![](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 = −0.561535 + 0.801719I
0.59754 − 9.28056I −1.67855 + 4.92481I
u = −0.561535 − 0.801719I
0.59754 + 9.28056I −1.67855 − 4.92481I
u = −0.741260 + 0.705629I
2.07770 − 1.55952I 0. + 4.24575I
u = −0.741260 − 0.705629I
2.07770 + 1.55952I 0. − 4.24575I
u = 0.858174 + 0.460652I
3.02036 + 0.76922I −4.00000 + 0.63988I
u = 0.858174 − 0.460652I
3.02036 − 0.76922I −4.00000 − 0.63988I
u = 0.552904 + 0.795056I
−4.60768 + 5.51677I −6.32456 − 4.07554I
u = 0.552904 − 0.795056I
−4.60768 − 5.51677I −6.32456 + 4.07554I
u = 0.787073 + 0.683095I
2.73226 − 1.63418I 0
u = 0.787073 − 0.683095I
2.73226 + 1.63418I 0
u = 0.744206 + 0.732824I
7.48690 + 4.59797I 0
u = 0.744206 − 0.732824I
7.48690 − 4.59797I 0
u = −0.891875 + 0.548288I
−1.16815 + 2.14250I 0
u = −0.891875 − 0.548288I
−1.16815 − 2.14250I 0
u = −0.540612 + 0.778681I
−2.67823 − 1.59684I −3.63668 − 0.69772I
u = −0.540612 − 0.778681I
−2.67823 + 1.59684I −3.63668 + 0.69772I
u = −0.923734 + 0.200980I
1.85137 + 5.82041I −6.32686 − 6.94483I
u = −0.923734 − 0.200980I
1.85137 − 5.82041I −6.32686 + 6.94483I
u = 0.582842 + 0.744201I
3.93389 + 1.07116I 0.776477 − 0.457625I
u = 0.582842 − 0.744201I
3.93389 − 1.07116I 0.776477 + 0.457625I
u = −0.930462
−0.771769 −9.37220
u = −0.519198 + 0.768041I
−2.80848 − 1.33304I −4.00000 + 1.12385I
u = −0.519198 − 0.768041I
−2.80848 + 1.33304I −4.00000 − 1.12385I
u = −0.805040 + 0.718870I
8.37556 + 3.79820I 0
u = −0.805040 − 0.718870I
8.37556 − 3.79820I 0
u = 0.900653 + 0.146018I
−3.07880 − 2.61927I −12.21002 + 6.26526I
u = 0.900653 − 0.146018I
−3.07880 + 2.61927I −12.21002 − 6.26526I
u = 0.493368 + 0.760092I
−4.98673 − 2.50951I −7.03178 + 3.70440I
u = 0.493368 − 0.760092I
−4.98673 + 2.50951I −7.03178 − 3.70440I
u = −1.09692
−1.56890 0
5