NumberDBbeta
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The advanced searchbar can be used to search for:
• Lists of real numbers
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:
• Lists of complex numbers
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 p-adic numbers in $\mathbb{Z}_p$ and $\mathbb{Q}_p$.
• Lists of polynomials over $\mathbb{Q}$
Similarly one can search for multivariate polynomials over $\mathbb{Q}$. As only expressions are accepted (mainly for safety reasons), we can define the variables as in the following example:
 Index Number Table -5, 1: -5 Integers (#-5) -5, 1: -5 Rational numbers (#-5) -5, 2: -2.5000000000000000? Rational numbers (#-5/2) -5, 3: -1.666666666666667? Rational numbers (#-5/3) -5, 3: -1.666666666666667? Generalized Bernoulli numbers (#11,1,2) -5, 4: -1.2500000000000000? Rational numbers (#-5/4) -4, 1: -4 Integers (#-4) -4, 1: -4 Rational numbers (#-4) -4, 3: -1.333333333333334? Rational numbers (#-4/3) -4, 5: -0.8000000000000000? Rational numbers (#-4/5) -3, 1: -3 Integers (#-3) -3, 1: -3 Rational numbers (#-3) -3, 2: -1.5000000000000000? Rational numbers (#-3/2) -3, 4: -0.75000000000000000? Rational numbers (#-3/4) -3, 5: -0.6000000000000000? Rational numbers (#-3/5) -2, 1: -2 Integers (#-2) -2, 1: -2 Rational numbers (#-2) -2, 1: -2 First known Mordell curves of given rank (#1,neg) -2, 3: -0.6666666666666667? Rational numbers (#-2/3) -2, 3: -0.6666666666666667? Generalized Bernoulli numbers (#5,1,2) -2, 5: -0.4000000000000000? Rational numbers (#-2/5) -1, 1: -1 Integers (#-1) -1, 1: -1 Rational numbers (#-1) -1, 1: -1 Generalized Bernoulli numbers (#7,1,2) -1, 1: -1 $j$-invariants of elliptic curves over quadratic fields with everywhere good reduction (#-6916) -1, 1: -1 First known Mordell curves of given rank (#0,neg) -1, 2: -0.50000000000000000? Bernoulli numbers (#1) -1, 2: -0.50000000000000000? Values of the Riemann zeta function at rational numbers (#0) -1, 2: -0.50000000000000000? Rational numbers (#-1/2) -1, 2: -0.50000000000000000? Generalized Bernoulli numbers (#4,3,1) -1, 2: -0.50000000000000000? $\cos(\pi x)$ for rational $x$ (#2/3) -1, 3: -0.3333333333333334? Rational numbers (#-1/3) -1, 3: -0.3333333333333334? Generalized Bernoulli numbers (#3,1,2) -1, 4: -0.25000000000000000? Rational numbers (#-1/4) -1, 4: -0.25000000000000000? Values of the Hurwitz zeta function at pairs of rational numbers (#3/4,0) -1, 5: -0.2000000000000000? Rational numbers (#-1/5) 0, 1: 0 Zero 0, 1: 0 Bernoulli numbers (#3) 0, 1: 0 Values of the Riemann zeta function at rational numbers (#-2) 0, 1: 0 Taylor coefficients of the completed Riemann zeta function at 1/2 (#a_n,1) 0, 1: 0 Local extrema of Bessel functions of the first kind $J_\alpha$ (#0,1) 0, 1: 0 Volume of the $d$-dimensional unit sphere (#-1) 0, 1: 0 Rational multiples of pi (#0) 0, 1: 0 Keiper-Li coefficients (#0) 0, 1: 0 Generalized Bernoulli numbers (#5,4,0) 0, 1: 0 $j$-invariants of elliptic curves over $\mathbb{Q}$ with good