The best known packings of equal spheres in a sphere

N	radius	distance	ratio	density	contacts	loose	boundary	reference
1	1.000000000000	–	1.0000000000	1.000000000000	1		1
2	0.500000000000	2.000000000000	2.0000000000	0.250000000000	3		2
3	0.464101615138	1.732050807571	2.1547005384	0.299888971118	6		3	[1]
4	0.449489742783	1.632993161854	2.2247448714	0.363261480388	10		4	[1]
5	0.414213562373	1.414213562373	2.4142135624	0.355339059327	12		5	[1]
6	0.414213562373	1.414213562373	2.4142135624	0.426406871193	18		6	[1]
7	0.385913557400	1.256870468483	2.5912538723	0.402316780932	19		7	[2]
8	0.378024844801	1.215562524133	2.6453287760	0.432166419789	24		8	[2]
9	0.366025403785	1.154700538382	2.7320508076	0.441342951092	27		9	[2]
10	0.353049430432	1.091426291402	2.8324645611	0.440054580178	29		10	[5]
11	0.344576516755	1.051462224237	2.9021130326	0.450038547852	36		11	[5]
12	0.344576516755	1.051462224237	2.9021130326	0.490951143111	42		12	[1]
13	0.333333333333	1.000000000000	3.0000000000	0.481481481481	24		12
14	0.323504674183	0.956413627226	3.0911454449	0.473990585425	37	1	13	[2]
15	0.318304823107	0.933862623344	3.1416426249	0.483749932003	42	1	14	[2]
16	0.310975923325	0.902656188230	3.2156830320	0.481171926089	45	1	15	[2]
17	0.305693961650	0.880574112178	3.2712455117	0.485634466608	48	1	16	[2]
18	0.301296589342	0.862444879318	3.3189887817	0.492328697969	51	1	17	[5]
19	0.295332333897	0.838217355793	3.3860159733	0.489425500215	52	1	18	[6]
20	0.287890825717	0.808558114721	3.4735389622	0.477214324831	52	2	19	[7]
21	0.286832818119	0.804391523913	3.4863514104	0.495570920187	57	3	20	[3]
22	0.279342624810	0.775243921527	3.5798331912	0.479550457554	61	1	21	[8]
23	0.275670701290	0.761175067144	3.6275164365	0.481836470826	64	1	22	[8]
24	0.271341339941	0.744769409368	3.6853949355	0.479467459313	68	1	22	[31]
25	0.271191827927	0.744206331155	3.6874267475	0.498620125704	84	1	24	[4]
26	0.266851272489	0.727959450724	3.7474057765	0.494061693011	77		24	[11]
27	0.262232080452	0.710879596426	3.8134159569	0.486879204757	78	1	24	[11]
28	0.260305475681	0.703818852575	3.8416402782	0.493864651913	82		25	[11]
29	0.257925462478	0.695147049080	3.8770891032	0.497600320836	76	3	26	[11]
30	0.255330557656	0.685755432242	3.9164916616	0.499378264835	86	1	27	[11]
31	0.253116209529	0.677792751050	3.9507544849	0.502714681184	85	2	27	[11]
32	0.250787448179	0.669469425117	3.9874403893	0.504739586490	93	1	28	[11]
33	0.248762350343	0.662273384345	4.0199009160	0.508004891658	94	1	29	[11]
34	0.247052663501	0.656228268632	4.0477199712	0.512681372527	102		30	[11]
35	0.244833658425	0.648423122022	4.0844057408	0.513666698068	100	1	30	[11]
36	0.243132164915	0.642469275729	4.1129893297	0.517403964757	98	4	32	[11]
37	0.240686558293	0.633958376272	4.1547812520	0.515890148167	110		32	[11]
38	0.240519372142	0.633378557187	4.1576692600	0.528729790846	116		32	[11]
39	0.236745240285	0.620357062361	4.2239497563	0.517497643020	97	6	33	[11]
40	0.234999237637	0.614376479603	4.2553329537	0.519109947837	98	7	34	[11]
41	0.232755981857	0.606732607497	4.2963450048	0.516995080282	100	7	35	[11]
42	0.232118623301	0.604568961677	4.3081420430	0.525265949758	108	6	36	[11]
43	0.229732967254	0.596502141433	4.3528798324	0.521360856683	127		36	[11]
44	0.228163038226	0.591220813529	4.3828308379	0.522623038233	127	1	36	[11]
45	0.226911569263	0.587026167360	4.4070031477	0.525753813707	119	5	38	[11]
46	0.225168199111	0.581205363158	4.4411244747	0.525144709692	138		38	[11]
47	0.223507049839	0.575683397493	4.4741318035	0.524773065591	133	2	38	[11]
48	0.222405942149	0.572036115512	4.4962827447	0.528056504400	139	1	39	[11]
49	0.221278177007	0.568311226097	4.5191984746	0.530898911129	142	1	40	[11]
50	0.219758275796	0.563308187652	4.5504543407	0.530647009782	142	2	41	[11]
51	0.218550295807	0.559345776534	4.5756057950	0.532383236403	145	2	42	[11]
52	0.216930407731	0.554051414773	4.6097732930	0.530841223195	142	4	42	[11]
53	0.216288057367	0.551958048873	4.6234637833	0.536257636148	142	5	43	[11]
54	0.214920670908	0.547513258709	4.6528795754	0.536078417223	160		44	[11]
55	0.213441688789	0.542723116002	4.6851203515	0.534811127622	151	4	43	[11]
56	0.213067869308	0.541515236189	4.6933402171	0.541678896170	154	4	44	[11]
57	0.211316523700	0.535871563308	4.7322376049	0.537867407396	157	4	45	[31]
58	0.210480101312	0.533185044891	4.7510429431	0.540830438196	165	3	45	[11]
59	0.209759450876	0.530874937027	4.7673656459	0.544523495682	163	4	46	[11]
60	0.209426996435	0.529810644914	4.7749335903	0.551123897404	156	12	48	[11]
61	0.209108659202	0.528792385035	4.7822027257	0.557758101350	204		48	[11]
62	0.206739154000	0.521238770431	4.8370131185	0.547847764413	184	1	48	[11]
63	0.205954921018	0.518748686868	4.8554314461	0.550372935465	204	1	48	[11]
64	0.204107219252	0.512901295725	4.8993857428	0.544195657340	172	6	48	[31]
65	0.203076051707	0.509649765557	4.9242635535	0.544364116868	192	1	50	[11]
66	0.202108764115	0.506607304417	4.9478309581	0.544878127391	187	3	50	[11]
67	0.201216632889	0.503807768599	4.9697680835	0.545841352947	178	7	52	[11]
68	0.200002230133	0.500006969185	4.9999442473	0.544018198088	193	3	52	[11]
69	0.199281532516	0.497756803692	5.0180264442	0.546072434137	184	7	52	[11]
70	0.198688729141	0.495908984103	5.0329981188	0.549057383073	199	3	53	[11]
71	0.197222141221	0.491349229589	5.0704246177	0.544659844168	196	5	54	[11]
72	0.196285915470	0.488447121304	5.0946090432	0.544502539950	211	1	54	[11]
73	0.195628064638	0.486411959537	5.1117410063	0.546532931293	208	3	55	[31]
74	0.195146793635	0.484925181615	5.1243475815	0.549940848873	212	3	56	[31]
75	0.193964427622	0.481280068198	5.1555845175	0.547302624777	212	5	56	[31]
76	0.192947595405	0.478153820759	5.1827544049	0.545923392558	217	3	57	[31]
77	0.192254073574	0.476026104953	5.2014502549	0.547163825196	217	4	58	[11]
78	0.191458926390	0.473591095466	5.2230523740	0.547421008606	173	20	59	[31]
79	0.190659742093	0.471148544090	5.2449457291	0.547525177852	233	1	58	[31]
80	0.189727102250	0.468304204119	5.2707282625	0.546359008245	229	3	58	[11]
81	0.188968327254	0.465994938556	5.2918921098	0.546577909205	235	2	60	[31]
82	0.188293592202	0.463945067805	5.3108551826	0.547419766291	238	2	61	[31]
83	0.187640284124	0.461963537721	5.3293460126	0.548348093717	247		61	[31]
84	0.186955560139	0.459890138775	5.3488647209	0.548901532648	238	4	61	[11]
85	0.186411240258	0.458244384588	5.3644833789	0.550598740536	244	3	60	[31]
86	0.185610957844	0.455828721252	5.3876129492	0.549932374075	250	2	63	[31]
87	0.184934302257	0.453789928270	5.4073256708	0.550264723511	252	3	60	[11]
88	0.184275052856	0.451806833912	5.4266705368	0.550658446830	247	5	64	[11]
89	0.183598057582	0.449773691224	5.4466807175	0.550800407839	256	3	62	[31]
90	0.182935895973	0.447788356070	5.4663957267	0.550984402483	259	3	64	[11]
91	0.182348262626	0.446029169366	5.4840116687	0.551755005487	265	2	64	[11]
