The advanced searchbar can be used to search for:

Use Sage syntax to enter
a number, a list of numbers, or a dictionary of the form {param: number}.
The lists and dictionaries may be nested.
The numbers might be given via formulas involving standard functions such as sin and sqrt, as well as standard constants such as e and pi.
Examples:

Similarly one can search for complex numbers.
Recommended parents are
CIF (complex interval field),
CBF (complex ball field),
and SR (symbolic ring),
although CC (complex field via floats) should work as well
unless too much precision is lost during the computation.

Similarly one can search for padic numbers in $\mathbb{Z}_p$ and $\mathbb{Q}_p$.
Examples:

Qp(2,prec=4)(5)
searches for $5 + O(2^4)$ = $2^0 + 2^2 + O(2^4)$,
that is, any $2$adic integer with first four $2$adic digits $1$, $0$, $1$, $0$.

{n: Qp(2)(n) for n in [1..10]}
searches $1$, ..., $10$ up to $O(2^{20})$ as $2$adic numbers;
note that 20 is the standard precision for Qp in sage.