['Ex 37 C4 0-0-3-0', C4(1,1,1,0), 23.353, 46.532, 40.812, 40, 13, 24, 6, 7, 13]

***************************************
SOLUTION TO GIT PROBLEM: NONSTABLE LOCI
***************************************
Group: C4 RepresentationC4(1,1,1,0)
Set of maximal non-stable states:
(1) 1-PS = (1, 0, 0, 0) yields a state with 27 characters
Maximal nonstable state={(0, 0, 0, 1), (0, 0, 1, 0), (0, -1, 1, 1), (0, 0, 0, -1), (1, 0, 1, -1), (1, 0, 1, 1), (0, 1, 0, 0), (1, 1, -1, 0), (1, -1, 0, -1), (0, 1, -1, -1), (1, 0, 0, 0), (1, -1, 0, 1), (1, -1, 1, 0), (0, 1, -1, 1), (0, 1, 1, -1), (0, 1, 1, 1), (0, -1, -1, -1), (0, -1, 0, 0), (0, 0, -1, 0), (0, -1, -1, 1), (1, 0, -1, -1), (1, -1, -1, 0), (1, 1, 1, 0), (1, 0, -1, 1), (1, 1, 0, -1), (1, 1, 0, 1), (0, -1, 1, -1)}
(2) 1-PS = (1, 1/2, 1/2, 0) yields a state with 24 characters
Maximal nonstable state={(0, 0, 0, 1), (0, 0, 1, 0), (0, -1, 1, 1), (0, 0, 0, -1), (1, 0, 1, -1), (1, 0, 1, 1), (0, 1, 0, 0), (1, 1, -1, 0), (-1, 1, 1, 0), (1, -1, 0, -1), (0, 1, -1, -1), (1, 0, 0, 0), (1, -1, 0, 1), (1, -1, 1, 0), (0, 1, -1, 1), (0, 1, 1, -1), (0, 1, 1, 1), (1, 0, -1, -1), (1, -1, -1, 0), (1, 1, 1, 0), (1, 0, -1, 1), (1, 1, 0, -1), (1, 1, 0, 1), (0, -1, 1, -1)}
(3) 1-PS = (1, 1/2, 1/2, 1/2) yields a state with 23 characters
Maximal nonstable state={(0, 0, 0, 1), (0, 0, 1, 0), (0, -1, 1, 1), (1, 0, 1, -1), (1, 0, 1, 1), (-1, 0, 1, 1), (0, 1, 0, 0), (1, 1, -1, 0), (-1, 1, 1, 0), (-1, 1, 0, 1), (1, -1, 0, -1), (1, 0, 0, 0), (1, -1, 0, 1), (1, -1, 1, 0), (0, 1, -1, 1), (0, 1, 1, -1), (0, 1, 1, 1), (1, 0, -1, -1), (1, -1, -1, 0), (1, 1, 1, 0), (1, 0, -1, 1), (1, 1, 0, -1), (1, 1, 0, 1)}
(4) 1-PS = (1, 1, 1, 0) yields a state with 27 characters
Maximal nonstable state={(0, 0, 0, 1), (0, 0, 1, 0), (0, -1, 1, 1), (-1, 0, 1, -1), (0, 0, 0, -1), (1, 0, 1, -1), (1, 0, 1, 1), (-1, 0, 1, 1), (0, 1, 0, 0), (1, 1, -1, 0), (-1, 1, 1, 0), (-1, 1, 0, -1), (1, -1, 0, -1), (-1, 1, 0, 1), (0, 1, -1, -1), (1, 0, 0, 0), (1, -1, 0, 1), (1, -1, 1, 0), (0, 1, -1, 1), (0, 1, 1, -1), (0, 1, 1, 1), (1, 0, -1, -1), (1, 1, 1, 0), (1, 0, -1, 1), (1, 1, 0, -1), (1, 1, 0, 1), (0, -1, 1, -1)}
(5) 1-PS = (1, 2/3, 1/3, 1/3) yields a state with 23 characters
Maximal nonstable state={(0, 0, 0, 1), (0, 0, 1, 0), (0, -1, 1, 1), (1, 0, 1, -1), (1, 0, 1, 1), (0, 1, 0, 0), (1, 1, -1, 0), (-1, 1, 1, 0), (-1, 1, 0, 1), (1, -1, 0, -1), (0, 1, -1, -1), (1, 0, 0, 0), (1, -1, 0, 1), (1, -1, 1, 0), (0, 1, -1, 1), (0, 1, 1, -1), (0, 1, 1, 1), (1, 0, -1, -1), (1, -1, -1, 0), (1, 1, 1, 0), (1, 0, -1, 1), (1, 1, 0, -1), (1, 1, 0, 1)}
(6) 1-PS = (1, 1, 0, 0) yields a state with 26 characters
