![](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 = −0.556433 + 0.835324I
−7.18763 + 2.08490I 0
u = −0.556433 − 0.835324I
−7.18763 − 2.08490I 0
u = −0.024996 + 0.994939I
3.43520 + 2.09623I 8.58300 + 0.I
u = −0.024996 − 0.994939I
3.43520 − 2.09623I 8.58300 + 0.I
u = −0.123552 + 0.999729I
1.18678 + 2.46011I 0
u = −0.123552 − 0.999729I
1.18678 − 2.46011I 0
u = 0.548923 + 0.847737I
−3.24727 − 6.11532I 0
u = 0.548923 − 0.847737I
−3.24727 + 6.11532I 0
u = −0.557501 + 0.853846I
−6.39706 + 10.87620I 0
u = −0.557501 − 0.853846I
−6.39706 − 10.87620I 0
u = 0.183246 + 1.004240I
−2.41430 + 1.30442I 0
u = 0.183246 − 1.004240I
−2.41430 − 1.30442I 0
u = −0.451800 + 0.860540I
0.69661 + 2.01708I 0
u = −0.451800 − 0.860540I
0.69661 − 2.01708I 0
u = 0.128657 + 1.032900I
−1.77995 − 7.01061I 0
u = 0.128657 − 1.032900I
−1.77995 + 7.01061I 0
u = 0.510603 + 0.767949I
−3.43520 − 2.09623I −8.58300 + 4.19142I
u = 0.510603 − 0.767949I
−3.43520 + 2.09623I −8.58300 − 4.19142I
u = −0.565146 + 0.686956I
−7.60942 + 2.39548I −8.03590 − 3.45801I
u = −0.565146 − 0.686956I
−7.60942 − 2.39548I −8.03590 + 3.45801I
u = −0.570856 + 0.661159I
−6.94292 − 6.37762I −6.79931 + 3.36470I
u = −0.570856 − 0.661159I
−6.94292 + 6.37762I −6.79931 − 3.36470I
u = 0.556299 + 0.668324I
−3.75583 + 1.68060I −3.85601 − 0.15656I
u = 0.556299 − 0.668324I
−3.75583 − 1.68060I −3.85601 + 0.15656I
u = −0.362656 + 0.775470I
0.22941 + 1.46786I 2.13380 − 4.56718I
u = −0.362656 − 0.775470I
0.22941 − 1.46786I 2.13380 + 4.56718I
u = 0.804947 + 0.154678I
−3.05581 + 11.52890I −3.10731 − 7.64918I
u = 0.804947 − 0.154678I
−3.05581 − 11.52890I −3.10731 + 7.64918I
u = −0.798246 + 0.151160I
− 6.69000I 0. + 4.60895I
u = −0.798246 − 0.151160I
6.69000I 0. − 4.60895I
5