Hyperbolic Arbitrary Triangles with Dirichlet Boundary Conditions

We analyzed hyperbolic arbitrary triangles of different angle measures to test our conjecture. The triangles were constructed as the region bounded by two circles and the y axis, as in the blue-shaded area of this image:

Here we find it easier to specify the triangles by the measurements of v, u, and s; r =sqrt(u^2+1). We can then find that alpha = acos(v/s), beta = acos(((u+v)^2-r^2-s^2)/(-2*s*r)), and gamma = atan(1/u). Next, we need to find the hyperbolic area and perimeter of the triangle. The area is the angle deficit, or pi-(alpha+beta+gamma). To find the perimeter we use the hyperbolic laws of sines and cosines to find Sa = acosh((cos(beta)*cos(gamma)+cos(alpha))/(sin(beta)*sin(gamma))), Sb = asinh(sinh(Sa)*sin(beta)/sin(alpha)), and Sc = asinh(sinh(Sa)*sin(gamma)/sin(alpha)). We then have N'(t) = Area/4pi*t - Perimeter/4pi*sqrt(t) + c where c = 1/24*sum(pi/theta-theta/pi)-Area/12.

Unlike the Euclidean and Spherical space, we do not have a region where the eigenvalue spectrum is known to use as a test case for accuracy in Hyperbolic space. After computing the eigenvalues for several Hyperbolic equilateral triangles and seeing that their multiplicity 2 eigenvalues are all very close to equal, we can assume that our computed eigenvalues for these arbitrary triangles are accurate; indeed we will observe in the counting graphs below that they conform very closely to our prediction N'(t).

Here for the set (u,v,s) we have 1: (5,10,11), 2: (3,4,6), 3: (2,2,sqrt(21)), and 4: (2,3,sqrt(5)+4.9).

Difference Graphs for the Hyperbolic Arbitrary Triangles

Calculated and Predicted Eigenvalue Spectrums for the Hyperbolic Arbitrary Triangles

	Hyperbolic Triangle 1
	u = 5	v = 10	s = 11
		Refinement
#	Initial	1	2	3	4	5		Predicted
1	322.147016	273.881435	260.4052933	256.9088076	256.0210751	255.797524		255.7205244
2	639.1805825	444.9434303	401.3008724	390.6629161	388.0191881	387.3589646		387.1315582
3	852.9799557	595.890452	531.0164299	514.4377025	510.2708675	509.2274064		508.8679981
4	1325.973591	763.4361238	664.6071602	639.7380651	633.4908644	631.9256565		631.3865385
5	2578.535641	953.3483781	815.2872721	779.2558903	770.1561533	767.8742903		767.0883286
6	0	1072.539658	916.7029921	879.1510626	869.8690434	867.5501677		866.7514574
7	0	1183.183592	985.8383102	935.5947902	922.9536791	919.7860927		918.6950538
8	0	1366.536933	1133.991027	1073.523483	1058.121265	1054.247046		1052.912616
9	0	1563.162893	1269.153095	1189.911535	1169.7553	1164.687091		1162.941404
10	0	1616.142987	1328.884312	1248.559275	1227.713972	1222.443275		1220.627844
11	0	1871.480592	1490.99641	1388.6116	1362.587482	1356.042106		1353.787626
12	0	2025.778004	1602.262082	1475.761735	1442.784721	1434.466403		1431.601254
13	0	2170.802876	1707.100835	1574.544878	1540.962416	1532.53286		1529.629396
14	0	2453.522575	1889.11031	1705.700375	1660.72023	1649.530489		1645.676311
15	0	2565.661881	1937.596984	1772.263439	1729.805582	1719.114266		1715.431765
16	0	2665.65527	2093.406413	1923.108809	1879.136208	1867.799696		1863.894964
17	0	2773.816128	2189.945427	1968.979729	1910.807776	1896.439589		1891.490631
18	0	3213.01797	2211.594224	1988.326651	1934.078481	1920.477314		1915.792548
19	0	3351.878503	2450.012726	2190.212096	2123.694539	2106.916053		2101.136895
20	0	3536.068629	2533.725296	2248.096145	2173.013909	2154.1129		2147.602663
21	0	3616.596525	2684.637176	2390.877106	2318.035732	2299.612017		2293.266179
22	0	3839.764266	2755.672972	2433.281152	2351.957003	2331.778787		2324.828631
23	0	3882.152687	2889.420938	2539.328987	2449.69439	2427.113469		2419.335729
24	0	4332.494639	3008.919612	2652.755893	2557.2576	2532.949634		2524.577034
25	0	4536.105892	3103.160127	2736.947238	2644.598571	2621.218084		2613.164942
26	0	4751.249365	3315.524989	2862.796489	2747.104123	2718.063306		2708.060529
27	0	5375.758156	3359.666231	2923.624336	2807.660732	2778.171106		2768.013741
28	0	5490.173	3498.696008	3043.675018	2925.882404	2895.980564		2885.681217
29	0	5744.155802	3689.553868	3154.034104	3012.604924	2976.64491		2964.258895
30	0	6190.108672	3819.980933	3230.555179	3081.30944	3044.297678		3031.5494
31	0	6237.986687	3868.452649	3353.70804	3215.062743	3178.530008		3165.946725
32	0	7262.771501	4028.892524	3429.506192	3274.332308	3235.689598		3222.379558
33	0	8357.058863	4069.242611	3477.335517	3319.978407	3280.597335		3267.032975
34	0	8530.344704	4282.2125	3600.638502	3422.882989	3378.574275		3363.312644
35	0	9972.732638	4423.170132	3716.761745	3521.743631	3472.148278		3455.065725
36	0	11911.78889	4507.271248	3777.354077	3587.372419	3539.867799		3523.505375
37	0	12246.72369	4681.040353	3920.246833	3723.587462	3673.65008		3656.449719
38	0	0	4820.791826	4025.364408	3802.247839	3745.142184		3725.472794
39	0	0	4895.136593	4140.496405	3925.065306	3865.741814		3845.308515
40	0	0	5062.077125	4165.9571	3947.126469	3896.57994		3879.169765
41	0	0	5189.407646	4278.360683	4039.81048	3979.586717		3958.843329
42	0	0	5279.457324	4355.87833	4102.862088	4038.508145		4016.342165
43	0	0	5475.538773	4546.152464	4283.53635	4215.106863		4191.537108
44	0	0	5535.623729	4609.65806	4343.844641	4273.422617		4249.166555
45	0	0	5665.989914	4650.251849	4366.01019	4294.229048		4269.504853
46	0	0	5826.314731	4750.915477	4475.286701	4408.647049		4385.693782
47	0	0	5973.345424	4918.956704	4617.219092	4539.456198		4512.671657
48	0	0	6116.672899	5015.600507	4678.192725	4591.545276		4561.700552
49	0	0	6152.411243	5063.650688	4727.699487	4641.112395		4611.28846
50	0	0	6445.276729	5145.365637	4830.962652	4751.893336		4724.658813
51	0	0	6515.18528	5305.825025	4953.990774	4862.192694		4830.573895
