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Fungrim entry: dc558b

Table of Im ⁣(ρn)\operatorname{Im}\!\left(\rho_{n}\right) to 10 digits for 1n5001 \le n \le 500
nn Im ⁣(ρn)\operatorname{Im}\!\left(\rho_{n}\right)
114.13472514
221.02203964
325.01085758
430.42487613
532.93506159
637.58617816
740.91871901
843.32707328
948.00515088
1049.77383248
1152.97032148
1256.44624770
1359.34704400
1460.83177852
1565.11254405
1667.07981053
1769.54640171
1872.06715767
1975.70469070
2077.14484007
2179.33737502
2282.91038085
2384.73549298
2487.42527461
2588.80911121
2692.49189927
2794.65134404
2895.87063423
2998.83119422
30101.3178510
31103.7255380
32105.4466231
33107.1686112
34111.0295355
35111.8746592
36114.3202209
37116.2266803
38118.7907829
39121.3701250
40122.9468293
41124.2568186
42127.5166839
43129.5787042
44131.0876885
45133.4977372
46134.7565098
47138.1160421
48139.7362090
49141.1237074
50143.1118458
51146.0009825
52147.4227653
53150.0535204
54150.9252576
55153.0246938
56156.1129093
57157.5975918
58158.8499882
59161.1889641
60163.0307097
61165.5370692
62167.1844400
63169.0945154
64169.9119765
65173.4115365
66174.7541915
67176.4414343
68178.3774078
69179.9164840
70182.2070785
71184.8744678
72185.5987837
73187.2289226
74189.4161587
75192.0266564
76193.0797266
77195.2653967
78196.8764818
79198.0153097
80201.2647519
81202.4935945
82204.1896718
83205.3946972
84207.9062589
85209.5765097
86211.6908626
87213.3479194
88214.5470448
89216.1695385
90219.0675963
91220.7149188
92221.4307056
93224.0070003
94224.9833247
95227.4214443
96229.3374133
97231.2501887
98231.9872353
99233.6934042
100236.5242297
nn Im ⁣(ρn)\operatorname{Im}\!\left(\rho_{n}\right)
101237.7698205
102239.5554776
103241.0491578
104242.8232719
105244.0708985
106247.1369901
107248.1019901
108249.5736896
109251.0149478
110253.0699867
111255.3062565
112256.3807137
113258.6104395
114259.8744070
115260.8050845
116263.5738939
117265.5578518
118266.6149738
119267.9219151
120269.9704490
121271.4940556
122273.4596092
123275.5874926
124276.4520495
125278.2507435
126279.2292509
127282.4651148
128283.2111857
129284.8359640
130286.6674454
131287.9119205
132289.5798549
133291.8462913
134293.5584341
135294.9653696
136295.5732549
137297.9792771
138299.8403261
139301.6493255
140302.6967496
141304.8643713
142305.7289126
143307.2194961
144310.1094631
145311.1651415
146312.4278012
147313.9852857
148315.4756161
149317.7348059
150318.8531043
151321.1601343
152322.1445587
153323.4669696
154324.8628661
155327.4439013
156329.0330717
157329.9532397
158331.4744676
159333.6453785
160334.2113548
161336.8418504
162338.3399929
163339.8582167
164341.0422611
165342.0548775
166344.6617029
167346.3478706
168347.2726776
169349.3162609
170350.4084193
171351.8786490
172353.4889005
173356.0175750
174357.1513023
175357.9526851
176359.7437550
177361.2893617
178363.3313306
179364.7360241
180366.2127103
181367.9935755
182368.9684381
183370.0509192
184373.0619284
185373.8648739
186375.8259128
187376.3240922
188378.4366802
189379.8729753
190381.4844686
191383.4435294
192384.9561168
193385.8613008
194387.2228902
195388.8461284
196391.4560836
197392.2450833
198393.4277438
199395.5828700
200396.3818542
nn Im ⁣(ρn)\operatorname{Im}\!\left(\rho_{n}\right)
201397.9187362
202399.9851199
203401.8392286
204402.8619178
205404.2364418
206405.1343875
207407.5814604
208408.9472455
209410.5138692
210411.9722678