92	0.181782421764	0.444337610433	5.5010819544	0.552641484079	259	5	65	[31]
93	0.181267379888	0.442799945758	5.5167123871	0.553913462523	268	3	64	[31]
94	0.180806842580	0.441426642648	5.5307641333	0.555613053163	268	4	60	[31]
95	0.180125543166	0.439397865526	5.5516834671	0.555200074327	274	3	66	[31]
96	0.179567219984	0.437737799751	5.5689451565	0.555843344889	274	4	65	[31]
97	0.179019633861	0.436111851744	5.5859794729	0.556510967846	288	1	66	[31]
98	0.178498681405	0.434566999138	5.6022822809	0.557353987401	289	1	67	[31]
99	0.177878571988	0.432730654930	5.6218126153	0.557193571755	289	2	68	[11]
100	0.177431405921	0.431408169965	5.6359808164	0.558587845356	282	6	69	[11]
101	0.176679757440	0.429188420998	5.6599579629	0.557034067440	298	1	70	[31]
102	0.176215110923	0.427818264840	5.6748822207	0.558122607519	298	2	68	[31]
103	0.175673094380	0.426221910706	5.6923913336	0.558409731670	286	7	69	[31]
104	0.175163370419	0.424722579326	5.7089561454	0.558937462075	300	4	72	[31]
105	0.174632819112	0.423163952131	5.7263005035	0.559199653725	295	6	72	[31]
106	0.174152753738	0.421755365841	5.7420854884	0.559882513029	307	3	72	[31]
107	0.173608230754	0.420159631823	5.7600955649	0.559879687186	307	4	70	[31]
108	0.173168180989	0.418871593975	5.7747329463	0.560825872313	307	5	71	[31]
109	0.172638823470	0.417323965318	5.7924398458	0.560843771142	313	4	73	[31]
110	0.172285229701	0.416291301987	5.8043281002	0.562518518025	325	1	73	[31]
111	0.171743879601	0.414712008450	5.8226237949	0.562298320367	325	2	73	[31]
112	0.171326945524	0.413497083316	5.8367934883	0.563242009507	334		75	[31]
113	0.170853998626	0.412120418703	5.8529505194	0.563577810665	331	2	76	[31]
114	0.170449483384	0.410944191993	5.8668408971	0.564536360556	337	1	77	[31]
115	0.169745356914	0.408899506501	5.8911773387	0.562459882260	331	4	77	[31]
116	0.169367420514	0.407803461354	5.9043232575	0.563569665507	328	6	77	[31]
117	0.169057633289	0.406905797711	5.9151425496	0.565314618649	337	4	78	[31]
118	0.168723599855	0.405938626011	5.9268531543	0.566773460390	334	6	78	[31]
119	0.168090670453	0.404108150932	5.9491701550	0.565168293742	337	6	79	[31]
120	0.167593810095	0.402673147141	5.9668074819	0.564878661167	346	4	77	[31]
121	0.167146216576	0.401381898966	5.9827857339	0.565034573186	355	2	79	[31]
122	0.166776063926	0.400315105473	5.9960642820	0.565927750478	355	3	77	[31]
123	0.166414865560	0.399275031870	6.0090785558	0.566867380471	334	11	78	[31]
124	0.166043033766	0.398205280342	6.0225351062	0.567653950274	343	9	79	[31]
125	0.165617291650	0.396981600871	6.0380168643	0.567841393747	349	8	80	[31]
126	0.165230418840	0.395870723057	6.0521543613	0.568382314745	355	7	80	[31]
127	0.164830084333	0.394722274452	6.0668536575	0.568739200886	367	4	80	[31]
128	0.164456462770	0.393651450684	6.0806366813	0.569328342446	340	14	75	[31]
129	0.164115580588	0.392675295236	6.0932666869	0.570215673737	361	8	76	[31]
130	0.163729008890	0.391569265538	6.1076531690	0.570584869402	385	1	83	[11]
131	0.163455162313	0.390786374978	6.1178856994	0.572093771176	352	13	78	[31]
132	0.163213627869	0.390096285754	6.1269393558	0.573909199081	382	4	79	[31]
133	0.162962154416	0.389378222922	6.1363940823	0.575588241935	370	9	79	[31]
134	0.162832399256	0.389007885903	6.1412839494	0.578531838360	373	9	80	[31]
135	0.162579700716	0.388286982905	6.1508293815	0.580139889296	373	10	81	[31]
136	0.162377283465	0.387709837041	6.1584969194	0.582257005914	376	10	82	[31]
137	0.161772816367	0.385987998303	6.1815082562	0.580012303665	394	5	82	[31]
138	0.161135258979	0.384174590013	6.2059663809	0.577365501645	402	3	84	[31]
139	0.160745199639	0.383066500352	6.2210255874	0.577336263825	373	14	85	[31]
140	0.160407273660	0.382107344734	6.2341312659	0.577830162437	406	4	84	[31]
141	0.160024538913	0.381021937726	6.2490415957	0.577801767737	406	5	85	[31]
142	0.159699976468	0.380102277748	6.2617416866	0.578366194897	406	6	86	[31]
143	0.159446486235	0.379384497534	6.2716966903	0.579670095928	409	6	87	[31]
144	0.159153628674	0.378555784032	6.2832371987	0.580513236652	411	5	88	[31]
145	0.158600757402	0.376992869431	6.3051401291	0.578473905632	415	4	90	[31]
146	0.158245529341	0.375989756769	6.3192938478	0.578558400878	400	12	90	[31]
147	0.157784117755	0.374688060582	6.3377734986	0.577440435470	422	6	91	[31]
148	0.157391538060	0.373581669707	6.3535817257	0.577039912876	427	5	90	[31]
149	0.157074962827	0.372690229618	6.3663869913	0.577440399581	424	7	91	[31]
150	0.156703678076	0.371645586497	6.3814711453	0.577203332042	418	10	94	[31]
151	0.156284188488	0.370466420934	6.3985999459	0.576397479835	418	11	93	[31]
152	0.156015192670	0.369710903123	6.4096321832	0.577223844761	428	8	93	[31]
153	0.155581386131	0.368493502099	6.4275041177	0.576188173801	415	14	93	[31]
154	0.155232190987	0.367514456235	6.4419628019	0.576057828083	430	10	93	[31]
155	0.154882847307	0.366535803500	6.4564928744	0.575892828008	439	8	94	[31]
156	0.154590492826	0.365717422183	6.4687030989	0.576332278156	426	13	95	[31]
157	0.154304605357	0.364917691014	6.4806879723	0.576814696187	442	9	95	[31]
158	0.154079300217	0.364287811509	6.4901644711	0.577949615306	449	7	96	[31]
159	0.153695958755	0.363216884865	6.5063519438	0.577277285755	460	5	97	[31]
160	0.153336259774	0.362212889223	6.5216146623	0.576838952415	439	13	98	[11]
161	0.153095571235	0.361541553060	6.5318675905	0.577715152779	457	8	98	[31]
162	0.152766222693	0.360623541660	6.5459496371	0.577559904144	481	1	99	[31]
163	0.152333352287	0.359418062980	6.5645506055	0.576199135780	462	8	100	[31]
164	0.152097125131	0.358760725170	6.5747462297	0.577041255291	459	10	99	[31]
165	0.151818107200	0.357984787199	6.5868295847	0.577370594951	463	10	99	[31]
166	0.151510034723	0.357128642467	6.6002228950	0.577340841944	472	8	101	[31]
167	0.151275315465	0.356476766193	6.6104638217	0.578123566156	477	7	101	[31]
168	0.150959747967	0.355600921406	6.6242823896	0.577953326846	481	6	102	[31]
169	0.150633585245	0.354696353960	6.6386257645	0.577633195437	490	5	103	[31]
170	0.150414852078	0.354090116678	6.6482796492	0.578523605552	480	9	102	[31]
171	0.150126724785	0.353292024030	6.6610392083	0.578588956932	484	9	102	[31]
172	0.149823942661	0.352453921438	6.6745006321	0.578458372460	484	10	104	[31]
173	0.149550842703	0.351698491132	6.6866891682	0.578645655624	481	12	104	[31]
174	0.149295833059	0.350993538908	6.6981105869	0.579018323663	483	12	104	[31]
175	0.149008670736	0.350200209125	6.7110188626	0.578992142861	487	12	105	[31]
176	0.148745774624	0.349474387768	6.7228800450	0.579224043324	490	12	106	[31]
177	0.148341239250	0.348358394433	6.7412137384	0.577775304058	505	8	106	[31]
178	0.148066413782	0.347600836913	6.7537260778	0.577816149121	505	9	106	[31]
179	0.147779767882	0.346811216896	6.7668261653	0.577694152012	519	5	109	[31]
180	0.147648144480	0.346448813419	6.7728585654	0.579370643052	522	4	109	[31]
181	0.147222317786	0.345277135780	6.7924484211	0.577563217473	517	8	109	[31]
