g~:  39
r: 4


 b =  4 



Example  # 1
-- C~ --
G~ Id: SmallGroup <160, 137>
G~ name: C40.C2^2
GrpPC : G of order 160 = 2^5 * 5
PC-Relations:
    G.1^2 = Id(G), 
    G.2^2 = Id(G), 
    G.3^2 = G.5, 
    G.4^2 = G.5, 
    G.5^2 = Id(G), 
    G.6^5 = Id(G), 
    G.2^G.1 = G.2 * G.5, 
    G.3^G.1 = G.3 * G.5, 
    G.3^G.2 = G.3 * G.4, 
    G.4^G.2 = G.4 * G.5, 
    G.4^G.3 = G.4 * G.5, 
    G.6^G.1 = G.6^4
generating vector: [ G.2 * G.5, G.1 * G.3 * G.5 * G.6, G.1 * G.5 * G.6^4, G.2 * 
G.3 * G.4 * G.5 * G.6^2 ]
signature: [ 2, 2, 2, 40 ]
genus: 39
decomp H^0(K_C~): [ 0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 1, 0, 0, 1, 1, 0, 0, 1, 0, 1, 
1, 0, 1, 1, 1, 1, 0, 2 ]
N~ = dim S^2H^0(K_C~)^G~ = 9
sigma: G.5
branch points: 4
verify (B1): false
verify (B2): false
-- C --
G Id: SmallGroup <80, 39>
G name: D4*D5
GrpPC : H of order 80 = 2^4 * 5
PC-Relations:
    H.1^2 = Id(H), 
    H.2^2 = Id(H), 
    H.3^2 = Id(H), 
    H.4^2 = Id(H), 
    H.5^5 = Id(H), 
    H.3^H.2 = H.3 * H.4, 
    H.5^H.1 = H.5^4
generating vector: [ H.2, H.1 * H.3 * H.5, H.1 * H.5^4, H.2 * H.3 * H.4 * H.5^2 
]
signature: [ 2, 2, 2, 20 ]
genus: 19
decomp H^0(K_C): [ 0, 0, 0, 0, 0, 0, 1, 0, 0, 1, 1, 1, 0, 0, 1, 0, 0, 1, 1, 1 ]
N = dim S^2H^0(K_C)^G = 8
1