We present a near-infrared (NIR) spectrum of WISE J1042+1641, an extremely red dust-obscured galaxy (DOG), which has been observed with the LIRIS on the 4.2m William Hershel Telescope. This object was selected as a hyper-luminous DOG candidate at z ~ 2 by combining the optical and IR photometric data based on the SDSS and WISE, although its redshift had not yet been confirmed. Based on the LIRIS observation, we confirmed its redshift of 2.521 and total IR luminosity of log(L_IR/L_sun) = 14.57, which satisfies the criterion for an extremely luminous IR galaxy (ELIRG). Moreover, we indicate that this object seems to have an extremely massive black hole with M_BH = 10^10.92 M_sun based on the broad Halpha line: the host stellar mass is derived as M_star = 10^13.55 M_sun by a fit of the spectral energy distribution. Very recently, it has been reported that this object is an anomalous gravitationally lensed quasar based on near-IR high-resolution imaging data obtained with the Hubble Space Telescope. Its magnification factor has also been estimated with some uncertainty (i.e., mu = 53-122). We investigate the ratio of the black hole to galaxy mass, which is less strongly affected by a lensing magnification factor, instead of the absolute values of the luminosities and masses. We find that the M_BH/M_star ratio (i.e., 0.0140-0.0204) is significantly higher than the local relation, following a sequence of unobscured quasars instead of obscured objects (e.g., submillimeter galaxies) at the same redshift. Moreover, the LIRIS spectrum shows strongly blueshifted oxygen lines with an outflowing velocity of ~ 1100 km/s, and our Swift X-ray observation also supports that this source is an absorbed AGN with an intrinsic column density of N_H = 4.9 x 10^23 cm^-2. These results imply that WISE J1042+1641 is in a blow-out phase at the end of the buried rapid black hole growth.
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