Characteristics of Long Gamma-Ray bursts in the Comoving Frame

TL;DR

This study analyzes the intrinsic properties and correlations of long gamma-ray bursts in the comoving frame, revealing narrow distributions and confirming that observed spectral-energy relations are influenced by Doppler effects.

Contribution

It provides the first comprehensive analysis of long GRBs in the comoving frame, demonstrating intrinsic parameter distributions and the impact of Doppler effects on observed correlations.

Findings

Distributions of duration, peak energy, isotropic energy, and luminosity are narrow in the comoving frame.

Confirmed key spectral-energy correlations and their persistence in the comoving frame.

Peak energies are independent of durations, with a weak anticorrelation between peak energy and Lorentz factor.

Abstract

We compile a sample of 93 long gamma-ray bursts (GRBs) from Fermi satellite and 131 from Konus-Wind, which have measured redshifts and well determined spectra, and estimate their pseudo Lorentz factors (${\Gamma_0}$) using the tight ${L_{{\rm{iso}}}}$-${E_{\rm p}}$-${\Gamma_0}$ correlation. The statistical properties and pair correlations of temporal and spectral parameters are studied in the observer frame, rest frame and comoving frame, respectively. We find that the distributions of the duration, peak energy, isotropic energy and luminosity in the different frames are basically lognormal, and their distributions in the comoving frame are narrow, clustering around $T'_{\rm 90}\sim 4000$ s, $E'_{\rm p,c}\sim 0.7$ keV, $E'_{\rm iso,c} \sim 8\times10^{49}$ erg and $L'_{\rm iso,c}\sim 2.5\times10^{46}$ erg s$^{-1}$, where the redshift evolution effect has been taken into account. We also find that the values of ${\Gamma_0}$ are broadly distributed between few tens and several hundreds with median values $\sim 270$. We further analyze the pair correlations of all the quantities, and well confirm ${E_{{\rm{iso}}}}$-${E_{\rm p}}$, ${L_{{\rm{iso}}}}$-${E_{\rm p}}$, ${L_{{\rm{iso}}}}$-${\Gamma_0}$ and $E_{\rm{iso}}$-${\Gamma_0}$ relations, and find that the corresponding relations in the comoving frame do still exist, but have large dispersions. This suggests not only the well-known spectrum-energy relations are intrinsic correlations, but also the observed correlations are governed by the Doppler effect. In addition, the peak energies of long GRBs are independent of durations both in the rest frame and in the comoving frame. And there is a weak anticorrelation between the peak energy and Lorentz factor.

Tables

Table 1. Table 1: Observed data of Fermi sample

GRB	$z$	$T_{90,\mathrm{obs}}$	$E_{p,\mathrm{obs}}$	$\alpha$	$\beta$	$F_p$	$S_{\gamma }$	emin	emax
		s	keV			($\times {10}^{-7}$ erg cm-2 s-1)	($\times {10}^{-7}$ erg cm-2)
080916A	0.689	46.34 $\pm$ 7.17	106.62 $\pm$ 19.25	-0.82 $\pm$ 0.13	-1.78 $\pm$ 0.05	8.42 $\pm$ 0.97	126.73 $\pm$ 3.95	10	1000
081109	0.9787	58.37 $\pm$ 5.22	32.44 $\pm$ 38.3	-0.67 $\pm$ 1.85	-1.65 $\pm$ 0.03	3.63 $\pm$ 0.5	66.75 $\pm$ 2.78	10	1000
081121	2.512	41.99 $\pm$ 8.51	160.84 $\pm$ 16.56	-0.43 $\pm$ 0.13	-2.09 $\pm$ 0.09	15.42 $\pm$ 0.94	147.54 $\pm$ 4.2	10	1000
081221	2.26	29.7 $\pm$ 0.41	86.94 $\pm$ 1.41	-0.9 $\pm$ 0.02	-3.86 $\pm$ 0.48	24.69 $\pm$ 0.9	301.64 $\pm$ 5.26	10	1000
081222	2.77	18.88 $\pm$ 2.32	142.72 $\pm$ 9.58	-0.86 $\pm$ 0.05	-2.31 $\pm$ 0.12	16.68 $\pm$ 0.88	117.92 $\pm$ 3.4	10	1000
090323	3.57	135.17 $\pm$ 1.45	632.9 $\pm$ 40.83	-1.29 $\pm$ 0.01	-2.44 $\pm$ 0.17	32.01 $\pm$ 1.36	1277.04 $\pm$ 14.7	10	1000
090328	0.736	61.7 $\pm$ 1.81	639.66 $\pm$ 45.71	-1.09 $\pm$ 0.02	-2.37 $\pm$ 0.18	39.98 $\pm$ 1.26	508.9 $\pm$ 8.15	10	1000
090423	8.26	7.17 $\pm$ 2.42	66.01 $\pm$ 16.18	-0.59 $\pm$ 0.5	-2.67 $\pm$ 0.74	1.52 $\pm$ 1.01	6.83 $\pm$ 1.36	10	1000
090424	0.544	14.14 $\pm$ 0.26	153.96 $\pm$ 3.83	-1.04 $\pm$ 0.02	-2.76 $\pm$ 0.12	109.69 $\pm$ 1.38	460.38 $\pm$ 5.28	10	1000
090516	4.109	123.07 $\pm$ 2.9	142.05 $\pm$ 26.45	-1.52 $\pm$ 0.05	-2.3 $\pm$ 0.27	5.28 $\pm$ 0.63	229.1 $\pm$ 9.11	10	1000
090618	0.54	112.39 $\pm$ 1.09	146.87 $\pm$ 3.65	-1.13 $\pm$ 0.01	-2.22 $\pm$ 0.02	134.01 $\pm$ 2.53	2698.41 $\pm$ 15.04	10	1000
090902B	1.822	19.33 $\pm$ 0.29	1054.71 $\pm$ 17.43	-1.01 $\pm$ 0	-11.78 $\pm$ 4018.05	191.87 $\pm$ 1.73	2660.43 $\pm$ 7.69	10	1000
090926A	2.1062	13.76 $\pm$ 0.29	339.83 $\pm$ 5.75	-0.86 $\pm$ 0.01	-2.4 $\pm$ 0.04	185.26 $\pm$ 1.99	1538.92 $\pm$ 7.23	10	1000
090926B	1.24	55.55 $\pm$ 7.64	82.49 $\pm$ 3	0.13 $\pm$ 0.12	-3.25 $\pm$ 0.34	3.86 $\pm$ 0.94	85.8 $\pm$ 4.04	10	1000
091003A	0.8969	20.22 $\pm$ 0.36	367.28 $\pm$ 26.76	-1.07 $\pm$ 0.02	-2.23 $\pm$ 0.11	83.54 $\pm$ 1.62	349.07 $\pm$ 5.16	10	1000
091020	1.71	24.26 $\pm$ 7.97	244.24 $\pm$ 36.72	-1.26 $\pm$ 0.06	-3.97 $\pm$ 11.13	12.39 $\pm$ 0.73	80.03 $\pm$ 4.41	10	1000
091024	1.092	93.95 $\pm$ 5.22	1730.32 $\pm$ 901.97	-1.32 $\pm$ 0.08	-6.17 $\pm$ 252.18	7.44 $\pm$ 1.68	93.7 $\pm$ 5.33	10	1000
091127	0.49	8.7 $\pm$ 0.57	35.49 $\pm$ 1.54	-1.26 $\pm$ 0.07	-2.22 $\pm$ 0.02	55.6 $\pm$ 0.85	183.26 $\pm$ 2.05	10	1000
091208B	1.063	12.48 $\pm$ 5.02	38.45 $\pm$ 5.75	-0.15 $\pm$ 0.39	-1.9 $\pm$ 0.04	26.9 $\pm$ 1.07	78.9 $\pm$ 2.86	10	1000
100414A	1.368	26.5 $\pm$ 2.07	663.56 $\pm$ 16.12	-0.62 $\pm$ 0.01	-3.54 $\pm$ 0.49	52.89 $\pm$ 1.44	914.55 $\pm$ 7.21	10	1000
100615A	1.398	37.38 $\pm$ 0.98	53.35 $\pm$ 9.93	-0.9 $\pm$ 0.18	-1.8 $\pm$ 0.03	7.92 $\pm$ 0.56	132.18 $\pm$ 3.16	10	1000
100728A	1.567	165.38 $\pm$ 2.9	290.37 $\pm$ 7.82	-0.64 $\pm$ 0.02	-2.7 $\pm$ 0.15	29.78 $\pm$ 1.29	1199.98 $\pm$ 12.08	10	1000
100728B	2.106	10.24 $\pm$ 1.85	109.84 $\pm$ 22.04	-0.78 $\pm$ 0.17	-1.98 $\pm$ 0.14	7.42 $\pm$ 0.71	33.91 $\pm$ 2.37	10	1000
100814A	1.44	150.53 $\pm$ 1.62	135.6 $\pm$ 10.46	-0.37 $\pm$ 0.1	-2.43 $\pm$ 0.21	10.02 $\pm$ 0.79	139.96 $\pm$ 7.35	10	1000
100906A	1.727	110.59 $\pm$ 2.83	69.67 $\pm$ 10.1	-0.9 $\pm$ 0.13	-1.86 $\pm$ 0.03	22.38 $\pm$ 1.22	260.27 $\pm$ 6.43	10	1000
101219B	0.55	51.01 $\pm$ 1.78	56.36 $\pm$ 6.64	1.37 $\pm$ 0.72	-2.26 $\pm$ 0.14	2.3 $\pm$ 0.63	30.86 $\pm$ 2.62	10	1000
110106B	0.618	35.52 $\pm$ 3.61	129.7 $\pm$ 20.61	-0.94 $\pm$ 0.16	-6.88 $\pm$ 559.1	3.26 $\pm$ 0.92	19.66 $\pm$ 3.7	10	1000
110128A	2.339	12.16 $\pm$ 4.97	192.79 $\pm$ 112.89	-1.26 $\pm$ 0.25	-10.48 $\pm$ 335258.1	2.75 $\pm$ 0.84	5.24 $\pm$ 1.34	10	1000
110213A	1.46	34.31 $\pm$ 1.64	74.73 $\pm$ 13.07	-1.42 $\pm$ 0.09	-2.13 $\pm$ 0.09	13.76 $\pm$ 0.98	117.06 $\pm$ 4.81	10	1000
110731A	2.83	7.49 $\pm$ 0.57	319.32 $\pm$ 19.69	-0.87 $\pm$ 0.03	-2.44 $\pm$ 0.16	24.1 $\pm$ 1.18	228.23 $\pm$ 3.67	10	1000
110818A	3.36	67.07 $\pm$ 3.92	183.36 $\pm$ 85.3	-1.11 $\pm$ 0.17	-1.76 $\pm$ 0.1	4.52 $\pm$ 0.51	63.23 $\pm$ 2.96	10	1000
111228A	0.714	99.84 $\pm$ 2.11	26.51 $\pm$ 1.25	-1.58 $\pm$ 0.08	-2.44 $\pm$ 0.06	13.7 $\pm$ 0.85	155.11 $\pm$ 3.75	10	1000
120119A	1.728	55.3 $\pm$ 6.23	183.25 $\pm$ 7.96	-0.96 $\pm$ 0.03	-2.37 $\pm$ 0.09	29.09 $\pm$ 0.88	393.77 $\pm$ 5.55	10	1000
120624B	2.1974	271.36 $\pm$ 4.58	637.65 $\pm$ 24.51	-0.92 $\pm$ 0.01	-2.22 $\pm$ 0.07	49.02 $\pm$ 1.52	1975.49 $\pm$ 17.74	10	1000
120711A	1.405	44.03 $\pm$ 0.72	1318.66 $\pm$ 45.86	-0.98 $\pm$ 0.01	-2.8 $\pm$ 0.09	78.14 $\pm$ 1.71	1973.8 $\pm$ 10.03	10	1000
120716A	2.486	237.06 $\pm$ 4.1	119.92 $\pm$ 6.46	-0.89 $\pm$ 0.05	-2.63 $\pm$ 0.22	11 $\pm$ 0.65	140.94 $\pm$ 4.82	10	1000
120811C	2.671	14.34 $\pm$ 6.56	55.57 $\pm$ 5.32	-0.71 $\pm$ 0.27	-2.85 $\pm$ 0.32	5.22 $\pm$ 0.66	36.8 $\pm$ 2.6	10	1000
120907A	0.97	5.76 $\pm$ 1.78	122.42 $\pm$ 34.15	-0.81 $\pm$ 0.31	-5.02 $\pm$ 54.06	4.08 $\pm$ 0.78	7 $\pm$ 2.52	10	1000
120909A	3.93	112.07 $\pm$ 10.42	195.01 $\pm$ 25.44	-0.83 $\pm$ 0.08	-1.92 $\pm$ 0.09	7.56 $\pm$ 0.98	181.72 $\pm$ 5.71	10	1000
121128A	2.2	17.34 $\pm$ 0.92	76.31 $\pm$ 3	-1 $\pm$ 0.06	-6.83 $\pm$ 122.22	15.59 $\pm$ 0.63	83.24 $\pm$ 7.17	10	1000
121211A	1.023	5.63 $\pm$ 1.72	100.23 $\pm$ 15.84	-0.27 $\pm$ 0.37	-4.8 $\pm$ 15.94	1.89 $\pm$ 0.7	5.09 $\pm$ 1.28	10	1000
130215A	0.597	143.75 $\pm$ 13.03	257.01 $\pm$ 130.5	-1.19 $\pm$ 0.11	-1.59 $\pm$ 0.04	4.95 $\pm$ 0.56	158.79 $\pm$ 3.59	10	1000
130420A	1.297	104.96 $\pm$ 8.81	57.29 $\pm$ 3.14	-1.13 $\pm$ 0.12	-10.59 $\pm$ 14049.05	2.97 $\pm$ 0.31	57.7 $\pm$ 9.68	10	1000
130427A	0.3399	138.24 $\pm$ 3.24	824.99 $\pm$ 5.45	-1.02 $\pm$ 0	-2.83 $\pm$ 0.03	1960.24 $\pm$ 6.24	14117.15 $\pm$ 18.24	10	1000
130518A	2.488	48.58 $\pm$ 0.92	398.03 $\pm$ 15.83	-0.91 $\pm$ 0.02	-2.25 $\pm$ 0.07	117.09 $\pm$ 2.05	1001.81 $\pm$ 9.76	10	1000
130610A	2.092	21.76 $\pm$ 1.64	271.93 $\pm$ 111.57	-1.58 $\pm$ 0.08	-16.38 $\pm$ 351940700	3.06 $\pm$ 0.6	56.4 $\pm$ 4.78	10	1000
130612A	2.006	7.42 $\pm$ 6.19	26.4 $\pm$ 6.77	1.01 $\pm$ 2.14	-2.23 $\pm$ 0.15	1.96 $\pm$ 0.34	5.69 $\pm$ 0.67	10	1000
130702A	0.145	58.88 $\pm$ 6.19	10.43 $\pm$ 1.13	1.82 $\pm$ 19.38	-2.49 $\pm$ 0.03	6.52 $\pm$ 0.45	68.36 $\pm$ 1.94	10	1000
130925A	0.347	215.56 $\pm$ 1.81	82.36 $\pm$ 2.3	-1.39 $\pm$ 0.02	-2.62 $\pm$ 0.08	7.85 $\pm$ 0.88	842.75 $\pm$ 10.9	10	1000
131011A	1.874	77.06 $\pm$ 3	217.64 $\pm$ 31.86	-0.88 $\pm$ 0.08	-2.08 $\pm$ 0.18	8.56 $\pm$ 0.58	118.17 $\pm$ 4.31	10	1000
131105A	1.686	112.64 $\pm$ 0.46	265.52 $\pm$ 17.19	-1.26 $\pm$ 0.02	-11.18 $\pm$ 42864.73	16.13 $\pm$ 0.88	245.51 $\pm$ 5.87	10	1000
131108A	2.4	18.18 $\pm$ 0.57	367.03 $\pm$ 17.62	-0.91 $\pm$ 0.02	-2.46 $\pm$ 0.15	44.77 $\pm$ 1.03	364.48 $\pm$ 4.53	10	1000
131231A	0.642	31.23 $\pm$ 0.57	178.15 $\pm$ 3.69	-1.21 $\pm$ 0.01	-2.3 $\pm$ 0.03	146.99 $\pm$ 1.61	1532.67 $\pm$ 6.69	10	1000
140206A	2.73	146.69 $\pm$ 4.42	477.33 $\pm$ 32.11	-1.4 $\pm$ 0.01	-2.04 $\pm$ 0.05	97.17 $\pm$ 1.42	1284.18 $\pm$ 10.02	10	1000
140213A	1.2076	18.62 $\pm$ 0.72	86.63 $\pm$ 3.56	-1.13 $\pm$ 0.03	-2.26 $\pm$ 0.05	29.24 $\pm$ 0.79	238.31 $\pm$ 4.01	10	1000
140304A	5.283	31.23 $\pm$ 8.72	123.36 $\pm$ 27.59	-0.8 $\pm$ 0.22	-2.35 $\pm$ 0.43	3.67 $\pm$ 0.68	22.27 $\pm$ 2.54	10	1000
140423A	3.26	95.23 $\pm$ 11.59	121.3 $\pm$ 15.19	-0.58 $\pm$ 0.12	-1.83 $\pm$ 0.05	4.53 $\pm$ 0.74	209.5 $\pm$ 6.18	10	1000
140506A	0.889	64.13 $\pm$ 2.01	197.56 $\pm$ 32.55	-1.18 $\pm$ 0.11	-9.8 $\pm$ 28454.34	20.64 $\pm$ 1.24	46.22 $\pm$ 3.5	10	1000
140508A	1.027	44.29 $\pm$ 0.23	263.18 $\pm$ 14.03	-1.19 $\pm$ 0.02	-2.36 $\pm$ 0.1	121.95 $\pm$ 2.08	640.52 $\pm$ 7.63	10	1000
140512A	0.725	147.97 $\pm$ 2.36	682.81 $\pm$ 70.35	-1.22 $\pm$ 0.02	-3.24 $\pm$ 1.64	24.13 $\pm$ 1.1	453.63 $\pm$ 8.23	10	1000
140606B	0.384	22.78 $\pm$ 2.06	554.63 $\pm$ 165.32	-1.24 $\pm$ 0.05	-2.2 $\pm$ 0.52	23.78 $\pm$ 1.2	94.48 $\pm$ 5.11	10	1000
140620A	2.04	45.83 $\pm$ 12.13	75.72 $\pm$ 11.14	-0.93 $\pm$ 0.16	-2.15 $\pm$ 0.09	5.87 $\pm$ 0.64	69.09 $\pm$ 3.06	10	1000
140623A	1.92	111.1 $\pm$ 4	282.97 $\pm$ 109.74	-1.41 $\pm$ 0.1	-6.54 $\pm$ 1429.42	2.46 $\pm$ 0.96	32.29 $\pm$ 3.48	10	1000
140703A	3.14	83.97 $\pm$ 3	208.03 $\pm$ 35.82	-1.27 $\pm$ 0.06	-2.61 $\pm$ 0.79	6.75 $\pm$ 0.62	91.67 $\pm$ 4.45	10	1000
140801A	1.32	7.17 $\pm$ 0.57	119.26 $\pm$ 2.64	-0.38 $\pm$ 0.04	-3.93 $\pm$ 0.66	25.81 $\pm$ 0.91	123.37 $\pm$ 3.21	10	1000
140808A	3.29	4.48 $\pm$ 0.36	117.28 $\pm$ 8.14	-0.42 $\pm$ 0.11	-3 $\pm$ 0.47	11.59 $\pm$ 0.89	34.78 $\pm$ 2.14	10	1000
140907A	1.21	35.84 $\pm$ 5.47	140.97 $\pm$ 9.81	-1.03 $\pm$ 0.06	-14.69 $\pm$ 3160631	3.97 $\pm$ 0.59	63.14 $\pm$ 2.4	10	1000
141004A	0.573	2.56 $\pm$ 0.61	27.84 $\pm$ 11.25	0.1 $\pm$ 1.68	-1.91 $\pm$ 0.08	9.2 $\pm$ 0.68	15.16 $\pm$ 1.21	10	1000
141028A	2.33	31.49 $\pm$ 2.43	294.17 $\pm$ 16.03	-0.84 $\pm$ 0.03	-1.97 $\pm$ 0.04	42.3 $\pm$ 1.1	399.04 $\pm$ 4.03	10	1000
141220A	1.3195	7.62 $\pm$ 0.92	180.56 $\pm$ 10.42	-0.83 $\pm$ 0.05	-11.14 $\pm$ 31688.58	21.17 $\pm$ 0.83	55.91 $\pm$ 1.9	10	1000
141221A	1.452	23.81 $\pm$ 1.72	183.78 $\pm$ 35.54	-1.19 $\pm$ 0.1	-19.96 $\pm$ 1954114000	7.9 $\pm$ 1.16	28.74 $\pm$ 2.66	10	1000
141225A	0.915	56.32 $\pm$ 4.89	178.96 $\pm$ 27.22	-0.3 $\pm$ 0.18	-2.06 $\pm$ 0.17	5.39 $\pm$ 0.69	63.78 $\pm$ 3.38	10	1000
150301B	1.5169	13.31 $\pm$ 1.56	182.97 $\pm$ 36.14	-1.05 $\pm$ 0.1	-2.22 $\pm$ 0.28	5.1 $\pm$ 0.62	42.17 $\pm$ 2.36	10	1000
150314A	1.758	10.69 $\pm$ 0.14	347.09 $\pm$ 6.91	-0.68 $\pm$ 0.01	-2.6 $\pm$ 0.08	159.43 $\pm$ 1.96	889.31 $\pm$ 6.11	10	1000
150403A	2.06	22.27 $\pm$ 0.81	428.67 $\pm$ 17.35	-0.87 $\pm$ 0.02	-2.11 $\pm$ 0.04	89.31 $\pm$ 1.77	642.44 $\pm$ 6.35	10	1000
150514A	0.807	10.81 $\pm$ 1.07	64.6 $\pm$ 5.64	-1.21 $\pm$ 0.1	-2.43 $\pm$ 0.13	12.87 $\pm$ 0.57	51.81 $\pm$ 2.05	10	1000
150727A	0.313	49.41 $\pm$ 3.97	148.56 $\pm$ 19.18	0.13 $\pm$ 0.28	-2.16 $\pm$ 0.16	3.71 $\pm$ 0.52	67 $\pm$ 3.49	10	1000
150821A	0.755	103.43 $\pm$ 5.75	281.03 $\pm$ 17.8	-1.24 $\pm$ 0.02	-2.13 $\pm$ 0.07	19.56 $\pm$ 0.87	711.02 $\pm$ 8.28	10	1000
151027A	0.81	123.39 $\pm$ 1.15	202.63 $\pm$ 34.13	-1.25 $\pm$ 0.05	-1.96 $\pm$ 0.08	17 $\pm$ 0.76	174.15 $\pm$ 4.35	10	1000
160509A	1.17	369.67 $\pm$ 0.81	355.18 $\pm$ 9.59	-1.02 $\pm$ 0.01	-2.23 $\pm$ 0.04	148.76 $\pm$ 1.63	2041.37 $\pm$ 11.07	10	1000
160625B	1.406	454.67 $\pm$ 11.01	471.46 $\pm$ 6.45	-0.93 $\pm$ 0	-2.18 $\pm$ 0.02	687.4 $\pm$ 4.31	6785.42 $\pm$ 22.77	10	1000
160629A	3.332	64.77 $\pm$ 0.92	277.55 $\pm$ 25.86	-1.02 $\pm$ 0.04	-2.65 $\pm$ 0.56	8.29 $\pm$ 0.79	190.05 $\pm$ 6.01	10	1000
160804A	0.736	131.59 $\pm$ 21.72	71.39 $\pm$ 4.18	-1.03 $\pm$ 0.09	-2.82 $\pm$ 0.9	4.18 $\pm$ 0.67	136.67 $\pm$ 6.43	10	1000
161014A	2.823	36.61 $\pm$ 1.49	169.02 $\pm$ 14.42	-0.76 $\pm$ 0.09	-19.19 $\pm$ 412864700	7.29 $\pm$ 0.72	50.74 $\pm$ 2.69	10	1000
161017A	2.013	32.26 $\pm$ 8.08	238.58 $\pm$ 40.77	-1.03 $\pm$ 0.1	-2.37 $\pm$ 0.78	7.98 $\pm$ 1.09	58.19 $\pm$ 3.49	10	1000
161117A	1.549	122.18 $\pm$ 0.66	80.67 $\pm$ 3.05	-0.81 $\pm$ 0.05	-3.02 $\pm$ 0.51	7.35 $\pm$ 0.79	332.52 $\pm$ 8.99	10	1000
161129A	0.645	36.1 $\pm$ 0.72	146.41 $\pm$ 42.61	-1.04 $\pm$ 0.1	-1.95 $\pm$ 0.16	8.39 $\pm$ 0.89	98.5 $\pm$ 3.99	10	1000
170113A	1.968	49.15 $\pm$ 4.14	112.51 $\pm$ 58.79	-1.7 $\pm$ 0.22	-20.46 $\pm$ 23839230000	3.85 $\pm$ 0.89	17.74 $\pm$ 3.02	10	1000
170214A	2.53	122.88 $\pm$ 0.72	481.39 $\pm$ 11.23	-0.98 $\pm$ 0.01	-2.51 $\pm$ 0.1	44.44 $\pm$ 1.25	2030.98 $\pm$ 13.25	10	1000
170607A	0.557	22.59 $\pm$ 2.85	111.79 $\pm$ 9.03	-1.29 $\pm$ 0.06	-2.38 $\pm$ 0	16.59 $\pm$ 0.89	97.71 $\pm$ 2.37	10	1000
170705A	2.01	22.78 $\pm$ 1.38	97.88 $\pm$ 7.64	-0.99 $\pm$ 0.07	-2.3 $\pm$ 0.11	30.51 $\pm$ 1.07	144.32 $\pm$ 4.32	10	1000
171010A	0.3285	107.27 $\pm$ 0.81	137.66 $\pm$ 1.43	-1.09 $\pm$ 0.01	-2.19 $\pm$ 0.01	201.74 $\pm$ 2.23	6718.16 $\pm$ 16.6	10	1000
171222A	2.409	80.38 $\pm$ 4.62	17.54 $\pm$ 4.14	-0.37 $\pm$ 1.11	-2.14 $\pm$ 0.1	1.61 $\pm$ 0.42	17.93 $\pm$ 1.61	10	1000

