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\begin{document}
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Notation:S:  semimagic squares (all positive values).s:   normalized squares (symmetry types).R:   reduced squares (least element is 0).r:   reduced normalized squares (reduced symmetry types).gf:  generating function in some form.gfsum:  generating function as a sum of simple terms.c:   Cubic (fixed strict upper bound; weak upper bound for reduced).a:   Affine (fixed magic sum).We start by recomputing rs from the semimagic count.  From the Latte results we get the closed Ehrhart g.f. of each flat, which depends on whether we're doing cubic or affine.  We also need p =  period (or truncated period in affine),d = degree/dimension,  RtoSfactor = the rational function that multiplies Rgf to Sgf and rgf to sgf.enddegree:  The number of terms of the sequences to print out.  \begin{mapleinput}
\mapleinline{active}{1d}{enddegree:=20;}{}
\end{mapleinput}
\mapleresult
\begin{maplelatex}
\mapleinline{inert}{2d}{enddegree := 20}{%
\[
{\it enddegree}\, := \,20
\]
}

\end{maplelatex}
This is for cubic: set up main constants.\begin{mapleinput}
\mapleinline{active}{1d}{d:=5; p:=60;
RtoSfactor:=x\symbol{94}2/(1-x)\symbol{94}2;}{}
\end{mapleinput}
\mapleresult
\begin{maplelatex}
\mapleinline{inert}{2d}{d := 5}{%
\[
d\, := \,5
\]
}
\mapleinline{inert}{2d}{p := 60}{%
\[
p\, := \,60
\]
}
\mapleinline{inert}{2d}{RtoSfactor := x^2/(1-x)^2}{%
\[
{\it RtoSfactor}\, := \,{\frac {{x}^{2}}{ \left( 1-x \right) ^{2}}}
\]
}

\end{maplelatex}
This is also for cubic: set up simplex data.\begin{mapleinput}
\mapleinline{active}{1d}{simplexname[1]:="OABC": ehrgf[1]:= 1/((1-x)\symbol{94}3*(1-x\symbol{94}2)) : dimen[1]:=3:
simplexname[2]:="OEE2": ehrgf[2]:= 1/((1-x)*(1-x\symbol{94}2)*(1-x\symbol{94}3)) : dimen[2]:=2:
simplexname[3]:="OAE2": ehrgf[3]:= 1/((1-x)*(1-x\symbol{94}2)\symbol{94}2) : dimen[3]:=2:
simplexname[4]:="ADE2": ehrgf[4]:= 1/((1-x\symbol{94}2)\symbol{94}3) : dimen[4]:=2:
simplexname[5]:="DE1E2": ehrgf[5]:= 1/((1-x\symbol{94}2)\symbol{94}2*(1-x\symbol{94}3)) : dimen[5]:=2:
simplexname[6]:="OCE": ehrgf[6]:= 1/((1-x)\symbol{94}2*(1-x\symbol{94}3)) : dimen[6]:=2:
simplexname[7]:="BDE1": ehrgf[7]:= 1/((1-x)*(1-x\symbol{94}2)*(1-x\symbol{94}3)) : dimen[7]:=2:
simplexname[8]:="ABD": ehrgf[8]:= 1/((1-x)*(1-x\symbol{94}2)\symbol{94}2) : dimen[8]:=2:
simplexname[9]:="FG1": ehrgf[9]:= 1/((1-x\symbol{94}3)*(1-x\symbol{94}5)) : dimen[9]:=1:
simplexname[10]:="EF": ehrgf[10]:= 1/((1-x\symbol{94}3)\symbol{94}2) : dimen[10]:=1:
simplexname[11]:="OG": ehrgf[11]:= 1/((1-x)*(1-x\symbol{94}4)) : dimen[11]:=1:
simplexname[12]:="FG": ehrgf[12]:= 1/((1-x\symbol{94}3)*(1-x\symbol{94}4)) : dimen[12]:=1:
simplexname[13]:="AF": ehrgf[13]:= 1/((1-x\symbol{94}2)*(1-x\symbol{94}3)) : dimen[13]:=1:
simplexname[14]:="DG": ehrgf[14]:= 1/((1-x\symbol{94}2)*(1-x\symbol{94}4)) : dimen[14]:=1:
simplexname[15]:="DG2": ehrgf[15]:= 1/((1-x\symbol{94}2)*(1-x\symbol{94}5)) : dimen[15]:=1:
simplexname[16]:="DE": ehrgf[16]:= 1/((1-x\symbol{94}2)*(1-x\symbol{94}3)) : dimen[16]:=1:
simplexname[17]:="H": ehrgf[17] := 1/(1-x\symbol{94}5) : dimen[17]:=0:
for n from 1 to 17 do print(simplexname[n], dimen[n], ehrgf[n]); od;}{}
\end{mapleinput}
\mapleresult
\begin{maplelatex}
\mapleinline{inert}{2d}{"OABC", 3, 1/((1-x)^3*(1-x^2))}{%
\[
{\it ``OABC''},\,3,\,{\frac {1}{ \left( 1-x \right) ^{3} \left( 1-{x}^{2} \right) }}
\]
}
\mapleinline{inert}{2d}{"OEE2", 2, 1/((1-x)*(1-x^2)*(1-x^3))}{%
\[
{\it ``OEE2''},\,2,\,{\frac {1}{ \left( 1-x \right)  \left( 1-{x}^{2} \right)  \left( 1-{x}^{3} \right) }}
\]
}
\mapleinline{inert}{2d}{"OAE2", 2, 1/((1-x)*(1-x^2)^2)}{%
\[
{\it ``OAE2''},\,2,\,{\frac {1}{ \left( 1-x \right)  \left( 1-{x}^{2} \right) ^{2}}}
\]
}
\mapleinline{inert}{2d}{"ADE2", 2, 1/(1-x^2)^3}{%
\[
{\it ``ADE2''},\,2,\, \left( 1-{x}^{2} \right) ^{-3}
\]
}
\mapleinline{inert}{2d}{"DE1E2", 2, 1/((1-x^2)^2*(1-x^3))}{%
\[
{\it ``DE1E2''},\,2,\,{\frac {1}{ \left( 1-{x}^{2} \right) ^{2} \left( 1-{x}^{3} \right) }}
\]
}
\mapleinline{inert}{2d}{"OCE", 2, 1/((1-x)^2*(1-x^3))}{%
\[
{\it ``OCE''},\,2,\,{\frac {1}{ \left( 1-x \right) ^{2} \left( 1-{x}^{3} \right) }}
\]
}
\mapleinline{inert}{2d}{"BDE1", 2, 1/((1-x)*(1-x^2)*(1-x^3))}{%
\[
{\it ``BDE1''},\,2,\,{\frac {1}{ \left( 1-x \right)  \left( 1-{x}^{2} \right)  \left( 1-{x}^{3} \right) }}
\]
}
\mapleinline{inert}{2d}{"ABD", 2, 1/((1-x)*(1-x^2)^2)}{%
\[
{\it ``ABD''},\,2,\,{\frac {1}{ \left( 1-x \right)  \left( 1-{x}^{2} \right) ^{2}}}
\]
}
\mapleinline{inert}{2d}{"FG1", 1, 1/((1-x^3)*(1-x^5))}{%
\[
{\it ``FG1''},\,1,\,{\frac {1}{ \left( 1-{x}^{3} \right)  \left( 1-{x}^{5} \right) }}
\]
}
\mapleinline{inert}{2d}{"EF", 1, 1/(1-x^3)^2}{%
\[
{\it ``EF''},\,1,\, \left( 1-{x}^{3} \right) ^{-2}
\]
}
\mapleinline{inert}{2d}{"OG", 1, 1/((1-x)*(1-x^4))}{%
\[
{\it ``OG''},\,1,\,{\frac {1}{ \left( 1-x \right)  \left( 1-{x}^{4} \right) }}
\]
}
\mapleinline{inert}{2d}{"FG", 1, 1/((1-x^3)*(1-x^4))}{%
\[
{\it ``FG''},\,1,\,{\frac {1}{ \left( 1-{x}^{3} \right)  \left( 1-{x}^{4} \right) }}
\]
}
\mapleinline{inert}{2d}{"AF", 1, 1/((1-x^2)*(1-x^3))}{%
\[
{\it ``AF''},\,1,\,{\frac {1}{ \left( 1-{x}^{2} \right)  \left( 1-{x}^{3} \right) }}
\]
}
\mapleinline{inert}{2d}{"DG", 1, 1/((1-x^2)*(1-x^4))}{%
\[
{\it ``DG''},\,1,\,{\frac {1}{ \left( 1-{x}^{2} \right)  \left( 1-{x}^{4} \right) }}
\]
}
\mapleinline{inert}{2d}{"DG2", 1, 1/((1-x^2)*(1-x^5))}{%
\[
{\it ``DG2''},\,1,\,{\frac {1}{ \left( 1-{x}^{2} \right)  \left( 1-{x}^{5} \right) }}
\]
}
\mapleinline{inert}{2d}{"DE", 1, 1/((1-x^2)*(1-x^3))}{%
\[
{\it ``DE''},\,1,\,{\frac {1}{ \left( 1-{x}^{2} \right)  \left( 1-{x}^{3} \right) }}
\]
}
\mapleinline{inert}{2d}{"H", 0, 1/(1-x^5)}{%
\[
``H'',\,0,\, \left( 1-{x}^{5} \right) ^{-1}
\]
}

\end{maplelatex}
The closed E.g.f. is converted to the open E.g.f.:\begin{mapleinput}
\mapleinline{active}{1d}{for n from 1 to 17 do 
  mu[n]:=(-1)\symbol{94}(dimen[1]-dimen[n]):
od:
mu[14]:=2*mu[14]:
for n from 1 to 17 do  
  openehrgf[n]:=simplify(-(-1)\symbol{94}dimen[n]*subs(x=1/x,ehrgf[n])):
od:
for n from 1 to 17 do 
  rgfterm[n]:=openehrgf[n]: 
od:}{}
\end{mapleinput}Now compute the number of reduced symmetry types:\begin{mapleinput}
\mapleinline{active}{1d}{rgfsum:=sum(mu[nn]*rgfterm[nn],nn=1..17);
rgf:=simplify(rgfsum):}{}
\end{mapleinput}
\mapleresult
\begin{maplelatex}
\mapleinline{inert}{2d}{rgfsum := x^5/((x-1)^3*(x^2-1))+2*x^6/((x-1)*(x^2-1)*(x^3-1))+2*x^5/((x-1)*(x^2-1)^2)+x^6/(x^2-1)^3+x^7/((x^2-1)^2*(x^3-1))+x^5/((x-1)^2*(x^3-1))+x^8/((x^3-1)*(x^5-1))+x^6/(x^3-1)^2+x^5/((x-1)*(x^4-1))+x^7/((x^3-1)*(x^4-1))+2*x^5/((x^2-1)*(x^3-1))+2*x^6/((x^2-1)*(x^4-1))+x^7/((x^2-1)*(x^5-1))+x^5/(x^5-1)}{%
${\it rgfsum}\, := \,{\frac {{x}^{5}}{ \left( x-1 \right) ^{3} \left( {x}^{2}-1 \right) }}+2\,{\frac {{x}^{6}}{ \left( x-1 \right)  \left( {x}^{2}-1 \right)  \left( {x}^{3}-1 \right) }}+2\,{\frac {{x}^{5}}{ \left( x-1 \right)  \left( {x}^{2}-1 \right) ^{2}}}\\
\mbox{}+{\frac {{x}^{6}}{ \left( {x}^{2}-1 \right) ^{3}}}+{\frac {{x}^{7}}{ \left( {x}^{2}-1 \right) ^{2} \left( {x}^{3}-1 \right) }}+{\frac {{x}^{5}}{ \left( x-1 \right) ^{2} \left( {x}^{3}-1 \right) }}+{\frac {{x}^{8}}{ \left( {x}^{3}-1 \right)  \left( {x}^{5}-1 \right) }}\\
\mbox{}+{\frac {{x}^{6}}{ \left( {x}^{3}-1 \right) ^{2}}}+{\frac {{x}^{5}}{ \left( x-1 \right)  \left( {x}^{4}-1 \right) }}+{\frac {{x}^{7}}{ \left( {x}^{3}-1 \right)  \left( {x}^{4}-1 \right) }}+2\,{\frac {{x}^{5}}{ \left( {x}^{2}-1 \right)  \left( {x}^{3}-1 \right) }}\\
\mbox{}+2\,{\frac {{x}^{6}}{ \left( {x}^{2}-1 \right)  \left( {x}^{4}-1 \right) }}+{\frac {{x}^{7}}{ \left( {x}^{2}-1 \right)  \left( {x}^{5}-1 \right) }}+{\frac {{x}^{5}}{{x}^{5}-1}}$}

\end{maplelatex}
We need the total number of reduced squares, Rgf:\begin{mapleinput}
\mapleinline{active}{1d}{Rgfsum:=72*rgfsum;
Rgf:=simplify(Rgfsum):}{}
\end{mapleinput}
\mapleresult
\begin{maplelatex}
\mapleinline{inert}{2d}{Rgfsum := 72*x^5/((x-1)^3*(x^2-1))+144*x^6/((x-1)*(x^2-1)*(x^3-1))+144*x^5/((x-1)*(x^2-1)^2)+72*x^6/(x^2-1)^3+72*x^7/((x^2-1)^2*(x^3-1))+72*x^5/((x-1)^2*(x^3-1))+72*x^8/((x^3-1)*(x^5-1))+72*x^6/(x^3-1)^2+72*x^5/((x-1)*(x^4-1))+72*x^7/((x^3-1)*(x^4-1))+144*x^5/((x^2-1)*(x^3-1))+144*x^6/((x^2-1)*(x^4-1))+72*x^7/((x^2-1)*(x^5-1))+72*x^5/(x^5-1)}{%
${\it Rgfsum}\, := \,72\,{\frac {{x}^{5}}{ \left( x-1 \right) ^{3} \left( {x}^{2}-1 \right) }}+144\,{\frac {{x}^{6}}{ \left( x-1 \right)  \left( {x}^{2}-1 \right)  \left( {x}^{3}-1 \right) }}+144\,{\frac {{x}^{5}}{ \left( x-1 \right)  \left( {x}^{2}-1 \right) ^{2}}}\\
\mbox{}+72\,{\frac {{x}^{6}}{ \left( {x}^{2}-1 \right) ^{3}}}+72\,{\frac {{x}^{7}}{ \left( {x}^{2}-1 \right) ^{2} \left( {x}^{3}-1 \right) }}+72\,{\frac {{x}^{5}}{ \left( x-1 \right) ^{2} \left( {x}^{3}-1 \right) }}\\
\mbox{}+72\,{\frac {{x}^{8}}{ \left( {x}^{3}-1 \right)  \left( {x}^{5}-1 \right) }}+72\,{\frac {{x}^{6}}{ \left( {x}^{3}-1 \right) ^{2}}}+72\,{\frac {{x}^{5}}{ \left( x-1 \right)  \left( {x}^{4}-1 \right) }}+72\,{\frac {{x}^{7}}{ \left( {x}^{3}-1 \right)  \left( {x}^{4}-1 \right) }}\\
\mbox{}+144\,{\frac {{x}^{5}}{ \left( {x}^{2}-1 \right)  \left( {x}^{3}-1 \right) }}+144\,{\frac {{x}^{6}}{ \left( {x}^{2}-1 \right)  \left( {x}^{4}-1 \right) }}+72\,{\frac {{x}^{7}}{ \left( {x}^{2}-1 \right)  \left( {x}^{5}-1 \right) }}\\
\mbox{}+72\,{\frac {{x}^{5}}{{x}^{5}-1}}$}

\end{maplelatex}
Hence Sgf, the g.f. of the number of semimagic squares, equals\begin{mapleinput}
\mapleinline{active}{1d}{Sgfsum:=RtoSfactor*Rgfsum;
Sgf:=simplify(Sgfsum):}{}
\end{mapleinput}
\mapleresult
\begin{maplelatex}
\mapleinline{inert}{2d}{Sgfsum := x^2*(72*x^5/((x-1)^3*(x^2-1))+144*x^6/((x-1)*(x^2-1)*(x^3-1))+144*x^5/((x-1)*(x^2-1)^2)+72*x^6/(x^2-1)^3+72*x^7/((x^2-1)^2*(x^3-1))+72*x^5/((x-1)^2*(x^3-1))+72*x^8/((x^3-1)*(x^5-1))+72*x^6/(x^3-1)^2+72*x^5/((x-1)*(x^4-1))+72*x^7/((x^3-1)*(x^4-1))+144*x^5/((x^2-1)*(x^3-1))+144*x^6/((x^2-1)*(x^4-1))+72*x^7/((x^2-1)*(x^5-1))+72*x^5/(x^5-1))/(1-x)^2}{%
${\it Sgfsum}\, := \,{x}^{2} \left( 72\,{\frac {{x}^{5}}{ \left( x-1 \right) ^{3} \left( {x}^{2}-1 \right) }}+144\,{\frac {{x}^{6}}{ \left( x-1 \right)  \left( {x}^{2}-1 \right)  \left( {x}^{3}-1 \right) }}+144\,{\frac {{x}^{5}}{ \left( x-1 \right)  \left( {x}^{2}-1 \right) ^{2}}}\\
\mbox{}+72\,{\frac {{x}^{6}}{ \left( {x}^{2}-1 \right) ^{3}}}+72\,{\frac {{x}^{7}}{ \left( {x}^{2}-1 \right) ^{2} \left( {x}^{3}-1 \right) }}+72\,{\frac {{x}^{5}}{ \left( x-1 \right) ^{2} \left( {x}^{3}-1 \right) }}\\
\mbox{}+72\,{\frac {{x}^{8}}{ \left( {x}^{3}-1 \right)  \left( {x}^{5}-1 \right) }}+72\,{\frac {{x}^{6}}{ \left( {x}^{3}-1 \right) ^{2}}}+72\,{\frac {{x}^{5}}{ \left( x-1 \right)  \left( {x}^{4}-1 \right) }}+72\,{\frac {{x}^{7}}{ \left( {x}^{3}-1 \right)  \left( {x}^{4}-1 \right) }}\\
\mbox{}+144\,{\frac {{x}^{5}}{ \left( {x}^{2}-1 \right)  \left( {x}^{3}-1 \right) }}+144\,{\frac {{x}^{6}}{ \left( {x}^{2}-1 \right)  \left( {x}^{4}-1 \right) }}+72\,{\frac {{x}^{7}}{ \left( {x}^{2}-1 \right)  \left( {x}^{5}-1 \right) }}\\
\mbox{}+72\,{\frac {{x}^{5}}{{x}^{5}-1}} \right)  \left( 1-x \right) ^{-2}$}

\end{maplelatex}
The g.f. of the total number of symmetry types, sgf:\begin{mapleinput}
\mapleinline{active}{1d}{sgfsum:=RtoSfactor*rgfsum;
sgf:=simplify(sgfsum):}{}
\end{mapleinput}
\mapleresult
\begin{maplelatex}
\mapleinline{inert}{2d}{sgfsum := x^2*(x^5/((x-1)^3*(x^2-1))+2*x^6/((x-1)*(x^2-1)*(x^3-1))+2*x^5/((x-1)*(x^2-1)^2)+x^6/(x^2-1)^3+x^7/((x^2-1)^2*(x^3-1))+x^5/((x-1)^2*(x^3-1))+x^8/((x^3-1)*(x^5-1))+x^6/(x^3-1)^2+x^5/((x-1)*(x^4-1))+x^7/((x^3-1)*(x^4-1))+2*x^5/((x^2-1)*(x^3-1))+2*x^6/((x^2-1)*(x^4-1))+x^7/((x^2-1)*(x^5-1))+x^5/(x^5-1))/(1-x)^2}{%
${\it sgfsum}\, := \,{x}^{2} \left( {\frac {{x}^{5}}{ \left( x-1 \right) ^{3} \left( {x}^{2}-1 \right) }}+2\,{\frac {{x}^{6}}{ \left( x-1 \right)  \left( {x}^{2}-1 \right)  \left( {x}^{3}-1 \right) }}+2\,{\frac {{x}^{5}}{ \left( x-1 \right)  \left( {x}^{2}-1 \right) ^{2}}}\\
\mbox{}+{\frac {{x}^{6}}{ \left( {x}^{2}-1 \right) ^{3}}}+{\frac {{x}^{7}}{ \left( {x}^{2}-1 \right) ^{2} \left( {x}^{3}-1 \right) }}+{\frac {{x}^{5}}{ \left( x-1 \right) ^{2} \left( {x}^{3}-1 \right) }}+{\frac {{x}^{8}}{ \left( {x}^{3}-1 \right)  \left( {x}^{5}-1 \right) }}\\
\mbox{}+{\frac {{x}^{6}}{ \left( {x}^{3}-1 \right) ^{2}}}+{\frac {{x}^{5}}{ \left( x-1 \right)  \left( {x}^{4}-1 \right) }}+{\frac {{x}^{7}}{ \left( {x}^{3}-1 \right)  \left( {x}^{4}-1 \right) }}+2\,{\frac {{x}^{5}}{ \left( {x}^{2}-1 \right)  \left( {x}^{3}-1 \right) }}\\
\mbox{}+2\,{\frac {{x}^{6}}{ \left( {x}^{2}-1 \right)  \left( {x}^{4}-1 \right) }}+{\frac {{x}^{7}}{ \left( {x}^{2}-1 \right)  \left( {x}^{5}-1 \right) }}+{\frac {{x}^{5}}{{x}^{5}-1}} \right)  \left( 1-x \right) ^{-2}$}

\end{maplelatex}
Expressing the rational function with standard denominator gives an orders-of-magnitude speedup in the series expansion.  Standard denominator (1-x\symbol{94}p)\symbol{94}{d+1}.  \begin{mapleinput}
\mapleinline{active}{1d}{pdenom:=(1-x\symbol{94}p):
standenom:=pdenom\symbol{94}(d+1);}{}
\end{mapleinput}
\mapleresult
\begin{maplelatex}
\mapleinline{inert}{2d}{standenom := (1-x^60)^6}{%
\[
{\it standenom}\, := \, \left( 1-{x}^{60} \right) ^{6}
\]
}

\end{maplelatex}
G.f. as rational function with standard denominator.\begin{mapleinput}
\mapleinline{active}{1d}{Sgfstandnum:=simplify(numer(Sgf)*simplify(standenom/denom(Sgf))):
Sgf:=Sgfstandnum/standenom;}{}
\end{mapleinput}
\mapleresult
\begin{maplelatex}
\mapleinline{inert}{2d}{Sgf := 72*x^10*(18*x^9+46*x^8+69*x^7+74*x^6+65*x^5+46*x^4+26*x^3+11*x^2+4*x+1)*(x^55+x^50+x^45+x^40+x^35+x^30+x^25+x^20+x^15+x^10+x^5+1)*(1+x+x^2+x^3+x^5+x^4+x^6+x^7+x^8+x^10+x^15+x^12+x^9+x^13+x^11+x^19+x^14+x^16+x^17+x^18+x^58+x^54+x^56+x^52+x^50+x^48+x^46+x^44+x^42+x^40+x^38+x^36+x^34+x^32+x^30+x^28+x^26+x^24+x^22+x^20+x^31+x^43+x^37+x^55+x^49+x^25+x^59+x^57+x^53+x^51+x^47+x^45+x^41+x^39+x^35+x^33+x^29+x^27+x^23+x^21)^2*(1+x^2+x^4+x^6+x^8+x^10+x^12+x^14+x^16+x^18+x^58+x^54+x^56+x^52+x^50+x^48+x^46+x^44+x^42+x^40+x^38+x^36+x^34+x^32+x^30+x^28+x^26+x^24+x^22+x^20)*(1-x+x^3-x^5+x^6+x^15+x^12-x^13-x^17+x^18+x^54+x^48+x^42+x^36+x^30+x^24-x^37-x^49-x^25-x^53+x^51-x^41+x^39-x^29+x^27)*(1-x+x^2+x^6-x^7+x^8+x^12-x^13-x^19+x^14+x^18+x^54+x^56+x^50+x^48+x^44+x^42+x^38+x^36+x^32+x^30+x^26+x^24+x^20-x^31-x^43-x^37-x^55-x^49-x^25)/(1-x^60)^6}{%
${\it Sgf}\, := \,72\,{\frac {{x}^{10} \left( 18\,{x}^{9}+46\,{x}^{8}+69\,{x}^{7}+74\,{x}^{6}+65\,{x}^{5}+46\,{x}^{4}+26\,{x}^{3}+11\,{x}^{2}+4\,x+1 \right)  \left( {x}^{55}+{x}^{50}+{x}^{45}+{x}^{40}+{x}^{35}+{x}^{30}+{x}^{25}+{x}^{20}+{x}^{15}+{x}^{10}+{x}^{5}+1 \right)  \left( 1+x+{x}^{41}+{x}^{7}+{x}^{6}+{x}^{2}+{x}^{3}+{x}^{5}+{x}^{4}+{x}^{8}+{x}^{10}+{x}^{9}+{x}^{55}+{x}^{50}+{x}^{45}+{x}^{40}+{x}^{35}+{x}^{30}+{x}^{25}+{x}^{20}\\
\mbox{}+{x}^{15}+{x}^{12}+{x}^{13}+{x}^{11}+{x}^{19}+{x}^{14}+{x}^{16}+{x}^{17}+{x}^{18}+{x}^{58}+{x}^{54}+{x}^{56}+{x}^{52}+{x}^{48}+{x}^{46}+{x}^{44}+{x}^{42}\\
\mbox{}+{x}^{38}+{x}^{36}+{x}^{34}+{x}^{32}+{x}^{28}+{x}^{26}+{x}^{24}+{x}^{22}+{x}^{31}+{x}^{43}+{x}^{37}+{x}^{49}+{x}^{59}+{x}^{51}+{x}^{47}+{x}^{57}+{x}^{53}\\
\mbox{}+{x}^{39}+{x}^{33}+{x}^{29}+{x}^{27}+{x}^{23}+{x}^{21} \right) ^{2}\\
\mbox{} \left( 1+{x}^{6}+{x}^{2}+{x}^{4}+{x}^{8}+{x}^{10}+{x}^{50}+{x}^{40}+{x}^{30}+{x}^{20}+{x}^{12}+{x}^{14}+{x}^{16}+{x}^{18}+{x}^{58}+{x}^{54}+{x}^{56}+{x}^{52}\\
\mbox{}+{x}^{48}+{x}^{46}+{x}^{44}+{x}^{42}+{x}^{38}+{x}^{36}+{x}^{34}+{x}^{32}+{x}^{28}+{x}^{26}+{x}^{24}+{x}^{22} \right)  \left( 1-x-{x}^{41}+{x}^{6}+{x}^{3}-{x}^{5}+{x}^{30}-{x}^{25}+{x}^{15}+{x}^{12}-{x}^{13}-{x}^{17}+{x}^{18}+{x}^{54}+{x}^{48}+{x}^{42}+{x}^{36}+{x}^{24}\\
\mbox{}-{x}^{37}-{x}^{49}+{x}^{51}-{x}^{53}+{x}^{39}-{x}^{29}+{x}^{27} \right) \\
\mbox{} \left( 1-x-{x}^{7}+{x}^{6}+{x}^{2}+{x}^{8}-{x}^{55}+{x}^{50}+{x}^{30}-{x}^{25}+{x}^{20}+{x}^{12}-{x}^{13}-{x}^{19}+{x}^{14}+{x}^{18}+{x}^{54}+{x}^{56}+{x}^{48}\\
\mbox{}+{x}^{44}+{x}^{42}+{x}^{38}+{x}^{36}+{x}^{32}+{x}^{26}+{x}^{24}-{x}^{31}-{x}^{43}-{x}^{37}-{x}^{49} \right) }{ \left( 1-{x}^{60} \right) ^{6}}}$}

