Statistics for Riemann zeta zeros

• The following table was produced by Agatha L. Lee as part of an undergraduate project using the data linked here.
  
  The table below contains summary statistics about the Hardy $Z$-function (the rotated zeta function) based on data obtained using the amortized algorithm. The 4th column displays the minimum (resp. maximum) normalized spacing of consecutive zeros of the $Z$-function for each dataset of 10 million zeros at heights $T = $ 1e12,...,1e28. The zero ordinate where the max (resp. min) normalized spacing occurs is expressed in the form $T+t$, where $T$ is given in the 2nd column and $t$ is given in the 3rd column. The 5th column displays the maximum of the $Z$-function between the consecutive zero ordinates where the max (resp. min) normalized spacing occurs. The derivatives of the $Z$-function at the consecutive zeros where the max (resp. min) normalized spacing occurs are shown in the 6th and 7th columns.

  Summary statistics for the $Z$-function at various heights $T$

  Row #	$T$	$t$	Normalized.Spacing	Max.between.consecutive.zeros	Derivative.Zeros.left	Derivative.Zeros.right
  1	1e12	1690521.47416274	0.00460625	0.00007948	-0.28329158	0.28339492
  2	1e12	206880.85325403	3.77365656	165.64638502	43.94693787	-24.91982357
  3	1e13	253301.81124073	0.00552191	0.00029029	-0.93922876	0.94132176
  4	1e13	1302815.08231513	3.73937893	251.30113621	-101.65507669	45.27135084
  5	1e14	389993.89907488	0.00407607	0.00002887	-0.13699606	0.13712265
  6	1e14	2026158.53608729	3.96710353	223.91026313	44.34761533	-76.01636763
  7	1e15	677902.54443196	0.00348682	0.00001511	0.09025437	-0.09016508
  8	1e15	742072.67642370	3.61295524	106.65130623	97.20378372	-25.93228269
  9	1e16	381734.48714284	0.00360112	0.00009780	0.60661266	-0.60377489
  10	1e16	1267101.54021076	3.73479966	117.22057915	-24.96801799	68.24640454
  11	1e17	419484.86315535	0.00241857	0.00000519	0.05095856	-0.05096247
  12	1e17	296191.94631050	3.68651602	305.36683221	-157.74261074	242.41183067
  13	1e18	941064.90769908	0.00569272	0.00005120	-0.22619900	0.22739615
  14	1e18	1246399.50185418	3.72077811	74.91980616	-22.48846801	23.35120343
  15	1e19	460628.14464702	0.00540438	0.00001095	0.05400934	-0.05414715
  16	1e19	578940.59483533	3.83964540	53.28273741	-22.25117391	16.08472455
  17	1e20	1383900.88093245	0.00462024	0.00003397	0.20755877	-0.20632409
  18	1e20	368718.16305013	3.84760292	483.50645996	-400.52110929	205.90560850
  19	1e21	959614.40713735	0.00398210	0.00005492	0.40809162	-0.40867713
  20	1e21	1104477.79613337	3.80635523	151.26620010	-56.01444379	114.99716592
  21	1e22	680742.43467852	0.00218283	0.00000709	0.10090500	-0.10111871
  22	1e22	48475.43844621	3.83366769	376.08174575	-312.16775699	243.03472023
  23	1e23	56641.20788677	0.00401394	0.00001603	0.12983660	-0.13012480
  24	1e23	523760.82226342	3.67153966	581.55602221	-566.42704945	635.74403848
  25	1e24	792252.53051333	0.00621630	0.00003088	-0.16903572	0.16883176
  26	1e24	710245.73832348	3.57551078	401.35098140	98.85842501	-821.65451449
  27	1e25	870877.33724656	0.00234681	0.00000979	-0.14786651	0.14815679
  28	1e25	209560.46958613	4.09737216	341.03621261	-177.74551811	130.58175584
  29	1e26	1050812.35659205	0.00384856	0.00002620	0.25184501	-0.25108456
  30	1e26	676401.29576434	3.68488266	58.43612078	-54.00554017	22.96289208
  31	1e27	779334.21581987	0.00252168	0.00000333	-0.05069822	0.05076840
  32	1e27	486245.57155325	3.68679489	105.24525813	66.38086481	-51.24806696
  33	1e28	289065.69360204	0.00255474	0.00000247	0.03847333	-0.03858979
  34	1e28	680627.75794282	3.62400200	699.30021929	-1398.39381919	495.10516602