182	0.146956187105	0.344545461518	6.8047492229	0.577610412993	524	6	107	[31]
183	0.146713480572	0.343878585287	6.8160062463	0.577911252205	529	6	108	[31]
184	0.146448929587	0.343152119805	6.8283189424	0.577931582438	517	11	109	[31]
185	0.146147309943	0.342324411798	6.8424112657	0.577489651564	532	7	109	[31]
186	0.145873754857	0.341574224388	6.8552427473	0.577356992910	547	3	110	[31]
187	0.145641283299	0.340937080531	6.8661850359	0.577690329525	523	12	112	[31]
188	0.145383154153	0.340230022049	6.8783760115	0.577696996722	532	10	111	[31]
189	0.145201386787	0.339732387354	6.8869865649	0.578594228038	539	8	112	[31]
190	0.144943777745	0.339027479066	6.8992268282	0.578565229663	540	9	112	[31]
191	0.144676708866	0.338297133648	6.9119625946	0.578401258999	559	4	114	[31]
192	0.144447612062	0.337670992679	6.9229251057	0.578671813415	527	15	114	[31]
193	0.144165689697	0.336900935056	6.9364631911	0.578286496167	556	7	115	[31]
194	0.143870419235	0.336094961481	6.9506991452	0.577718476528	562	6	112	[31]
195	0.143614018530	0.335395538081	6.9631085477	0.577597247624	568	5	116	[31]
196	0.143322983399	0.334602144383	6.9772480051	0.577036906367	563	5	115	[31]
197	0.143104594387	0.334007145912	6.9878958414	0.577333764513	577	4	115	[31]
198	0.142899447497	0.333448501648	6.9979276863	0.577772462939	559	11	116	[31]
199	0.142650446091	0.332770794457	7.0101428170	0.577660243157	575	6	117	[31]
200	0.142396339034	0.332079596940	7.0226524557	0.577466064231	581	5	118	[31]
201	0.142224083682	0.331611277436	7.0311579735	0.578249799131	583	6	118	[31]
202	0.141939049418	0.330836753081	7.0452775617	0.577639717069	585	6	118	[31]
203	0.141748016525	0.330317946837	7.0547724371	0.578158625904	598	3	118	[31]
204	0.141533175867	0.329734759430	7.0654812476	0.578368888188	598	4	118	[31]
205	0.141255065371	0.328980258689	7.0793921434	0.577784587040	598	5	120	[31]
206	0.141051658936	0.328428735915	7.0896011259	0.578098463915	592	7	120	[31]
207	0.140838253195	0.327850381418	7.1003436731	0.578272094507	601	6	120	[31]
208	0.140618552118	0.327255265900	7.1114371819	0.578350613573	598	8	117	[31]
209	0.140398612826	0.326659809816	7.1225774947	0.578408593535	613	4	118	[31]
210	0.140173476026	0.326050597692	7.1340172788	0.578384737356	602	7	118	[31]
211	0.139951366100	0.325449888724	7.1453393266	0.578380818514	609	7	119	[31]
212	0.139719673249	0.324823592739	7.1571882237	0.578240551221	597	12	121	[31]
213	0.139523883133	0.324294609456	7.1672317136	0.578529178363	621	5	119	[31]
214	0.139339364720	0.323796300210	7.1767228307	0.578942259578	618	7	120	[31]
215	0.139163141260	0.323320591694	7.1858107754	0.579443545831	616	9	120	[31]
216	0.138962105620	0.322778141420	7.1962064445	0.579619395389	619	9	121	[31]
217	0.138817477406	0.322388050764	7.2037038757	0.580486572376	641	2	123	[31]
218	0.138657850737	0.321957658419	7.2119969745	0.581152199775	644	2	124	[31]
219	0.138410295838	0.321290505606	7.2248960523	0.580696629857	628	8	123	[31]
220	0.138186822072	0.320688579872	7.2365800516	0.580527194453	636	7	123	[31]
221	0.138002112058	0.320191299742	7.2462659092	0.580830579610	639	5	124	[31]
222	0.137834010655	0.319738918859	7.2551034048	0.581329221953	643	7	125	[31]
223	0.137634296744	0.319201694186	7.2656309049	0.581413173203	630	12	125	[31]
224	0.137413481321	0.318607996637	7.2773063486	0.581213971697	646	8	125	[31]
225	0.137285232553	0.318263318847	7.2841046441	0.582175586373	661	4	126	[31]
226	0.137130906453	0.317848692179	7.2923021211	0.582793204869	669	2	127	[31]
227	0.136859964105	0.317121112249	7.3067387277	0.581909064677	649	10	127	[31]
228	0.136680119570	0.316638415652	7.3163529791	0.582171441386	670	4	128	[31]
229	0.136416453724	0.315931108952	7.3304940328	0.581347418988	672	4	129	[31]
230	0.136262665884	0.315518759007	7.3387673249	0.581913563557	668	3	130	[31]
231	0.136093380525	0.315065025448	7.3478959531	0.582268084193	678	4	129	[31]
232	0.135857677632	0.314433569832	7.3606440021	0.581755562071	671	5	131	[31]
233	0.135757390409	0.314165001593	7.3660814854	0.582970212500	669	8	132	[31]
234	0.135532096038	0.313561892621	7.3783260883	0.582562227227	683	5	132	[31]
235	0.135372821059	0.313135706016	7.3870071716	0.582991604058	679	8	133	[31]
236	0.135241202949	0.312783641889	7.3941962819	0.583766378053	700	2	134	[31]
237	0.135074436669	0.312337714122	7.4033253417	0.584073955423	694	3	134	[31]
238	0.134859880066	0.311764249418	7.4151037322	0.583747810171	694	6	135	[31]
239	0.134579925724	0.311016417863	7.4305286960	0.582557440875	684	10	132	[31]
240	0.134414860778	0.310575712746	7.4396535786	0.582845035151	702	5	131	[31]
241	0.134240473825	0.310110301455	7.4493181639	0.582998546216	681	13	132	[31]
242	0.134078338355	0.309677755608	7.4583263208	0.583298988326	696	9	133	[31]
243	0.133935543756	0.309296941562	7.4662779719	0.583839950445	709	6	133	[31]
244	0.133769310544	0.308853778035	7.4755562089	0.584062458789	703	8	134	[31]
245	0.133590861995	0.308378238721	7.4855419380	0.584112285564	718	5	135	[31]
246	0.133496533034	0.308126944954	7.4908312394	0.585254913053	715	6	135	[31]
247	0.133376993241	0.307808567741	7.4975449341	0.586056816350	721	4	136	[31]
248	0.133205378474	0.307351649782	7.5072043746	0.586161059206	725	5	136	[31]
249	0.132972838465	0.306732809223	7.5203328104	0.585447782378	727	6	137	[31]
250	0.132854110725	0.306416976355	7.5270535066	0.586225895733	735	4	138	[31]
251	0.132731105487	0.306089855930	7.5340290155	0.586937497614	716	11	138	[31]
252	0.132582652149	0.305695182320	7.5424648986	0.587300874660	729	8	138	[31]
253	0.132412960680	0.305244211081	7.5521308100	0.587370336544	736	7	137	[31]
254	0.132238264513	0.304780123633	7.5621077128	0.587361044494	744	5	138	[31]
255	0.132067893549	0.304327706205	7.5718630254	0.587397283107	751	4	140	[31]
256	0.131938045013	0.303983014704	7.5793149724	0.587963138232	747	6	140	[31]
257	0.131711352310	0.303381491075	7.5923599786	0.587222583850	749	6	140	[31]
258	0.131437440755	0.302655092270	7.6081822216	0.585837258485	753	6	141	[31]
259	0.131177140298	0.301965213814	7.6232794657	0.584620770298	749	8	143	[31]
260	0.131055631094	0.301643317533	7.6303474460	0.585248630733	758	6	142	[31]
261	0.130907926034	0.301252145670	7.6389568630	0.585515416683	761	6	143	[31]
262	0.130744385418	0.300819191098	7.6485119939	0.585558696253	763	7	144	[31]
263	0.130501548432	0.300176609163	7.6627443277	0.584524531697	755	10	141	[31]
264	0.130355113444	0.299789294364	7.6713523051	0.584774118076	760	10	142	[31]
265	0.130147682532	0.299240870935	7.6835789969	0.584191443589	756	10	135	[31]
266	0.130032631517	0.298936802063	7.6903773179	0.584842185637	779	4	133	[31]
267	0.129963082823	0.298753030491	7.6944927612	0.586099397770	769	9	134	[31]
268	0.129888967208	0.298557223878	7.6988832962	0.587288619020	763	13	135	[31]
269	0.129795710556	0.298310895799	7.7044148510	0.588211215315	778	6	137	[31]
