Actual and conjectured gap count

Gap size : 4 (r=2)

Generated by program gapCounts : Wed Jul 16 14:36:35 2008

π(r,x) = actual gap count
L(r,x) = conjectured gap count
D(r,x) = L(r,x) - π(r,x)
S(r,x) = D(r,x)*ln(x)/x^½

x	π(r,x)	L(r,x)	D(r,x)	S(r,x)
1.0000e+02	7	11	4.00	1.84
2.0000e+02	13	16	3.32	1.24
3.0000e+02	16	21	4.67	1.54
4.0000e+02	20	25	4.52	1.36
5.0000e+02	25	28	3.06	0.85
6.0000e+02	26	31	5.38	1.41
7.0000e+02	29	35	5.53	1.37
8.0000e+02	32	38	5.55	1.31
9.0000e+02	37	40	3.45	0.78
1.0000e+03	40	43	3.26	0.71
1.1000e+03	43	46	2.99	0.63
1.2000e+03	43	49	5.64	1.16
1.3000e+03	45	51	6.24	1.24
1.4000e+03	47	54	6.78	1.31
1.5000e+03	52	56	4.27	0.81
1.6000e+03	55	59	3.72	0.69
1.7000e+03	59	61	2.13	0.38
1.8000e+03	60	63	3.50	0.62
1.9000e+03	62	66	3.83	0.66
2.0000e+03	63	68	5.13	0.87
2.1000e+03	65	70	5.40	0.90
2.2000e+03	66	73	6.64	1.09
2.3000e+03	70	75	4.86	0.78
2.4000e+03	73	77	4.05	0.64
2.5000e+03	75	79	4.22	0.66
2.6000e+03	76	81	5.36	0.83
2.7000e+03	80	83	3.49	0.53
2.8000e+03	82	86	3.59	0.54
2.9000e+03	85	88	2.68	0.40
3.0000e+03	86	90	3.75	0.55
3.1000e+03	89	92	2.80	0.40
3.2000e+03	91	94	2.84	0.40
3.3000e+03	93	96	2.85	0.40
3.4000e+03	95	98	2.86	0.40
3.5000e+03	97	100	2.85	0.39
3.6000e+03	98	102	3.82	0.52
3.7000e+03	100	104	3.79	0.51
3.8000e+03	102	106	3.74	0.50
3.9000e+03	104	108	3.67	0.49
4.0000e+03	107	110	2.60	0.34
4.1000e+03	108	112	3.51	0.46
4.2000e+03	110	113	3.41	0.44
4.3000e+03	110	115	5.31	0.68
4.4000e+03	110	117	7.19	0.91
4.5000e+03	111	119	8.06	1.01
4.6000e+03	113	121	7.92	0.98
4.7000e+03	114	123	8.77	1.08
4.8000e+03	117	125	7.61	0.93
4.9000e+03	118	126	8.45	1.03
5.0000e+03	120	128	8.27	1.00
5.2000e+03	123	132	8.89	1.06
5.4000e+03	126	135	9.48	1.11
5.6000e+03	132	139	7.04	0.81
5.8000e+03	137	143	5.58	0.63
6.0000e+03	140	146	6.08	0.68
6.2000e+03	142	150	7.55	0.84
6.4000e+03	144	153	9.00	0.99
6.6000e+03	147	156	9.43	1.02
6.8000e+03	148	160	11.83	1.27
7.0000e+03	152	163	11.21	1.19
7.2000e+03	154	167	12.57	1.32
7.4000e+03	156	170	13.91	1.44
7.6000e+03	159	173	14.22	1.46
7.8000e+03	167	177	9.52	0.97
8.0000e+03	170	180	9.80	0.98
8.2000e+03	172	183	11.06	1.10
8.4000e+03	176	186	10.30	1.02
8.6000e+03	179	190	10.53	1.03
8.8000e+03	184	193	8.74	0.85
9.0000e+03	187	196	8.93	0.86
9.2000e+03	190	199	9.11	0.87
9.4000e+03	194	202	8.27	0.78
9.6000e+03	197	205	8.42	0.79
9.8000e+03	200	209	8.55	0.79
1.0000e+04	202	212	9.67	0.89
1.0500e+04	211	219	8.41	0.76
1.1000e+04	216	227	11.08	0.98
1.1500e+04	224	235	10.66	0.93
1.2000e+04	231	242	11.18	0.96
1.2500e+04	242	250	7.63	0.64
1.3000e+04	248	257	9.02	0.75
1.3500e+04	257	264	7.34	0.60
1.4000e+04	264	272	7.62	0.61
1.4500e+04	271	279	7.83	0.62
1.5000e+04	282	286	4.00	0.31
1.5500e+04	288	293	5.11	0.40
1.6000e+04	296	300	4.18	0.32
1.6500e+04	306	307	1.20	0.09
1.7000e+04	312	314	2.18	0.16
1.7500e+04	318	321	3.12	0.23
1.8000e+04	321	328	7.01	0.51
1.8500e+04	330	335	4.87	0.35
1.9000e+04	334	342	7.69	0.55
1.9500e+04	341	348	7.47	0.53
2.0000e+04	343	355	12.22	0.86
2.1000e+04	356	369	12.62	0.87
2.2000e+04	372	382	9.88	0.67
2.3000e+04	385	395	10.03	0.66
2.4000e+04	399	408	9.07	0.59
2.5000e+04	411	421	9.99	0.64
2.6000e+04	422	434	11.82	0.75
2.7000e+04	433	447	13.55	0.84
