tomleslie

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9 years, 61 days

MaplePrimes Activity


These are answers submitted by tomleslie

using Maple2018.2 (Build ID 1362973) on Windows 7.

See the attached

restart;

interface(version);
with(TimeSeriesAnalysis):
esm2 := ExponentialSmoothingModel(seasonal = {A, M}, constraints = admissible);

`Standard Worksheet Interface, Maple 2018.2, Windows 7, November 16 2018 Build ID 1362973`

 

_m652943904

(1)

 

Download timeSer.mw

Not so much a singularity, more the fact that the system is inconsistent.

Each differential in 'odesys' is multiplied by the factor sqrt(t). Hence at t=0, all of these differential terms disappear, and you are left with a set of linear equations in S(0), M(0)., N(0)., U(0). Into these equations just substitute your boundary conditions, using

eval([eval(odesys, t=0)], [ICS])

which will return

[32.619 = 0, -5.19 = 0, -22.81 = 0, -0.30 = 0]

This is definitely not good!

see the attached

restart;

interface(rtablesize=10):

with(Groebner):
Jugdement := proc (F, P)
                   local f, N1, N2, i, j, k, q, LTF, LTPj, F__loc:=F;
                   N1 := nops(F__loc);
                   N2 := numelems(P);
                   for i to N1 do
                       LTF := LeadingTerm(F__loc, plex(w, t, s, x, y, z));
                       for j to N2 do
                           LTPj := LeadingTerm(P[j], plex(w, t, s, x, y, z));
                           f := divide(LTF[2], LTPj[2], 'q');
                           if   f = true
                           then k := j;
                                break
                           end if
                       end do;
                       if   f = true
                       then break
                       end if;
                       if   f = false
                       then F__loc := F__loc-LTF[1]*LTF[2]
                       end if
                   end do;
                   return k, f, q, P[k], LTF[1]
             end proc:
F := x^2+y^2+z^2;
P := {z, x*z, y*x};
Jugdement(F, P);

x^2+y^2+z^2

 

{z, x*z, y*x}

 

1, true, z, z, 1

(1)

 


 

Download formPar.mw

The GraphTheory() package does not permit Graphs with loops.

From the help page of ?GraphTheory (with my emphasis)

The GraphTheory package is a collection of routines for creating graphs, drawing graphs, manipulating graphs, and testing graphs for properties. The graphs are sets of vertices (nodes) connected by edges. The package supports both directed and undirected graphs but not multigraphs or graphs with loops (self-incident vertices). The edges in the graphs can be weighted or unweighted.

 

 

 - but you don't have to!

  1. The attached generates the desired plot from the original expresssion (ie using Cartesian coordinates)
  2. Then uses changecoords() to convert the expression to spherical polars,  and produces the "same" plot using the polar coordinates

  restart:

  interface(rtablesize=10):
  with(plots):

#
# Produce plot using cartesian coordinates
#
  expr1:=x^2+y^2/4+z^2/9=1:
  implicitplot3d( expr1,
                  x=-4..4,
                  y=-4..4,
                  z=-4..4,
                  axes=none,
                  style=surface,
                  scaling=constrained,
                  grid=[ 40, 40, 40]
               )

 

#
# Convert expression to spherical polars
#
  expr2:= :-changecoords( expr1,
                          [ x, y, z ],
                          spherical,
                          [ r, theta, phi ]
                        );
#
# Produce plot using spherical coordinates
#
  implicitplot3d( expr2,
                  r=0..4,
                  theta=0..2*Pi,
                  phi=0..Pi,
                  style=surface,
                  coords=spherical,
                  axes=none,
                  scaling=constrained,
                  style=surface,
                  grid=[40, 40, 40]
                );

r^2*sin(phi)^2*cos(theta)^2+(1/4)*r^2*sin(phi)^2*sin(theta)^2+(1/9)*r^2*cos(phi)^2 = 1

 

 

 


 

Download elliPlot.mw

The attached "just works" - and it isn't a version issue, becuase I've checked it in Maple 2018, Maple 2017 ,Maple 2016, Maple 2015, and Maple 18.

  restart;

  kernelopts(version);
  Physics:-Version();
  interface(rtablesize=10):

`Maple 2019.0, X86 64 WINDOWS, Mar 9 2019, Build ID 1384062`

 

"C:\Users\TomLeslie\maple\toolbox\2019\Physics Updates\lib\Physics Updates.maple", `2019, April 16, 8:7 hours, version in the MapleCloud: 344, version installed in this computer: 344.`

(1)

  PDE:=[ diff(f(x,xp),x)=-(1/2)*(L*xp+2*x)*kl,
         diff(f(x,xp),xp)=-(1/4)*kl*L*(L*xp+2*x)
       ];
  sol:=pdsolve(PDE);
  pdetest(sol[], PDE);

[diff(f(x, xp), x) = -(1/2)*(L*xp+2*x)*kl, diff(f(x, xp), xp) = -(1/4)*kl*L*(L*xp+2*x)]

 

{f(x, xp) = -(1/8)*(L*xp+2*x)^2*kl+_C1}

 

[0, 0]

(2)

 

 


 

Download pdprob.mw

which are fixed in the attached

#
# Restar should be in its own execution group
#
  restart;

#
# redefining built-in variables is really not
# advisable!
#
  local gamma;
  local I;
  local pi ;

gamma

 

I

 

Warning, The imaginary unit, I, has been renamed _I

 

I

 

pi

(1)

#
# Added this execution group so worksheet displays
# correctly on Mapleprimes website
#
  interface(rtablesize=10):

#
# Set up numerical values for all problem parameters
#
# Changed beta[*] to beta[star] in this execution group
# (and everywhere subsequently).
#
# rmoved excess comma character after final entry in params
#
  params:=[       psi=0.142,        mu[1]=0.112,      phi=0.4e-3,
                 mu[v]=0.002, beta[o]=0.081,  M[h]=10,
            omega=0.2e-2,     eta=0.5e-1, mu[e]=0.092,
                pi=0.598e-2,    beta[star]=.5,      eta=0.213
             
          ]:

#
# Define main function
#
  R:= sqrt((psi+mu[1]+phi)*(mu[1])^(2)*mu[v]*psi*beta[o]*(M[h])^(2)*(omega+mu[1]+eta)*mu[e]*pi*beta[star]/(psi+mu[1]+phi)*(omega+mu[1]+eta)*mu[v]*mu[e]*(mu[1])^2);

(mu[1]^4*mu[v]^2*psi*beta[o]*M[h]^2*(omega+mu[1]+eta)^2*mu[e]^2*pi*beta[star])^(1/2)

(2)

#
# Compute "all" derivatives and evaluate numerically.
#
# For the purposes of this calculation "all"
# derivatives, means the derivatives with respect to
# every variable returned by indets(R, name)
#
# Output a list of two element lists where each of
# the latter is
#
# [ varName,
#   eval( diff( R, varName), params )
# ]
#
 [ seq( [j, eval( diff( R, j), params )],j in indets(R, name))];

[[eta, 0.1353555737e-6], [omega, 0.1353555737e-6], [pi, 0.1856046329e-5], [psi, 0.7816307780e-7], [M[h], 0.2219831409e-8], [beta[o], 0.1370266302e-6], [beta[star], 0.2219831409e-7], [mu[1], 0.5317540395e-6], [mu[e], 0.2412860227e-6], [mu[v], 0.1109915705e-4]]

(3)

#
# Compute all "sensitivities" (where the sensitivity
# is as defined in Rouben Rostamian response to the
# OP's earlier post) and evaluate numerically.
#
# For the purposes of this calculation "all" sensitivities
# means the sensitivity with respect to every variable
# returned by indets(R, name)
#
# Output a list of two element lists where each of
# the latter is
#
# [ varName,
#   eval( varName*diff( R, varName)/R, params )
# ]
#
  seq( [j, eval( j*diff( R, j)/R, params )],j in indets(R, name));

[eta, .3048780488], [omega, 0.1219512195e-1], [pi, 1/2], [psi, 1/2], [M[h], 1], [beta[o], 1/2], [beta[star], 1/2], [mu[1], 2.682926826], [mu[e], 1], [mu[v], 1]

(4)

 

NULL


 

Download sens.mw

  1. You have used x both as the independent variable in all of the ODEs, but also as an index in a for-loop. The latter use will result on 5.2 being assigned to 'x' after the loop has executed. This will effectively substitute 5.2 everywhere you use 'x' in your ODEs. You really do not want this, so I have changed the offending loop index at the point highlighted in the attached
  2. Second problem is more subtle. Location is also highlighted in the attached. The loop which solves the ODEs for coefficients of p0, p1,p2,...etc. For p0 one gets an explicit expression fro c[0](x), whihc is good. However for p1, the relevant ODE contains c[0](x) (which will be correctly substituted from the previous loop iteration), c[1](x) and f(x). It is therefore not possible to get an explicit expression for c[1](x). Maple will provide a 'formal' solution for c[1](x) in terms of double integrals of the unknown f(x) - but I'm guessing that this is not what you want! It gets worse! This formal soultion for c[1](x) is used in the ODE for p2 which also contains the two unknowns c[2](x) and f(x). Maple will provide another 'formal' solution, but this contains the previous 'formal' solution for c[1](x) - so ones gets an even more complicated formal solution containing a formal solution. This situation gets worse at each loop iteration, and the expression complexity "explodes". I'm guessing thsat this is not what you want, but it is an inevitable consequence of the way the problem is formulated. Can only suggest that you check the logic of your algorithm very carefully

NULL

#
# added restart, just because it's always a good idea
#
  restart;

#
# Added this just so that worksheet will display
# correctly ion the MApleprimes website
#
  interface(rtablesize=10):

de1 := (1-p)*(diff(f(x), `$`(x, 3)))+p*(diff(f(x), `$`(x, 3))+(1/2)*f(x)*(diff(f(x), `$`(x, 2))))

(1-p)*(diff(diff(diff(f(x), x), x), x))+p*(diff(diff(diff(f(x), x), x), x)+(1/2)*f(x)*(diff(diff(f(x), x), x)))

(1)

de2 := (1-p)*(diff(g(x), `$`(x, 2)))/Pr+p*((diff(g(x), `$`(x, 2)))/Pr+(1/2)*f(x)*(diff(g(x), x)))

(1-p)*(diff(diff(g(x), x), x))/Pr+p*((diff(diff(g(x), x), x))/Pr+(1/2)*f(x)*(diff(g(x), x)))

(2)

ibvc := f(0), (D(f))(0), (D(f))(5)-1, g(0)-1, g(5); n := 5; F := unapply(add(b[k](x)*p^k, k = 0 .. n), x); G := unapply(add(c[k](x)*p^k, k = 0 .. n), x)

f(0), (D(f))(0), (D(f))(5)-1, g(0)-1, g(5)

 

5

 

proc (x) options operator, arrow; b[0](x)+b[1](x)*p+b[2](x)*p^2+b[3](x)*p^3+b[4](x)*p^4+b[5](x)*p^5 end proc

 

proc (x) options operator, arrow; c[0](x)+c[1](x)*p+c[2](x)*p^2+c[3](x)*p^3+c[4](x)*p^4+c[5](x)*p^5 end proc

(3)

DE1 := series(eval(de1, f = F), p = 0, n+1)

series(diff(diff(diff(b[0](x), x), x), x)+(diff(diff(diff(b[1](x), x), x), x)+(1/2)*b[0](x)*(diff(diff(b[0](x), x), x)))*p+(diff(diff(diff(b[2](x), x), x), x)+(1/2)*b[0](x)*(diff(diff(b[1](x), x), x))+(1/2)*b[1](x)*(diff(diff(b[0](x), x), x)))*p^2+(diff(diff(diff(b[3](x), x), x), x)+(1/2)*b[0](x)*(diff(diff(b[2](x), x), x))+(1/2)*b[1](x)*(diff(diff(b[1](x), x), x))+(1/2)*b[2](x)*(diff(diff(b[0](x), x), x)))*p^3+(diff(diff(diff(b[4](x), x), x), x)+(1/2)*b[0](x)*(diff(diff(b[3](x), x), x))+(1/2)*b[1](x)*(diff(diff(b[2](x), x), x))+(1/2)*b[2](x)*(diff(diff(b[1](x), x), x))+(1/2)*b[3](x)*(diff(diff(b[0](x), x), x)))*p^4+(diff(diff(diff(b[5](x), x), x), x)+(1/2)*b[0](x)*(diff(diff(b[4](x), x), x))+(1/2)*b[1](x)*(diff(diff(b[3](x), x), x))+(1/2)*b[2](x)*(diff(diff(b[2](x), x), x))+(1/2)*b[3](x)*(diff(diff(b[1](x), x), x))+(1/2)*b[4](x)*(diff(diff(b[0](x), x), x)))*p^5+O(p^6),p,6)

(4)

DE2 := series(eval(de2, g = G), p = 0, n+1)

series((diff(diff(c[0](x), x), x))/Pr+((diff(diff(c[1](x), x), x))/Pr+(1/2)*f(x)*(diff(c[0](x), x)))*p+((diff(diff(c[2](x), x), x))/Pr+(1/2)*f(x)*(diff(c[1](x), x)))*p^2+((diff(diff(c[3](x), x), x))/Pr+(1/2)*f(x)*(diff(c[2](x), x)))*p^3+((diff(diff(c[4](x), x), x))/Pr+(1/2)*f(x)*(diff(c[3](x), x)))*p^4+((diff(diff(c[5](x), x), x))/Pr+(1/2)*f(x)*(diff(c[4](x), x)))*p^5+O(p^6),p,6)

(5)

CO := map(coeffs, eval([ibvc], f = F), p); CT := map(coeffs, eval([ibvc], g = G), p)

[b[0](0), b[1](0), b[2](0), b[3](0), b[4](0), b[5](0), (D(b[0]))(0), (D(b[1]))(0), (D(b[2]))(0), (D(b[3]))(0), (D(b[4]))(0), (D(b[5]))(0), (D(b[0]))(5)-1, (D(b[1]))(5), (D(b[2]))(5), (D(b[3]))(5), (D(b[4]))(5), (D(b[5]))(5), g(0)-1, g(5)]

 

[f(0), (D(f))(0), (D(f))(5)-1, c[0](0)-1, c[1](0), c[2](0), c[3](0), c[4](0), c[5](0), c[0](5), c[1](5), c[2](5), c[3](5), c[4](5), c[5](5)]

(6)

NULL

for k from 0 to n do IBVC1 := select(has, CO, b[k]); slv := dsolve({coeff(DE1, p, k), op(IBVC1)}); b[k] := unapply(rhs(slv), x) end do

F(x) = F(x)+O(p^(n+1))

(1/10)*x^2+(-(1/6000)*x^5+(5/96)*x^2)*p+((11/20160000)*x^8-(1/5760)*x^5+(325/16128)*x^2)*p^2+(-(1/532224000)*x^11+(11/12902400)*x^8-(29/258048)*x^5+(3125/1548288)*x^2)*p^3+((9299/1452971520000000)*x^14-(1/255467520)*x^11+(671/867041280)*x^8-(775/18579456)*x^5-(157028125/37196070912)*x^2)*p^4+(-(1272379/59281238016000000000)*x^17+(9299/557941063680000)*x^14-(157/34334834688)*x^11+(5665/12485394432)*x^8+(484625/127529385984)*x^5-(11930796875/3570822807552)*x^2)*p^5 = (1/10)*x^2+(-(1/6000)*x^5+(5/96)*x^2)*p+((11/20160000)*x^8-(1/5760)*x^5+(325/16128)*x^2)*p^2+(-(1/532224000)*x^11+(11/12902400)*x^8-(29/258048)*x^5+(3125/1548288)*x^2)*p^3+((9299/1452971520000000)*x^14-(1/255467520)*x^11+(671/867041280)*x^8-(775/18579456)*x^5-(157028125/37196070912)*x^2)*p^4+(-(1272379/59281238016000000000)*x^17+(9299/557941063680000)*x^14-(157/34334834688)*x^11+(5665/12485394432)*x^8+(484625/127529385984)*x^5-(11930796875/3570822807552)*x^2)*p^5+O(p^6)

(7)

plot(eval(F(x), p = 1), x = 0 .. 5, color = blue); plot(eval(diff(F(x), x), p = 1), x = 0 .. 5, color = red)

 

 

for k from 0 by .2 to 5 do NM1 := subs[eval](p = 1, F(k)) end do

``

``

for k from 0 to 1 do IBVC2 := select(has, CT, c[k]); sol := dsolve({coeff(DE2, p, k), op(IBVC2)}); c[k] := unapply(rhs(sol), x) end do

[c[0](0)-1, c[0](5)]

 

c[0](x) = -(1/5)*x+1

 

proc (x) options operator, arrow; -(1/5)*x+1 end proc

 

[c[1](0), c[1](5)]

 

c[1](x) = Int(Int((1/10)*f(_z1)*Pr, _z1 = 0 .. _z1), _z1 = 0 .. x)-(1/5)*(Int(Int((1/10)*f(_z1)*Pr, _z1 = 0 .. _z1), _z1 = 0 .. 5))*x

 

proc (x) options operator, arrow; Int(Int((1/10)*f(_z1)*Pr, _z1 = 0 .. _z1), _z1 = 0 .. x)-(1/5)*(Int(Int((1/10)*f(_z1)*Pr, _z1 = 0 .. _z1), _z1 = 0 .. 5))*x end proc

(8)

 

NULL

Download hpm2.mw

it is possible to use the 'parameters' option with the dsolve/numeric command.

