![](data:image/png;base64,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)
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.595719 + 0.578948I
−7.70647 + 11.34340I −8.26251 − 9.40428I
u = −0.595719 − 0.578948I
−7.70647 − 11.34340I −8.26251 + 9.40428I
u = −0.599254 + 0.561085I
−8.54295 + 2.41798I −9.80276 − 3.05774I
u = −0.599254 − 0.561085I
−8.54295 − 2.41798I −9.80276 + 3.05774I
u = 0.589572 + 0.570914I
−4.51819 − 6.51331I −5.31750 + 6.37538I
u = 0.589572 − 0.570914I
−4.51819 + 6.51331I −5.31750 − 6.37538I
u = 0.538749 + 0.569567I
−0.93086 − 6.41545I −3.67996 + 9.86351I
u = 0.538749 − 0.569567I
−0.93086 + 6.41545I −3.67996 − 9.86351I
u = 0.220912 + 0.733421I
−2.38478 − 6.60693I −2.78190 + 7.82097I
u = 0.220912 − 0.733421I
−2.38478 + 6.60693I −2.78190 − 7.82097I
u = 0.569041 + 0.489543I
−4.59319 − 1.95369I −11.39399 + 3.79158I
u = 0.569041 − 0.489543I
−4.59319 + 1.95369I −11.39399 − 3.79158I
u = −0.621187 + 0.418285I
−8.96370 + 1.72981I −11.03048 − 3.35966I
u = −0.621187 − 0.418285I
−8.96370 − 1.72981I −11.03048 + 3.35966I
u = −0.505578 + 0.547288I
−0.07972 + 2.16929I −1.40597 − 3.65142I
u = −0.505578 − 0.547288I
−0.07972 − 2.16929I −1.40597 + 3.65142I
u = −0.624357 + 0.395701I
−8.24591 − 7.19806I −9.88810 + 3.21124I
u = −0.624357 − 0.395701I
−8.24591 + 7.19806I −9.88810 − 3.21124I
u = 0.613226 + 0.403101I
−5.01179 + 2.41777I −6.90071 − 0.01179I
u = 0.613226 − 0.403101I
−5.01179 − 2.41777I −6.90071 + 0.01179I
u = 0.274381 + 0.668482I
−2.83652 + 1.62881I −4.05285 + 1.38314I
u = 0.274381 − 0.668482I
−2.83652 − 1.62881I −4.05285 − 1.38314I
u = −0.043462 + 0.719036I
2.69348 + 2.02135I 4.11374 − 4.67175I
u = −0.043462 − 0.719036I
2.69348 − 2.02135I 4.11374 + 4.67175I
u = −0.195350 + 0.687690I
0.60698 + 2.16613I 0.97582 − 4.91748I
u = −0.195350 − 0.687690I
0.60698 − 2.16613I 0.97582 + 4.91748I
u = 0.537336 + 0.377380I
−1.48399 + 2.68474I −5.93567 − 3.09855I
u = 0.537336 − 0.377380I
−1.48399 − 2.68474I −5.93567 + 3.09855I
u = −0.463936 + 0.448567I
−0.422225 + 1.251880I −2.42688 − 4.39107I
u = −0.463936 − 0.448567I
−0.422225 − 1.251880I −2.42688 + 4.39107I
5