\end{maplelatex}
G.f. as rational function with standard denominator.\begin{mapleinput}
\mapleinline{active}{1d}{Rgfstandnum:=simplify(numer(Rgf)*standenom/denom(Rgf)):
Rgf:=Rgfstandnum/standenom;}{}
\end{mapleinput}
\mapleresult
\begin{maplelatex}
\mapleinline{inert}{2d}{Rgf := 72*(18*x^9+46*x^8+69*x^7+74*x^6+65*x^5+46*x^4+26*x^3+11*x^2+4*x+1)*x^8*(x^57+x^54+x^51+x^48+x^45+x^42+x^39+x^36+x^33+x^30+x^27+x^24+x^21+x^18+x^15+x^12+x^9+x^6+x^3+1)^2*(-1+x-x^2+x^3+x^5-x^4-x^6+x^7-x^8-x^10+x^15-x^12+x^9+x^13+x^11+x^19-x^14-x^16+x^17-x^18-x^58-x^54-x^56-x^52-x^50-x^48-x^46-x^44-x^42-x^40-x^38-x^36-x^34-x^32-x^30-x^28-x^26-x^24-x^22-x^20+x^31+x^43+x^37+x^55+x^49+x^25+x^59+x^57+x^53+x^51+x^47+x^45+x^41+x^39+x^35+x^33+x^29+x^27+x^23+x^21)*(-1+x^60)*(1+x^2+x^4+x^6+x^8+x^10+x^12+x^14+x^16+x^18+x^58+x^54+x^56+x^52+x^50+x^48+x^46+x^44+x^42+x^40+x^38+x^36+x^34+x^32+x^30+x^28+x^26+x^24+x^22+x^20)*(x^52-x^51+x^48-x^46+x^44-x^41+x^40+x^32-x^31+x^28-x^26+x^24-x^21+x^20+x^12-x^11+x^8-x^6+x^4-x+1)/(1-x^60)^6}{%
${\it Rgf}\, := \,72\,{\frac { \left( 18\,{x}^{9}+46\,{x}^{8}+69\,{x}^{7}+74\,{x}^{6}+65\,{x}^{5}+46\,{x}^{4}+26\,{x}^{3}+11\,{x}^{2}+4\,x+1 \right) {x}^{8} \left( {x}^{57}+{x}^{54}+{x}^{51}+{x}^{48}+{x}^{45}+{x}^{42}+{x}^{39}+{x}^{36}+{x}^{33}+{x}^{30}+{x}^{27}+{x}^{24}+{x}^{21}+{x}^{18}+{x}^{15}+{x}^{12}\\
\mbox{}+{x}^{9}+{x}^{6}+{x}^{3}+1 \right) ^{2} \left( -1+x+{x}^{41}+{x}^{7}-{x}^{6}-{x}^{2}+{x}^{3}+{x}^{5}-{x}^{4}-{x}^{8}-{x}^{10}+{x}^{9}+{x}^{55}-{x}^{50}+{x}^{45}-{x}^{40}+{x}^{35}-{x}^{30}+{x}^{25}\\
\mbox{}-{x}^{20}+{x}^{15}-{x}^{12}+{x}^{13}+{x}^{11}+{x}^{19}-{x}^{14}-{x}^{16}+{x}^{17}-{x}^{18}-{x}^{58}-{x}^{54}-{x}^{56}-{x}^{52}-{x}^{48}-{x}^{46}-{x}^{44}\\
\mbox{}-{x}^{42}-{x}^{38}-{x}^{36}-{x}^{34}-{x}^{32}-{x}^{28}-{x}^{26}-{x}^{24}-{x}^{22}+{x}^{31}+{x}^{43}+{x}^{37}+{x}^{49}+{x}^{59}+{x}^{51}+{x}^{47}+{x}^{57}\\
\mbox{}+{x}^{53}+{x}^{39}+{x}^{33}+{x}^{29}+{x}^{27}+{x}^{23}+{x}^{21} \right) \\
\mbox{} \left( -1+{x}^{60} \right)  \left( 1+{x}^{6}+{x}^{2}+{x}^{4}+{x}^{8}+{x}^{10}+{x}^{50}+{x}^{40}+{x}^{30}+{x}^{20}+{x}^{12}+{x}^{14}+{x}^{16}+{x}^{18}+{x}^{58}+{x}^{54}+{x}^{56}+{x}^{52}\\
\mbox{}+{x}^{48}+{x}^{46}+{x}^{44}+{x}^{42}+{x}^{38}+{x}^{36}+{x}^{34}+{x}^{32}+{x}^{28}+{x}^{26}+{x}^{24}+{x}^{22} \right)  \left( {x}^{52}-{x}^{51}+{x}^{48}-{x}^{46}+{x}^{44}-{x}^{41}+{x}^{40}+{x}^{32}-{x}^{31}+{x}^{28}-{x}^{26}+{x}^{24}-{x}^{21}+{x}^{20}+{x}^{12}-{x}^{11}\\
\mbox{}+{x}^{8}-{x}^{6}+{x}^{4}-x+1 \right) }{ \left( 1-{x}^{60} \right) ^{6}}}$}

\end{maplelatex}
G.f. as rational function with standard denominator.\begin{mapleinput}
\mapleinline{active}{1d}{sgfstandnum:=simplify(numer(sgf)*simplify(standenom/denom(sgf))): 
sgf:=sgfstandnum/standenom;}{}
\end{mapleinput}
\mapleresult
\begin{maplelatex}
\mapleinline{inert}{2d}{sgf := x^10*(18*x^9+46*x^8+69*x^7+74*x^6+65*x^5+46*x^4+26*x^3+11*x^2+4*x+1)*(x^55+x^50+x^45+x^40+x^35+x^30+x^25+x^20+x^15+x^10+x^5+1)*(1+x+x^2+x^3+x^5+x^4+x^6+x^7+x^8+x^10+x^15+x^12+x^9+x^13+x^11+x^19+x^14+x^16+x^17+x^18+x^58+x^54+x^56+x^52+x^50+x^48+x^46+x^44+x^42+x^40+x^38+x^36+x^34+x^32+x^30+x^28+x^26+x^24+x^22+x^20+x^31+x^43+x^37+x^55+x^49+x^25+x^59+x^57+x^53+x^51+x^47+x^45+x^41+x^39+x^35+x^33+x^29+x^27+x^23+x^21)^2*(1+x^2+x^4+x^6+x^8+x^10+x^12+x^14+x^16+x^18+x^58+x^54+x^56+x^52+x^50+x^48+x^46+x^44+x^42+x^40+x^38+x^36+x^34+x^32+x^30+x^28+x^26+x^24+x^22+x^20)*(1-x+x^3-x^5+x^6+x^15+x^12-x^13-x^17+x^18+x^54+x^48+x^42+x^36+x^30+x^24-x^37-x^49-x^25-x^53+x^51-x^41+x^39-x^29+x^27)*(1-x+x^2+x^6-x^7+x^8+x^12-x^13-x^19+x^14+x^18+x^54+x^56+x^50+x^48+x^44+x^42+x^38+x^36+x^32+x^30+x^26+x^24+x^20-x^31-x^43-x^37-x^55-x^49-x^25)/(1-x^60)^6}{%
${\it sgf}\, := \,{\frac {{x}^{10} \left( 18\,{x}^{9}+46\,{x}^{8}+69\,{x}^{7}+74\,{x}^{6}+65\,{x}^{5}+46\,{x}^{4}+26\,{x}^{3}+11\,{x}^{2}+4\,x+1 \right)  \left( {x}^{55}+{x}^{50}+{x}^{45}+{x}^{40}+{x}^{35}+{x}^{30}+{x}^{25}+{x}^{20}+{x}^{15}+{x}^{10}+{x}^{5}+1 \right)  \left( 1+x+{x}^{41}+{x}^{7}+{x}^{6}+{x}^{2}+{x}^{3}+{x}^{5}+{x}^{4}+{x}^{8}+{x}^{10}+{x}^{9}+{x}^{55}+{x}^{50}+{x}^{45}+{x}^{40}+{x}^{35}+{x}^{30}+{x}^{25}+{x}^{20}\\
\mbox{}+{x}^{15}+{x}^{12}+{x}^{13}+{x}^{11}+{x}^{19}+{x}^{14}+{x}^{16}+{x}^{17}+{x}^{18}+{x}^{58}+{x}^{54}+{x}^{56}+{x}^{52}+{x}^{48}+{x}^{46}+{x}^{44}+{x}^{42}\\
\mbox{}+{x}^{38}+{x}^{36}+{x}^{34}+{x}^{32}+{x}^{28}+{x}^{26}+{x}^{24}+{x}^{22}+{x}^{31}+{x}^{43}+{x}^{37}+{x}^{49}+{x}^{59}+{x}^{51}+{x}^{47}+{x}^{57}+{x}^{53}\\
\mbox{}+{x}^{39}+{x}^{33}+{x}^{29}+{x}^{27}+{x}^{23}+{x}^{21} \right) ^{2}\\
\mbox{} \left( 1+{x}^{6}+{x}^{2}+{x}^{4}+{x}^{8}+{x}^{10}+{x}^{50}+{x}^{40}+{x}^{30}+{x}^{20}+{x}^{12}+{x}^{14}+{x}^{16}+{x}^{18}+{x}^{58}+{x}^{54}+{x}^{56}+{x}^{52}\\
\mbox{}+{x}^{48}+{x}^{46}+{x}^{44}+{x}^{42}+{x}^{38}+{x}^{36}+{x}^{34}+{x}^{32}+{x}^{28}+{x}^{26}+{x}^{24}+{x}^{22} \right)  \left( 1-x-{x}^{41}+{x}^{6}+{x}^{3}-{x}^{5}+{x}^{30}-{x}^{25}+{x}^{15}+{x}^{12}-{x}^{13}-{x}^{17}+{x}^{18}+{x}^{54}+{x}^{48}+{x}^{42}+{x}^{36}+{x}^{24}\\
\mbox{}-{x}^{37}-{x}^{49}+{x}^{51}-{x}^{53}+{x}^{39}-{x}^{29}+{x}^{27} \right) \\
\mbox{} \left( 1-x-{x}^{7}+{x}^{6}+{x}^{2}+{x}^{8}-{x}^{55}+{x}^{50}+{x}^{30}-{x}^{25}+{x}^{20}+{x}^{12}-{x}^{13}-{x}^{19}+{x}^{14}+{x}^{18}+{x}^{54}+{x}^{56}+{x}^{48}\\
\mbox{}+{x}^{44}+{x}^{42}+{x}^{38}+{x}^{36}+{x}^{32}+{x}^{26}+{x}^{24}-{x}^{31}-{x}^{43}-{x}^{37}-{x}^{49} \right) }{ \left( 1-{x}^{60} \right) ^{6}}}$}

\end{maplelatex}
G.f. as rational function with standard denominator.\begin{mapleinput}
\mapleinline{active}{1d}{rgfstandnum:=simplify(numer(rgf)*standenom/denom(rgf)):
rgf:=rgfstandnum/standenom;}{}
\end{mapleinput}
\mapleresult
\begin{maplelatex}
\mapleinline{inert}{2d}{rgf := (18*x^9+46*x^8+69*x^7+74*x^6+65*x^5+46*x^4+26*x^3+11*x^2+4*x+1)*x^8*(x^57+x^54+x^51+x^48+x^45+x^42+x^39+x^36+x^33+x^30+x^27+x^24+x^21+x^18+x^15+x^12+x^9+x^6+x^3+1)^2*(-1+x-x^2+x^3+x^5-x^4-x^6+x^7-x^8-x^10+x^15-x^12+x^9+x^13+x^11+x^19-x^14-x^16+x^17-x^18-x^58-x^54-x^56-x^52-x^50-x^48-x^46-x^44-x^42-x^40-x^38-x^36-x^34-x^32-x^30-x^28-x^26-x^24-x^22-x^20+x^31+x^43+x^37+x^55+x^49+x^25+x^59+x^57+x^53+x^51+x^47+x^45+x^41+x^39+x^35+x^33+x^29+x^27+x^23+x^21)*(-1+x^60)*(1+x^2+x^4+x^6+x^8+x^10+x^12+x^14+x^16+x^18+x^58+x^54+x^56+x^52+x^50+x^48+x^46+x^44+x^42+x^40+x^38+x^36+x^34+x^32+x^30+x^28+x^26+x^24+x^22+x^20)*(x^52-x^51+x^48-x^46+x^44-x^41+x^40+x^32-x^31+x^28-x^26+x^24-x^21+x^20+x^12-x^11+x^8-x^6+x^4-x+1)/(1-x^60)^6}{%
${\it rgf}\, := \,{\frac { \left( 18\,{x}^{9}+46\,{x}^{8}+69\,{x}^{7}+74\,{x}^{6}+65\,{x}^{5}+46\,{x}^{4}+26\,{x}^{3}+11\,{x}^{2}+4\,x+1 \right) {x}^{8} \left( {x}^{57}+{x}^{54}+{x}^{51}+{x}^{48}+{x}^{45}+{x}^{42}+{x}^{39}+{x}^{36}+{x}^{33}+{x}^{30}+{x}^{27}+{x}^{24}+{x}^{21}+{x}^{18}+{x}^{15}+{x}^{12}\\
\mbox{}+{x}^{9}+{x}^{6}+{x}^{3}+1 \right) ^{2} \left( -1+x+{x}^{41}+{x}^{7}-{x}^{6}-{x}^{2}+{x}^{3}+{x}^{5}-{x}^{4}-{x}^{8}-{x}^{10}+{x}^{9}+{x}^{55}-{x}^{50}+{x}^{45}-{x}^{40}+{x}^{35}-{x}^{30}+{x}^{25}\\
\mbox{}-{x}^{20}+{x}^{15}-{x}^{12}+{x}^{13}+{x}^{11}+{x}^{19}-{x}^{14}-{x}^{16}+{x}^{17}-{x}^{18}-{x}^{58}-{x}^{54}-{x}^{56}-{x}^{52}-{x}^{48}-{x}^{46}-{x}^{44}\\
\mbox{}-{x}^{42}-{x}^{38}-{x}^{36}-{x}^{34}-{x}^{32}-{x}^{28}-{x}^{26}-{x}^{24}-{x}^{22}+{x}^{31}+{x}^{43}+{x}^{37}+{x}^{49}+{x}^{59}+{x}^{51}+{x}^{47}+{x}^{57}\\
\mbox{}+{x}^{53}+{x}^{39}+{x}^{33}+{x}^{29}+{x}^{27}+{x}^{23}+{x}^{21} \right) \\
\mbox{} \left( -1+{x}^{60} \right)  \left( 1+{x}^{6}+{x}^{2}+{x}^{4}+{x}^{8}+{x}^{10}+{x}^{50}+{x}^{40}+{x}^{30}+{x}^{20}+{x}^{12}+{x}^{14}+{x}^{16}+{x}^{18}+{x}^{58}+{x}^{54}+{x}^{56}+{x}^{52}\\
\mbox{}+{x}^{48}+{x}^{46}+{x}^{44}+{x}^{42}+{x}^{38}+{x}^{36}+{x}^{34}+{x}^{32}+{x}^{28}+{x}^{26}+{x}^{24}+{x}^{22} \right)  \left( {x}^{52}-{x}^{51}+{x}^{48}-{x}^{46}+{x}^{44}-{x}^{41}+{x}^{40}+{x}^{32}-{x}^{31}+{x}^{28}-{x}^{26}+{x}^{24}-{x}^{21}+{x}^{20}+{x}^{12}-{x}^{11}\\
\mbox{}+{x}^{8}-{x}^{6}+{x}^{4}-x+1 \right) }{ \left( 1-{x}^{60} \right) ^{6}}}$}

\end{maplelatex}
Expand the series to find the first few values of the number of squares.\begin{mapleinput}
\mapleinline{active}{1d}{Sseries:=series(Sgf,x=0,enddegree+1);}{}
\end{mapleinput}
\mapleresult
\begin{maplelatex}
\mapleinline{inert}{2d}{Sseries := series(72*x^10+288*x^11+936*x^12+2592*x^13+5760*x^14+11520*x^15+20952*x^16+35712*x^17+57168*x^18+88272*x^19+131112*x^20+O(x^21),x,21)}{%
${\it Sseries}\, := \,{\it series} \left( 72\,{x}^{10}+288\,{x}^{11}+936\,{x}^{12}+2592\,{x}^{13}+5760\,{x}^{14}+11520\,{x}^{15}\\
\mbox{}+20952\,{x}^{16}+35712\,{x}^{17}+57168\,{x}^{18}+88272\,{x}^{19}+131112\,{x}^{20}+O \left( {x}^{21} \right) ,x,21\\
\mbox{} \right) $}

\end{maplelatex}
Expand the series to find the first few values of the number of reduced squares.\begin{mapleinput}
\mapleinline{active}{1d}{Rseries:=series(Rgf,x=0,enddegree+1);}{}
\end{mapleinput}
\mapleresult
\begin{maplelatex}
\mapleinline{inert}{2d}{Rseries := series(72*x^8+144*x^9+432*x^10+1008*x^11+1512*x^12+2592*x^13+3672*x^14+5328*x^15+6696*x^16+9648*x^17+11736*x^18+15552*x^19+17856*x^20+O(x^21),x,21)}{%
${\it Rseries}\, := \,{\it series} \left( 72\,{x}^{8}+144\,{x}^{9}+432\,{x}^{10}+1008\,{x}^{11}+1512\,{x}^{12}+2592\,{x}^{13}\\
\mbox{}+3672\,{x}^{14}+5328\,{x}^{15}+6696\,{x}^{16}+9648\,{x}^{17}+11736\,{x}^{18}+15552\,{x}^{19}+17856\,{x}^{20}\\
\mbox{}+O \left( {x}^{21} \right) ,x,21 \right) $}

\end{maplelatex}
Expand the series to find the first few values of the number of symmetry types.\begin{mapleinput}
\mapleinline{active}{1d}{sseries:=series(sgf,x=0,enddegree+1);}{}
\end{mapleinput}
\mapleresult
\begin{maplelatex}
\mapleinline{inert}{2d}{sseries := series(x^10+4*x^11+13*x^12+36*x^13+80*x^14+160*x^15+291*x^16+496*x^17+794*x^18+1226*x^19+1821*x^20+O(x^21),x,21)}{%
${\it sseries}\, := \,{\it series} \left( {x}^{10}+4\,{x}^{11}+13\,{x}^{12}+36\,{x}^{13}+80\,{x}^{14}+160\,{x}^{15}+291\,{x}^{16}+496\,{x}^{17}\\
\mbox{}+794\,{x}^{18}+1226\,{x}^{19}+1821\,{x}^{20}+O \left( {x}^{21} \right) ,x,21 \right) $}

\end{maplelatex}
Expand the series to find the first few values of the number of reduced symmetry types.\begin{mapleinput}
\mapleinline{active}{1d}{rseries:=series(rgf,x=0,enddegree+1);}{}
\end{mapleinput}
\mapleresult
\begin{maplelatex}
\mapleinline{inert}{2d}{rseries := series(x^8+2*x^9+6*x^10+14*x^11+21*x^12+36*x^13+51*x^14+74*x^15+93*x^16+134*x^17+163*x^18+216*x^19+248*x^20+O(x^21),x,21)}{%
${\it rseries}\, := \,{\it series} \left( {x}^{8}+2\,{x}^{9}+6\,{x}^{10}+14\,{x}^{11}+21\,{x}^{12}+36\,{x}^{13}+51\,{x}^{14}+74\,{x}^{15}+93\,{x}^{16}\\
\mbox{}+134\,{x}^{17}+163\,{x}^{18}+216\,{x}^{19}+248\,{x}^{20}+O \left( {x}^{21} \right) ,x,21 \right) $}

\end{maplelatex}
Casculate the zeroth constituent of the .  Find its constant term.\begin{mapleinput}
\mapleinline{active}{1d}{Szeroth:=expand(
sum(coeff(Sgfstandnum,x,p*jj)*binomial(d+t/p-jj,d),jj=0..d+1) );
print(subs(t=0,Szeroth)):  }{}
\end{mapleinput}
\mapleresult
\begin{maplelatex}
\mapleinline{inert}{2d}{Szeroth := -1296+1464*t-5989/10*t^2+331/3*t^3-75/8*t^4+3/10*t^5}{%
${\it Szeroth}\, := \,-1296+1464\,t-{\frac {5989}{10}}\,{t}^{2}+{\frac {331}{3}}\,{t}^{3}\\
\mbox{}-{\frac {75}{8}}\,{t}^{4}+3/10\,{t}^{5}$}
\mapleinline{inert}{2d}{-1296}{%
\[
-1296
\]
}

\end{maplelatex}
Extract the constituents of the total semimagic counting function.\begin{mapleinput}
\mapleinline{active}{1d}{Sconstituent[0]:=Szeroth:
for r from 1 to p do
  Sconstituent[r]:=expand(sum( coeff(Sgfstandnum,x,p*jj+r)*binomial(d+(t-r)/p-jj,d), jj=0..d)):
#  print(r):
#  print( Sconstituent[r] ):
  print( factor(Sconstituent[r]) ):
od;}{}
\end{mapleinput}
\mapleresult
\begin{maplelatex}
\mapleinline{inert}{2d}{Sconstituent[1] := 2831/2*t-11933/20*t^2-110413/120+331/3*t^3-75/8*t^4+3/10*t^5}{%
${\it Sconstituent}_{{1}}\, := \,{\frac {2831}{2}}\,t-{\frac {11933}{20}}\,{t}^{2}-{\frac {110413}{120}}\\
\mbox{}+{\frac {331}{3}}\,{t}^{3}-{\frac {75}{8}}\,{t}^{4}+3/10\,{t}^{5}$}

\end{maplelatex}

\mapleresult
\begin{maplelatex}
\mapleinline{inert}{2d}{1/120*(t-1)*(36*t^4-1089*t^3+12151*t^2-59447*t+110413)}{%
\[
{\frac {1}{120}}\, \left( t-1 \right)  \left( 36\,{t}^{4}-1089\,{t}^{3}+12151\,{t}^{2}-59447\,t+110413 \right) 
\]
}
\mapleinline{inert}{2d}{Sconstituent[2] := 1464*t-5989/10*t^2+331/3*t^3-75/8*t^4+3/10*t^5-3824/3}{%
${\it Sconstituent}_{{2}}\, := \,1464\,t-{\frac {5989}{10}}\,{t}^{2}+{\frac {331}{3}}\,{t}^{3}-{\frac {75}{8}}\,{t}^{4}\\
\mbox{}+3/10\,{t}^{5}-{\frac {3824}{3}}$}
\mapleinline{inert}{2d}{1/120*(t-2)*(36*t^4-1053*t^3+11134*t^2-49600*t+76480)}{%
\[
{\frac {1}{120}}\, \left( t-2 \right)  \left( 36\,{t}^{4}-1053\,{t}^{3}+11134\,{t}^{2}-49600\,t+76480 \right) 
\]
}
\mapleinline{inert}{2d}{Sconstituent[3] := 2847/2*t-11933/20*t^2+331/3*t^3-75/8*t^4+3/10*t^5-47727/40}{%
${\it Sconstituent}_{{3}}\, := \,{\frac {2847}{2}}\,t-{\frac {11933}{20}}\,{t}^{2}+{\frac {331}{3}}\,{t}^{3}\\
\mbox{}-{\frac {75}{8}}\,{t}^{4}+3/10\,{t}^{5}-{\frac {47727}{40}}$}
\mapleinline{inert}{2d}{1/120*(t-3)*(36*t^4-1017*t^3+10189*t^2-41031*t+47727)}{%
\[
{\frac {1}{120}}\, \left( t-3 \right)  \left( 36\,{t}^{4}-1017\,{t}^{3}+10189\,{t}^{2}-41031\,t+47727 \right) 
\]
}
\mapleinline{inert}{2d}{Sconstituent[4] := 1456*t-5989/10*t^2+331/3*t^3-75/8*t^4+3/10*t^5-18152/15}{%
${\it Sconstituent}_{{4}}\, := \,1456\,t-{\frac {5989}{10}}\,{t}^{2}+{\frac {331}{3}}\,{t}^{3}-{\frac {75}{8}}\,{t}^{4}\\
\mbox{}+3/10\,{t}^{5}-{\frac {18152}{15}}$}

