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The last Greek lettered star in Aquarius is ω, completely immersed in the water gushing out from the Urn:

Gb2-32 Gb2-33 Gb2-34 (60) Gb2-35 Gb3-1 (291)
JANUARY 2 3 4 5 (370) 6
Simmah (351.7) φ Aquarii (352.0), ψ Aquarii (352.4), χ Aquarii (352.6), γ Tucanae, φ Gruis (352.8) ο Cephei (353.3), Kerb (353.6) κ Piscium (354.2), θ Piscium (354.4), υ Pegasi (354.9) ο Gruis, Snowball Nebula (355.0)
March 7 8 (432) 9 (68) 10 11
'February 8 9 (40) 10 11 12 (408)
"January 25 26 27 (392) 28 29 (*314)
NAKSHATRA DATES:
JULY 4 5 (186) 6 7 8
Al Zubrah-9 / Purva Phalguni-11 φ Leonis (170.0), Alula (170.5), Labrum (170.6) σ Leonis (171.1), λ Crateris (171.6), ι Leonis, ε Crateris (171.9) γ Crateris, π Centauri (172.0), κ Crateris (172.5), τ Leonis (172.8)

Gredi

ο¹ Centauri (173.8)
Zosma (169.2), COXA (169.4)
September 6 7 (250) 8 9 10
'August 10 (222) 11 12 (*144) 13 14
"July 27 28 29 (210) 30 31
Gb3-2 (63) Gb3-3 Gb3-4 Gb3-5 (295) Gb3-6
JANUARY 7 8 (*293) 9 10 (375) 11
no star listed (356) ι Phoenicis (357.3), ι Piscium (357.4), λ Andromedae (357.9) λ Piscium (358.0), Manus Catenata (358.1), Alrai, θ Phoenicis (358.4), κ Andromedae (358.7) ω Aquarii (359.2) ψ Andromedae (360.1), σ Phoenicis (360.4)
March 12 13 (72) π 15 16 (440)
'February 13 2-14 (45) 15 (*331) 16 17 (413)
"January 30 31 "February 1 2 (33) 3 (399)
NAKSHATRA DATES:
JULY 9 10 (*111) 11 12 (193) 13
ξ Hydrae (174.3), ο² Centauri, λ Centauri (174.8) θ Crateris (175.0), υ Leonis (175.2), ω Virginis (175.3), ι Crateris (175.5) ο Hydrae (176.1) ζ Crateris, ξ Virginis  (177.0), λ Muscae (177.1), ν Virginis (177.2), μ Muscae (177.8) Al Sarfah-10 / Uttara Phalguni-12 / Zibbat A.-17 / Shēpu-arkū sha-A.-18
93 Leonis (178.0), DENEBOLA (178.3), Alaraph (178.6)
September 11 12 (*175) 13 (256) 14 15
'August 15 16 (*148) 17 (229) 18 19
"August 1 2 (214) 3 (*135) 4 5

Greek omega Ω (ω)

Omega  ...  is the 24th and last letter of the Greek alphabet. In the Greek numeric system, it has a value of 800. The word literally means 'great O' (ō mega, mega meaning 'great'), as opposed to omicron, which means 'little O' (o mikron, micron meaning 'little') ...

The form of the uppercase letter derives from that of an omicron (Ο) broken up at the side ... with the edges subsequently turned outward

The modern lowercase shape goes back to the uncial form

a form that developed during the 3rd century BC in ancient handwriting on papyrus, from a flattened-out form of the letter ... that had its edges curved even further upward

Possibly, I think, this flattened out form alluded to the high sky 'carapace' in summer. As to the 'broken up omikron' it could have been turned at is side as an allusion to the orientation of the Gemini pair. The uncial form could reflect a pair of twins joined together (at the star ω Gemini).

Ga2-9 Ga2-10 Ga2-11 Ga2-12
APRIL 29 30 MAY 1 (121) 2
θ Gemini (103.0), ψ8 Aurigae (103.2), Alhena (103.8), ψ9 Aurigae (103.9) Adara (104.8) ω Gemini (105.4), Alzirr (105.7), Muliphein (105.8), Mekbuda (105.9) 7h (106.5)
no star listed (106)
July 2 3 4 (185) 5
'June 5 6 (157) 7 (*78) 8
"May 22 23 (143) 24 (*64) 25
NAKSHATRA DATES:
OCTOBER 29 30 31 (304) NOVEMBER 1
Ain al Rami (286.2), δ Lyrae (286.3), κ Pavonis (286.5), Alya (286.6) ξ Sagittarii (287.1), ω Pavonis (287.3), ε Aquilae, ε Cor. Austr., Sulaphat (287.4), λ Lyrae (287.7), Ascella, Bered (Ant.) (287.9)  Al Na'ām-18 / Uttara Ashadha-21 19h (289.2)
NUNKI (288.4), ζ Cor. Austr. (288.5), Manubrium (288.8), ζ Aquilae (288.9) λ Aquilae (Ant.) (289.1), γ Cor. Austr (289.3), τ Sagittarii (289.4), ι Lyrae (289.5), δ Cor. Austr. (289.8)
January 1 2 3 (368) 4
'December 5 6 (340) 7 (*261) 8
"November 21 22 (326) 23 (*247) 24

From ω Aquarii to ω Gemini there were 185 (July 5) - March 15 (74) = 111 days (= 471 - 360 = 472 - 19 * 19).