reduction outside $\{2, 3, 5\}$ 0, 1: 0 $q$-expansion of the modular discriminant $\Delta$ (#0) 0, 1: 0 Rational singular moduli (#-3) 0, 1: 0 Number of elliptic curves over $\mathbb{Q}$ with good redution outside $S$ (#1,Q) 0, 1: 0 Values of the Hurwitz zeta function at pairs of rational numbers (#1/2,0) 0, 1: 0 Gegenbauer polynomials (#0,1) 1, 1: 1 One 1, 1: 1 Diagonal Ramsey numbers (#1) 1, 1: 1 Factorial of natural numbers (#0) 1, 1: 1 Bernoulli numbers (#0) 1, 1: 1 Area of the regular n-gon (#unit-s,4) 1, 1: 1 Pólya's random walk constants (#1) 1, 1: 1 Complete elliptic integral of the second kind $E(m)$ (#1) 1, 1: 1 Volume of the $d$-dimensional unit ball (#0) 1, 1: 1 Laurent series coefficients of the logarithmic derivative of the Riemann zeta function at 1 (#eta_n,-1) 1, 1: 1 $abc$-triples of high quality (#1.401189,a) 1, 1: 1 $j$-invariants of elliptic curves over quadratic fields with everywhere good reduction (#5181) 1, 1: 1 $q$-expansion of the $j$-invariant (#-1) 1, 1: 1 $q$-expansion of the modular discriminant $\Delta$ (#1) 1, 1: 1 $q$-expansion of the Eisenstein series $E_4$ (#0) 1, 1: 1 $q$-expansion of the Eisenstein series $E_6$ (#0) 1, 1: 1 Volume of the Platonic solids (#unit-a,cube) 1, 1: 1 First known Mordell curves of given rank (#0,pos) 1, 1: 1 Values of the Barnes $G$-function at rational numbers (#1) 1, 1: 1 Chebyshev polynomials of the first kind $T_n$ (#0) 1, 1: 1 Chebyshev polynomials of the second kind $U_n$ (#0) 1, 1: 1 Legendre polynomials (#0) 1, 1: 1 Laguerre polynomials (#0) 1, 1: 1 Hermite polynomials in physicist's convention (#0) 1, 1: 1 Hermite polynomials in probabilist's convention (#0) 1, 1: 1 Gegenbauer polynomials (#0,0) 1, 1: 1 Jacobi polynomials (#0,1,0) 1, 2: 0.50000000000000000? Rational numbers (#1/2) 1, 2: 0.50000000000000000? Generalized Bernoulli numbers (#2,1,0) 1, 2: 0.50000000000000000? $\cos(\pi x)$ for rational $x$ (#1/3) 1, 3: 0.3333333333333334? Rational numbers (#1/3) 1, 3: 0.3333333333333334? Generalized Bernoulli numbers (#6,1,0) 1, 4: 0.25000000000000000? Rational numbers (#1/4) 1, 4: 0.25000000000000000? Values of the Hurwitz zeta function at pairs of rational numbers (#1/4,0) 1, 5: 0.2000000000000000? Rational numbers (#1/5) 2, 1: 2 Integers (#2) 2, 1: 2 Diagonal Ramsey numbers (#2) 2, 1: 2 Factorial of natural numbers (#2) 2, 1: 2 Area of the regular n-gon (#unit-R,4) 2, 1: 2 Volume of the $d$-dimensional unit ball (#1) 2, 1: 2 Volume of the $d$-dimensional unit sphere (#0) 2, 1: 2 Rational numbers (#2) 2, 1: 2 Generalized Bernoulli numbers (#8,5,2) 2, 1: 2 $abc$-triples of high quality (#1.629911,a) 2, 1: 2 Number of elliptic curves over $\mathbb{Q}$ with good redution outside $S$ (#3,Qbar) 2, 1: 2 First known Mordell curves of given rank (#1,pos) 2, 1: 2 Values of the Barnes $G$-function at rational numbers (#4) 2, 3: 0.6666666666666667? Rational numbers (#2/3) 2, 3: 0.6666666666666667? Generalized Bernoulli numbers (#3,1,0) 2, 5: 0.4000000000000000? Rational numbers (#2/5)