\end{maplelatex}

\mapleresult
\begin{maplelatex}
\mapleinline{inert}{2d}{1/120*(t-4)*(36*t^4-981*t^3+9316*t^2-34604*t+36304)}{%
\[
{\frac {1}{120}}\, \left( t-4 \right)  \left( 36\,{t}^{4}-981\,{t}^{3}+9316\,{t}^{2}-34604\,t+36304 \right) 
\]
}
\mapleinline{inert}{2d}{Sconstituent[5] := 2847/2*t-11933/20*t^2+331/3*t^3-75/8*t^4+3/10*t^5-25705/24}{%
${\it Sconstituent}_{{5}}\, := \,{\frac {2847}{2}}\,t-{\frac {11933}{20}}\,{t}^{2}+{\frac {331}{3}}\,{t}^{3}\\
\mbox{}-{\frac {75}{8}}\,{t}^{4}+3/10\,{t}^{5}-{\frac {25705}{24}}$}
\mapleinline{inert}{2d}{1/120*(t-5)*(36*t^4-945*t^3+8515*t^2-29023*t+25705)}{%
\[
{\frac {1}{120}}\, \left( t-5 \right)  \left( 36\,{t}^{4}-945\,{t}^{3}+8515\,{t}^{2}-29023\,t+25705 \right) 
\]
}
\mapleinline{inert}{2d}{Sconstituent[6] := 1464*t-6192/5-5989/10*t^2+331/3*t^3-75/8*t^4+3/10*t^5}{%
${\it Sconstituent}_{{6}}\, := \,1464\,t-{\frac {6192}{5}}-{\frac {5989}{10}}\,{t}^{2}+{\frac {331}{3}}\,{t}^{3}\\
\mbox{}-{\frac {75}{8}}\,{t}^{4}+3/10\,{t}^{5}$}
\mapleinline{inert}{2d}{1/120*(t-6)*(36*t^4-909*t^3+7786*t^2-25152*t+24768)}{%
\[
{\frac {1}{120}}\, \left( t-6 \right)  \left( 36\,{t}^{4}-909\,{t}^{3}+7786\,{t}^{2}-25152\,t+24768 \right) 
\]
}
\mapleinline{inert}{2d}{Sconstituent[7] := 2831/2*t-11933/20*t^2+331/3*t^3-75/8*t^4+3/10*t^5-25193/24}{%
${\it Sconstituent}_{{7}}\, := \,{\frac {2831}{2}}\,t-{\frac {11933}{20}}\,{t}^{2}+{\frac {331}{3}}\,{t}^{3}\\
\mbox{}-{\frac {75}{8}}\,{t}^{4}+3/10\,{t}^{5}-{\frac {25193}{24}}$}
\mapleinline{inert}{2d}{1/120*(t-7)*(36*t^4-873*t^3+7129*t^2-21695*t+17995)}{%
\[
{\frac {1}{120}}\, \left( t-7 \right)  \left( 36\,{t}^{4}-873\,{t}^{3}+7129\,{t}^{2}-21695\,t+17995 \right) 
\]
}
\mapleinline{inert}{2d}{Sconstituent[8] := 1464*t-19552/15-5989/10*t^2+331/3*t^3-75/8*t^4+3/10*t^5}{%
${\it Sconstituent}_{{8}}\, := \,1464\,t-{\frac {19552}{15}}-{\frac {5989}{10}}\,{t}^{2}+{\frac {331}{3}}\,{t}^{3}\\
\mbox{}-{\frac {75}{8}}\,{t}^{4}+3/10\,{t}^{5}$}
\mapleinline{inert}{2d}{1/120*(t-8)*(36*t^4-837*t^3+6544*t^2-19516*t+19552)}{%
\[
{\frac {1}{120}}\, \left( t-8 \right)  \left( 36\,{t}^{4}-837\,{t}^{3}+6544\,{t}^{2}-19516\,t+19552 \right) 
\]
}

\end{maplelatex}

\mapleresult
\begin{maplelatex}
\mapleinline{inert}{2d}{Sconstituent[9] := 2847/2*t-11933/20*t^2+331/3*t^3-75/8*t^4+3/10*t^5-44847/40}{%
${\it Sconstituent}_{{9}}\, := \,{\frac {2847}{2}}\,t-{\frac {11933}{20}}\,{t}^{2}+{\frac {331}{3}}\,{t}^{3}\\
\mbox{}-{\frac {75}{8}}\,{t}^{4}+3/10\,{t}^{5}-{\frac {44847}{40}}$}
\mapleinline{inert}{2d}{1/120*(t-9)*(36*t^4-801*t^3+6031*t^2-17319*t+14949)}{%
\[
{\frac {1}{120}}\, \left( t-9 \right)  \left( 36\,{t}^{4}-801\,{t}^{3}+6031\,{t}^{2}-17319\,t+14949 \right) 
\]
}
\mapleinline{inert}{2d}{Sconstituent[10] := 1456*t-3544/3-5989/10*t^2+331/3*t^3-75/8*t^4+3/10*t^5}{%
${\it Sconstituent}_{{10}}\, := \,1456\,t-{\frac {3544}{3}}-{\frac {5989}{10}}\,{t}^{2}+{\frac {331}{3}}\,{t}^{3}\\
\mbox{}-{\frac {75}{8}}\,{t}^{4}+3/10\,{t}^{5}$}
\mapleinline{inert}{2d}{1456*t-3544/3-5989/10*t^2+331/3*t^3-75/8*t^4+3/10*t^5}{%
$1456\,t-{\frac {3544}{3}}-{\frac {5989}{10}}\,{t}^{2}+{\frac {331}{3}}\,{t}^{3}\\
\mbox{}-{\frac {75}{8}}\,{t}^{4}+3/10\,{t}^{5}$}
\mapleinline{inert}{2d}{Sconstituent[11] := 2847/2*t-11933/20*t^2+331/3*t^3-75/8*t^4+3/10*t^5-130253/120}{%
${\it Sconstituent}_{{11}}\, := \,{\frac {2847}{2}}\,t-{\frac {11933}{20}}\,{t}^{2}+{\frac {331}{3}}\,{t}^{3}\\
\mbox{}-{\frac {75}{8}}\,{t}^{4}+3/10\,{t}^{5}-{\frac {130253}{120}}$}
\mapleinline{inert}{2d}{2847/2*t-11933/20*t^2+331/3*t^3-75/8*t^4+3/10*t^5-130253/120}{%
${\frac {2847}{2}}\,t-{\frac {11933}{20}}\,{t}^{2}+{\frac {331}{3}}\,{t}^{3}\\
\mbox{}-{\frac {75}{8}}\,{t}^{4}+3/10\,{t}^{5}-{\frac {130253}{120}}$}
\mapleinline{inert}{2d}{Sconstituent[12] := -1296+1464*t-5989/10*t^2+331/3*t^3-75/8*t^4+3/10*t^5}{%
${\it Sconstituent}_{{12}}\, := \,-1296+1464\,t-{\frac {5989}{10}}\,{t}^{2}+{\frac {331}{3}}\,{t}^{3}\\
\mbox{}-{\frac {75}{8}}\,{t}^{4}+3/10\,{t}^{5}$}
\mapleinline{inert}{2d}{-1296+1464*t-5989/10*t^2+331/3*t^3-75/8*t^4+3/10*t^5}{%
$-1296+1464\,t-{\frac {5989}{10}}\,{t}^{2}+{\frac {331}{3}}\,{t}^{3}\\
\mbox{}-{\frac {75}{8}}\,{t}^{4}+3/10\,{t}^{5}$}
\mapleinline{inert}{2d}{Sconstituent[13] := 2831/2*t-11933/20*t^2+331/3*t^3-75/8*t^4+3/10*t^5-120781/120}{%
${\it Sconstituent}_{{13}}\, := \,{\frac {2831}{2}}\,t-{\frac {11933}{20}}\,{t}^{2}+{\frac {331}{3}}\,{t}^{3}\\
\mbox{}-{\frac {75}{8}}\,{t}^{4}+3/10\,{t}^{5}-{\frac {120781}{120}}$}
\mapleinline{inert}{2d}{2831/2*t-11933/20*t^2+331/3*t^3-75/8*t^4+3/10*t^5-120781/120}{%
${\frac {2831}{2}}\,t-{\frac {11933}{20}}\,{t}^{2}+{\frac {331}{3}}\,{t}^{3}\\
\mbox{}-{\frac {75}{8}}\,{t}^{4}+3/10\,{t}^{5}-{\frac {120781}{120}}$}
\mapleinline{inert}{2d}{Sconstituent[14] := 1464*t-19552/15-5989/10*t^2+331/3*t^3-75/8*t^4+3/10*t^5}{%
${\it Sconstituent}_{{14}}\, := \,1464\,t-{\frac {19552}{15}}-{\frac {5989}{10}}\,{t}^{2}+{\frac {331}{3}}\,{t}^{3}\\
\mbox{}-{\frac {75}{8}}\,{t}^{4}+3/10\,{t}^{5}$}
\mapleinline{inert}{2d}{1/120*(t-8)*(36*t^4-837*t^3+6544*t^2-19516*t+19552)}{%
\[
{\frac {1}{120}}\, \left( t-8 \right)  \left( 36\,{t}^{4}-837\,{t}^{3}+6544\,{t}^{2}-19516\,t+19552 \right) 
\]
}
\mapleinline{inert}{2d}{Sconstituent[15] := 2847/2*t-11933/20*t^2+331/3*t^3-75/8*t^4+3/10*t^5-9315/8}{%
${\it Sconstituent}_{{15}}\, := \,{\frac {2847}{2}}\,t-{\frac {11933}{20}}\,{t}^{2}+{\frac {331}{3}}\,{t}^{3}\\
\mbox{}-{\frac {75}{8}}\,{t}^{4}+3/10\,{t}^{5}-{\frac {9315}{8}}$}
\mapleinline{inert}{2d}{2847/2*t-11933/20*t^2+331/3*t^3-75/8*t^4+3/10*t^5-9315/8}{%
${\frac {2847}{2}}\,t-{\frac {11933}{20}}\,{t}^{2}+{\frac {331}{3}}\,{t}^{3}\\
\mbox{}-{\frac {75}{8}}\,{t}^{4}+3/10\,{t}^{5}-{\frac {9315}{8}}$}

\end{maplelatex}

\mapleresult
\begin{maplelatex}
\mapleinline{inert}{2d}{Sconstituent[16] := 1456*t-5989/10*t^2+331/3*t^3-75/8*t^4+3/10*t^5-16856/15}{%
${\it Sconstituent}_{{16}}\, := \,1456\,t-{\frac {5989}{10}}\,{t}^{2}+{\frac {331}{3}}\,{t}^{3}-{\frac {75}{8}}\,{t}^{4}\\
\mbox{}+3/10\,{t}^{5}-{\frac {16856}{15}}$}
\mapleinline{inert}{2d}{1456*t-5989/10*t^2+331/3*t^3-75/8*t^4+3/10*t^5-16856/15}{%
$1456\,t-{\frac {5989}{10}}\,{t}^{2}+{\frac {331}{3}}\,{t}^{3}-{\frac {75}{8}}\,{t}^{4}\\
\mbox{}+3/10\,{t}^{5}-{\frac {16856}{15}}$}
\mapleinline{inert}{2d}{Sconstituent[17] := 2847/2*t-11933/20*t^2+331/3*t^3-75/8*t^4+3/10*t^5-25705/24}{%
${\it Sconstituent}_{{17}}\, := \,{\frac {2847}{2}}\,t-{\frac {11933}{20}}\,{t}^{2}+{\frac {331}{3}}\,{t}^{3}\\
\mbox{}-{\frac {75}{8}}\,{t}^{4}+3/10\,{t}^{5}-{\frac {25705}{24}}$}
\mapleinline{inert}{2d}{1/120*(t-5)*(36*t^4-945*t^3+8515*t^2-29023*t+25705)}{%
\[
{\frac {1}{120}}\, \left( t-5 \right)  \left( 36\,{t}^{4}-945\,{t}^{3}+8515\,{t}^{2}-29023\,t+25705 \right) 
\]
}
\mapleinline{inert}{2d}{Sconstituent[18] := 1464*t-5989/10*t^2+331/3*t^3-75/8*t^4+3/10*t^5-6624/5}{%
${\it Sconstituent}_{{18}}\, := \,1464\,t-{\frac {5989}{10}}\,{t}^{2}+{\frac {331}{3}}\,{t}^{3}-{\frac {75}{8}}\,{t}^{4}\\
\mbox{}+3/10\,{t}^{5}-{\frac {6624}{5}}$}
\mapleinline{inert}{2d}{1464*t-5989/10*t^2+331/3*t^3-75/8*t^4+3/10*t^5-6624/5}{%
$1464\,t-{\frac {5989}{10}}\,{t}^{2}+{\frac {331}{3}}\,{t}^{3}-{\frac {75}{8}}\,{t}^{4}\\
\mbox{}+3/10\,{t}^{5}-{\frac {6624}{5}}$}
\mapleinline{inert}{2d}{Sconstituent[19] := -129421/120+2831/2*t-11933/20*t^2+331/3*t^3-75/8*t^4+3/10*t^5}{%
${\it Sconstituent}_{{19}}\, := \,-{\frac {129421}{120}}+{\frac {2831}{2}}\,t\\
\mbox{}-{\frac {11933}{20}}\,{t}^{2}+{\frac {331}{3}}\,{t}^{3}-{\frac {75}{8}}\,{t}^{4}\\
\mbox{}+3/10\,{t}^{5}$}
\mapleinline{inert}{2d}{-129421/120+2831/2*t-11933/20*t^2+331/3*t^3-75/8*t^4+3/10*t^5}{%
$-{\frac {129421}{120}}+{\frac {2831}{2}}\,t\\
\mbox{}-{\frac {11933}{20}}\,{t}^{2}+{\frac {331}{3}}\,{t}^{3}-{\frac {75}{8}}\,{t}^{4}\\
\mbox{}+3/10\,{t}^{5}$}

\end{maplelatex}

\mapleresult
\begin{maplelatex}
\mapleinline{inert}{2d}{Sconstituent[20] := 1464*t-5989/10*t^2+331/3*t^3-75/8*t^4+3/10*t^5-3824/3}{%
${\it Sconstituent}_{{20}}\, := \,1464\,t-{\frac {5989}{10}}\,{t}^{2}+{\frac {331}{3}}\,{t}^{3}-{\frac {75}{8}}\,{t}^{4}\\
\mbox{}+3/10\,{t}^{5}-{\frac {3824}{3}}$}
\mapleinline{inert}{2d}{1/120*(t-2)*(36*t^4-1053*t^3+11134*t^2-49600*t+76480)}{%
\[
{\frac {1}{120}}\, \left( t-2 \right)  \left( 36\,{t}^{4}-1053\,{t}^{3}+11134\,{t}^{2}-49600\,t+76480 \right) 
\]
}
\mapleinline{inert}{2d}{Sconstituent[21] := 2847/2*t-11933/20*t^2+331/3*t^3-75/8*t^4+3/10*t^5-41391/40}{%
${\it Sconstituent}_{{21}}\, := \,{\frac {2847}{2}}\,t-{\frac {11933}{20}}\,{t}^{2}+{\frac {331}{3}}\,{t}^{3}\\
\mbox{}-{\frac {75}{8}}\,{t}^{4}+3/10\,{t}^{5}-{\frac {41391}{40}}$}
\mapleinline{inert}{2d}{2847/2*t-11933/20*t^2+331/3*t^3-75/8*t^4+3/10*t^5-41391/40}{%
${\frac {2847}{2}}\,t-{\frac {11933}{20}}\,{t}^{2}+{\frac {331}{3}}\,{t}^{3}\\
\mbox{}-{\frac {75}{8}}\,{t}^{4}+3/10\,{t}^{5}-{\frac {41391}{40}}$}
\mapleinline{inert}{2d}{Sconstituent[22] := 1456*t-3544/3-5989/10*t^2+331/3*t^3-75/8*t^4+3/10*t^5}{%
${\it Sconstituent}_{{22}}\, := \,1456\,t-{\frac {3544}{3}}-{\frac {5989}{10}}\,{t}^{2}+{\frac {331}{3}}\,{t}^{3}\\
\mbox{}-{\frac {75}{8}}\,{t}^{4}+3/10\,{t}^{5}$}
\mapleinline{inert}{2d}{1456*t-3544/3-5989/10*t^2+331/3*t^3-75/8*t^4+3/10*t^5}{%
$1456\,t-{\frac {3544}{3}}-{\frac {5989}{10}}\,{t}^{2}+{\frac {331}{3}}\,{t}^{3}\\
\mbox{}-{\frac {75}{8}}\,{t}^{4}+3/10\,{t}^{5}$}
\mapleinline{inert}{2d}{Sconstituent[23] := 2847/2*t-11933/20*t^2-140621/120+331/3*t^3-75/8*t^4+3/10*t^5}{%
${\it Sconstituent}_{{23}}\, := \,{\frac {2847}{2}}\,t-{\frac {11933}{20}}\,{t}^{2}-{\frac {140621}{120}}\\
\mbox{}+{\frac {331}{3}}\,{t}^{3}-{\frac {75}{8}}\,{t}^{4}+3/10\,{t}^{5}$}
\mapleinline{inert}{2d}{2847/2*t-11933/20*t^2-140621/120+331/3*t^3-75/8*t^4+3/10*t^5}{%
${\frac {2847}{2}}\,t-{\frac {11933}{20}}\,{t}^{2}-{\frac {140621}{120}}\\
\mbox{}+{\frac {331}{3}}\,{t}^{3}-{\frac {75}{8}}\,{t}^{4}+3/10\,{t}^{5}$}

\end{maplelatex}

\mapleresult
\begin{maplelatex}
\mapleinline{inert}{2d}{Sconstituent[24] := 1464*t-5989/10*t^2+331/3*t^3-75/8*t^4+3/10*t^5-6624/5}{%
${\it Sconstituent}_{{24}}\, := \,1464\,t-{\frac {5989}{10}}\,{t}^{2}+{\frac {331}{3}}\,{t}^{3}-{\frac {75}{8}}\,{t}^{4}\\
\mbox{}+3/10\,{t}^{5}-{\frac {6624}{5}}$}
\mapleinline{inert}{2d}{1464*t-5989/10*t^2+331/3*t^3-75/8*t^4+3/10*t^5-6624/5}{%
$1464\,t-{\frac {5989}{10}}\,{t}^{2}+{\frac {331}{3}}\,{t}^{3}-{\frac {75}{8}}\,{t}^{4}\\
\mbox{}+3/10\,{t}^{5}-{\frac {6624}{5}}$}
\mapleinline{inert}{2d}{Sconstituent[25] := 2831/2*t-11933/20*t^2+331/3*t^3-75/8*t^4+3/10*t^5-23465/24}{%
${\it Sconstituent}_{{25}}\, := \,{\frac {2831}{2}}\,t-{\frac {11933}{20}}\,{t}^{2}+{\frac {331}{3}}\,{t}^{3}\\
\mbox{}-{\frac {75}{8}}\,{t}^{4}+3/10\,{t}^{5}-{\frac {23465}{24}}$}
\mapleinline{inert}{2d}{2831/2*t-11933/20*t^2+331/3*t^3-75/8*t^4+3/10*t^5-23465/24}{%
${\frac {2831}{2}}\,t-{\frac {11933}{20}}\,{t}^{2}+{\frac {331}{3}}\,{t}^{3}\\
\mbox{}-{\frac {75}{8}}\,{t}^{4}+3/10\,{t}^{5}-{\frac {23465}{24}}$}
\mapleinline{inert}{2d}{Sconstituent[26] := 1464*t-18256/15-5989/10*t^2+331/3*t^3-75/8*t^4+3/10*t^5}{%
${\it Sconstituent}_{{26}}\, := \,1464\,t-{\frac {18256}{15}}-{\frac {5989}{10}}\,{t}^{2}+{\frac {331}{3}}\,{t}^{3}\\
\mbox{}-{\frac {75}{8}}\,{t}^{4}+3/10\,{t}^{5}$}
\mapleinline{inert}{2d}{1464*t-18256/15-5989/10*t^2+331/3*t^3-75/8*t^4+3/10*t^5}{%
$1464\,t-{\frac {18256}{15}}-{\frac {5989}{10}}\,{t}^{2}+{\frac {331}{3}}\,{t}^{3}\\
\mbox{}-{\frac {75}{8}}\,{t}^{4}+3/10\,{t}^{5}$}
\mapleinline{inert}{2d}{Sconstituent[27] := 2847/2*t-11933/20*t^2+331/3*t^3-75/8*t^4+3/10*t^5-9315/8}{%
${\it Sconstituent}_{{27}}\, := \,{\frac {2847}{2}}\,t-{\frac {11933}{20}}\,{t}^{2}+{\frac {331}{3}}\,{t}^{3}\\
\mbox{}-{\frac {75}{8}}\,{t}^{4}+3/10\,{t}^{5}-{\frac {9315}{8}}$}
\mapleinline{inert}{2d}{2847/2*t-11933/20*t^2+331/3*t^3-75/8*t^4+3/10*t^5-9315/8}{%
${\frac {2847}{2}}\,t-{\frac {11933}{20}}\,{t}^{2}+{\frac {331}{3}}\,{t}^{3}\\
\mbox{}-{\frac {75}{8}}\,{t}^{4}+3/10\,{t}^{5}-{\frac {9315}{8}}$}
\mapleinline{inert}{2d}{Sconstituent[28] := 1456*t-5989/10*t^2+331/3*t^3-75/8*t^4+3/10*t^5-18152/15}{%
${\it Sconstituent}_{{28}}\, := \,1456\,t-{\frac {5989}{10}}\,{t}^{2}+{\frac {331}{3}}\,{t}^{3}-{\frac {75}{8}}\,{t}^{4}\\
\mbox{}+3/10\,{t}^{5}-{\frac {18152}{15}}$}
\mapleinline{inert}{2d}{1/120*(t-4)*(36*t^4-981*t^3+9316*t^2-34604*t+36304)}{%
\[
{\frac {1}{120}}\, \left( t-4 \right)  \left( 36\,{t}^{4}-981\,{t}^{3}+9316\,{t}^{2}-34604\,t+36304 \right) 
\]
}
\mapleinline{inert}{2d}{Sconstituent[29] := 2847/2*t-11933/20*t^2+331/3*t^3-75/8*t^4+3/10*t^5-131981/120}{%
${\it Sconstituent}_{{29}}\, := \,{\frac {2847}{2}}\,t-{\frac {11933}{20}}\,{t}^{2}+{\frac {331}{3}}\,{t}^{3}\\
\mbox{}-{\frac {75}{8}}\,{t}^{4}+3/10\,{t}^{5}-{\frac {131981}{120}}$}
\mapleinline{inert}{2d}{2847/2*t-11933/20*t^2+331/3*t^3-75/8*t^4+3/10*t^5-131981/120}{%
${\frac {2847}{2}}\,t-{\frac {11933}{20}}\,{t}^{2}+{\frac {331}{3}}\,{t}^{3}\\
\mbox{}-{\frac {75}{8}}\,{t}^{4}+3/10\,{t}^{5}-{\frac {131981}{120}}$}
\mapleinline{inert}{2d}{Sconstituent[30] := -1296+1464*t-5989/10*t^2+331/3*t^3-75/8*t^4+3/10*t^5}{%
${\it Sconstituent}_{{30}}\, := \,-1296+1464\,t-{\frac {5989}{10}}\,{t}^{2}+{\frac {331}{3}}\,{t}^{3}\\
\mbox{}-{\frac {75}{8}}\,{t}^{4}+3/10\,{t}^{5}$}
\mapleinline{inert}{2d}{-1296+1464*t-5989/10*t^2+331/3*t^3-75/8*t^4+3/10*t^5}{%
$-1296+1464\,t-{\frac {5989}{10}}\,{t}^{2}+{\frac {331}{3}}\,{t}^{3}\\
\mbox{}-{\frac {75}{8}}\,{t}^{4}+3/10\,{t}^{5}$}

\end{maplelatex}

\mapleresult
\begin{maplelatex}
\mapleinline{inert}{2d}{Sconstituent[31] := 2831/2*t-11933/20*t^2+331/3*t^3-75/8*t^4+3/10*t^5-119053/120}{%
${\it Sconstituent}_{{31}}\, := \,{\frac {2831}{2}}\,t-{\frac {11933}{20}}\,{t}^{2}+{\frac {331}{3}}\,{t}^{3}\\
\mbox{}-{\frac {75}{8}}\,{t}^{4}+3/10\,{t}^{5}-{\frac {119053}{120}}$}
\mapleinline{inert}{2d}{2831/2*t-11933/20*t^2+331/3*t^3-75/8*t^4+3/10*t^5-119053/120}{%
${\frac {2831}{2}}\,t-{\frac {11933}{20}}\,{t}^{2}+{\frac {331}{3}}\,{t}^{3}\\
\mbox{}-{\frac {75}{8}}\,{t}^{4}+3/10\,{t}^{5}-{\frac {119053}{120}}$}
\mapleinline{inert}{2d}{Sconstituent[32] := 1464*t-5989/10*t^2+331/3*t^3-75/8*t^4+3/10*t^5-3824/3}{%
${\it Sconstituent}_{{32}}\, := \,1464\,t-{\frac {5989}{10}}\,{t}^{2}+{\frac {331}{3}}\,{t}^{3}-{\frac {75}{8}}\,{t}^{4}\\
\mbox{}+3/10\,{t}^{5}-{\frac {3824}{3}}$}
\mapleinline{inert}{2d}{1/120*(t-2)*(36*t^4-1053*t^3+11134*t^2-49600*t+76480)}{%
\[
{\frac {1}{120}}\, \left( t-2 \right)  \left( 36\,{t}^{4}-1053\,{t}^{3}+11134\,{t}^{2}-49600\,t+76480 \right) 
\]
}
\mapleinline{inert}{2d}{Sconstituent[33] := 2847/2*t-11933/20*t^2+331/3*t^3-75/8*t^4+3/10*t^5-44847/40}{%
${\it Sconstituent}_{{33}}\, := \,{\frac {2847}{2}}\,t-{\frac {11933}{20}}\,{t}^{2}+{\frac {331}{3}}\,{t}^{3}\\
\mbox{}-{\frac {75}{8}}\,{t}^{4}+3/10\,{t}^{5}-{\frac {44847}{40}}$}

