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These are answers submitted by acer

From the Help page for topic I,

"

I is implemented as Complex(1), and therefore, unlike many other Maple constants, type(I, name) returns false."

It is not a protected name, because it is not implemented to evaluate as a name.

That distinguishes it from other initially known names and constants.

dismantle(I);

COMPLEX(2)
   INTPOS(2): 1

type(I, name);

             false

Complex(1);

               I

dismantle(Pi);

NAME(4): Pi #[protected]

Pi;                                                                                
               Pi

[edit] Also,

op(0,I), [op(I)];

           Complex, [1]

It is like that by design. From one point of view this is beneficial because it allows you to construct an exploration for which you can subsequently redefine variables or assigned names.

If you upload and attach your worksheet then we may be able to show you more than one way to work with the design, so that your example works more as you want.

You mentioned "variables", which could mean parameters (in the Explore sense) or additional variables with assigned values. An explicit example from you would make you meaning more clear. Explore parameters have to be unassigned global names -- but even for them it is often possible to programmatically work around some issues.

In one sense this is part of a broader Maple worksheet subject: execution of previous parts can be re-executed out-of-order, and if that is the intention then the burden is on the user to set up examples which guard against collision in the namespace. [edit. I see that Carl made this same point, while I was typing.]

I have not yet pinpointed the precise cause of the problem.

But here is something quick, in my Maple 2020.1.

restart;

(-1)^v*(alpha*GAMMA(k-v)/v!/GAMMA(k-2*v-1)/GAMMA(k-2*v))^(1/2)
*exp(-1/2*k*exp(-alpha*x))*(k*exp(-alpha*x))^(1/2*k-v-1/2)
*LaguerreL(v,k-2*v-1,k/exp(alpha*x))/binomial(k-v-1,v):

CodeTools:-Usage(
  seq((evalf[15](Int(unapply(simplify(eval(%, [k=30.5, v=j, alpha=2.5]))^2, x),
                     -1..infinity))), j=0..5) );

memory used=27.47MiB, alloc change=34.00MiB, cpu time=260.00ms, real time=261.00ms, gc time=24.22ms

     0.999999999999992, 0.999999999999994, 1.00000000000001,
     1.00000000000001, 1.00000000000001, 0.999999999999959

Here is a way to substitute names c[i] for the _Cn constants, which also forces the reordering so that specified names c[i] are first in the product subterms. It uses subs for the substitution, as opposed to alias.

This uses sort, and can forcibly correct the example even when the "uniquified" expression (stored by the kernel as the sole representation) has been inadvertantly reordered in a manner contrary to your goal.

sorting_fun.mw

Unfortunately inlining of uploaded worksheets is currently broken on Mapleprimes.

It also finds the _Cn names as they appear, alleviating need to hard code a fixed number of replacements up front. (Other Answers hard-coded 10 substitutions.)

If you come across an example which it cannot handle directly then the procedure could be adjusted accordingly.

Some of the other suggestions (in other Answers) are not always assured to produce the desired ordering of the terms, eg. in cases where the misordered expression have previously existed in the session. So the ability to force the ordering seems useful.

The vertical view is negative, ie. the squares are placed with position at negative y-values. That why you don't see your y-tickmarks, which you've created to be placed at positive vertical postions. They are out of viewing range.

You can adjust this, naturally.

restart;

M := LinearAlgebra:-RandomMatrix(20,density=0.25,generator=0 .. 1):

plots:-sparsematrixplot(
   M, matrixview
  ,axis[1]=[tickmarks=[seq(i=i-1, i in [seq](1..20, 5))]]
  ,axis[2]=[tickmarks=[seq(-j=j-1, j in [seq](1..20, 5))]]
);

 

Download sparsematrixplot_yticks.mw

If you are allowed to let Maple do all the work, then you could get by with something short, eg.

is( sin(2*x) = 2*sin(x)*cos(x) );

           true

simplify( sin(2*x) - 2*sin(x)*cos(x) );

             0

Let's suppose that you don't want the work to be hidden in calls to combine and expand or other powerful simplification commands, but that you do know and are allowed to use the sum rule for sin(A+B). Then you can get by with only making various kinds of substitutions.

restart;

This identity you should know, sometimes called a sum rule.

rule := sin(x + y) = sin(x)*cos(y) + cos(x)*sin(y);

sin(x+y) = sin(x)*cos(y)+cos(x)*sin(y)

expr := sin(2*x);

sin(2*x)

Turn one of the two x's into y.

eval( expr, x = (x+y)/2 );

sin(x+y)

applyrule( rule, % );

sin(x)*cos(y)+cos(x)*sin(y)

Turn y back into x.

eval( %, y = x );

2*sin(x)*cos(x)


Now the other direction, for fun...

Here we'll use the reverse of the rule.

revrule := (rhs = lhs)(rule)

sin(x)*cos(y)+cos(x)*sin(y) = sin(x+y)

expr := 2*sin(x)*cos(x);

2*sin(x)*cos(x)

Change some of the x's into y's.
Take half of expr and change one of the x's into y.
Take the other half of expr and change another of the x's into y.

eval( expr/2, cos(x)=cos(y) ) + eval( expr/2, sin(x)=sin(y) );

sin(x)*cos(y)+cos(x)*sin(y)

Use the reverse of the given sum rule.

applyrule( revrule, % );

sin(x+y)

Turn y back into x.

eval( %, y = x );

sin(2*x)

Download double_angle_sine.mw

Your expression assigned to A is a product of terms.

I believe that the only one of those multiplicative terms which attains zero for real-valued lambda (if evaluated at adequate working precision to avoid spurious roots due to numeric roundoff error) is this one. This behaves well even at default Digits=10.

restart;
p:=-.1141301418e17*lambda^9+.9737052862e16*lambda^8
   -.3682582968e16*lambda^7+.8102838405e15*lambda^6
   -.1142983789e15*lambda^5+.1071802621e14*lambda^4
   -.6680654662e12*lambda^3+.2668788927e11*lambda^2
   -619949976.6*lambda+6379681.930:

fsolve(p);
           0.07016568203, 0.07350618818, 0.1121166384

You can also achieve those with the following, using your A, even at default Digits=10,

Digits := 10;
sols := [fsolve(numer(A), lambda = -0.1 .. 1, maxsols = 4)];

  sols := [0.07016568203, 0.07350618818, 0.1121166384]

You can use higher working precision to show accurately the residual errors.

forget(evalf);
seq(evalf[max(20, Digits)](A), lambda = sols);

                            -9                           -8  
   -7.4318703347473954061 10  , -1.2463236113255786800 10  , 

                             -8
     3.8410294096271317263 10  

I get the following, in Maple 2019.0 or Maple 2019.2.

restart;
kernelopts(version);

   Maple 2019.2, X86 64 LINUX, Oct 30 2019, Build ID 1430966

assume(x, 'real'); assume(y, 'real');
verify(x^2 + y^2, 0, {'greater_equal'});

                    true

restart;
verify(x^2 + y^2, 0, {'greater_equal'}) assuming x::real, y::real;

                    true

T__e_np := sqrt(r^2+1)/(r^2+sqrt(r^2+1)*r+1);

(r^2+1)^(1/2)/(r^2+(r^2+1)^(1/2)*r+1)

evala(T__e_np);

(r^2+1)^(1/2)-r

1/evala(1/T__e_np);

1/((r^2+1)^(1/2)+r)

Download simp_ex_2.mw

There is also this (but it's easier to let evala figure it out.

factor(T__e_np, sqrt(r^2 + 1));
1/factor(1/T__e_np, sqrt(r^2 + 1));

See https://oeis.org/A000399 which gives several formulations, eg.

seq(coeff(expand(mul((x+i),i=1..n)),x,2), n=1..10);

    0, 1, 6, 35, 225, 1624, 13132, 118124, 1172700, 12753576

seq(1/2*n!*(harmonic(n)^2+Psi(1,n+1)-1/6*Pi^2), n=1..10);

    0, 1, 6, 35, 225, 1624, 13132, 118124, 1172700, 12753576

seq((-1)^n*(Stirling1(n+1, 3)), n=1..10);

    0, 1, 6, 35, 225, 1624, 13132, 118124, 1172700, 12753576

Also,

1/2*(Sum(1/i,i = 1 .. n)^2-Sum(1/i^2,i = 1 .. n))*n!

If it doesn't both you that the result is not always true (and you could lose a sign, etc),

 

ee := sqrt(4*n^2+5*n-7)/n;

(4*n^2+5*n-7)^(1/2)/n

sqrt(expand(ee^2));

(4+5/n-7/n^2)^(1/2)

Download rad_rat.mw

That was a problem in Maple 2015, and that particular issue was corrected by Maple 2016.2.

As a kind of workaround you could pass the inert=false option to InertForm:-Display here. I prefer that option because operators get rendered in the usual color of output, rather than in dull gray. For this example the separating brackets get properly shown (though the output appears as implicit multiplication in Maple 2015.2 so it's not quite perfect).

ps. I added the Maple 2015 product marker on your Question, since that's the version in which your atteched worksheet was saved. It might be helpful if you could add that yourself when asking about problems when running in older versions.

These may be close enough to your goals, that you can adjust to taste.

restart

with(Statistics)

