![](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 = 1.044500 + 0.281512I
−2.20764 − 0.64085I −5.73049 + 0.77381I
u = 1.044500 − 0.281512I
−2.20764 + 0.64085I −5.73049 − 0.77381I
u = 0.601217 + 0.686706I
8.50588 − 6.50884I 1.27031 + 5.73425I
u = 0.601217 − 0.686706I
8.50588 + 6.50884I 1.27031 − 5.73425I
u = 0.974822 + 0.492221I
−0.225106 − 0.871265I −4.08839 − 0.80386I
u = 0.974822 − 0.492221I
−0.225106 + 0.871265I −4.08839 + 0.80386I
u = −0.586774 + 0.690510I
8.78157 + 0.18779I 1.88251 − 0.64861I
u = −0.586774 − 0.690510I
8.78157 − 0.18779I 1.88251 + 0.64861I
u = 1.109660 + 0.186764I
2.94416 + 0.20510I −5.58587 + 0.61243I
u = 1.109660 − 0.186764I
2.94416 − 0.20510I −5.58587 − 0.61243I
u = −1.102420 + 0.258443I
−4.56669 − 2.49112I −11.89781 + 4.18392I
u = −1.102420 − 0.258443I
−4.56669 + 2.49112I −11.89781 − 4.18392I
u = −1.122120 + 0.196280I
2.54225 − 6.40452I −6.41624 + 4.33917I
u = −1.122120 − 0.196280I
2.54225 + 6.40452I −6.41624 − 4.33917I
u = 0.971931 + 0.595508I
7.41049 + 1.56089I 0
u = 0.971931 − 0.595508I
7.41049 − 1.56089I 0
u = 0.366014 + 0.773541I
7.29360 + 8.95041I −0.09124 − 5.62138I
u = 0.366014 − 0.773541I
7.29360 − 8.95041I −0.09124 + 5.62138I
u = −0.376178 + 0.768520I
7.69936 − 2.64631I 0.774092 + 0.704677I
u = −0.376178 − 0.768520I
7.69936 + 2.64631I 0.774092 − 0.704677I
u = −1.098220 + 0.328717I
−5.25608 + 2.82044I −13.7464 − 4.6104I
u = −1.098220 − 0.328717I
−5.25608 − 2.82044I −13.7464 + 4.6104I
u = −0.983871 + 0.595556I
7.60812 + 4.77001I 0. − 5.11123I
u = −0.983871 − 0.595556I
7.60812 − 4.77001I 0. + 5.11123I
u = 0.592887 + 0.582181I
0.88261 − 3.44954I −2.55100 + 7.40984I
u = 0.592887 − 0.582181I
0.88261 + 3.44954I −2.55100 − 7.40984I
u = −1.038830 + 0.540274I
0.66178 + 4.72185I 0. − 6.22617I
u = −1.038830 − 0.540274I
0.66178 − 4.72185I 0. + 6.22617I
u = 1.108380 + 0.429410I
0.525380 − 0.893417I −6.66537 + 0.I
u = 1.108380 − 0.429410I
0.525380 + 0.893417I −6.66537 + 0.I
5