Performance Tuning :: Function Based Index Is Not Being Used

I have a table which has 4M records

This table has a query where one of the condition is
AND STATUS <> 'C'

Now the data is as following

select count(*) record_count, status from new_business group by status;

record_countstatus
4298025C
15N
13Q
122S

I want to know if following index would be useful in this case while the condition in where clause is

"AND STATUS <> 'C'"

create index nb_index_1 on new_business(case when status in('N','Q','S') then 1 else NULL end);
Or
create index nb_index_1 on new_business(case when status ='N' then 'N' when status='Q' then 'Q' when status='S' then 'S' else NULL end);

I tried it on a sample table but the index is simply not picked up even when hinted following are the db level settings

query_rewrite_enabled string TRUE
query_rewrite_integrity string enforced

I tried it 'query_rewrite_integrity' with 'trusted' as well .