Equation of State Tables

The following tables contain the equation of state from PIMC simulations of hydrogen and deuterium using different time steps and nodal surfaces. It should be noted that all simulations have been performed using order $n_{\rm A}=1$ in the action expansion for the off-diagonal pair density matrix (Eq. 2.38) and order $n_{\rm E}=2$ in the energy expansion. As discussed in section  , there are corrections to pressure and energy due to higher orders. They are particularly substantial for the pressure at low temperatures. In the following table, we list the raw simulation data without the corrections.

Table D.1: Equation of state table with pressure and internal energy per atom for hydrogen at the density of $0.000983\,\rm gcm^{-3}$ ($r_s=14$) calculated with PIMC simulations of $N_P=32$ pairs of protons and electrons, using free particle nodes, a time step of $\tau^{-1}=10^6\rm K$, $n_{\rm A}=1$ orders in the action expansion formula 2.38 and $n_{\rm E}=2$ orders in the energy expansion.

$T \:(\rm{K})$	$p \:(\rm{GPa})$	$E \:(\rm{eV})$
166$\,$667	2.641 $\pm$ 0.001	41.091 $\pm$ 0.018
125$\,$000	1.956 $\pm$ 0.001	29.979 $\pm$ 0.026
62$\,$500	0.902 $\pm$ 0.002	11.827 $\pm$ 0.042
31$\,$250	0.343 $\pm$ 0.001	-2.880 $\pm$ 0.046
15$\,$625	0.143 $\pm$ 0.001	-11.298 $\pm$ 0.064
12$\,$500	0.117 $\pm$ 0.001	-11.903 $\pm$ 0.032
10$\,$000	0.094 $\pm$ 0.001	-12.429 $\pm$ 0.027
8929	0.085 $\pm$ 0.001	-12.652 $\pm$ 0.032
7812	0.076 $\pm$ 0.002	-12.971 $\pm$ 0.084
6944	0.063 $\pm$ 0.001	-13.476 $\pm$ 0.053
6250	0.059 $\pm$ 0.001	-14.189 $\pm$ 0.037
5000	0.053 $\pm$ 0.001	-14.708 $\pm$ 0.026

Table D.2: EOS table for hydrogen at the density of $0.00270\,\rm gcm^{-3}$ ($r_s$=10) calculated with PIMC simulations using FP nodes, $N_P=32$, $\tau^{-1}=10^6\rm K$, $n_{\rm A}=1$ and $n_{\rm E}=2$ (see Tab. D.1)

$T \:(\rm{K})$	$p \:(\rm{GPa})$	$E \:(\rm{eV})$
166$\,$667	7.166 $\pm$ 0.004	39.979 $\pm$ 0.024
125$\,$000	5.264 $\pm$ 0.004	28.594 $\pm$ 0.027
62$\,$500	2.342 $\pm$ 0.005	9.466 $\pm$ 0.053
31$\,$250	0.879 $\pm$ 0.006	-4.885 $\pm$ 0.068
15$\,$625	0.397 $\pm$ 0.006	-11.382 $\pm$ 0.043
12$\,$500	0.323 $\pm$ 0.005	-11.945 $\pm$ 0.046
10$\,$000	0.270 $\pm$ 0.003	-12.491 $\pm$ 0.039
8929	0.234 $\pm$ 0.004	-12.903 $\pm$ 0.033
7812	0.203 $\pm$ 0.004	-13.543 $\pm$ 0.028
6944	0.191 $\pm$ 0.004	-13.715 $\pm$ 0.035
6250	0.168 $\pm$ 0.004	-14.282 $\pm$ 0.073
5000	0.151 $\pm$ 0.004	-14.759 $\pm$ 0.018

Table D.3: EOS table for hydrogen at the density of $0.0105\,\rm gcm^{-3}$ ($r_s=8$) calculated with PIMC simulations using FP nodes, $N_P=32$, $\tau=10^6\rm K$, $n_{\rm A}=1$ and $n_{\rm E}=2$ (see Tab. D.1)