211413.2627361
212415.0188098
213415.4552150
214418.3877058
215419.8613648
216420.6438276
217422.0767101
218423.7165796
219425.0698825
220427.2088251
221428.1279141
222430.3287454
223431.3013069
224432.1386417
225433.8892185
226436.1610064
227437.5816982
228438.6217387
229439.9184422
230441.6831992
231442.9045463
232444.3193363
233446.8606227
234447.4417042
235449.1485457
236450.1269458
237451.4033084
238453.9867378
239454.9746838
240456.3284267
241457.9038931
242459.5134153
243460.0879444
244462.0653673
245464.0572869
246465.6715392
247466.5702869
248467.4390462
249469.5360046
250470.7736555
251472.7991747
252473.8352323
253475.6003394
254476.7690152
255478.0752638
256478.9421815
257481.8303394
258482.8347828
259483.8514272
260485.5391481
261486.5287183
262488.3805671
263489.6617616
264491.3988216
265493.3144416
266493.9579978
267495.3588288
268496.4296962
269498.5807824
270500.3090849
271501.6044470
272502.2762703
273504.4997733
274505.4152317
275506.4641527
276508.8007003
277510.2642279
278511.5622897
279512.6231445
280513.6689856
281515.4350572
282517.5896686
283518.2342231
284520.1063104
285521.5251934
286522.4566962
287523.9605309
288525.0773857
289527.9036416
290528.4062139
291529.8062263
292530.8669179
293532.6881830
294533.7796308
295535.6643141
296537.0697591
297538.4285262
298540.2131664
299540.6313902
300541.8474371
nn Im ⁣(ρn)\operatorname{Im}\!\left(\rho_{n}\right)
301544.3238901
302545.6368332
303547.0109121
304547.9316134
305549.4975676
306550.9700100
307552.0495722
308553.7649721
309555.7920206
310556.8994764
311557.5646592
312559.3162370
313560.2408075
314562.5592076
315564.1608791
316564.5060559
317566.6987877
318567.7317579
319568.9239552
320570.0511148
321572.4199841
322573.6146105
323575.0938860
324575.8072471
325577.0390035
326579.0988347
327580.1369594
328581.9465763
329583.2360882
330584.5617059
331585.9845632
332586.7427719
333588.1396633
334590.6603975
335591.7258581
336592.5713583
337593.9747147
338595.7281537
339596.3627683
340598.4930773
341599.5456404
342601.6021367
343602.5791679
344603.6256189
345604.6162185
346606.3834604
347608.4132173
348609.3895752
349610.8391629
350611.7742096
351613.5997787
352614.6462379
353615.5385634
354618.1128314
355619.1844826
356620.2728937
357621.7092945
358622.3750027
359624.2699000
360626.0192834
361627.2683969
362628.3258624
363630.4738874
364630.8057809
365632.2251412
366633.5468583
367635.5238003
368637.3971932
369637.9255140
370638.9279383
371640.6947947
372641.9454997
373643.2788838
374644.9905782
375646.3481916
376647.7617530
377648.7864009
378650.1975193
379650.6686839
380653.6495716
381654.3019206
382655.7094630
383656.9640846
384658.1756144
385659.6638460
386660.7167326
387662.2965864
388664.2446047
389665.3427631
390666.5151477
391667.1484949
392668.9758488
393670.3235852
394672.4581836
395673.0435783
396674.3558978
397676.1396744
398677.2301807
399677.8004447
400679.7421979
nn Im ⁣(ρn)\operatorname{Im}\!\left(\rho_{n}\right)
401681.8949915
402682.6027350
403684.0135498
404684.9726299
405686.1632236
406687.9615432
407689.3689414
408690.4747350
409692.4516844
410693.1769701
411694.5339087
412695.7263359
413696.6260699
414699.1320955
415700.2967391
416701.3017430
417702.2273431
418704.0338393
419705.1258140
420706.1846548
421708.2690709
422709.2295886
423711.1302742
424711.9002899
425712.7493835
426714.0827718
427716.1123965
428717.4825697
429718.7427865
