685376293570.286-3.10744320276378E21

22464.17818097953575.285-3.13677677140212E21

22495.58782433013580.284-3.16608713061913E21

22526.99746768073585.283-3.19536776658459E21

22558.40711103133590.282-3.22461204173366E21

22589.81675438193595.281-3.25381319427996E21

22621.22639773253600.28-3.28296433632329E21

22652.63604108313605.279-3.31205845337281E21

22684.04568443373610.278-3.3410884023128E21

22715.45532778433615.277-3.37004691148766E21

22746.86497113493620.276-3.39892657870632E21

22778.27461448553625.275-3.42771987038654E21

22809.6842578363630.274-3.45641912073464E21

22841.09390118663635.273-3.48501653039755E21

22872.50354453723640.272-3.51350416540097E21

22903.91318788783645.271-3.54187395578553E21

22935.32283123843650.27-3.57011769523727E21

22966.7324745893655.269-3.59822703935523E21

22998.14211793963660.268-3.62619350462658E21

23029.55176129023665.267-3.65400846780171E21

23060.96140464083670.266-3.68166316436989E21

23092.37104799143675.265-3.70914868783514E21

23123.78069134193680.264-3.73645598828103E21

23155.19033469253685.263-3.76357587140369E21

23186.59997804313690.262-3.79049899778448E21

23218.00962139373695.261-3.81721588177211E21

23249.41926474433700.26-3.84371688980536E21

23280.82890809493705.259-3.86999224014717E21

23312.23855144553710.258-3.89603200186941E21

23343.64819479613715.257-3.9218260927139E21

23375.05783814673720.256-3.94736427975959E21

23406.46748149733725.255-3.97263617692372E21

23437.87712484793730.254-3.9976312448317E21

23469.28676819843735.253-4.02233878948553E21

23500.6964115493740.252-4.04674796128227E21

23532.10605489963745.251-4.0708477545338E21

23563.51569825023750.25-4.09462700526859E21

23594.92534160083755.249-4.1180743915668E21

23626.33498495143760.248-4.14117843207313E21

23657.7446283023765.247-4.16392748442973E21

23689.15427165263770.246-4.18630974609137E21

23720.56391500323775.245-4.20831325125212E21

23751.97355835383780.244-4.22992587177582E21

23783.38320170443785.243-4.25113531391094E21

23814.79284505493790.242-4.27192912079821E21

23846.20248840553795.241-4.29229466870244E21

23877.61213175613800.24-4.31221916688179E21

23909.02177510673805.239-4.33168965705881E21

23940.43141845733810.238-4.35069301354528E21

23971.84106180793815.237-4.36921593936397E21

24003.25070515853820.236-4.38724496945358E21

24034.66034850913825.235-4.40476646544738E21

24066.06999185973830.234-4.42176661911189E21

24097.47963521033835.233-4.43823144814624E21

24128.88927856093840.232-4.45414679786502E21

24160.29892191143845.231-4.46949833876952E21

24191.7085652623850.23-4.48427156666386E21

24223.11820861263855.229-4.49845180067759E21

24254.52785196323860.228-4.51202418556257E21

24285.93749531383865.227-4.5249736865417E21

24317.34713866443870.226-4.53728509230233E21

24348.7567820153875.225-4.54894301303302E21

24380.16642536563880.224-4.55993187828974E21

24411.57606871623885.223-4.57023593939791E21

24442.98571206683890.222-4.57983926570036E21

24474.39535541733895.221-4.58872574698141E21

24505.80499876793900.22-4.59687908946194E21

24537.21464211853905.219-4.60428281821058E21

24568.62428546913910.218-4.61092027437942E21

24600.03392881973915.217-4.61677461613307E21

24631.44357217033920.216-4.6218288167894E21

24662.85321552093925.215-4.62606566690502E21

24694.26285887153930.214-4.62946776977261E21

24725.67250222213935.213-4.63201754412923E21

24757.08214557273940.212-4.63369722283322E21

24788.49178892333945.211-4.63448885071567E21

24819.90143227383950.21-4.63437428821495E21

24851.31107562443955.209-4.63333520616218E21

24882.7207189753960.208-4.63135308864263E21

24914.13036232563965.207-4.62840923107614E21

24945.54000567623970.206-4.62448474075574E21

24976.94964902683975.205-4.61956053677328E21

25008.35929237743980.204-4.61361734737146E21

25039.7689357283985.203-4.6066357135241E21

25071.17857907863990.202-4.59859598590237E21

25102.58822242923995.201-4.58947832376057E21

