Theoretical ISM pressure and electron density diagnostics for local and high-redshift galaxies

TL;DR

This paper develops new theoretical diagnostics using UV, optical, and IR emission lines to measure ISM pressure and electron density in star-forming galaxies across different redshifts, accounting for metallicity and ionization effects.

Contribution

It introduces self-consistent UV, optical, and IR diagnostics for ISM pressure and electron density, considering metallicity and ionization dependencies, and discusses implications for high-redshift galaxy observations.

Findings

Line ratios depend on metallicity and ionization parameter.

[S II] ratio is strongly metallicity-dependent.

ISM pressure diagnostics cover a wide range (4 < log(P/k) < 9).

Abstract

We derive new self-consistent theoretical UV, optical, and IR diagnostics for the ISM pressure and electron density in the ionized nebulae of star-forming galaxies. Our UV diagnostics utilize the inter-combination, forbidden and resonance lines of silicon, carbon, aluminum, neon, and nitrogen. We also calibrate the optical and IR forbidden lines of oxygen, argon, nitrogen and sulfur. We show that line ratios used as ISM pressure diagnostics depend on the gas-phase metallicity with a residual dependence on the ionization parameter of the gas. In addition, the traditional electron density diagnostic [S II] {\lambda}6731/[S II] {\lambda}6717 is strongly dependent on the gas-phase metallicity. We show how different emission-line ratios are produced in different ionization zones in our theoretical nebulae. The [S II] and [O II] ratios are produced in different zones, and should not be used interchangeably to measure the electron density of the gas unless the electron temperature is known to be constant. We review the temperature and density distributions observed within H II regions and discuss the implications of these distributions on measuring the electron density of the gas. Many H II regions contain radial variations in density. We suggest that the ISM pressure is a more meaningful quantity to measure in H II regions or galaxies. Specific combinations of line ratios can cover the full range of ISM pressures (4 < log(P/k) < 9). As H II regions become resolved at increasingly high redshift through the next generation telescopes, we anticipate that these diagnostics will be important for understanding the conditions around the young, hot stars from the early universe to the present day.