430719.6971010
431721.3511622
432722.2775050
433723.8458210
434724.5626139
435727.0564032
436728.4054816
437728.7587498
438730.4164821
439731.4173549
440732.8180527
441734.7896433
442735.7654592
443737.0529289
444738.5804212
445739.9095237
446740.5738074
447741.7573356
448743.8950131
449745.3449896
450746.4993059
451747.6745636
452748.2427545
453750.6559504
454750.9663811
455752.8876216
456754.3223705
457755.8393090
458756.7682484
459758.1017292
460758.9002382
461760.2823670
462762.7000332
463763.5930662
464764.3075227
465766.0875401
466767.2184722
467768.2814618
468769.6934073
469771.0708393
470772.9616176
471774.1177446
472775.0478471
473775.9997120
474777.2997485
475779.1570769
476780.3489250
477782.1376644
478782.5979439
479784.2888226
480785.7390897
481786.4611475
482787.4684638
483790.0590924
484790.8316205
485792.4277076
486792.8886526
487794.4837919
488795.6065962
489797.2634700
490798.7075702
491799.6543362
492801.6042465
493802.5419849
494803.2430962
495804.7622391
496805.8616357
497808.1518149
498809.1977834
499810.0818049
500811.1843588
Table data: (n,y)\left(n, y\right) such that Re ⁣(ρn)=12andIm ⁣(ρn)  (nearest 10D)=y\operatorname{Re}\!\left(\rho_{n}\right) = \frac{1}{2} \,\mathbin{\operatorname{and}}\, \operatorname{Im}\!\left(\rho_{n}\right) \; (\text{nearest } 10 \text{D}) = y
Definitions:
Fungrim symbol Notation Short description
ImIm(z)\operatorname{Im}(z) Imaginary part
RiemannZetaZeroρn\rho_{n} Nontrivial zero of the Riemann zeta function
ReRe(z)\operatorname{Re}(z) Real part
Source code for this entry:
Entry(ID("dc558b"),
    Description("Table of", Im(RiemannZetaZero(n)), "to 10 digits for", LessEqual(1, n, 500)),
    Table(TableRelation(Tuple(n, y), And(Equal(Re(RiemannZetaZero(n)), Div(1, 2)), Equal(NearestDecimal(Im(RiemannZetaZero(n)), 10), y))), TableHeadings(n, Im(RiemannZetaZero(n))), TableSplit(5), List(Tuple(1, Decimal("14.13472514")), Tuple(2, Decimal("21.02203964")), Tuple(3, Decimal("25.01085758")), Tuple(4, Decimal("30.42487613")), Tuple(5, Decimal("32.93506159")), Tuple(6, Decimal("37.58617816")), Tuple(7, Decimal("40.91871901")), Tuple(8, Decimal("43.32707328")), Tuple(9, Decimal("48.00515088")), Tuple(10, Decimal("49.77383248")), Tuple(11, Decimal("52.97032148")), Tuple(12, Decimal("56.44624770")), Tuple(13, Decimal("59.34704400")), Tuple(14, Decimal("60.83177852")), Tuple(15, Decimal("65.11254405")), Tuple(16, Decimal("67.07981053")), Tuple(17, Decimal("69.54640171")), Tuple(18, Decimal("72.06715767")), Tuple(19, Decimal("75.70469070")), Tuple(20, Decimal("77.14484007")), Tuple(21, Decimal("79.33737502")), Tuple(22, Decimal("82.91038085")), Tuple(23, Decimal("84.73549298")), Tuple(24, Decimal("87.42527461")), Tuple(25, Decimal("88.80911121")), Tuple(26, Decimal("92.49189927")), Tuple(27, Decimal("94.65134404")), Tuple(28, Decimal("95.87063423")), Tuple(29, Decimal("98.83119422")), Tuple(30, Decimal("101.3178510")), Tuple(31, Decimal("103.7255380")), Tuple(32, Decimal("105.4466231")), Tuple(33, Decimal("107.1686112")), Tuple(34, Decimal("111.0295355")), Tuple(35, Decimal("111.8746592")), Tuple(36, Decimal("114.3202209")), Tuple(37, Decimal("116.2266803")), Tuple(38, Decimal("118.7907829")), Tuple(39, Decimal("121.3701250")), Tuple(40, Decimal("122.9468293")), Tuple(41, Decimal("124.2568186")), Tuple(42, Decimal("127.5166839")), Tuple(43, Decimal("129.5787042")), Tuple(44