2.8000e+04	445	459	14.18	0.87
2.9000e+04	457	472	14.73	0.89
3.0000e+04	467	484	17.20	1.02
3.1000e+04	475	497	21.58	1.27
3.2000e+04	489	509	19.89	1.15
3.3000e+04	504	521	17.12	0.98
3.4000e+04	518	533	15.28	0.86
3.5000e+04	526	545	19.38	1.08
3.6000e+04	536	557	21.40	1.18
3.7000e+04	548	569	21.37	1.17
3.8000e+04	558	581	23.27	1.26
3.9000e+04	567	593	26.11	1.40
4.0000e+04	580	605	24.90	1.32
4.1000e+04	593	617	23.63	1.24
4.2000e+04	605	628	23.31	1.21
4.3000e+04	617	640	22.93	1.18
4.4000e+04	627	652	24.51	1.25
4.5000e+04	642	663	21.03	1.06
4.6000e+04	652	675	22.51	1.13
4.7000e+04	662	686	23.94	1.19
4.8000e+04	671	697	26.33	1.30
4.9000e+04	681	709	27.67	1.35
5.0000e+04	692	720	27.97	1.35
5.2000e+04	715	742	27.44	1.31
5.4000e+04	742	765	22.76	1.07
5.6000e+04	765	787	21.92	1.01
5.8000e+04	786	809	22.95	1.04
6.0000e+04	807	831	23.83	1.07
6.2000e+04	825	853	27.58	1.22
6.4000e+04	844	874	30.20	1.32
6.6000e+04	865	896	30.70	1.33
6.8000e+04	888	917	29.09	1.24
7.0000e+04	905	938	33.36	1.41
7.2000e+04	922	960	37.52	1.56
7.4000e+04	944	981	36.58	1.51
7.6000e+04	969	1002	32.54	1.33
7.8000e+04	992	1022	30.39	1.23
8.0000e+04	1013	1043	30.16	1.20
8.2000e+04	1033	1064	30.83	1.22
8.4000e+04	1053	1084	31.41	1.23
8.6000e+04	1066	1105	38.91	1.51
8.8000e+04	1091	1125	34.32	1.32
9.0000e+04	1112	1146	33.66	1.28
9.2000e+04	1135	1166	30.91	1.16
9.4000e+04	1156	1186	30.08	1.12
9.6000e+04	1177	1206	29.19	1.08
9.8000e+04	1197	1226	29.21	1.07
1.0000e+05	1215	1246	31.17	1.13
1.0500e+05	1264	1296	31.76	1.13
1.1000e+05	1317	1345	27.95	0.98
1.1500e+05	1368	1394	25.75	0.88
1.2000e+05	1412	1442	30.19	1.02
1.2500e+05	1462	1490	28.29	0.94
1.3000e+05	1508	1538	30.06	0.98
1.3500e+05	1557	1586	28.52	0.92
1.4000e+05	1604	1633	28.68	0.91
1.4500e+05	1650	1680	29.56	0.92
1.5000e+05	1686	1726	40.16	1.24
1.5500e+05	1731	1773	41.51	1.26
1.6000e+05	1779	1819	39.61	1.19
1.6500e+05	1817	1864	47.46	1.40
1.7000e+05	1863	1910	47.09	1.38
1.7500e+05	1909	1955	46.49	1.34
1.8000e+05	1957	2001	43.68	1.25
1.8500e+05	1990	2046	55.66	1.57
1.9000e+05	2035	2090	55.45	1.55
1.9500e+05	2084	2135	51.03	1.41
2.0000e+05	2134	2179	45.44	1.24
2.1000e+05	2224	2268	43.70	1.17
2.2000e+05	2315	2355	40.28	1.06
2.3000e+05	2402	2442	40.21	1.04
2.4000e+05	2485	2529	43.54	1.10
2.5000e+05	2578	2614	36.28	0.90
2.6000e+05	2661	2699	38.48	0.94
2.7000e+05	2737	2784	47.15	1.13
2.8000e+05	2810	2868	58.32	1.38
2.9000e+05	2891	2952	61.02	1.43
3.0000e+05	2974	3035	61.25	1.41
3.1000e+05	3055	3118	63.05	1.43
3.2000e+05	3144	3200	56.42	1.26
3.3000e+05	3220	3282	62.39	1.38
3.4000e+05	3306	3364	57.97	1.27
3.5000e+05	3392	3445	53.17	1.15
3.6000e+05	3474	3526	52.01	1.11
3.7000e+05	3562	3607	44.50	0.94
3.8000e+05	3641	3687	45.66	0.95
3.9000e+05	3720	3766	46.48	0.96
4.0000e+05	3812	3846	33.99	0.69
4.1000e+05	3877	3925	48.19	0.97
4.2000e+05	3958	4004	46.09	0.92
4.3000e+05	4043	4083	39.70	0.79
4.4000e+05	4121	4161	40.03	0.78
4.5000e+05	4194	4239	45.08	0.87
4.6000e+05	4265	4317	51.87	1.00
4.7000e+05	4340	4394	54.40	1.04
4.8000e+05	4417	4472	54.68	1.03
4.9000e+05	4483	4549	65.72	1.23
5.0000e+05	4558	4626	67.51	1.25
5.2000e+05	4709	4778	69.40	1.27
5.4000e+05	4866	4930	64.40	1.16
5.6000e+05	5018	5082	63.55	1.12
