Racket, 443 434434 386 Bytes
Just for kicks.
(require file/gunzip net/base64)(define(f n)(let([odefine o(open-output-bytes)])(gunzip-through-ports(open-input-bytes(base64-decode(if(even? n)#"H4sIALHztlUAA21OwQ0AIQj7O0UXICzUpIs4/AkcmEvOSIu2DQC/Rxqs9qNIWoCzCtjnsig93p/1ak/gCpFRbWGS2VjMMuAS8Son573ADGJQbsfAXZpfT+YeCYucBeEAAAA="#"H4sIAOvztlUAA22O0Q0AIQhD/5miC5AuRMIiDn9A5b40Ck3pU4HnylS1WIfAmU01WZIlohHu5FgZYCgzAKe5#"H4sIAK8Lt1UAA22Q3Q3AIAiE352CBcwtRHLpHg7f8lubahRUDuVD5DjItrH9REgOEWgskfVMDeca1GWcSmN2WFBtlUTdzdmSOT0BpEpGnjxUAf2RmvPq1OyKGF6N5V1nvgYcWjeod/xH34TfTk+YQ1BF3n53Hj8JotBRtH0qM48OeoWrBxJH23KL/RNeSuuBm2suT9gEg2MyyyQAAAA==")dOMh4IDXe8MUbT1AqtKkBAAA="))o)(list-ref(string-split(get-output-string o)"a")(modulo n 2))) Prettified
Just for kicks.
(require file/gunzip net/base64) (define (f n) (letdefine ([oo (open-output-bytes)]) (gunzip-through-ports (open-input-bytes (base64-decode (if (even? n) #"H4sIALHztlUAA21OwQ0AIQj7O0UXICzUpIs4/AkcmEvOSIu2DQC/Rxqs9qNIWoCzCtjnsig93p/1ak/gCpFRbWGS2VjMMuAS8Son573ADGJQbsfAXZpfT+YeCYucBeEAAAA=" base64-decode #"H4sIAOvztlUAA22O0Q0AIQhD/5miC5AuRMIiDn9A5b40Ck3pU4HnylS1WIfAmU01WZIlohHu5FgZYCgzAKe5#"H4sIAK8Lt1UAA22Q3Q3AIAiE352CBcwtRHLpHg7f8lubahRUDuVD5DjItrH9REgOEWgskfVMDeca1GWcSmN2WFBtlUTdzdmSOT0BpEpGnjxUAf2RmvPq1OyKGF6N5V1nvgYcWjeod/xH34TfTk+YQ1BF3n53Hj8JotBRtH0qM48OeoWrBxJH23KL/RNeSuuBm2suT9gEg2MyyyQAAAA==")dOMh4IDXe8MUbT1AqtKkBAAA=")) o) (list-ref (string-split (get-output-string o) "a") (modulo n 2))) N.B. you may need the #lang racket line to run in DrRacket.