![](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 = 0.598747 + 0.574890I
−6.17596 − 9.61051I −8.07514 + 7.89257I
u = 0.598747 − 0.574890I
−6.17596 + 9.61051I −8.07514 − 7.89257I
u = −0.579767 + 0.568232I
1.46262 + 7.21330I −5.14859 − 9.60886I
u = −0.579767 − 0.568232I
1.46262 − 7.21330I −5.14859 + 9.60886I
u = −0.799600 + 0.134077I
−10.62720 + 4.36353I −13.8919 − 4.2573I
u = −0.799600 − 0.134077I
−10.62720 − 4.36353I −13.8919 + 4.2573I
u = 0.552380 + 0.559106I
2.72755 − 3.55040I −1.47416 + 3.94014I
u = 0.552380 − 0.559106I
2.72755 + 3.55040I −1.47416 − 3.94014I
u = −0.486892 + 0.584883I
−1.98087 + 1.99888I −4.50156 − 3.58150I
u = −0.486892 − 0.584883I
−1.98087 − 1.99888I −4.50156 + 3.58150I
u = 0.619098 + 0.438297I
−8.73729 − 0.86802I −11.01246 + 3.92491I
u = 0.619098 − 0.438297I
−8.73729 + 0.86802I −11.01246 − 3.92491I
u = 0.726133 + 0.110853I
−2.87515 − 2.61799I −12.7473 + 6.4736I
u = 0.726133 − 0.110853I
−2.87515 + 2.61799I −12.7473 − 6.4736I
u = 0.418082 + 0.569716I
3.12275 − 0.32958I 0.04870 + 3.38032I
u = 0.418082 − 0.569716I
3.12275 + 0.32958I 0.04870 − 3.38032I
u = 0.359261 + 0.608239I
−5.47474 + 5.57708I −6.11056 − 1.82524I
u = 0.359261 − 0.608239I
−5.47474 − 5.57708I −6.11056 + 1.82524I
u = −0.528151 + 0.466800I
−0.81474 + 1.58943I −9.19847 − 3.59943I
u = −0.528151 − 0.466800I
−0.81474 − 1.58943I −9.19847 + 3.59943I
u = −0.381969 + 0.589199I
2.04130 − 3.25118I −3.15587 + 3.30820I
u = −0.381969 − 0.589199I
2.04130 + 3.25118I −3.15587 − 3.30820I
u = −0.607541
−1.09411 −8.24150
u = −1.43710 + 0.11460I
−11.13960 − 3.09747I 0
u = −1.43710 − 0.11460I
−11.13960 + 3.09747I 0
u = 1.46424 + 0.12360I
−3.87403 + 0.83702I 0
u = 1.46424 − 0.12360I
−3.87403 − 0.83702I 0
u = 0.167534 + 0.493668I
−7.46565 − 2.28896I −6.43563 + 2.79578I
u = 0.167534 − 0.493668I
−7.46565 + 2.28896I −6.43563 − 2.79578I
u = −1.48768 + 0.13710I
−3.08950 + 2.74865I 0
5