5.8000e+05	5182	5232	49.88	0.87
6.0000e+05	5333	5381	48.44	0.83
6.2000e+05	5481	5530	49.25	0.83
6.4000e+05	5630	5678	48.34	0.81
6.6000e+05	5774	5826	51.74	0.85
6.8000e+05	5936	5972	36.47	0.59
7.0000e+05	6084	6119	34.56	0.56
7.2000e+05	6215	6264	49.03	0.78
7.4000e+05	6364	6409	44.91	0.71
7.6000e+05	6495	6553	58.21	0.90
7.8000e+05	6644	6697	52.94	0.81
8.0000e+05	6797	6840	43.14	0.66
8.2000e+05	6924	6983	58.81	0.88
8.4000e+05	7067	7125	57.97	0.86
8.6000e+05	7202	7267	64.63	0.95
8.8000e+05	7342	7408	65.81	0.96
9.0000e+05	7470	7549	78.52	1.13
9.2000e+05	7610	7689	78.78	1.13
9.4000e+05	7750	7829	78.60	1.11
9.6000e+05	7885	7968	82.98	1.17
9.8000e+05	8019	8107	87.94	1.23
1.0000e+06	8143	8245	102.49	1.42
1.0500e+06	8511	8590	79.14	1.07
1.1000e+06	8843	8932	89.42	1.19
1.1500e+06	9196	9272	76.48	1.00
1.2000e+06	9548	9610	62.42	0.80
1.2500e+06	9873	9946	73.35	0.92
1.3000e+06	10214	10280	66.38	0.82
1.3500e+06	10548	10613	64.59	0.78
1.4000e+06	10891	10943	52.05	0.62
1.4500e+06	11202	11272	69.85	0.82
1.5000e+06	11531	11599	68.06	0.79
1.5500e+06	11848	11925	76.74	0.88
1.6000e+06	12188	12249	60.94	0.69
1.6500e+06	12528	12572	43.73	0.49
1.7000e+06	12879	12893	14.16	0.16
1.7500e+06	13200	13213	13.27	0.14
1.8000e+06	13497	13532	35.11	0.38
1.8500e+06	13828	13850	21.72	0.23
1.9000e+06	14133	14166	33.14	0.35
1.9500e+06	14444	14481	37.42	0.39
2.0000e+06	14741	14796	54.58	0.56
2.1000e+06	15334	15421	86.69	0.87
2.2000e+06	15940	16042	101.72	1.00
2.3000e+06	16549	16659	109.89	1.06
2.4000e+06	17141	17272	131.42	1.25
2.5000e+06	17795	17882	87.47	0.81
2.6000e+06	18399	18489	90.21	0.83
2.7000e+06	19018	19093	74.81	0.67
2.8000e+06	19636	19693	57.39	0.51
2.9000e+06	20228	20291	63.08	0.55
3.0000e+06	20825	20886	61.02	0.53
3.1000e+06	21398	21478	80.29	0.68
3.2000e+06	21998	22068	70.02	0.59
3.3000e+06	22567	22655	88.29	0.73
3.4000e+06	23134	23240	106.20	0.87
3.5000e+06	23720	23823	102.82	0.83
3.6000e+06	24300	24403	103.23	0.82
3.7000e+06	24885	24982	96.51	0.76
3.8000e+06	25478	25558	79.73	0.62
3.9000e+06	26096	26132	35.95	0.28
4.0000e+06	26628	26704	76.24	0.58
4.1000e+06	27213	27275	61.64	0.46
4.2000e+06	27792	27843	51.22	0.38
4.3000e+06	28362	28410	48.02	0.35
4.4000e+06	28931	28975	44.11	0.32
4.5000e+06	29501	29539	37.51	0.27
4.6000e+06	30074	30100	26.29	0.19
4.7000e+06	30638	30660	22.47	0.16
4.8000e+06	31186	31219	33.10	0.23
4.9000e+06	31739	31776	37.23	0.26
5.0000e+06	32307	32332	24.88	0.17
5.2000e+06	33430	33439	8.89	0.06
5.4000e+06	34525	34540	15.41	0.10
5.6000e+06	35621	35637	15.67	0.10
5.8000e+06	36706	36728	21.91	0.14
6.0000e+06	37786	37814	28.33	0.18
6.2000e+06	38870	38896	26.11	0.16
6.4000e+06	39930	39973	43.44	0.27
6.6000e+06	40984	41046	62.48	0.38
6.8000e+06	42055	42115	60.38	0.36
7.0000e+06	43124	43180	56.30	0.34
7.2000e+06	44174	44241	67.36	0.40
7.4000e+06	45199	45299	99.69	0.58
7.6000e+06	46265	46352	87.42	0.50
7.8000e+06	47263	47403	139.65	0.79
8.0000e+06	48287	48449	162.49	0.91
8.2000e+06	49360	49493	133.05	0.74
8.4000e+06	50391	50533	142.41	0.78
8.6000e+06	51437	51571	133.67	0.73
8.8000e+06	52489	52605	115.91	0.62
9.0000e+06	53468	53636	168.21	0.90
9.2000e+06	54471	54665	193.66	1.02
9.4000e+06	55512	55690	178.32	0.93