Array3 := Matrix(101, 31, {(1, 1) = 0., (1, 2) = "RPM 0 - 100", (1, 3) = "RPM 101 - 200", (1, 4) = "RPM 201 - 300", (1, 5) = "RPM 301 - 400", (1, 6) = "RPM 401 - 500", (1, 7) = "RPM 501 - 600", (1, 8) = "RPM 601 - 700", (1, 9) = "RPM 701 - 800", (1, 10) = "RPM 801 - 900", (1, 11) = "RPM 901 - 1000", (1, 12) = "RPM 1001 - 1100", (1, 13) = "RPM 1101 - 1200", (1, 14) = "RPM 1201 - 1300", (1, 15) = "RPM 1301 - 1400", (1, 16) = "RPM 1401 - 1500", (1, 17) = "RPM 1501 - 1600", (1, 18) = "RPM 1601 - 1700", (1, 19) = "RPM 1701 - 1800", (1, 20) = "RPM 1801 - 1900", (1, 21) = "RPM 1901 - 2000", (1, 22) = "RPM 2001 - 2100", (1, 23) = "RPM 2101 - 2200", (1, 24) = "RPM 2201 - 2300", (1, 25) = "RPM 2301 - 2400", (1, 26) = "RPM 2401 - 2500", (1, 27) = "RPM 2501 - 2600", (1, 28) = "RPM 2601 - 2700", (1, 29) = "RPM 2701 - 2800", (1, 30) = "RPM 2801 - 2900", (1, 31) = "RPM 2901 - 3000", (2, 1) = "0 - 40", (2, 2) = 0., (2, 3) = 0., (2, 4) = 0., (2, 5) = 0., (2, 6) = 11.0, (2, 7) = 13.0, (2, 8) = 0., (2, 9) = 0., (2, 10) = 0., (2, 11) = 0., (2, 12) = 0., (2, 13) = 0., (2, 14) = 0., (2, 15) = 0., (2, 16) = 0., (2, 17) = 0., (2, 18) = 0., (2, 19) = 0., (2, 20) = 0., (2, 21) = 0., (2, 22) = 0., (2, 23) = 0., (2, 24) = 0., (2, 25) = 0., (2, 26) = 0., (2, 27) = 0., (2, 28) = 0., (2, 29) = 0., (2, 30) = 0., (2, 31) = 0., (3, 1) = "41 - 80", (3, 2) = 0., (3, 3) = 0., (3, 4) = 0., (3, 5) = 0., (3, 6) = 10.0, (3, 7) = 1.0, (3, 8) = 0., (3, 9) = 0., (3, 10) = 0., (3, 11) = 0., (3, 12) = 0., (3, 13) = 0., (3, 14) = 0., (3, 15) = 0., (3, 16) = 0., (3, 17) = 0., (3, 18) = 0., (3, 19) = 0., (3, 20) = 0., (3, 21) = 0., (3, 22) = 0., (3, 23) = 0., (3, 24) = 0., (3, 25) = 0., (3, 26) = 0., (3, 27) = 0., (3, 28) = 0., (3, 29) = 0., (3, 30) = 0., (3, 31) = 0., (4, 1) = "81 - 120", (4, 2) = 13.0, (4, 3) = 0., (4, 4) = 0., (4, 5) = 1.0, (4, 6) = 8.0, (4, 7) = 6.0, (4, 8) = 0., (4, 9) = 0., (4, 10) = 19.0, (4, 11) = 0., (4, 12) = 0., (4, 13) = 0., (4, 14) = 0., (4, 15) = 0., (4, 16) = 0., (4, 17) = 0., (4, 18) = 0., (4, 19) = 0., (4, 20) = 0., (4, 21) = 0., (4, 22) = 0., (4, 23) = 0., (4, 24) = 0., (4, 25) = 0., (4, 26) = 0., (4, 27) = 0., (4, 28) = 0., (4, 29) = 0., (4, 30) = 0., (4, 31) = 0., (5, 1) = "121 - 160", (5, 2) = 17.0, (5, 3) = 0., (5, 4) = 0., (5, 5) = 0., (5, 6) = 9.0, (5, 7) = 3.0, (5, 8) = 0., (5, 9) = 0., (5, 10) = 37.0, (5, 11) = 12.0, (5, 12) = 0., (5, 13) = 1.0, (5, 14) = 0., (5, 15) = 0., (5, 16) = 0., (5, 17) = 0., (5, 18) = 0., (5, 19) = 0., (5, 20) = 0., (5, 21) = 0., (5, 22) = 0., (5, 23) = 0., (5, 24) = 0., (5, 25) = 0., (5, 26) = 0., (5, 27) = 0., (5, 28) = 0., (5, 29) = 0., (5, 30) = 0., (5, 31) = 0., (6, 1) = "161 - 200", (6, 2) = 58.0, (6, 3) = 0., (6, 4) = 0., (6, 5) = 0., (6, 6) = 27.0, (6, 7) = 12.0, (6, 8) = 1.0, (6, 9) = 0., (6, 10) = 43.0, (6, 11) = 3.0, (6, 12) = 0., (6, 13) = 2.0, (6, 14) = 5.0, (6, 15) = 7.0, (6, 16) = 0., (6, 17) = 0., (6, 18) = 0., (6, 19) = 0., (6, 20) = 0., (6, 21) = 0., (6, 22) = 0., (6, 23) = 0., (6, 24) = 0., (6, 25) = 0., (6, 26) = 0., (6, 27) = 0., (6, 28) = 0., (6, 29) = 0., (6, 30) = 0., (6, 31) = 0., (7, 1) = "201 - 240", (7, 2) = 43.0, (7, 3) = 0., (7, 4) = 0., (7, 5) = 0., (7, 6) = 27.0, (7, 7) = 41.0, (7, 8) = 3.0, (7, 9) = 0., (7, 10) = 22.0, (7, 11) = 0., (7, 12) = 0., (7, 13) = 5.0, (7, 14) = 10.0, (7, 15) = 3.0, (7, 16) = 0., (7, 17) = 0., (7, 18) = 0., (7, 19) = 0., (7, 20) = 0., (7, 21) = 0., (7, 22) = 0., (7, 23) = 0., (7, 24) = 0., (7, 25) = 0., (7, 26) = 0., (7, 27) = 0., (7, 28) = 0., (7, 29) = 0., (7, 30) = 0., (7, 31) = 0., (8, 1) = "241 - 280", (8, 2) = 17.0, (8, 3) = 0., (8, 4) = 1.0, (8, 5) = 0., (8, 6) = 18.0, (8, 7) = 57.0, (8, 8) = 11.0, (8, 9) = 6.0, (8, 10) = 12.0, (8, 11) = 0., (8, 12) = 1.0, (8, 13) = 10.0, (8, 14) = 9.0, (8, 15) = 4.0, (8, 16) = 0., (8, 17) = 0., (8, 18) = 0., (8, 19) = 0., (8, 20) = 0., (8, 21) = 0., (8, 22) = 0., (8, 23) = 0., (8, 24) = 0., (8, 25) = 0., (8, 26) = 0., (8, 27) = 0., (8, 28) = 0., (8, 29) = 0., (8, 30) = 0., (8, 31) = 0., (9, 1) = "281 - 320", (9, 2) = 33.0, (9, 3) = 0., (9, 4) = 1.0, (9, 5) = 0., (9, 6) = 3.0, (9, 7) = 77.0, (9, 8) = 15.0, (9, 9) = 31.0, (9, 10) = 14.0, (9, 11) = 3.0, (9, 12) = 13.0, (9, 13) = 10.0, (9, 14) = 11.0, (9, 15) = 0., (9, 16) = 0., (9, 17) = 0., (9, 18) = 0., (9, 19) = 0., (9, 20) = 0., (9, 21) = 0., (9, 22) = 0., (9, 23) = 0., (9, 24) = 0., (9, 25) = 0., (9, 26) = 0., (9, 27) = 0., (9, 28) = 0., (9, 29) = 0., (9, 30) = 0., (9, 31) = 0., (10, 1) = "321 - 360", (10, 2) = 16.0, (10, 3) = 1.0, (10, 4) = 1.0, (10, 5) = 3.0, (10, 6) = 5.0, (10, 7) = 29.0, (10, 8) = 23.0, (10, 9) = 87.0, (10, 10) = 20.0, (10, 11) = 13.0, (10, 12) = 9.0, (10, 13) = 6.0, (10, 14) = 3.0, (10, 15) = 1.0, (10, 16) = 0., (10, 17) = 0., (10, 18) = 0., (10, 19) = 0., (10, 20) = 0., (10, 21) = 0., (10, 22) = 0., (10, 23) = 0., (10, 24) = 0., (10, 25) = 0., (10, 26) = 0., (10, 27) = 0., (10, 28) = 0., (10, 29) = 0., (10, 30) = 0., (10, 31) = 0., (11, 1) = "361 - 400", (11, 2) = 29.0, (11, 3) = 2.0, (11, 4) = 0., (11, 5) = 2.0, (11, 6) = 6.0, (11, 7) = 9.0, (11, 8) = 12.0, (11, 9) = 122.0, (11, 10) = 21.0, (11, 11) = 10.0, (11, 12) = 5.0, (11, 13) = 4.0, (11, 14) = 0., (11, 15) = 0., (11, 16) = 0., (11, 17) = 0., (11, 18) = 0., (11, 19) = 0., (11, 20) = 0., (11, 21) = 0., (11, 22) = 0., (11, 23) = 0., (11, 24) = 0., (11, 25) = 0., (11, 26) = 0., (11, 27) = 0., (11, 28) = 0., (11, 29) = 0., (11, 30) = 0., (11, 31) = 0., (12, 1) = "401 - 440", (12, 2) = 16.0, (12, 3) = 0., (12, 4) = 1.0, (12, 5) = 3.0, (12, 6) = 2.0, (12, 7) = 2.0, (12, 8) = 5.0, (12, 9) = 83.0, (12, 10) = 2.0, (12, 11) = 11.0, (12, 12) = 0., (12, 13) = 1.0, (12, 14) = 0., (12, 15) = 0., (12, 16) = 0., (12, 17) = 0., (12, 18) = 0., (12, 19) = 0., (12, 20) = 0., (12, 21) = 0., (12, 22) = 0., (12, 23) = 0., (12, 24) = 0., (12, 25) = 0., (12, 26) = 0., (12, 27) = 0., (12, 28) = 0., (12, 29) = 0., (12, 30) = 0., (12, 31) = 0., (13, 1) = "441 - 480", (13, 2) = 22.0, (13, 3) = 0., (13, 4) = 2.0, (13, 5) = 15.0, (13, 6) = 3.0, (13, 7) = 2.0, (13, 8) = 2.0, (13, 9) = 11.0, (13, 10) = 0., (13, 11) = 1.0, (13, 12) = 0., (13, 13) = 1.0, (13, 14) = 0., (13, 15) = 0., (13, 16) = 0., (13, 17) = 0., (13, 18) = 0., (13, 19) = 0., (13, 20) = 0., (13, 21) = 0., (13, 22) = 0., (13, 23) = 0., (13, 24) = 0., (13, 25) = 0., (13, 26) = 0., (13, 27) = 0., (13, 28) = 0., (13, 29) = 0., (13, 30) = 0., (13, 31) = 0., (14, 1) = "481 - 520", (14, 2) = 24.0, (14, 3) = 1.0, (14, 4) = 1.0, (14, 5) = 7.0, (14, 6) = 1.0, (14, 7) = 6.0, (14, 8) = 8.0, (14, 9) = 6.0, (14, 10) = 0., (14, 11) = 0., (14, 12) = 0., (14, 13) = 1.0, (14, 14) = 0., (14, 15) = 0., (14, 16) = 0., (14, 17) = 0., (14, 18) = 0., (14, 19) = 0., (14, 20) = 0., (14, 21) = 0., (14, 22) = 0., (14, 23) = 0., (14, 24) = 0., (14, 25) = 0., (14, 26) = 0., (14, 27) = 0., (14, 28) = 0., (14, 29) = 0., (14, 30) = 0., (14, 31) = 0., (15, 1) = "521 - 560", (15, 2) = 19.0, (15, 3) = 6.0, (15, 4) = 2.0, (15, 5) = 15.0, (15, 6) = 3.0, (15, 7) = 5.0, (15, 8) = 7.0, (15, 9) = 6.0, (15, 10) = 0., (15, 11) = 0., (15, 12) = 0., (15, 13) = 0., (15, 14) = 0., (15, 15) = 0., (15, 16) = 0., (15, 17) = 0., (15, 18) = 0., (15, 19) = 0., (15, 20) = 0., (15, 21) = 0., (15, 22) = 0., (15, 23) = 0., (15, 24) = 0., (15, 25) = 0., (15, 26) = 0., (15, 27) = 0., (15, 28) = 0., (15, 29) = 0., (15, 30) = 0., (15, 31) = 0., (16, 1) = "561 - 600", (16, 2) = 26.0, (16, 3) = 3.0, (16, 4) = 8.0, (16, 5) = 17.0, (16, 6) = 2.0, (16, 7) = 5.0, (16, 8) = 9.0, (16, 9) = 1.0, (16, 10) = 0., (16, 11) = 0., (16, 12) = 0., (16, 13) = 0., (16, 14) = 0., (16, 15) = 0., (16, 16) = 0., (16, 17) = 0., (16, 18) = 0., (16, 19) = 0., (16, 20) = 0., (16, 21) = 0., (16, 22) = 0., (16, 23) = 0., (16, 24) = 0., (16, 25) = 0., (16, 26) = 0., (16, 27) = 0., (16, 28) = 0., (16, 29) = 0., (16, 30) = 0., (16, 31) = 0., (17, 1) = "601 - 640", (17, 2) = 21.0, (17, 3) = 4.0, (17, 4) = 8.0, (17, 5) = 13.0, (17, 6) = 2.0, (17, 7) = 1.0, (17, 8) = 1.0, (17, 9) = 1.0, (17, 10) = 