270	0.129730440741	0.298138523542	7.7082910864	0.589507649340	771	7	137	[31]
271	0.129662548876	0.297959254100	7.7123271806	0.590762547645	772	12	137	[31]
272	0.129504298770	0.297541500978	7.7217513975	0.590774114568	786	7	138	[31]
273	0.129393946194	0.297250278994	7.7283368304	0.591431594455	794	6	139	[31]
274	0.129221616623	0.296795646492	7.7386433178	0.591229468993	777	14	139	[31]
275	0.129077536225	0.296415677845	7.7472814344	0.591404596208	801	6	140	[31]
276	0.128809944144	0.295710317808	7.7633757754	0.589871288540	783	13	139	[31]
277	0.128723663012	0.295482977208	7.7685794251	0.590819659807	792	11	140	[31]
278	0.128612047560	0.295188950455	7.7753213557	0.591411483818	794	12	141	[31]
279	0.128488061420	0.294862424098	7.7828242480	0.591823946036	793	13	141	[31]
280	0.128376338034	0.294568272147	7.7895974859	0.592397177789	795	13	142	[31]
281	0.128253970819	0.294246183007	7.7970295470	0.592814448346	817	8	143	[31]
282	0.128050030279	0.293709581342	7.8094475872	0.592090597976	823	6	144	[31]
283	0.127927013754	0.293386025646	7.8169572685	0.592479354935	817	10	144	[31]
284	0.127812148072	0.293083990540	7.8239824233	0.592972757901	832	5	145	[31]
285	0.127700864366	0.292791449972	7.8308005585	0.593507717611	826	9	146	[31]
286	0.127535355781	0.292356502068	7.8409629540	0.593277430582	831	8	147	[31]
287	0.127390664731	0.291976396727	7.8498687648	0.593327814612	833	8	148	[31]
288	0.127202821777	0.291483118761	7.8614608232	0.592765234197	829	10	149	[31]
289	0.127063199605	0.291116606718	7.8700993136	0.592866900223	840	8	146	[31]
290	0.126919078579	0.290738408010	7.8790360850	0.592896285372	836	9	147	[31]
291	0.126762134512	0.290326701399	7.8887911114	0.592736429330	846	7	148	[31]
292	0.126624068271	0.289964638756	7.8973927600	0.592832002235	864	3	149	[31]
293	0.126497466240	0.289632740262	7.9052966809	0.593079756020	842	10	150	[31]
294	0.126356900687	0.289264347847	7.9140909168	0.593122262129	849	10	151	[31]
295	0.126238610117	0.288954425267	7.9215067329	0.593469806991	859	8	154	[31]
296	0.126100367140	0.288592333486	7.9301910270	0.593527388109	856	9	154	[31]
297	0.125882407804	0.288021677925	7.9439217715	0.592449821635	856	11	154	[31]
298	0.125687060993	0.287510467672	7.9562684663	0.591681481797	862	9	155	[31]
299	0.125604349113	0.287294084744	7.9615077588	0.592495723826	860	11	152	[31]
300	0.125444098089	0.286874967775	7.9716783431	0.592204843253	864	11	153	[31]
301	0.125294923934	0.286484959016	7.9811692972	0.592061642985	874	9	154	[31]
302	0.125131371140	0.286057510836	7.9916010741	0.591705427896	884	6	155	[31]
303	0.125026422276	0.285783309254	7.9983093317	0.592172233220	878	8	155	[31]
304	0.124884086246	0.285411530709	8.0074253659	0.592099760236	886	8	156	[31]
305	0.124794376498	0.285177272967	8.0131815877	0.592768184735	892	6	157	[31]
306	0.124667948785	0.284847215664	8.0213078802	0.592906031288	899	5	158	[31]
307	0.124531316162	0.284490624190	8.0301086572	0.592889978916	891	9	158	[31]
308	0.124407676829	0.284168039250	8.0380891717	0.593051293010	897	8	158	[31]
309	0.124302943140	0.283894851915	8.0448618089	0.593475389691	899	8	159	[31]
310	0.124148769392	0.283492824017	8.0548522945	0.593183348021	885	14	160	[31]
311	0.124060183015	0.283261887653	8.0606039399	0.593823857082	912	6	161	[31]
312	0.123962061703	0.283006149127	8.0669842552	0.594320849499	900	11	160	[31]
313	0.123828999645	0.282659434277	8.0756527378	0.594307801087	907	7	160	[31]
314	0.123621072616	0.282117857363	8.0892357495	0.593208233921	905	11	161	[31]
315	0.123435880317	0.281635712768	8.1013721248	0.592426954249	911	10	162	[31]
316	0.123284337546	0.281241325610	8.1113304407	0.592121458554	916	8	163	[31]
317	0.123151897501	0.280896764559	8.1200535298	0.592082991497	925	7	164	[31]
318	0.123027850330	0.280574133115	8.1282408602	0.592157762673	926	8	165	[31]
319	0.122899912029	0.280241476918	8.1367023254	0.592168632878	920	11	165	[31]
320	0.122749461479	0.279850410091	8.1466752518	0.591846065403	921	11	165	[31]
321	0.122603374679	0.279470814318	8.1563823395	0.591578396043	931	10	163	[31]
322	0.122473763911	0.279134136107	8.1650140248	0.591541293368	932	10	164	[31]
323	0.122363440653	0.278847637668	8.1723756268	0.591776292517	942	8	165	[31]
324	0.122254876984	0.278565779013	8.1796327858	0.592029829388	958	4	166	[31]
325	0.122126639414	0.278232931758	8.1882217082	0.591990286838	948	7	166	[31]
326	0.121988143481	0.277873567595	8.1975179838	0.591793874737	948	7	166	[31]
327	0.121864670472	0.277553279943	8.2058236905	0.591808513010	966	4	167	[31]
328	0.121748636245	0.277252370493	8.2136443647	0.591924286513	945	12	168	[31]
329	0.121679866694	0.277074069192	8.2182864526	0.592723400982	951	10	169	[31]
330	0.121508428489	0.276629696697	8.2298817657	0.592015601522	955	11	169	[31]
331	0.121397545044	0.276342376143	8.2373988670	0.592185414815	955	12	168	[31]
332	0.121290007254	0.276063794098	8.2447022853	0.592397408229	959	9	169	[31]
333	0.121125861928	0.275638698833	8.2558752036	0.591772630279	961	12	169	[31]
334	0.121004422608	0.275324303603	8.2641607509	0.591766257278	957	14	170	[31]
335	0.120895240137	0.275041714382	8.2716242498	0.591932811085	963	13	170	[31]
336	0.120790826424	0.274771533451	8.2787743871	0.592162819053	959	15	171	[31]
337	0.120682229095	0.274490595068	8.2862241400	0.592324737827	982	8	172	[31]
338	0.120573412828	0.274209159893	8.2937023722	0.592476817136	973	12	172	[31]
339	0.120452988193	0.273897782781	8.3019941224	0.592450995401	976	11	172	[31]
340	0.120330982817	0.273582405351	8.3104116379	0.592394896818	1001	5	172	[31]
341	0.120241747884	0.273351793165	8.3165790385	0.592816415591	988	11	172	[31]
342	0.120153250085	0.273123132173	8.3227045402	0.593243070826	981	12	172	[31]
343	0.120025125494	0.272792164802	8.3315888726	0.593076377477	977	16	173	[31]
344	0.119887157332	0.272435877583	8.3411770056	0.592756644098	1012	6	173	[31]
345	0.119733990337	0.272040471909	8.3518472673	0.592204174022	995	12	173	[31]
346	0.119629883791	0.271771795949	8.3591153674	0.592372844436	1003	10	174	[31]
347	0.119513267248	0.271470909901	8.3672718772	0.592349235985	1006	11	175	[31]
348	0.119409379294	0.271202932410	8.3745515295	0.592508474632	1006	12	176	[31]
349	0.119280053909	0.270869427764	8.3836313552	0.592282508564	1031	4	176	[31]
350	0.119149402841	0.270532603884	8.3928242707	0.592029918515	1006	13	176	[31]
351	0.119036952378	0.270242781918	8.4007527076	0.592041996728	1005	15	176	[31]
352	0.118864433845	0.269798288506	8.4129454678	0.591151018148	1024	10	178	[31]
353	0.118781276684	0.269584096527	8.4188352568	0.591587068147	1032	8	178	[31]
354	0.118628767297	0.269191375655	8.4296585287	0.590980722573	1022	12	178	[31]
355	0.118508158962	0.268880898143	8.4382375759	0.590844377525	1019	12	176	[31]
356	0.118426010154	0.268669474187	8.4440909450	0.591277416383	1046	6	177	[31]
357	0.118317089585	0.268389209288	8.4518644222	0.591303773568	1034	9	177	[31]