9.6000e+06	56576	56713	137.27	0.71
9.8000e+06	57571	57734	162.56	0.84
1.0000e+07	58621	58751	130.28	0.66
1.0500e+07	61159	61285	125.65	0.63
1.1000e+07	63657	63803	146.14	0.71
1.1500e+07	66193	66308	114.55	0.55
1.2000e+07	68726	68799	72.58	0.34
1.2500e+07	71235	71277	41.91	0.19
1.3000e+07	73655	73743	88.14	0.40
1.3500e+07	76087	76198	110.80	0.50
1.4000e+07	78583	78641	58.42	0.26
1.4500e+07	81044	81074	30.44	0.13
1.5000e+07	83471	83497	26.31	0.11
1.5500e+07	85899	85910	11.43	0.05
1.6000e+07	88281	88314	33.15	0.14
1.6500e+07	90683	90709	25.83	0.11
1.7000e+07	93098	93095	-3.20	-0.01
1.7500e+07	95483	95472	-10.65	-0.04
1.8000e+07	97800	97842	41.76	0.16
1.8500e+07	100158	100203	45.31	0.18
1.9000e+07	102476	102557	81.24	0.31
1.9500e+07	104773	104904	130.79	0.50
2.0000e+07	107081	107243	162.18	0.61
2.1000e+07	111741	111901	160.31	0.59
2.2000e+07	116324	116533	209.19	0.75
2.3000e+07	120898	121140	242.23	0.86
2.4000e+07	125574	125724	149.68	0.52
2.5000e+07	130175	130285	109.70	0.37
2.6000e+07	134691	134824	133.35	0.45
2.7000e+07	139175	139344	168.59	0.56
2.8000e+07	143724	143843	119.29	0.39
2.9000e+07	148189	148324	135.29	0.43
3.0000e+07	152576	152787	211.34	0.66
3.1000e+07	157011	157233	222.13	0.69
3.2000e+07	161420	161662	242.33	0.74
3.3000e+07	165868	166076	207.53	0.63
3.4000e+07	170206	170473	267.30	0.79
3.5000e+07	174590	174856	266.18	0.78
3.6000e+07	178923	179225	301.67	0.87
3.7000e+07	183189	183579	390.22	1.12
3.8000e+07	187536	187920	384.29	1.09
3.9000e+07	191927	192248	321.29	0.90
4.0000e+07	196233	196564	330.60	0.91
4.1000e+07	200426	200867	440.60	1.21
4.2000e+07	204693	205158	464.65	1.26
4.3000e+07	209028	209437	409.07	1.10
4.4000e+07	213258	213705	447.17	1.19
4.5000e+07	217485	217962	477.27	1.25
4.6000e+07	221689	222209	519.64	1.35
4.7000e+07	225956	226445	488.56	1.26
4.8000e+07	230168	230670	502.29	1.28
4.9000e+07	234317	234886	569.08	1.44
5.0000e+07	238610	239092	482.16	1.21
5.2000e+07	247051	247476	425.09	1.05
5.4000e+07	255353	255824	470.79	1.14
5.6000e+07	263724	264137	412.82	0.98
5.8000e+07	272020	272417	396.63	0.93
6.0000e+07	280205	280665	459.55	1.06
6.2000e+07	288362	288882	519.82	1.18
6.4000e+07	296601	297070	468.59	1.05
6.6000e+07	304730	305229	498.93	1.11
6.8000e+07	312964	313361	396.85	0.87
7.0000e+07	321199	321466	267.29	0.58
7.2000e+07	329310	329546	236.12	0.50
7.4000e+07	337319	337601	282.18	0.59
7.6000e+07	345291	345632	341.24	0.71
7.8000e+07	353283	353640	357.03	0.73
8.0000e+07	361346	361625	279.26	0.57
8.2000e+07	369341	369589	247.57	0.50
8.4000e+07	377295	377531	235.60	0.47
8.6000e+07	385152	385452	299.92	0.59
8.8000e+07	393083	393353	270.09	0.53
9.0000e+07	401024	401235	210.66	0.41
9.2000e+07	408906	409097	191.12	0.37
9.4000e+07	416745	416941	195.96	0.37
9.6000e+07	424659	424767	107.64	0.20
9.8000e+07	432493	432575	81.60	0.15
1.0000e+08	440257	440365	108.26	0.20
1.0500e+08	459820	459769	-51.21	-0.09
1.1000e+08	479234	479072	-161.51	-0.29
1.1500e+08	498394	498282	-112.39	-0.19
1.2000e+08	517473	517401	-72.09	-0.12
1.2500e+08	536534	536435	-99.27	-0.17
1.3000e+08	555608	555387	-220.98	-0.36
1.3500e+08	574474	574261	-212.58	-0.34
1.4000e+08	593197	593061	-135.73	-0.22