$T \:(\rm{K})$	$p \:(\rm{GPa})$	$E \:(\rm{eV})$
166$\,$667	13.770 $\pm$ 0.010	38.683 $\pm$ 0.036
125$\,$000	10.060 $\pm$ 0.010	27.120 $\pm$ 0.037
625$\,$00	4.337 $\pm$ 0.006	7.412 $\pm$ 0.034
31$\,$250	1.639 $\pm$ 0.009	-5.848 $\pm$ 0.041
15$\,$625	0.723 $\pm$ 0.012	-11.593 $\pm$ 0.037
12$\,$500	0.630 $\pm$ 0.008	-12.062 $\pm$ 0.037
10$\,$000	0.480 $\pm$ 0.006	-12.865 $\pm$ 0.028
8929	0.432 $\pm$ 0.005	-13.223 $\pm$ 0.025
7812	0.371 $\pm$ 0.007	-13.881 $\pm$ 0.044
6944	0.344 $\pm$ 0.006	-14.081 $\pm$ 0.050
6250	0.308 $\pm$ 0.004	-14.559 $\pm$ 0.019
5000	0.297 $\pm$ 0.006	-14.797 $\pm$ 0.019

Table D.4: EOS table for hydrogen at the density of $0.0125\,\rm gcm^{-3}$ ($r_s=6$) calculated with PIMC simulations using FP nodes, $N_P=32$, $\tau=10^6\rm K$, $n_{\rm A}=1$ and $n_{\rm E}=2$ (see Tab. D.1)

$T \:(\rm{K})$	$p \:(\rm{GPa})$	$E \:(\rm{eV})$
166$\,$667	31.912 $\pm$ 0.021	36.602 $\pm$ 0.028
125$\,$000	23.036 $\pm$ 0.018	24.734 $\pm$ 0.032
62$\,$500	9.586 $\pm$ 0.020	4.727 $\pm$ 0.034
31$\,$250	3.716 $\pm$ 0.012	-6.923 $\pm$ 0.027
15$\,$625	1.672 $\pm$ 0.026	-11.783 $\pm$ 0.048
12$\,$500	1.380 $\pm$ 0.025	-12.461 $\pm$ 0.059
10$\,$000	1.096 $\pm$ 0.012	-13.171 $\pm$ 0.037
8929	0.992 $\pm$ 0.011	-13.472 $\pm$ 0.038
7812	0.884 $\pm$ 0.011	-13.843 $\pm$ 0.030
6944	0.808 $\pm$ 0.014	-14.269 $\pm$ 0.029
6250	0.769 $\pm$ 0.013	-14.368 $\pm$ 0.022
5000	0.676 $\pm$ 0.016	-14.938 $\pm$ 0.019

Table D.5: EOS table for hydrogen at the density of $0.0421\,\rm gcm^{-3}$ ($r_s=4$) calculated with PIMC simulations using FP nodes, $N_P=32$, $\tau=10^6\rm K$, $n_{\rm A}=1$ and $n_{\rm E}=2$ (see Tab. D.1)

$T \:(\rm{K})$	$p \:(\rm{GPa})$	$E \:(\rm{eV})$
166$\,$667	102.747 $\pm$ 0.131	32.261 $\pm$ 0.050
125$\,$000	73.082 $\pm$ 0.111	20.229 $\pm$ 0.046
62$\,$500	29.462 $\pm$ 0.131	1.051 $\pm$ 0.050
31$\,$250	11.863 $\pm$ 0.066	-8.144 $\pm$ 0.017
25$\,$000	9.075 $\pm$ 0.131	-9.809 $\pm$ 0.051
20$\,$000	7.320 $\pm$ 0.141	-10.985 $\pm$ 0.053
15$\,$625	5.530 $\pm$ 0.111	-12.057 $\pm$ 0.053
12$\,$500	4.325 $\pm$ 0.162	-12.982 $\pm$ 0.059
10$\,$000	3.700 $\pm$ 0.049	-13.543 $\pm$ 0.034
8929	3.353 $\pm$ 0.069	-13.909 $\pm$ 0.035
7812	3.065 $\pm$ 0.086	-14.222 $\pm$ 0.033
6944	2.893 $\pm$ 0.064	-14.382 $\pm$ 0.036
6250	2.622 $\pm$ 0.075	-14.605 $\pm$ 0.035
5000	2.307 $\pm$ 0.100	-14.943 $\pm$ 0.028

Table D.6: EOS table for hydrogen at the density of $0.0999\,\rm gcm^{-3}$ ($r_s=3$) calculated with PIMC simulations using FP nodes, $N_P=32$, $\tau=10^6\rm K$, $n_{\rm A}=1$ and $n_{\rm E}=2$ (see Tab. D.1). The last column shows the fraction of permuting electrons given by $1-P_1$ (see section 2.6.8)