0., (17, 11) = 0., (17, 12) = 0., (17, 13) = 0., (17, 14) = 0., (17, 15) = 0., (17, 16) = 0., (17, 17) = 0., (17, 18) = 0., (17, 19) = 0., (17, 20) = 0., (17, 21) = 0., (17, 22) = 0., (17, 23) = 0., (17, 24) = 0., (17, 25) = 0., (17, 26) = 0., (17, 27) = 0., (17, 28) = 0., (17, 29) = 0., (17, 30) = 0., (17, 31) = 0., (18, 1) = "641 - 680", (18, 2) = 19.0, (18, 3) = 6.0, (18, 4) = 8.0, (18, 5) = 0., (18, 6) = 1.0, (18, 7) = 0., (18, 8) = 3.0, (18, 9) = 0., (18, 10) = 0., (18, 11) = 0., (18, 12) = 0., (18, 13) = 0., (18, 14) = 0., (18, 15) = 0., (18, 16) = 0., (18, 17) = 0., (18, 18) = 0., (18, 19) = 0., (18, 20) = 0., (18, 21) = 0., (18, 22) = 0., (18, 23) = 0., (18, 24) = 0., (18, 25) = 0., (18, 26) = 0., (18, 27) = 0., (18, 28) = 0., (18, 29) = 0., (18, 30) = 0., (18, 31) = 0., (19, 1) = "681 - 720", (19, 2) = 25.0, (19, 3) = 17.0, (19, 4) = 2.0, (19, 5) = 8.0, (19, 6) = 7.0, (19, 7) = 0., (19, 8) = 0., (19, 9) = 0., (19, 10) = 0., (19, 11) = 0., (19, 12) = 0., (19, 13) = 0., (19, 14) = 0., (19, 15) = 0., (19, 16) = 0., (19, 17) = 0., (19, 18) = 0., (19, 19) = 0., (19, 20) = 0., (19, 21) = 0., (19, 22) = 0., (19, 23) = 0., (19, 24) = 0., (19, 25) = 0., (19, 26) = 0., (19, 27) = 0., (19, 28) = 0., (19, 29) = 0., (19, 30) = 0., (19, 31) = 0., (20, 1) = "721 - 760", (20, 2) = 27.0, (20, 3) = 11.0, (20, 4) = 4.0, (20, 5) = 3.0, (20, 6) = 6.0, (20, 7) = 0., (20, 8) = 1.0, (20, 9) = 0., (20, 10) = 0., (20, 11) = 0., (20, 12) = 0., (20, 13) = 0., (20, 14) = 0., (20, 15) = 0., (20, 16) = 0., (20, 17) = 0., (20, 18) = 0., (20, 19) = 0., (20, 20) = 0., (20, 21) = 0., (20, 22) = 0., (20, 23) = 0., (20, 24) = 0., (20, 25) = 0., (20, 26) = 0., (20, 27) = 0., (20, 28) = 0., (20, 29) = 0., (20, 30) = 0., (20, 31) = 0., (21, 1) = "761 - 800", (21, 2) = 23.0, (21, 3) = 5.0, (21, 4) = 0., (21, 5) = 12.0, (21, 6) = 1.0, (21, 7) = 1.0, (21, 8) = 5.0, (21, 9) = 0., (21, 10) = 0., (21, 11) = 0., (21, 12) = 0., (21, 13) = 0., (21, 14) = 0., (21, 15) = 0., (21, 16) = 0., (21, 17) = 0., (21, 18) = 0., (21, 19) = 0., (21, 20) = 0., (21, 21) = 0., (21, 22) = 0., (21, 23) = 0., (21, 24) = 0., (21, 25) = 0., (21, 26) = 0., (21, 27) = 0., (21, 28) = 0., (21, 29) = 0., (21, 30) = 0., (21, 31) = 0., (22, 1) = "801 - 840", (22, 2) = 23.0, (22, 3) = 2.0, (22, 4) = 5.0, (22, 5) = 14.0, (22, 6) = 0., (22, 7) = 3.0, (22, 8) = 7.0, (22, 9) = 0., (22, 10) = 0., (22, 11) = 0., (22, 12) = 0., (22, 13) = 0., (22, 14) = 0., (22, 15) = 0., (22, 16) = 0., (22, 17) = 0., (22, 18) = 0., (22, 19) = 0., (22, 20) = 0., (22, 21) = 0., (22, 22) = 0., (22, 23) = 0., (22, 24) = 0., (22, 25) = 0., (22, 26) = 0., (22, 27) = 0., (22, 28) = 0., (22, 29) = 0., (22, 30) = 0., (22, 31) = 0., (23, 1) = "841 - 880", (23, 2) = 16.0, (23, 3) = 4.0, (23, 4) = 5.0, (23, 5) = 2.0, (23, 6) = 0., (23, 7) = 8.0, (23, 8) = 6.0, (23, 9) = 0., (23, 10) = 0., (23, 11) = 0., (23, 12) = 0., (23, 13) = 0., (23, 14) = 0., (23, 15) = 0., (23, 16) = 0., (23, 17) = 0., (23, 18) = 0., (23, 19) = 0., (23, 20) = 0., (23, 21) = 0., (23, 22) = 0., (23, 23) = 0., (23, 24) = 0., (23, 25) = 0., (23, 26) = 0., (23, 27) = 0., (23, 28) = 0., (23, 29) = 0., (23, 30) = 0., (23, 31) = 0., (24, 1) = "881 - 920", (24, 2) = 16.0, (24, 3) = 13.0, (24, 4) = 3.0, (24, 5) = 3.0, (24, 6) = 6.0, (24, 7) = 16.0, (24, 8) = 10.0, (24, 9) = 0., (24, 10) = 0., (24, 11) = 0., (24, 12) = 0., (24, 13) = 0., (24, 14) = 0., (24, 15) = 0., (24, 16) = 0., (24, 17) = 0., (24, 18) = 0., (24, 19) = 0., (24, 20) = 0., (24, 21) = 0., (24, 22) = 0., (24, 23) = 0., (24, 24) = 0., (24, 25) = 0., (24, 26) = 0., (24, 27) = 0., (24, 28) = 0., (24, 29) = 0., (24, 30) = 0., (24, 31) = 0., (25, 1) = "921 - 960", (25, 2) = 16.0, (25, 3) = 11.0, (25, 4) = 5.0, (25, 5) = 0., (25, 6) = 10.0, (25, 7) = 25.0, (25, 8) = 3.0, (25, 9) = 0., (25, 10) = 0., (25, 11) = 0., (25, 12) = 0., (25, 13) = 0., (25, 14) = 0., (25, 15) = 0., (25, 16) = 0., (25, 17) = 0., (25, 18) = 0., (25, 19) = 0., (25, 20) = 0., (25, 21) = 0., (25, 22) = 0., (25, 23) = 0., (25, 24) = 0., (25, 25) = 0., (25, 26) = 0., (25, 27) = 0., (25, 28) = 0., (25, 29) = 0., (25, 30) = 0., (25, 31) = 0., (26, 1) = "961 - 1000", (26, 2) = 9.0, (26, 3) = 0., (26, 4) = 7.0, (26, 5) = 1.0, (26, 6) = 6.0, (26, 7) = 5.0, (26, 8) = 1.0, (26, 9) = 0., (26, 10) = 0., (26, 11) = 0., (26, 12) = 0., (26, 13) = 0., (26, 14) = 0., (26, 15) = 0., (26, 16) = 0., (26, 17) = 0., (26, 18) = 0., (26, 19) = 0., (26, 20) = 0., (26, 21) = 0., (26, 22) = 0., (26, 23) = 0., (26, 24) = 0., (26, 25) = 0., (26, 26) = 0., (26, 27) = 0., (26, 28) = 0., (26, 29) = 0., (26, 30) = 0., (26, 31) = 0., (27, 1) = "1001 - 1040", (27, 2) = 7.0, (27, 3) = 2.0, (27, 4) = 2.0, (27, 5) = 6.0, (27, 6) = 8.0, (27, 7) = 4.0, (27, 8) = 0., (27, 9) = 0., (27, 10) = 0., (27, 11) = 0., (27, 12) = 0., (27, 13) = 0., (27, 14) = 0., (27, 15) = 0., (27, 16) = 0., (27, 17) = 0., (27, 18) = 0., (27, 19) = 0., (27, 20) = 0., (27, 21) = 0., (27, 22) = 0., (27, 23) = 0., (27, 24) = 0., (27, 25) = 0., (27, 26) = 0., (27, 27) = 0., (27, 28) = 0., (27, 29) = 0., (27, 30) = 0., (27, 31) = 0., (28, 1) = "1041 - 1080", (28, 2) = 6.0, (28, 3) = 0., (28, 4) = 0., (28, 5) = 8.0, (28, 6) = 0., (28, 7) = 2.0, (28, 8) = 0., (28, 9) = 0., (28, 10) = 0., (28, 11) = 0., (28, 12) = 0., (28, 13) = 0., (28, 14) = 0., (28, 15) = 0., (28, 16) = 0., (28, 17) = 0., (28, 18) = 0., (28, 19) = 0., (28, 20) = 0., (28, 21) = 0., (28, 22) = 0., (28, 23) = 0., (28, 24) = 0., (28, 25) = 0., (28, 26) = 0., (28, 27) = 0., (28, 28) = 0., (28, 29) = 0., (28, 30) = 0., (28, 31) = 0., (29, 1) = "1081 - 1120", (29, 2) = 14.0, (29, 3) = 9.0, (29, 4) = 8.0, (29, 5) = 6.0, (29, 6) = 0., (29, 7) = 0., (29, 8) = 0., (29, 9) = 0., (29, 10) = 0., (29, 11) = 0., (29, 12) = 0., (29, 13) = 0., (29, 14) = 0., (29, 15) = 0., (29, 16) = 0., (29, 17) = 0., (29, 18) = 0., (29, 19) = 0., (29, 20) = 0., (29, 21) = 0., (29, 22) = 0., (29, 23) = 0., (29, 24) = 0., (29, 25) = 0., (29, 26) = 0., (29, 27) = 0., (29, 28) = 0., (29, 29) = 0., (29, 30) = 0., (29, 31) = 0., (30, 1) = "1121 - 1160", (30, 2) = 15.0, (30, 3) = 7.0, (30, 4) = 13.0, (30, 5) = 7.0, (30, 6) = 0., (30, 7) = 0., (30, 8) = 0., (30, 9) = 0., (30, 10) = 0., (30, 11) = 0., (30, 12) = 0., (30, 13) = 0., (30, 14) = 0., (30, 15) = 0., (30, 16) = 0., (30, 17) = 0., (30, 18) = 0., (30, 19) = 0., (30, 20) = 0., (30, 21) = 0., (30, 22) = 0., (30, 23) = 0., (30, 24) = 0., (30, 25) = 0., (30, 26) = 0., (30, 27) = 0., (30, 28) = 0., (30, 29) = 0., (30, 30) = 0., (30, 31) = 0., (31, 1) = "1161 - 1200", (31, 2) = 5.0, (31, 3) = 6.0, (31, 4) = 2.0, (31, 5) = 0., (31, 6) = 0., (31, 7) = 0., (31, 8) = 0., (31, 9) = 0., (31, 10) = 0., (31, 11) = 0., (31, 12) = 0., (31, 13) = 0., (31, 14) = 0., (31, 15) = 0., (31, 16) = 0., (31, 17) = 0., (31, 18) = 0., (31, 19) = 0., (31, 20) = 0., (31, 21) = 0., (31, 22) = 0., (31, 23) = 0., (31, 24) = 0., (31, 25) = 0., (31, 26) = 0., (31, 27) = 0., (31, 28) = 0., (31, 29) = 0., (31, 30) = 0., (31, 31) = 0., (32, 1) = "1201 - 1240", (32, 2) = 4.0, (32, 3) = 3.0, (32, 4) = 2.0, (32, 5) = 0., (32, 6) = 0., (32, 7) = 0., (32, 8) = 0., (32, 9) = 0., (32, 10) = 0., (32, 11) = 0., (32, 12) = 0., (32, 13) = 0., (32, 14) = 0., (32, 15) = 0., (32, 16) = 0., (32, 17) = 0., (32, 18) = 0., (32, 19) = 0., (32, 20) = 0., (32, 21) = 0., (32, 22) = 0., (32, 23) = 0., (32, 24) = 0., (32, 25) = 0., (32, 26) = 0., (32, 27) = 0., (32, 28) = 0., (32, 29) = 0., (32, 30) = 0., (32, 31) = 0., (33, 1) = "1241 - 1280", (33, 2) = 2.0, (33, 3) = 1.0, (33, 4) = 0., (33, 5) = 0., (33, 6) = 0., (33, 7) = 0., (33, 8) = 0., (33, 9) = 0., (33, 10) = 0., (33, 11) = 0., (33, 12) = 0., (33, 13) = 0., (33, 14) = 0., (33, 15) = 0., (33, 16) = 0., (33, 17) = 0., (33, 18) = 0., (33, 19) = 0., (33, 20) = 0., (33, 21) = 0., (33, 22) = 0., (33, 23) = 0., (33, 24) = 0., (33, 25) = 0., (33, 26) = 0., (33, 27) = 0., (33, 28) = 0., (33, 29) = 0., (33, 30) = 0., (33, 31) = 0., (34, 1) = "1281 - 1320", (34, 2) = 1.0, (34, 3) = 1.0, (34, 4) = 0., (34, 