**Table 1:** Parameters of computed 2D models for progenitor stars with different masses. $\Omega _{{\rm i}}$ is the angular velocity of the Fe-core, which is assumed to rotate uniformly, prior to collapse, $\theta _0$ and $\theta _1$ are the polar angles of the lateral grid boundaries, and $N_{\theta }$ is the number of grid points in the lateral direction. $t_{\rm 2D}$ denotes the time (relative to the bounce time) when the simulation was started or continued in 2D.
Model $~^\ast$	Progenitor	$\Omega _{{\rm i}}$	$[\theta_0,\theta_1]$	$N_{\theta }$	Resolution	Collapse	$t_{\rm 2D}$	Perturbation	Boundary
		(rad s^-1)	(degrees)		(degrees)	in 2D	[ms]	(%)	conditions
s112_32	s11.2	-	[46.8,133.2]	32	2.70	-	6.4	$v,\pm1$	periodic
s112_64	s11.2	-	[46.8,133.2]	64	1.35	-	7.3	$v,\pm1$	periodic
s112_128_f	s11.2	-	[0,180]	128	1.41	-	6.4	$v,\pm1$	reflecting
s15_32 $^\dagger$	s15s7b2	-	[46.8,133.2]	32	2.70	-	6.5	$v,\pm1$	periodic
s15_64_p	s15s7b2	-	[46.8,133.2]	64	1.35	+	-175	$\rho,\pm2$	periodic
s15_64_r	s15s7b2	0.5	[0,90]	64	1.41	+	-175	$\rho,\pm1$	reflecting
s20_32	s20.0	-	[46.8,133.2]	32	2.70	-	6.5	$v,\pm1$	periodic
s15_mix $^\ddagger$	s15s7b2	-	-	1	-	-		-	-

$^\ast$ Models s112_32, s112_64, s15_32, s15_64_p, s15_64_r, and s20_32 were discussed in overview in Buras et al. (2003).
$^\dagger$ This is Model s15Gio_32.b from Buras et al. (2006). Different from the other models presented in this paper, Model s15_32 was computed with an older implementation of the gravitational potential, which contained a slightly different treatment of the relativistic corrections in the potential (see also the comment in Table B.1). This affects only the neutrino luminosities and average neutrino energies by a few percent. We have corrected this difference in our plots for the luminosities and mean energies. The correction was calculated as $\Delta L = L_{\rm 1D,new} - L_{\rm 1D,old}$ , where $L_{\rm 1D,new}$ and $L_{\rm 1D,old}$ are the luminosities of the 1D simulations with the "new'' and "old'' versions of the gravitational potential, respectively. Then the corrected luminosity is given by $L_{\rm 2D,corr} = L_{\rm 2D,old} + \Delta L$ , where $L_{\rm 2D,old}$ is the luminosity of the 2D model which was simulated with the old version of the gravitational potential. For the average neutrino energies the procedure is analogous.
$^\ddagger$ This model was calculated in 1D using the mixing algorithm described in Appendix D for treating effects from PNS convection.

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