$T \:(\rm{K})$	$p \:(\rm{GPa})$	$E \:(\rm{eV})$	$1-P_1$
166$\,$667	234.381 $\pm$ 0.242	28.422 $\pm$ 0.042	0.00031 $\pm$ 0.00003
125$\,$000	164.852 $\pm$ 0.212	16.489 $\pm$ 0.027	0.00065 $\pm$ 0.00004
62$\,$500	67.526 $\pm$ 0.303	-1.166 $\pm$ 0.044	0.006 $\pm$ 0.001
31$\,$250	27.763 $\pm$ 0.192	-8.961 $\pm$ 0.030	0.033 $\pm$ 0.006
25$\,$000	21.410 $\pm$ 0.242	-10.282 $\pm$ 0.037	0.039 $\pm$ 0.002
20$\,$000	17.428 $\pm$ 0.293	-11.297 $\pm$ 0.049	0.046 $\pm$ 0.004
15$\,$625	13.602 $\pm$ 0.343	-12.260 $\pm$ 0.050	0.047 $\pm$ 0.005
12$\,$500	11.462 $\pm$ 0.454	-13.087 $\pm$ 0.079	0.036 $\pm$ 0.004
10$\,$000	10.600 $\pm$ 0.172	-13.593 $\pm$ 0.028	0.036 $\pm$ 0.003
8929	10.257 $\pm$ 0.151	-13.866 $\pm$ 0.027	0.022 $\pm$ 0.001
7812	9.433 $\pm$ 0.131	-14.220 $\pm$ 0.032	0.024 $\pm$ 0.002
6944	9.055 $\pm$ 0.141	-14.438 $\pm$ 0.028	0.016 $\pm$ 0.001
6250	8.498 $\pm$ 0.212	-14.593 $\pm$ 0.040	0.025 $\pm$ 0.005
5000	7.996 $\pm$ 0.212	-14.835 $\pm$ 0.018	0.017 $\pm$ 0.002

Table D.7: EOS table for deuterium at the density of $0.307\,\rm gcm^{-3}$ ($r_s$=2.6) calculated with PIMC simulations using FP nodes, $N_P=32$, $\tau=10^6\rm K$, $n_{\rm A}=1$ and $n_{\rm E}=2$ (see Tab. D.6)

$T \:(\rm{K})$	$p \:(\rm{GPa})$	$E \:(\rm{eV})$	$1-P_1$
125$\,$000	248.561 $\pm$ 0.161	14.675 $\pm$ 0.020	0.003 $\pm$ 0.001
62$\,$500	103.121 $\pm$ 0.344	-2.143 $\pm$ 0.038	0.017 $\pm$ 0.001
50$\,$000	77.568 $\pm$ 0.217	-5.167 $\pm$ 0.025	0.030 $\pm$ 0.001
31$\,$250	44.905 $\pm$ 0.235	-9.160 $\pm$ 0.022	0.076 $\pm$ 0.002
25$\,$000	35.512 $\pm$ 0.366	-10.384 $\pm$ 0.029	0.105 $\pm$ 0.003
20$\,$000	29.997 $\pm$ 0.228	-11.228 $\pm$ 0.024	0.129 $\pm$ 0.003
15$\,$625	24.503 $\pm$ 0.325	-12.211 $\pm$ 0.023	0.136 $\pm$ 0.006
12$\,$500	21.402 $\pm$ 0.399	-12.823 $\pm$ 0.030	0.134 $\pm$ 0.008
10$\,$000	20.200 $\pm$ 0.309	-13.547 $\pm$ 0.024	0.092 $\pm$ 0.005
8929	19.038 $\pm$ 0.402	-13.822 $\pm$ 0.051	0.073 $\pm$ 0.007
7812	18.311 $\pm$ 0.455	-14.167 $\pm$ 0.045	0.063 $\pm$ 0.002
6944	17.574 $\pm$ 0.540	-14.374 $\pm$ 0.055	0.065 $\pm$ 0.004
6250	17.029 $\pm$ 0.413	-14.529 $\pm$ 0.042	0.060 $\pm$ 0.004
5000	15.817 $\pm$ 0.445	-14.736 $\pm$ 0.043	0.057 $\pm$ 0.003