\end{maplelatex}

\mapleresult
\begin{maplelatex}
\mapleinline{inert}{2d}{1/120*(t-9)*(36*t^4-801*t^3+6031*t^2-17319*t+14949)}{%
\[
{\frac {1}{120}}\, \left( t-9 \right)  \left( 36\,{t}^{4}-801\,{t}^{3}+6031\,{t}^{2}-17319\,t+14949 \right) 
\]
}
\mapleinline{inert}{2d}{Sconstituent[34] := 1456*t-5989/10*t^2+331/3*t^3-75/8*t^4+3/10*t^5-18152/15}{%
${\it Sconstituent}_{{34}}\, := \,1456\,t-{\frac {5989}{10}}\,{t}^{2}+{\frac {331}{3}}\,{t}^{3}-{\frac {75}{8}}\,{t}^{4}\\
\mbox{}+3/10\,{t}^{5}-{\frac {18152}{15}}$}
\mapleinline{inert}{2d}{1/120*(t-4)*(36*t^4-981*t^3+9316*t^2-34604*t+36304)}{%
\[
{\frac {1}{120}}\, \left( t-4 \right)  \left( 36\,{t}^{4}-981\,{t}^{3}+9316\,{t}^{2}-34604\,t+36304 \right) 
\]
}
\mapleinline{inert}{2d}{Sconstituent[35] := 2847/2*t-27433/24-11933/20*t^2+331/3*t^3-75/8*t^4+3/10*t^5}{%
${\it Sconstituent}_{{35}}\, := \,{\frac {2847}{2}}\,t-{\frac {27433}{24}}-{\frac {11933}{20}}\,{t}^{2}\\
\mbox{}+{\frac {331}{3}}\,{t}^{3}-{\frac {75}{8}}\,{t}^{4}+3/10\,{t}^{5}$}
\mapleinline{inert}{2d}{2847/2*t-27433/24-11933/20*t^2+331/3*t^3-75/8*t^4+3/10*t^5}{%
${\frac {2847}{2}}\,t-{\frac {27433}{24}}-{\frac {11933}{20}}\,{t}^{2}\\
\mbox{}+{\frac {331}{3}}\,{t}^{3}-{\frac {75}{8}}\,{t}^{4}+3/10\,{t}^{5}$}
\mapleinline{inert}{2d}{Sconstituent[36] := 1464*t-6192/5-5989/10*t^2+331/3*t^3-75/8*t^4+3/10*t^5}{%
${\it Sconstituent}_{{36}}\, := \,1464\,t-{\frac {6192}{5}}-{\frac {5989}{10}}\,{t}^{2}+{\frac {331}{3}}\,{t}^{3}\\
\mbox{}-{\frac {75}{8}}\,{t}^{4}+3/10\,{t}^{5}$}
\mapleinline{inert}{2d}{1/120*(t-6)*(36*t^4-909*t^3+7786*t^2-25152*t+24768)}{%
\[
{\frac {1}{120}}\, \left( t-6 \right)  \left( 36\,{t}^{4}-909\,{t}^{3}+7786\,{t}^{2}-25152\,t+24768 \right) 
\]
}

\end{maplelatex}

\mapleresult
\begin{maplelatex}
\mapleinline{inert}{2d}{Sconstituent[37] := 2831/2*t-11933/20*t^2+331/3*t^3-75/8*t^4+3/10*t^5-23465/24}{%
${\it Sconstituent}_{{37}}\, := \,{\frac {2831}{2}}\,t-{\frac {11933}{20}}\,{t}^{2}+{\frac {331}{3}}\,{t}^{3}\\
\mbox{}-{\frac {75}{8}}\,{t}^{4}+3/10\,{t}^{5}-{\frac {23465}{24}}$}
\mapleinline{inert}{2d}{2831/2*t-11933/20*t^2+331/3*t^3-75/8*t^4+3/10*t^5-23465/24}{%
${\frac {2831}{2}}\,t-{\frac {11933}{20}}\,{t}^{2}+{\frac {331}{3}}\,{t}^{3}\\
\mbox{}-{\frac {75}{8}}\,{t}^{4}+3/10\,{t}^{5}-{\frac {23465}{24}}$}
\mapleinline{inert}{2d}{Sconstituent[38] := 1464*t-19552/15-5989/10*t^2+331/3*t^3-75/8*t^4+3/10*t^5}{%
${\it Sconstituent}_{{38}}\, := \,1464\,t-{\frac {19552}{15}}-{\frac {5989}{10}}\,{t}^{2}+{\frac {331}{3}}\,{t}^{3}\\
\mbox{}-{\frac {75}{8}}\,{t}^{4}+3/10\,{t}^{5}$}
\mapleinline{inert}{2d}{1/120*(t-8)*(36*t^4-837*t^3+6544*t^2-19516*t+19552)}{%
\[
{\frac {1}{120}}\, \left( t-8 \right)  \left( 36\,{t}^{4}-837\,{t}^{3}+6544\,{t}^{2}-19516\,t+19552 \right) 
\]
}
\mapleinline{inert}{2d}{Sconstituent[39] := 2847/2*t-11933/20*t^2+331/3*t^3-75/8*t^4+3/10*t^5-47727/40}{%
${\it Sconstituent}_{{39}}\, := \,{\frac {2847}{2}}\,t-{\frac {11933}{20}}\,{t}^{2}+{\frac {331}{3}}\,{t}^{3}\\
\mbox{}-{\frac {75}{8}}\,{t}^{4}+3/10\,{t}^{5}-{\frac {47727}{40}}$}
\mapleinline{inert}{2d}{1/120*(t-3)*(36*t^4-1017*t^3+10189*t^2-41031*t+47727)}{%
\[
{\frac {1}{120}}\, \left( t-3 \right)  \left( 36\,{t}^{4}-1017\,{t}^{3}+10189\,{t}^{2}-41031\,t+47727 \right) 
\]
}
\mapleinline{inert}{2d}{Sconstituent[40] := 1456*t-3544/3-5989/10*t^2+331/3*t^3-75/8*t^4+3/10*t^5}{%
${\it Sconstituent}_{{40}}\, := \,1456\,t-{\frac {3544}{3}}-{\frac {5989}{10}}\,{t}^{2}+{\frac {331}{3}}\,{t}^{3}\\
\mbox{}-{\frac {75}{8}}\,{t}^{4}+3/10\,{t}^{5}$}
\mapleinline{inert}{2d}{1456*t-3544/3-5989/10*t^2+331/3*t^3-75/8*t^4+3/10*t^5}{%
$1456\,t-{\frac {3544}{3}}-{\frac {5989}{10}}\,{t}^{2}+{\frac {331}{3}}\,{t}^{3}\\
\mbox{}-{\frac {75}{8}}\,{t}^{4}+3/10\,{t}^{5}$}
\mapleinline{inert}{2d}{Sconstituent[41] := 2847/2*t-11933/20*t^2+331/3*t^3-75/8*t^4+3/10*t^5-121613/120}{%
${\it Sconstituent}_{{41}}\, := \,{\frac {2847}{2}}\,t-{\frac {11933}{20}}\,{t}^{2}+{\frac {331}{3}}\,{t}^{3}\\
\mbox{}-{\frac {75}{8}}\,{t}^{4}+3/10\,{t}^{5}-{\frac {121613}{120}}$}
\mapleinline{inert}{2d}{2847/2*t-11933/20*t^2+331/3*t^3-75/8*t^4+3/10*t^5-121613/120}{%
${\frac {2847}{2}}\,t-{\frac {11933}{20}}\,{t}^{2}+{\frac {331}{3}}\,{t}^{3}\\
\mbox{}-{\frac {75}{8}}\,{t}^{4}+3/10\,{t}^{5}-{\frac {121613}{120}}$}
\mapleinline{inert}{2d}{Sconstituent[42] := -1296+1464*t-5989/10*t^2+331/3*t^3-75/8*t^4+3/10*t^5}{%
${\it Sconstituent}_{{42}}\, := \,-1296+1464\,t-{\frac {5989}{10}}\,{t}^{2}+{\frac {331}{3}}\,{t}^{3}\\
\mbox{}-{\frac {75}{8}}\,{t}^{4}+3/10\,{t}^{5}$}
\mapleinline{inert}{2d}{-1296+1464*t-5989/10*t^2+331/3*t^3-75/8*t^4+3/10*t^5}{%
$-1296+1464\,t-{\frac {5989}{10}}\,{t}^{2}+{\frac {331}{3}}\,{t}^{3}\\
\mbox{}-{\frac {75}{8}}\,{t}^{4}+3/10\,{t}^{5}$}
\mapleinline{inert}{2d}{Sconstituent[43] := -129421/120+2831/2*t-11933/20*t^2+331/3*t^3-75/8*t^4+3/10*t^5}{%
${\it Sconstituent}_{{43}}\, := \,-{\frac {129421}{120}}+{\frac {2831}{2}}\,t\\
\mbox{}-{\frac {11933}{20}}\,{t}^{2}+{\frac {331}{3}}\,{t}^{3}-{\frac {75}{8}}\,{t}^{4}\\
\mbox{}+3/10\,{t}^{5}$}
\mapleinline{inert}{2d}{-129421/120+2831/2*t-11933/20*t^2+331/3*t^3-75/8*t^4+3/10*t^5}{%
$-{\frac {129421}{120}}+{\frac {2831}{2}}\,t\\
\mbox{}-{\frac {11933}{20}}\,{t}^{2}+{\frac {331}{3}}\,{t}^{3}-{\frac {75}{8}}\,{t}^{4}\\
\mbox{}+3/10\,{t}^{5}$}

\end{maplelatex}

\mapleresult
\begin{maplelatex}
\mapleinline{inert}{2d}{Sconstituent[44] := 1464*t-19552/15-5989/10*t^2+331/3*t^3-75/8*t^4+3/10*t^5}{%
${\it Sconstituent}_{{44}}\, := \,1464\,t-{\frac {19552}{15}}-{\frac {5989}{10}}\,{t}^{2}+{\frac {331}{3}}\,{t}^{3}\\
\mbox{}-{\frac {75}{8}}\,{t}^{4}+3/10\,{t}^{5}$}
\mapleinline{inert}{2d}{1/120*(t-8)*(36*t^4-837*t^3+6544*t^2-19516*t+19552)}{%
\[
{\frac {1}{120}}\, \left( t-8 \right)  \left( 36\,{t}^{4}-837\,{t}^{3}+6544\,{t}^{2}-19516\,t+19552 \right) 
\]
}
\mapleinline{inert}{2d}{Sconstituent[45] := 2847/2*t-11933/20*t^2+331/3*t^3-75/8*t^4+3/10*t^5-8739/8}{%
${\it Sconstituent}_{{45}}\, := \,{\frac {2847}{2}}\,t-{\frac {11933}{20}}\,{t}^{2}+{\frac {331}{3}}\,{t}^{3}\\
\mbox{}-{\frac {75}{8}}\,{t}^{4}+3/10\,{t}^{5}-{\frac {8739}{8}}$}
\mapleinline{inert}{2d}{2847/2*t-11933/20*t^2+331/3*t^3-75/8*t^4+3/10*t^5-8739/8}{%
${\frac {2847}{2}}\,t-{\frac {11933}{20}}\,{t}^{2}+{\frac {331}{3}}\,{t}^{3}\\
\mbox{}-{\frac {75}{8}}\,{t}^{4}+3/10\,{t}^{5}-{\frac {8739}{8}}$}

\end{maplelatex}

\mapleresult
\begin{maplelatex}
\mapleinline{inert}{2d}{Sconstituent[46] := 1456*t-5989/10*t^2+331/3*t^3-75/8*t^4+3/10*t^5-16856/15}{%
${\it Sconstituent}_{{46}}\, := \,1456\,t-{\frac {5989}{10}}\,{t}^{2}+{\frac {331}{3}}\,{t}^{3}-{\frac {75}{8}}\,{t}^{4}\\
\mbox{}+3/10\,{t}^{5}-{\frac {16856}{15}}$}
\mapleinline{inert}{2d}{1456*t-5989/10*t^2+331/3*t^3-75/8*t^4+3/10*t^5-16856/15}{%
$1456\,t-{\frac {5989}{10}}\,{t}^{2}+{\frac {331}{3}}\,{t}^{3}-{\frac {75}{8}}\,{t}^{4}\\
\mbox{}+3/10\,{t}^{5}-{\frac {16856}{15}}$}
\mapleinline{inert}{2d}{Sconstituent[47] := 2847/2*t-27433/24-11933/20*t^2+331/3*t^3-75/8*t^4+3/10*t^5}{%
${\it Sconstituent}_{{47}}\, := \,{\frac {2847}{2}}\,t-{\frac {27433}{24}}-{\frac {11933}{20}}\,{t}^{2}\\
\mbox{}+{\frac {331}{3}}\,{t}^{3}-{\frac {75}{8}}\,{t}^{4}+3/10\,{t}^{5}$}
\mapleinline{inert}{2d}{2847/2*t-27433/24-11933/20*t^2+331/3*t^3-75/8*t^4+3/10*t^5}{%
${\frac {2847}{2}}\,t-{\frac {27433}{24}}-{\frac {11933}{20}}\,{t}^{2}\\
\mbox{}+{\frac {331}{3}}\,{t}^{3}-{\frac {75}{8}}\,{t}^{4}+3/10\,{t}^{5}$}
\mapleinline{inert}{2d}{Sconstituent[48] := 1464*t-5989/10*t^2+331/3*t^3-75/8*t^4+3/10*t^5-6624/5}{%
${\it Sconstituent}_{{48}}\, := \,1464\,t-{\frac {5989}{10}}\,{t}^{2}+{\frac {331}{3}}\,{t}^{3}-{\frac {75}{8}}\,{t}^{4}\\
\mbox{}+3/10\,{t}^{5}-{\frac {6624}{5}}$}
\mapleinline{inert}{2d}{1464*t-5989/10*t^2+331/3*t^3-75/8*t^4+3/10*t^5-6624/5}{%
$1464\,t-{\frac {5989}{10}}\,{t}^{2}+{\frac {331}{3}}\,{t}^{3}-{\frac {75}{8}}\,{t}^{4}\\
\mbox{}+3/10\,{t}^{5}-{\frac {6624}{5}}$}
\mapleinline{inert}{2d}{Sconstituent[49] := 2831/2*t-11933/20*t^2+331/3*t^3-75/8*t^4+3/10*t^5-120781/120}{%
${\it Sconstituent}_{{49}}\, := \,{\frac {2831}{2}}\,t-{\frac {11933}{20}}\,{t}^{2}+{\frac {331}{3}}\,{t}^{3}\\
\mbox{}-{\frac {75}{8}}\,{t}^{4}+3/10\,{t}^{5}-{\frac {120781}{120}}$}
\mapleinline{inert}{2d}{2831/2*t-11933/20*t^2+331/3*t^3-75/8*t^4+3/10*t^5-120781/120}{%
${\frac {2831}{2}}\,t-{\frac {11933}{20}}\,{t}^{2}+{\frac {331}{3}}\,{t}^{3}\\
\mbox{}-{\frac {75}{8}}\,{t}^{4}+3/10\,{t}^{5}-{\frac {120781}{120}}$}
\mapleinline{inert}{2d}{Sconstituent[50] := 1464*t-5989/10*t^2+331/3*t^3-75/8*t^4+3/10*t^5-3824/3}{%
${\it Sconstituent}_{{50}}\, := \,1464\,t-{\frac {5989}{10}}\,{t}^{2}+{\frac {331}{3}}\,{t}^{3}-{\frac {75}{8}}\,{t}^{4}\\
\mbox{}+3/10\,{t}^{5}-{\frac {3824}{3}}$}
\mapleinline{inert}{2d}{1/120*(t-2)*(36*t^4-1053*t^3+11134*t^2-49600*t+76480)}{%
\[
{\frac {1}{120}}\, \left( t-2 \right)  \left( 36\,{t}^{4}-1053\,{t}^{3}+11134\,{t}^{2}-49600\,t+76480 \right) 
\]
}
\mapleinline{inert}{2d}{Sconstituent[51] := 2847/2*t-11933/20*t^2+331/3*t^3-75/8*t^4+3/10*t^5-44271/40}{%
${\it Sconstituent}_{{51}}\, := \,{\frac {2847}{2}}\,t-{\frac {11933}{20}}\,{t}^{2}+{\frac {331}{3}}\,{t}^{3}\\
\mbox{}-{\frac {75}{8}}\,{t}^{4}+3/10\,{t}^{5}-{\frac {44271}{40}}$}
\mapleinline{inert}{2d}{2847/2*t-11933/20*t^2+331/3*t^3-75/8*t^4+3/10*t^5-44271/40}{%
${\frac {2847}{2}}\,t-{\frac {11933}{20}}\,{t}^{2}+{\frac {331}{3}}\,{t}^{3}\\
\mbox{}-{\frac {75}{8}}\,{t}^{4}+3/10\,{t}^{5}-{\frac {44271}{40}}$}
\mapleinline{inert}{2d}{Sconstituent[52] := 1456*t-3544/3-5989/10*t^2+331/3*t^3-75/8*t^4+3/10*t^5}{%
${\it Sconstituent}_{{52}}\, := \,1456\,t-{\frac {3544}{3}}-{\frac {5989}{10}}\,{t}^{2}+{\frac {331}{3}}\,{t}^{3}\\
\mbox{}-{\frac {75}{8}}\,{t}^{4}+3/10\,{t}^{5}$}
\mapleinline{inert}{2d}{1456*t-3544/3-5989/10*t^2+331/3*t^3-75/8*t^4+3/10*t^5}{%
$1456\,t-{\frac {3544}{3}}-{\frac {5989}{10}}\,{t}^{2}+{\frac {331}{3}}\,{t}^{3}\\
\mbox{}-{\frac {75}{8}}\,{t}^{4}+3/10\,{t}^{5}$}

\end{maplelatex}

\mapleresult
\begin{maplelatex}
\mapleinline{inert}{2d}{Sconstituent[53] := 2847/2*t-11933/20*t^2+331/3*t^3-75/8*t^4+3/10*t^5-131981/120}{%
${\it Sconstituent}_{{53}}\, := \,{\frac {2847}{2}}\,t-{\frac {11933}{20}}\,{t}^{2}+{\frac {331}{3}}\,{t}^{3}\\
\mbox{}-{\frac {75}{8}}\,{t}^{4}+3/10\,{t}^{5}-{\frac {131981}{120}}$}
\mapleinline{inert}{2d}{2847/2*t-11933/20*t^2+331/3*t^3-75/8*t^4+3/10*t^5-131981/120}{%
${\frac {2847}{2}}\,t-{\frac {11933}{20}}\,{t}^{2}+{\frac {331}{3}}\,{t}^{3}\\
\mbox{}-{\frac {75}{8}}\,{t}^{4}+3/10\,{t}^{5}-{\frac {131981}{120}}$}
\mapleinline{inert}{2d}{Sconstituent[54] := 1464*t-5989/10*t^2+331/3*t^3-75/8*t^4+3/10*t^5-6624/5}{%
${\it Sconstituent}_{{54}}\, := \,1464\,t-{\frac {5989}{10}}\,{t}^{2}+{\frac {331}{3}}\,{t}^{3}-{\frac {75}{8}}\,{t}^{4}\\
\mbox{}+3/10\,{t}^{5}-{\frac {6624}{5}}$}
\mapleinline{inert}{2d}{1464*t-5989/10*t^2+331/3*t^3-75/8*t^4+3/10*t^5-6624/5}{%
$1464\,t-{\frac {5989}{10}}\,{t}^{2}+{\frac {331}{3}}\,{t}^{3}-{\frac {75}{8}}\,{t}^{4}\\
\mbox{}+3/10\,{t}^{5}-{\frac {6624}{5}}$}
\mapleinline{inert}{2d}{Sconstituent[55] := 2831/2*t-11933/20*t^2+331/3*t^3-75/8*t^4+3/10*t^5-25193/24}{%
${\it Sconstituent}_{{55}}\, := \,{\frac {2831}{2}}\,t-{\frac {11933}{20}}\,{t}^{2}+{\frac {331}{3}}\,{t}^{3}\\
\mbox{}-{\frac {75}{8}}\,{t}^{4}+3/10\,{t}^{5}-{\frac {25193}{24}}$}
\mapleinline{inert}{2d}{1/120*(t-7)*(36*t^4-873*t^3+7129*t^2-21695*t+17995)}{%
\[
{\frac {1}{120}}\, \left( t-7 \right)  \left( 36\,{t}^{4}-873\,{t}^{3}+7129\,{t}^{2}-21695\,t+17995 \right) 
\]
}
\mapleinline{inert}{2d}{Sconstituent[56] := 1464*t-18256/15-5989/10*t^2+331/3*t^3-75/8*t^4+3/10*t^5}{%
${\it Sconstituent}_{{56}}\, := \,1464\,t-{\frac {18256}{15}}-{\frac {5989}{10}}\,{t}^{2}+{\frac {331}{3}}\,{t}^{3}\\
\mbox{}-{\frac {75}{8}}\,{t}^{4}+3/10\,{t}^{5}$}
\mapleinline{inert}{2d}{1464*t-18256/15-5989/10*t^2+331/3*t^3-75/8*t^4+3/10*t^5}{%
$1464\,t-{\frac {18256}{15}}-{\frac {5989}{10}}\,{t}^{2}+{\frac {331}{3}}\,{t}^{3}\\
\mbox{}-{\frac {75}{8}}\,{t}^{4}+3/10\,{t}^{5}$}
\mapleinline{inert}{2d}{Sconstituent[57] := 2847/2*t-11933/20*t^2+331/3*t^3-75/8*t^4+3/10*t^5-8739/8}{%
${\it Sconstituent}_{{57}}\, := \,{\frac {2847}{2}}\,t-{\frac {11933}{20}}\,{t}^{2}+{\frac {331}{3}}\,{t}^{3}\\
\mbox{}-{\frac {75}{8}}\,{t}^{4}+3/10\,{t}^{5}-{\frac {8739}{8}}$}
\mapleinline{inert}{2d}{2847/2*t-11933/20*t^2+331/3*t^3-75/8*t^4+3/10*t^5-8739/8}{%
${\frac {2847}{2}}\,t-{\frac {11933}{20}}\,{t}^{2}+{\frac {331}{3}}\,{t}^{3}\\
\mbox{}-{\frac {75}{8}}\,{t}^{4}+3/10\,{t}^{5}-{\frac {8739}{8}}$}
\mapleinline{inert}{2d}{Sconstituent[58] := 1456*t-5989/10*t^2+331/3*t^3-75/8*t^4+3/10*t^5-18152/15}{%
${\it Sconstituent}_{{58}}\, := \,1456\,t-{\frac {5989}{10}}\,{t}^{2}+{\frac {331}{3}}\,{t}^{3}-{\frac {75}{8}}\,{t}^{4}\\
\mbox{}+3/10\,{t}^{5}-{\frac {18152}{15}}$}
\mapleinline{inert}{2d}{1/120*(t-4)*(36*t^4-981*t^3+9316*t^2-34604*t+36304)}{%
\[
{\frac {1}{120}}\, \left( t-4 \right)  \left( 36\,{t}^{4}-981\,{t}^{3}+9316\,{t}^{2}-34604\,t+36304 \right) 
\]
}

\end{maplelatex}

\mapleresult
\begin{maplelatex}
\mapleinline{inert}{2d}{Sconstituent[59] := 2847/2*t-11933/20*t^2-140621/120+331/3*t^3-75/8*t^4+3/10*t^5}{%
${\it Sconstituent}_{{59}}\, := \,{\frac {2847}{2}}\,t-{\frac {11933}{20}}\,{t}^{2}-{\frac {140621}{120}}\\
\mbox{}+{\frac {331}{3}}\,{t}^{3}-{\frac {75}{8}}\,{t}^{4}+3/10\,{t}^{5}$}
\mapleinline{inert}{2d}{2847/2*t-11933/20*t^2-140621/120+331/3*t^3-75/8*t^4+3/10*t^5}{%
${\frac {2847}{2}}\,t-{\frac {11933}{20}}\,{t}^{2}-{\frac {140621}{120}}\\
\mbox{}+{\frac {331}{3}}\,{t}^{3}-{\frac {75}{8}}\,{t}^{4}+3/10\,{t}^{5}$}
\mapleinline{inert}{2d}{Sconstituent[60] := -1296+1464*t-5989/10*t^2+331/3*t^3-75/8*t^4+3/10*t^5}{%
${\it Sconstituent}_{{60}}\, := \,-1296+1464\,t-{\frac {5989}{10}}\,{t}^{2}+{\frac {331}{3}}\,{t}^{3}\\
\mbox{}-{\frac {75}{8}}\,{t}^{4}+3/10\,{t}^{5}$}
\mapleinline{inert}{2d}{-1296+1464*t-5989/10*t^2+331/3*t^3-75/8*t^4+3/10*t^5}{%
$-1296+1464\,t-{\frac {5989}{10}}\,{t}^{2}+{\frac {331}{3}}\,{t}^{3}\\
\mbox{}-{\frac {75}{8}}\,{t}^{4}+3/10\,{t}^{5}$}

