All the signature papers shall be filed in the office of the City Administrator as one instrument. Within five days after the filing of the petition, the City Administrator shall ascertain by examination the number of registered voters whose signatures are appended thereto and whether this number is at least fifty. If he finds the petition insufficient or irregular, he shall at once notify one or more of the committee of sponsors of that fact, certifying the reasons for his findings. The committee shall then be given 30 days in which to file additional signature papers and to correct the petition in all other particulars. If at the end of that period the petition is found to be still insufficient or irregular, the Administrator shall file it in his office and shall notify each member of the committee of that fact. The final finding of the insufficiency or irregularity of a petition shall not prejudice the filing of a new petition for the same purpose, nor shall it prevent the Council from referring the ordinance to the registered voters at the next regular or any special election at its option.