newa1p = a1 + 2*d
newb1p = b1
newa3p = (6*a3 - a1*b1*d - b1*d^2)/6
newb3p = (6*b3 - b1^2*d)/6
newa5p = (180*a5 + 30*a3*b1*d + a1^2*b1^2*d - 30*a1*b3*d + 2*a1*b1^2*d^2 - 
     30*b3*d^2 + 3*b1^2*d^3)/180
newb5p = (360*b5 + a1*b1^3*d + 60*b1*b3*d - 4*b1^3*d^2)/360
newc5p = (180*c5 + a1*b1^3*d - 60*b1*b3*d + 6*b1^3*d^2)/180
newd5p = (b1^4*d + 360*d5)/360
newa7p = (7560*a7 + 1260*a5*b1*d - 84*a1*a3*b1^2*d - 2*a1^3*b1^3*d + 
     1260*a3*b3*d + 84*a1^2*b1*b3*d - 1260*a1*c5*d - 84*a3*b1^2*d^2 - 
     6*a1^2*b1^3*d^2 + 168*a1*b1*b3*d^2 - 1260*c5*d^2 - 15*a1*b1^3*d^3 + 
     252*b1*b3*d^3 - 18*b1^3*d^4)/7560
newb7p = (45360*b7 - 2520*a5*b1*d + 294*a1*a3*b1^2*d - a1^3*b1^3*d - 
     5040*a3*b3*d - 252*a1^2*b1*b3*d - 7560*a1*b5*d + 504*a3*b1^2*d^2 - 
     24*a1^2*b1^3*d^2 - 504*a1*b1*b3*d^2 - 7560*b5*d^2 - 39*a1*b1^3*d^3 - 
     756*b1*b3*d^3 + 12*b1^3*d^4)/45360
newc7p = (15120*c7 + 42*a3*b1^3*d + a1^2*b1^4*d - 2520*b3^2*d - 
     2520*b1*c5*d - 12*a1*b1^4*d^2 + 840*b1^2*b3*d^2 - 57*b1^4*d^3 - 
     2520*a1*d*d5 - 2520*d^2*d5)/15120
newd7p = (-84*a3*b1^3*d - 5*a1^2*b1^4*d - 42*a1*b1^2*b3*d + 5040*b3^2*d + 
     2520*b1*b5*d + 5040*b1*c5*d + 18*a1*b1^4*d^2 - 1512*b1^2*b3*d^2 + 
     96*b1^4*d^3 + 15120*d7)/15120
newe7p = (252*a3*b1^3*d - a1^2*b1^4*d - 168*a1*b1^2*b3*d - 2520*b3^2*d - 
     15120*b1*b5*d - 30*a1*b1^4*d^2 - 1008*b1^2*b3*d^2 + 36*b1^4*d^3 + 
     45360*e7)/45360
newf7p = (-21*a3*b1^3*d - a1^2*b1^4*d + 63*a1*b1^2*b3*d - 630*b3^2*d - 
     1260*b1*c5*d - 9*a1*b1^4*d^2 + 378*b1^2*b3*d^2 - 27*b1^4*d^3 + 3780*f7)/
   3780
newg7p = (-(a1*b1^5*d) - 42*b1^3*b3*d + 6*b1^5*d^2 + 2520*b1*d*d5 + 15120*g7)/
   15120
newh7p = (a1*b1^5*d - 6*b1^5*d^2 - 5040*b1*d*d5 + 15120*h7)/15120
newi7p = (-5*a1*b1^5*d + 84*b1^3*b3*d - 12*b1^5*d^2 + 15120*i7)/15120
newj7p = (-(b1^6*d) + 15120*j7)/15120