25133.99786577984000.2-4.57926269862655E21

25165.40750913034005.199-4.56792889044603E21

25196.81715248094010.198-4.55545648727904E21

25228.22679583154015.197-4.54182489116062E21

25259.63643918214020.196-4.52701330887849E21

25291.04608253274025.195-4.5110007580002E21

25322.45572588334030.194-4.49376606646368E21

25353.86536923394035.193-4.47528786873398E21

25385.27501258454040.192-4.45554461249597E21

25416.68465593514045.191-4.43451455070794E21

25448.09429928574050.19-4.41217574729043E21

25479.50394263634055.189-4.38850607462978E21

25510.91358598684060.188-4.36348321406614E21

25542.32322933744065.187-4.3370846607374E21

25573.7328726884070.186-4.30928771276082E21

25605.14251603864075.185-4.28006948338137E21

25636.55215938924080.184-4.24940689303863E21

25667.96180273984085.183-4.21727667422685E21

25699.37144609044090.182-4.18365536877752E21

25730.7810894414095.181-4.14851932984854E21

25762.19073279164100.18-4.11184472332166E21

25793.60037614224105.179-4.07360752396197E21

25825.01001949284110.178-4.03378352126821E21

25856.41966284334115.177-3.99234831686287E21

25887.82930619394120.176-3.94927732138763E21

25919.23894954454125.175-3.90454576607373E21

25950.64859289514130.174-3.85812868801316E21

25982.05823624574135.173-3.81000094827083E21

26013.46787959634140.172-3.76013721412085E21

26044.87752294694145.171-3.70851197338661E21

26076.28716629754150.17-3.65509953053212E21

26107.69680964814155.169-3.599874006739E21

26139.10645299874160.168-3.54280933986249E21

26170.51609634924165.167-3.48387928658862E21

26201.92573969984170.166-3.4230574260328E21

26233.33538305044175.165-3.36031715577077E21

26264.7450264014180.164-3.29563169598943E21

26296.15466975164185.163-3.2289740858986E21

26327.56431310224190.162-3.16031719224803E21

26358.97395645284195.161-3.08963370342604E21

26390.38359980344200.16-3.01689613507765E21

26421.7932431544205.159-2.94207682773505E21

26453.20288650464210.158-2.86514795157248E21

26484.61252985524215.157-2.78608150260377E21

26516.02217320574220.156-2.70484930977092E21

26547.43181655634225.155-2.62142303247131E21

26578.84145990694230.154-2.53577416401434E21

26610.25110325754235.153-2.44787402730548E21

26641.66074660814240.152-2.35769378676994E21

26673.07038995874245.151-2.26520443891637E21

26704.48003330934250.15-2.1703768218209E21

26735.88967665994255.149-2.07318161121288E21

26767.29932001054260.148-1.9735893255413E21

26798.70896336114265.147-1.87157032663727E21

26830.11860671174270.146-1.76709482078536E21

26861.52825006224275.145-1.6601328595574E21

26892.93789341284280.144-1.5506543443444E21

26924.34753676344285.143-1.43862902510678E21

26955.7571801144290.142-1.32402650663076E21

26987.16682346464295.141-1.20681624382942E21

27018.57646681524300.14-1.08696755186243E21

27049.98611016584305.139-9.64449598364832E20

27081.39575351644310.138-8.3923141692845E20

27112.8053968674315.137-7.11281898713239E20

27144.21504021764320.136-5.80569799707949E20

27175.62468356824325.135-4.47063742221545E20

27207.03432691874330.134-3.10732217899886E20

27238.44397026934335.133-1.71543591987945E20

27269.85361361994340.132-2.94661011071597E19

27301.26325697054345.1311.15532147537522E20

27332.67290032114350.132.63483160527184E20

27364.08254367174355.1294.14419064359471E20

27395.49218702234360.1285.68372110927893E20

27426.90183037294365.1277.25374656665465E20

27458.31147372354370.1268.85459172000075E20

27489.72111707414375.1251.04865823565775E21

27521.13076042474380.1241.21500453455152E21

27552.54040377524385.1231.38453085469004E21

27583.95004712584390.1221.55727008497438E21

27615.35969047644395.1211.73325521189957E21

27646.7693338274400.121.91251930910287E21

27678.17897717764405.1192.09509554999578E21

27709.58862052824410.1182.28101718972409E21

27740.99826387884415.1172.47031757039755E21

27772.40790722944420.1162.6630301111465E21

27803.817550584425.1152.859188318943E21

27835.22719393064430.1143.05882576015263E21