\end{maplelatex}
Extract the coefficients of the constituents.\begin{mapleinput}
\mapleinline{active}{1d}{for r from 1 to p do
 for coeffdeg from 0 to d do 
  Sc[coeffdeg,r]:=coeff(Sconstituent[r],t,coeffdeg):
  #print( r, Sc[coeffdeg,r] ):
 od:
od:}{}
\end{mapleinput}Print and analyze the constituent coefficients for periods.  First the higher coefficients, which ought to be constant.  Print the first coefficient, then any that don't repeat the preceding value.\begin{mapleinput}
\mapleinline{active}{1d}{for coeffdeg from 3 to d do
  print("degree", coeffdeg, "coeff", Sc[coeffdeg,1]):
  print(1,Sc[coeffdeg,1]);
  for r from 2 to p do
    stepdifference:=Sc[coeffdeg,r]-Sc[coeffdeg,r-1]:
    if( stepdifference<\TEXTsymbol{>}0 ) then 
    print(r,Sc[coeffdeg,r],stepdifference):
    fi: 
  od: 
  print("Compared all coefficients of degree", coeffdeg); 
od: }{}
\end{mapleinput}
\mapleresult
\begin{maplelatex}
\mapleinline{inert}{2d}{"degree", 3, "coeff", 331/3}{%
\[
{\it ``degree''},\,3,\,{\it ``coeff''},\,{\frac {331}{3}}
\]
}
\mapleinline{inert}{2d}{1, 331/3}{%
\[
1,\,{\frac {331}{3}}
\]
}
\mapleinline{inert}{2d}{"Compared all coefficients of degree", 3}{%
$\mbox {{\tt ``Compared all coefficients of degree''}},\,3$}
\mapleinline{inert}{2d}{"degree", 4, "coeff", (-75)/8}{%
\[
{\it ``degree''},\,4,\,{\it ``coeff''},\,-{\frac {75}{8}}
\]
}
\mapleinline{inert}{2d}{1, (-75)/8}{%
\[
1,\,-{\frac {75}{8}}
\]
}
\mapleinline{inert}{2d}{"Compared all coefficients of degree", 4}{%
$\mbox {{\tt ``Compared all coefficients of degree''}},\,4$}
\mapleinline{inert}{2d}{"degree", 5, "coeff", 3/10}{%
\[
{\it ``degree''},\,5,\,{\it ``coeff''},\,3/10
\]
}
\mapleinline{inert}{2d}{1, 3/10}{%
\[
1,\,3/10
\]
}
\mapleinline{inert}{2d}{"Compared all coefficients of degree", 5}{%
$\mbox {{\tt ``Compared all coefficients of degree''}},\,5$}

\end{maplelatex}
Next, the constant terms, whose period is expected to be p.  Print all constant terms up to the presumed period "stepsize".  Print the difference (at step "stepsize") if they are not repeating.Note that the even terms repeat at step 30 (a period of 15, half the expected period).\begin{mapleinput}
\mapleinline{active}{1d}{stepsize:=30; lcd:=120;
for r from 1 to stepsize do
  print(r, Sc[0,r], "With sign adjusted:", -Sc[0,r]*lcd, "/l.c.d."); 
od: 
for r from stepsize+1 to p do 
  stepdifference:=Sc[0,r]-Sc[0,r-stepsize]:
  if( stepdifference<\TEXTsymbol{>}0 ) then print(r,Sc[0,r],stepdifference, "With sign adjusted:", -Sc[0,r]*lcd, "/l.c.d."): fi:
  #print(r,Sc[0,r],stepdifference);
od:
print("Constant terms completed."); }{}
\end{mapleinput}
\mapleresult
\begin{maplelatex}
\mapleinline{inert}{2d}{stepsize := 30}{%
\[
{\it stepsize}\, := \,30
\]
}
\mapleinline{inert}{2d}{lcd := 120}{%
\[
{\it lcd}\, := \,120
\]
}
\mapleinline{inert}{2d}{1, (-110413)/120, "With sign adjusted:", 110413, "/l.c.d."}{%
$1,\,-{\frac {110413}{120}},\,\mbox {{\tt ``With sign adjusted:''}},\,110413,\,\mbox {{\tt ``/l.c.d.''}}$}
\mapleinline{inert}{2d}{2, (-3824)/3, "With sign adjusted:", 152960, "/l.c.d."}{%
$2,\,-{\frac {3824}{3}},\,\mbox {{\tt ``With sign adjusted:''}},\,152960,\,\mbox {{\tt ``/l.c.d.''}}$}
\mapleinline{inert}{2d}{3, (-47727)/40, "With sign adjusted:", 143181, "/l.c.d."}{%
$3,\,-{\frac {47727}{40}},\,\mbox {{\tt ``With sign adjusted:''}},\,143181,\,\mbox {{\tt ``/l.c.d.''}}$}
\mapleinline{inert}{2d}{4, (-18152)/15, "With sign adjusted:", 145216, "/l.c.d."}{%
$4,\,-{\frac {18152}{15}},\,\mbox {{\tt ``With sign adjusted:''}},\,145216,\,\mbox {{\tt ``/l.c.d.''}}$}
\mapleinline{inert}{2d}{5, (-25705)/24, "With sign adjusted:", 128525, "/l.c.d."}{%
$5,\,-{\frac {25705}{24}},\,\mbox {{\tt ``With sign adjusted:''}},\,128525,\,\mbox {{\tt ``/l.c.d.''}}$}
\mapleinline{inert}{2d}{6, (-6192)/5, "With sign adjusted:", 148608, "/l.c.d."}{%
$6,\,-{\frac {6192}{5}},\,\mbox {{\tt ``With sign adjusted:''}},\,148608,\,\mbox {{\tt ``/l.c.d.''}}$}
\mapleinline{inert}{2d}{7, (-25193)/24, "With sign adjusted:", 125965, "/l.c.d."}{%
$7,\,-{\frac {25193}{24}},\,\mbox {{\tt ``With sign adjusted:''}},\,125965,\,\mbox {{\tt ``/l.c.d.''}}$}
\mapleinline{inert}{2d}{8, (-19552)/15, "With sign adjusted:", 156416, "/l.c.d."}{%
$8,\,-{\frac {19552}{15}},\,\mbox {{\tt ``With sign adjusted:''}},\,156416,\,\mbox {{\tt ``/l.c.d.''}}$}
\mapleinline{inert}{2d}{9, (-44847)/40, "With sign adjusted:", 134541, "/l.c.d."}{%
$9,\,-{\frac {44847}{40}},\,\mbox {{\tt ``With sign adjusted:''}},\,134541,\,\mbox {{\tt ``/l.c.d.''}}$}
\mapleinline{inert}{2d}{10, (-3544)/3, "With sign adjusted:", 141760, "/l.c.d."}{%
$10,\,-{\frac {3544}{3}},\,\mbox {{\tt ``With sign adjusted:''}},\,141760,\,\mbox {{\tt ``/l.c.d.''}}$}
\mapleinline{inert}{2d}{11, (-130253)/120, "With sign adjusted:", 130253, "/l.c.d."}{%
$11,\,-{\frac {130253}{120}},\,\mbox {{\tt ``With sign adjusted:''}},\,130253,\,\mbox {{\tt ``/l.c.d.''}}$}
\mapleinline{inert}{2d}{12, -1296, "With sign adjusted:", 155520, "/l.c.d."}{%
$12,\,-1296,\,\mbox {{\tt ``With sign adjusted:''}},\,155520,\,\mbox {{\tt ``/l.c.d.''}}$}
\mapleinline{inert}{2d}{13, (-120781)/120, "With sign adjusted:", 120781, "/l.c.d."}{%
$13,\,-{\frac {120781}{120}},\,\mbox {{\tt ``With sign adjusted:''}},\,120781,\,\mbox {{\tt ``/l.c.d.''}}$}
\mapleinline{inert}{2d}{14, (-19552)/15, "With sign adjusted:", 156416, "/l.c.d."}{%
$14,\,-{\frac {19552}{15}},\,\mbox {{\tt ``With sign adjusted:''}},\,156416,\,\mbox {{\tt ``/l.c.d.''}}$}
\mapleinline{inert}{2d}{15, (-9315)/8, "With sign adjusted:", 139725, "/l.c.d."}{%
$15,\,-{\frac {9315}{8}},\,\mbox {{\tt ``With sign adjusted:''}},\,139725,\,\mbox {{\tt ``/l.c.d.''}}$}
\mapleinline{inert}{2d}{16, (-16856)/15, "With sign adjusted:", 134848, "/l.c.d."}{%
$16,\,-{\frac {16856}{15}},\,\mbox {{\tt ``With sign adjusted:''}},\,134848,\,\mbox {{\tt ``/l.c.d.''}}$}
\mapleinline{inert}{2d}{17, (-25705)/24, "With sign adjusted:", 128525, "/l.c.d."}{%
$17,\,-{\frac {25705}{24}},\,\mbox {{\tt ``With sign adjusted:''}},\,128525,\,\mbox {{\tt ``/l.c.d.''}}$}
\mapleinline{inert}{2d}{18, (-6624)/5, "With sign adjusted:", 158976, "/l.c.d."}{%
$18,\,-{\frac {6624}{5}},\,\mbox {{\tt ``With sign adjusted:''}},\,158976,\,\mbox {{\tt ``/l.c.d.''}}$}
\mapleinline{inert}{2d}{19, (-129421)/120, "With sign adjusted:", 129421, "/l.c.d."}{%
$19,\,-{\frac {129421}{120}},\,\mbox {{\tt ``With sign adjusted:''}},\,129421,\,\mbox {{\tt ``/l.c.d.''}}$}
\mapleinline{inert}{2d}{20, (-3824)/3, "With sign adjusted:", 152960, "/l.c.d."}{%
$20,\,-{\frac {3824}{3}},\,\mbox {{\tt ``With sign adjusted:''}},\,152960,\,\mbox {{\tt ``/l.c.d.''}}$}
\mapleinline{inert}{2d}{21, (-41391)/40, "With sign adjusted:", 124173, "/l.c.d."}{%
$21,\,-{\frac {41391}{40}},\,\mbox {{\tt ``With sign adjusted:''}},\,124173,\,\mbox {{\tt ``/l.c.d.''}}$}
\mapleinline{inert}{2d}{22, (-3544)/3, "With sign adjusted:", 141760, "/l.c.d."}{%
$22,\,-{\frac {3544}{3}},\,\mbox {{\tt ``With sign adjusted:''}},\,141760,\,\mbox {{\tt ``/l.c.d.''}}$}
\mapleinline{inert}{2d}{23, (-140621)/120, "With sign adjusted:", 140621, "/l.c.d."}{%
$23,\,-{\frac {140621}{120}},\,\mbox {{\tt ``With sign adjusted:''}},\,140621,\,\mbox {{\tt ``/l.c.d.''}}$}
\mapleinline{inert}{2d}{24, (-6624)/5, "With sign adjusted:", 158976, "/l.c.d."}{%
$24,\,-{\frac {6624}{5}},\,\mbox {{\tt ``With sign adjusted:''}},\,158976,\,\mbox {{\tt ``/l.c.d.''}}$}
\mapleinline{inert}{2d}{25, (-23465)/24, "With sign adjusted:", 117325, "/l.c.d."}{%
$25,\,-{\frac {23465}{24}},\,\mbox {{\tt ``With sign adjusted:''}},\,117325,\,\mbox {{\tt ``/l.c.d.''}}$}
\mapleinline{inert}{2d}{26, (-18256)/15, "With sign adjusted:", 146048, "/l.c.d."}{%
$26,\,-{\frac {18256}{15}},\,\mbox {{\tt ``With sign adjusted:''}},\,146048,\,\mbox {{\tt ``/l.c.d.''}}$}
\mapleinline{inert}{2d}{27, (-9315)/8, "With sign adjusted:", 139725, "/l.c.d."}{%
$27,\,-{\frac {9315}{8}},\,\mbox {{\tt ``With sign adjusted:''}},\,139725,\,\mbox {{\tt ``/l.c.d.''}}$}
\mapleinline{inert}{2d}{28, (-18152)/15, "With sign adjusted:", 145216, "/l.c.d."}{%
$28,\,-{\frac {18152}{15}},\,\mbox {{\tt ``With sign adjusted:''}},\,145216,\,\mbox {{\tt ``/l.c.d.''}}$}
\mapleinline{inert}{2d}{29, (-131981)/120, "With sign adjusted:", 131981, "/l.c.d."}{%
$29,\,-{\frac {131981}{120}},\,\mbox {{\tt ``With sign adjusted:''}},\,131981,\,\mbox {{\tt ``/l.c.d.''}}$}
\mapleinline{inert}{2d}{30, -1296, "With sign adjusted:", 155520, "/l.c.d."}{%
$30,\,-1296,\,\mbox {{\tt ``With sign adjusted:''}},\,155520,\,\mbox {{\tt ``/l.c.d.''}}$}
\mapleinline{inert}{2d}{31, (-119053)/120, -72, "With sign adjusted:", 119053, "/l.c.d."}{%
$31,\,-{\frac {119053}{120}},\,-72,\,\mbox {{\tt ``With sign adjusted:''}},\,119053,\,\mbox {{\tt ``/l.c.d.''}}$}
\mapleinline{inert}{2d}{33, (-44847)/40, 72, "With sign adjusted:", 134541, "/l.c.d."}{%
$33,\,-{\frac {44847}{40}},\,72,\,\mbox {{\tt ``With sign adjusted:''}},\,134541,\,\mbox {{\tt ``/l.c.d.''}}$}
\mapleinline{inert}{2d}{35, (-27433)/24, -72, "With sign adjusted:", 137165, "/l.c.d."}{%
$35,\,-{\frac {27433}{24}},\,-72,\,\mbox {{\tt ``With sign adjusted:''}},\,137165,\,\mbox {{\tt ``/l.c.d.''}}$}
\mapleinline{inert}{2d}{37, (-23465)/24, 72, "With sign adjusted:", 117325, "/l.c.d."}{%
$37,\,-{\frac {23465}{24}},\,72,\,\mbox {{\tt ``With sign adjusted:''}},\,117325,\,\mbox {{\tt ``/l.c.d.''}}$}
\mapleinline{inert}{2d}{39, (-47727)/40, -72, "With sign adjusted:", 143181, "/l.c.d."}{%
$39,\,-{\frac {47727}{40}},\,-72,\,\mbox {{\tt ``With sign adjusted:''}},\,143181,\,\mbox {{\tt ``/l.c.d.''}}$}
\mapleinline{inert}{2d}{41, (-121613)/120, 72, "With sign adjusted:", 121613, "/l.c.d."}{%
$41,\,-{\frac {121613}{120}},\,72,\,\mbox {{\tt ``With sign adjusted:''}},\,121613,\,\mbox {{\tt ``/l.c.d.''}}$}
\mapleinline{inert}{2d}{43, (-129421)/120, -72, "With sign adjusted:", 129421, "/l.c.d."}{%
$43,\,-{\frac {129421}{120}},\,-72,\,\mbox {{\tt ``With sign adjusted:''}},\,129421,\,\mbox {{\tt ``/l.c.d.''}}$}
\mapleinline{inert}{2d}{45, (-8739)/8, 72, "With sign adjusted:", 131085, "/l.c.d."}{%
$45,\,-{\frac {8739}{8}},\,72,\,\mbox {{\tt ``With sign adjusted:''}},\,131085,\,\mbox {{\tt ``/l.c.d.''}}$}
\mapleinline{inert}{2d}{47, (-27433)/24, -72, "With sign adjusted:", 137165, "/l.c.d."}{%
$47,\,-{\frac {27433}{24}},\,-72,\,\mbox {{\tt ``With sign adjusted:''}},\,137165,\,\mbox {{\tt ``/l.c.d.''}}$}
\mapleinline{inert}{2d}{49, (-120781)/120, 72, "With sign adjusted:", 120781, "/l.c.d."}{%
$49,\,-{\frac {120781}{120}},\,72,\,\mbox {{\tt ``With sign adjusted:''}},\,120781,\,\mbox {{\tt ``/l.c.d.''}}$}
\mapleinline{inert}{2d}{51, (-44271)/40, -72, "With sign adjusted:", 132813, "/l.c.d."}{%
$51,\,-{\frac {44271}{40}},\,-72,\,\mbox {{\tt ``With sign adjusted:''}},\,132813,\,\mbox {{\tt ``/l.c.d.''}}$}
\mapleinline{inert}{2d}{53, (-131981)/120, 72, "With sign adjusted:", 131981, "/l.c.d."}{%
$53,\,-{\frac {131981}{120}},\,72,\,\mbox {{\tt ``With sign adjusted:''}},\,131981,\,\mbox {{\tt ``/l.c.d.''}}$}
\mapleinline{inert}{2d}{55, (-25193)/24, -72, "With sign adjusted:", 125965, "/l.c.d."}{%
$55,\,-{\frac {25193}{24}},\,-72,\,\mbox {{\tt ``With sign adjusted:''}},\,125965,\,\mbox {{\tt ``/l.c.d.''}}$}
\mapleinline{inert}{2d}{57, (-8739)/8, 72, "With sign adjusted:", 131085, "/l.c.d."}{%
$57,\,-{\frac {8739}{8}},\,72,\,\mbox {{\tt ``With sign adjusted:''}},\,131085,\,\mbox {{\tt ``/l.c.d.''}}$}
\mapleinline{inert}{2d}{59, (-140621)/120, -72, "With sign adjusted:", 140621, "/l.c.d."}{%
$59,\,-{\frac {140621}{120}},\,-72,\,\mbox {{\tt ``With sign adjusted:''}},\,140621,\,\mbox {{\tt ``/l.c.d.''}}$}
\mapleinline{inert}{2d}{"Constant terms completed."}{%
$\mbox {{\tt ``Constant terms completed.''}}$}

\end{maplelatex}
Now, the linear terms.  First print all linear coefficients up to the presumed period "stepsize"..  Then analyze for period and print the difference (at step "stepsize") if they are not repeating.\begin{mapleinput}
\mapleinline{active}{1d}{stepsize:=6; lcd:=2;
for r from 1 to stepsize do
  print(r, Sc[1,r], "With sign adjusted:", Sc[1,r]*lcd, "/l.c.d."); 
od: 
for r from stepsize+1 to p do 
  stepdifference:=Sc[1,r]-Sc[1,r-stepsize]:
  if( stepdifference<\TEXTsymbol{>}0 ) then print(r,Sc[1,r],stepdifference): fi:
od:
print("Linear coefficients completed."); }{}
\end{mapleinput}
\mapleresult
\begin{maplelatex}
\mapleinline{inert}{2d}{stepsize := 6}{%
\[
{\it stepsize}\, := \,6
\]
}
\mapleinline{inert}{2d}{lcd := 2}{%
\[
{\it lcd}\, := \,2
\]
}
\mapleinline{inert}{2d}{1, 2831/2, "With sign adjusted:", 2831, "/l.c.d."}{%
$1,\,{\frac {2831}{2}},\,\mbox {{\tt ``With sign adjusted:''}},\,2831,\,\mbox {{\tt ``/l.c.d.''}}$}
\mapleinline{inert}{2d}{2, 1464, "With sign adjusted:", 2928, "/l.c.d."}{%
$2,\,1464,\,\mbox {{\tt ``With sign adjusted:''}},\,2928,\,\mbox {{\tt ``/l.c.d.''}}$}
\mapleinline{inert}{2d}{3, 2847/2, "With sign adjusted:", 2847, "/l.c.d."}{%
$3,\,{\frac {2847}{2}},\,\mbox {{\tt ``With sign adjusted:''}},\,2847,\,\mbox {{\tt ``/l.c.d.''}}$}
\mapleinline{inert}{2d}{4, 1456, "With sign adjusted:", 2912, "/l.c.d."}{%
$4,\,1456,\,\mbox {{\tt ``With sign adjusted:''}},\,2912,\,\mbox {{\tt ``/l.c.d.''}}$}
\mapleinline{inert}{2d}{5, 2847/2, "With sign adjusted:", 2847, "/l.c.d."}{%
$5,\,{\frac {2847}{2}},\,\mbox {{\tt ``With sign adjusted:''}},\,2847,\,\mbox {{\tt ``/l.c.d.''}}$}
\mapleinline{inert}{2d}{6, 1464, "With sign adjusted:", 2928, "/l.c.d."}{%
$6,\,1464,\,\mbox {{\tt ``With sign adjusted:''}},\,2928,\,\mbox {{\tt ``/l.c.d.''}}$}
\mapleinline{inert}{2d}{"Linear coefficients completed."}{%
$\mbox {{\tt ``Linear coefficients completed.''}}$}

\end{maplelatex}
The quadratic terms.  First print all quadratic coefficients up to the presumed period "stepsize"..  Then analyze for period and print the difference (at step "stepsize") if they are not repeating.\begin{mapleinput}
\mapleinline{active}{1d}{stepsize:=2; lcd:=20;
for r from 1 to stepsize do
  print(r, Sc[2,r], "With sign adjusted:", -Sc[2,r]*lcd, "/l.c.d."); 
od: 
for r from stepsize+1 to p do 
  stepdifference:=Sc[2,r]-Sc[2,r-stepsize]:
  if( stepdifference<\TEXTsymbol{>}0 ) then print(r,Sc[2,r],stepdifference): fi:
od:
print("Quadratic coefficients completed."); }{}
\end{mapleinput}
\mapleresult
\begin{maplelatex}
\mapleinline{inert}{2d}{stepsize := 2}{%
\[
{\it stepsize}\, := \,2
\]
}
\mapleinline{inert}{2d}{lcd := 20}{%
\[
{\it lcd}\, := \,20
\]
}
\mapleinline{inert}{2d}{1, (-11933)/20, "With sign adjusted:", 11933, "/l.c.d."}{%
$1,\,-{\frac {11933}{20}},\,\mbox {{\tt ``With sign adjusted:''}},\,11933,\,\mbox {{\tt ``/l.c.d.''}}$}
\mapleinline{inert}{2d}{2, (-5989)/10, "With sign adjusted:", 11978, "/l.c.d."}{%
$2,\,-{\frac {5989}{10}},\,\mbox {{\tt ``With sign adjusted:''}},\,11978,\,\mbox {{\tt ``/l.c.d.''}}$}
\mapleinline{inert}{2d}{"Quadratic coefficients completed."}{%
$\mbox {{\tt ``Quadratic coefficients completed.''}}$}

\end{maplelatex}
Casculate the zeroth constituent of the .  Find its constant term.\begin{mapleinput}
\mapleinline{active}{1d}{szeroth:=expand(
sum(coeff(sgfstandnum,x,p*jj)*binomial(d+t/p-jj,d),jj=0..d+1) );
print(subs(t=0,szeroth)):  }{}
\end{mapleinput}
\mapleresult
\begin{maplelatex}
\mapleinline{inert}{2d}{szeroth := -18+61/3*t-5989/720*t^2+331/216*t^3-25/192*t^4+1/240*t^5}{%
${\it szeroth}\, := \,-18+{\frac {61}{3}}\,t-{\frac {5989}{720}}\,{t}^{2}+{\frac {331}{216}}\,{t}^{3}\\
\mbox{}-{\frac {25}{192}}\,{t}^{4}+{\frac {1}{240}}\,{t}^{5}$}
\mapleinline{inert}{2d}{-18}{%
\[
-18
\]
}

\end{maplelatex}
Extract the constituents of the semimagic symmetry-type counting function.\begin{mapleinput}
\mapleinline{active}{1d}{sconstituent[0]:=szeroth:
for r from 1 to p do
  sconstituent[r]:=expand(sum( coeff(sgfstandnum,x,p*jj+r)*binomial(d+(t-r)/p-jj,d), jj=0..d)):
#  print(r):
#  print( sconstituent[r] ):
  print( factor(sconstituent[r]) ):
od; }{}
\end{mapleinput}
\mapleresult
\begin{maplelatex}
\mapleinline{inert}{2d}{sconstituent[1] := 2831/144*t-11933/1440*t^2+331/216*t^3-25/192*t^4+1/240*t^5-110413/8640}{%
${\it sconstituent}_{{1}}\, := \,{\frac {2831}{144}}\,t-{\frac {11933}{1440}}\,{t}^{2}+{\frac {331}{216}}\,{t}^{3}\\
\mbox{}-{\frac {25}{192}}\,{t}^{4}+{\frac {1}{240}}\,{t}^{5}-{\frac {110413}{8640}}$}

\end{maplelatex}

\mapleresult
\begin{maplelatex}
\mapleinline{inert}{2d}{1/8640*(t-1)*(36*t^4-1089*t^3+12151*t^2-59447*t+110413)}{%
\[
{\frac {1}{8640}}\, \left( t-1 \right)  \left( 36\,{t}^{4}-1089\,{t}^{3}+12151\,{t}^{2}-59447\,t+110413 \right) 
\]
}

