Fungrim entry: 71d9d9

Table of

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

to 50 digits for

1 \le n \le 50

$n$	$\operatorname{Im}\!\left(\rho_{n}\right)$
1	14.134725141734693790457251983562470270784257115699
2	21.022039638771554992628479593896902777334340524903
3	25.010857580145688763213790992562821818659549672558
4	30.424876125859513210311897530584091320181560023715
5	32.935061587739189690662368964074903488812715603517
6	37.586178158825671257217763480705332821405597350831
7	40.918719012147495187398126914633254395726165962777
8	43.327073280914999519496122165406805782645668371837
9	48.005150881167159727942472749427516041686844001144
10	49.773832477672302181916784678563724057723178299677
11	52.970321477714460644147296608880990063825017888821
12	56.446247697063394804367759476706127552782264471717
13	59.347044002602353079653648674992219031098772806467
14	60.831778524609809844259901824524003802910090451219
15	65.112544048081606660875054253183705029348149295167
16	67.079810529494173714478828896522216770107144951746
17	69.546401711173979252926857526554738443012474209603
18	72.067157674481907582522107969826168390480906621457
19	75.704690699083933168326916762030345922811903530697
20	77.144840068874805372682664856304637015796032449234
21	79.337375020249367922763592877116228190613246743120
22	82.910380854086030183164837494770609497508880593782
23	84.735492980517050105735311206827741417106627934241
24	87.425274613125229406531667850919213252171886401269
25	88.809111207634465423682348079509378395444893409819
26	92.491899270558484296259725241810684878721794027731
27	94.651344040519886966597925815208153937728027015655
28	95.870634228245309758741029219246781695256461224988
29	98.831194218193692233324420138622327820658039063428
30	101.31785100573139122878544794029230890633286638430
31	103.72553804047833941639840810869528083448117306950
32	105.44662305232609449367083241411180899728275392854
33	107.16861118427640751512335196308619121347670788140
34	111.02953554316967452465645030994435041534596839007
35	111.87465917699263708561207871677059496031174987339
36	114.32022091545271276589093727619107980991765772383
37	116.22668032085755438216080431206475512732985123238
38	118.79078286597621732297913970269982434730621059281
39	121.37012500242064591894553297049992272300131063173
40	122.94682929355258820081746033077001649621438987386
41	124.25681855434576718473200796612992444157353877469
42	127.51668387959649512427932376690607626808830988155
43	129.57870419995605098576803390617997360864095326466
44	131.08768853093265672356637246150134905920354750298
45	133.49773720299758645013049204264060766497417494390
46	134.75650975337387133132606415716973617839606861365
47	138.11604205453344320019155519028244785983527462415
48	139.73620895212138895045004652338246084679005256538
49	141.12370740402112376194035381847535509030066087975
50	143.11184580762063273940512386891392996623310243035

Table data:

\left(n, y\right)

such that

\operatorname{Re}\!\left(\rho_{n}\right) = \frac{1}{2} \,\mathbin{\operatorname{and}}\, \operatorname{NearestDecimal}\!\left(\operatorname{Im}\!\left(\rho_{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
`Re`	$\operatorname{Re}\!\left(z\right)$	Real part

Source code for this entry:

