We carried out the energy scan between E(CM) = 58 and 60 GeV. at the T
RISTAN e+ e- collider to search for the possible narrow resonance sugg
ested by the L3 experiment at LEP. The total cross sections are measur
ed for gammagamma, multihadron, e+ e- and mu+ mu- productions at ten e
nergy points covering this energy range almost uniformly. The results
are in good agreement with the Standard Model predictions, and 95% con
fidence level upper limits are set to GAMMA(ee) x BR of the hypothetic
al scalar and tensor resonances.