We present the results of a 7 mm spectral survey of molecular absorption lines originating in the disk of a z=0.89 spiral galaxy located in front of the quasar PKS 1830-211. [...] A total of 28 different species, plus 8 isotopic variants, were detected toward the south-west absorption region, located about 2 kpc from the center of the z=0.89 galaxy, which therefore has the largest number of detected molecular species of any extragalactic object so far. The results of our rotation diagram analysis show that the rotation temperatures are close to the cosmic microwave background temperature of 5.14 K that we expect to measure at z=0.89, whereas the kinetic temperature is one order of magnitude higher, indicating that the gas is subthermally excited. The molecular fractional abundances are found to be in-between those in typical Galactic diffuse and translucent clouds, and clearly deviate from those observed in the dark cloud TMC 1 or in the Galactic center giant molecular cloud Sgr B2. The isotopic ratios of carbon, nitrogen, oxygen, and silicon deviate significantly from the solar values, which can be linked to the young age of the z=0.89 galaxy and a release of nucleosynthesis products dominated by massive stars. [...] We also report the discovery of several new absorption components, with velocities spanning between -300 and +170 km/s. Finally, the line centroids of several species (e.g., CH3OH, NH3) are found to be significantly offset from the average velocity. If caused by a variation in the proton-to-electron mass ratio mu with redshift, these offsets yield an upper limit |Delta_mu/mu|<4e-6, which takes into account the kinematical noise produced by the velocity dispersion measured from a large number of molecular species.
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