5) = 0., (34, 6) = 0., (34, 7) = 0., (34, 8) = 0., (34, 9) = 0., (34, 10) = 0., (34, 11) = 0., (34, 12) = 0., (34, 13) = 0., (34, 14) = 0., (34, 15) = 0., (34, 16) = 0., (34, 17) = 0., (34, 18) = 0., (34, 19) = 0., (34, 20) = 0., (34, 21) = 0., (34, 22) = 0., (34, 23) = 0., (34, 24) = 0., (34, 25) = 0., (34, 26) = 0., (34, 27) = 0., (34, 28) = 0., (34, 29) = 0., (34, 30) = 0., (34, 31) = 0., (35, 1) = "1321 - 1360", (35, 2) = 0., (35, 3) = 1.0, (35, 4) = 0., (35, 5) = 0., (35, 6) = 0., (35, 7) = 0., (35, 8) = 0., (35, 9) = 0., (35, 10) = 0., (35, 11) = 0., (35, 12) = 0., (35, 13) = 0., (35, 14) = 0., (35, 15) = 0., (35, 16) = 0., (35, 17) = 0., (35, 18) = 0., (35, 19) = 0., (35, 20) = 0., (35, 21) = 0., (35, 22) = 0., (35, 23) = 0., (35, 24) = 0., (35, 25) = 0., (35, 26) = 0., (35, 27) = 0., (35, 28) = 0., (35, 29) = 0., (35, 30) = 0., (35, 31) = 0., (36, 1) = "1361 - 1400", (36, 2) = 2.0, (36, 3) = 0., (36, 4) = 0., (36, 5) = 0., (36, 6) = 0., (36, 7) = 0., (36, 8) = 0., (36, 9) = 0., (36, 10) = 0., (36, 11) = 0., (36, 12) = 0., (36, 13) = 0., (36, 14) = 0., (36, 15) = 0., (36, 16) = 0., (36, 17) = 0., (36, 18) = 0., (36, 19) = 0., (36, 20) = 0., (36, 21) = 0., (36, 22) = 0., (36, 23) = 0., (36, 24) = 0., (36, 25) = 0., (36, 26) = 0., (36, 27) = 0., (36, 28) = 0., (36, 29) = 0., (36, 30) = 0., (36, 31) = 0., (37, 1) = "1401 - 1440", (37, 2) = 3.0, (37, 3) = 1.0, (37, 4) = 0., (37, 5) = 0., (37, 6) = 0., (37, 7) = 0., (37, 8) = 0., (37, 9) = 0., (37, 10) = 0., (37, 11) = 0., (37, 12) = 0., (37, 13) = 0., (37, 14) = 0., (37, 15) = 0., (37, 16) = 0., (37, 17) = 0., (37, 18) = 0., (37, 19) = 0., (37, 20) = 0., (37, 21) = 0., (37, 22) = 0., (37, 23) = 0., (37, 24) = 0., (37, 25) = 0., (37, 26) = 0., (37, 27) = 0., (37, 28) = 0., (37, 29) = 0., (37, 30) = 0., (37, 31) = 0., (38, 1) = "1441 - 1480", (38, 2) = 1.0, (38, 3) = 0., (38, 4) = 0., (38, 5) = 0., (38, 6) = 0., (38, 7) = 0., (38, 8) = 0., (38, 9) = 0., (38, 10) = 0., (38, 11) = 0., (38, 12) = 0., (38, 13) = 0., (38, 14) = 0., (38, 15) = 0., (38, 16) = 0., (38, 17) = 0., (38, 18) = 0., (38, 19) = 0., (38, 20) = 0., (38, 21) = 0., (38, 22) = 0., (38, 23) = 0., (38, 24) = 0., (38, 25) = 0., (38, 26) = 0., (38, 27) = 0., (38, 28) = 0., (38, 29) = 0., (38, 30) = 0., (38, 31) = 0., (39, 1) = "1481 - 1520", (39, 2) = 0., (39, 3) = 0., (39, 4) = 0., (39, 5) = 0., (39, 6) = 0., (39, 7) = 0., (39, 8) = 0., (39, 9) = 0., (39, 10) = 0., (39, 11) = 0., (39, 12) = 0., (39, 13) = 0., (39, 14) = 0., (39, 15) = 0., (39, 16) = 0., (39, 17) = 0., (39, 18) = 0., (39, 19) = 0., (39, 20) = 0., (39, 21) = 0., (39, 22) = 0., (39, 23) = 0., (39, 24) = 0., (39, 25) = 0., (39, 26) = 0., (39, 27) = 0., (39, 28) = 0., (39, 29) = 0., (39, 30) = 0., (39, 31) = 0., (40, 1) = "1521 - 1560", (40, 2) = 0., (40, 3) = 0., (40, 4) = 0., (40, 5) = 0., (40, 6) = 0., (40, 7) = 0., (40, 8) = 0., (40, 9) = 0., (40, 10) = 0., (40, 11) = 0., (40, 12) = 0., (40, 13) = 0., (40, 14) = 0., (40, 15) = 0., (40, 16) = 0., (40, 17) = 0., (40, 18) = 0., (40, 19) = 0., (40, 20) = 0., (40, 21) = 0., (40, 22) = 0., (40, 23) = 0., (40, 24) = 0., (40, 25) = 0., (40, 26) = 0., (40, 27) = 0., (40, 28) = 0., (40, 29) = 0., (40, 30) = 0., (40, 31) = 0., (41, 1) = "1561 - 1600", (41, 2) = 0., (41, 3) = 0., (41, 4) = 0., (41, 5) = 0., (41, 6) = 0., (41, 7) = 0., (41, 8) = 0., (41, 9) = 0., (41, 10) = 0., (41, 11) = 0., (41, 12) = 0., (41, 13) = 0., (41, 14) = 0., (41, 15) = 0., (41, 16) = 0., (41, 17) = 0., (41, 18) = 0., (41, 19) = 0., (41, 20) = 0., (41, 21) = 0., (41, 22) = 0., (41, 23) = 0., (41, 24) = 0., (41, 25) = 0., (41, 26) = 0., (41, 27) = 0., (41, 28) = 0., (41, 29) = 0., (41, 30) = 0., (41, 31) = 0., (42, 1) = "1601 - 1640", (42, 2) = 0., (42, 3) = 0., (42, 4) = 0., (42, 5) = 0., (42, 6) = 0., (42, 7) = 0., (42, 8) = 0., (42, 9) = 0., (42, 10) = 0., (42, 11) = 0., (42, 12) = 0., (42, 13) = 0., (42, 14) = 0., (42, 15) = 0., (42, 16) = 0., (42, 17) = 0., (42, 18) = 0., (42, 19) = 0., (42, 20) = 0., (42, 21) = 0., (42, 22) = 0., (42, 23) = 0., (42, 24) = 0., (42, 25) = 0., (42, 26) = 0., (42, 27) = 0., (42, 28) = 0., (42, 29) = 0., (42, 30) = 0., (42, 31) = 0., (43, 1) = "1641 - 1680", (43, 2) = 0., (43, 3) = 0., (43, 4) = 0., (43, 5) = 0., (43, 6) = 0., (43, 7) = 0., (43, 8) = 0., (43, 9) = 0., (43, 10) = 0., (43, 11) = 0., (43, 12) = 0., (43, 13) = 0., (43, 14) = 0., (43, 15) = 0., (43, 16) = 0., (43, 17) = 0., (43, 18) = 0., (43, 19) = 0., (43, 20) = 0., (43, 21) = 0., (43, 22) = 0., (43, 23) = 0., (43, 24) = 0., (43, 25) = 0., (43, 26) = 0., (43, 27) = 0., (43, 28) = 0., (43, 29) = 0., (43, 30) = 0., (43, 31) = 0., (44, 1) = "1681 - 1720", (44, 2) = 0., (44, 3) = 0., (44, 4) = 0., (44, 5) = 0., (44, 6) = 0., (44, 7) = 0., (44, 8) = 0., (44, 9) = 0., (44, 10) = 0., (44, 11) = 0., (44, 12) = 0., (44, 13) = 0., (44, 14) = 0., (44, 15) = 0., (44, 16) = 0., (44, 17) = 0., (44, 18) = 0., (44, 19) = 0., (44, 20) = 0., (44, 21) = 0., (44, 22) = 0., (44, 23) = 0., (44, 24) = 0., (44, 25) = 0., (44, 26) = 0., (44, 27) = 0., (44, 28) = 0., (44, 29) = 0., (44, 30) = 0., (44, 31) = 0., (45, 1) = "1721 - 1760", (45, 2) = 0., (45, 3) = 0., (45, 4) = 0., (45, 5) = 0., (45, 6) = 0., (45, 7) = 0., (45, 8) = 0., (45, 9) = 0., (45, 10) = 0., (45, 11) = 0., (45, 12) = 0., (45, 13) = 0., (45, 14) = 0., (45, 15) = 0., (45, 16) = 0., (45, 17) = 0., (45, 18) = 0., (45, 19) = 0., (45, 20) = 0., (45, 21) = 0., (45, 22) = 0., (45, 23) = 0., (45, 24) = 0., (45, 25) = 0., (45, 26) = 0., (45, 27) = 0., (45, 28) = 0., (45, 29) = 0., (45, 30) = 0., (45, 31) = 0., (46, 1) = "1761 - 1800", (46, 2) = 0., (46, 3) = 0., (46, 4) = 0., (46, 5) = 0., (46, 6) = 0., (46, 7) = 0., (46, 8) = 0., (46, 9) = 0., (46, 10) = 0., (46, 11) = 0., (46, 12) = 0., (46, 13) = 0., (46, 14) = 0., (46, 15) = 0., (46, 16) = 0., (46, 17) = 0., (46, 18) = 0., (46, 19) = 0., (46, 20) = 0., (46, 21) = 0., (46, 22) = 0., (46, 23) = 0., (46, 24) = 0., (46, 25) = 0., (46, 26) = 0., (46, 27) = 0., (46, 28) = 0., (46, 29) = 0., (46, 30) = 0., (46, 31) = 0., (47, 1) = "1801 - 1840", (47, 2) = 0., (47, 3) = 0., (47, 4) = 0., (47, 5) = 0., (47, 6) = 0., (47, 7) = 0., (47, 8) = 0., (47, 9) = 0., (47, 10) = 0., (47, 11) = 0., (47, 12) = 0., (47, 13) = 0., (47, 14) = 0., (47, 15) = 0., (47, 16) = 0., (47, 17) = 0., (47, 18) = 0., (47, 19) = 0., (47, 20) = 0., (47, 21) = 0., (47, 22) = 0., (47, 23) = 0., (47, 24) = 0., (47, 25) = 0., (47, 26) = 0., (47, 27) = 0., (47, 28) = 0., (47, 29) = 0., (47, 30) = 0., (47, 31) = 0., (48, 1) = "1841 - 1880", (48, 2) = 0., (48, 3) = 0., (48, 4) = 0., (48, 5) = 0., (48, 6) = 0., (48, 7) = 0., (48, 8) = 0., (48, 9) = 0., (48, 10) = 0., (48, 11) = 0., (48, 12) = 0., (48, 13) = 0., (48, 14) = 0., (48, 15) = 0., (48, 16) = 0., (48, 17) = 0., (48, 18) = 0., (48, 19) = 0., (48, 20) = 0., (48, 21) = 0., (48, 22) = 0., (48, 23) = 0., (48, 24) = 0., (48, 25) = 0., (48, 26) = 0., (48, 27) = 0., (48, 28) = 0., (48, 29) = 0., (48, 30) = 0., (48, 31) = 0., (49, 1) = "1881 - 1920", (49, 2) = 0., (49, 3) = 0., (49, 4) = 0., (49, 5) = 0., (49, 6) = 0., (49, 7) = 0., (49, 8) = 0., (49, 9) = 0., (49, 10) = 0., (49, 11) = 0., (49, 12) = 0., (49, 13) = 0., (49, 14) = 0., (49, 15) = 0., (49, 16) = 0., (49, 17) = 0., (49, 18) = 0., (49, 19) = 0., (49, 20) = 0., (49, 21) = 0., (49, 22) = 0., (49, 23) = 0., (49, 24) = 0., (49, 25) = 0., (49, 26) = 0., (49, 27) = 0., (49, 28) = 0., (49, 29) = 0., (49, 30) = 0., (49, 31) = 0., (50, 1) = "1921 - 1960", (50, 2) = 0., (50, 3) = 0., (50, 4) = 0., (50, 5) = 0., (50, 6) = 0., (50, 7) = 0., (50, 8) = 0., (50, 9) = 0., (50, 10) = 0., (50, 11) = 0., (50, 12) = 0., (50, 13) = 0., (50, 14) = 0., (50, 15) = 0., (50, 16) = 0., (50, 17) = 0., (50, 18) = 0., (50, 19) = 0., (50, 20) = 0., (50, 21) = 0., (50, 22) = 0., (50, 23) = 0., (50, 24) = 0., (50, 25) = 0., (50, 26) = 0., (50, 27) = 0., (50, 28) = 0., (50, 29) = 0., (50, 30) = 0., (50, 31) = 0., (51, 1) = "1961 - 2000", (51, 2) = 0., (51, 3) = 0., (51, 4) = 