Newbie question about eigenvalues calculating

Dear list! I recently installed Maxima for my university studying. I 
study S-splines and have to calculate optimal parameters for them. 
Here's description of the task.
A0: 
matrix([S5,S6,S7,S8,S9],[S6,S7,S8,S9,S10],[S7,S8,S9,S10,S11],[S8,S9,S10,S11,S12],[S9,S10,S11,S12,S13]);
A1: 
matrix([S10,S11,S12,S13,S14],[S11,S12,S13,S14,S15],[S12,S13,S14,S15,S16],[S13,S14,S15,S16,S17],[S14,S15,S16,S17,S18]);
where Si: sum(k^i,k,0,M); and k is a range from 0 to some K; M is a 
number.
B0: 
matrix([1,m,m^2,m^3,m^4],[0,1,2*m,3*m^2,4*m^3],[0,0,1,3*m,6*m^2],[0,0,0,1,4*m],[0,0,0,0,1]);
B1: 
matrix([m^5,m^6,m^7,m^8,m^9],[5*m^4,6*m^5,7*m^6,8*m^7,9*m^8],[10*m^3,15*m^4,21*m^5,28*m^6,36*m^7],[10*m^2,20*m^3,35*m^4,56*m^5,84*m^6],[5*m,15*m^2,35*m^3,70*m^4,126*m^5]); 
where m is a number.
Matrix U is B0 - B1.(invert(A1)).A0;
The task is to calculate the eigenvalues of U. I need to do it with 
different m and M to find out the best couple. The problem is: I can't 
do it. When I'm trying eigenvalues(U); Maxima is calculating but it 
takes so long time and I didn't saw results yet even when it's been 
running all night. I was trying to calculate eigenvalues of A0 for 
example but received the following error: solve is unable to find the 
roots of the characteristic polynomial. Is it too big or am I doing 
something wrong?
Thanks for Re:!

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Hiisi.
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