Table 2. Table 2: Observed data of Konus-Wind sample

GRB	$z$	$T_{90,\mathrm{obs}}$	$E_{p,\mathrm{obs}}$	$\alpha$	$\beta$	$F_p$	$S_{\gamma }$	emin	emax
		s	keV			($\times {10}^{-7}$ erg cm-2 s-1)	($\times {10}^{-7}$ erg cm-2)
970228	0.69	53.44 $\pm$ 2.89	159${}_{}{}^{+38}{}_{-36}{}^{}$	-1.24${}_{}{}^{+0.31}{}_{-0.22}{}^{}$	-2.82${}_{}{}^{+0.6}{}_{-7.18}{}^{}$	22.4${}_{}{}^{+4.3}{}_{-3.4}{}^{}$	80.7${}_{}{}^{+4.9}{}_{-4.1}{}^{}$	10	10000
970828	0.96	66.21 $\pm$ 2.78	271${}_{}{}^{+24}{}_{-22}{}^{}$	-0.73${}_{}{}^{+0.06}{}_{-0.06}{}^{}$	-2.18${}_{}{}^{+0.11}{}_{-0.15}{}^{}$	43${}_{}{}^{+4.6}{}_{-4.4}{}^{}$	1018${}_{}{}^{+35}{}_{-36}{}^{}$	10	10000
971214	3.42	15.89 $\pm$ 2.13	154${}_{}{}^{+20}{}_{-19}{}^{}$	-0.32${}_{}{}^{+0.26}{}_{-0.22}{}^{}$	-2.39${}_{}{}^{+0.23}{}_{-0.35}{}^{}$	6.04${}_{}{}^{+0.71}{}_{-0.68}{}^{}$	57.2${}_{}{}^{+2.4}{}_{-2.2}{}^{}$	10	10000
990123	1.6	62.02 $\pm$ 1.18	675${}_{}{}^{+40}{}_{-45}{}^{}$	-0.92${}_{}{}^{+0.02}{}_{-0.02}{}^{}$	-2.53${}_{}{}^{+0.25}{}_{-0.34}{}^{}$	256${}_{}{}^{+11}{}_{-11}{}^{}$	3106${}_{}{}^{+80}{}_{-78}{}^{}$	10	10000
990506	1.31	128.61 $\pm$ 0.65	296${}_{}{}^{+27}{}_{-25}{}^{}$	-1.19${}_{}{}^{+0.05}{}_{-0.04}{}^{}$	-2.09${}_{}{}^{+0.07}{}_{-0.08}{}^{}$	93.2${}_{}{}^{+4.7}{}_{-4.6}{}^{}$	2610${}_{}{}^{+88}{}_{-88}{}^{}$	10	10000
990510	1.62	55.89 $\pm$ 8.11	136${}_{}{}^{+12}{}_{-10}{}^{}$	-1.35${}_{}{}^{+0.08}{}_{-0.08}{}^{}$	-2.82${}_{}{}^{+0}{}_0{}^{}$	35.6${}_{}{}^{+3.5}{}_{-3.3}{}^{}$	217.2${}_{}{}^{+8.9}{}_{-8.2}{}^{}$	10	10000
990705	0.84	33.23 $\pm$ 1.12	299${}_{}{}^{+9}{}_{-9}{}^{}$	-0.72${}_{}{}^{+0.03}{}_{-0.03}{}^{}$	-2.68${}_{}{}^{+0.12}{}_{-0.15}{}^{}$	48${}_{}{}^{+4.4}{}_{-4.2}{}^{}$	1090${}_{}{}^{+38}{}_{-38}{}^{}$	10	10000
990712	0.43	16.63 $\pm$ 1.78	103${}_{}{}^{+14}{}_{-11}{}^{}$	-1.44${}_{}{}^{+0.13}{}_{-0.13}{}^{}$	-3.47${}_{}{}^{+0.81}{}_{-6.53}{}^{}$	8.02${}_{}{}^{+1.18}{}_{-0.87}{}^{}$	62.5${}_{}{}^{+3.8}{}_{-3.3}{}^{}$	10	10000
991208	0.71	63.06 $\pm$ 0.48	185${}_{}{}^{+5}{}_{-5}{}^{}$	-1.27${}_{}{}^{+0.02}{}_{-0.02}{}^{}$	-2.92${}_{}{}^{+0.16}{}_{-0.25}{}^{}$	185.9${}_{}{}^{+5.5}{}_{-5.3}{}^{}$	1549${}_{}{}^{+29}{}_{-30}{}^{}$	10	10000
991216	1.02	14.53 $\pm$ 0.14	353${}_{}{}^{+15}{}_{-15}{}^{}$	-1.2${}_{}{}^{+0.02}{}_{-0.02}{}^{}$	-2.23${}_{}{}^{+0.03}{}_{-0.04}{}^{}$	476${}_{}{}^{+32}{}_{-31}{}^{}$	2970${}_{}{}^{+38}{}_{-37}{}^{}$	10	10000
000131	4.5	96.47 $\pm$ 3.13	133${}_{}{}^{+13}{}_{-12}{}^{}$	-0.9${}_{}{}^{+0.1}{}_{-0.09}{}^{}$	-2.26${}_{}{}^{+0.09}{}_{-0.11}{}^{}$	30.9${}_{}{}^{+2.7}{}_{-2.6}{}^{}$	453${}_{}{}^{+13}{}_{-13}{}^{}$	10	10000
000210	0.85	7.97 $\pm$ 0.41	372${}_{}{}^{+21}{}_{-20}{}^{}$	-0.99${}_{}{}^{+0.03}{}_{-0.03}{}^{}$	-2.25${}_{}{}^{+0.07}{}_{-0.08}{}^{}$	295${}_{}{}^{+15}{}_{-15}{}^{}$	952${}_{}{}^{+24}{}_{-23}{}^{}$	10	10000
000301C	2.03	3.66 $\pm$ 0.55	116${}_{}{}^{+27}{}_{-24}{}^{}$	-1.11${}_{}{}^{+0.3}{}_{-0.23}{}^{}$	-2.33${}_{}{}^{+0.23}{}_{-0.33}{}^{}$	12.4${}_{}{}^{+2.2}{}_{-1.8}{}^{}$	27.9${}_{}{}^{+4.2}{}_{-3}{}^{}$	10	10000
000418	1.12	27.75 $\pm$ 1.3	92${}_{}{}^{+15}{}_{-11}{}^{}$	-1.32${}_{}{}^{+0.18}{}_{-0.17}{}^{}$	-2.37${}_{}{}^{+0.1}{}_{-0.21}{}^{}$	26.3${}_{}{}^{+1.9}{}_{-1.8}{}^{}$	219.3${}_{}{}^{+8.8}{}_{-8}{}^{}$	10	10000
000911	1.06	23.35 $\pm$ 0.23	1083${}_{}{}^{+52}{}_{-50}{}^{}$	-0.82${}_{}{}^{+0.03}{}_{-0.03}{}^{}$	-2.75${}_{}{}^{+0.16}{}_{-0.23}{}^{}$	188${}_{}{}^{+10}{}_{-10}{}^{}$	2084${}_{}{}^{+65}{}_{-65}{}^{}$	10	10000
000926	2.04	54.68 $\pm$ 9.47	108${}_{}{}^{+8}{}_{-7}{}^{}$	-1.51${}_{}{}^{+0.06}{}_{-0.06}{}^{}$	-3.17${}_{}{}^{+0}{}_0{}^{}$	19.2${}_{}{}^{+1.6}{}_{-1.5}{}^{}$	210.1${}_{}{}^{+5.8}{}_{-5.5}{}^{}$	10	10000
010222	1.48	89.76 $\pm$ 7.88	285${}_{}{}^{+22}{}_{-20}{}^{}$	-1.26${}_{}{}^{+0.03}{}_{-0.03}{}^{}$	-2.17${}_{}{}^{+0.06}{}_{-0.08}{}^{}$	103.4${}_{}{}^{+8.4}{}_{-8.1}{}^{}$	1751${}_{}{}^{+48}{}_{-49}{}^{}$	10	10000
010921	0.45	19.79 $\pm$ 2.41	80${}_{}{}^{+10}{}_{-8}{}^{}$	-1.52${}_{}{}^{+0.13}{}_{-0.11}{}^{}$	-2.45${}_{}{}^{+0.12}{}_{-0.27}{}^{}$	11.3${}_{}{}^{+1.1}{}_{-1}{}^{}$	146.6${}_{}{}^{+4.9}{}_{-4.4}{}^{}$	10	10000
011121	0.36	57.01 $\pm$ 3.78	819${}_{}{}^{+108}{}_{-96}{}^{}$	-1.26${}_{}{}^{+0.02}{}_{-0.02}{}^{}$	-2.01${}_{}{}^{+0.09}{}_{-0.12}{}^{}$	112.3${}_{}{}^{+7.6}{}_{-7}{}^{}$	2785${}_{}{}^{+75}{}_{-76}{}^{}$	10	10000
020405	0.69	41.54 $\pm$ 2.03	161${}_{}{}^{+7}{}_{-7}{}^{}$	-0.97${}_{}{}^{+0.06}{}_{-0.06}{}^{}$	-2.6${}_{}{}^{+0.11}{}_{-0.15}{}^{}$	60.3${}_{}{}^{+5.9}{}_{-5.4}{}^{}$	837${}_{}{}^{+12}{}_{-12}{}^{}$	10	10000
020813	1.25	89.41 $\pm$ 0.73	227${}_{}{}^{+18}{}_{-17}{}^{}$	-0.9${}_{}{}^{+0.1}{}_{-0.09}{}^{}$	-2.24${}_{}{}^{+0.08}{}_{-0.09}{}^{}$	125${}_{}{}^{+11}{}_{-11}{}^{}$	1730${}_{}{}^{+110}{}_{-100}{}^{}$	10	10000
020819B	0.41	8.2 $\pm$ 2	161${}_{}{}^{+40}{}_{-28}{}^{}$	-1.42${}_{}{}^{+0.24}{}_{-0.19}{}^{}$	-2.64${}_{}{}^{+0}{}_0{}^{}$	22.4${}_{}{}^{+4.3}{}_{-3.4}{}^{}$	66.8${}_{}{}^{+6.5}{}_{-5.2}{}^{}$	10	10000
030329	0.17	21.81 $\pm$ 1.15	97${}_{}{}^{+2}{}_{-2}{}^{}$	-1.53${}_{}{}^{+0.03}{}_{-0.03}{}^{}$	-2.78${}_{}{}^{+0.06}{}_{-0.07}{}^{}$	216.7${}_{}{}^{+6.2}{}_{-6.1}{}^{}$	1873${}_{}{}^{+26}{}_{-27}{}^{}$	10	10000
041006	0.72	6.85 $\pm$ 1.98	85${}_{}{}^{+5}{}_{-5}{}^{}$	0.08${}_{}{}^{+0.5}{}_{-0.42}{}^{}$	-3.77${}_{}{}^{+0}{}_0{}^{}$	13.2${}_{}{}^{+1.6}{}_{-1.5}{}^{}$	47.2${}_{}{}^{+2.5}{}_{-2.4}{}^{}$	10	10000
050401	2.9	33.06 $\pm$ 0.68	105${}_{}{}^{+14}{}_{-11}{}^{}$	-0.82${}_{}{}^{+0.26}{}_{-0.23}{}^{}$	-2.31${}_{}{}^{+0.1}{}_{-0.15}{}^{}$	22.3${}_{}{}^{+1.7}{}_{-1.6}{}^{}$	232${}_{}{}^{+9.8}{}_{-10.2}{}^{}$	10	10000
050525A	0.61	7.05 $\pm$ 0.19	80${}_{}{}^{+2}{}_{-2}{}^{}$	-1.05${}_{}{}^{+0.06}{}_{-0.06}{}^{}$	-3.2${}_{}{}^{+0.16}{}_{-0.24}{}^{}$	58.9${}_{}{}^{+2}{}_{-2}{}^{}$	246.2${}_{}{}^{+4.4}{}_{-4.5}{}^{}$	10	10000
050603	2.82	11.2 $\pm$ 3.5	239${}_{}{}^{+64}{}_{-34}{}^{}$	-0.69${}_{}{}^{+0.17}{}_{-0.18}{}^{}$	-1.94${}_{}{}^{+0.09}{}_{-0.17}{}^{}$	156${}_{}{}^{+11}{}_{-11}{}^{}$	512${}_{}{}^{+31}{}_{-36}{}^{}$	10	10000
050820A	2.61	440.83 $\pm$ 76.52	478${}_{}{}^{+139}{}_{-90}{}^{}$	-1.33${}_{}{}^{+0.09}{}_{-0.08}{}^{}$	-2.74${}_{}{}^{+0.55}{}_{-7.26}{}^{}$	18.3${}_{}{}^{+2.9}{}_{-2.3}{}^{}$	605${}_{}{}^{+20}{}_{-15}{}^{}$	10	10000
050922C	2.2	6.25 $\pm$ 1.47	734${}_{}{}^{+717}{}_{-314}{}^{}$	-1.37${}_{}{}^{+0.2}{}_{-0.16}{}^{}$	-2.06${}_{}{}^{+0}{}_0{}^{}$	29.1${}_{}{}^{+10.5}{}_{-7.5}{}^{}$	81${}_{}{}^{+22}{}_{-15}{}^{}$	10	10000
051008	2.77	208.84 $\pm$ 25.77	322${}_{}{}^{+93}{}_{-74}{}^{}$	-0.7${}_{}{}^{+0.24}{}_{-0.18}{}^{}$	-1.96${}_{}{}^{+0.15}{}_{-0.22}{}^{}$	42.6${}_{}{}^{+3.5}{}_{-3.2}{}^{}$	461${}_{}{}^{+43}{}_{-34}{}^{}$	10	10000
051022	0.81	153.79 $\pm$ 2.21	432${}_{}{}^{+20}{}_{-20}{}^{}$	-1.16${}_{}{}^{+0.03}{}_{-0.02}{}^{}$	-3.08${}_{}{}^{+0.34}{}_{-0.81}{}^{}$	137.4${}_{}{}^{+6.5}{}_{-6.6}{}^{}$	2608${}_{}{}^{+55}{}_{-52}{}^{}$	10	10000
051109A	2.35	39.64 $\pm$ 3.45	170${}_{}{}^{+80}{}_{-42}{}^{}$	-1.31${}_{}{}^{+0.3}{}_{-0.26}{}^{}$	-2.48${}_{}{}^{+0}{}_0{}^{}$	6.9${}_{}{}^{+1.7}{}_{-1.3}{}^{}$	47.2${}_{}{}^{+4.6}{}_{-3.8}{}^{}$	10	10000
060124	2.3	238.12 $\pm$ 19.11	223${}_{}{}^{+37}{}_{-29}{}^{}$	-1.14${}_{}{}^{+0.11}{}_{-0.1}{}^{}$	-2.56${}_{}{}^{+0.32}{}_{-1.73}{}^{}$	24.4${}_{}{}^{+2}{}_{-1.8}{}^{}$	237${}_{}{}^{+10.7}{}_{-9.4}{}^{}$	10	10000
060502A	1.5	10.57 $\pm$ 2.22	129${}_{}{}^{+42}{}_{-38}{}^{}$	-1.29${}_{}{}^{+0.27}{}_{-0.23}{}^{}$	-3.26${}_{}{}^{+1.08}{}_{-6.74}{}^{}$	5.56${}_{}{}^{+1.04}{}_{-0.93}{}^{}$	34${}_{}{}^{+3.7}{}_{-3}{}^{}$	10	10000
060614	0.13	123.65 $\pm$ 18.94	73${}_{}{}^{+13}{}_{-12}{}^{}$	-1.92${}_{}{}^{+0.01}{}_{-0.04}{}^{}$	-2.31${}_{}{}^{+0}{}_0{}^{}$	17.4${}_{}{}^{+3.6}{}_{-2.8}{}^{}$	470${}_{}{}^{+26}{}_{-20}{}^{}$	10	10000
060814	1.92	145.83 $\pm$ 26.52	261${}_{}{}^{+161}{}_{-82}{}^{}$	-1.31${}_{}{}^{+0.21}{}_{-0.16}{}^{}$	-1.93${}_{}{}^{+0.16}{}_{-0.3}{}^{}$	20.9${}_{}{}^{+1.7}{}_{-1.6}{}^{}$	400${}_{}{}^{+17}{}_{-13}{}^{}$	10	10000
061007	1.26	57.55 $\pm$ 0.51	399${}_{}{}^{+12}{}_{-11}{}^{}$	-0.7${}_{}{}^{+0.02}{}_{-0.02}{}^{}$	-2.61${}_{}{}^{+0.1}{}_{-0.12}{}^{}$	133.5${}_{}{}^{+8.8}{}_{-8.9}{}^{}$	2536${}_{}{}^{+93}{}_{-91}{}^{}$	10	10000
061021	0.35	18.68 $\pm$ 5.43	521${}_{}{}^{+265}{}_{-139}{}^{}$	-1.27${}_{}{}^{+0.15}{}_{-0.14}{}^{}$	-2.39${}_{}{}^{+0}{}_0{}^{}$	40.3${}_{}{}^{+5.8}{}_{-4.8}{}^{}$	136${}_{}{}^{+30}{}_{-21}{}^{}$	10	10000
061121	1.31	17.76 $\pm$ 1.45	606${}_{}{}^{+52}{}_{-45}{}^{}$	-1.32${}_{}{}^{+0.03}{}_{-0.03}{}^{}$	-3.08${}_{}{}^{+0}{}_0{}^{}$	133.6${}_{}{}^{+6.6}{}_{-6.2}{}^{}$	616${}_{}{}^{+23}{}_{-22}{}^{}$	10	10000
061222A	2.09	60.16 $\pm$ 4.78	268${}_{}{}^{+27}{}_{-23}{}^{}$	-0.83${}_{}{}^{+0.09}{}_{-0.08}{}^{}$	-2.41${}_{}{}^{+0.22}{}_{-0.4}{}^{}$	30.6${}_{}{}^{+1.9}{}_{-1.8}{}^{}$	231.6${}_{}{}^{+6}{}_{-5.8}{}^{}$	10	10000
070125	1.55	124.21 $\pm$ 15.65	372${}_{}{}^{+36}{}_{-31}{}^{}$	-1.1${}_{}{}^{+0.06}{}_{-0.05}{}^{}$	-2.09${}_{}{}^{+0.06}{}_{-0.08}{}^{}$	129${}_{}{}^{+13}{}_{-13}{}^{}$	1958${}_{}{}^{+98}{}_{-97}{}^{}$	10	10000
070328	2.06	53.8 $\pm$ 12.9	386${}_{}{}^{+59}{}_{-47}{}^{}$	-0.8${}_{}{}^{+0.09}{}_{-0.09}{}^{}$	-2${}_{}{}^{+0.1}{}_{-0.14}{}^{}$	54${}_{}{}^{+5.8}{}_{-5.8}{}^{}$	720${}_{}{}^{+80}{}_{-78}{}^{}$	10	10000
070508	0.82	14.75 $\pm$ 1.12	186${}_{}{}^{+5}{}_{-5}{}^{}$	-0.8${}_{}{}^{+0.05}{}_{-0.05}{}^{}$	-3.77${}_{}{}^{+0.52}{}_{-6.23}{}^{}$	67${}_{}{}^{+1.9}{}_{-1.9}{}^{}$	412.5${}_{}{}^{+6.3}{}_{-6.2}{}^{}$	10	10000
070521	1.7	31.78 $\pm$ 6.82	216${}_{}{}^{+16}{}_{-16}{}^{}$	-0.91${}_{}{}^{+0.08}{}_{-0.08}{}^{}$	-3.43${}_{}{}^{+0.74}{}_{-6.57}{}^{}$	19.4${}_{}{}^{+1.3}{}_{-1.2}{}^{}$	187.6${}_{}{}^{+5.8}{}_{-5.6}{}^{}$	10	10000
071003	1.6	21.36 $\pm$ 1.02	769${}_{}{}^{+77}{}_{-74}{}^{}$	-0.96${}_{}{}^{+0.05}{}_{-0.04}{}^{}$	-2.79${}_{}{}^{+0.42}{}_{-1.41}{}^{}$	71.1${}_{}{}^{+4}{}_{-3.9}{}^{}$	558${}_{}{}^{+27}{}_{-25}{}^{}$	10	10000
071010B	0.95	8.52 $\pm$ 1.27	55${}_{}{}^{+4}{}_{-5}{}^{}$	-0.95${}_{}{}^{+0.38}{}_{-0.31}{}^{}$	-2.76${}_{}{}^{+0.2}{}_{-0.28}{}^{}$	8.55${}_{}{}^{+1.02}{}_{-0.91}{}^{}$	50.9${}_{}{}^{+3.4}{}_{-3.4}{}^{}$	10	10000
071020	2.15	2.73 $\pm$ 0.07	271${}_{}{}^{+50}{}_{-44}{}^{}$	-0.46${}_{}{}^{+0.29}{}_{-0.24}{}^{}$	-2.39${}_{}{}^{+0.27}{}_{-0.56}{}^{}$	32.5${}_{}{}^{+3.3}{}_{-2.9}{}^{}$	73.1${}_{}{}^{+6.3}{}_{-5.6}{}^{}$	10	10000
071112C	0.82	5.25 $\pm$ 0.83	407${}_{}{}^{+175}{}_{-100}{}^{}$	-1.13${}_{}{}^{+0.26}{}_{-0.22}{}^{}$	-2.45${}_{}{}^{+0}{}_0{}^{}$	21.1${}_{}{}^{+4.9}{}_{-3.9}{}^{}$	60.2${}_{}{}^{+11.1}{}_{-8.3}{}^{}$	10	10000
071117	1.33	2.27 $\pm$ 0.35	278${}_{}{}^{+101}{}_{-55}{}^{}$	-1.54${}_{}{}^{+0.11}{}_{-0.09}{}^{}$	-2.21${}_{}{}^{+0}{}_0{}^{}$	46${}_{}{}^{+6.4}{}_{-4.7}{}^{}$	67.8${}_{}{}^{+4.2}{}_{-5.3}{}^{}$	10	10000
080319B	0.94	44.56 $\pm$ 0.52	652${}_{}{}^{+9}{}_{-9}{}^{}$	-0.83${}_{}{}^{+0.01}{}_{-0.01}{}^{}$	-3.52${}_{}{}^{+0.18}{}_{-0.25}{}^{}$	210.6${}_{}{}^{+4.5}{}_{-4.4}{}^{}$	6350${}_{}{}^{+78}{}_{-78}{}^{}$	10	10000
080319C	1.95	10.23 $\pm$ 0.64	363${}_{}{}^{+162}{}_{-118}{}^{}$	-1.06${}_{}{}^{+0.17}{}_{-0.11}{}^{}$	-1.92${}_{}{}^{+0.16}{}_{-0.33}{}^{}$	31.8${}_{}{}^{+3.9}{}_{-3.4}{}^{}$	155${}_{}{}^{+18}{}_{-15}{}^{}$	10	10000
080411	1.03	42.85 $\pm$ 0.81	266${}_{}{}^{+21}{}_{-18}{}^{}$	-1.52${}_{}{}^{+1.52}{}_{-0.02}{}^{}$	-2.49${}_{}{}^{+0}{}_0{}^{}$	130.5${}_{}{}^{+8.2}{}_{-7.9}{}^{}$	706${}_{}{}^{+22}{}_{-20}{}^{}$	10	10000
080413A	2.43	17.85 $\pm$ 1.6	133${}_{}{}^{+42}{}_{-36}{}^{}$	0.32${}_{}{}^{+1.91}{}_{-0.9}{}^{}$	-2.27${}_{}{}^{+0.3}{}_{-0.52}{}^{}$	10.4${}_{}{}^{+5.7}{}_{-3}{}^{}$	49.2${}_{}{}^{+9.3}{}_{-6.9}{}^{}$	10	10000
080514B	1.8	5.72 $\pm$ 0.09	196${}_{}{}^{+12}{}_{-12}{}^{}$	-0.53${}_{}{}^{+0.1}{}_{-0.1}{}^{}$	-2.46${}_{}{}^{+0.1}{}_{-0.13}{}^{}$	104.4${}_{}{}^{+6.7}{}_{-6.5}{}^{}$	337${}_{}{}^{+15}{}_{-15}{}^{}$	10	10000
080603B	2.69	12.56 $\pm$ 1.16	85${}_{}{}^{+32}{}_{-18}{}^{}$	-0.93${}_{}{}^{+0.65}{}_{-0.49}{}^{}$	-2.5${}_{}{}^{+0.37}{}_{-7.5}{}^{}$	13.2${}_{}{}^{+2}{}_{-1.7}{}^{}$	51.4${}_{}{}^{+7.6}{}_{-6.1}{}^{}$	10	10000
080605	1.64	13.74 $\pm$ 2.8	253${}_{}{}^{+10}{}_{-10}{}^{}$	-0.87${}_{}{}^{+0.05}{}_{-0.04}{}^{}$	-3.23${}_{}{}^{+0.32}{}_{-0.54}{}^{}$	89.5${}_{}{}^{+9.2}{}_{-8.4}{}^{}$	328.7${}_{}{}^{+6.4}{}_{-6.3}{}^{}$	10	10000
080607	3.04	28.74 $\pm$ 3.45	334${}_{}{}^{+17}{}_{-16}{}^{}$	-0.71${}_{}{}^{+0.05}{}_{-0.04}{}^{}$	-2.52${}_{}{}^{+0.11}{}_{-0.15}{}^{}$	125${}_{}{}^{+13}{}_{-12}{}^{}$	1038${}_{}{}^{+28}{}_{-29}{}^{}$	10	10000
080721	2.59	19.74 $\pm$ 1.97	490${}_{}{}^{+41}{}_{-41}{}^{}$	-0.93${}_{}{}^{+0.06}{}_{-0.05}{}^{}$	-2.45${}_{}{}^{+0.16}{}_{-0.22}{}^{}$	163${}_{}{}^{+13}{}_{-13}{}^{}$	938${}_{}{}^{+39}{}_{-39}{}^{}$	10	10000
080916A	0.69	6.57 $\pm$ 1.48	129${}_{}{}^{+18}{}_{-14}{}^{}$	-1.02${}_{}{}^{+0.23}{}_{-0.17}{}^{}$	-3.36${}_{}{}^{+0}{}_0{}^{}$	8.12${}_{}{}^{+1}{}_{-0.94}{}^{}$	59.9${}_{}{}^{+4.8}{}_{-4.4}{}^{}$	10	10000
080916C	4.35	61.28 $\pm$ 2.05	505${}_{}{}^{+46}{}_{-43}{}^{}$	-1.04${}_{}{}^{+0.04}{}_{-0.04}{}^{}$	-2.26${}_{}{}^{+0.14}{}_{-0.2}{}^{}$	86.6${}_{}{}^{+6.9}{}_{-6.9}{}^{}$	1290${}_{}{}^{+100}{}_{-100}{}^{}$	10	10000
081121	2.51	19.44 $\pm$ 2.92	235${}_{}{}^{+22}{}_{-20}{}^{}$	-0.73${}_{}{}^{+0.1}{}_{-0.09}{}^{}$	-2.53${}_{}{}^{+0.23}{}_{-0.38}{}^{}$	15.7${}_{}{}^{+1.3}{}_{-1.2}{}^{}$	152.5${}_{}{}^{+6.7}{}_{-6.1}{}^{}$	10	10000
081221	2.26	29.2 $\pm$ 0.96	81${}_{}{}^{+2}{}_{-2}{}^{}$	-1.02${}_{}{}^{+0.09}{}_{-0.09}{}^{}$	-3.44${}_{}{}^{+0}{}_0{}^{}$	24.3${}_{}{}^{+1.2}{}_{-1.2}{}^{}$	278.2${}_{}{}^{+5.5}{}_{-5.4}{}^{}$	10	10000
081222	2.77	11.97 $\pm$ 2.31	165${}_{}{}^{+26}{}_{-18}{}^{}$	-0.67${}_{}{}^{+0.22}{}_{-0.21}{}^{}$	-2.35${}_{}{}^{+0.2}{}_{-0.4}{}^{}$	15.9${}_{}{}^{+1.4}{}_{-1.3}{}^{}$	96.4${}_{}{}^{+6.7}{}_{-5.9}{}^{}$	10	10000
090102	1.55	15.26 $\pm$ 0.69	432${}_{}{}^{+42}{}_{-36}{}^{}$	-0.92${}_{}{}^{+0.1}{}_{-0.06}{}^{}$	-3.07${}_{}{}^{+0}{}_0{}^{}$	30.3${}_{}{}^{+2.2}{}_{-2.1}{}^{}$	308${}_{}{}^{+16}{}_{-15}{}^{}$	10	10000
090201	2.1	67.29 $\pm$ 4.12	156${}_{}{}^{+7}{}_{-6}{}^{}$	-0.9${}_{}{}^{+0.05}{}_{-0.05}{}^{}$	-2.71${}_{}{}^{+0.14}{}_{-0.21}{}^{}$	42.7${}_{}{}^{+1.8}{}_{-1.8}{}^{}$	828${}_{}{}^{+23}{}_{-24}{}^{}$	10	10000
090323	3.6	132.99 $\pm$ 1.64	417${}_{}{}^{+45}{}_{-45}{}^{}$	-0.96${}_{}{}^{+0.07}{}_{-0.06}{}^{}$	-2.1${}_{}{}^{+0.1}{}_{-0.12}{}^{}$	51.9${}_{}{}^{+4.6}{}_{-4.4}{}^{}$	2100${}_{}{}^{+160}{}_{-160}{}^{}$	10	10000
090328	0.74	52.8 $\pm$ 3.65	592${}_{}{}^{+134}{}_{-90}{}^{}$	-1.04${}_{}{}^{+0.06}{}_{-0.06}{}^{}$	-2.05${}_{}{}^{+0.15}{}_{-0.34}{}^{}$	78.8${}_{}{}^{+6.6}{}_{-7}{}^{}$	708${}_{}{}^{+57}{}_{-49}{}^{}$	10	10000
090424	0.54	4.3 $\pm$ 0.06	162${}_{}{}^{+6}{}_{-6}{}^{}$	-0.87${}_{}{}^{+0.06}{}_{-0.05}{}^{}$	-3.01${}_{}{}^{+0.18}{}_{-0.24}{}^{}$	86.6${}_{}{}^{+4.7}{}_{-4.4}{}^{}$	459.4${}_{}{}^{+7.8}{}_{-7.9}{}^{}$	10	10000
090618	0.54	104.32 $\pm$ 1.05	187${}_{}{}^{+6}{}_{-6}{}^{}$	-1.29${}_{}{}^{+0.02}{}_{-0.02}{}^{}$	-2.61${}_{}{}^{+0.1}{}_{-0.13}{}^{}$	192${}_{}{}^{+16}{}_{-16}{}^{}$	2909${}_{}{}^{+53}{}_{-54}{}^{}$	10	10000
090709A	1.8	77.34 $\pm$ 2.23	260${}_{}{}^{+15}{}_{-14}{}^{}$	-0.83${}_{}{}^{+0.04}{}_{-0.04}{}^{}$	-2.68${}_{}{}^{+0.23}{}_{-0.48}{}^{}$	29.9${}_{}{}^{+2}{}_{-1.9}{}^{}$	772${}_{}{}^{+14}{}_{-14}{}^{}$	10	10000
090715B	3	71.34 $\pm$ 6.66	135${}_{}{}^{+26}{}_{-18}{}^{}$	-1.13${}_{}{}^{+0.17}{}_{-0.19}{}^{}$	-2.94${}_{}{}^{+0}{}_0{}^{}$	8.14${}_{}{}^{+0.87}{}_{-0.84}{}^{}$	91.8${}_{}{}^{+8}{}_{-6.9}{}^{}$	10	10000
090812	2.45	32.79 $\pm$ 3.49	376${}_{}{}^{+238}{}_{-256}{}^{}$	-0.81${}_{}{}^{+2.28}{}_{-0.37}{}^{}$	-3.02${}_{}{}^{+1.38}{}_{-6.98}{}^{}$	18.3${}_{}{}^{+6.8}{}_{-4.1}{}^{}$	184.9${}_{}{}^{+5.6}{}_{-5.2}{}^{}$	10	10000
090926A	2.11	13.2 $\pm$ 0.54	327${}_{}{}^{+8}{}_{-8}{}^{}$	-0.79${}_{}{}^{+0.02}{}_{-0.02}{}^{}$	-2.61${}_{}{}^{+0.07}{}_{-0.08}{}^{}$	239.7${}_{}{}^{+9}{}_{-8.9}{}^{}$	1873${}_{}{}^{+47}{}_{-46}{}^{}$	10	10000
091003	0.9	20.14 $\pm$ 0.3	358${}_{}{}^{+32}{}_{-28}{}^{}$	-1.02${}_{}{}^{+0.05}{}_{-0.04}{}^{}$	-2.62${}_{}{}^{+0.28}{}_{-0.71}{}^{}$	80.3${}_{}{}^{+3.9}{}_{-3.6}{}^{}$	354${}_{}{}^{+12}{}_{-12}{}^{}$	10	10000
091020	1.71	29.22 $\pm$ 5.22	496${}_{}{}^{+534}{}_{-173}{}^{}$	-1.6${}_{}{}^{+0.1}{}_{-0.08}{}^{}$	-2.93${}_{}{}^{+1.03}{}_{-7.07}{}^{}$	15${}_{}{}^{+4.3}{}_{-2.5}{}^{}$	112.1${}_{}{}^{+5.3}{}_{-8.8}{}^{}$	10	10000
091127	0.49	4.84 $\pm$ 1.71	33${}_{}{}^{+3}{}_{-13}{}^{}$	-1.9${}_{}{}^{+0.05}{}_{-0.06}{}^{}$	-3.02${}_{}{}^{+0}{}_0{}^{}$	95${}_{}{}^{+14}{}_{-13}{}^{}$	147.8${}_{}{}^{+3.8}{}_{-4.9}{}^{}$	10	10000
100414A	1.37	21.73 $\pm$ 0.53	547${}_{}{}^{+22}{}_{-21}{}^{}$	-0.46${}_{}{}^{+0.04}{}_{-0.04}{}^{}$	-3.18${}_{}{}^{+0.27}{}_{-0.52}{}^{}$	74.9${}_{}{}^{+4.2}{}_{-4}{}^{}$	1051${}_{}{}^{+21}{}_{-21}{}^{}$	10	10000
100606A	1.55	59.05 $\pm$ 8.03	742${}_{}{}^{+275}{}_{-142}{}^{}$	-0.96${}_{}{}^{+0.11}{}_{-0.05}{}^{}$	-2.04${}_{}{}^{+0.27}{}_{-7.96}{}^{}$	38${}_{}{}^{+3.8}{}_{-3.5}{}^{}$	451${}_{}{}^{+35}{}_{-36}{}^{}$	10	10000
100621A	0.54	46.26 $\pm$ 8.21	97${}_{}{}^{+8}{}_{-7}{}^{}$	-1.64${}_{}{}^{+0.07}{}_{-0.07}{}^{}$	-2.45${}_{}{}^{+0.11}{}_{-0.18}{}^{}$	18.5${}_{}{}^{+1.6}{}_{-1.5}{}^{}$	406${}_{}{}^{+17}{}_{-15}{}^{}$	10	10000
100728A	1.57	159.94 $\pm$ 5.2	305${}_{}{}^{+16}{}_{-16}{}^{}$	-0.65${}_{}{}^{+0.06}{}_{-0.05}{}^{}$	-2.48${}_{}{}^{+0.13}{}_{-0.17}{}^{}$	31.5${}_{}{}^{+2}{}_{-1.9}{}^{}$	1730${}_{}{}^{+110}{}_{-100}{}^{}$	10	10000
100814A	1.44	148.42 $\pm$ 43.32	128${}_{}{}^{+13}{}_{-11}{}^{}$	-0.42${}_{}{}^{+0.39}{}_{-0.35}{}^{}$	-3.57${}_{}{}^{+0}{}_0{}^{}$	6.78${}_{}{}^{+0.71}{}_{-0.71}{}^{}$	132.6${}_{}{}^{+10.3}{}_{-9.5}{}^{}$	10	10000
100906A	1.73	90.14 $\pm$ 14.08	185${}_{}{}^{+60}{}_{-53}{}^{}$	-1.58${}_{}{}^{+0.14}{}_{-0.09}{}^{}$	-2.62${}_{}{}^{+0.51}{}_{-7.38}{}^{}$	29.3${}_{}{}^{+3.1}{}_{-3.1}{}^{}$	260${}_{}{}^{+29}{}_{-22}{}^{}$	10	10000
101213A	0.41	30.54 $\pm$ 4.62	232${}_{}{}^{+43}{}_{-53}{}^{}$	-0.84${}_{}{}^{+0.29}{}_{-0.17}{}^{}$	-2.63${}_{}{}^{+0.52}{}_{-7.37}{}^{}$	6.83${}_{}{}^{+1}{}_{-0.94}{}^{}$	112.3${}_{}{}^{+8.9}{}_{-7.6}{}^{}$	10	10000
110213A	1.46	29.25 $\pm$ 2.6	89${}_{}{}^{+16}{}_{-18}{}^{}$	-1.62${}_{}{}^{+0.28}{}_{-0.14}{}^{}$	-2.92${}_{}{}^{+0.61}{}_{-7.08}{}^{}$	12.3${}_{}{}^{+1.6}{}_{-1.4}{}^{}$	105.3${}_{}{}^{+6.5}{}_{-5.2}{}^{}$	10	10000
110422A	1.77	22.3 $\pm$ 0.27	155${}_{}{}^{+3}{}_{-3}{}^{}$	-0.7${}_{}{}^{+0.05}{}_{-0.04}{}^{}$	-3.21${}_{}{}^{+0.13}{}_{-0.17}{}^{}$	106.9${}_{}{}^{+8.6}{}_{-8}{}^{}$	888${}_{}{}^{+13}{}_{-13}{}^{}$	10	10000
110503A	1.61	6.67 $\pm$ 2.1	220${}_{}{}^{+12}{}_{-12}{}^{}$	-0.98${}_{}{}^{+0.05}{}_{-0.05}{}^{}$	-2.71${}_{}{}^{+0.16}{}_{-0.23}{}^{}$	90${}_{}{}^{+6.7}{}_{-6.2}{}^{}$	298${}_{}{}^{+13}{}_{-13}{}^{}$	10	10000
110715A	0.82	2.84 $\pm$ 0.18	119${}_{}{}^{+7}{}_{-7}{}^{}$	-1.23${}_{}{}^{+0.09}{}_{-0.08}{}^{}$	-2.66${}_{}{}^{+0.14}{}_{-0.21}{}^{}$	68.1${}_{}{}^{+2.5}{}_{-2.5}{}^{}$	240${}_{}{}^{+16}{}_{-14}{}^{}$	10	10000
110731A	2.83	6.7 $\pm$ 0.86	288${}_{}{}^{+18}{}_{-16}{}^{}$	-0.74${}_{}{}^{+0.1}{}_{-0.09}{}^{}$	-3.39${}_{}{}^{+0}{}_0{}^{}$	31.2${}_{}{}^{+2}{}_{-2}{}^{}$	167.9${}_{}{}^{+6.4}{}_{-6.1}{}^{}$	10	10000
110918A	0.98	19.55 $\pm$ 0.1	336${}_{}{}^{+40}{}_{-35}{}^{}$	-1.64${}_{}{}^{+0.04}{}_{-0.03}{}^{}$	-2.25${}_{}{}^{+0.05}{}_{-0.05}{}^{}$	3401${}_{}{}^{+90}{}_{-90}{}^{}$	8760${}_{}{}^{+290}{}_{-290}{}^{}$	10	10000
111228A	0.72	50.58 $\pm$ 2.18	44${}_{}{}^{+18}{}_{-14}{}^{}$	-1.54${}_{}{}^{+0.64}{}_{-0.44}{}^{}$	-2.78${}_{}{}^{+0}{}_0{}^{}$	11.9${}_{}{}^{+3.6}{}_{-2.4}{}^{}$	78.5${}_{}{}^{+8.1}{}_{-7.1}{}^{}$	10	10000
120119A	1.73	39.64 $\pm$ 4.14	153${}_{}{}^{+12}{}_{-12}{}^{}$	-0.85${}_{}{}^{+0.12}{}_{-0.1}{}^{}$	-2.34${}_{}{}^{+0.1}{}_{-0.12}{}^{}$	36.1${}_{}{}^{+2.9}{}_{-2.8}{}^{}$	500${}_{}{}^{+36}{}_{-34}{}^{}$	10	10000
120624B	2.2	267.9 $\pm$ 4.16	531${}_{}{}^{+54}{}_{-52}{}^{}$	-1.02${}_{}{}^{+0.07}{}_{-0.06}{}^{}$	-2.6${}_{}{}^{+0.29}{}_{-0.58}{}^{}$	48.1${}_{}{}^{+3.2}{}_{-3.1}{}^{}$	2309${}_{}{}^{+98}{}_{-90}{}^{}$	10	10000
120711A	1.41	41.34 $\pm$ 0.6	1061${}_{}{}^{+38}{}_{-36}{}^{}$	-0.97${}_{}{}^{+0.01}{}_{-0.01}{}^{}$	-2.71${}_{}{}^{+0.14}{}_{-0.18}{}^{}$	127.5${}_{}{}^{+7}{}_{-6.9}{}^{}$	3793${}_{}{}^{+86}{}_{-86}{}^{}$	10	10000
120716A	2.49	208.58 $\pm$ 5.32	175${}_{}{}^{+48}{}_{-38}{}^{}$	-1.47${}_{}{}^{+0.16}{}_{-0.13}{}^{}$	-2.44${}_{}{}^{+0.31}{}_{-7.56}{}^{}$	8.6${}_{}{}^{+1.3}{}_{-1.2}{}^{}$	150.4${}_{}{}^{+13.2}{}_{-9.9}{}^{}$	10	10000
121128A	2.2	10.02 $\pm$ 3.17	76${}_{}{}^{+3}{}_{-3}{}^{}$	-0.94${}_{}{}^{+0.13}{}_{-0.12}{}^{}$	-3.36${}_{}{}^{+0.33}{}_{-0.58}{}^{}$	22.3${}_{}{}^{+1.3}{}_{-1.2}{}^{}$	74${}_{}{}^{+2.2}{}_{-2.1}{}^{}$	10	10000
130408A	3.76	4.24 $\pm$ 0.29	271${}_{}{}^{+37}{}_{-43}{}^{}$	-0.7${}_{}{}^{+0.19}{}_{-0.13}{}^{}$	-2.3${}_{}{}^{+0.22}{}_{-0.28}{}^{}$	31.5${}_{}{}^{+5.9}{}_{-4.8}{}^{}$	110${}_{}{}^{+23}{}_{-17}{}^{}$	10	10000
130427A	0.34	61.74 $\pm$ 6.25	1056${}_{}{}^{+10}{}_{-10}{}^{}$	-0.95${}_{}{}^{+0.01}{}_{-0.01}{}^{}$	-4.13${}_{}{}^{+0}{}_0{}^{}$	5090${}_{}{}^{+110}{}_{-110}{}^{}$	28630${}_{}{}^{+150}{}_{-150}{}^{}$	10	10000
130505A	2.27	14.69 $\pm$ 0.47	593${}_{}{}^{+26}{}_{-24}{}^{}$	-0.49${}_{}{}^{+0.04}{}_{-0.04}{}^{}$	-2.04${}_{}{}^{+0.03}{}_{-0.03}{}^{}$	707${}_{}{}^{+28}{}_{-28}{}^{}$	3445${}_{}{}^{+80}{}_{-79}{}^{}$	10	10000
130518A	2.49	28.63 $\pm$ 5.69	332${}_{}{}^{+54}{}_{-45}{}^{}$	-0.88${}_{}{}^{+0.09}{}_{-0.08}{}^{}$	-1.96${}_{}{}^{+0.07}{}_{-0.08}{}^{}$	177${}_{}{}^{+16}{}_{-16}{}^{}$	1440${}_{}{}^{+93}{}_{-91}{}^{}$	10	10000
130701A	1.16	3.66 $\pm$ 0.32	89${}_{}{}^{+4}{}_{-4}{}^{}$	-1.1${}_{}{}^{+0.11}{}_{-0.11}{}^{}$	-3.77${}_{}{}^{+0}{}_0{}^{}$	29.6${}_{}{}^{+1.8}{}_{-1.7}{}^{}$	62.8${}_{}{}^{+1.9}{}_{-1.9}{}^{}$	10	10000
130831A	0.48	17.53 $\pm$ 2.81	55${}_{}{}^{+7}{}_{-9}{}^{}$	-1.6${}_{}{}^{+0.14}{}_{-0.13}{}^{}$	-3.27${}_{}{}^{+0.5}{}_{-6.73}{}^{}$	15.9${}_{}{}^{+1.4}{}_{-1.3}{}^{}$	89.3${}_{}{}^{+4}{}_{-3.7}{}^{}$	10	10000
130907A	1.24	180.29 $\pm$ 0.41	387${}_{}{}^{+16}{}_{-16}{}^{}$	-0.9${}_{}{}^{+0.03}{}_{-0.03}{}^{}$	-2.22${}_{}{}^{+0.05}{}_{-0.05}{}^{}$	190${}_{}{}^{+6.4}{}_{-6.3}{}^{}$	9030${}_{}{}^{+300}{}_{-300}{}^{}$	10	10000
131030A	1.29	15.71 $\pm$ 0.56	196${}_{}{}^{+6}{}_{-6}{}^{}$	-0.52${}_{}{}^{+0.07}{}_{-0.07}{}^{}$	-3.05${}_{}{}^{+0.16}{}_{-0.22}{}^{}$	72.3${}_{}{}^{+2.7}{}_{-2.6}{}^{}$	707${}_{}{}^{+28}{}_{-26}{}^{}$	10	10000
131105A	1.69	110.95 $\pm$ 3.2	154${}_{}{}^{+31}{}_{-21}{}^{}$	-0.89${}_{}{}^{+0.24}{}_{-0.22}{}^{}$	-2.29${}_{}{}^{+0.17}{}_{-0.29}{}^{}$	12.6${}_{}{}^{+1.5}{}_{-1.4}{}^{}$	191${}_{}{}^{+15}{}_{-12}{}^{}$	10	10000
131108A	2.4	17.69 $\pm$ 0.47	332${}_{}{}^{+31}{}_{-29}{}^{}$	-1.12${}_{}{}^{+0.08}{}_{-0.07}{}^{}$	-2.68${}_{}{}^{+0.24}{}_{-0.41}{}^{}$	77${}_{}{}^{+13}{}_{-12}{}^{}$	370${}_{}{}^{+17}{}_{-15}{}^{}$	10	10000
131231A	0.64	29.16 $\pm$ 3.04	162${}_{}{}^{+6}{}_{-6}{}^{}$	-1.28${}_{}{}^{+0.05}{}_{-0.04}{}^{}$	-2.47${}_{}{}^{+0.05}{}_{-0.06}{}^{}$	171.5${}_{}{}^{+7.3}{}_{-7.1}{}^{}$	1692${}_{}{}^{+45}{}_{-45}{}^{}$	10	10000
140213A	1.21	16.4 $\pm$ 2.87	99${}_{}{}^{+4}{}_{-4}{}^{}$	-1.39${}_{}{}^{+0.06}{}_{-0.06}{}^{}$	-3.52${}_{}{}^{+0.52}{}_{-2.19}{}^{}$	35.7${}_{}{}^{+1.6}{}_{-1.6}{}^{}$	182.8${}_{}{}^{+3.8}{}_{-3.7}{}^{}$	10	10000
140419A	3.96	53.47 $\pm$ 3.81	282${}_{}{}^{+38}{}_{-38}{}^{}$	-0.43${}_{}{}^{+0.18}{}_{-0.14}{}^{}$	-2.08${}_{}{}^{+0.18}{}_{-0.24}{}^{}$	19.8${}_{}{}^{+2.1}{}_{-2}{}^{}$	717${}_{}{}^{+58}{}_{-57}{}^{}$	10	10000
140506A	0.89	61.04 $\pm$ 5.23	186${}_{}{}^{+104}{}_{-49}{}^{}$	-1.3${}_{}{}^{+0.42}{}_{-0.25}{}^{}$	-2.24${}_{}{}^{+0.3}{}_{-2.36}{}^{}$	21.9${}_{}{}^{+5}{}_{-3.4}{}^{}$	57.4${}_{}{}^{+5.2}{}_{-3.4}{}^{}$	10	10000
140508A	1.03	149.68 $\pm$ 20.98	220${}_{}{}^{+14}{}_{-13}{}^{}$	-1.17${}_{}{}^{+0.04}{}_{-0.04}{}^{}$	-2.54${}_{}{}^{+0.15}{}_{-0.22}{}^{}$	220${}_{}{}^{+10}{}_{-10}{}^{}$	731${}_{}{}^{+50}{}_{-47}{}^{}$	10	10000
140512A	0.72	141.17 $\pm$ 6.13	479${}_{}{}^{+117}{}_{-79}{}^{}$	-1.27${}_{}{}^{+0.12}{}_{-0.11}{}^{}$	-1.97${}_{}{}^{+0}{}_0{}^{}$	26.8${}_{}{}^{+3.8}{}_{-3.1}{}^{}$	473${}_{}{}^{+43}{}_{-35}{}^{}$	10	10000
140606B	0.38	6.73 $\pm$ 0.71	254${}_{}{}^{+20}{}_{-17}{}^{}$	-0.59${}_{}{}^{+0.12}{}_{-0.11}{}^{}$	-3.28${}_{}{}^{+0}{}_0{}^{}$	18.7${}_{}{}^{+1.4}{}_{-1.3}{}^{}$	67.9${}_{}{}^{+3.4}{}_{-3.2}{}^{}$	10	10000
140801A	1.32	6.16 $\pm$ 0.19	108${}_{}{}^{+3}{}_{-3}{}^{}$	-0.44${}_{}{}^{+0.11}{}_{-0.1}{}^{}$	-4.99${}_{}{}^{+0}{}_0{}^{}$	14.9${}_{}{}^{+1.3}{}_{-1.3}{}^{}$	113.2${}_{}{}^{+2.5}{}_{-2.4}{}^{}$	10	10000
140808A	3.29	5.2 $\pm$ 1.12	123${}_{}{}^{+14}{}_{-13}{}^{}$	-0.92${}_{}{}^{+0.19}{}_{-0.16}{}^{}$	-3.91${}_{}{}^{+1.1}{}_{-6.09}{}^{}$	11.5${}_{}{}^{+1.1}{}_{-1}{}^{}$	33.4${}_{}{}^{+1.9}{}_{-1.8}{}^{}$	10	10000
141220A	1.32	6.89 $\pm$ 0.31	138${}_{}{}^{+10}{}_{-9}{}^{}$	-0.55${}_{}{}^{+0.17}{}_{-0.16}{}^{}$	-3.58${}_{}{}^{+0}{}_0{}^{}$	13${}_{}{}^{+1.5}{}_{-1.4}{}^{}$	46.9${}_{}{}^{+2.4}{}_{-2.3}{}^{}$	10	10000
150206A	2.09	35.17 $\pm$ 4.74	228${}_{}{}^{+23}{}_{-22}{}^{}$	-0.73${}_{}{}^{+0.1}{}_{-0.09}{}^{}$	-2.2${}_{}{}^{+0.1}{}_{-0.12}{}^{}$	56.6${}_{}{}^{+5.3}{}_{-5.1}{}^{}$	558${}_{}{}^{+41}{}_{-40}{}^{}$	10	10000
150314A	1.76	10.25 $\pm$ 0.22	350${}_{}{}^{+10}{}_{-10}{}^{}$	-0.78${}_{}{}^{+0.02}{}_{-0.02}{}^{}$	-2.9${}_{}{}^{+0.12}{}_{-0.15}{}^{}$	194.6${}_{}{}^{+7.5}{}_{-7.3}{}^{}$	941${}_{}{}^{+26}{}_{-26}{}^{}$	10	10000
150323A	0.59	153.17 $\pm$ 9.4	95${}_{}{}^{+9}{}_{-8}{}^{}$	-1.21${}_{}{}^{+0.17}{}_{-0.17}{}^{}$	-3.22${}_{}{}^{+0}{}_0{}^{}$	6.71${}_{}{}^{+0.99}{}_{-0.94}{}^{}$	112${}_{}{}^{+3.6}{}_{-3.4}{}^{}$	10	10000
150403A	2.06	21.04 $\pm$ 1.55	373${}_{}{}^{+34}{}_{-31}{}^{}$	-0.93${}_{}{}^{+0.05}{}_{-0.05}{}^{}$	-2.06${}_{}{}^{+0.05}{}_{-0.07}{}^{}$	153.9${}_{}{}^{+7.4}{}_{-7.3}{}^{}$	1074${}_{}{}^{+57}{}_{-57}{}^{}$	10	10000
150821A	0.76	110.96 $\pm$ 13.79	351${}_{}{}^{+104}{}_{-96}{}^{}$	-1.47${}_{}{}^{+0.09}{}_{-0.06}{}^{}$	-2.21${}_{}{}^{+0.23}{}_{-0.54}{}^{}$	22.4${}_{}{}^{+1.6}{}_{-1.5}{}^{}$	880${}_{}{}^{+71}{}_{-57}{}^{}$	10	10000
151021A	2.33	57.01 $\pm$ 2.86	170${}_{}{}^{+13}{}_{-11}{}^{}$	-1.14${}_{}{}^{+0.09}{}_{-0.08}{}^{}$	-2.46${}_{}{}^{+0.12}{}_{-0.16}{}^{}$	33.3${}_{}{}^{+2.9}{}_{-2.9}{}^{}$	801${}_{}{}^{+69}{}_{-63}{}^{}$	10	10000
151027A	0.81	117.33 $\pm$ 2.72	151${}_{}{}^{+46}{}_{-39}{}^{}$	-1.37${}_{}{}^{+0.2}{}_{-0.14}{}^{}$	-2.37${}_{}{}^{+0.3}{}_{-0.71}{}^{}$	15.8${}_{}{}^{+1.4}{}_{-1.3}{}^{}$	156${}_{}{}^{+21}{}_{-15}{}^{}$	10	10000
160131A	0.97	109.87 $\pm$ 7.94	651${}_{}{}^{+230}{}_{-156}{}^{}$	-0.93${}_{}{}^{+0.11}{}_{-0.09}{}^{}$	-1.58${}_{}{}^{+0.04}{}_{-0.06}{}^{}$	162.1${}_{}{}^{+7.4}{}_{-7.4}{}^{}$	3300${}_{}{}^{+250}{}_{-250}{}^{}$	10	10000
160509A	1.17	28.51 $\pm$ 3.82	288${}_{}{}^{+29}{}_{-27}{}^{}$	-0.99${}_{}{}^{+0.06}{}_{-0.05}{}^{}$	-2.08${}_{}{}^{+0.08}{}_{-0.1}{}^{}$	219.5${}_{}{}^{+9.6}{}_{-9.5}{}^{}$	2940${}_{}{}^{+270}{}_{-260}{}^{}$	10	10000
160623A	0.37	21.6 $\pm$ 0.59	552${}_{}{}^{+14}{}_{-14}{}^{}$	-1.03${}_{}{}^{+0.02}{}_{-0.02}{}^{}$	-2.65${}_{}{}^{+0.05}{}_{-0.06}{}^{}$	1125${}_{}{}^{+14}{}_{-14}{}^{}$	6882${}_{}{}^{+91}{}_{-91}{}^{}$	10	10000
160625B	1.41	20.99 $\pm$ 0.57	571${}_{}{}^{+12}{}_{-11}{}^{}$	-0.8${}_{}{}^{+0.01}{}_{-0.01}{}^{}$	-2.28${}_{}{}^{+0.02}{}_{-0.02}{}^{}$	1088${}_{}{}^{+47}{}_{-47}{}^{}$	9500${}_{}{}^{+120}{}_{-110}{}^{}$	10	10000
160629A	3.33	64.57 $\pm$ 11.2	228${}_{}{}^{+24}{}_{-26}{}^{}$	-0.79${}_{}{}^{+0.13}{}_{-0.11}{}^{}$	-2.92${}_{}{}^{+0.5}{}_{-4.17}{}^{}$	8.52${}_{}{}^{+0.9}{}_{-0.88}{}^{}$	157.1${}_{}{}^{+5.8}{}_{-5.4}{}^{}$	10	10000
161023A	2.708	50 $\pm$ 0	163${}_{}{}^{+37}{}_{-28}{}^{}$	-1.11${}_{}{}^{+0.22}{}_{-0.18}{}^{}$	-2.27${}_{}{}^{+0.16}{}_{-0.32}{}^{}$	53${}_{}{}^{+8}{}_{-8}{}^{}$aaPeak energy flux calculated on the 64-ms time scale	420${}_{}{}^{+60}{}_{-60}{}^{}$	20	10000
170214A	2.53	150 $\pm$ 0	330${}_{}{}^{+21}{}_{-19}{}^{}$	-0.7${}_{}{}^{+0.07}{}_{-0.06}{}^{}$	-2.61${}_{}{}^{+0.16}{}_{-0.27}{}^{}$	87.7${}_{}{}^{+1.3}{}_{-1.3}{}^{}$aaPeak energy flux calculated on the 64-ms time scale	2410${}_{}{}^{+170}{}_{-170}{}^{}$	20	10000
171010A	0.3285	155 $\pm$ 0	171${}_{}{}^{+7}{}_{-6}{}^{}$	-1.09${}_{}{}^{+0.04}{}_{-0.04}{}^{}$	-2.42${}_{}{}^{+0.06}{}_{-0.07}{}^{}$	245${}_{}{}^{+17}{}_{-17}{}^{}$aaPeak energy flux calculated on the 64-ms time scale	6500${}_{}{}^{+200}{}_{-200}{}^{}$	20	10000
180325A	2.248	10 $\pm$ 0	306${}_{}{}^{+50}{}_{-39}{}^{}$	-0.5${}_{}{}^{+0.21}{}_{-0.19}{}^{}$	-2.65${}_{}{}^{+0.31}{}_{-1.06}{}^{}$	82${}_{}{}^{+13}{}_{-13}{}^{}$aaPeak energy flux calculated on the 64-ms time scale	190${}_{}{}^{+30}{}_{-30}{}^{}$	20	10000

