![](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 = −0.249709 + 0.948226I
4.63631 − 2.12088I −1.01844 + 2.80811I
u = −0.249709 − 0.948226I
4.63631 + 2.12088I −1.01844 − 2.80811I
u = 0.295729 + 0.994644I
−2.13539 + 4.89833I −5.01649 − 2.19451I
u = 0.295729 − 0.994644I
−2.13539 − 4.89833I −5.01649 + 2.19451I
u = 0.230603 + 0.853532I
4.74743 − 1.96048I −0.34668 + 4.23406I
u = 0.230603 − 0.853532I
4.74743 + 1.96048I −0.34668 − 4.23406I
u = −0.273056 + 0.774265I
−1.78828 + 4.72311I −4.06394 − 4.26663I
u = −0.273056 − 0.774265I
−1.78828 − 4.72311I −4.06394 + 4.26663I
u = 0.777766 + 0.178377I
−4.65007 − 8.93459I −8.10474 + 6.18574I
u = 0.777766 − 0.178377I
−4.65007 + 8.93459I −8.10474 − 6.18574I
u = −0.761639 + 0.184556I
2.23741 + 6.02041I −4.49356 − 6.91985I
u = −0.761639 − 0.184556I
2.23741 − 6.02041I −4.49356 + 6.91985I
u = 0.775098 + 0.060463I
−11.25330 − 3.44491I −12.79521 + 3.55577I
u = 0.775098 − 0.060463I
−11.25330 + 3.44491I −12.79521 − 3.55577I
u = 0.742257 + 0.192170I
2.53020 − 1.80186I −3.57173 + 0.69342I
u = 0.742257 − 0.192170I
2.53020 + 1.80186I −3.57173 − 0.69342I
u = 0.318281 + 1.201370I
−7.76752 − 0.51963I 0
u = 0.318281 − 1.201370I
−7.76752 + 0.51963I 0
u = −0.275754 + 1.221110I
−0.186542 + 1.326290I 0
u = −0.275754 − 1.221110I
−0.186542 − 1.326290I 0
u = −0.716310 + 0.207468I
−3.73927 − 1.03700I −7.10850 − 0.87605I
u = −0.716310 − 0.207468I
−3.73927 + 1.03700I −7.10850 + 0.87605I
u = 0.063850 + 1.258910I
4.32614 − 1.52805I 0
u = 0.063850 − 1.258910I
4.32614 + 1.52805I 0
u = −0.731823 + 0.057552I
−3.72646 + 2.32596I −11.41052 − 5.70564I
u = −0.731823 − 0.057552I
−3.72646 − 2.32596I −11.41052 + 5.70564I
u = 0.267337 + 1.286100I
2.27908 − 3.39012I 0
u = 0.267337 − 1.286100I
2.27908 + 3.39012I 0
u = −0.145806 + 1.317740I
−1.58295 + 3.13834I 0
u = −0.145806 − 1.317740I
−1.58295 − 3.13834I 0
5