![](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 = −1.14724
−1.35276 0
u = 1.151380 + 0.058161I
2.53228 + 3.79612I 0
u = 1.151380 − 0.058161I
2.53228 − 3.79612I 0
u = 0.481555 + 0.664903I
11.99140 + 2.20783I 4.22893 − 3.07025I
u = 0.481555 − 0.664903I
11.99140 − 2.20783I 4.22893 + 3.07025I
u = −0.443054 + 0.686901I
7.60131 − 10.06700I 0.80807 + 7.84045I
u = −0.443054 − 0.686901I
7.60131 + 10.06700I 0.80807 − 7.84045I
u = −0.515153 + 0.627947I
7.87503 + 5.69223I 1.58915 − 1.87939I
u = −0.515153 − 0.627947I
7.87503 − 5.69223I 1.58915 + 1.87939I
u = 0.438326 + 0.675169I
2.65616 + 6.14445I −3.69389 − 6.69694I
u = 0.438326 − 0.675169I
2.65616 − 6.14445I −3.69389 + 6.69694I
u = 0.501005 + 0.618665I
2.90568 − 1.85234I −2.97160 + 0.63684I
u = 0.501005 − 0.618665I
2.90568 + 1.85234I −2.97160 − 0.63684I
u = −0.442362 + 0.648377I
5.01043 − 2.20484I −0.34907 + 2.50917I
u = −0.442362 − 0.648377I
5.01043 + 2.20484I −0.34907 − 2.50917I
u = −0.466755 + 0.626215I
5.10910 − 1.98014I 0.15978 + 4.14976I
u = −0.466755 − 0.626215I
5.10910 + 1.98014I 0.15978 − 4.14976I
u = −1.307560 + 0.189347I
4.08058 − 1.65712I 0
u = −1.307560 − 0.189347I
4.08058 + 1.65712I 0
u = 1.331250 + 0.207988I
0.86765 + 5.45245I 0
u = 1.331250 − 0.207988I
0.86765 − 5.45245I 0
u = 0.188380 + 0.617055I
0.49984 + 6.30818I −4.83696 − 8.02356I
u = 0.188380 − 0.617055I
0.49984 − 6.30818I −4.83696 + 8.02356I
u = 1.354390 + 0.050533I
3.56112 + 0.15774I 0
u = 1.354390 − 0.050533I
3.56112 − 0.15774I 0
u = −1.351690 + 0.130313I
4.61294 − 2.74721I 0
u = −1.351690 − 0.130313I
4.61294 + 2.74721I 0
u = −1.345480 + 0.220131I
5.32159 − 9.34589I 0
u = −1.345480 − 0.220131I
5.32159 + 9.34589I 0
u = −0.155934 + 0.602452I
−3.78873 − 2.51425I −10.60618 + 5.42125I
5