0., (51, 5) = 0., (51, 6) = 0., (51, 7) = 0., (51, 8) = 0., (51, 9) = 0., (51, 10) = 0., (51, 11) = 0., (51, 12) = 0., (51, 13) = 0., (51, 14) = 0., (51, 15) = 0., (51, 16) = 0., (51, 17) = 0., (51, 18) = 0., (51, 19) = 0., (51, 20) = 0., (51, 21) = 0., (51, 22) = 0., (51, 23) = 0., (51, 24) = 0., (51, 25) = 0., (51, 26) = 0., (51, 27) = 0., (51, 28) = 0., (51, 29) = 0., (51, 30) = 0., (51, 31) = 0., (52, 1) = "2001 - 2040", (52, 2) = 0., (52, 3) = 0., (52, 4) = 0., (52, 5) = 0., (52, 6) = 0., (52, 7) = 0., (52, 8) = 0., (52, 9) = 0., (52, 10) = 0., (52, 11) = 0., (52, 12) = 0., (52, 13) = 0., (52, 14) = 0., (52, 15) = 0., (52, 16) = 0., (52, 17) = 0., (52, 18) = 0., (52, 19) = 0., (52, 20) = 0., (52, 21) = 0., (52, 22) = 0., (52, 23) = 0., (52, 24) = 0., (52, 25) = 0., (52, 26) = 0., (52, 27) = 0., (52, 28) = 0., (52, 29) = 0., (52, 30) = 0., (52, 31) = 0., (53, 1) = "2041 - 2080", (53, 2) = 0., (53, 3) = 0., (53, 4) = 0., (53, 5) = 0., (53, 6) = 0., (53, 7) = 0., (53, 8) = 0., (53, 9) = 0., (53, 10) = 0., (53, 11) = 0., (53, 12) = 0., (53, 13) = 0., (53, 14) = 0., (53, 15) = 0., (53, 16) = 0., (53, 17) = 0., (53, 18) = 0., (53, 19) = 0., (53, 20) = 0., (53, 21) = 0., (53, 22) = 0., (53, 23) = 0., (53, 24) = 0., (53, 25) = 0., (53, 26) = 0., (53, 27) = 0., (53, 28) = 0., (53, 29) = 0., (53, 30) = 0., (53, 31) = 0., (54, 1) = "2081 - 2120", (54, 2) = 0., (54, 3) = 0., (54, 4) = 0., (54, 5) = 0., (54, 6) = 0., (54, 7) = 0., (54, 8) = 0., (54, 9) = 0., (54, 10) = 0., (54, 11) = 0., (54, 12) = 0., (54, 13) = 0., (54, 14) = 0., (54, 15) = 0., (54, 16) = 0., (54, 17) = 0., (54, 18) = 0., (54, 19) = 0., (54, 20) = 0., (54, 21) = 0., (54, 22) = 0., (54, 23) = 0., (54, 24) = 0., (54, 25) = 0., (54, 26) = 0., (54, 27) = 0., (54, 28) = 0., (54, 29) = 0., (54, 30) = 0., (54, 31) = 0., (55, 1) = "2121 - 2160", (55, 2) = 0., (55, 3) = 0., (55, 4) = 0., (55, 5) = 0., (55, 6) = 0., (55, 7) = 0., (55, 8) = 0., (55, 9) = 0., (55, 10) = 0., (55, 11) = 0., (55, 12) = 0., (55, 13) = 0., (55, 14) = 0., (55, 15) = 0., (55, 16) = 0., (55, 17) = 0., (55, 18) = 0., (55, 19) = 0., (55, 20) = 0., (55, 21) = 0., (55, 22) = 0., (55, 23) = 0., (55, 24) = 0., (55, 25) = 0., (55, 26) = 0., (55, 27) = 0., (55, 28) = 0., (55, 29) = 0., (55, 30) = 0., (55, 31) = 0., (56, 1) = "2161 - 2200", (56, 2) = 0., (56, 3) = 0., (56, 4) = 0., (56, 5) = 0., (56, 6) = 0., (56, 7) = 0., (56, 8) = 0., (56, 9) = 0., (56, 10) = 0., (56, 11) = 0., (56, 12) = 0., (56, 13) = 0., (56, 14) = 0., (56, 15) = 0., (56, 16) = 0., (56, 17) = 0., (56, 18) = 0., (56, 19) = 0., (56, 20) = 0., (56, 21) = 0., (56, 22) = 0., (56, 23) = 0., (56, 24) = 0., (56, 25) = 0., (56, 26) = 0., (56, 27) = 0., (56, 28) = 0., (56, 29) = 0., (56, 30) = 0., (56, 31) = 0., (57, 1) = "2201 - 2240", (57, 2) = 0., (57, 3) = 0., (57, 4) = 0., (57, 5) = 0., (57, 6) = 0., (57, 7) = 0., (57, 8) = 0., (57, 9) = 0., (57, 10) = 0., (57, 11) = 0., (57, 12) = 0., (57, 13) = 0., (57, 14) = 0., (57, 15) = 0., (57, 16) = 0., (57, 17) = 0., (57, 18) = 0., (57, 19) = 0., (57, 20) = 0., (57, 21) = 0., (57, 22) = 0., (57, 23) = 0., (57, 24) = 0., (57, 25) = 0., (57, 26) = 0., (57, 27) = 0., (57, 28) = 0., (57, 29) = 0., (57, 30) = 0., (57, 31) = 0., (58, 1) = "2241 - 2280", (58, 2) = 0., (58, 3) = 0., (58, 4) = 0., (58, 5) = 0., (58, 6) = 0., (58, 7) = 0., (58, 8) = 0., (58, 9) = 0., (58, 10) = 0., (58, 11) = 0., (58, 12) = 0., (58, 13) = 0., (58, 14) = 0., (58, 15) = 0., (58, 16) = 0., (58, 17) = 0., (58, 18) = 0., (58, 19) = 0., (58, 20) = 0., (58, 21) = 0., (58, 22) = 0., (58, 23) = 0., (58, 24) = 0., (58, 25) = 0., (58, 26) = 0., (58, 27) = 0., (58, 28) = 0., (58, 29) = 0., (58, 30) = 0., (58, 31) = 0., (59, 1) = "2281 - 2320", (59, 2) = 0., (59, 3) = 0., (59, 4) = 0., (59, 5) = 0., (59, 6) = 0., (59, 7) = 0., (59, 8) = 0., (59, 9) = 0., (59, 10) = 0., (59, 11) = 0., (59, 12) = 0., (59, 13) = 0., (59, 14) = 0., (59, 15) = 0., (59, 16) = 0., (59, 17) = 0., (59, 18) = 0., (59, 19) = 0., (59, 20) = 0., (59, 21) = 0., (59, 22) = 0., (59, 23) = 0., (59, 24) = 0., (59, 25) = 0., (59, 26) = 0., (59, 27) = 0., (59, 28) = 0., (59, 29) = 0., (59, 30) = 0., (59, 31) = 0., (60, 1) = "2321 - 2360", (60, 2) = 0., (60, 3) = 0., (60, 4) = 0., (60, 5) = 0., (60, 6) = 0., (60, 7) = 0., (60, 8) = 0., (60, 9) = 0., (60, 10) = 0., (60, 11) = 0., (60, 12) = 0., (60, 13) = 0., (60, 14) = 0., (60, 15) = 0., (60, 16) = 0., (60, 17) = 0., (60, 18) = 0., (60, 19) = 0., (60, 20) = 0., (60, 21) = 0., (60, 22) = 0., (60, 23) = 0., (60, 24) = 0., (60, 25) = 0., (60, 26) = 0., (60, 27) = 0., (60, 28) = 0., (60, 29) = 0., (60, 30) = 0., (60, 31) = 0., (61, 1) = "2361 - 2400", (61, 2) = 0., (61, 3) = 0., (61, 4) = 0., (61, 5) = 0., (61, 6) = 0., (61, 7) = 0., (61, 8) = 0., (61, 9) = 0., (61, 10) = 0., (61, 11) = 0., (61, 12) = 0., (61, 13) = 0., (61, 14) = 0., (61, 15) = 0., (61, 16) = 0., (61, 17) = 0., (61, 18) = 0., (61, 19) = 0., (61, 20) = 0., (61, 21) = 0., (61, 22) = 0., (61, 23) = 0., (61, 24) = 0., (61, 25) = 0., (61, 26) = 0., (61, 27) = 0., (61, 28) = 0., (61, 29) = 0., (61, 30) = 0., (61, 31) = 0., (62, 1) = "2401 - 2440", (62, 2) = 0., (62, 3) = 0., (62, 4) = 0., (62, 5) = 0., (62, 6) = 0., (62, 7) = 0., (62, 8) = 0., (62, 9) = 0., (62, 10) = 0., (62, 11) = 0., (62, 12) = 0., (62, 13) = 0., (62, 14) = 0., (62, 15) = 0., (62, 16) = 0., (62, 17) = 0., (62, 18) = 0., (62, 19) = 0., (62, 20) = 0., (62, 21) = 0., (62, 22) = 0., (62, 23) = 0., (62, 24) = 0., (62, 25) = 0., (62, 26) = 0., (62, 27) = 0., (62, 28) = 0., (62, 29) = 0., (62, 30) = 0., (62, 31) = 0., (63, 1) = "2441 - 2480", (63, 2) = 0., (63, 3) = 0., (63, 4) = 0., (63, 5) = 0., (63, 6) = 0., (63, 7) = 0., (63, 8) = 0., (63, 9) = 0., (63, 10) = 0., (63, 11) = 0., (63, 12) = 0., (63, 13) = 0., (63, 14) = 0., (63, 15) = 0., (63, 16) = 0., (63, 17) = 0., (63, 18) = 0., (63, 19) = 0., (63, 20) = 0., (63, 21) = 0., (63, 22) = 0., (63, 23) = 0., (63, 24) = 0., (63, 25) = 0., (63, 26) = 0., (63, 27) = 0., (63, 28) = 0., (63, 29) = 0., (63, 30) = 0., (63, 31) = 0., (64, 1) = "2481 - 2520", (64, 2) = 0., (64, 3) = 0., (64, 4) = 0., (64, 5) = 0., (64, 6) = 0., (64, 7) = 0., (64, 8) = 0., (64, 9) = 0., (64, 10) = 0., (64, 11) = 0., (64, 12) = 0., (64, 13) = 0., (64, 14) = 0., (64, 15) = 0., (64, 16) = 0., (64, 17) = 0., (64, 18) = 0., (64, 19) = 0., (64, 20) = 0., (64, 21) = 0., (64, 22) = 0., (64, 23) = 0., (64, 24) = 0., (64, 25) = 0., (64, 26) = 0., (64, 27) = 0., (64, 28) = 0., (64, 29) = 0., (64, 30) = 0., (64, 31) = 0., (65, 1) = "2521 - 2560", (65, 2) = 0., (65, 3) = 0., (65, 4) = 0., (65, 5) = 0., (65, 6) = 0., (65, 7) = 0., (65, 8) = 0., (65, 9) = 0., (65, 10) = 0., (65, 11) = 0., (65, 12) = 0., (65, 13) = 0., (65, 14) = 0., (65, 15) = 0., (65, 16) = 0., (65, 17) = 0., (65, 18) = 0., (65, 19) = 0., (65, 20) = 0., (65, 21) = 0., (65, 22) = 0., (65, 23) = 0., (65, 24) = 0., (65, 25) = 0., (65, 26) = 0., (65, 27) = 0., (65, 28) = 0., (65, 29) = 0., (65, 30) = 0., (65, 31) = 0., (66, 1) = "2561 - 2600", (66, 2) = 0., (66, 3) = 0., (66, 4) = 0., (66, 5) = 0., (66, 6) = 0., (66, 7) = 0., (66, 8) = 0., (66, 9) = 0., (66, 10) = 0., (66, 11) = 0., (66, 12) = 0., (66, 13) = 0., (66, 14) = 0., (66, 15) = 0., (66, 16) = 0., (66, 17) = 0., (66, 18) = 0., (66, 19) = 0., (66, 20) = 0., (66, 21) = 0., (66, 22) = 0., (66, 23) = 0., (66, 24) = 0., (66, 25) = 0., (66, 26) = 0., (66, 27) = 0., (66, 28) = 0., (66, 29) = 0., (66, 30) = 0., (66, 31) = 0., (67, 1) = "2601 - 2640", (67, 2) = 0., (67, 3) = 0., (67, 4) = 0., (67, 5) = 0., (67, 6) = 0., (67, 7) = 0., (67, 8) = 0., (67, 9) = 0., (67, 10) = 0., (67, 11) = 0., (67, 12) = 0., (67, 13) = 0., (67, 14) = 0., (67, 15) = 0., (67, 16) = 0., (67, 17) = 0., (67, 18) = 0., (67, 19) = 0., (67, 20) = 0., (67, 21) = 0., (67, 22) = 0., (67, 23) = 0., (67, 24) = 0., (67, 25) = 0., (67, 26) = 0., (67, 27) = 0., (67, 28) = 0., (67, 29) = 0., (67, 30) = 0., (67, 31) = 0., (68, 1) = "2641 - 2680", (68, 2) = 0., (68, 3) = 0., (68, 4) = 