![](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 = −1.165530 + 0.155856I
3.73352 − 1.14194I −3.26529 + 0.I
u = −1.165530 − 0.155856I
3.73352 + 1.14194I −3.26529 + 0.I
u = 0.386832 + 0.683926I
1.91287 − 9.38652I −5.20305 + 7.91054I
u = 0.386832 − 0.683926I
1.91287 + 9.38652I −5.20305 − 7.91054I
u = −0.397188 + 0.664692I
−3.31119 + 5.72979I −10.05626 − 7.33064I
u = −0.397188 − 0.664692I
−3.31119 − 5.72979I −10.05626 + 7.33064I
u = 0.528416 + 0.546036I
1.33332 + 5.27035I −6.71990 − 1.90933I
u = 0.528416 − 0.546036I
1.33332 − 5.27035I −6.71990 + 1.90933I
u = 1.240960 + 0.124497I
−1.94572 − 1.01820I 0
u = 1.240960 − 0.124497I
−1.94572 + 1.01820I 0
u = −0.494882 + 0.561225I
−3.73492 − 1.67350I −11.57713 + 0.85623I
u = −0.494882 − 0.561225I
−3.73492 + 1.67350I −11.57713 − 0.85623I
u = 0.441277 + 0.595069I
−1.58749 − 1.92674I −8.17224 + 4.16982I
u = 0.441277 − 0.595069I
−1.58749 + 1.92674I −8.17224 − 4.16982I
u = 0.407690 + 0.618254I
−1.47350 − 1.99549I −7.38990 + 2.72369I
u = 0.407690 − 0.618254I
−1.47350 + 1.99549I −7.38990 − 2.72369I
u = 1.263800 + 0.221984I
2.87934 − 7.34272I 0
u = 1.263800 − 0.221984I
2.87934 + 7.34272I 0
u = −1.276900 + 0.186164I
−2.59332 + 4.30245I 0
u = −1.276900 − 0.186164I
−2.59332 − 4.30245I 0
u = −0.297294 + 0.620737I
4.69829 + 1.24621I −1.93786 − 3.60564I
u = −0.297294 − 0.620737I
4.69829 − 1.24621I −1.93786 + 3.60564I
u = −0.062298 + 0.646826I
6.95779 + 4.17599I 1.17304 − 4.31736I
u = −0.062298 − 0.646826I
6.95779 − 4.17599I 1.17304 + 4.31736I
u = −1.37176
−5.91200 0
u = 1.386810 + 0.059846I
−2.09433 − 3.02163I 0
u = 1.386810 − 0.059846I
−2.09433 + 3.02163I 0
u = 0.057342 + 0.580744I
1.51039 − 1.50155I −2.27260 + 5.37426I
u = 0.057342 − 0.580744I
1.51039 + 1.50155I −2.27260 − 5.37426I
u = −0.506673 + 0.270240I
3.63229 + 1.96690I −5.76565 − 3.43589I
5