This will produce a solution module with explicit values of 'p', 'lambda' and 'rho' as yet unspecified

These parameters can be subsequently given values, and relevant outputs obtained, as in the following.

Note that depending on the parameter values which are used, the ode system may (or may not) exhibit a singularity in the solution process

  restart;

  with(plots):
  interface(rtablesize=10):

  N:= 10:
  beta:= 1:
  alpha:= (N + 2)/(N - 2):
  ics:= {U(0) = beta, V(0) = 1, X(0) = 0, Y(0) = 1}:
  sys_ode:= { diff(U(r), r) = r^(N - 1)*rho^(N - 2)*p*X(r),
              diff(V(r), r) = r^(N - 1)*rho^(N - 2)*p*Y(r),
              diff(X(r), r) = -r^(N - 1)*rho^N*(U(r)^(alpha - 1) + lambda*U(r)),
              diff(Y(r), r) = -r^(N - 1)*rho^N*(lambda + (2^alpha - 1)*U(r)^(alpha - 2))*V(r)
            }:
  sol:= dsolve( [ sys_ode[], ics[] ],
                  numeric,
                  parameters = [lambda, p, rho]
              ):

#
# List the unknown parameters (just as a check!)
#
  sol(parameters);
#
# Supply one set of parameter values. Note
# this is dependent on order.
#
# Then plot the solution
#
  sol( parameters = [1, 1, 1] ):
  odeplot( sol,
           [ [r, U(r)], [r, V(r)], [r,X(r)], [r, Y(r)] ],
             r=0..1,
             color=[red, blue, green ,black]
         );
#
# Supply another set of parameter values and
# plot the solution
#
  sol( parameters = [2, 2, 2] ):
  odeplot( sol,
           [ [r, U(r)], [r, V(r)], [r,X(r)], [r, Y(r)]],
             r=0..1,
             color=[red, blue, green ,black]
         );
#
# Supply another set of parameter values and
# plot the solution
#
  sol( parameters = [1, 2, 3] ):
  odeplot( sol,
           [ [r, U(r)], [r, V(r)], [r,X(r)], [r, Y(r)]],
           r=0..1,
           color=[red, blue, green ,black]
         );
                  

[lambda = undefined, p = undefined, rho = undefined]

 

 

Warning, cannot evaluate the solution further right of .64415942, probably a singularity

 

 

Warning, cannot evaluate the solution further right of .45598040, probably a singularity

 

 

 

NULL


 

Download odePars.mw

.

that this PDE is separable, in either the original or simplified (with supplied time dependency) versions.

Output of the PDETools:-separability() command suggests otherwise.

This command returns the conditions which have to be satisfied in order for the PDE to be separable. So if it returns exactly 0 conditions, then PDE is separable. For your case the original PDE returns 3 (lengthy) conditions: the "simplified" version returns 1 condition

See the attached

restart

interface(rtablesize=10):

with(PDEtools)

Do := proc (f) options operator, arrow; diff(f, r, r)+(diff(f, phi, phi))/r^2-cos(phi)*(diff(f, phi))/(r^2*sin(phi)) end proc

Do(f(t, r, phi))

diff(diff(f(t, r, phi), r), r)+(diff(diff(f(t, r, phi), phi), phi))/r^2-cos(phi)*(diff(f(t, r, phi), phi))/(r^2*sin(phi))

(1)

PDE := Do(Do(f(t, r, phi))-(diff(f(t, r, phi), t))/alpha)+sin(phi)*(diff(f(t, r, phi), r))*(diff(Do(f(t, r, phi))/(r^2*sin(phi)^2), phi))/alpha-(diff(f(t, r, phi), phi))*(diff(Do(f(t, r, phi))/(r^2*sin(phi)^2), r)) = 0

 

NULL

NULL

NULL

#
# Check separability of original PDE. Returns
# three conditions which would have to be met
# for PDE to be separable
#
  sep:=[PDETools:-separability(PDE, f(t,r,phi), `*`)]:
  numelems(sep);

3

(2)

#
# Simplify the PDE using an explicit time function
#
  PDE2:=simplify(expand(subs( f(t,r,phi)=exp(-lambda^2*alpha*t)*g(r,phi), PDE))):
#
# Check the separability of this simplified PDE
#
# Still doesn't separate - one condition left
#
  sep:=[PDETools:-separability(PDE2, g(r,phi), `*`)]:
  numelems(sep);

1

(3)

 

Download PDEIssue.mw

the boundary condition

theta(infinity) = 0

when looking for the nummeric solution to an ODE. Just change it ot something like

theta(100) = 0

as in the attached


 

  restart;

  interface(rtablesize=10):

  BVP1 := { diff( theta(eta), eta, eta) +2 * eta * diff(theta(eta), eta), theta(infinity) = 0, theta(0) = 1 };
  #Analytically:  
  sol1 := dsolve(BVP1);
  plot( rhs(sol1), eta=0..10);

{diff(diff(theta(eta), eta), eta)+2*eta*(diff(theta(eta), eta)), theta(0) = 1, theta(infinity) = 0}

 

theta(eta) = 1-erf(eta)

 

 

#
# Define "infinity" as 100 to make
# the boundary condition
#
# theta(infinity) = 0
#
# usable in a "numerical" context
#
  inf:=100:
  BVP2 := { diff( theta(eta), eta, eta) +2 * eta * diff(theta(eta), eta), theta(inf) = 0, theta(0) = 1 }:
  sol:=dsolve(BVP2, numeric, maxmesh=1024);
  plots:-odeplot(sol, [eta, theta(eta)], eta=0..10);