Table 3. Table 3: The intrinsic properties of Fermi sample

GRB	$z$	$E_{iso}$	$L_{iso}$	$E_{p,z}$	$T_{90,z}$	$E_{iso}^{\prime }$	$L_{iso}^{\prime }$	$E_p^{\prime }$	$T_{90}^{\prime }$	${\Gamma }_0$
		($\times {10}^{52}$ erg)	($\times {10}^{52}$ erg s-1)	(keV)	(s)	($\times {10}^{50}$ erg)	($\times {10}^{46}$ erg s-1)	(keV)	(s)
171222A	2.409	3.35 $\pm$ 0.3	1.02 $\pm$ 0.27	59.8 $\pm$ 14.1	23.58 $\pm$ 1.35	0.9 $\pm$ 0.16	5.54 $\pm$ 2.28	0.16 $\pm$ 0.05	8776.99 $\pm$ 1473.85	372.22 $\pm$ 58.74
171010A	0.3285	25.32 $\pm$ 0.06	1.01 $\pm$ 0.01	182.88 $\pm$ 1.9	80.74 $\pm$ 0.61	11.07 $\pm$ 0.08	14.48 $\pm$ 0.25	0.8 $\pm$ 0.01	18465.91 $\pm$ 187.13	228.7 $\pm$ 1.55
170705A	2.01	17.88 $\pm$ 0.54	11.38 $\pm$ 0.4	294.61 $\pm$ 23.01	7.57 $\pm$ 0.46	3.15 $\pm$ 0.15	26.49 $\pm$ 2.18	0.52 $\pm$ 0.04	4295.37 $\pm$ 304.94	567.54 $\pm$ 21.13
170607A	0.557	1.03 $\pm$ 0.02	0.27 $\pm$ 0.01	174.06 $\pm$ 14.06	14.51 $\pm$ 1.83	0.81 $\pm$ 0.04	12.5 $\pm$ 1.26	1.36 $\pm$ 0.12	1853.23 $\pm$ 246.86	127.74 $\pm$ 5.44
170214A	2.53	392.53 $\pm$ 2.56	30.32 $\pm$ 0.85	1699.3 $\pm$ 39.63	34.81 $\pm$ 0.21	93.6 $\pm$ 1.65	129.31 $\pm$ 5.59	4.05 $\pm$ 0.12	14597.94 $\pm$ 254.27	419.35 $\pm$ 6.87
170113A	1.968	2.39 $\pm$ 0.41	1.54 $\pm$ 0.36	333.92 $\pm$ 174.49	16.56 $\pm$ 1.39	1.12 $\pm$ 0.34	25.14 $\pm$ 13.79	1.56 $\pm$ 0.9	3550.59 $\pm$ 931.95	214.4 $\pm$ 53.3
161129A	0.645	1.73 $\pm$ 0.07	0.24 $\pm$ 0.03	240.84 $\pm$ 70.09	21.94 $\pm$ 0.44	1.64 $\pm$ 0.23	16.37 $\pm$ 4.73	2.29 $\pm$ 0.73	2312.55 $\pm$ 314.13	105.39 $\pm$ 14.16
161117A	1.549	22.88 $\pm$ 0.62	1.29 $\pm$ 0.14	205.62 $\pm$ 7.76	47.93 $\pm$ 0.26	9.41 $\pm$ 0.55	16.33 $\pm$ 2.45	0.85 $\pm$ 0.05	11657.44 $\pm$ 611.49	243.21 $\pm$ 12.69
161017A	2.013	7.32 $\pm$ 0.44	3.03 $\pm$ 0.41	718.83 $\pm$ 122.83	10.71 $\pm$ 2.68	3.48 $\pm$ 0.4	51.32 $\pm$ 12.13	3.42 $\pm$ 0.67	2252.25 $\pm$ 604.84	210.38 $\pm$ 20.32
161014A	2.823	9.49 $\pm$ 0.5	5.21 $\pm$ 0.52	646.18 $\pm$ 55.13	9.58 $\pm$ 0.39	3.36 $\pm$ 0.27	48.9 $\pm$ 7.51	2.29 $\pm$ 0.24	2706.59 $\pm$ 193.21	282.64 $\pm$ 16.56
160804A	0.736	2.29 $\pm$ 0.11	0.12 $\pm$ 0.02	123.93 $\pm$ 7.25	75.8 $\pm$ 12.51	2.24 $\pm$ 0.2	8.75 $\pm$ 1.95	1.21 $\pm$ 0.12	7735.39 $\pm$ 1411.64	102.05 $\pm$ 7.94
160629A	3.332	52.68 $\pm$ 1.67	9.96 $\pm$ 0.95	1202.36 $\pm$ 112.01	14.95 $\pm$ 0.21	18.07 $\pm$ 1.22	87.85 $\pm$ 13.44	4.12 $\pm$ 0.46	4358.83 $\pm$ 267.01	291.54 $\pm$ 17.37
160625B	1.406	522.34 $\pm$ 1.75	127.32 $\pm$ 0.8	1134.34 $\pm$ 15.51	188.97 $\pm$ 4.58	54.11 $\pm$ 0.4	102.45 $\pm$ 1.49	1.17 $\pm$ 0.02	182432.46 $\pm$ 4576.71	965.4 $\pm$ 6.32
160509A	1.17	104.9 $\pm$ 0.57	16.59 $\pm$ 0.18	770.74 $\pm$ 20.82	170.35 $\pm$ 0.37	23.5 $\pm$ 0.32	62.43 $\pm$ 1.72	1.73 $\pm$ 0.05	76049.24 $\pm$ 977.43	446.42 $\pm$ 5.65
151027A	0.81	4.87 $\pm$ 0.12	0.86 $\pm$ 0.04	366.76 $\pm$ 61.78	68.17 $\pm$ 0.63	3.09 $\pm$ 0.25	26.01 $\pm$ 4.09	2.33 $\pm$ 0.43	10740.11 $\pm$ 814.99	157.54 $\pm$ 11.86
150821A	0.755	15.96 $\pm$ 0.19	0.77 $\pm$ 0.03	493.2 $\pm$ 31.25	58.93 $\pm$ 3.28	12.11 $\pm$ 0.44	33.27 $\pm$ 2.7	3.74 $\pm$ 0.27	7769.02 $\pm$ 506.57	131.83 $\pm$ 4.49
150727A	0.313	0.24 $\pm$ 0.01	0.02 $\pm$ 0	195.05 $\pm$ 25.18	37.63 $\pm$ 3.03	0.69 $\pm$ 0.07	11.05 $\pm$ 2.44	5.7 $\pm$ 0.88	1286.77 $\pm$ 150.82	34.19 $\pm$ 2.92
150514A	0.807	1.15 $\pm$ 0.05	0.52 $\pm$ 0.02	116.72 $\pm$ 10.19	5.98 $\pm$ 0.59	0.56 $\pm$ 0.03	9.33 $\pm$ 0.9	0.57 $\pm$ 0.06	1219.38 $\pm$ 131.66	203.78 $\pm$ 8.71
150403A	2.06	97.03 $\pm$ 0.96	41.27 $\pm$ 0.82	1311.74 $\pm$ 53.09	7.28 $\pm$ 0.26	17.96 $\pm$ 0.4	106.09 $\pm$ 4.67	2.43 $\pm$ 0.11	3931.64 $\pm$ 162.52	540.18 $\pm$ 10.61
150314A	1.758	86.69 $\pm$ 0.6	42.86 $\pm$ 0.53	957.28 $\pm$ 19.06	3.88 $\pm$ 0.05	13.77 $\pm$ 0.17	81.16 $\pm$ 1.94	1.52 $\pm$ 0.03	2439.04 $\pm$ 41.12	629.39 $\pm$ 6.46
150301B	1.5169	3.32 $\pm$ 0.19	1.01 $\pm$ 0.12	460.51 $\pm$ 90.95	5.29 $\pm$ 0.62	2.16 $\pm$ 0.25	32.05 $\pm$ 7.6	3 $\pm$ 0.67	812.9 $\pm$ 126	153.69 $\pm$ 15.63
141225A	0.915	2.12 $\pm$ 0.11	0.34 $\pm$ 0.04	342.71 $\pm$ 52.13	29.41 $\pm$ 2.55	2 $\pm$ 0.2	22.8 $\pm$ 4.94	3.22 $\pm$ 0.57	3125.59 $\pm$ 385.93	106.28 $\pm$ 9.33
141221A	1.452	1.72 $\pm$ 0.16	1.16 $\pm$ 0.17	450.62 $\pm$ 87.15	9.71 $\pm$ 0.7	1.04 $\pm$ 0.15	31.8 $\pm$ 8.25	2.73 $\pm$ 0.6	1604.11 $\pm$ 207.06	165.21 $\pm$ 17.69
141220A	1.3195	2.64 $\pm$ 0.09	2.32 $\pm$ 0.09	418.8 $\pm$ 24.17	3.28 $\pm$ 0.4	1.13 $\pm$ 0.05	31.57 $\pm$ 2.3	1.78 $\pm$ 0.12	770.99 $\pm$ 96.39	234.81 $\pm$ 7.2
141028A	2.33	74.67 $\pm$ 0.75	26.36 $\pm$ 0.69	979.59 $\pm$ 53.39	9.46 $\pm$ 0.73	14.99 $\pm$ 0.42	79.62 $\pm$ 4.68	1.97 $\pm$ 0.12	4711.92 $\pm$ 384.07	498.29 $\pm$ 13.12
141004A	0.573	0.21 $\pm$ 0.02	0.2 $\pm$ 0.01	43.79 $\pm$ 17.7	1.63 $\pm$ 0.39	0.1 $\pm$ 0.02	3.72 $\pm$ 1.34	0.22 $\pm$ 0.1	324.37 $\pm$ 95.99	199.31 $\pm$ 35.29
140907A	1.21	2.61 $\pm$ 0.1	0.36 $\pm$ 0.05	311.54 $\pm$ 21.69	16.22 $\pm$ 2.48	2.3 $\pm$ 0.19	21.1 $\pm$ 4.48	2.74 $\pm$ 0.28	1840.64 $\pm$ 313.25	113.5 $\pm$ 8.53
140808A	3.29	8.62 $\pm$ 0.53	12.33 $\pm$ 0.95	503.15 $\pm$ 34.92	1.04 $\pm$ 0.08	1.84 $\pm$ 0.14	42.25 $\pm$ 5.09	1.08 $\pm$ 0.09	488.17 $\pm$ 45.49	467.78 $\pm$ 21.66
140801A	1.32	5.8 $\pm$ 0.15	2.82 $\pm$ 0.1	276.69 $\pm$ 6.13	3.09 $\pm$ 0.25	1.89 $\pm$ 0.06	22.45 $\pm$ 1.16	0.9 $\pm$ 0.03	947.77 $\pm$ 77.72	306.76 $\pm$ 5.79
140703A	3.14	23.73 $\pm$ 1.15	7.23 $\pm$ 0.67	861.25 $\pm$ 148.3	20.28 $\pm$ 0.72	8.17 $\pm$ 0.8	64.27 $\pm$ 12.48	2.97 $\pm$ 0.57	5891.16 $\pm$ 545.24	290.46 $\pm$ 24.8
140623A	1.92	3.5 $\pm$ 0.38	0.78 $\pm$ 0.3	826.26 $\pm$ 320.43	38.05 $\pm$ 1.37	3.3 $\pm$ 0.88	51.9 $\pm$ 32.44	7.78 $\pm$ 3.57	4041.3 $\pm$ 999.27	106.21 $\pm$ 25.98
140620A	2.04	9.17 $\pm$ 0.41	2.37 $\pm$ 0.26	230.19 $\pm$ 33.87	15.07 $\pm$ 3.99	2.99 $\pm$ 0.28	18.9 $\pm$ 3.67	0.75 $\pm$ 0.13	4621.28 $\pm$ 1278.68	306.57 $\pm$ 24.7
140606B	0.384	0.57 $\pm$ 0.03	0.2 $\pm$ 0.01	767.61 $\pm$ 228.8	16.46 $\pm$ 1.49	0.97 $\pm$ 0.14	43.65 $\pm$ 11.58	13.16 $\pm$ 4.28	960.05 $\pm$ 152.31	58.32 $\pm$ 7.6
140512A	0.725	8.72 $\pm$ 0.16	0.8 $\pm$ 0.04	1177.84 $\pm$ 121.35	85.78 $\pm$ 1.37	9.46 $\pm$ 0.49	70.54 $\pm$ 7.62	12.77 $\pm$ 1.46	7912.53 $\pm$ 407.57	92.24 $\pm$ 4.52
140508A	1.027	23.78 $\pm$ 0.28	9.18 $\pm$ 0.16	533.46 $\pm$ 28.44	21.85 $\pm$ 0.11	5.97 $\pm$ 0.16	43.39 $\pm$ 2.23	1.34 $\pm$ 0.08	8701.49 $\pm$ 215.71	398.26 $\pm$ 9.65
140506A	0.889	1.05 $\pm$ 0.08	0.88 $\pm$ 0.05	373.19 $\pm$ 61.49	33.95 $\pm$ 1.06	0.66 $\pm$ 0.07	26.46 $\pm$ 4.33	2.36 $\pm$ 0.43	5371.64 $\pm$ 441.65	158.23 $\pm$ 12.03
140423A	3.26	65.67 $\pm$ 1.94	6.05 $\pm$ 0.99	516.74 $\pm$ 64.73	22.36 $\pm$ 2.72	19.7 $\pm$ 1.92	40.83 $\pm$ 10.11	1.55 $\pm$ 0.24	7452.9 $\pm$ 1140.03	333.39 $\pm$ 30.92
140304A	5.283	12.24 $\pm$ 1.4	12.65 $\pm$ 2.34	775.06 $\pm$ 173.37	4.97 $\pm$ 1.39	3.11 $\pm$ 0.53	61.39 $\pm$ 19.42	1.97 $\pm$ 0.51	1954.54 $\pm$ 600.57	393.2 $\pm$ 50.48
140213A	1.2076	11.99 $\pm$ 0.2	3.25 $\pm$ 0.09	191.24 $\pm$ 7.85	8.44 $\pm$ 0.32	3.12 $\pm$ 0.09	16.52 $\pm$ 0.84	0.5 $\pm$ 0.02	3238.49 $\pm$ 142.86	383.87 $\pm$ 8.3
140206A	2.73	310.14 $\pm$ 2.42	87.53 $\pm$ 1.28	1780.44 $\pm$ 119.77	39.33 $\pm$ 1.18	46.33 $\pm$ 1.42	146.52 $\pm$ 8.96	2.66 $\pm$ 0.2	26324.96 $\pm$ 1113.57	669.39 $\pm$ 19.88
131231A	0.642	22.23 $\pm$ 0.1	3.5 $\pm$ 0.04	292.52 $\pm$ 6.06	19.02 $\pm$ 0.35	6.72 $\pm$ 0.07	23.96 $\pm$ 0.56	0.88 $\pm$ 0.02	6296.12 $\pm$ 132.08	331.01 $\pm$ 3.39
131108A	2.4	62.78 $\pm$ 0.78	26.22 $\pm$ 0.6	1247.9 $\pm$ 59.91	5.35 $\pm$ 0.17	14.02 $\pm$ 0.37	98.01 $\pm$ 5.07	2.79 $\pm$ 0.15	2394.52 $\pm$ 93.61	447.92 $\pm$ 10.39
131105A	1.686	19.86 $\pm$ 0.48	3.51 $\pm$ 0.19	713.18 $\pm$ 46.18	41.94 $\pm$ 0.17	8.8 $\pm$ 0.39	51.57 $\pm$ 4.8	3.16 $\pm$ 0.24	9468.64 $\pm$ 357.86	225.78 $\pm$ 8.48
131011A	1.874	14.36 $\pm$ 0.52	2.99 $\pm$ 0.2	625.5 $\pm$ 91.56	26.81 $\pm$ 1.04	6.47 $\pm$ 0.51	45.48 $\pm$ 7.12	2.82 $\pm$ 0.46	5951.5 $\pm$ 478.44	221.97 $\pm$ 15.62
130925A	0.347	3.25 $\pm$ 0.04	0.04 $\pm$ 0	110.94 $\pm$ 3.1	160.03 $\pm$ 1.34	5.01 $\pm$ 0.27	7.29 $\pm$ 1.13	1.71 $\pm$ 0.1	10364.89 $\pm$ 557.07	64.77 $\pm$ 3.44
130702A	0.145	0.05 $\pm$ 0	0.01 $\pm$ 0	11.94 $\pm$ 1.29	51.42 $\pm$ 5.41	0.07 $\pm$ 0	0.91 $\pm$ 0.12	0.18 $\pm$ 0.02	3368.67 $\pm$ 401.84	65.51 $\pm$ 3.69
130612A	2.006	0.67 $\pm$ 0.08	0.7 $\pm$ 0.12	79.35 $\pm$ 20.35	2.47 $\pm$ 2.06	0.24 $\pm$ 0.04	6.86 $\pm$ 2.21	0.29 $\pm$ 0.08	683.42 $\pm$ 577.51	276.72 $\pm$ 37.58
130610A	2.092	7.76 $\pm$ 0.66	1.3 $\pm$ 0.26	840.81 $\pm$ 344.98	7.04 $\pm$ 0.53	5.81 $\pm$ 1.25	54.89 $\pm$ 24.29	6.3 $\pm$ 2.87	938.89 $\pm$ 199.09	133.41 $\pm$ 26.45
130518A	2.488	194.34 $\pm$ 1.89	79.23 $\pm$ 1.39	1388.34 $\pm$ 55.23	13.93 $\pm$ 0.26	27.31 $\pm$ 0.58	117.36 $\pm$ 4.89	1.95 $\pm$ 0.09	9909.65 $\pm$ 264.65	711.55 $\pm$ 13.46
130427A	0.3399	63.73 $\pm$ 0.08	11.86 $\pm$ 0.04	1105.4 $\pm$ 7.3	103.17 $\pm$ 2.42	19.45 $\pm$ 0.07	82.87 $\pm$ 0.59	3.37 $\pm$ 0.02	33796.49 $\pm$ 798.94	327.57 $\pm$ 1.05
130420A	1.297	3.09 $\pm$ 0.52	0.37 $\pm$ 0.04	131.59 $\pm$ 7.2	45.7 $\pm$ 3.84	1.87 $\pm$ 0.33	10.06 $\pm$ 1.52	0.8 $\pm$ 0.06	7544.28 $\pm$ 752.56	165.1 $\pm$ 8.9
130215A	0.597	3.58 $\pm$ 0.08	0.18 $\pm$ 0.02	410.45 $\pm$ 208.41	90.01 $\pm$ 8.16	4.92 $\pm$ 1.11	25.26 $\pm$ 11.69	5.65 $\pm$ 3.13	6543.45 $\pm$ 1583.39	72.7 $\pm$ 16.31
121211A	1.023	0.14 $\pm$ 0.04	0.11 $\pm$ 0.04	202.76 $\pm$ 32.05	2.78 $\pm$ 0.85	0.18 $\pm$ 0.06	13.24 $\pm$ 6.87	2.59 $\pm$ 0.62	218.34 $\pm$ 77.6	78.43 $\pm$ 14.33
121128A	2.2	11.08 $\pm$ 0.95	6.64 $\pm$ 0.27	244.19 $\pm$ 9.61	5.42 $\pm$ 0.29	2.31 $\pm$ 0.21	21.59 $\pm$ 1.4	0.51 $\pm$ 0.02	2603.4 $\pm$ 153.32	480.33 $\pm$ 12.12
120909A	3.93	72.54 $\pm$ 2.28	14.88 $\pm$ 1.93	961.41 $\pm$ 125.42	22.73 $\pm$ 2.11	18.78 $\pm$ 1.65	74.85 $\pm$ 15.63	2.49 $\pm$ 0.38	8778.91 $\pm$ 1087.43	386.2 $\pm$ 31.61
120907A	0.97	0.18 $\pm$ 0.07	0.21 $\pm$ 0.04	241.16 $\pm$ 67.27	2.92 $\pm$ 0.9	0.19 $\pm$ 0.07	16.21 $\pm$ 5.73	2.44 $\pm$ 0.77	289.02 $\pm$ 99.02	98.85 $\pm$ 14.7
120811C	2.671	6.88 $\pm$ 0.49	3.58 $\pm$ 0.45	203.98 $\pm$ 19.55	3.91 $\pm$ 1.79	1.76 $\pm$ 0.18	17.6 $\pm$ 3.34	0.52 $\pm$ 0.06	1525.23 $\pm$ 705.95	390.56 $\pm$ 27.71
120716A	2.486	23.42 $\pm$ 0.8	6.37 $\pm$ 0.38	418.05 $\pm$ 22.52	68 $\pm$ 1.18	6.26 $\pm$ 0.31	34.17 $\pm$ 3.18	1.12 $\pm$ 0.07	25427.07 $\pm$ 1011.39	373.91 $\pm$ 13.39
120711A	1.405	188.04 $\pm$ 0.96	17.9 $\pm$ 0.39	3171.38 $\pm$ 110.29	18.31 $\pm$ 0.3	74.72 $\pm$ 1.4	212.02 $\pm$ 8.94	12.6 $\pm$ 0.49	4607.46 $\pm$ 112.43	251.65 $\pm$ 4.54
120624B	2.1974	340.78 $\pm$ 3.06	27.04 $\pm$ 0.84	2038.82 $\pm$ 78.37	84.87 $\pm$ 1.43	92.64 $\pm$ 2.19	149.86 $\pm$ 8.02	5.54 $\pm$ 0.24	31220.85 $\pm$ 861.33	367.87 $\pm$ 8.03
120119A	1.728	37.14 $\pm$ 0.52	7.48 $\pm$ 0.23	499.91 $\pm$ 21.71	20.27 $\pm$ 2.28	9.96 $\pm$ 0.27	40.37 $\pm$ 2.25	1.34 $\pm$ 0.07	7558.12 $\pm$ 869.43	372.87 $\pm$ 8.69
111228A	0.714	3.34 $\pm$ 0.08	0.5 $\pm$ 0.03	45.43 $\pm$ 2.15	58.25 $\pm$ 1.23	1.1 $\pm$ 0.05	4.14 $\pm$ 0.39	0.15 $\pm$ 0.01	17623.57 $\pm$ 720.8	302.55 $\pm$ 10.59
110818A	3.36	21.7 $\pm$ 1.02	6.76 $\pm$ 0.76	799.45 $\pm$ 371.9	15.38 $\pm$ 0.9	7.46 $\pm$ 1.58	59.96 $\pm$ 25.69	2.75 $\pm$ 1.4	4474.65 $\pm$ 960.92	290.87 $\pm$ 60.11
110731A	2.83	50.75 $\pm$ 0.82	20.52 $\pm$ 1	1223.01 $\pm$ 75.4	1.95 $\pm$ 0.15	12.57 $\pm$ 0.48	94.46 $\pm$ 8.02	3.03 $\pm$ 0.21	788.92 $\pm$ 66.23	403.68 $\pm$ 14.03
110213A	1.46	9.35 $\pm$ 0.38	2.7 $\pm$ 0.19	183.83 $\pm$ 32.15	13.95 $\pm$ 0.67	2.61 $\pm$ 0.24	15.74 $\pm$ 2.81	0.51 $\pm$ 0.1	5006.15 $\pm$ 475.07	358.99 $\pm$ 29.43
110128A	2.339	0.76 $\pm$ 0.2	1.33 $\pm$ 0.41	643.72 $\pm$ 376.93	3.64 $\pm$ 1.49	0.5 $\pm$ 0.19	43.71 $\pm$ 28.49	4.26 $\pm$ 2.78	550.83 $\pm$ 275.5	151.25 $\pm$ 43.58
110106B	0.618	0.21 $\pm$ 0.04	0.06 $\pm$ 0.02	209.85 $\pm$ 33.35	21.95 $\pm$ 2.23	0.37 $\pm$ 0.09	12.93 $\pm$ 5.28	3.7 $\pm$ 0.8	1246.81 $\pm$ 222.88	56.79 $\pm$ 8.35
101219B	0.55	0.3 $\pm$ 0.03	0.03 $\pm$ 0.01	87.36 $\pm$ 10.29	32.91 $\pm$ 1.15	0.45 $\pm$ 0.07	5.86 $\pm$ 2.25	1.31 $\pm$ 0.23	2196.59 $\pm$ 306.17	66.75 $\pm$ 9.01
100906A	1.727	29.97 $\pm$ 0.74	7.03 $\pm$ 0.38	189.99 $\pm$ 27.53	40.56 $\pm$ 1.04	5.46 $\pm$ 0.39	17.48 $\pm$ 2.54	0.35 $\pm$ 0.06	22268.81 $\pm$ 1600.73	549.1 $\pm$ 36.89
100814A	1.44	8.99 $\pm$ 0.47	1.57 $\pm$ 0.12	330.87 $\pm$ 25.52	61.69 $\pm$ 0.66	4.14 $\pm$ 0.3	24.98 $\pm$ 3.14	1.52 $\pm$ 0.14	13392.5 $\pm$ 673.15	217.08 $\pm$ 10.66
100728B	2.106	5.09 $\pm$ 0.36	3.46 $\pm$ 0.33	341.16 $\pm$ 68.46	3.3 $\pm$ 0.59	1.65 $\pm$ 0.2	27.32 $\pm$ 5.91	1.11 $\pm$ 0.25	1015.6 $\pm$ 207.87	308.05 $\pm$ 29.86
100728A	1.567	90.72 $\pm$ 0.91	5.78 $\pm$ 0.25	745.38 $\pm$ 20.08	64.42 $\pm$ 1.13	32.54 $\pm$ 0.82	55.75 $\pm$ 3.53	2.67 $\pm$ 0.09	17963.56 $\pm$ 520.11	278.83 $\pm$ 6.43
100615A	1.398	11.03 $\pm$ 0.26	1.58 $\pm$ 0.11	127.93 $\pm$ 23.81	15.59 $\pm$ 0.41	3.36 $\pm$ 0.3	11.04 $\pm$ 2.06	0.39 $\pm$ 0.08	5113.71 $\pm$ 461.28	328.08 $\pm$ 28.32
100414A	1.368	59.23 $\pm$ 0.47	8.11 $\pm$ 0.22	1571.32 $\pm$ 38.18	11.19 $\pm$ 0.88	25.05 $\pm$ 0.45	108.79 $\pm$ 4.61	6.64 $\pm$ 0.19	2646 $\pm$ 211.45	236.47 $\pm$ 3.85
091208B	1.063	3.61 $\pm$ 0.13	2.54 $\pm$ 0.1	79.33 $\pm$ 11.87	6.05 $\pm$ 2.43	0.72 $\pm$ 0.05	7.6 $\pm$ 1.06	0.16 $\pm$ 0.03	3028.12 $\pm$ 1234.29	500.56 $\pm$ 33.49
091127	0.49	1.64 $\pm$ 0.02	0.74 $\pm$ 0.01	52.88 $\pm$ 2.29	5.84 $\pm$ 0.38	0.48 $\pm$ 0.01	4.86 $\pm$ 0.21	0.16 $\pm$ 0.01	1973.48 $\pm$ 135.33	337.95 $\pm$ 6.72
091024	1.092	5.62 $\pm$ 0.32	0.93 $\pm$ 0.21	3619.83 $\pm$ 1886.93	44.91 $\pm$ 2.5	9.2 $\pm$ 2.33	187.58 $\pm$ 101.95	59.22 $\pm$ 34.16	2745.15 $\pm$ 695.31	61.12 $\pm$ 15.1
091020	1.71	6.71 $\pm$ 0.37	2.81 $\pm$ 0.17	661.88 $\pm$ 99.5	8.95 $\pm$ 2.94	3.18 $\pm$ 0.28	47.52 $\pm$ 7.23	3.14 $\pm$ 0.52	1886.51 $\pm$ 634.05	210.77 $\pm$ 14.78
091003A	0.8969	10.84 $\pm$ 0.16	4.92 $\pm$ 0.1	696.69 $\pm$ 50.76	10.66 $\pm$ 0.19	4.07 $\pm$ 0.15	51.93 $\pm$ 3.53	2.61 $\pm$ 0.21	2842.61 $\pm$ 105.66	266.62 $\pm$ 8.69
090926B	1.24	3.59 $\pm$ 0.17	0.36 $\pm$ 0.09	184.77 $\pm$ 6.72	24.8 $\pm$ 3.41	2.53 $\pm$ 0.31	13.46 $\pm$ 4.46	1.3 $\pm$ 0.15	3521.32 $\pm$ 626.32	141.99 $\pm$ 16.02
090926A	2.1062	214.34 $\pm$ 1.01	80.15 $\pm$ 0.86	1055.58 $\pm$ 17.85	4.43 $\pm$ 0.09	26.63 $\pm$ 0.27	92.81 $\pm$ 1.91	1.31 $\pm$ 0.02	3565.22 $\pm$ 80.47	804.82 $\pm$ 7.08
090902B	1.822	355.03 $\pm$ 1.03	72.26 $\pm$ 0.65	2976.4 $\pm$ 49.17	6.85 $\pm$ 0.1	72.26 $\pm$ 0.63	224.46 $\pm$ 4.21	6.06 $\pm$ 0.11	3365.29 $\pm$ 56.97	491.35 $\pm$ 4.04
090618	0.54	28.07 $\pm$ 0.16	2.15 $\pm$ 0.04	226.19 $\pm$ 5.62	72.98 $\pm$ 0.71	9.51 $\pm$ 0.14	18.47 $\pm$ 0.62	0.77 $\pm$ 0.02	21545.69 $\pm$ 362.25	295.24 $\pm$ 4.06
090516	4.109	101.12 $\pm$ 4.02	11.9 $\pm$ 1.42	725.74 $\pm$ 135.14	24.09 $\pm$ 0.57	25.72 $\pm$ 2.7	57.73 $\pm$ 13.14	1.85 $\pm$ 0.39	9470.97 $\pm$ 945.53	393.16 $\pm$ 38.14
090424	0.544	4.1 $\pm$ 0.05	1.51 $\pm$ 0.02	237.72 $\pm$ 5.92	9.16 $\pm$ 0.17	1.67 $\pm$ 0.03	18.74 $\pm$ 0.51	0.97 $\pm$ 0.03	2250.02 $\pm$ 50.15	245.62 $\pm$ 2.99
090423	8.26	6.93 $\pm$ 1.38	14.27 $\pm$ 9.49	611.22 $\pm$ 149.84	0.77 $\pm$ 0.26	1.5 $\pm$ 0.57	50.53 $\pm$ 46.88	1.33 $\pm$ 0.54	356.21 $\pm$ 166.38	460.17 $\pm$ 148.86
090328	0.736	11.22 $\pm$ 0.18	1.53 $\pm$ 0.05	1110.45 $\pm$ 79.35	35.54 $\pm$ 1.04	8.8 $\pm$ 0.33	70.63 $\pm$ 5.29	8.71 $\pm$ 0.69	4531.47 $\pm$ 203.37	127.5 $\pm$ 4.33
090323	3.57	443.12 $\pm$ 5.1	50.76 $\pm$ 2.15	2892.34 $\pm$ 186.6	29.58 $\pm$ 0.32	104.79 $\pm$ 3.75	212.9 $\pm$ 17.02	6.84 $\pm$ 0.5	12506.84 $\pm$ 444.7	422.85 $\pm$ 14.34
081222	2.77	24.82 $\pm$ 0.72	13.23 $\pm$ 0.7	538.05 $\pm$ 36.12	5.01 $\pm$ 0.61	5.29 $\pm$ 0.25	45.01 $\pm$ 4.15	1.15 $\pm$ 0.09	2351.73 $\pm$ 302.08	469.6 $\pm$ 17.73
081221	2.26	40.88 $\pm$ 0.71	10.91 $\pm$ 0.4	283.43 $\pm$ 4.59	9.11 $\pm$ 0.13	7.22 $\pm$ 0.18	25.54 $\pm$ 1.32	0.5 $\pm$ 0.01	5155.8 $\pm$ 117.79	565.98 $\pm$ 10.3
081121	2.512	28.38 $\pm$ 0.81	10.42 $\pm$ 0.63	564.88 $\pm$ 58.16	11.95 $\pm$ 2.42	6.89 $\pm$ 0.41	46.04 $\pm$ 5.58	1.37 $\pm$ 0.16	4924.37 $\pm$ 1030.93	411.92 $\pm$ 21.58
081109	0.9787	3.42 $\pm$ 0.14	0.37 $\pm$ 0.05	64.2 $\pm$ 75.78	29.5 $\pm$ 2.64	1.52 $\pm$ 0.78	5.43 $\pm$ 5.61	0.28 $\pm$ 0.37	6652.45 $\pm$ 3454.75	225.52 $\pm$ 115.37
080916A	0.689	2.94 $\pm$ 0.09	0.33 $\pm$ 0.04	180.09 $\pm$ 32.52	27.43 $\pm$ 4.25	2.14 $\pm$ 0.21	13.07 $\pm$ 2.89	1.31 $\pm$ 0.27	3774.68 $\pm$ 683.89	137.59 $\pm$ 12.95