358	0.118248107320	0.268211745961	8.4567949768	0.591923552895	1060	3	180	[31]
359	0.118143750077	0.267943329964	8.4642649260	0.592006812612	1035	13	181	[31]
360	0.118033769573	0.267660519192	8.4721516869	0.591999489482	1048	10	180	[31]
361	0.117916830316	0.267359891604	8.4805536014	0.591881262550	1040	13	179	[31]
362	0.117812440315	0.267091592989	8.4880679606	0.591945912666	1044	12	179	[31]
363	0.117695431659	0.266790937918	8.4965064991	0.591814284192	1048	12	180	[31]
364	0.117605334466	0.266559486496	8.5030156544	0.592082803744	1062	9	181	[31]
365	0.117480180108	0.266238054852	8.5120741140	0.591815963384	1071	7	181	[31]
366	0.117361088611	0.265932278980	8.5207116927	0.591634475581	1067	9	182	[31]
367	0.117272910770	0.265705929275	8.5271184405	0.591914771746	1059	13	182	[31]
368	0.117162653607	0.265422966270	8.5351429761	0.591855130887	1078	7	182	[31]
369	0.117049783806	0.265133371415	8.5433733193	0.591749928052	1060	10	181	[31]
370	0.116960492536	0.264904325452	8.5498955957	0.591996705065	1068	13	183	[31]
371	0.116849082906	0.264618607407	8.5580474842	0.591902036371	1093	5	182	[31]
372	0.116759146054	0.264388010433	8.5646395490	0.592128097937	1074	12	182	[31]
373	0.116661197072	0.264136923874	8.5718304380	0.592226882606	1069	14	182	[31]
374	0.116567867650	0.263897731091	8.5786934269	0.592390599885	1093	9	183	[31]
375	0.116474388770	0.263658205919	8.5855784311	0.592546705569	1087	12	184	[31]
376	0.116359036848	0.263362704311	8.5940896993	0.592363374089	1089	11	185	[31]
377	0.116271712298	0.263139052842	8.6005441929	0.592602603176	1102	8	185	[31]
378	0.116185186701	0.262917491205	8.6069492023	0.592848984716	1073	18	186	[31]
379	0.116077311357	0.262641321121	8.6149479886	0.592763195441	1099	12	186	[31]
380	0.115991094867	0.262420648013	8.6213515024	0.593003887171	1130	2	186	[31]
381	0.115887474336	0.262155485805	8.6290602650	0.592972386172	1131	3	187	[31]
382	0.115755769778	0.261818547007	8.6388782340	0.592504025155	1121	6	187	[31]
383	0.115662444510	0.261579854416	8.6458487389	0.592619413614	1125	7	188	[31]
384	0.115556189631	0.261308153839	8.6537986688	0.592530708614	1123	9	189	[31]
385	0.115476816431	0.261105234043	8.6597468731	0.592850426401	1123	10	190	[31]
386	0.115354942253	0.260793730192	8.6688960219	0.592510325431	1115	9	191	[31]
387	0.115283018913	0.260609938268	8.6743044156	0.592934864355	1128	10	192	[31]
388	0.115198161480	0.260393133162	8.6806940940	0.593155237437	1123	13	192	[31]
389	0.115109404337	0.260166409048	8.6873874968	0.593310481891	1146	6	193	[31]
390	0.114999815965	0.259886535708	8.6956660896	0.593138402385	1137	8	194	[31]
391	0.114902600384	0.259638318753	8.7030232271	0.593152451411	1128	14	195	[31]
392	0.114807220622	0.259394842110	8.7102535414	0.593189802682	1148	7	196	[31]
393	0.114662281461	0.259024955246	8.7212637605	0.592453523516	1155	7	196	[31]
394	0.114557173753	0.258756794583	8.7292656343	0.592329133240	1153	8	195	[31]
395	0.114484466548	0.258571334377	8.7348094475	0.592702542397	1157	7	196	[31]
396	0.114408864214	0.258378521624	8.7405814827	0.593026647225	1146	12	197	[31]
397	0.114329633323	0.258176490092	8.7466387404	0.593289877541	1152	10	197	[31]
398	0.114241058331	0.257950674742	8.7534203080	0.593402983275	1173	3	198	[31]
399	0.114161665991	0.257748308259	8.7595077675	0.593654534567	1153	13	198	[31]
400	0.114057861481	0.257483771280	8.7674798301	0.593520419446	1169	8	199	[31]
401	0.113923230762	0.257140768648	8.7778409488	0.592899727361	1184	3	199	[31]
402	0.113829818286	0.256902840188	8.7850443325	0.592917379849	1178	8	192	[31]
403	0.113742497220	0.256680472353	8.7917886845	0.593025438132	1151	15	192	[31]
404	0.113674911422	0.256508391530	8.7970158718	0.593437844466	1163	15	192	[31]
405	0.113578308717	0.256262476052	8.8044980709	0.593391355573	1187	8	193	[31]
406	0.113482989836	0.256019881254	8.8118933194	0.593360102900	1173	13	194	[31]
407	0.113394114812	0.255793733622	8.8187998263	0.593425158704	1170	16	196	[31]
408	0.113272154676	0.255483472801	8.8282950285	0.592965803851	1189	9	194	[31]
409	0.113216834497	0.255342769013	8.8326087233	0.593548664294	1192	8	195	[31]
410	0.113126840761	0.255113912475	8.8396351677	0.593582151497	1197	8	196	[31]
411	0.113042614054	0.254899763721	8.8462214747	0.593701843256	1199	10	196	[31]
412	0.112961076461	0.254692490856	8.8526068565	0.593859465448	1189	13	197	[31]
413	0.112886218623	0.254502231829	8.8584772543	0.594118161573	1200	11	198	[31]
414	0.112801261865	0.254286344235	8.8651490548	0.594213090419	1203	12	198	[31]
415	0.112676302265	0.253968878669	8.8749806295	0.593671027939	1200	13	199	[31]
416	0.112594791156	0.253761844158	8.8814055227	0.593810988208	1215	9	196	[31]
417	0.112507287994	0.253539632432	8.8883130847	0.593851726182	1200	14	197	[31]
418	0.112438348270	0.253364592873	8.8937628077	0.594182221615	1222	7	198	[31]
419	0.112372828151	0.253198260970	8.8989484064	0.594563105505	1207	14	199	[31]
420	0.112267548097	0.252931044384	8.9072934873	0.594308585084	1227	9	198	[31]
421	0.112194049553	0.252744531610	8.9131286729	0.594554358674	1228	9	199	[31]
422	0.112130710029	0.252583823533	8.9181634518	0.594957806755	1241	6	200	[31]
423	0.112061868670	0.252409181937	8.9236420191	0.595269934405	1231	12	200	[31]
424	0.111975345672	0.252189722721	8.9305372892	0.595296174924	1258	4	201	[31]
425	0.111862604876	0.251903828147	8.9395379368	0.594899651938	1253	6	202	[31]
426	0.111761439909	0.251647350004	8.9476298875	0.594683056053	1228	13	203	[31]
427	0.111642720577	0.251346441714	8.9571446739	0.594181476066	1240	12	204	[31]
428	0.111564690005	0.251148707734	8.9634094798	0.594325080875	1250	9	204	[31]
429	0.111490795579	0.250961487004	8.9693502931	0.594530768982	1236	15	205	[31]
430	0.111415066881	0.250769651224	8.9754467506	0.594703139952	1262	7	206	[31]
431	0.111323260162	0.250537130481	8.9828486746	0.594613848077	1253	10	207	[31]
432	0.111273684316	0.250411588702	8.9868508098	0.595197571654	1259	8	207	[31]
433	0.111181328085	0.250177750756	8.9943160171	0.595091118688	1258	8	207	[31]
434	0.111117393831	0.250015903247	8.9994911285	0.595437071433	1240	19	208	[31]
435	0.111047596454	0.249839240011	9.0051476298	0.595685112067	1256	14	208	[31]
436	0.110944561345	0.249578499880	9.0135107830	0.595394120107	1259	14	209	[31]
437	0.110875029546	0.249402577209	9.0191633237	0.595638392216	1252	15	210	[31]
438	0.110776193899	0.249152560107	9.0272103130	0.595406304125	1264	13	210	[31]
439	0.110677296244	0.248902441771	9.0352767364	0.595168782390	1274	13	211	[31]
440	0.110575255473	0.248644432603	9.0436146471	0.594876113593	1295	6	206	[31]
441	0.110478623674	0.248400154542	9.0515247814	0.594666337816	1277	12	207	[31]
442	0.110393832316	0.248185851956	9.0584770817	0.594643532431	1293	8	207	[31]
443	0.110332045492	0.248029717004	9.0635499010	0.594988724633	1283	13	207	[31]
444	0.110278472285	0.247894355368	9.0679529674	0.595463565259	1294	10	208	[31]
