w:=(x,y)->x^6+a2*x^4*y^2+a4*x^2*y^4+a6*y^6;

Zio2JEkieEc2IkkieUdGJUYlNiRJKW9wZXJhdG9yR0YlSSZhcnJvd0dGJUYlLCoqJClGJCIiJyIiIkYuKihJI2EyR0YlRi4pRiQiIiVGLilGJiIiI0YuRi4qKEkjYTRHRiVGLilGJEY0Ri4pRiZGMkYuRi4qJkkjYTZHRiVGLilGJkYtRi5GLkYlRiVGJQ==

w(x,y);

LCoqJClJInhHNiIiIiciIiJGKCooSSNhMkdGJkYoKUYlIiIlRigpSSJ5R0YmIiIjRihGKCooSSNhNEdGJkYoKUYlRi9GKClGLkYsRihGKComSSNhNkdGJkYoKUYuRidGKEYo

pol:=w(x,y)-1/4^3*w(x+3*y,x-y);

LDIqJClJInhHNiIiIiciIiJGKCooSSNhMkdGJkYoKUYlIiIlRigpSSJ5R0YmIiIjRihGKCooSSNhNEdGJkYoKUYlRi9GKClGLkYsRihGKComSSNhNkdGJkYoKUYuRidGKEYoKiYjRigiI2tGKCksJkYlRigqJiIiJEYoRi5GKEYoRidGKCEiIioqRjhGKEYqRigpRjtGLEYoKSwmRiVGKEYuRj5GL0YoRj4qKkY4RihGMUYoKUY7Ri9GKClGQkYsRihGPiooRjhGKEY1RigpRkJGJ0YoRj4=

eqs:={seq(coeff(coeff(pol,x,2*k),y,6-2*k)=0,k=0..3),w(1,1)=64};

PCcvLCoiIiJGJUkjYTJHNiJGJUkjYTRHRidGJUkjYTZHRidGJSIjay8sKiomIyIjakYqRiVGKUYlRiUjIiRIKEYqISIiKiYjIiMiKUYqRiVGJkYlRjIqJiMiIipGKkYlRihGJUYyIiIhLywqKiYjIiNMRipGJUYoRiVGJSMiJTo3RipGMkYzRiUqJiMiIzpGKkYlRilGJUYyRjkvLCoqJkY9RiVGJkYlRiUjIiROIkYqRjJGNkYlRkFGMkY5LywqRi5GJSomI0YlRipGJUYmRiVGMiomRkxGJUYoRiVGMiomRkxGJUYpRiVGMkY5

solve(eqs,{a2,a4,a6});

PCUvSSNhNkc2IkYkL0kjYTRHRiUsJiomIiIjIiIiRiRGKyEiIiIjIilGKy9JI2EyR0YlLCYiIz1GLEYkRis=

M:=Matrix(3,3,[[0,1,0],[0,0,1],[-1,1,0]]);

LUknTWF0cml4RzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliRzYiNiMvSSQlaWRHRiciKi85T04i

M^3-M+M^0;

LUknTWF0cml4RzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliRzYiNiMvSSQlaWRHRiciKiM0QXc4

a:=array(1..5,);

PTYiNiM7IiIiIiImRVxbbCZGJkYmIiIjRiYiIiQiIiFGJ0YmIiIlRik=

b:=array(1..5,);

PTYiNiM7IiIiIiImRVxbbCZGJkYnIiIjIiIhIiIkRilGJ0YmIiIlRik=

A:=Matrix(2,5,[[1,1,0,2,1],[5,0,2,2,1]]);

LUknTWF0cml4RzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliRzYiNiMvSSQlaWRHRiciKm9TYlIi

with(LinearAlgebra);

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

NullSpace(A) mod 7;

PCUtJkknVmVjdG9yRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliRzYiNiNJJ2NvbHVtbkdGKTYjL0kkJWlkR0YpIipfQ2tPIi1GJDYjL0YuIiohKXAkcDgtRiQ2Iy9GLiIqcyRlKVEi