Maximal nonstable state={(0, 0, 0, 1), (0, 0, 1, 0), (0, 0, 0, -1), (1, 0, 1, -1), (1, 0, 1, 1), (0, 1, 0, 0), (1, 1, -1, 0), (-1, 1, 1, 0), (-1, 1, 0, -1), (1, -1, 0, -1), (-1, 1, 0, 1), (0, 1, -1, -1), (1, 0, 0, 0), (1, -1, 0, 1), (1, -1, 1, 0), (0, 1, -1, 1), (0, 1, 1, -1), (0, 1, 1, 1), (0, 0, -1, 0), (1, 0, -1, -1), (1, -1, -1, 0), (1, 1, 1, 0), (1, 0, -1, 1), (1, 1, 0, -1), (-1, 1, -1, 0), (1, 1, 0, 1)}


**************************************
SOLUTION TO GIT PROBLEM: UNSTABLE LOCI
**************************************
Group: C4 RepresentationC4(1,1,1,0)
Set of maximal unstable states:
(1) 1-PS = (1, 3/5, 1/5, 1/5) yields a state with 20 characters
Maximal unstable state={(0, 0, 0, 1), (0, 0, 1, 0), (1, 0, 1, -1), (1, 0, 1, 1), (0, 1, 0, 0), (1, 1, -1, 0), (1, -1, 0, -1), (0, 1, -1, -1), (1, 0, 0, 0), (1, -1, 0, 1), (0, 1, -1, 1), (1, -1, 1, 0), (0, 1, 1, -1), (0, 1, 1, 1), (1, 0, -1, -1), (1, -1, -1, 0), (1, 1, 1, 0), (1, 0, -1, 1), (1, 1, 0, -1), (1, 1, 0, 1)}
(2) 1-PS = (1, 3/5, 3/5, 1/5) yields a state with 20 characters
Maximal unstable state={(0, 0, 0, 1), (0, 0, 1, 0), (1, 0, 1, -1), (0, -1, 1, 1), (1, 0, 1, 1), (0, 1, 0, 0), (1, 1, -1, 0), (-1, 1, 1, 0), (1, -1, 0, -1), (1, 0, 0, 0), (1, -1, 0, 1), (0, 1, -1, 1), (1, -1, 1, 0), (0, 1, 1, -1), (0, 1, 1, 1), (1, 0, -1, -1), (1, 1, 1, 0), (1, 0, -1, 1), (1, 1, 0, -1), (1, 1, 0, 1)}
(3) 1-PS = (1, 5/7, 3/7, 3/7) yields a state with 20 characters
Maximal unstable state={(0, 0, 0, 1), (0, 0, 1, 0), (1, 0, 1, -1), (0, -1, 1, 1), (1, 0, 1, 1), (0, 1, 0, 0), (1, 1, -1, 0), (-1, 1, 1, 0), (-1, 1, 0, 1), (1, 0, 0, 0), (1, -1, 0, 1), (0, 1, -1, 1), (1, -1, 1, 0), (0, 1, 1, -1), (0, 1, 1, 1), (1, 0, -1, -1), (1, 1, 1, 0), (1, 0, -1, 1), (1, 1, 0, -1), (1, 1, 0, 1)}
(4) 1-PS = (1, 1/3, 1/3, 1/3) yields a state with 20 characters
Maximal unstable state={(0, 0, 0, 1), (0, 0, 1, 0), (1, 0, 1, -1), (0, -1, 1, 1), (1, 0, 1, 1), (0, 1, 0, 0), (1, 1, -1, 0), (1, -1, 0, -1), (1, 0, 0, 0), (1, -1, 0, 1), (0, 1, -1, 1), (1, -1, 1, 0), (0, 1, 1, -1), (0, 1, 1, 1), (1, 0, -1, -1), (1, -1, -1, 0), (1, 1, 1, 0), (1, 0, -1, 1), (1, 1, 0, -1), (1, 1, 0, 1)}
(5) 1-PS = (1, 5/7, 3/7, 1/7) yields a state with 20 characters
Maximal unstable state={(0, 0, 0, 1), (0, 0, 1, 0), (1, 0, 1, -1), (1, 0, 1, 1), (0, 1, 0, 0), (1, 1, -1, 0), (-1, 1, 1, 0), (1, -1, 0, -1), (0, 1, -1, -1), (1, 0, 0, 0), (1, -1, 0, 1), (0, 1, -1, 1), (1, -1, 1, 0), (0, 1, 1, -1), (0, 1, 1, 1), (1, 0, -1, -1), (1, 1, 1, 0), (1, 0, -1, 1), (1, 1, 0, -1), (1, 1, 0, 1)}
(6) 1-PS = (1, 1, 1, 1) yields a state with 20 characters
Maximal unstable state={(0, 0, 0, 1), (0, 0, 1, 0), (1, 0, 1, -1), (0, -1, 1, 1), (1, 0, 1, 1), (-1, 0, 1, 1), (0, 1, 0, 0), (1, 1, -1, 0), (-1, 1, 1, 0), (-1, 1, 0, 1), (1, 0, 0, 0), (1, -1, 0, 1), (0, 1, -1, 1), (1, -1, 1, 0), (0, 1, 1, -1), (0, 1, 1, 1), (1, 1, 1, 0), (1, 0, -1, 1), (1, 1, 0, -1), (1, 1, 0, 1)}