proc (x_bvp) local res, data, solnproc, _ndsol, outpoint, i; option `Copyright (c) 2000 by Waterloo Maple Inc. All rights reserved.`; _EnvDSNumericSaveDigits := Digits; Digits := 15; if _EnvInFsolve = true then outpoint := evalf[_EnvDSNumericSaveDigits](x_bvp) else outpoint := evalf(x_bvp) end if; data := Array(1..4, {(1) = proc (outpoint) local X, Y, YP, yout, errproc, L, V, i; option `Copyright (c) 2000 by Waterloo Maple Inc. All rights reserved.`; X := Vector(287, {(1) = .0, (2) = .34272785551155327, (3) = .68545605600652, (4) = 1.0281851233132908, (5) = 1.3709157576421804, (6) = 1.7136488383912685, (7) = 2.056385953711714, (8) = 2.3991290298258354, (9) = 2.741880351570709, (10) = 3.084643587088239, (11) = 3.4274437035919227, (12) = 3.770301567818841, (13) = 4.113191803804626, (14) = 4.456115474905258, (15) = 4.799079776109701, (16) = 5.14209466044807, (17) = 5.485169427579998, (18) = 5.828314040472344, (19) = 6.171541537977492, (20) = 6.514863445697707, (21) = 6.858291813544751, (22) = 7.201841545499454, (23) = 7.545525083034571, (24) = 7.889355083423169, (25) = 8.233346219155038, (26) = 8.577509952977802, (27) = 8.92185754467095, (28) = 9.266400979153765, (29) = 9.611148801757508, (30) = 9.956108953659863, (31) = 10.301288730821417, (32) = 10.6466924395304, (33) = 10.992323534142638, (34) = 11.33818376225298, (35) = 11.684272903420274, (36) = 12.0305898603869, (37) = 12.377131283060706, (38) = 12.72389312270968, (39) = 13.070870623217946, (40) = 13.418056712046997, (41) = 13.765444778211265, (42) = 14.113027773901806, (43) = 14.460796576462846, (44) = 14.808743348757957, (45) = 15.156860091762422, (46) = 15.505137090682709, (47) = 15.853566351414612, (48) = 16.202139937083167, (49) = 16.550848548706988, (50) = 16.899684722744254, (51) = 17.24864119730986, (52) = 17.597709643967587, (53) = 17.94688347580373, (54) = 18.29615638472377, (55) = 18.645521225125222, (56) = 18.994972391968034, (57) = 19.34450458700878, (58) = 19.694111846926504, (59) = 20.043789512092907, (60) = 20.393533226676, (61) = 20.743338099741614, (62) = 21.09320031234754, (63) = 21.443116329359093, (64) = 21.793082179871465, (65) = 22.14309475882787, (66) = 22.493151217183122, (67) = 22.843248346986332, (68) = 23.193383632461526, (69) = 23.54355478391626, (70) = 23.893759213342307, (71) = 24.24399488277774, (72) = 24.59425995148581, (73) = 24.944552329348667, (74) = 25.294870361999827, (75) = 25.645212565905318, (76) = 25.995577247975383, (77) = 26.34596306071336, (78) = 26.696368804056206, (79) = 27.04679310067058, (80) = 27.39723484828554, (81) = 27.74769307187836, (82) = 28.09816664618133, (83) = 28.448654665485446, (84) = 28.799156334035786, (85) = 29.149670728749008, (86) = 29.500197102624572, (87) = 29.850734803822537, (88) = 30.20128307266724, (89) = 30.55184129119914, (90) = 30.902408923959488, (91) = 31.252985344565516, (92) = 31.603570040897964, (93) = 31.954162572236804, (94) = 32.30476242101317, (95) = 32.655369162567034, (96) = 33.00598243385484, (97) = 33.35660180652833, (98) = 33.70722692767758, (99) = 34.05785749763447, (100) = 34.40849316164718, (101) = 34.75913362556661, (102) = 35.10977864120253, (103) = 35.4604279138097, (104) = 35.811081197479595, (105) = 36.161738285857474, (106) = 36.51239893269488, (107) = 36.863062932270076, (108) = 37.213730132427244, (109) = 37.564400411682485, (110) = 37.91507429726012, (111) = 38.26575278180425, (112) = 38.61643836750501, (113) = 38.96713357867858, (114) = 39.31784005437529, (115) = 39.66855847947291, (116) = 40.01928849985208, (117) = 40.37002941059889, (118) = 40.72077953261957, (119) = 41.07153580382777, (120) = 41.42229565140575, (121) = 41.7730562000106, (122) = 42.12381643485321, (123) = 42.474584871545844, (124) = 42.82539298957335, (125) = 43.17621628319367, (126) = 43.52703866350971, (127) = 43.87786013580987, (128) = 44.228680706087246, (129) = 44.57950038004278, (130) = 44.93031916638373, (131) = 45.28113707488388, (132) = 45.631954114395405, (133) = 45.9827702976725, (134) = 46.33358563911399, (135) = 46.68440015137355, (136) = 47.03521385201806, (137) = 47.38602675988438, (138) = 47.736838891351844, (139) = 48.087650269059495, (140) = 48.438460915923294, (141) = 48.789270851395536, (142) = 49.14008010179399, (143) = 49.49088869330937, (144) = 49.84169664757439, (145) = 50.19250399298156, (146) = 50.54331075723062, (147) = 50.89411696274616, (148) = 51.24492263837032, (149) = 51.595727811628926, (150) = 51.94653250438395, (151) = 52.29733674423571, (152) = 52.648140557097435, (153) = 52.998943963278634, (154) = 53.34974698812261, (155) = 53.70054965478789, (156) = 54.05135198128938, (157) = 54.40215399004583, (158) = 54.75295570130227, (159) = 55.103757130533914, (160) = 55.454558296681114, (161) = 55.805359217100936, (162) = 56.156159904884326, (163) = 56.50696037582576, (164) = 56.85776064430965, (165) = 57.208560721202716, (166) = 57.55936061969085, (167) = 57.91016035151163, (168) = 58.26095992552927, (169) = 58.61175935255006, (170) = 58.96255864229041, (171) = 59.31335780196695, (172) = 59.664156843110334, (173) = 60.014955838602745, (174) = 60.365754970062234, (175) = 60.71655460864663, (176) = 61.06735477766199, (177) = 61.418155330543456, (178) = 61.76895590733981, (179) = 62.11975643197004, (180) = 62.470556882346905, (181) = 62.82135726316636, (182) = 63.172157578783505, (183) = 63.522957832393786, (184) = 63.873758027797514, (185) = 64.22455816856692, (186) = 64.57535825733743, (187) = 64.92615829725554, (188) = 65.2769582912228, (189) = 65.62775824139982, (190) = 65.97855815038982, (191) = 66.32935802061039, (192) = 66.68015785383814, (193) = 67.03095765218829, (194) = 67.38175741768679, (195) = 67.73255715181558, (196) = 68.08335685632655, (197) = 68.43415653288562, (198) = 68.78495618272667, (199) = 69.13575580732001, (200) = 69.48655540804855, (201) = 69.83735498593576, (202) = 70.188154542199, (203) = 70.53895407800616, (204) = 70.88975359420964, (205) = 71.24055309180984, (206) = 71.59135257178401, (207) = 71.9421520348469, (208) = 72.29295148183436, (209) = 72.64375091354758, (210) = 72.99455033057936, (211) = 73.34534973362636, (212) = 73.69614912335479, (213) = 74.0469485002512, (214) = 74.39774786488076, (215) = 74.74854721779742, (216) = 75.09934655940131, (217) = 75.45014589015119, (218) = 75.80094521049713, (219) = 76.15174452077865, (220) = 76.5025438214065, (221) = 76.85334311291608, (222) = 77.20414239582111, (223) = 77.55494167082877, (224) = 77.9057409389566, (225) = 78.25654020112306, (226) = 78.60733945850832, (227) = 78.95813871242063, (228) = 79.30893796382937, (229) = 79.65973721381565, (230) = 80.01053646321836, (231) = 80.36133571253576, (232) = 80.71213496221912, (233) = 81.06293421237899, (234) = 81.41373346301715, (235) = 81.76453271407989, (236) = 82.11533196543857, (237) = 82.46613121700742, (238) = 82.81693046870076, (239) = 83.16772972046982, (240) = 83.51852897231515, (241) = 83.86932822426833, (242) = 84.22012747644777, (243) = 84.5709267290116, (244) = 84.92172598219018, (245) = 85.27252523636308, (246) = 85.62332449191798, (247) = 85.97412374935872, (248) = 86.32492300939072, (249) = 86.67572227265899, (250) = 87.02652153994809, (251) = 87.37732081223929, (252) = 87.72812009034146, (253) = 88.07891937517155, (254) = 88.42971866772481, (255) = 88.78051796870106, (256) = 89.13131727880436, (257) = 89.48211659858173, (258) = 89.83291592823649, (259) = 90.18371526783567, (260) = 90.5345146170466, (261) = 90.88531397531379, (262) = 91.23611334185617, (263) = 91.58691271541277, (264) = 91.9377120947821, (265) = 92.2885114785654, (266) = 92.63931086503187, (267) = 92.99011025279923, (268) = 93.34090964040644, (269) = 93.6917090263214, (270) = 94.04250840948134, (271) = 94.39330778886179, (272) = 94.74410716357119, (273) = 95.0949065331069, (274) = 95.4457058970584, (275) = 95.79650525522254, (276) = 96.14730460760524, (277) = 96.49810395429898, (278) = 96.84890329558608, (279) = 97.1997026317924, (280) = 97.55050196330045, (281) = 97.9013012906382, (282) = 98.25210061427734, (283) = 98.60289993472414, (284) = 98.9536992526252, (285) = 99.30449856847163, (286) = 99.65462188610245, (287) = 100.0}, datatype = float[8], order = C_order); Y := Matrix(287, 2, {(1, 1) = 1.0, (1, 2) = -1.1283791674267003, (2, 1) = .6278959892458038, (2, 2) = -1.0033253703961789, (3, 1) = .33235500334966966, (3, 2) = -.7053453282628015, (4, 1) = .14592597488181203, (4, 2) = -.39204353119670143, (5, 1) = 0.52529635312474274e-1, (5, 2) = -.17228110960073115, (6, 1) = 0.15373214118391612e-1, (6, 2) = -0.5985620188681629e-1, (7, 1) = 0.36355201421329046e-2, (7, 2) = -0.16441596235870857e-1, (8, 1) = 0.6916183250017865e-3, (8, 2) = -0.3570546546451321e-2, (9, 1) = 0.1054896681900158e-3, (9, 2) = -0.613010429971097e-3, (10, 1) = 0.12867290774246585e-4, (10, 2) = -0.8320011967798202e-4, (11, 1) = 0.1252625952662034e-5, (11, 2) = -0.8926065654300458e-5, (12, 1) = 0.9717729069973927e-7, (12, 2) = -0.7569281526541e-6, (13, 1) = 0.5992258191644407e-8, (13, 2) = -0.50658788319881446e-7, (14, 1) = 0.2911295659347868e-9, (14, 2) = -0.26550358456016295e-8, (15, 1) = 0.11007598727149347e-10, (15, 2) = -0.10770675490806924e-9, (16, 1) = 0.31240769206886714e-12, (16, 2) = -0.3267009632232186e-11, (17, 1) = 0.7542834019921173e-14, (17, 2) = -0.834115632859287e-13, (18, 1) = -0.11907747909096325e-15, (18, 2) = 0.12683415337118029e-14, (19, 1) = 0.6904857416399427e-16, (19, 2) = -0.817059679151158e-15, (20, 1) = -0.22252788831734182e-16, (20, 2) = 0.2773102100486827e-15, (21, 1) = 0.7808467941825095e-17, (21, 2) = -0.10231193556036214e-15, (22, 1) = -0.29058057015387957e-17, (22, 2) = 0.3993760642405087e-16, (23, 1) = 0.11396813889080552e-17, (23, 2) = -0.16395676869190798e-16, (24, 1) = -0.4685042927395025e-18, (24, 2) = 0.7041137238700602e-17, (25, 1) = 0.20092653563966487e-18, (25, 2) = -0.31489972453048688e-17, (26, 1) = -0.8954323657563221e-19, (26, 2) = 0.14610229257044495e-17, (27, 1) = 0.41325748021944154e-19, (27, 2) = -0.7009247704997067e-18, (28, 1) = -0.19693306464512285e-19, (28, 2) = 0.34672237753843374e-18, (29, 1) = 0.9665055914308937e-20, (29, 2) = -0.1764044787503365e-18, (30, 1) = -0.48740654542791846e-20, (30, 2) = 0.9210998103278941e-19, (31, 1) = 0.25206119022799273e-20, (31, 2) = -0.4926461264321781e-19, (32, 1) = -0.1334350153725337e-20, (32, 2) = 0.2694312645875299e-19, (33, 1) = 0.7219159386625533e-21, (33, 2) = -0.1504450897646322e-19, (34, 1) = -0.39859339519367384e-21, (34, 2) = 0.8564958899379675e-20, (35, 1) = 0.2243028650008971e-21, (35, 2) = -0.4965329866849897e-20, (36, 1) = -0.12849561282991317e-21, (36, 2) = 0.2927898717529516e-20, (37, 1) = 0.7485554122237656e-22, (37, 2) = -0.17542949821763707e-20, (38, 1) = -0.44301317619966274e-22, (38, 2) = 0.1067040242941133e-20, (39, 1) = 0.26611958577655334e-22, (39, 2) = -0.6582916866586792e-21, (40, 1) = -0.16212379562429503e-22, (40, 2) = 0.4115978269794636e-21, (41, 1) = 0.10009171319080252e-22, (41, 2) = -0.26063379893418916e-21, (42, 1) = -0.6257884060571396e-23, (42, 2) = 0.16703281395311855e-21, (43, 1) = 0.3959628066760292e-23, (43, 2) = -0.108272441820325e-21, (44, 1) = -0.25340776228252934e-23, (44, 2) = 0.709465850707304e-22, (45, 1) = 0.16393932951174192e-23, (45, 2) = -0.46969163692355056e-22, (46, 1) = -0.10715691168169637e-23, (46, 2) = 0.31401311549727865e-22, (47, 1) = 0.7073321829535418e-24, (47, 2) = -0.21190336179670446e-22, (48, 1) = -0.4713011632550308e-24, (48, 2) = 0.1442772768225402e-22, (49, 1) = 0.31685754347936943e-24, (49, 2) = -0.9907284650668217e-23, (50, 1) = -0.21485780399282117e-24, (50, 2) = 0.6858774277914486e-23, (51, 1) = 0.14689292625831301e-24, (51, 2) = -0.4785445615929058e-23, (52, 1) = -0.1012195527230076e-24, (52, 2) = 0.3363876400166692e-23, (53, 1) = 0.7027527663288349e-25, (53, 2) = -0.23815872724042558e-23, (54, 1) = -0.4914551595762221e-25, (54, 2) = 0.16977621629232046e-23, (55, 1) = 0.34608662387799014e-25, (55, 2) = -0.12182967522129127e-23, (56, 1) = -0.24535185969406646e-25, (56, 2) = 0.879801111225021e-24, (57, 1) = 0.17506028044445155e-25, (57, 2) = -0.6392440775077309e-24, (58, 1) = -0.12568282134016417e-25, (58, 2) = 0.4671978208851588e-24, (59, 1) = 0.9077299238956611e-26, (59, 2) = -0.34339476722044436e-24, (60, 1) = -0.6593819064231566e-26, (60, 2) = 0.25377989982035854e-24, (61, 1) = 0.48164740975560784e-26, (61, 2) = -0.18854185403906826e-24, (62, 1) = -0.35371244560964856e-26, (62, 2) = 0.14078820558740098e-24, (63, 1) = 0.2611086890962957e-26, (63, 2) = -0.10564713717008403e-24, (64, 1) = -0.1937167473445816e-26, (64, 2) = 0.7965457613734174e-25, (65, 1) = 0.144416506112663e-26, (65, 2) = -0.6033337034151309e-25, (66, 1) = -0.10816890901391561e-26, (66, 2) = 0.4590224592727788e-25, (67, 1) = 0.8138782324739687e-27, (67, 2) = -0.35073437798067597e-25, (68, 1) = -0.61507271045299695e-27, (68, 2) = 0.2691115880360668e-25, (69, 1) = 0.4668150088774256e-27, (69, 2) = -0.20731964916069545e-25, (70, 1) = -0.35576112122845236e-27, (70, 2) = 0.16034273733499025e-25, (71, 1) = 0.27221632733528296e-27, (71, 2) = -0.12448245790793749e-25, (72, 1) = -0.209103223171459e-27, (72, 2) = 0.9699929766691817e-26, (73, 1) = 0.16123126856243842e-27, (73, 2) = -0.7585498993214902e-26, (74, 1) = -0.12477660360774168e-27, (74, 2) = 0.59526520055462384e-26, (75, 1) = 0.9690977385787812e-28, (75, 2) = -0.4687110058305257e-26, (76, 1) = -0.7552828095411554e-28, (76, 2) = 0.3702775371411829e-26, (77, 1) = 0.5906336420632986e-28, (77, 2) = -0.2934527113249145e-26, (78, 1) = -0.46339764189709166e-28, (78, 2) = 0.23329209444090234e-26, (79, 1) = 0.364735986484968e-28, (79, 2) = -0.18602747059014177e-26, (80, 1) = -0.2879759715979879e-28, (80, 2) = 0.1487766600046391e-26, (81, 1) = 0.22806137823595994e-28, (81, 2) = -0.11932736675971883e-26, (82, 1) = -0.18114712358619493e-28, (82, 2) = 0.9597562033283948e-27, (83, 1) = 0.1442989184308751e-28, (83, 2) = -0.7740459798159293e-27, (84, 1) = -0.11526978428476326e-28, (84, 2) = 0.6259333024702297e-27, (85, 1) = 0.9233336799269078e-29, (85, 2) = -0.5074770248344675e-27, (86, 1) = -0.7415899190780214e-29, (86, 2) = 0.4124813997922176e-27, (87, 1) = 0.5971769996123965e-29, (87, 2) = -0.33609778033473564e-27, (88, 1) = -0.4821137860740975e-29, (88, 2) = 0.2745204809092725e-27, (89, 1) = 0.3901911703857373e-29, (89, 2) = -0.224753856688445e-27, (90, 1) = -0.3165641103043791e-29, (90, 2) = 0.18443323295458422e-27, (91, 1) = 0.25744127634320616e-29, (91, 2) = -0.1516868556793934e-27, (92, 1) = -0.2098474021983308e-29, (92, 2) = 0.12502917875111128e-27, (93, 1) = 0.1714413121636603e-29, (93, 2) = -0.1032780756739323e-27, (94, 1) = -0.14037569874266477e-29, (94, 2) = 0.8549044615870961e-28, (95, 1) = 0.11518927675602182e-29, (95, 2) = -0.7091200568913816e-28, (96, 1) = -0.9472296628774523e-30, (96, 2) = 0.5893800126695704e-28, (97, 1) = 0.7805525024204847e-30, (97, 2) = -0.4908240114923678e-28, (98, 1) = -0.64451529365802755e-30, (98, 2) = 0.4095367499631458e-28, (99, 1) = 0.5332494475506717e-30, (99, 2) = -0.34235694066394926e-28, (100, 1) = -0.4420540688747581e-30, (100, 2) = 0.28672634648741913e-28, (101, 1) = 0.3671565341678221e-30, (101, 2) = -0.240570201586333e-28, (102, 1) = -0.30552070870133636e-30, (102, 2) = 0.20220221043440877e-28, (103, 1) = 0.25469937145279508e-30, (103, 2) = -0.1702489098620906e-28, (104, 1) = -0.21271412894956033e-30, (104, 2) = 0.14358932775235093e-28, (105, 1) = 0.17796376867207694e-30, (105, 2) = -0.12130670974346276e-28, (106, 1) = -0.1491480636392607e-30, (106, 2) = 0.102649821081355e-28, (107, 1) = 0.12521064644697341e-30, (107, 2) = -0.8700186689053147e-29, (108, 1) = -0.10528994112083141e-30, (108, 2) = 0.7385546554677987e-29, (109, 1) = 0.8868347671531742e-31, (109, 2) = -0.6279245682826614e-29, (110, 1) = -0.74815839566361e-31, (110, 2) = 0.5346759273053952e-29, (111, 1) = 0.6321632344950137e-31, (111, 2) = -0.4559530120998722e-29, (112, 1) = -0.5349769734008354e-31, (112, 2) = 0.3893896712905444e-29, (113, 1) = 0.4534217465326631e-31, (113, 2) = -0.3330217091147198e-29, (114, 1) = -0.38487133819798027e-31, (114, 2) = 0.28521574356674197e-29, (115, 1) = 0.32716552973782056e-31, (115, 