Tables

Table 1. Table 1 Theoretical flux ratios for our MAPPINGS v5.1 Pressure Models

log	log(q)	log(O/H)	[N IV]	SiIII]	C III]	[Ne IV]	[Al II]	[O II]	[Ar IV]	[N I]	[Cl III]	[S II]	[S III]	[O III]	[N II]
($\frac{P}{k}$)		+12	$\frac{\lambda 1483}{\lambda 1486}$	$\frac{\lambda 1883}{\lambda 1892}$	$\frac{\lambda 1906}{\lambda 1908}$	$\frac{\lambda 2425}{\lambda 2423}$	$\frac{\lambda 2660}{\lambda 2669}$	$\frac{\lambda 3729}{\lambda 3726}$	$\frac{\lambda 4711}{\lambda 4740}$	$\frac{\lambda 5198}{\lambda 5200}$	$\frac{\lambda 5517}{\lambda 5537}$	$\frac{\lambda 6717}{\lambda 6731}$	$\frac{\lambda 33\mu m}{\lambda 18\mu m}$	$\frac{\lambda 52\mu m}{\lambda 88\mu m}$	$\frac{\lambda 205\mu m}{\lambda 122\mu m}$
4.0	6.50	7.63	$\cdots$	1.5647	1.4862	$\cdots$	1.5352	1.4533	$\cdots$	0.69806	1.4216	1.4460	1.7769	1.5924	1.7000
4.0	6.50	8.23	$\cdots$	1.5638	1.4813	$\cdots$	1.5331	1.4537	$\cdots$	0.69670	1.4263	1.4478	1.7929	1.6182	1.7301
4.0	6.50	8.53	$\cdots$	1.5622	1.4728	$\cdots$	1.5290	1.4544	$\cdots$	0.69366	1.4341	1.4514	1.8192	1.6712	1.7865
4.0	6.50	8.93	$\cdots$	1.5513	1.4479	$\cdots$	1.5117	1.4573	$\cdots$	0.68227	1.4482	1.4637	1.8778	1.8575	1.9474
4.0	6.50	9.23	$\cdots$	$\cdots$	$\cdots$	$\cdots$	$\cdots$	1.4618	$\cdots$	0.66746	1.4398	1.4633	1.9378	1.9830	2.1429
4.0	6.75	7.63	$\cdots$	1.5654	1.4898	$\cdots$	1.5370	1.4531	$\cdots$	0.69893	1.4177	1.4444	1.7648	1.5707	1.6761
4.0	6.75	8.23	$\cdots$	1.5642	1.4837	$\cdots$	1.5344	1.4535	1.3706	0.69749	1.4239	1.4465	1.7855	1.6011	1.7130
4.0	6.75	8.53	$\cdots$	1.5624	1.4738	$\cdots$	1.5297	1.4543	1.3842	0.69435	1.4331	1.4506	1.8165	1.6604	1.7783
4.0	6.75	8.93	$\cdots$	1.5518	1.4485	$\cdots$	1.5126	1.4572	$\cdots$	0.68274	1.4480	1.4633	1.8765	1.8474	1.9425
4.0	6.75	9.23	$\cdots$	$\cdots$	$\cdots$	$\cdots$	$\cdots$	1.4618	$\cdots$	0.66745	1.4400	1.4634	1.9362	1.9748	2.1322
4.0	7.00	7.63	$\cdots$	1.5662	1.4935	$\cdots$	1.5388	1.4527	1.3556	0.69965	1.4136	1.4428	1.7522	1.5512	1.6517
4.0	7.00	8.23	$\cdots$	1.5645	1.4856	$\cdots$	1.5355	1.4533	1.3679	0.69818	1.4217	1.4454	1.7792	1.5869	1.6979
4.0	7.00	8.53	$\cdots$	1.5624	1.4743	$\cdots$	1.5301	1.4542	1.3839	0.69496	1.4325	1.4500	1.8156	1.6533	1.7736
4.0	7.00	8.93	$\cdots$	1.5518	1.4486	$\cdots$	1.5128	1.4570	$\cdots$	0.68315	1.4480	1.4630	1.8763	1.8416	1.9405
4.0	7.00	9.23	$\cdots$	$\cdots$	$\cdots$	$\cdots$	$\cdots$	1.4618	$\cdots$	0.66749	1.4398	1.4634	1.9363	1.9666	2.1305
4.0	7.25	7.63	$\cdots$	1.5670	1.4973	$\cdots$	1.5406	1.4525	1.3495	0.70011	1.4093	1.4413	1.7397	1.5353	1.6271
4.0	7.25	8.23	1.4825	1.5648	1.4871	$\cdots$	1.5364	1.4532	1.3660	0.69867	1.4200	1.4445	1.7752	1.5764	1.6861
4.0	7.25	8.53	$\cdots$	1.5624	1.4742	$\cdots$	1.5303	1.4541	1.3846	0.69549	1.4326	1.4497	1.8171	1.6502	1.7737
4.0	7.25	8.93	$\cdots$	1.5512	1.4480	$\cdots$	1.5128	1.4571	1.4036	0.68342	1.4481	1.4629	1.8780	1.8403	1.9427
4.0	7.25	9.23	$\cdots$	$\cdots$	$\cdots$	$\cdots$	$\cdots$	1.4619	$\cdots$	0.66762	1.4389	1.4632	1.9386	1.9583	2.1350
4.0	7.50	7.63	1.4876	1.5680	1.5012	$\cdots$	1.5423	1.4523	1.3433	0.70041	1.4049	1.4398	1.7274	1.5228	1.6028
4.0	7.50	8.23	1.4826	1.5649	1.4879	$\cdots$	1.5369	1.4531	1.3652	0.69903	1.4189	1.4438	1.7730	1.5688	1.6783
4.0	7.50	8.53	$\cdots$	1.5623	1.4735	$\cdots$	1.5302	1.4542	1.3863	0.69597	1.4332	1.4495	1.8205	1.6497	1.7788
4.0	7.50	8.93	$\cdots$	1.5499	1.4468	$\cdots$	1.5122	1.4571	1.4040	0.68359	1.4483	1.4628	1.8820	1.8427	1.9508
4.0	7.50	9.23	$\cdots$	$\cdots$	$\cdots$	$\cdots$	$\cdots$	1.4621	$\cdots$	0.66829	1.4372	1.4630	1.9449	1.9458	2.1475
4.0	7.75	7.63	1.4887	1.5690	1.5051	1.4783	1.5439	1.4521	1.3369	0.70057	1.4003	1.4384	1.7151	1.5132	1.5787
4.0	7.75	8.23	1.4827	1.5650	1.4885	$\cdots$	1.5373	1.4530	1.3648	0.69934	1.4181	1.4432	1.7716	1.5626	1.6728
4.0	7.75	8.53	1.4757	1.5621	1.4729	$\cdots$	1.5300	1.4542	1.3880	0.69648	1.4340	1.4493	1.8240	1.6488	1.7861
4.0	7.75	8.93	$\cdots$	1.5485	1.4459	$\cdots$	1.5119	1.4571	1.4040	0.68379	1.4486	1.4629	1.8873	1.8447	1.9638
4.0	7.75	9.23	$\cdots$	$\cdots$	$\cdots$	$\cdots$	$\cdots$	1.4613	$\cdots$	0.66955	1.4364	1.4629	1.9564	1.9191	2.1682
4.0	8.00	7.63	1.4900	1.5702	1.5092	1.4751	1.5454	1.4520	1.3308	0.70067	1.3960	1.4372	1.7024	1.5057	1.5556
4.0	8.00	8.23	1.4828	1.5652	1.4891	1.4920	1.5378	1.4530	1.3644	0.69958	1.4173	1.4426	1.7699	1.5562	1.6681
4.0	8.00	8.53	1.4754	1.5619	1.4725	$\cdots$	1.5301	1.4542	1.3892	0.69695	1.4345	1.4492	1.8261	1.6450	1.7919
4.0	8.00	8.93	$\cdots$	1.5482	1.4461	$\cdots$	1.5123	1.4570	1.4037	0.68402	1.4486	1.4626	1.8920	1.8403	1.9773
4.0	8.00	9.23	$\cdots$	$\cdots$	$\cdots$	$\cdots$	$\cdots$	1.4598	$\cdots$	0.67058	1.4378	1.4628	1.9701	1.8594	2.1922
4.0	8.25	7.63	1.4910	1.5715	1.5133	1.4722	1.5466	1.4517	1.3249	0.70080	1.3919	1.4361	1.6896	1.5000	1.5340
4.0	8.25	8.23	1.4830	1.5653	1.4898	1.4918	1.5383	1.4528	1.3638	0.69984	1.4165	1.4421	1.7678	1.5494	1.6629
4.0	8.25	8.53	1.4752	1.5619	1.4724	$\cdots$	1.5305	1.4540	1.3897	0.69746	1.4347	1.4487	1.8270	1.6375	1.7947
4.0	8.25	8.93	$\cdots$	1.5486	1.4470	$\cdots$	1.5131	1.4566	1.4030	0.68436	1.4483	1.4621	1.8947	1.8234	1.9873
4.0	8.25	9.23	$\cdots$	$\cdots$	$\cdots$	$\cdots$	$\cdots$	1.4570	$\cdots$	0.67131	1.4396	1.4617	1.9785	1.7409	2.2101
4.0	8.50	7.63	1.4920	1.5722	1.5169	1.4696	1.5476	1.4516	1.3197	0.70093	1.3884	1.4354	1.6771	1.4960	1.5149
4.0	8.50	8.23	1.4833	1.5655	1.4908	1.4916	1.5390	1.4527	1.3630	0.70004	1.4153	1.4416	1.7653	1.5419	1.6574
4.0	8.50	8.53	1.4752	1.5619	1.4726	$\cdots$	1.5312	1.4538	1.3898	0.69791	1.4345	1.4481	1.8264	1.6253	1.7941
4.0	8.50	8.93	$\cdots$	1.5493	1.4482	$\cdots$	1.5140	1.4560	1.4025	0.68476	1.4480	1.4612	1.8944	1.7876	1.9916
4.0	8.50	9.23	$\cdots$	$\cdots$	$\cdots$	$\cdots$	$\cdots$	1.4522	$\cdots$	0.67182	1.4407	1.4584	1.9718	1.5456	2.2135
4.5	6.50	7.63	$\cdots$	1.5647	1.4862	$\cdots$	1.5350	1.4520	$\cdots$	0.69787	1.4213	1.4449	1.7702	1.5221	1.6980
4.5	6.50	8.23	$\cdots$	1.5638	1.4813	$\cdots$	1.5330	1.4522	$\cdots$	0.69651	1.4260	1.4465	1.7854	1.5396	1.7279
4.5	6.50	8.53	$\cdots$	1.5622	1.4728	$\cdots$	1.5288	1.4526	$\cdots$	0.69346	1.4336	1.4497	1.8100	1.5739	1.7834
4.5	6.50	8.93	$\cdots$	1.5516	1.4482	$\cdots$	1.5119	1.4538	$\cdots$	0.68213	1.4474	1.4605	1.8605	1.6612	1.9391
4.5	6.50	9.23	$\cdots$	$\cdots$	$\cdots$	$\cdots$	$\cdots$	1.4525	$\cdots$	0.66808	1.4407	1.4572	1.8941	1.5546	2.1055
4.5	6.75	7.63	$\cdots$	1.5654	1.4897	$\cdots$	1.5368	1.4518	$\cdots$	0.69876	1.4174	1.4433	1.7586	1.5039	1.6742
4.5	6.75	8.23	$\cdots$	1.5642	1.4836	$\cdots$	1.5343	1.4520	1.3704	0.69733	1.4235	1.4452	1.7783	1.5248	1.7107
4.5	6.75	8.53	$\cdots$	1.5623	1.4738	$\cdots$	1.5295	1.4525	1.3840	0.69414	1.4327	1.4490	1.8075	1.5634	1.7753
4.5	6.75	8.93	$\cdots$	1.5520	1.4488	$\cdots$	1.5126	1.4537	$\cdots$	0.68262	1.4472	1.4600	1.8592	1.6509	1.9343
4.5	6.75	9.23	$\cdots$	$\cdots$	$\cdots$	$\cdots$	$\cdots$	1.4522	$\cdots$	0.66818	1.4407	1.4572	1.8924	1.5508	2.0972
4.5	7.00	7.63	$\cdots$	1.5661	1.4935	$\cdots$	1.5387	1.4516	1.3554	0.69946	1.4134	1.4417	1.7464	1.4879	1.6499
4.5	7.00	8.23	$\cdots$	1.5646	1.4856	$\cdots$	1.5354	1.4519	1.3677	0.69799	1.4214	1.4442	1.7724	1.5129	1.6958
4.5	7.00	8.53	$\cdots$	1.5624	1.4743	$\cdots$	1.5300	1.4524	1.3836	0.69475	1.4321	1.4484	1.8064	1.5565	1.7705
4.5	7.00	8.93	$\cdots$	1.5520	1.4490	$\cdots$	1.5129	1.4536	$\cdots$	0.68300	1.4472	1.4597	1.8589	1.6437	1.9325
4.5	7.00	9.23	$\cdots$	$\cdots$	$\cdots$	$\cdots$	$\cdots$	1.4520	$\cdots$	0.66825	1.4403	1.4571	1.8918	1.5403	2.0964
4.5	7.25	7.63	$\cdots$	1.5670	1.4972	$\cdots$	1.5405	1.4514	1.3494	0.69994	1.4091	1.4402	1.7342	1.4750	1.6255
4.5	7.25	8.23	1.4825	1.5647	1.4870	$\cdots$	1.5362	1.4517	1.3659	0.69849	1.4197	1.4432	1.7683	1.5043	1.6841
4.5	7.25	8.53	$\cdots$	1.5623	1.4742	$\cdots$	1.5301	1.4524	1.3843	0.69527	1.4322	1.4481	1.8077	1.5528	1.7706
4.5	7.25	8.93	$\cdots$	1.5513	1.4483	$\cdots$	1.5127	1.4535	1.4032	0.68322	1.4473	1.4596	1.8601	1.6386	1.9348
4.5	7.25	9.23	$\cdots$	$\cdots$	$\cdots$	$\cdots$	$\cdots$	1.4517	$\cdots$	0.66839	1.4396	1.4567	1.8921	1.5234	2.1008
4.5	7.50	7.63	1.4876	1.5679	1.5012	$\cdots$	1.5422	1.4512	1.3432	0.70024	1.4046	1.4388	1.7222	1.4653	1.6013
4.5	7.50	8.23	1.4826	1.5649	1.4879	$\cdots$	1.5368	1.4517	1.3651	0.69884	1.4186	1.4425	1.7662	1.4983	1.6762
4.5	7.50	8.53	$\cdots$	1.5622	1.4735	$\cdots$	1.5300	1.4524	1.3860	0.69576	1.4328	1.4479	1.8108	1.5510	1.7757
4.5	7.50	8.93	$\cdots$	1.5500	1.4470	$\cdots$	1.5123	1.4534	1.4035	0.68340	1.4476	1.4595	1.8629	1.6335	1.9428
4.5	7.50	9.23	$\cdots$	$\cdots$	$\cdots$	$\cdots$	$\cdots$	1.4514	$\cdots$	0.66902	1.4379	1.4561	1.8937	1.4940	2.1119
4.5	7.75	7.63	1.4888	1.5690	1.5052	1.4783	1.5438	1.4511	1.3369	0.70040	1.4002	1.4374	1.7103	1.4576	1.5774
4.5	7.75	8.23	1.4827	1.5650	1.4885	$\cdots$	1.5372	1.4517	1.3647	0.69914	1.4178	1.4420	1.7648	1.4931	1.6708
4.5	7.75	8.53	1.4758	1.5620	1.4729	$\cdots$	1.5298	1.4523	1.3877	0.69627	1.4335	1.4477	1.8139	1.5486	1.7828
4.5	7.75	8.93	$\cdots$	1.5487	1.4462	$\cdots$	1.5119	1.4532	1.4036	0.68354	1.4477	1.4593	1.8665	1.6241	1.9553
4.5	7.75	9.23	$\cdots$	$\cdots$	$\cdots$	$\cdots$	$\cdots$	1.4505	$\cdots$	0.67017	1.4371	1.4556	1.8955	1.4414	2.1297
4.5	8.00	7.63	1.4900	1.5701	1.5092	1.4752	1.5453	1.4508	1.3307	0.70053	1.3958	1.4362	1.6979	1.4513	1.5543
4.5	8.00	8.23	1.4828	1.5651	1.4891	1.4919	1.5377	1.4516	1.3642	0.69942	1.4170	1.4414	1.7631	1.4874	1.6660
4.5	8.00	8.53	1.4754	1.5617	1.4724	$\cdots$	1.5300	1.4522	1.3889	0.69675	1.4341	1.4475	1.8158	1.5433	1.7885
4.5	8.00	8.93	$\cdots$	1.5483	1.4464	$\cdots$	1.5122	1.4528	1.4032	0.68376	1.4475	1.4589	1.8687	1.6048	1.9681
4.5	8.00	9.23	$\cdots$	$\cdots$	$\cdots$	$\cdots$	$\cdots$	1.4479	$\cdots$	0.67118	1.4381	1.4542	1.8930	1.3492	2.1480
4.5	8.25	7.63	1.4910	1.5714	1.5132	1.4722	1.5466	1.4507	1.3248	0.70064	1.3917	1.4352	1.6853	1.4459	1.5328
4.5	8.25	8.23	1.4830	1.5653	1.4898	1.4918	1.5382	1.4515	1.3636	0.69965	1.4161	1.4409	1.7609	1.4803	1.6609
4.5	8.25	8.53	1.4753	1.5617	1.4723	$\cdots$	1.5304	1.4520	1.3895	0.69723	1.4342	1.4470	1.8162	1.5330	1.7912
4.5	8.25	8.93	$\cdots$	1.5487	1.4473	$\cdots$	1.5130	1.4520	1.4025	0.68407	1.4473	1.4578	1.8682	1.5662	1.9769
4.5	8.25	9.23	$\cdots$	$\cdots$	$\cdots$	$\cdots$	$\cdots$	1.4420	$\cdots$	0.67186	1.4393	1.4500	1.8768	1.1955	2.1572
4.5	8.50	7.63	1.4920	1.5721	1.5169	1.4695	1.5475	1.4506	1.3196	0.70075	1.3881	1.4344	1.6731	1.4407	1.5138
4.5	8.50	8.23	1.4832	1.5654	1.4907	1.4915	1.5388	1.4513	1.3629	0.69985	1.4150	1.4403	1.7583	1.4703	1.6553
4.5	8.50	8.53	1.4751	1.5618	1.4726	$\cdots$	1.5310	1.4517	1.3895	0.69766	1.4339	1.4462	1.8148	1.5147	1.7903
4.5	8.50	8.93	$\cdots$	1.5494	1.4484	$\cdots$	1.5138	1.4503	1.4020	0.68436	1.4468	1.4560	1.8633	1.4953	1.9793
4.5	8.50	9.23	$\cdots$	$\cdots$	$\cdots$	$\cdots$	$\cdots$	1.4307	$\cdots$	0.67215	1.4392	1.4408	1.8328	0.98048	2.1456
5.0	6.50	7.63	$\cdots$	1.5645	1.4861	$\cdots$	1.5347	1.4477	$\cdots$	0.69731	1.4203	1.4413	1.7493	1.3382	1.6917
5.0	6.50	8.23	$\cdots$	1.5636	1.4812	$\cdots$	1.5325	1.4474	$\cdots$	0.69591	1.4249	1.4424	1.7622	1.3373	1.7206
5.0	6.50	8.53	$\cdots$	1.5619	1.4728	$\cdots$	1.5283	1.4470	$\cdots$	0.69281	1.4323	1.4448	1.7817	1.3334	1.7739
5.0	6.50	8.93	$\cdots$	1.5519	1.4491	$\cdots$	1.5118	1.4436	$\cdots$	0.68152	1.4451	1.4509	1.8106	1.2652	1.9163
5.0	6.50	9.23	$\cdots$	$\cdots$	$\cdots$	$\cdots$	1.4818	1.4304	$\cdots$	0.66883	1.4397	1.4399	1.7958	1.0230	2.0400
5.0	6.75	7.63	$\cdots$	1.5652	1.4896	$\cdots$	1.5365	1.4477	$\cdots$	0.69818	1.4165	1.4397	1.7390	1.3275	1.6682
5.0	6.75	8.23	$\cdots$	1.5640	1.4835	$\cdots$	1.5338	1.4475	1.3699	0.69672	1.4225	1.4412	1.7558	1.3277	1.7038
5.0	6.75	8.53	$\cdots$	1.5621	1.4738	$\cdots$	1.5291	1.4468	1.3833	0.69351	1.4314	1.4440	1.7791	1.3240	1.7658
5.0	6.75	8.93	$\cdots$	1.5522	1.4496	$\cdots$	1.5125	1.4433	$\cdots$	0.68195	1.4449	1.4504	1.8089	1.2543	1.9118
5.0	6.75	9.23	$\cdots$	$\cdots$	$\cdots$	$\cdots$	1.4816	1.4296	$\cdots$	0.66901	1.4396	1.4395	1.7920	1.0125	2.0346
5.0	7.00	7.63	$\cdots$	1.5660	1.4934	$\cdots$	1.5383	1.4476	1.3550	0.69888	1.4124	1.4382	1.7281	1.3197	1.6443
5.0	7.00	8.23	$\cdots$	1.5644	1.4855	$\cdots$	1.5349	1.4474	1.3672	0.69739	1.4204	1.4401	1.7505	1.3211	1.6890
5.0	7.00	8.53	$\cdots$	1.5622	1.4743	$\cdots$	1.5295	1.4467	1.3830	0.69410	1.4308	1.4434	1.7781	1.3175	1.7611
5.0	7.00	8.93	$\cdots$	1.5521	1.4496	$\cdots$	1.5127	1.4430	$\cdots$	0.68225	1.4449	1.4500	1.8080	1.2449	1.9103
5.0	7.00	9.23	$\cdots$	$\cdots$	$\cdots$	$\cdots$	$\cdots$	1.4287	$\cdots$	0.66905	1.4390	1.4388	1.7883	0.99695	2.0340
5.0	7.25	7.63	$\cdots$	1.5669	1.4972	$\cdots$	1.5401	1.4477	1.3491	0.69939	1.4083	1.4368	1.7172	1.3143	1.6204
5.0	7.25	8.23	1.4823	1.5646	1.4869	$\cdots$	1.5358	1.4474	1.3654	0.69788	1.4187	1.4393	1.7470	1.3169	1.6776
5.0	7.25	8.53	$\cdots$	1.5621	1.4741	$\cdots$	1.5296	1.4467	1.3836	0.69460	1.4308	1.4430	1.7789	1.3128	1.7611
5.0	7.25	8.93	$\cdots$	1.5515	1.4489	$\cdots$	1.5125	1.4427	1.4019	0.68249	1.4449	1.4496	1.8076	1.2345	1.9126
5.0	7.25	9.23	$\cdots$	$\cdots$	$\cdots$	$\cdots$	$\cdots$	1.4274	$\cdots$	0.66921	1.4380	1.4380	1.7833	0.97516	2.0369
5.0	7.50	7.63	1.4876	1.5678	1.5011	$\cdots$	1.5419	1.4477	1.3429	0.69968	1.4038	1.4355	1.7064	1.3105	1.5965
5.0	7.50	8.23	1.4826	1.5647	1.4877	$\cdots$	1.5363	1.4474	1.3646	0.69827	1.4176	1.4386	1.7451	1.3141	1.6699
5.0	7.50	8.53	$\cdots$	1.5619	1.4735	$\cdots$	1.5295	1.4465	1.3853	0.69511	1.4315	1.4428	1.7810	1.3085	1.7659
5.0	7.50	8.93	$\cdots$	1.5501	1.4476	$\cdots$	1.5118	1.4422	1.4022	0.68262	1.4451	1.4493	1.8070	1.2197	1.9198
5.0	7.50	9.23	$\cdots$	$\cdots$	$\cdots$	$\cdots$	$\cdots$	1.4258	$\cdots$	0.66976	1.4363	1.4367	1.7732	0.94118	2.0441
5.0	7.75	7.63	1.4888	1.5689	1.5051	1.4782	1.5435	1.4477	1.3365	0.69983	1.3995	1.4342	1.6953	1.3073	1.5730
5.0	7.75	8.23	1.4827	1.5648	1.4884	$\cdots$	1.5368	1.4473	1.3642	0.69856	1.4168	1.4381	1.7437	1.3112	1.6645
5.0	7.75	8.53	1.4757	1.5617	1.4728	$\cdots$	1.5293	1.4464	1.3870	0.69560	1.4321	1.4426	1.7829	1.3033	1.7726
5.0	7.75	8.93	$\cdots$	1.5489	1.4467	$\cdots$	1.5115	1.4415	1.4022	0.68273	1.4451	1.4487	1.8050	1.1973	1.9307
5.0	7.75	9.23	$\cdots$	$\cdots$	$\cdots$	$\cdots$	$\cdots$	1.4240	$\cdots$	0.67065	1.4352	1.4348	1.7530	0.88771	2.0548
5.0	8.00	7.63	1.4899	1.5700	1.5091	1.4751	1.5450	1.4476	1.3304	0.69997	1.3951	1.4331	1.6838	1.3040	1.5503
5.0	8.00	8.23	1.4828	1.5649	1.4891	1.4918	1.5372	1.4473	1.3638	0.69879	1.4160	1.4376	1.7420	1.3071	1.6597
5.0	8.00	8.53	1.4753	1.5616	1.4723	$\cdots$	1.5294	1.4462	1.3881	0.69610	1.4326	1.4422	1.7838	1.2951	1.7780
5.0	8.00	8.93	$\cdots$	1.5484	1.4468	$\cdots$	1.5117	1.4403	1.4018	0.68287	1.4448	1.4474	1.8003	1.1627	1.9411
5.0	8.00	9.23	$\cdots$	$\cdots$	$\cdots$	$\cdots$	$\cdots$	1.4187	$\cdots$	0.67128	1.4352	1.4306	1.7159	0.80561	2.0614
5.0	8.25	7.63	1.4910	1.5713	1.5131	1.4721	1.5462	1.4475	1.3246	0.70009	1.3910	1.4320	1.6721	1.2994	1.5291
5.0	8.25	8.23	1.4830	1.5651	1.4898	1.4917	1.5377	1.4471	1.3632	0.69904	1.4152	1.4369	1.7396	1.2994	1.6545
5.0	8.25	8.53	1.4752	1.5615	1.4722	$\cdots$	1.5298	1.4458	1.3887	0.69657	1.4327	1.4416	1.7827	1.2803	1.7801
5.0	8.25	8.93	$\cdots$	1.5487	1.4476	$\cdots$	1.5123	1.4380	1.4010	0.68297	1.4441	1.4450	1.7915	1.1055	1.9464
5.0	8.25	9.23	$\cdots$	$\cdots$	$\cdots$	$\cdots$	$\cdots$	1.4056	$\cdots$	0.67122	1.4344	1.4195	1.6529	0.68389	2.0512
5.0	8.50	7.63	1.4920	1.5720	1.5168	1.4695	1.5472	1.4473	1.3193	0.70018	1.3875	1.4312	1.6604	1.2918	1.5102
5.0	8.50	8.23	1.4832	1.5652	1.4906	1.4914	1.5384	1.4468	1.3624	0.69919	1.4140	1.4362	1.7364	1.2845	1.6487
5.0	8.50	8.53	1.4750	1.5615	1.4724	$\cdots$	1.5304	1.4449	1.3886	0.69687	1.4323	1.4404	1.7794	1.2516	1.7785
5.0	8.50	8.93	$\cdots$	1.5491	1.4486	$\cdots$	1.5129	1.4335	1.4002	0.68298	1.4430	1.4405	1.7744	1.0118	1.9434
5.0	8.50	9.23	$\cdots$	$\cdots$	$\cdots$	$\cdots$	1.4868	1.3790	$\cdots$	0.66994	1.4302	1.3966	1.5507	0.53472	2.0081
5.5	6.50	7.63	$\cdots$	1.5641	1.4858	$\cdots$	1.5333	1.4344	$\cdots$	0.69561	1.4174	1.4299	1.6868	0.98013	1.6722
5.5	6.50	8.23	$\cdots$	1.5630	1.4809	$\cdots$	1.5311	1.4328	$\cdots$	0.69405	1.4216	1.4298	1.6927	0.95824	1.6984
5.5	6.50	8.53	$\cdots$	1.5613	1.4726	$\cdots$	1.5267	1.4296	$\cdots$	0.69072	1.4283	1.4296	1.6986	0.91670	1.7456
5.5	6.50	8.93	$\cdots$	1.5517	1.4499	$\cdots$	1.5104	1.4140	$\cdots$	0.67901	1.4385	1.4239	1.6768	0.76184	1.8592
5.5	6.50	9.23	$\cdots$	$\cdots$	$\cdots$	$\cdots$	1.4834	1.3776	$\cdots$	0.66730	1.4315	1.3945	1.5848	0.56450	1.9275
5.5	6.75	7.63	$\cdots$	1.5647	1.4893	$\cdots$	1.5352	1.4349	$\cdots$	0.69644	1.4136	1.4284	1.6799	0.97939	1.6497
5.5	6.75	8.23	$\cdots$	1.5634	1.4832	$\cdots$	1.5324	1.4331	1.3684	0.69485	1.4193	1.4286	1.6886	0.95513	1.6822
5.5	6.75	8.53	$\cdots$	1.5614	1.4736	$\cdots$	1.5275	1.4294	1.3811	0.69142	1.4273	1.4286	1.6964	0.90904	1.7375
5.5	6.75	8.93	$\cdots$	1.5519	1.4503	$\cdots$	1.5108	1.4133	$\cdots$	0.67937	1.4382	1.4230	1.6739	0.75179	1.8546
5.5	6.75	9.23	$\cdots$	$\cdots$	1.4249	$\cdots$	1.4831	1.3754	$\cdots$	0.66743	1.4309	1.3930	1.5752	0.55371	1.9217
5.5	7.00	7.63	$\cdots$	1.5655	1.4930	$\cdots$	1.5370	1.4355	1.3538	0.69713	1.4098	1.4273	1.6728	0.98243	1.6270
5.5	7.00	8.23	$\cdots$	1.5638	1.4852	$\cdots$	1.5335	1.4334	1.3657	0.69551	1.4172	1.4277	1.6854	0.95519	1.6682
5.5	7.00	8.53	$\cdots$	1.5615	1.4740	$\cdots$	1.5278	1.4293	1.3808	0.69197	1.4268	1.4279	1.6952	0.90363	1.7328
5.5	7.00	8.93	$\cdots$	1.5517	1.4501	$\cdots$	1.5109	1.4125	$\cdots$	0.67961	1.4380	1.4222	1.6708	0.74236	1.8526
5.5	7.00	9.23	$\cdots$	$\cdots$	1.4240	$\cdots$	1.4823	1.3727	$\cdots$	0.66749	1.4299	1.3911	1.5646	0.54123	1.9188
5.5	7.25	7.63	$\cdots$	1.5664	1.4969	$\cdots$	1.5389	1.4362	1.3479	0.69765	1.4056	1.4262	1.6654	0.98717	1.6044
5.5	7.25	8.23	1.4822	1.5641	1.4866	$\cdots$	1.5344	1.4337	1.3639	0.69603	1.4156	1.4270	1.6832	0.95641	1.6574
5.5	7.25	8.53	$\cdots$	1.5615	1.4739	$\cdots$	1.5280	1.4290	1.3815	0.69252	1.4268	1.4275	1.6944	0.89851	1.7324
5.5	7.25	8.93	$\cdots$	1.5510	1.4494	$\cdots$	1.5105	1.4113	1.3981	0.67972	1.4379	1.4213	1.6660	0.73103	1.8538
5.5	7.25	9.23	$\cdots$	$\cdots$	1.4222	$\cdots$	1.4810	1.3691	$\cdots$	0.66758	1.4285	1.3888	1.5492	0.52585	1.9173
5.5	7.50	7.63	1.4874	1.5673	1.5007	$\cdots$	1.5407	1.4367	1.3418	0.69796	1.4014	1.4252	1.6578	0.99176	1.5818
5.5	7.50	8.23	1.4824	1.5642	1.4875	$\cdots$	1.5351	1.4339	1.3631	0.69642	1.4145	1.4265	1.6817	0.95758	1.6500
5.5	7.50	8.53	$\cdots$	1.5612	1.4732	$\cdots$	1.5278	1.4286	1.3831	0.69303	1.4273	1.4271	1.6938	0.89261	1.7363
5.5	7.50	8.93	$\cdots$	1.5497	1.4480	$\cdots$	1.5098	1.4096	1.3983	0.67975	1.4378	1.4200	1.6567	0.71516	1.8582
5.5	7.50	9.23	$\cdots$	$\cdots$	$\cdots$	$\cdots$	1.4805	1.3648	$\cdots$	0.66793	1.4263	1.3858	1.5200	0.50429	1.9157
5.5	7.75	7.63	1.4886	1.5685	1.5048	1.4781	1.5424	1.4370	1.3356	0.69814	1.3971	1.4243	1.6497	0.99523	1.5594
5.5	7.75	8.23	1.4826	1.5643	1.4881	$\cdots$	1.5354	1.4340	1.3627	0.69672	1.4137	1.4261	1.6805	0.95792	1.6448
5.5	7.75	8.53	1.4755	1.5610	1.4725	$\cdots$	1.5276	1.4282	1.3847	0.69357	1.4278	1.4267	1.6925	0.88588	1.7419
5.5	7.75	8.93	$\cdots$	1.5484	1.4470	$\cdots$	1.5092	1.4073	1.3981	0.67970	1.4374	1.4179	1.6422	0.69336	1.8641
5.5	7.75	9.23	$\cdots$	$\cdots$	$\cdots$	$\cdots$	1.4820	1.3601	$\cdots$	0.66822	1.4241	1.3813	1.4674	0.47336	1.9104
5.5	8.00	7.63	1.4899	1.5697	1.5088	1.4749	1.5440	1.4372	1.3295	0.69824	1.3929	1.4233	1.6410	0.99639	1.5377
5.5	8.00	8.23	1.4826	1.5644	1.4888	1.4916	1.5359	1.4340	1.3622	0.69696	1.4129	1.4256	1.6786	0.95610	1.6400
5.5	8.00	8.53	1.4751	1.5608	1.4720	$\cdots$	1.5276	1.4276	1.3858	0.69403	1.4282	1.4261	1.6901	0.87671	1.7458
5.5	8.00	8.93	$\cdots$	1.5476	1.4469	$\cdots$	1.5092	1.4040	1.3973	0.67961	1.4364	1.4146	1.6228	0.66305	1.8674
5.5	8.00	9.23	$\cdots$	$\cdots$	$\cdots$	$\cdots$	1.4832	1.3490	$\cdots$	0.66785	1.4220	1.3710	1.3883	0.42860	1.8925
5.5	8.25	7.63	1.4910	1.5710	1.5129	1.4719	1.5452	1.4373	1.3237	0.69829	1.3890	1.4224	1.6316	0.99349	1.5174
5.5	8.25	8.23	1.4828	1.5646	1.4894	1.4913	1.5364	1.4336	1.3616	0.69714	1.4120	1.4247	1.6758	0.94867	1.6348
5.5	8.25	8.53	1.4750	1.5607	1.4718	$\cdots$	1.5279	1.4266	1.3862	0.69442	1.4281	1.4249	1.6856	0.86026	1.7464
5.5	8.25	8.93	$\cdots$	1.5476	1.4475	$\cdots$	1.5093	1.3980	1.3961	0.67914	1.4348	1.4085	1.5964	0.61699	1.8634
5.5	8.25	9.23	$\cdots$	$\cdots$	$\cdots$	$\cdots$	1.4824	1.3209	$\cdots$	0.66574	1.4168	1.3461	1.2829	0.36484	1.8465
5.5	8.50	7.63	1.4919	1.5717	1.5166	1.4693	1.5462	1.4370	1.3185	0.69831	1.3854	1.4214	1.6217	0.98345	1.4991
5.5	8.50	8.23	1.4831	1.5647	1.4903	1.4911	1.5369	1.4327	1.3608	0.69715	1.4108	1.4234	1.6709	0.92967	1.6285
5.5	8.50	8.53	1.4749	1.5606	1.4721	$\cdots$	1.5283	1.4244	1.3861	0.69449	1.4273	1.4225	1.6768	0.82766	1.7425
5.5	8.50	8.93	$\cdots$	1.5475	1.4481	$\cdots$	1.5090	1.3859	1.3947	0.67809	1.4319	1.3971	1.5556	0.54746	1.8468
5.5	8.50	9.23	$\cdots$	$\cdots$	1.4257	$\cdots$	1.4783	1.2666	$\cdots$	0.66067	1.4042	1.2976	1.1479	0.29125	1.7545
6.0	6.50	7.63	$\cdots$	1.5623	1.4847	$\cdots$	1.5292	1.3943	$\cdots$	0.69034	1.4080	1.3957	1.5167	0.56279	1.6133
6.0	6.50	8.23	$\cdots$	1.5611	1.4798	$\cdots$	1.5266	1.3891	$\cdots$	0.68833	1.4113	1.3920	1.5073	0.53904	1.6323
6.0	6.50	8.53	$\cdots$	1.5590	1.4715	$\cdots$	1.5216	1.3785	$\cdots$	0.68424	1.4162	1.3848	1.4843	0.49881	1.6644
6.0	6.50	8.93	$\cdots$	1.5489	1.4494	$\cdots$	1.5032	1.3337	$\cdots$	0.67038	1.4195	1.3516	1.3751	0.38781	1.7188
6.0	6.50	9.23	$\cdots$	$\cdots$	1.4265	$\cdots$	1.4745	1.2545	$\cdots$	0.65778	1.4037	1.2855	1.1975	0.29259	1.7022
6.0	6.75	7.63	$\cdots$	1.5631	1.4884	$\cdots$	1.5311	1.3964	$\cdots$	0.69110	1.4047	1.3947	1.5182	0.56566	1.5939
6.0	6.75	8.23	$\cdots$	1.5616	1.4822	$\cdots$	1.5280	1.3903	1.3634	0.68903	1.4092	1.3910	1.5084	0.53856	1.6183
6.0	6.75	8.53	$\cdots$	1.5592	1.4725	$\cdots$	1.5223	1.3783	1.3749	0.68482	1.4151	1.3835	1.4828	0.49362	1.6564
6.0	6.75	8.93	$\cdots$	1.5490	1.4496	$\cdots$	1.5033	1.3319	$\cdots$	0.67055	1.4189	1.3496	1.3691	0.38144	1.7122
6.0	6.75	9.23	$\cdots$	$\cdots$	1.4260	$\cdots$	1.4739	1.2494	$\cdots$	0.65771	1.4021	1.2816	1.1821	0.28668	1.6913
6.0	7.00	7.63	$\cdots$	1.5640	1.4921	$\cdots$	1.5331	1.3989	1.3499	0.69178	1.4012	1.3942	1.5202	0.57227	1.5749
6.0	7.00	8.23	$\cdots$	1.5620	1.4842	$\cdots$	1.5292	1.3917	1.3609	0.68970	1.4073	1.3905	1.5098	0.54068	1.6063
6.0	7.00	8.53	$\cdots$	1.5593	1.4730	$\cdots$	1.5226	1.3780	1.3745	0.68542	1.4145	1.3826	1.4810	0.48992	1.6515
6.0	7.00	8.93	$\cdots$	1.5487	1.4494	$\cdots$	1.5032	1.3298	$\cdots$	0.67062	1.4183	1.3475	1.3625	0.37555	1.7080
6.0	7.00	9.23	$\cdots$	$\cdots$	1.4249	$\cdots$	1.4728	1.2435	$\cdots$	0.65761	1.4002	1.2773	1.1659	0.28063	1.6822
6.0	7.25	7.63	$\cdots$	1.5650	1.4960	$\cdots$	1.5352	1.4013	1.3443	0.69233	1.3975	1.3941	1.5216	0.58029	1.5559
6.0	7.25	8.23	1.4817	1.5623	1.4856	$\cdots$	1.5301	1.3927	1.3593	0.69028	1.4059	1.3904	1.5106	0.54342	1.5971
6.0	7.25	8.53	$\cdots$	1.5592	1.4728	$\cdots$	1.5226	1.3773	1.3751	0.68605	1.4143	1.3819	1.4772	0.48627	1.6500
6.0	7.25	8.93	$\cdots$	1.5479	1.4485	$\cdots$	1.5026	1.3266	1.3873	0.67048	1.4177	1.3450	1.3507	0.36885	1.7051
6.0	7.25	9.23	$\cdots$	$\cdots$	1.4233	$\cdots$	1.4712	1.2364	$\cdots$	0.65758	1.3977	1.2726	1.1438	0.27393	1.6726
6.0	7.50	7.63	1.4871	1.5661	1.4999	$\cdots$	1.5372	1.4033	1.3385	0.69266	1.3938	1.3941	1.5221	0.58789	1.5370
6.0	7.50	8.23	1.4819	1.5625	1.4865	$\cdots$	1.5307	1.3934	1.3584	0.69074	1.4049	1.3901	1.5105	0.54576	1.5907
6.0	7.50	8.53	1.4754	1.5589	1.4721	$\cdots$	1.5224	1.3763	1.3764	0.68664	1.4145	1.3811	1.4709	0.48214	1.6513
6.0	7.50	8.93	$\cdots$	1.5465	1.4471	$\cdots$	1.5015	1.3221	1.3869	0.67020	1.4166	1.3415	1.3297	0.36019	1.7021
6.0	7.50	9.23	$\cdots$	$\cdots$	1.4213	$\cdots$	1.4699	1.2274	$\cdots$	0.65754	1.3941	1.2665	1.1056	0.26531	1.6584
6.0	7.75	7.63	1.4882	1.5673	1.5040	1.4773	1.5391	1.4048	1.3325	0.69284	1.3899	1.3940	1.5215	0.59404	1.5181
6.0	7.75	8.23	1.4819	1.5627	1.4872	$\cdots$	1.5311	1.3939	1.3580	0.69109	1.4042	1.3900	1.5096	0.54734	1.5859
6.0	7.75	8.53	1.4748	1.5587	1.4713	$\cdots$	1.5221	1.3750	1.3777	0.68724	1.4146	1.3802	1.4634	0.47766	1.6533
6.0	7.75	8.93	$\cdots$	1.5450	1.4459	$\cdots$	1.5005	1.3163	1.3858	0.66977	1.4149	1.3363	1.3000	0.34922	1.6964
6.0	7.75	9.23	$\cdots$	$\cdots$	1.4208	$\cdots$	1.4697	1.2169	$\cdots$	0.65702	1.3892	1.2571	1.0440	0.25355	1.6328
6.0	8.00	7.63	1.4895	1.5685	1.5081	1.4743	1.5408	1.4059	1.3266	0.69292	1.3861	1.3937	1.5197	0.59761	1.4995
6.0	8.00	8.23	1.4821	1.5627	1.4878	1.4906	1.5316	1.3939	1.3575	0.69131	1.4034	1.3895	1.5076	0.54706	1.5813
6.0	8.00	8.53	1.4744	1.5584	1.4708	$\cdots$	1.5219	1.3736	1.3785	0.68765	1.4145	1.3788	1.4550	0.47184	1.6535
6.0	8.00	8.93	$\cdots$	1.5439	1.4454	$\cdots$	1.4998	1.3084	1.3841	0.66891	1.4123	1.3283	1.2647	0.33445	1.6850
6.0	8.00	9.23	$\cdots$	$\cdots$	1.4219	$\cdots$	1.4688	1.1971	$\cdots$	0.65464	1.3826	1.2378	0.96239	0.23634	1.5866
6.0	8.25	7.63	1.4906	1.5699	1.5121	1.4713	1.5421	1.4063	1.3210	0.69288	1.3824	1.3930	1.5163	0.59683	1.4816
6.0	8.25	8.23	1.4823	1.5628	1.4885	1.4903	1.5320	1.3932	1.3568	0.69128	1.4023	1.3882	1.5035	0.54198	1.5756
6.0	8.25	8.53	1.4742	1.5581	1.4708	$\cdots$	1.5220	1.3710	1.3786	0.68778	1.4138	1.3761	1.4438	0.46120	1.6501
6.0	8.25	8.93	$\cdots$	1.5430	1.4454	$\cdots$	1.4986	1.2942	1.3818	0.66712	1.4080	1.3144	1.2219	0.31229	1.6633
6.0	8.25	9.23	$\cdots$	$\cdots$	1.4225	$\cdots$	1.4637	1.1522	$\cdots$	0.64869	1.3693	1.1959	0.86782	0.21135	1.5069
6.0	8.50	7.63	1.4916	1.5707	1.5159	1.4688	1.5432	1.4058	1.3160	0.69261	1.3791	1.3915	1.5109	0.58872	1.4650
6.0	8.50	8.23	1.4825	1.5630	1.4893	1.4901	1.5324	1.3908	1.3559	0.69086	1.4007	1.3853	1.4951	0.52710	1.5678
6.0	8.50	8.53	1.4741	1.5580	1.4708	$\cdots$	1.5219	1.3649	1.3780	0.68719	1.4120	1.3704	1.4246	0.43972	1.6401
6.0	8.50	8.93	$\cdots$	1.5418	1.4454	$\cdots$	1.4959	1.2668	1.3788	0.66339	1.4007	1.2888	1.1613	0.27984	1.6222
6.0	8.50	9.23	$\cdots$	$\cdots$	1.4212	$\cdots$	1.4512	1.0723	$\cdots$	0.63680	1.3421	1.1215	0.76054	0.18201	1.3805
6.5	6.50	7.63	$\cdots$	1.5570	1.4814	$\cdots$	1.5162	1.2856	$\cdots$	0.67493	1.3794	1.3027	1.1579	0.28838	1.4531
6.5	6.50	8.23	$\cdots$	1.5552	1.4763	$\cdots$	1.5125	1.2721	$\cdots$	0.67158	1.3802	1.2906	1.1290	0.27551	1.4561
6.5	6.50	8.53	$\cdots$	1.5521	1.4678	$\cdots$	1.5055	1.2463	$\cdots$	0.66537	1.3800	1.2684	1.0744	0.25523	1.4566
6.5	6.50	8.93	$\cdots$	1.5384	1.4447	$\cdots$	1.4791	1.1511	$\cdots$	0.64535	1.3657	1.1859	0.90343	0.20654	1.4088
6.5	6.50	9.23	$\cdots$	$\cdots$	1.4210	$\cdots$	1.4396	1.0240	$\cdots$	0.62826	1.3263	1.0746	0.72146	0.17196	1.2902
6.5	6.75	7.63	$\cdots$	1.5581	1.4852	$\cdots$	1.5184	1.2914	$\cdots$	0.67549	1.3771	1.3023	1.1714	0.28914	1.4413
6.5	6.75	8.23	$\cdots$	1.5559	1.4788	$\cdots$	1.5140	1.2755	1.3484	0.67213	1.3786	1.2897	1.1370	0.27455	1.4467
6.5	6.75	8.53	$\cdots$	1.5523	1.4688	$\cdots$	1.5059	1.2460	1.3562	0.66585	1.3788	1.2662	1.0739	0.25220	1.4488
6.5	6.75	8.93	$\cdots$	1.5383	1.4449	$\cdots$	1.4788	1.1474	$\cdots$	0.64501	1.3640	1.1816	0.89660	0.20355	1.3984
6.5	6.75	9.23	$\cdots$	$\cdots$	1.4204	$\cdots$	1.4380	1.0164	$\cdots$	0.62764	1.3226	1.0680	0.70872	0.16957	1.2734
6.5	7.00	7.63	$\cdots$	1.5593	1.4891	$\cdots$	1.5209	1.2982	1.3378	0.67616	1.3749	1.3035	1.1866	0.29243	1.4311
6.5	7.00	8.23	$\cdots$	1.5566	1.4809	$\cdots$	1.5154	1.2793	1.3464	0.67282	1.3774	1.2902	1.1449	0.27525	1.4399
6.5	7.00	8.53	$\cdots$	1.5524	1.4693	$\cdots$	1.5062	1.2457	1.3558	0.66649	1.3780	1.2648	1.0721	0.25012	1.4437
6.5	7.00	8.93	$\cdots$	1.5379	1.4447	$\cdots$	1.4782	1.1433	$\cdots$	0.64455	1.3625	1.1775	0.88917	0.20095	1.3903
6.5	7.00	9.23	$\cdots$	$\cdots$	1.4194	$\cdots$	1.4360	1.0084	$\cdots$	0.62717	1.3189	1.0616	0.69680	0.16736	1.2590
6.5	7.25	7.63	$\cdots$	1.5606	1.4931	$\cdots$	1.5236	1.3048	1.3330	0.67672	1.3728	1.3055	1.2015	0.29688	1.4214
6.5	7.25	8.23	1.4800	1.5569	1.4824	$\cdots$	1.5166	1.2823	1.3449	0.67353	1.3765	1.2910	1.1500	0.27655	1.4347
6.5	7.25	8.53	$\cdots$	1.5522	1.4691	$\cdots$	1.5061	1.2442	1.3559	0.66724	1.3773	1.2635	1.0659	0.24834	1.4399
6.5	7.25	8.93	$\cdots$	1.5370	1.4437	$\cdots$	1.4771	1.1377	1.3561	0.64383	1.3606	1.1726	0.87683	0.19830	1.3817
6.5	7.25	9.23	$\cdots$	$\cdots$	1.4179	$\cdots$	1.4337	0.99953	$\cdots$	0.62682	1.3147	1.0552	0.68249	0.16518	1.2444
6.5	7.50	7.63	1.4858	1.5620	1.4972	$\cdots$	1.5263	1.3104	1.3280	0.67713	1.3705	1.3078	1.2150	0.30135	1.4117
6.5	7.50	8.23	1.4802	1.5572	1.4834	$\cdots$	1.5173	1.2842	1.3441	0.67417	1.3758	1.2918	1.1520	0.27780	1.4309
6.5	7.50	8.53	1.4732	1.5517	1.4685	$\cdots$	1.5055	1.2419	1.3564	0.66811	1.3766	1.2620	1.0553	0.24658	1.4362
6.5	7.50	8.93	$\cdots$	1.5353	1.4422	$\cdots$	1.4752	1.1298	1.3542	0.64287	1.3575	1.1660	0.85576	0.19518	1.3692