27866.63683728114435.1133.2619760851779E21

27898.04648063174440.1123.46867300460399E21

27929.45612398234445.1113.67895029542383E21

27960.86576733294450.113.89284179197673E21

27992.27541068354455.1094.11038138987937E21

28023.68505403414460.1084.33160303198609E21

28055.09469738474465.1074.55654071511483E21

28086.50434073534470.1064.78522847525845E21

28117.91398408594475.1055.01770039455171E21

28149.32362743654480.1045.2539905890623E21

28180.73327078714485.1035.49413320670726E21

28212.14291413764490.1025.73816242583344E21

28243.55255748824495.1015.98611244608216E21

28274.96220083884500.16.23801749615342E21

28306.37184418944505.0996.49391180378404E21

28337.781487544510.0986.7538296220469E21

28369.19113089064515.0977.01780520741108E21

28400.60077424124520.0967.28587282085863E21

28432.01041759184525.0957.55806670401739E21

28463.42006094244530.0947.83442112302228E21

28494.8297042934535.0938.11497029420486E21

28526.23934764364540.0928.39974844371177E21

28557.64899099414545.0918.68878976494801E21

28589.05863434474550.098.98212843550348E21

28620.46827769534555.0899.27979858391523E21

28651.87792104594560.0889.5818343139115E21

28683.28756439654565.0879.88826967954498E21

28714.69720774714570.0861.01991386907257E22

28746.10685109774575.0851.0514475304701E22

28777.51649444834580.0841.08343134147511E22

28808.92613779894585.0831.11586868742849E22

28840.33578114954590.0821.148762941662E22

28871.74542450014595.0811.18211747440509E22

28903.15506785064600.081.21593564724537E22

28934.56471120124605.0791.25022081133579E22

28965.97435455184610.0781.2849763096185E22

28997.38399790244615.0771.32020547486573E22

29028.7936412534620.0761.35591162873119E22

29060.20328460364625.0751.39209808407607E22

29091.61292795424630.0741.42876813927504E22

29123.02257130484635.0731.46592508179605E22

29154.43221465544640.0721.50357218554662E22

29185.8418580064645.0711.54171271125101E22

29217.25150135654650.071.58034990507739E22

29248.66114470714655.0691.61948699860521E22

29280.07078805774660.0681.65912720772496E22

29311.48043140834665.0671.69927372958763E22

29342.89007475894670.0661.73992974952684E22

29374.29971810954675.0651.78109843030689E22

29405.70936146014680.0641.82278291962556E22

29437.11900481074685.0631.8649863420385E22

29468.52864816134690.0621.90771180776108E22

29499.93829151194695.0611.95096240243547E22

29531.34793486254700.061.9947411911408E22

29562.7575782134705.0592.03905121860496E22

29594.16722156364710.0582.08389550393074E22

29625.57686491424715.0572.12927704490719E22

29656.98650826484720.0562.17519881579141E22

29688.39615161544725.0552.22166376204665E22

29719.8057949664730.0542.26867480756574E22

29751.21543831664735.0532.31623484774525E22

29782.62508166724740.0522.36434674923019E22

29814.03472501784745.0512.4130133507386E22

29845.44436836844750.052.46223746539311E22

29876.8540117194755.0492.51202187256711E22

29908.26365506954760.0482.56236932003274E22

29939.67329842014765.0472.61328252830515E22

29971.08294177074770.0462.66476418305919E22

30002.49258512134775.0452.71681693596214E22

30033.90222847194780.0442.7694434061293E22

30065.31187182254785.0432.82264617450293E22

30096.72151517314790.0422.87642779083375E22

30128.13115852374795.0412.93079076329869E22

30159.54080187434800.042.98573756601345E22

30190.95044522494805.0393.04127063232053E22

30222.36008857554810.0383.09739235585094E22

30253.7697319264815.0373.15410509171135E22

30285.17937527664820.0363.21141115085099E22

30316.58901862724825.0353.26931280288435E22

30347.99866197784830.0343.32781227480695E22

30379.40830532844835.0333.38691174757526E22

30410.8179486794840.0323.4466133599578E22

30442.22759202964845.0313.50691920211221E22

30473.63723538024850.033.56783131433779E22

30505.04687873084855.0293.62935169276141E22

30536.45652208144860.0283.69148228425823E22

30567.8661654324865.0273.75422498111482E22

30599.27580878254870.0263.81758162833918E22

