We carried out the energy scan between E CM = 58 and 60 GeV at the TRISTAN e + e − collider to search for the possible narrow resonance suggested by the L3 experiment at LEP. The total cross sections are measured for γγ, multihadron, e + e − and μ + μ − production at ten energy points covering this energy range almost uniformly. The results are in good agreement with the Standard Model predictions, and 95% confidence level upper limits are set to Γ ee × BR of the hypothetical scalar and tensor resonances.