Simple DTMF decoding: find the phone key!

JavaScript (ES6), 39 35 bytes

a=>b=>"310*58# 47269"[a%b%83%16%13]

Maps the two inputs into numbers in the range [0, 13) by calculating:
col % row % 83 % 16 % 13.
Takes input in currying syntax (f(col)(row)) and returns a single-char string.

Test Cases

let f=
a=>b=>"310*58# 47269"[a%b%83%16%13]

console.log( f(1336)(941) )
console.log( f(1209)(697) )
console.log( f(1336)(697) )
console.log( f(1477)(697) )
console.log( f(1209)(770) )
console.log( f(1336)(770) )
console.log( f(1477)(770) )
console.log( f(1209)(852) )
console.log( f(1336)(852) )
console.log( f(1477)(852) )
console.log( f(1209)(941) )
console.log( f(1477)(941) )

.as-console-wrapper{max-height:100%!important}

History

Started with the range of [0, 20) with calculation col % row % 29 % 20, which required 8 wasted characters in the mapping.

Haskell, 42 37 bytes

x#y="_1425__#9__*70836"!!mod(2*x+y)18

Just some math to index a string. Input order is <column> # <row>, e.g. 1336 # 697.

Try it online!

Edit: @flawr found a formula that works on shorter string. Overall -5 bytes. Thanks!

MATL, 23 bytes

13*+79\'186#294*3750'w)

Inputs are: column frequency, then row frequency.

Try it online!

Explanation

Multiplying the column frequency by 13, adding the row frequency, and computing modulo 79 gives a different value for each of the 12 pairs of inputs.

13*               % First input (implicit) times 13
+                 % Add to second input (implicit)
79\               % Modulo 79
'186#294*3750'    % Push this string
w                 % Swap
)                 % Index