συν-

• ξῠν- (xŭn-) — Old Attic
• σῠ- (sŭ-), ξῠ- (xŭ-) — before ζ (z) and before σ (s) plus consonant
• σῠγ- (sŭg-), ξῠγ- (xŭg-) — before the velar consonants γ (g), κ (k), ξ (x), χ (kh)
• σῠλ- (sŭl-), ξῠλ- (xŭl-) — before λ (l)
• σῠμ- (sŭm-), ξῠμ- (xŭm-) — before the labial consonants β (b), μ (m), π (p), φ (ph)
• σῠρ- (sŭr-), ξῠρ- (xŭr-) — before ρ (r)
• σῠσ- (sŭs-), ξῠσ- (xŭs-) — before σ (s) plus a vowel

Prefix version of the preposition σῠ́ν (sŭ́n, “with”).

σῠν- • (sŭn-)

1. with, together, co-, syn-
2. indicates completeness

• “σύν”, in Liddell & Scott (1940), A Greek–English Lexicon, Oxford: Clarendon Press

• συν- or σύν- before vowels, dental consontants and [n]
• συ-, σύ- (sy-, sý-) before sibilants [s] (+consonant) and [z] and colloquially before [v, γ, δ, f, x, θ, ks, ps]
• συγ-, σύγ- (syg-, sýg-) before the consonants κ, γ, χ (k, g, ch) pronounced /siŋ/
• συλ-, σύλ- (syl-, sýl-) before [l] λ (l) pronounced /sil/ (only one [l])
• συμ-, σύμ- (sym-, sým-) before the labial consonants [p, v, f, m] π, β, φ, μ (p, v, f, m)
• συρ-, σύρ- (syr-, sýr-) before [r] ρ (r)
• συσ-, σύσ- (sys-, sýs-) often before [s] σ (s)

From Ancient Greek σῠν- from preposition σύν (sún, “with”).

• IPA^(key): /sin/

συν- • (syn-)

1. with, together, co-, syn-

   ‎συν- (syn-) + ‎αγωνίζομαι (agonízomai, “strive”) → ‎συναγωνίζομαι (synagonízomai, “compete”)

2. indicates completeness
3. indicates similarity

and

• "συν-", in Λεξικό της κοινής νεοελληνικής [Dictionary of Standard Modern Greek], Triantafyllidis Foundation, 1998 at the Centre for the Greek language