6.5	7.50	9.23	$\cdots$	$\cdots$	1.4159	$\cdots$	1.4310	0.98837	$\cdots$	0.62621	1.3087	1.0473	0.65987	0.16261	1.2247
6.5	7.75	7.63	1.4870	1.5634	1.5014	1.4753	1.5287	1.3148	1.3228	0.67735	1.3679	1.3098	1.2269	0.30518	1.4016
6.5	7.75	8.23	1.4804	1.5574	1.4842	$\cdots$	1.5179	1.2855	1.3437	0.67465	1.3752	1.2923	1.1520	0.27876	1.4274
6.5	7.75	8.53	1.4725	1.5513	1.4677	$\cdots$	1.5049	1.2393	1.3569	0.66888	1.3757	1.2601	1.0429	0.24484	1.4316
6.5	7.75	8.93	$\cdots$	1.5333	1.4408	$\cdots$	1.4730	1.1199	1.3513	0.64146	1.3531	1.1569	0.82796	0.19139	1.3508
6.5	7.75	9.23	$\cdots$	$\cdots$	1.4140	$\cdots$	1.4281	0.97376	$\cdots$	0.62426	1.2999	1.0351	0.62531	0.15908	1.1932
6.5	8.00	7.63	1.4884	1.5650	1.5057	1.4723	1.5308	1.3180	1.3176	0.67730	1.3652	1.3111	1.2369	0.30771	1.3909
6.5	8.00	8.23	1.4805	1.5575	1.4848	1.4875	1.5183	1.2858	1.3431	0.67472	1.3743	1.2918	1.1503	0.27880	1.4232
6.5	8.00	8.53	1.4720	1.5509	1.4671	$\cdots$	1.5043	1.2363	1.3569	0.66924	1.3743	1.2573	1.0301	0.24254	1.4251
6.5	8.00	8.93	$\cdots$	1.5313	1.4396	$\cdots$	1.4705	1.1065	1.3476	0.63904	1.3469	1.1434	0.79676	0.18623	1.3248
6.5	8.00	9.23	$\cdots$	$\cdots$	1.4131	$\cdots$	1.4230	0.94991	1.3005	0.61890	1.2862	1.0115	0.58109	0.15370	1.1424
6.5	8.25	7.63	1.4897	1.5666	1.5099	1.4695	1.5325	1.3196	1.3125	0.67692	1.3624	1.3110	1.2443	0.30793	1.3796
6.5	8.25	8.23	1.4807	1.5576	1.4855	1.4873	1.5186	1.2843	1.3423	0.67422	1.3729	1.2894	1.1452	0.27645	1.4168
6.5	8.25	8.53	1.4718	1.5504	1.4668	$\cdots$	1.5038	1.2305	1.3564	0.66866	1.3720	1.2519	1.0142	0.23802	1.4141
6.5	8.25	8.93	$\cdots$	1.5290	1.4385	$\cdots$	1.4664	1.0832	1.3432	0.63422	1.3373	1.1202	0.75992	0.17821	1.2865
6.5	8.25	9.23	$\cdots$	1.4923	1.4117	$\cdots$	1.4105	0.90405	1.2847	0.60736	1.2616	0.96555	0.52997	0.14548	1.0633
6.5	8.50	7.63	1.4906	1.5674	1.5136	1.4670	1.5335	1.3186	1.3078	0.67599	1.3594	1.3083	1.2474	0.30416	1.3676
6.5	8.50	8.23	1.4809	1.5575	1.4862	1.4871	1.5184	1.2783	1.3410	0.67266	1.3704	1.2827	1.1328	0.26916	1.4059
6.5	8.50	8.53	1.4716	1.5496	1.4666	$\cdots$	1.5023	1.2171	1.3548	0.66634	1.3674	1.2396	0.98805	0.22859	1.3934
6.5	8.50	8.93	$\cdots$	1.5254	1.4370	$\cdots$	1.4581	1.0407	1.3366	0.62526	1.3209	1.0797	0.70888	0.16632	1.2248
6.5	8.50	9.23	$\cdots$	1.4823	1.4071	$\cdots$	1.3842	0.82997	1.2622	0.58650	1.2165	0.89190	0.47099	0.13513	0.94888
7.0	6.50	7.63	$\cdots$	1.5404	1.4710	$\cdots$	1.4766	1.0565	$\cdots$	0.63609	1.2973	1.1036	0.68647	0.16718	1.1136
7.0	6.50	8.23	$\cdots$	1.5370	1.4654	$\cdots$	1.4698	1.0336	$\cdots$	0.62985	1.2918	1.0805	0.65631	0.16198	1.0950
7.0	6.50	8.53	$\cdots$	1.5307	1.4556	$\cdots$	1.4572	0.99309	$\cdots$	0.61903	1.2800	1.0413	0.60542	0.15418	1.0587
7.0	6.50	8.93	$\cdots$	1.5061	1.4283	$\cdots$	1.4091	0.86830	$\cdots$	0.58664	1.2279	0.92269	0.47714	0.13708	0.92756
7.0	6.50	9.23	$\cdots$	$\cdots$	1.3986	$\cdots$	1.3402	0.74431	$\cdots$	0.56113	1.1464	0.80770	0.37237	0.12631	0.77770
7.0	6.75	7.63	$\cdots$	1.5424	1.4751	$\cdots$	1.4797	1.0670	$\cdots$	0.63610	1.2979	1.1035	0.70330	0.16646	1.1133
7.0	6.75	8.23	$\cdots$	1.5383	1.4681	$\cdots$	1.4717	1.0397	1.3038	0.63010	1.2918	1.0794	0.66581	0.16085	1.0928
7.0	6.75	8.53	$\cdots$	1.5310	1.4567	$\cdots$	1.4572	0.99298	1.3021	0.61931	1.2786	1.0378	0.60598	0.15261	1.0523
7.0	6.75	8.93	$\cdots$	1.5056	1.4282	$\cdots$	1.4076	0.86389	$\cdots$	0.58539	1.2244	0.91694	0.47310	0.13587	0.91605
7.0	6.75	9.23	$\cdots$	$\cdots$	1.3975	$\cdots$	1.3365	0.73792	$\cdots$	0.55958	1.1397	0.80125	0.36648	0.12542	0.76263
7.0	7.00	7.63	$\cdots$	1.5446	1.4795	$\cdots$	1.4837	1.0797	1.3009	0.63656	1.2992	1.1065	0.72279	0.16710	1.1168
7.0	7.00	8.23	$\cdots$	1.5395	1.4705	$\cdots$	1.4738	1.0465	1.3031	0.63072	1.2924	1.0806	0.67526	0.16062	1.0937
7.0	7.00	8.53	$\cdots$	1.5312	1.4573	$\cdots$	1.4571	0.99280	1.3015	0.62007	1.2776	1.0359	0.60530	0.15159	1.0480
7.0	7.00	8.93	$\cdots$	1.5050	1.4279	$\cdots$	1.4058	0.85962	1.2746	0.58401	1.2213	0.91168	0.46929	0.13489	0.90712
7.0	7.00	9.23	$\cdots$	$\cdots$	1.3965	$\cdots$	1.3328	0.73204	$\cdots$	0.55841	1.1341	0.79569	0.36192	0.12470	0.75097
7.0	7.25	7.63	$\cdots$	1.5469	1.4841	$\cdots$	1.4881	1.0922	1.2988	0.63713	1.3008	1.1112	0.74278	0.16847	1.1222
7.0	7.25	8.23	1.4747	1.5404	1.4723	$\cdots$	1.4756	1.0521	1.3025	0.63165	1.2931	1.0826	0.68192	0.16086	1.0951
7.0	7.25	8.53	$\cdots$	1.5309	1.4571	$\cdots$	1.4565	0.99124	1.3009	0.62116	1.2762	1.0343	0.60107	0.15083	1.0429
7.0	7.25	8.93	$\cdots$	1.5037	1.4270	$\cdots$	1.4034	0.85424	1.2724	0.58225	1.2177	0.90600	0.46336	0.13402	0.89772
7.0	7.25	9.23	$\cdots$	1.4585	1.3952	$\cdots$	1.3292	0.72631	$\cdots$	0.55750	1.1287	0.79074	0.35754	0.12407	0.74076
7.0	7.50	7.63	1.4819	1.5493	1.4886	$\cdots$	1.4926	1.1032	1.2962	0.63765	1.3023	1.1165	0.76205	0.17006	1.1280
7.0	7.50	8.23	1.4750	1.5408	1.4735	$\cdots$	1.4769	1.0559	1.3021	0.63259	1.2934	1.0846	0.68520	0.16122	1.0957
7.0	7.50	8.53	1.4658	1.5301	1.4564	$\cdots$	1.4553	0.98826	1.2999	0.62258	1.2739	1.0324	0.59317	0.15021	1.0356
7.0	7.50	8.93	$\cdots$	1.5014	1.4254	$\cdots$	1.4000	0.84686	1.2683	0.58002	1.2121	0.89889	0.45335	0.13308	0.88458
7.0	7.50	9.23	$\cdots$	1.4551	1.3934	$\cdots$	1.3246	0.71937	$\cdots$	0.55612	1.1216	0.78512	0.35105	0.12340	0.72852
7.0	7.75	7.63	1.4835	1.5515	1.4933	1.4689	1.4967	1.1120	1.2933	0.63782	1.3034	1.1216	0.78049	0.17152	1.1332
7.0	7.75	8.23	1.4753	1.5412	1.4743	1.4786	1.4777	1.0583	1.3017	0.63317	1.2932	1.0859	0.68625	0.16154	1.0951
7.0	7.75	8.53	1.4651	1.5292	1.4555	$\cdots$	1.4538	0.98506	1.2986	0.62375	1.2708	1.0302	0.58406	0.14966	1.0261
7.0	7.75	8.93	$\cdots$	1.4982	1.4233	$\cdots$	1.3955	0.83735	1.2625	0.57708	1.2040	0.88961	0.44006	0.13195	0.86604
7.0	7.75	9.23	$\cdots$	1.4499	1.3907	$\cdots$	1.3179	0.70916	1.1965	0.55263	1.1105	0.77614	0.34049	0.12245	0.70967
7.0	8.00	7.63	1.4850	1.5538	1.4980	1.4663	1.5003	1.1186	1.2901	0.63746	1.3038	1.1253	0.79768	0.17256	1.1368
7.0	8.00	8.23	1.4754	1.5413	1.4751	1.4784	1.4782	1.0592	1.3011	0.63296	1.2925	1.0855	0.68551	0.16152	1.0925
7.0	8.00	8.53	1.4645	1.5282	1.4547	$\cdots$	1.4523	0.98083	1.2971	0.62396	1.2670	1.0265	0.57463	0.14888	1.0146
7.0	8.00	8.93	$\cdots$	1.4946	1.4211	$\cdots$	1.3894	0.82412	1.2555	0.57244	1.1927	0.87587	0.42488	0.13035	0.84112
7.0	8.00	9.23	$\cdots$	1.4433	1.3872	$\cdots$	1.3059	0.69222	1.1823	0.54440	1.0915	0.75886	0.32548	0.12085	0.67844
7.0	8.25	7.63	1.4864	1.5560	1.5025	1.4638	1.5028	1.1222	1.2866	0.63633	1.3034	1.1261	0.81237	0.17274	1.1379
7.0	8.25	8.23	1.4756	1.5414	1.4757	1.4782	1.4780	1.0566	1.3001	0.63141	1.2904	1.0816	0.68144	0.16060	1.0862
7.0	8.25	8.53	1.4640	1.5267	1.4539	$\cdots$	1.4499	0.97252	1.2950	0.62205	1.2614	1.0186	0.56272	0.14724	0.99840
7.0	8.25	8.93	$\cdots$	1.4896	1.4184	$\cdots$	1.3789	0.80149	1.2470	0.56392	1.1754	0.85274	0.40589	0.12771	0.80524
7.0	8.25	9.23	$\cdots$	1.4324	1.3817	$\cdots$	1.2811	0.66237	1.1623	0.52817	1.0577	0.72698	0.30566	0.11826	0.62867
7.0	8.50	7.63	1.4877	1.5573	1.5065	1.4615	1.5039	1.1209	1.2829	0.63405	1.3016	1.1218	0.82216	0.17141	1.1348
7.0	8.50	8.23	1.4756	1.5409	1.4761	1.4781	1.4762	1.0463	1.2979	0.62760	1.2856	1.0703	0.67042	0.15781	1.0723
7.0	8.50	8.53	1.4634	1.5245	1.4529	$\cdots$	1.4445	0.95333	1.2909	0.61652	1.2509	1.0005	0.54340	0.14379	0.97055
7.0	8.50	8.93	$\cdots$	1.4809	1.4139	$\cdots$	1.3585	0.76237	1.2340	0.54928	1.1455	0.81440	0.37882	0.12370	0.75004
7.0	8.50	9.23	$\cdots$	1.4113	1.3708	$\cdots$	1.2336	0.61734	1.1328	0.50191	1.0002	0.67929	0.27990	0.11475	0.55743
7.5	6.50	7.63	$\cdots$	1.4904	1.4392	$\cdots$	1.3643	0.75564	$\cdots$	0.56475	1.1003	0.83453	0.34157	0.12221	0.66331
7.5	6.50	8.23	$\cdots$	1.4826	1.4318	$\cdots$	1.3504	0.73535	$\cdots$	0.55486	1.0849	0.80992	0.32613	0.12034	0.63985
7.5	6.50	8.53	$\cdots$	1.4684	1.4189	$\cdots$	1.3251	0.70207	$\cdots$	0.53828	1.0567	0.77174	0.30157	0.11777	0.60025
7.5	6.50	8.93	$\cdots$	1.4162	1.3789	$\cdots$	1.2335	0.61332	$\cdots$	0.49274	0.96020	0.67688	0.24439	0.11282	0.49026
7.5	6.50	9.23	$\cdots$	$\cdots$	1.3312	$\cdots$	1.1124	0.54105	$\cdots$	0.46047	0.84542	0.60568	0.20223	0.11007	0.39581
7.5	6.75	7.63	$\cdots$	1.4951	1.4444	$\cdots$	1.3695	0.76598	$\cdots$	0.56383	1.1059	0.83234	0.35143	0.12138	0.66888
7.5	6.75	8.23	$\cdots$	1.4858	1.4353	$\cdots$	1.3532	0.74111	1.1835	0.55459	1.0879	0.80726	0.33169	0.11955	0.64146
7.5	6.75	8.53	$\cdots$	1.4693	1.4200	$\cdots$	1.3243	0.70224	1.1626	0.53853	1.0554	0.76776	0.30232	0.11704	0.59606
7.5	6.75	8.93	$\cdots$	1.4149	1.3782	$\cdots$	1.2292	0.61028	$\cdots$	0.49093	0.95481	0.67213	0.24278	0.11234	0.48219
7.5	6.75	9.23	$\cdots$	1.3355	1.3290	$\cdots$	1.1051	0.53766	$\cdots$	0.45836	0.83747	0.60157	0.20021	0.10973	0.38721
7.5	7.00	7.63	$\cdots$	1.5002	1.4502	$\cdots$	1.3773	0.77894	1.1983	0.56359	1.1138	0.83391	0.36314	0.12118	0.67955
7.5	7.00	8.23	$\cdots$	1.4887	1.4385	$\cdots$	1.3573	0.74790	1.1864	0.55494	1.0922	0.80737	0.33734	0.11920	0.64621
7.5	7.00	8.53	$\cdots$	1.4698	1.4207	$\cdots$	1.3239	0.70250	1.1625	0.53943	1.0546	0.76556	0.30247	0.11656	0.59362
7.5	7.00	8.93	$\cdots$	1.4137	1.3774	$\cdots$	1.2253	0.60763	1.0843	0.48888	0.95063	0.66798	0.24149	0.11197	0.47642
7.5	7.00	9.23	$\cdots$	1.3330	1.3275	$\cdots$	1.0990	0.53489	$\cdots$	0.45676	0.83158	0.59833	0.19895	0.10948	0.38130
7.5	7.25	7.63	$\cdots$	1.5052	1.4561	$\cdots$	1.3863	0.79230	1.2027	0.56375	1.1227	0.83788	0.37556	0.12138	0.69319
7.5	7.25	8.23	1.4582	1.4909	1.4411	$\cdots$	1.3610	0.75367	1.1884	0.55578	1.0959	0.80872	0.34152	0.11911	0.65119
7.5	7.25	8.53	$\cdots$	1.4691	1.4205	$\cdots$	1.3226	0.70164	1.1609	0.54098	1.0526	0.76407	0.30082	0.11624	0.59014
7.5	7.25	8.93	$\cdots$	1.4117	1.3762	$\cdots$	1.2208	0.60463	1.0810	0.48628	0.94600	0.66378	0.23964	0.11167	0.47097
7.5	7.25	9.23	$\cdots$	1.3313	1.3264	$\cdots$	1.0939	0.53266	$\cdots$	0.45555	0.82724	0.59579	0.19818	0.10929	0.37699
7.5	7.50	7.63	1.4695	1.5102	1.4622	$\cdots$	1.3955	0.80436	1.2064	0.56391	1.1317	0.84304	0.38799	0.12175	0.70825
7.5	7.50	8.23	1.4588	1.4923	1.4427	$\cdots$	1.3637	0.75755	1.1894	0.55666	1.0984	0.81022	0.34373	0.11913	0.65459
7.5	7.50	8.53	1.4438	1.4675	1.4193	$\cdots$	1.3199	0.69955	1.1574	0.54279	1.0486	0.76260	0.29737	0.11601	0.58420
7.5	7.50	8.93	$\cdots$	1.4079	1.3738	$\cdots$	1.2148	0.60063	1.0746	0.48306	0.93908	0.65902	0.23641	0.11139	0.46374
7.5	7.50	9.23	$\cdots$	1.3288	1.3250	$\cdots$	1.0884	0.53021	0.97161	0.45396	0.82229	0.59322	0.19715	0.10911	0.37252
7.5	7.75	7.63	1.4721	1.5150	1.4681	1.4492	1.4042	0.81448	1.2094	0.56371	1.1401	0.84844	0.40035	0.12214	0.72354
7.5	7.75	8.23	1.4592	1.4930	1.4438	1.4519	1.3652	0.76006	1.1896	0.55694	1.0994	0.81113	0.34465	0.11916	0.65609
7.5	7.75	8.53	1.4424	1.4652	1.4179	$\cdots$	1.3167	0.69710	1.1532	0.54414	1.0430	0.76085	0.29326	0.11581	0.57637
7.5	7.75	8.93	$\cdots$	1.4025	1.3706	$\cdots$	1.2066	0.59535	1.0653	0.47925	0.92898	0.65316	0.23190	0.11106	0.45373
7.5	7.75	9.23	$\cdots$	1.3233	1.3219	$\cdots$	1.0791	0.52620	0.96441	0.45037	0.81357	0.58899	0.19494	0.10884	0.36547
7.5	8.00	7.63	1.4745	1.5196	1.4740	1.4477	1.4114	0.82231	1.2114	0.56272	1.1471	0.85263	0.41240	0.12243	0.73769
7.5	8.00	8.23	1.4594	1.4933	1.4446	1.4519	1.3657	0.76090	1.1892	0.55609	1.0990	0.81045	0.34450	0.11910	0.65544
7.5	8.00	8.53	1.4412	1.4628	1.4162	$\cdots$	1.3128	0.69389	1.1489	0.54389	1.0361	0.75802	0.28896	0.11553	0.56705
7.5	8.00	8.93	$\cdots$	1.3954	1.3663	$\cdots$	1.1948	0.58768	1.0544	0.47387	0.91460	0.64478	0.22642	0.11055	0.43996
7.5	8.00	9.23	$\cdots$	1.3126	1.3159	$\cdots$	1.0603	0.51867	0.95102	0.44258	0.79662	0.58067	0.19090	0.10835	0.35265
7.5	8.25	7.63	1.4766	1.5236	1.4794	1.4462	1.4162	0.82693	1.2122	0.56063	1.1517	0.85394	0.42336	0.0000	0.74886
7.5	8.25	8.23	1.4595	1.4930	1.4449	1.4518	1.3643	0.75833	1.1876	0.55326	1.0960	0.80630	0.34249	0.11873	0.65100
7.5	8.25	8.53	1.4400	1.4593	1.4140	$\cdots$	1.3064	0.68703	1.1438	0.54057	1.0261	0.75130	0.28341	0.11494	0.55434
7.5	8.25	8.93	$\cdots$	1.3846	1.3599	$\cdots$	1.1738	0.57447	1.0407	0.46510	0.89212	0.63103	0.21906	0.10968	0.41984
7.5	8.25	9.23	$\cdots$	1.2926	1.3041	$\cdots$	1.0223	0.50512	0.92969	0.42845	0.76506	0.56559	0.18436	0.10750	0.33080
7.5	8.50	7.63	1.4783	1.5262	1.4841	1.4448	1.4175	0.82636	1.2115	0.55673	1.1525	0.84952	0.43138	0.0000	0.75428
7.5	8.50	8.23	1.4593	1.4912	1.4443	1.4518	1.3586	0.74841	1.1836	0.54721	1.0876	0.79497	0.33672	0.11773	0.63904
7.5	8.50	8.53	1.4383	1.4532	1.4105	$\cdots$	1.2923	0.67161	1.1348	0.53234	1.0080	0.73597	0.27435	0.11372	0.53316
7.5	8.50	8.93	$\cdots$	1.3649	1.3482	$\cdots$	1.1336	0.55231	1.0190	0.45170	0.85396	0.60914	0.20815	0.10832	0.38897
7.5	8.50	9.23	$\cdots$	1.2538	1.2806	$\cdots$	0.95293	0.48464	0.89565	0.40772	0.71222	0.54350	0.17465	0.10629	0.29853
8.0	6.50	7.63	$\cdots$	1.3519	1.3472	$\cdots$	1.1011	0.53514	$\cdots$	0.48172	0.77677	0.62732	0.18195	0.10646	0.32962
8.0	6.50	8.23	$\cdots$	1.3359	1.3359	$\cdots$	1.0779	0.52556	$\cdots$	0.47052	0.75836	0.61060	0.17688	0.10592	0.31721
8.0	6.50	8.53	$\cdots$	1.3070	1.3159	$\cdots$	1.0379	0.51057	$\cdots$	0.45166	0.72722	0.58627	0.16895	0.10530	0.29761
8.0	6.50	8.93	$\cdots$	1.2051	1.2485	$\cdots$	0.90290	0.47175	$\cdots$	0.40362	0.63303	0.53546	0.14981	0.10451	0.24686
8.0	6.50	9.23	$\cdots$	1.0711	1.1634	$\cdots$	0.74561	0.44159	$\cdots$	0.37204	0.53923	0.50368	0.13565	0.10435	0.20718
8.0	6.75	7.63	$\cdots$	1.3633	1.3555	$\cdots$	1.1097	0.54057	$\cdots$	0.47985	0.78566	0.62239	0.18573	0.10589	0.33265
8.0	6.75	8.23	$\cdots$	1.3439	1.3415	$\cdots$	1.0826	0.52868	0.92939	0.46971	0.76350	0.60649	0.17913	0.10546	0.31796
8.0	6.75	8.53	$\cdots$	1.3099	1.3177	$\cdots$	1.0367	0.51083	0.88947	0.45212	0.72692	0.58279	0.16942	0.10494	0.29529
8.0	6.75	8.93	$\cdots$	1.2024	1.2463	$\cdots$	0.89559	0.47021	$\cdots$	0.40247	0.62796	0.53252	0.14921	0.10429	0.24255
8.0	6.75	9.23	$\cdots$	1.0650	1.1588	$\cdots$	0.73572	0.44011	$\cdots$	0.37048	0.53323	0.50151	0.13497	0.10422	0.20317
8.0	7.00	7.63	$\cdots$	1.3755	1.3648	$\cdots$	1.1237	0.54776	0.96677	0.47842	0.79814	0.62031	0.19032	0.10559	0.33941
8.0	7.00	8.23	$\cdots$	1.3513	1.3470	$\cdots$	1.0900	0.53242	0.93789	0.46932	0.77033	0.60449	0.18144	0.10517	0.32093
8.0	7.00	8.53	$\cdots$	1.3114	1.3189	$\cdots$	1.0361	0.51114	0.89058	0.45299	0.72696	0.58067	0.16963	0.10470	0.29412
8.0	7.00	8.93	$\cdots$	1.1999	1.2443	$\cdots$	0.88918	0.46895	0.77066	0.40091	0.62414	0.52997	0.14875	0.10414	0.23964
8.0	7.00	9.23	$\cdots$	1.0614	1.1559	$\cdots$	0.72813	0.43899	$\cdots$	0.36927	0.52920	0.49990	0.13459	0.10412	0.20060
8.0	7.25	7.63	$\cdots$	1.3875	1.3745	$\cdots$	1.1406	0.55545	0.98167	0.47748	0.81253	0.62036	0.19525	0.10546	0.34857
8.0	7.25	8.23	1.4096	1.3566	1.3512	$\cdots$	1.0970	0.53563	0.94395	0.46923	0.77627	0.60373	0.18311	0.10502	0.32413
8.0	7.25	8.53	$\cdots$	1.3101	1.3181	$\cdots$	1.0338	0.51075	0.88776	0.45421	0.72500	0.57923	0.16902	0.10455	0.29234
8.0	7.25	8.93	$\cdots$	1.1960	1.2416	$\cdots$	0.88239	0.46756	0.76645	0.39861	0.62002	0.52745	0.14812	0.10403	0.23706
8.0	7.25	9.23	$\cdots$	1.0602	1.1547	$\cdots$	0.72274	0.43819	0.0000	0.36842	0.52670	0.49874	0.13444	0.10406	0.19891
8.0	7.50	7.63	1.4319	1.3992	1.3843	$\cdots$	1.1584	0.56261	0.99601	0.47665	0.82752	0.62168	0.20027	0.0000	0.35918
8.0	7.50	8.23	1.4108	1.3597	1.3538	$\cdots$	1.1017	0.53769	0.94697	0.46912	0.78002	0.60337	0.18394	0.10495	0.32631
8.0	7.50	8.53	1.3802	1.3059	1.3154	$\cdots$	1.0287	0.50956	0.88091	0.45545	0.72016	0.57807	0.16765	0.10446	0.28907
8.0	7.50	8.93	$\cdots$	1.1890	1.2371	$\cdots$	0.87354	0.46580	0.75830	0.39564	0.61401	0.52482	0.14701	0.10394	0.23386
8.0	7.50	9.23	$\cdots$	1.0586	1.1535	$\cdots$	0.71767	0.43742	0.64475	0.36749	0.52431	0.49768	0.13430	0.10399	0.19741
8.0	7.75	7.63	1.4373	1.4104	1.3938	1.3907	1.1753	0.56881	1.0094	0.47575	0.84225	0.62375	0.20536	0.0000	0.37052
8.0	7.75	8.23	1.4113	1.3613	1.3552	1.3767	1.1041	0.53885	0.94801	0.46843	0.78173	0.60288	0.18423	0.10490	0.32733
8.0	7.75	8.53	1.3768	1.3004	1.3119	$\cdots$	1.0223	0.50820	0.87277	0.45594	0.71346	0.57691	0.16602	0.10437	0.28481
8.0	7.75	8.93	$\cdots$	1.1788	1.2305	$\cdots$	0.86188	0.46354	0.74677	0.39242	0.60540	0.52192	0.14548	0.10384	0.22955
8.0	7.75	9.23	$\cdots$	1.0526	1.1494	$\cdots$	0.70851	0.43608	0.64063	0.36549	0.51959	0.49602	0.13382	0.10389	0.19504
8.0	8.00	7.63	1.4421	1.4209	1.4029	1.3927	1.1896	0.57386	1.0210	0.47416	0.85540	0.62547	0.21047	0.0000	0.38172
8.0	8.00	8.23	1.4117	1.3618	1.3559	1.3771	1.1044	0.53917	0.94784	0.46676	0.78157	0.60169	0.18412	0.10483	0.32711
8.0	8.00	8.53	1.3737	1.2943	1.3078	$\cdots$	1.0147	0.50638	0.86514	0.45480	0.70557	0.57513	0.16434	0.10425	0.27994
8.0	8.00	8.93	$\cdots$	1.1654	1.2216	$\cdots$	0.84511	0.46021	0.73373	0.38871	0.59344	0.51809	0.14360	0.10366	0.22373
8.0	8.00	9.23	$\cdots$	1.0380	1.1392	$\cdots$	0.68882	0.43329	0.63046	0.36125	0.50931	0.49277	0.13266	0.10371	0.19045
8.0	8.25	7.63	1.4463	1.4299	1.4111	1.3941	1.1989	0.57716	1.0299	0.47163	0.86517	0.62577	0.21523	0.0000	0.39139
8.0	8.25	8.23	1.4117	1.3607	1.3553	1.3774	1.1009	0.53756	0.94578	0.46347	0.77817	0.59865	0.18330	0.10467	0.32486
8.0	8.25	8.53	1.3706	1.2861	1.3022	$\cdots$	1.0026	0.50278	0.85679	0.45098	0.69467	0.57121	0.16222	0.10402	0.27353
8.0	8.25	8.93	$\cdots$	1.1449	1.2074	$\cdots$	0.81603	0.45455	0.71791	0.38364	0.57524	0.51215	0.14102	0.10336	0.21529
8.0	8.25	9.23	$\cdots$	1.0078	1.1173	$\cdots$	0.64880	0.42811	0.61251	0.35383	0.48954	0.48687	0.13050	0.10341	0.18231
8.0	8.50	7.63	1.4495	1.4360	1.4175	1.3950	1.2007	0.57739	1.0350	0.46742	0.86926	0.62284	0.21886	0.0000	0.39747
8.0	8.50	8.23	1.4105	1.3559	1.3523	1.3778	1.0886	0.53203	0.93919	0.45751	0.76807	0.59171	0.18104	0.0000	0.31855
8.0	8.50	8.53	1.3659	1.2717	1.2924	$\cdots$	0.97723	0.49502	0.84315	0.44319	0.67578	0.56280	0.15884	0.10358	0.26332
8.0	8.50	8.93	1.2737	1.1082	1.1815	$\cdots$	0.76308	0.44523	0.69376	0.37744	0.54575	0.50325	0.13714	0.10288	0.20258
8.0	8.50	9.23	$\cdots$	0.95019	1.0739	$\cdots$	0.57967	0.42016	0.58347	0.34347	0.45719	0.47826	0.12708	0.10296	0.17008
8.5	6.50	7.63	$\cdots$	1.0461	1.1212	$\cdots$	0.68724	0.43251	$\cdots$	0.41451	0.47421	0.52154	0.12367	0.0000	0.17266
8.5	6.50	8.23	$\cdots$	1.0224	1.1047	$\cdots$	0.66403	0.42944	$\cdots$	0.40510	0.46364	0.51184	0.12244	0.10119	0.16835
8.5	6.50	8.53	$\cdots$	0.98141	1.0760	$\cdots$	0.62626	0.42477	$\cdots$	0.38908	0.44663	0.49788	0.12051	0.10120	0.16179
8.5	6.50	8.93	$\cdots$	0.84210	0.97535	$\cdots$	0.50804	0.41212	$\cdots$	0.34991	0.39639	0.47378	0.11545	0.10164	0.14477
8.5	6.50	9.23	$\cdots$	0.68221	0.85125	$\cdots$	0.38520	0.40185	$\cdots$	0.32340	0.34940	0.46185	0.11159	0.10230	0.13197
8.5	6.75	7.63	$\cdots$	1.0675	1.1350	$\cdots$	0.69612	0.43430	$\cdots$	0.41221	0.48020	0.51599	0.12475	0.0000	0.17280
8.5	6.75	8.23	$\cdots$	1.0379	1.1146	$\cdots$	0.66918	0.43052	0.58602	0.40403	0.46730	0.50766	0.12312	0.10089	0.16786
8.5	6.75	8.53	$\cdots$	0.98817	1.0799	$\cdots$	0.62568	0.42491	0.55109	0.38947	0.44697	0.49512	0.12070	0.10097	0.16042
8.5	6.75	8.93	$\cdots$	0.83820	0.97109	$\cdots$	0.50073	0.41146	$\cdots$	0.34977	0.39335	0.47217	0.11522	0.10153	0.14272
8.5	6.75	9.23	$\cdots$	0.67509	0.84404	$\cdots$	0.37714	0.40124	$\cdots$	0.32271	0.34622	0.46076	0.11135	0.10224	0.13018
8.5	7.00	7.63	$\cdots$	1.0906	1.1513	$\cdots$	0.71234	0.43691	0.62566	0.41027	0.48922	0.51224	0.12610	0.0000	0.17496
8.5	7.00	8.23	$\cdots$	1.0523	1.1245	$\cdots$	0.67805	0.43193	0.59657	0.40303	0.47234	0.50479	0.12383	0.10066	0.16867
8.5	7.00	8.53	$\cdots$	0.99197	1.0823	$\cdots$	0.62586	0.42508	0.55315	0.38978	0.44745	0.49316	0.12078	0.10082	0.15974
8.5	7.00	8.93	$\cdots$	0.83411	0.96717	$\cdots$	0.49438	0.41091	0.45469	0.34913	0.39100	0.47071	0.11504	0.10146	0.14135
8.5	7.00	9.23	$\cdots$	0.67069	0.83952	$\cdots$	0.37110	0.40079	$\cdots$	0.32221	0.34414	0.46001	0.11120	0.10220	0.12907
8.5	7.25	7.63	$\cdots$	1.1138	1.1682	$\cdots$	0.73289	0.43981	0.64493	0.40884	0.49996	0.51000	0.12759	0.0000	0.17840
8.5	7.25	8.23	1.2786	1.0623	1.1318	$\cdots$	0.68631	0.43311	0.60389	0.40214	0.47666	0.50285	0.12434	0.10051	0.16973
8.5	7.25	8.53	1.2267	0.98934	1.0804	$\cdots$	0.62318	0.42484	0.54994	0.39013	0.44611	0.49184	0.12055	0.10073	0.15884
8.5	7.25	8.93	$\cdots$	0.82728	0.96154	$\cdots$	0.48745	0.41030	0.45037	0.34772	0.38831	0.46930	0.11478	0.10142	0.14016
8.5	7.25	9.23	$\cdots$	0.66878	0.83730	$\cdots$	0.36683	0.40046	0.0000	0.32202	0.34284	0.45947	0.11114	0.10217	0.12835
8.5	7.50	7.63	1.3253	1.1366	1.1851	$\cdots$	0.75521	0.44256	0.66445	0.40758	0.51161	0.50874	0.12910	0.0000	0.18264
8.5	7.50	8.23	1.2808	1.0674	1.1357	$\cdots$	0.69122	0.43380	0.60698	0.40121	0.47911	0.50148	0.12453	0.10043	0.17038
8.5	7.50	8.53	1.2185	0.98064	1.0742	$\cdots$	0.61657	0.42426	0.54168	0.39021	0.44242	0.49085	0.12003	0.10069	0.15731
8.5	7.50	8.93	$\cdots$	0.81584	0.95259	$\cdots$	0.47863	0.40953	0.44261	0.34585	0.38446	0.46792	0.11436	0.10141	0.13878
8.5	7.50	9.23	$\cdots$	0.66654	0.83498	$\cdots$	0.36287	0.40013	0.36921	0.32197	0.34158	0.45904	0.11106	0.10215	0.12772
8.5	7.75	7.63	1.3377	1.1589	1.2017	1.2371	0.77721	0.44505	0.68371	0.40665	0.52345	0.50831	0.13067	0.0000	0.18739
8.5	7.75	8.23	1.2815	1.0694	1.1372	1.1910	0.69317	0.43408	0.60765	0.39989	0.47996	0.50028	0.12454	0.10037	0.17055
8.5	7.75	8.53	1.2095	0.96953	1.0662	$\cdots$	0.60828	0.42357	0.53236	0.38966	0.43748	0.48999	0.11943	0.10067	0.15539
8.5	7.75	8.93	$\cdots$	0.80069	0.94055	$\cdots$	0.46770	0.40862	0.43276	0.34383	0.37930	0.46653	0.11384	0.10139	0.13705
8.5	7.75	9.23	$\cdots$	0.65943	0.82860	$\cdots$	0.35617	0.39963	0.36628	0.32172	0.33923	0.45844	0.11088	0.10211	0.12679
8.5	8.00	7.63	1.3488	1.1798	1.2175	1.2466	0.79625	0.44710	0.70164	0.40523	0.53455	0.50793	0.13225	0.0000	0.19227
8.5	8.00	8.23	1.2816	1.0697	1.1373	1.1920	0.69266	0.43403	0.60731	0.39804	0.47960	0.49895	0.12443	0.0000	0.17031
8.5	8.00	8.53	1.2017	0.95790	1.0574	$\cdots$	0.59905	0.42272	0.52444	0.38803	0.43203	0.48889	0.11883	0.10062	0.15332
8.5	8.00	8.93	$\cdots$	0.78198	0.92490	$\cdots$	0.45307	0.40734	0.42273	0.34208	0.37263	0.46496	0.11321	0.10133	0.13485
8.5	8.00	9.23	$\cdots$	0.64337	0.81361	$\cdots$	0.34248	0.39860	0.35981	0.32050	0.33431	0.45722	0.11049	0.10203	0.12509
8.5	8.25	7.63	1.3585	1.1978	1.2315	1.2545	0.80900	0.44853	0.71663	0.40304	0.54334	0.50717	0.13374	$\cdots$	0.19668
8.5	8.25	8.23	1.2809	1.0672	1.1349	1.1932	0.68775	0.43328	0.60520	0.39526	0.47717	0.49698	0.12409	0.0000	0.16933
8.5	8.25	8.53	1.1942	0.94370	1.0458	$\cdots$	0.58552	0.42120	0.51671	0.38500	0.42511	0.48688	0.11809	0.10053	0.15078
8.5	8.25	8.93	1.0413	0.75507	0.90114	$\cdots$	0.42918	0.40521	0.41172	0.34023	0.36311	0.46273	0.11235	0.10122	0.13176
8.5	8.25	9.23	$\cdots$	0.61190	0.78291	$\cdots$	0.31605	0.39670	0.34915	0.31793	0.32521	0.45501	0.10975	0.10191	0.12215
8.5	8.50	7.63	1.3658	1.2107	1.2417	1.2609	0.81148	0.44882	0.72667	0.39994	0.54764	0.50538	0.13487	$\cdots$	0.19969
8.5	8.50	8.23	1.2778	1.0580	1.1274	1.1945	0.67270	0.43100	0.59874	0.39105	0.47033	0.49362	0.12328	0.0000	0.16684
8.5	8.50	8.53	1.1835	0.92032	1.0263	$\cdots$	0.55930	0.41809	0.50521	0.37977	0.41389	0.48298	0.11694	0.0000	0.14692
8.5	8.50	8.93	1.0169	0.71058	0.86039	$\cdots$	0.38857	0.40175	0.39615	0.33934	0.34861	0.45986	0.11105	0.10105	0.12722
8.5	8.50	9.23	$\cdots$	0.55632	0.72617	$\cdots$	0.27321	0.39378	0.33299	0.31454	0.31089	0.45186	0.10856	0.10173	0.11777
9.0	6.50	7.63	$\cdots$	0.61072	0.73320	$\cdots$	0.31775	0.39468	$\cdots$	0.36679	0.30794	0.47322	0.10432	0.0000	0.11394
9.0	6.50	8.23	$\cdots$	0.59036	0.71637	$\cdots$	0.30443	0.39390	$\cdots$	0.36105	0.30411	0.46839	0.10415	0.099991	0.11268
9.0	6.50	8.53	$\cdots$	0.55674	0.68812	$\cdots$	0.28377	0.39273	$\cdots$	0.35069	0.29816	0.46105	0.10390	0.10014	0.11086
9.0	6.50	8.93	$\cdots$	0.44902	0.59195	$\cdots$	0.22318	0.38960	$\cdots$	0.32450	0.28069	0.44971	0.10327	0.10079	0.10652
9.0	6.50	9.23	$\cdots$	0.34019	0.48368	$\cdots$	0.16413	0.38701	$\cdots$	0.30397	0.26428	0.44582	0.10293	0.10156	0.10397
9.0	6.75	7.63	$\cdots$	0.63409	0.75036	$\cdots$	0.32193	0.39496	$\cdots$	0.36529	0.30994	0.46909	0.10443	0.0000	0.11318
9.0	6.75	8.23	$\cdots$	0.60771	0.72910	$\cdots$	0.30689	0.39404	0.0000	0.36031	0.30535	0.46517	0.10420	0.099755	0.11185
9.0	6.75	8.53	$\cdots$	0.56558	0.69414	$\cdots$	0.28346	0.39268	0.0000	0.35087	0.29827	0.45888	0.10388	0.099969	0.10992
9.0	6.75	8.93	$\cdots$	0.44629	0.58776	$\cdots$	0.21895	0.38933	0.0000	0.32482	0.27937	0.44869	0.10317	0.10073	0.10555
9.0	6.75	9.23	$\cdots$	0.33546	0.47737	$\cdots$	0.16003	0.38675	$\cdots$	0.30400	0.26298	0.44529	0.10283	0.10153	0.10317
9.0	7.00	7.63	$\cdots$	0.66025	0.77098	$\cdots$	0.33187	0.39559	0.34295	0.36429	0.31355	0.46609	0.10463	0.0000	0.11337
9.0	7.00	8.23	$\cdots$	0.62416	0.74220	$\cdots$	0.31246	0.39438	0.32786	0.35968	0.30741	0.46278	0.10429	0.0000	0.11173
9.0	7.00	8.53	$\cdots$	0.57077	0.69807	$\cdots$	0.28393	0.39268	0.30633	0.35088	0.29854	0.45726	0.10386	0.099846	0.10945
9.0	7.00	8.93	$\cdots$	0.44266	0.58338	$\cdots$	0.21522	0.38910	0.25913	0.32506	0.27829	0.44794	0.10311	0.10069	0.10495
9.0	7.00	9.23	$\cdots$	0.33217	0.47311	$\cdots$	0.15692	0.38659	$\cdots$	0.30425	0.26210	0.44500	0.10278	0.10151	0.10270
9.0	7.25	7.63	1.0485	0.68744	0.79311	$\cdots$	0.34547	0.39638	0.35534	0.36314	0.31813	0.46363	0.10487	0.0000	0.11417
9.0	7.25	8.23	0.99359	0.63567	0.75178	$\cdots$	0.31782	0.39466	0.33255	0.35902	0.30922	0.46101	0.10436	0.0000	0.11185
9.0	7.25	8.53	0.91519	0.56826	0.69585	$\cdots$	0.28224	0.39258	0.30450	0.35076	0.29795	0.45612	0.10380	0.099784	0.10902
9.0	7.25	8.93	$\cdots$	0.43589	0.57634	$\cdots$	0.21094	0.38887	0.25630	0.32452	0.27702	0.44712	0.10303	0.10068	0.10446
9.0	7.25	9.23	$\cdots$	0.32978	0.47011	$\cdots$	0.15456	0.38645	0.0000	0.30479	0.26148	0.44479	0.10274	0.10150	0.10238
9.0	7.50	7.63	1.0739	0.71491	0.81563	$\cdots$	0.36089	0.39715	0.36829	0.36238	0.32325	0.46196	0.10513	$\cdots$	0.11534
9.0	7.50	8.23	0.99727	0.64109	0.75635	$\cdots$	0.32083	0.39481	0.33436	0.35819	0.31017	0.45961	0.10436	0.0000	0.11191
9.0	7.50	8.53	0.90021	0.55874	0.68757	$\cdots$	0.27767	0.39235	0.29936	0.35048	0.29623	0.45536	0.10368	0.099778	0.10844
9.0	7.50	8.93	$\cdots$	0.42511	0.56552	$\cdots$	0.20555	0.38860	0.25159	0.32389	0.27523	0.44651	0.10295	0.10070	0.10398
9.0	7.50	9.23	$\cdots$	0.32642	0.46618	$\cdots$	0.15217	0.38633	0.22089	0.30561	0.26079	0.44469	0.10269	0.10150	0.10211
9.0	7.75	7.63	1.0982	0.74265	0.83824	0.93220	0.37667	0.39786	0.38163	0.36224	0.32864	0.46101	0.10542	$\cdots$	0.11676
9.0	7.75	8.23	0.99801	0.64299	0.75779	0.85928	0.32180	0.39483	0.33467	0.35717	0.31044	0.45847	0.10433	0.0000	0.11185
9.0	7.75	8.53	0.88428	0.54682	0.67697	$\cdots$	0.27199	0.39207	0.29373	0.34967	0.29400	0.45468	0.10354	0.0000	0.10778
9.0	7.75	8.93	0.0000	0.41205	0.55200	$\cdots$	0.19925	0.38826	0.24616	0.32240	0.27299	0.44564	0.10284	0.10071	0.10341
9.0	7.75	9.23	$\cdots$	0.31983	0.45851	$\cdots$	0.14843	0.38610	0.21874	0.30617	0.25965	0.44446	0.10263	0.10148	0.10173
9.0	8.00	7.63	1.1210	0.76979	0.86006	0.95023	0.39084	0.39845	0.39467	0.36150	0.33383	0.46006	0.10570	$\cdots$	0.11828
9.0	8.00	8.23	0.99817	0.64317	0.75742	0.86080	0.32123	0.39475	0.33449	0.35569	0.31019	0.45736	0.10426	0.0000	0.11169
9.0	8.00	8.53	0.87129	0.53492	0.66570	$\cdots$	0.26598	0.39176	0.28923	0.34863	0.29161	0.45408	0.10339	0.0000	0.10708
9.0	8.00	8.93	0.68638	0.39691	0.53559	$\cdots$	0.19132	0.38779	0.24112	0.32214	0.27022	0.44511	0.10269	0.10071	0.10271
9.0	8.00	9.23	$\cdots$	0.30819	0.44427	$\cdots$	0.14163	0.38569	0.21527	0.30623	0.25756	0.44392	0.10251	0.10145	0.10109
9.0	8.25	7.63	1.1409	0.79397	0.87947	0.96615	0.40071	0.39885	0.40613	0.35976	0.33810	0.45887	0.10596	$\cdots$	0.11969
9.0	8.25	8.23	0.99703	0.64053	0.75409	0.86292	0.31787	0.39442	0.33340	0.35397	0.30908	0.45619	0.10411	0.0000	0.11131
9.0	8.25	8.53	0.85945	0.52136	0.65173	$\cdots$	0.25765	0.39115	0.28520	0.34681	0.28868	0.45300	0.10316	0.0000	0.10622
9.0	8.25	8.93	0.66594	0.37658	0.51230	$\cdots$	0.17899	0.38703	0.23609	0.32180	0.26644	0.44435	0.10242	0.10068	0.10170
9.0	8.25	9.23	$\cdots$	0.28775	0.41824	$\cdots$	0.12934	0.38497	0.21042	0.30600	0.25394	0.44308	0.10227	0.10139	0.10000
9.0	8.50	7.63	1.1563	0.81205	0.89368	0.97969	0.40302	0.39888	0.41435	0.0000	0.34034	0.45779	0.10611	$\cdots$	0.12068
9.0	8.50	8.23	0.99145	0.63091	0.74404	0.86522	0.30809	0.39358	0.32988	0.35178	0.30608	0.45471	0.10381	$\cdots$	0.11042
9.0	8.50	8.53	0.84371	0.50052	0.62951	$\cdots$	0.24240	0.39006	0.27952	0.34415	0.28409	0.45132	0.10278	0.0000	0.10491
9.0	8.50	8.93	0.63920	0.34562	0.47541	$\cdots$	0.15904	0.38578	0.22941	0.32248	0.26089	0.44367	0.10199	0.10064	0.10017
9.0	8.50	9.23	$\cdots$	0.25459	0.37452	$\cdots$	0.11028	0.38388	0.20371	0.30523	0.24848	0.44188	0.10185	0.10132	0.098425

