![](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 = 0.133466 + 1.000640I
−1.27367 − 1.16757I 0
u = 0.133466 − 1.000640I
−1.27367 + 1.16757I 0
u = −0.532862 + 0.830572I
−0.02430 − 6.14834I 0
u = −0.532862 − 0.830572I
−0.02430 + 6.14834I 0
u = 0.524056 + 0.795819I
4.00847 + 2.15498I 0. − 3.78589I
u = 0.524056 − 0.795819I
4.00847 − 2.15498I 0. + 3.78589I
u = −0.284834 + 0.897551I
−0.67768 − 1.28884I −8.00000 + 4.92802I
u = −0.284834 − 0.897551I
−0.67768 + 1.28884I −8.00000 − 4.92802I
u = −0.170246 + 1.062460I
−6.83445 + 2.33727I 0
u = −0.170246 − 1.062460I
−6.83445 − 2.33727I 0
u = −0.749314 + 0.538316I
4.42162 − 7.61184I −4.45987 + 5.77896I
u = −0.749314 − 0.538316I
4.42162 + 7.61184I −4.45987 − 5.77896I
u = 0.752586 + 0.529461I
8.86798 + 3.35426I 0. − 3.38737I
u = 0.752586 − 0.529461I
8.86798 − 3.35426I 0. + 3.38737I
u = −0.525332 + 0.751819I
0.19898 + 1.80626I −5.15609 + 0.I
u = −0.525332 − 0.751819I
0.19898 − 1.80626I −5.15609 + 0.I
u = −0.755993 + 0.517707I
5.56056 + 0.94896I −3.15680 + 0.I
u = −0.755993 − 0.517707I
5.56056 − 0.94896I −3.15680 + 0.I
u = 0.287923 + 1.044900I
−4.82508 + 3.82270I 0
u = 0.287923 − 1.044900I
−4.82508 − 3.82270I 0
u = 0.081808 + 1.082030I
−0.0248733 − 0.0847749I 0
u = 0.081808 − 1.082030I
−0.0248733 + 0.0847749I 0
u = −0.098958 + 1.094980I
3.18345 + 4.26960I 0
u = −0.098958 − 1.094980I
3.18345 − 4.26960I 0
u = 0.781133 + 0.445371I
5.16257 − 1.98343I −3.74120 + 0.I
u = 0.781133 − 0.445371I
5.16257 + 1.98343I −3.74120 + 0.I
u = −0.785449 + 0.435883I
8.35181 + 6.28657I −0.78678 − 3.84368I
u = −0.785449 − 0.435883I
8.35181 − 6.28657I −0.78678 + 3.84368I
u = 0.787695 + 0.428827I
3.81832 − 10.53440I −5.33981 + 6.01257I
u = 0.787695 − 0.428827I
3.81832 + 10.53440I −5.33981 − 6.01257I
5