1.4500e+08	611753	611790	36.64	0.06
1.5000e+08	630330	630449	119.39	0.18
1.5500e+08	648820	649043	223.17	0.34
1.6000e+08	667181	667573	392.44	0.59
1.6500e+08	685715	686042	327.49	0.48
1.7000e+08	704197	704452	255.47	0.37
1.7500e+08	722414	722805	391.38	0.56
1.8000e+08	740833	741103	270.11	0.38
1.8500e+08	759208	759347	139.43	0.20
1.9000e+08	777391	777540	149.02	0.21
1.9500e+08	795573	795682	109.44	0.15
2.0000e+08	813714	813776	62.17	0.08
2.1000e+08	849710	849823	113.15	0.15
2.2000e+08	885590	885691	101.35	0.13
2.3000e+08	921401	921390	-10.87	-0.01
2.4000e+08	956872	956928	55.98	0.07
2.5000e+08	992478	992313	-165.36	-0.20
2.6000e+08	1027720	1027551	-168.83	-0.20
2.7000e+08	1062643	1062650	7.04	0.01
2.8000e+08	1097685	1097615	-69.79	-0.08
2.9000e+08	1132502	1132452	-49.82	-0.06
3.0000e+08	1167213	1167166	-46.96	-0.05
3.1000e+08	1201676	1201762	85.52	0.09
3.2000e+08	1235985	1236243	258.00	0.28
3.3000e+08	1270461	1270615	153.60	0.17
3.4000e+08	1304721	1304880	159.14	0.17
3.5000e+08	1338978	1339043	65.21	0.07
3.6000e+08	1373082	1373107	25.18	0.03
3.7000e+08	1406927	1407075	148.22	0.15
3.8000e+08	1440792	1440950	158.30	0.16
3.9000e+08	1474759	1474735	-23.75	-0.02
4.0000e+08	1508304	1508433	128.71	0.13
4.1000e+08	1542098	1542045	-52.79	-0.05
4.2000e+08	1575559	1575575	16.12	0.02
4.3000e+08	1609019	1609025	5.71	0.01
4.4000e+08	1642348	1642396	48.12	0.05
4.5000e+08	1675683	1675691	8.39	0.01
4.6000e+08	1708789	1708912	123.47	0.11
4.7000e+08	1741869	1742061	192.20	0.18
4.8000e+08	1775255	1775139	-115.63	-0.11
4.9000e+08	1808205	1808149	-56.35	-0.05
5.0000e+08	1841265	1841091	-174.34	-0.16
5.2000e+08	1906950	1906779	-171.00	-0.15
5.4000e+08	1972307	1972216	-91.03	-0.08
5.6000e+08	2037538	2037412	-125.75	-0.11
5.8000e+08	2102631	2102378	-253.30	-0.21
6.0000e+08	2167272	2167121	-150.55	-0.12
6.2000e+08	2231846	2231652	-194.04	-0.16
6.4000e+08	2295925	2295977	52.11	0.04
6.6000e+08	2360216	2360104	-111.74	-0.09
6.8000e+08	2423999	2424040	41.28	0.03
7.0000e+08	2487947	2487792	-155.38	-0.12
7.2000e+08	2551197	2551364	167.31	0.13
7.4000e+08	2614454	2614764	310.04	0.23
7.6000e+08	2677809	2677996	187.16	0.14
7.8000e+08	2740965	2741066	100.72	0.07
8.0000e+08	2804043	2803977	-65.51	-0.05
8.2000e+08	2866947	2866736	-211.01	-0.15
8.4000e+08	2929524	2929345	-178.51	-0.13
8.6000e+08	2992037	2991810	-226.94	-0.16
8.8000e+08	3054445	3054134	-311.45	-0.22
9.0000e+08	3116320	3116320	-0.38	-0.00
9.2000e+08	3178298	3178372	73.78	0.05
9.4000e+08	3240293	3240293	0.36	0.00
9.6000e+08	3301759	3302088	328.52	0.22
9.8000e+08	3363238	3363757	519.30	0.34
1.0000e+09	3424679	3425306	626.62	0.41
1.0500e+09	3577934	3578663	728.90	0.47
1.1000e+09	3730514	3731318	804.37	0.50
1.1500e+09	3881855	3883308	1453.43	0.89
1.2000e+09	4033416	4034666	1250.09	0.75
1.2500e+09	4184331	4185421	1090.42	0.65
1.3000e+09	4334692	4335602	909.90	0.53
1.3500e+09	4483798	4485233	1434.75	0.82
1.4000e+09	4632478	4634337	1859.18	1.05
1.4500e+09	4780808	4782937	2128.62	1.18
1.5000e+09	4928915	4931051	2135.94	1.17
1.5500e+09	5076682	5078699	2016.55	1.08
1.6000e+09	5224119	5225897	1777.62	0.94
1.6500e+09	5370843	5372661	1818.16	0.95
1.7000e+09	5517492	5519007	1515.13	0.78
