![](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 = −0.923130 + 0.285145I
−0.30787 − 2.25346I 5.12843 + 3.26342I
u = −0.923130 − 0.285145I
−0.30787 + 2.25346I 5.12843 − 3.26342I
u = 0.995096 + 0.286789I
4.18097 + 4.67479I 11.82536 − 4.59597I
u = 0.995096 − 0.286789I
4.18097 − 4.67479I 11.82536 + 4.59597I
u = 1.024000 + 0.199158I
5.17530 + 2.55443I 13.5240 − 4.2251I
u = 1.024000 − 0.199158I
5.17530 − 2.55443I 13.5240 + 4.2251I
u = −0.994663 + 0.317611I
2.00397 − 9.65728I 8.40249 + 8.58483I
u = −0.994663 − 0.317611I
2.00397 + 9.65728I 8.40249 − 8.58483I
u = −1.049710 + 0.138664I
3.94362 + 2.17455I 11.37017 − 2.11968I
u = −1.049710 − 0.138664I
3.94362 − 2.17455I 11.37017 + 2.11968I
u = 0.674179 + 0.268506I
−1.71251 + 3.16112I 3.99113 − 5.83038I
u = 0.674179 − 0.268506I
−1.71251 − 3.16112I 3.99113 + 5.83038I
u = −0.691311
1.07542 9.42760
u = 0.472191 + 0.368747I
−0.77973 − 3.66810I 5.58740 + 1.24735I
u = 0.472191 − 0.368747I
−0.77973 + 3.66810I 5.58740 − 1.24735I
u = 0.201428 + 0.536486I
−1.68498 + 6.75016I 2.91272 − 7.90487I
u = 0.201428 − 0.536486I
−1.68498 − 6.75016I 2.91272 + 7.90487I
u = −0.210047 + 0.484113I
0.46489 − 2.03480I 6.34842 + 4.41097I
u = −0.210047 − 0.484113I
0.46489 + 2.03480I 6.34842 − 4.41097I
u = 0.100349 + 0.504234I
−3.42760 − 0.43485I −1.35617 − 0.72368I
u = 0.100349 − 0.504234I
−3.42760 + 0.43485I −1.35617 + 0.72368I
u = −0.332629 + 0.351120I
1.029420 − 0.669064I 9.01560 + 4.71804I
u = −0.332629 − 0.351120I
1.029420 + 0.669064I 9.01560 − 4.71804I
u = −1.64665 + 0.02163I
6.41597 − 3.89056I 0
u = −1.64665 − 0.02163I
6.41597 + 3.89056I 0
u = 1.66590
9.58969 0
u = 1.70003 + 0.06962I
8.97882 + 3.61851I 0
u = 1.70003 − 0.06962I
8.97882 − 3.61851I 0
u = 1.71726 + 0.08303I
11.6119 + 11.2693I 0
u = 1.71726 − 0.08303I
11.6119 − 11.2693I 0
5