, Decimal("131.0876885")), Tuple(45, Decimal("133.4977372")), Tuple(46, Decimal("134.7565098")), Tuple(47, Decimal("138.1160421")), Tuple(48, Decimal("139.7362090")), Tuple(49, Decimal("141.1237074")), Tuple(50, Decimal("143.1118458")), Tuple(51, Decimal("146.0009825")), Tuple(52, Decimal("147.4227653")), Tuple(53, Decimal("150.0535204")), Tuple(54, Decimal("150.9252576")), Tuple(55, Decimal("153.0246938")), Tuple(56, Decimal("156.1129093")), Tuple(57, Decimal("157.5975918")), Tuple(58, Decimal("158.8499882")), Tuple(59, Decimal("161.1889641")), Tuple(60, Decimal("163.0307097")), Tuple(61, Decimal("165.5370692")), Tuple(62, Decimal("167.1844400")), Tuple(63, Decimal("169.0945154")), Tuple(64, Decimal("169.9119765")), Tuple(65, Decimal("173.4115365")), Tuple(66, Decimal("174.7541915")), Tuple(67, Decimal("176.4414343")), Tuple(68, Decimal("178.3774078")), Tuple(69, Decimal("179.9164840")), Tuple(70, Decimal("182.2070785")), Tuple(71, Decimal("184.8744678")), Tuple(72, Decimal("185.5987837")), Tuple(73, Decimal("187.2289226")), Tuple(74, Decimal("189.4161587")), Tuple(75, Decimal("192.0266564")), Tuple(76, Decimal("193.0797266")), Tuple(77, Decimal("195.2653967")), Tuple(78, Decimal("196.8764818")), Tuple(79, Decimal("198.0153097")), Tuple(80, Decimal("201.2647519")), Tuple(81, Decimal("202.4935945")), Tuple(82, Decimal("204.1896718")), Tuple(83, Decimal("205.3946972")), Tuple(84, Decimal("207.9062589")), Tuple(85, Decimal("209.5765097")), Tuple(86, Decimal("211.6908626")), Tuple(87, Decimal("213.3479194")), Tuple(88, Decimal("214.5470448")), Tuple(89, Decimal("216.1695385")), Tuple(90, Decimal("219.0675963")), Tuple(91, Decimal("220.7149188")), Tuple(92, Decimal("221.4307056")), Tuple(93, Decimal("224.0070003")), Tuple(94, Decimal("224.9833247")), Tuple(95, Decimal("227.4214443")), Tuple(96, Decimal("229.3374133")), Tuple(97, Decimal("231.2501887")), Tuple(98, Decimal("231.9872353")), Tuple(99, Decimal("233.6934042")), Tuple(100, Decimal("236.5242297")), Tuple(101, Decimal("237.7698205")), Tuple(102, Decimal("239.5554776")), Tuple(103, Decimal("241.0491578")), Tuple(104, Decimal("242.8232719")), Tuple(105, Decimal("244.0708985")), Tuple(106, Decimal("247.1369901")), Tuple(107, Decimal("248.1019901")), Tuple(108, Decimal("249.5736896")), Tuple(109, Decimal("251.0149478")), Tuple(110, Decimal("253.0699867")), Tuple(111, Decimal("255.3062565")), Tuple(112, Decimal("256.3807137")), Tuple(113, Decimal("258.6104395")), Tuple(114, Decimal("259.8744070")), Tuple(115, Decimal("260.8050845")), Tuple(116, Decimal("263.5738939")), Tuple(117, Decimal("265.5578518")), Tuple(118, Decimal("266.6149738")), Tuple(119, Decimal("267.9219151")), Tuple(120, Decimal("269.9704490")), Tuple(121, Decimal("271.4940556")), Tuple(122, Decimal("273.4596092")), Tuple(123, Decimal("275.5874926")), Tuple(124, Decimal("276.4520495")), Tuple(125, Decimal("278.2507435")), Tuple(126, Decimal("279.2292509")), Tuple(127, Decimal("282.4651148")), Tuple(128, Decimal("283.2111857")), Tuple(129, Decimal("284.8359640")), Tuple(130, Decimal("286.6674454")), Tuple(131, Decimal("287.9119205")), Tuple(132, Decimal("289.5798549")), Tuple(133, Decimal("291.8462913")), Tuple(134, Decimal("293.5584341")), Tuple(135, Decimal("294.9653696")), Tuple(136, Decimal("295.5732549")), Tuple(137, Decimal("297.9792771")), Tuple(138, Decimal("299.8403261")), Tuple(139, Decimal("