52	0	0	6638.635336	5382.372129	5013.279759	4919.360652		4887.011289
53	0	0	6695.63263	5423.078674	5073.417358	4981.648185		4950.039342
54	0	0	6971.894959	5564.800249	5193.358022	5102.358897		5071.015289
55	0	0	7113.886644	5704.345754	5286.446642	5177.999199		5140.645717
56	0	0	7153.144123	5743.666772	5339.584986	5233.46236		5196.909634
57	0	0	7266.847076	5783.009767	5369.101633	5268.07287		5233.274667
58	0	0	7492.467468	6031.734039	5568.475143	5449.00591		5407.856097
59	0	0	7626.360866	6112.003868	5628.704879	5504.679105		5461.959845
60	0	0	7778.798258	6167.048872	5694.132677	5573.524016		5531.981741
61	0	0	7789.514267	6199.683883	5775.001144	5667.707688		5630.751683
62	0	0	8002.88529	6382.036056	5925.714977	5807.856489		5767.261479
63	0	0	8094.236895	6524.16382	5981.006416	5843.64495		5796.332362
64	0	0	8227.519541	6574.085884	6039.785096	5905.207532		5858.853828
65	0	0	8421.306825	6617.145265	6079.305758	5940.25417		5892.35944
66	0	0	8609.53289	6756.592703	6234.787296	6102.715496		6057.224874
67	0	0	8693.936391	6923.558707	6342.471752	6179.19135		6122.951281
68	0	0	8878.556597	6982.288486	6391.271326	6250.463243		6201.963507
69	0	0	9044.175117	7084.645673	6483.997616	6329.204549		6275.887846
70	0	0	9212.423048	7137.054312	6547.960137	6408.753561		6360.805446
71	0	0	9444.936917	7302.856336	6696.06201	6533.912889		6478.062477
72	0	0	9671.342479	7410.776558	6726.574702	6549.989995		6489.167411
73	0	0	9700.082794	7464.968868	6827.597849	6665.005708		6609.002702
74	0	0	9907.64751	7589.31619	6919.633696	6749.532112		6690.942565
75	0	0	9950.508446	7679.392366	6984.006029	6809.533822		6749.438863
76	0	0	9998.777117	7848.475253	7093.414478	6897.435268		6829.932468
77	0	0	10361.56655	7903.221066	7165.230418	6971.420216		6904.664507
78	0	0	10399.53254	7941.500079	7254.197202	7079.046837		7018.718295
79	0	0	10496.67478	8098.405226	7346.35635	7149.826626		7082.134208
80	0	0	10603.7404	8192.707178	7476.380424	7260.079586		7185.577233
81	0	0	10761.36598	8340.519654	7484.439255	7297.965941		7233.737338
82	0	0	11050.27935	8402.20875	7611.719604	7406.345378		7335.606573
83	0	0	11224.92387	8484.508318	7642.687049	7425.353344		7350.495233
84	0	0	11307.44116	8654.281627	7825.98173	7590.369979		7509.216204
85	0	0	11388.71668	8776.445989	7885.71552	7647.18203		7565.021895
86	0	0	11692.37222	8868.205787	7910.240764	7684.424881		7606.645181
87	0	0	11980.49197	8933.673346	8043.283766	7820.76623		7744.122607
88	0	0	12239.12908	9052.237042	8104.626422	7866.235381		7784.124311
89	0	0	12291.09125	9158.654572	8296.053359	8022.817051		7928.703927
90	0	0	12437.14951	9338.420057	8325.863405	8066.700064		7977.434213
91	0	0	12672.29648	9397.323828	8366.015514	8125.372923		8042.486332
92	0	0	12805.46364	9467.242264	8484.579866	8232.700758		8145.943877
93	0	0	0	9563.327062	8562.795773	8321.176901		8237.954042
94	0	0	0	9679.50124	8616.747916	8342.356324		8247.845275
95	0	0	0	9853.841849	8734.880875	8436.393331		8333.582707
96	0	0	0	9929.728006	8829.172184	8525.606506		8421.046777
97	0	0	0	10039.22178	8944.081	8649.951705		8548.64223
98	0	0	0	10147.80033	9023.791923	8737.972701		8639.525536
99	0	0	0	10194.47214	9122.532536	8827.075637		8725.308884
100	0	0	0	10350.04438	9161.676615	8860.82622		8757.201739
101	0	0	0	10412.39665	9189.884171	8908.984002		8812.231148
102	0	0	0	10549.28116	9322.50369	8997.050111		8884.951344
103	0	0	0	10665.80879	9477.592023	9154.444379		9043.139865
104	0	0	0	10777.588	9506.299918	9186.291234		9076.067899
105	0	0	0	10884.49287	9644.092881	9275.65711		9148.753619
106	0	0	0	10995.48875	9678.589618	9365.971622		9258.293925
107	0	0	0	11074.74493	9743.784109	9433.212143		9326.239178
108	0	0	0	11144.0729	9791.673089	9441.683975		9321.134224
109	0	0	0	11340.44496	9983.166106	9620.323391		9495.346363
110	0	0	0	11394.90141	10064.40562	9691.53806		9563.108088
111	0	0	0	11595.33628	10130.01676	9740.73925		9606.657058
112	0	0	0	11624.90697	10182.95919	9841.793954		9724.283486
113	0	0	0	11659.90886	10287.38837	9919.866458		9793.277736
114	0	0	0	11778.24603	10367.96751	10015.15554		9893.633486
115	0	0	0	12005.06757	10485.63154	10096.32078		9962.22714
116	0	0	0	12079.15235	10602.99359	10160.84112		10008.54675
117	0	0	0	12216.10854	10637.27012	10267.96838		10140.76661
118	0	0	0	12287.92046	10679.55673	10276.89303		10138.20011
119	0	0	0	12343.06046	10823.00218	10387.62284		10237.6614
120	0	0	0	12481.82769	10932.29875	10505.55799		10358.57201
121	0	0	0	12651.9662	11022.17486	10601.8722		10457.10375
122	0	0	0	12769.71193	11125.73131	10655.79728		10493.93388
123	0	0	0	12865.88958	11143.45513	10745.76242		10608.78172
124	0	0	0	12890.39273	11217.68435	10811.46956		10671.55351
125	0	0	0	0	11356.05742	10901.62806		10745.10507
126	0	0	0	0	11467.07942	10987.22212		10821.94075
127	0	0	0	0	11504.03741	11045.92343		10888.1313
128	0	0	0	0	11634.54518	11114.47996		10935.34944
129	0	0	0	0	11743.81781	11247.51184		11076.56492
130	0	0	0	0	11777.48293	11315.09869		11155.83572
131	0	0	0	0	11838.50619	11395.58483		11243.02563
132	0	0	0	0	12000.80721	11462.38287		11276.92876
133	0	0	0	0	12039.23298	11512.2409		11330.72451
134	0	0	0	0	12167.90538	11615.13983		11424.74606
135	0	0	0	0	12196.10052	11720.78482		11557.06777
136	0	0	0	0	12345.13841	11818.69641		11637.36948
137	0	0	0	0	12421.48848	11886.14775		11701.75576
138	0	0	0	0	12458.62828	11938.07623		11758.77802
139	0	0	0	0	12567.14822	12027.91977		11842.18869
140	0	0	0	0	12673.3096	12065.55185		11856.21664
141	0	0	0	0	12748.88483	12181.37131		11985.89776
142	0	0	0	0	12812.39849	12270.44231		12083.77169

	Hyperbolic Triangle 2
	u = 3	v = 4	s = 6
		Refinement