1.7500e+09	5663558	5664949	1390.56	0.71
1.8000e+09	5809371	5810499	1127.62	0.57
1.8500e+09	5954361	5955670	1308.68	0.65
1.9000e+09	6099508	6100473	965.41	0.47
1.9500e+09	6243482	6244921	1438.83	0.70
2.0000e+09	6386967	6389022	2055.32	0.98
2.1000e+09	6673887	6676226	2339.41	1.10
2.2000e+09	6959846	6962159	2312.50	1.06
2.3000e+09	7244540	7246884	2344.32	1.05
2.4000e+09	7528480	7530463	1983.48	0.87
2.5000e+09	7811714	7812950	1236.28	0.54
2.6000e+09	8093771	8094394	623.36	0.27
2.7000e+09	8374147	8374841	694.28	0.29
2.8000e+09	8654259	8654333	74.00	0.03
2.9000e+09	8932967	8932908	-58.75	-0.02
3.0000e+09	9211041	9210603	-438.07	-0.17
3.1000e+09	9488317	9487450	-866.64	-0.34
3.2000e+09	9765146	9763482	-1664.44	-0.64
3.3000e+09	10039988	10038726	-1262.50	-0.48
3.4000e+09	10314335	10313209	-1125.75	-0.42
3.5000e+09	10588520	10586958	-1561.82	-0.58
3.6000e+09	10861416	10859996	-1419.88	-0.52
3.7000e+09	11133547	11132345	-1201.53	-0.44
3.8000e+09	11405221	11404027	-1193.66	-0.43
3.9000e+09	11676142	11675062	-1080.34	-0.38
4.0000e+09	11946708	11945467	-1240.74	-0.43
4.1000e+09	12216276	12215262	-1014.02	-0.35
4.2000e+09	12485039	12484463	-576.31	-0.20
4.3000e+09	12753860	12753085	-774.56	-0.26
4.4000e+09	13021834	13021145	-688.53	-0.23
4.5000e+09	13289486	13288657	-828.72	-0.27
4.6000e+09	13556030	13555635	-395.33	-0.13
4.7000e+09	13821892	13822091	198.81	0.06
4.8000e+09	14088228	14088038	-189.72	-0.06
4.9000e+09	14354015	14353489	-525.93	-0.17
5.0000e+09	14618743	14618455	-288.31	-0.09
5.2000e+09	15146353	15146974	620.88	0.19
5.4000e+09	15672698	15673678	980.44	0.30
5.6000e+09	16197529	16198644	1115.44	0.33
5.8000e+09	16720020	16721942	1922.14	0.57
6.0000e+09	17241682	17243637	1954.62	0.57
6.2000e+09	17761543	17763788	2245.33	0.64
6.4000e+09	18280158	18282454	2295.57	0.65
6.6000e+09	18797467	18799685	2217.88	0.62
6.8000e+09	19313650	19315531	1881.39	0.52
7.0000e+09	19827779	19830039	2260.16	0.61
7.2000e+09	20340508	20343251	2743.43	0.73
7.4000e+09	20852471	20855209	2737.88	0.72
7.6000e+09	21363385	21365950	2564.85	0.67
7.8000e+09	21873456	21875511	2054.53	0.53
8.0000e+09	22383209	22383925	716.10	0.18
8.2000e+09	22890247	22891226	978.96	0.25
8.4000e+09	23395911	23397444	1532.79	0.38
8.6000e+09	23901010	23902608	1597.72	0.39
8.8000e+09	24404437	24406745	2308.45	0.56
9.0000e+09	24907869	24909883	2014.32	0.49
9.2000e+09	25410206	25412046	1840.43	0.44
9.4000e+09	25911484	25913259	1774.70	0.42
9.6000e+09	26411887	26413543	1655.99	0.39
9.8000e+09	26911722	26912921	1199.13	0.28
1.0000e+10	27409998	27411414	1415.99	0.33
1.0500e+10	28653104	28653902	798.22	0.18
1.1000e+10	29889603	29891271	1667.63	0.37
1.1500e+10	31121858	31123782	1923.58	0.42
1.2000e+10	32349742	32351673	1931.13	0.41
1.2500e+10	33572724	33575162	2438.19	0.51
1.3000e+10	34791558	34794447	2889.20	0.59
1.3500e+10	36007278	36009710	2432.35	0.49
1.4000e+10	37218424	37221119	2695.45	0.53
1.4500e+10	38426212	38428830	2617.53	0.51
1.5000e+10	39630644	39632984	2340.26	0.45
1.5500e+10	40831473	40833717	2244.11	0.42
1.6000e+10	42029395	42031152	1757.36	0.33
1.6500e+10	43224737	43225406	669.04	0.12
1.7000e+10	44415280	44416587	1306.68	0.24