0., (68, 5) = 0., (68, 6) = 0., (68, 7) = 0., (68, 8) = 0., (68, 9) = 0., (68, 10) = 0., (68, 11) = 0., (68, 12) = 0., (68, 13) = 0., (68, 14) = 0., (68, 15) = 0., (68, 16) = 0., (68, 17) = 0., (68, 18) = 0., (68, 19) = 0., (68, 20) = 0., (68, 21) = 0., (68, 22) = 0., (68, 23) = 0., (68, 24) = 0., (68, 25) = 0., (68, 26) = 0., (68, 27) = 0., (68, 28) = 0., (68, 29) = 0., (68, 30) = 0., (68, 31) = 0., (69, 1) = "2681 - 2720", (69, 2) = 0., (69, 3) = 0., (69, 4) = 0., (69, 5) = 0., (69, 6) = 0., (69, 7) = 0., (69, 8) = 0., (69, 9) = 0., (69, 10) = 0., (69, 11) = 0., (69, 12) = 0., (69, 13) = 0., (69, 14) = 0., (69, 15) = 0., (69, 16) = 0., (69, 17) = 0., (69, 18) = 0., (69, 19) = 0., (69, 20) = 0., (69, 21) = 0., (69, 22) = 0., (69, 23) = 0., (69, 24) = 0., (69, 25) = 0., (69, 26) = 0., (69, 27) = 0., (69, 28) = 0., (69, 29) = 0., (69, 30) = 0., (69, 31) = 0., (70, 1) = "2721 - 2760", (70, 2) = 0., (70, 3) = 0., (70, 4) = 0., (70, 5) = 0., (70, 6) = 0., (70, 7) = 0., (70, 8) = 0., (70, 9) = 0., (70, 10) = 0., (70, 11) = 0., (70, 12) = 0., (70, 13) = 0., (70, 14) = 0., (70, 15) = 0., (70, 16) = 0., (70, 17) = 0., (70, 18) = 0., (70, 19) = 0., (70, 20) = 0., (70, 21) = 0., (70, 22) = 0., (70, 23) = 0., (70, 24) = 0., (70, 25) = 0., (70, 26) = 0., (70, 27) = 0., (70, 28) = 0., (70, 29) = 0., (70, 30) = 0., (70, 31) = 0., (71, 1) = "2761 - 2800", (71, 2) = 0., (71, 3) = 0., (71, 4) = 0., (71, 5) = 0., (71, 6) = 0., (71, 7) = 0., (71, 8) = 0., (71, 9) = 0., (71, 10) = 0., (71, 11) = 0., (71, 12) = 0., (71, 13) = 0., (71, 14) = 0., (71, 15) = 0., (71, 16) = 0., (71, 17) = 0., (71, 18) = 0., (71, 19) = 0., (71, 20) = 0., (71, 21) = 0., (71, 22) = 0., (71, 23) = 0., (71, 24) = 0., (71, 25) = 0., (71, 26) = 0., (71, 27) = 0., (71, 28) = 0., (71, 29) = 0., (71, 30) = 0., (71, 31) = 0., (72, 1) = "2801 - 2840", (72, 2) = 0., (72, 3) = 0., (72, 4) = 0., (72, 5) = 0., (72, 6) = 0., (72, 7) = 0., (72, 8) = 0., (72, 9) = 0., (72, 10) = 0., (72, 11) = 0., (72, 12) = 0., (72, 13) = 0., (72, 14) = 0., (72, 15) = 0., (72, 16) = 0., (72, 17) = 0., (72, 18) = 0., (72, 19) = 0., (72, 20) = 0., (72, 21) = 0., (72, 22) = 0., (72, 23) = 0., (72, 24) = 0., (72, 25) = 0., (72, 26) = 0., (72, 27) = 0., (72, 28) = 0., (72, 29) = 0., (72, 30) = 0., (72, 31) = 0., (73, 1) = "2841 - 2880", (73, 2) = 0., (73, 3) = 0., (73, 4) = 0., (73, 5) = 0., (73, 6) = 0., (73, 7) = 0., (73, 8) = 0., (73, 9) = 0., (73, 10) = 0., (73, 11) = 0., (73, 12) = 0., (73, 13) = 0., (73, 14) = 0., (73, 15) = 0., (73, 16) = 0., (73, 17) = 0., (73, 18) = 0., (73, 19) = 0., (73, 20) = 0., (73, 21) = 0., (73, 22) = 0., (73, 23) = 0., (73, 24) = 0., (73, 25) = 0., (73, 26) = 0., (73, 27) = 0., (73, 28) = 0., (73, 29) = 0., (73, 30) = 0., (73, 31) = 0., (74, 1) = "2881 - 2920", (74, 2) = 0., (74, 3) = 0., (74, 4) = 0., (74, 5) = 0., (74, 6) = 0., (74, 7) = 0., (74, 8) = 0., (74, 9) = 0., (74, 10) = 0., (74, 11) = 0., (74, 12) = 0., (74, 13) = 0., (74, 14) = 0., (74, 15) = 0., (74, 16) = 0., (74, 17) = 0., (74, 18) = 0., (74, 19) = 0., (74, 20) = 0., (74, 21) = 0., (74, 22) = 0., (74, 23) = 0., (74, 24) = 0., (74, 25) = 0., (74, 26) = 0., (74, 27) = 0., (74, 28) = 0., (74, 29) = 0., (74, 30) = 0., (74, 31) = 0., (75, 1) = "2921 - 2960", (75, 2) = 0., (75, 3) = 0., (75, 4) = 0., (75, 5) = 0., (75, 6) = 0., (75, 7) = 0., (75, 8) = 0., (75, 9) = 0., (75, 10) = 0., (75, 11) = 0., (75, 12) = 0., (75, 13) = 0., (75, 14) = 0., (75, 15) = 0., (75, 16) = 0., (75, 17) = 0., (75, 18) = 0., (75, 19) = 0., (75, 20) = 0., (75, 21) = 0., (75, 22) = 0., (75, 23) = 0., (75, 24) = 0., (75, 25) = 0., (75, 26) = 0., (75, 27) = 0., (75, 28) = 0., (75, 29) = 0., (75, 30) = 0., (75, 31) = 0., (76, 1) = "2961 - 3000", (76, 2) = 0., (76, 3) = 0., (76, 4) = 0., (76, 5) = 0., (76, 6) = 0., (76, 7) = 0., (76, 8) = 0., (76, 9) = 0., (76, 10) = 0., (76, 11) = 0., (76, 12) = 0., (76, 13) = 0., (76, 14) = 0., (76, 15) = 0., (76, 16) = 0., (76, 17) = 0., (76, 18) = 0., (76, 19) = 0., (76, 20) = 0., (76, 21) = 0., (76, 22) = 0., (76, 23) = 0., (76, 24) = 0., (76, 25) = 0., (76, 26) = 0., (76, 27) = 0., (76, 28) = 0., (76, 29) = 0., (76, 30) = 0., (76, 31) = 0., (77, 1) = "3001 - 3040", (77, 2) = 0., (77, 3) = 0., (77, 4) = 0., (77, 5) = 0., (77, 6) = 0., (77, 7) = 0., (77, 8) = 0., (77, 9) = 0., (77, 10) = 0., (77, 11) = 0., (77, 12) = 0., (77, 13) = 0., (77, 14) = 0., (77, 15) = 0., (77, 16) = 0., (77, 17) = 0., (77, 18) = 0., (77, 19) = 0., (77, 20) = 0., (77, 21) = 0., (77, 22) = 0., (77, 23) = 0., (77, 24) = 0., (77, 25) = 0., (77, 26) = 0., (77, 27) = 0., (77, 28) = 0., (77, 29) = 0., (77, 30) = 0., (77, 31) = 0., (78, 1) = "3041 - 3080", (78, 2) = 0., (78, 3) = 0., (78, 4) = 0., (78, 5) = 0., (78, 6) = 0., (78, 7) = 0., (78, 8) = 0., (78, 9) = 0., (78, 10) = 0., (78, 11) = 0., (78, 12) = 0., (78, 13) = 0., (78, 14) = 0., (78, 15) = 0., (78, 16) = 0., (78, 17) = 0., (78, 18) = 0., (78, 19) = 0., (78, 20) = 0., (78, 21) = 0., (78, 22) = 0., (78, 23) = 0., (78, 24) = 0., (78, 25) = 0., (78, 26) = 0., (78, 27) = 0., (78, 28) = 0., (78, 29) = 0., (78, 30) = 0., (78, 31) = 0., (79, 1) = "3081 - 3120", (79, 2) = 0., (79, 3) = 0., (79, 4) = 0., (79, 5) = 0., (79, 6) = 0., (79, 7) = 0., (79, 8) = 0., (79, 9) = 0., (79, 10) = 0., (79, 11) = 0., (79, 12) = 0., (79, 13) = 0., (79, 14) = 0., (79, 15) = 0., (79, 16) = 0., (79, 17) = 0., (79, 18) = 0., (79, 19) = 0., (79, 20) = 0., (79, 21) = 0., (79, 22) = 0., (79, 23) = 0., (79, 24) = 0., (79, 25) = 0., (79, 26) = 0., (79, 27) = 0., (79, 28) = 0., (79, 29) = 0., (79, 30) = 0., (79, 31) = 0., (80, 1) = "3121 - 3160", (80, 2) = 0., (80, 3) = 0., (80, 4) = 0., (80, 5) = 0., (80, 6) = 0., (80, 7) = 0., (80, 8) = 0., (80, 9) = 0., (80, 10) = 0., (80, 11) = 0., (80, 12) = 0., (80, 13) = 0., (80, 14) = 0., (80, 15) = 0., (80, 16) = 0., (80, 17) = 0., (80, 18) = 0., (80, 19) = 0., (80, 20) = 0., (80, 21) = 0., (80, 22) = 0., (80, 23) = 0., (80, 24) = 0., (80, 25) = 0., (80, 26) = 0., (80, 27) = 0., (80, 28) = 0., (80, 29) = 0., (80, 30) = 0., (80, 31) = 0., (81, 1) = "3161 - 3200", (81, 2) = 0., (81, 3) = 0., (81, 4) = 0., (81, 5) = 0., (81, 6) = 0., (81, 7) = 0., (81, 8) = 0., (81, 9) = 0., (81, 10) = 0., (81, 11) = 0., (81, 12) = 0., (81, 13) = 0., (81, 14) = 0., (81, 15) = 0., (81, 16) = 0., (81, 17) = 0., (81, 18) = 0., (81, 19) = 0., (81, 20) = 0., (81, 21) = 0., (81, 22) = 0., (81, 23) = 0., (81, 24) = 0., (81, 25) = 0., (81, 26) = 0., (81, 27) = 0., (81, 28) = 0., (81, 29) = 0., (81, 30) = 0., (81, 31) = 0., (82, 1) = "3201 - 3240", (82, 2) = 0., (82, 3) = 0., (82, 4) = 0., (82, 5) = 0., (82, 6) = 0., (82, 7) = 0., (82, 8) = 0., (82, 9) = 0., (82, 10) = 0., (82, 11) = 0., (82, 12) = 0., (82, 13) = 0., (82, 14) = 0., (82, 15) = 0., (82, 16) = 0., (82, 17) = 0., (82, 18) = 0., (82, 19) = 0., (82, 20) = 0., (82, 21) = 0., (82, 22) = 0., (82, 23) = 0., (82, 24) = 0., (82, 25) = 0., (82, 26) = 0., (82, 27) = 0., (82, 28) = 0., (82, 29) = 0., (82, 30) = 0., (82, 31) = 0., (83, 1) = "3241 - 3280", (83, 2) = 0., (83, 3) = 0., (83, 4) = 0., (83, 5) = 0., (83, 6) = 0., (83, 7) = 0., (83, 8) = 0., (83, 9) = 0., (83, 10) = 0., (83, 11) = 0., (83, 12) = 0., (83, 13) = 0., (83, 14) = 0., (83, 15) = 0., (83, 16) = 0., (83, 17) = 0., (83, 18) = 0., (83, 19) = 0., (83, 20) = 0., (83, 21) = 0., (83, 22) = 0., (83, 23) = 0., (83, 24) = 0., (83, 25) = 0., (83, 26) = 0., (83, 27) = 0., (83, 28) = 0., (83, 29) = 0., (83, 30) = 0., (83, 31) = 0., (84, 1) = "3281 - 3320", (84, 2) = 0., (84, 3) = 0., (84, 4) = 0., (84, 5) = 0., (84, 6) = 0., (84, 7) = 0., (84, 8) = 0., (84, 9) = 0., (84, 10) = 0., (84, 11) = 0., (84, 12) = 0., (84, 13) = 0., (84, 14) = 0., (84, 15) = 0., (84, 16) = 0., (84, 17) = 0., (84, 18) = 0., (84, 19) = 0., (84, 20) = 0., (84, 21) = 0., (84, 22) = 0., (84, 23) = 0., (84, 24) = 0., (84, 25) = 0., (84, 26) = 0., (84, 27) = 0., (84, 28) = 0., (84, 29) = 0., (84, 30) = 0., (84, 31) = 0., (85, 1) = "3321 - 3360", (85, 2) = 0., (85, 3) = 0., (85, 4) = 