#	Initial	1	2	3	4	5		Predicted
1	100.8948206	95.44613618	94.06148874	93.71202428	93.62434033	93.60239328		93.59478935
2	195.6822731	173.6835141	167.7392065	166.2014088	165.812628	165.7151166		165.6813321
3	299.2786952	254.8749989	241.8719626	238.406229	237.5230234	237.3010677		237.2241674
4	366.7246962	296.6999833	279.5705005	275.3723828	274.3280642	274.0672606		273.9769008
5	474.8833462	374.5436065	346.4052899	339.0821495	337.2299431	336.7654159		336.6044726
6	613.7685123	436.8363558	399.883377	391.0235661	388.8258585	388.2772256		388.0871425
7	639.6001761	510.5479861	470.9848249	459.3361745	456.2708124	455.4944203		455.2254262
8	796.3200412	546.362244	496.8855703	485.4100898	482.628257	481.937971		481.6988098
9	912.7437705	624.4492474	563.1127872	547.8756993	544.0280694	543.0620914		542.7274121
10	973.3823718	691.9108997	622.5058191	602.3884438	597.1381367	595.813037		595.3539338
11	1078.544915	724.480102	639.1952141	619.970771	615.3135922	614.1552218		613.7538848
12	1218.908176	833.1447024	731.8992497	704.5083427	697.4428392	695.6599785		695.0422764
13	1282.235135	888.7761953	789.2815755	759.1412763	750.9128015	748.8098551		748.0812539
14	1401.018948	951.0895656	813.4228588	782.2095841	774.7801089	772.93734		772.2988816
15	1718.026963	990.1338093	867.6027804	834.8716659	826.3955159	824.2540709		823.5121312
16	1935.432936	1088.084313	929.0469641	888.0055417	877.5605357	874.9277268		874.0155458
17	2387.861124	1147.747013	980.779961	933.6252688	920.9298138	917.6862836		916.5625079
18	2895.346712	1237.426328	1031.745912	983.482035	971.2518477	968.1523896		967.0785301
19	0	1276.440998	1068.071097	1010.254945	995.6780769	992.0635934		990.8112947
20	0	1395.296331	1147.862512	1082.70666	1066.093089	1061.910488		1060.461355
21	0	1417.779188	1198.490167	1136.737282	1119.166637	1114.568181		1112.974968
22	0	1538.15754	1263.017055	1186.325256	1166.08896	1161.096622		1159.366942
23	0	1565.709912	1281.803365	1196.66919	1177.208015	1172.439473		1170.787331
24	0	1644.63196	1355.742848	1281.08754	1261.965412	1257.096776		1255.409956
25	0	1709.172301	1384.99903	1300.487465	1279.492262	1274.227283		1272.403143
26	0	1759.659882	1447.463513	1365.668086	1340.205904	1333.28907		1330.892617
27	0	1867.40358	1499.19055	1384.397337	1359.445389	1353.684677		1351.688781
28	0	1954.529862	1543.155821	1432.805727	1405.537105	1398.734496		1396.377617
29	0	2016.620137	1640.115024	1522.381267	1492.734841	1485.16864		1482.547201
30	0	2112.613209	1656.459236	1541.503513	1510.170534	1502.134483		1499.350258
31	0	2148.011186	1714.617198	1598.171347	1562.804748	1553.177404		1549.841849
32	0	2281.842478	1762.153961	1617.47319	1584.038202	1576.34345		1573.677474
33	0	2308.011249	1828.750381	1686.368201	1650.110192	1640.902408		1637.712216
34	0	2449.592006	1871.24836	1728.82148	1691.397327	1681.825054		1678.508578
35	0	2543.533011	1963.093989	1813.538783	1770.408671	1758.987997		1755.031112
36	0	2609.28845	1980.575846	1819.784128	1780.500861	1769.608817		1765.835085
37	0	2665.280948	2024.566848	1849.25844	1798.660788	1786.960438		1782.906655
38	0	2710.484823	2097.483734	1908.824598	1868.357206	1858.545792		1855.146461
39	0	2777.553168	2151.327211	1956.170714	1904.680467	1891.571564		1887.029763
40	0	2865.758281	2167.748274	1977.075807	1926.405951	1913.292955		1908.749736
41	0	3019.083825	2281.489235	2092.908689	2033.674249	2015.485948		2009.184304
42	0	3057.650331	2338.599953	2104.330119	2041.952236	2028.361909		2023.653312
43	0	3204.071715	2367.448487	2144.30391	2088.328115	2074.126569		2069.206204
44	0	3280.579291	2449.759606	2187.163169	2125.312772	2110.214294		2104.983172
45	0	3387.12054	2468.673513	2232.668365	2172.830505	2157.636921		2152.372848
46	0	3391.028921	2547.849709	2280.348292	2210.044266	2192.330827		2186.193707
47	0	3484.007084	2577.738572	2353.294745	2285.548389	2266.831447		2260.346647
48	0	3654.983462	2667.436886	2393.884084	2318.665138	2299.598179		2292.99211
49	0	3731.257542	2709.105431	2425.150614	2352.61938	2334.492945		2328.212736
50	0	3771.816306	2735.668123	2462.92384	2391.979528	2372.718735		2366.045509
51	0	3880.884491	2831.848679	2498.333859	2413.454923	2394.346604		2387.726204
52	0	3962.074547	2875.631784	2578.800372	2499.467716	2478.724763		2471.538017
53	0	4067.68847	2905.231733	2588.314918	2504.274314	2483.124587		2475.796907
54	0	4108.81707	3020.954965	2654.690646	2565.24916	2543.546718		2536.027541
55	0	4248.854876	3041.819785	2720.569719	2618.98152	2590.344276		2580.42242
56	0	4398.338102	3107.328972	2739.534185	2646.790822	2625.070794		2617.545525
57	0	4425.609227	3155.689262	2791.438445	2704.717929	2683.220235		2675.771997
58	0	4624.266704	3235.195866	2833.767407	2724.449556	2696.776617		2687.18886
59	0	4669.749086	3302.020805	2917.100282	2807.226623	2779.659978		2770.10905
60	0	4690.167509	3359.466846	2941.614945	2831.845444	2803.478413		2793.650177
61	0	4809.537168	3387.02192	2978.380294	2869.242132	2841.589881		2832.009292
62	0	4894.229034	3462.707999	3036.879292	2932.37337	2901.185946		2890.380538
63	0	4956.572228	3525.817925	3076.9591	2960.055646	2934.223288		2925.273232
64	0	5122.186001	3570.761433	3133.121432	3015.24905	2986.062748		2975.950661
65	0	5235.127269	3592.151363	3144.200798	3025.529188	2991.198126		2979.30355
66	0	5324.93082	3690.83732	3214.679552	3092.241569	3064.077993		3054.320247
67	0	5515.206856	3794.495019	3270.138006	3132.767488	3098.042679		3086.011684
68	0	5603.789747	3816.49816	3305.463604	3173.15806	3138.872258		3126.993363
69	0	5675.686744	3878.398054	3335.389575	3186.71344	3148.679455		3135.50194
70	0	5866.585261	3923.096929	3437.452086	3297.221694	3258.864577		3245.575108
71	0	6009.906047	4019.861894	3463.3514	3339.322854	3297.460658		3282.956794
