Table 4: Semi-major axis and eccentricity variation ranges for the 3 known planet of Gl 581, plus additional outer planets (see text), computed over 105 yr integrations.

Planet		 Semi-major axis (AU) Eccentricity

With a $1~M_{\rm J}$ planet at 5 AU:

Gl 581 b		 0.04060120-0.04061199 0.00367502-0.0895939
Gl 581 c 0.07286312-0.0729903 0.09259277-0.164875
Gl 581 d 0.25222823-0.25281971 0.11884516-0.1228305

With a $29.6~M_\oplus$ planet at 5 AU:

Gl 581 b		 0.04060139-0.04061188 0.00347993-0.0895106
Gl 581 c 0.07286522-0.0729892 0.09258738-0.1647922
Gl 581 d 0.25222915-0.2528203 0.11887163-0.1226443

With a $26.5~M_\oplus$ planet at 4 AU:

Gl 581 b		 0.04060141-0.04061174 0.00354749-0.08949917
Gl 581 c 0.07286447-0.07298892 0.09258812-0.16479787
Gl 581 d 0.25222689-0.25282013 0.11884819-0.1226468

With a $22.9~M_\oplus$ planet at 3 AU:

Gl 581 b		 0.04060137-0.04061170 0.00372438-0.0895144
Gl 581 c 0.07286369-0.07298806 0.09258945-0.16479738
Gl 581 d 0.25222659-0.25281951 0.11884226-0.12267108

With a $18.7~M_\oplus$ planet at 2 AU:

Gl 581 b		 0.04060140-0.04061177 0.00405747-0.08955927
Gl 581 c 0.07286632-0.07298852 0.09259499-0.16492574
Gl 581 d 0.25222099-0.25281587 0.11886586-0.12266511

With a $13.2~M_\oplus$ planet at 1 AU:

Gl 581 b		 0.04060131-0.04061176 0.00475611-0.08969945
Gl 581 c 0.07286289-0.07298820 0.09258994-0.16491917
Gl 581 d 0.25222239-0.25280011 0.11882570-0.12246267


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