30630.68545213314875.0253.88155401540668E22

30662.09509548374880.0243.94614388324408E22

30693.50473883434885.0234.0113529134333E22

30724.91438218494890.0224.07718273017978E22

30756.32402553554895.0214.14363490693449E22

30787.73366888614900.024.21071095663488E22

30819.14331223674905.0194.27841233405723E22

30850.55295558734910.0184.34674043204269E22

30881.96259893794915.0174.41569658315985E22

30913.37224228844920.0164.48528205981208E22

30944.7818856394925.0154.55549806682232E22

30976.19152898964930.0144.6263457489892E22

31007.60117234024935.0134.69782618241463E22

31039.01081569084940.0124.76994037853377E22

31070.42045904144945.0114.84268927921705E22

31101.8301023924950.014.91607375638965E22

31133.23974574264955.0094.990094612595E22

31164.64938909324960.0085.06475258358674E22

31196.05903244384965.0075.1400483229932E22

31227.46867579444970.0065.2159824166638E22

31258.87831914494975.0055.29255537590453E22

31290.28796249554980.0045.36976763245451E22

31321.69760584614985.0035.44761954203067E22

31353.10724919674990.0025.5261113795165E22

31384.51689254734995.0015.60524334503299E22

1051.3863414014167.3333333333-403847574428219

1052.4314445575167.4996666667-405655137362965

1053.4765477136167.666-407458998752214

1054.5216508697167.8323333333-409259145337230

1055.5667540258167.9986666667-411055563861153

1056.6118571818168.165-412848241069044

1057.656960338168.3313333333-414637163707933

1058.702063494168.4976666667-416422318526849

1059.7471666501168.664-418203692276870

1060.7922698062168.8303333333-419981271711161

1061.8373729623168.9966666667-421755043585021

1062.8824761184169.163-423524994655914

1063.9275792745169.3293333333-425291111683526

1064.9726824306169.4956666667-427053381429796

1066.0177855867169.662-428811790658956

1067.0628887428169.8283333333-430566326137589

1068.1079918989169.9946666667-432316974634651

1069.153095055170.161-434063722921524

1070.1981982111170.3273333333-435806557772059

1071.2433013672170.4936666667-437545465962614

1072.2884045233170.66-439280434272095

1073.3335076794170.8263333333-441011449482004

1074.3786108355170.9926666667-442738498376478

1075.4237139915171.159-444461567742325

1076.4688171476171.3253333333-446180644369082

1077.5139203037171.4916666667-447895715049042

1078.5590234598171.658-449606766577297

1079.6041266159171.8243333333-451313785751796

1080.649229772171.9906666667-453016759373367

1081.6943329281172.157-454715674245778

1082.7394360842172.3233333333-456410517175759

1083.7845392403172.4896666667-458101274973062

1084.8296423964172.656-459787934450502

1085.8747455525172.8223333333-461470482423985

1086.9198487086172.9886666667-463148905712564

1087.9649518647173.155-464823191138480

1089.0100550208173.3213333333-466493325527198

1090.0551581769173.4876666667-468159295707459

1091.100261333173.654-469821088511309

1092.1453644891173.8203333333-471478690774158

1093.1904676451173.9866666667-473132089334812

1094.2355708013174.153-474781271035515

1095.2806739573174.3193333333-476426222722001

1096.3257771134174.4856666667-478066931243525

1097.3708802695174.652-479703383452913

1098.4159834256174.8183333333-481335566206605

1099.4610865817174.9846666667-482963466364694

1100.5061897378175.151-484587070790970

1101.5512928939175.3173333333-486206366352968

1102.59639605175.4836666667-487821339922002

1103.6414992061175.65-489431978373213

1104.6866023622175.8163333333-491038268585614

1105.7317055183175.9826666667-492640197442126

1106.7768086744176.149-494237751829629

1107.8219118305176.3153333333-495830918638999

1108.8670149866176.4816666667-497419684765156

1109.9121181427176.648-499004037107099

1110.9572212988176.8143333333-500583962567959

1112.0023244548176.9806666667-502159448055037

1113.0474276109177.147-503730480479845

1114.092530767177.3133333333-505297046758153

1115.1376339231177.4796666667-506859133810029

1116.1827370792177.646-508416728559890