72	0	6045.197712	4049.95607	3504.594734	3343.997018	3310.649144		3299.095211
73	0	6206.491116	4066.001292	3515.353568	3355.177603	3314.266506		3300.092167
74	0	6323.346758	4201.159989	3598.74192	3428.143064	3387.752246		3373.758167
75	0	6463.45582	4225.138121	3632.796224	3473.009254	3432.490799		3418.452497
76	0	6692.898255	4278.46732	3690.726904	3532.946698	3491.680543		3477.383188
77	0	6800.254487	4382.380117	3735.866937	3549.929145	3501.501259		3484.722602
78	0	0	4428.459483	3800.97098	3650.094178	3602.533211		3586.054912
79	0	0	4482.814025	3852.99265	3677.204176	3632.086296		3616.454446
80	0	0	4563.104066	3914.368949	3708.520141	3657.601369		3639.959702
81	0	0	4582.420879	3923.701312	3736.198181	3685.554107		3668.007614
82	0	0	4650.458537	3962.575985	3762.719785	3715.225617		3698.770462
83	0	0	4713.386878	3985.534375	3795.789059	3752.299009		3737.231148
84	0	0	4815.159313	4051.722664	3879.232352	3835.308381		3820.090181
85	0	0	4849.711952	4133.249499	3932.513826	3879.087843		3860.577511
86	0	0	4923.526004	4151.771602	3935.997266	3880.100404		3860.733994
87	0	0	5011.113894	4213.111789	3986.541594	3929.400087		3909.602449
88	0	0	5067.807093	4260.277869	4052.474701	3982.936938		3958.844408
89	0	0	5130.187416	4338.733729	4096.742453	4043.400642		4024.919473
90	0	0	5157.839092	4374.247165	4129.465861	4072.701728		4053.034838
91	0	0	5273.469284	4387.530016	4155.347578	4099.419512		4080.042291
92	0	0	5335.380614	4423.596099	4191.477427	4130.151941		4108.904692
93	0	0	5370.176889	4499.034888	4272.772996	4211.900173		4190.809758
94	0	0	5507.400264	4543.680188	4312.022353	4250.879371		4229.695355
95	0	0	5509.993925	4608.294367	4346.320954	4281.55001		4259.109025
96	0	0	5554.673502	4650.869506	4380.847166	4312.122406		4288.311555
97	0	0	5578.32717	4688.745222	4427.170775	4344.422852		4315.75344
98	0	0	5662.339687	4766.606885	4464.740454	4406.996841		4386.990593
99	0	0	5734.575872	4782.53349	4543.15991	4475.200126		4451.654314
100	0	0	5794.62538	4864.143307	4584.446785	4509.632612		4483.711981
101	0	0	5876.277647	4869.971392	4603.960546	4530.409958		4504.927117
102	0	0	5947.614806	4918.987113	4641.267848	4570.891273		4546.508122
103	0	0	6011.002367	4947.505754	4650.795933	4585.784812		4563.260614
104	0	0	6098.913599	5032.029092	4759.60765	4680.950788		4653.698792
105	0	0	6147.493971	5087.032923	4784.760268	4704.65182		4676.896898
106	0	0	6187.299952	5117.484893	4804.644528	4724.257144		4696.405581
107	0	0	6216.991387	5174.743592	4832.567601	4752.023269		4724.117327
108	0	0	6278.835661	5200.390571	4904.89098	4835.291298		4811.177315
109	0	0	6417.451449	5262.313806	4950.575076	4866.315711		4837.122634
110	0	0	6510.201929	5318.825885	5004.306277	4914.66718		4883.610204
111	0	0	6515.56215	5371.836678	5015.052487	4929.276471		4899.557924
112	0	0	6590.587106	5411.318196	5073.564505	4983.726593		4952.600735
113	0	0	6686.430545	5462.839253	5096.43272	5012.53485		4983.467019
114	0	0	6696.673262	5527.325044	5190.406307	5088.141586		5052.71025
115	0	0	6811.814495	5582.128204	5217.956378	5123.401526		5090.641404
116	0	0	6847.829167	5620.680266	5250.195483	5151.920452		5117.871411
117	0	0	0	5654.776315	5301.305893	5224.518606		5197.914356
118	0	0	0	5706.922083	5350.657465	5239.293402		5200.709445
119	0	0	0	5752.445355	5359.575394	5274.075177		5244.452186
120	0	0	0	5771.289967	5434.917792	5337.044096		5303.134104
121	0	0	0	5840.243299	5458.20198	5347.918313		5309.708677
122	0	0	0	5915.004659	5522.433118	5414.012409		5376.448227
123	0	0	0	5950.740825	5550.162615	5454.480453		5421.329755
124	0	0	0	5984.881503	5583.282311	5486.826456		5453.407699
125	0	0	0	6063.737092	5651.136059	5532.651287		5491.600241
126	0	0	0	6116.192811	5665.909274	5566.02003		5531.411718
127	0	0	0	6187.566793	5742.714407	5621.656501		5579.713949
128	0	0	0	6191.322576	5776.905181	5664.066355		5624.971442
129	0	0	0	6229.362827	5795.571113	5683.009568		5644.010724
130	0	0	0	6281.639462	5867.248152	5763.557534		5727.632171
131	0	0	0	6336.467794	5905.139799	5776.687381		5732.182876
132	0	0	0	6407.475433	5923.021677	5805.268322		5764.470688
133	0	0	0	6425.942244	5984.754344	5865.53784		5824.233273
134	0	0	0	6532.635933	6014.867388	5891.977127		5849.399725
135	0	0	0	6549.392956	6055.101316	5925.900726		5881.137004
136	0	0	0	6605.463367	6117.328692	5987.934343		5943.103489
137	0	0	0	6618.950027	6161.842188	6043.257372		6002.171664
138	0	0	0	6703.911991	6201.776562	6066.132721		6019.136626
139	0	0	0	6779.942163	6249.660033	6109.948323		6061.542847
140	0	0	0	6811.729585	6296.528314	6160.350507		6113.16941
141	0	0	0	6844.003875	6350.848714	6198.050407		6145.110858
142	0	0	0	0	6413.31921	6279.276701		6232.835414
143	0	0	0	0	6425.781057	6308.982529		6268.51571
144	0	0	0	0	6446.038467	6312.625988		6266.402987
145	0	0	0	0	6483.719995	6334.49257		6282.790214
146	0	0	0	0	6536.15116	6381.350003		6327.716533
147	0	0	0	0	6587.581019	6456.148966		6410.612115
148	0	0	0	0	6610.411099	6478.979845		6433.443271
149	0	0	0	0	6688.240467	6521.97248		6464.366133
150	0	0	0	0	6739.462532	6591.188448		6539.816393
151	0	0	0	0	6783.145189	6621.588009		6565.613801
152	0	0	0	0	6818.629883	6640.692885		6579.043613
153	0	0	0	0	6833.566414	6699.611707		6653.200841

	Hyperbolic Triangle 3
	u = 2	v = 2	s = sqrt(21)
		Refinement
#	Initial	1	2	3	4	5		Predicted
1	55.71135881	54.11132512	53.69907727	53.59473803	53.56854055	53.56198213		53.5598725
2	117.4263225	108.8342198	106.6453839	106.0950231	105.9571538	105.9226636		105.9115692
3	150.8710863	141.4237559	138.9917064	138.374504	138.2193516	138.1804936		138.1679942
4	198.5701575	176.3210382	170.4970434	169.0249596	168.6556428	168.5632119		168.5334799