445	0.110194692365	0.247682704114	9.0748472412	0.595445532768	1305	8	209	[31]
446	0.110124591676	0.247505641005	9.0806239077	0.595645399865	1309	8	210	[31]
447	0.110044469557	0.247303299531	9.0872354061	0.595678859225	1309	10	211	[31]
448	0.109965274119	0.247103334109	9.0937799047	0.595723452092	1299	13	212	[31]
449	0.109860500143	0.246838838543	9.1024526440	0.595348215882	1306	10	212	[31]
450	0.109770115411	0.246610717774	9.1099476051	0.595202677540	1295	16	213	[31]
451	0.109681879273	0.246388064489	9.1172763143	0.595087997336	1289	19	213	[31]
452	0.109596660874	0.246173067996	9.1243655786	0.595018409004	1316	12	214	[31]
453	0.109542039748	0.246035286645	9.1289152758	0.595443656081	1315	11	214	[31]
454	0.109475553468	0.245867598345	9.1344594142	0.595672157892	1323	12	214	[31]
455	0.109394347733	0.245662819351	9.1412401164	0.595656720471	1311	14	213	[31]
456	0.109329526213	0.245499383735	9.1466599613	0.595905290101	1319	15	213	[31]
457	0.109251422025	0.245302489898	9.1531989375	0.595933082659	1332	10	215	[31]
458	0.109158767985	0.245068961926	9.1609681792	0.595718866050	1342	7	213	[31]
459	0.109065951652	0.244835073604	9.1687642647	0.595497942041	1343	10	214	[31]
460	0.108969002458	0.244590822898	9.1769216699	0.595205255638	1320	17	215	[31]
461	0.108883112224	0.244374478180	9.1841606983	0.595089795390	1331	16	216	[31]
462	0.108820388914	0.244216513844	9.1894543842	0.595350601383	1350	9	216	[31]
463	0.108756943334	0.244056753139	9.1948152398	0.595596271170	1349	10	216	[31]
464	0.108682687764	0.243869800961	9.2010974385	0.595660896768	1363	8	217	[31]
465	0.108605312265	0.243675026920	9.2076527303	0.595670590749	1364	7	217	[31]
466	0.108552761588	0.243542762624	9.2121101792	0.596085483972	1344	16	217	[31]
467	0.108505275327	0.243423258319	9.2161417681	0.596581031163	1369	8	217	[31]
468	0.108440455926	0.243260153843	9.2216506419	0.596787691815	1353	16	218	[31]
469	0.108340189369	0.243007900720	9.2301850848	0.596405464253	1369	9	218	[31]
470	0.108279132992	0.242854321342	9.2353897964	0.596667203331	1362	14	219	[31]
471	0.108216050315	0.242695667159	9.2407734073	0.596892255329	1375	12	220	[31]
472	0.108130654558	0.242480930891	9.2480712716	0.596744595574	1354	18	220	[31]
473	0.108052942589	0.242285552021	9.2547225095	0.596720469849	1377	12	221	[31]
474	0.107934639322	0.241988186247	9.2648662772	0.596020058147	1373	13	217	[31]
475	0.107890818608	0.241878059005	9.2686292764	0.596550308206	1372	14	217	[31]
476	0.107826194413	0.241715669610	9.2741843060	0.596732629131	1372	17	218	[31]
477	0.107768218627	0.241570006532	9.2791735146	0.597022215237	1389	12	219	[31]
478	0.107706599323	0.241415209932	9.2844821607	0.597248184557	1378	16	220	[31]
479	0.107627557535	0.241216676834	9.2913006938	0.597180980291	1394	9	220	[31]
480	0.107559878114	0.241046711093	9.2971470174	0.597299486816	1401	10	221	[31]
481	0.107494798404	0.240883298409	9.3027757142	0.597458060980	1406	9	222	[31]
482	0.107415820111	0.240685018918	9.3096156503	0.597381520631	1405	12	222	[31]
483	0.107343910041	0.240504515117	9.3158521952	0.597419456580	1407	11	222	[31]
484	0.107325823151	0.240459119205	9.3174221323	0.598353789419	1401	12	221	[31]
485	0.107262823140	0.240301011138	9.3228946500	0.598534803302	1418	10	222	[31]
486	0.107204026782	0.240153472905	9.3280078185	0.598783142208	1417	12	223	[31]
487	0.107134705137	0.239979548434	9.3340435177	0.598851990163	1391	19	224	[31]
488	0.107009271262	0.239664909877	9.3449846748	0.597976396202	1422	12	226	[31]
489	0.106895274880	0.239379037808	9.3549504514	0.597288818062	1428	11	226	[31]
490	0.106823335858	0.239198671767	9.3612504419	0.597302713542	1420	15	221	[31]
491	0.106759174457	0.239037830346	9.3668764777	0.597443874350	1398	23	221	[31]
492	0.106695223529	0.238877539535	9.3724907913	0.597585478704	1419	16	222	[31]
493	0.106623751545	0.238698424610	9.3787733550	0.597597533693	1453	7	222	[31]
494	0.106572831570	0.238570832264	9.3832544868	0.597952193639	1452	9	222	[31]
495	0.106501040929	0.238390968110	9.3895795879	0.597952597165	1442	8	222	[31]
496	0.106448377583	0.238259043826	9.3942249070	0.598272190873	1461	7	222	[31]
497	0.106388133700	0.238108148990	9.3995445283	0.598461146085	1443	12	222	[31]
498	0.106320579777	0.237938968653	9.4055168068	0.598523699052	1450	10	223	[31]
499	0.106249875183	0.237761925247	9.4117757623	0.598529873051	1453	12	223	[31]
500	0.106171752886	0.237566340578	9.4187010463	0.598407416023	1453	13	224	[31]
501	0.106087527163	0.237355513848	9.4261788049	0.598178370037	1462	9	225	[31]
502	0.105967582145	0.237055346157	9.4368483243	0.597341643737	1465	10	226	[31]
503	0.105892708452	0.236868012268	9.4435208488	0.597263747177	1442	16	229	[31]
504	0.105786103007	0.236601339707	9.4530375123	0.596645531732	1459	14	234	[31]
505	0.105681137957	0.236338832697	9.4624264966	0.596051549414	1465	12	229	[31]
506	0.105638030921	0.236231044193	9.4662877685	0.596501320049	1463	15	230	[31]
507	0.105575052709	0.236073586787	9.4719346506	0.596611856817	1467	16	233	[31]
508	0.105502767764	0.235892888121	9.4784243219	0.596561567931	1464	18	225	[31]
509	0.105436694437	0.235727742869	9.4843641043	0.596613570869	1459	20	232	[31]
510	0.105408587453	0.235657498997	9.4868930907	0.597307759590	1492	9	233	[31]
511	0.105348915247	0.235508383196	9.4922666992	0.597463122878	1498	8	231	[31]
512	0.105300496351	0.235387403081	9.4966313992	0.597807302570	1503	8	233	[31]
513	0.105166901059	0.235053667960	9.5086951306	0.596698018314	1472	18	232	[31]
514	0.105087755811	0.234856001788	9.5158564600	0.596512394277	1482	17	232	[31]
515	0.105054747482	0.234773573437	9.5188463536	0.597109909399	1494	14	233	[31]
516	0.105042290468	0.234742467380	9.5199751980	0.598056549475	1506	11	232	[31]
517	0.104996423894	0.234627942719	9.5241338982	0.598430976475	1513	9	233	[31]
518	0.104893119691	0.234370044513	9.5335137609	0.597820449023	1533	3	233	[31]
519	0.104749349753	0.234011222944	9.5465986410	0.596514994520	1512	13	233	[31]
531	0.104259399184	0.232789267538	9.5914613726	0.601783359883	1557	9	239	[31]
555	0.102459917003	0.228312738214	9.7599142108	0.596973402925	1596	22	245	[31]
600	0.099989418385	0.222196095085	10.0010582735	0.599809551084	1742	15	262	[31]
603	0.099871802157	0.221905729420	10.0128362401	0.600683872785	1732	23	236	[31]
627	0.098602073035	0.218775903705	10.1417746019	0.601070865910	1807	16	248	[31]
675	0.096275781053	0.213064514671	10.3868282247	0.602358335610	1953	20	291	[31]
683	0.095949205989	0.212265077636	10.4221810873	0.603316022440	1987	17	290	[31]
700	0.095086541322	0.210156099260	10.5167354506	0.601804168994	2040	15	289	[31]
767	0.092373240519	0.203548957882	10.8256459813	0.604552333312	2251	10	313	[31]
791	0.091485908502	0.201396784834	10.9306451275	0.605674234526	2305	19	322	[31]
800	0.091105594839	0.200475642323	10.9762743086	0.604957870229	2314	21	321	[31]
887	0.088299173741	0.193702081204	11.3251342865	0.610651655601	2572	24	351	[31]
