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I've always liked sqlite3explorer.

Regarding:  "What I dislike is that every cell is treated as text, which disturbs re-sorting by clicking on a column header; it will not sort numerical."

Numerical sorting works for me.  I'm using the same version of sqlite3explorer and sqlite3.dll.  Does it fail for you using this simple example (in a fresh database)?

<code>
create table t(myNum INTEGER, myTxt TEXT, myReal REAL);
insert into t values (10, '10', 10.0);
insert into t values (2, '2', 2.);
</code>

If I display the contents of table "t", then click on the myNum or myReal columns, it sorts numerically.  Clicking on the myTxt column sorts lexically.

If this doesn't work for you, you might check to see if you've changed some of the "Options / Format Settings" described on the man page at:

<http://web.archive.org/web/20150424004100/http://www.singular.gr/sqlite/>

under the "Use of datatypes" section.