Table 2. Table 2 Theoretical flux ratios for our MAPPINGS v5.1 Density Models

log($n_e$)	log(q)	log(O/H)	[N IV]	SiIII]	C III]	[Ne IV]	[Al II]	[O II]	[Ar IV]	[N I]	[Cl III]	[S II]	[S III]	[O III]	[N II]
		+12	$\frac{\lambda 1483}{\lambda 1486}$	$\frac{\lambda 1883}{\lambda 1892}$	$\frac{\lambda 1906}{\lambda 1908}$	$\frac{\lambda 2425}{\lambda 2423}$	$\frac{\lambda 2660}{\lambda 2669}$	$\frac{\lambda 3729}{\lambda 3726}$	$\frac{\lambda 4711}{\lambda 4740}$	$\frac{\lambda 5198}{\lambda 5200}$	$\frac{\lambda 5517}{\lambda 5537}$	$\frac{\lambda 6717}{\lambda 6731}$	$\frac{\lambda 33\mu m}{\lambda 18\mu m}$	$\frac{\lambda 52\mu m}{\lambda 88\mu m}$	$\frac{\lambda 205\mu m}{\lambda 122\mu m}$
0.0	6.50	7.63	$\cdots$	1.5648	1.4863	$\cdots$	1.5355	1.4524	$\cdots$	0.69952	1.4211	1.4443	1.7721	1.5437	1.6956
0.0	6.50	8.23	$\cdots$	1.5638	1.4814	$\cdots$	1.5333	1.4528	$\cdots$	0.69787	1.4259	1.4463	1.7882	1.5701	1.7266
0.0	6.50	8.53	$\cdots$	1.5622	1.4729	$\cdots$	1.5291	1.4536	$\cdots$	0.69439	1.4338	1.4503	1.8147	1.6240	1.7837
0.0	6.50	8.93	$\cdots$	1.5514	1.4480	$\cdots$	1.5120	1.4568	$\cdots$	0.68253	1.4481	1.4631	1.8748	1.8250	1.9453
0.0	6.50	9.23	$\cdots$	$\cdots$	$\cdots$	$\cdots$	$\cdots$	1.4634	$\cdots$	0.66730	1.4394	1.4642	1.9449	2.1001	2.1523
0.0	6.75	7.63	$\cdots$	1.5654	1.4899	$\cdots$	1.5373	1.4521	$\cdots$	0.70067	1.4172	1.4426	1.7598	1.5200	1.6716
0.0	6.75	8.23	$\cdots$	1.5642	1.4837	$\cdots$	1.5346	1.4526	1.3704	0.69878	1.4235	1.4451	1.7806	1.5510	1.7097
0.0	6.75	8.53	$\cdots$	1.5624	1.4739	$\cdots$	1.5297	1.4534	1.3841	0.69512	1.4328	1.4495	1.8119	1.6110	1.7760
0.0	6.75	8.93	$\cdots$	1.5518	1.4486	$\cdots$	1.5126	1.4566	$\cdots$	0.68297	1.4479	1.4626	1.8733	1.8108	1.9406
0.0	6.75	9.23	$\cdots$	$\cdots$	$\cdots$	$\cdots$	$\cdots$	1.4632	$\cdots$	0.66736	1.4397	1.4644	1.9426	2.0723	2.1402
0.0	7.00	7.63	$\cdots$	1.5662	1.4936	$\cdots$	1.5390	1.4518	1.3553	0.70159	1.4130	1.4408	1.7471	1.4992	1.6471
0.0	7.00	8.23	$\cdots$	1.5645	1.4857	$\cdots$	1.5355	1.4524	1.3677	0.69952	1.4213	1.4439	1.7743	1.5358	1.6951
0.0	7.00	8.53	$\cdots$	1.5624	1.4743	$\cdots$	1.5302	1.4533	1.3838	0.69569	1.4323	1.4489	1.8109	1.6027	1.7716
0.0	7.00	8.93	$\cdots$	1.5519	1.4487	$\cdots$	1.5130	1.4564	$\cdots$	0.68331	1.4478	1.4624	1.8729	1.8026	1.9387
0.0	7.00	9.23	$\cdots$	$\cdots$	$\cdots$	$\cdots$	$\cdots$	1.4632	$\cdots$	0.66744	1.4395	1.4644	1.9425	2.0576	2.1378
0.0	7.25	7.63	$\cdots$	1.5670	1.4974	$\cdots$	1.5408	1.4516	1.3494	0.70220	1.4086	1.4391	1.7344	1.4825	1.6224
0.0	7.25	8.23	1.4825	1.5648	1.4871	$\cdots$	1.5364	1.4522	1.3659	0.70009	1.4197	1.4430	1.7701	1.5251	1.6837
0.0	7.25	8.53	$\cdots$	1.5624	1.4742	$\cdots$	1.5303	1.4533	1.3845	0.69623	1.4324	1.4486	1.8122	1.5990	1.7720
0.0	7.25	8.93	$\cdots$	1.5512	1.4481	$\cdots$	1.5128	1.4564	1.4035	0.68354	1.4480	1.4622	1.8746	1.8007	1.9412
0.0	7.25	9.23	$\cdots$	$\cdots$	$\cdots$	$\cdots$	$\cdots$	1.4635	$\cdots$	0.66761	1.4387	1.4642	1.9455	2.0526	2.1425
0.0	7.50	7.63	1.4876	1.5679	1.5014	$\cdots$	1.5425	1.4513	1.3431	0.70258	1.4042	1.4374	1.7219	1.4696	1.5978
0.0	7.50	8.23	1.4826	1.5649	1.4879	$\cdots$	1.5369	1.4521	1.3651	0.70052	1.4186	1.4423	1.7679	1.5179	1.6762
0.0	7.50	8.53	$\cdots$	1.5621	1.4735	$\cdots$	1.5301	1.4533	1.3862	0.69671	1.4330	1.4485	1.8157	1.5984	1.7772
0.0	7.50	8.93	$\cdots$	1.5499	1.4468	$\cdots$	1.5122	1.4565	1.4039	0.68368	1.4482	1.4623	1.8790	1.8045	1.9494
0.0	7.50	9.23	$\cdots$	$\cdots$	$\cdots$	$\cdots$	$\cdots$	1.4639	$\cdots$	0.66824	1.4370	1.4641	1.9535	2.0554	2.1554
0.0	7.75	7.63	1.4887	1.5691	1.5055	1.4783	1.5441	1.4511	1.3368	0.70281	1.3996	1.4358	1.7092	1.4594	1.5734
0.0	7.75	8.23	1.4828	1.5650	1.4886	$\cdots$	1.5373	1.4521	1.3647	0.70088	1.4178	1.4417	1.7665	1.5121	1.6709
0.0	7.75	8.53	1.4758	1.5620	1.4728	$\cdots$	1.5300	1.4533	1.3879	0.69726	1.4338	1.4483	1.8194	1.5978	1.7846
0.0	7.75	8.93	$\cdots$	1.5486	1.4460	$\cdots$	1.5120	1.4566	1.4040	0.68389	1.4484	1.4624	1.8849	1.8104	1.9625
0.0	7.75	9.23	$\cdots$	$\cdots$	$\cdots$	$\cdots$	$\cdots$	1.4636	$\cdots$	0.66923	1.4360	1.4643	1.9694	2.0618	2.1772
0.0	8.00	7.63	1.4900	1.5703	1.5096	1.4751	1.5456	1.4509	1.3304	0.70300	1.3950	1.4343	1.6962	1.4512	1.5497
0.0	8.00	8.23	1.4828	1.5651	1.4892	1.4919	1.5378	1.4519	1.3642	0.70119	1.4171	1.4411	1.7648	1.5064	1.6661
0.0	8.00	8.53	1.4753	1.5618	1.4724	$\cdots$	1.5301	1.4531	1.3892	0.69787	1.4344	1.4481	1.8217	1.5951	1.7906
0.0	8.00	8.93	$\cdots$	1.5481	1.4462	$\cdots$	1.5124	1.4565	1.4036	0.68418	1.4484	1.4622	1.8907	1.8143	1.9768
0.0	8.00	9.23	$\cdots$	$\cdots$	$\cdots$	$\cdots$	$\cdots$	1.4629	$\cdots$	0.67017	1.4372	1.4648	1.9920	2.0658	2.2059
0.0	8.25	7.63	1.4911	1.5716	1.5137	1.4722	1.5469	1.4506	1.3245	0.70314	1.3907	1.4329	1.6829	1.4449	1.5274
0.0	8.25	8.23	1.4830	1.5652	1.4900	1.4918	1.5383	1.4519	1.3636	0.70156	1.4161	1.4405	1.7626	1.5007	1.6609
0.0	8.25	8.53	1.4751	1.5618	1.4723	$\cdots$	1.5306	1.4531	1.3896	0.69847	1.4345	1.4477	1.8226	1.5898	1.7935
0.0	8.25	8.93	$\cdots$	1.5486	1.4472	$\cdots$	1.5133	1.4564	1.4029	0.68454	1.4483	1.4618	1.8950	1.8134	1.9887
0.0	8.25	9.23	$\cdots$	$\cdots$	$\cdots$	$\cdots$	$\cdots$	1.4622	$\cdots$	0.67096	1.4393	1.4654	2.0186	2.0634	2.2375
0.0	8.50	7.63	1.4921	1.5723	1.5175	1.4695	1.5480	1.4505	1.3190	0.70328	1.3869	1.4319	1.6699	1.4406	1.5073
0.0	8.50	8.23	1.4833	1.5655	1.4909	1.4915	1.5391	1.4518	1.3628	0.70188	1.4149	1.4398	1.7600	1.4949	1.6548
0.0	8.50	8.53	1.4752	1.5619	1.4726	$\cdots$	1.5314	1.4530	1.3897	0.69911	1.4342	1.4470	1.8222	1.5819	1.7927
0.0	8.50	8.93	$\cdots$	1.5494	1.4486	$\cdots$	1.5145	1.4562	1.4024	0.68518	1.4480	1.4613	1.8972	1.8073	1.9957
0.0	8.50	9.23	$\cdots$	$\cdots$	$\cdots$	$\cdots$	$\cdots$	1.4616	$\cdots$	0.67154	1.4415	1.4658	2.0450	2.0532	2.2697
0.50	6.50	7.63	$\cdots$	1.5646	1.4862	$\cdots$	1.5352	1.4492	$\cdots$	0.69917	1.4204	1.4417	1.7557	1.4005	1.6909
0.50	6.50	8.23	$\cdots$	1.5636	1.4813	$\cdots$	1.5330	1.4495	$\cdots$	0.69747	1.4252	1.4435	1.7710	1.4178	1.7216
0.50	6.50	8.53	$\cdots$	1.5621	1.4729	$\cdots$	1.5287	1.4501	$\cdots$	0.69403	1.4329	1.4472	1.7962	1.4546	1.7777
0.50	6.50	8.93	$\cdots$	1.5517	1.4486	$\cdots$	1.5121	1.4523	$\cdots$	0.68235	1.4470	1.4589	1.8514	1.5854	1.9344
0.50	6.50	9.23	$\cdots$	$\cdots$	$\cdots$	$\cdots$	$\cdots$	1.4556	$\cdots$	0.66796	1.4405	1.4597	1.9079	1.7284	2.1184
0.50	6.75	7.63	$\cdots$	1.5652	1.4899	$\cdots$	1.5369	1.4488	$\cdots$	0.70024	1.4164	1.4398	1.7434	1.3765	1.6669
0.50	6.75	8.23	$\cdots$	1.5641	1.4837	$\cdots$	1.5342	1.4491	1.3701	0.69837	1.4227	1.4421	1.7633	1.3970	1.7046
0.50	6.75	8.53	$\cdots$	1.5622	1.4739	$\cdots$	1.5294	1.4497	1.3837	0.69474	1.4320	1.4464	1.7929	1.4374	1.7697
0.50	6.75	8.93	$\cdots$	1.5520	1.4490	$\cdots$	1.5127	1.4518	$\cdots$	0.68280	1.4468	1.4584	1.8492	1.5645	1.9296
0.50	6.75	9.23	$\cdots$	$\cdots$	$\cdots$	$\cdots$	$\cdots$	1.4553	$\cdots$	0.66803	1.4406	1.4597	1.9049	1.6945	2.1088
0.50	7.00	7.63	$\cdots$	1.5660	1.4936	$\cdots$	1.5387	1.4485	1.3550	0.70112	1.4123	1.4380	1.7308	1.3574	1.6424
0.50	7.00	8.23	$\cdots$	1.5644	1.4856	$\cdots$	1.5352	1.4489	1.3673	0.69910	1.4205	1.4410	1.7569	1.3817	1.6898
0.50	7.00	8.53	$\cdots$	1.5623	1.4744	$\cdots$	1.5299	1.4496	1.3833	0.69530	1.4314	1.4457	1.7916	1.4263	1.7653
0.50	7.00	8.93	$\cdots$	1.5521	1.4491	$\cdots$	1.5129	1.4516	$\cdots$	0.68310	1.4468	1.4580	1.8486	1.5512	1.9278
0.50	7.00	9.23	$\cdots$	$\cdots$	$\cdots$	$\cdots$	$\cdots$	1.4551	$\cdots$	0.66811	1.4403	1.4595	1.9043	1.6727	2.1075
0.50	7.25	7.63	$\cdots$	1.5669	1.4974	$\cdots$	1.5405	1.4483	1.3490	0.70179	1.4080	1.4363	1.7184	1.3433	1.6179
0.50	7.25	8.23	1.4824	1.5646	1.4870	$\cdots$	1.5360	1.4488	1.3655	0.69966	1.4189	1.4401	1.7527	1.3717	1.6785
0.50	7.25	8.53	$\cdots$	1.5622	1.4742	$\cdots$	1.5300	1.4494	1.3840	0.69584	1.4315	1.4453	1.7928	1.4207	1.7655
0.50	7.25	8.93	$\cdots$	1.5514	1.4484	$\cdots$	1.5127	1.4515	1.4029	0.68328	1.4468	1.4578	1.8498	1.5445	1.9304
0.50	7.25	9.23	$\cdots$	$\cdots$	$\cdots$	$\cdots$	$\cdots$	1.4552	$\cdots$	0.66825	1.4394	1.4593	1.9064	1.6600	2.1125
0.50	7.50	7.63	1.4876	1.5678	1.5013	$\cdots$	1.5421	1.4481	1.3428	0.70217	1.4034	1.4346	1.7064	1.3334	1.5934
0.50	7.50	8.23	1.4826	1.5648	1.4878	$\cdots$	1.5366	1.4486	1.3647	0.70009	1.4178	1.4393	1.7506	1.3656	1.6710
0.50	7.50	8.53	$\cdots$	1.5621	1.4735	$\cdots$	1.5298	1.4494	1.3857	0.69631	1.4321	1.4452	1.7960	1.4185	1.7708
0.50	7.50	8.93	$\cdots$	1.5501	1.4472	$\cdots$	1.5122	1.4515	1.4033	0.68343	1.4471	1.4578	1.8536	1.5433	1.9387
0.50	7.50	9.23	$\cdots$	$\cdots$	$\cdots$	$\cdots$	$\cdots$	1.4557	$\cdots$	0.66882	1.4378	1.4592	1.9133	1.6540	2.1256
0.50	7.75	7.63	1.4888	1.5689	1.5054	1.4782	1.5438	1.4479	1.3364	0.70240	1.3989	1.4330	1.6940	1.3263	1.5691
0.50	7.75	8.23	1.4827	1.5649	1.4885	$\cdots$	1.5370	1.4486	1.3643	0.70049	1.4170	1.4387	1.7492	1.3615	1.6657
0.50	7.75	8.53	1.4758	1.5618	1.4728	$\cdots$	1.5296	1.4493	1.3874	0.69688	1.4329	1.4449	1.7993	1.4174	1.7780
0.50	7.75	8.93	$\cdots$	1.5487	1.4463	$\cdots$	1.5120	1.4515	1.4035	0.68360	1.4473	1.4578	1.8589	1.5445	1.9517
0.50	7.75	9.23	$\cdots$	$\cdots$	$\cdots$	$\cdots$	$\cdots$	1.4558	$\cdots$	0.66980	1.4369	1.4594	1.9269	1.6516	2.1472
0.50	8.00	7.63	1.4900	1.5702	1.5095	1.4751	1.5453	1.4477	1.3301	0.70256	1.3944	1.4316	1.6814	1.3212	1.5456
0.50	8.00	8.23	1.4828	1.5650	1.4891	1.4918	1.5374	1.4486	1.3639	0.70082	1.4162	1.4381	1.7474	1.3580	1.6610
0.50	8.00	8.53	1.4753	1.5617	1.4723	$\cdots$	1.5297	1.4493	1.3886	0.69746	1.4334	1.4448	1.8015	1.4154	1.7839
0.50	8.00	8.93	$\cdots$	1.5483	1.4465	$\cdots$	1.5123	1.4514	1.4031	0.68385	1.4473	1.4576	1.8640	1.5452	1.9660
0.50	8.00	9.23	$\cdots$	$\cdots$	$\cdots$	$\cdots$	$\cdots$	1.4555	$\cdots$	0.67072	1.4379	1.4599	1.9468	1.6496	2.1759
0.50	8.25	7.63	1.4910	1.5715	1.5136	1.4721	1.5466	1.4476	1.3242	0.70274	1.3900	1.4302	1.6685	1.3176	1.5235
0.50	8.25	8.23	1.4830	1.5652	1.4899	1.4917	1.5380	1.4485	1.3632	0.70116	1.4153	1.4375	1.7454	1.3549	1.6558
0.50	8.25	8.53	1.4751	1.5616	1.4723	$\cdots$	1.5302	1.4493	1.3892	0.69807	1.4336	1.4444	1.8023	1.4123	1.7868
0.50	8.25	8.93	$\cdots$	1.5487	1.4475	$\cdots$	1.5132	1.4514	1.4025	0.68428	1.4472	1.4572	1.8677	1.5437	1.9778
0.50	8.25	9.23	$\cdots$	$\cdots$	$\cdots$	$\cdots$	$\cdots$	1.4550	$\cdots$	0.67143	1.4398	1.4604	1.9704	1.6463	2.2083
0.50	8.50	7.63	1.4921	1.5722	1.5174	1.4694	1.5476	1.4475	1.3187	0.70287	1.3862	1.4292	1.6558	1.3157	1.5036
0.50	8.50	8.23	1.4832	1.5654	1.4908	1.4914	1.5387	1.4484	1.3624	0.70148	1.4141	1.4369	1.7429	1.3522	1.6497
0.50	8.50	8.53	1.4751	1.5617	1.4726	$\cdots$	1.5310	1.4492	1.3891	0.69872	1.4333	1.4438	1.8019	1.4079	1.7861
0.50	8.50	8.93	$\cdots$	1.5494	1.4488	$\cdots$	1.5144	1.4512	1.4020	0.68488	1.4470	1.4567	1.8695	1.5395	1.9847
0.50	8.50	9.23	$\cdots$	$\cdots$	$\cdots$	$\cdots$	$\cdots$	1.4544	$\cdots$	0.67202	1.4418	1.4606	1.9943	1.6412	2.2419
1.0	6.50	7.63	$\cdots$	1.5642	1.4860	$\cdots$	1.5342	1.4392	$\cdots$	0.69796	1.4181	1.4334	1.7059	1.0922	1.6762
1.0	6.50	8.23	$\cdots$	1.5633	1.4811	$\cdots$	1.5320	1.4390	$\cdots$	0.69625	1.4228	1.4348	1.7191	1.0948	1.7057
1.0	6.50	8.53	$\cdots$	1.5616	1.4728	$\cdots$	1.5278	1.4390	$\cdots$	0.69285	1.4303	1.4378	1.7403	1.1046	1.7594
1.0	6.50	8.93	$\cdots$	1.5520	1.4494	$\cdots$	1.5118	1.4384	$\cdots$	0.68156	1.4439	1.4467	1.7832	1.1386	1.9049
1.0	6.50	9.23	$\cdots$	$\cdots$	$\cdots$	$\cdots$	$\cdots$	1.4354	$\cdots$	0.66893	1.4402	1.4447	1.8148	1.1504	2.0539
1.0	6.75	7.63	$\cdots$	1.5648	1.4896	$\cdots$	1.5359	1.4387	$\cdots$	0.69900	1.4141	1.4312	1.6935	1.0691	1.6521
1.0	6.75	8.23	$\cdots$	1.5636	1.4834	$\cdots$	1.5332	1.4385	1.3688	0.69710	1.4203	1.4331	1.7107	1.0728	1.6885
1.0	6.75	8.53	$\cdots$	1.5618	1.4737	$\cdots$	1.5283	1.4383	1.3821	0.69346	1.4293	1.4365	1.7358	1.0830	1.7509
1.0	6.75	8.93	$\cdots$	1.5522	1.4499	$\cdots$	1.5124	1.4375	$\cdots$	0.68191	1.4435	1.4455	1.7790	1.1121	1.8995
1.0	6.75	9.23	$\cdots$	$\cdots$	$\cdots$	$\cdots$	$\cdots$	1.4344	$\cdots$	0.66904	1.4400	1.4440	1.8090	1.1160	2.0468
1.0	7.00	7.63	$\cdots$	1.5656	1.4933	$\cdots$	1.5376	1.4383	1.3539	0.69987	1.4100	1.4293	1.6816	1.0535	1.6279
1.0	7.00	8.23	$\cdots$	1.5640	1.4854	$\cdots$	1.5342	1.4381	1.3661	0.69780	1.4181	1.4317	1.7044	1.0582	1.6737
1.0	7.00	8.53	$\cdots$	1.5618	1.4742	$\cdots$	1.5287	1.4379	1.3818	0.69405	1.4287	1.4356	1.7337	1.0689	1.7460
1.0	7.00	8.93	$\cdots$	1.5521	1.4498	$\cdots$	1.5125	1.4368	$\cdots$	0.68212	1.4434	1.4447	1.7769	1.0941	1.8977
1.0	7.00	9.23	$\cdots$	$\cdots$	$\cdots$	$\cdots$	$\cdots$	1.4336	$\cdots$	0.66914	1.4395	1.4435	1.8059	1.0917	2.0460
1.0	7.25	7.63	$\cdots$	1.5665	1.4971	$\cdots$	1.5394	1.4381	1.3479	0.70047	1.4056	1.4275	1.6700	1.0441	1.6037
1.0	7.25	8.23	1.4822	1.5643	1.4867	$\cdots$	1.5350	1.4380	1.3643	0.69836	1.4164	1.4306	1.7001	1.0498	1.6624
1.0	7.25	8.53	$\cdots$	1.5617	1.4740	$\cdots$	1.5288	1.4376	1.3825	0.69455	1.4287	1.4350	1.7340	1.0609	1.7460
1.0	7.25	8.93	$\cdots$	1.5515	1.4491	$\cdots$	1.5122	1.4364	1.4011	0.68229	1.4435	1.4442	1.7770	1.0829	1.9001
1.0	7.25	9.23	$\cdots$	$\cdots$	$\cdots$	$\cdots$	$\cdots$	1.4333	$\cdots$	0.66926	1.4385	1.4431	1.8055	1.0751	2.0505
1.0	7.50	7.63	1.4874	1.5675	1.5010	$\cdots$	1.5411	1.4381	1.3417	0.70088	1.4012	1.4259	1.6590	1.0393	1.5796
1.0	7.50	8.23	1.4824	1.5643	1.4876	$\cdots$	1.5355	1.4379	1.3634	0.69882	1.4153	1.4299	1.6979	1.0458	1.6548
1.0	7.50	8.53	$\cdots$	1.5616	1.4734	$\cdots$	1.5287	1.4375	1.3842	0.69505	1.4293	1.4347	1.7364	1.0569	1.7509
1.0	7.50	8.93	$\cdots$	1.5502	1.4478	$\cdots$	1.5116	1.4361	1.4016	0.68239	1.4437	1.4440	1.7790	1.0763	1.9080
1.0	7.50	9.23	$\cdots$	$\cdots$	$\cdots$	$\cdots$	$\cdots$	1.4335	$\cdots$	0.66975	1.4371	1.4431	1.8082	1.0636	2.0623
1.0	7.75	7.63	1.4886	1.5686	1.5052	1.4780	1.5428	1.4380	1.3353	0.70115	1.3965	1.4243	1.6478	1.0374	1.5559
1.0	7.75	8.23	1.4826	1.5645	1.4882	$\cdots$	1.5359	1.4378	1.3630	0.69920	1.4145	1.4293	1.6964	1.0443	1.6496
1.0	7.75	8.53	1.4756	1.5613	1.4726	$\cdots$	1.5285	1.4373	1.3860	0.69562	1.4301	1.4347	1.7389	1.0551	1.7578
1.0	7.75	8.93	$\cdots$	1.5488	1.4469	$\cdots$	1.5113	1.4360	1.4017	0.68256	1.4439	1.4438	1.7821	1.0723	1.9205
1.0	7.75	9.23	$\cdots$	$\cdots$	$\cdots$	$\cdots$	$\cdots$	1.4342	$\cdots$	0.67057	1.4365	1.4434	1.8152	1.0552	2.0825
1.0	8.00	7.63	1.4899	1.5698	1.5092	1.4748	1.5442	1.4380	1.3291	0.70128	1.3921	1.4229	1.6364	1.0372	1.5329
1.0	8.00	8.23	1.4827	1.5645	1.4889	1.4916	1.5363	1.4378	1.3626	0.69955	1.4137	1.4288	1.6950	1.0444	1.6449
1.0	8.00	8.53	1.4752	1.5612	1.4722	$\cdots$	1.5286	1.4374	1.3872	0.69624	1.4306	1.4344	1.7407	1.0544	1.7634
1.0	8.00	8.93	$\cdots$	1.5484	1.4470	$\cdots$	1.5116	1.4360	1.4014	0.68277	1.4439	1.4436	1.7851	1.0697	1.9341
1.0	8.00	9.23	$\cdots$	$\cdots$	$\cdots$	$\cdots$	$\cdots$	1.4346	$\cdots$	0.67134	1.4372	1.4439	1.8266	1.0491	2.1097
1.0	8.25	7.63	1.4909	1.5711	1.5133	1.4719	1.5456	1.4379	1.3232	0.70150	1.3879	1.4218	1.6246	1.0381	1.5113
1.0	8.25	8.23	1.4829	1.5647	1.4897	1.4914	1.5369	1.4379	1.3619	0.69993	1.4128	1.4283	1.6930	1.0455	1.6398
1.0	8.25	8.53	1.4751	1.5612	1.4721	$\cdots$	1.5291	1.4374	1.3877	0.69689	1.4308	1.4342	1.7412	1.0546	1.7661
1.0	8.25	8.93	$\cdots$	1.5487	1.4478	$\cdots$	1.5124	1.4359	1.4008	0.68313	1.4438	1.4433	1.7871	1.0676	1.9454
1.0	8.25	9.23	$\cdots$	$\cdots$	$\cdots$	$\cdots$	$\cdots$	1.4346	$\cdots$	0.67199	1.4387	1.4444	1.8413	1.0455	2.1413
1.0	8.50	7.63	1.4920	1.5718	1.5172	1.4692	1.5467	1.4380	1.3178	0.70163	1.3840	1.4208	1.6132	1.0399	1.4918
1.0	8.50	8.23	1.4831	1.5649	1.4906	1.4912	1.5376	1.4380	1.3611	0.70024	1.4116	1.4278	1.6908	1.0474	1.6339
1.0	8.50	8.53	1.4750	1.5612	1.4724	$\cdots$	1.5299	1.4375	1.3877	0.69749	1.4305	1.4338	1.7408	1.0554	1.7654
1.0	8.50	8.93	$\cdots$	1.5492	1.4491	$\cdots$	1.5135	1.4360	1.4003	0.68370	1.4436	1.4429	1.7881	1.0658	1.9522
1.0	8.50	9.23	$\cdots$	$\cdots$	$\cdots$	$\cdots$	$\cdots$	1.4344	$\cdots$	0.67253	1.4401	1.4447	1.8568	1.0439	2.1751
1.5	6.50	7.63	$\cdots$	1.5629	1.4852	$\cdots$	1.5311	1.4086	$\cdots$	0.69427	1.4110	1.4081	1.5664	0.67306	1.6316
1.5	6.50	8.23	$\cdots$	1.5619	1.4803	$\cdots$	1.5288	1.4075	$\cdots$	0.69247	1.4154	1.4083	1.5743	0.66606	1.6580
1.5	6.50	8.53	$\cdots$	1.5602	1.4722	$\cdots$	1.5247	1.4056	$\cdots$	0.68907	1.4225	1.4093	1.5864	0.65867	1.7056
1.5	6.50	8.93	$\cdots$	1.5512	1.4500	$\cdots$	1.5093	1.3981	$\cdots$	0.67826	1.4347	1.4110	1.6031	0.64102	1.8294
1.5	6.50	9.23	$\cdots$	$\cdots$	$\cdots$	$\cdots$	1.4837	1.3834	$\cdots$	0.66801	1.4325	1.4013	1.5986	0.61336	1.9395
1.5	6.75	7.63	$\cdots$	1.5636	1.4887	$\cdots$	1.5327	1.4075	$\cdots$	0.69507	1.4069	1.4051	1.5539	0.65455	1.6073
1.5	6.75	8.23	$\cdots$	1.5622	1.4826	$\cdots$	1.5298	1.4061	1.3650	0.69311	1.4127	1.4056	1.5646	0.64747	1.6401
1.5	6.75	8.53	$\cdots$	1.5603	1.4731	$\cdots$	1.5251	1.4038	1.3779	0.68957	1.4211	1.4068	1.5788	0.63918	1.6955
1.5	6.75	8.93	$\cdots$	1.5513	1.4503	$\cdots$	1.5096	1.3957	$\cdots$	0.67838	1.4340	1.4083	1.5941	0.61915	1.8218
1.5	6.75	9.23	$\cdots$	$\cdots$	1.4249	$\cdots$	1.4833	1.3804	$\cdots$	0.66808	1.4316	1.3988	1.5857	0.58959	1.9312
1.5	7.00	7.63	$\cdots$	1.5643	1.4925	$\cdots$	1.5344	1.4071	1.3504	0.69581	1.4027	1.4027	1.5436	0.64387	1.5837
1.5	7.00	8.23	$\cdots$	1.5625	1.4846	$\cdots$	1.5308	1.4054	1.3623	0.69375	1.4104	1.4037	1.5579	0.63616	1.6250
1.5	7.00	8.53	$\cdots$	1.5604	1.4736	$\cdots$	1.5254	1.4026	1.3774	0.68998	1.4203	1.4051	1.5747	0.62653	1.6895
1.5	7.00	8.93	$\cdots$	1.5511	1.4502	$\cdots$	1.5095	1.3937	$\cdots$	0.67847	1.4336	1.4064	1.5887	0.60402	1.8182
1.5	7.00	9.23	$\cdots$	$\cdots$	1.4238	$\cdots$	1.4824	1.3780	$\cdots$	0.66812	1.4308	1.3970	1.5768	0.57256	1.9283
1.5	7.25	7.63	$\cdots$	1.5651	1.4963	$\cdots$	1.5361	1.4072	1.3445	0.69642	1.3983	1.4007	1.5344	0.63909	1.5605
1.5	7.25	8.23	1.4818	1.5628	1.4860	$\cdots$	1.5316	1.4051	1.3605	0.69429	1.4086	1.4023	1.5538	0.63038	1.6137
1.5	7.25	8.53	$\cdots$	1.5603	1.4734	$\cdots$	1.5253	1.4019	1.3781	0.69050	1.4203	1.4040	1.5730	0.61904	1.6884
1.5	7.25	8.93	$\cdots$	1.5504	1.4493	$\cdots$	1.5090	1.3923	1.3958	0.67839	1.4335	1.4050	1.5854	0.59392	1.8193
1.5	7.25	9.23	$\cdots$	$\cdots$	$\cdots$	$\cdots$	1.4813	1.3763	$\cdots$	0.66827	1.4298	1.3961	1.5704	0.56071	1.9302
1.5	7.50	7.63	1.4871	1.5662	1.5003	$\cdots$	1.5378	1.4075	1.3384	0.69686	1.3939	1.3991	1.5260	0.63829	1.5378
1.5	7.50	8.23	1.4820	1.5630	1.4868	$\cdots$	1.5320	1.4051	1.3596	0.69480	1.4075	1.4014	1.5516	0.62837	1.6062
1.5	7.50	8.53	1.4758	1.5601	1.4727	$\cdots$	1.5251	1.4013	1.3797	0.69105	1.4207	1.4034	1.5732	0.61510	1.6920
1.5	7.50	8.93	$\cdots$	1.5492	1.4480	$\cdots$	1.5084	1.3912	1.3962	0.67841	1.4336	1.4041	1.5833	0.58719	1.8254
1.5	7.50	9.23	$\cdots$	$\cdots$	$\cdots$	$\cdots$	1.4809	1.3760	$\cdots$	0.66865	1.4286	1.3959	1.5645	0.55221	1.9376
1.5	7.75	7.63	1.4883	1.5673	1.5044	1.4772	1.5394	1.4079	1.3320	0.69717	1.3894	1.3978	1.5178	0.63987	1.5156
1.5	7.75	8.23	1.4822	1.5631	1.4874	$\cdots$	1.5324	1.4051	1.3592	0.69525	1.4066	1.4009	1.5501	0.62884	1.6009
1.5	7.75	8.53	1.4751	1.5599	1.4720	$\cdots$	1.5249	1.4012	1.3813	0.69167	1.4214	1.4032	1.5738	0.61360	1.6977
1.5	7.75	8.93	$\cdots$	1.5479	1.4470	$\cdots$	1.5080	1.3906	1.3964	0.67845	1.4337	1.4035	1.5814	0.58266	1.8354
1.5	7.75	9.23	$\cdots$	$\cdots$	$\cdots$	$\cdots$	1.4824	1.3774	$\cdots$	0.66925	1.4278	1.3966	1.5582	0.54593	1.9517
1.5	8.00	7.63	1.4895	1.5685	1.5085	1.4741	1.5410	1.4083	1.3259	0.69741	1.3851	1.3967	1.5094	0.64280	1.4941
1.5	8.00	8.23	1.4823	1.5632	1.4882	1.4907	1.5329	1.4054	1.3587	0.69566	1.4059	1.4006	1.5489	0.63106	1.5963
1.5	8.00	8.53	1.4747	1.5597	1.4715	$\cdots$	1.5250	1.4012	1.3825	0.69238	1.4218	1.4032	1.5742	0.61395	1.7023
1.5	8.00	8.93	$\cdots$	1.5473	1.4469	$\cdots$	1.5082	1.3905	1.3960	0.67862	1.4336	1.4030	1.5796	0.57978	1.8461
1.5	8.00	9.23	$\cdots$	$\cdots$	$\cdots$	$\cdots$	1.4842	1.3789	$\cdots$	0.66979	1.4284	1.3977	1.5526	0.54173	1.9721
1.5	8.25	7.63	1.4906	1.5699	1.5126	1.4712	1.5424	1.4087	1.3201	0.69763	1.3810	1.3957	1.5008	0.64641	1.4740
1.5	8.25	8.23	1.4825	1.5634	1.4890	1.4906	1.5334	1.4058	1.3581	0.69608	1.4050	1.4003	1.5474	0.63447	1.5914
1.5	8.25	8.53	1.4746	1.5596	1.4714	$\cdots$	1.5254	1.4016	1.3830	0.69306	1.4220	1.4033	1.5742	0.61595	1.7045
1.5	8.25	8.93	$\cdots$	1.5474	1.4476	$\cdots$	1.5089	1.3908	1.3955	0.67894	1.4334	1.4028	1.5780	0.57819	1.8552
1.5	8.25	9.23	$\cdots$	$\cdots$	$\cdots$	$\cdots$	1.4858	1.3798	$\cdots$	0.67021	1.4297	1.3988	1.5487	0.53976	1.9968
1.5	8.50	7.63	1.4916	1.5707	1.5164	1.4685	1.5435	1.4092	1.3148	0.69777	1.3772	1.3951	1.4923	0.65020	1.4558
1.5	8.50	8.23	1.4827	1.5635	1.4898	1.4904	1.5342	1.4063	1.3572	0.69642	1.4038	1.4002	1.5458	0.63868	1.5859
1.5	8.50	8.53	1.4747	1.5597	1.4717	$\cdots$	1.5263	1.4022	1.3830	0.69367	1.4217	1.4034	1.5738	0.61937	1.7037
1.5	8.50	8.93	$\cdots$	1.5477	1.4486	$\cdots$	1.5099	1.3912	1.3951	0.67942	1.4332	1.4026	1.5770	0.57768	1.8603
1.5	8.50	9.23	$\cdots$	$\cdots$	$\cdots$	$\cdots$	1.4875	1.3804	$\cdots$	0.67056	1.4308	1.3996	1.5473	0.53966	2.0233
2.0	6.50	7.63	$\cdots$	1.5586	1.4827	$\cdots$	1.5213	1.3227	$\cdots$	0.68332	1.3891	1.3367	1.2502	0.35357	1.5059
2.0	6.50	8.23	$\cdots$	1.5575	1.4779	$\cdots$	1.5189	1.3190	$\cdots$	0.68125	1.3929	1.3337	1.2493	0.34703	1.5247
2.0	6.50	8.53	$\cdots$	1.5556	1.4698	$\cdots$	1.5144	1.3129	$\cdots$	0.67766	1.3987	1.3297	1.2471	0.33918	1.5590
2.0	6.50	8.93	$\cdots$	1.5466	1.4486	$\cdots$	1.4987	1.2904	$\cdots$	0.66695	1.4078	1.3161	1.2278	0.32167	1.6429
2.0	6.50	9.23	$\cdots$	$\cdots$	1.4265	$\cdots$	1.4748	1.2560	$\cdots$	0.65905	1.4035	1.2907	1.1877	0.30465	1.7048
2.0	6.75	7.63	$\cdots$	1.5593	1.4861	$\cdots$	1.5225	1.3203	$\cdots$	0.68352	1.3845	1.3313	1.2384	0.34171	1.4813
2.0	6.75	8.23	$\cdots$	1.5579	1.4801	$\cdots$	1.5195	1.3158	1.3533	0.68135	1.3894	1.3284	1.2380	0.33524	1.5051
2.0	6.75	8.53	$\cdots$	1.5557	1.4707	$\cdots$	1.5144	1.3084	1.3649	0.67770	1.3965	1.3242	1.2354	0.32706	1.5449
2.0	6.75	8.93	$\cdots$	1.5465	1.4487	$\cdots$	1.4982	1.2843	$\cdots$	0.66650	1.4059	1.3098	1.2126	0.30940	1.6289
2.0	6.75	9.23	$\cdots$	$\cdots$	1.4259	$\cdots$	1.4739	1.2487	$\cdots$	0.65879	1.4013	1.2843	1.1670	0.29280	1.6884
2.0	7.00	7.63	$\cdots$	1.5602	1.4898	$\cdots$	1.5239	1.3198	1.3395	0.68393	1.3801	1.3276	1.2310	0.33507	1.4592
2.0	7.00	8.23	$\cdots$	1.5582	1.4820	$\cdots$	1.5202	1.3143	1.3506	0.68172	1.3867	1.3250	1.2314	0.32817	1.4896
2.0	7.00	8.53	$\cdots$	1.5556	1.4711	$\cdots$	1.5143	1.3055	1.3644	0.67791	1.3952	1.3206	1.2283	0.31922	1.5360
2.0	7.00	8.93	$\cdots$	1.5462	1.4485	$\cdots$	1.4977	1.2796	$\cdots$	0.66610	1.4048	1.3051	1.2027	0.30087	1.6205
2.0	7.00	9.23	$\cdots$	$\cdots$	1.4249	$\cdots$	1.4727	1.2429	$\cdots$	0.65868	1.3994	1.2798	1.1523	0.28442	1.6788
2.0	7.25	7.63	$\cdots$	1.5611	1.4936	$\cdots$	1.5256	1.3204	1.3338	0.68445	1.3759	1.3253	1.2263	0.33242	1.4389
2.0	7.25	8.23	1.4804	1.5584	1.4834	$\cdots$	1.5208	1.3136	1.3487	0.68223	1.3848	1.3229	1.2278	0.32472	1.4784
2.0	7.25	8.53	$\cdots$	1.5555	1.4709	$\cdots$	1.5140	1.3035	1.3648	0.67837	1.3946	1.3182	1.2240	0.31463	1.5322
2.0	7.25	8.93	$\cdots$	1.5455	1.4476	$\cdots$	1.4970	1.2760	1.3798	0.66569	1.4040	1.3015	1.1954	0.29518	1.6170
2.0	7.25	9.23	$\cdots$	$\cdots$	1.4232	$\cdots$	1.4716	1.2385	$\cdots$	0.65883	1.3979	1.2772	1.1406	0.27870	1.6744
2.0	7.50	7.63	1.4858	1.5622	1.4976	$\cdots$	1.5274	1.3215	1.3279	0.68499	1.3717	1.3237	1.2229	0.33238	1.4198
2.0	7.50	8.23	1.4806	1.5586	1.4844	$\cdots$	1.5212	1.3136	1.3477	0.68284	1.3835	1.3217	1.2257	0.32371	1.4710
2.0	7.50	8.53	1.4742	1.5553	1.4702	$\cdots$	1.5137	1.3022	1.3661	0.67902	1.3947	1.3170	1.2210	0.31229	1.5326
2.0	7.50	8.93	$\cdots$	1.5443	1.4463	$\cdots$	1.4961	1.2732	1.3800	0.66535	1.4036	1.2988	1.1883	0.29144	1.6177
2.0	7.50	9.23	$\cdots$	$\cdots$	1.4214	$\cdots$	1.4710	1.2367	$\cdots$	0.65923	1.3964	1.2763	1.1281	0.27483	1.6743
2.0	7.75	7.63	1.4871	1.5634	1.5016	1.4751	1.5292	1.3230	1.3220	0.68547	1.3675	1.3228	1.2199	0.33388	1.4015
2.0	7.75	8.23	1.4808	1.5587	1.4850	$\cdots$	1.5215	1.3139	1.3472	0.68349	1.3826	1.3213	1.2245	0.32438	1.4657
2.0	7.75	8.53	1.4737	1.5550	1.4696	$\cdots$	1.5135	1.3017	1.3674	0.67986	1.3950	1.3166	1.2188	0.31159	1.5350
2.0	7.75	8.93	$\cdots$	1.5430	1.4451	$\cdots$	1.4954	1.2715	1.3799	0.66516	1.4033	1.2971	1.1811	0.28904	1.6212
2.0	7.75	9.23	$\cdots$	$\cdots$	1.4212	$\cdots$	1.4721	1.2380	$\cdots$	0.65963	1.3954	1.2771	1.1123	0.27222	1.6777
2.0	8.00	7.63	1.4883	1.5647	1.5058	1.4719	1.5308	1.3245	1.3160	0.68582	1.3635	1.3223	1.2171	0.33617	1.3841
2.0	8.00	8.23	1.4810	1.5588	1.4857	1.4882	1.5220	1.3149	1.3467	0.68410	1.3818	1.3214	1.2237	0.32616	1.4614
2.0	8.00	8.53	1.4733	1.5548	1.4690	$\cdots$	1.5135	1.3021	1.3684	0.68074	1.3952	1.3169	1.2175	0.31218	1.5372
2.0	8.00	8.93	$\cdots$	1.5421	1.4447	$\cdots$	1.4955	1.2711	1.3795	0.66511	1.4029	1.2960	1.1746	0.28760	1.6256
2.0	8.00	9.23	$\cdots$	$\cdots$	1.4225	$\cdots$	1.4737	1.2410	$\cdots$	0.65983	1.3957	1.2791	1.0938	0.27064	1.6847
2.0	8.25	7.63	1.4895	1.5662	1.5100	1.4690	1.5323	1.3261	1.3104	0.68614	1.3598	1.3221	1.2142	0.33881	1.3679
2.0	8.25	8.23	1.4812	1.5591	1.4864	1.4880	1.5227	1.3161	1.3461	0.68462	1.3809	1.3218	1.2231	0.32873	1.4571
2.0	8.25	8.53	1.4731	1.5548	1.4690	$\cdots$	1.5140	1.3032	1.3688	0.68156	1.3952	1.3179	1.2166	0.31386	1.5380
2.0	8.25	8.93	$\cdots$	1.5418	1.4449	$\cdots$	1.4961	1.2717	1.3789	0.66525	1.4024	1.2957	1.1699	0.28691	1.6292
2.0	8.25	9.23	$\cdots$	$\cdots$	1.4241	$\cdots$	1.4753	1.2436	$\cdots$	0.65998	1.3970	1.2812	1.0763	0.27004	1.6937
2.0	8.50	7.63	1.4905	1.5671	1.5139	1.4663	1.5336	1.3276	1.3053	0.68630	1.3564	1.3222	1.2113	0.34143	1.3533
2.0	8.50	8.23	1.4814	1.5593	1.4874	1.4877	1.5235	1.3175	1.3452	0.68501	1.3798	1.3225	1.2226	0.33171	1.4527
2.0	8.50	8.53	1.4732	1.5548	1.4693	$\cdots$	1.5149	1.3048	1.3687	0.68227	1.3949	1.3193	1.2163	0.31647	1.5370
2.0	8.50	8.93	$\cdots$	1.5420	1.4456	$\cdots$	1.4971	1.2728	1.3786	0.66566	1.4021	1.2961	1.1675	0.28686	1.6309
2.0	8.50	9.23	$\cdots$	$\cdots$	1.4260	$\cdots$	1.4767	1.2455	$\cdots$	0.65997	1.3982	1.2830	1.0626	0.27016	1.7036
2.5	6.50	7.63	$\cdots$	1.5457	1.4745	$\cdots$	1.4913	1.1260	$\cdots$	0.65437	1.3249	1.1705	0.78319	0.19797	1.2165
2.5	6.50	8.23	$\cdots$	1.5441	1.4699	$\cdots$	1.4882	1.1184	$\cdots$	0.65138	1.3267	1.1618	0.77672	0.19434	1.2222
2.5	6.50	8.53	$\cdots$	1.5414	1.4620	$\cdots$	1.4830	1.1064	$\cdots$	0.64694	1.3299	1.1496	0.76643	0.18990	1.2343
2.5	6.50	8.93	$\cdots$	1.5307	1.4411	$\cdots$	1.4640	1.0654	$\cdots$	0.63509	1.3314	1.1141	0.73265	0.18093	1.2598
2.5	6.50	9.23	$\cdots$	$\cdots$	1.4202	$\cdots$	1.4373	1.0122	$\cdots$	0.62939	1.3194	1.0704	0.68934	0.17428	1.2680
2.5	6.75	7.63	$\cdots$	1.5463	1.4779	$\cdots$	1.4912	1.1214	$\cdots$	0.65324	1.3189	1.1607	0.77402	0.19111	1.1923
2.5	6.75	8.23	$\cdots$	1.5442	1.4719	$\cdots$	1.4875	1.1123	1.3180	0.65037	1.3216	1.1520	0.76685	0.18780	1.2004
2.5	6.75	8.53	$\cdots$	1.5411	1.4626	$\cdots$	1.4815	1.0981	1.3267	0.64597	1.3254	1.1393	0.75472	0.18361	1.2144
2.5	6.75	8.93	$\cdots$	1.5300	1.4409	$\cdots$	1.4619	1.0545	$\cdots$	0.63326	1.3265	1.1024	0.71793	0.17521	1.2370
2.5	6.75	9.23	$\cdots$	$\cdots$	1.4193	$\cdots$	1.4346	1.0003	$\cdots$	0.62815	1.3136	1.0592	0.67120	0.16928	1.2413
2.5	7.00	7.63	$\cdots$	1.5472	1.4815	$\cdots$	1.4921	1.1205	1.3065	0.65287	1.3140	1.1546	0.77032	0.18708	1.1739
2.5	7.00	8.23	$\cdots$	1.5445	1.4737	$\cdots$	1.4874	1.1094	1.3151	0.65014	1.3180	1.1459	0.76187	0.18378	1.1853
2.5	7.00	8.53	$\cdots$	1.5409	1.4629	$\cdots$	1.4804	1.0926	1.3256	0.64568	1.3225	1.1325	0.74768	0.17952	1.2016
2.5	7.00	8.93	$\cdots$	1.5294	1.4405	$\cdots$	1.4601	1.0464	$\cdots$	0.63169	1.3231	1.0936	0.70855	0.17124	1.2221
2.5	7.00	9.23	$\cdots$	$\cdots$	1.4184	$\cdots$	1.4323	0.99119	$\cdots$	0.62751	1.3094	1.0514	0.65903	0.16578	1.2241
2.5	7.25	7.63	$\cdots$	1.5483	1.4853	$\cdots$	1.4936	1.1219	1.3014	0.65322	1.3101	1.1512	0.76953	0.18529	1.1593
2.5	7.25	8.23	1.4761	1.5448	1.4751	$\cdots$	1.4877	1.1085	1.3131	0.65058	1.3156	1.1425	0.75932	0.18174	1.1749
2.5	7.25	8.53	$\cdots$	1.5406	1.4627	$\cdots$	1.4796	1.0889	1.3253	0.64610	1.3208	1.1282	0.74296	0.17715	1.1940
2.5	7.25	8.93	$\cdots$	1.5285	1.4397	$\cdots$	1.4584	1.0403	1.3333	0.63026	1.3209	1.0869	0.70173	0.16866	1.2128
2.5	7.25	9.23	$\cdots$	$\cdots$	1.4170	$\cdots$	1.4305	0.98476	$\cdots$	0.62755	1.3062	1.0469	0.65018	0.16350	1.2134
2.5	7.50	7.63	1.4819	1.5497	1.4892	$\cdots$	1.4955	1.1245	1.2962	0.65393	1.3066	1.1496	0.77023	0.18494	1.1471
2.5	7.50	8.23	1.4763	1.5450	1.4762	$\cdots$	1.4879	1.1085	1.3120	0.65154	1.3140	1.1408	0.75796	0.18110	1.1680
2.5	7.50	8.53	1.4693	1.5402	1.4622	$\cdots$	1.4788	1.0867	1.3258	0.64711	1.3199	1.1259	0.73921	0.17600	1.1900
2.5	7.50	8.93	$\cdots$	1.5272	1.4385	$\cdots$	1.4569	1.0356	1.3327	0.62910	1.3192	1.0819	0.69538	0.16702	1.2072
2.5	7.50	9.23	$\cdots$	$\cdots$	1.4153	$\cdots$	1.4294	0.98076	$\cdots$	0.62793	1.3038	1.0450	0.64171	0.16205	1.2067
2.5	7.75	7.63	1.4832	1.5512	1.4933	1.4681	1.4975	1.1275	1.2910	0.65472	1.3033	1.1492	0.77164	0.18546	1.1365