900	0.087723944140	0.192318856944	11.3993962515	0.607570891046	2614	22	353	[31]
935	0.086955379489	0.190473450115	11.5001510646	0.614753450711	2553	52	329	[31]
959	0.086113522460	0.188455622392	11.6125780416	0.612396458069	2750	32	360	[31]
1000	0.084864364119	0.185468384776	11.7835090191	0.611189781043	2919	17	379	[31]
1055	0.083447520229	0.182089999363	11.9835795870	0.613045580732	3087	20	377	[31]
1061	0.083260872596	0.181645726919	12.0104434270	0.612404337722	3068	31	380	[31]
1157	0.080893782384	0.176027059405	12.3618895115	0.612461489305	3364	28	426	[31]
1205	0.079803276753	0.173448295863	12.5308137797	0.612419793834	3404	45	377	[31]
1253	0.078827079542	0.171145021290	12.6859958000	0.613730040158	3583	42	421	[31]
1289	0.078167551985	0.169591669621	12.7930320780	0.615647968543	3649	54	393	[31]
1409	0.076154441092	0.164864008616	13.1312105461	0.622295554446	4056	34	463	[31]
1433	0.075771336694	0.163966645274	13.1976027299	0.623391730215	4140	38	470	[31]
1481	0.074822911994	0.161748303031	13.3648901566	0.620381555455	4264	39	496	[31]
1505	0.074408668802	0.160780824742	13.4392943201	0.620022007168	4352	32	496	[31]
1553	0.073607102421	0.158911197643	13.5856455031	0.619342127044	4507	34	513	[31]
1601	0.072845698692	0.157138242446	13.7276464905	0.618875188136	4664	40	526	[31]
1721	0.070978933493	0.152803711459	14.0886873159	0.615416702369	4990	52	563	[31]
1745	0.070734553387	0.152237562786	14.1373621818	0.617575812766	5017	55	561	[31]
1865	0.069573892291	0.149552751615	14.3732076368	0.628084010835	5332	49	493	[31]
1961	0.068197437850	0.146377442218	14.6633074720	0.621987661744	5667	47	615	[31]
1985	0.068194753127	0.146371258062	14.6638847440	0.629525600068	5599	64	593	[31]
2000	0.067800362008	0.145463180299	14.7491837858	0.623341488610	5792	54	624	[31]
2093	0.067066559198	0.143775657008	14.9105606722	0.631374889582	5966	58	622	[31]
2123	0.066647726127	0.142813657807	15.0042628325	0.628501045803	6149	43	630	[31]
2171	0.066106943195	0.141572833663	15.1270040887	0.627192780478	6232	58	649	[31]
2243	0.065343938138	0.139824563932	15.3036383863	0.625813875897	6497	48	681	[31]
2315	0.064672251950	0.138287893382	15.4625820170	0.626188296896	6746	44	695	[31]
2347	0.064360750075	0.137575994338	15.5374199156	0.625714731748	6770	64	695	[31]
2491	0.063250369853	0.135042209396	15.8101842301	0.630322682375	7051	67	697	[31]
2587	0.062638988538	0.133649656369	15.9644978845	0.635814807150	7339	54	698	[31]
2659	0.062109131997	0.132444262154	16.1006919248	0.637066424323	7421	82	710	[31]
2731	0.061511257082	0.131085764312	16.2571868539	0.635602370147	7727	65	751	[31]
2779	0.061214170962	0.130411365550	16.3360866330	0.637447560061	7948	62	749	[31]
2899	0.060321948580	0.128388544329	16.5777138097	0.636318136328	8287	84	795	[31]
3000	0.059419702784	0.126346900865	16.8294345671	0.629379626189	8772	45	834	[31]
3043	0.059355142043	0.126200959992	16.8477399866	0.636322087314	9550	133	680	[31]
3055	0.059202488875	0.125855964062	16.8911817560	0.633915117936	8736	81	824	[31]
3103	0.058933552990	0.125248441653	16.9682625477	0.635140270341	8828	55	825	[31]
3151	0.058662130326	0.124635653607	17.0467726700	0.636094871950	8944	69	820	[31]
3319	0.057609871322	0.122263316580	17.3581363238	0.634596931717	9481	85	878	[31]
3367	0.057404156158	0.121800146973	17.4203414339	0.636902755705	9588	76	882	[31]
3463	0.056864051634	0.120585058246	17.5858028275	0.636745512550	10692	66	901	[31]
3511	0.056641776761	0.120085404178	17.6548134113	0.638030490521	9968	97	903	[31]
3559	0.056405574270	0.119554700053	17.7287442409	0.638695804761	10161	74	928	[31]
3589	0.056324917885	0.119373540644	17.7541315202	0.641320555509	10039	94	907	[31]
3781	0.055466051920	0.117446391488	18.0290459729	0.645191205420	12895	103	918	[31]
3805	0.055358103561	0.117204421633	18.0642026312	0.645503011095	10821	101	920	[31]
3925	0.054738886050	0.115817492632	18.2685485979	0.643765244814	10934	106	958	[31]
3997	0.054426950305	0.115119504140	18.3732506489	0.644430592353	10702	90	976	[31]
4000	0.054116708972	0.114425763697	18.4785811812	0.633948713105	11770	67	1022	[31]
4093	0.054033689415	0.114240198219	18.5069724245	0.645707173226	11319	130	971	[31]
4189	0.053572966969	0.113210982145	18.6661306360	0.644091336399	11614	99	990	[31]
4213	0.053462475289	0.112964301770	18.7047082013	0.643781728683	11900	80	984	[31]
4321	0.053056320422	0.112058027454	18.8478958218	0.645350496353	11928	120	1002	[31]
4417	0.052684186064	0.111228347060	18.9810277943	0.645904371518	12141	122	1023	[31]
4537	0.052223435092	0.110201997022	19.1484914435	0.646197218166	12701	112	1068	[31]
4585	0.052091737452	0.109908816095	19.1969024056	0.648105741741	12945	102	1053	[31]
4729	0.051529819168	0.108658807012	19.4062392639	0.647060917536	13019	110	1111	[31]
4753	0.051456493109	0.108495799582	19.4338933647	0.647572456045	11545	185	1096	[31]
4897	0.051085445393	0.107671328562	19.5750471060	0.652862398976	12909	155	1011	[31]
4921	0.050865749062	0.107183465377	19.6595944902	0.647634085980	13590	101	1134	[31]
5000	0.050363856639	0.106069797345	19.8555088259	0.638744158561	14617	93	1198	[31]
5017	0.050574237403	0.106536475827	19.7729130749	0.648981220182	18163	181	1142	[31]
5089	0.050442769936	0.106244823037	19.8244466208	0.653174514388	18443	175	1135	[31]
5233	0.049858809486	0.104950316824	20.0566361353	0.648599258364	14245	128	1190	[31]
5281	0.049766460614	0.104745746285	20.0938541271	0.650918225875	15662	119	1186	[31]
5425	0.049435571481	0.104013089482	20.2283491430	0.655418083246	14933	106	1113	[31]
5473	0.049133604238	0.103344916714	20.3526693290	0.649174299819	15485	146	1226	[31]
5481	0.049137823467	0.103354249817	20.3509217429	0.650290709288	15577	124	1221	[31]
5721	0.048362204502	0.101639940597	20.6773039049	0.647128035614	17862	137	1288	[31]
5775	0.048230928332	0.101350064353	20.7335839179	0.647931138621	16291	127	1295	[31]
5895	0.048058151421	0.100968670497	20.8081245416	0.654312163465	16279	172	1200	[31]
5979	0.047700111454	0.100178760972	20.9643116025	0.648913388677	16845	146	1324	[31]
6000	0.047187699337	0.099049307622	21.1919634575	0.630431146186	17494	128	1355	[31]
6051	0.047556166041	0.099861355275	21.0277674432	0.650800169036	16724	137	1345	[31]
6099	0.047420954441	0.099563295376	21.0877240196	0.650383486283	17126	132	1341	[31]
6339	0.046983761482	0.098600127853	21.2839493573	0.657452076017	16848	167	1303	[31]
6363	0.046766323549	0.098121425427	21.3829081294	0.650821082854	17994	124	1404	[31]
6459	0.046705520909	0.097987603901	21.4107450369	0.658066745676	24730	166	1276	[31]
6531	0.046382821560	0.097277655245	21.5597060801	0.651705184715	18827	162	1413	[31]
6603	0.046253017236	0.096992217164	21.6202111723	0.653373479790	22534	167	1414	[31]
7000	0.044845910117		22.2985774488	0.631344739890	20469	110	1495	[31]
8000	0.043021472466	0.089911050726	23.2442067337	0.637009338072	23348	132	1647	[31]