\end{maplelatex}

\mapleresult
\begin{maplelatex}
\mapleinline{inert}{2d}{sconstituent[2] := 61/3*t-5989/720*t^2+331/216*t^3-25/192*t^4+1/240*t^5-478/27}{%
${\it sconstituent}_{{2}}\, := \,{\frac {61}{3}}\,t-{\frac {5989}{720}}\,{t}^{2}+{\frac {331}{216}}\,{t}^{3}\\
\mbox{}-{\frac {25}{192}}\,{t}^{4}+{\frac {1}{240}}\,{t}^{5}-{\frac {478}{27}}$}
\mapleinline{inert}{2d}{1/8640*(t-2)*(36*t^4-1053*t^3+11134*t^2-49600*t+76480)}{%
\[
{\frac {1}{8640}}\, \left( t-2 \right)  \left( 36\,{t}^{4}-1053\,{t}^{3}+11134\,{t}^{2}-49600\,t+76480 \right) 
\]
}
\mapleinline{inert}{2d}{sconstituent[3] := 949/48*t-11933/1440*t^2+331/216*t^3-25/192*t^4+1/240*t^5-5303/320}{%
${\it sconstituent}_{{3}}\, := \,{\frac {949}{48}}\,t-{\frac {11933}{1440}}\,{t}^{2}+{\frac {331}{216}}\,{t}^{3}\\
\mbox{}-{\frac {25}{192}}\,{t}^{4}+{\frac {1}{240}}\,{t}^{5}-{\frac {5303}{320}}$}
\mapleinline{inert}{2d}{1/8640*(t-3)*(36*t^4-1017*t^3+10189*t^2-41031*t+47727)}{%
\[
{\frac {1}{8640}}\, \left( t-3 \right)  \left( 36\,{t}^{4}-1017\,{t}^{3}+10189\,{t}^{2}-41031\,t+47727 \right) 
\]
}
\mapleinline{inert}{2d}{sconstituent[4] := 182/9*t-2269/135-5989/720*t^2+331/216*t^3-25/192*t^4+1/240*t^5}{%
${\it sconstituent}_{{4}}\, := \,{\frac {182}{9}}\,t-{\frac {2269}{135}}-{\frac {5989}{720}}\,{t}^{2}\\
\mbox{}+{\frac {331}{216}}\,{t}^{3}-{\frac {25}{192}}\,{t}^{4}+{\frac {1}{240}}\,{t}^{5}$}
\mapleinline{inert}{2d}{1/8640*(t-4)*(36*t^4-981*t^3+9316*t^2-34604*t+36304)}{%
\[
{\frac {1}{8640}}\, \left( t-4 \right)  \left( 36\,{t}^{4}-981\,{t}^{3}+9316\,{t}^{2}-34604\,t+36304 \right) 
\]
}

\end{maplelatex}

\mapleresult
\begin{maplelatex}
\mapleinline{inert}{2d}{sconstituent[5] := 949/48*t-11933/1440*t^2+331/216*t^3-25/192*t^4+1/240*t^5-25705/1728}{%
${\it sconstituent}_{{5}}\, := \,{\frac {949}{48}}\,t-{\frac {11933}{1440}}\,{t}^{2}+{\frac {331}{216}}\,{t}^{3}\\
\mbox{}-{\frac {25}{192}}\,{t}^{4}+{\frac {1}{240}}\,{t}^{5}-{\frac {25705}{1728}}$}
\mapleinline{inert}{2d}{1/8640*(t-5)*(36*t^4-945*t^3+8515*t^2-29023*t+25705)}{%
\[
{\frac {1}{8640}}\, \left( t-5 \right)  \left( 36\,{t}^{4}-945\,{t}^{3}+8515\,{t}^{2}-29023\,t+25705 \right) 
\]
}
\mapleinline{inert}{2d}{sconstituent[6] := 61/3*t-5989/720*t^2+331/216*t^3-25/192*t^4+1/240*t^5-86/5}{%
${\it sconstituent}_{{6}}\, := \,{\frac {61}{3}}\,t-{\frac {5989}{720}}\,{t}^{2}+{\frac {331}{216}}\,{t}^{3}\\
\mbox{}-{\frac {25}{192}}\,{t}^{4}+{\frac {1}{240}}\,{t}^{5}-{\frac {86}{5}}$}
\mapleinline{inert}{2d}{1/8640*(t-6)*(36*t^4-909*t^3+7786*t^2-25152*t+24768)}{%
\[
{\frac {1}{8640}}\, \left( t-6 \right)  \left( 36\,{t}^{4}-909\,{t}^{3}+7786\,{t}^{2}-25152\,t+24768 \right) 
\]
}

\end{maplelatex}

\mapleresult
\begin{maplelatex}
\mapleinline{inert}{2d}{sconstituent[7] := -25193/1728+2831/144*t-11933/1440*t^2+331/216*t^3-25/192*t^4+1/240*t^5}{%
${\it sconstituent}_{{7}}\, := \,-{\frac {25193}{1728}}+{\frac {2831}{144}}\,t\\
\mbox{}-{\frac {11933}{1440}}\,{t}^{2}+{\frac {331}{216}}\,{t}^{3}-{\frac {25}{192}}\,{t}^{4}\\
\mbox{}+{\frac {1}{240}}\,{t}^{5}$}
\mapleinline{inert}{2d}{1/8640*(t-7)*(36*t^4-873*t^3+7129*t^2-21695*t+17995)}{%
\[
{\frac {1}{8640}}\, \left( t-7 \right)  \left( 36\,{t}^{4}-873\,{t}^{3}+7129\,{t}^{2}-21695\,t+17995 \right) 
\]
}
\mapleinline{inert}{2d}{sconstituent[8] := 61/3*t-2444/135-5989/720*t^2+331/216*t^3-25/192*t^4+1/240*t^5}{%
${\it sconstituent}_{{8}}\, := \,{\frac {61}{3}}\,t-{\frac {2444}{135}}-{\frac {5989}{720}}\,{t}^{2}\\
\mbox{}+{\frac {331}{216}}\,{t}^{3}-{\frac {25}{192}}\,{t}^{4}+{\frac {1}{240}}\,{t}^{5}$}
\mapleinline{inert}{2d}{1/8640*(t-8)*(36*t^4-837*t^3+6544*t^2-19516*t+19552)}{%
\[
{\frac {1}{8640}}\, \left( t-8 \right)  \left( 36\,{t}^{4}-837\,{t}^{3}+6544\,{t}^{2}-19516\,t+19552 \right) 
\]
}
\mapleinline{inert}{2d}{sconstituent[9] := 949/48*t-11933/1440*t^2+331/216*t^3-25/192*t^4+1/240*t^5-4983/320}{%
${\it sconstituent}_{{9}}\, := \,{\frac {949}{48}}\,t-{\frac {11933}{1440}}\,{t}^{2}+{\frac {331}{216}}\,{t}^{3}\\
\mbox{}-{\frac {25}{192}}\,{t}^{4}+{\frac {1}{240}}\,{t}^{5}-{\frac {4983}{320}}$}
\mapleinline{inert}{2d}{1/8640*(t-9)*(36*t^4-801*t^3+6031*t^2-17319*t+14949)}{%
\[
{\frac {1}{8640}}\, \left( t-9 \right)  \left( 36\,{t}^{4}-801\,{t}^{3}+6031\,{t}^{2}-17319\,t+14949 \right) 
\]
}

\end{maplelatex}

\mapleresult
\begin{maplelatex}
\mapleinline{inert}{2d}{sconstituent[10] := 182/9*t-5989/720*t^2+331/216*t^3-25/192*t^4+1/240*t^5-443/27}{%
${\it sconstituent}_{{10}}\, := \,{\frac {182}{9}}\,t-{\frac {5989}{720}}\,{t}^{2}+{\frac {331}{216}}\,{t}^{3}\\
\mbox{}-{\frac {25}{192}}\,{t}^{4}+{\frac {1}{240}}\,{t}^{5}-{\frac {443}{27}}$}
\mapleinline{inert}{2d}{182/9*t-5989/720*t^2+331/216*t^3-25/192*t^4+1/240*t^5-443/27}{%
${\frac {182}{9}}\,t-{\frac {5989}{720}}\,{t}^{2}+{\frac {331}{216}}\,{t}^{3}\\
\mbox{}-{\frac {25}{192}}\,{t}^{4}+{\frac {1}{240}}\,{t}^{5}-{\frac {443}{27}}$}
\mapleinline{inert}{2d}{sconstituent[11] := 949/48*t-11933/1440*t^2+331/216*t^3-25/192*t^4+1/240*t^5-130253/8640}{%
${\it sconstituent}_{{11}}\, := \,{\frac {949}{48}}\,t-{\frac {11933}{1440}}\,{t}^{2}+{\frac {331}{216}}\,{t}^{3}\\
\mbox{}-{\frac {25}{192}}\,{t}^{4}+{\frac {1}{240}}\,{t}^{5}-{\frac {130253}{8640}}$}
\mapleinline{inert}{2d}{949/48*t-11933/1440*t^2+331/216*t^3-25/192*t^4+1/240*t^5-130253/8640}{%
${\frac {949}{48}}\,t-{\frac {11933}{1440}}\,{t}^{2}+{\frac {331}{216}}\,{t}^{3}\\
\mbox{}-{\frac {25}{192}}\,{t}^{4}+{\frac {1}{240}}\,{t}^{5}-{\frac {130253}{8640}}$}
\mapleinline{inert}{2d}{sconstituent[12] := -18+61/3*t-5989/720*t^2+331/216*t^3-25/192*t^4+1/240*t^5}{%
${\it sconstituent}_{{12}}\, := \,-18+{\frac {61}{3}}\,t-{\frac {5989}{720}}\,{t}^{2}+{\frac {331}{216}}\,{t}^{3}\\
\mbox{}-{\frac {25}{192}}\,{t}^{4}+{\frac {1}{240}}\,{t}^{5}$}
\mapleinline{inert}{2d}{-18+61/3*t-5989/720*t^2+331/216*t^3-25/192*t^4+1/240*t^5}{%
$-18+{\frac {61}{3}}\,t-{\frac {5989}{720}}\,{t}^{2}+{\frac {331}{216}}\,{t}^{3}\\
\mbox{}-{\frac {25}{192}}\,{t}^{4}+{\frac {1}{240}}\,{t}^{5}$}
\mapleinline{inert}{2d}{sconstituent[13] := 2831/144*t-120781/8640-11933/1440*t^2+331/216*t^3-25/192*t^4+1/240*t^5}{%
${\it sconstituent}_{{13}}\, := \,{\frac {2831}{144}}\,t-{\frac {120781}{8640}}-{\frac {11933}{1440}}\,{t}^{2}\\
\mbox{}+{\frac {331}{216}}\,{t}^{3}-{\frac {25}{192}}\,{t}^{4}+{\frac {1}{240}}\,{t}^{5}$}

\end{maplelatex}

\mapleresult
\begin{maplelatex}
\mapleinline{inert}{2d}{2831/144*t-120781/8640-11933/1440*t^2+331/216*t^3-25/192*t^4+1/240*t^5}{%
${\frac {2831}{144}}\,t-{\frac {120781}{8640}}-{\frac {11933}{1440}}\,{t}^{2}\\
\mbox{}+{\frac {331}{216}}\,{t}^{3}-{\frac {25}{192}}\,{t}^{4}+{\frac {1}{240}}\,{t}^{5}$}
\mapleinline{inert}{2d}{sconstituent[14] := 61/3*t-2444/135-5989/720*t^2+331/216*t^3-25/192*t^4+1/240*t^5}{%
${\it sconstituent}_{{14}}\, := \,{\frac {61}{3}}\,t-{\frac {2444}{135}}-{\frac {5989}{720}}\,{t}^{2}\\
\mbox{}+{\frac {331}{216}}\,{t}^{3}-{\frac {25}{192}}\,{t}^{4}+{\frac {1}{240}}\,{t}^{5}$}
\mapleinline{inert}{2d}{1/8640*(t-8)*(36*t^4-837*t^3+6544*t^2-19516*t+19552)}{%
\[
{\frac {1}{8640}}\, \left( t-8 \right)  \left( 36\,{t}^{4}-837\,{t}^{3}+6544\,{t}^{2}-19516\,t+19552 \right) 
\]
}
\mapleinline{inert}{2d}{sconstituent[15] := 949/48*t-11933/1440*t^2+331/216*t^3-25/192*t^4+1/240*t^5-1035/64}{%
${\it sconstituent}_{{15}}\, := \,{\frac {949}{48}}\,t-{\frac {11933}{1440}}\,{t}^{2}+{\frac {331}{216}}\,{t}^{3}\\
\mbox{}-{\frac {25}{192}}\,{t}^{4}+{\frac {1}{240}}\,{t}^{5}-{\frac {1035}{64}}$}
\mapleinline{inert}{2d}{949/48*t-11933/1440*t^2+331/216*t^3-25/192*t^4+1/240*t^5-1035/64}{%
${\frac {949}{48}}\,t-{\frac {11933}{1440}}\,{t}^{2}+{\frac {331}{216}}\,{t}^{3}\\
\mbox{}-{\frac {25}{192}}\,{t}^{4}+{\frac {1}{240}}\,{t}^{5}-{\frac {1035}{64}}$}
\mapleinline{inert}{2d}{sconstituent[16] := 182/9*t-5989/720*t^2+331/216*t^3-25/192*t^4+1/240*t^5-2107/135}{%
${\it sconstituent}_{{16}}\, := \,{\frac {182}{9}}\,t-{\frac {5989}{720}}\,{t}^{2}+{\frac {331}{216}}\,{t}^{3}\\
\mbox{}-{\frac {25}{192}}\,{t}^{4}+{\frac {1}{240}}\,{t}^{5}-{\frac {2107}{135}}$}
\mapleinline{inert}{2d}{182/9*t-5989/720*t^2+331/216*t^3-25/192*t^4+1/240*t^5-2107/135}{%
${\frac {182}{9}}\,t-{\frac {5989}{720}}\,{t}^{2}+{\frac {331}{216}}\,{t}^{3}\\
\mbox{}-{\frac {25}{192}}\,{t}^{4}+{\frac {1}{240}}\,{t}^{5}-{\frac {2107}{135}}$}

\end{maplelatex}

\mapleresult
\begin{maplelatex}
\mapleinline{inert}{2d}{sconstituent[17] := 949/48*t-11933/1440*t^2+331/216*t^3-25/192*t^4+1/240*t^5-25705/1728}{%
${\it sconstituent}_{{17}}\, := \,{\frac {949}{48}}\,t-{\frac {11933}{1440}}\,{t}^{2}+{\frac {331}{216}}\,{t}^{3}\\
\mbox{}-{\frac {25}{192}}\,{t}^{4}+{\frac {1}{240}}\,{t}^{5}-{\frac {25705}{1728}}$}
\mapleinline{inert}{2d}{1/8640*(t-5)*(36*t^4-945*t^3+8515*t^2-29023*t+25705)}{%
\[
{\frac {1}{8640}}\, \left( t-5 \right)  \left( 36\,{t}^{4}-945\,{t}^{3}+8515\,{t}^{2}-29023\,t+25705 \right) 
\]
}
\mapleinline{inert}{2d}{sconstituent[18] := 61/3*t-92/5-5989/720*t^2+331/216*t^3-25/192*t^4+1/240*t^5}{%
${\it sconstituent}_{{18}}\, := \,{\frac {61}{3}}\,t-{\frac {92}{5}}-{\frac {5989}{720}}\,{t}^{2}\\
\mbox{}+{\frac {331}{216}}\,{t}^{3}-{\frac {25}{192}}\,{t}^{4}+{\frac {1}{240}}\,{t}^{5}$}
\mapleinline{inert}{2d}{61/3*t-92/5-5989/720*t^2+331/216*t^3-25/192*t^4+1/240*t^5}{%
${\frac {61}{3}}\,t-{\frac {92}{5}}-{\frac {5989}{720}}\,{t}^{2}\\
\mbox{}+{\frac {331}{216}}\,{t}^{3}-{\frac {25}{192}}\,{t}^{4}+{\frac {1}{240}}\,{t}^{5}$}
\mapleinline{inert}{2d}{sconstituent[19] := 2831/144*t-11933/1440*t^2+331/216*t^3-25/192*t^4+1/240*t^5-129421/8640}{%
${\it sconstituent}_{{19}}\, := \,{\frac {2831}{144}}\,t-{\frac {11933}{1440}}\,{t}^{2}+{\frac {331}{216}}\,{t}^{3}\\
\mbox{}-{\frac {25}{192}}\,{t}^{4}+{\frac {1}{240}}\,{t}^{5}-{\frac {129421}{8640}}$}
\mapleinline{inert}{2d}{2831/144*t-11933/1440*t^2+331/216*t^3-25/192*t^4+1/240*t^5-129421/8640}{%
${\frac {2831}{144}}\,t-{\frac {11933}{1440}}\,{t}^{2}+{\frac {331}{216}}\,{t}^{3}\\
\mbox{}-{\frac {25}{192}}\,{t}^{4}+{\frac {1}{240}}\,{t}^{5}-{\frac {129421}{8640}}$}
\mapleinline{inert}{2d}{sconstituent[20] := 61/3*t-5989/720*t^2+331/216*t^3-25/192*t^4+1/240*t^5-478/27}{%
${\it sconstituent}_{{20}}\, := \,{\frac {61}{3}}\,t-{\frac {5989}{720}}\,{t}^{2}+{\frac {331}{216}}\,{t}^{3}\\
\mbox{}-{\frac {25}{192}}\,{t}^{4}+{\frac {1}{240}}\,{t}^{5}-{\frac {478}{27}}$}
\mapleinline{inert}{2d}{1/8640*(t-2)*(36*t^4-1053*t^3+11134*t^2-49600*t+76480)}{%
\[
{\frac {1}{8640}}\, \left( t-2 \right)  \left( 36\,{t}^{4}-1053\,{t}^{3}+11134\,{t}^{2}-49600\,t+76480 \right) 
\]
}
\mapleinline{inert}{2d}{sconstituent[21] := 949/48*t-11933/1440*t^2+331/216*t^3-25/192*t^4+1/240*t^5-4599/320}{%
${\it sconstituent}_{{21}}\, := \,{\frac {949}{48}}\,t-{\frac {11933}{1440}}\,{t}^{2}+{\frac {331}{216}}\,{t}^{3}\\
\mbox{}-{\frac {25}{192}}\,{t}^{4}+{\frac {1}{240}}\,{t}^{5}-{\frac {4599}{320}}$}
\mapleinline{inert}{2d}{949/48*t-11933/1440*t^2+331/216*t^3-25/192*t^4+1/240*t^5-4599/320}{%
${\frac {949}{48}}\,t-{\frac {11933}{1440}}\,{t}^{2}+{\frac {331}{216}}\,{t}^{3}\\
\mbox{}-{\frac {25}{192}}\,{t}^{4}+{\frac {1}{240}}\,{t}^{5}-{\frac {4599}{320}}$}
\mapleinline{inert}{2d}{sconstituent[22] := 182/9*t-5989/720*t^2+331/216*t^3-25/192*t^4+1/240*t^5-443/27}{%
${\it sconstituent}_{{22}}\, := \,{\frac {182}{9}}\,t-{\frac {5989}{720}}\,{t}^{2}+{\frac {331}{216}}\,{t}^{3}\\
\mbox{}-{\frac {25}{192}}\,{t}^{4}+{\frac {1}{240}}\,{t}^{5}-{\frac {443}{27}}$}
\mapleinline{inert}{2d}{182/9*t-5989/720*t^2+331/216*t^3-25/192*t^4+1/240*t^5-443/27}{%
${\frac {182}{9}}\,t-{\frac {5989}{720}}\,{t}^{2}+{\frac {331}{216}}\,{t}^{3}\\
\mbox{}-{\frac {25}{192}}\,{t}^{4}+{\frac {1}{240}}\,{t}^{5}-{\frac {443}{27}}$}

\end{maplelatex}

\mapleresult
\begin{maplelatex}
\mapleinline{inert}{2d}{sconstituent[23] := 949/48*t-11933/1440*t^2+331/216*t^3-25/192*t^4+1/240*t^5-140621/8640}{%
${\it sconstituent}_{{23}}\, := \,{\frac {949}{48}}\,t-{\frac {11933}{1440}}\,{t}^{2}+{\frac {331}{216}}\,{t}^{3}\\
\mbox{}-{\frac {25}{192}}\,{t}^{4}+{\frac {1}{240}}\,{t}^{5}-{\frac {140621}{8640}}$}
\mapleinline{inert}{2d}{949/48*t-11933/1440*t^2+331/216*t^3-25/192*t^4+1/240*t^5-140621/8640}{%
${\frac {949}{48}}\,t-{\frac {11933}{1440}}\,{t}^{2}+{\frac {331}{216}}\,{t}^{3}\\
\mbox{}-{\frac {25}{192}}\,{t}^{4}+{\frac {1}{240}}\,{t}^{5}-{\frac {140621}{8640}}$}
\mapleinline{inert}{2d}{sconstituent[24] := 61/3*t-92/5-5989/720*t^2+331/216*t^3-25/192*t^4+1/240*t^5}{%
${\it sconstituent}_{{24}}\, := \,{\frac {61}{3}}\,t-{\frac {92}{5}}-{\frac {5989}{720}}\,{t}^{2}\\
\mbox{}+{\frac {331}{216}}\,{t}^{3}-{\frac {25}{192}}\,{t}^{4}+{\frac {1}{240}}\,{t}^{5}$}
\mapleinline{inert}{2d}{61/3*t-92/5-5989/720*t^2+331/216*t^3-25/192*t^4+1/240*t^5}{%
${\frac {61}{3}}\,t-{\frac {92}{5}}-{\frac {5989}{720}}\,{t}^{2}\\
\mbox{}+{\frac {331}{216}}\,{t}^{3}-{\frac {25}{192}}\,{t}^{4}+{\frac {1}{240}}\,{t}^{5}$}
\mapleinline{inert}{2d}{sconstituent[25] := 2831/144*t-11933/1440*t^2+331/216*t^3-25/192*t^4+1/240*t^5-23465/1728}{%
${\it sconstituent}_{{25}}\, := \,{\frac {2831}{144}}\,t-{\frac {11933}{1440}}\,{t}^{2}+{\frac {331}{216}}\,{t}^{3}\\
\mbox{}-{\frac {25}{192}}\,{t}^{4}+{\frac {1}{240}}\,{t}^{5}-{\frac {23465}{1728}}$}

\end{maplelatex}

\mapleresult
\begin{maplelatex}
\mapleinline{inert}{2d}{2831/144*t-11933/1440*t^2+331/216*t^3-25/192*t^4+1/240*t^5-23465/1728}{%
${\frac {2831}{144}}\,t-{\frac {11933}{1440}}\,{t}^{2}+{\frac {331}{216}}\,{t}^{3}\\
\mbox{}-{\frac {25}{192}}\,{t}^{4}+{\frac {1}{240}}\,{t}^{5}-{\frac {23465}{1728}}$}
\mapleinline{inert}{2d}{sconstituent[26] := 61/3*t-2282/135-5989/720*t^2+331/216*t^3-25/192*t^4+1/240*t^5}{%
${\it sconstituent}_{{26}}\, := \,{\frac {61}{3}}\,t-{\frac {2282}{135}}-{\frac {5989}{720}}\,{t}^{2}\\
\mbox{}+{\frac {331}{216}}\,{t}^{3}-{\frac {25}{192}}\,{t}^{4}+{\frac {1}{240}}\,{t}^{5}$}
\mapleinline{inert}{2d}{61/3*t-2282/135-5989/720*t^2+331/216*t^3-25/192*t^4+1/240*t^5}{%
${\frac {61}{3}}\,t-{\frac {2282}{135}}-{\frac {5989}{720}}\,{t}^{2}\\
\mbox{}+{\frac {331}{216}}\,{t}^{3}-{\frac {25}{192}}\,{t}^{4}+{\frac {1}{240}}\,{t}^{5}$}
\mapleinline{inert}{2d}{sconstituent[27] := 949/48*t-11933/1440*t^2+331/216*t^3-25/192*t^4+1/240*t^5-1035/64}{%
${\it sconstituent}_{{27}}\, := \,{\frac {949}{48}}\,t-{\frac {11933}{1440}}\,{t}^{2}+{\frac {331}{216}}\,{t}^{3}\\
\mbox{}-{\frac {25}{192}}\,{t}^{4}+{\frac {1}{240}}\,{t}^{5}-{\frac {1035}{64}}$}
\mapleinline{inert}{2d}{949/48*t-11933/1440*t^2+331/216*t^3-25/192*t^4+1/240*t^5-1035/64}{%
${\frac {949}{48}}\,t-{\frac {11933}{1440}}\,{t}^{2}+{\frac {331}{216}}\,{t}^{3}\\
\mbox{}-{\frac {25}{192}}\,{t}^{4}+{\frac {1}{240}}\,{t}^{5}-{\frac {1035}{64}}$}
\mapleinline{inert}{2d}{sconstituent[28] := 182/9*t-2269/135-5989/720*t^2+331/216*t^3-25/192*t^4+1/240*t^5}{%
${\it sconstituent}_{{28}}\, := \,{\frac {182}{9}}\,t-{\frac {2269}{135}}-{\frac {5989}{720}}\,{t}^{2}\\
\mbox{}+{\frac {331}{216}}\,{t}^{3}-{\frac {25}{192}}\,{t}^{4}+{\frac {1}{240}}\,{t}^{5}$}
\mapleinline{inert}{2d}{1/8640*(t-4)*(36*t^4-981*t^3+9316*t^2-34604*t+36304)}{%
\[
{\frac {1}{8640}}\, \left( t-4 \right)  \left( 36\,{t}^{4}-981\,{t}^{3}+9316\,{t}^{2}-34604\,t+36304 \right) 
\]
}
\mapleinline{inert}{2d}{sconstituent[29] := 949/48*t-11933/1440*t^2+331/216*t^3-25/192*t^4+1/240*t^5-131981/8640}{%
${\it sconstituent}_{{29}}\, := \,{\frac {949}{48}}\,t-{\frac {11933}{1440}}\,{t}^{2}+{\frac {331}{216}}\,{t}^{3}\\
\mbox{}-{\frac {25}{192}}\,{t}^{4}+{\frac {1}{240}}\,{t}^{5}-{\frac {131981}{8640}}$}
\mapleinline{inert}{2d}{949/48*t-11933/1440*t^2+331/216*t^3-25/192*t^4+1/240*t^5-131981/8640}{%
${\frac {949}{48}}\,t-{\frac {11933}{1440}}\,{t}^{2}+{\frac {331}{216}}\,{t}^{3}\\
\mbox{}-{\frac {25}{192}}\,{t}^{4}+{\frac {1}{240}}\,{t}^{5}-{\frac {131981}{8640}}$}
\mapleinline{inert}{2d}{sconstituent[30] := -18+61/3*t-5989/720*t^2+331/216*t^3-25/192*t^4+1/240*t^5}{%
${\it sconstituent}_{{30}}\, := \,-18+{\frac {61}{3}}\,t-{\frac {5989}{720}}\,{t}^{2}+{\frac {331}{216}}\,{t}^{3}\\
\mbox{}-{\frac {25}{192}}\,{t}^{4}+{\frac {1}{240}}\,{t}^{5}$}
\mapleinline{inert}{2d}{-18+61/3*t-5989/720*t^2+331/216*t^3-25/192*t^4+1/240*t^5}{%
$-18+{\frac {61}{3}}\,t-{\frac {5989}{720}}\,{t}^{2}+{\frac {331}{216}}\,{t}^{3}\\
\mbox{}-{\frac {25}{192}}\,{t}^{4}+{\frac {1}{240}}\,{t}^{5}$}
\mapleinline{inert}{2d}{sconstituent[31] := 2831/144*t-11933/1440*t^2+331/216*t^3-25/192*t^4+1/240*t^5-119053/8640}{%
${\it sconstituent}_{{31}}\, := \,{\frac {2831}{144}}\,t-{\frac {11933}{1440}}\,{t}^{2}+{\frac {331}{216}}\,{t}^{3}\\
\mbox{}-{\frac {25}{192}}\,{t}^{4}+{\frac {1}{240}}\,{t}^{5}-{\frac {119053}{8640}}$}
\mapleinline{inert}{2d}{2831/144*t-11933/1440*t^2+331/216*t^3-25/192*t^4+1/240*t^5-119053/8640}{%
${\frac {2831}{144}}\,t-{\frac {11933}{1440}}\,{t}^{2}+{\frac {331}{216}}\,{t}^{3}\\
\mbox{}-{\frac {25}{192}}\,{t}^{4}+{\frac {1}{240}}\,{t}^{5}-{\frac {119053}{8640}}$}
\mapleinline{inert}{2d}{sconstituent[32] := 61/3*t-5989/720*t^2+331/216*t^3-25/192*t^4+1/240*t^5-478/27}{%
${\it sconstituent}_{{32}}\, := \,{\frac {61}{3}}\,t-{\frac {5989}{720}}\,{t}^{2}+{\frac {331}{216}}\,{t}^{3}\\
\mbox{}-{\frac {25}{192}}\,{t}^{4}+{\frac {1}{240}}\,{t}^{5}-{\frac {478}{27}}$}