2) = -0.24461126903776633e-29, (116, 1) = -0.2785105617233275e-31, (116, 2) = 0.21007324512945432e-29, (117, 1) = 0.2374285864166079e-31, (117, 2) = -0.18065328684506685e-29, (118, 1) = -0.2026857253651624e-31, (118, 2) = 0.1555576826441944e-29, (119, 1) = 0.17326450882075263e-31, (119, 2) = -0.13412113168013998e-29, (120, 1) = -0.1483106220936951e-31, (120, 2) = 0.11578521705736434e-29, (121, 1) = 0.12711942739685214e-31, (121, 2) = -0.10008048341008604e-29, (122, 1) = -0.10909540875605854e-31, (122, 2) = 0.8661174820645636e-30, (123, 1) = 0.9374868935744178e-32, (123, 2) = -0.7504604976299958e-30, (124, 1) = -0.8066227238650816e-32, (124, 2) = 0.6510266745333979e-30, (125, 1) = 0.6948765419748539e-32, (125, 2) = -0.5654280673060794e-30, (126, 1) = -0.5993365662887184e-32, (126, 2) = 0.4916463942499053e-30, (127, 1) = 0.51754787996125515e-32, (127, 2) = -0.4279738693655604e-30, (128, 1) = -0.4474449387989862e-32, (128, 2) = 0.37296040091373637e-30, (129, 1) = 0.3872833298645834e-32, (129, 2) = -0.32537308864860904e-30, (130, 1) = -0.3355919445930876e-32, (130, 2) = 0.2841623381071453e-30, (131, 1) = 0.29112440346245147e-32, (131, 2) = -0.24843346949066983e-30, (132, 1) = -0.25282744838832053e-32, (132, 2) = 0.21742289756358993e-30, (133, 1) = 0.21980576170857237e-32, (133, 2) = -0.19047811949310133e-30, (134, 1) = -0.19130143172258835e-32, (134, 2) = 0.1670408780234418e-30, (135, 1) = 0.16666794659082184e-32, (135, 2) = -0.14663297779105465e-30, (136, 1) = -0.14535727114435306e-32, (136, 2) = 0.1288443214665143e-30, (137, 1) = 0.12690015878679633e-32, (137, 2) = -0.11332280422320707e-30, (138, 1) = -0.11089848733563927e-32, (138, 2) = 0.9976576757640353e-31, (139, 1) = 0.9700995203606845e-33, (139, 2) = -0.879127632223075e-31, (140, 1) = -0.8494405218850026e-33, (140, 2) = 0.7753941760972859e-31, (141, 1) = 0.7444983690660507e-33, (141, 2) = -0.6845222406256883e-31, (142, 1) = -0.653144447545612e-33, (142, 2) = 0.6048411709261702e-31, (143, 1) = 0.5735298488823994e-33, (143, 2) = -0.53490706291992e-31, (144, 1) = -0.5040886997031859e-33, (144, 2) = 0.47347068238839457e-31, (145, 1) = 0.4434520277694964e-33, (145, 2) = -0.41945010728481444e-31, (146, 1) = -0.3904637271877708e-33, (146, 2) = 0.37190736638344014e-31, (147, 1) = 0.34410508000313353e-33, (147, 2) = -0.330028471675096e-31, (148, 1) = -0.30351969943448955e-33, (148, 2) = 0.29310633361188766e-31, (149, 1) = 0.26794561272266985e-33, (149, 2) = -0.26052612352840926e-31, (150, 1) = -0.23674660567586e-33, (150, 2) = 0.23175272175688602e-31, (151, 1) = 0.20934971766872374e-33, (151, 2) = -0.20631994343396363e-31, (152, 1) = -0.18528115956777264e-33, (152, 2) = 0.1838212782103803e-31, (153, 1) = 0.16410769479011934e-33, (153, 2) = -0.16390192462363818e-31, (154, 1) = -0.14547585374442733e-33, (154, 2) = 0.1462519315158425e-31, (155, 1) = 0.1290561096400749e-33, (155, 2) = -0.13060028519318333e-31, (156, 1) = -0.11458447602642792e-33, (156, 2) = 0.11670980800642499e-31, (157, 1) = 0.10180871040733443e-33, (157, 2) = -0.10437275285666425e-31, (158, 1) = -0.9053163663448727e-34, (158, 2) = 0.9340699408924997e-32, (159, 1) = 0.8055882404373701e-34, (159, 2) = -0.836527316249834e-32, (160, 1) = -0.7174316927339181e-34, (160, 2) = 0.7496963658343102e-32, (161, 1) = 0.6393365011415715e-34, (161, 2) = -0.6723437641220817e-32, (162, 1) = -0.5702082930544001e-34, (162, 2) = 0.6033846750257689e-32, (163, 1) = 0.5088639788642299e-34, (163, 2) = -0.5418641035725452e-32, (164, 1) = -0.4544935470701293e-34, (164, 2) = 0.4869406834681102e-32, (165, 1) = 0.4061613110465909e-34, (165, 2) = -0.4378725723240617e-32, (166, 1) = -0.3632726966926779e-34, (166, 2) = 0.3940051703632741e-32, (167, 1) = 0.32507977500950117e-34, (167, 2) = -0.354760415635001e-32, (168, 1) = -0.2911517471670078e-34, (168, 2) = 0.319627446964658e-32, (169, 1) = 0.26088366096164375e-34, (169, 2) = -0.28815445324760868e-32, (170, 1) = -0.2339696373223238e-34, (170, 2) = 0.25994155129731338e-32, (171, 1) = 0.20991395775100583e-34, (171, 2) = -0.2346345582313922e-32, (172, 1) = -0.1885063387834065e-34, (172, 2) = 0.2119195419510833e-32, (173, 1) = 0.16933479565648127e-34, (173, 2) = -0.19151805055355112e-32, (174, 1) = -0.15226243857344396e-34, (174, 2) = 0.17318292909006743e-32, (175, 1) = 0.13694166743486085e-34, (175, 2) = -0.1566946506428353e-32, (176, 1) = -0.12329204226420526e-34, (176, 2) = 0.1418580722894358e-32, (177, 1) = 0.11101562178114172e-34, (177, 2) = -0.12849961762790793e-32, (178, 1) = -0.10007561354834203e-34, (178, 2) = 0.11646478933559064e-32, (179, 1) = 0.902125267480869e-35, (179, 2) = -0.10561599482497915e-32, (180, 1) = -0.814233758051135e-35, (180, 2) = 0.9583060815464538e-33, (181, 1) = 0.7347846653076577e-35, (181, 2) = -0.869992698320368e-33, (182, 1) = -0.6640108620353482e-35, (182, 2) = 0.7902438802565789e-33, (183, 1) = 0.5998472462962716e-35, (183, 2) = -0.7181881679060695e-33, (184, 1) = -0.5427314094324073e-35, (184, 2) = 0.6530468897255713e-33, (185, 1) = 0.4907791425375297e-35, (185, 2) = -0.5941238488337791e-33, (186, 1) = -0.4445879876917691e-35, (186, 2) = 0.5407962038204935e-33, (187, 1) = 0.4024152656056052e-35, (187, 2) = -0.4925064001194972e-33, (188, 1) = -0.3649838309699928e-35, (188, 2) = 0.44875502556004435e-33, (189, 1) = 0.33066203244449404e-35, (189, 2) = -0.4090944803938618e-33, (190, 1) = -0.300271161281962e-35, (190, 2) = 0.37312336537600703e-33, (191, 1) = 0.27226689508525247e-35, (191, 2) = -0.3404815028800537e-33, (192, 1) = -0.24754804988472075e-35, (192, 2) = 0.31084551701385013e-33, (193, 1) = 0.22463916855192684e-35, (193, 2) = -0.2839249075575462e-33, (194, 1) = -0.20450027808407193e-35, (194, 2) = 0.25945856015130854e-33, (195, 1) = 0.18571036277316037e-35, (195, 2) = -0.23721164244332213e-33, (196, 1) = -0.1692779001421108e-35, (196, 2) = 0.2169728418770345e-33, (197, 1) = 0.15382501929998294e-35, (197, 2) = -0.1985519058823843e-33, (198, 1) = -0.1403986411443119e-35, (198, 2) = 0.1817774501166719e-33, (199, 1) = 0.12765516956295374e-35, (199, 2) = -0.16649500441747457e-33, (200, 1) = -0.116672101488836e-35, (200, 2) = 0.152565269574885e-33, (201, 1) = 0.10613313325097669e-35, (201, 2) = -0.13986256131726767e-33, (202, 1) = -0.9714013740701731e-36, (202, 2) = 0.1282734206226106e-33, (203, 1) = 0.8839859315713982e-36, (203, 2) = -0.1176953718154862e-33, (204, 1) = -0.8102985002375465e-36, (204, 2) = 0.10803581213224918e-33, (205, 1) = 0.737568121793428e-36, (205, 2) = -0.99211018296342e-34, (206, 1) = -0.67716426890013375e-36, (206, 2) = 0.9114525724790876e-34, (207, 1) = 0.616455681457523e-36, (207, 2) = -0.8376998968584803e-34, (208, 1) = -0.56693701851589065e-36, (208, 2) = 0.7702315635908218e-34, (209, 1) = 0.5160892619996105e-36, (209, 2) = -0.7084853814361585e-34, (210, 1) = -0.4755077609222527e-36, (210, 2) = 0.6519518198178588e-34, (211, 1) = 0.4327638719710652e-36, (211, 2) = -0.6001688563917718e-34, (212, 1) = -0.3995341025953953e-36, (212, 2) = 0.5527173499789222e-34, (213, 1) = 0.36346272932557852e-36, (213, 2) = -0.5092168832066444e-34, (214, 1) = -0.33629181092554216e-36, (214, 2) = 0.46932202530175474e-34, (215, 1) = 0.3057245810583775e-36, (215, 2) = -0.43271897078376966e-34, (216, 1) = -0.28355615152901516e-36, (216, 2) = 0.39912251476459205e-34, (217, 1) = 0.2575375200944625e-36, (217, 2) = -0.36827332982078095e-34, (218, 1) = -0.23950682208861803e-36, (218, 2) = 0.3399355131059267e-34, (219, 1) = 0.21725382772685473e-36, (219, 2) = -0.31389437582723705e-34, (220, 1) = -0.202651630763349e-36, (220, 2) = 0.2899544501923474e-34, (221, 1) = 0.18352153605820425e-36, (221, 2) = -0.26793769154040974e-34, (222, 1) = -0.17176509707138881e-36, (222, 2) = 0.247681855770903e-34, (223, 1) = 0.1552293154465942e-36, (223, 2) = -0.22903903431632305e-34, (224, 1) = -0.1458389575220295e-36, (224, 2) = 0.2118743307195669e-34, (225, 1) = 0.13146200366463421e-36, (225, 2) = -0.1960646645604042e-34, (226, 1) = -0.12404218863538449e-36, (226, 2) = 0.18149769003459984e-34, (227, 1) = 0.11146465124639577e-36, (227, 2) = -0.16807081769919906e-34, (228, 1) = -0.10568865443115907e-36, (228, 2) = 0.1556903291545131e-34, (229, 1) = 0.9461339617312092e-37, (229, 2) = -0.14427057551409482e-34, (230, 1) = -0.9021087405820194e-37, (230, 2) = 0.13373325135813107e-34, (231, 1) = 0.8039182610849166e-37, (231, 2) = -0.12400673680607734e-34, (232, 1) = -0.7713871195738574e-37, (232, 2) = 0.11502550105896189e-34, (233, 1) = 0.6837175841154187e-37, (233, 2) = -0.10672956141242531e-34, (234, 1) = -0.6608203489740537e-37, (234, 2) = 0.9906399239741777e-35, (235, 1) = 0.5819758372368783e-37, (235, 2) = -0.9197848019951062e-35, (236, 1) = -0.567165717841207e-37, (236, 2) = 0.8542691801329093e-35, (237, 1) = 0.4957348947770027e-37, (237, 2) = -0.7936703842195946e-35, (238, 1) = -0.4877236423020021e-37, (238, 2) = 0.7376007927177813e-35, (239, 1) = 0.42253015139052195e-37, (239, 2) = -0.6857047986925733e-35, (240, 1) = -0.42024316718898565e-37, (240, 2) = 0.6376560463565193e-35, (241, 1) = 0.3603049884620755e-37, (241, 2) = -0.5931549163623772e-35, (242, 1) = -0.362844513817845e-37, (242, 2) = 0.551926236552634e-35, (243, 1) = 0.30734061006484985e-37, (243, 2) = -0.51371719711001646e-35, (244, 1) = -0.31395549168175364e-37, (244, 2) = 0.47829545113324e-35, (245, 1) = 0.26219839019630753e-37, (245, 2) = -0.4454473834692155e-35, (246, 1) = -0.27225920567851103e-37, (246, 2) = 0.41497653226806024e-35, (247, 1) = 0.22367242223868057e-37, (247, 2) = -0.3867021492756001e-35, (248, 1) = -0.2366509820207582e-37, (248, 2) = 0.3604578861481759e-35, (249, 1) = 0.19075040204359506e-37, (249, 2) = -0.33609059528887656e-35, (250, 1) = -0.2062028306659192e-37, (250, 2) = 0.31345923486572987e-35, (251, 1) = 0.1625813294813756e-37, (251, 2) = -0.2924338685507586e-35, (252, 1) = -0.18013407937527606e-37, (252, 2) = 0.27289475144022434e-35, (253, 1) = 0.13844879819579717e-37, (253, 2) = -0.25473149448117235e-35, (254, 1) = -0.1577870696865216e-37, (254, 2) = 0.23784230033677894e-35, (255, 1) = 0.11774887272445758e-37, (255, 2) = -0.22213326433560898e-35, (256, 1) = -0.13860701161406586e-37, (256, 2) = 0.20751773477467816e-35, (257, 1) = 0.999717371380926e-38, (257, 2) = -0.19391572728483876e-35, (258, 1) = -0.12212526037503027e-37, (258, 2) = 0.1812533885208609e-35, (259, 1) = 0.8468644963760476e-38, (259, 2) = -0.16946250486360973e-35, (260, 1) = -0.10794541316236845e-37, (260, 2) = 0.15848005217473686e-35, (261, 1) = 0.7152825879791159e-38, (261, 2) = -0.14824778305960624e-35, (262, 1) = -0.9573173366764231e-38, (262, 2) = 0.13871184836769757e-35, (263, 1) = 0.6018803573149819e-38, (263, 2) = -0.12982244997348811e-35, (264, 1) = -0.8519950073356736e-38, (264, 2) = 0.12153352216943357e-35, (265, 1) = 0.5040345667523102e-38, (265, 2) = -0.11380243918140815e-35, (266, 1) = -0.7610694997775041e-38, (266, 2) = 0.10658974659791437e-35, (267, 1) = 0.4195163568149325e-38, (267, 2) = -0.9985891468793657e-36, (268, 1) = -0.6824853605648358e-38, (268, 2) = 0.9357611171672236e-36, (269, 1) = 0.3464296053348906e-38, (269, 2) = -0.877099955990111e-36, (270, 1) = -0.6144929138239997e-38, (270, 2) = 0.8223152234456637e-36, (271, 1) = 0.28315928283239162e-38, (271, 2) = -0.7711376986597443e-36, (272, 1) = -0.5556009659776911e-38, (272, 2) = 0.7233177588719506e-36, (273, 1) = 0.2283281251428981e-38, (273, 2) = -0.6786238877194185e-36, (274, 1) = -0.50453710100602925e-38, (274, 2) = 0.6368413019191564e-36, (275, 1) = 0.1807602365687846e-38, (275, 2) = -0.5977706866728063e-36, (276, 1) = -0.4602143046017932e-38, (276, 2) = 0.5612270307728243e-36, (277, 1) = 0.13945047476884989e-38, (277, 2) = -0.5270385532273333e-36, (278, 1) = -0.4217028724972452e-38, (278, 2) = 0.4950457139473309e-36, (279, 1) = 0.10353866617935568e-38, (279, 2) = -0.4651003016009631e-36, (280, 1) = -0.3882067361165364e-38, (280, 2) = 0.43706459240037096e-36, (281, 1) = 0.7228786241120215e-39, (281, 2) = -0.4108105740690065e-36, (282, 1) = -0.359043486077201e-38, (282, 2) = 0.386219229706459e-36, (283, 1) = 0.4506598152330236e-39, (283, 2) = -0.36317987677465306e-36, (284, 1) = -0.3336274950575199e-38, (284, 2) = 0.34158955676795585e-36, (285, 1) = 0.21330288295354805e-39, (285, 2) = -0.3213524714990403e-36, (286, 1) = -0.31136570187821304e-38, (286, 2) = 0.3023479680329675e-36, (287, 1) = .0, (287, 2) = -0.2843175434432687e-36}, datatype = float[8], order = C_order); YP := Matrix(287, 2, {(1, 1) = -1.1283791674267003, (1, 2) = .0, (2, 1) = -1.0033253703961789, (2, 2) = .6877351051524345, (3, 1) = -.7053453282628015, (3, 2) = .9669664536672883, (4, 1) = -.39204353119670143, (4, 2) = .8061866529353169, (5, 1) = -.17228110960073115, (5, 2) = .47236577579144373, (6, 1) = -0.5985620188681629e-1, (6, 2) = .20514502166771198, (7, 1) = -0.16441596235870857e-1, (7, 2) = 0.6762053511208845e-1, (8, 1) = -0.3570546546451321e-2, (8, 2) = 0.1713240374387149e-1, (9, 1) = -0.613010429971097e-3, (9, 2) = 0.3361602506491326e-2, (10, 1) = -0.8320011967798202e-4, (10, 2) = 0.5132854312193224e-3, (11, 1) = -0.8926065654300458e-5, (11, 2) = 0.6118717504936045e-4, (12, 1) = -0.7569281526541e-6, (12, 2) = 0.5707694801355945e-5, (13, 1) = -0.50658788319881446e-7, (13, 2) = 0.4167386258160198e-6, (14, 1) = -0.26550358456016295e-8, (14, 2) = 0.23662292636027178e-7, (15, 1) = -0.10770675490806924e-9, (15, 2) = 0.10337866184594388e-8, (16, 1) = -0.3267009632232186e-11, (16, 2) = 0.3359854557106707e-10, (17, 1) = -0.834115632859287e-13, (17, 2) = 0.9150531136852606e-12, (18, 1) = 0.12683415337118029e-14, (18, 2) = -0.14784585538093455e-13, (19, 1) = -0.817059679151158e-15, (19, 2) = 0.10085035497775869e-13, (20, 1) = 0.2773102100486827e-15, (20, 2) = -0.3613276301129832e-14, (21, 1) = -0.10231193556036214e-15, (21, 2) = 0.14033702201630997e-14, (22, 1) = 0.3993760642405087e-16, (22, 2) = -0.5752486263450709e-15, (23, 1) = -0.16395676869190798e-16, (23, 2) = 0.2474279821396178e-15, (24, 1) = 0.7041137238700602e-17, (24, 2) = -0.11110006373444555e-15, (25, 1) = -0.31489972453048688e-17, (25, 2) = 0.5185356912752094e-16, (26, 1) = 0.14610229257044495e-17, (26, 2) = -0.2506387737351733e-16, (27, 1) = -0.7009247704997067e-18, (27, 2) = 0.12507101903859123e-16, (28, 1) = 0.34672237753843374e-18, (28, 2) = -0.64257371574333276e-17, (29, 1) = -0.1764044787503365e-18, (29, 2) = 0.3390899389131909e-17, (30, 1) = 0.9210998103278941e-19, (30, 2) = -0.18341140137639894e-17, (31, 1) = -0.4926461264321781e-19, (31, 2) = 0.1014977998099724e-17, (32, 1) = 0.2694312645875299e-19, (32, 2) = -0.5737103615314339e-18, (33, 1) = -0.1504450897646322e-19, (33, 2) = 0.3307482201631937e-18, (34, 1) = 0.8564958899379675e-20, (34, 2) = -0.19422215583462156e-18, (35, 1) = -0.4965329866849897e-20, (35, 2) = 0.1160325384395553e-18, (36, 1) = 0.2927898717529516e-20, (36, 2) = -0.704486972467008e-19, (37, 1) = -0.17542949821763707e-20, (37, 2) = 0.43426278607223165e-19, (38, 1) = 0.1067040242941133e-20, (38, 2) = -0.271538120176263e-19, (39, 1) = -0.6582916866586792e-21, (39, 2) = 0.17208890937311046e-19, (40, 1) = 0.4115978269794636e-21, (40, 2) = -0.11045685969931501e-19, (41, 1) = -0.26063379893418916e-21, (41, 2) = 0.7175480333127997e-20, (42, 1) = 0.16703281395311855e-21, (42, 2) = -0.471467748494667e-20, (43, 1) = -0.108272441820325e-21, (43, 2) = 0.31314115120012567e-20, (44, 1) = 0.709465850707304e-22, (44, 2) = -0.21012595395665388e-20, (45, 1) = -0.46969163692355056e-22, (45, 2) = 0.14238100854242258e-20, (46, 1) = 0.31401311549727865e-22, (46, 2) = -0.9737632808115377e-21, (47, 1) = -0.21190336179670446e-22, (47, 2) = 0.671884801266374e-21, (48, 1) = 0.1442772768225402e-22, (48, 2) = -0.4675201257640165e-21, (49, 1) = -0.9907284650668217e-23, (49, 2) = 0.32794793556427816e-21, (50, 1) = 0.6858774277914486e-23, (50, 2) = -0.2318222457624454e-21, (51, 1) = -0.4785445615929058e-23, (51, 2) = 0.1650848687967996e-21, (52, 1) = 0.3363876400166692e-23, (52, 2) = -0.11839304033665674e-21, (53, 1) = -0.23815872724042558e-23, (53, 2) = 0.8548413853059283e-22, (54, 1) = 0.16977621629232046e-23, (54, 2) = -0.6212504407381965e-22, (55, 1) = -0.12182967522129127e-23, (55, 2) = 