![](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 = −1.196810 + 0.224203I
4.01809 + 0.23438I −4.86393 − 0.79093I
u = −1.196810 − 0.224203I
4.01809 − 0.23438I −4.86393 + 0.79093I
u = 0.356883 + 0.692055I
3.38201 − 9.13654I −5.22617 + 8.05199I
u = 0.356883 − 0.692055I
3.38201 + 9.13654I −5.22617 − 8.05199I
u = −0.341594 + 0.685182I
3.89441 + 3.00577I −4.12276 − 3.17486I
u = −0.341594 − 0.685182I
3.89441 − 3.00577I −4.12276 + 3.17486I
u = −1.233130 + 0.069457I
−2.15848 + 0.53603I −5.34890 + 0.I
u = −1.233130 − 0.069457I
−2.15848 − 0.53603I −5.34890 + 0.I
u = 1.217450 + 0.233216I
3.86157 − 6.43991I −5.27816 + 6.02462I
u = 1.217450 − 0.233216I
3.86157 + 6.43991I −5.27816 − 6.02462I
u = 0.396277 + 0.634373I
−3.48205 − 4.78463I −11.04017 + 7.62920I
u = 0.396277 − 0.634373I
−3.48205 + 4.78463I −11.04017 − 7.62920I
u = 0.556137 + 0.493828I
2.57048 + 5.10842I −7.05988 − 2.20532I
u = 0.556137 − 0.493828I
2.57048 − 5.10842I −7.05988 + 2.20532I
u = 0.454805 + 0.560740I
−3.76676 + 0.88407I −12.38985 − 0.56473I
u = 0.454805 − 0.560740I
−3.76676 − 0.88407I −12.38985 + 0.56473I
u = −0.553895 + 0.455920I
3.00179 + 0.90271I −6.25769 − 2.96370I
u = −0.553895 − 0.455920I
3.00179 − 0.90271I −6.25769 + 2.96370I
u = 1.305380 + 0.145441I
−3.32923 − 3.99615I −9.76353 + 7.26560I
u = 1.305380 − 0.145441I
−3.32923 + 3.99615I −9.76353 − 7.26560I
u = −0.011445 + 0.679358I
7.60462 + 3.09519I −0.01509 − 2.78190I
u = −0.011445 − 0.679358I
7.60462 − 3.09519I −0.01509 + 2.78190I
u = −0.361045 + 0.570627I
−0.76961 + 1.72495I −4.78052 − 3.91512I
u = −0.361045 − 0.570627I
−0.76961 − 1.72495I −4.78052 + 3.91512I
u = 1.34637
−5.74682 −16.7140
u = 1.44469 + 0.15665I
−3.29340 − 3.04757I 0
u = 1.44469 − 0.15665I
−3.29340 + 3.04757I 0
u = 1.43643 + 0.22136I
−6.53816 − 4.66456I 0
u = 1.43643 − 0.22136I
−6.53816 + 4.66456I 0
u = 1.43871 + 0.26142I
−1.81787 − 6.45853I 0
5