Table 4: Coefficients of correlation (r), number of stars used in the fit (N), parameters (a and b) of the linear, exponential and power law weighted fits to the lower envelope of the $L_{\rm X}$ / $L_{\rm bol}$ - $A_{{\rm max}}$ distribution in the fast rotation regime ( $P \ge 1.1$ d) and reduced chi-squares ( $\chi ^2_{\rm\nu }$ ).
Linear Exponential Power

Sp. type r N a b $\chi^2_{\nu}$ log(a) b $\chi^2_{\nu}$ log(a) b $\chi^2_{\nu}$

F 0.74 12 -8.9e-6 $\pm$ 1.2e-6 0.001 $\pm$ 0.0001 16.6 -5.52 $\pm$ 0.08 26.40 $\pm$ 1.35 7.1 -0.66 $\pm$ 0.17 2.65 $\pm$ 0.13 6.9

G 0.79 14 -1.1e-4 $\pm$ 8.0e-6 0.003 $\pm$ 0.0001 89.2 -5.63 $\pm$ 0.09 20.59 $\pm$ 0.76 26.9 0.20 $\pm$ 0.13 3.66 $\pm$ 0.14 23.7

K 0.72 15 -2.9e-5 $\pm$ 4.0e-6 0.002 $\pm$ 0.0001 14.8 -5.01 $\pm$ 0.07 11.41 $\pm$ 0.47 9.7 -1.27 $\pm$ 0.09 2.39 $\pm$ 0.10 9.5

M(env 1) 0.96 9 -7.1e-5 $\pm$ 1.2e-5 0.004 $\pm$ 0.0002 2.62 -4.16 $\pm$ 0.02 4.12 $\pm$ 0.11 0.1 -2.24 $\pm$ 0.04 1.28 $\pm$ 0.04 0.9

M(env 2) 0.86 4 7.8e-5 $\pm$ 1.0e-4 0.006 $\pm$ 0.0009 2.29 -3.41 $\pm$ 0.14 2.72 $\pm$ 1.05 2.1 -2.42 $\pm$ 0.20 0.71 $\pm$ 0.22 1.5

**Table 4:** Coefficients of correlation (r), number of stars used in the fit (N), parameters (a and b) of the linear, exponential and power law weighted fits to the lower envelope of the $L_{\rm X}$ / $L_{\rm bol}$ - $A_{{\rm max}}$ distribution in the fast rotation regime ( $P \ge 1.1$ d) and reduced chi-squares ( $\chi ^2_{\rm\nu }$ ).
		Linear	Exponential	Power
Sp. type	r	N	a	b	$\chi^2_{\nu}$	log(a)	b	$\chi^2_{\nu}$	log(a)	b	$\chi^2_{\nu}$
F	0.74	12	-8.9e-6 $\pm$ 1.2e-6	0.001 $\pm$ 0.0001	16.6	-5.52 $\pm$ 0.08	26.40 $\pm$ 1.35	7.1	-0.66 $\pm$ 0.17	2.65 $\pm$ 0.13	6.9
G	0.79	14	-1.1e-4 $\pm$ 8.0e-6	0.003 $\pm$ 0.0001	89.2	-5.63 $\pm$ 0.09	20.59 $\pm$ 0.76	26.9	0.20 $\pm$ 0.13	3.66 $\pm$ 0.14	23.7
K	0.72	15	-2.9e-5 $\pm$ 4.0e-6	0.002 $\pm$ 0.0001	14.8	-5.01 $\pm$ 0.07	11.41 $\pm$ 0.47	9.7	-1.27 $\pm$ 0.09	2.39 $\pm$ 0.10	9.5
M(env 1)	0.96	9	-7.1e-5 $\pm$ 1.2e-5	0.004 $\pm$ 0.0002	2.62	-4.16 $\pm$ 0.02	4.12 $\pm$ 0.11	0.1	-2.24 $\pm$ 0.04	1.28 $\pm$ 0.04	0.9
M(env 2)	0.86	4	7.8e-5 $\pm$ 1.0e-4	0.006 $\pm$ 0.0009	2.29	-3.41 $\pm$ 0.14	2.72 $\pm$ 1.05	2.1	-2.42 $\pm$ 0.20	0.71 $\pm$ 0.22	1.5

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