5	277.3845066	241.833391	232.7554778	230.4658845	229.8912902	229.7474571		229.7011906
6	292.8354984	255.7348	244.3130737	241.3609159	240.6177061	240.4315638		240.3716879
7	310.9029166	271.2549286	262.0284892	259.7586968	259.1918459	259.0501033		259.0045092
8	439.5900836	356.9985703	333.4398508	327.315212	325.7720957	325.3855192		325.2611701
9	455.1851417	361.4121067	337.6404307	331.9439296	330.5317384	330.1793138		330.0659502
10	505.1419693	419.9709698	396.4987363	390.5417993	389.0429321	388.6674192		388.5466288
11	521.505947	436.2271999	413.9365465	408.2663957	406.8385113	406.4807464		406.365665
12	540.4956757	478.0449143	438.3752748	428.1946104	425.6374606	424.9972312		424.7912901
13	616.246651	495.5647846	456.982751	447.3268156	444.9148752	444.3119817		444.1180503
14	769.0873854	581.9382416	531.4820187	518.4365083	515.1267032	514.2954851		514.0281092
15	801.3317149	622.4517034	560.8099101	544.925318	540.967155	539.9788795		539.6609833
16	845.3470867	634.48163	574.434117	558.3022887	554.2395961	553.222759		552.8956754
17	863.9712361	654.7164967	607.2087885	594.9786608	591.8491323	591.0614311		590.8080531
18	999.073056	682.2258895	617.7093057	603.5315945	600.1273137	599.2847047		599.0136646
19	1162.025341	767.1893091	675.2511289	650.6923155	644.4620757	642.8991063		642.3963497
20	1199.768766	810.0199617	713.2088587	688.9870027	682.9045244	681.3807484		680.8905991
21	1264.710011	830.5912178	725.2539522	699.4165534	693.0777896	691.5021728		690.9953478
22	1438.668395	879.8452789	784.2486602	759.9656321	753.8563392	752.3258396		751.8335274
23	1470.11897	922.5191495	821.9140131	785.9059294	776.4355899	774.0517859		773.2849934
24	1519.016643	954.5952996	838.4405291	811.0963021	804.4818652	802.8277612		802.2956894
25	1548.755385	985.1008841	852.2831343	827.9548187	821.997046	820.507689		820.0286111
26	1645.872127	1034.797971	888.0025466	849.0846821	839.476869	837.0883517		836.3200431
27	1837.630782	1044.022072	900.9820593	867.6426004	859.4017102	857.3480449		856.6874473
28	2040.069703	1146.907945	987.6066268	935.956745	921.7521621	918.1817775		917.0333005
29	2159.307641	1169.031333	995.2208583	948.8618706	938.3160564	935.6844593		934.8379597
30	2448.445855	1200.557679	1031.643056	991.4315584	980.9381836	978.2824378		977.4281703
31	2632.906104	1267.480854	1073.656788	1018.46705	1004.742616	1001.319002		1000.217737
32	2986.601859	1281.40404	1091.294269	1044.791361	1033.308248	1030.447709		1029.527566
33	3314.574508	1288.235874	1124.938745	1083.600711	1072.829101	1069.93347		1069.002039
34	3419.191424	1340.388491	1146.074209	1098.244464	1079.613517	1074.984719		1073.495785
35	0	1444.660202	1178.827491	1105.15747	1093.843433	1091.18289		1090.327079
36	0	1452.679735	1210.963499	1148.411902	1132.591053	1128.622734		1127.346255
37	0	1505.271898	1258.344655	1189.1734	1171.476137	1167.019625		1165.586109
38	0	1557.995602	1286.8481	1211.870337	1193.376054	1188.773667		1187.293229
39	0	1573.921722	1339.16309	1269.0202	1246.25647	1239.923431		1237.886297
40	0	1622.97272	1362.242166	1278.200292	1256.000122	1251.034749		1249.437549
41	0	1698.225548	1385.477047	1299.853747	1283.524902	1279.398053		1278.07058
42	0	1716.432776	1421.65459	1340.173365	1319.620873	1314.491096		1312.841012
43	0	1750.270513	1470.335343	1390.407815	1366.546705	1360.320594		1358.317856
44	0	1769.35934	1471.179651	1394.635711	1374.313956	1369.216749		1367.577142
45	0	1840.315807	1497.463022	1406.433388	1387.199742	1382.505032		1380.994897
46	0	1851.199739	1532.448997	1443.129529	1421.907872	1416.351414		1414.564081
47	0	1952.827243	1611.421608	1469.130332	1433.950866	1425.615126		1422.933789
48	0	1994.303139	1620.754602	1508.656742	1480.533038	1473.444993		1471.164999
49	0	2007.478317	1648.940892	1537.990056	1509.485569	1502.337043		1500.037594
50	0	2046.930949	1694.649809	1583.761996	1554.277101	1546.67524		1544.229967
51	0	2122.971675	1719.764218	1616.167697	1579.352911	1570.029846		1567.030917
52	0	2188.671916	1755.576117	1626.467049	1602.837973	1596.845248		1594.917583
53	0	2205.708904	1793.622627	1671.730609	1631.040711	1620.276124		1616.813505
54	0	2231.834736	1838.69284	1680.238931	1647.375411	1640.110123		1637.773116
55	0	2300.687496	1864.055306	1726.20213	1692.849721	1683.894057		1681.01331
56	0	2337.469994	1869.146162	1746.684108	1710.768709	1701.922671		1699.077187
57	0	2453.592418	1912.269728	1765.356833	1735.926219	1728.769564		1726.467501
58	0	2462.271124	1940.950546	1795.58417	1760.000615	1750.844746		1747.8996
59	0	2525.465701	1998.900594	1837.776536	1792.60216	1780.669159		1776.830699
60	0	2562.509186	2054.570879	1859.898208	1812.368628	1801.161578		1797.556633
61	0	2587.833526	2064.107669	1906.660173	1854.643122	1842.127454		1838.101568
62	0	2620.996764	2105.243482	1916.278198	1876.5071	1866.330284		1863.056732
63	0	2668.635243	2134.786903	1960.856618	1921.167027	1910.57712		1907.17069
64	0	2729.444186	2153.947584	1985.805872	1931.245979	1918.021846		1913.76807
65	0	2799.987364	2202.423246	2003.078277	1966.486358	1956.941224		1953.870864
66	0	2833.393824	2236.071157	2040.517854	1989.089853	1975.714724		1971.412379
67	0	2885.116587	2277.419417	2087.618724	2028.73099	2013.197939		2008.20146
68	0	2896.485552	2309.996878	2105.37105	2046.43449	2032.869871		2028.506573
69	0	2967.308293	2329.630042	2146.155951	2091.206058	2077.391234		2072.947453
70	0	3029.46871	2373.762792	2150.637276	2107.765229	2096.952408		2093.474273
71	0	3069.977724	2420.437011	2177.664131	2130.433735	2118.936097		2115.237679
72	0	3145.911932	2440.379644	2212.06067	2151.631177	2135.981343		2130.947298
73	0	3163.459763	2483.384376	2240.705973	2173.574575	2157.56837		2152.419692