Table 4. Table 4: The intrinsic properties of Konus-Wind sample

GRB	$z$	$E_{iso}$	$L_{iso}$	$E_p$	$T_{90}$	$E_{iso}^{\prime }$	$L_{iso}^{\prime }$	$E_p^{\prime }$	$T_{90}^{\prime }$	${\Gamma }_0$
		($\times {10}^{52}$ erg)	($\times {10}^{52}$ erg s-1)	(keV)	(s)	($\times {10}^{50}$ erg)	($\times {10}^{46}$ erg s-1)	(keV)	(s)
970228	0.69	1.08${}_{}{}^{+0.07}{}_{-0.05}{}^{}$	0.51${}_{}{}^{+0.1}{}_{-0.08}{}^{}$	268.71${}_{}{}^{+64.22}{}_{-60.84}{}^{}$	31.62 $\pm$ 1.71	0.77${}_{}{}^{+0.11}{}_{-0.1}{}^{}$	19.09${}_{}{}^{+6.34}{}_{-5.41}{}^{}$	1.9${}_{}{}^{+0.52}{}_{-0.49}{}^{}$	4466.88${}_{}{}^{+651.69}{}_{-587.19}{}^{}$	141.26${}_{}{}^{+19.14}{}_{-16.92}{}^{}$
970828	0.96	22.71${}_{}{}^{+0.78}{}_{-0.8}{}^{}$	1.88${}_{}{}^{+0.2}{}_{-0.19}{}^{}$	531.16${}_{}{}^{+47.04}{}_{-43.12}{}^{}$	33.78 $\pm$ 1.42	11.8${}_{}{}^{+0.84}{}_{-0.81}{}^{}$	38.08${}_{}{}^{+6.25}{}_{-5.92}{}^{}$	2.76${}_{}{}^{+0.3}{}_{-0.28}{}^{}$	6499.83${}_{}{}^{+487.97}{}_{-468.64}{}^{}$	192.42${}_{}{}^{+11.97}{}_{-11.28}{}^{}$
971214	3.42	12.59${}_{}{}^{+0.53}{}_{-0.48}{}^{}$	5.88${}_{}{}^{+0.69}{}_{-0.66}{}^{}$	680.68${}_{}{}^{+88.4}{}_{-83.98}{}^{}$	3.6 $\pm$ 0.48	4.31${}_{}{}^{+0.38}{}_{-0.36}{}^{}$	51.63${}_{}{}^{+10.06}{}_{-9.61}{}^{}$	2.33${}_{}{}^{+0.35}{}_{-0.34}{}^{}$	1050.39${}_{}{}^{+162.92}{}_{-161.06}{}^{}$	292.14${}_{}{}^{+22.71}{}_{-21.66}{}^{}$
990123	1.6	184.25${}_{}{}^{+4.75}{}_{-4.63}{}^{}$	39.48${}_{}{}^{+1.7}{}_{-1.7}{}^{}$	1755${}_{}{}^{+104}{}_{-117}{}^{}$	23.85 $\pm$ 0.45	39.45${}_{}{}^{+1.63}{}_{-1.69}{}^{}$	135.79${}_{}{}^{+10.52}{}_{-11.11}{}^{}$	3.76${}_{}{}^{+0.25}{}_{-0.28}{}^{}$	11138.88${}_{}{}^{+416.99}{}_{-441.9}{}^{}$	466.99${}_{}{}^{+15.06}{}_{-16.26}{}^{}$
990506	1.31	105.57${}_{}{}^{+3.56}{}_{-3.56}{}^{}$	8.71${}_{}{}^{+0.44}{}_{-0.43}{}^{}$	683.76${}_{}{}^{+62.37}{}_{-57.75}{}^{}$	55.67 $\pm$ 0.28	30.21${}_{}{}^{+1.71}{}_{-1.65}{}^{}$	53.49${}_{}{}^{+5.57}{}_{-5.29}{}^{}$	1.96${}_{}{}^{+0.2}{}_{-0.19}{}^{}$	19454.23${}_{}{}^{+892.02}{}_{-839.08}{}^{}$	349.43${}_{}{}^{+15.92}{}_{-14.97}{}^{}$
990510	1.62	16.31${}_{}{}^{+0.67}{}_{-0.62}{}^{}$	7${}_{}{}^{+0.69}{}_{-0.65}{}^{}$	356.32${}_{}{}^{+31.44}{}_{-26.2}{}^{}$	21.33 $\pm$ 3.09	3.9${}_{}{}^{+0.28}{}_{-0.25}{}^{}$	30.01${}_{}{}^{+4.61}{}_{-4.23}{}^{}$	0.85${}_{}{}^{+0.09}{}_{-0.08}{}^{}$	8924.45${}_{}{}^{+1397.8}{}_{-1378.67}{}^{}$	418.37${}_{}{}^{+24.7}{}_{-22.21}{}^{}$
990705	0.84	19.91${}_{}{}^{+0.69}{}_{-0.69}{}^{}$	1.61${}_{}{}^{+0.15}{}_{-0.14}{}^{}$	550.16${}_{}{}^{+16.56}{}_{-16.56}{}^{}$	18.06 $\pm$ 0.61	11.27${}_{}{}^{+0.63}{}_{-0.62}{}^{}$	38.77${}_{}{}^{+4.93}{}_{-4.72}{}^{}$	3.11${}_{}{}^{+0.17}{}_{-0.16}{}^{}$	3190.77${}_{}{}^{+177.12}{}_{-172.52}{}^{}$	176.67${}_{}{}^{+7.79}{}_{-7.47}{}^{}$
990712	0.43	0.35${}_{}{}^{+0.02}{}_{-0.02}{}^{}$	0.06${}_{}{}^{+0.01}{}_{-0.01}{}^{}$	147.29${}_{}{}^{+20.02}{}_{-15.73}{}^{}$	11.63 $\pm$ 1.24	0.49${}_{}{}^{+0.05}{}_{-0.04}{}^{}$	9.64${}_{}{}^{+2.23}{}_{-1.67}{}^{}$	2.09${}_{}{}^{+0.34}{}_{-0.26}{}^{}$	821.15${}_{}{}^{+114.42}{}_{-103.93}{}^{}$	70.61${}_{}{}^{+6.31}{}_{-4.79}{}^{}$
991208	0.71	22.02${}_{}{}^{+0.41}{}_{-0.43}{}^{}$	4.52${}_{}{}^{+0.13}{}_{-0.13}{}^{}$	316.35${}_{}{}^{+8.55}{}_{-8.55}{}^{}$	36.87 $\pm$ 0.28	6.12${}_{}{}^{+0.16}{}_{-0.16}{}^{}$	26.16${}_{}{}^{+1.21}{}_{-1.18}{}^{}$	0.88${}_{}{}^{+0.03}{}_{-0.03}{}^{}$	13272.68${}_{}{}^{+258.21}{}_{-253.66}{}^{}$	359.94${}_{}{}^{+6.44}{}_{-6.31}{}^{}$
991216	1.02	77.26${}_{}{}^{+0.99}{}_{-0.96}{}^{}$	25.01${}_{}{}^{+1.68}{}_{-1.63}{}^{}$	713.06${}_{}{}^{+30.3}{}_{-30.3}{}^{}$	7.19 $\pm$ 0.07	13.86${}_{}{}^{+0.53}{}_{-0.52}{}^{}$	60.34${}_{}{}^{+5.94}{}_{-5.78}{}^{}$	1.28${}_{}{}^{+0.07}{}_{-0.07}{}^{}$	4010.21${}_{}{}^{+149.14}{}_{-145.93}{}^{}$	557.59${}_{}{}^{+20.03}{}_{-19.57}{}^{}$
000131	4.5	150.35${}_{}{}^{+4.31}{}_{-4.31}{}^{}$	56.4${}_{}{}^{+4.93}{}_{-4.75}{}^{}$	731.5${}_{}{}^{+71.5}{}_{-66}{}^{}$	17.54 $\pm$ 0.57	18.75${}_{}{}^{+1.22}{}_{-1.16}{}^{}$	65.82${}_{}{}^{+9.58}{}_{-9.1}{}^{}$	0.91${}_{}{}^{+0.1}{}_{-0.1}{}^{}$	14061.34${}_{}{}^{+936.05}{}_{-895.15}{}^{}$	801.66${}_{}{}^{+46.62}{}_{-43.93}{}^{}$
000210	0.85	17.02${}_{}{}^{+0.43}{}_{-0.41}{}^{}$	9.76${}_{}{}^{+0.5}{}_{-0.5}{}^{}$	688.2${}_{}{}^{+38.85}{}_{-37}{}^{}$	4.31 $\pm$ 0.22	4.64${}_{}{}^{+0.2}{}_{-0.19}{}^{}$	54.28${}_{}{}^{+4.58}{}_{-4.51}{}^{}$	1.87${}_{}{}^{+0.12}{}_{-0.12}{}^{}$	1581.49${}_{}{}^{+97.45}{}_{-96.74}{}^{}$	367.19${}_{}{}^{+12.38}{}_{-12.08}{}^{}$
000301C	2.03	2.8${}_{}{}^{+0.42}{}_{-0.3}{}^{}$	3.78${}_{}{}^{+0.67}{}_{-0.55}{}^{}$	351.48${}_{}{}^{+81.81}{}_{-72.72}{}^{}$	1.21 $\pm$ 0.18	0.89${}_{}{}^{+0.18}{}_{-0.14}{}^{}$	28.23${}_{}{}^{+8.85}{}_{-7.5}{}^{}$	1.11${}_{}{}^{+0.3}{}_{-0.26}{}^{}$	382.43${}_{}{}^{+75.48}{}_{-71.19}{}^{}$	316.78${}_{}{}^{+40.91}{}_{-35.24}{}^{}$
000418	1.12	7.92${}_{}{}^{+0.32}{}_{-0.29}{}^{}$	2.01${}_{}{}^{+0.15}{}_{-0.14}{}^{}$	195.04${}_{}{}^{+31.8}{}_{-23.32}{}^{}$	13.09 $\pm$ 0.61	2.59${}_{}{}^{+0.23}{}_{-0.18}{}^{}$	16.18${}_{}{}^{+2.77}{}_{-2.24}{}^{}$	0.64${}_{}{}^{+0.12}{}_{-0.09}{}^{}$	3999.26${}_{}{}^{+362.08}{}_{-304.88}{}^{}$	305.49${}_{}{}^{+23.7}{}_{-18.42}{}^{}$
000911	1.06	57.1${}_{}{}^{+1.78}{}_{-1.78}{}^{}$	10.61${}_{}{}^{+0.56}{}_{-0.56}{}^{}$	2230.98${}_{}{}^{+107.12}{}_{-103}{}^{}$	11.34 $\pm$ 0.11	24.81${}_{}{}^{+1.11}{}_{-1.1}{}^{}$	150.25${}_{}{}^{+12.51}{}_{-12.39}{}^{}$	9.69${}_{}{}^{+0.56}{}_{-0.54}{}^{}$	2608.86${}_{}{}^{+87.26}{}_{-85.99}{}^{}$	230.14${}_{}{}^{+7.37}{}_{-7.25}{}^{}$
000926	2.04	26.67${}_{}{}^{+0.74}{}_{-0.7}{}^{}$	7.41${}_{}{}^{+0.62}{}_{-0.58}{}^{}$	328.32${}_{}{}^{+24.32}{}_{-21.28}{}^{}$	17.99 $\pm$ 3.12	6${}_{}{}^{+0.34}{}_{-0.31}{}^{}$	28.1${}_{}{}^{+3.65}{}_{-3.37}{}^{}$	0.74${}_{}{}^{+0.07}{}_{-0.06}{}^{}$	7999.27${}_{}{}^{+1441.73}{}_{-1432.47}{}^{}$	444.72${}_{}{}^{+22.16}{}_{-20.23}{}^{}$
010222	1.48	91.99${}_{}{}^{+2.52}{}_{-2.57}{}^{}$	13.47${}_{}{}^{+1.09}{}_{-1.06}{}^{}$	706.8${}_{}{}^{+54.56}{}_{-49.6}{}^{}$	36.2 $\pm$ 3.18	21.85${}_{}{}^{+1.25}{}_{-1.2}{}^{}$	56.99${}_{}{}^{+7.34}{}_{-6.97}{}^{}$	1.68${}_{}{}^{+0.15}{}_{-0.14}{}^{}$	15239.8${}_{}{}^{+1539.78}{}_{-1517.82}{}^{}$	421.05${}_{}{}^{+21.04}{}_{-19.79}{}^{}$
010921	0.45	0.9${}_{}{}^{+0.03}{}_{-0.03}{}^{}$	0.1${}_{}{}^{+0.01}{}_{-0.01}{}^{}$	116${}_{}{}^{+14.5}{}_{-11.6}{}^{}$	13.65 $\pm$ 1.66	0.94${}_{}{}^{+0.07}{}_{-0.06}{}^{}$	8.14${}_{}{}^{+1.39}{}_{-1.2}{}^{}$	1.2${}_{}{}^{+0.17}{}_{-0.14}{}^{}$	1316.05${}_{}{}^{+184.77}{}_{-178.14}{}^{}$	96.42${}_{}{}^{+6.75}{}_{-5.71}{}^{}$
011121	0.36	8.51${}_{}{}^{+0.23}{}_{-0.23}{}^{}$	0.47${}_{}{}^{+0.03}{}_{-0.03}{}^{}$	1113.84${}_{}{}^{+146.88}{}_{-130.56}{}^{}$	41.92 $\pm$ 2.78	11.54${}_{}{}^{+0.81}{}_{-0.74}{}^{}$	64.39${}_{}{}^{+9.4}{}_{-8.48}{}^{}$	15.11${}_{}{}^{+2.22}{}_{-1.98}{}^{}$	3090.21${}_{}{}^{+286.41}{}_{-272.37}{}^{}$	73.72${}_{}{}^{+4.77}{}_{-4.27}{}^{}$
020405	0.69	10.65${}_{}{}^{+0.15}{}_{-0.15}{}^{}$	1.3${}_{}{}^{+0.13}{}_{-0.12}{}^{}$	272.09${}_{}{}^{+11.83}{}_{-11.83}{}^{}$	24.58 $\pm$ 1.2	4.92${}_{}{}^{+0.25}{}_{-0.23}{}^{}$	20.79${}_{}{}^{+2.87}{}_{-2.65}{}^{}$	1.26${}_{}{}^{+0.08}{}_{-0.08}{}^{}$	5314.68${}_{}{}^{+366.73}{}_{-353.84}{}^{}$	216.24${}_{}{}^{+10.54}{}_{-9.78}{}^{}$
020813	1.25	65.85${}_{}{}^{+4.19}{}_{-3.81}{}^{}$	10.71${}_{}{}^{+0.94}{}_{-0.94}{}^{}$	510.75${}_{}{}^{+40.5}{}_{-38.25}{}^{}$	39.74 $\pm$ 0.32	15.12${}_{}{}^{+1.25}{}_{-1.17}{}^{}$	42.31${}_{}{}^{+5.82}{}_{-5.75}{}^{}$	1.17${}_{}{}^{+0.11}{}_{-0.11}{}^{}$	17309.1${}_{}{}^{+926.86}{}_{-906.34}{}^{}$	435.59${}_{}{}^{+23.05}{}_{-22.53}{}^{}$
020819B	0.41	0.31${}_{}{}^{+0.03}{}_{-0.02}{}^{}$	0.15${}_{}{}^{+0.03}{}_{-0.02}{}^{}$	227.01${}_{}{}^{+56.4}{}_{-39.48}{}^{}$	5.81 $\pm$ 1.42	0.36${}_{}{}^{+0.06}{}_{-0.05}{}^{}$	14.96${}_{}{}^{+5.04}{}_{-3.81}{}^{}$	2.63${}_{}{}^{+0.75}{}_{-0.53}{}^{}$	501.26${}_{}{}^{+140.74}{}_{-132.71}{}^{}$	86.25${}_{}{}^{+11.95}{}_{-8.82}{}^{}$
030329	0.17	1.53${}_{}{}^{+0.02}{}_{-0.02}{}^{}$	0.21${}_{}{}^{+0.01}{}_{-0.01}{}^{}$	113.49${}_{}{}^{+2.34}{}_{-2.34}{}^{}$	18.64 $\pm$ 0.98	1.13${}_{}{}^{+0.02}{}_{-0.02}{}^{}$	8.47${}_{}{}^{+0.36}{}_{-0.36}{}^{}$	0.84${}_{}{}^{+0.02}{}_{-0.02}{}^{}$	2526.23${}_{}{}^{+138.78}{}_{-138.66}{}^{}$	135.53${}_{}{}^{+2.15}{}_{-2.13}{}^{}$
041006	0.72	0.65${}_{}{}^{+0.03}{}_{-0.03}{}^{}$	0.31${}_{}{}^{+0.04}{}_{-0.04}{}^{}$	146.2${}_{}{}^{+8.6}{}_{-8.6}{}^{}$	3.98 $\pm$ 1.15	0.44${}_{}{}^{+0.04}{}_{-0.03}{}^{}$	10.88${}_{}{}^{+1.87}{}_{-1.77}{}^{}$	0.99${}_{}{}^{+0.08}{}_{-0.08}{}^{}$	585.31${}_{}{}^{+173.35}{}_{-172.97}{}^{}$	147.03${}_{}{}^{+9}{}_{-8.54}{}^{}$
050401	2.9	40.85${}_{}{}^{+1.73}{}_{-1.8}{}^{}$	15.31${}_{}{}^{+1.17}{}_{-1.1}{}^{}$	409.5${}_{}{}^{+54.6}{}_{-42.9}{}^{}$	8.48 $\pm$ 0.18	7.23${}_{}{}^{+0.57}{}_{-0.51}{}^{}$	36.01${}_{}{}^{+5.56}{}_{-4.78}{}^{}$	0.73${}_{}{}^{+0.11}{}_{-0.09}{}^{}$	4786.6${}_{}{}^{+336.55}{}_{-285.01}{}^{}$	564.73${}_{}{}^{+37.95}{}_{-31.54}{}^{}$
050525A	0.61	2.66${}_{}{}^{+0.05}{}_{-0.05}{}^{}$	1.02${}_{}{}^{+0.03}{}_{-0.03}{}^{}$	128.8${}_{}{}^{+3.22}{}_{-3.22}{}^{}$	4.38 $\pm$ 0.12	0.99${}_{}{}^{+0.03}{}_{-0.03}{}^{}$	10.72${}_{}{}^{+0.55}{}_{-0.55}{}^{}$	0.48${}_{}{}^{+0.02}{}_{-0.02}{}^{}$	1171.74${}_{}{}^{+38.47}{}_{-38.47}{}^{}$	267.51${}_{}{}^{+5.07}{}_{-5.07}{}^{}$
050603	2.82	66.35${}_{}{}^{+4.02}{}_{-4.67}{}^{}$	77.23${}_{}{}^{+5.45}{}_{-5.45}{}^{}$	912.98${}_{}{}^{+244.48}{}_{-129.88}{}^{}$	2.93 $\pm$ 0.92	7.88${}_{}{}^{+1.06}{}_{-0.78}{}^{}$	81.67${}_{}{}^{+20.37}{}_{-12.69}{}^{}$	1.08${}_{}{}^{+0.32}{}_{-0.17}{}^{}$	2469.51${}_{}{}^{+826.62}{}_{-790.73}{}^{}$	842.13${}_{}{}^{+100.74}{}_{-58.31}{}^{}$
050820A	2.61	92.7${}_{}{}^{+3.06}{}_{-2.3}{}^{}$	10.12${}_{}{}^{+1.6}{}_{-1.27}{}^{}$	1725.58${}_{}{}^{+501.79}{}_{-324.9}{}^{}$	122.11 $\pm$ 21.2	36.86${}_{}{}^{+5.47}{}_{-3.78}{}^{}$	120.02${}_{}{}^{+39.61}{}_{-28.25}{}^{}$	6.86${}_{}{}^{+2.23}{}_{-1.46}{}^{}$	30711.7${}_{}{}^{+6941.04}{}_{-6144.41}{}^{}$	251.5${}_{}{}^{+36.4}{}_{-25.02}{}^{}$
050922C	2.2	7.73${}_{}{}^{+2.1}{}_{-1.43}{}^{}$	8.89${}_{}{}^{+3.21}{}_{-2.29}{}^{}$	2348.8${}_{}{}^{+2294.4}{}_{-1004.8}{}^{}$	1.95 $\pm$ 0.46	3.73${}_{}{}^{+1.96}{}_{-1.07}{}^{}$	154.84${}_{}{}^{+150.61}{}_{-78.65}{}^{}$	11.32${}_{}{}^{+12.18}{}_{-5.44}{}^{}$	405.42${}_{}{}^{+206.52}{}_{-130.36}{}^{}$	207.48${}_{}{}^{+93.71}{}_{-45.41}{}^{}$
051008	2.77	57.65${}_{}{}^{+5.38}{}_{-4.25}{}^{}$	20.08${}_{}{}^{+1.65}{}_{-1.51}{}^{}$	1213.94${}_{}{}^{+350.61}{}_{-278.98}{}^{}$	55.39 $\pm$ 6.84	14.38${}_{}{}^{+2.3}{}_{-1.84}{}^{}$	93.69${}_{}{}^{+25.51}{}_{-20.84}{}^{}$	3.03${}_{}{}^{+0.96}{}_{-0.76}{}^{}$	22210.81${}_{}{}^{+3978.38}{}_{-3594.51}{}^{}$	400.96${}_{}{}^{+52.05}{}_{-41.97}{}^{}$
051022	0.81	45.8${}_{}{}^{+0.97}{}_{-0.91}{}^{}$	4.37${}_{}{}^{+0.21}{}_{-0.21}{}^{}$	781.92${}_{}{}^{+36.2}{}_{-36.2}{}^{}$	84.97 $\pm$ 1.22	19.07${}_{}{}^{+0.69}{}_{-0.68}{}^{}$	56.81${}_{}{}^{+4.3}{}_{-4.34}{}^{}$	3.26${}_{}{}^{+0.18}{}_{-0.18}{}^{}$	20402.95${}_{}{}^{+669.44}{}_{-673.99}{}^{}$	240.13${}_{}{}^{+7.08}{}_{-7.14}{}^{}$
051109A	2.35	6.38${}_{}{}^{+0.62}{}_{-0.51}{}^{}$	3.12${}_{}{}^{+0.77}{}_{-0.59}{}^{}$	569.5${}_{}{}^{+268}{}_{-140.7}{}^{}$	11.83 $\pm$ 1.03	2.7${}_{}{}^{+0.68}{}_{-0.43}{}^{}$	42.11${}_{}{}^{+22.12}{}_{-14.01}{}^{}$	2.41${}_{}{}^{+1.27}{}_{-0.68}{}^{}$	2790.93${}_{}{}^{+691.46}{}_{-453.36}{}^{}$	235.89${}_{}{}^{+54.71}{}_{-32.34}{}^{}$
060124	2.3	29.57${}_{}{}^{+1.34}{}_{-1.17}{}^{}$	10.05${}_{}{}^{+0.82}{}_{-0.74}{}^{}$	735.9${}_{}{}^{+122.1}{}_{-95.7}{}^{}$	72.16 $\pm$ 5.79	8.18${}_{}{}^{+0.76}{}_{-0.63}{}^{}$	57.64${}_{}{}^{+10.43}{}_{-8.66}{}^{}$	2.04${}_{}{}^{+0.38}{}_{-0.3}{}^{}$	26090.24${}_{}{}^{+2969.16}{}_{-2701.05}{}^{}$	361.58${}_{}{}^{+29.18}{}_{-23.65}{}^{}$
060502A	1.5	2.23${}_{}{}^{+0.24}{}_{-0.2}{}^{}$	0.91${}_{}{}^{+0.17}{}_{-0.15}{}^{}$	322.5${}_{}{}^{+105}{}_{-95}{}^{}$	4.23 $\pm$ 0.89	1.3${}_{}{}^{+0.26}{}_{-0.22}{}^{}$	23.4${}_{}{}^{+8.85}{}_{-7.96}{}^{}$	1.89${}_{}{}^{+0.69}{}_{-0.62}{}^{}$	722.83${}_{}{}^{+192.56}{}_{-185.6}{}^{}$	170.91${}_{}{}^{+28.09}{}_{-25.33}{}^{}$
060614	0.13	0.25${}_{}{}^{+0.01}{}_{-0.01}{}^{}$	0.01${}_{}{}^{+0}{}_{-0}{}^{}$	82.49${}_{}{}^{+14.69}{}_{-13.56}{}^{}$	109.42 $\pm$ 16.76	0.64${}_{}{}^{+0.09}{}_{-0.07}{}^{}$	5.07${}_{}{}^{+1.62}{}_{-1.32}{}^{}$	2.09${}_{}{}^{+0.45}{}_{-0.4}{}^{}$	4317.52${}_{}{}^{+846}{}_{-795.51}{}^{}$	39.46${}_{}{}^{+4.82}{}_{-4.04}{}^{}$
060814	1.92	30.31${}_{}{}^{+1.29}{}_{-0.99}{}^{}$	4.62${}_{}{}^{+0.38}{}_{-0.35}{}^{}$	762.12${}_{}{}^{+470.12}{}_{-239.44}{}^{}$	49.94 $\pm$ 9.08	12.16${}_{}{}^{+3.3}{}_{-1.74}{}^{}$	55.82${}_{}{}^{+30.25}{}_{-16.16}{}^{}$	3.06${}_{}{}^{+2.06}{}_{-1.05}{}^{}$	12448.79${}_{}{}^{+4030.78}{}_{-2854.37}{}^{}$	249.27${}_{}{}^{+66.77}{}_{-34.8}{}^{}$
061007	1.26	100.36${}_{}{}^{+3.68}{}_{-3.6}{}^{}$	11.94${}_{}{}^{+0.79}{}_{-0.8}{}^{}$	901.74${}_{}{}^{+27.12}{}_{-24.86}{}^{}$	25.47 $\pm$ 0.23	27.98${}_{}{}^{+1.38}{}_{-1.36}{}^{}$	69.6${}_{}{}^{+6.49}{}_{-6.52}{}^{}$	2.51${}_{}{}^{+0.11}{}_{-0.11}{}^{}$	9134.43${}_{}{}^{+311.97}{}_{-311.21}{}^{}$	358.7${}_{}{}^{+11.82}{}_{-11.79}{}^{}$
061021	0.35	0.41${}_{}{}^{+0.09}{}_{-0.06}{}^{}$	0.17${}_{}{}^{+0.02}{}_{-0.02}{}^{}$	703.35${}_{}{}^{+357.75}{}_{-187.65}{}^{}$	13.83 $\pm$ 4.02	0.74${}_{}{}^{+0.24}{}_{-0.15}{}^{}$	39.91${}_{}{}^{+19.12}{}_{-11.21}{}^{}$	12.62${}_{}{}^{+7.04}{}_{-3.73}{}^{}$	771.14${}_{}{}^{+285.07}{}_{-244.59}{}^{}$	55.74${}_{}{}^{+12.74}{}_{-7.09}{}^{}$
061121	1.31	27.92${}_{}{}^{+1.04}{}_{-1}{}^{}$	13.99${}_{}{}^{+0.69}{}_{-0.65}{}^{}$	1399.86${}_{}{}^{+120.12}{}_{-103.95}{}^{}$	7.69 $\pm$ 0.63	8.74${}_{}{}^{+0.5}{}_{-0.46}{}^{}$	102.89${}_{}{}^{+10.26}{}_{-9.23}{}^{}$	4.38${}_{}{}^{+0.42}{}_{-0.37}{}^{}$	2455.01${}_{}{}^{+227.17}{}_{-221.76}{}^{}$	319.32${}_{}{}^{+13.84}{}_{-12.26}{}^{}$
061222A	2.09	22.73${}_{}{}^{+0.59}{}_{-0.57}{}^{}$	9.28${}_{}{}^{+0.58}{}_{-0.55}{}^{}$	828.12${}_{}{}^{+83.43}{}_{-71.07}{}^{}$	19.47 $\pm$ 1.55	6.86${}_{}{}^{+0.4}{}_{-0.36}{}^{}$	63.39${}_{}{}^{+7.67}{}_{-6.9}{}^{}$	2.5${}_{}{}^{+0.28}{}_{-0.24}{}^{}$	6450.94${}_{}{}^{+611.98}{}_{-591.29}{}^{}$	331.33${}_{}{}^{+17.19}{}_{-15.16}{}^{}$
070125	1.55	104.44${}_{}{}^{+5.23}{}_{-5.17}{}^{}$	17.55${}_{}{}^{+1.77}{}_{-1.77}{}^{}$	948.6${}_{}{}^{+91.8}{}_{-79.05}{}^{}$	48.71 $\pm$ 6.14	24.93${}_{}{}^{+1.99}{}_{-1.91}{}^{}$	74.97${}_{}{}^{+12.01}{}_{-11.59}{}^{}$	2.26${}_{}{}^{+0.26}{}_{-0.23}{}^{}$	20407.02${}_{}{}^{+2868.34}{}_{-2835.66}{}^{}$	418.96${}_{}{}^{+26.1}{}_{-24.55}{}^{}$
070328	2.06	57.91${}_{}{}^{+6.43}{}_{-6.27}{}^{}$	13.29${}_{}{}^{+1.43}{}_{-1.43}{}^{}$	1181.16${}_{}{}^{+180.54}{}_{-143.82}{}^{}$	17.58 $\pm$ 4.22	17.26${}_{}{}^{+2.39}{}_{-2.24}{}^{}$	88.54${}_{}{}^{+17.39}{}_{-15.9}{}^{}$	3.52${}_{}{}^{+0.61}{}_{-0.5}{}^{}$	5898.88${}_{}{}^{+1495.42}{}_{-1476.94}{}^{}$	335.52${}_{}{}^{+27.59}{}_{-24.15}{}^{}$
070508	0.82	7.51${}_{}{}^{+0.11}{}_{-0.11}{}^{}$	2.22${}_{}{}^{+0.06}{}_{-0.06}{}^{}$	338.52${}_{}{}^{+9.1}{}_{-9.1}{}^{}$	8.1 $\pm$ 0.61	2.98${}_{}{}^{+0.07}{}_{-0.07}{}^{}$	26.2${}_{}{}^{+1.18}{}_{-1.18}{}^{}$	1.34${}_{}{}^{+0.04}{}_{-0.04}{}^{}$	2043.48${}_{}{}^{+158.53}{}_{-158.53}{}^{}$	252.14${}_{}{}^{+4.39}{}_{-4.39}{}^{}$