Table D.8: EOS table for deuterium at the density of $0.390\,\rm gcm^{-3}$ ($r_s$=2.4) calculated with PIMC simulations using VDM nodes, $N_P=32$, $\tau_B^{-1}=2\cdot10^6\rm K$, $\tau_F^{-1}=8\cdot10^6\rm K$, $n_{\rm A}=1$ and $n_{\rm E}=2$ (see Tab. D.6)

$T \:(\rm{K})$	$p \:(\rm{GPa})$	$E \:(\rm{eV})$	$1-P_1$
125$\,$000	308 $\pm$ 5	13.2 $\pm$ 0.4	0.002 $\pm$ 0.000
62$\,$500	134 $\pm$ 1	-2.5 $\pm$ 0.1	0.020 $\pm$ 0.002
31$\,$250	60 $\pm$ 3	-9.4 $\pm$ 0.2	0.102 $\pm$ 0.004
15$\,$625	34 $\pm$ 4	-12.1 $\pm$ 0.3	0.204 $\pm$ 0.008
10$\,$000	17 $\pm$ 5	-14.0 $\pm$ 0.4	0.225 $\pm$ 0.014

Table D.9: EOS table for deuterium at the density of $0.506\,\rm gcm^{-3}$ ($r_s$=2.2) calculated with PIMC simulations using VDM nodes, $N_P=32$, $\tau_B^{-1}=2\cdot10^6\rm K$, $\tau_F^{-1}=8\cdot10^6\rm K$, $n_{\rm A}=1$ and $n_{\rm E}=2$ (see Tab. D.6)

$T \:(\rm{K})$	$p \:(\rm{GPa})$	$E \:(\rm{eV})$	$1-P_1$
125$\,$000	411 $\pm$ 2	13.3 $\pm$ 0.1	0.004 $\pm$ 0.000
62$\,$500	183 $\pm$ 5	-2.5 $\pm$ 0.3	0.032 $\pm$ 0.001
31$\,$250	84 $\pm$ 3	-9.4 $\pm$ 0.2	0.172 $\pm$ 0.005
15$\,$625	50 $\pm$ 5	-12.0 $\pm$ 0.3	0.302 $\pm$ 0.005
10$\,$000	36 $\pm$ 5	-13.5 $\pm$ 0.3	0.320 $\pm$ 0.010

Table D.10: EOS table for deuterium at the density of $0.674\,\rm gcm^{-3}$ ($r_s$=2.0) calculated with PIMC simulations using FP nodes, $N_P=32$, $\tau_B^{-1}=2\cdot10^6\rm K$, $\tau_F^{-1}=8\cdot10^6\rm K$, $n_{\rm A}=1$ and $n_{\rm E}=2$ (see Tab. D.6)

$T \:(\rm{K})$	$p \:(\rm{GPa})$	$E \:(\rm{eV})$	$1-P_1$
1$\,$000$\,$000	5433 $\pm$ 5	245.7 $\pm$ 0.3	0.000 $\pm$ 0.000
500$\,$000	2624 $\pm$ 4	113.2 $\pm$ 0.2	0.000 $\pm$ 0.000
250$\,$000	1225 $\pm$ 3	45.7 $\pm$ 0.1	0.000 $\pm$ 0.000
125$\,$000	548 $\pm$ 2	12.2 $\pm$ 0.1	0.008 $\pm$ 0.000
62$\,$500	246 $\pm$ 2	-3.1 $\pm$ 0.1	0.081 $\pm$ 0.001
31$\,$250	125 $\pm$ 2	-9.1 $\pm$ 0.1	0.365 $\pm$ 0.003
15$\,$625	75 $\pm$ 3	-11.7 $\pm$ 0.1	0.701 $\pm$ 0.003
10$\,$000	63 $\pm$ 5	-12.5 $\pm$ 0.2	0.829 $\pm$ 0.004
7812	51 $\pm$ 4	-13.5 $\pm$ 0.2	0.833 $\pm$ 0.010
5000	68 $\pm$ 9	-14.4 $\pm$ 0.4	0.629 $\pm$ 0.007

Table D.11: EOS table for deuterium at the density of $0.674\,\rm gcm^{-3}$ ($r_s$=2.0) calculated with PIMC simulations using VDM nodes, $N_P=32$, $\tau_B^{-1}=2\cdot10^6\rm K$, $\tau_F^{-1}=8\cdot10^6\rm K$, $n_{\rm A}=1$ and $n_{\rm E}=2$ (see Tab. D.6)