0.45431555903773976e-22, (56, 1) = 0.879801111225021e-24, (56, 2) = -0.3342359563628414e-22, (57, 1) = -0.6392440775077309e-24, (57, 2) = 0.24731719979132994e-22, (58, 1) = 0.4671978208851588e-24, (58, 2) = -0.18402092278305307e-22, (59, 1) = -0.34339476722044436e-24, (59, 2) = 0.13765864867441455e-22, (60, 1) = 0.25377989982035854e-24, (60, 2) = -0.10350937638497976e-22, (61, 1) = -0.18854185403906826e-24, (61, 2) = 0.7821974848569054e-23, (62, 1) = 0.14078820558740098e-24, (62, 2) = -0.5939347644142032e-23, (63, 1) = -0.10564713717008403e-24, (63, 2) = 0.45308077044037375e-23, (64, 1) = 0.7965457613734174e-25, (64, 2) = -0.34718374475278344e-23, (65, 1) = -0.6033337034151309e-25, (65, 2) = 0.2671935073183159e-23, (66, 1) = 0.4590224592727788e-25, (66, 2) = -0.2064972317701179e-23, (67, 1) = -0.35073437798067597e-25, (67, 2) = 0.16023825000076712e-23, (68, 1) = 0.2691115880360668e-25, (68, 2) = -0.12483216602522881e-23, (69, 1) = -0.20731964916069545e-25, (69, 2) = 0.9762083035594264e-24, (70, 1) = 0.16034273733499025e-25, (70, 2) = -0.7662381514980898e-24, (71, 1) = -0.12448245790793749e-25, (71, 2) = 0.6035904145031264e-24, (72, 1) = 0.9699929766691817e-26, (72, 2) = -0.4771251883863473e-24, (73, 1) = -0.7585498993214902e-26, (73, 2) = 0.37843375316094148e-24, (74, 1) = 0.59526520055462384e-26, (74, 2) = -0.30114312158078074e-24, (75, 1) = -0.4687110058305257e-26, (75, 2) = 0.2404038675300624e-24, (76, 1) = 0.3702775371411829e-26, (76, 2) = -0.19251156639887388e-24, (77, 1) = -0.2934527113249145e-26, (77, 2) = 0.15462588585264756e-24, (78, 1) = 0.23329209444090234e-26, (78, 2) = -0.1245610358453008e-24, (79, 1) = -0.18602747059014177e-26, (79, 2) = 0.10062893016185291e-24, (80, 1) = 0.1487766600046391e-26, (80, 2) = -0.8152138188181255e-25, (81, 1) = -0.11932736675971883e-26, (81, 2) = 0.6622118295848277e-25, (82, 1) = 0.9597562033283948e-27, (82, 2) = -0.5393477948165506e-25, (83, 1) = -0.7740459798159293e-27, (83, 2) = 0.4404113354998138e-25, (84, 1) = 0.6259333024702297e-27, (84, 2) = -0.3605270206503891e-25, (85, 1) = -0.5074770248344675e-27, (85, 2) = 0.2958557635265982e-25, (86, 1) = 0.4124813997922176e-27, (86, 2) = -0.24336565190073814e-25, (87, 1) = -0.33609778033473564e-27, (87, 2) = 0.2006553141785119e-25, (88, 1) = 0.2745204809092725e-27, (88, 2) = -0.16581741506371362e-25, (89, 1) = -0.224753856688445e-27, (89, 2) = 0.13733288318260578e-25, (90, 1) = 0.18443323295458422e-27, (90, 2) = -0.11398862367860886e-25, (91, 1) = -0.1516868556793934e-27, (91, 2) = 0.9481334155022612e-26, (92, 1) = 0.12502917875111128e-27, (92, 2) = -0.7902736815633393e-26, (93, 1) = -0.1032780756739323e-27, (93, 2) = 0.6600328840465215e-26, (94, 1) = 0.8549044615870961e-28, (94, 2) = -0.5523497104847064e-26, (95, 1) = -0.7091200568913816e-28, (95, 2) = 0.4631315447673721e-26, (96, 1) = 0.5893800126695704e-28, (96, 2) = -0.3890613269007397e-26, (97, 1) = -0.4908240114923678e-28, (97, 2) = 0.32744442216867594e-26, (98, 1) = 0.4095367499631458e-28, (98, 2) = -0.2760869633246262e-26, (99, 1) = -0.34235694066394926e-28, (99, 2) = 0.2331988779691777e-26, (100, 1) = 0.28672634648741913e-28, (100, 2) = -0.19731643064752883e-26, (101, 1) = -0.240570201586333e-28, (101, 2) = 0.1672402356653769e-26, (102, 1) = 0.20220221043440877e-28, (102, 2) = -0.1419854969822789e-26, (103, 1) = -0.1702489098620906e-28, (103, 2) = 0.120741983911387e-26, (104, 1) = 0.14358932775235093e-28, (104, 2) = -0.10284178150461898e-26, (105, 1) = -0.12130670974346276e-28, (105, 2) = 0.8773322980123154e-27, (106, 1) = 0.102649821081355e-28, (106, 2) = -0.7495982435384373e-27, (107, 1) = -0.8700186689053147e-29, (107, 2) = 0.6414310588821291e-27, (108, 1) = 0.7385546554677987e-29, (108, 2) = -0.5496874727325289e-27, (109, 1) = -0.6279245682826614e-29, (109, 2) = 0.47175219822605505e-27, (110, 1) = 0.5346759273053952e-29, (110, 2) = -0.4054455501748101e-27, (111, 1) = -0.4559530120998722e-29, (111, 2) = 0.34894770482265425e-27, (112, 1) = 0.3893896712905444e-29, (112, 2) = -0.30073684484668686e-27, (113, 1) = -0.3330217091147198e-29, (113, 2) = 0.2595380284734626e-27, (114, 1) = 0.28521574356674197e-29, (114, 2) = -0.2242813397309376e-27, (115, 1) = -0.24461126903776633e-29, (115, 2) = 0.1940675286112543e-27, (116, 1) = 0.21007324512945432e-29, (116, 2) = -0.16813963605871556e-27, (117, 1) = -0.18065328684506685e-29, (117, 2) = 0.14585957006113413e-27, (118, 1) = 0.1555576826441944e-29, (118, 2) = -0.12668860199118883e-27, (119, 1) = -0.13412113168013998e-29, (119, 2) = 0.11017121723701536e-27, (120, 1) = 0.11578521705736434e-29, (120, 2) = -0.9592178986024667e-28, (121, 1) = -0.10008048341008604e-29, (121, 2) = 0.8361335316027506e-28, (122, 1) = 0.8661174820645636e-30, (122, 2) = -0.7296834765100989e-28, (123, 1) = -0.7504604976299958e-30, (123, 2) = 0.6375099619865557e-28, (124, 1) = 0.6510266745333979e-30, (124, 2) = -0.5576094636717566e-28, (125, 1) = -0.5654280673060794e-30, (125, 2) = 0.4882608905319094e-28, (126, 1) = 0.4916463942499053e-30, (126, 2) = -0.42799823222581524e-28, (127, 1) = -0.4279738693655604e-30, (127, 2) = 0.3755715516360685e-28, (128, 1) = 0.37296040091373637e-30, (128, 2) = -0.32991092976055873e-28, (129, 1) = -0.32537308864860904e-30, (129, 2) = 0.2900993945813272e-28, (130, 1) = 0.2841623381071453e-30, (130, 2) = -0.2553500909243977e-28, (131, 1) = -0.24843346949066983e-30, (131, 2) = 0.22498699971992007e-28, (132, 1) = 0.21742289756358993e-30, (132, 2) = -0.19842863370081256e-28, (133, 1) = -0.19047811949310133e-30, (133, 2) = 0.17517423230767786e-28, (134, 1) = 0.1670408780234418e-30, (134, 2) = -0.1547920565426387e-28, (135, 1) = -0.14663297779105465e-30, (135, 2) = 0.13690945221170133e-28, (136, 1) = 0.1288443214665143e-30, (136, 2) = -0.12120440427591322e-28, (137, 1) = -0.11332280422320707e-30, (137, 2) = 0.10739834866852058e-28, (138, 1) = 0.9976576757640353e-31, (138, 2) = -0.9525004747333658e-29, (139, 1) = -0.879127632223075e-31, (139, 2) = 0.8455036424041919e-29, (140, 1) = 0.7753941760972859e-31, (140, 2) = -0.7511780098664585e-29, (141, 1) = -0.6845222406256883e-31, (141, 2) = 0.667946820033817e-29, (142, 1) = 0.6048411709261702e-31, (142, 2) = -0.59443887176349745e-29, (143, 1) = -0.53490706291992e-31, (143, 2) = 0.5294605182446958e-29, (144, 1) = 0.47347068238839457e-31, (144, 2) = -0.47197164246244804e-29, (145, 1) = -0.41945010728481444e-31, (145, 2) = 0.4210650236949918e-29, (146, 1) = 0.37190736638344014e-31, (146, 2) = -0.3759485918404288e-29, (147, 1) = -0.330028471675096e-31, (147, 2) = 0.3359301527693739e-29, (148, 1) = 0.29310633361188766e-31, (148, 2) = -0.3004042278151509e-29, (149, 1) = -0.26052612352840926e-31, (149, 2) = 0.26884069914781236e-29, (150, 1) = 0.23175272175688602e-31, (150, 2) = -0.2407750058744706e-29, (151, 1) = -0.20631994343396363e-31, (151, 2) = 0.21579967117635317e-29, (152, 1) = 0.1838212782103803e-31, (152, 2) = -0.1935569698521083e-29, (153, 1) = -0.16390192462363818e-31, (153, 2) = 0.17373257837203437e-29, (154, 1) = 0.1462519315158425e-31, (154, 2) = -0.15605007085788865e-29, (155, 1) = -0.13060028519318333e-31, (155, 2) = 0.14026614199892003e-29, (156, 1) = 0.11670980800642499e-31, (156, 2) = -0.12616645824447964e-29, (157, 1) = -0.10437275285666425e-31, (157, 2) = 0.1135620514654649e-29, (158, 1) = 0.9340699408924997e-32, (158, 2) = -0.10228618019121014e-29, (159, 1) = -0.836527316249834e-32, (159, 2) = 0.9219159613537638e-30, (160, 1) = 0.7496963658343102e-32, (160, 2) = -0.8314816164793746e-30, (161, 1) = -0.6723437641220817e-32, (161, 2) = 0.750407705484211e-30, (162, 1) = 0.6033846750257689e-32, (162, 2) = -0.67767532589807485e-30, (163, 1) = -0.5418641035725452e-32, (163, 2) = 0.6123818685931232e-30, (164, 1) = 0.4869406834681102e-32, (164, 2) = -0.5537271365721272e-30, (165, 1) = -0.4378725723240617e-32, (165, 2) = 0.5010011928390063e-30, (166, 1) = 0.3940051703632741e-32, (166, 2) = -0.4535737137392484e-30, (167, 1) = -0.354760415635001e-32, (167, 2) = 0.41088465111583645e-30, (168, 1) = 0.319627446964658e-32, (168, 2) = -0.3724360375741434e-30, (169, 1) = -0.28815445324760868e-32, (169, 2) = 0.33778478940228954e-30, (170, 1) = 0.25994155129731338e-32, (170, 2) = -0.30653637923871564e-30, (171, 1) = -0.2346345582313922e-32, (171, 2) = 0.27833927010170032e-30, (172, 1) = 0.2119195419510833e-32, (172, 2) = -0.25288001578179066e-30, (173, 1) = -0.19151805055355112e-32, (173, 2) = 0.22987894692533316e-30, (174, 1) = 0.17318292909006743e-32, (174, 2) = -0.20908636524897344e-30, (175, 1) = -0.1566946506428353e-32, (175, 2) = 0.1902791862527703e-30, (176, 1) = 0.1418580722894358e-32, (176, 2) = -0.17325794457148393e-30, (177, 1) = -0.12849961762790793e-32, (177, 2) = 0.15784418950772578e-30, (178, 1) = 0.11646478933559064e-32, (178, 2) = -0.14387816874455436e-30, (179, 1) = -0.10561599482497915e-32, (179, 2) = 0.13121679747695827e-30, (180, 1) = 0.9583060815464538e-33, (180, 2) = -0.11973182915589342e-30, (181, 1) = -0.869992698320368e-33, (181, 2) = 0.1093082442350599e-30, (182, 1) = 0.7902438802565789e-33, (182, 2) = -0.9984282185847586e-31, (183, 1) = -0.7181881679060695e-33, (183, 2) = 0.912428734112428e-31, (184, 1) = 0.6530468897255713e-33, (184, 2) = -0.8342511803027381e-31, (185, 1) = -0.5941238488337791e-33, (185, 2) = 0.763146833775158e-31, (186, 1) = 0.5407962038204935e-33, (186, 2) = -0.6984421721183288e-31, (187, 1) = -0.4925064001194972e-33, (187, 2) = 0.639530969931399e-31, (188, 1) = 0.44875502556004435e-33, (188, 2) = -0.5858672617291927e-31, (189, 1) = -0.4090944803938618e-33, (189, 2) = 0.5369590731435888e-31, (190, 1) = 0.37312336537600703e-33, (190, 2) = -0.4923628331946005e-31, (191, 1) = -0.3404815028800537e-33, (191, 2) = 0.45167839007853136e-31, (192, 1) = 0.31084551701385013e-33, (192, 2) = -0.4145445628528291e-31, (193, 1) = -0.2839249075575462e-33, (193, 2) = 0.38063516909782707e-31, (194, 1) = 0.25945856015130854e-33, (194, 2) = -0.34965547520115533e-31, (195, 1) = -0.23721164244332213e-33, (195, 2) = 0.3213390225773672e-31, (196, 1) = 0.2169728418770345e-33, (196, 2) = -0.295444788432909e-31, (197, 1) = -0.1985519058823843e-33, (197, 2) = 0.27175464414115723e-31, (198, 1) = 0.1817774501166719e-33, (198, 2) = -0.2500710788256612e-31, (199, 1) = -0.16649500441747457e-33, (199, 2) = 0.23021515937090376e-31, (200, 1) = 0.152565269574885e-33, (200, 2) = -0.21202470115318217e-31, (201, 1) = -0.13986256131726767e-33, (201, 2) = 0.19535262687912457e-31, (202, 1) = 0.1282734206226106e-33, (202, 2) = -0.18006549340632579e-31, (203, 1) = -0.1176953718154862e-33, (203, 2) = 0.16604216855372883e-31, (204, 1) = 0.10803581213224918e-33, (204, 2) = -0.15317264202810937e-31, (205, 1) = -0.99211018296342e-34, (205, 2) = 0.1413569563246614e-31, (206, 1) = 0.9114525724790876e-34, (206, 2) = -0.13050424493761976e-31, (207, 1) = -0.8376998968584803e-34, (207, 2) = 0.12053186667873671e-31, (208, 1) = 0.7702315635908218e-34, (208, 2) = -0.1113646261128974e-31, (209, 1) = -0.7084853814361585e-34, (209, 2) = 0.10293407114987609e-31, (210, 1) = 0.6519518198178588e-34, (210, 2) = -0.9517785984961501e-32, (211, 1) = -0.6001688563917718e-34, (211, 2) = 0.8803918934257016e-32, (212, 1) = 0.5527173499789222e-34, (212, 2) = -0.8146628049422425e-32, (213, 1) = -0.5092168832066444e-34, (213, 2) = 0.7541191265252166e-32, (214, 1) = 0.46932202530175474e-34, (214, 2) = -0.6983300341167028e-32, (215, 1) = -0.43271897078376966e-34, (215, 2) = 0.6469022883933462e-32, (216, 1) = 0.39912251476459205e-34, (216, 2) = -0.5994768011193173e-32, (217, 1) = -0.36827332982078095e-34, (217, 2) = 0.5557255292485938e-32, (218, 1) = 0.3399355131059267e-34, (218, 2) = -0.5153486640808916e-32, (219, 1) = -0.31389437582723705e-34, (219, 2) = 0.47807208629010065e-32, (220, 1) = 0.2899544501923474e-34, (220, 2) = -0.44364506064103776e-32, (221, 1) = -0.26793769154040974e-34, (221, 2) = 0.4118381468167556e-32, (222, 1) = 0.247681855770903e-34, (222, 2) = -0.3824413052359604e-32, (223, 1) = -0.22903903431632305e-34, (223, 2) = 0.3552621789349076e-32, (224, 1) = 0.2118743307195669e-34, (224, 2) = -0.3301245344130679e-32, (225, 1) = -0.1960646645604042e-34, (225, 2) = 0.3068668460838196e-32, (226, 1) = 0.18149769003459984e-34, (226, 2) = -0.28534101062969824e-32, (227, 1) = -0.16807081769919906e-34, (227, 2) = 0.2654111787480664e-32, (228, 1) = 0.1556903291545131e-34, (228, 2) = -0.2469526931296691e-32, (229, 1) = -0.14427057551409482e-34, (229, 2) = 0.22985112266277478e-32, (230, 1) = 0.13373325135813107e-34, (230, 2) = -0.21400138368268982e-32, (231, 1) = -0.12400673680607734e-34, (231, 2) = 0.1993069401417849e-32, (232, 1) = 0.11502550105896189e-34, (232, 2) = -0.18567907531135622e-32, (233, 1) = -0.10672956141242531e-34, (233, 2) = 0.1730362283058299e-32, (234, 1) = 0.9906399239741777e-35, (234, 2) = -0.16130338945651454e-32, (235, 1) = -0.9197848019951062e-35, (235, 2) = 0.15041154906528471e-32, (236, 1) = 0.8542691801329093e-35, (236, 2) = -0.14029719462891378e-32, (237, 1) = -0.7936703842195946e-35, (237, 2) = 0.13090185209621157e-32, (238, 1) = 0.7376007927177813e-35, (238, 2) = -0.12217166712833413e-32, (239, 1) = -0.6857047986925733e-35, (239, 2) = 0.11405702273138622e-32, (240, 1) = 0.6376560463565193e-35, (240, 2) = -0.10651218996399778e-32, (241, 1) = -0.5931549163623772e-35, (241, 2) = 0.9949500873646928e-33, (242, 1) = 0.551926236552634e-35, (242, 2) = -0.9296659600011781e-33, (243, 1) = -0.51371719711001646e-35, (243, 2) = 0.8689107887244882e-33, (244, 1) = 0.47829545113324e-35, (244, 2) = -0.8123535047933009e-33, (245, 1) = -0.4454473834692155e-35, (245, 2) = 0.7596884649670116e-33, (246, 1) = 0.41497653226806024e-35, (246, 2) = -0.7106334055783799e-33, (247, 1) = -0.3867021492756001e-35, (247, 2) = 0.6649275687192687e-33, (248, 1) = 0.3604578861481759e-35, (248, 2) = -0.6223299853973802e-33, (249, 1) = -0.33609059528887656e-35, (249, 2) = 0.58261790191422595e-33, (250, 1) = 0.31345923486572987e-35, (250, 2) = -0.5455853370987617e-33, (251, 1) = -0.2924338685507586e-35, (251, 2) = 0.511041758974477e-33, (252, 1) = 0.27289475144022434e-35, (252, 2) = -0.4788108705274377e-33, (253, 1) = -0.25473149448117235e-35, (253, 2) = 0.4487294952944828e-33, (254, 1) = 0.23784230033677894e-35, (254, 2) = -0.4206465541213175e-33, (255, 1) = -0.22213326433560898e-35, (255, 2) = 0.3944221253158751e-33, (256, 1) = 0.20751773477467816e-35, (256, 2) = -0.36992658118361226e-33, (257, 1) = -0.19391572728483876e-35, (257, 2) = 0.34703979438401436e-33, (258, 1) = 0.1812533885208609e-35, (258, 2) = -0.32565040825404966e-33, (259, 1) = -0.16946250486360973e-35, (259, 2) = 0.3056551657438799e-33, (260, 1) = 0.15848005217473686e-35, (260, 2) = -0.28695829200248043e-33, (261, 1) = -0.14824778305960624e-35, (261, 2) = 0.2694709261903304e-33, (262, 1) = 0.13871184836769757e-35, (262, 2) = -0.25311059839067244e-33, (263, 1) = -0.12982244997348811e-35, (263, 2) = 0.2378007478844579e-33, (264, 1) = 0.12153352216943357e-35, (264, 2) = -0.223470279421564e-33, (265, 1) = -0.11380243918140815e-35, (265, 2) = 0.21005315429364256e-33, (266, 1) = 0.10658974659791437e-35, (266, 2) = -0.19748801340218325e-33, (267, 1) = -0.9985891468793657e-36, (267, 2) = 0.18571782973112188e-33, (268, 1) = 0.9357611171672236e-36, (268, 2) = -0.1746895877650232e-33, (269, 1) = -0.877099955990111e-36, (269, 2) = 0.1643539877272496e-33, (270, 1) = 0.8223152234456637e-36, (270, 2) = -0.15466517263226672e-33, (271, 1) = -0.7711376986597443e-36, (271, 2) = 0.1455804762743676e-33, (272, 1) = 0.7233177588719506e-36, (272, 2) = -0.13706019051975646e-33, (273, 1) = -0.6786238877194185e-36, (273, 2) = 0.12906735034762346e-33, (274, 1) = 0.6368413019191564e-36, (274, 2) = -0.12156753521215117e-33, (275, 1) = -0.5977706866728063e-36, (275, 2) = 0.11452868545453896e-33, (276, 1) = 0.5612270307728243e-36, (276, 2) = -0.10792093256347315e-33, (277, 1) = -0.5270385532273333e-36, (277, 2) = 0.1017164421945091e-33, (278, 1) = 0.4950457139473309e-36, (278, 2) = -0.9588926895395885e-34, (279, 1) = -0.4651003016009631e-36, (279, 2) = 0.9041522201914115e-34, (280, 1) = 0.43706459240037096e-36, (280, 2) = -0.8527174075808299e-34, (281, 1) = -0.4108105740690065e-36, (281, 2) = 0.804377795706197e-34, (282, 1) = 0.386219229706459e-36, (282, 2) = -0.758937012325754e-34, (283, 1) = -0.36317987677465306e-36, (283, 2) = 0.7162117809583311e-34, (284, 1) = 0.34158955676795585e-36, (284, 2) = -0.6760310053650769e-34, (285, 1) = -0.3213524714990403e-36, (285, 2) = 0.6382349209190253e-34, (286, 1) = 0.3023479680329675e-36, (286, 2) = -0.6026074486471353e-34, (287, 1) = -0.2843175434432687e-36, (287, 2) = 0.5686350868865374e-34}, datatype = float[8], order = C_order); errproc := proc (x_bvp) local outpoint, X, Y, yout, L, V, i; option `Copyright (c) 2000 by Waterloo Maple Inc. All rights reserved.