DedekindEta[(3 I)/4] == ((1 + Sqrt[2] - Sqrt[2] 3^(3/4) + Sqrt[3] (-1 + Sqrt[2]) + 2 3^(1/4) (1 + Sqrt[2]))^(1/4) Gamma[1/4])/( 2 2^(1/48) 3^(3/8) (-1 + Sqrt[3])^(1/12) \[Pi]^(3/4)) PSLQ its log, along with every imaginable binomial "factor": DedekindEta[(3 I)/4] == ( Sqrt[1 + 3^(1/4)] (Sqrt[2] + 3^(1/4))^(3/8) (1 + Sqrt[3])^(5/24)Gamma[1/4])/( 2 2^(1/24) 3^(3/8) ((1 + Sqrt[2]) (Sqrt[2] + Sqrt[3]))^(1/4) \[Pi]^(3/4)) Still, the rhs looks disproportionately weird. --rwg