2.5	7.75	8.23	1.4764	1.5452	1.4768	1.4806	1.4883	1.1094	1.3113	0.65262	1.3129	1.1406	0.75729	0.18134	1.1634
2.5	7.75	8.53	1.4688	1.5399	1.4615	$\cdots$	1.4783	1.0859	1.3265	0.64843	1.3194	1.1253	0.73640	0.17573	1.1880
2.5	7.75	8.93	$\cdots$	1.5259	1.4372	$\cdots$	1.4559	1.0327	1.3319	0.62826	1.3178	1.0786	0.68920	0.16605	1.2037
2.5	7.75	9.23	$\cdots$	$\cdots$	1.4142	$\cdots$	1.4298	0.97994	$\cdots$	0.62809	1.3019	1.0449	0.63173	0.16118	1.2021
2.5	8.00	7.63	1.4846	1.5528	1.4976	1.4649	1.4995	1.1308	1.2859	0.65532	1.3003	1.1495	0.77336	0.18638	1.1270
2.5	8.00	8.23	1.4767	1.5453	1.4776	1.4804	1.4887	1.1113	1.3108	0.65354	1.3120	1.1412	0.75711	0.18215	1.1600
2.5	8.00	8.53	1.4684	1.5396	1.4611	$\cdots$	1.4782	1.0867	1.3270	0.64980	1.3191	1.1263	0.73453	0.17608	1.1869
2.5	8.00	8.93	$\cdots$	1.5248	1.4363	$\cdots$	1.4555	1.0318	1.3309	0.62785	1.3166	1.0769	0.68403	0.16552	1.2012
2.5	8.00	9.23	$\cdots$	$\cdots$	1.4146	$\cdots$	1.4314	0.98217	1.3092	0.62792	1.3013	1.0465	0.62045	0.16071	1.1984
2.5	8.25	7.63	1.4859	1.5546	1.5017	1.4620	1.5013	1.1342	1.2811	0.65578	1.2974	1.1504	0.77518	0.18747	1.1184
2.5	8.25	8.23	1.4769	1.5456	1.4784	1.4802	1.4895	1.1137	1.3102	0.65428	1.3113	1.1427	0.75727	0.18330	1.1572
2.5	8.25	8.53	1.4683	1.5395	1.4610	$\cdots$	1.4788	1.0887	1.3272	0.65104	1.3189	1.1286	0.73368	0.17693	1.1859
2.5	8.25	8.93	$\cdots$	1.5242	1.4361	$\cdots$	1.4559	1.0325	1.3302	0.62765	1.3157	1.0764	0.68058	0.16528	1.1994
2.5	8.25	9.23	$\cdots$	$\cdots$	1.4161	$\cdots$	1.4333	0.98560	1.3044	0.62750	1.3016	1.0488	0.60961	0.16055	1.1950
2.5	8.50	7.63	1.4870	1.5557	1.5057	1.4594	1.5028	1.1375	1.2766	0.65593	1.2949	1.1517	0.77698	0.18856	1.1109
2.5	8.50	8.23	1.4772	1.5459	1.4794	1.4799	1.4905	1.1165	1.3095	0.65468	1.3105	1.1446	0.75766	0.18462	1.1547
2.5	8.50	8.53	1.4683	1.5397	1.4613	$\cdots$	1.4800	1.0919	1.3271	0.65184	1.3185	1.1320	0.73357	0.17816	1.1849
2.5	8.50	8.93	$\cdots$	1.5242	1.4365	$\cdots$	1.4570	1.0344	1.3299	0.62811	1.3151	1.0776	0.67906	0.16532	1.1981
2.5	8.50	9.23	$\cdots$	1.5046	1.4180	$\cdots$	1.4349	0.98849	1.3009	0.62700	1.3024	1.0511	0.60137	0.16056	1.1918
3.0	6.50	7.63	$\cdots$	1.5058	1.4497	$\cdots$	1.4036	0.83001	$\cdots$	0.59610	1.1614	0.91189	0.39739	0.13600	0.77688
3.0	6.50	8.23	$\cdots$	1.5029	1.4451	$\cdots$	1.3989	0.82167	$\cdots$	0.59106	1.1596	0.89918	0.39286	0.13431	0.77211
3.0	6.50	8.53	$\cdots$	1.4982	1.4372	$\cdots$	1.3916	0.80909	$\cdots$	0.58368	1.1574	0.88178	0.38593	0.13218	0.76709
3.0	6.50	8.93	$\cdots$	1.4817	1.4156	$\cdots$	1.3639	0.76849	$\cdots$	0.56582	1.1451	0.83729	0.36578	0.12839	0.75380
3.0	6.50	9.23	$\cdots$	$\cdots$	1.3937	$\cdots$	1.3261	0.72231	$\cdots$	0.56001	1.1196	0.79399	0.34319	0.12645	0.73608
3.0	6.75	7.63	$\cdots$	1.5063	1.4524	$\cdots$	1.4003	0.82424	$\cdots$	0.59327	1.1525	0.89842	0.39234	0.13223	0.75634
3.0	6.75	8.23	$\cdots$	1.5027	1.4464	$\cdots$	1.3948	0.81451	1.2191	0.58868	1.1510	0.88634	0.38723	0.13087	0.75215
3.0	6.75	8.53	$\cdots$	1.4971	1.4371	$\cdots$	1.3863	0.79977	1.2212	0.58160	1.1485	0.86899	0.37920	0.12915	0.74686
3.0	6.75	8.93	$\cdots$	1.4794	1.4145	$\cdots$	1.3575	0.75748	$\cdots$	0.56207	1.1348	0.82414	0.35769	0.12598	0.73075
3.0	6.75	9.23	$\cdots$	$\cdots$	1.3918	$\cdots$	1.3190	0.71154	$\cdots$	0.55699	1.1078	0.78258	0.33401	0.12448	0.71094
3.0	7.00	7.63	$\cdots$	1.5076	1.4557	$\cdots$	1.3995	0.82294	1.2128	0.59190	1.1470	0.89005	0.39073	0.12989	0.74339
3.0	7.00	8.23	$\cdots$	1.5030	1.4480	$\cdots$	1.3928	0.81118	1.2161	0.58768	1.1457	0.87839	0.38461	0.12868	0.73962
3.0	7.00	8.53	$\cdots$	1.4963	1.4370	$\cdots$	1.3828	0.79384	1.2188	0.58083	1.1429	0.86067	0.37526	0.12714	0.73405
3.0	7.00	8.93	$\cdots$	1.4778	1.4135	$\cdots$	1.3524	0.74953	1.2120	0.55867	1.1278	0.81428	0.35278	0.12430	0.71586
3.0	7.00	9.23	$\cdots$	1.4484	1.3904	$\cdots$	1.3135	0.70373	$\cdots$	0.55525	1.0997	0.77493	0.32830	0.12315	0.69501
3.0	7.25	7.63	$\cdots$	1.5093	1.4594	$\cdots$	1.4006	0.82442	1.2094	0.59187	1.1436	0.88524	0.39098	0.12869	0.73537
3.0	7.25	8.23	1.4621	1.5033	1.4493	$\cdots$	1.3920	0.81007	1.2142	0.58806	1.1425	0.87385	0.38341	0.12751	0.73184
3.0	7.25	8.53	$\cdots$	1.4956	1.4366	$\cdots$	1.3802	0.79005	1.2174	0.58136	1.1393	0.85562	0.37265	0.12598	0.72581
3.0	7.25	8.93	$\cdots$	1.4764	1.4124	$\cdots$	1.3485	0.74387	1.2097	0.55559	1.1231	0.80682	0.34949	0.12322	0.70624
3.0	7.25	9.23	$\cdots$	1.4464	1.3892	$\cdots$	1.3097	0.69851	$\cdots$	0.55473	1.0945	0.77053	0.32466	0.12229	0.68527
3.0	7.50	7.63	1.4694	1.5114	1.4634	$\cdots$	1.4027	0.82731	1.2063	0.59262	1.1415	0.88271	0.39217	0.12827	0.73043
3.0	7.50	8.23	1.4625	1.5036	1.4502	$\cdots$	1.3917	0.81021	1.2131	0.58930	1.1405	0.87173	0.38281	0.12705	0.72700
3.0	7.50	8.53	1.4537	1.4947	1.4359	$\cdots$	1.3783	0.78779	1.2166	0.58294	1.1368	0.85306	0.37060	0.12543	0.72038
3.0	7.50	8.93	$\cdots$	1.4747	1.4112	$\cdots$	1.3454	0.73983	1.2076	0.55289	1.1196	0.80133	0.34672	0.12256	0.69966
3.0	7.50	9.23	$\cdots$	1.4443	1.3880	$\cdots$	1.3074	0.69525	1.1812	0.55473	1.0911	0.76845	0.32191	0.12179	0.67917
3.0	7.75	7.63	1.4712	1.5138	1.4677	1.4465	1.4054	0.83086	1.2032	0.59350	1.1401	0.88181	0.39381	0.12828	0.72741
3.0	7.75	8.23	1.4628	1.5039	1.4509	1.4573	1.3919	0.81136	1.2124	0.59073	1.1393	0.87117	0.38257	0.12702	0.72390
3.0	7.75	8.53	1.4529	1.4941	1.4351	$\cdots$	1.3771	0.78709	1.2161	0.58500	1.1351	0.85265	0.36904	0.12527	0.71667
3.0	7.75	8.93	$\cdots$	1.4731	1.4100	$\cdots$	1.3433	0.73735	1.2055	0.55104	1.1169	0.79777	0.34423	0.12219	0.69488
3.0	7.75	9.23	$\cdots$	1.4420	1.3867	$\cdots$	1.3065	0.69359	1.1777	0.55452	1.0886	0.76784	0.31921	0.12151	0.67479
3.0	8.00	7.63	1.4730	1.5163	1.4719	1.4435	1.4083	0.83476	1.2003	0.59411	1.1391	0.88207	0.39571	0.12850	0.72561
3.0	8.00	8.23	1.4630	1.5042	1.4517	1.4571	1.3924	0.81331	1.2120	0.59190	1.1386	0.87181	0.38261	0.12725	0.72203
3.0	8.00	8.53	1.4525	1.4937	1.4346	$\cdots$	1.3768	0.78794	1.2159	0.58697	1.1340	0.85396	0.36809	0.12538	0.71424
3.0	8.00	8.93	$\cdots$	1.4718	1.4090	$\cdots$	1.3423	0.73649	1.2037	0.55002	1.1147	0.79597	0.34229	0.12199	0.69133
3.0	8.00	9.23	$\cdots$	1.4407	1.3859	$\cdots$	1.3072	0.69351	1.1734	0.55390	1.0867	0.76820	0.31642	0.12136	0.67091
3.0	8.25	7.63	1.4746	1.5189	1.4763	1.4407	1.4109	0.83883	1.1975	0.59438	1.1384	0.88303	0.39777	0.0000	0.72461
3.0	8.25	8.23	1.4633	1.5047	1.4526	1.4568	1.3935	0.81601	1.2115	0.59263	1.1382	0.87341	0.38287	0.12764	0.72088
3.0	8.25	8.53	1.4524	1.4936	1.4346	$\cdots$	1.3777	0.79012	1.2157	0.58847	1.1334	0.85688	0.36765	0.12567	0.71280
3.0	8.25	8.93	$\cdots$	1.4711	1.4086	$\cdots$	1.3425	0.73699	1.2024	0.54950	1.1132	0.79558	0.34110	0.12189	0.68884
3.0	8.25	9.23	$\cdots$	1.4413	1.3862	$\cdots$	1.3090	0.69471	1.1691	0.55290	1.0855	0.76919	0.31400	0.12129	0.66732
3.0	8.50	7.63	1.4760	1.5208	1.4804	1.4382	1.4133	0.84279	1.1948	0.59426	1.1379	0.88460	0.39983	0.0000	0.72408
3.0	8.50	8.23	1.4637	1.5052	1.4536	1.4565	1.3951	0.81915	1.2112	0.59284	1.1381	0.87571	0.38325	0.12809	0.72025
3.0	8.50	8.53	1.4524	1.4938	1.4349	$\cdots$	1.3795	0.79341	1.2156	0.58926	1.1331	0.86086	0.36763	0.12609	0.71206
3.0	8.50	8.93	$\cdots$	1.4711	1.4088	$\cdots$	1.3439	0.73875	1.2019	0.55089	1.1125	0.79751	0.34071	0.12192	0.68747
3.0	8.50	9.23	$\cdots$	1.4434	1.3876	$\cdots$	1.3110	0.69634	1.1660	0.55174	1.0846	0.77029	0.31244	0.12125	0.66394
3.5	6.50	7.63	$\cdots$	1.3924	1.3765	$\cdots$	1.1844	0.57975	$\cdots$	0.52026	0.86103	0.68161	0.20427	0.11234	0.40037
3.5	6.50	8.23	$\cdots$	1.3867	1.3714	$\cdots$	1.1767	0.57498	$\cdots$	0.51286	0.85597	0.67010	0.20265	0.11164	0.39499
3.5	6.50	8.53	$\cdots$	1.3776	1.3634	$\cdots$	1.1654	0.56815	$\cdots$	0.50075	0.84921	0.65443	0.20032	0.11080	0.38864
3.5	6.50	8.93	$\cdots$	1.3469	1.3390	$\cdots$	1.1240	0.54665	$\cdots$	0.47009	0.82697	0.62011	0.19343	0.10982	0.37478
3.5	6.50	9.23	$\cdots$	$\cdots$	1.3118	$\cdots$	1.0683	0.52307	$\cdots$	0.45754	0.79459	0.59352	0.18574	0.10981	0.36241
3.5	6.75	7.63	$\cdots$	1.3926	1.3772	$\cdots$	1.1746	0.57528	$\cdots$	0.51664	0.84980	0.66874	0.20200	0.11042	0.38665
3.5	6.75	8.23	$\cdots$	1.3856	1.3710	$\cdots$	1.1661	0.56995	0.99290	0.51013	0.84461	0.65868	0.20023	0.10995	0.38165
3.5	6.75	8.53	$\cdots$	1.3744	1.3613	$\cdots$	1.1533	0.56214	0.98557	0.49888	0.83708	0.64423	0.19755	0.10943	0.37514
3.5	6.75	8.93	$\cdots$	1.3411	1.3350	$\cdots$	1.1099	0.54004	$\cdots$	0.46595	0.81307	0.61093	0.19022	0.10886	0.36034
3.5	6.75	9.23	$\cdots$	1.2967	1.3068	$\cdots$	1.0536	0.51714	$\cdots$	0.45359	0.77975	0.58630	0.18227	0.10908	0.34768
3.5	7.00	7.63	$\cdots$	1.3948	1.3796	$\cdots$	1.1705	0.57391	0.99500	0.51444	0.84391	0.66012	0.20120	0.10916	0.37874
3.5	7.00	8.23	$\cdots$	1.3859	1.3716	$\cdots$	1.1603	0.56754	0.99021	0.50870	0.83824	0.65121	0.19911	0.10883	0.37373
3.5	7.00	8.53	$\cdots$	1.3724	1.3599	$\cdots$	1.1453	0.55841	0.98169	0.49832	0.82960	0.63760	0.19598	0.10851	0.36683
3.5	7.00	8.93	$\cdots$	1.3372	1.3324	$\cdots$	1.0993	0.53540	0.95305	0.46203	0.80401	0.60398	0.18834	0.10820	0.35129
3.5	7.00	9.23	$\cdots$	1.2914	1.3035	$\cdots$	1.0429	0.51301	$\cdots$	0.45118	0.77019	0.58153	0.18022	0.10859	0.33869
3.5	7.25	7.63	$\cdots$	1.3982	1.3830	$\cdots$	1.1705	0.57448	0.99467	0.51362	0.84137	0.65446	0.20119	0.10846	0.37450
3.5	7.25	8.23	1.4201	1.3865	1.3725	$\cdots$	1.1576	0.56670	0.98887	0.50860	0.83466	0.64668	0.19860	0.10821	0.36904
3.5	7.25	8.53	$\cdots$	1.3708	1.3587	$\cdots$	1.1397	0.55614	0.97882	0.49909	0.82473	0.63361	0.19496	0.10798	0.36152
3.5	7.25	8.93	$\cdots$	1.3342	1.3304	$\cdots$	1.0916	0.53222	0.94924	0.45807	0.79803	0.59859	0.18715	0.10777	0.34558
3.5	7.25	9.23	$\cdots$	1.2882	1.3016	$\cdots$	1.0359	0.51042	$\cdots$	0.45007	0.76452	0.57879	0.17904	0.10828	0.33340
3.5	7.50	7.63	1.4316	1.4021	1.3870	$\cdots$	1.1730	0.57607	0.99516	0.51342	0.84081	0.65069	0.20157	0.0000	0.37260
3.5	7.50	8.23	1.4206	1.3870	1.3731	$\cdots$	1.1562	0.56667	0.98807	0.50924	0.83261	0.64413	0.19832	0.10792	0.36620
3.5	7.50	8.53	1.4061	1.3689	1.3573	$\cdots$	1.1357	0.55477	0.97638	0.50076	0.82124	0.63167	0.19418	0.10773	0.35791
3.5	7.50	8.93	$\cdots$	1.3313	1.3285	$\cdots$	1.0859	0.53008	0.94571	0.45436	0.79380	0.59458	0.18625	0.10752	0.34179
3.5	7.50	9.23	$\cdots$	1.2863	1.3004	$\cdots$	1.0319	0.50890	0.90468	0.44950	0.76130	0.57740	0.17835	0.10810	0.33027
3.5	7.75	7.63	1.4345	1.4066	1.3915	1.3831	1.1769	0.57814	0.99611	0.51334	0.84144	0.64832	0.20217	0.0000	0.37216
3.5	7.75	8.23	1.4209	1.3874	1.3737	1.3900	1.1559	0.56726	0.98762	0.50994	0.83146	0.64295	0.19820	0.10783	0.36449
3.5	7.75	8.53	1.4048	1.3672	1.3562	$\cdots$	1.1333	0.55433	0.97439	0.50269	0.81868	0.63137	0.19359	0.10764	0.35538
3.5	7.75	8.93	$\cdots$	1.3287	1.3268	$\cdots$	1.0821	0.52881	0.94234	0.45159	0.79053	0.59198	0.18549	0.10738	0.33914
3.5	7.75	9.23	$\cdots$	1.2845	1.2994	$\cdots$	1.0299	0.50812	0.90221	0.44900	0.75931	0.57682	0.17782	0.10799	0.32819
3.5	8.00	7.63	1.4373	1.4113	1.3961	1.3806	1.1812	0.58050	0.99714	0.51312	0.84274	0.64716	0.20289	0.0000	0.37265
3.5	8.00	8.23	1.4213	1.3880	1.3743	1.3899	1.1565	0.56842	0.98748	0.51027	0.83095	0.64269	0.19819	0.10785	0.36351
3.5	8.00	8.53	1.4039	1.3662	1.3554	$\cdots$	1.1325	0.55478	0.97305	0.50423	0.81699	0.63234	0.19323	0.10764	0.35368
3.5	8.00	8.93	$\cdots$	1.3267	1.3256	$\cdots$	1.0803	0.52835	0.93955	0.45025	0.78812	0.59070	0.18494	0.10731	0.33723
3.5	8.00	9.23	$\cdots$	1.2831	1.2987	$\cdots$	1.0296	0.50791	0.89935	0.44820	0.75789	0.57677	0.17735	0.10792	0.32654
3.5	8.25	7.63	1.4400	1.4161	1.4008	1.3782	1.1855	0.58300	0.99806	0.51266	0.84427	0.64678	0.20367	$\cdots$	0.37367
3.5	8.25	8.23	1.4218	1.3889	1.3751	1.3896	1.1581	0.57001	0.98750	0.51024	0.83093	0.64320	0.19827	0.10793	0.36308
3.5	8.25	8.53	1.4036	1.3658	1.3552	$\cdots$	1.1336	0.55600	0.97244	0.50498	0.81611	0.63420	0.19306	0.10770	0.35272
3.5	8.25	8.93	$\cdots$	1.3257	1.3250	$\cdots$	1.0804	0.52859	0.93781	0.45038	0.78660	0.59062	0.18462	0.10725	0.33597
3.5	8.25	9.23	$\cdots$	1.2829	1.2985	$\cdots$	1.0309	0.50816	0.89672	0.44722	0.75685	0.57700	0.17699	0.10787	0.32506
3.5	8.50	7.63	1.4423	1.4201	1.4052	1.3760	1.1894	0.58545	0.99884	0.51186	0.84595	0.64713	0.20446	$\cdots$	0.37497
3.5	8.50	8.23	1.4224	1.3901	1.3761	1.3894	1.1606	0.57188	0.98777	0.50960	0.83134	0.64419	0.19840	$\cdots$	0.36300
3.5	8.50	8.53	1.4037	1.3661	1.3554	$\cdots$	1.1364	0.55788	0.97235	0.50484	0.81597	0.63662	0.19305	0.10779	0.35231
3.5	8.50	8.93	1.3706	1.3258	1.3253	$\cdots$	1.0826	0.52953	0.93726	0.45407	0.78602	0.59266	0.18456	0.10723	0.33530
3.5	8.50	9.23	$\cdots$	1.2841	1.2993	$\cdots$	1.0331	0.50877	0.89512	0.44612	0.75618	0.57737	0.17683	0.10780	0.32375
4.0	6.50	7.63	$\cdots$	1.1248	1.1869	$\cdots$	0.79600	0.45153	$\cdots$	0.45309	0.53735	0.55424	0.13130	$\cdots$	0.20479
4.0	6.50	8.23	$\cdots$	1.1157	1.1810	$\cdots$	0.78632	0.44971	$\cdots$	0.44542	0.53288	0.54560	0.13099	0.10329	0.20200
4.0	6.50	8.53	$\cdots$	1.1011	1.1720	$\cdots$	0.77298	0.44731	$\cdots$	0.43156	0.52727	0.53323	0.13060	0.10310	0.19881
4.0	6.50	8.93	$\cdots$	1.0521	1.1428	$\cdots$	0.72883	0.44001	$\cdots$	0.39271	0.51115	0.51018	0.12942	0.10338	0.19311
4.0	6.50	9.23	$\cdots$	0.98934	1.1057	$\cdots$	0.66958	0.43155	$\cdots$	0.37102	0.48943	0.49710	0.12788	0.10412	0.18954
4.0	6.75	7.63	$\cdots$	1.1246	1.1835	$\cdots$	0.78001	0.44888	$\cdots$	0.44952	0.52783	0.54405	0.13025	$\cdots$	0.19679
4.0	6.75	8.23	$\cdots$	1.1134	1.1767	$\cdots$	0.77027	0.44704	0.65054	0.44284	0.52354	0.53693	0.12996	0.10249	0.19444
4.0	6.75	8.53	$\cdots$	1.0955	1.1659	$\cdots$	0.75609	0.44445	0.63994	0.43055	0.51766	0.52647	0.12956	0.10249	0.19154
4.0	6.75	8.93	$\cdots$	1.0414	1.1337	$\cdots$	0.71037	0.43708	$\cdots$	0.39038	0.50069	0.50517	0.12830	0.10300	0.18597
4.0	6.75	9.23	$\cdots$	0.97576	1.0948	$\cdots$	0.65156	0.42904	$\cdots$	0.36823	0.47901	0.49348	0.12670	0.10385	0.18262
4.0	7.00	7.63	$\cdots$	1.1284	1.1840	$\cdots$	0.77268	0.44776	0.65703	0.44661	0.52302	0.53641	0.12973	$\cdots$	0.19212
4.0	7.00	8.23	$\cdots$	1.1140	1.1753	$\cdots$	0.76154	0.44568	0.64890	0.44092	0.51847	0.53085	0.12943	0.10194	0.18997
4.0	7.00	8.53	$\cdots$	1.0920	1.1623	$\cdots$	0.74530	0.44274	0.63619	0.43011	0.51191	0.52189	0.12899	0.10207	0.18719
4.0	7.00	8.93	$\cdots$	1.0342	1.1277	$\cdots$	0.69687	0.43504	0.60167	0.38776	0.49405	0.50123	0.12765	0.10274	0.18161
4.0	7.00	9.23	$\cdots$	0.96698	1.0878	$\cdots$	0.63890	0.42733	$\cdots$	0.36636	0.47253	0.49107	0.12601	0.10366	0.17848
4.0	7.25	7.63	$\cdots$	1.1344	1.1866	$\cdots$	0.77124	0.44762	0.65909	0.44487	0.52115	0.53098	0.12951	$\cdots$	0.18955
4.0	7.25	8.23	1.3026	1.1150	1.1750	$\cdots$	0.75712	0.44509	0.64826	0.43978	0.51572	0.52673	0.12916	0.10161	0.18733
4.0	7.25	8.53	1.2797	1.0887	1.1594	$\cdots$	0.73798	0.44167	0.63290	0.43032	0.50819	0.51913	0.12864	0.10184	0.18446
4.0	7.25	8.93	$\cdots$	1.0287	1.1234	$\cdots$	0.68720	0.43365	0.59769	0.38452	0.48973	0.49801	0.12726	0.10259	0.17895
4.0	7.25	9.23	$\cdots$	0.96206	1.0839	$\cdots$	0.63093	0.42624	$\cdots$	0.36538	0.46887	0.48963	0.12562	0.10355	0.17608
4.0	7.50	7.63	1.3238	1.1415	1.1904	$\cdots$	0.77340	0.44802	0.66232	0.44350	0.52095	0.52683	0.12942	$\cdots$	0.18829
4.0	7.50	8.23	1.3032	1.1155	1.1749	$\cdots$	0.75482	0.44495	0.64778	0.43906	0.51412	0.52409	0.12901	0.10144	0.18573
4.0	7.50	8.53	1.2762	1.0847	1.1567	$\cdots$	0.73269	0.44106	0.62945	0.43088	0.50545	0.51769	0.12841	0.10174	0.18266
4.0	7.50	8.93	$\cdots$	1.0237	1.1198	$\cdots$	0.68030	0.43274	0.59385	0.38099	0.48668	0.49551	0.12700	0.10251	0.17726
4.0	7.50	9.23	$\cdots$	0.95959	1.0819	$\cdots$	0.62643	0.42565	0.55604	0.36492	0.46689	0.48885	0.12540	0.10347	0.17468
4.0	7.75	7.63	1.3296	1.1496	1.1951	1.2179	0.77763	0.44869	0.66613	0.44206	0.52179	0.52359	0.12940	$\cdots$	0.18784
4.0	7.75	8.23	1.3036	1.1161	1.1749	1.2183	0.75386	0.44510	0.64744	0.43835	0.51319	0.52245	0.12892	0.10136	0.18476
4.0	7.75	8.53	1.2728	1.0811	1.1543	$\cdots$	0.72924	0.44083	0.62641	0.43130	0.50337	0.51730	0.12825	0.10170	0.18142
4.0	7.75	8.93	$\cdots$	1.0191	1.1169	$\cdots$	0.67572	0.43219	0.59008	0.37830	0.48438	0.49385	0.12680	0.10247	0.17614
4.0	7.75	9.23	$\cdots$	0.95778	1.0806	$\cdots$	0.62416	0.42532	0.55456	0.36471	0.46576	0.48851	0.12526	0.10342	0.17377
4.0	8.00	7.63	1.3352	1.1581	1.2003	1.2166	0.78275	0.44954	0.67017	0.44114	0.52324	0.52152	0.12943	$\cdots$	0.18793
4.0	8.00	8.23	1.3042	1.1169	1.1752	1.2180	0.75421	0.44550	0.64743	0.43745	0.51277	0.52143	0.12887	$\cdots$	0.18418
4.0	8.00	8.53	1.2707	1.0786	1.1528	$\cdots$	0.72790	0.44097	0.62451	0.43115	0.50197	0.51749	0.12816	0.10168	0.18062
4.0	8.00	8.93	$\cdots$	1.0158	1.1149	$\cdots$	0.67342	0.43201	0.58719	0.37696	0.48270	0.49302	0.12667	0.10244	0.17538
4.0	8.00	9.23	$\cdots$	0.95646	1.0796	$\cdots$	0.62354	0.42522	0.55281	0.36444	0.46498	0.48836	0.12516	0.10339	0.17307
4.0	8.25	7.63	1.3406	1.1663	1.2056	1.2152	0.78792	0.45044	0.67403	0.44005	0.52492	0.52011	0.12948	$\cdots$	0.18834
4.0	8.25	8.23	1.3051	1.1184	1.1759	1.2179	0.75589	0.44609	0.64780	0.43642	0.51280	0.52089	0.12885	$\cdots$	0.18389
4.0	8.25	8.53	1.2698	1.0776	1.1519	$\cdots$	0.72883	0.44140	0.62364	0.43042	0.50125	0.51801	0.12811	0.10167	0.18013
4.0	8.25	8.93	1.2114	1.0140	1.1139	$\cdots$	0.67332	0.43205	0.58560	0.37779	0.48167	0.49308	0.12660	0.10240	0.17490
4.0	8.25	9.23	$\cdots$	0.95629	1.0794	$\cdots$	0.62434	0.42526	0.55132	0.36410	0.46444	0.48835	0.12510	0.10334	0.17246
4.0	8.50	7.63	1.3453	1.1743	$\cdots$	1.2137	0.79269	0.45135	0.67758	0.43899	0.52668	0.51945	0.12954	$\cdots$	0.18892
4.0	8.50	8.23	1.3063	1.1204	1.1770	1.2177	0.75881	0.44678	0.64840	0.43512	0.51317	0.52071	0.12885	$\cdots$	0.18380
4.0	8.50	8.53	1.2700	1.0780	1.1519	$\cdots$	0.73186	0.44211	0.62361	0.42922	0.50111	0.51867	0.12809	0.10166	0.17990
4.0	8.50	8.93	1.2110	1.0140	1.1140	$\cdots$	0.67564	0.43238	0.58522	0.38435	0.48128	0.49516	0.12657	0.10236	0.17462
4.0	8.50	9.23	$\cdots$	0.95771	1.0802	$\cdots$	0.62619	0.42541	0.55061	0.36388	0.46408	0.48844	0.12507	0.10327	0.17192
4.5	6.50	7.63	$\cdots$	0.69999	0.82703	$\cdots$	0.39582	0.40187	$\cdots$	0.40142	0.33818	0.49608	0.10678	$\cdots$	0.12744
4.5	6.50	8.23	$\cdots$	0.69080	0.82068	$\cdots$	0.38838	0.40131	$\cdots$	0.39504	0.33594	0.49004	0.10684	0.10059	0.12627
4.5	6.50	8.53	$\cdots$	0.67670	0.81179	$\cdots$	0.37875	0.40066	$\cdots$	0.38334	0.33336	0.48075	0.10700	0.10064	0.12500
4.5	6.50	8.93	$\cdots$	0.62919	0.78294	$\cdots$	0.35110	0.39903	$\cdots$	0.34921	0.32713	0.46504	0.10758	0.10125	0.12353
4.5	6.50	9.23	$\cdots$	0.56988	0.74217	$\cdots$	0.31434	0.39698	$\cdots$	0.32437	0.31884	0.45883	0.10811	0.10215	0.12405
4.5	6.75	7.63	$\cdots$	0.69950	0.81942	$\cdots$	0.38128	0.40037	$\cdots$	0.39832	0.33236	0.48849	0.10619	$\cdots$	0.12288
4.5	6.75	8.23	$\cdots$	0.68833	0.81254	$\cdots$	0.37462	0.39991	0.35771	0.39275	0.33048	0.48374	0.10631	0.10020	0.12205
4.5	6.75	8.53	$\cdots$	0.67097	0.80222	$\cdots$	0.36530	0.39936	0.35170	0.38254	0.32814	0.47617	0.10655	0.10035	0.12114
4.5	6.75	8.93	$\cdots$	0.61792	0.76989	$\cdots$	0.33750	0.39783	$\cdots$	0.34856	0.32197	0.46241	0.10720	0.10110	0.12017
4.5	6.75	9.23	$\cdots$	0.55664	0.72755	$\cdots$	0.30199	0.39602	$\cdots$	0.32303	0.31397	0.45711	0.10773	0.10204	0.12095
4.5	7.00	7.63	$\cdots$	0.70385	0.81750	$\cdots$	0.37424	0.39954	0.36192	0.39567	0.32927	0.48249	0.10577	$\cdots$	0.12010
4.5	7.00	8.23	$\cdots$	0.68924	0.80908	$\cdots$	0.36717	0.39912	0.35701	0.39077	0.32748	0.47895	0.10597	0.099899	0.11952
4.5	7.00	8.53	$\cdots$	0.66758	0.79667	$\cdots$	0.35703	0.39856	0.34968	0.38185	0.32510	0.47295	0.10630	0.10014	0.11887
4.5	7.00	8.93	$\cdots$	0.61026	0.76131	$\cdots$	0.32783	0.39705	0.33001	0.34737	0.31876	0.46024	0.10699	0.10100	0.11819
4.5	7.00	9.23	$\cdots$	0.54807	0.71827	$\cdots$	0.29360	0.39537	$\cdots$	0.32206	0.31104	0.45595	0.10750	0.10198	0.11913
4.5	7.25	7.63	1.0593	0.71084	0.81884	$\cdots$	0.37214	0.39918	0.36365	0.39420	0.32782	0.47819	0.10546	$\cdots$	0.11845
4.5	7.25	8.23	1.0346	0.69057	0.80771	$\cdots$	0.36336	0.39873	0.35686	0.38917	0.32586	0.47552	0.10577	$\cdots$	0.11801
4.5	7.25	8.53	0.99894	0.66375	0.79252	$\cdots$	0.35158	0.39812	0.34763	0.38130	0.32323	0.47084	0.10620	0.10004	0.11753
4.5	7.25	8.93	$\cdots$	0.60409	0.75521	$\cdots$	0.32101	0.39653	0.32744	0.34542	0.31671	0.45842	0.10690	0.10096	0.11704
4.5	7.25	9.23	$\cdots$	0.54315	0.71290	$\cdots$	0.28835	0.39497	$\cdots$	0.32165	0.30937	0.45528	0.10736	0.10194	0.11810
4.5	7.50	7.63	1.0697	0.71943	0.82210	$\cdots$	0.37305	0.39908	0.36613	0.39251	0.32731	0.47445	0.10520	$\cdots$	0.11749
4.5	7.50	8.23	1.0354	0.69116	0.80679	$\cdots$	0.36130	0.39856	0.35658	0.38788	0.32489	0.47313	0.10567	$\cdots$	0.11711
4.5	7.50	8.53	0.99185	0.65886	0.78873	$\cdots$	0.34760	0.39787	0.34525	0.38075	0.32190	0.46964	0.10620	0.099995	0.11674
4.5	7.50	8.93	$\cdots$	0.59824	0.75032	$\cdots$	0.31617	0.39620	0.32483	0.34275	0.31529	0.45688	0.10689	0.10095	0.11639
4.5	7.50	9.23	$\cdots$	0.54029	0.70990	$\cdots$	0.28533	0.39472	0.30525	0.32183	0.30844	0.45497	0.10727	0.10191	0.11749
4.5	7.75	7.63	1.0803	0.72904	$\cdots$	0.90070	0.37569	0.39915	0.36908	0.39092	0.32737	0.47141	0.10496	$\cdots$	0.11695
4.5	7.75	8.23	1.0358	0.69150	0.80633	0.89452	0.36031	0.39855	0.35635	0.38662	0.32431	0.47141	0.10561	$\cdots$	0.11655
4.5	7.75	8.53	0.98522	0.65421	0.78547	$\cdots$	0.34493	0.39780	0.34310	0.38010	0.32091	0.46907	0.10623	0.099993	0.11625
4.5	7.75	8.93	$\cdots$	0.59302	0.74639	$\cdots$	0.31297	0.39601	0.32235	0.34035	0.31424	0.45577	0.10690	0.10095	0.11604
4.5	7.75	9.23	$\cdots$	0.53816	0.70785	$\cdots$	0.28372	0.39458	0.30422	0.32213	0.30789	0.45476	0.10724	0.10189	0.11709
4.5	8.00	7.63	1.0908	0.73920	$\cdots$	0.90064	0.37917	0.39927	0.37222	0.38990	0.32778	0.46927	0.10473	$\cdots$	0.11668
4.5	8.00	8.23	1.0367	0.69241	0.80634	0.89427	0.36033	0.39864	0.35637	0.38538	0.32403	0.47018	0.10556	$\cdots$	0.11621
4.5	8.00	8.53	0.98090	0.65092	0.78318	$\cdots$	0.34377	0.39782	0.34176	0.37911	0.32025	0.46874	0.10625	$\cdots$	0.11596
4.5	8.00	8.93	0.89404	0.58919	0.74362	$\cdots$	0.31129	0.39593	0.32054	0.33946	0.31348	0.45529	0.10693	0.10094	0.11584
4.5	8.00	9.23	$\cdots$	0.53668	0.70649	$\cdots$	0.28320	0.39453	0.30311	0.32258	0.30748	0.45468	0.10722	0.10187	0.11679
4.5	8.25	7.63	1.1009	0.74966	$\cdots$	0.90032	0.38281	0.39944	0.37529	$\cdots$	0.32836	0.46770	0.10450	$\cdots$	0.11658
4.5	8.25	8.23	1.0383	0.69408	0.80689	0.89416	0.36137	0.39877	0.35663	0.38409	0.32393	0.46923	0.10551	$\cdots$	0.11600
4.5	8.25	8.53	0.97915	0.64940	0.78195	$\cdots$	0.34420	0.39793	0.34119	0.37794	0.31989	0.46852	0.10625	$\cdots$	0.11576
4.5	8.25	8.93	0.89063	0.58705	0.74218	$\cdots$	0.31107	0.39592	0.31962	0.34119	0.31299	0.45554	0.10693	0.10092	0.11570
4.5	8.25	9.23	$\cdots$	0.53638	0.70606	$\cdots$	0.28355	0.39452	0.30227	0.32285	0.30717	0.45462	0.10722	0.10182	0.11652
4.5	8.50	7.63	1.1100	0.75967	$\cdots$	0.89974	0.38624	0.39961	0.37815	$\cdots$	0.32904	0.46683	0.10428	$\cdots$	0.11659
4.5	8.50	8.23	1.0405	0.69651	0.80790	0.89416	0.36329	0.39895	0.35715	0.38278	0.32402	0.46862	0.10546	$\cdots$	0.11587
4.5	8.50	8.53	0.97945	0.64971	0.78166	$\cdots$	0.34606	0.39812	0.34120	0.37691	0.31978	0.46833	0.10623	$\cdots$	0.11565
4.5	8.50	8.93	0.89026	0.58675	0.74206	$\cdots$	0.31244	0.39596	0.31947	0.34792	0.31279	0.45739	0.10692	0.10087	0.11561
4.5	8.50	9.23	$\cdots$	0.53741	0.70665	$\cdots$	0.28447	0.39450	0.30198	0.32304	0.30692	0.45456	0.10721	0.10176	0.11626
5.0	6.50	7.63	$\cdots$	0.31917	0.42296	$\cdots$	0.15656	0.38459	$\cdots$	0.36263	0.25397	0.46613	0.098995	$\cdots$	0.099460
5.0	6.50	8.23	$\cdots$	0.31394	0.41836	$\cdots$	0.15270	0.38448	$\cdots$	0.35864	0.25313	0.46301	0.099134	$\cdots$	0.099089
5.0	6.50	8.53	$\cdots$	0.30627	0.41235	$\cdots$	0.14779	0.38439	$\cdots$	0.35040	0.25224	0.45714	0.099389	0.10026	0.098697
5.0	6.50	8.93	$\cdots$	0.28128	0.39430	$\cdots$	0.13557	0.38450	$\cdots$	0.32701	0.25080	0.44742	0.10030	0.10077	0.098772
5.0	6.50	9.23	$\cdots$	0.25045	0.36833	$\cdots$	0.12061	0.38466	$\cdots$	0.30550	0.24915	0.44432	0.10132	0.10148	0.10040
5.0	6.75	7.63	$\cdots$	0.31879	0.41574	$\cdots$	0.14788	0.38372	$\cdots$	0.36089	0.25072	0.46135	0.098575	$\cdots$	0.096938
5.0	6.75	8.23	$\cdots$	0.31249	0.41108	$\cdots$	0.14479	0.38371	$\cdots$	0.35738	0.25017	0.45901	0.098779	$\cdots$	0.096761
5.0	6.75	8.53	$\cdots$	0.30305	0.40446	$\cdots$	0.14056	0.38374	$\cdots$	0.34977	0.24960	0.45400	0.099113	0.10011	0.096614
5.0	6.75	8.93	$\cdots$	0.27485	0.38438	$\cdots$	0.12901	0.38404	$\cdots$	0.32719	0.24862	0.44597	0.10014	0.10070	0.097176
5.0	6.75	9.23	$\cdots$	0.24327	0.35788	$\cdots$	0.11512	0.38432	$\cdots$	0.30532	0.24729	0.44359	0.10118	0.10144	0.099017
5.0	7.00	7.63	$\cdots$	0.32162	0.41336	$\cdots$	0.14348	0.38312	$\cdots$	0.35928	0.24880	0.45732	0.098209	$\cdots$	0.095329
5.0	7.00	8.23	$\cdots$	0.31332	0.40793	$\cdots$	0.14050	0.38317	0.20666	0.35575	0.24846	0.45540	0.098503	$\cdots$	0.095307
5.0	7.00	8.53	$\cdots$	0.30140	0.40010	$\cdots$	0.13627	0.38332	0.20417	0.34927	0.24811	0.45179	0.098949	0.10000	0.095401
5.0	7.00	8.93	$\cdots$	0.27044	0.37803	$\cdots$	0.12451	0.38372	$\cdots$	0.32724	0.24733	0.44492	0.10008	0.10066	0.096282
5.0	7.00	9.23	$\cdots$	0.23863	0.35136	$\cdots$	0.11150	0.38408	$\cdots$	0.30533	0.24621	0.44314	0.10110	0.10141	0.098212
5.0	7.25	7.63	$\cdots$	0.32628	0.41375	$\cdots$	0.14186	0.38274	0.20902	0.35898	0.24766	0.45465	0.097880	$\cdots$	0.094285
5.0	7.25	8.23	0.62917	0.31451	0.40664	$\cdots$	0.13832	0.38289	0.20663	0.35477	0.24748	0.45297	0.098320	$\cdots$	0.094435
5.0	7.25	8.53	0.59486	0.29934	0.39707	$\cdots$	0.13357	0.38313	0.20342	0.34862	0.24727	0.45016	0.098916	$\cdots$	0.094724
5.0	7.25	8.93	$\cdots$	0.26672	0.37353	$\cdots$	0.12139	0.38357	0.19626	0.32645	0.24658	0.44383	0.10010	0.10065	0.095816
5.0	7.25	9.23	$\cdots$	0.23571	0.34745	$\cdots$	0.10927	0.38395	$\cdots$	0.30585	0.24559	0.44292	0.10106	0.10140	0.097803
5.0	7.50	7.63	0.66639	0.33200	$\cdots$	$\cdots$	0.14193	0.38250	0.21000	0.35773	0.24696	0.45186	0.097578	$\cdots$	0.093582
5.0	7.50	8.23	0.63084	0.31521	0.40596	$\cdots$	0.13720	0.38274	0.20658	0.35360	0.24691	0.45099	0.098216	$\cdots$	0.093895
5.0	7.50	8.53	0.58768	0.29644	0.39430	$\cdots$	0.13168	0.38305	0.20250	0.34815	0.24679	0.44928	0.098984	$\cdots$	0.094400
5.0	7.50	8.93	$\cdots$	0.26309	0.36987	$\cdots$	0.11919	0.38348	0.19513	0.32519	0.24613	0.44296	0.10019	0.10067	0.095647
5.0	7.50	9.23	$\cdots$	0.23366	0.34490	$\cdots$	0.10796	0.38385	0.18832	0.30609	0.24524	0.44269	0.10105	0.10140	0.097560
5.0	7.75	7.63	0.67916	0.33854	$\cdots$	$\cdots$	0.14296	0.38234	0.21116	$\cdots$	0.24656	0.44964	0.097281	$\cdots$	0.093087
5.0	7.75	8.23	0.63192	0.31575	$\cdots$	$\cdots$	0.13668	0.38269	0.20655	0.35274	0.24656	0.44966	0.098157	$\cdots$	0.093572
5.0	7.75	8.53	0.58084	0.29362	0.39198	$\cdots$	0.13040	0.38303	0.20169	0.34739	0.24649	0.44862	0.099080	$\cdots$	0.094259
5.0	7.75	8.93	$\cdots$	0.25988	0.36693	$\cdots$	0.11774	0.38343	0.19406	0.32360	0.24582	0.44218	0.10030	0.10068	0.095639
5.0	7.75	9.23	$\cdots$	0.23204	0.34308	$\cdots$	0.10725	0.38381	0.18770	0.30733	0.24502	0.44272	0.10108	0.10138	0.097442
5.0	8.00	7.63	0.69214	0.34555	$\cdots$	$\cdots$	0.14447	0.38222	0.21243	$\cdots$	0.24631	0.44779	0.096976	$\cdots$	0.092727
5.0	8.00	8.23	0.63349	0.31663	$\cdots$	$\cdots$	0.13666	0.38266	0.20661	0.35208	0.24634	0.44878	0.098099	$\cdots$	0.093354
5.0	8.00	8.53	0.57652	0.29161	0.39030	$\cdots$	0.12981	0.38302	0.20117	0.34665	0.24631	0.44814	0.099136	$\cdots$	0.094187
5.0	8.00	8.93	0.49662	0.25747	0.36483	$\cdots$	0.11697	0.38343	0.19331	0.32335	0.24563	0.44192	0.10038	0.10069	0.095680
5.0	8.00	9.23	$\cdots$	0.23099	0.34187	$\cdots$	0.10701	0.38378	0.18710	0.30758	0.24486	0.44257	0.10113	0.10137	0.097362
5.0	8.25	7.63	0.70478	0.35289	$\cdots$	0.53729	0.14611	0.38212	0.21368	$\cdots$	0.24618	0.44652	0.096665	$\cdots$	0.092460
5.0	8.25	8.23	0.63578	0.31793	$\cdots$	0.53222	0.13709	0.38265	0.20676	0.35117	0.24620	0.44780	0.098030	$\cdots$	0.093190
5.0	8.25	8.53	0.57486	0.29074	0.38941	$\cdots$	0.12991	0.38304	0.20097	0.34594	0.24619	0.44775	0.099150	$\cdots$	0.094129
5.0	8.25	8.93	0.49334	0.25602	0.36365	$\cdots$	0.11680	0.38338	0.19295	0.32488	0.24550	0.44218	0.10042	0.10067	0.095702
5.0	8.25	9.23	$\cdots$	0.23065	0.34139	$\cdots$	0.10714	0.38374	0.18667	0.30786	0.24470	0.44244	0.10116	0.10134	0.097267
5.0	8.50	7.63	0.71641	0.35998	$\cdots$	0.53691	0.14767	0.38203	0.21488	$\cdots$	0.24612	0.44549	0.096359	$\cdots$	0.092261
5.0	8.50	8.23	0.63863	0.31966	$\cdots$	0.53223	0.13791	0.38263	0.20698	0.35006	0.24612	0.44706	0.097952	$\cdots$	0.093071
5.0	8.50	8.53	0.57535	0.29098	0.38924	$\cdots$	0.13065	0.38304	0.20100	0.34526	0.24612	0.44731	0.099129	$\cdots$	0.094060
5.0	8.50	8.93	0.49306	0.25562	0.36339	$\cdots$	0.11732	0.38338	0.19292	0.32915	0.24542	0.44350	0.10041	$\cdots$	0.095677
5.0	8.50	9.23	$\cdots$	0.23091	0.34158	$\cdots$	0.10745	0.38369	0.18652	0.30825	0.24454	0.44234	0.10116	0.10129	0.097155