070521	1.7	14.16${}_{}{}^{+0.44}{}_{-0.42}{}^{}$	3.95${}_{}{}^{+0.26}{}_{-0.24}{}^{}$	583.2${}_{}{}^{+43.2}{}_{-43.2}{}^{}$	11.77 $\pm$ 2.53	5.44${}_{}{}^{+0.29}{}_{-0.28}{}^{}$	43.79${}_{}{}^{+4.87}{}_{-4.62}{}^{}$	2.24${}_{}{}^{+0.19}{}_{-0.19}{}^{}$	3062.79${}_{}{}^{+670.88}{}_{-669.9}{}^{}$	260.18${}_{}{}^{+11.53}{}_{-11.11}{}^{}$
071003	1.6	34.02${}_{}{}^{+1.65}{}_{-1.52}{}^{}$	11.27${}_{}{}^{+0.63}{}_{-0.62}{}^{}$	1999.4${}_{}{}^{+200.2}{}_{-192.4}{}^{}$	8.22 $\pm$ 0.39	13.72${}_{}{}^{+0.96}{}_{-0.91}{}^{}$	137.4${}_{}{}^{+15.82}{}_{-15.3}{}^{}$	8.06${}_{}{}^{+0.9}{}_{-0.87}{}^{}$	2037.77${}_{}{}^{+141.5}{}_{-138.91}{}^{}$	248.04${}_{}{}^{+12.46}{}_{-12.02}{}^{}$
071010B	0.95	1.37${}_{}{}^{+0.09}{}_{-0.09}{}^{}$	0.45${}_{}{}^{+0.05}{}_{-0.05}{}^{}$	107.25${}_{}{}^{+7.8}{}_{-9.75}{}^{}$	4.37 $\pm$ 0.65	0.69${}_{}{}^{+0.06}{}_{-0.06}{}^{}$	8.58${}_{}{}^{+1.49}{}_{-1.41}{}^{}$	0.54${}_{}{}^{+0.05}{}_{-0.06}{}^{}$	866.03${}_{}{}^{+139.79}{}_{-139.61}{}^{}$	198.14${}_{}{}^{+12.52}{}_{-12.41}{}^{}$
071020	2.15	7.35${}_{}{}^{+0.63}{}_{-0.56}{}^{}$	10.29${}_{}{}^{+1.05}{}_{-0.92}{}^{}$	853.65${}_{}{}^{+157.5}{}_{-138.6}{}^{}$	0.87 $\pm$ 0.02	2.14${}_{}{}^{+0.27}{}_{-0.24}{}^{}$	65.61${}_{}{}^{+13.8}{}_{-12.13}{}^{}$	2.49${}_{}{}^{+0.51}{}_{-0.45}{}^{}$	297.06${}_{}{}^{+28.48}{}_{-25.34}{}^{}$	343.01${}_{}{}^{+31.58}{}_{-27.78}{}^{}$
071112C	0.82	1.04${}_{}{}^{+0.19}{}_{-0.14}{}^{}$	0.66${}_{}{}^{+0.15}{}_{-0.12}{}^{}$	740.74${}_{}{}^{+318.5}{}_{-182}{}^{}$	2.88 $\pm$ 0.45	1.01${}_{}{}^{+0.28}{}_{-0.19}{}^{}$	46.64${}_{}{}^{+22.67}{}_{-15.31}{}^{}$	7.17${}_{}{}^{+3.44}{}_{-2.01}{}^{}$	297.9${}_{}{}^{+79.02}{}_{-61.89}{}^{}$	103.31${}_{}{}^{+22.06}{}_{-14.01}{}^{}$
071117	1.33	3.2${}_{}{}^{+0.2}{}_{-0.25}{}^{}$	5.06${}_{}{}^{+0.7}{}_{-0.52}{}^{}$	647.74${}_{}{}^{+235.33}{}_{-128.15}{}^{}$	0.98 $\pm$ 0.15	1.15${}_{}{}^{+0.21}{}_{-0.14}{}^{}$	48.89${}_{}{}^{+17.85}{}_{-10.74}{}^{}$	2.32${}_{}{}^{+0.93}{}_{-0.51}{}^{}$	271.73${}_{}{}^{+62.43}{}_{-49.9}{}^{}$	278.67${}_{}{}^{+47.05}{}_{-27.08}{}^{}$
080319B	0.94	146.96${}_{}{}^{+1.81}{}_{-1.81}{}^{}$	9.46${}_{}{}^{+0.2}{}_{-0.2}{}^{}$	1264.88${}_{}{}^{+17.46}{}_{-17.46}{}^{}$	22.97 $\pm$ 0.27	52.76${}_{}{}^{+0.89}{}_{-0.88}{}^{}$	91.39${}_{}{}^{+2.87}{}_{-2.81}{}^{}$	4.54${}_{}{}^{+0.08}{}_{-0.08}{}^{}$	6398.48${}_{}{}^{+104.96}{}_{-104.13}{}^{}$	278.57${}_{}{}^{+3.2}{}_{-3.15}{}^{}$
080319C	1.95	11.27${}_{}{}^{+1.31}{}_{-1.09}{}^{}$	6.82${}_{}{}^{+0.84}{}_{-0.73}{}^{}$	1070.85${}_{}{}^{+477.9}{}_{-348.1}{}^{}$	3.47 $\pm$ 0.22	4.38${}_{}{}^{+1.01}{}_{-0.77}{}^{}$	77.15${}_{}{}^{+32.28}{}_{-24.31}{}^{}$	4.16${}_{}{}^{+2.03}{}_{-1.49}{}^{}$	892.77${}_{}{}^{+187.14}{}_{-143.64}{}^{}$	257.55${}_{}{}^{+51.51}{}_{-38.16}{}^{}$
080411	1.03	21.41${}_{}{}^{+0.67}{}_{-0.61}{}^{}$	8.03${}_{}{}^{+0.5}{}_{-0.49}{}^{}$	539.98${}_{}{}^{+42.63}{}_{-36.54}{}^{}$	21.11 $\pm$ 0.4	5.74${}_{}{}^{+0.31}{}_{-0.28}{}^{}$	43.38${}_{}{}^{+4.73}{}_{-4.37}{}^{}$	1.45${}_{}{}^{+0.13}{}_{-0.11}{}^{}$	7866.46${}_{}{}^{+380.95}{}_{-349.99}{}^{}$	372.69${}_{}{}^{+16.62}{}_{-15.01}{}^{}$
080413A	2.43	6${}_{}{}^{+1.13}{}_{-0.84}{}^{}$	4.35${}_{}{}^{+2.39}{}_{-1.26}{}^{}$	456.19${}_{}{}^{+144.06}{}_{-123.48}{}^{}$	5.2 $\pm$ 0.47	1.99${}_{}{}^{+0.68}{}_{-0.45}{}^{}$	35.73${}_{}{}^{+28.32}{}_{-16.29}{}^{}$	1.51${}_{}{}^{+0.64}{}_{-0.49}{}^{}$	1572.52${}_{}{}^{+471.89}{}_{-311.35}{}^{}$	302.24${}_{}{}^{+86.55}{}_{-53.35}{}^{}$
080514B	1.8	25.85${}_{}{}^{+1.15}{}_{-1.15}{}^{}$	22.42${}_{}{}^{+1.44}{}_{-1.4}{}^{}$	548.8${}_{}{}^{+33.6}{}_{-33.6}{}^{}$	2.04 $\pm$ 0.03	4.36${}_{}{}^{+0.26}{}_{-0.26}{}^{}$	47.75${}_{}{}^{+4.86}{}_{-4.76}{}^{}$	0.92${}_{}{}^{+0.07}{}_{-0.07}{}^{}$	1211.87${}_{}{}^{+51.28}{}_{-50.54}{}^{}$	593.43${}_{}{}^{+23.47}{}_{-23.09}{}^{}$
080603B	2.69	8.72${}_{}{}^{+1.29}{}_{-1.03}{}^{}$	8.26${}_{}{}^{+1.25}{}_{-1.06}{}^{}$	313.65${}_{}{}^{+118.08}{}_{-66.42}{}^{}$	3.4 $\pm$ 0.31	1.83${}_{}{}^{+0.42}{}_{-0.29}{}^{}$	27.25${}_{}{}^{+10.46}{}_{-6.88}{}^{}$	0.66${}_{}{}^{+0.27}{}_{-0.16}{}^{}$	1622.81${}_{}{}^{+322.74}{}_{-231.16}{}^{}$	476.84${}_{}{}^{+84.04}{}_{-51.8}{}^{}$
080605	1.64	22.87${}_{}{}^{+0.45}{}_{-0.44}{}^{}$	16.44${}_{}{}^{+1.69}{}_{-1.54}{}^{}$	667.92${}_{}{}^{+26.4}{}_{-26.4}{}^{}$	5.21 $\pm$ 1.06	4.84${}_{}{}^{+0.26}{}_{-0.24}{}^{}$	55.16${}_{}{}^{+7.93}{}_{-7.28}{}^{}$	1.41${}_{}{}^{+0.09}{}_{-0.09}{}^{}$	2460.99${}_{}{}^{+515.76}{}_{-513.58}{}^{}$	472.78${}_{}{}^{+23.76}{}_{-21.94}{}^{}$
080607	3.04	188.52${}_{}{}^{+5.09}{}_{-5.27}{}^{}$	91.72${}_{}{}^{+9.54}{}_{-8.8}{}^{}$	1349.36${}_{}{}^{+68.68}{}_{-64.64}{}^{}$	7.11 $\pm$ 0.85	24.47${}_{}{}^{+1.45}{}_{-1.37}{}^{}$	115.87${}_{}{}^{+17.14}{}_{-15.85}{}^{}$	1.75${}_{}{}^{+0.13}{}_{-0.12}{}^{}$	5480.5${}_{}{}^{+718.73}{}_{-710.46}{}^{}$	770.5${}_{}{}^{+40.54}{}_{-37.55}{}^{}$
080721	2.59	127.15${}_{}{}^{+5.29}{}_{-5.29}{}^{}$	79.32${}_{}{}^{+6.33}{}_{-6.33}{}^{}$	1759.1${}_{}{}^{+147.19}{}_{-147.19}{}^{}$	5.5 $\pm$ 0.55	19.77${}_{}{}^{+1.31}{}_{-1.31}{}^{}$	143.87${}_{}{}^{+18.72}{}_{-18.72}{}^{}$	2.74${}_{}{}^{+0.27}{}_{-0.27}{}^{}$	3536.64${}_{}{}^{+396.76}{}_{-396.76}{}^{}$	643.06${}_{}{}^{+33.04}{}_{-33.04}{}^{}$
080916A	0.69	0.8${}_{}{}^{+0.06}{}_{-0.06}{}^{}$	0.18${}_{}{}^{+0.02}{}_{-0.02}{}^{}$	218.01${}_{}{}^{+30.42}{}_{-23.66}{}^{}$	3.89 $\pm$ 0.88	0.83${}_{}{}^{+0.09}{}_{-0.08}{}^{}$	14.69${}_{}{}^{+3.03}{}_{-2.69}{}^{}$	2.26${}_{}{}^{+0.37}{}_{-0.29}{}^{}$	375.55${}_{}{}^{+90.16}{}_{-88.74}{}^{}$	96.54${}_{}{}^{+7.97}{}_{-6.84}{}^{}$
080916C	4.35	356.05${}_{}{}^{+27.6}{}_{-27.6}{}^{}$	127.88${}_{}{}^{+10.19}{}_{-10.19}{}^{}$	2701.75${}_{}{}^{+246.1}{}_{-230.05}{}^{}$	11.45 $\pm$ 0.38	53.46${}_{}{}^{+5.04}{}_{-4.98}{}^{}$	216.18${}_{}{}^{+28.89}{}_{-28.26}{}^{}$	4.06${}_{}{}^{+0.43}{}_{-0.4}{}^{}$	7629.3${}_{}{}^{+482.12}{}_{-470.28}{}^{}$	666.07${}_{}{}^{+35.73}{}_{-34.51}{}^{}$
081121	2.51	20.98${}_{}{}^{+0.92}{}_{-0.84}{}^{}$	7.58${}_{}{}^{+0.63}{}_{-0.58}{}^{}$	824.85${}_{}{}^{+77.22}{}_{-70.2}{}^{}$	5.54 $\pm$ 0.83	6.94${}_{}{}^{+0.49}{}_{-0.45}{}^{}$	62.16${}_{}{}^{+8.6}{}_{-7.9}{}^{}$	2.73${}_{}{}^{+0.3}{}_{-0.27}{}^{}$	1674.98${}_{}{}^{+268.4}{}_{-265.8}{}^{}$	302.41${}_{}{}^{+16.76}{}_{-15.35}{}^{}$
081221	2.26	38.35${}_{}{}^{+0.76}{}_{-0.74}{}^{}$	10.92${}_{}{}^{+0.54}{}_{-0.54}{}^{}$	264.06${}_{}{}^{+6.52}{}_{-6.52}{}^{}$	8.96 $\pm$ 0.3	6.57${}_{}{}^{+0.21}{}_{-0.21}{}^{}$	24.03${}_{}{}^{+1.69}{}_{-1.69}{}^{}$	0.45${}_{}{}^{+0.02}{}_{-0.02}{}^{}$	5228.95${}_{}{}^{+216.77}{}_{-216.77}{}^{}$	583.78${}_{}{}^{+14.64}{}_{-14.64}{}^{}$
081222	2.77	15.22${}_{}{}^{+1.06}{}_{-0.93}{}^{}$	9.46${}_{}{}^{+0.83}{}_{-0.77}{}^{}$	622.05${}_{}{}^{+98.02}{}_{-67.86}{}^{}$	3.18 $\pm$ 0.61	4.02${}_{}{}^{+0.42}{}_{-0.35}{}^{}$	49.64${}_{}{}^{+8.97}{}_{-7.22}{}^{}$	1.65${}_{}{}^{+0.29}{}_{-0.2}{}^{}$	1200.66${}_{}{}^{+250.31}{}_{-242.65}{}^{}$	378.09${}_{}{}^{+29.85}{}_{-22.73}{}^{}$
090102	1.55	18.77${}_{}{}^{+0.98}{}_{-0.91}{}^{}$	4.71${}_{}{}^{+0.34}{}_{-0.33}{}^{}$	1101.6${}_{}{}^{+107.1}{}_{-91.8}{}^{}$	5.99 $\pm$ 0.27	8.75${}_{}{}^{+0.65}{}_{-0.6}{}^{}$	76.74${}_{}{}^{+9.92}{}_{-9.08}{}^{}$	5.13${}_{}{}^{+0.57}{}_{-0.49}{}^{}$	1284.14${}_{}{}^{+89.9}{}_{-84.58}{}^{}$	214.53${}_{}{}^{+11.48}{}_{-10.29}{}^{}$
090201	2.1	89.84${}_{}{}^{+2.5}{}_{-2.6}{}^{}$	14.36${}_{}{}^{+0.61}{}_{-0.61}{}^{}$	483.6${}_{}{}^{+21.7}{}_{-18.6}{}^{}$	21.71 $\pm$ 1.33	17.6${}_{}{}^{+0.69}{}_{-0.68}{}^{}$	41.33${}_{}{}^{+2.85}{}_{-2.73}{}^{}$	0.95${}_{}{}^{+0.05}{}_{-0.04}{}^{}$	11081.53${}_{}{}^{+743.7}{}_{-735.5}{}^{}$	510.49${}_{}{}^{+13.96}{}_{-13.01}{}^{}$
090323	3.6	417.28${}_{}{}^{+31.79}{}_{-31.79}{}^{}$	47.44${}_{}{}^{+4.2}{}_{-4.02}{}^{}$	1918.2${}_{}{}^{+207}{}_{-207}{}^{}$	28.91 $\pm$ 0.36	85.32${}_{}{}^{+8.37}{}_{-8.31}{}^{}$	148.74${}_{}{}^{+22.62}{}_{-22}{}^{}$	3.92${}_{}{}^{+0.49}{}_{-0.49}{}^{}$	14139.87${}_{}{}^{+890.69}{}_{-874.68}{}^{}$	489.08${}_{}{}^{+30.21}{}_{-29.65}{}^{}$
090328	0.74	9.12${}_{}{}^{+0.73}{}_{-0.63}{}^{}$	1.77${}_{}{}^{+0.15}{}_{-0.16}{}^{}$	1030.08${}_{}{}^{+233.16}{}_{-156.6}{}^{}$	30.34 $\pm$ 2.09	6.49${}_{}{}^{+0.86}{}_{-0.67}{}^{}$	66.97${}_{}{}^{+15.1}{}_{-11.92}{}^{}$	7.32${}_{}{}^{+1.83}{}_{-1.25}{}^{}$	4268.63${}_{}{}^{+535.26}{}_{-441.74}{}^{}$	140.67${}_{}{}^{+14.73}{}_{-10.84}{}^{}$
090424	0.54	3.55${}_{}{}^{+0.06}{}_{-0.06}{}^{}$	1.03${}_{}{}^{+0.06}{}_{-0.05}{}^{}$	249.48${}_{}{}^{+9.24}{}_{-9.24}{}^{}$	2.79 $\pm$ 0.04	1.76${}_{}{}^{+0.06}{}_{-0.06}{}^{}$	18.95${}_{}{}^{+1.52}{}_{-1.44}{}^{}$	1.24${}_{}{}^{+0.06}{}_{-0.06}{}^{}$	563.76${}_{}{}^{+18.4}{}_{-17.72}{}^{}$	202${}_{}{}^{+5.98}{}_{-5.71}{}^{}$
090618	0.54	23.22${}_{}{}^{+0.42}{}_{-0.43}{}^{}$	2.36${}_{}{}^{+0.2}{}_{-0.2}{}^{}$	287.98${}_{}{}^{+9.24}{}_{-9.24}{}^{}$	67.74 $\pm$ 0.68	8.35${}_{}{}^{+0.37}{}_{-0.37}{}^{}$	22.91${}_{}{}^{+2.67}{}_{-2.67}{}^{}$	1.04${}_{}{}^{+0.05}{}_{-0.05}{}^{}$	18830.2${}_{}{}^{+790.09}{}_{-790.09}{}^{}$	277.98${}_{}{}^{+11.32}{}_{-11.32}{}^{}$
090709A	1.8	61.18${}_{}{}^{+1.11}{}_{-1.11}{}^{}$	6.63${}_{}{}^{+0.44}{}_{-0.42}{}^{}$	728${}_{}{}^{+42}{}_{-39.2}{}^{}$	27.62 $\pm$ 0.8	20.38${}_{}{}^{+0.89}{}_{-0.85}{}^{}$	55.24${}_{}{}^{+5.72}{}_{-5.41}{}^{}$	2.43${}_{}{}^{+0.17}{}_{-0.16}{}^{}$	8290.59${}_{}{}^{+405.54}{}_{-390.72}{}^{}$	300.14${}_{}{}^{+11.86}{}_{-11.19}{}^{}$
090715B	3	19.53${}_{}{}^{+1.7}{}_{-1.47}{}^{}$	6.93${}_{}{}^{+0.74}{}_{-0.71}{}^{}$	540${}_{}{}^{+104}{}_{-72}{}^{}$	17.83 $\pm$ 1.66	5.61${}_{}{}^{+0.73}{}_{-0.59}{}^{}$	42.87${}_{}{}^{+9.44}{}_{-7.77}{}^{}$	1.55${}_{}{}^{+0.33}{}_{-0.24}{}^{}$	6208.44${}_{}{}^{+832.57}{}_{-741.08}{}^{}$	348.11${}_{}{}^{+33.53}{}_{-25.91}{}^{}$
090812	2.45	25.35${}_{}{}^{+0.77}{}_{-0.71}{}^{}$	8.66${}_{}{}^{+3.22}{}_{-1.94}{}^{}$	1297.2${}_{}{}^{+821.1}{}_{-883.2}{}^{}$	9.5 $\pm$ 1.01	9.58${}_{}{}^{+3.09}{}_{-2.99}{}^{}$	92.73${}_{}{}^{+68.85}{}_{-61.2}{}^{}$	4.9${}_{}{}^{+3.48}{}_{-3.67}{}^{}$	2514.84${}_{}{}^{+851.52}{}_{-825.24}{}^{}$	264.6${}_{}{}^{+85.04}{}_{-82.13}{}^{}$
090926A	2.11	191.21${}_{}{}^{+4.8}{}_{-4.7}{}^{}$	76.1${}_{}{}^{+2.86}{}_{-2.83}{}^{}$	1016.97${}_{}{}^{+24.88}{}_{-24.88}{}^{}$	4.24 $\pm$ 0.17	23.94${}_{}{}^{+0.77}{}_{-0.76}{}^{}$	89.51${}_{}{}^{+4.94}{}_{-4.89}{}^{}$	1.27${}_{}{}^{+0.04}{}_{-0.04}{}^{}$	3389.37${}_{}{}^{+154.21}{}_{-153.97}{}^{}$	798.56${}_{}{}^{+16.15}{}_{-16.02}{}^{}$
091003	0.9	7.46${}_{}{}^{+0.25}{}_{-0.25}{}^{}$	3.21${}_{}{}^{+0.16}{}_{-0.14}{}^{}$	680.2${}_{}{}^{+60.8}{}_{-53.2}{}^{}$	10.6 $\pm$ 0.16	3.37${}_{}{}^{+0.19}{}_{-0.18}{}^{}$	49.17${}_{}{}^{+4.98}{}_{-4.46}{}^{}$	3.07${}_{}{}^{+0.31}{}_{-0.27}{}^{}$	2347.72${}_{}{}^{+110.07}{}_{-99}{}^{}$	221.44${}_{}{}^{+9.84}{}_{-8.74}{}^{}$
091020	1.71	9.07${}_{}{}^{+0.43}{}_{-0.71}{}^{}$	3.29${}_{}{}^{+0.94}{}_{-0.55}{}^{}$	1344.16${}_{}{}^{+1447.14}{}_{-468.83}{}^{}$	10.78 $\pm$ 1.93	5.43${}_{}{}^{+2.63}{}_{-1.01}{}^{}$	88.49${}_{}{}^{+88.89}{}_{-33.26}{}^{}$	8.05${}_{}{}^{+9.49}{}_{-3.12}{}^{}$	1800.19${}_{}{}^{+924.3}{}_{-442.03}{}^{}$	166.97${}_{}{}^{+80.37}{}_{-28.13}{}^{}$
091127	0.49	1.47${}_{}{}^{+0.04}{}_{-0.05}{}^{}$	1.41${}_{}{}^{+0.21}{}_{-0.19}{}^{}$	49.17${}_{}{}^{+4.47}{}_{-19.37}{}^{}$	3.25 $\pm$ 1.14	0.31${}_{}{}^{+0.03}{}_{-0.06}{}^{}$	4.81${}_{}{}^{+1.03}{}_{-1.86}{}^{}$	0.1${}_{}{}^{+0.01}{}_{-0.05}{}^{}$	1523.68${}_{}{}^{+549.93}{}_{-603.34}{}^{}$	468.87${}_{}{}^{+36.69}{}_{-84.73}{}^{}$
100414A	1.37	50${}_{}{}^{+1}{}_{-1}{}^{}$	8.44${}_{}{}^{+0.47}{}_{-0.45}{}^{}$	1296.39${}_{}{}^{+52.14}{}_{-49.77}{}^{}$	9.17 $\pm$ 0.22	19.11${}_{}{}^{+0.71}{}_{-0.68}{}^{}$	92.5${}_{}{}^{+7.74}{}_{-7.37}{}^{}$	4.95${}_{}{}^{+0.25}{}_{-0.24}{}^{}$	2398.95${}_{}{}^{+94.67}{}_{-91.94}{}^{}$	261.67${}_{}{}^{+8.13}{}_{-7.74}{}^{}$
100606A	1.55	22.25${}_{}{}^{+1.73}{}_{-1.78}{}^{}$	4.78${}_{}{}^{+0.48}{}_{-0.44}{}^{}$	1892.1${}_{}{}^{+701.25}{}_{-362.1}{}^{}$	23.16 $\pm$ 3.15	13${}_{}{}^{+2.38}{}_{-1.59}{}^{}$	122.35${}_{}{}^{+42.39}{}_{-25.3}{}^{}$	11.05${}_{}{}^{+4.49}{}_{-2.35}{}^{}$	3964.17${}_{}{}^{+850.31}{}_{-652.13}{}^{}$	171.18${}_{}{}^{+28.39}{}_{-15.84}{}^{}$
100621A	0.54	3.76${}_{}{}^{+0.16}{}_{-0.14}{}^{}$	0.26${}_{}{}^{+0.02}{}_{-0.02}{}^{}$	149.38${}_{}{}^{+12.32}{}_{-10.78}{}^{}$	30.04 $\pm$ 5.33	2.79${}_{}{}^{+0.19}{}_{-0.17}{}^{}$	10.93${}_{}{}^{+1.5}{}_{-1.38}{}^{}$	1.11${}_{}{}^{+0.11}{}_{-0.1}{}^{}$	4041.19${}_{}{}^{+748.79}{}_{-743.47}{}^{}$	134.52${}_{}{}^{+7.17}{}_{-6.53}{}^{}$
100728A	1.57	102.21${}_{}{}^{+6.5}{}_{-5.91}{}^{}$	4.78${}_{}{}^{+0.3}{}_{-0.29}{}^{}$	783.85${}_{}{}^{+41.12}{}_{-41.12}{}^{}$	62.23 $\pm$ 2.02	40.87${}_{}{}^{+3}{}_{-2.78}{}^{}$	57.34${}_{}{}^{+5.58}{}_{-5.36}{}^{}$	3.13${}_{}{}^{+0.2}{}_{-0.2}{}^{}$	15565.54${}_{}{}^{+765.8}{}_{-752.53}{}^{}$	250.11${}_{}{}^{+9.23}{}_{-8.94}{}^{}$
100814A	1.44	7.28${}_{}{}^{+0.57}{}_{-0.52}{}^{}$	0.91${}_{}{}^{+0.1}{}_{-0.1}{}^{}$	312.32${}_{}{}^{+31.72}{}_{-26.84}{}^{}$	60.83 $\pm$ 17.75	4.21${}_{}{}^{+0.43}{}_{-0.4}{}^{}$	22.75${}_{}{}^{+3.8}{}_{-3.65}{}^{}$	1.81${}_{}{}^{+0.22}{}_{-0.19}{}^{}$	10523.83${}_{}{}^{+3146.83}{}_{-3137.29}{}^{}$	173.01${}_{}{}^{+11.25}{}_{-10.5}{}^{}$
100906A	1.73	22.76${}_{}{}^{+2.54}{}_{-1.93}{}^{}$	7${}_{}{}^{+0.74}{}_{-0.74}{}^{}$	505.05${}_{}{}^{+163.8}{}_{-144.69}{}^{}$	33.02 $\pm$ 5.16	6.32${}_{}{}^{+1.17}{}_{-0.99}{}^{}$	40.51${}_{}{}^{+12.71}{}_{-11.56}{}^{}$	1.4${}_{}{}^{+0.5}{}_{-0.44}{}^{}$	11888.57${}_{}{}^{+2556.22}{}_{-2435.22}{}^{}$	360.07${}_{}{}^{+53.18}{}_{-47.69}{}^{}$
101213A	0.41	0.48${}_{}{}^{+0.04}{}_{-0.03}{}^{}$	0.04${}_{}{}^{+0.01}{}_{-0.01}{}^{}$	327.12${}_{}{}^{+60.63}{}_{-74.73}{}^{}$	21.66 $\pm$ 3.28	1.17${}_{}{}^{+0.15}{}_{-0.16}{}^{}$	18.47${}_{}{}^{+4.71}{}_{-5.01}{}^{}$	8.04${}_{}{}^{+1.71}{}_{-2.06}{}^{}$	881.77${}_{}{}^{+162.09}{}_{-168.6}{}^{}$	40.71${}_{}{}^{+4.25}{}_{-4.76}{}^{}$
110213A	1.46	7.64${}_{}{}^{+0.47}{}_{-0.38}{}^{}$	2.2${}_{}{}^{+0.29}{}_{-0.25}{}^{}$	218.94${}_{}{}^{+39.36}{}_{-44.28}{}^{}$	11.89 $\pm$ 1.06	2.53${}_{}{}^{+0.29}{}_{-0.29}{}^{}$	17.99${}_{}{}^{+4.22}{}_{-4.19}{}^{}$	0.72${}_{}{}^{+0.15}{}_{-0.16}{}^{}$	3596.99${}_{}{}^{+475.1}{}_{-485.18}{}^{}$	302.53${}_{}{}^{+29.57}{}_{-30.71}{}^{}$
110422A	1.77	71.81${}_{}{}^{+1.05}{}_{-1.05}{}^{}$	23.95${}_{}{}^{+1.93}{}_{-1.79}{}^{}$	429.35${}_{}{}^{+8.31}{}_{-8.31}{}^{}$	8.05 $\pm$ 0.1	10.56${}_{}{}^{+0.43}{}_{-0.4}{}^{}$	38.87${}_{}{}^{+4.3}{}_{-4.01}{}^{}$	0.63${}_{}{}^{+0.03}{}_{-0.03}{}^{}$	5473.29${}_{}{}^{+218.15}{}_{-205.09}{}^{}$	679.74${}_{}{}^{+25.78}{}_{-24.07}{}^{}$
110503A	1.61	19.76${}_{}{}^{+0.86}{}_{-0.86}{}^{}$	15.58${}_{}{}^{+1.16}{}_{-1.07}{}^{}$	574.2${}_{}{}^{+31.32}{}_{-31.32}{}^{}$	2.55 $\pm$ 0.8	4.01${}_{}{}^{+0.24}{}_{-0.24}{}^{}$	48.22${}_{}{}^{+5.38}{}_{-5.05}{}^{}$	1.17${}_{}{}^{+0.08}{}_{-0.08}{}^{}$	1257.13${}_{}{}^{+398.9}{}_{-398.56}{}^{}$	492.22${}_{}{}^{+20.43}{}_{-19.41}{}^{}$
110715A	0.82	4.63${}_{}{}^{+0.31}{}_{-0.27}{}^{}$	2.39${}_{}{}^{+0.09}{}_{-0.09}{}^{}$	216.58${}_{}{}^{+12.74}{}_{-12.74}{}^{}$	1.56 $\pm$ 0.1	1.46${}_{}{}^{+0.11}{}_{-0.1}{}^{}$	17.95${}_{}{}^{+1.28}{}_{-1.28}{}^{}$	0.69${}_{}{}^{+0.05}{}_{-0.05}{}^{}$	493.61${}_{}{}^{+35.31}{}_{-35.31}{}^{}$	316.11${}_{}{}^{+9.61}{}_{-9.61}{}^{}$
