  Breakthrough Listen (BL) is a ten-year initiative to search for signatures of
technologically capable life beyond Earth via radio and optical observations of
the local Universe. A core part of the BL program is a comprehensive survey of
1702 nearby stars at radio wavelengths (1-10 GHz). Here, we report on
observations with the 64-m CSIRO Parkes radio telescope in New South Wales,
Australia, and the 100-m Robert C. Byrd Green Bank radio telescope in West
Virginia, USA. Over 2016 January to 2019 March, a sample of 1138 stars was
observed at Green Bank using the 1.10-1.90 GHz and 1.80-2.80 GHz receivers, and
189 stars were observed with Parkes over 2.60-3.45 GHz. We searched these data
for the presence of engineered signals with Doppler-acceleration drift rates
between -4 to 4 Hz/s. Here, we detail our data analysis techniques and provide
examples of detected events. After excluding events with characteristics
consistent with terrestrial radio interference, we are left with zero
candidates. Given the sensitivity of our observations, we can put an upper
limit on the power of potential radio transmitters at these frequencies at
2x10^12 W, and 9x10^12 W for GBT and Parkes respectively. These observations
constitute the most comprehensive search over 1.10-3.45 GHz for
technosignatures to date. All data products, totalling ~219 TB, are available
for download as part of the first BL data release (DR1), as described in a
companion paper (Lebofsky et. al., 2019)
