g~:  14
r: 4


 b =  2 



Example  # 1
-- C~ --
G~ Id: SmallGroup <18, 2>
G~ name: C18
GrpPC : G of order 18 = 2 * 3^2
PC-Relations:
    G.1^2 = Id(G), 
    G.2^3 = G.3, 
    G.3^3 = Id(G)
generating vector: [ G.3, G.2 * G.3^2, G.1 * G.2 * G.3, G.1 * G.2 * G.3 ]
signature: [ 3, 9, 18, 18 ]
genus: 14
decomp H^0(K_C~): [ 0, 0, 0, 1, 1, 2, 0, 1, 1, 2, 1, 0, 1, 0, 1, 0, 2, 1 ]
N~ = dim S^2H^0(K_C~)^G~ = 3
sigma: G.1
branch points: 2
verify (B1): true
verify (B2): false
-- C --
G Id: SmallGroup <9, 1>
G name: C9
GrpPC : H of order 9 = 3^2
PC-Relations:
    H.1^3 = H.2
generating vector: [ H.2, H.1 * H.2^2, H.1 * H.2, H.1 * H.2 ]
signature: [ 3, 9, 9, 9 ]
genus: 7
decomp H^0(K_C): [ 0, 0, 1, 0, 1, 1, 1, 1, 2 ]
N = dim S^2H^0(K_C)^G = 2
1


 b =  6 



Example  # 1
-- C~ --
G~ Id: SmallGroup <16, 1>
G~ name: C16
GrpPC : G of order 16 = 2^4
PC-Relations:
    G.1^2 = G.2, 
    G.2^2 = G.3, 
    G.3^2 = G.4
generating vector: [ G.2, G.2, G.1 * G.2, G.1 * G.4 ]
signature: [ 8, 8, 16, 16 ]
genus: 14
decomp H^0(K_C~): [ 0, 0, 0, 1, 1, 2, 1, 2, 0, 0, 1, 0, 1, 1, 2, 2 ]
N~ = dim S^2H^0(K_C~)^G~ = 3
sigma: G.4
branch points: 6
verify (B1): true
verify (B2): false
-- C --
G Id: SmallGroup <8, 1>
G name: C8
GrpPC : H of order 8 = 2^3
PC-Relations:
    H.1^2 = H.2, 
    H.2^2 = H.3
generating vector: [ H.2, H.2, H.1 * H.2, H.1 ]
signature: [ 4, 4, 8, 8 ]
genus: 6
decomp H^0(K_C): [ 0, 0, 1, 1, 0, 1, 1, 2 ]
N = dim S^2H^0(K_C)^G = 2
1