301.6493255")), Tuple(140, Decimal("302.6967496")), Tuple(141, Decimal("304.8643713")), Tuple(142, Decimal("305.7289126")), Tuple(143, Decimal("307.2194961")), Tuple(144, Decimal("310.1094631")), Tuple(145, Decimal("311.1651415")), Tuple(146, Decimal("312.4278012")), Tuple(147, Decimal("313.9852857")), Tuple(148, Decimal("315.4756161")), Tuple(149, Decimal("317.7348059")), Tuple(150, Decimal("318.8531043")), Tuple(151, Decimal("321.1601343")), Tuple(152, Decimal("322.1445587")), Tuple(153, Decimal("323.4669696")), Tuple(154, Decimal("324.8628661")), Tuple(155, Decimal("327.4439013")), Tuple(156, Decimal("329.0330717")), Tuple(157, Decimal("329.9532397")), Tuple(158, Decimal("331.4744676")), Tuple(159, Decimal("333.6453785")), Tuple(160, Decimal("334.2113548")), Tuple(161, Decimal("336.8418504")), Tuple(162, Decimal("338.3399929")), Tuple(163, Decimal("339.8582167")), Tuple(164, Decimal("341.0422611")), Tuple(165, Decimal("342.0548775")), Tuple(166, Decimal("344.6617029")), Tuple(167, Decimal("346.3478706")), Tuple(168, Decimal("347.2726776")), Tuple(169, Decimal("349.3162609")), Tuple(170, Decimal("350.4084193")), Tuple(171, Decimal("351.8786490")), Tuple(172, Decimal("353.4889005")), Tuple(173, Decimal("356.0175750")), Tuple(174, Decimal("357.1513023")), Tuple(175, Decimal("357.9526851")), Tuple(176, Decimal("359.7437550")), Tuple(177, Decimal("361.2893617")), Tuple(178, Decimal("363.3313306")), Tuple(179, Decimal("364.7360241")), Tuple(180, Decimal("366.2127103")), Tuple(181, Decimal("367.9935755")), Tuple(182, Decimal("368.9684381")), Tuple(183, Decimal("370.0509192")), Tuple(184, Decimal("373.0619284")), Tuple(185, Decimal("373.8648739")), Tuple(186, Decimal("375.8259128")), Tuple(187, Decimal("376.3240922")), Tuple(188, Decimal("378.4366802")), Tuple(189, Decimal("379.8729753")), Tuple(190, Decimal("381.4844686")), Tuple(191, Decimal("383.4435294")), Tuple(192, Decimal("384.9561168")), Tuple(193, Decimal("385.8613008")), Tuple(194, Decimal("387.2228902")), Tuple(195, Decimal("388.8461284")), Tuple(196, Decimal("391.4560836")), Tuple(197, Decimal("392.2450833")), Tuple(198, Decimal("393.4277438")), Tuple(199, Decimal("395.5828700")), Tuple(200, Decimal("396.3818542")), Tuple(201, Decimal("397.9187362")), Tuple(202, Decimal("399.9851199")), Tuple(203, Decimal("401.8392286")), Tuple(204, Decimal("402.8619178")), Tuple(205, Decimal("404.2364418")), Tuple(206, Decimal("405.1343875")), Tuple(207, Decimal("407.5814604")), Tuple(208, Decimal("408.9472455")), Tuple(209, Decimal("410.5138692")), Tuple(210, Decimal("411.9722678")), Tuple(211, Decimal("413.2627361")), Tuple(212, Decimal("415.0188098")), Tuple(213, Decimal("415.4552150")), Tuple(214, Decimal("418.3877058")), Tuple(215, Decimal("419.8613648")), Tuple(216, Decimal("420.6438276")), Tuple(217, Decimal("422.0767101")), Tuple(218, 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Decimal("802.5419849")), Tuple(494, Decimal("803.2430962")), Tuple(495, Decimal("804.7622391")), Tuple(496, Decimal("805.8616357")), Tuple(497, Decimal("808.1518149")), Tuple(498, Decimal("809.1977834")), Tuple(499, Decimal("810.0818049")), Tuple(500, Decimal("811.1843588")))))

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Copyright (C) Fredrik Johansson and contributors. Fungrim is provided under the MIT license. The source code is on GitHub.

2019-10-05 13:11:19.856591 UTC