![](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 = −0.571105 + 0.602504I
7.23980 − 9.54989I 3.31919 + 7.94832I
u = −0.571105 − 0.602504I
7.23980 + 9.54989I 3.31919 − 7.94832I
u = 0.119738 + 0.805469I
2.92614 + 4.24554I −2.30656 − 4.16682I
u = 0.119738 − 0.805469I
2.92614 − 4.24554I −2.30656 + 4.16682I
u = 0.549622 + 0.599161I
6.94310I 0. − 9.44534I
u = 0.549622 − 0.599161I
− 6.94310I 0. + 9.44534I
u = −0.041579 + 0.787901I
−3.70641 − 1.86423I −6.68982 + 4.28103I
u = −0.041579 − 0.787901I
−3.70641 + 1.86423I −6.68982 − 4.28103I
u = −0.518355 + 0.592676I
−0.74026 − 3.08667I −2.29165 + 3.31825I
u = −0.518355 − 0.592676I
−0.74026 + 3.08667I −2.29165 − 3.31825I
u = −0.590762 + 0.488652I
11.79350 − 2.01666I 7.44353 + 3.51119I
u = −0.590762 − 0.488652I
11.79350 + 2.01666I 7.44353 − 3.51119I
u = 0.447929 + 0.612038I
4.96768 + 0.96718I 0.97174 − 3.83444I
u = 0.447929 − 0.612038I
4.96768 − 0.96718I 0.97174 + 3.83444I
u = 0.539062 + 0.483661I
3.70641 + 1.86423I 6.68982 − 4.28103I
u = 0.539062 − 0.483661I
3.70641 − 1.86423I 6.68982 + 4.28103I
u = −0.605762 + 0.352402I
7.97171 + 5.53571I 5.39099 − 1.87938I
u = −0.605762 − 0.352402I
7.97171 − 5.53571I 5.39099 + 1.87938I
u = 0.572553 + 0.344141I
0.74026 − 3.08667I 2.29165 + 3.31825I
u = 0.572553 − 0.344141I
0.74026 + 3.08667I 2.29165 − 3.31825I
u = −0.503120 + 0.331554I
− 0.502173I 0. + 3.98649I
u = −0.503120 − 0.331554I
0.502173I 0. − 3.98649I
u = −0.10770 + 1.43493I
2.35576 + 3.09747I 0
u = −0.10770 − 1.43493I
2.35576 − 3.09747I 0
u = 0.08834 + 1.46597I
−4.96768 − 0.96718I 0
u = 0.08834 − 1.46597I
−4.96768 + 0.96718I 0
u = 0.493520 + 0.181034I
6.17159 + 2.22513I 5.27781 − 2.91607I
u = 0.493520 − 0.181034I
6.17159 − 2.22513I 5.27781 + 2.91607I
u = −0.09667 + 1.51117I
−6.17159 − 2.22513I 0
u = −0.09667 − 1.51117I
−6.17159 + 2.22513I 0
5