1.7500e+10	45602543	45604796	2253.04	0.40
1.8000e+10	46788555	46790130	1574.64	0.28
1.8500e+10	47971101	47972677	1576.41	0.27
1.9000e+10	49149983	49152524	2541.07	0.44
1.9500e+10	50328204	50329750	1545.59	0.26
2.0000e+10	51501939	51504430	2490.61	0.42
2.1000e+10	53844565	53846436	1870.74	0.31
2.2000e+10	56176051	56179072	3021.27	0.49
2.3000e+10	58499396	58502818	3421.73	0.54
2.4000e+10	60813974	60818106	4132.46	0.64
2.5000e+10	63121587	63125334	3747.27	0.57
2.6000e+10	65421526	65424863	3337.33	0.50
2.7000e+10	67713562	67717026	3464.18	0.51
2.8000e+10	69999129	70002129	3000.19	0.43
2.9000e+10	72277589	72280455	2866.44	0.41
3.0000e+10	74548841	74552267	3426.30	0.48
3.1000e+10	76813275	76817809	4533.50	0.62
3.2000e+10	79075132	79077306	2174.10	0.29
3.3000e+10	81330893	81330972	79.06	0.01
3.4000e+10	83578551	83579005	453.67	0.06
3.5000e+10	85820783	85821590	806.86	0.10
3.6000e+10	88058441	88058902	461.25	0.06
3.7000e+10	90291209	90291106	-102.84	-0.01
3.8000e+10	92519367	92518356	-1010.54	-0.13
3.9000e+10	94740446	94740799	353.37	0.04
4.0000e+10	96957511	96958573	1062.14	0.13
4.1000e+10	99171311	99171809	497.68	0.06
4.2000e+10	101379269	101380630	1361.11	0.16
4.3000e+10	103583222	103585155	1933.28	0.23
4.4000e+10	105783893	105785496	1603.21	0.19
4.5000e+10	107981616	107981760	143.51	0.02
4.6000e+10	110174676	110174047	-629.24	-0.07
4.7000e+10	112365011	112362455	-2556.15	-0.29
4.8000e+10	114550485	114547076	-3408.72	-0.38
4.9000e+10	116731541	116727999	-3541.51	-0.39
5.0000e+10	118908266	118905309	-2956.96	-0.33
5.2000e+10	123253565	123249408	-4157.21	-0.45
5.4000e+10	127581668	127579981	-1686.84	-0.18
5.6000e+10	131901796	131897590	-4206.04	-0.44
5.8000e+10	136205903	136202752	-3150.51	-0.32
6.0000e+10	140499927	140495949	-3977.91	-0.40
6.2000e+10	144781518	144777626	-3891.85	-0.39
6.4000e+10	149053736	149048200	-5536.50	-0.54
6.6000e+10	153314379	153308057	-6321.61	-0.61
6.8000e+10	157562750	157557563	-5186.90	-0.50
7.0000e+10	161805194	161797057	-8136.75	-0.77
7.2000e+10	166035035	166026860	-8175.19	-0.76
7.4000e+10	170252188	170247272	-4916.12	-0.45
7.6000e+10	174464261	174458577	-5683.68	-0.52
7.8000e+10	178666912	178661044	-5867.87	-0.53
8.0000e+10	182860245	182854926	-5319.28	-0.47
8.2000e+10	187044018	187040462	-3555.92	-0.31
8.4000e+10	191220885	191217881	-3004.22	-0.26
8.6000e+10	195389715	195387398	-2317.11	-0.20
8.8000e+10	199549014	199549219	204.83	0.02
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9.2000e+10	207852174	207850545	-1628.97	-0.14
9.4000e+10	211992986	211990414	-2571.70	-0.21
9.6000e+10	216125211	216123317	-1894.38	-0.15
9.8000e+10	220252502	220249414	-3087.83	-0.25
1.0000e+11	224373160	224368862	-4297.86	-0.34
1.0500e+11	234644656	234639350	-5305.84	-0.42
1.1000e+11	244873053	244871350	-1702.66	-0.13
1.1500e+11	255067162	255066815	-347.11	-0.03
1.2000e+11	265225667	265227516	1849.20	0.14
1.2500e+11	275351868	275355070	3202.20	0.23
1.3000e+11	285446790	285450956	4165.93	0.30
1.3500e+11	295515788	295516532	743.90	0.05
1.4000e+11	305552719	305553050	331.08	0.02
1.4500e+11	315562701	315561668	-1033.29	-0.07
1.5000e+11	325546175	325543458	-2717.45	-0.18
1.5500e+11	335503460	335499417	-4043.39	-0.26
