The following section is not a solution, but a possible direction the Zodiac Killer may have taken when constructing the first two lines of the 340 Cipher.
Freemasonry and Rosicrucianism have been suggested as Zodiac influences, with both employing variations of a cipher within their secret society, dating back as far as the 18th century. The Pigpen Cipher is commonly known as the Freemasons Cipher and uses geometric simple substitution to replace letters with symbols. The 340 Cipher is constructed using 63 symbols and could quite possibly have been formulated using a combination or variant of the Pigpen Cipher, alongside any other technique the Zodiac Killer decided to choose. The reasoning behind this is the Zodiac Killer's extensive use of directional arrows, such as the normal, sideward and upside down V's, as well as the forward and backwards L's throughout the 340 Cipher, in a seemingly natural progression from the 408 Cipher.
To find out what is written on the first line of the cipher, it is a question of trial and error, until something exhibits a small glimmer of promise, as well as finding the key, or one of the keys to unlock the mind of this serial killer.
So lets start with something we do know.
He opened up the 408 Cipher with the words 'I like killing people because it is so much fun', and his San Francisco Chronicle Letter with 'I am the murderer of the 2 teenagers last Christmas', but a change was about to occur, when he sent the Debut of Zodiac Letter on August 4th 1969, in that he had now adopted the Zodiac persona, opening his correspondence with the line 'This is the Zodiac speaking'. This was to become his opening phrase in virtually every confirmed letter thereafter, culminating with the Los Angeles Times Letter on March 13th 1971. So let us adopt this known trait and apply it to the opening section of the 340 Cipher, using the first word THIS as the key, to shine some light on a possible solution, albeit, still a theory in its infancy.
The next question would be how are the other symbols arranged within the Pigpen design, if indeed this is the answer at all.