0., (85, 5) = 0., (85, 6) = 0., (85, 7) = 0., (85, 8) = 0., (85, 9) = 0., (85, 10) = 0., (85, 11) = 0., (85, 12) = 0., (85, 13) = 0., (85, 14) = 0., (85, 15) = 0., (85, 16) = 0., (85, 17) = 0., (85, 18) = 0., (85, 19) = 0., (85, 20) = 0., (85, 21) = 0., (85, 22) = 0., (85, 23) = 0., (85, 24) = 0., (85, 25) = 0., (85, 26) = 0., (85, 27) = 0., (85, 28) = 0., (85, 29) = 0., (85, 30) = 0., (85, 31) = 0., (86, 1) = "3361 - 3400", (86, 2) = 0., (86, 3) = 0., (86, 4) = 0., (86, 5) = 0., (86, 6) = 0., (86, 7) = 0., (86, 8) = 0., (86, 9) = 0., (86, 10) = 0., (86, 11) = 0., (86, 12) = 0., (86, 13) = 0., (86, 14) = 0., (86, 15) = 0., (86, 16) = 0., (86, 17) = 0., (86, 18) = 0., (86, 19) = 0., (86, 20) = 0., (86, 21) = 0., (86, 22) = 0., (86, 23) = 0., (86, 24) = 0., (86, 25) = 0., (86, 26) = 0., (86, 27) = 0., (86, 28) = 0., (86, 29) = 0., (86, 30) = 0., (86, 31) = 0., (87, 1) = "3401 - 3440", (87, 2) = 0., (87, 3) = 0., (87, 4) = 0., (87, 5) = 0., (87, 6) = 0., (87, 7) = 0., (87, 8) = 0., (87, 9) = 0., (87, 10) = 0., (87, 11) = 0., (87, 12) = 0., (87, 13) = 0., (87, 14) = 0., (87, 15) = 0., (87, 16) = 0., (87, 17) = 0., (87, 18) = 0., (87, 19) = 0., (87, 20) = 0., (87, 21) = 0., (87, 22) = 0., (87, 23) = 0., (87, 24) = 0., (87, 25) = 0., (87, 26) = 0., (87, 27) = 0., (87, 28) = 0., (87, 29) = 0., (87, 30) = 0., (87, 31) = 0., (88, 1) = "3441 - 3480", (88, 2) = 0., (88, 3) = 0., (88, 4) = 0., (88, 5) = 0., (88, 6) = 0., (88, 7) = 0., (88, 8) = 0., (88, 9) = 0., (88, 10) = 0., (88, 11) = 0., (88, 12) = 0., (88, 13) = 0., (88, 14) = 0., (88, 15) = 0., (88, 16) = 0., (88, 17) = 0., (88, 18) = 0., (88, 19) = 0., (88, 20) = 0., (88, 21) = 0., (88, 22) = 0., (88, 23) = 0., (88, 24) = 0., (88, 25) = 0., (88, 26) = 0., (88, 27) = 0., (88, 28) = 0., (88, 29) = 0., (88, 30) = 0., (88, 31) = 0., (89, 1) = "3481 - 3520", (89, 2) = 0., (89, 3) = 0., (89, 4) = 0., (89, 5) = 0., (89, 6) = 0., (89, 7) = 0., (89, 8) = 0., (89, 9) = 0., (89, 10) = 0., (89, 11) = 0., (89, 12) = 0., (89, 13) = 0., (89, 14) = 0., (89, 15) = 0., (89, 16) = 0., (89, 17) = 0., (89, 18) = 0., (89, 19) = 0., (89, 20) = 0., (89, 21) = 0., (89, 22) = 0., (89, 23) = 0., (89, 24) = 0., (89, 25) = 0., (89, 26) = 0., (89, 27) = 0., (89, 28) = 0., (89, 29) = 0., (89, 30) = 0., (89, 31) = 0., (90, 1) = "3521 - 3560", (90, 2) = 0., (90, 3) = 0., (90, 4) = 0., (90, 5) = 0., (90, 6) = 0., (90, 7) = 0., (90, 8) = 0., (90, 9) = 0., (90, 10) = 0., (90, 11) = 0., (90, 12) = 0., (90, 13) = 0., (90, 14) = 0., (90, 15) = 0., (90, 16) = 0., (90, 17) = 0., (90, 18) = 0., (90, 19) = 0., (90, 20) = 0., (90, 21) = 0., (90, 22) = 0., (90, 23) = 0., (90, 24) = 0., (90, 25) = 0., (90, 26) = 0., (90, 27) = 0., (90, 28) = 0., (90, 29) = 0., (90, 30) = 0., (90, 31) = 0., (91, 1) = "3561 - 3600", (91, 2) = 0., (91, 3) = 0., (91, 4) = 0., (91, 5) = 0., (91, 6) = 0., (91, 7) = 0., (91, 8) = 0., (91, 9) = 0., (91, 10) = 0., (91, 11) = 0., (91, 12) = 0., (91, 13) = 0., (91, 14) = 0., (91, 15) = 0., (91, 16) = 0., (91, 17) = 0., (91, 18) = 0., (91, 19) = 0., (91, 20) = 0., (91, 21) = 0., (91, 22) = 0., (91, 23) = 0., (91, 24) = 0., (91, 25) = 0., (91, 26) = 0., (91, 27) = 0., (91, 28) = 0., (91, 29) = 0., (91, 30) = 0., (91, 31) = 0., (92, 1) = "3601 - 3640", (92, 2) = 0., (92, 3) = 0., (92, 4) = 0., (92, 5) = 0., (92, 6) = 0., (92, 7) = 0., (92, 8) = 0., (92, 9) = 0., (92, 10) = 0., (92, 11) = 0., (92, 12) = 0., (92, 13) = 0., (92, 14) = 0., (92, 15) = 0., (92, 16) = 0., (92, 17) = 0., (92, 18) = 0., (92, 19) = 0., (92, 20) = 0., (92, 21) = 0., (92, 22) = 0., (92, 23) = 0., (92, 24) = 0., (92, 25) = 0., (92, 26) = 0., (92, 27) = 0., (92, 28) = 0., (92, 29) = 0., (92, 30) = 0., (92, 31) = 0., (93, 1) = "3641 - 3680", (93, 2) = 0., (93, 3) = 0., (93, 4) = 0., (93, 5) = 0., (93, 6) = 0., (93, 7) = 0., (93, 8) = 0., (93, 9) = 0., (93, 10) = 0., (93, 11) = 0., (93, 12) = 0., (93, 13) = 0., (93, 14) = 0., (93, 15) = 0., (93, 16) = 0., (93, 17) = 0., (93, 18) = 0., (93, 19) = 0., (93, 20) = 0., (93, 21) = 0., (93, 22) = 0., (93, 23) = 0., (93, 24) = 0., (93, 25) = 0., (93, 26) = 0., (93, 27) = 0., (93, 28) = 0., (93, 29) = 0., (93, 30) = 0., (93, 31) = 0., (94, 1) = "3681 - 3720", (94, 2) = 0., (94, 3) = 0., (94, 4) = 0., (94, 5) = 0., (94, 6) = 0., (94, 7) = 0., (94, 8) = 0., (94, 9) = 0., (94, 10) = 0., (94, 11) = 0., (94, 12) = 0., (94, 13) = 0., (94, 14) = 0., (94, 15) = 0., (94, 16) = 0., (94, 17) = 0., (94, 18) = 0., (94, 19) = 0., (94, 20) = 0., (94, 21) = 0., (94, 22) = 0., (94, 23) = 0., (94, 24) = 0., (94, 25) = 0., (94, 26) = 0., (94, 27) = 0., (94, 28) = 0., (94, 29) = 0., (94, 30) = 0., (94, 31) = 0., (95, 1) = "3721 - 3760", (95, 2) = 0., (95, 3) = 0., (95, 4) = 0., (95, 5) = 0., (95, 6) = 0., (95, 7) = 0., (95, 8) = 0., (95, 9) = 0., (95, 10) = 0., (95, 11) = 0., (95, 12) = 0., (95, 13) = 0., (95, 14) = 0., (95, 15) = 0., (95, 16) = 0., (95, 17) = 0., (95, 18) = 0., (95, 19) = 0., (95, 20) = 0., (95, 21) = 0., (95, 22) = 0., (95, 23) = 0., (95, 24) = 0., (95, 25) = 0., (95, 26) = 0., (95, 27) = 0., (95, 28) = 0., (95, 29) = 0., (95, 30) = 0., (95, 31) = 0., (96, 1) = "3761 - 3800", (96, 2) = 0., (96, 3) = 0., (96, 4) = 0., (96, 5) = 0., (96, 6) = 0., (96, 7) = 0., (96, 8) = 0., (96, 9) = 0., (96, 10) = 0., (96, 11) = 0., (96, 12) = 0., (96, 13) = 0., (96, 14) = 0., (96, 15) = 0., (96, 16) = 0., (96, 17) = 0., (96, 18) = 0., (96, 19) = 0., (96, 20) = 0., (96, 21) = 0., (96, 22) = 0., (96, 23) = 0., (96, 24) = 0., (96, 25) = 0., (96, 26) = 0., (96, 27) = 0., (96, 28) = 0., (96, 29) = 0., (96, 30) = 0., (96, 31) = 0., (97, 1) = "3801 - 3840", (97, 2) = 0., (97, 3) = 0., (97, 4) = 0., (97, 5) = 0., (97, 6) = 0., (97, 7) = 0., (97, 8) = 0., (97, 9) = 0., (97, 10) = 0., (97, 11) = 0., (97, 12) = 0., (97, 13) = 0., (97, 14) = 0., (97, 15) = 0., (97, 16) = 0., (97, 17) = 0., (97, 18) = 0., (97, 19) = 0., (97, 20) = 0., (97, 21) = 0., (97, 22) = 0., (97, 23) = 0., (97, 24) = 0., (97, 25) = 0., (97, 26) = 0., (97, 27) = 0., (97, 28) = 0., (97, 29) = 0., (97, 30) = 0., (97, 31) = 0., (98, 1) = "3841 - 3880", (98, 2) = 0., (98, 3) = 0., (98, 4) = 0., (98, 5) = 0., (98, 6) = 0., (98, 7) = 0., (98, 8) = 0., (98, 9) = 0., (98, 10) = 0., (98, 11) = 0., (98, 12) = 0., (98, 13) = 0., (98, 14) = 0., (98, 15) = 0., (98, 16) = 0., (98, 17) = 0., (98, 18) = 0., (98, 19) = 0., (98, 20) = 0., (98, 21) = 0., (98, 22) = 0., (98, 23) = 0., (98, 24) = 0., (98, 25) = 0., (98, 26) = 0., (98, 27) = 0., (98, 28) = 0., (98, 29) = 0., (98, 30) = 0., (98, 31) = 0., (99, 1) = "3881 - 3920", (99, 2) = 0., (99, 3) = 0., (99, 4) = 0., (99, 5) = 0., (99, 6) = 0., (99, 7) = 0., (99, 8) = 0., (99, 9) = 0., (99, 10) = 0., (99, 11) = 0., (99, 12) = 0., (99, 13) = 0., (99, 14) = 0., (99, 15) = 0., (99, 16) = 0., (99, 17) = 0., (99, 18) = 0., (99, 19) = 0., (99, 20) = 0., (99, 21) = 0., (99, 22) = 0., (99, 23) = 0., (99, 24) = 0., (99, 25) = 0., (99, 26) = 0., (99, 27) = 0., (99, 28) = 0., (99, 29) = 0., (99, 30) = 0., (99, 31) = 0., (100, 1) = "3921 - 3960", (100, 2) = 0., (100, 3) = 0., (100, 4) = 0., (100, 5) = 0., (100, 6) = 0., (100, 7) = 0., (100, 8) = 0., (100, 9) = 0., (100, 10) = 0., (100, 11) = 0., (100, 12) = 0., (100, 13) = 0., (100, 14) = 0., (100, 15) = 0., (100, 16) = 0., (100, 17) = 0., (100, 18) = 0., (100, 19) = 0., (100, 20) = 0., (100, 21) = 0., (100, 22) = 0., (100, 23) = 0., (100, 24) = 0., (100, 25) = 0., (100, 26) = 0., (100, 27) = 0., (100, 28) = 0., (100, 29) = 0., (100, 30) = 0., (100, 31) = 0., (101, 1) = "3961 - 4000", (101, 2) = 0., (101, 3) = 0., (101, 4) = 0., (101, 5) = 0., (101, 6) = 0., (101, 7) = 0., (101, 8) = 0., (101, 9) = 0., (101, 10) = 0., (101, 11) = 0., (101, 12) = 0., (101, 13) = 0., (101, 14) = 0., (101, 15) = 0., (101, 16) = 0., (101, 17) = 0., (101, 18) = 0., (101, 19) = 0., (101, 20) = 0., (101, 21) = 0., (101, 22) = 0., (101, 23) = 0., (101, 24) = 0., (101, 25) = 0., (101, 26) = 0., (101, 27) = 0., (101, 28) = 0., (101, 29) = 0., (101, 30) = 0., (101, 31) = 0.})