110731A	2.83	30.32${}_{}{}^{+1.16}{}_{-1.1}{}^{}$	21.58${}_{}{}^{+1.38}{}_{-1.38}{}^{}$	1103.04${}_{}{}^{+68.94}{}_{-61.28}{}^{}$	1.75 $\pm$ 0.22	7.02${}_{}{}^{+0.39}{}_{-0.37}{}^{}$	86.78${}_{}{}^{+8.88}{}_{-8.62}{}^{}$	2.55${}_{}{}^{+0.19}{}_{-0.17}{}^{}$	755.69${}_{}{}^{+101.23}{}_{-100.8}{}^{}$	431.85${}_{}{}^{+17.23}{}_{-16.39}{}^{}$
110918A	0.98	239.5${}_{}{}^{+7.93}{}_{-7.93}{}^{}$	184.11${}_{}{}^{+4.87}{}_{-4.87}{}^{}$	665.28${}_{}{}^{+79.2}{}_{-69.3}{}^{}$	9.87 $\pm$ 0.05	16.64${}_{}{}^{+1.03}{}_{-0.95}{}^{}$	66.69${}_{}{}^{+7.24}{}_{-6.44}{}^{}$	0.46${}_{}{}^{+0.06}{}_{-0.05}{}^{}$	14207.64${}_{}{}^{+750.82}{}_{-663.15}{}^{}$	1438.93${}_{}{}^{+75.71}{}_{-66.79}{}^{}$
111228A	0.72	1.47${}_{}{}^{+0.15}{}_{-0.13}{}^{}$	0.38${}_{}{}^{+0.12}{}_{-0.08}{}^{}$	75.68${}_{}{}^{+30.96}{}_{-24.08}{}^{}$	29.4 $\pm$ 1.26	0.69${}_{}{}^{+0.17}{}_{-0.13}{}^{}$	6.28${}_{}{}^{+3.4}{}_{-2.43}{}^{}$	0.35${}_{}{}^{+0.16}{}_{-0.13}{}^{}$	6298.73${}_{}{}^{+1438.52}{}_{-1075.88}{}^{}$	214.21${}_{}{}^{+48.05}{}_{-35.41}{}^{}$
120119A	1.73	36.03${}_{}{}^{+2.59}{}_{-2.45}{}^{}$	7.1${}_{}{}^{+0.57}{}_{-0.55}{}^{}$	417.69${}_{}{}^{+32.76}{}_{-32.76}{}^{}$	14.52 $\pm$ 1.52	9.16${}_{}{}^{+0.8}{}_{-0.77}{}^{}$	34.44${}_{}{}^{+4.42}{}_{-4.31}{}^{}$	1.06${}_{}{}^{+0.1}{}_{-0.1}{}^{}$	5709.44${}_{}{}^{+661.58}{}_{-659.3}{}^{}$	393.22${}_{}{}^{+19.67}{}_{-19.31}{}^{}$
120624B	2.2	247.24${}_{}{}^{+10.49}{}_{-9.64}{}^{}$	16.48${}_{}{}^{+1.1}{}_{-1.06}{}^{}$	1699.2${}_{}{}^{+172.8}{}_{-166.4}{}^{}$	83.72 $\pm$ 1.3	78.04${}_{}{}^{+5.32}{}_{-5.04}{}^{}$	123.15${}_{}{}^{+15.49}{}_{-14.96}{}^{}$	5.36${}_{}{}^{+0.62}{}_{-0.59}{}^{}$	26524.27${}_{}{}^{+1474.48}{}_{-1426.79}{}^{}$	316.82${}_{}{}^{+16.91}{}_{-16.32}{}^{}$
120711A	1.41	177.41${}_{}{}^{+4.02}{}_{-4.02}{}^{}$	14.37${}_{}{}^{+0.79}{}_{-0.78}{}^{}$	2557.01${}_{}{}^{+91.58}{}_{-86.76}{}^{}$	17.15 $\pm$ 0.25	71.1${}_{}{}^{+2.65}{}_{-2.61}{}^{}$	173.11${}_{}{}^{+13.97}{}_{-13.7}{}^{}$	10.25${}_{}{}^{+0.48}{}_{-0.46}{}^{}$	4280.29${}_{}{}^{+141.22}{}_{-138.44}{}^{}$	249.54${}_{}{}^{+7.38}{}_{-7.2}{}^{}$
120716A	2.49	23.3${}_{}{}^{+2.05}{}_{-1.53}{}^{}$	4.65${}_{}{}^{+0.7}{}_{-0.65}{}^{}$	610.75${}_{}{}^{+167.52}{}_{-132.62}{}^{}$	59.76 $\pm$ 1.53	8.48${}_{}{}^{+1.38}{}_{-1.11}{}^{}$	46.16${}_{}{}^{+14.44}{}_{-12.29}{}^{}$	2.22${}_{}{}^{+0.68}{}_{-0.54}{}^{}$	16427.11${}_{}{}^{+2287.86}{}_{-1907.92}{}^{}$	274.86${}_{}{}^{+37.63}{}_{-31.14}{}^{}$
121128A	2.2	9.64${}_{}{}^{+0.29}{}_{-0.27}{}^{}$	9.3${}_{}{}^{+0.54}{}_{-0.5}{}^{}$	243.2${}_{}{}^{+9.6}{}_{-9.6}{}^{}$	3.13 $\pm$ 0.99	1.72${}_{}{}^{+0.07}{}_{-0.07}{}^{}$	22.1${}_{}{}^{+1.9}{}_{-1.78}{}^{}$	0.43${}_{}{}^{+0.02}{}_{-0.02}{}^{}$	1758.25${}_{}{}^{+558.69}{}_{-558.39}{}^{}$	561.68${}_{}{}^{+17.83}{}_{-16.86}{}^{}$
130408A	3.76	26.17${}_{}{}^{+5.47}{}_{-4.04}{}^{}$	35.67${}_{}{}^{+6.68}{}_{-5.44}{}^{}$	1289.96${}_{}{}^{+176.12}{}_{-204.68}{}^{}$	0.89 $\pm$ 0.06	5.14${}_{}{}^{+1.2}{}_{-0.94}{}^{}$	103.36${}_{}{}^{+28.97}{}_{-25.63}{}^{}$	2.54${}_{}{}^{+0.44}{}_{-0.47}{}^{}$	452.75${}_{}{}^{+56.35}{}_{-53.93}{}^{}$	508.75${}_{}{}^{+53.04}{}_{-49.77}{}^{}$
130427A	0.34	81.56${}_{}{}^{+0.43}{}_{-0.43}{}^{}$	19.43${}_{}{}^{+0.42}{}_{-0.42}{}^{}$	1415.04${}_{}{}^{+13.4}{}_{-13.4}{}^{}$	46.08 $\pm$ 4.66	22.06${}_{}{}^{+0.26}{}_{-0.26}{}^{}$	106.61${}_{}{}^{+3.25}{}_{-3.25}{}^{}$	3.83${}_{}{}^{+0.05}{}_{-0.05}{}^{}$	17035.36${}_{}{}^{+1734.08}{}_{-1734.08}{}^{}$	369.71${}_{}{}^{+3.97}{}_{-3.97}{}^{}$
130505A	2.27	311.23${}_{}{}^{+7.23}{}_{-7.14}{}^{}$	208.86${}_{}{}^{+8.27}{}_{-8.27}{}^{}$	1939.11${}_{}{}^{+85.02}{}_{-78.48}{}^{}$	4.49 $\pm$ 0.14	32.33${}_{}{}^{+1.13}{}_{-1.1}{}^{}$	169.04${}_{}{}^{+11.11}{}_{-10.83}{}^{}$	2.01${}_{}{}^{+0.1}{}_{-0.1}{}^{}$	4323.96${}_{}{}^{+178.64}{}_{-175.87}{}^{}$	962.65${}_{}{}^{+25.24}{}_{-24.25}{}^{}$
130518A	2.49	155.4${}_{}{}^{+10.04}{}_{-9.82}{}^{}$	66.66${}_{}{}^{+6.03}{}_{-6.03}{}^{}$	1158.68${}_{}{}^{+188.46}{}_{-157.05}{}^{}$	8.2 $\pm$ 1.63	21.88${}_{}{}^{+2.27}{}_{-2.09}{}^{}$	99.08${}_{}{}^{+18.44}{}_{-16.78}{}^{}$	1.63${}_{}{}^{+0.3}{}_{-0.25}{}^{}$	5827.19${}_{}{}^{+1252.01}{}_{-1231.58}{}^{}$	710.36${}_{}{}^{+57.8}{}_{-50.86}{}^{}$
130701A	1.16	2.51${}_{}{}^{+0.08}{}_{-0.08}{}^{}$	2.56${}_{}{}^{+0.16}{}_{-0.15}{}^{}$	192.24${}_{}{}^{+8.64}{}_{-8.64}{}^{}$	1.69 $\pm$ 0.15	0.73${}_{}{}^{+0.03}{}_{-0.03}{}^{}$	16.28${}_{}{}^{+1.49}{}_{-1.42}{}^{}$	0.56${}_{}{}^{+0.03}{}_{-0.03}{}^{}$	581.02${}_{}{}^{+54.38}{}_{-54.12}{}^{}$	343.08${}_{}{}^{+11.66}{}_{-11.23}{}^{}$
130831A	0.48	0.73${}_{}{}^{+0.03}{}_{-0.03}{}^{}$	0.19${}_{}{}^{+0.02}{}_{-0.02}{}^{}$	81.4${}_{}{}^{+10.36}{}_{-13.32}{}^{}$	11.84 $\pm$ 1.9	0.48${}_{}{}^{+0.04}{}_{-0.04}{}^{}$	6.32${}_{}{}^{+1.02}{}_{-1.13}{}^{}$	0.54${}_{}{}^{+0.08}{}_{-0.1}{}^{}$	1784.83${}_{}{}^{+310.93}{}_{-319.67}{}^{}$	150.69${}_{}{}^{+10.26}{}_{-12.02}{}^{}$
130907A	1.24	327.56${}_{}{}^{+10.88}{}_{-10.88}{}^{}$	15.44${}_{}{}^{+0.52}{}_{-0.51}{}^{}$	866.88${}_{}{}^{+35.84}{}_{-35.84}{}^{}$	80.49 $\pm$ 0.18	79.77${}_{}{}^{+3.25}{}_{-3.24}{}^{}$	68.67${}_{}{}^{+3.98}{}_{-3.94}{}^{}$	2.11${}_{}{}^{+0.1}{}_{-0.1}{}^{}$	33048.76${}_{}{}^{+783.04}{}_{-777.83}{}^{}$	410.62${}_{}{}^{+9.68}{}_{-9.62}{}^{}$
131030A	1.29	30.84${}_{}{}^{+1.22}{}_{-1.13}{}^{}$	7.22${}_{}{}^{+0.27}{}_{-0.26}{}^{}$	448.84${}_{}{}^{+13.74}{}_{-13.74}{}^{}$	6.86 $\pm$ 0.25	8.03${}_{}{}^{+0.36}{}_{-0.34}{}^{}$	36.69${}_{}{}^{+2.1}{}_{-2.04}{}^{}$	1.17${}_{}{}^{+0.04}{}_{-0.04}{}^{}$	2636.24${}_{}{}^{+110.21}{}_{-109.53}{}^{}$	384.23${}_{}{}^{+8.32}{}_{-8.12}{}^{}$
131105A	1.69	13.07${}_{}{}^{+1.03}{}_{-0.82}{}^{}$	2.32${}_{}{}^{+0.28}{}_{-0.26}{}^{}$	414.26${}_{}{}^{+83.39}{}_{-56.49}{}^{}$	41.24 $\pm$ 1.19	5.54${}_{}{}^{+0.72}{}_{-0.55}{}^{}$	31.27${}_{}{}^{+7.41}{}_{-5.98}{}^{}$	1.76${}_{}{}^{+0.4}{}_{-0.28}{}^{}$	9728.48${}_{}{}^{+1035.11}{}_{-806.96}{}^{}$	235.88${}_{}{}^{+24.16}{}_{-18.35}{}^{}$
131108A	2.4	48.83${}_{}{}^{+2.24}{}_{-1.98}{}^{}$	34.55${}_{}{}^{+5.83}{}_{-5.38}{}^{}$	1128.8${}_{}{}^{+105.4}{}_{-98.6}{}^{}$	5.2 $\pm$ 0.14	9.2${}_{}{}^{+0.91}{}_{-0.83}{}^{}$	91.92${}_{}{}^{+22.34}{}_{-20.65}{}^{}$	2.13${}_{}{}^{+0.27}{}_{-0.25}{}^{}$	2762.93${}_{}{}^{+252.23}{}_{-235.11}{}^{}$	530.97${}_{}{}^{+46.42}{}_{-42.97}{}^{}$
131231A	0.64	19.08${}_{}{}^{+0.51}{}_{-0.51}{}^{}$	3.17${}_{}{}^{+0.14}{}_{-0.13}{}^{}$	265.68${}_{}{}^{+9.84}{}_{-9.84}{}^{}$	17.78 $\pm$ 1.85	5.79${}_{}{}^{+0.21}{}_{-0.21}{}^{}$	21.88${}_{}{}^{+1.44}{}_{-1.41}{}^{}$	0.81${}_{}{}^{+0.04}{}_{-0.04}{}^{}$	5863.38${}_{}{}^{+628.28}{}_{-627.72}{}^{}$	329.73${}_{}{}^{+8.32}{}_{-8.19}{}^{}$
140213A	1.21	8.44${}_{}{}^{+0.18}{}_{-0.17}{}^{}$	3.64${}_{}{}^{+0.16}{}_{-0.16}{}^{}$	218.79${}_{}{}^{+8.84}{}_{-8.84}{}^{}$	7.42 $\pm$ 1.3	2.21${}_{}{}^{+0.08}{}_{-0.07}{}^{}$	18.72${}_{}{}^{+1.31}{}_{-1.31}{}^{}$	0.57${}_{}{}^{+0.03}{}_{-0.03}{}^{}$	2835.03${}_{}{}^{+501.75}{}_{-501.75}{}^{}$	381.99${}_{}{}^{+10.3}{}_{-10.3}{}^{}$
140419A	3.96	160.08${}_{}{}^{+12.95}{}_{-12.73}{}^{}$	21.93${}_{}{}^{+2.33}{}_{-2.21}{}^{}$	1398.72${}_{}{}^{+188.48}{}_{-188.48}{}^{}$	10.78 $\pm$ 0.77	40.75${}_{}{}^{+4.52}{}_{-4.43}{}^{}$	106.58${}_{}{}^{+19.71}{}_{-19.15}{}^{}$	3.56${}_{}{}^{+0.55}{}_{-0.55}{}^{}$	4234.78${}_{}{}^{+440.22}{}_{-435.69}{}^{}$	392.81${}_{}{}^{+29.75}{}_{-29.17}{}^{}$
140506A	0.89	1.21${}_{}{}^{+0.11}{}_{-0.07}{}^{}$	0.87${}_{}{}^{+0.2}{}_{-0.14}{}^{}$	351.54${}_{}{}^{+196.56}{}_{-92.61}{}^{}$	32.3 $\pm$ 2.77	0.75${}_{}{}^{+0.21}{}_{-0.11}{}^{}$	25.11${}_{}{}^{+14.37}{}_{-7.77}{}^{}$	2.18${}_{}{}^{+1.35}{}_{-0.64}{}^{}$	5213.08${}_{}{}^{+1438.82}{}_{-828.74}{}^{}$	161.4${}_{}{}^{+42.35}{}_{-21.61}{}^{}$
140508A	1.03	20.81${}_{}{}^{+1.42}{}_{-1.34}{}^{}$	12.72${}_{}{}^{+0.58}{}_{-0.58}{}^{}$	446.6${}_{}{}^{+28.42}{}_{-26.39}{}^{}$	73.73 $\pm$ 10.33	4.17${}_{}{}^{+0.32}{}_{-0.3}{}^{}$	38.22${}_{}{}^{+3.15}{}_{-3.06}{}^{}$	0.89${}_{}{}^{+0.06}{}_{-0.06}{}^{}$	36830.7${}_{}{}^{+5315.21}{}_{-5302.04}{}^{}$	499.51${}_{}{}^{+17.2}{}_{-16.44}{}^{}$
140512A	0.72	5.86${}_{}{}^{+0.53}{}_{-0.43}{}^{}$	0.57${}_{}{}^{+0.08}{}_{-0.07}{}^{}$	823.88${}_{}{}^{+201.24}{}_{-135.88}{}^{}$	82.08 $\pm$ 3.56	6.36${}_{}{}^{+0.98}{}_{-0.73}{}^{}$	50.49${}_{}{}^{+14.39}{}_{-10.69}{}^{}$	8.95${}_{}{}^{+2.45}{}_{-1.68}{}^{}$	7557.32${}_{}{}^{+990.25}{}_{-746.01}{}^{}$	92.08${}_{}{}^{+11.38}{}_{-8.16}{}^{}$
140606B	0.38	0.25${}_{}{}^{+0.01}{}_{-0.01}{}^{}$	0.09${}_{}{}^{+0.01}{}_{-0.01}{}^{}$	350.52${}_{}{}^{+27.6}{}_{-23.46}{}^{}$	4.88 $\pm$ 0.51	0.43${}_{}{}^{+0.03}{}_{-0.03}{}^{}$	20.95${}_{}{}^{+2.56}{}_{-2.32}{}^{}$	6.06${}_{}{}^{+0.56}{}_{-0.48}{}^{}$	282.07${}_{}{}^{+32.54}{}_{-31.94}{}^{}$	57.84${}_{}{}^{+2.79}{}_{-2.49}{}^{}$
140801A	1.32	5.32${}_{}{}^{+0.12}{}_{-0.11}{}^{}$	1.62${}_{}{}^{+0.14}{}_{-0.14}{}^{}$	250.56${}_{}{}^{+6.96}{}_{-6.96}{}^{}$	2.65 $\pm$ 0.08	2.14${}_{}{}^{+0.1}{}_{-0.1}{}^{}$	19.72${}_{}{}^{+2.39}{}_{-2.39}{}^{}$	1.01${}_{}{}^{+0.05}{}_{-0.05}{}^{}$	659.47${}_{}{}^{+34.24}{}_{-34.24}{}^{}$	248.53${}_{}{}^{+10.41}{}_{-10.41}{}^{}$
140808A	3.29	8.3${}_{}{}^{+0.47}{}_{-0.45}{}^{}$	12.26${}_{}{}^{+1.17}{}_{-1.07}{}^{}$	527.67${}_{}{}^{+60.06}{}_{-55.77}{}^{}$	1.21 $\pm$ 0.26	1.82${}_{}{}^{+0.16}{}_{-0.15}{}^{}$	43.99${}_{}{}^{+7.16}{}_{-6.56}{}^{}$	1.15${}_{}{}^{+0.15}{}_{-0.14}{}^{}$	554.42${}_{}{}^{+124.82}{}_{-124}{}^{}$	457.22${}_{}{}^{+30.09}{}_{-27.68}{}^{}$
141220A	1.32	2.19${}_{}{}^{+0.11}{}_{-0.11}{}^{}$	1.41${}_{}{}^{+0.16}{}_{-0.15}{}^{}$	320.16${}_{}{}^{+23.2}{}_{-20.88}{}^{}$	2.97 $\pm$ 0.13	1.04${}_{}{}^{+0.08}{}_{-0.08}{}^{}$	24.07${}_{}{}^{+4.06}{}_{-3.77}{}^{}$	1.53${}_{}{}^{+0.15}{}_{-0.13}{}^{}$	621.66${}_{}{}^{+47.56}{}_{-45.28}{}^{}$	209.33${}_{}{}^{+12.88}{}_{-11.92}{}^{}$
150206A	2.09	51.69${}_{}{}^{+3.8}{}_{-3.71}{}^{}$	16.2${}_{}{}^{+1.52}{}_{-1.46}{}^{}$	704.52${}_{}{}^{+71.07}{}_{-67.98}{}^{}$	11.38 $\pm$ 1.54	11.26${}_{}{}^{+1.08}{}_{-1.04}{}^{}$	57.68${}_{}{}^{+8.88}{}_{-8.53}{}^{}$	1.54${}_{}{}^{+0.18}{}_{-0.17}{}^{}$	5224.09${}_{}{}^{+773.64}{}_{-768.37}{}^{}$	458.97${}_{}{}^{+28.06}{}_{-26.92}{}^{}$
150314A	1.76	71.82${}_{}{}^{+1.98}{}_{-1.98}{}^{}$	40.99${}_{}{}^{+1.58}{}_{-1.54}{}^{}$	966${}_{}{}^{+27.6}{}_{-27.6}{}^{}$	3.71 $\pm$ 0.08	11.69${}_{}{}^{+0.41}{}_{-0.41}{}^{}$	81.5${}_{}{}^{+4.71}{}_{-4.61}{}^{}$	1.57${}_{}{}^{+0.06}{}_{-0.06}{}^{}$	2280.96${}_{}{}^{+68.94}{}_{-68.31}{}^{}$	614.19${}_{}{}^{+13.25}{}_{-13.01}{}^{}$
150323A	0.59	1.14${}_{}{}^{+0.04}{}_{-0.03}{}^{}$	0.11${}_{}{}^{+0.02}{}_{-0.02}{}^{}$	151.05${}_{}{}^{+14.31}{}_{-12.72}{}^{}$	96.33 $\pm$ 5.91	1.28${}_{}{}^{+0.11}{}_{-0.1}{}^{}$	10.28${}_{}{}^{+2.23}{}_{-2.09}{}^{}$	1.69${}_{}{}^{+0.21}{}_{-0.19}{}^{}$	8589.73${}_{}{}^{+860.49}{}_{-825.4}{}^{}$	89.17${}_{}{}^{+7.06}{}_{-6.59}{}^{}$
150403A	2.06	90.06${}_{}{}^{+4.78}{}_{-4.78}{}^{}$	39.49${}_{}{}^{+1.9}{}_{-1.87}{}^{}$	1141.38${}_{}{}^{+104.04}{}_{-94.86}{}^{}$	6.87 $\pm$ 0.51	16.03${}_{}{}^{+1.12}{}_{-1.08}{}^{}$	93.79${}_{}{}^{+9.57}{}_{-9.03}{}^{}$	2.03${}_{}{}^{+0.21}{}_{-0.19}{}^{}$	3862.98${}_{}{}^{+333.06}{}_{-326.91}{}^{}$	561.93${}_{}{}^{+25.29}{}_{-23.53}{}^{}$
150821A	0.76	13.51${}_{}{}^{+1.09}{}_{-0.88}{}^{}$	0.61${}_{}{}^{+0.04}{}_{-0.04}{}^{}$	617.76${}_{}{}^{+183.04}{}_{-168.96}{}^{}$	63.05 $\pm$ 7.83	12.62${}_{}{}^{+1.95}{}_{-1.74}{}^{}$	39.6${}_{}{}^{+10.8}{}_{-9.99}{}^{}$	5.77${}_{}{}^{+1.87}{}_{-1.73}{}^{}$	6750.8${}_{}{}^{+1221.66}{}_{-1173.48}{}^{}$	107.08${}_{}{}^{+14.09}{}_{-13.02}{}^{}$
151021A	2.33	102.51${}_{}{}^{+8.83}{}_{-8.06}{}^{}$	14.19${}_{}{}^{+1.24}{}_{-1.24}{}^{}$	566.1${}_{}{}^{+43.29}{}_{-36.63}{}^{}$	17.12 $\pm$ 0.86	21.61${}_{}{}^{+2.17}{}_{-2}{}^{}$	47.28${}_{}{}^{+6.4}{}_{-6.18}{}^{}$	1.19${}_{}{}^{+0.11}{}_{-0.1}{}^{}$	8122.01${}_{}{}^{+586.16}{}_{-568.62}{}^{}$	474.45${}_{}{}^{+24.59}{}_{-23.14}{}^{}$
151027A	0.81	2.88${}_{}{}^{+0.39}{}_{-0.28}{}^{}$	0.53${}_{}{}^{+0.05}{}_{-0.04}{}^{}$	273.31${}_{}{}^{+83.26}{}_{-70.59}{}^{}$	64.82 $\pm$ 1.5	2.02${}_{}{}^{+0.39}{}_{-0.31}{}^{}$	19.42${}_{}{}^{+5.6}{}_{-4.83}{}^{}$	1.92${}_{}{}^{+0.64}{}_{-0.54}{}^{}$	9248.52${}_{}{}^{+1286.72}{}_{-1106.06}{}^{}$	142.67${}_{}{}^{+19.57}{}_{-16.74}{}^{}$
160131A	0.97	59.15${}_{}{}^{+4.48}{}_{-4.48}{}^{}$	5.72${}_{}{}^{+0.26}{}_{-0.26}{}^{}$	1282.47${}_{}{}^{+453.1}{}_{-307.32}{}^{}$	55.77 $\pm$ 4.03	26.91${}_{}{}^{+4.6}{}_{-3.49}{}^{}$	88.84${}_{}{}^{+27.55}{}_{-19.12}{}^{}$	5.83${}_{}{}^{+2.25}{}_{-1.53}{}^{}$	12259.32${}_{}{}^{+2078.29}{}_{-1564.08}{}^{}$	219.82${}_{}{}^{+33.71}{}_{-23.12}{}^{}$
160509A	1.17	94.17${}_{}{}^{+8.65}{}_{-8.33}{}^{}$	15.26${}_{}{}^{+0.67}{}_{-0.66}{}^{}$	624.96${}_{}{}^{+62.93}{}_{-58.59}{}^{}$	13.14 $\pm$ 1.76	20.03${}_{}{}^{+2.07}{}_{-1.99}{}^{}$	51.78${}_{}{}^{+5.44}{}_{-5.17}{}^{}$	1.33${}_{}{}^{+0.15}{}_{-0.14}{}^{}$	6176.62${}_{}{}^{+877.49}{}_{-871.86}{}^{}$	470.09${}_{}{}^{+22.44}{}_{-21.14}{}^{}$
160623A	0.37	23.26${}_{}{}^{+0.31}{}_{-0.31}{}^{}$	5.21${}_{}{}^{+0.06}{}_{-0.06}{}^{}$	756.24${}_{}{}^{+19.18}{}_{-19.18}{}^{}$	15.77 $\pm$ 0.43	8.8${}_{}{}^{+0.16}{}_{-0.16}{}^{}$	55.98${}_{}{}^{+1.55}{}_{-1.55}{}^{}$	2.86${}_{}{}^{+0.08}{}_{-0.08}{}^{}$	4164.68${}_{}{}^{+124.96}{}_{-124.96}{}^{}$	264.15${}_{}{}^{+3.25}{}_{-3.25}{}^{}$
160625B	1.41	429.4${}_{}{}^{+5.42}{}_{-4.97}{}^{}$	118.52${}_{}{}^{+5.12}{}_{-5.12}{}^{}$	1376.11${}_{}{}^{+28.92}{}_{-26.51}{}^{}$	8.71 $\pm$ 0.24	49.95${}_{}{}^{+1.26}{}_{-1.22}{}^{}$	120.28${}_{}{}^{+7.39}{}_{-7.34}{}^{}$	1.6${}_{}{}^{+0.05}{}_{-0.05}{}^{}$	7487.81${}_{}{}^{+261.43}{}_{-260.03}{}^{}$	859.64${}_{}{}^{+18.77}{}_{-18.51}{}^{}$
160629A	3.33	36.49${}_{}{}^{+1.35}{}_{-1.25}{}^{}$	8.57${}_{}{}^{+0.91}{}_{-0.88}{}^{}$	987.24${}_{}{}^{+103.92}{}_{-112.58}{}^{}$	14.91 $\pm$ 2.59	12.32${}_{}{}^{+0.94}{}_{-0.94}{}^{}$	73.26${}_{}{}^{+12.43}{}_{-12.54}{}^{}$	3.33${}_{}{}^{+0.41}{}_{-0.44}{}^{}$	4416.25${}_{}{}^{+820.52}{}_{-823.51}{}^{}$	296.16${}_{}{}^{+19.67}{}_{-20.22}{}^{}$
161023A	2.708	68.17${}_{}{}^{+9.74}{}_{-9.74}{}^{}$	31.9${}_{}{}^{+4.81}{}_{-4.81}{}^{}$	604.4${}_{}{}^{+137.2}{}_{-103.82}{}^{}$	13.48 $\pm$ 0	10.18${}_{}{}^{+1.9}{}_{-1.78}{}^{}$	53.37${}_{}{}^{+15.11}{}_{-13.49}{}^{}$	0.9${}_{}{}^{+0.23}{}_{-0.18}{}^{}$	9027.68${}_{}{}^{+1081.37}{}_{-915.19}{}^{}$	669.49${}_{}{}^{+80.19}{}_{-67.87}{}^{}$
170214A	2.53	336.95${}_{}{}^{+23.77}{}_{-23.77}{}^{}$	43.28${}_{}{}^{+0.64}{}_{-0.64}{}^{}$	1164.9${}_{}{}^{+74.13}{}_{-67.07}{}^{}$	42.49 $\pm$ 0	57.99${}_{}{}^{+4.41}{}_{-4.35}{}^{}$	96.16${}_{}{}^{+5.61}{}_{-5.14}{}^{}$	2${}_{}{}^{+0.14}{}_{-0.13}{}^{}$	24689.85${}_{}{}^{+696.26}{}_{-634.02}{}^{}$	581.03${}_{}{}^{+16.39}{}_{-14.92}{}^{}$
171010A	0.3285	18.59${}_{}{}^{+0.57}{}_{-0.57}{}^{}$	0.93${}_{}{}^{+0.06}{}_{-0.06}{}^{}$	227.17${}_{}{}^{+9.3}{}_{-7.97}{}^{}$	116.67 $\pm$ 0	9.26${}_{}{}^{+0.44}{}_{-0.43}{}^{}$	17.34${}_{}{}^{+1.75}{}_{-1.72}{}^{}$	1.13${}_{}{}^{+0.06}{}_{-0.06}{}^{}$	23410.41${}_{}{}^{+853.32}{}_{-826.5}{}^{}$	200.65${}_{}{}^{+7.31}{}_{-7.08}{}^{}$
180325A	2.248	21.83${}_{}{}^{+3.45}{}_{-3.45}{}^{}$	30.6${}_{}{}^{+4.85}{}_{-4.85}{}^{}$	993.89${}_{}{}^{+162.4}{}_{-126.67}{}^{}$	3.08 $\pm$ 0	4.12${}_{}{}^{+0.77}{}_{-0.75}{}^{}$	81.59${}_{}{}^{+20.98}{}_{-19.72}{}^{}$	1.87${}_{}{}^{+0.36}{}_{-0.29}{}^{}$	1632.78${}_{}{}^{+165.35}{}_{-148.95}{}^{}$	530.33${}_{}{}^{+53.7}{}_{-48.38}{}^{}$