\end{maplelatex}

\mapleresult
\begin{maplelatex}
\mapleinline{inert}{2d}{1/8640*(t-2)*(36*t^4-1053*t^3+11134*t^2-49600*t+76480)}{%
\[
{\frac {1}{8640}}\, \left( t-2 \right)  \left( 36\,{t}^{4}-1053\,{t}^{3}+11134\,{t}^{2}-49600\,t+76480 \right) 
\]
}
\mapleinline{inert}{2d}{sconstituent[33] := 949/48*t-11933/1440*t^2+331/216*t^3-25/192*t^4+1/240*t^5-4983/320}{%
${\it sconstituent}_{{33}}\, := \,{\frac {949}{48}}\,t-{\frac {11933}{1440}}\,{t}^{2}+{\frac {331}{216}}\,{t}^{3}\\
\mbox{}-{\frac {25}{192}}\,{t}^{4}+{\frac {1}{240}}\,{t}^{5}-{\frac {4983}{320}}$}
\mapleinline{inert}{2d}{1/8640*(t-9)*(36*t^4-801*t^3+6031*t^2-17319*t+14949)}{%
\[
{\frac {1}{8640}}\, \left( t-9 \right)  \left( 36\,{t}^{4}-801\,{t}^{3}+6031\,{t}^{2}-17319\,t+14949 \right) 
\]
}
\mapleinline{inert}{2d}{sconstituent[34] := 182/9*t-2269/135-5989/720*t^2+331/216*t^3-25/192*t^4+1/240*t^5}{%
${\it sconstituent}_{{34}}\, := \,{\frac {182}{9}}\,t-{\frac {2269}{135}}-{\frac {5989}{720}}\,{t}^{2}\\
\mbox{}+{\frac {331}{216}}\,{t}^{3}-{\frac {25}{192}}\,{t}^{4}+{\frac {1}{240}}\,{t}^{5}$}
\mapleinline{inert}{2d}{1/8640*(t-4)*(36*t^4-981*t^3+9316*t^2-34604*t+36304)}{%
\[
{\frac {1}{8640}}\, \left( t-4 \right)  \left( 36\,{t}^{4}-981\,{t}^{3}+9316\,{t}^{2}-34604\,t+36304 \right) 
\]
}
\mapleinline{inert}{2d}{sconstituent[35] := 949/48*t-11933/1440*t^2+331/216*t^3-25/192*t^4+1/240*t^5-27433/1728}{%
${\it sconstituent}_{{35}}\, := \,{\frac {949}{48}}\,t-{\frac {11933}{1440}}\,{t}^{2}+{\frac {331}{216}}\,{t}^{3}\\
\mbox{}-{\frac {25}{192}}\,{t}^{4}+{\frac {1}{240}}\,{t}^{5}-{\frac {27433}{1728}}$}
\mapleinline{inert}{2d}{949/48*t-11933/1440*t^2+331/216*t^3-25/192*t^4+1/240*t^5-27433/1728}{%
${\frac {949}{48}}\,t-{\frac {11933}{1440}}\,{t}^{2}+{\frac {331}{216}}\,{t}^{3}\\
\mbox{}-{\frac {25}{192}}\,{t}^{4}+{\frac {1}{240}}\,{t}^{5}-{\frac {27433}{1728}}$}
\mapleinline{inert}{2d}{sconstituent[36] := 61/3*t-5989/720*t^2+331/216*t^3-25/192*t^4+1/240*t^5-86/5}{%
${\it sconstituent}_{{36}}\, := \,{\frac {61}{3}}\,t-{\frac {5989}{720}}\,{t}^{2}+{\frac {331}{216}}\,{t}^{3}\\
\mbox{}-{\frac {25}{192}}\,{t}^{4}+{\frac {1}{240}}\,{t}^{5}-{\frac {86}{5}}$}
\mapleinline{inert}{2d}{1/8640*(t-6)*(36*t^4-909*t^3+7786*t^2-25152*t+24768)}{%
\[
{\frac {1}{8640}}\, \left( t-6 \right)  \left( 36\,{t}^{4}-909\,{t}^{3}+7786\,{t}^{2}-25152\,t+24768 \right) 
\]
}
\mapleinline{inert}{2d}{sconstituent[37] := 2831/144*t-11933/1440*t^2+331/216*t^3-25/192*t^4+1/240*t^5-23465/1728}{%
${\it sconstituent}_{{37}}\, := \,{\frac {2831}{144}}\,t-{\frac {11933}{1440}}\,{t}^{2}+{\frac {331}{216}}\,{t}^{3}\\
\mbox{}-{\frac {25}{192}}\,{t}^{4}+{\frac {1}{240}}\,{t}^{5}-{\frac {23465}{1728}}$}
\mapleinline{inert}{2d}{2831/144*t-11933/1440*t^2+331/216*t^3-25/192*t^4+1/240*t^5-23465/1728}{%
${\frac {2831}{144}}\,t-{\frac {11933}{1440}}\,{t}^{2}+{\frac {331}{216}}\,{t}^{3}\\
\mbox{}-{\frac {25}{192}}\,{t}^{4}+{\frac {1}{240}}\,{t}^{5}-{\frac {23465}{1728}}$}
\mapleinline{inert}{2d}{sconstituent[38] := 61/3*t-2444/135-5989/720*t^2+331/216*t^3-25/192*t^4+1/240*t^5}{%
${\it sconstituent}_{{38}}\, := \,{\frac {61}{3}}\,t-{\frac {2444}{135}}-{\frac {5989}{720}}\,{t}^{2}\\
\mbox{}+{\frac {331}{216}}\,{t}^{3}-{\frac {25}{192}}\,{t}^{4}+{\frac {1}{240}}\,{t}^{5}$}
\mapleinline{inert}{2d}{1/8640*(t-8)*(36*t^4-837*t^3+6544*t^2-19516*t+19552)}{%
\[
{\frac {1}{8640}}\, \left( t-8 \right)  \left( 36\,{t}^{4}-837\,{t}^{3}+6544\,{t}^{2}-19516\,t+19552 \right) 
\]
}
\mapleinline{inert}{2d}{sconstituent[39] := 949/48*t-11933/1440*t^2+331/216*t^3-25/192*t^4+1/240*t^5-5303/320}{%
${\it sconstituent}_{{39}}\, := \,{\frac {949}{48}}\,t-{\frac {11933}{1440}}\,{t}^{2}+{\frac {331}{216}}\,{t}^{3}\\
\mbox{}-{\frac {25}{192}}\,{t}^{4}+{\frac {1}{240}}\,{t}^{5}-{\frac {5303}{320}}$}
\mapleinline{inert}{2d}{1/8640*(t-3)*(36*t^4-1017*t^3+10189*t^2-41031*t+47727)}{%
\[
{\frac {1}{8640}}\, \left( t-3 \right)  \left( 36\,{t}^{4}-1017\,{t}^{3}+10189\,{t}^{2}-41031\,t+47727 \right) 
\]
}
\mapleinline{inert}{2d}{sconstituent[40] := 182/9*t-5989/720*t^2+331/216*t^3-25/192*t^4+1/240*t^5-443/27}{%
${\it sconstituent}_{{40}}\, := \,{\frac {182}{9}}\,t-{\frac {5989}{720}}\,{t}^{2}+{\frac {331}{216}}\,{t}^{3}\\
\mbox{}-{\frac {25}{192}}\,{t}^{4}+{\frac {1}{240}}\,{t}^{5}-{\frac {443}{27}}$}
\mapleinline{inert}{2d}{182/9*t-5989/720*t^2+331/216*t^3-25/192*t^4+1/240*t^5-443/27}{%
${\frac {182}{9}}\,t-{\frac {5989}{720}}\,{t}^{2}+{\frac {331}{216}}\,{t}^{3}\\
\mbox{}-{\frac {25}{192}}\,{t}^{4}+{\frac {1}{240}}\,{t}^{5}-{\frac {443}{27}}$}
\mapleinline{inert}{2d}{sconstituent[41] := 949/48*t-11933/1440*t^2+331/216*t^3-25/192*t^4+1/240*t^5-121613/8640}{%
${\it sconstituent}_{{41}}\, := \,{\frac {949}{48}}\,t-{\frac {11933}{1440}}\,{t}^{2}+{\frac {331}{216}}\,{t}^{3}\\
\mbox{}-{\frac {25}{192}}\,{t}^{4}+{\frac {1}{240}}\,{t}^{5}-{\frac {121613}{8640}}$}
\mapleinline{inert}{2d}{949/48*t-11933/1440*t^2+331/216*t^3-25/192*t^4+1/240*t^5-121613/8640}{%
${\frac {949}{48}}\,t-{\frac {11933}{1440}}\,{t}^{2}+{\frac {331}{216}}\,{t}^{3}\\
\mbox{}-{\frac {25}{192}}\,{t}^{4}+{\frac {1}{240}}\,{t}^{5}-{\frac {121613}{8640}}$}
\mapleinline{inert}{2d}{sconstituent[42] := -18+61/3*t-5989/720*t^2+331/216*t^3-25/192*t^4+1/240*t^5}{%
${\it sconstituent}_{{42}}\, := \,-18+{\frac {61}{3}}\,t-{\frac {5989}{720}}\,{t}^{2}+{\frac {331}{216}}\,{t}^{3}\\
\mbox{}-{\frac {25}{192}}\,{t}^{4}+{\frac {1}{240}}\,{t}^{5}$}
\mapleinline{inert}{2d}{-18+61/3*t-5989/720*t^2+331/216*t^3-25/192*t^4+1/240*t^5}{%
$-18+{\frac {61}{3}}\,t-{\frac {5989}{720}}\,{t}^{2}+{\frac {331}{216}}\,{t}^{3}\\
\mbox{}-{\frac {25}{192}}\,{t}^{4}+{\frac {1}{240}}\,{t}^{5}$}
\mapleinline{inert}{2d}{sconstituent[43] := 2831/144*t-11933/1440*t^2+331/216*t^3-25/192*t^4+1/240*t^5-129421/8640}{%
${\it sconstituent}_{{43}}\, := \,{\frac {2831}{144}}\,t-{\frac {11933}{1440}}\,{t}^{2}+{\frac {331}{216}}\,{t}^{3}\\
\mbox{}-{\frac {25}{192}}\,{t}^{4}+{\frac {1}{240}}\,{t}^{5}-{\frac {129421}{8640}}$}
\mapleinline{inert}{2d}{2831/144*t-11933/1440*t^2+331/216*t^3-25/192*t^4+1/240*t^5-129421/8640}{%
${\frac {2831}{144}}\,t-{\frac {11933}{1440}}\,{t}^{2}+{\frac {331}{216}}\,{t}^{3}\\
\mbox{}-{\frac {25}{192}}\,{t}^{4}+{\frac {1}{240}}\,{t}^{5}-{\frac {129421}{8640}}$}

\end{maplelatex}

\mapleresult
\begin{maplelatex}
\mapleinline{inert}{2d}{sconstituent[44] := 61/3*t-2444/135-5989/720*t^2+331/216*t^3-25/192*t^4+1/240*t^5}{%
${\it sconstituent}_{{44}}\, := \,{\frac {61}{3}}\,t-{\frac {2444}{135}}-{\frac {5989}{720}}\,{t}^{2}\\
\mbox{}+{\frac {331}{216}}\,{t}^{3}-{\frac {25}{192}}\,{t}^{4}+{\frac {1}{240}}\,{t}^{5}$}
\mapleinline{inert}{2d}{1/8640*(t-8)*(36*t^4-837*t^3+6544*t^2-19516*t+19552)}{%
\[
{\frac {1}{8640}}\, \left( t-8 \right)  \left( 36\,{t}^{4}-837\,{t}^{3}+6544\,{t}^{2}-19516\,t+19552 \right) 
\]
}
\mapleinline{inert}{2d}{sconstituent[45] := 949/48*t-11933/1440*t^2+331/216*t^3-25/192*t^4+1/240*t^5-971/64}{%
${\it sconstituent}_{{45}}\, := \,{\frac {949}{48}}\,t-{\frac {11933}{1440}}\,{t}^{2}+{\frac {331}{216}}\,{t}^{3}\\
\mbox{}-{\frac {25}{192}}\,{t}^{4}+{\frac {1}{240}}\,{t}^{5}-{\frac {971}{64}}$}
\mapleinline{inert}{2d}{949/48*t-11933/1440*t^2+331/216*t^3-25/192*t^4+1/240*t^5-971/64}{%
${\frac {949}{48}}\,t-{\frac {11933}{1440}}\,{t}^{2}+{\frac {331}{216}}\,{t}^{3}\\
\mbox{}-{\frac {25}{192}}\,{t}^{4}+{\frac {1}{240}}\,{t}^{5}-{\frac {971}{64}}$}
\mapleinline{inert}{2d}{sconstituent[46] := 182/9*t-5989/720*t^2+331/216*t^3-25/192*t^4+1/240*t^5-2107/135}{%
${\it sconstituent}_{{46}}\, := \,{\frac {182}{9}}\,t-{\frac {5989}{720}}\,{t}^{2}+{\frac {331}{216}}\,{t}^{3}\\
\mbox{}-{\frac {25}{192}}\,{t}^{4}+{\frac {1}{240}}\,{t}^{5}-{\frac {2107}{135}}$}

\end{maplelatex}

\mapleresult
\begin{maplelatex}
\mapleinline{inert}{2d}{182/9*t-5989/720*t^2+331/216*t^3-25/192*t^4+1/240*t^5-2107/135}{%
${\frac {182}{9}}\,t-{\frac {5989}{720}}\,{t}^{2}+{\frac {331}{216}}\,{t}^{3}\\
\mbox{}-{\frac {25}{192}}\,{t}^{4}+{\frac {1}{240}}\,{t}^{5}-{\frac {2107}{135}}$}
\mapleinline{inert}{2d}{sconstituent[47] := 949/48*t-11933/1440*t^2+331/216*t^3-25/192*t^4+1/240*t^5-27433/1728}{%
${\it sconstituent}_{{47}}\, := \,{\frac {949}{48}}\,t-{\frac {11933}{1440}}\,{t}^{2}+{\frac {331}{216}}\,{t}^{3}\\
\mbox{}-{\frac {25}{192}}\,{t}^{4}+{\frac {1}{240}}\,{t}^{5}-{\frac {27433}{1728}}$}
\mapleinline{inert}{2d}{949/48*t-11933/1440*t^2+331/216*t^3-25/192*t^4+1/240*t^5-27433/1728}{%
${\frac {949}{48}}\,t-{\frac {11933}{1440}}\,{t}^{2}+{\frac {331}{216}}\,{t}^{3}\\
\mbox{}-{\frac {25}{192}}\,{t}^{4}+{\frac {1}{240}}\,{t}^{5}-{\frac {27433}{1728}}$}
\mapleinline{inert}{2d}{sconstituent[48] := 61/3*t-92/5-5989/720*t^2+331/216*t^3-25/192*t^4+1/240*t^5}{%
${\it sconstituent}_{{48}}\, := \,{\frac {61}{3}}\,t-{\frac {92}{5}}-{\frac {5989}{720}}\,{t}^{2}\\
\mbox{}+{\frac {331}{216}}\,{t}^{3}-{\frac {25}{192}}\,{t}^{4}+{\frac {1}{240}}\,{t}^{5}$}

\end{maplelatex}

\mapleresult
\begin{maplelatex}
\mapleinline{inert}{2d}{61/3*t-92/5-5989/720*t^2+331/216*t^3-25/192*t^4+1/240*t^5}{%
${\frac {61}{3}}\,t-{\frac {92}{5}}-{\frac {5989}{720}}\,{t}^{2}\\
\mbox{}+{\frac {331}{216}}\,{t}^{3}-{\frac {25}{192}}\,{t}^{4}+{\frac {1}{240}}\,{t}^{5}$}

\end{maplelatex}

\mapleresult
\begin{maplelatex}
\mapleinline{inert}{2d}{sconstituent[49] := 2831/144*t-120781/8640-11933/1440*t^2+331/216*t^3-25/192*t^4+1/240*t^5}{%
${\it sconstituent}_{{49}}\, := \,{\frac {2831}{144}}\,t-{\frac {120781}{8640}}-{\frac {11933}{1440}}\,{t}^{2}\\
\mbox{}+{\frac {331}{216}}\,{t}^{3}-{\frac {25}{192}}\,{t}^{4}+{\frac {1}{240}}\,{t}^{5}$}
\mapleinline{inert}{2d}{2831/144*t-120781/8640-11933/1440*t^2+331/216*t^3-25/192*t^4+1/240*t^5}{%
${\frac {2831}{144}}\,t-{\frac {120781}{8640}}-{\frac {11933}{1440}}\,{t}^{2}\\
\mbox{}+{\frac {331}{216}}\,{t}^{3}-{\frac {25}{192}}\,{t}^{4}+{\frac {1}{240}}\,{t}^{5}$}
\mapleinline{inert}{2d}{sconstituent[50] := 61/3*t-5989/720*t^2+331/216*t^3-25/192*t^4+1/240*t^5-478/27}{%
${\it sconstituent}_{{50}}\, := \,{\frac {61}{3}}\,t-{\frac {5989}{720}}\,{t}^{2}+{\frac {331}{216}}\,{t}^{3}\\
\mbox{}-{\frac {25}{192}}\,{t}^{4}+{\frac {1}{240}}\,{t}^{5}-{\frac {478}{27}}$}
\mapleinline{inert}{2d}{1/8640*(t-2)*(36*t^4-1053*t^3+11134*t^2-49600*t+76480)}{%
\[
{\frac {1}{8640}}\, \left( t-2 \right)  \left( 36\,{t}^{4}-1053\,{t}^{3}+11134\,{t}^{2}-49600\,t+76480 \right) 
\]
}
\mapleinline{inert}{2d}{sconstituent[51] := 949/48*t-11933/1440*t^2+331/216*t^3-25/192*t^4+1/240*t^5-4919/320}{%
${\it sconstituent}_{{51}}\, := \,{\frac {949}{48}}\,t-{\frac {11933}{1440}}\,{t}^{2}+{\frac {331}{216}}\,{t}^{3}\\
\mbox{}-{\frac {25}{192}}\,{t}^{4}+{\frac {1}{240}}\,{t}^{5}-{\frac {4919}{320}}$}
\mapleinline{inert}{2d}{949/48*t-11933/1440*t^2+331/216*t^3-25/192*t^4+1/240*t^5-4919/320}{%
${\frac {949}{48}}\,t-{\frac {11933}{1440}}\,{t}^{2}+{\frac {331}{216}}\,{t}^{3}\\
\mbox{}-{\frac {25}{192}}\,{t}^{4}+{\frac {1}{240}}\,{t}^{5}-{\frac {4919}{320}}$}

\end{maplelatex}

\mapleresult
\begin{maplelatex}
\mapleinline{inert}{2d}{sconstituent[52] := 182/9*t-5989/720*t^2+331/216*t^3-25/192*t^4+1/240*t^5-443/27}{%
${\it sconstituent}_{{52}}\, := \,{\frac {182}{9}}\,t-{\frac {5989}{720}}\,{t}^{2}+{\frac {331}{216}}\,{t}^{3}\\
\mbox{}-{\frac {25}{192}}\,{t}^{4}+{\frac {1}{240}}\,{t}^{5}-{\frac {443}{27}}$}
\mapleinline{inert}{2d}{182/9*t-5989/720*t^2+331/216*t^3-25/192*t^4+1/240*t^5-443/27}{%
${\frac {182}{9}}\,t-{\frac {5989}{720}}\,{t}^{2}+{\frac {331}{216}}\,{t}^{3}\\
\mbox{}-{\frac {25}{192}}\,{t}^{4}+{\frac {1}{240}}\,{t}^{5}-{\frac {443}{27}}$}
\mapleinline{inert}{2d}{sconstituent[53] := 949/48*t-11933/1440*t^2+331/216*t^3-25/192*t^4+1/240*t^5-131981/8640}{%
${\it sconstituent}_{{53}}\, := \,{\frac {949}{48}}\,t-{\frac {11933}{1440}}\,{t}^{2}+{\frac {331}{216}}\,{t}^{3}\\
\mbox{}-{\frac {25}{192}}\,{t}^{4}+{\frac {1}{240}}\,{t}^{5}-{\frac {131981}{8640}}$}
\mapleinline{inert}{2d}{949/48*t-11933/1440*t^2+331/216*t^3-25/192*t^4+1/240*t^5-131981/8640}{%
${\frac {949}{48}}\,t-{\frac {11933}{1440}}\,{t}^{2}+{\frac {331}{216}}\,{t}^{3}\\
\mbox{}-{\frac {25}{192}}\,{t}^{4}+{\frac {1}{240}}\,{t}^{5}-{\frac {131981}{8640}}$}
\mapleinline{inert}{2d}{sconstituent[54] := 61/3*t-92/5-5989/720*t^2+331/216*t^3-25/192*t^4+1/240*t^5}{%
${\it sconstituent}_{{54}}\, := \,{\frac {61}{3}}\,t-{\frac {92}{5}}-{\frac {5989}{720}}\,{t}^{2}\\
\mbox{}+{\frac {331}{216}}\,{t}^{3}-{\frac {25}{192}}\,{t}^{4}+{\frac {1}{240}}\,{t}^{5}$}
\mapleinline{inert}{2d}{61/3*t-92/5-5989/720*t^2+331/216*t^3-25/192*t^4+1/240*t^5}{%
${\frac {61}{3}}\,t-{\frac {92}{5}}-{\frac {5989}{720}}\,{t}^{2}\\
\mbox{}+{\frac {331}{216}}\,{t}^{3}-{\frac {25}{192}}\,{t}^{4}+{\frac {1}{240}}\,{t}^{5}$}
\mapleinline{inert}{2d}{sconstituent[55] := -25193/1728+2831/144*t-11933/1440*t^2+331/216*t^3-25/192*t^4+1/240*t^5}{%
${\it sconstituent}_{{55}}\, := \,-{\frac {25193}{1728}}+{\frac {2831}{144}}\,t\\
\mbox{}-{\frac {11933}{1440}}\,{t}^{2}+{\frac {331}{216}}\,{t}^{3}-{\frac {25}{192}}\,{t}^{4}\\
\mbox{}+{\frac {1}{240}}\,{t}^{5}$}
\mapleinline{inert}{2d}{1/8640*(t-7)*(36*t^4-873*t^3+7129*t^2-21695*t+17995)}{%
\[
{\frac {1}{8640}}\, \left( t-7 \right)  \left( 36\,{t}^{4}-873\,{t}^{3}+7129\,{t}^{2}-21695\,t+17995 \right) 
\]
}
\mapleinline{inert}{2d}{sconstituent[56] := 61/3*t-2282/135-5989/720*t^2+331/216*t^3-25/192*t^4+1/240*t^5}{%
${\it sconstituent}_{{56}}\, := \,{\frac {61}{3}}\,t-{\frac {2282}{135}}-{\frac {5989}{720}}\,{t}^{2}\\
\mbox{}+{\frac {331}{216}}\,{t}^{3}-{\frac {25}{192}}\,{t}^{4}+{\frac {1}{240}}\,{t}^{5}$}
\mapleinline{inert}{2d}{61/3*t-2282/135-5989/720*t^2+331/216*t^3-25/192*t^4+1/240*t^5}{%
${\frac {61}{3}}\,t-{\frac {2282}{135}}-{\frac {5989}{720}}\,{t}^{2}\\
\mbox{}+{\frac {331}{216}}\,{t}^{3}-{\frac {25}{192}}\,{t}^{4}+{\frac {1}{240}}\,{t}^{5}$}

