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We report a search for time variations of the solar $^8$B neutrino flux using5,804 live days of Super-Kamiokande data collected between May 31, 1996, andMay 30, 2018. Super-Kamiokande measured the precise time of each solar neutrinointeraction over 22 calendar years to search for solar neutrino fluxmodulations with unprecedented precision. Periodic modulations are searched forin a data set comprised of five-day interval solar neutrino flux measurementswith a maximum likelihood method. We also applied the Lomb-Scargle method tothis data set to compare it with previous reports. The only significantmodulation found is due to the elliptic orbit of the Earth around the Sun. Theobserved modulation is consistent with astronomical data: we measured aneccentricity of (1.53$\pm$0.35)\,\%, and a perihelion shift is($-$1.5$\pm$13.5)\,days.

Search for Periodic Time Variations of the Solar $^8$B Neutrino Flux Between 1996 and 2018 in Super-Kamiokande