`; Digits := 15; outpoint := evalf(x_bvp); X := Vector(287, {(1) = .0, (2) = .34272785551155327, (3) = .68545605600652, (4) = 1.0281851233132908, (5) = 1.3709157576421804, (6) = 1.7136488383912685, (7) = 2.056385953711714, (8) = 2.3991290298258354, (9) = 2.741880351570709, (10) = 3.084643587088239, (11) = 3.4274437035919227, (12) = 3.770301567818841, (13) = 4.113191803804626, (14) = 4.456115474905258, (15) = 4.799079776109701, (16) = 5.14209466044807, (17) = 5.485169427579998, (18) = 5.828314040472344, (19) = 6.171541537977492, (20) = 6.514863445697707, (21) = 6.858291813544751, (22) = 7.201841545499454, (23) = 7.545525083034571, (24) = 7.889355083423169, (25) = 8.233346219155038, (26) = 8.577509952977802, (27) = 8.92185754467095, (28) = 9.266400979153765, (29) = 9.611148801757508, (30) = 9.956108953659863, (31) = 10.301288730821417, (32) = 10.6466924395304, (33) = 10.992323534142638, (34) = 11.33818376225298, (35) = 11.684272903420274, (36) = 12.0305898603869, (37) = 12.377131283060706, (38) = 12.72389312270968, (39) = 13.070870623217946, (40) = 13.418056712046997, (41) = 13.765444778211265, (42) = 14.113027773901806, (43) = 14.460796576462846, (44) = 14.808743348757957, (45) = 15.156860091762422, (46) = 15.505137090682709, (47) = 15.853566351414612, (48) = 16.202139937083167, (49) = 16.550848548706988, (50) = 16.899684722744254, (51) = 17.24864119730986, (52) = 17.597709643967587, (53) = 17.94688347580373, (54) = 18.29615638472377, (55) = 18.645521225125222, (56) = 18.994972391968034, (57) = 19.34450458700878, (58) = 19.694111846926504, (59) = 20.043789512092907, (60) = 20.393533226676, (61) = 20.743338099741614, (62) = 21.09320031234754, (63) = 21.443116329359093, (64) = 21.793082179871465, (65) = 22.14309475882787, (66) = 22.493151217183122, (67) = 22.843248346986332, (68) = 23.193383632461526, (69) = 23.54355478391626, (70) = 23.893759213342307, (71) = 24.24399488277774, (72) = 24.59425995148581, (73) = 24.944552329348667, (74) = 25.294870361999827, (75) = 25.645212565905318, (76) = 25.995577247975383, (77) = 26.34596306071336, (78) = 26.696368804056206, (79) = 27.04679310067058, (80) = 27.39723484828554, (81) = 27.74769307187836, (82) = 28.09816664618133, (83) = 28.448654665485446, (84) = 28.799156334035786, (85) = 29.149670728749008, (86) = 29.500197102624572, (87) = 29.850734803822537, (88) = 30.20128307266724, (89) = 30.55184129119914, (90) = 30.902408923959488, (91) = 31.252985344565516, (92) = 31.603570040897964, (93) = 31.954162572236804, (94) = 32.30476242101317, (95) = 32.655369162567034, (96) = 33.00598243385484, (97) = 33.35660180652833, (98) = 33.70722692767758, (99) = 34.05785749763447, (100) = 34.40849316164718, (101) = 34.75913362556661, (102) = 35.10977864120253, (103) = 35.4604279138097, (104) = 35.811081197479595, (105) = 36.161738285857474, (106) = 36.51239893269488, (107) = 36.863062932270076, (108) = 37.213730132427244, (109) = 37.564400411682485, (110) = 37.91507429726012, (111) = 38.26575278180425, (112) = 38.61643836750501, (113) = 38.96713357867858, (114) = 39.31784005437529, (115) = 39.66855847947291, (116) = 40.01928849985208, (117) = 40.37002941059889, (118) = 40.72077953261957, (119) = 41.07153580382777, (120) = 41.42229565140575, (121) = 41.7730562000106, (122) = 42.12381643485321, (123) = 42.474584871545844, (124) = 42.82539298957335, (125) = 43.17621628319367, (126) = 43.52703866350971, (127) = 43.87786013580987, (128) = 44.228680706087246, (129) = 44.57950038004278, (130) = 44.93031916638373, (131) = 45.28113707488388, (132) = 45.631954114395405, (133) = 45.9827702976725, (134) = 46.33358563911399, (135) = 46.68440015137355, (136) = 47.03521385201806, (137) = 47.38602675988438, (138) = 47.736838891351844, (139) = 48.087650269059495, (140) = 48.438460915923294, (141) = 48.789270851395536, (142) = 49.14008010179399, (143) = 49.49088869330937, (144) = 49.84169664757439, (145) = 50.19250399298156, (146) = 50.54331075723062, (147) = 50.89411696274616, (148) = 51.24492263837032, (149) = 51.595727811628926, (150) = 51.94653250438395, (151) = 52.29733674423571, (152) = 52.648140557097435, (153) = 52.998943963278634, (154) = 53.34974698812261, (155) = 53.70054965478789, (156) = 54.05135198128938, (157) = 54.40215399004583, (158) = 54.75295570130227, (159) = 55.103757130533914, (160) = 55.454558296681114, (161) = 55.805359217100936, (162) = 56.156159904884326, (163) = 56.50696037582576, (164) = 56.85776064430965, (165) = 57.208560721202716, (166) = 57.55936061969085, (167) = 57.91016035151163, (168) = 58.26095992552927, (169) = 58.61175935255006, (170) = 58.96255864229041, (171) = 59.31335780196695, (172) = 59.664156843110334, (173) = 60.014955838602745, (174) = 60.365754970062234, (175) = 60.71655460864663, (176) = 61.06735477766199, (177) = 61.418155330543456, (178) = 61.76895590733981, (179) = 62.11975643197004, (180) = 62.470556882346905, (181) = 62.82135726316636, (182) = 63.172157578783505, (183) = 63.522957832393786, (184) = 63.873758027797514, (185) = 64.22455816856692, (186) = 64.57535825733743, (187) = 64.92615829725554, (188) = 65.2769582912228, (189) = 65.62775824139982, (190) = 65.97855815038982, (191) = 66.32935802061039, (192) = 66.68015785383814, (193) = 67.03095765218829, (194) = 67.38175741768679, (195) = 67.73255715181558, (196) = 68.08335685632655, (197) = 68.43415653288562, (198) = 68.78495618272667, (199) = 69.13575580732001, (200) = 69.48655540804855, (201) = 69.83735498593576, (202) = 70.188154542199, (203) = 70.53895407800616, (204) = 70.88975359420964, (205) = 71.24055309180984, (206) = 71.59135257178401, (207) = 71.9421520348469, (208) = 72.29295148183436, (209) = 72.64375091354758, (210) = 72.99455033057936, (211) = 73.34534973362636, (212) = 73.69614912335479, (213) = 74.0469485002512, (214) = 74.39774786488076, (215) = 74.74854721779742, (216) = 75.09934655940131, (217) = 75.45014589015119, (218) = 75.80094521049713, (219) = 76.15174452077865, (220) = 76.5025438214065, (221) = 76.85334311291608, (222) = 77.20414239582111, (223) = 77.55494167082877, (224) = 77.9057409389566, (225) = 78.25654020112306, (226) = 78.60733945850832, (227) = 78.95813871242063, (228) = 79.30893796382937, (229) = 79.65973721381565, (230) = 80.01053646321836, (231) = 80.36133571253576, (232) = 80.71213496221912, (233) = 81.06293421237899, (234) = 81.41373346301715, (235) = 81.76453271407989, (236) = 82.11533196543857, (237) = 82.46613121700742, (238) = 82.81693046870076, (239) = 83.16772972046982, (240) = 83.51852897231515, (241) = 83.86932822426833, (242) = 84.22012747644777, (243) = 84.5709267290116, (244) = 84.92172598219018, (245) = 85.27252523636308, (246) = 85.62332449191798, (247) = 85.97412374935872, (248) = 86.32492300939072, (249) = 86.67572227265899, (250) = 87.02652153994809, (251) = 87.37732081223929, (252) = 87.72812009034146, (253) = 88.07891937517155, (254) = 88.42971866772481, (255) = 88.78051796870106, (256) = 89.13131727880436, (257) = 89.48211659858173, (258) = 89.83291592823649, (259) = 90.18371526783567, (260) = 90.5345146170466, (261) = 90.88531397531379, (262) = 91.23611334185617, (263) = 91.58691271541277, (264) = 91.9377120947821, (265) = 92.2885114785654, (266) = 92.63931086503187, (267) = 92.99011025279923, (268) = 93.34090964040644, (269) = 93.6917090263214, (270) = 94.04250840948134, (271) = 94.39330778886179, (272) = 94.74410716357119, (273) = 95.0949065331069, (274) = 95.4457058970584, (275) = 95.79650525522254, (276) = 96.14730460760524, (277) = 96.49810395429898, (278) = 96.84890329558608, (279) = 97.1997026317924, (280) = 97.55050196330045, (281) = 97.9013012906382, (282) = 98.25210061427734, (283) = 98.60289993472414, (284) = 98.9536992526252, (285) = 99.30449856847163, (286) = 99.65462188610245, (287) = 100.0}, datatype = float[8], order = C_order); Y := Matrix(287, 2, {(1, 1) = .0, (1, 2) = 0.3337473770689716e-9, (2, 1) = 0.11814765668358296e-8, (2, 2) = -0.1114592631425331e-8, (3, 1) = 0.1511543972188e-9, (3, 2) = -0.1206492417902728e-8, (4, 1) = -0.25141053825953208e-8, (4, 2) = 0.5407350326297658e-8, (5, 1) = 0.7113925387067616e-9, (5, 2) = -0.1759125288537426e-9, (6, 1) = 0.2330632692087437e-8, (6, 2) = -0.7510279655112322e-8, (7, 1) = -0.9319663398877757e-9, (7, 2) = 0.25105448540246094e-8, (8, 1) = -0.10925492928389412e-8, (8, 2) = 0.4552867706214881e-8, (9, 1) = 0.4076493832666734e-9, (9, 2) = -0.18380528251927653e-8, (10, 1) = 0.2986518631089414e-9, (10, 2) = -0.15088298020185389e-8, (11, 1) = -0.7005046864020264e-10, (11, 2) = 0.4822203195435165e-9, (12, 1) = -0.4697021592525276e-10, (12, 2) = 0.3008072883341392e-9, (13, 1) = 0.16721729915836829e-11, (13, 2) = -0.311577845677934e-10, (14, 1) = 0.29246964534049903e-11, (14, 2) = -0.28599926294300703e-10, (15, 1) = 0.4402540168328618e-12, (15, 2) = -0.4453066753332934e-11, (16, 1) = 0.4007343244129068e-13, (16, 2) = -0.4231821160635797e-12, (17, 1) = 0.925084606169142e-15, (17, 2) = -0.10955593999150281e-13, (18, 1) = 0.2870488914253043e-15, (18, 2) = -0.32469165417556614e-14, (19, 1) = -0.6962697216651804e-16, (19, 2) = 0.8224017028812664e-15, (20, 1) = 0.23204181301376128e-16, (20, 2) = -0.2891831955614606e-15, (21, 1) = -0.8133633844802188e-17, (21, 2) = 0.1065723465978877e-15, (22, 1) = 0.30268819841325116e-17, (22, 2) = -0.41601688523960707e-16, (23, 1) = -0.11871681092704418e-17, (23, 2) = 0.17078830008648408e-16, (24, 1) = 0.4880253049487869e-18, (24, 2) = -0.733451795716719e-17, (25, 1) = -0.20929847462463454e-18, (25, 2) = 0.3280205463859045e-17, (26, 1) = 0.9327420476628717e-19, (26, 2) = -0.15218988809421989e-17, (27, 1) = -0.4304765418952763e-19, (27, 2) = 0.7301299692705559e-18, (28, 1) = 0.2051386090053452e-19, (28, 2) = -0.36116914326921613e-18, (29, 1) = -0.1006776657740541e-19, (29, 2) = 0.18375466536494282e-18, (30, 1) = 0.5077151514874421e-20, (30, 2) = -0.9594789690915855e-19, (31, 1) = -0.26256373982083428e-20, (31, 2) = 0.5131730483668789e-19, (32, 1) = 0.13899480767972848e-20, (32, 2) = -0.280657567278695e-19, (33, 1) = -0.7519957694401982e-21, (33, 2) = 0.15671363517149912e-19, (34, 1) = 0.41520145332676e-21, (34, 2) = -0.8921832186854169e-20, (35, 1) = -0.23364881770927607e-21, (35, 2) = 0.5172218611302253e-20, (36, 1) = 0.13384959669783403e-21, (36, 2) = -0.3049894497426686e-20, (37, 1) = -0.7797452210664558e-22, (37, 2) = 0.18273906064338e-20, (38, 1) = 0.46147205854133144e-22, (38, 2) = -0.11115002530637308e-20, (39, 1) = -0.2772079018505821e-22, (39, 2) = 0.6857205069361473e-21, (40, 1) = 0.1688789537753143e-22, (40, 2) = -0.4287477364369552e-21, (41, 1) = -0.10426220124042319e-22, (41, 2) = 0.2714935405564624e-21, (42, 1) = 0.65186292297620775e-23, (42, 2) = -0.17399251453450416e-21, (43, 1) = -0.4124612569542049e-23, (43, 2) = 0.1127837935628437e-21, (44, 1) = 0.26396641904431163e-23, (44, 2) = -0.7390269278201417e-22, (45, 1) = -0.1707701349080691e-23, (45, 2) = 0.4892621217953827e-22, (46, 1) = 0.11162178300177267e-23, (46, 2) = -0.32709699530967695e-22, (47, 1) = -0.7368043572433129e-24, (47, 2) = 0.22073266853824346e-22, (48, 1) = 0.4909387117240077e-24, (48, 2) = -0.15028883002348628e-22, (49, 1) = -0.3300599411243533e-24, (49, 2) = 0.10320088177779745e-22, (50, 1) = 0.22381021249253716e-24, (50, 2) = -0.7144556539494561e-23, (51, 1) = -0.1530134648524169e-24, (51, 2) = 0.498483918325963e-23, (52, 1) = 0.10543703408647383e-24, (52, 2) = -0.3504037916840427e-23, (53, 1) = -0.7320341315925612e-25, (53, 2) = 0.2480820075421193e-23, (54, 1) = 0.5119324578919227e-25, (54, 2) = -0.1768502253045044e-23, (55, 1) = -0.3605068998729239e-25, (55, 2) = 0.1269059116888513e-23, (56, 1) = 0.25557485384799628e-25, (56, 2) = -0.91645949085942e-24, (57, 1) = -0.1823544587963114e-25, (57, 2) = 0.6658792474039049e-24, (58, 1) = 0.13091960556268006e-25, (58, 2) = -0.4866643967553924e-24, (59, 1) = -0.9455520040580005e-26, (59, 2) = 0.35770288252130434e-24, (60, 1) = 0.686856152524142e-26, (60, 2) = -0.26435406231287835e-24, (61, 1) = -0.50171605182877446e-26, (61, 2) = 0.19639776462403663e-24, (62, 1) = 0.3684504641767209e-26, (62, 2) = -0.1466543808202158e-24, (63, 1) = -0.27198821780865398e-26, (63, 2) = 0.11004910121884334e-24, (64, 1) = 0.20178827848394655e-26, (64, 2) = -0.8297351680973491e-25, (65, 1) = -0.1504338605340296e-26, (65, 2) = 0.6284726077241137e-25, (66, 1) = 0.11267594688949902e-26, (66, 2) = -0.47814839507583096e-25, (67, 1) = -0.8477898254937608e-27, (67, 2) = 0.36534831039655415e-25, (68, 1) = 0.6407007400552214e-27, (68, 2) = -0.28032457087091865e-25, (69, 1) = -0.4862656342473373e-27, (69, 2) = 0.21595796787573645e-25, (70, 1) = 0.3705845012796548e-27, (70, 2) = -0.16702368472395702e-25, (71, 1) = -0.28355867430759805e-27, (71, 2) = 0.1296692269874396e-25, (72, 1) = 0.21781585747028026e-27, (72, 2) = -0.10104093506970917e-25, (73, 1) = -0.16794923808588196e-27, (73, 2) = 0.7901561451265935e-26, (74, 1) = 0.12997562875807102e-27, (74, 2) = -0.6200679172444172e-26, (75, 1) = -0.10094768110196078e-27, (75, 2) = 0.4882406310734796e-26, (76, 1) = 0.786752926605406e-28, (76, 2) = -0.3857057678554118e-26, (77, 1) = -0.615243377149303e-28, (77, 2) = 0.30567990763013615e-26, (78, 1) = 0.4827058769761561e-28, (78, 2) = -0.24301259837595366e-26, (79, 1) = -0.3799333192551861e-28, (79, 2) = 0.19377861519806835e-26, (80, 1) = 0.2999749704145833e-28, (80, 2) = -0.15497568750483856e-26, (81, 1) = -0.23756393566246672e-28, (81, 2) = 0.12429934037471303e-26, (82, 1) = 0.1886949204022922e-28, (82, 2) = -0.9997460451337635e-27, (83, 1) = -0.1503113733655041e-28, (83, 2) = 0.8062978956416159e-27, (84, 1) = 0.120072691963301e-28, (84, 2) = -0.6520138567398338e-27, (85, 1) = -0.9618059165905672e-29, (85, 2) = 0.5286219008692601e-27, (86, 1) = 0.7724894990396434e-29, (86, 2) = -0.4296681247835735e-27, (87, 1) = -0.6220593745962619e-29, (87, 2) = 0.35010185451536685e-27, (88, 1) = 0.50220186049387665e-29, (88, 2) = -0.2859588342805069e-27, (89, 1) = -0.4064491358184905e-29, (89, 2) = 0.23411860071713875e-27, (90, 1) = 0.3297542815670744e-29, (90, 2) = -0.19211795099436772e-27, (91, 1) = -0.26816799619085238e-29, (91, 2) = 0.15800714133270899e-27, (92, 1) = 0.21859104395660753e-29, (92, 2) = -0.1302387278657487e-27, (93, 1) = -0.1785847001704855e-29, (93, 2) = 0.1075813288270173e-27, (94, 1) = 0.14622468619028246e-29, (94, 2) = -0.8905254808199302e-28, (95, 1) = -0.11998882995419452e-29, (95, 2) = 0.7386667259285517e-28, (96, 1) = 0.9866975654973794e-30, (96, 2) = -0.6139375131975005e-28, (97, 1) = -0.8130755233546983e-30, (97, 2) = 0.5112750119712382e-28, (98, 1) = 0.6713700975604642e-30, (98, 2) = -0.42660078121162386e-28, (99, 1) = -0.55546817453196835e-30, (99, 2) = 0.356621813191627e-28, (100, 1) = 0.4604729884112169e-30, (100, 2) = -0.29867327759107367e-28, (101, 1) = -0.3824547230914971e-30, (101, 2) = 0.25059395998577682e-28, (102, 1) = 0.318250738230565e-30, (102, 2) = -0.21062730253585154e-28, (103, 1) = -0.26531184526334304e-30, (103, 2) = 0.17734261443968678e-28, (104, 1) = 0.22157721765580087e-30, (104, 2) = -0.1495722164087073e-28, (105, 1) = -0.18537892570008996e-30, (105, 2) = 0.12636115598278117e-28, (106, 1) = 0.15536256629090588e-30, (106, 2) = -0.10692689695974917e-28, (107, 1) = -0.13042775671560108e-30, (107, 2) = 0.9062694467764165e-29, (108, 1) = 0.10967702200086956e-30, (108, 2) = -0.769327766112338e-29, (109, 1) = -0.9237862157846045e-31, (109, 2) = 0.6540880919611225e-29, (110, 1) = 0.7793316621496255e-31, (110, 2) = -0.55695409094313936e-29, (111, 1) = -0.6585033692656705e-31, (111, 2) = 0.4749510542707245e-29, (112, 1) = 