Entry(ID("71d9d9"),
    Description("Table of", Im(RiemannZetaZero(n)), "to 50 digits for", LessEqual(1, n, 50)),
    Table(TableRelation(Tuple(n, y), And(Equal(Re(RiemannZetaZero(n)), Div(1, 2)), Equal(NearestDecimal(Im(RiemannZetaZero(n)), 50), y))), TableHeadings(n, Im(RiemannZetaZero(n))), TableSplit(1), List(Tuple(1, Decimal("14.134725141734693790457251983562470270784257115699")), Tuple(2, Decimal("21.022039638771554992628479593896902777334340524903")), Tuple(3, Decimal("25.010857580145688763213790992562821818659549672558")), Tuple(4, Decimal("30.424876125859513210311897530584091320181560023715")), Tuple(5, Decimal("32.935061587739189690662368964074903488812715603517")), Tuple(6, Decimal("37.586178158825671257217763480705332821405597350831")), Tuple(7, Decimal("40.918719012147495187398126914633254395726165962777")), Tuple(8, Decimal("43.327073280914999519496122165406805782645668371837")), Tuple(9, Decimal("48.005150881167159727942472749427516041686844001144")), Tuple(10, Decimal("49.773832477672302181916784678563724057723178299677")), Tuple(11, Decimal("52.970321477714460644147296608880990063825017888821")), Tuple(12, Decimal("56.446247697063394804367759476706127552782264471717")), Tuple(13, Decimal("59.347044002602353079653648674992219031098772806467")), Tuple(14, Decimal("60.831778524609809844259901824524003802910090451219")), Tuple(15, Decimal("65.112544048081606660875054253183705029348149295167")), Tuple(16, Decimal("67.079810529494173714478828896522216770107144951746")), Tuple(17, Decimal("69.546401711173979252926857526554738443012474209603")), Tuple(18, Decimal("72.067157674481907582522107969826168390480906621457")), Tuple(19, Decimal("75.704690699083933168326916762030345922811903530697")), Tuple(20, Decimal("77.144840068874805372682664856304637015796032449234")), Tuple(21, Decimal("79.337375020249367922763592877116228190613246743120")), Tuple(22, Decimal("82.910380854086030183164837494770609497508880593782")), Tuple(23, Decimal("84.735492980517050105735311206827741417106627934241")), Tuple(24, Decimal("87.425274613125229406531667850919213252171886401269")), Tuple(25, Decimal("88.809111207634465423682348079509378395444893409819")), Tuple(26, Decimal("92.491899270558484296259725241810684878721794027731")), Tuple(27, Decimal("94.651344040519886966597925815208153937728027015655")), Tuple(28, Decimal("95.870634228245309758741029219246781695256461224988")), Tuple(29, Decimal("98.831194218193692233324420138622327820658039063428")), Tuple(30, Decimal("101.31785100573139122878544794029230890633286638430")), Tuple(31, Decimal("103.72553804047833941639840810869528083448117306950")), Tuple(32, Decimal("105.44662305232609449367083241411180899728275392854")), Tuple(33, Decimal("107.16861118427640751512335196308619121347670788140")), Tuple(34, Decimal("111.02953554316967452465645030994435041534596839007")), Tuple(35, Decimal("111.87465917699263708561207871677059496031174987339")), Tuple(36, Decimal("114.32022091545271276589093727619107980991765772383")), Tuple(37, Decimal("116.22668032085755438216080431206475512732985123238")), Tuple(38, Decimal("118.79078286597621732297913970269982434730621059281")), Tuple(39, Decimal("121.37012500242064591894553297049992272300131063173")), Tuple(40, Decimal("122.94682929355258820081746033077001649621438987386")), Tuple(41, Decimal("124.25681855434576718473200796612992444157353877469")), Tuple(42, Decimal("127.51668387959649512427932376690607626808830988155")), Tuple(43, Decimal("129.57870419995605098576803390617997360864095326466")), Tuple(44, Decimal("131.08768853093265672356637246150134905920354750298")), Tuple(45, Decimal("133.49773720299758645013049204264060766497417494390")), Tuple(46, Decimal("134.75650975337387133132606415716973617839606861365")), Tuple(47, Decimal("138.11604205453344320019155519028244785983527462415")), Tuple(48, Decimal("139.73620895212138895045004652338246084679005256538")), Tuple(49, Decimal("141.12370740402112376194035381847535509030066087975")), Tuple(50, Decimal("143.11184580762063273940512386891392996623310243035")))))

Fungrim entry: 71d9d9

Topics using this entry