Table 3. Table 3 Density-sensitive lines and their ionization potentials

Ion	Line ratio	Ionization	min neaaaMinimum and maximum values of ne for which the line ratio is density sensitive.	max neaaaMinimum and maximum values of ne for which the line ratio is density sensitive.	$\Delta$nebbbThe uncertainty in $n_e$ due to the electron temperature, defined as the difference between the ne at log(Te)=3.5 and 4.5, divided by 2$\times$ the value at log(Te) at 4.0, at the mid-point of the values of the flux ratio over which the ratio is density sensitive.	CasecccThe case for which electron density sensitivity can arise in line ratios, as described in Section III.2.
		potential (eV)
UV
S v	1188/1199	47.222	60000	80000000	88%	2
O v	1214/1218	77.414	8000	4000000	41%	2
N iv	1483/1486	47.445	2500	2500000	93%	2
Si iii	1883/1892	16.346	900	450000	75%	2
C iii	1906/1909	24.385	1800	630000	39%	2
Ne iv	2423/2425	63.423	2500	660000	23%	1
Al ii	2661/2670	5.986	450	180000	52%	2
Optical
O ii	3727/3729	13.618	40	10000	59%	1
Ar iv	4711/4740	40.735	350	80000	40%	1
N i	5200/5198	0.000	200	6300	3.5%	1
Cl iii	5517/5537	23.813	250	50000	31%	1
S ii	6717/6731	10.360	40	5000	47%	1
IR
S iii	335$\mu$/187$\mu$	23.338	400	12000	14%	3
O iii	88$\mu$/52$\mu$	35.121	60	3000	26%	3
N ii	205$\mu$/122$\mu$	14.534	10	200	18%	3

Equations

$$R_{ij}=n_e{N}_i{\alpha }_{ij},$$

$$R_{ij}=n_e{N}_i{\left(\frac{2\pi {\hslash }^4}{k{m}_e^3}\right)}^{1/2}\frac{{\Omega }_{ij}}{g_i}{T}^{-1/2}exp\left(\frac{-E_{ij}}{kT}\right)$$

$$R_{ji}^{rad}=n_e{N}_j{A}_{ji}$$

$$R_{ji}^{coll}=n_e{N}_j{\left(\frac{2\pi {\hslash }^4}{k{m}_e^3}\right)}^{1/2}\frac{{\Omega }_{ji}}{g_j}{T}^{-1/2}$$

Full text

I. Introduction

The Interstellar Medium (ISM) pressure and electron density of the gas are two of the main physical quantities that govern the emission from H II regions. The nebular emission-lines and derived quantities, such as the gas-phase metallicity, ionization parameter, and star formation rate, depend critically on assumptions about the density and pressure of the nebula.