0.5572676806259021e-31, (112, 2) = -0.4056142409276652e-29, (113, 1) = -0.4723143193048704e-31, (113, 2) = 0.3468976136611732e-29, (114, 1) = 0.40090764395624516e-31, (114, 2) = -0.2970997328820372e-29, (115, 1) = -0.34079742681023814e-31, (115, 2) = 0.25480340524767877e-29, (116, 1) = 0.29011516846181336e-31, (116, 2) = -0.2188262970098597e-29, (117, 1) = -0.247321444183979e-31, (117, 2) = 0.18818050713028952e-29, (118, 1) = 0.21113096392205004e-31, (118, 2) = -0.16203925275437173e-29, (119, 1) = -0.180483863354958e-31, (119, 2) = 0.13970951216681748e-29, (120, 1) = 0.15449023134760425e-31, (120, 2) = -0.12060960110142806e-29, (121, 1) = -0.13241607020505873e-31, (121, 2) = 0.10425050355217693e-29, (122, 1) = 0.11364105078756676e-31, (122, 2) = -0.9022057104839553e-30, (123, 1) = -0.9765488474733964e-32, (123, 2) = 0.7817296850312761e-30, (124, 1) = 0.8402320040261645e-32, (124, 2) = -0.67815278597230635e-30, (125, 1) = -0.723829731223821e-32, (125, 2) = 0.5889875701105122e-30, (126, 1) = 0.6243089232174535e-32, (126, 2) = -0.5121316606770032e-30, (127, 1) = -0.539112374959662e-32, (127, 2) = 0.4458061139224835e-30, (128, 1) = 0.46608847791563504e-32, (128, 2) = -0.3885004176184961e-30, (129, 1) = -0.40342013527562426e-32, (129, 2) = 0.3389303006756524e-30, (130, 1) = 0.3495749422844784e-32, (130, 2) = -0.29600243552828953e-30, (131, 1) = -0.30325458694006873e-32, (131, 2) = 0.25878486405279445e-30, (132, 1) = 0.26336192540451217e-32, (132, 2) = -0.22648218496208407e-30, (133, 1) = -0.2289643351131066e-32, (133, 2) = 0.19841470780532246e-30, (134, 1) = 0.19927232471103483e-32, (134, 2) = -0.17400091460775773e-30, (135, 1) = -0.17361244436544725e-32, (135, 2) = 0.15274268519902317e-30, (136, 1) = 0.15141382410870842e-32, (136, 2) = -0.13421283486095642e-30, (137, 1) = -0.13218766540291868e-32, (137, 2) = 0.11804458773251245e-30, (138, 1) = 0.11551925764129571e-32, (138, 2) = -0.10392267455875862e-30, (139, 1) = -0.10105203337090825e-32, (139, 2) = 0.9157579502324023e-31, (140, 1) = 0.8848338769635796e-33, (140, 2) = -0.8077022667680521e-31, (141, 1) = -0.7755191344438287e-33, (141, 2) = 0.7130440006517806e-31, (142, 1) = 0.6803587995267088e-33, (142, 2) = -0.6300428863814429e-31, (143, 1) = -0.59742692591919096e-33, (143, 2) = 0.5571948572082767e-31, (144, 1) = 0.52509239552417015e-33, (144, 2) = -0.4931986274879284e-31, (145, 1) = -0.4619291955932403e-33, (145, 2) = 0.43692719508835927e-31, (146, 1) = 0.40673304915394185e-33, (146, 2) = -0.38740350664942923e-31, (147, 1) = -0.35844279166994104e-33, (147, 2) = 0.34377965799490294e-31, (148, 1) = 0.31616635357760217e-33, (148, 2) = -0.30531909751239395e-31, (149, 1) = -0.2791100132527961e-33, (149, 2) = 0.27138137867544806e-31, (150, 1) = 0.24661104757903347e-33, (150, 2) = -0.24140908516343437e-31, (151, 1) = -0.21807262257159595e-33, (151, 2) = 0.2149166077437237e-31, (152, 1) = 0.19300120788310715e-33, (152, 2) = -0.19148049813581943e-31, (153, 1) = -0.17094551540637902e-33, (153, 2) = 0.17073117148296364e-31, (154, 1) = 0.15153734765045163e-33, (154, 2) = -0.15234576199567748e-31, (155, 1) = -0.1344334475417537e-33, (155, 2) = 0.1360419637429045e-31, (156, 1) = 0.11935882919419917e-33, (156, 2) = -0.12157271667336315e-31, (157, 1) = -0.10605074000764487e-33, (157, 2) = 0.1087216175590277e-31, (158, 1) = 0.9430378816092739e-34, (158, 2) = -0.9729895217630775e-32, (159, 1) = -0.8391544171222988e-34, (159, 2) = 0.8713826210936183e-32, (160, 1) = 0.7473246799311917e-34, (160, 2) = -0.7809337144107723e-32, (161, 1) = -0.6659755220225075e-34, (161, 2) = 0.7003580876271684e-32, (162, 1) = 0.5939669719316928e-34, (162, 2) = -0.628525703151869e-32, (163, 1) = -0.5300666446502691e-34, (163, 2) = 0.564441774554753e-32, (164, 1) = 0.47343077819806993e-34, (164, 2) = -0.5072298786126305e-32, (165, 1) = -0.4230846990068872e-34, (165, 2) = 0.45611726283758844e-32, (166, 1) = 0.378409059054885e-34, (166, 2) = -0.4104220524617655e-32, (167, 1) = -0.3386247656349131e-34, (167, 2) = 0.3695420996198015e-32, (168, 1) = 0.3032830699656366e-34, (168, 2) = -0.3329452572548598e-32, (169, 1) = -0.27175381350172327e-34, (169, 2) = 0.30016088879960467e-32, (170, 1) = 0.2437183722107732e-34, (170, 2) = -0.27077244926804838e-32, (171, 1) = -0.21866037265730772e-34, (171, 2) = 0.24441099815771403e-32, (172, 1) = 0.19636076956605462e-34, (172, 2) = -0.2207495228657229e-32, (173, 1) = -0.17639041214217496e-34, (173, 2) = 0.1994979693266219e-32, (174, 1) = 0.15860670684734346e-34, (174, 2) = -0.18039888446883172e-32, (175, 1) = -0.14264757024465028e-34, (175, 2) = 0.16322359441962506e-32, (176, 1) = 0.1284292106918877e-34, (176, 2) = -0.14776882530149972e-32, (177, 1) = -0.11564127268869396e-34, (177, 2) = 0.13385376836240854e-32, (178, 1) = 0.10424543077952786e-34, (178, 2) = -0.12131748889124417e-32, (179, 1) = -0.9397138202926179e-35, (179, 2) = 0.11001666127602455e-32, (180, 1) = 0.8481601646366298e-35, (180, 2) = -0.9982355016109226e-33, (181, 1) = -0.7654006930288358e-35, (181, 2) = 0.9062423940837592e-33, (182, 1) = 0.691677981286831e-35, (182, 2) = -0.823170708600617e-33, (183, 1) = -0.6248408815586368e-35, (183, 2) = 0.7481126749021843e-33, (184, 1) = 0.5653452181587884e-35, (184, 2) = -0.6802571767975036e-33, (185, 1) = -0.5112282734766252e-35, (185, 2) = 0.6188790092018786e-33, (186, 1) = 0.4631124871789453e-35, (186, 2) = -0.5633293789797099e-33, (187, 1) = -0.419182568339192e-35, (187, 2) = 0.5130275001245018e-33, (188, 1) = 0.38019149059375494e-35, (188, 2) = -0.4674531516250693e-33, (189, 1) = -0.34443961712968836e-35, (189, 2) = 0.4261400837436245e-33, (190, 1) = 0.31278245966872795e-35, (190, 2) = -0.38867017226668485e-33, (191, 1) = -0.28361134904715077e-35, (191, 2) = 0.3546682321667413e-33, (192, 1) = 0.25786255196326492e-35, (192, 2) = -0.323797413556105e-33, (193, 1) = -0.2339991339082681e-35, (193, 2) = 0.29575511203911674e-33, (194, 1) = 0.21302112300425164e-35, (194, 2) = -0.270269333490964e-33, (195, 1) = -0.19344829455538694e-35, (195, 2) = 0.2470954608784735e-33, (196, 1) = 0.17633114598137155e-35, (196, 2) = -0.22601337695524923e-33, (197, 1) = -0.16023439510415835e-35, (197, 2) = 0.20682490196082456e-33, (198, 1) = 0.14624858452532997e-35, (198, 2) = -0.1893515105382064e-33, (199, 1) = -0.1329741349614128e-35, (199, 2) = 0.1734322962682068e-33, (200, 1) = 0.1215334390508763e-35, (200, 2) = -0.15892215580717671e-33, (201, 1) = -0.11055534713643871e-35, (201, 2) = 0.14569016803882635e-33, (202, 1) = 0.10118764313231196e-35, (202, 2) = -0.13361814648189295e-33, (203, 1) = -0.9208186787202561e-36, (203, 2) = 0.122599345641135e-33, (204, 1) = 0.8440609377474686e-36, (204, 2) = -0.1125373043044295e-33, (205, 1) = -0.7683001268681995e-36, (205, 2) = 0.10334481072536028e-33, (206, 1) = 0.7053794467710106e-36, (206, 2) = -0.9494297629990978e-34, (207, 1) = -0.6421413348516116e-36, (207, 2) = 0.8726040592276175e-34, (208, 1) = 0.5905593942874108e-36, (208, 2) = -0.8023245454071526e-34, (209, 1) = -0.537592981249624e-36, (209, 2) = 0.7380056056626958e-34, (210, 1) = 0.49532058429402855e-36, (210, 2) = -0.6791164789769716e-34, (211, 1) = -0.4507956999698665e-36, (211, 2) = 0.6251758920747775e-34, (212, 1) = 0.4161813568702299e-36, (212, 2) = -0.5757472395614066e-34, (213, 1) = -0.3786070097141604e-36, (213, 2) = 0.5304342533402869e-34, (214, 1) = 0.3503039697141173e-36, (214, 2) = -0.4888771096893547e-34, (215, 1) = -0.3184631052691592e-36, (215, 2) = 0.4507489278997771e-34, (216, 1) = 0.2953709911760705e-36, (216, 2) = -0.4157526195464645e-34, (217, 1) = -0.26826825009841395e-36, (217, 2) = 0.38361805189665645e-34, (218, 1) = 0.24948627300898547e-36, (218, 2) = -0.3540994928186896e-34, (219, 1) = -0.22630607054881833e-36, (219, 2) = 0.3269733081533858e-34, (220, 1) = 0.2110954487118299e-36, (220, 2) = -0.3020358856170453e-34, (221, 1) = -0.19116826672730477e-36, (221, 2) = 0.2791017620212669e-34, (222, 1) = 0.17892197611603809e-36, (222, 2) = -0.2580019330947062e-34, (223, 1) = -0.16169720359020907e-36, (223, 2) = 0.2385823274128465e-34, (224, 1) = 0.15191558075211895e-36, (224, 2) = -0.22070242783288896e-34, (225, 1) = -0.13693958715066484e-36, (225, 2) = 0.20423402558376064e-34, (226, 1) = 0.1292106131618646e-36, (226, 2) = -0.18906009378604668e-34, (227, 1) = -0.1161090117149979e-36, (227, 2) = 0.17507376843667124e-34, (228, 1) = 0.1100923483657934e-36, (228, 2) = -0.1621774262026243e-34, (229, 1) = -0.9855562101367198e-37, (229, 2) = 0.15028184949385224e-34, (230, 1) = 0.939696604772997e-37, (230, 2) = -0.13930547016472725e-34, (231, 1) = -0.8374148552968004e-37, (231, 2) = 0.12917368417300073e-34, (232, 1) = 0.8035282495561473e-37, (232, 2) = -0.11981823026975501e-34, (233, 1) = -0.7122058167869287e-37, (233, 2) = 0.11117662647128212e-34, (234, 1) = 0.6883545301813345e-37, (234, 2) = -0.10319165874731565e-34, (235, 1) = -0.6062248304551106e-37, (235, 2) = 0.9581091687449441e-35, (236, 1) = 0.590797622751285e-37, (236, 2) = -0.8898637293051614e-35, (237, 1) = -0.5163905153927267e-37, (237, 2) = 0.8267399835621295e-35, (238, 1) = 0.5080454607312584e-37, (238, 2) = -0.7683341590810539e-35, (239, 1) = -0.4401355743651424e-37, (239, 2) = 0.7142758319714514e-35, (240, 1) = 0.4377532991552011e-37, (240, 2) = -0.664225048288068e-35, (241, 1) = -0.37531769631467134e-37, (241, 2) = 0.6178697045441746e-35, (242, 1) = 0.3779630352269319e-37, (242, 2) = -0.57492316307567976e-35, (243, 1) = -0.32014646881756663e-37, (243, 2) = 0.5351220803229526e-35, (244, 1) = 0.32703697050184e-37, (244, 2) = -0.498224428263812e-35, (245, 1) = -0.27312332312116314e-37, (245, 2) = 0.464007691113782e-35, (246, 1) = 0.2836033392484572e-37, (246, 2) = -0.4322672211125852e-35, (247, 1) = -0.2329921064986339e-37, (247, 2) = 0.4028147388287664e-35, (248, 1) = 0.2465114396049633e-37, (248, 2) = -0.3754769647377042e-35, (249, 1) = -0.19869833546208911e-37, (249, 2) = 0.3500943700925948e-35, (250, 1) = 0.2147946152770067e-37, (250, 2) = -0.3265200363184777e-35, (251, 1) = -0.16935555154310478e-37, (251, 2) = 0.3046186130737151e-35, (252, 1) = 0.18763966601592173e-37, (252, 2) = -0.28426536608357577e-35, (253, 1) = -0.14421749812062591e-37, (253, 2) = 0.26534530675123343e-35, (254, 1) = 0.1643615309234645e-37, (254, 2) = -0.24775239618415717e-35, (255, 1) = -0.12265507575464846e-37, (255, 2) = 0.2313888170162637e-35, (256, 1) = 0.14438230376465493e-37, (256, 2) = -0.21616430705696473e-35, (257, 1) = -0.10413722618551834e-37, (257, 2) = 0.20199554925505035e-35, (258, 1) = 0.127213812890663e-37, (258, 2) = -0.18880561304257172e-35, (259, 1) = -0.8821505170584356e-38, (259, 2) = 0.17652344256626342e-35, (260, 1) = 0.11244313871080417e-37, (260, 2) = -0.16508338768202428e-35, (261, 1) = -0.7450860291449383e-38, (261, 2) = 0.1544247740204293e-35, (262, 1) = 0.9972055590379809e-38, (262, 2) = -0.14449150871635847e-35, (263, 1) = -0.6269587055364527e-38, (263, 2) = 0.13523171872238832e-35, (264, 1) = 0.8874947993080264e-38, (264, 2) = -0.1265974189265001e-35, (265, 1) = -0.52503600703367265e-38, (265, 2) = 0.11854420748063925e-35, (266, 1) = 0.7927807289349354e-38, (266, 2) = -0.11103098603949768e-35, (267, 1) = -0.4369962050155763e-38, (267, 2) = 0.10401970279993729e-35, (268, 1) = 0.7109222505883944e-38, (268, 2) = -0.97475116371589e-36, (269, 1) = -0.3608641722238596e-38, (269, 2) = 0.9136457874897461e-36, (270, 1) = 0.640096785233356e-38, (270, 2) = -0.8565783577559522e-36, (271, 1) = -0.2949575862837564e-38, (271, 2) = 0.8032684361039455e-36, (272, 1) = 0.5787510062267883e-38, (272, 2) = -0.753455998824992e-36, (273, 1) = -0.23784179702385838e-38, (273, 2) = 0.7068998830410939e-36, (274, 1) = 0.52555948021463534e-38, (274, 2) = -0.6633763561658139e-36, (275, 1) = -0.18829191309249274e-38, (275, 2) = 0.6226777986175264e-36, (276, 1) = 0.47938990062688373e-38, (276, 2) = -0.5846114903883851e-36, (277, 1) = -0.14526091121756108e-38, (277, 2) = 0.5489984929451629e-36, (278, 1) = 0.43927382551798036e-38, (278, 2) = -0.5156726186951453e-36, (279, 1) = -0.10785277727016811e-38, (279, 2) = 0.4844794808343455e-36, (280, 1) = 0.4043820167880682e-38, (280, 2) = -0.4552756170837254e-36, (281, 1) = -0.7529985667834077e-39, (281, 2) = 0.4279276813218819e-36, (282, 1) = 0.3740036313304319e-38, (282, 2) = -0.4023116976109102e-36, (283, 1) = -0.4694373075344152e-39, (283, 2) = 0.37831237164027825e-36, (284, 1) = 0.3475286406849295e-38, (284, 2) = -0.35582245496663687e-36, (285, 1) = -0.22219050307662627e-39, (285, 2) = 0.3347421578115095e-36, (286, 1) = 0.3243392727898204e-38, (286, 2) = -0.31494580003435276e-36, (287, 1) = .0, (287, 2) = 0.2961641077534191e-36}, datatype = float[8], order = C_order); if not type(outpoint, 'numeric') then if outpoint = "start" or outpoint = "left" then return X[1] elif outpoint = "right" then return X[287] elif outpoint = "order" then return 8 elif outpoint = "error" then return HFloat(7.510279655112322e-9) elif outpoint = "errorproc" then error "this is already the error procedure" elif outpoint = "rawdata" then return [2, 287, [theta(eta), diff(theta(eta), eta)], X, Y] else return ('procname')(x_bvp) end if end if; if outpoint < X[1] or X[287] < outpoint then error "solution is only defined in the range %1..%2", X[1], X[287] end if; V := array([1 = 4, 2 = 0]); if Digits <= trunc(evalhf(Digits)) then L := Vector(4, 'datatype' = 'float'[8]); yout := Vector(2, 'datatype' = 'float'[8]); evalhf(`dsolve/numeric/lagrange`(287, 2, X, Y, outpoint, var(yout), var(L), var(V))) else L := Vector(4, 'datatype' = 'sfloat'); yout := Vector(2, 'datatype' = 'sfloat'); `dsolve/numeric/lagrange`(287, 2, X, Y, outpoint, yout, L, V) end if; [eta = outpoint, seq('[theta(eta), diff(theta(eta), eta)]'[i] = yout[i], i = 1 .. 2)] end proc; if not type(outpoint, 'numeric') then if outpoint = "start" or outpoint = "left" then return X[1] elif outpoint = "method" then return "bvp" elif outpoint = "right" then return X[287] elif outpoint = "order" then return 8 elif outpoint = "error" then return HFloat(7.510279655112322e-9) elif outpoint = "errorproc" then return eval(errproc) elif outpoint = "rawdata" then return [2, 287, "depnames", X, Y, YP] else error "non-numeric value" end if end if; if outpoint < X[1] or X[287] < outpoint then error "solution is only defined in the range %1..%2", X[1], X[287] end if; if Digits <= trunc(evalhf(Digits)) and (_EnvInFsolve <> true or _EnvDSNumericSaveDigits <= trunc(evalhf(Digits))) then V := array( 1 .. 6, [( 1 ) = (7), ( 2 ) = (0), ( 3 ) = (false), ( 4 ) = (false), ( 5 ) = (false), ( 6 ) = (false)  ] ); L := Matrix(7, 2, {(1, 1) = .0, (1, 2) = .0, (2, 1) = .0, (2, 2) = .0, (3, 1) = .0, (3, 2) = .0, (4, 1) = .0, (4, 2) = .0, (5, 1) = .0, (5, 2) = .0, (6, 1) = .0, (6, 2) = .0, (7, 1) = .0, (7, 2) = .0}, datatype = float[8], order = C_order); yout := Vector(2, {(1) = .0, (2) = .0}, datatype = float[8]); evalhf(`dsolve/numeric/hermite`(287, 2, X, Y, YP, outpoint, var(yout), var(L), var(V))) else if _EnvInFsolve = true then Digits := _EnvDSNumericSaveDigits end if; V := array( 1 .. 6, [( 1 ) = (7), ( 2 ) = (0), ( 3 ) = (false), ( 4 ) = (false), ( 5 ) = (false), ( 6 ) = (false)  ] ); L := Matrix(7, 2, {(1, 1) = 0., (1, 2) = 0., (2, 1) = 0., (2, 2) = 0., (3, 1) = 0., (3, 2) = 0., (4, 1) = 0., (4, 2) = 0., (5, 1) = 0., (5, 2) = 0., (6, 1) = 0., (6, 2) = 0., (7, 1) = 0., (7, 2) = 0.}, order = C_order); yout := Vector(2, {(1) = 0., (2) = 0.}); `dsolve/numeric/hermite`(287, 2, X, Y, YP, outpoint, yout, L, V) end if; [outpoint, seq(yout[i], i = 1 .. 2)] end proc, (2) = Array(0..0, {}), (3) = [eta, theta(eta), diff(theta(eta), eta)], (4) = 0}); solnproc := data[1]; if not type(outpoint, 'numeric') then if outpoint = "solnprocedure" then return eval(solnproc) elif member(outpoint, ["start", "left", "right", "errorproc", "rawdata", "order", "error"]) then return solnproc(x_bvp) elif outpoint = "sysvars" then return data[3] elif procname <> unknown then return ('procname')(x_bvp) else _ndsol := pointto(data[2][0]); return ('_ndsol')(x_bvp) end if end if; try res := solnproc(outpoint); [eta = res[1], seq('[theta(eta), diff(theta(eta), eta)]'[i] = res[i+1], i = 1 .. 2)] catch: error  end try end proc

