Fungrim entry: 2e1cc7

Table of

\operatorname{Im}\!\left(\rho_{{10}^{n}}\right)

to 50 digits for

0 \le n \le 16

$n$	$\operatorname{Im}\!\left(\rho_{{10}^{n}}\right)$
0	14.134725141734693790457251983562470270784257115699
1	49.773832477672302181916784678563724057723178299677
2	236.52422966581620580247550795566297868952949521219
3	1419.4224809459956864659890380799168192321006010642
4	9877.7826540055011427740990706901235776224680517811
5	74920.827498994186793849200946918346620223555216802
6	600269.67701244495552123391427049074396819125790619
7	4992381.0140031786660182508391600932712387635814368
8	42653549.760951553903050309232819667982595130452178
9	371870203.83702805273405479598662519100082698522485
10	3293531632.3971367042089917031338769677069644102625
11	29538618431.613072810689561192671546108506486777642
12	267653395648.62594824214264940920070899588029633790
13	2445999556030.2468813938032396773514175248139258741
14	22514484222485.729124253904444090280880182979014905
15	208514052006405.46942460229754774510609948399247941
16	1941393531395154.7112809113883108073327538053720311

Table data:

\left(n, y\right)

such that

\operatorname{Re}\!\left(\rho_{{10}^{n}}\right) = \frac{1}{2} \,\mathbin{\operatorname{and}}\, \operatorname{NearestDecimal}\!\left(\operatorname{Im}\!\left(\rho_{{10}^{n}}\right), 50\right) = y

Definitions:

Fungrim symbol	Notation	Short description
`Im`	$\operatorname{Im}\!\left(z\right)$	Imaginary part
`RiemannZetaZero`	$\rho_{n}$	Nontrivial zero of the Riemann zeta function
`Pow`	${a}^{b}$	Power
`Re`	$\operatorname{Re}\!\left(z\right)$	Real part

Source code for this entry:

Entry(ID("2e1cc7"),
    Description("Table of", Im(RiemannZetaZero(Pow(10, n))), "to 50 digits for", LessEqual(0, n, 16)),
    Table(TableRelation(Tuple(n, y), And(Equal(Re(RiemannZetaZero(Pow(10, n))), Div(1, 2)), Equal(NearestDecimal(Im(RiemannZetaZero(Pow(10, n))), 50), y))), TableHeadings(n, Im(RiemannZetaZero(Pow(10, n)))), TableSplit(1), List(Tuple(0, Decimal("14.134725141734693790457251983562470270784257115699")), Tuple(1, Decimal("49.773832477672302181916784678563724057723178299677")), Tuple(2, Decimal("236.52422966581620580247550795566297868952949521219")), Tuple(3, Decimal("1419.4224809459956864659890380799168192321006010642")), Tuple(4, Decimal("9877.7826540055011427740990706901235776224680517811")), Tuple(5, Decimal("74920.827498994186793849200946918346620223555216802")), Tuple(6, Decimal("600269.67701244495552123391427049074396819125790619")), Tuple(7, Decimal("4992381.0140031786660182508391600932712387635814368")), Tuple(8, Decimal("42653549.760951553903050309232819667982595130452178")), Tuple(9, Decimal("371870203.83702805273405479598662519100082698522485")), Tuple(10, Decimal("3293531632.3971367042089917031338769677069644102625")), Tuple(11, Decimal("29538618431.613072810689561192671546108506486777642")), Tuple(12, Decimal("267653395648.62594824214264940920070899588029633790")), Tuple(13, Decimal("2445999556030.2468813938032396773514175248139258741")), Tuple(14, Decimal("22514484222485.729124253904444090280880182979014905")), Tuple(15, Decimal("208514052006405.46942460229754774510609948399247941")), Tuple(16, Decimal("1941393531395154.7112809113883108073327538053720311")))))

Topics using this entry

Zeros of the Riemann zeta function