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Table E.1

Relevant versions of the multi-resonant model with assumed observed characteristic frequency ratio set νU:νM:νL = 3:2:1. The radius of marginally stable orbit xms and corresponding resonant radii x1 and x2 are given.

Set νU νM νL a x ms x 1 x 2

“Magic” ν K 0.983043* 1.571 2.395
T45 0.885010 2.419 3.720 4.299
B15 0.616894 3.758 4.241 5.833
B15 0.999667 1.121 1.411 4.250
B22 ν r 0.913806 2.225 2.885 3.935
B24 0.980124 1.612 2.551 3.519
B25 0.475159 4.330 4.988 6.359
B45 0.922985 2.158 3.794 4.594
M14 0.544870 4.055 4.347 5.477
M24 0.535413 4.093 4.394 5.832
M54 0.336030 4.849 5.327 6.857
T1(DC1) }   0.865670* 2.539 2.880
B1(DC11)
T1(DC3) 0.986666* 1.514 1.753
T1(DC9) }   0.892290 2.372 3.601 5.034
M(DC11)
T1(DC11) 0.772687 3.046 3.792 6.036
T1(DC11) 0.927324 2.125 2.131 2.419
B1(DC9) }     0.868917 2.520 2.648 3.510
M1(DC1)
B1(DC12) 0.851581 2.623 2.675 3.640
M1(DC7) 0.987594 1.498 1.502 2.326

Notes.An asterisk denotes the special values of the black hole spin when the resonance points share the same radius (x1 = x2 ≡ x3:2:1).

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