74	0	3274.922454	2515.514019	2263.855538	2205.737698	2190.340389		2185.387573
75	0	3298.599825	2535.315652	2314.844597	2243.185577	2223.447908		2217.098939
76	0	3413.343233	2585.529855	2352.144172	2282.885587	2266.045218		2260.628216
77	0	3498.078677	2611.721849	2364.561641	2297.814926	2281.767981		2276.606198
78	0	3553.396285	2657.049889	2401.466533	2332.771092	2316.218572		2310.894163
79	0	3627.229749	2714.554728	2406.527563	2354.950753	2342.128944		2338.004583
80	0	3643.082219	2751.546192	2466.342574	2399.179551	2380.303362		2374.231503
81	0	3682.735479	2784.798568	2493.569669	2412.602628	2393.743258		2387.676809
82	0	3754.713024	2803.533305	2511.193393	2426.719476	2406.294794		2399.724835
83	0	3793.872427	2834.018937	2546.773258	2470.48181	2448.235211		2441.079201
84	0	3923.123721	2862.374102	2576.867601	2493.908525	2472.389035		2465.466912
85	0	3949.163591	2873.886193	2599.644796	2533.478331	2514.406702		2508.271977
86	0	3975.045813	2944.507575	2626.882249	2540.47897	2523.627239		2518.206583
87	0	4014.451357	2996.202661	2667.87542	2585.490257	2565.282779		2558.782688
88	0	4122.972041	3016.330856	2681.601175	2603.222473	2584.553384		2578.548142
89	0	4275.542604	3073.573339	2712.964359	2633.216947	2612.775105		2606.199626
90	0	4336.241987	3097.913949	2779.240291	2676.887274	2648.907901		2639.907843
91	0	4371.593057	3106.712113	2792.888262	2695.221633	2669.289126		2660.947478
92	0	4416.02607	3165.232776	2799.585251	2706.132421	2684.532314		2677.584259
93	0	4538.370871	3210.901747	2818.217045	2738.437988	2715.779488		2708.490982
94	0	0	3238.967203	2861.671092	2763.336259	2735.31606		2726.302869
95	0	0	3285.098123	2897.590052	2794.55705	2774.477979		2768.019192
96	0	0	3355.600957	2924.469116	2820.86895	2796.648727		2788.857866
97	0	0	3363.127958	2976.730986	2872.061407	2845.689624		2837.206675
98	0	0	3374.048409	2991.410747	2891.573518	2866.733745		2858.743595
99	0	0	3440.43103	3041.323443	2939.019323	2912.112296		2903.457176
100	0	0	3463.971637	3070.342624	2958.103314	2923.379212		2912.209593
101	0	0	3473.762739	3086.03513	2977.150209	2944.612152		2934.145713
102	0	0	3531.193467	3103.586329	2985.921403	2963.209919		2955.90437
103	0	0	3596.626995	3118.848599	3012.52716	2986.664836		2978.345763
104	0	0	3609.410446	3142.170247	3037.083412	3009.091909		3000.087949
105	0	0	3627.24034	3206.100238	3059.348069	3027.197059		3016.855121
106	0	0	3667.10884	3223.007057	3114.140388	3088.27939		3079.960745
107	0	0	3717.381339	3258.954774	3136.747303	3105.999436		3096.108843
108	0	0	3771.368528	3290.363528	3172.177423	3141.115917		3131.124437
109	0	0	3803.888647	3310.906097	3201.670023	3173.163618		3163.99403
110	0	0	3867.602783	3356.960981	3244.45357	3204.201147		3191.253246
111	0	0	3905.525078	3412.118877	3246.467799	3214.435873		3204.13224
112	0	0	3938.861184	3437.006635	3261.273924	3225.098315		3213.461793
113	0	0	3977.132975	3438.625392	3283.904245	3249.211802		3238.052367
114	0	0	4009.183692	3514.997897	3307.220001	3277.690985		3268.192457
115	0	0	4029.25442	3552.627488	3344.823334	3301.058679		3286.981007
116	0	0	4056.202862	3556.961525	3396.029724	3358.350388		3346.230167
117	0	0	4067.708614	3585.489297	3429.474334	3396.513564		3385.911152
118	0	0	4114.673732	3623.042629	3445.715864	3409.942579		3398.435471
119	0	0	4210.625599	3653.728604	3502.178818	3465.298137		3453.434815
120	0	0	4227.708076	3671.035139	3514.225436	3475.916095		3463.593221
121	0	0	4284.239045	3729.679263	3523.435874	3491.348484		3481.02701
122	0	0	4296.728829	3749.374718	3555.013814	3504.210888		3487.869232
123	0	0	4356.515422	3766.978598	3577.974576	3536.348858		3522.959212
124	0	0	4391.336249	3779.870582	3597.07216	3557.650858		3544.970302
125	0	0	4445.304248	3823.347948	3614.976261	3576.648848		3564.32016
126	0	0	4471.650215	3858.191128	3661.886203	3614.095696		3598.723038
127	0	0	4504.660537	3885.983758	3673.878285	3634.898586		3622.360079
128	0	0	0	3892.537989	3726.891363	3684.257		3670.542906
129	0	0	0	3945.155559	3733.815075	3698.598231		3687.270113
130	0	0	0	4000.261711	3775.56126	3734.987874		3721.936729
131	0	0	0	4018.950558	3799.695776	3749.906838		3733.89135
132	0	0	0	4057.04588	3853.660423	3790.019574		3769.548373
133	0	0	0	4094.271191	3860.4667	3817.478163		3803.650143
134	0	0	0	4119.737609	3881.689871	3832.331919		3816.455063
135	0	0	0	4151.416884	3918.686364	3870.981578		3855.636493
136	0	0	0	4163.256684	3933.396937	3880.990281		3864.132756
137	0	0	0	4186.276249	3982.804472	3925.331063		3906.843728
138	0	0	0	4206.772986	4003.909819	3961.610464		3948.004132
139	0	0	0	4259.439665	4020.614426	3973.980997		3958.980533
140	0	0	0	4266.013732	4056.024059	4013.805427		4000.22506
141	0	0	0	4324.79273	4085.336281	4037.238567		4021.767089
142	0	0	0	4354.472606	4115.556917	4065.790044		4049.781652
143	0	0	0	4382.999564	4140.121097	4075.714744		4054.997306
144	0	0	0	4388.200218	4170.028907	4114.581199		4096.745466
145	0	0	0	4434.647003	4195.090765	4126.045673		4103.836103
146	0	0	0	4487.168139	4203.326807	4156.673123		4141.666144
147	0	0	0	4509.374146	4233.249079	4186.158529		4171.011024
148	0	0	0	4526.275977	4278.824089	4214.577004		4193.910797
149	0	0	0	0	4301.801463	4241.240263		4221.759687
150	0	0	0	0	4323.017727	4269.684129		4252.528438
151	0	0	0	0	4334.245435	4274.869579		4255.770289
152	0	0	0	0	4369.548059	4315.45459		4298.054473
153	0	0	0	0	4408.174484	4345.975391		4325.967957
154	0	0	0	0	4473.556037	4399.107334		4375.159597
155	0	0	0	0	4481.248735	4408.65594		4385.305189
156	0	0	0	0	4502.074618	4432.123773		4409.622852

	Hyperbolic Triangle 4
	u = 2	v = 3	s = sqrt(5)+4.9
		Refinement
#	Initial	1	2	3	4	5		Predicted
1	25.19613802	24.51130907	24.33580168	24.29148489	24.28036885	24.27758701		24.27663364