9000	0.041348250525	0.086263339211	24.1848200904	0.636229681916	26241	181	1794	[31]
9909	0.040692765852	0.084837817132	24.5743925010	0.667700123925	37798	267	1813	[31]
10000	0.039927779623	0.083176616874	25.0452193796	0.636539677077	29162	179	1936	[31]
10005	0.040579698283	0.084592119242	24.6428643463	0.668564841143	28329	348	1788	[31]
20000	0.031511804440	0.065074214811	31.7341395636	0.625820540730	58668	333	3513	[31]
20113	0.032360307172	0.066885034609	30.9020552458	0.681576738151	52293	384	3275	[31]
30000	0.027569300128	0.056701830026	36.2722301748	0.628634886153	88002	416	6699	[31]
30093	0.028353902321	0.058362612455	35.2685139660	0.685968229323	71212	733	4981	[31]
40000	0.025100123336	0.051492720302	39.8404416828	0.632539364395	117150	649	9016	[31]
40143	0.025842262077	0.053055600897	38.6963028631	0.692789672540	99231	1012	6827	[31]
50000	0.023292291593	0.047695521173	42.9326584723	0.631839335086	146380	719	10666	[31]
50141	0.024014688109	0.049211167046	41.6411820741	0.694422594361	58221	14485	8515	[31]
60000	0.021962913560	0.044912230558	45.5312997189	0.635654472887	175839	986	12268	[31]
60047	0.022656242323	0.046362893598	44.1379459905	0.698320767542	143629	1088	9762	[31]
70000	0.020874072304	0.042638176998	47.9063205989	0.636677629119	204695	1135	13752	[31]
70009	0.021542499588	0.044033592831	46.4198685912	0.699909928541	133282	3628	11006	[31]
80000	0.019966505753	0.040746578296	50.0838760858	0.636789934232	233889	1322	15085	[31]
80341	0.020583242024	0.042031631287	48.5832114705	0.700613618715	190100	1080	12567	[31]
90000	0.019199467294	0.039150605355	52.0847784309	0.636956899751	263186	1448	16480	[31]
90183	0.019807115279	0.040414729770	50.4869076549	0.700790758367	167090	6098	14020	[31]
100000	0.018537044699	0.037774313537	53.9460316484	0.636973685874	292221	1566	17729	[31]
100281	0.019150716641	0.039049254490	52.2173670441	0.704326043302	241716	1440	15346	[31]
110109	0.018570913333	0.037844636124	53.8476477742	0.705216732460	259230	2168	16636	[31]
120119	0.018039268987	0.036741324612	55.4346188152	0.705128894497	160346	30268	17944	[31]
130055	0.017580785179	0.035790800737	56.8802809328	0.706711006654	225072	14314	19668	[31]
180000	0.015060083171	0.030580714445	66.4006957097	0.614829385217	155200	106084	30217	[31]
500000	0.010670618461	0.021571417286	93.7152802956	0.607489504278	1320897	1909	81156	[31]
1030719	0.008879072967	0.017917234365	112.6243701022	0.721511332383	6102348		148028	[31]
1565879	0.007732295227	0.015585099041	129.3277055056	0.723908176976	9286272		224212	[31]
2005059	0.007124757201	0.014351767259	140.3556601002	0.725165882674	11901828		286814	[31]
2519011	0.006606203613	0.013300271528	151.3728698934	0.726249638858	14964828		360170	[31]
2982989	0.006246686016	0.012571904774	160.0848829985	0.727110946851	17730708		427090	[31]

14-Feb-2022:	First presentation for N=1–519, 531, 555, 600, 603, 627, 675, 683, 700, 767, 791, 800, 887, 900, 935, 959, 1000, 1055, 1061, 1157, 1205, 1253, 1289, 1409, 1433, 1481, 1505, 1553, 1601, 1721, 1745, 1865, 1961, 1985, 2000, 2093, 2123, 2171, 2243, 2315, 2347, 2491, 2587, 2659, 2731, 2779, 2899, 3000, 3043, 3055, 3103, 3151, 3319, 3367, 3463, 3511, 3559, 3589, 3781, 3805, 3925, 3997, 4000, 4093, 4189, 4213, 4321, 4417, 4537, 4585, 4729, 4753, 4897, 4921, 5000, 5017, 5089, 5233, 5281, 5425, 5473, 5481, 5721, 5775, 5895, 5979, 6000, 6051, 6099, 6339, 6363, 6459, 6531, 6603, 7000, 8000, 9000, 9909, 10000, 10005, 20000, 20113, 30000, 30093, 40000, 40143, 50000, 50141, 60000, 60047, 70000, 70009, 80000, 80341, 90000, 90183, 100000, 100281, 110109, 120119, 130055, 180000, and 500000.
16-Feb-2022:	First improvements for N= 94, 138, 148, 149, 156, 162, 165, 167, 190, 199, 210, 217, 219, 220, 223, 231, 232, 234, 236, 238, 239, 242, 243, 245, 250, 252, 253, 256, 258, 261, 270, 271, 272, 275, 281, 287, 293, 297, 299, 307, 312, 313, 323, 332, 355, 356, 358, 362, 363, 364, 376, 401, 407, 408, 410, 413, 419, 420, 424, 430, 431, 437, 439, 446, 449, 451, 458, 462, 482, 488, 489, 490, 501, 503, 507, 509, 510, 511, 513, 515, 516, and 518 by Eckard Specht [31].
17-Feb-2022:	Further small improvements for N= 120, 161, 165, 170, 182, 183, 190, 191, 206, 213, 221, 232, 233, 237, 239, 252, 266, 275, 290, 295, 299, 316, 332, 342, 351, 355, 357, 362, 369, 391, 397, 404, 412, 414, 424, 427, 428, 430, 433, 452, 461, 471, 478, 484, 490, 503, 504, 509, 510, and 514 by Eckard Specht [31].
22-Feb-2022:	Contact figures added. They are displayed at the right hand side. The colors indicate the number of contacting neighbors for each sphere. Furthermore, the size of the (equal) spheres are scaled linearly such that innermost spheres are larger than those near the container. This allows a pretty look at the spheres near the center.
25-Feb-2022:	Small improvements for N= 935, 1055, 9909, 100281, 110109, 120119, 130055, and 500000. New high density packings added for N= 1030719, 1565879, 2005059, 2519011, and 2982989 by Eckard Specht [31].

[1]	L. Fejes, Über eine Abschätzung des kürzesten Abstandes zweier Punkte eines auf einer Kugelfläche liegenden Punktsystems, Jahresbericht der Deutschen Mathematiker-Vereinigung 53 (1943), 66–68.
[2]	K. Schütte, B.L. van der Waerden, Auf welcher Kugel haben 5, 6, 7, 8 oder 9 Punkte mit Mindestabstand Eins Platz?, Math. Annalen 123 (1951), 96–124.
[3]	B.L. van der Waerden, Punkte auf der Kugel. Drei Zusätze, Math. Annalen 125 (1952), 213–222.
[4]	Raphael M. Robinson, Arrangement Of 24 Points On A Sphere, Math. Annalen 144 (1961), 17–48.
[5]	Ludwig Danzer, Endliche Punktmengen auf der 2-Sphäre mit möglichst großem Minimalabstand (Finite Point-Set on S² with Minimum Distance as Large as Possible), Habilitationsschrift, Univ. Göttingen, Germany (1963). Engl. transl.: Discrete Math. 60 (1986), 3–66.
[6]	T. Tarnai, Ts. Gáspár, Improved packing of equal circles on a sphere and rigidity of its graph, Math. Proc. Cambridge Phil. Soc. 93 (1983), 191–218.
[7]	D. Lazić, V. Šenk, I.P. Šeškar, Arrangements of Points on a Sphere Which Maximizes the Distance, Bulletin for Applied Mathematics, Technical University Budapest XLVII-4/9/87 (1987), 7–21.
[8]	D.A. Kottwitz, The Densest Packing of Equal Circles on a Sphere, Acta Cryst. A47 (1991), 158–165.
[9]	Th. Gensane, Dense Packings of Equal Spheres in a Larger Sphere, Les Cahiers du LMPA J. Liouville 188 (2003).
[10]	H. Pfoertner, Densest Packings of n Equal Spheres in a Sphere of Radius 1, August 25, 2013.
[11]	, Serial Symmetrical Relocation Algorithm for the Equal Sphere Packing Problem, Jisuanji Yingyong Yanjiu (Application Research of Computers) 29 (2012) 5, 1695–1697 (in Chinese), arxiv:1202.4149 (2012) (in English).
[31]	, program ssp, April 2010–February 2022.

The best known packings of equal spheres in a sphere (complete up to N = 519)

Last update: 25-Feb-2022

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