 

 

 


 

Download odeProb.mw

 

with no errors - see the attached

Problem *may* be a Maple version issue. What version are you running?

restart:

interface(rtablesize=10):
kernelopts(version);
Physics:-Version();
with(geometry):
with(plots):
S:=segment:
L:=line:
Per:=PerpendicularLine:
R:=5: xA:=0: yA:=0:
point(A,xA,yA):
xI:=R/3:
yI:=0:
point(I1,xI,yI):
circle(C,[A,R]):
quadri:=proc(t)
              local xM,yM,xN,yN,xE,yE,dr1:
              xM:=evalf(R*cos(t)):
              yM:=evalf(R*sin(t)):
              point(M,xM,yM):
              L(lMI,[M,I1]):
              intersection('h',C,lMI,[M,N]):
              L(lAM,[A,M]):
              L(lAN,[A,N]):
              Per(lME,M,lAM):
              Per(lNE,N,lAN):
              intersection(E,lME,lNE):
              S(sAM,[A,M]):
              S(sAN,[A,N]):
              S(sME,[M,E]):
              S(sNE,[N,E]):
              dr1:=draw({lMI(color=blue),sAM(color=black),sAN(color=black),
                         sME,sNE}):
              display({dr1}):
         end:
  
 dr:=draw({C},view=[-6..17,-10..6]):
 display([dr,quadri(0.7),quadri(1),quadri(1.2)],view=[-6..17,-10..6]);

`Maple 2019.0, X86 64 WINDOWS, Mar 9 2019, Build ID 1384062`

 

"C:\Users\TomLeslie\maple\toolbox\2019\Physics Updates\lib\Physics Updates.maple", `2019, March 18, 10:15 hours, version in the MapleCloud: 344, version installed in this computer: 333.`

 

 

 

Download geo.mw

The help page at ?fsolve/details states (my emphasis), for the option 'fulldigits'

fulldigits
Prevent fsolve from decreasing Digits for intermediate calculations at high settings of Digits.  With this option, fsolve may escape ill-conditioning problems, but is slower.

without specifying how "high" the setting of "Digits" has to be before reduction of accuracy for intermediate calculations is applied. I doubt that this is likely to affect your calculations, but it is probably safer to use the 'fulldigits' for fsolve() in your calculation.

Based on the desired number of digits (ND) , you can define an acceptable "tolerance" as 1.0*10-ND, but this will no take account of "rounding" in intermediate calculations, so a better definition of the tolerance might be 1.0*10-ND-2.

The just keep incrementing the setting of Digits until the difference between the value obtained with the current setting and that obtained with the previous setting is less than the specified tolerance. Once this criterion is met, round the value obtained to the desired number of digits. See the attached.

  restart:

  interface(rtablesize=10):
#
# Specify required number of digits numDig
# so the "best case error" will be
#
# 1.0*10^(-numDig)
#
# However the worst case error may be
# substantially greater than this, due to
# rounding at every stage of the calculation
# so define the "desired" error to be a couple
# of digits better, as in
#
  numDig:= 10:
  eps:= 1.0*10^(-numDig-2):

  f:= 2*sin(x^2/2)-sin(1*x/2)^2:
  df:= diff(f,x):
  dff:= diff(f,x,x):
#
# Define a function whih computes the required
# quantity.Use the 'fulldigits' option to ensure
# that fsolve() is always using the current
# setting of Digits internally
#
  do_dff:= ()-> eval
                ( dff,
                  x = fsolve
                      ( df,
                        x = 1..2,
                        fulldigits
                      )
                ):
#
# Compute the desired answer using default
# Digits setting.
#
  old:= do_dff():
#
# Increment 'Digits' and repeat the calculation
# until the difference between the value on the
# current setting of Digits and that on the previous
# setting is less than the desired error
#
  for j from 1 do
      Digits:= Digits+1:
      new:= do_dff();
      if   abs(new-old) < eps
      then break
      else old:= new:
      fi:
  od:
#
# Out of idle curiosity, check the value of Digits
# where the error criterion was met, and the value
# obtained.
#
  Digits;
  new;
#
# Round the obtained value to the required number
# of Digits
#
  evalf[numDig](new);

15

 

-5.27792158987530

 

-5.277921590

(1)

 

Download dff10.mw

the code

assume(x, posint);
 binomial(x, -1);
assume(x, Non(integer));
binomial(x, -1);

returns

0
0

in Maple 2017 and later versions: but returns

                               0
                        binomial(x~, -1)


in earlier versions. Before investigating furthr for a workaround, it would be useful to know precisely which Maple version your are running

 

you can use the about() function which will show (for your example) that the two instances of the variable 'b' have different associated assumptions.

Should additionally() work this way - well I can think of arguments for and against. But it is certainly a trap for the unwary!

A couple of useful general rules

  1. If you are going to make assumptions on variables in a worksheet, do all of them right at the start
  2. Certain commands (such as solve() ) will ignore pre-existing assumptions unless you invoke the 'useassumptions' option

 

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