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tokens: those integrated orbits. Both these quantities correlate with age, with OCs younger than 300 Myr being all contained within 180 pc of the plane, while half the older clusters have orbits that extend beyond this limit. The oldest OC in our sample is NGC 2682, one of the oldest known open clusters, and its orbit strays more than 400 pc from the Galactic plane. We also computed the eccentricity of each orbit ( where r p and r a are the perigalacticon and apogalacticon of the orbit), and found no apparent correlation of eccentricity with age (bottom panel of Fig. 12 ). The orbital parameters of the integrated orbits are listed in Table 3 . 6 Discussion The two-million-star TGAS sample allows us to identify members and derive mean parallaxes in clusters located further than 1000 pc from us, thus enabling studies of the Galactic disk on a larger scale than the works based on the results of the H IPPARCOS catalogue (e.g. Robichon et al. 1999 ; Bouy Alves 2015 ), which is severely incomplete beyond 100 pc and for which the relative parallax error reaches 50% at 350 pc. The distribution of OCs identified in this paper is shown in Fig. 13 , along with the schematic location of the spiral arms of the Milky Way in the model of Reid et al. (2014) . We remark that almost all OCs in this study are located in the inter-arm region. In order to trace the spiral structure of the thin disk, our sample would require a significant number of objects younger than 20 Myr (log t 7.3), as clusters drift away from their birthplace over this timescale (see e.g. Dias Lépine 2005 ). These young clusters and associations are often sparsely populated and/or embedded in their progenitor molecular cloud (thus requiring the use of infrared photometry). Due to the magnitude limits of the TGAS solution, even nearby clusters such as Chamaeleon I (2 Myr old, 160 pc from us, Whittet et al. 1997 ) are not present in the catalogue. Hints of objects such as IC 2395 (6 Myr, 800 pc Clariá et al. 2003 ) can be seen, but not with a sufficient number of stars for our method to establish secure membership. Another common tracer of the spiral structure of the disk are the so-called OB associations, which are even sparser groups of bright, short-lived blue stars, whose identification requires the use of multi-band photometry (and ideally spectroscopy). Such a search is well beyond the scope of this paper, aimed at identifying stellar clusters from astrometric data. Fig. 13 Position of the OCs studied in this paper in Galactic rectangular XY Z coordinates. Black dots: OCs from this study with relative parallax errors under 50% (considering an additional 0.3 mas calibration error for all OCs). Crosses: OCs from this study with relative parallax error over 50%. Open symbols: OCs from Gaia Collaboration (2017) . The spiral arms are traced according to the model of Reid et al. (2014) . Out of the 128 OCs for which we derived mean astrometric parameters, 67 have mean proper motions obtained from