Direct measurements of the electron density (assuming a constant electron temperature) are now being made for increasing numbers of galaxies, particularly at high redshift. Some high-z studies find large electron densities (Hainline et al., 2009; Bian et al., 2010; Liu et al., 2008; Brinchmann et al., 2008; Shirazi et al., 2013a, b) while others have relatively low electron densities (see Rigby et al., 2011; Bayliss et al., 2013). Selection effects may play a key role in electron density measurements at high redshift. Kaasinen et al. (2016) showed that the larger electron density seen in many high-z galaxies disappears when high-z and low-z samples are matched in star formation rate. This result implies that the observed large electron densities are a result of selecting samples of the most luminous galaxies at a given epoch.

One major disadvantage with measuring the electron density is the assumption of a constant nebular temperature. Under this assumption, the ISM pressure is related to the mean electron temperature through $n=\frac{P}{T_{e}k}$, where the total density $n$ is related to the electron density, $n_{e}$, through $n=2n_{e}(1+{\rm He/H})$. In a fully ionized plasma, the electron temperature is assumed to be $\sim 10^{4}$ K, and the ISM pressure is then directly proportional to the electron density (see e.g., Dopita et al., 2006b, for a discussion). However, in real H II regions, the electron temperature is not constant, and the nebular gas contains temperature fluctuations and gradients, with a complex ionization structure (see e.g., Wang et al., 2004, for a discussion).

Another major disadvantage with measuring the electron density is the assumption that the electron density is a single value across an entire H II region or galaxy. Both H II regions and galaxies are known to have gradients and clumps in electron density (e.g., Binette et al., 2002; Phillips, 2007; Herrera-Camus et al., 2016). In these cases, a constant electron density may not be a realistic assumption.

The ISM pressure provides a useful alternative measure of the ISM conditions. The ISM pressure is a key determinant of fully self-consistent models that include a detailed nebular temperature and density structure. The pressure is determined by the combination of the mechanical energy produced by the stellar population, as well as the strength and shape of the radiation field. Models with a constant pressure are applicable when the sound crossing time is less than the heating and cooling timescales, which occurs in the majority of H II regions (Field, 1965; Begelman, 1990).

It is now possible to measure the ISM pressure in H II regions and galaxies. The application of detailed stellar evolution synthesis and photoionization models allows the complex temperature and ionization structure of a nebula to be modeled. For example, Lehnert et al. (2009) applied photoionization models to galaxies at $z\sim 2$, suggesting that high ISM pressures from large (10-20 kpc) intense star-forming regions exist in most high-z star-forming galaxies.

In this paper, we calibrate a suite of UV, optical, and IR emission-line ratios to measure the ISM pressure and electron density of the gas. We use detailed, self-consistent photoionization models that calculate the detailed temperature and ionization structure of nebulae. We investigate the dependence of ISM pressure and electron density diagnostics on the gas-phase metallicity and ionization parameter. We show that the dependence on the metallicity is large (typically an order of magnitude in $\log(P/k)$), while the effect of ionization parameter is relatively small (typically $<0.1$ dex).

We provide our model data for calculating the ISM pressure, as a function of metallicity and ionization parameter. We anticipate that these models and resulting diagnostics will be useful for understanding the physical properties of galaxies across large swathes of cosmic time in the coming era of large-scale infrared spectroscopy with space and 8-10m class ground-based telescopes.

In Section II, we describe the stellar evolution and photoionization models used to calculate the ISM pressure and electron density diagnostics. We investigate the effect of temperature on the density-sensitive emission-lines in Section III. Section IV gives the UV, optical, and infrared pressure and electron density diagnostic calibrations for our models. We explain the dependence of the calibrations on metallicity and ionization parameter as well as the pressure and density regimes over which each diagnostic is valid. In Section V, we discuss the ionization and density structure of H II regions and the effect on our diagnostics. We also briefly discuss the potential contributions to the emission-lines from Diffuse Ionized Gas (DIG) and shocks. We present our conclusions in Section VI. Throughout this paper, we use Z to denote $\log(O/H)+12$, the gas-phase oxygen abundance111Asplund et al. (2009) gives a bulk solar abundance of \log({\rm O/H})+12$$=8.72, and a surface solar abundance of \log({\rm O/H})+12$$=8.69. The solar bulk abundance is an estimate of the abundance when the Sun formed, whereas the solar surface abundance shows evidence of evolution and mixing. Nicholls et al. (2017) argues that local B stars (\log({\rm O/H})+12$$=8.76) may be more representative of local present-day galactic abundances.. We use the term ISM pressure when referring to the pressure within the ionized gaseous nebulae surrounding young hot stars.

II. Theoretical Models

We combine current stellar evolution synthesis models with our photoionization models to create synthetic spectra of star-forming regions for a broad range of input parameters. We select our range of parameters to fully cover the expected pressure, density, metallicity and ionization parameter that might exist in galaxies.

II.1. Stellar Radiation Field

We use Starburst99 to generate the stellar ionizing radiation field for input into our photoionization models. The Starburst99 (SB99) models that we use are described in detail in Levesque et al. (2010) and Nicholls et al. (2012). Briefly, we apply a Salpeter IMF (Salpeter, 1955) with an upper mass limit of 100 ${\rm M}_{\odot}$. The choice of IMF makes negligible difference on the emission-line ratios used in this analysis. We use the Pauldrach/Hillier model atmospheres, which employ the WMBASIC wind models of Pauldrach et al. (2001) for younger ages when O stars dominate the luminosity ($<3$ Myr), and the CMFGEN atmospheres from Hillier & Miller (1998) for later ages when Wolf-Rayet (W-R) stars dominate. These stellar atmosphere models include the effects of metal opacities. We use the Geneva group “high” mass-loss evolutionary tracks (Meynet et al., 1994). These tracks include enhanced mass-loss rates that are applicable to low-luminosity W-R stars and can reproduce the blue-to-red supergiant ratios observed in the Magellanic Clouds (Schaller et al., 1992; Meynet, 1993). Starburst99 generates a synthetic FUV spectrum using isochrone synthesis (e.g., Charlot & Bruzual, 1991), in which isochrones are fitted to the evolutionary tracks across different masses rather than discretely assigning stellar mass bins to specific tracks. To match the nebular metallicities of our photoionization code, we interpolate between the Starburst99 model grids as a function of metallicity.

II.2. Photoionization Models

We use our MAPPINGS version 5.1 photoionization code (Binette et al., 1985; Sutherland & Dopita, 1993; Dopita et al., 2013) to model the interstellar medium surrounding the ionizing radiation field.

The relative metallicity of individual elements were chosen to maximise compatibility between stellar atmospheres, evolutionary tracks and nebulae. Nebular element abundances at sub-solar metallicities were scaled as described in Nicholls et al. (2017). Briefly, we use the standard local B-star scale of Nieva & Przybilla (2012) for the present day local region of the Milky Way. This scale is based on an ensemble average of 29 stars, and is most relevant to the present day abundances of the Milky Way local region because B star photospheric abundances represent the bulk abundances of the nebulae in which they recently formed. The Nieva & Pryzbilla abundance scale includes the elements He, C, N, O, Ne, Mg, Si, and Fe. We supplement these elements with recent solar and meteoric abundances (Grevesse et al., 2015; Scott et al., 2015a, b; Lodders et al., 2009). Together, these measurements provide local region elemental abundances for 30 elements. The full abundance sets are given in Tables 1 & 2 of Nicholls et al. (2017).

The $\alpha$-element abundances are assumed to scale linearly with metallicity, with the exception of helium, carbon, and nitrogen. The abundance scaling is described in full detail in Nicholls et al. (2017). For helium, we include the stellar yield in addition to the primordial abundance from Pagel et al. (1992). For nitrogen, we assume primary and secondary nucleosynthetic component fits to the stellar abundances from Izotov & Thuan (1999), Israelian et al. (2004), Spite et al. (2005), and Nieva & Przybilla (2012). For carbon, we assume primary and secondary nucleosynthetic component fits to the stellar abundances from Gustafsson et al. (1999), Akerman et al. (2004), Spite et al. (2005), Fabbian et al. (2009), Nieva & Przybilla (2012) and Nissen et al. (2014).

Some metals are depleted out of gas phase and onto dust grains. For nebular dust depletion we use the parametric models from Jenkins (2009), with a value of Fe depletion of -1.5 dex, derived from Wide Integral Field Spectrograph (WiFeS) observations of local and Magellanic Cloud HII regions (Dopita et al., in prep).

We use the latest available atomic data for the lightest 30 elements, taken from the CHIANTI 8 database (Del Zanna et al., 2015). We use spline interpolation between these values where needed.

MAPPINGS uses either a plane parallel or spherical geometry with the ionization parameter defined at the initial edge of the nebula. The ionization parameter $q$ has units of velocity (cm/s) and can be thought of as the maximum velocity ionization front that an ionizing radiation field is able to drive through a nebula. This dimensional ionization parameter is related to the dimensionless ionization parameter $U$ through the identity $U\equiv q/c$. The dimensionless ionization parameter is $-3.2<\log U<-2.9$ for local H II regions (Dopita et al., 2000) and star-forming galaxies (Moustakas, 2006; Moustakas et al., 2010).

Here, we utilize both spherical and plane parallel models. Our density and pressure models are calculated using a plane parallel model, to account for the fact that in a real H II region, one typically views an H II region from one direction, not a sum of the light emitted in all directions, i.e. one does not typically view the emission from the far side of the H II region. We utilize spherical models to investigate how well one can reproduce the density structure of an H II region using our diagnostics. To minimize small uncertainties produced by particular geometries, we calculate spherical models in which $q$ is determined at the inner radius. The average ionization parameter is lower than this initial value, and is dependent on the ionization parameter of the initial radius. In practice, all models with a similar effective ionization parameter produce very similar spectra, assuming all other parameters are held constant (e.g., Dopita et al., 2000). We have verified that our spherical and plane parallel models used here produce almost identical spectra if they have a similar effective ionization parameter.

Detailed photoionization, excitation, and recombination are calculated at linear increments (step size $0.02$) throughout the nebula. The model completes when the hydrogen gas is fully recombined. A full description of the models, including geometry, is given in López-Sánchez et al. (2012). These models include a sophisticated treatment of dust, including the effects of absorption, grain charging, radiation pressure, and photoelectric heating of the small grains (Groves et al., 2004).

For the purposes of developing ISM pressure and density diagnostics, we calculate three dimensional grids of models in metallicity, ionization parameter, and a third parameter (pressure, density, or temperature) by holding metallicity fixed at each of \log({\rm O/H})+12$$=[7.63,8.23,8.53,8.93,9.23], and the ionization parameter fixed at each of $\log(\frac{q}{cms^{-1}})=[6.5,6.75,7.0,7.25,7.5,7.75,8.0,8.25,8.5]$, while varying the third parameter. Using this approach, we develop three sets of three dimensional grids, one set for constant pressures, and one set for constant electron densities, and one set for constant electron temperatures, as described below.

Pressure Models: Our pressure models are plane parallel models calculated at constant pressures of $\log(P/k)=4.0$ to $\log(P/k)=9.0$ dex in increments of 0.5 dex in $\log(P/k)$, where $P/k$ is in units of $cm^{-3}k$. This pressure represents the pressure from the mechanical energy flux produced by the stellar population by the combination of stellar winds and supernovae. The purpose of these models is to calibrate emission-line ratios as a function of ISM pressure. Therefore, we use the ISM pressure as a variable input parameter into our photoionization models rather than constraining the pressure by the mechanical luminosity of the stellar evolution models, as in Dopita et al. (2006b). Our pressure models calculate a detailed electron temperature and density structure which varies through the nebula based on the metallicity and the ionizing radiation field. The model metallicities are constrained by the stellar tracks used by the stellar evolutionary synthesis models. These tracks are based on a coarse model grid with metallicities \log({\rm O/H})+12$$=7.63,8.23,8.53,8.93,9.23. The model parameters and resulting fluxes are provided in Table 1. 2. 2.

Density Models: We calculate constant density plane parallel models with electron density $\log(n_{e}/{\rm cm^{3}})=0$ to $\log(n_{e}/{\rm cm^{3}})=5$ in increments of 0.5 dex, for the model metallicities \log({\rm O/H})+12$$=[7.63,8.23,8.53,8.93,9.23]. Like the pressure models, our density models include a changing temperature structure determined by the metallicity and by the ionizing radiation field, but they do not account for a changing density. Our density models assume a constant density throughout the nebulae. The model parameters and resulting fluxes from our density models are provided in Table 2. 3. 3.

Temperature Models: We calculate single model atoms for the density-sensitive species by fixing the electron density ($\log(n_{e}/{\rm cm^{3}})=0$ to $\log(n_{e}/{\rm cm^{3}})=5$ in increments of 0.5 dex). For each electron density, we calculate a model for each electron temperature from $\log(T_{e}/K)=0$ to $\log(T_{e}/K)=5$ in increments of 0.5 dex. This approach is different to our Pressure and Density models where temperature structure is an output of the model. The electron density calibrations in Osterbrock (1989) and in the IRAF Temden task are based on such models, assuming $\log(T_{e}/K)=4$. We emphasize that these single atom fixed temperature, fixed density models do not represent the physical conditions in a nebula and they are illustrative rather than diagnostic.

Of these three sets of models, we consider our Pressure Models to be the most realistic simulations of H II regions because the sound crossing time in a typical H II region nebula is comparable with the cluster lifetime, sufficient for the pressure to equalize across the nebula. Therefore an H II region can reasonably be assumed to have a constant pressure. We use our Pressure Models to derive calibrations of ISM pressure for star-forming regions. We use our Density Models to derive calibrations of the electron density that take the temperature structure of a nebula into account. The combination of metallicity, ionization parameter, and the shape of the ionizing radiation field produces a complex temperature structure. Therefore, to isolate the effect of temperature on density-sensitive line ratios, we use our simple temperature models.

III. The effect of electron temperature

To understand the relationship between density-sensitive line ratios and metallicity or ionization parameter, it is important to understand the relationship between emission-line fluxes and the electron temperature within the line-emitting zone for the atomic species being considered. The electron temperature is sensitive to the metallicity of the gas because metals act as coolants for the nebula. Therefore, an observed relationship between a line ratio of the same species and metallicity can often be traced to the temperature sensitivity of the emission-lines.

III.1. Electron temperature and collisional excitation

In this paper, we utilize many collisionally-excited lines. The collisional excitation rate per unit volume ($R_{ij}$ in cm${}^{3}{\rm s}^{-1}$) from energy level i to energy level j is given by

[TABLE]

where $n_{e}$ is the electron density per unit volume and $N_{i}$ is the electron density in the lower level. The collisional coefficient $\alpha_{ij}$ depends on the temperature, $T$, of the gas through an exponential thermal excitation term ($e^{\frac{-E_{ij}}{kT}}$) and a power law term ($T^{-1/2}$), i.e.

[TABLE]

where $\Omega_{ij}$ is the collision strength for the transition from level i to level j, $g_{i}$ is the statistical weight of level i, and $E_{ij}$ is the energy difference between levels i and j. The relative importance of each of the two temperature terms governs whether a line ratio pair is sensitive to the electron density of the gas.

The upper energy level can be depopulated by collisional de-excitation or by radiation. The radiative depopulation rate is given by

[TABLE]

where $A_{ji}$ is the spontaneous transition probability and $N_{j}$ is the number of electrons in the upper energy level.

The collisional de-excitation rate is given by

[TABLE]

where $\Omega_{ji}$ is the collision strength for the transition from level j to level i, and $g_{j}$ is the statistical weight of level j. The collision strength $\Omega_{ji}$ has a residual dependence on temperature that becomes important for the mid-IR fine structure lines.

The critical density is a useful parameter when considering the emission-line strengths from H II regions. The critical density is defined as the density where the collisional de-excitation probability equals the radiative de-excitation probability for the excited state.

III.2. Density-sensitive line ratios and electron temperature

The most commonly used density diagnostics are the optical line ratios of [S ii] and [O ii]. However, there are many potential choices for emission line pairs that can be density diagnostics. We use our simple temperature models as a guide to determine (a) which ratios may be used as density diagnostics, (b) the range of electron densities over which the ratios are useful, and (c) their dependence on the electron temperature. Table 3 gives the line ratios considered here, their ionization potentials, and the range over which each ratio can be used as a reliable density or ISM pressure diagnostic.

There are three different scenarios where useful nebula density diagnostic line pair ratios might be expected:

Case 1: The flux ratio of two forbidden lines of the same atom where both lines have low radiative transition probabilities, $A_{ji}$ (s*-1*), giving rise to critical densities that are also low. Here, the radiative transition probability $A_{ji}$ is small, and is comparable to the collisional de-excitation rate at low densities (where forbidden transitions occur). In this case, the line fluxes depend on $n_{e}^{2}$ at low density and on $n_{e}$ at high density, giving a double exponential shaped curve for the line ratios between these two limits. In this scenario, the two atomic transitions arise from closely spaced upper energy levels, where the energy difference between these closely spaced levels is small compared to their energies above the ground state. The thermal excitation term $\exp(E_{ij}/kT)$ (i.e. the exponential term in equation 2) is similar for the two lines. Therefore, the two energy levels are populated by a similar number of electrons at a given temperature, reducing the temperature sensitivity of the line ratio. In this case, the de-excitation rate is only dependent on $T^{-1/2}$ from the Maxwell-Boltzmann electron velocity distribution, and the radiative depopulation rate is constant ($A_{ji}$ s*-1*).

Figure 1 gives examples of how Case 1 line ratios depend on electron density and temperature, using our Temperature Models. All line ratios show the typical double exponential shaped curve, with a strong dependence on electron density. The line ratios typically vary by 1 to 1.5 dex with electron density, and can probe different density regimes. Each line ratio has a unique dependence on temperature (shown as coloured curves in Figure 1). Multi-level effects cause the low density limit to be sensitive to the electron temperature for the majority of these line ratios (with the exception of the [O II] ratio). Varying the temperature from $\log({\rm T_{e}})=3.5$ to $\log({\rm T_{e}})=4.5$ causes a small change ($<0.15$ dex) change in the line ratios between the low and high density limits.

The high excitation species such as [Ar IV] and [Ne IV] are particularly sensitive to the electron temperature, and these lines typically arise from high excitation sources such as WR stars or AGN. The presence of an AGN would need to be ruled out prior to the use of these lines as pressure or density diagnostics because our diagnostics assume a stellar ionizing radiation field only.

The N i ratio shows a different dependence on electron density and temperature to the other Case 1 line ratios, and is only a weak function of electron density. Unfortunately, the [N I] ratio suffers from additional collisions between the two upper energy levels, as well as transitions from higher energy levels, reducing the sensitivity of this line ratio to the electron density.

Case 2: The flux ratio of one line with a small radiative transition probability $A_{ji}$ and one line with a large radiative transition probability from the same atom. The line with a small radiative transition probability will be weak, with a low critical density, and will be predominantly collisionally de-excited. For this line, the line flux will be proportional to $n_{e}$. The line with a large radiative transition probability will be strong, with a high critical density. For ISM densities less than this high critical density, this stronger line will be produced predominantly by radiative de-excitation, and the line flux will be proportional to $n_{e}^{2}$. The ratio of these two lines produces a low density limit, but the flux ratio at the high density limit is extremely sensitive to the electron temperature. The ratio of forbidden lines to intercombination lines show this type of behaviour. These ratios can be used to measure electron density wherever the forbidden line is detectable.

More accurate densities will be achieved when the electron temperature has been constrained prior to or in conjunction with the application of these density diagnostics. In Nicholls et al. (in prep), we present electron temperature diagnostics for temperature-sensitive line ratios in the UV. We note that the electron temperature is different for different regions of the nebula. Therefore, the electron temperature should be estimated in the zone where the density-sensitive lines are produced.

In Figure 2, we give examples of emission-line ratios that are produced via Scenario 2. The low excitation species [Al II], Si III], and C III] are produced at densities of typical H II regions, while the higher excitation species ([N IV] and [O V]) can be produced in the ISM surrounding WR stars or an AGN.

Case 3: The flux ratio of two low energy infrared lines for which the temperature term $\exp(-E_{ij}$/kT) $\sim$ 1 (i.e. $E_{ij}<<kT$). Both collisional excitation and de-excitation are then dominated by the $T^{-1/2}$ term in equations 2 and 4. This gives only a very weak dependence on temperature except in the low density limit, and therefore these line ratios are ideal tracers of the electron density of the gas. The triplet fine structure levels in many ions satisfy this criteria, with low critical densities similar to densities in H ii regions. The disadvantage of these line ratios is that the energy levels differ significantly, producing lines that are separated in wavelength by a few tens to hundreds of microns. IR satellites with a large wavelength coverage are often required to reliably measure these line ratios to avoid errors from aperture effects and relative flux calibration issues. In Figure 3, we give the relationship between the IR line ratios [N ii], [O iii] and [S iii] and electron density, as a function of temperature. In the low density limit, the line ratios are an extremely strong function of temperature. The dashed lines in Figure 3 indicate the regime over which the line ratios can be used to reliably estimate the electron density. The IR line ratios each cover a relatively small, but complementary range of electron densities. Together, these three line ratios can probe the range of electron densities seen in most H II regions and galaxies.

IV. Measuring the ISM Pressure and Density

Recent integral field spectroscopic studies of local H II regions show that the gas within H II regions spans a range of temperatures, with electron temperature gradients (Zahid et al. 2017, in prep) and/or fluctuations (see Stasińska, 2002, for a review). Assuming a constant temperature becomes particularly problematic when fixed-size apertures capture the light from an ensemble of H II regions. Nuclear or global fiber-based or slit-based spectra of nearby or distant galaxies represent the luminosity-weighted average of multiple (up to hundreds or thousands) of H II regions, each of which may contain a complex electron temperature structure. In these cases, it is unclear what an electron density that assumes a fixed electron temperature means for the ensemble.

Electron temperature gradients also exist in spiral galaxies (Quireza et al., 2006). The electron temperature is extremely sensitive to the metallicity of the gas. Disk galaxies often have steep metallicity gradients that cause a radial variation in the electron temperature (see e.g., Shields, 1990, for a review). However, not all galaxies have strong metallicity gradients. Many barred spiral galaxies have weaker metallicity gradients than spirals of similar type (e.g., Pagel et al., 1979; Roy & Walsh, 1997), and mergers and irregular galaxies have flat gradients compared with isolated spiral galaxies (e.g., Kewley et al., 2010; Rupke et al., 2010b; Rich et al., 2012). These results suggest that radial gas flows suppress or mix metallicity gradients (e.g., Roberts et al., 1979; Martin & Roy, 1994; Roy & Walsh, 1997; Rupke et al., 2010a; Torrey et al., 2012). A constant temperature might be a reasonable assumption in some of these cases.

IV.1. Theoretical density and temperature distributions

The optical density-sensitive line ratios have traditionally been calibrated assuming a simple model atom and a single electron temperature (typically $T_{e}=10^{4}$ K) (e.g., De Robertis et al., 1987; Osterbrock, 1989; Rubin et al., 1994; Shaw & Dufour, 1995). More recently, calibrations have been based on photoionization models, which assume a constant temperature throughout the photoionized nebula (e.g., Proxauf et al., 2014, and references therein). Our models take into account all available atomic levels, rather than simple model level atoms, and our pressure models allow the electron temperature and electron density to vary through the nebula.

Figure 4 shows how the electron temperature and density vary through the nebula for our pressure models for a variety of pressure, ionization parameters (different panels), and metallicity (coloured curves). The electron temperature and density vary with distance through the nebula, and only reflect isothermal or constant electron density conditions for some metallicities (usually, but not always, \log({\rm O/H})+12$$\sim 8.23). At metallicities at or above \log({\rm O/H})+12$$\sim 8.5, the nebula becomes hotter towards the outer edges. The cause of this heating is twofold; (1) in the outer zones, the soft ionizing photons have already been absorbed by metals closer to the ionising source, leaving predominantly hard ionising photons, yielding more heat per ionisation, and (2) the dominant coolant, [O III], dominates the cooling in the inner nebula zone, but is not a significant coolant in the outer edge of the nebula. A metal-rich nebula absorbs more soft ionizing photons, as well as cooling more strongly in the inner nebula, causing a larger temperature difference between the inner zone and the outer edge of the nebula.

IV.2. UV Pressure and Density Diagnostics

The UV contains relatively few ISM pressure diagnostics. Some pressure-sensitive lines (such as the [C II] complex at 2326Å and the N III] complex at $1746-1753$Å) are strongly blended and do not have useful diagnostic capability with modern instruments. Three of the five [C II] lines between 2323Å and 2329Å are separated by 1Å or less. The [C II] lines may also be blended with Fe II at 2327Å and Si II at 2329Å, depending on the metallicity of the gas. Similarly, three of the five N III] lines between 1746Å and 1756Å are also separated by 1Å or less.

The [O V] and [S V] emission-lines shown in Figure 2 are not produced in our pressure models for star-forming regions at detectable levels (i.e. with fluxes $>1\times 10^{-5}$ H$\beta$). If the [O V] and [S V] lines are observed in a spectrum, an AGN or shocks are likely to be present in the galaxy. In this Section, we provide UV pressure and density diagnostics for sets of emission-lines that are currently available, or are likely to be available in the near future.

IV.3. The [Si III],Si III] ratio

The [Si III] $\lambda 1883$ and Si III] $\lambda 1892$ lines are produced by the ${}^{1}S_{0}\rightarrow{}^{3}P_{2}$ and ${}^{1}S_{0}\rightarrow{}^{3}P_{1}$ transitions, respectively. The [Si III] $\lambda 1883$/Si III] $\lambda 1892$ ratio probes high density, high pressure regions of the nebula ($\log({\rm P/k})>7.5$). Dufton et al. (1984) first proposed these Si III lines as density diagnostics. This ratio has been used to derive electron densities in planetary nebulae (Dufton et al., 1984; Clegg et al., 1987), and more recently to derive the electron density in the gas around quasars (Negrete et al., 2012).

Figure 5 indicates how the [Si III]/Si III] ratio depends on ISM pressure, metallicity, and ionization parameter. The [Si III]/Si III] ratio is extremely sensitive to the ISM pressure in the high pressure regime, varying by over an order of magnitude between $7.5<\log({\rm P/k})<9.0$. For the same [Si III]/Si III] ratio, the estimated ISM pressure can vary by up to $\sim 1$ dex when the metallicity is changed from \log({\rm O/H})+12$$=7.63 to \log({\rm O/H})+12$$=9.23. The estimated pressure also has a minor dependence on ionization parameter ($\sim 0.2$ dex). Both of our ISM pressure and density calibrations are only valid for [Si III]/Si III] ratios below [Si III]/Si III]$<1.4$, above which the [Si III]/Si III] ratio saturates (called the low density limit).

IV.4. The [C III],C III] ratio

The [C III] $\lambda 1907$/C III] $\lambda 1909$ ratio was first proposed as a density diagnostic by Nussbaumer & Schild (1979). Revised density calibrations were calculated by Keenan et al. (1992). The [C III] $\lambda 1907$ and C III] $\lambda 1909$ lines are based on the ${}^{1}S_{0}\rightarrow{}^{3}P^{o}_{1}$ and the ${}^{1}S_{0}\rightarrow{}^{3}P^{o}_{2}$ transitions, respectively. The C III] $\lambda 1909$ line is an intercombination line, while the weaker [C III] $\lambda 1907$ line is forbidden. There is a large difference in lifetimes for these transitions, producing a large difference in critical densities and therefore the ratio is extremely sensitive to the electron density of the gas.

Figure 6 shows how the [C III]/C III] ratio depends on ISM pressure (left panel) and electron density (right panel) as a function of metallicity and ionization parameter. The [C III]/C III] lines probe the high density, high pressure regions of a nebula ($\log({\rm P/k})>7.5$). In this high pressure regime, the [C III]/C III] ratio is an extremely sensitive function of pressure or density, with the [C III]/C III] ratio changing by almost an order of magnitude between $7.5<\log({\rm P/k})<9.0$. At lower pressures ($\log({\rm P/k})<7.5$), the [C III]/C III] ratio is primarily sensitive to the metallicity. Like Si III], for the same [C III]/C III]  ratio, the estimated ISM pressure can vary by up to $\sim 1$ dex when the metallicity is changed from \log({\rm O/H})+12$$=7.63 to \log({\rm O/H})+12$$=9.23. The estimated pressure also has a minor dependence on ionization parameter ($\sim 0.2$ dex). The metallicity dependence is primarily caused by the fact that the C*++* transitions depend on the electron temperature of the gas through their recombination coefficients.

The [C III]/C III] ratio is a sensitive electron density diagnostic for dense environments ($\log(n_{e})>3.5$), where the electron density is uniform throughout the nebula. Metallicity variations may introduce a scatter in the estimated density of up to 0.3 dex. For [C III]/C III] ratios $>1.4$, the [C III]/C III] ratio is in its low density limit, where every collisional excitation is followed by the emission of a photon. In this regime, the [C III]/C III] ratio is not a useful pressure or density indicator.

IV.5. The [Al II] , Al II] ratio

The [Al II] $\lambda 2660$ and Al II] $\lambda 2669$ lines are produced by the ${}^{3}P^{0}_{2}\rightarrow{}^{1}S_{0}$ and ${}^{3}P^{0}_{0}\rightarrow{}^{1}S_{0}$ transitions. The Al II] $\lambda 2669$ intercombination line was first predicted by Aller (1961), and subsequently observed in planetary nebulae (Gurzadian, 1975). The [Al II] $\lambda 2660$ transition produces a forbidden line, which has been observed in nearby H II regions (Park et al., 2010).

In Figure 7 we show that the relationship between the Al II ratio and pressure is a sensitive function of metallicity, with a secondary dependence on ionization parameter ($<0.1$ dex). The Al II ratio is useful in probing the high pressure regime, varying by over an order of magnitude between $7.0<\log({\rm P/k})<9.0$. Both of our ISM pressure and density calibrations are only valid for Al II ratios below [Al II]$/$Al II]$<1.44$, above which the Al II ratio is in its low density limit. The value at which the Al II ratio enters the low density limit depends on metallicity, as a result of the electron temperature dependence for Case 2 flux ratios.

IV.6. The high-ionization [Ne IV] and [N IV],N IV] ratios

Two high ionization UV line ratios are produced by our stellar photoionization models. These ratios probe the highest pressure regions of a nebula ($\log(P/k)>8.0$ dex), providing a set of complementary diagnostics to the C III] and [Al II] lines, which probe lower pressure regions of a nebula.

The [Ne IV] $\lambda 2425$/[Ne IV] $\lambda 2423$ ratio is produced by the ${}^{2}D^{0}_{3/2}\rightarrow{}^{4}S^{0}_{3/2}$ and the ${}^{2}D^{0}_{5/2}\rightarrow{}^{4}S^{0}_{3/2}$transitions. The [Ne IV] lines are only produced at detectable levels (i.e. $1\times 10^{-5}$H$\beta$) for the lowest metallicity, highest ionization parameter models (i.e. \log({\rm O/H})+12$$\leq 7.63 and $\log(q)\geq 7.75$ dex), as shown in Figure 8.

The [N IV] $\lambda 1483$/N IV] $\lambda 1486$ ratio is produced by the ${}^{3}P^{0}_{2}\rightarrow{}^{1}S_{0}$ and the ${}^{2}P^{o}_{1}\rightarrow{}^{1}S_{0}$ transitions. The [N IV] and N IV] lines are produced at detectable levels in our high temperature (i.e. low metallicity), high ionization parameter models (i.e. \log({\rm O/H})+12$$\leq 8.93 and $\log(q)\geq 7.5$ dex; Figure 9).

Both ratios probe the highest pressure regions of a nebula, and are most commonly observed in regions surrounding AGN, or in gas associated with shocks. The presence of an AGN or shocks must be ruled out prior to applying our Ne IV and N V calibrations.

IV.7. Optical Pressure and Density Diagnostics

There are a large number of ISM pressure diagnostics in the optical. Many of these diagnostic lines are weak relative to H$\beta$ and require deep, high S/N spectra to observe. Here, we calibrate the traditional electron density diagnostic lines [S II] and [O II] with ISM pressure, in addition to the weak optical lines.

IV.7.1 The [O II] ratio

The [O II] $\lambda 3729/$[O II] $\lambda 3726$ ratio has been used for several decades to determine the electron density of the gas in planetary nebulae, H II regions, and galaxies (see e.g., Pradhan et al., 2006, and references therein). This doublet is produced by the ${}^{2}{\rm D}^{0}_{3/2}\rightarrow{}^{4}{\rm S}^{0}_{3/2}$ and ${}^{2}{\rm D}^{0}_{5/2}\rightarrow{}^{4}{\rm S}^{0}_{3/2}$ transitions. At temperatures typical of H II regions ($T_{e}=1-2\times 10^{4}$ K), the difference in excitation potential between the two upper D levels and the lower S level is $\sim kT$ and therefore the [O II] transitions are sensitive to the collisional excitation and de-excitation rates, which depend critically on the ISM pressure (or electron density) of the gas.

The [O II] lines have similar ionization potentials to Hydrogen, and are readily observable in optical spectra of H II regions and galaxies, although the close proximity of the two lines requires high resolution spectroscopy to resolve the doublet. The [O II] doublet is observable in the optical to $z\sim 1.5$ and is available in the near-infrared (K-band) to $z\sim 5$, and is used to measure the electron density in increasing numbers of galaxies at high redshift (e.g., Kaasinen et al., 2016).

In Figure 10, we show how the [O II] ratio varies with ISM pressure and electron density, for the metallicities and ionization parameters covered by our models. The relationship between the [O II] doublet and ISM pressure depends on metallicity (up to 0.4 dex), and there is a secondary dependence on ionization parameter which becomes largest (up to 0.2 dex) at the highest metallicities (\log({\rm O/H})+12$$>8.9).