(7) 1-PS = (1, 1, 1/3, 1/3) yields a state with 20 characters
Maximal unstable state={(0, 0, 0, 1), (0, 0, 1, 0), (1, 0, 1, -1), (1, 0, 1, 1), (0, 1, 0, 0), (1, 1, -1, 0), (-1, 1, 1, 0), (-1, 1, 0, 1), (0, 1, -1, -1), (1, 0, 0, 0), (1, -1, 0, 1), (0, 1, -1, 1), (1, -1, 1, 0), (0, 1, 1, -1), (0, 1, 1, 1), (1, 0, -1, -1), (1, 1, 1, 0), (1, 0, -1, 1), (1, 1, 0, -1), (1, 1, 0, 1)}


*************************************************************
SOLUTION TO GIT PROBLEM: STRICTLY POLYSTABLE LOCI
*************************************************************
Group: C4 RepresentationC4(1,1,1,0)
Set of strictly polystable states:
(1) A state with 6 characters
Strictly polystable state={(-1, 1, 1, 0), (-1, 1, 0, 1), (1, -1, 0, -1), (-1, 0, 1, 1), (1, 0, -1, -1), (1, -1, -1, 0)}
(2) A state with 4 characters
Strictly polystable state={(0, 0, -1, 0), (0, 0, 1, 0), (-1, 1, 0, 1), (1, -1, 0, -1)}
(3) A state with 6 characters
Strictly polystable state={(1, -1, 0, -1), (-1, 1, 1, 0), (0, -1, 1, 1), (-1, 1, 0, 1), (0, 1, -1, -1), (1, -1, -1, 0)}
(4) A state with 2 characters
Strictly polystable state={(-1, 1, 0, -1), (1, -1, 0, 1)}
(5) A state with 14 characters
Strictly polystable state={(0, 0, 0, 1), (0, 1, 1, -1), (0, 0, 1, 0), (0, -1, 1, 1), (0, 0, 0, -1), (0, 1, 1, 1), (0, -1, -1, -1), (0, -1, 0, 0), (0, 0, -1, 0), (0, 1, 0, 0), (0, -1, -1, 1), (0, 1, -1, -1), (0, 1, -1, 1), (0, -1, 1, -1)}
(6) A state with 4 characters
Strictly polystable state={(-1, 1, 0, -1), (1, -1, 0, 1), (-1, 0, 1, -1), (1, 0, -1, 1)}
(7) A state with 14 characters
Strictly polystable state={(0, 0, 0, 1), (1, -1, 0, -1), (0, -1, 1, 1), (-1, 0, 1, -1), (0, 0, 0, -1), (-1, 0, 1, 1), (1, 0, -1, -1), (1, 0, -1, 1), (-1, 1, 0, -1), (-1, 1, 0, 1), (0, 1, -1, -1), (1, -1, 0, 1), (0, 1, -1, 1), (0, -1, 1, -1)}
(8) A state with 6 characters
Strictly polystable state={(0, 0, 0, 1), (0, 1, 1, -1), (0, 0, 0, -1), (0, 1, 1, 1), (0, -1, -1, -1), (0, -1, -1, 1)}
(9) A state with 2 characters
Strictly polystable state={(0, 0, 0, 1), (0, 0, 0, -1)}
(10) A state with 4 characters
Strictly polystable state={(0, 0, -1, 0), (0, 1, 0, 0), (0, 0, 1, 0), (0, -1, 0, 0)}
(11) A state with 4 characters
Strictly polystable state={(-1, 0, 1, 1), (1, 0, -1, -1), (0, 1, -1, 1), (0, -1, 1, -1)}
(12) A state with 8 characters
Strictly polystable state={(0, 0, 0, 1), (0, -1, 1, 1), (0, 0, 0, -1), (1, -1, -1, 0), (-1, 1, 1, 0), (0, 1, -1, -1), (0, 1, -1, 1), (0, -1, 1, -1)}
(13) A state with 12 characters
Strictly polystable state={(0, 0, 0, 1), (1, -1, 0, -1), (0, 0, 1, 0), (0, 0, 0, -1), (0, 0, -1, 0), (1, -1, -1, 0), (-1, 1, 1, 0), (-1, 1, 0, -1), (-1, 1, 0, 1), (-1, 1, -1, 0), (1, -1, 0, 1), (1, -1, 1, 0)}