We present spectroscopic identification of 32 new quasars and luminous galaxies discovered at 5.7 < z < 6.8. This is the second in a series of papers presenting the results of the Subaru High-z Exploration of Low-Luminosity Quasars (SHELLQs) project, which exploits the deep multi-band imaging data produced by the Hyper Suprime-Cam (HSC) Subaru Strategic Program survey. The photometric candidates were selected by a Bayesian probabilistic algorithm, and then observed with spectrographs on the Gran Telescopio Canarias and the Subaru Telescope. Combined with the sample presented in the previous paper, we have now identified 64 HSC sources over about 430 deg2, which include 33 high-z quasars, 14 high-z luminous galaxies, 2 [O III] emitters at z ~ 0.8, and 15 Galactic brown dwarfs. The new quasars have considerably lower luminosity (M1450 ~ -25 to -22 mag) than most of the previously known high-z quasars. Several of these quasars have luminous (> 10^(43) erg/s) and narrow (< 500 km/s) Ly alpha lines, and also a possible mini broad absorption line system of N V 1240 in the composite spectrum, which clearly separate them from typical quasars. On the other hand, the high-z galaxies have extremely high luminosity (M1450 ~ -24 to -22 mag) compared to other galaxies found at similar redshift. With the discovery of these new classes of objects, we are opening up new parameter spaces in the high-z Universe. Further survey observations and follow-up studies of the identified objects, including the construction of the quasar luminosity function at z ~ 6, are ongoing.
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