The [O II] ratio can be used to determine the electron density, with errors of up to 0.4 dex due to the residual dependence of the [O II] ratio on the electron temperature. Recall that the electron temperature is sensitive to the metallicity of the nebula. Therefore, a nebula with the same electron density can give rise to different [O II] ratios, depending on the metallicity of the gas. For electron densities more accurate than 0.4 dex, the metallicity should be calculated using consistent strong line calibrations to determine which [O II]-density calibration should be applied.

The [O II] electron density relation from Osterbrock (1989) (thick solid black line) is shown for comparison in Figure 10. The Osterbrock [O II] relation has a different shape to our calibration because the atomic datasets for oxygen have changed substantially over the past two decades (Proxauf et al., 2014).

IV.7.2 The [Ar IV] ratio

The [Ar IV] $\lambda 4711,40$ doublet is weak ($\sim 1\times 10^{-4}\times$H$\beta$) for ionization parameters and metallicities typical of star-forming galaxies. The [Ar IV] lines are produced by the ${}^{2}D^{0}_{5/2}\rightarrow{}^{4}S^{0}_{3/2}$ and ${}^{2}D^{0}_{3/2}\rightarrow{}^{4}S^{0}_{3/2}$ transitions. The relationship between [Ar IV] and electron density was first calibrated theoretically by Stanghellini & Kaler (1989), and updated by Proxauf et al. (2014). The observed relationship between [Ar IV] and electron density has been investigated primarily for planetary nebulae (e.g., Meatheringham & Dopita, 1991; Copetti & Writzl, 2002; Wang et al., 2004, and references therein).

The [Ar IV] lines are produced in thin hot regions of the nebula that are optically thin to UV photons because the ionization potential of the [Ar IV] ratio is large (40.73 eV). Therefore, the [Ar IV] ratio traces a similar ionization zone to the Auroral [O III]$~{}\lambda 4363$ line, and can be used to probe the ISM pressure where the [O III]$~{}\lambda 4363$ Auroral line is produced. However, care must be taken when measuring the [Ar IV] ratio because the [Ar IV] $\lambda 4711$ line is very close to the He I $\lambda 4713$ emission-line and may be blended.

Figure 11 (left) confirms that the [Ar IV] ratio traces the ISM pressure in the high ionization zone close to the stellar ionizing sources, and is sensitive to pressures above $\log({P/k})>7$. This ratio is less affected by collisional de-excitation than the other optical pressure-sensitive lines, and is less sensitive to ionization parameter variations (ionization parameter causes the ISM pressure to vary within 0.2 dex for this ratio).

The [Ar IV] ratio is a highly sensitive density diagnostic for nebulae with constant electron density; the variation of [Ar IV] with electron temperature (or metallicity) is less than 0.2 dex, and the ratio changes by an order of magnitude between $3<\log(n_{e})<5$.

IV.7.3 The [N I] ratio

The [N I] $\lambda 5198$/ [N I] $\lambda 5200$ ratio is a result of the ${}^{2}D^{0}_{3/2}\rightarrow{}^{4}S^{0}_{3/2}$ and ${}^{2}D^{0}_{5/2}\rightarrow{}^{4}S^{0}_{3/2}$ transitions, respectively. This ratio probes the conditions in the outer edges of nebulae where Hydrogen is partially ionized. The [N I] ratio was first calibrated as a density diagnostic by Dopita et al. (1976). The [N I] $\lambda 5198,5200$ doublet is weak ($\sim 1\times 10^{-4}\times$H$\beta$) for ionization parameters and metallicities typical of star-forming galaxies, and has been traditionally measured in planetary nebulae (e.g., Lee & Hyung, 2013). However, with high resolution, high S/N spectroscopy, it is possible to observe this ratio in H II regions (e.g., Esteban et al., 1999), allowing one to probe the H II region outer recombination zones at the interface between H I and H II regions.

Figure 12 (left) shows how the [N I] ratio depends on ISM pressure as a function of metallicity and ionization parameter. There is relatively little dependence on metallicity and ionization parameter for \log({\rm O/H})+12$$<8.5 (with differences within $\pm 0.2$ dex). However, at higher metallicities (\log({\rm O/H})+12$$>8.5), there is a stronger dependence on metallicity and ionization parameter (up to 0.1 and 0.04 dex, respectively). This behaviour is primarily due to collisional effects between the upper levels in the pair, as well as transitions from higher levels.

Figure 12 (right) shows how the [N I] ratio depends on the electron density as a function of metallicity and ionization parameter. While the effect of ionization parameter is minimal ($<0.1$ dex), there is a bimodal dependence on the metallicity, with one curve for low metallicity (\log({\rm O/H})+12$$<8.5), and different curves for high metallicity (\log({\rm O/H})+12$$>8.5). The saturation at the low density limit occurs at different [N I] ratios due to multi-level effects and depends on the electron temperature and metallicity.

IV.7.4 The [Cl III] ratio

The [Cl III] $\lambda 5517/$[Cl III] $\lambda 5537$ ratio is produced by the ${}^{2}D^{0}_{5/2}\rightarrow{}^{4}S^{0}_{3/2}$ and ${}^{2}D^{0}_{3/2}\rightarrow{}^{4}S^{0}_{3/2}$ transitions and traces high pressure regimes ($\log({P/k})>7$). The potential use of [Cl III] as a density diagnostic was first identified by Weedman (1968). The first calibration of the [Cl III] ratio in terms of electron density was made by Aller et al. (1970), with subsequent revisions by Saraph & Seaton (1970) and Keenan et al. (1992). The [Cl III] ratio has primarily been used to measure the electron density in planetary nebulae (e.g., Dopita & Gibbons, 1975; Kaler, 1978; Stanghellini & Kaler, 1989).

Figure 13 shows how the [Cl III] ratio is related to the ISM pressure and electron density. The relationship between the [Cl III] ratio and pressure is primarily sensitive to metallicity, with only minor dependence on the ionization parameter of the gas ($\Delta\log({\rm P/k})\lesssim 0.3$ dex).

Like [Ar IV], the [Cl III] ratio is a highly sensitive density diagnostic, with variations $<0.1$ dex due to metallicity for all but the highest metallicities (\log({\rm O/H})+12$$>9.2), where the variation with metallicity is $\sim 0.2$ dex.

IV.7.5 The [S II] ratio

The [S II] $\lambda 6731$/[S II] $\lambda 6717$ ratio is produced by the transitions ${}^{2}D^{0}_{5/2}\rightarrow^{4}S^{0}_{3/2}$ and ${}^{2}D^{0}_{3/2}\rightarrow^{4}S^{0}_{3/2}$. The [S II] lines have similar ionization potentials to Hydrogen, and are readily observable in optical spectra of H II regions and galaxies.

The theoretical relationship between the [S II] ratio and ISM pressure depends primarily on the metallicity, with a secondary effect from ionization parameter at metallicities above \log({\rm O/H})+12$$>8.9 (Figure 14, left panel). The [S II] ratio can be used to calculate the ISM pressure up to the [S II] critical density of $\sim 3\times 10^{3}{\rm cm}^{-3}$, above which the lines are collisionally de-excited.

The relationship between the [S II] ratio and electron density (Figure 14, right panel) has a smaller, but still important dependence on metallicity. The metallicity can change the [S II] density estimate by up to 0.4 dex. This metallicity dependence should be taken into account when comparing the electron density of H II regions or galaxies where the metallicity is likely to be different, particularly when comparing electron densities derived in galaxies at different redshifts.

The [S II] electron density relation from Osterbrock (1989) (thick solid black line) is shown for comparison in Figure 14. The Osterbrock [S II] relation is consistent with our calibration, and agrees with our \log({\rm O/H})+12$$\sim 8.93 curves, except in the high density limit, where the Osterbock relation more closely correlates with our \log({\rm O/H})+12$$\sim 9.23 curves.

IV.8. Infrared Pressure and Density Diagnostics

The infrared fine structure lines were first used to measure the electron density in planetary nebulae over a decade ago (e.g., Liu et al., 2001). These lines are now accessible in local H II regions and galaxies, thanks to the Spitzer and Herschel satellites (Stacey et al., 1991; Malhotra et al., 2001; Luhman et al., 2003; Brauher et al., 2008; Fischer et al., 2010). Infrared and sub-millimeter instruments now allow the strong infrared fine structure lines to be detected in high-redshift galaxies, probing the ISM conditions over the past 12 billion years (Maiolino et al., 2005, 2009; Ferkinhoff et al., 2010; Sturm et al., 2010; Stacey et al., 2010; Ivison et al., 2010; Ferkinhoff et al., 2011; Valtchanov et al., 2011; Spinoglio et al., 2015). Here, we calibrate the [S III] 18 and 33$\mu$m, [O III] 88 and $52\mu$m, and [N II] $122\mu$m and $205\mu$m lines for pressure and density. These lines trace a broad range of ISM pressures and densities, providing a complementary suite of diagnostics that can be used to build a comprehensive picture of the pressure or density structure of the ionized gas at a given redshift.

IV.8.1 The [S III] ratio

The [S III] $33\mu$m/[S III] $18\mu$m ratio is readily observable in the rest-frame infrared spectrum. The [S III] ratio is produced by the ${}^{3}P_{1}\rightarrow^{3}P_{0}$ and ${}^{3}P_{2}\rightarrow^{3}P_{1}$ transitions and traces the high ionization, high pressure regions of a nebula ($7<\log({\rm P/k})<8$) as shown in Figure 15.

For all pressures between $6<\log({\rm P/k})<8$, the metallicity dependence is strong (up to an order of magnitude in $\log({\rm P/k})$ across the full metallicity range of our models). The dependence on ionization parameter is only important in the most metal-rich nebulae (\log({\rm O/H})+12$$>9.2). At low pressures, the saturation value depends strongly on the metallicity, with a strong dependence on the ionization parameter at the lowest metallicities (\log({\rm O/H})+12$$<8.0) due to multi-level effects.

Figure 15 indicates that the infrared [S III] ratio is a sensitive diagnostic of the electron density for high density environments ($2.5<\log(\frac{n_{e}}{cm^{3}})<4$). In this regime, there is no residual dependence on metallicity or ionization parameter. However, below $\log(\frac{n_{e}}{cm^{3}})<2.5$, the [S III] ratio is much more sensitive to metallicity than the electron density, and the saturation value is also metallicity dependent.

IV.8.2 The [O III] ratio

The Herschel Observatory has allowed the [O III] $88\mu$m/[O III] $52\mu$m ratio to be measured for increasing numbers of star-forming galaxies in the local universe, and is now also possible to observe the [O III] lines in galaxies at high redshift (Ferkinhoff et al., 2010). These lines probe H II regions with densities up to $300\,{\rm cm}^{-3}$, and are produced by the transitions ${}^{3}P_{2}\rightarrow^{3}P_{1}$ and ${}^{3}P_{1}\rightarrow^{3}P_{0}$.

The [O III] ratio is strongly affected by metallicity, with the [O III]-pressure calibration varying by up to an order of magnitude in $\log({\rm P/k})$ from \log({\rm O/H})+12$$=7.6 to \log({\rm O/H})+12$$=9.23 (Figure 16, left panel). The dependence on ionization parameter is $\sim 0.2$ dex for metallicities \log({\rm O/H})+12$$<8.9, rising to 0.5 dex above \log({\rm O/H})+12$$>8.9. At low pressures, the [O III] ratio saturation value depends on the metallicity. As for [S III], the stronger metallicity (i.e. temperature) sensitivity at low density is due to multi-level effects.

The relationship between the [O III] ratio and electron density is largely independent of metallicity (to within 0.1 dex) except in the most metal-rich galaxies (\log({\rm O/H})+12$$>9.2) where there is a 0.2 dex offset from the [O III]-electron density relationship. Therefore, the [O III] ratio is a robust indicator of the electron density for electron densities $>100$ cm*-3*, below which the [O III] ratio enters the low density limit.

IV.8.3 The [N II] ratio

The infrared fine structure lines of [N II] $205\mu$m and [N II] $122\mu$m are produced by the ${}^{3}P_{1}\rightarrow^{3}P_{0}$ and the ${}^{3}P_{2}\rightarrow^{3}P_{1}$ transitions. These lines have a low ionization potential (14.5 eV) and are produced within H II regions around late O-type and early B-type stars. They are sensitive to the low to intermediate pressure regime ($4<\log({\rm P}/k)<6.5$), providing a complementary diagnostic to the IR [S III] and [O III] ratios. With Herschel, the [N II] ratio provides estimates of the electron density in both galaxies (Zhao et al., 2016; Herrera-Camus et al., 2016) and H II regions (Goldsmith et al., 2015). Sub-mm observations now allow the [N II] lines to be detected in high redshift galaxies (Ferkinhoff et al., 2011; Decarli et al., 2012; Ferkinhoff et al., 2015).

Figure 17 shows that the [N II]  ratio is extremely sensitive to the ISM pressure, varying by $\sim 1.5$ orders of magnitude across the pressures probed by our models. The [N II] ratio is also sensitive to the gas-phase metallicity. The ISM pressure can vary with metallicity by up to $\sim 1.5$ dex for $\log({\rm P}/k)<5$), depending on the ionization parameter. The [N II] ratio remains sensitive to both the ISM pressure and metallicity even at the lowest pressures ($\log({\rm P}/k)<4$). Therefore, the [N II] ratio can provide a powerful probe of the ISM pressure across a broad range of potential pressures, provided that the gas-phase metallicity is known. For the most metal-rich H II regions and galaxies (\log({\rm O/H})+12$$>9.0), the ISM pressure calibration also depends on the ionization parameter of the gas ($\pm 0.2$ dex) and calculation of the ISM pressure should include the effect of ionization parameter as well as metallicity.

The [N II] ratio is a robust diagnostic of the electron density for a large range of possible electron densities ($1<\log({\rm P}/k)<2.5$). The [N II] ratio can also potentially be used to calculate the electron density in low density regimes ($\log({\rm P}/k)<1$), providing the electron density can be corrected for metallicity.

V. Discussion

Several important issues affect the ISM pressure or electron density derived from the spectra of H II regions or galaxies. Different species and ionization states of elements will produce different ISM pressure or density estimates, and should not be directly compared unless it is clear that the different species are probing the same zones within the ionized nebula. The ionization and density structure of the nebula may lead to different species probing different regions of gas within an H II region. The atomic data used to calculate the line ratio calibrations can also cause intrinsic offsets among ISM pressures or densities of different species, even if those species probe the same regions within a nebula. In addition, some density-sensitive lines may be contaminated by emission from the diffuse ionized gas, or from shock excitation. We discuss each of these issues below.

V.1. Density Structure

H II regions have extremely complex density structures. H II regions can trigger the formation of new stars through “collect and collapse” (Elmegreen et al., 1995) and “radiation-driven implosion” (Bertoldi, 1989). In the “collect and collapse” model proposed by Elmegreen et al., the expansion of an H II region into a supersonically turbulent cloud causes coagulation of clumps which are gravitationally unstable. These unstable clumps can then collapse and form new stars. In the radiation-driven implosion scenario, hot stars penetrate the ISM and heat the cold low-density gas. This heating amplifies overdensities created by the turbulent ISM, which can then collapse and form stars (Gritschneder et al., 2009; Dale et al., 2012). These processes can create globules of dense gas (e.g., Tremblin et al., 2013; Walch et al., 2015; Schneider et al., 2016), while stellar winds can drive outflows that create horse-shoe or other complex geometries (Park et al., 2010).

Ionized gas or radio continuum density measurements within H II regions show many complex radial gradients (Franco et al., 2000; Pérez et al., 2001; Binette et al., 2002; Phillips, 2007; Herrera-Camus et al., 2016) and in some cases little to no gradient (Ramos-Larios et al., 2010; García-Benito et al., 2010). The density gradients in H II regions are related to H II region size. Ultracompact H II regions often show steep density gradients (de Pree et al., 1995; Franco et al., 2000; Kurtz, 2002; Johnson & Kobulnicky, 2003; Phillips, 2007), while larger H II regions typically have more shallow or flat density gradients (Phillips, 2008). Density gradients can be approximated by $n\propto r^{-\beta}$ where $n$ is the density and $r$ is the distance of the gas from the central stellar source. Franco et al. (2000) found steep gradients in three ultra-compact H II regions with exponents $1.6<\beta<2.4$. On the other hand, in normal Galactic H II regions, large-scale density gradients appear to be relatively modest. Phillips (2008) found that $\beta\leq 1$ and that density variations are small ($\Delta n\sim 10^{2}{\rm cm}^{-3}$ on average).

The density structure of nearby Seyfert galaxies has recently been measured by Spinoglio et al. (2015) using Herschel data. They find an anti-correlation of the electron temperature with the gas density, and they find significant density stratification within the galaxies. On average, electron densities increase with the ionization potential of the ions. In a clumpy nebula with high density gas clumps, the clumps are likely to be unresolved with standard integral field or integrated spectroscopy. A clumpy ISM has also been observed in high redshift galaxies (Carniani et al., 2017).

Where density gradients or complex density structures are expected, we recommend the use of constant pressure diagnostics rather than constant density diagnostics. Our pressure models allow a unique density to be calculated at each step through a nebula, and can produce density gradients or other profiles. If our constant density diagnostics are applied to H II regions or galaxies that contain density gradients or clumps, the density derived will likely be dominated by the regions that produce the largest emission-line strengths, and will not necessarily represent an average electron density for the nebulae.

Emission-lines produced by different ions and different energy levels are sensitive to different density regimes, depending on the critical density of the transition. Lines with low critical densities, like [O II] and [S II], are affected by collisional de-excitation and are therefore weak in the high density regions, while C III], [Ar IV]  trace higher density regions of a nebula. The [O III] fine structure lines have a significantly lower critical density than the [Ar IV] or the [Cl III] lines, and therefore trace lower density regions. In addition, where the density varies through a nebula, the density estimated from diagnostics from species predominantly in the outer regions of the nebula, such as the [S II] or [N I] ratios, may not give reliable estimates of the density in regions where the electron temperature has been calculated (typically the [O III] lines) (Nicholls et al., in prep). Where possible, co-spatial species should be used. In the case of [O III], the the [Cl III] density diagnostic may be a better choice, if observed.

In Figure 18, we show how the line ratios vary as a function of radius throughout a nominal spherical model with \log({\rm O/H})+12$$=8.23, $\log(q/cms^{-1})=8.0$ cm/s, and $\log({\rm P/k})=6$. The line ratios are relatively constant with radius (i.e. constant to within $\pm 0.01$ dex, until the partially ionized zone that occurs in the last $\sim 10$% of the nebula).

To test how well our density diagnostics (which have been derived using plane parallel models) could be used to map the density structure of a roughly spherical HII region using integral field observations, we use our spherical pressure models and derive the density at each radial step throughout the nebula for our nominal spherical model. This test is based on the assumption that the H II region is roughly spherical, is well resolved, that the metallicity and ionization parameter of the H II region are known, and that the H II region does not contain any additional power sources such as shocked ionizing radiation fields from supernovae or stellar winds. However, this model is useful because for a pressure of $\log({\rm P/k})=6$, the electron density is constant at $\sim 40$ cm*-3* throughout the nebula until the gas begins to recombine at the edge of the nebula. An electron density of $\sim 40$ cm*-3* is close to (but not within) the low density limit of the commonly-used [S II] and [O II] doublets, and provides a useful test of how well our models are able to reproduce the density within this regime, which is difficult to fit analytically. Figure 19 shows how well the electron diagnostics using [S II] $\lambda 6717/$[S II] $\lambda 6731$, [O II] $\lambda 3729/$[O II] $\lambda 3727$, [N I] $\lambda 5198/$[N I] $\lambda 5200$, and [N II] $205\mu$m/[N II] $122\mu$m track the electron density through the spherical nebula. The [S II] and [N II] ratios provide the best match to the true density throughout the nebula, within 3% on average. The [O II] and [N II] ratios agree with the true density to within 5% and 7% on average. We emphasize that these electron densities have been derived using plane parallel diagnostics. Spherical models have a larger partially ionized zone than plane parallel models. Lines that are produced in the partially ionized zone (such as [NI]) will give the poorest fit to the average density of the spherical model. This effect will become larger for models with high ionization parameters.

Modelling a clumpy ISM in nebulae may overcome much of these problems. Monte Carlo simulations are needed to track individual lines of sight throughout a nebula. Monte Carlo photoionization models have been developed over the past two decades (Ercolano et al., 2003, 2005, 2008; Robitaille, 2011; Lomax & Whitworth, 2016). These models successfully reproduce properties in individual star forming regions, but the physics included in these models has been constrained by computation time. For example, the models currently don’t include clumpy dust distributions, which are modeled with separate dust Monte Carlo codes which have simple photoionization calculations (e.g., Gordon et al., 2001; Steinacker et al., 2013; Gordon et al., 2017). We expect significant advances to be made in this area in the coming years.

V.2. Ionization structure

Different ionization lines of different species probe different zones of a nebula. Thus, by observing several different ionization lines of different species, we can derive a picture of the pressures within the different ionization zones of an H II region. Figure 20 shows the ionization energy and critical densities of the species considered here, where the ionization energy is the energy required to create the ion in its ground state, not the energy required to ionize the atom into a higher ionization state.

We use ionization data from NIST (Kramida et al., 2015), as given in Table 3. The uncertainties in the critical densities represent the potential variation due to electron temperature (as in our Temperature Models). The density-sensitive species in the optical and UV cover a wide range of critical densities and ionization energies.

In Figure 21, we show the MAPPINGS v5.1 ionization zones for the species considered here. The [Ne IV], [O V], [Ar IV], [N IV], and [S V] ratios ratios trace regions of high ionization. Therefore, electron densities derived for these regions will be larger than for the lower ionization lines, if the H II regions have negative density gradients.

The ionization potential of higher levels of ionization (i.e. higher than the ionization state of the ion used for our diagnostics) also play a role in defining the regions where each line is observable. For example, the ionization potential of the S I $\rightarrow$ S II transition (12.20 eV) is lower than the ionization potential of hydrogen. Therefore, the [S II] states can be readily achieved by thermal absorption of Lyman photons from hydrogen recombination or by collisional excitation. The higher ionization state [S III] requires a significantly larger energy to achieve (23.3 eV). This higher [S III] level can be achieved in regions that are optically thin to UV photons or from photons from He recombination. Therefore, the majority of the [S II] photons are likely to be produced in high pressure clumps or on the outskirts of nebulae, and not in the same zone as the [O II] lines (see e.g., Proxauf et al., 2014, for a discussion). Figure 21 highlights the fact that the [S II] lines are produced in the extended partially ionized zone of the nebula, while the [O II] lines are produced closer to the ionizing source. Therefore, the [S II] and [O II] lines should not be used interchangeably to measure the ISM pressure or density unless the density is constant across the H II regions or galaxies within the sample(s) being studied.

Low ionization species, such as [N I] can probe the pressure at the very edge of the nebula, where the H II region transitions into an H I region. Note that some additional pressure-sensitive lines such as the infrared [O I] and [C I] lines are produced partially or predominantly in the photo-dissociation region or in neutral gas, which are not tracked by our MAPPINGS v5.1 models. We refer the reader to Tielens & Hollenbach (1985) for a description of the use of photodissociation models to derive electron densities in the outer nebula zones.

Only a few sets of lines trace the same region of the nebula. The [Cl III] and [S III] lines are both produced throughout the nebula, and derived pressures may be considered as broadly representative of the overall ISM pressure within the nebula. Both the [S II] and [N I] lines trace the very outer edge of the nebula, while the high ionization species (such as [Ar IV], [S V], [Ne IV]) trace the inner zones close to the ionizing source.

The [N II] and [O II] lines trace similar regions of the nebula, and may be used to trace intermediate-zone pressures at optical and UV wavelengths, respectively. Therefore, the [N II] and [O II] lines can be used to trace or compare the ISM pressure in local and high redshift galaxies.

V.3. Atomic Data

The pressures or densities derived for different species are critically dependent on the atomic data used in the theoretical models. Different atomic datasets are available for different emission-lines, and these may introduce errors in the estimated quantities. Copetti & Writzl (2002) compared different electron density indicators in planetary nebulae and concluded that atomic data was the cause of differences in [O II] densities when compared with other indicators. In this work, we include the most recent atomic data available, but we are still constrained to the accuracy of the atomic data and the fact that this data comes from different sources for different species. We refer the reader to Proxauf et al. (2014) for a detailed comparison and discussion of atomic datasets on electron density estimates.

V.4. Metallicity Calibration Discrepancies

The electron temperature in a nebula is fundamentally linked to the gas-phase metallicity because metals act as coolants in the nebula. Therefore, many of the ISM pressure diagnostics have a strong dependence on the gas-phase metallicity. Different metallicity calibrations exhibit extremely large systematic discrepancies (up to 1 dex in $\log({\rm O/H})+12$) (see Kewley & Ellison, 2008, for a review and discussion). Due to these discrepancies, our ISM pressure calibrations should only be used with metallicity calibrations that have been constructed using consistent theoretical models (i.e with Starburst99 and MAPPINGS v5 photoionization models), such as the metallicity surface fits in Kewley et al. (ARAA, submitted), or the code NebulaBayes, which calculates the gas-phase metallicity of both star-forming and AGN regions using MAPPINGS v5 models (Thomas et al., 2018).

V.5. Diffuse Ionized Gas

The ionizing radiation produced by the star clusters is partially absorbed by the H II regions. Superbubble models suggest that the combined effects of supernovae, stellar winds, and large-scale ionization by OB associations create a complex density and ionization structure that can be porous to ionizing radiation, allowing some radiation to escape (Shields, 1990). The absorption by the H II region produces a hard ionizing radiation field incident on gas outside H II regions in the disk, as well as on gas up to several kpc above the disk. The gas that receives ionizing radiation that has leaked from nearby H II regions is referred to as Diffuse Ionized Gas (DIG).

The radiation in the DIG may come from a variety of sources. Martin (1997) showed that the DIG has a radial gradient that is consistent with the dilution of radiation from a centralized source, indicating that the dominant excitation mechanism of the DIG is photoionization by the radiation from massive stars. However, in some galaxies, 30-50% of the DIG emission may come from shock excitation (Martin, 1997; Ramirez-Ballinas & Hidalgo-Gámez, 2014), and a very minor component ($<20$% of H$\alpha$) may come from dust scattered radiation (Barnes et al., 2015; Ascasibar et al., 2016). The DIG can also be produced by evolved stars (Zhang et al., 2017). Hot evolved stars, such as post-AGB stars, are characterized by very high temperatures. Zhang et al. used photoionization models to show that high temperature evolved stars can produce a hard ionizing spectrum. By comparing their models with spatially resolved data of nearby galaxies, they conclude that hot evolved stars make a major contribution to the DIG.

The DIG has a different emission-line spectrum to star-forming regions. The escaped hard radiation field produces strong emission in low-ionization species, such as [O I], [N II], [C II], and [S II], but weak emission in high ionization species such as [O III] (see reviews by Rand, 1998; Mathis, 2000; Haffner et al., 2009). The DIG may contribute between 10-50% of the H$\alpha$ emission, but may contaminate the [N II], [S II] and other low ionization lines up to 2-3$\times$ more (Madsen et al., 2006; Oey et al., 2007; Blanc et al., 2009).

Theoretical models are needed to help remove the DIG component from spectra. Our photoionization models were calculated assuming a normal star forming source, and do not include a hard component that would be typical of the DIG. Current models can only partially reproduce the DIG line ratios (e.g., Bland-Hawthorn et al., 1997). For example, Martin (1996) used a combination of photo-ionized gas with shock-ionized gas using various shock speeds, and turbulent mixing layers of various temperatures to model the DIG in irregular galaxies. However, a fully self-consistent model of the effect of the DIG on the UV-IR emission-lines is still lacking.

Care must be taken to account for the DIG when using global spectra of galaxies, or when using integral field data where H II regions are not spatially resolved. The pressure or density derived using low ionization lines may not represent a luminosity-weighted average H II region within a galaxy. Instead, the pressure or density estimates may include a component from the pressure or density within the DIG, depending on the surface brightness of the DIG, and the sensitivity of the observations. We are currently investigating the effect of the DIG on multiple emission-line diagnostics, including our pressure and density diagnostics (Poetrodjojo et al., in prep). With such information, DIG models might allow reliable ISM pressures to be calculated for the global spectra of galaxies, taking into account possible DIG contamination.

V.6. Shock excitation

Shock excitation can be produced by many phenomena, including supernovae, stellar winds, galaxy interactions, and AGN related activity such as jets. The effect of shocks on the optical emission-lines has been observed in both interacting and isolated galaxies with high spectral resolution integral field spectroscopy (Ho et al., 2014; Rich et al., 2015; Dopita et al., 2015; Ho et al., 2016). Gas outflows and mergers can produce widespread shocks throughout galaxies which significantly affect the emission-line spectrum of a galaxy at both kpc-scales and sub-kpc scales within a galaxy (Medling et al., 2015).

Shock excitation can contaminate both low ionization line ratios and high ionization line ratios, depending on the shock velocity. Fast shocks ($v>500\,{\rm kms}^{-1}$) produce strong high ionization lines such as [O III] (Allen et al., 1998, 2008), while slow shocks produce relatively weak high ionization lines, but strong low ionization species such as [S II] and [N II] (Rich et al., 2011, 2015). This difference occurs because fast shocks produce a photoionizing precursor which produces significant ionization in front of the shock.

Shocks can be identified using a combination of morphological information, velocity maps, velocity dispersion, and emission-line ratios (see Ho et al., 2014; Yuan et al., 2012, for examples of how shocks can be identified at low and high redshift). We recommend that these tools be used to identify galaxies containing shocks prior to the application of the pressure and density diagnostics given here, because our pressure and density diagnostics have been produced using the ionizing radiation from pure stellar populations, not the harder radiation field from shocks, which changes the ionizing spectrum, and may change the electron density distribution. For example, shocked regions from galactic outflows can have higher electron densities, as seen in edge-on disk galaxies from the SAMI galaxy survey (Ho et al., 2014).

High resolution integral field spectroscopy allows the shock component to be resolved and separated from the H II region component to optical emission-line spectra by identifying emission-lines with different velocity dispersions (e.g., Ho et al. (2014), D’Agostino et al., in prep). In these cases, it is feasible to apply our pressure and density diagnostics to the H II region component of the spectra. For galaxies where shocks have been identified, but the shock and H II region components cannot be reliably separated, our pressure and density diagnostics should not be used because the diagnostics may yield unreliable densities and pressures.

V.7. Measuring ISM pressure and electron density in global spectra

Understanding the ISM pressures derived for global spectra of galaxies (or for large spaxels within galaxies where H II regions are unresolved) is non-trivial. The main complication with measuring the electron density or ISM pressure for global spectra is saturation. If the emission-line ratios are saturated (i.e. in the low density limit or the high density limit) in some, but not all regions of the galaxy, the resulting density or pressure estimate will not represent the luminosity-weighted average density or pressure. In this case, the line ratios will be strongly affected by the fraction of regions that are in the low density limit and the fraction of regions that are in the high density limit. To overcome this problem, several line ratios that cover a range of critical densities could be used together to identify which line ratios (if any) can sample the full set of pressures across the galaxy without being saturated.

If a line ratio, or a set of line ratios have been identified that sample the full set of pressures across the galaxy with no saturation, the resulting global pressure will represent the ISM pressure within a luminosity-weighted equivalent H II region. In the global spectrum of a galaxy, the electron density derived from our calibrations is the density that exists within an equivalent luminosity-weighted H II region with a temperature structure that is the same as our stellar photoionization model at the model metallicity and density across the H II region.

For ultracompact H II regions or H II regions with complex geometries, this constant density assumption is likely to be invalid. In these cases, our density diagnostics would only provide an average estimate of the density, at best. We recommend the use of tailored H II region models for ultracompact H II regions for these cases, such as in Dopita et al. (2006a).

Modeling how well the integrated properties of an entire galaxy can be calculated using these diagnostics is significantly more complicated. Realistic simulations of observed integrated spectra requires modeling of the star formation, metallicity, pressure, dust, and ionization parameter distributions within galaxies, weighting by surface brightness to simulate integrated data at different redshifts, and convolving the output spectrum through given instrument response functions.

VI. Conclusions

We have used new self-consistent stellar evolution and photoionization models to produce new ISM pressure and density diagnostics from the UV to the far-infrared. Our ISM pressure diagnostics take into account the temperature and density structure of the nebula, while our electron density diagnostics take the temperature structure into account and assume a constant density. We anticipate that these diagnostics will provide a useful probe of the pressure and density within H II regions and galaxies.

We show that our pressure diagnostics primarily depend on the gas-phase metallicity (through its effect on the electron temperature of the gas), with only a minor effect from the ionization parameter.

We show how different species probe different zones within a nebula. We anticipate that measuring multiple lines with different ionization states and different species will provide an unprecedented a picture of the detailed pressure or density structure within H II regions.

We show that the [S II] and [O II] lines do not probe similar regions of a nebula and that they are likely to only yield comparable results under constant electron temperature and density conditions. The UV [N II] and optical [O II] lines probe similar nebular zones, and may be used to compare the ISM pressure or electron density in galaxies across cosmic time.

In the near future, JWST and the ELTs will enable the measurement of multiple ISM pressure-sensitive line ratios for galaxies across cosmic time, providing an important probe of how the luminosity-weighted average pressure in galaxies has changed over time.

We wish to thank the referee for his/her extensive and insightful comments which have significantly improved this paper. Parts of this research were supported by the Australian Research Council Centre of Excellence for All Sky Astrophysics in 3 Dimensions (ASTRO 3D), through project number CE170100013. L.J.K. gratefully acknowledges the support of an ARC Laureate Fellowship (FL150100113). This research has made use of NASA’s Astrophysics Data System Bibliographic Services.