Table 5. Table 5: The properties of distributions

Parameter	Median(log10)			$\sigma$			Median(real)			paaP-Value of normal distribution test.
	Fermi	KW	All	Fermi	KW	All	Fermi	KW	All	Fermi	KW
$T_{90,\mathrm{obs}}$ (s)	1.61	1.48	1.53	0.47	0.50	0.49	41.07	30.00	34.18	0.27	0.006
$E_{p,\mathrm{obs}}$(keV)	2.21	2.36	2.30	0.41	0.30	0.36	161.58	230.64	198.96	0.75	0.72
$S_{\gamma }$ (erg cm-2)	-4.79	-4.38	-4.55	0.71	0.64	0.70	1.62E-05	4.20E-05	2.82E-05	0.11	0.10
$F_p$(erg cm-2 s-1)	-5.80	-5.32	-5.52	0.61	0.55	0.63	1.58E-06	4.83E-06	3.03E-06	0.01	0.04
$z$bbRedshift of our sample.	0.14	0.12	0.13	0.31	0.30	0.30	1.37	1.31	1.33
$z$ccRedshift of 412 long GRBs.	0.17			0.38			1.48
$E_{\mathrm{iso}}$ (erg)	52.99	53.24	53.14	0.86	0.77	0.82	9.88E+52	1.75E+53	1.38E+53	0.76	0.02
$L_{\mathrm{iso}}$ (erg s-1)	52.38	52.69	52.56	0.87	0.80	0.84	2.42E+52	4.91E+52	3.66E+52	0.69	0.0001
$E_p$ (keV)	2.61	2.75	2.69	0.46	0.36	0.41	406	562	491	0.41	-
$T_{90}$ (s)	1.21	1.09	1.14	0.51	0.51	0.51	16.34	12.30	13.84	0.76	0.52
${\Gamma }_0$	2.38	2.47	2.43	0.30	0.28	0.29	243	292	270
$E_{\mathrm{iso}}^{\prime }$ (erg)	50.61	50.78	50.71	0.67	0.58	0.62	4.07E+50	6E+50	5.11E+50	0.78	0.30
$L_{\mathrm{iso}}^{\prime }$ (erg s-1)	47.49	47.64	47.57	0.45	0.35	0.40	3.08E+47	4.32E+47	3.76E+47	0.58	0.35
$E_p^{\prime }$ (keV)	0.22	0.28	0.26	0.47	0.37	0.41	1.67	1.93	1.82	0.10	0.45
$T_{90}^{\prime }$ (s)	3.60	3.56	3.57	0.52	0.52	0.52	3965.47	3592.07	3742.62	0.70	0.14
$E_{\mathrm{iso},c}$ (erg)	52.02	52.57	52.34	0.75	0.65	0.74	1.05E+52	3.72E+52	2.19E+52	0.57	0.41
$L_{\mathrm{iso},c}$ (erg s-1)	51.32	51.44	51.39	0.66	0.56	0.60	2.09E+51	2.75E+51	2.45E+51	0.47	0.54
$E_{p,c}$ (keV)	2.19	2.34	2.27	0.41	0.30	0.36	155	219	186	0.74	0.85
$E_{\mathrm{iso},c}^{\prime }$ (erg)	49.63	50.11	49.91	0.64	0.52	0.62	4.27E+49	1.29E+50	8.13E+49	0.31	0.10
$L_{\mathrm{iso},c}^{\prime }$ (erg s-1)	46.43	46.38	46.40	0.44	0.40	0.42	2.69E+46	2.40E+46	2.51E+46	0.65	0.85
$E_{p,c}^{\prime }$ (keV)	-0.20	-0.13	-0.16	0.49	0.40	0.44	0.63	0.74	0.69	0.43	0.004

Table 6. Table 6: The results of regression analysis for correlations in the rest frame and comoving frame, in which r 𝑟 r is the correlation coefficient, p 𝑝 p is the chance probability, and σ 𝜎 \sigma is the dispersion

Relations	Expressions	$r$	$p$	$\sigma$
$E_p\left(E_{\mathrm{iso}}\right)$	$\log E_p=\left(2.28\pm 0.04\right)+\left(0.36\pm 0.03\right)\times \log E_{\mathrm{iso},52}$	0.71		0.58
$E_p\left(L_{\mathrm{iso}}\right)$	$\log E_p=\left(2.50\pm 0.03\right)+\left(0.34\pm 0.03\right)\times \log L_{\mathrm{iso},52}$	0.72		0.57
$T_{90}\left(E_{\mathrm{iso}}\right)$	$\log T_{90}=\left(1.03\pm 0.06\right)+\left(0.10\pm 0.05\right)\times \log E_{\mathrm{iso},52}$	0.17	0.023	0.99
$T_{90}\left(L_{\mathrm{iso}}\right)$	$\log T_{90}=\left(1.20\pm 0.04\right)+\left(-0.12\pm 0.04\right)\times \log L_{\mathrm{iso},52}$	-0.20	0.008	0.98
$L_{\mathrm{iso}}\left(E_{\mathrm{iso}}\right)$	$\log L_{\mathrm{iso},52}=\left(-0.51\pm 0.05\right)+\left(0.94\pm 0.03\right)\times \log E_{\mathrm{iso},52}$	0.90		0.75
$E_{\mathrm{iso}}\left({\Gamma }_0\right)$	$\log E_{\mathrm{iso},52}=\left(-4.10\pm 0.33\right)+\left(2.15\pm 0.13\right)\times \log {\Gamma }_0$	0.77		1.04
$T_{90}\left({\Gamma }_0\right)$	$\log T_{90}=\left(2.20\pm 0.30\right)+\left(-0.44\pm 0.12\right)\times \log {\Gamma }_0$	-0.26	0.001	0.97
$L_{\mathrm{iso}}\left({\Gamma }_0\right)$	$\log L_{\mathrm{iso},52}=\left(-5.86\pm 0.23\right)+\left(2.64\pm 0.09\right)\times \log {\Gamma }_0$	0.91		0.72
$E_p\left({\Gamma }_0\right)$	$\log E_p=\left(1.47\pm 0.24\right)+\left(0.50\pm 0.10\right)\times \log {\Gamma }_0$	0.36		0.77
$E_p^{\prime }\left(E_{\mathrm{iso}}^{\prime }\right)$	$\log E_p^{\prime }=\left(0.09\pm 0.04\right)+\left(0.25\pm 0.05\right)\times \log E_{\mathrm{iso},50}^{\prime }$	0.38		0.76
$E_p^{\prime }\left(L_{\mathrm{iso}}^{\prime }\right)$	$\log E_p^{\prime }=\left(-0.79\pm 0.09\right)+\left(0.67\pm 0.06\right)\times \log L_{\mathrm{iso},46}^{\prime }$	0.66		0.62
$T_{90}^{\prime }\left(E_{\mathrm{iso}}^{\prime }\right)$	$\log T_{90}^{\prime }=\left(3.19\pm 0.04\right)+\left(0.54\pm 0.05\right)\times \log E_{\mathrm{iso},50}^{\prime }$	0.65		0.78
$T_{90}^{\prime }\left(L_{\mathrm{iso}}^{\prime }\right)$	$\log T_{90}^{\prime }=\left(3.13\pm 0.15\right)+\left(0.28\pm 0.09\right)\times \log L_{\mathrm{iso},46}^{\prime }$	0.22	0.004	1.00
$L_{\mathrm{iso}}^{\prime }\left(E_{\mathrm{iso}}^{\prime }\right)$	$\log L_{\mathrm{iso},46}^{\prime }=\left(1.21\pm 0.03\right)+\left(0.52\pm 0.03\right)\times \log E_{\mathrm{iso},46}^{\prime }$	0.80		0.49
$E_{\mathrm{iso}}^{\prime }\left({\Gamma }_0\right)$	$\log E_{\mathrm{iso},50}^{\prime }=\left(-2.10\pm 0.33\right)+\left(1.15\pm 0.13\right)\times \log {\Gamma }_0$	0.54		1.04
$T_{90}^{\prime }\left({\Gamma }_0\right)$	$\log T_{90}^{\prime }=\left(2.20\pm 0.30\right)+\left(0.56\pm 0.12\right)\times \log {\Gamma }_0$	0.32		0.97
$L_{\mathrm{iso}}^{\prime }\left({\Gamma }_0\right)$	$\log L_{\mathrm{iso},46}^{\prime }=\left(0.01\pm 0.23\right)+\left(0.64\pm 0.09\right)\times \log {\Gamma }_0$	0.46		0.72
$E_p^{\prime }\left({\Gamma }_0\right)$	$\log E_p^{\prime }=\left(1.47\pm 0.24\right)+\left(-0.50\pm 0.10\right)\times \log {\Gamma }_0$	-0.36		0.77

Table 7. Table 7: The results of regression analysis for correlations in the rest frame and comoving frame after eliminating the redshit evolution, in which r 𝑟 r is the correlation coefficient, p 𝑝 p is the chance probability, and σ 𝜎 \sigma is the dispersion

Relations	Expressions	$r$	$p$	$\sigma$
$E_{p,c}\left(E_{\mathrm{iso},c}\right)$	$\log E_{p,c}=\left(2.18\pm 0.02\right)+\left(0.30\pm 0.03\right)\times \log E_{\mathrm{iso},c,52}$	0.62		0.56
$E_{p,c}\left(L_{\mathrm{iso},c}\right)$	$\log E_{p,c}=\left(2.48\pm 0.03\right)+\left(0.34\pm 0.04\right)\times \log L_{\mathrm{iso},c,52}$	0.58		0.58
$T_{90}\left(E_{\mathrm{iso},c}\right)$	$\log T_{90}=\left(1.08\pm 0.04\right)+\left(0.21\pm 0.05\right)\times \log E_{\mathrm{iso},c,52}$	0.31		0.95
$T_{90,c}\left(L_{\mathrm{iso},c}\right)$	$\log T_{90,c}=\left(1.13\pm 0.05\right)+\left(-0.01\pm 0.06\right)\times \log L_{\mathrm{iso},c,52}$	-0.02	0.839	1.00
$L_{\mathrm{iso},c}\left(E_{\mathrm{iso},c}\right)$	$\log L_{\mathrm{iso},c,52}=\left(-0.81\pm 0.03\right)+\left(0.68\pm 0.03\right)\times \log E_{\mathrm{iso},c,52}$	0.83		0.68
$E_{\mathrm{iso},c}\left({\Gamma }_0\right)$	$\log E_{\mathrm{iso},c,52}=\left(-3.33\pm 0.37\right)+\left(1.49\pm 0.15\right)\times \log {\Gamma }_0$	0.59		1.19
$L_{\mathrm{iso},c}\left({\Gamma }_0\right)$	$\log L_{\mathrm{iso},c,52}=\left(-4.44\pm 0.25\right)+\left(1.58\pm 0.10\right)\times \log {\Gamma }_0$	0.76		0.79
$E_{p,c}\left({\Gamma }_0\right)$	$\log E_{p,c}=\left(1.94\pm 0.22\right)+\left(0.13\pm 0.09\right)\times \log {\Gamma }_0$	0.11	0.153	0.71
$E_{p,c}^{\prime }\left(E_{\mathrm{iso},c}^{\prime }\right)$	$\log E_{p,c}^{\prime }=\left(-0.12\pm 0.03\right)+\left(0.29\pm 0.05\right)\times \log E_{\mathrm{iso},c,50}^{\prime }$	0.41		0.80
$E_{p,c}^{\prime }\left(L_{\mathrm{iso},c}^{\prime }\right)$	$\log E_{p,c}^{\prime }=\left(-0.50\pm 0.03\right)+\left(0.83\pm 0.05\right)\times \log L_{\mathrm{iso},c,46}^{\prime }$	0.78		0.55
$T_{90}^{\prime }\left(E_{\mathrm{iso},c}^{\prime }\right)$	$\log T_{90}^{\prime }=\left(3.64\pm 0.03\right)+\left(0.52\pm 0.05\right)\times \log E_{\mathrm{iso},c,50}^{\prime }$	0.62		0.80
$T_{90}^{\prime }\left(L_{\mathrm{iso},c}^{\prime }\right)$	$\log T_{90}^{\prime }=\left(3.48\pm 0.05\right)+\left(0.20\pm 0.09\right)\times \log L_{\mathrm{iso},c,46}^{\prime }$	0.16	0.0031	1.01
$L_{\mathrm{iso},c}^{\prime }\left(E_{\mathrm{iso},c}^{\prime }\right)$	$\log L_{\mathrm{iso},c,46}^{\prime }=\left(0.47\pm 0.03\right)+\left(0.40\pm 0.04\right)\times \log E_{\mathrm{iso},c,46}^{\prime }$	0.59		0.66
$E_{\mathrm{iso},c}^{\prime }\left({\Gamma }_0\right)$	$\log E_{\mathrm{iso},c,50}^{\prime }=\left(-1.33\pm 0.37\right)+\left(0.49\pm 0.15\right)\times \log {\Gamma }_0$	0.23	0.002	1.19
$L_{\mathrm{iso},c}^{\prime }\left({\Gamma }_0\right)$	$\log L_{\mathrm{iso},c,46}^{\prime }=\left(1.43\pm 0.25\right)+\left(-0.42\pm 0.10\right)\times \log {\Gamma }_0$	-0.3		0.79
$E_{p,c}^{\prime }\left({\Gamma }_0\right)$	$\log E_{p,c}^{\prime }=\left(1.94\pm 0.22\right)+\left(-0.87\pm 0.09\right)\times \log {\Gamma }_0$	-0.58		0.71