1.6000e+11	345435474	345430474	-5000.20	-0.32
1.6500e+11	355345473	355337497	-7976.43	-0.51
1.7000e+11	365230863	365221297	-9566.32	-0.60
1.7500e+11	375094725	375082635	-12089.62	-0.75
1.8000e+11	384933062	384922228	-10834.15	-0.66
1.8500e+11	394749000	394740747	-8252.81	-0.50
1.9000e+11	404547727	404538828	-8898.99	-0.53
1.9500e+11	414321363	414317070	-4293.44	-0.25
2.0000e+11	424077103	424076039	-1064.43	-0.06
2.1000e+11	443540248	443538278	-1969.87	-0.11
2.2000e+11	462933062	462929520	-3541.86	-0.20
2.3000e+11	482261351	482253356	-7995.07	-0.44
2.4000e+11	501519361	501513047	-6314.45	-0.34
2.5000e+11	520711417	520711566	148.61	0.01
2.6000e+11	539855154	539851635	-3518.85	-0.18
2.7000e+11	558937945	558935756	-2189.23	-0.11
2.8000e+11	577963642	577966232	2590.22	0.13
2.9000e+11	596943455	596945195	1740.14	0.09
3.0000e+11	615875308	615874620	-688.15	-0.03
3.1000e+11	634759981	634756342	-3638.60	-0.17
3.2000e+11	653592075	653592074	-1.37	-0.00
3.3000e+11	672388699	672383411	-5287.70	-0.24
3.4000e+11	691137025	691131851	-5174.15	-0.24
3.5000e+11	709844592	709838795	-5797.30	-0.26
3.6000e+11	728510321	728505561	-4760.46	-0.21
3.7000e+11	747134806	747133389	-1417.27	-0.06
3.8000e+11	765726620	765723449	-3171.29	-0.14
3.9000e+11	784277119	784276845	-274.11	-0.01
4.0000e+11	802794951	802794622	-329.17	-0.01
4.1000e+11	821278066	821277769	-297.14	-0.01
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4.3000e+11	858145360	858143879	-1480.63	-0.06
4.4000e+11	876530395	876528581	-1813.72	-0.07
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4.6000e+11	913212964	913205314	-7649.67	-0.30
4.7000e+11	931507621	931498848	-8773.38	-0.34
4.8000e+11	949767470	949763437	-4033.00	-0.16
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5.0000e+11	986220868	986208434	-12434.45	-0.47
5.2000e+11	1022558693	1022545325	-13368.12	-0.50
5.4000e+11	1058791137	1058778724	-12412.93	-0.46
5.6000e+11	1094927369	1094912883	-14485.65	-0.52
5.8000e+11	1130968892	1130951734	-17157.76	-0.61
6.0000e+11	1166918775	1166898922	-19853.00	-0.70
6.2000e+11	1202775564	1202757835	-17728.73	-0.61
6.4000e+11	1238545335	1238531632	-13703.07	-0.47
6.6000e+11	1274230059	1274223261	-6797.55	-0.23
6.8000e+11	1309856275	1309835485	-20790.38	-0.69
7.0000e+11	1345389342	1345370891	-18451.22	-0.60
7.2000e+11	1380845752	1380831913	-13838.90	-0.45
7.4000e+11	1416230672	1416220842	-9829.96	-0.31
7.6000e+11	1451547940	1451539837	-8102.59	-0.25
7.8000e+11	1486806214	1486790939	-15275.01	-0.47
8.0000e+11	1521984604	1521976076	-8527.80	-0.26
8.2000e+11	1557107691	1557097077	-10614.38	-0.32
8.4000e+11	1592164661	1592155674	-8987.26	-0.27
8.6000e+11	1627159160	1627153514	-5646.05	-0.17
8.8000e+11	1662099741	1662092163	-7578.18	-0.22
9.0000e+11	1696975691	1696973111	-2580.19	-0.07
9.2000e+11	1731800690	1731797778	-2911.52	-0.08
9.4000e+11	1766574609	1766567521	-7087.77	-0.20
9.6000e+11	1801302719	1801283634	-19085.41	-0.54
9.8000e+11	1835969214	1835947353	-21860.83	-0.61
1.0000e+12	1870585458	1870559864	-25593.72	-0.71
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1.0000e+18	808675898548205	808675901493604	2945398.76	0.12