How do you summon a Pharaonic Egregor?

The summon spell Pharaonic Egregor is presented in Major Arcana p11. The element is that of the Egregor’s Arcanum, listed in the Exaltation table on p9. The table lists elements, planets and zodiac months. These are copied almost verbatim from the astrological correspondences proposed by the Golden Dawn (cheat sheet herecolor coded here, secondary correspondences here). I've reproduced and merged both tables below:

ARCANUM EXALTATION EGREGOR DYNASTY
0 Fool Air Unknown
I Magician Mercury Djoser (Zoser) III
II High Priestess Moon Khafre (Chephren) IV
III Empress Venus Netaqerti (Nitocris) VI
IV Emperor Aries Narmer (Menes) I
V Hierophant Taurus Unas V
VI Lovers Gemini Yaqub-Har XVI
VII Chariot Cancer Sheshi XV
VIII Strength Leo Sekhemre II XVII
IX Hermit Virgo Uatchkare I VIII
X Wheel Jupiter Amenemhat I XII
XI Justice Libra Habmerire Khati IX
XII Hanged Man Water Adoniram, a stonemason in Akhet-Aton
XIII Unnamed Scorpio Nephren-Ka, a Selenim
XIV Temperance Sagittarius Uahkare-Khati II X
XV Devil Capricorn Peribsen II
XVI Tower Mars Khendjer XIII
XVII Star Aquarius Sankhkare II XIV
XVIII Moon Pisces Wahankh Intef II XI
XIX Sun Sun Akhenaton XVIII
XX Judgment Fire Menkare VII
XXI The World Unknown

The table doesn't list one Ka-element per Arcanum! Is The Sun’s element Solar-Ka? Is The Unnamed Arcanum’s element Fire-Ka? Is the Star’s element Saturnian-Ka? That doesn’t make sense!

As my own unofficial errata, I'm giving each Arcanum an element that's actually usable. The short easy answer is that Pharaonic Egregor simply uses the summoner's Dominant Ka-element. A longer answer that makes the book's statement make sense would assign a Ka-element to each Arcanum, but after a few tries I've found that it's too much work for too little gain. The Exaltations are easy enough because they're based on correspondences already given by the Golden Dawn, but trying to assign the Major Arcana into a five Ka-element framework is... well, I gave up already. 

Hope you enjoyed!

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