2	52.09799763	48.65407372	47.76872123	47.54492784	47.48876799	47.47471158		47.46989434
3	64.42270104	60.10285408	58.96540639	58.67457157	58.60133328	58.58298474		58.57669654
4	89.80674145	80.03420923	77.48691805	76.84092324	76.67867188	76.63805318		76.62413283
5	107.2008287	93.84062229	90.20754798	89.2732153	89.03760173	88.97855352		88.95831723
6	131.6504187	117.0695426	112.6905014	111.3459379	110.9873898	110.8963501		110.8651501
7	145.7165672	121.5366642	115.4051605	114.049831	113.7278304	113.648345		113.6211048
8	161.7167005	135.0034115	127.8373978	126.0245542	125.5694225	125.4554823		125.4164341
9	203.5030056	162.4348209	149.3532268	145.9955089	145.1511922	144.9397757		144.8673216
10	215.6757932	172.1366321	161.9206173	159.2737868	158.6017245	158.4329325		158.3750862
11	232.451564	192.2348032	179.2692082	175.717508	174.8115347	174.5838525		174.5058241
12	244.232048	196.6036351	184.2109229	180.8321411	179.9488427	179.7253282		179.648728
13	282.1494497	212.9722031	193.5643433	189.1899578	188.1421212	187.8830512		187.7942658
14	318.4415043	228.0475633	208.3511901	203.252353	201.9625869	201.6390933		201.5282295
15	334.7305068	257.87178	233.7506346	227.5381122	225.9800192	225.5900655		225.4564253
16	357.6753229	265.7258806	239.3960024	232.4654076	230.6903608	230.2432303		230.0899952
17	369.7406623	277.2962524	248.3059549	240.7386165	238.8342377	238.3574896		238.1941042
18	392.8667053	292.3047824	268.6128209	262.1671473	260.5163261	260.1009705		259.9586249
19	423.5642624	301.2935078	276.0641766	269.6956375	268.0376709	267.6156429		267.4710106
20	466.4996196	321.6760523	287.1643987	278.2944522	276.0361261	275.4695908		275.2754346
21	514.9040034	341.5770654	297.3936652	286.5865109	283.9698063	283.3222991		283.1003933
22	522.8670764	352.5421091	310.8081288	299.935709	297.1607826	296.4621048		296.2226624
23	550.3713143	380.0273092	337.6465315	324.3224407	320.7761523	319.8802383		319.5732014
24	592.3299821	390.640482	341.0454458	329.0952182	326.1667184	325.4327137		325.1811645
25	662.3571781	404.4369396	352.7410731	339.5258268	336.2012472	335.3683978		335.0829737
26	688.112951	421.3895669	370.0402577	357.5304277	354.3294425	353.5177362		353.239558
27	736.0884666	421.6573628	376.41569	361.9065181	357.8667967	356.8329444		356.478635
28	776.0761933	449.1698551	391.5559602	376.2715969	372.3477628	371.3619945		371.0241639
29	830.8934127	473.2213409	399.3961523	382.8114309	379.0592157	378.1423201		377.8280927
30	859.3779017	482.2271132	418.4076983	398.5574688	393.4753471	392.1981506		391.7604453
31	942.8445534	499.1739354	425.6486653	409.2855599	405.0447992	403.9652917		403.5953359
32	1024.392951	521.9598489	447.1661358	426.9662713	420.6912185	419.1020594		418.557442
33	1050.508282	536.1722979	452.7272707	427.4577632	422.178944	420.8676557		420.4182669
34	1092.551431	556.2816232	473.1934206	450.9227777	445.013016	443.5087211		442.9931874
35	1219.767918	570.5494771	484.6626135	458.6774783	451.8942899	450.1857963		449.600282
36	1278.353908	573.8226881	499.9848196	478.575833	472.806229	471.1606933		470.5967552
37	1452.292974	597.0946557	500.7944167	479.5460416	473.5833332	472.1677472		471.6826148
38	1581.043385	605.8731345	520.4949456	491.5003288	484.6086486	482.974004		482.4137984
39	0	627.9341267	530.9195911	506.1948308	497.8513347	495.733877		495.0082075
40	0	665.1231872	538.1289662	507.6472438	502.1770874	500.8114395		500.3434212
41	0	671.3233331	560.854504	525.3900146	516.3858335	514.1217173		513.3457867
42	0	683.4088753	570.3922159	538.5375621	530.3015268	528.2280118		527.5174019
43	0	703.9307666	589.6089793	554.2976832	543.1322324	540.3274166		539.3661841
44	0	710.6621077	596.811313	558.875343	550.7986559	548.7508989		548.0491164
45	0	742.9730735	613.4481746	578.2926586	567.8844527	565.1479513		564.2101306
46	0	757.9727885	627.892493	585.5555795	576.5347925	574.3927389		573.6586402
47	0	770.2450986	641.3642815	603.2983558	591.8476558	588.9063448		587.8983342
48	0	782.4372617	646.9897393	609.5055405	599.1359221	596.3536444		595.4001359
49	0	803.2970771	656.8395461	618.2841148	608.6793687	606.3352607		605.5319164
50	0	827.1566375	684.370942	636.4279945	625.1319576	622.3903718		621.4508087
51	0	854.5923035	687.4482018	644.485887	633.9508315	631.2024644		630.2605772
52	0	865.0436198	698.7448278	652.2955586	639.5430626	636.241705		635.1103037
53	0	888.6221116	710.9391477	658.7064593	646.1557905	643.1770733		642.1562434
54	0	902.5236054	727.2235717	679.1277976	665.0831279	661.3874735		660.1209436
55	0	907.9077977	740.4034493	689.3859274	674.3678902	670.5728773		669.2722964
56	0	938.2241143	751.6618342	690.4197449	678.235526	675.3185819		674.3189221
57	0	961.5065981	781.5123037	724.1504192	708.9945521	705.0845838		703.7446068
58	0	984.1219963	791.8360997	732.0845864	714.5158778	709.9947117		708.4452723
59	0	1004.974423	796.5649033	738.5738994	720.8090137	716.238193		714.6717366
60	0	1009.422044	807.8300256	743.2481118	729.098199	725.6197971		724.4277212
61	0	1031.902029	816.6100524	757.5686532	742.7045987	738.9501539		737.663476
62	0	1054.829349	838.4167206	775.800293	759.6730927	755.6035843		754.2089316
63	0	1080.239063	850.105309	784.3293778	764.9718656	760.0219354		758.3255552
64	0	1108.247833	855.5707615	789.7972446	775.9019029	772.4561412		771.2752514
65	0	1123.553132	860.6630795	804.2023091	788.576079	783.6850586		782.0088673
66	0	1149.841219	902.5832316	817.8650365	795.5938358	790.4918725		788.7433893
67	0	1157.36826	908.8143235	823.7070259	801.4090313	796.2062054		794.4231558
68	0	1164.778749	910.5710182	827.445145	807.6930684	802.7652789		801.0764866
69	0	1181.665189	933.757327	864.0455741	844.2937814	838.6091639		836.6610007