1117.2278402353177.8123333333-509969817936534

1118.2729433914177.9786666667-511518388873186

1119.3180465475178.145-513062428307551

1120.3631497036178.3113333333-514601923181844

1121.4082528597178.4776666667-516136860442841

1122.4533560158178.644-517667227041923

1123.4984591719178.8103333333-519193009935115

1124.543562328178.9766666667-520714196083130

1125.5886654841179.143-522230772451415

1126.6337686402179.3093333333-523742726010192

1127.6788717963179.4756666667-525250043734508

1128.7239749524179.642-526752712604266

1129.7690781085179.8083333333-528250719604279

1130.8141812645179.9746666667-529744051724309

1131.8592844206180.141-531232695959113

1132.9043875767180.3073333333-532716639308487

1133.9494907328180.4736666667-534195868777301

1134.9945938889180.64-535670371375556

1136.039697045180.8063333333-537140134118420

1137.0848002011180.9726666667-538605144026269

1138.1299033572181.139-540065388124740

1139.1750065133181.3053333333-541520853444760

1140.2201096694181.4716666667-542971527022611

1141.2652128255181.638-544417395899953

1142.3103159816181.8043333333-545858447123882

1143.3554191377181.9706666667-547294667746959

1144.4005222938182.137-548726044827274

1145.4456254499182.3033333333-550152565428471

1146.490728606182.4696666667-551574216619803

1147.5358317621182.636-552990985476171

1148.5809349181182.8023333333-554402859078174

1149.6260380742182.9686666667-555809824512143

1150.6711412303183.135-557211868870192

1151.7162443864183.3013333333-558608979250259

1152.7613475425183.4676666667-560001142756156

1153.8064506986183.634-561388346497604

1154.8515538547183.8003333333-562770577590282

1155.8966570108183.9666666667-564147823155875

1156.9417601669184.133-565520070322105

1157.986863323184.2993333333-566887306222793

1159.0319664791184.4656666667-568249517997886

1160.0770696352184.632-569606692793514

1161.1221727913184.7983333333-570958817762029

1162.1672759474184.9646666667-572305880062046

1163.2123791035185.131-573647866858495

1164.2574822596185.2973333333-574984765322654

1165.3025854156185.4636666667-576316562632211

1166.3476885718185.63-577643245971287

1167.3927917278185.7963333333-578964802530497

1168.4378948839185.9626666667-580281219506981

1169.48299804186.129-581592484104469

1170.5281011961186.2953333333-582898583533296

1171.5732043522186.4616666667-584199505010473

1172.6183075083186.628-585495235759716

1173.6634106644186.7943333333-586785763011495

1174.7085138205186.9606666667-588071074003082

1175.7536169766187.127-589351155978588

1176.7987201327187.2933333333-590625996189013

1177.8438232888187.4596666667-591895581892289

1178.8889264449187.626-593159900353327

1179.934029601187.7923333333-594418938844057

1180.9791327571187.9586666667-595672684643472

1182.0242359132188.125-596921125037680

1183.0693390692188.2913333333-598164247319945

1184.1144422254188.4576666667-599402038790724

1185.1595453814188.624-600634486757724

1186.2046485375188.7903333333-601861578535937

1187.2497516936188.9566666667-603083301447694

1188.2948548497189.123-604299642822706

1189.3399580058189.2893333333-605510589998094

1190.3850611619189.4556666667-606716130318461

1191.430164318189.622-607916251135919

1192.4752674741189.7883333333-609110939810134

1193.5203706302189.9546666667-610300183708381

1194.5654737863190.121-611483970205573

1195.6105769424190.2873333333-612662286684327

1196.6556800985190.4536666667-613835120534986

1197.7007832546190.62-615002459155687

1198.7458864107190.7863333333-616164289952380

1199.7909895668190.9526666667-617320600338901

1200.8360927229191.119-618471377736991

1201.8811958789191.2853333333-619616609576363

1202.926299035191.4516666667-620756283294729

1203.9714021911191.618-621890386337862

1205.0165053472191.7843333333-623018906159621

1206.0616085033191.9506666667-624141830222018

1207.1067116594192.117-625259145995247

1208.1518148155192.2833333333-62637084095773