Upon proof being filed of the publication of such notice and of such personal service where required, the court, at the time and place therein fixed or to which the hearing may be adjourned, shall proceed to hear the allegations and proofs of all persons interested which touch the matters committed to it, and it shall regulate the order of proof as it may deem best. The testimony taken by it shall be under oath. The court shall determine the truth of the matters alleged and set forth in the petition and also the compensation to be paid to such owner for the lands, rights-of-way, or other rights or easements in lands to be appropriated. In the event that the petitioner has theretofore taken possession of such lands, rights-of-way, or other rights or easements in lands, the value thereof shall be determined without considering the value of any improvements that may have been constructed by such corporation and as of the date when such corporation took possession. The court shall file among its records its findings in writing and shall give notice to the petitioner that its findings have been filed. The petitioner shall cause a notice to be published in one or more newspapers of general circulation in the state of Colorado once a week for two weeks, setting forth that the findings of the court have been filed and stating the amount of the compensation fixed by the court. If the owner has appeared in said proceeding by attorney, a copy of said notice shall be served prior to the last publication of said notice upon the attorney so appearing.