$T \:(\rm{K})$	$p \:(\rm{GPa})$	$E \:(\rm{eV})$	$1-P_1$
125$\,$000	540 $\pm$ 14	11.7 $\pm$ 0.6	0.008 $\pm$ 0.001
62$\,$500	236 $\pm$ 7	-3.7 $\pm$ 0.3	0.071 $\pm$ 0.005
31$\,$250	128 $\pm$ 5	-9.2 $\pm$ 0.2	0.271 $\pm$ 0.006
15$\,$625	59 $\pm$ 9	-12.8 $\pm$ 0.4	0.459 $\pm$ 0.009
10$\,$000	48 $\pm$ 10	-13.6 $\pm$ 0.5	0.534 $\pm$ 0.010
7812	53 $\pm$ 12	-13.7 $\pm$ 0.5	0.557 $\pm$ 0.011
5000	26 $\pm$ 25	-15.3 $\pm$ 1.2	0.666 $\pm$ 0.016

Table D.12: EOS table for deuterium at the density of $0.838\,\rm gcm^{-3}$ ($r_s$=1.86) calculated with PIMC simulations using FP nodes, $N_P=32$, $\tau_B^{-1}=2\cdot10^6\rm K$, $\tau_F^{-1}=8\cdot10^6\rm K$, $n_{\rm A}=1$ and $n_{\rm E}=2$ (see Tab. D.6)

$T \:(\rm{K})$	$p \:(\rm{GPa})$	$E \:(\rm{eV})$	$1-P_1$
1$\,$000$\,$000	6752 $\pm$ 8	245.3 $\pm$ 0.3	0.000 $\pm$ 0.000
500$\,$000	3245 $\pm$ 5	111.9 $\pm$ 0.2	0.000 $\pm$ 0.000
250$\,$000	1506 $\pm$ 3	44.3 $\pm$ 0.1	0.000 $\pm$ 0.000
125$\,$000	688 $\pm$ 3	11.7 $\pm$ 0.1	0.013 $\pm$ 0.000
62$\,$500	307 $\pm$ 1	-3.6 $\pm$ 0.0	0.133 $\pm$ 0.001
31$\,$250	166 $\pm$ 3	-9.1 $\pm$ 0.1	0.488 $\pm$ 0.002
15$\,$625	107 $\pm$ 7	-11.5 $\pm$ 0.3	0.804 $\pm$ 0.002
10$\,$000	85 $\pm$ 5	-12.4 $\pm$ 0.2	0.896 $\pm$ 0.001
7812	69 $\pm$ 7	-13.0 $\pm$ 0.3	0.919 $\pm$ 0.001
5000	93 $\pm$ 12	-14.4 $\pm$ 0.5	0.864 $\pm$ 0.005

Table D.13: EOS table for deuterium at the density of $0.838\,\rm gcm^{-3}$ ($r_s$=1.86) calculated with PIMC simulations using VDM nodes, $N_P=32$, $\tau_B^{-1}=2\cdot10^6\rm K$, $\tau_F^{-1}=8\cdot10^6\rm K$, $n_{\rm A}=1$ and $n_{\rm E}=2$ (see Tab. D.6)

$T \:(\rm{K})$	$p \:(\rm{GPa})$	$E \:(\rm{eV})$	$1-P_1$
125$\,$000	654 $\pm$ 16	10.3 $\pm$ 0.6	0.017 $\pm$ 0.002
62$\,$500	322 $\pm$ 5	-3.1 $\pm$ 0.2	0.122 $\pm$ 0.004
31$\,$250	169 $\pm$ 6	-9.3 $\pm$ 0.2	0.351 $\pm$ 0.005
15$\,$625	102 $\pm$ 10	-12.2 $\pm$ 0.4	0.562 $\pm$ 0.010
10$\,$000	97 $\pm$ 13	-12.5 $\pm$ 0.5	0.674 $\pm$ 0.009
7812	69 $\pm$ 27	-13.8 $\pm$ 1.0	0.689 $\pm$ 0.015
5000	49 $\pm$ 25	-14.7 $\pm$ 1.0	0.777 $\pm$ 0.009

