(1) Theorem 1.2(b)
   [ok] p=3: relation, surjectivity, b, (1-J)^-1, Jb, w(b,Jb)=al and kappa = -c1-(1+al)/2 for all c1 and all 4 solutions (al,be)
   [ok] p=7: relation, surjectivity, b, (1-J)^-1, Jb, w(b,Jb)=al and kappa = -c1-(1+al)/2 for all c1 and all 8 solutions (al,be)
   [ok] p=11: relation, surjectivity, b, (1-J)^-1, Jb, w(b,Jb)=al and kappa = -c1-(1+al)/2 for all c1 and all 12 solutions (al,be)
   [ok] p=19: relation, surjectivity, b, (1-J)^-1, Jb, w(b,Jb)=al and kappa = -c1-(1+al)/2 for all c1 and all 20 solutions (al,be)
   [ok] p=23: relation, surjectivity, b, (1-J)^-1, Jb, w(b,Jb)=al and kappa = -c1-(1+al)/2 for all c1 and all 24 solutions (al,be)
   [ok] p=31: relation, surjectivity, b, (1-J)^-1, Jb, w(b,Jb)=al and kappa = -c1-(1+al)/2 for all c1 and all 32 solutions (al,be)
   [ok] p=43: relation, surjectivity, b, (1-J)^-1, Jb, w(b,Jb)=al and kappa = -c1-(1+al)/2 for all c1 and all 44 solutions (al,be)
   [ok] p=47: relation, surjectivity, b, (1-J)^-1, Jb, w(b,Jb)=al and kappa = -c1-(1+al)/2 for all c1 and all 48 solutions (al,be)
   [ok] p=59: relation, surjectivity, b, (1-J)^-1, Jb, w(b,Jb)=al and kappa = -c1-(1+al)/2 for all c1 and all 60 solutions (al,be)
   [ok] p=67: relation, surjectivity, b, (1-J)^-1, Jb, w(b,Jb)=al and kappa = -c1-(1+al)/2 for all c1 and all 68 solutions (al,be)
   [ok] p=71: relation, surjectivity, b, (1-J)^-1, Jb, w(b,Jb)=al and kappa = -c1-(1+al)/2 for all c1 and all 72 solutions (al,be)
   [ok] p=79: relation, surjectivity, b, (1-J)^-1, Jb, w(b,Jb)=al and kappa = -c1-(1+al)/2 for all c1 and all 80 solutions (al,be)
   [ok] p=83: relation, surjectivity, b, (1-J)^-1, Jb, w(b,Jb)=al and kappa = -c1-(1+al)/2 for all c1 and all 84 solutions (al,be)
(2) Proposition 6.1
   [ok] p=5: be=2, be^2=-1, IJ = diag(3,2)
   [ok] p=5: [x,u][v,w] = 1 ; [x,u] = t_(3, 0), [v,w] = t_(2, 0)
   [ok] p=5: x,u,v,w generate the group of order 200
   [ok] p=5: J has order 10 and preserves the line z2 = 3: intransitive
   [ok] p=5: kappa = 4 (as stated: 4)
   [ok] p=5: the value does not depend on the lifts
   [ok] p=5: [x,u] = t_(3,0)
   [ok] p=5: w v w^-1 = rho_(4,3)
   [ok] p=5: [v,w] = t_(2,0)
   [ok] p=5: u x u^-1 = t_(3,0)
   [ok] p=5: v = rho_(0,3) = (-1|(0,1)), lift (0,1),0,-1
   [ok] p=5: [x~,u~] = [(3,0),0;1]
   [ok] p=5: v~ w~ = [(0,3),0;J]
   [ok] p=5: w~ v~ = [(3,3),3;J]
   [ok] p=5: [v~,w~] = [(2,0),4;1]
   [ok] p=13: be=5, be^2=-1, IJ = diag(8,5)
   [ok] p=13: [x,u][v,w] = 1 ; [x,u] = t_(6, 0), [v,w] = t_(7, 0)
   [ok] p=13: x,u,v,w generate the group of order 1352
   [ok] p=13: J has order 26 and preserves the line z2 = 7: intransitive
   [ok] p=13: kappa = 3 (as stated: 3)
   [ok] p=13: the value does not depend on the lifts
(3) hypothesis (E) for Q_8
   [ok] for the odd primes below 100: (E) holds for Q_8 exactly when p = 3 mod 4

r2_family.py: 35 checks, 0 failed