70	0	1198.897155	947.3469913	872.9443364	849.9464804	844.3359313		842.4131518
71	0	1233.158464	958.3094989	874.9507779	853.7567124	848.2554092		846.3700692
72	0	1241.581534	969.3887187	887.0113261	864.3467979	858.8543709		856.9720729
73	0	1261.169972	981.0623473	892.5495624	870.3754565	864.3422404		862.2746096
74	0	1272.488725	1005.779204	905.2669627	881.6411869	875.8045364		873.8042702
75	0	1299.140894	1020.070881	917.9738213	891.0281182	884.4536729		882.2005586
76	0	1320.019765	1024.444914	927.1912997	903.1993704	897.2977775		895.275255
77	0	1327.980569	1029.407337	954.7996628	925.5641618	917.3642859		914.5541237
78	0	1358.90277	1042.494117	958.6469149	939.2285878	934.2483335		932.541561
79	0	1383.886376	1085.313041	969.8808251	944.2811782	938.0902565		935.9685787
80	0	1399.044994	1090.580252	981.1030649	953.1017994	946.4904747		944.2247215
81	0	1437.057637	1094.953906	994.8402077	966.7288571	959.1714754		956.581501
82	0	1462.323939	1104.607304	1004.879955	976.700498	968.7171494		965.9811928
83	0	1475.221017	1115.756083	1007.82811	978.7710049	971.5721616		969.1050611
84	0	1500.204484	1137.878253	1019.648996	987.9759553	980.5601301		978.0186682
85	0	1522.923862	1148.374317	1029.618192	1004.455557	996.6318757		993.9506384
86	0	1546.59348	1158.085264	1045.141328	1006.914886	998.7961969		996.0138582
87	0	1573.685881	1176.427799	1060.911525	1028.867553	1021.020205		1018.330857
88	0	1591.333007	1203.422293	1067.100596	1041.106291	1034.071548		1031.660686
89	0	1615.694756	1210.071925	1087.345589	1052.43589	1043.131318		1039.942568
90	0	1625.871124	1227.214122	1097.96929	1062.481421	1053.711303		1050.705714
91	0	1649.741506	1244.957407	1115.653451	1076.996463	1066.14073		1062.420384
92	0	1704.189515	1250.115328	1126.114887	1085.635083	1076.290239		1073.087687
93	0	1708.093108	1266.524772	1126.953062	1095.480854	1087.557818		1084.84253
94	0	1724.488518	1275.907293	1141.165951	1107.742738	1098.954574		1095.942801
95	0	0	1289.261833	1155.912713	1111.979877	1100.994956		1097.230337
96	0	0	1307.775227	1163.274073	1133.654319	1125.549898		1122.772449
97	0	0	1312.979563	1175.517692	1138.959919	1129.126336		1125.75629
98	0	0	1337.055447	1184.205771	1148.937805	1137.835916		1134.031211
99	0	0	1349.862624	1193.808215	1152.029518	1144.002817		1141.252003
100	0	0	1358.902895	1209.859105	1167.785618	1157.02149		1153.332539
101	0	0	1377.097438	1218.714798	1172.153994	1160.567436		1156.596632
102	0	0	1381.020998	1235.994737	1190.581502	1179.834166		1176.150969
103	0	0	1417.630006	1246.534674	1209.091591	1198.310972		1194.616368
104	0	0	1424.8161	1261.92041	1215.108073	1202.044836		1197.567962
105	0	0	1442.938204	1274.034833	1230.076737	1218.718826		1214.82638
106	0	0	1455.963681	1285.414803	1239.118046	1227.503372		1223.522931
107	0	0	1458.84896	1293.83245	1246.98517	1235.49455		1231.556624
108	0	0	1484.380814	1302.588513	1249.772294	1237.008461		1232.634195
109	0	0	1501.512301	1310.024764	1263.938358	1250.935574		1246.479418
110	0	0	1505.443342	1326.715871	1281.323327	1270.835664		1267.241459
111	0	0	1515.858895	1341.062507	1287.27687	1273.88166		1269.291015
112	0	0	1533.043616	1358.725453	1305.051857	1290.675567		1285.748699
113	0	0	1551.909792	1362.455349	1316.051906	1303.191036		1298.783514
114	0	0	1565.138379	1377.771766	1320.622679	1305.581654		1300.426977
115	0	0	1577.90112	1385.072808	1332.323798	1319.129273		1314.607406
116	0	0	1605.904584	1400.340529	1351.618545	1340.309047		1336.433193
117	0	0	1615.07231	1414.767426	1359.098752	1343.579619		1338.26109
118	0	0	1630.337786	1427.289202	1368.230881	1352.723279		1347.408701
119	0	0	1650.957757	1434.531002	1378.50566	1363.516855		1358.380074
120	0	0	1660.929594	1438.023041	1381.041399	1366.623593		1361.682497
121	0	0	1665.255894	1450.653696	1397.086681	1384.237467		1379.83394
122	0	0	1680.378681	1471.492933	1410.903496	1396.15033		1391.094304
123	0	0	1684.713653	1480.110882	1418.265295	1403.258912		1398.116106
124	0	0	1723.535125	1493.786631	1427.576403	1408.53982		1402.015833
125	0	0	1743.495507	1497.092753	1432.078994	1415.867006		1410.31103
126	0	0	0	1508.602142	1455.471835	1441.72206		1437.009904
127	0	0	0	1538.286096	1465.202885	1446.624952		1440.258147
128	0	0	0	1545.554164	1479.679192	1463.25138		1457.62144
129	0	0	0	1553.801983	1490.39041	1474.047984		1468.447305
130	0	0	0	1570.786586	1499.459571	1480.638718		1474.188663
131	0	0	0	1576.33679	1504.927319	1486.302149		1479.919156
132	0	0	0	1587.935557	1520.918686	1503.339253		1497.314642
133	0	0	0	1595.703076	1531.437803	1513.99892		1508.022477
134	0	0	0	1612.931797	1542.556033	1522.635901		1515.809115
135	0	0	0	1629.26022	1548.156739	1528.83951		1522.219343
136	0	0	0	1632.11826	1557.093975	1539.502239		1533.473411
137	0	0	0	1640.591358	1573.080309	1550.815267		1543.18486
138	0	0	0	1655.374069	1586.508027	1568.747942		1562.66142
139	0	0	0	1663.322352	1592.359013	1579.498932		1575.091681
140	0	0	0	1683.880564	1602.160586	1581.15398		1573.954851
141	0	0	0	1694.928347	1622.539419	1601.882706		1594.803487
142	0	0	0	1707.365442	1626.192119	1605.309358		1598.152671
143	0	0	0	1717.716496	1641.092645	1619.137903		1611.613839
144	0	0	0	1723.589131	1645.010861	1625.568268		1618.905137
145	0	0	0	1744.817516	1659.629184	1635.438791		1627.148552
146	0	0	0	0	1670.259089	1647.8978		1640.234409
147	0	0	0	0	1682.964068	1662.417789		1655.376417
148	0	0	0	0	1691.739008	1669.312111		1661.626237
149	0	0	0	0	1701.780973	1679.51501		1671.884289
150	0	0	0	0	1705.070505	1680.913085		1672.634147
151	0	0	0	0	1722.565104	1699.358217		1691.405033
152	0	0	0	0	1732.128889	1714.358775		1708.268817
153	0	0	0	0	1743.264562	1718.364926		1709.831625