Table D.14: EOS table for deuterium at the density of $1.01\,\rm gcm^{-3}$ ($r_s$=1.75) calculated with PIMC simulations using VDM nodes, $N_P=32$, $\tau_B^{-1}=2\cdot10^6\rm K$, $\tau_F^{-1}=4\cdot10^6\rm K$, $n_{\rm A}=1$ and $n_{\rm E}=2$ (see Tab. D.6)

$T \:(\rm{K})$	$p \:(\rm{GPa})$	$E \:(\rm{eV})$	$1-P_1$
125$\,$000	815 $\pm$ 6	10.6 $\pm$ 0.2	0.023 $\pm$ 0.001
62$\,$500	377 $\pm$ 9	-4.0 $\pm$ 0.3	0.177 $\pm$ 0.007
31$\,$250	199 $\pm$ 15	-9.9 $\pm$ 0.4	0.435 $\pm$ 0.009
15$\,$625	162 $\pm$ 16	-11.3 $\pm$ 0.5	0.675 $\pm$ 0.017
10$\,$000	138 $\pm$ 37	-12.3 $\pm$ 1.1	0.755 $\pm$ 0.015

Table D.15: EOS table for deuterium at the density of $1.60\,\rm gcm^{-3}$ ($r_s$=1.50) calculated with PIMC simulations using VDM nodes, $N_P=32$, $\tau_B^{-1}=4\cdot10^6\rm K$, $\tau_F^{-1}=8\cdot10^6\rm K$, $n_{\rm A}=1$ and $n_{\rm E}=2$ (see Tab. D.6)

$T \:(\rm{K})$	$p \:(\rm{GPa})$	$E \:(\rm{eV})$	$1-P_1$
250$\,$000	2865 $\pm$ 12	41.2 $\pm$ 0.2	0.006 $\pm$ 0.000
125$\,$000	1328 $\pm$ 24	9.5 $\pm$ 0.5	0.070 $\pm$ 0.003
62$\,$500	676 $\pm$ 26	-3.9 $\pm$ 0.5	0.340 $\pm$ 0.005
31$\,$250	409 $\pm$ 58	-9.3 $\pm$ 1.1	0.650 $\pm$ 0.011
15$\,$625	403 $\pm$ 104	-9.9 $\pm$ 2.0	0.821 $\pm$ 0.013

Table D.16: EOS table for deuterium at the density of $2.76\,\rm gcm^{-3}$ ($r_s$=1.25) calculated with PIMC simulations using VDM nodes, $N_P=32$, $\tau_B^{-1}=4\cdot10^6\rm K$, $\tau_F^{-1}=8\cdot10^6\rm K$, $n_{\rm A}=1$ and $n_{\rm E}=2$ (see Tab. D.6)

$T \:(\rm{K})$	$p \:(\rm{GPa})$	$E \:(\rm{eV})$	$1-P_1$
250$\,$000	5043 $\pm$ 37	39.5 $\pm$ 0.4	0.024 $\pm$ 0.001
125$\,$000	2477 $\pm$ 30	9.2 $\pm$ 0.3	0.222 $\pm$ 0.005
62$\,$500	1509 $\pm$ 88	-2.1 $\pm$ 1.0	0.568 $\pm$ 0.008
31$\,$250	1068 $\pm$ 93	-7.3 $\pm$ 1.1	0.813 $\pm$ 0.008
15$\,$625	960 $\pm$ 174	-8.9 $\pm$ 2.0	0.911 $\pm$ 0.002

Table D.17: EOS table for deuterium at the density of $5.39\,\rm gcm^{-3}$ ($r_s$=1.0) calculated with PIMC simulations using VDM nodes, $N_P=32$, $\tau_B^{-1}=8\cdot10^6\rm K$, $\tau_F^{-1}=16\cdot10^6\rm K$, $n_{\rm A}=1$ and $n_{\rm E}=2$ (see Tab. D.6)

$T \:(\rm{K})$	$p \:(\rm{GPa})$	$E \:(\rm{eV})$	$1-P_1$
500$\,$000	20814 $\pm$ 143	101.5 $\pm$ 0.8	0.009 $\pm$ 0.000
250$\,$000	10545 $\pm$ 153	39.8 $\pm$ 0.9	0.122 $\pm$ 0.003
125$\,$000	6343 $\pm$ 221	14.6 $\pm$ 1.3	0.485 $\pm$ 0.007
62$\,$500	4877 $\pm$ 404	5.9 $\pm$ 2.3	0.785 $\pm$ 0.003