ArrayDims(Array3)

1 .. 101, 1 .. 31

Array3[2 .. 101, 2 .. 31]

_rtable[18446884555240406662]

C_List := ["HTML 1", "HTML 83", "HTML 80", "HTML 53", "HTML 49", "HTML 72", "HTML 141", "HTML 101", "HTML 16", "HTML 115"]

["HTML 1", "HTML 83", "HTML 80", "HTML 53", "HTML 49", "HTML 72", "HTML 141", "HTML 101", "HTML 16", "HTML 115"]

Plt1 := HeatMap(Array3[2 .. 101, 2 .. 31], color = C_List, size = [750, 450], transparency = 0, columnlabels = subsindets(convert(Array3[1, 2 .. ()], list), string, proc (u) options operator, arrow; u[5 .. ()] end proc), rowlabels = convert(Array3[2 .. (), 1], list), axis[1] = [tickmarks = [rotation = (1/3)*Pi]], axesfont = ["LucidaSans", 10])

plots:-display(Plt1, plots:-textplot([17, -5, "RPM"]))

Plt2 := HeatMap(ArrayTools:-FlipDimension(Array3[2 .. 101, 2 .. 31], 1), color = C_List, size = [750, 450], transparency = 0, columnlabels = subsindets(convert(Array3[1, 2 .. ()], list), string, proc (u) options operator, arrow; u[5 .. ()] end proc), rowlabels = ListTools:-Reverse(convert(Array3[2 .. (), 1], list)), axis[1] = [tickmarks = [rotation = (1/3)*Pi]], axesfont = ["LucidaSans", 8])

plots:-display(Plt2, plots:-textplot([17, -5, "RPM"]))

 

Download Static_Array_Heat-map_test_ac.mw

A proper fix consists of teaching Tabulate:-CellHandler and Layout:-Plot about the _DUALAXES plotting substructure and where to find the ROOT substructure within it.

But, for now, this might serve as terse workaround (Maple 2015.2 or Maple 2020.1, say).

restart:

interface(version)

`Standard Worksheet Interface, Maple 2015.2, Linux, December 21 2015 Build ID 1097895`

wp := 800:  wt := 90:
q := plot(x^2, x=0..1, axes=boxed, size=[wp, 400]):
p := plot(x, x=0..1, axes=boxed, size=[wp, 400]):
r := plots:-display(plots:-dualaxisplot(p, q), size=[wp, 400]):
rr := subsop(-1=[op(-1,r),indets(r,specfunc(ROOT))[]][],r):

DocumentTools:-Tabulate([rr, p], width=wt):

 

 
 

dualaxes_size_Tabulate.mw

(I will file a bug report.)

Your aux2 equation does not look quite right, for your suggested "desired" expression. Or perhaps your "desired" expression is not quite right.

restart;

eq9_13_m3 := 2*R__R*s*omega__s*L__sigma_S/(s^2*L__sigma_S^2*omega__s^2 + R__R^2);

2*R__R*s*omega__s*L__sigma_S/(s^2*L__sigma_S^2*omega__s^2+R__R^2)

aux2 := s_hat = R__R/(L__sigma_S*omega__s);

s_hat = R__R/(L__sigma_S*omega__s)

temp := simplify(eq9_13_m3, {(rhs=lhs)(aux2)}):
expand(numer(temp)/s_hat)/(s_hat*expand(denom(temp)/s_hat^2));

2*s/(s_hat*(s^2/s_hat^2+1))


verification

desired := 2*(s/s_hat) / (1+(s/s_hat)^2);

2*s/(s_hat*(s^2/s_hat^2+1))

simplify( eq9_13_m3 - eval(desired,aux2));

0


Or perhaps your "desired" expression is not quite right.

aux3 := s_hat = R__R/(L__sigma_S*omega__s*s);

s_hat = R__R/(L__sigma_S*omega__s*s)

temp := simplify(eq9_13_m3, {(rhs=lhs)(aux3)}):
expand(numer(temp)/s_hat)/(s_hat*expand(denom(temp)/s_hat^2));

2/(s_hat*(1+1/s_hat^2))

Download subst_ex.mw

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