Equations

$$E_{\mathrm{iso}}=4\pi D_L^2{S}_{\gamma }k/(1+z),$$

$$k=\frac{{\int }_{1keV/(1+z)}^{{10}^{4}keV/(1+z)}EN(E)dE}{{\int }_{e_{\min }}^{e_{\max }}EN(E)dE}.$$

$$N(E)=\left\{{\begin{array}[]{*{20}{l}}{A{{\left({\frac{E}{{100keV}}}\right)}^{\alpha}}\exp\left({-\frac{E}{{{E_{0}}}}}\right)}\\ {A{{\left({\frac{E}{{100keV}}}\right)}^{\beta}}{{\left[{\frac{{\left({\alpha-\beta}\right){E_{0}}}}{{100keV}}}\right]}^{\alpha-\beta}}\exp\left({\beta-\alpha}\right)},\end{array}}\right.$$

$$L_{iso}=4\pi D_L^2{F}_{p}k,$$

$$E_{\mathrm{p}}=E_{\mathrm{p},\mathrm{obs}}(1+z),$$

$$T_{90}=T_{90,\mathrm{obs}}/(1+z).$$

$${\Gamma }_0=10^{3.33}{L}_{\mathrm{iso},52}^{0.46}{E_{\mathrm{p}}}^{-0.43}.$$

$$L_{\mathrm{iso}}^{\prime }=3/4L_{\mathrm{iso}}/{\Gamma }_0^2,$$

$$E_{\mathrm{iso}}^{\prime }=E_{\mathrm{iso}}/{\Gamma }_0,$$

$$E_{\mathrm{p}}^{\prime }=E_{\mathrm{p}}/{\Gamma }_0,$$

$$T_{90}^{\prime }=T_{90}{\Gamma }_0.$$

$$J_i=\{j|E_{\mathrm{iso},j}>E_{\mathrm{iso},i},z_j<z_{i,\lim }\},\mathrm{for}1\le i\le 93.$$

$$R_i=\mathrm{Number}\{j\in J_i|z_j\le z_i\}$$

$$\tau =\frac{{\sum }_i(R_i-E_i)}{\sqrt{{\sum }_i{V}_i}},$$

Full text

gamma-rays burst: general - methods: data analysis

1 Introduction

Gamma-ray bursts (GRBs) are the most luminous explosions in the universe (see e.g., Piran, 2004; Mészáros, 2006; Zhang, 2007). According to the traditional classification schemes, GRBs can be divided into long bursts (longer than 2.0 seconds) and short ones (shorter than 2.0 seconds), based on the well-known bimodal distribution of their durations (Kouveliotou et al., 1993). The observed spectra of GRBs are typically fitted by an empirical smoothly jointed broken power-law function, the so-called Band function (Band et al., 1993), characterized by a peak energy ($E_{\rm p,obs}$) in the $\nu F_{\nu}$ spectrum. A variety of empirical relations involved the rest frame peak energy, $E_{\rm p}=E_{\rm p,obs}(1+z)$, have been discussed. For example, Amati et al. (2002) found a tight correlation between the rest frame isotropic gamma-ray energy $E_{\rm iso}$ and $E_{\rm p}$ (so called Amati relation). A similar correlation was found between the isotropic luminosity $L_{\rm iso}$ and $E_{\rm p}$ (Wei & Gao 2003; Yonetoku et al. 2004, so called Yonetoku relation). Ghirlanda et al. (2004) found a tighter relation by replacing $E_{\rm iso}$ with the geometrically corrected energy of the GRB jets. These correlations not only give important clues to understand GRB physics (even though some correlations still lack straightforward theoretical interpretations; see e.g., Fan et al. 2012), but also provide new ways to constrain cosmological parameters (e.g., Wang et al. 2015 for a recent review).

The intrinsic properties of GRBs with measured redshifts have been extensively investigated, but the additional correction of the initial Lorentz factor ($\Gamma_{0}$) is still to be considered. $\Gamma_{0}$ is a key parameter to better understand the physics of GRBs. Several methods have been developed to estimate the value of $\Gamma_{0}$ based on different hypotheses (Lithwick & Sari, 2001; Pe’er et al., 2007; Molinari et al., 2007; Gupta & Zhang, 2008; Liang et al., 2010; Ryde et al., 2010; Zou et al., 2015). Although the number of GRBs with estimated $\Gamma_{0}$ is still limited, several interesting correlations involving $\Gamma_{0}$ have been reported in the literature. For example, Liang et al. (2010) discovered a correlation between $\Gamma_{0}$ and $E_{\rm iso}$ (see also Ghirlanda et al. 2012 ). Lü et al. (2012) and Fan et al. (2012) showed that $L_{\rm iso}$ is also correlated with $\Gamma_{0}$. Ghirlanda et al. (2012) further analyzed the spectrum-energy correlation in the comoving frame and found that these correlations still exist (see also Ghirlanda et al. 2018). Recently, Liang et al. (2015) reported a strong three-parameter correlation among $L_{\rm iso}(E_{\rm iso})$, $E_{\rm p}$ and $\Gamma_{0}$. This correlaion provides a simple way to estimate the initial Lorentz factor of GRBs, and gives us an opportunity to analyze the intrinsic properties of GRBs in the comoving frame with a reasonable large sample.

In this paper, we compile a long GRB sample with known redshift and well measured spectra observed by two satellites, Fermi (Atwood et al., 2009) and Konus-Wind (hereafter KW, Aptekar et al. 1995), and obtain the pseudo values of $\Gamma_{0}$ for 225 long GRBs using the ${L_{{\rm{iso}}}}$-${E_{\rm p}}$-${\Gamma_{0}}$ correlation found by Liang et al. (2015). We analyze the distributions of temporal and spectral characteristics of long GRBs in different frames, and study the pair correlations of all quantities. The data selection and sample are presented in section 2. The results are shown in section 3. Summary and discussion are given in section 4. The cosmological constants in this paper are $h=0.71$, $\Omega_{M}=0.27$, $\Omega_{\Lambda}=0.73$. The symbolic notation $Q_{n}=Q/10^{n}$ is adopted.

2 Sample and Data Analysis

In order to investigate the intrinsic properties of GRBs, a sample of GRBs with measured redshift $z$ and well constrained spectral parameters is needed. We concentrate our analysis on the GRBs detected by the Fermi and KW detectors. Some GRBs observed by other detectors such as BeppoSAX, HETE-2, Integral, are not considered in this paper to minimize the influence of different instruments (with different sensitivities and energy bands). The Fermi GRBs are selected from the Fermi catalog111https://heasarc.gsfc.nasa.gov/W3Browse/fermi/fermigbrst.html till the end of December 2017, in total there are 2233 events. Firstly, we choose the bursts with well measured spectral parameters and known redshifts.222http://www.mpe.mpg.de/ jcg/grbgen.html The traditional criteria of long GRBs ($T_{\rm 90}>$ 2 s) has been used and then we have 95 long GRBs. Among them, GRB 100816A and GRB 170817A with durations of 2.045 s and 2.048 s, have been classified as short bursts, which are thus excluded from our sample. Our Fermi sample thus contains 93 GRBs, as summarized in Table 1. Using the same selection criteria, we have a KW sample consisting of 131 long GRBs (see Table 2). The KW data are mainly taken from Tsvetkova et al. (2017) and the GCN reports (GCN Circular Archive). In addition, we note that there are 46 overlapped GRBs in the two samples.

Below we estimate the rest frame parameters. In this paper, both $E_{\rm iso}$ and $L_{\rm iso}$ are corrected to the energy band of $1-10^{4}$ keV in the rest frame. The isotropic energy $E_{\rm iso}$ is estimated as

[TABLE]

where $S_{\rm\gamma}$ is the time integral fluence, in units of erg cm*-2*, $D_{\rm L}$ is the luminosity distance, and $k$ is the $k$-correction factor defined as

[TABLE]

Here $e_{\rm min}$ and $e_{\rm max}$ are the observational energy band of fluence, $N(E)$ denotes the photon spectrum of GRBs. All the GRB spectra are assumed to be a Band function (Band et al. 1993), defined as

[TABLE]

where $\alpha$ is the low energy photon index, and $\beta$ is the high energy photon index. $E_{\rm 0}$ is the break energy, $E_{\rm 0}=E_{\rm p}/(2+\alpha)$. The isotropic luminosity $L_{\rm iso}$ is estimated as

[TABLE]

here $F_{\rm p}$ is the peak flux, in units of erg cm*-2* s*-1*. The rest frame peak energy $E_{\rm p}$ and duration $T_{\rm 90}$ are estimated as

[TABLE]

and

[TABLE]

All the errors of these quantities are calculated by the error propagation formula. The initial Lorentz factor $\Gamma_{0}$ can be derived from $L_{\rm iso}$ and $E_{\rm p}$ (Liang et al., 2015) as

[TABLE]

Using the pseudo values of $\Gamma_{0}$, we can further estimate the comoving frame isotropic energy $E^{\prime}_{\rm iso}$, isotropic luminosity $L^{\prime}_{\rm iso}$, spectrum peak energy $E^{\prime}_{\rm p}$ and duration $T^{\prime}_{\rm 90}$ (Ghirlanda et al., 2012), which are defied as

[TABLE]

[TABLE]

[TABLE]

and

[TABLE]

The derived temporal and spectral results of Fermi sample and KW sample in the rest frame and comoving frame are listed in Table 3 and Table 4, respectively.

3 Results

3.1 Observer Frame

We analyze the distributions of the observed duration ($T_{\rm 90,obs}$), spectrum peak energy ($E_{\rm p,obs}$), fluence ($S_{\rm\gamma}$), peak flux ($F_{\rm p}$) and redshift ($z$) (see Figure 1). The Fermi sample and KW sample are shown as red and green step lines, respectively. It is clear that all the parameters follow the logarithm normal distributions.333To confirm this result, we make the normal statistic test by using the software Mathematica tool called ”DistributionFitTest”, and report the p-value in Table 5. The lognormal distribution can be accepted. We find that the values of $E_{\rm p,obs}$, $S_{\rm\gamma}$ and $F_{\rm p}$ of Fermi GRBs are systematically smaller than those of KW GRBs. On the contrary, the observed durations of Fermi GRBs are longer. To give a quantitative result, we make a Gaussian fitting and list the results in Table 5. For Fermi (KW) sample, the median values of $T_{\rm 90,obs}$, $E_{\rm p,obs}$, $S_{\rm\gamma}$ and $F_{\rm p}$ are $\sim$41 (30) s, $\sim$162 (231) keV, $\sim 1.6~{}(4.2)\times 10^{-5}$ erg cm*-2* and $\sim 1.6~{}(4.8)\times 10^{-6}$ erg cm*-2* s*-1*, respectively. In addition, the dispersions of $E_{\rm p,obs}$, $S_{\rm\gamma}$ and $F_{\rm p}$ distributions for Fermi GRBs are larger than those of KW GRBs. This indicates that the ranges of the parameter distributions of Fermi GRBs are wider than those of KW sample. We also present the distribution of $z$ (see the last panel in Figure 1). It shows that the distribution ranges of redshift in two samples are basically consistent. The median value of $z$ is $\sim$1.3. To check if the samples have selection effect, the distribution of $z$ for all 412 long GRBs with measured redshift is analyzed and showed in the last panel of Figure 1. The typical value of $z$ for all long GRBs is $\sim$1.48. From the figure, one can find that the $z$ distributions of our samples are basically consistent with all long GRBs.

The difference of observed properties for two samples may be due to the different energy band of instruments. The detected energy band of Fermi/GBM (8-1000 keV) is lower than KW (10-10000 keV), so that, on average, the values of $E_{\rm p}$, $S_{\rm\gamma}$ and $F_{\rm p}$ are smaller for Fermi GRBs. It is known that the durations of GRBs strongly depend on the energy band, with an index of -0.4 (Fenimore et al., 1995; Norris et al., 1996; Zhang et al., 2007; Bissaldi, 2011; Qin et al., 2013), and the instrument selection biases (e.g., Bromberg et al. 2013; Kocevski & Petrosian 2013). The energy band to calculate the duration of Fermi/GBM (8-1000 keV) is lower than that of KW (80-1200 keV). Therefore, the durations of Fermi GRBs should be longer. To further confirm this result, we make the distribution analysis of 46 GRBs observed simultaneously by two detectors (see in Figure 2). From the Figure 2 one can find that the most GRB durations derived from Fermi detector are obviously longer than those calculated from KW. In addition, $S_{\rm\gamma}$ and $F_{\rm p}$ derived from Fermi detector are smaller.

3.2 Rest Frame

The statistical properties and correlations of GRBs in the rest frame have been widely studied. We firstly present the distributions of $E_{\rm iso}$, $L_{\rm iso}$, $E_{\rm p}$ and $T_{\rm 90}$ in Figure 3. It shows that these four quantities are basically logarithmic normal distributions and are similar with those in the observer frame. This indicates that the observed distribution profiles are not significantly affected by the redshift distribution. In the same way, we make a lognormal test and a Gaussian fit and show the results in Table 5. From the results, we have $E_{\rm iso}\sim 0.99~{}(1.75)\times 10^{53}$ erg, $\sigma\sim$0.86 (0.77), $L_{\rm iso}\sim$ 2.4 (4.9)$\times 10^{52}$ erg s*-1*, $\sigma\sim$0.87 (0.80), $E_{\rm p}\sim$406 (562) keV, $\sigma\sim$0.46 (0.36), and $T_{\rm 90}\sim$16.3 (12.3) s, $\sigma\sim$ 0.51 (0.51) for Fermi (KW) sample, respectively.

The spectrum-energy correlation of GRBs is a very important relation in GRB research field and has been discussed extensively. The $E_{\rm p}$-$E_{\rm iso}$ and $E_{\rm p}$-$L_{\rm iso}$ relations are analyzed and shown in the top panel of Figure 4. From this figure, one can find the two samples almost have the same properties, so we combine two samples together to make a quantitative analysis and obtain $E_{\rm p}\propto{E_{\rm iso}}^{0.36\pm 0.03}$, with the correlation coefficient $r=0.71$, the chance probability $p<10^{-4}$ and the dispersion $\sigma=0.58$, and $E_{\rm p}\propto{L_{\rm iso}}^{0.34\pm 0.03}$ ($r=0.71$, $p<10^{-4}$ and $\sigma=0.57$), where the data of 46 overlapped bursts are taken from Fermi. Our results are consistent with the previous finding presented in the literature (e.g., Amati et al. 2008; Ghirlanda et al. 2009; Zhang et al. 2009; Zhang et al. 2012).

In addition, we analyze the relations of other quantities and also present the results in Figure 4. We find that $E_{\rm p}$ is not correlated with $T_{\rm 90}$, which indicate that the spectral hardness is independent of the duration for long GRBs. There exists a weak correlation between $E_{\rm iso}$ and $T_{\rm 90}$ with $r=0.17$, but $L_{\rm iso}$ and $T_{\rm 90}$ are anti-correlated, with $r=-0.20$. There is a tight correlation between $E_{\rm iso}$ and $L_{\rm iso}$ with $r=0.9$, but GRB 130925A deviates this relation.

3.3 Properties of $\Gamma_{0}$

The pseudo Lorentz factors have been estimated from the three-parameter correlation ${L_{{\rm{iso}}}}$-${E_{\rm p}}$-${\Gamma_{0}}$ (Liang et al. 2015), so we can study the distribution of $\Gamma_{0}$ and the relations between $\Gamma_{0}$ and other quantities. Figure 5 shows the distribution of $\Gamma_{0}$ for Fermi and KW sample. There is a typical value of $\Gamma_{0}$ as $\sim 240~{}(300)$ for Fermi (KW) sample, and a small dispersion $\sigma\sim 0.3~{}(0.28)$ shown in Table 1. Ghirlanda et al. (2012) discussed the distribution of $\Gamma_{0}$ in homogeneous ISM (H) and wind density profile (W) case and obtained $\Gamma_{0}$ (H, W) $\sim 138~{}(66)$, $\sigma\sim 0.17~{}(0.2)$. The reconstructed distribution of $\Gamma_{0}$ by Ghirlanda et al. (2018) has the median value $\sim 300~{}(150)$. Our results are consistent with the previous findings and the theoretical predictions (see Piran 2004).

The values of $\Gamma_{0}$ are derived from $L_{\rm iso}$ and $E_{\rm p}$, so these three quantities should be correlated (see in Table 6). The relations between $\Gamma_{0}$ and $E_{\rm iso}$ ($T_{\rm 90}$) are analyzed and shown in Figure 6. From this figure we find that there is a tight correlation between $\Gamma_{0}$ and $E_{\rm iso}$, with a correlation coefficient $r=0.77$. We parametrize the correlation and obtain $\log E_{iso,52}=(-4.10\pm 0.33)+(2.15\pm 0.13)\times\log\Gamma_{0}$, which is consistent with the result of Liang et al. (2015). We also find there is a trend that the intrinsic duration is anticorrelated with the $\Gamma_{0}$. The parameterized result is $\log T_{90}=(2.20\pm 0.30)+(-0.44\pm 0.12)\times\log\Gamma_{0}$, where the correlation coefficient is $r=-0.26$.

3.4 Comoving Frame

The properties of GRBs in the rest frame can not fully reflect the real physical processes, so the intrinsic properties in the comoving frame need to be investigated. Using the pseudo Lorentz factor, we obtain the parameters in the comoving frame and analyze their properties. We show the distributions of the isotropic energy $E^{\prime}_{\rm iso}$, isotropic luminosity $L^{\prime}_{\rm iso}$, spectrum peak energy $E^{\prime}_{\rm p}$ and duration $T^{\prime}_{\rm 90}$ in the comoving frame (see in Figure 7). As shown in Figure 7, these four quantities basically follow the lognormal distributions. Fitting these distributions we have the median value of $E^{\prime}_{\rm iso}\sim 4~{}(6)\times 10^{50}$ erg , with a dispersion of $\sigma\sim 0.67~{}(0.58)$ and the median value of $L^{\prime}_{\rm iso}\sim 3~{}(4)\times 10^{47}$ erg s*-1* , with a dispersion of $\sigma\sim 0.45~{}(0.35)$ for Fermi (KW) sample. The typical values of the comoving frame isotropic energy and isotropic luminosity are consistent with the results of Ghirlanda et al. (2018). We also find that the dispersions in the comoving frame are smaller than those in the rest frame. This indicates that the intrinsic energy and luminosity tend to be concentrated. In addition, we obtain the typical values of $E^{\prime}_{\rm p}$ and $T^{\prime}_{\rm 90}$ are $\sim 2$ keV and $\sim 4000$ s, respectively. The dispersions of these two quantities are large and similar to which in the rest frame, even a little bigger than those in the observer frame. This shows that the intrinsic peak energies and durations are not the same for the different long GRBs.

It is well known that long GRBs basically comply with $E_{\rm p}$-$E_{\rm iso}$ and $E_{\rm p}$-$L_{\rm iso}$ correlations. Ghirlanda et al. (2012) found that these two correlations still exist in the comoving frame (see also Liang et al. 2015). The pair relations of $E^{\prime}_{\rm iso}$, $L^{\prime}_{\rm iso}$, $E^{\prime}_{\rm p}$ and $T^{\prime}_{\rm 90}$ are studied and shown in Figure 8. The results of the regression analysis are listed in Table 6. We have $E^{\prime}_{\rm p}=(-0.79\pm 0.09){L^{\prime}_{\rm iso,46}}^{0.67\pm 0.06}$ with a correlation coefficient of $r=0.66$ and a dispersion of $\sigma=0.62$, and $E^{\prime}_{\rm p}=(0.09\pm 0.04){E^{\prime}_{\rm iso,50}}^{0.25\pm 0.05}$ with $r=0.38$ and $\sigma=0.76$. This results further confirm that the spectrum-energy relations do exist in the comoving frame, but have very large dispersions, suggesting that the observed strong spectrum-energy correlations in the rest frame are likely governed by the Doppler boosting effect. From Figure 8, we also find that the comoving peak energy $E^{\prime}_{\rm p}$ is independent of the duration $T^{\prime}_{\rm 90}$. This is consistent with the result in the rest frame. It further confirms that the hardness and duration of long GRBs are independent quantities and describe the different physical processes. In addition, we also find there exists a tight relation between the isotropic energy $E^{\prime}_{\rm iso}$ and the duration $T^{\prime}_{\rm 90}$, $T^{\prime}_{\rm 90}=(3.19\pm 0.04){E^{\prime}_{\rm iso,50}}^{0.54\pm 0.05}$ with $r=0.65$ and $\sigma$ = 0.78. This shows the isotropic energy is strongly related to duration in the comoving frame. For the isotropic luminosity $L^{\prime}_{\rm iso}$ and duration $T^{\prime}_{\rm 90}$, there is a weak correlation as $T^{\prime}_{\rm 90}=(3.13\pm 0.15){L^{\prime}_{\rm iso,46}}^{0.28\pm 0.09}$ with $r=0.22$ and $\sigma=1.00$.

We also analyze the relations between $\Gamma_{0}$ and all the comoving frame quantities and report the results in Figure 9 and Table 6. It is found that $E^{\prime}_{\rm iso}$, $L^{\prime}_{\rm iso}$ and $T^{\prime}_{\rm 90}$ are weakly correlated with $\Gamma_{0}$, but $E^{\prime}_{\rm p}$ is anticorrelated with $\Gamma_{0}$. This indicate that the harder the spectra of long GRBs, the slower the bulk motion of fireball.

3.5 The redshift dependence

It is known that the distributions of the isotropic energy, luminosity and peak energy, and their statistical correlations in the rest frame are affected by the severe truncation mainly due to the detection flux and energy limit of the telescope. Figure 10. shows the relations between $T_{\rm 90}$, $E_{\rm p}$, $E_{\rm iso}$ and $L_{\rm iso}$ and $z$. From this figure we can find that $T_{\rm 90}$ does not significantly depend on $z$ 444The previous studies found that the intrinsic duration of GRBs is independent with redshift (see, Sakamoto et al. 2011; Gruber et al. 2011; Zhang et al. 2013) or has a smaller redshift evolution (Pélangeon et al. 2008; Dainotti et al. 2015)., but $E_{\rm iso}$, $L_{\rm iso}$ and $E_{\rm p}$ all depend on $z$, which are consistent with the previous results reported by many authors (e.g., Lloyd-Ronning et al. 2002; Wei & Gao 2003; Yonetoku et al. 2004; Wu et al. 2012; Salvaterra et al. 2012; Zhang et al. 2014). To obtain the intrinsic distributions and correlations, the first step is to remove the effect of redshift evolution. A nonparametric $\tau$ statistical technique was widely used to resolve this problem (e.g., Lloyd-Ronning et al. 2002; Yonetoku et al. 2004; Wu et al. 2012; Dainotti et al. 2013, 2015, 2017, Zhang et al. 2014; Petrosian et al. 2015; Tsvetkova et al. 2017). We firstly consider $E_{\rm iso}$ observed by Fermi as an example.

Consider a set of observable $E_{{\rm iso},i}$ and $z_{i}$, where $i$ indexes the $i$th burst and in our case $i$ runs from 1 to 93. For the $i$th sample of ($z_{i},E_{{\rm iso},i}$), we consider an associated set of

[TABLE]

in which the number of samples in the $J_{i}$ set is $N_{i}$. The $z_{i,\rm lim}$ is the redshift of the crossing point between two lines of $E=E_{{\rm iso},i}$ and the fluence limit corresponding to its “isotropic-equivalent-energy” limit. If $z_{i}$ and $E_{{\rm iso},i}$ are independent to each other, one would expect the number of the following sample

[TABLE]

to be uniformly distributed between 1 and $N_{i}$. To estimate the correlation degree between $E_{\rm iso}$ and $z$, one may introduce the test statistic $\tau$ parameterized as

[TABLE]

where $E_{i}=(N_{i}+1)/2$ and $V_{i}=(N_{i}^{2}-1)/12$ are the expected mean and the variance of the uniform distribution, respectively.

If $R_{i}$ follows an ideal uniform distribution, then the samples of $R_{i}\leq E_{i}$ and $R_{i}\geq E_{i}$ should be equal, and thus the statistic parameter $\tau$ tends to be zero. Note that the $\tau$ value here has been normalized by the square root of variance, so the correlation degree $z$ and $E_{\rm iso}$ can be measured in units of standard deviation.

We take the simple form of $g(z)=(1+z)^{q}$ in order to separate the isotropic energy evolution. The value $E_{\rm iso,c}\equiv E_{\rm iso}/g(z)$ represents the isotropic energy after removing the evolution effect. When $\tau$ is not equal to zero, we change the $q$ values until $\tau=0$ with a proper $q$. Finally, we find that the null hypothesis of the evolution is rejected at about 4.1 $\sigma$ confidence level and there is a significant evolution for the isotropic energy, $q_{\rm E}=2.44^{+0.59}_{-0.47}$. The de-evolved isotropic energy $E_{\rm iso,c}$ for Fermi sample can be obtained from $E_{\rm iso,c}=E_{\rm iso}/(1+z)^{2.44}$.

Using the same $\tau$ statistical method, we obtain $q_{\rm L}=2.65^{+0.56}_{-0.69}$ (2.9$\sigma$, for $L_{\rm iso}$), and $q_{\rm Ep}=1.05^{+0.34}_{-0.29}$ (3.6$\sigma$, for $E_{\rm{p}}$ ) for Fermi data, and $q_{\rm E}=1.73^{+1.2}_{-0.77}$ (2.6$\sigma$), $q_{\rm L}=3.24^{+0.29}_{-0.67}$ (4.6$\sigma$), and $q_{\rm Ep}=1.07^{+0.26}_{-0.18}$ (4.1$\sigma$) for KW data. As shown in Figure 10, we choose $5\times 10^{-7}{\rm erg}\,{\rm cm}^{-2}$ as the fluence limit, $2\times 10^{-7}{\rm erg}\,{\rm cm}^{-2}\,{\rm s}^{-1}$ as the flux limit and 30 keV as the lower limit of the observed peak energy for Fermi data, and $4\times 10^{-6}{\rm erg}\,{\rm cm}^{-2}$ as the fluence limit, $6\times 10^{-7}{\rm erg}\,{\rm cm}^{-2}\,{\rm s}^{-1}$ as the flux limit and 60 keV as the lower limit of the observed peak energy for KW data.555The result is not significantly affected by the chosen value of flux/fluence and peak energy limit as long as it is around the instrumental sensitivity (see Wu et al. 2012, Zhang et al. 2014) Meanwhile, we can obtain the de-evolved luminosity and peak energy from $L_{\rm iso,c}=L_{\rm iso}/(1+z)^{q_{\rm L}}$ and $E_{\rm p,c}=E_{\rm p}/(1+z)^{q_{\rm Ep}}$.

After eliminating the redshift evolution effect, the intrinsic distributions and correlations are analyzed and shown in Figures 11-14. The statistical analysis results are listed in Table 5 and Table 7. From these results, we find that the main conclusions are not significantly changed when the instrument biases are taken into account. But the pair correlations become slightly weaker in the rest frame and tighter in the comving frame. We also find that the isotropic energy, luminosity and peak energy both in the rest frame and comving frame are more concentrated. The median values are $E_{\rm iso,c}\sim 1~{}(4)\times 10^{52}$ erg, with a dispersion of $\sigma\sim 0.75~{}(0.65)$, $L_{\rm iso,c}\sim 2~{}(3)\times 10^{51}$ erg s*-1*, $\sigma\sim 0.66~{}(0.65)$ and $E_{\rm p,c}\sim 160~{}(220)$ keV, $\sigma\sim 0.41~{}(0.30)$ for Fermi (KW) sample in the rest frame. In the comoving frame, we have $E^{\prime}_{\rm iso,c}\sim 4~{}(13)\times 10^{49}$ erg, $\sigma\sim 0.64~{}(0.52)$, $L^{\prime}_{\rm iso,c}\sim 2.7~{}(2.4)\times 10^{46}$ erg s*-1*, $\sigma\sim 0.44~{}(0.4)$ and $E^{\prime}_{\rm p,c}\sim 0.6~{}(0.7)$ keV, $\sigma\sim 0.49~{}(0.4)$ for Fermi (KW) sample.

4 Summary and Discussion

We compile a long GRB sample with the measured redshifts and well determined spectra observed by Fermi and Konus-Wind instruments. Using a tight ${L_{{\rm{iso}}}}$-${E_{\rm p}}$-${\Gamma_{0}}$ three-parameter correlation, we estimate the GRB initial Lorentz factors in our samples. The properties and correlations in the observer frame, rest frame and comoving frame are studied. We find that the distributions of the isotropic energy, luminosity, peak energy and duration in the different frame are basically lognormal and the comoving frame quantities are more concentrated. When the redshift evolution effect has been taken into account, we obtain the median values are $E^{\prime}_{\rm iso,c}\sim 8\times 10^{49}$ erg, $L^{\prime}_{\rm iso,c}\sim 2.5\times 10^{46}$ erg s*-1*, $E^{\prime}_{\rm p,c}\sim 0.7$ KeV. The central value of ${\Gamma_{0}}$ is $\sim 270$, which is consistent with the previous finding and the theoretical prediction. We further confirm the Amati relation, Yonetoku relation, and ${L_{{\rm{iso}}}}$ ($E_{\rm{iso}}$)-${\Gamma_{0}}$ relation, and find that the corresponding relations in the comoving frame still exist with large dispersions. This indicates these correlations are not a good standard candle and we need caution to make cosmological studies (e.g., Dainotti et al. 2013; Dainotti & Amati 2018). In addition, the peak energies of long GRBs are independent of durations both in the rest frame and in the comoving frame. And there is a weak anticorrelation between the peak energy and Lorentz factor.

It is known that short GRBs are also comply with the similar ${E_{{\rm{iso}}}}$-${E_{\rm p}}$ and ${L_{{\rm{iso}}}}$-${E_{\rm p}}$ correlations (e.g., Zhang et al. 2012), but both correlations for short GRBs are dimmer than those of Long GRBs (e.g., Tsutsui et al. 2013). We wonder if the spectrum-energy correlation in the comoving frame also exist for short GRBs. However the Lorentz factors of short GRBs are not derived now, we cannot analyze the intrinsic properties of short GRBs in the comoving frame and this question need to be investigated in the future.

Acknowledgments

We thank the anonymous referee for constructive comments. We also thank Dr. Yi-Zhong Fan for stimulating suggestions/discussions. We acknowledgment the use of public data from Fermi and Konus-Wind. This work was supported in part by NSFC under grants 11763003, and by the Guangxi Natural Science Foundation (No. 2017GXNSFAA198094).