\end{maplelatex}

\mapleresult
\begin{maplelatex}
\mapleinline{inert}{2d}{sconstituent[57] := 949/48*t-11933/1440*t^2+331/216*t^3-25/192*t^4+1/240*t^5-971/64}{%
${\it sconstituent}_{{57}}\, := \,{\frac {949}{48}}\,t-{\frac {11933}{1440}}\,{t}^{2}+{\frac {331}{216}}\,{t}^{3}\\
\mbox{}-{\frac {25}{192}}\,{t}^{4}+{\frac {1}{240}}\,{t}^{5}-{\frac {971}{64}}$}
\mapleinline{inert}{2d}{949/48*t-11933/1440*t^2+331/216*t^3-25/192*t^4+1/240*t^5-971/64}{%
${\frac {949}{48}}\,t-{\frac {11933}{1440}}\,{t}^{2}+{\frac {331}{216}}\,{t}^{3}\\
\mbox{}-{\frac {25}{192}}\,{t}^{4}+{\frac {1}{240}}\,{t}^{5}-{\frac {971}{64}}$}
\mapleinline{inert}{2d}{sconstituent[58] := 182/9*t-2269/135-5989/720*t^2+331/216*t^3-25/192*t^4+1/240*t^5}{%
${\it sconstituent}_{{58}}\, := \,{\frac {182}{9}}\,t-{\frac {2269}{135}}-{\frac {5989}{720}}\,{t}^{2}\\
\mbox{}+{\frac {331}{216}}\,{t}^{3}-{\frac {25}{192}}\,{t}^{4}+{\frac {1}{240}}\,{t}^{5}$}
\mapleinline{inert}{2d}{1/8640*(t-4)*(36*t^4-981*t^3+9316*t^2-34604*t+36304)}{%
\[
{\frac {1}{8640}}\, \left( t-4 \right)  \left( 36\,{t}^{4}-981\,{t}^{3}+9316\,{t}^{2}-34604\,t+36304 \right) 
\]
}
\mapleinline{inert}{2d}{sconstituent[59] := 949/48*t-11933/1440*t^2+331/216*t^3-25/192*t^4+1/240*t^5-140621/8640}{%
${\it sconstituent}_{{59}}\, := \,{\frac {949}{48}}\,t-{\frac {11933}{1440}}\,{t}^{2}+{\frac {331}{216}}\,{t}^{3}\\
\mbox{}-{\frac {25}{192}}\,{t}^{4}+{\frac {1}{240}}\,{t}^{5}-{\frac {140621}{8640}}$}
\mapleinline{inert}{2d}{949/48*t-11933/1440*t^2+331/216*t^3-25/192*t^4+1/240*t^5-140621/8640}{%
${\frac {949}{48}}\,t-{\frac {11933}{1440}}\,{t}^{2}+{\frac {331}{216}}\,{t}^{3}\\
\mbox{}-{\frac {25}{192}}\,{t}^{4}+{\frac {1}{240}}\,{t}^{5}-{\frac {140621}{8640}}$}
\mapleinline{inert}{2d}{sconstituent[60] := -18+61/3*t-5989/720*t^2+331/216*t^3-25/192*t^4+1/240*t^5}{%
${\it sconstituent}_{{60}}\, := \,-18+{\frac {61}{3}}\,t-{\frac {5989}{720}}\,{t}^{2}+{\frac {331}{216}}\,{t}^{3}\\
\mbox{}-{\frac {25}{192}}\,{t}^{4}+{\frac {1}{240}}\,{t}^{5}$}
\mapleinline{inert}{2d}{-18+61/3*t-5989/720*t^2+331/216*t^3-25/192*t^4+1/240*t^5}{%
$-18+{\frac {61}{3}}\,t-{\frac {5989}{720}}\,{t}^{2}+{\frac {331}{216}}\,{t}^{3}\\
\mbox{}-{\frac {25}{192}}\,{t}^{4}+{\frac {1}{240}}\,{t}^{5}$}

\end{maplelatex}
Extract the coefficients of the constituents.\begin{mapleinput}
\mapleinline{active}{1d}{for r from 1 to p do
 for coeffdeg from 0 to d do 
  sc[coeffdeg,r]:=coeff(sconstituent[r],t,coeffdeg):
  #print( r, sc[coeffdeg,r] ):
 od:
od: }{}
\end{mapleinput}Print and analyze the constituent coefficients for periods.  First the higher coefficients, which are constant.  Print the first coefficient, then any that don't repeat the preceding value (there are none).\begin{mapleinput}
\mapleinline{active}{1d}{for coeffdeg from 3 to d do
  print("degree", coeffdeg, "coeff", sc[coeffdeg,1]):
  for r from 2 to p do
    stepdifference:=sc[coeffdeg,r]-sc[coeffdeg,r-1]:
    if( stepdifference<\TEXTsymbol{>}0 ) then 
    print(r,sc[coeffdeg,r],stepdifference):
    fi: 
  od: 
od: }{}
\end{mapleinput}
\mapleresult
\begin{maplelatex}
\mapleinline{inert}{2d}{"degree", 3, "coeff", 331/216}{%
\[
{\it ``degree''},\,3,\,{\it ``coeff''},\,{\frac {331}{216}}
\]
}
\mapleinline{inert}{2d}{"degree", 4, "coeff", (-25)/192}{%
\[
{\it ``degree''},\,4,\,{\it ``coeff''},\,-{\frac {25}{192}}
\]
}
\mapleinline{inert}{2d}{"degree", 5, "coeff", 1/240}{%
\[
{\it ``degree''},\,5,\,{\it ``coeff''},\,{\frac {1}{240}}
\]
}

\end{maplelatex}
Next, the constant terms, whose period is expected to be 60.  Print all constant terms up to the presumed period "stepsize".  Print the difference (at step "stepsize") if they are not repeating.\begin{mapleinput}
\mapleinline{active}{1d}{stepsize:=30; lcd:=8640;
for r from 1 to stepsize do
  print(r, sc[0,r], "With sign adjusted:", -sc[0,r]*lcd, "/l.c.d."); 
od: 
for r from stepsize+1 to p do 
  stepdifference:=sc[0,r]-sc[0,r-stepsize]:
  if( stepdifference<\TEXTsymbol{>}0 ) then print(r,sc[0,r],stepdifference, "With sign adjusted:", -sc[0,r]*lcd, "/l.c.d."): fi:
od:
print("Constant terms completed."); }{}
\end{mapleinput}
\mapleresult
\begin{maplelatex}
\mapleinline{inert}{2d}{stepsize := 30}{%
\[
{\it stepsize}\, := \,30
\]
}
\mapleinline{inert}{2d}{lcd := 8640}{%
\[
{\it lcd}\, := \,8640
\]
}
\mapleinline{inert}{2d}{1, (-110413)/8640, "With sign adjusted:", 110413, "/l.c.d."}{%
$1,\,-{\frac {110413}{8640}},\,\mbox {{\tt ``With sign adjusted:''}},\,110413,\,\mbox {{\tt ``/l.c.d.''}}$}
\mapleinline{inert}{2d}{2, (-478)/27, "With sign adjusted:", 152960, "/l.c.d."}{%
$2,\,-{\frac {478}{27}},\,\mbox {{\tt ``With sign adjusted:''}},\,152960,\,\mbox {{\tt ``/l.c.d.''}}$}
\mapleinline{inert}{2d}{3, (-5303)/320, "With sign adjusted:", 143181, "/l.c.d."}{%
$3,\,-{\frac {5303}{320}},\,\mbox {{\tt ``With sign adjusted:''}},\,143181,\,\mbox {{\tt ``/l.c.d.''}}$}
\mapleinline{inert}{2d}{4, (-2269)/135, "With sign adjusted:", 145216, "/l.c.d."}{%
$4,\,-{\frac {2269}{135}},\,\mbox {{\tt ``With sign adjusted:''}},\,145216,\,\mbox {{\tt ``/l.c.d.''}}$}
\mapleinline{inert}{2d}{5, (-25705)/1728, "With sign adjusted:", 128525, "/l.c.d."}{%
$5,\,-{\frac {25705}{1728}},\,\mbox {{\tt ``With sign adjusted:''}},\,128525,\,\mbox {{\tt ``/l.c.d.''}}$}
\mapleinline{inert}{2d}{6, (-86)/5, "With sign adjusted:", 148608, "/l.c.d."}{%
$6,\,-{\frac {86}{5}},\,\mbox {{\tt ``With sign adjusted:''}},\,148608,\,\mbox {{\tt ``/l.c.d.''}}$}
\mapleinline{inert}{2d}{7, (-25193)/1728, "With sign adjusted:", 125965, "/l.c.d."}{%
$7,\,-{\frac {25193}{1728}},\,\mbox {{\tt ``With sign adjusted:''}},\,125965,\,\mbox {{\tt ``/l.c.d.''}}$}
\mapleinline{inert}{2d}{8, (-2444)/135, "With sign adjusted:", 156416, "/l.c.d."}{%
$8,\,-{\frac {2444}{135}},\,\mbox {{\tt ``With sign adjusted:''}},\,156416,\,\mbox {{\tt ``/l.c.d.''}}$}
\mapleinline{inert}{2d}{9, (-4983)/320, "With sign adjusted:", 134541, "/l.c.d."}{%
$9,\,-{\frac {4983}{320}},\,\mbox {{\tt ``With sign adjusted:''}},\,134541,\,\mbox {{\tt ``/l.c.d.''}}$}
\mapleinline{inert}{2d}{10, (-443)/27, "With sign adjusted:", 141760, "/l.c.d."}{%
$10,\,-{\frac {443}{27}},\,\mbox {{\tt ``With sign adjusted:''}},\,141760,\,\mbox {{\tt ``/l.c.d.''}}$}
\mapleinline{inert}{2d}{11, (-130253)/8640, "With sign adjusted:", 130253, "/l.c.d."}{%
$11,\,-{\frac {130253}{8640}},\,\mbox {{\tt ``With sign adjusted:''}},\,130253,\,\mbox {{\tt ``/l.c.d.''}}$}
\mapleinline{inert}{2d}{12, -18, "With sign adjusted:", 155520, "/l.c.d."}{%
$12,\,-18,\,\mbox {{\tt ``With sign adjusted:''}},\,155520,\,\mbox {{\tt ``/l.c.d.''}}$}
\mapleinline{inert}{2d}{13, (-120781)/8640, "With sign adjusted:", 120781, "/l.c.d."}{%
$13,\,-{\frac {120781}{8640}},\,\mbox {{\tt ``With sign adjusted:''}},\,120781,\,\mbox {{\tt ``/l.c.d.''}}$}
\mapleinline{inert}{2d}{14, (-2444)/135, "With sign adjusted:", 156416, "/l.c.d."}{%
$14,\,-{\frac {2444}{135}},\,\mbox {{\tt ``With sign adjusted:''}},\,156416,\,\mbox {{\tt ``/l.c.d.''}}$}
\mapleinline{inert}{2d}{15, (-1035)/64, "With sign adjusted:", 139725, "/l.c.d."}{%
$15,\,-{\frac {1035}{64}},\,\mbox {{\tt ``With sign adjusted:''}},\,139725,\,\mbox {{\tt ``/l.c.d.''}}$}
\mapleinline{inert}{2d}{16, (-2107)/135, "With sign adjusted:", 134848, "/l.c.d."}{%
$16,\,-{\frac {2107}{135}},\,\mbox {{\tt ``With sign adjusted:''}},\,134848,\,\mbox {{\tt ``/l.c.d.''}}$}
\mapleinline{inert}{2d}{17, (-25705)/1728, "With sign adjusted:", 128525, "/l.c.d."}{%
$17,\,-{\frac {25705}{1728}},\,\mbox {{\tt ``With sign adjusted:''}},\,128525,\,\mbox {{\tt ``/l.c.d.''}}$}
\mapleinline{inert}{2d}{18, (-92)/5, "With sign adjusted:", 158976, "/l.c.d."}{%
$18,\,-{\frac {92}{5}},\,\mbox {{\tt ``With sign adjusted:''}},\,158976,\,\mbox {{\tt ``/l.c.d.''}}$}
\mapleinline{inert}{2d}{19, (-129421)/8640, "With sign adjusted:", 129421, "/l.c.d."}{%
$19,\,-{\frac {129421}{8640}},\,\mbox {{\tt ``With sign adjusted:''}},\,129421,\,\mbox {{\tt ``/l.c.d.''}}$}
\mapleinline{inert}{2d}{20, (-478)/27, "With sign adjusted:", 152960, "/l.c.d."}{%
$20,\,-{\frac {478}{27}},\,\mbox {{\tt ``With sign adjusted:''}},\,152960,\,\mbox {{\tt ``/l.c.d.''}}$}
\mapleinline{inert}{2d}{21, (-4599)/320, "With sign adjusted:", 124173, "/l.c.d."}{%
$21,\,-{\frac {4599}{320}},\,\mbox {{\tt ``With sign adjusted:''}},\,124173,\,\mbox {{\tt ``/l.c.d.''}}$}
\mapleinline{inert}{2d}{22, (-443)/27, "With sign adjusted:", 141760, "/l.c.d."}{%
$22,\,-{\frac {443}{27}},\,\mbox {{\tt ``With sign adjusted:''}},\,141760,\,\mbox {{\tt ``/l.c.d.''}}$}
\mapleinline{inert}{2d}{23, (-140621)/8640, "With sign adjusted:", 140621, "/l.c.d."}{%
$23,\,-{\frac {140621}{8640}},\,\mbox {{\tt ``With sign adjusted:''}},\,140621,\,\mbox {{\tt ``/l.c.d.''}}$}
\mapleinline{inert}{2d}{24, (-92)/5, "With sign adjusted:", 158976, "/l.c.d."}{%
$24,\,-{\frac {92}{5}},\,\mbox {{\tt ``With sign adjusted:''}},\,158976,\,\mbox {{\tt ``/l.c.d.''}}$}
\mapleinline{inert}{2d}{25, (-23465)/1728, "With sign adjusted:", 117325, "/l.c.d."}{%
$25,\,-{\frac {23465}{1728}},\,\mbox {{\tt ``With sign adjusted:''}},\,117325,\,\mbox {{\tt ``/l.c.d.''}}$}
\mapleinline{inert}{2d}{26, (-2282)/135, "With sign adjusted:", 146048, "/l.c.d."}{%
$26,\,-{\frac {2282}{135}},\,\mbox {{\tt ``With sign adjusted:''}},\,146048,\,\mbox {{\tt ``/l.c.d.''}}$}
\mapleinline{inert}{2d}{27, (-1035)/64, "With sign adjusted:", 139725, "/l.c.d."}{%
$27,\,-{\frac {1035}{64}},\,\mbox {{\tt ``With sign adjusted:''}},\,139725,\,\mbox {{\tt ``/l.c.d.''}}$}
\mapleinline{inert}{2d}{28, (-2269)/135, "With sign adjusted:", 145216, "/l.c.d."}{%
$28,\,-{\frac {2269}{135}},\,\mbox {{\tt ``With sign adjusted:''}},\,145216,\,\mbox {{\tt ``/l.c.d.''}}$}
\mapleinline{inert}{2d}{29, (-131981)/8640, "With sign adjusted:", 131981, "/l.c.d."}{%
$29,\,-{\frac {131981}{8640}},\,\mbox {{\tt ``With sign adjusted:''}},\,131981,\,\mbox {{\tt ``/l.c.d.''}}$}
\mapleinline{inert}{2d}{30, -18, "With sign adjusted:", 155520, "/l.c.d."}{%
$30,\,-18,\,\mbox {{\tt ``With sign adjusted:''}},\,155520,\,\mbox {{\tt ``/l.c.d.''}}$}
\mapleinline{inert}{2d}{31, (-119053)/8640, -1, "With sign adjusted:", 119053, "/l.c.d."}{%
$31,\,-{\frac {119053}{8640}},\,-1,\,\mbox {{\tt ``With sign adjusted:''}},\,119053,\,\mbox {{\tt ``/l.c.d.''}}$}
\mapleinline{inert}{2d}{33, (-4983)/320, 1, "With sign adjusted:", 134541, "/l.c.d."}{%
$33,\,-{\frac {4983}{320}},\,1,\,\mbox {{\tt ``With sign adjusted:''}},\,134541,\,\mbox {{\tt ``/l.c.d.''}}$}
\mapleinline{inert}{2d}{35, (-27433)/1728, -1, "With sign adjusted:", 137165, "/l.c.d."}{%
$35,\,-{\frac {27433}{1728}},\,-1,\,\mbox {{\tt ``With sign adjusted:''}},\,137165,\,\mbox {{\tt ``/l.c.d.''}}$}
\mapleinline{inert}{2d}{37, (-23465)/1728, 1, "With sign adjusted:", 117325, "/l.c.d."}{%
$37,\,-{\frac {23465}{1728}},\,1,\,\mbox {{\tt ``With sign adjusted:''}},\,117325,\,\mbox {{\tt ``/l.c.d.''}}$}
\mapleinline{inert}{2d}{39, (-5303)/320, -1, "With sign adjusted:", 143181, "/l.c.d."}{%
$39,\,-{\frac {5303}{320}},\,-1,\,\mbox {{\tt ``With sign adjusted:''}},\,143181,\,\mbox {{\tt ``/l.c.d.''}}$}
\mapleinline{inert}{2d}{41, (-121613)/8640, 1, "With sign adjusted:", 121613, "/l.c.d."}{%
$41,\,-{\frac {121613}{8640}},\,1,\,\mbox {{\tt ``With sign adjusted:''}},\,121613,\,\mbox {{\tt ``/l.c.d.''}}$}
\mapleinline{inert}{2d}{43, (-129421)/8640, -1, "With sign adjusted:", 129421, "/l.c.d."}{%
$43,\,-{\frac {129421}{8640}},\,-1,\,\mbox {{\tt ``With sign adjusted:''}},\,129421,\,\mbox {{\tt ``/l.c.d.''}}$}
\mapleinline{inert}{2d}{45, (-971)/64, 1, "With sign adjusted:", 131085, "/l.c.d."}{%
$45,\,-{\frac {971}{64}},\,1,\,\mbox {{\tt ``With sign adjusted:''}},\,131085,\,\mbox {{\tt ``/l.c.d.''}}$}
\mapleinline{inert}{2d}{47, (-27433)/1728, -1, "With sign adjusted:", 137165, "/l.c.d."}{%
$47,\,-{\frac {27433}{1728}},\,-1,\,\mbox {{\tt ``With sign adjusted:''}},\,137165,\,\mbox {{\tt ``/l.c.d.''}}$}
\mapleinline{inert}{2d}{49, (-120781)/8640, 1, "With sign adjusted:", 120781, "/l.c.d."}{%
$49,\,-{\frac {120781}{8640}},\,1,\,\mbox {{\tt ``With sign adjusted:''}},\,120781,\,\mbox {{\tt ``/l.c.d.''}}$}
\mapleinline{inert}{2d}{51, (-4919)/320, -1, "With sign adjusted:", 132813, "/l.c.d."}{%
$51,\,-{\frac {4919}{320}},\,-1,\,\mbox {{\tt ``With sign adjusted:''}},\,132813,\,\mbox {{\tt ``/l.c.d.''}}$}
\mapleinline{inert}{2d}{53, (-131981)/8640, 1, "With sign adjusted:", 131981, "/l.c.d."}{%
$53,\,-{\frac {131981}{8640}},\,1,\,\mbox {{\tt ``With sign adjusted:''}},\,131981,\,\mbox {{\tt ``/l.c.d.''}}$}
\mapleinline{inert}{2d}{55, (-25193)/1728, -1, "With sign adjusted:", 125965, "/l.c.d."}{%
$55,\,-{\frac {25193}{1728}},\,-1,\,\mbox {{\tt ``With sign adjusted:''}},\,125965,\,\mbox {{\tt ``/l.c.d.''}}$}
\mapleinline{inert}{2d}{57, (-971)/64, 1, "With sign adjusted:", 131085, "/l.c.d."}{%
$57,\,-{\frac {971}{64}},\,1,\,\mbox {{\tt ``With sign adjusted:''}},\,131085,\,\mbox {{\tt ``/l.c.d.''}}$}
\mapleinline{inert}{2d}{59, (-140621)/8640, -1, "With sign adjusted:", 140621, "/l.c.d."}{%
$59,\,-{\frac {140621}{8640}},\,-1,\,\mbox {{\tt ``With sign adjusted:''}},\,140621,\,\mbox {{\tt ``/l.c.d.''}}$}
\mapleinline{inert}{2d}{"Constant terms completed."}{%
$\mbox {{\tt ``Constant terms completed.''}}$}

\end{maplelatex}
Now, the linear terms.  First print all linear coefficients up to the presumed period "stepsize".  Then analyze for period and print the difference (at step "stepsize") if they are not repeating.\begin{mapleinput}
\mapleinline{active}{1d}{stepsize:=6; lcd:=144;
for r from 1 to stepsize do
  print(r, sc[1,r], "equals", sc[1,r]*lcd, "/l.c.d."); 
od: 
for r from stepsize+1 to p do 
  stepdifference:=sc[1,r]-sc[1,r-stepsize]:
  if( stepdifference<\TEXTsymbol{>}0 ) then print(r,sc[1,r],stepdifference): fi:
od:
print("Linear coefficients completed."); }{}
\end{mapleinput}
\mapleresult
\begin{maplelatex}
\mapleinline{inert}{2d}{stepsize := 6}{%
\[
{\it stepsize}\, := \,6
\]
}
\mapleinline{inert}{2d}{lcd := 144}{%
\[
{\it lcd}\, := \,144
\]
}
\mapleinline{inert}{2d}{1, 2831/144, "equals", 2831, "/l.c.d."}{%
$1,\,{\frac {2831}{144}},\,{\it ``equals''},\,2831,\,\mbox {{\tt ``/l.c.d.''}}$}
\mapleinline{inert}{2d}{2, 61/3, "equals", 2928, "/l.c.d."}{%
$2,\,{\frac {61}{3}},\,{\it ``equals''},\,2928,\,\mbox {{\tt ``/l.c.d.''}}$}
\mapleinline{inert}{2d}{3, 949/48, "equals", 2847, "/l.c.d."}{%
$3,\,{\frac {949}{48}},\,{\it ``equals''},\,2847,\,\mbox {{\tt ``/l.c.d.''}}$}
\mapleinline{inert}{2d}{4, 182/9, "equals", 2912, "/l.c.d."}{%
$4,\,{\frac {182}{9}},\,{\it ``equals''},\,2912,\,\mbox {{\tt ``/l.c.d.''}}$}
\mapleinline{inert}{2d}{5, 949/48, "equals", 2847, "/l.c.d."}{%
$5,\,{\frac {949}{48}},\,{\it ``equals''},\,2847,\,\mbox {{\tt ``/l.c.d.''}}$}
\mapleinline{inert}{2d}{6, 61/3, "equals", 2928, "/l.c.d."}{%
$6,\,{\frac {61}{3}},\,{\it ``equals''},\,2928,\,\mbox {{\tt ``/l.c.d.''}}$}
\mapleinline{inert}{2d}{"Linear coefficients completed."}{%
$\mbox {{\tt ``Linear coefficients completed.''}}$}

\end{maplelatex}
The quadratic terms.  First print all quadratic coefficients up to the presumed period "stepsize".  Then analyze for period and print the difference (at step "stepsize") if they are not repeating.\begin{mapleinput}
\mapleinline{active}{1d}{stepsize:=2; lcd:=1440;
for r from 1 to stepsize do
  print(r, sc[2,r], "With sign adjusted:", -sc[2,r]*lcd, "/l.c.d."); 
od: 
for r from stepsize+1 to p do 
  stepdifference:=sc[2,r]-sc[2,r-stepsize]:
  if( stepdifference<\TEXTsymbol{>}0 ) then print(r,sc[2,r],stepdifference): fi:
od:
print("Quadratic coefficients completed.");}{}
\end{mapleinput}
\mapleresult
\begin{maplelatex}
\mapleinline{inert}{2d}{stepsize := 2}{%
\[
{\it stepsize}\, := \,2
\]
}
\mapleinline{inert}{2d}{lcd := 1440}{%
\[
{\it lcd}\, := \,1440
\]
}
\mapleinline{inert}{2d}{1, (-11933)/1440, "With sign adjusted:", 11933, "/l.c.d."}{%
$1,\,-{\frac {11933}{1440}},\,\mbox {{\tt ``With sign adjusted:''}},\,11933,\,\mbox {{\tt ``/l.c.d.''}}$}
\mapleinline{inert}{2d}{2, (-5989)/720, "With sign adjusted:", 11978, "/l.c.d."}{%
$2,\,-{\frac {5989}{720}},\,\mbox {{\tt ``With sign adjusted:''}},\,11978,\,\mbox {{\tt ``/l.c.d.''}}$}
\mapleinline{inert}{2d}{"Quadratic coefficients completed."}{%
$\mbox {{\tt ``Quadratic coefficients completed.''}}$}

\end{maplelatex}
\begin{mapleinput}
\mapleinline{active}{1d}{}{}
\end{mapleinput}\end{document}
%% End of Maple 9.00 Output