![](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 = 0.276142 + 0.973147I
4.50590 − 2.85550I 12.05805 + 4.41993I
u = 0.276142 − 0.973147I
4.50590 + 2.85550I 12.05805 − 4.41993I
u = −0.311087 + 0.967783I
1.20301 + 5.52787I 4.00000 − 8.08112I
u = −0.311087 − 0.967783I
1.20301 − 5.52787I 4.00000 + 8.08112I
u = −0.225553 + 0.996987I
7.62104 − 4.67869I 10.89032 + 2.00709I
u = −0.225553 − 0.996987I
7.62104 + 4.67869I 10.89032 − 2.00709I
u = 0.236153 + 0.997386I
8.32399 − 1.19963I 12.16015 + 3.25993I
u = 0.236153 − 0.997386I
8.32399 + 1.19963I 12.16015 − 3.25993I
u = 0.304523 + 1.001500I
7.92106 − 4.82325I 11.07978 + 4.36296I
u = 0.304523 − 1.001500I
7.92106 + 4.82325I 11.07978 − 4.36296I
u = −0.312943 + 1.002150I
7.10672 + 10.70210I 9.44810 − 9.41252I
u = −0.312943 − 1.002150I
7.10672 − 10.70210I 9.44810 + 9.41252I
u = 0.456777 + 0.785683I
1.23819 − 6.54922I 4.17677 + 9.67765I
u = 0.456777 − 0.785683I
1.23819 + 6.54922I 4.17677 − 9.67765I
u = −0.397793 + 0.800537I
1.82221 + 1.25981I 6.09781 − 4.41931I
u = −0.397793 − 0.800537I
1.82221 − 1.25981I 6.09781 + 4.41931I
u = 0.784027 + 0.781220I
1.10586 − 5.81643I 0
u = 0.784027 − 0.781220I
1.10586 + 5.81643I 0
u = −0.023490 + 0.865695I
3.89741 + 2.71211I 12.15997 − 3.32953I
u = −0.023490 − 0.865695I
3.89741 − 2.71211I 12.15997 + 3.32953I
u = −0.836827 + 0.807352I
−2.60329 − 1.13595I 0
u = −0.836827 − 0.807352I
−2.60329 + 1.13595I 0
u = −0.858606 + 0.795301I
0.37310 − 3.30299I 0
u = −0.858606 − 0.795301I
0.37310 + 3.30299I 0
u = 0.863434 + 0.797395I
−0.53580 + 9.14737I 0
u = 0.863434 − 0.797395I
−0.53580 − 9.14737I 0
u = 0.827585 + 0.837312I
−4.93871 − 2.14028I 0
u = 0.827585 − 0.837312I
−4.93871 + 2.14028I 0
u = 0.854921 + 0.812716I
−6.26873 + 3.63660I 0
u = 0.854921 − 0.812716I
−6.26873 − 3.63660I 0
5