![](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 = −0.886995 + 0.045862I
14.3413 − 2.3988I 10.05032 + 0.51244I
u = −0.886995 − 0.045862I
14.3413 + 2.3988I 10.05032 − 0.51244I
u = 0.885350 + 0.051007I
13.9632 + 8.8219I 9.36443 − 5.35751I
u = 0.885350 − 0.051007I
13.9632 − 8.8219I 9.36443 + 5.35751I
u = −0.864228 + 0.018685I
7.62020 − 1.13554I 10.36949 + 0.23646I
u = −0.864228 − 0.018685I
7.62020 + 1.13554I 10.36949 − 0.23646I
u = 0.079677 + 1.134880I
−1.86120 + 1.73369I 0. − 4.71715I
u = 0.079677 − 1.134880I
−1.86120 − 1.73369I 0. + 4.71715I
u = 0.856539 + 0.039628I
5.73343 + 5.16675I 5.71941 − 6.13440I
u = 0.856539 − 0.039628I
5.73343 − 5.16675I 5.71941 + 6.13440I
u = 0.124104 + 0.821653I
5.01486 + 3.10577I 5.36912 − 3.19461I
u = 0.124104 − 0.821653I
5.01486 − 3.10577I 5.36912 + 3.19461I
u = 0.830617
3.31017 1.79020
u = −0.134449 + 0.719876I
4.98402 + 3.12049I 4.83515 − 1.88613I
u = −0.134449 − 0.719876I
4.98402 − 3.12049I 4.83515 + 1.88613I
u = 0.140602 + 1.264520I
−3.20902 + 2.28111I 0
u = 0.140602 − 1.264520I
−3.20902 − 2.28111I 0
u = 0.398432 + 1.236750I
2.03590 − 0.66546I 0
u = 0.398432 − 1.236750I
2.03590 + 0.66546I 0
u = 0.431188 + 1.231470I
10.32020 − 4.11571I 0
u = 0.431188 − 1.231470I
10.32020 + 4.11571I 0
u = −0.091117 + 1.302380I
−6.13952 − 0.32984I 0
u = −0.091117 − 1.302380I
−6.13952 + 0.32984I 0
u = −0.431390 + 1.236960I
10.66320 − 2.31354I 0
u = −0.431390 − 1.236960I
10.66320 + 2.31354I 0
u = −0.151057 + 1.311240I
−5.41307 − 5.33764I 0
u = −0.151057 − 1.311240I
−5.41307 + 5.33764I 0
u = −0.404078 + 1.258270I
3.77988 − 3.40970I 0
u = −0.404078 − 1.258270I
3.77988 + 3.40970I 0
u = −0.010529 + 1.328650I
−0.68155 + 2.96620I 0
5