![](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 = −0.981563 + 0.214317I
−1.74298 + 0.40841I −5.87200 − 0.75563I
u = −0.981563 − 0.214317I
−1.74298 − 0.40841I −5.87200 + 0.75563I
u = 0.803335 + 0.491088I
1.74384 − 2.05721I 4.27298 + 4.01793I
u = 0.803335 − 0.491088I
1.74384 + 2.05721I 4.27298 − 4.01793I
u = −0.527198 + 0.744803I
6.35994 + 2.92383I 5.29020 − 3.29300I
u = −0.527198 − 0.744803I
6.35994 − 2.92383I 5.29020 + 3.29300I
u = 1.085860 + 0.107562I
0.74814 + 3.77265I −1.89193 − 3.49106I
u = 1.085860 − 0.107562I
0.74814 − 3.77265I −1.89193 + 3.49106I
u = −0.433290 + 0.779547I
5.84506 − 5.78082I 4.37527 + 3.72629I
u = −0.433290 − 0.779547I
5.84506 + 5.78082I 4.37527 − 3.72629I
u = −1.062920 + 0.387157I
−2.96425 + 1.34320I −6.02964 − 0.62000I
u = −1.062920 − 0.387157I
−2.96425 − 1.34320I −6.02964 + 0.62000I
u = 0.452781 + 0.717874I
2.63437 + 1.18290I 1.39246 − 0.39910I
u = 0.452781 − 0.717874I
2.63437 − 1.18290I 1.39246 + 0.39910I
u = 1.083310 + 0.462291I
−2.43992 − 5.71321I −4.10823 + 7.50361I
u = 1.083310 − 0.462291I
−2.43992 + 5.71321I −4.10823 − 7.50361I
u = −1.041780 + 0.614710I
4.82981 + 2.24524I 3.02697 − 1.89383I
u = −1.041780 − 0.614710I
4.82981 − 2.24524I 3.02697 + 1.89383I
u = 1.075010 + 0.585259I
0.79700 − 6.17959I −1.78521 + 5.04555I
u = 1.075010 − 0.585259I
0.79700 + 6.17959I −1.78521 − 5.04555I
u = −1.097340 + 0.604979I
3.87224 + 11.00000I 1.31825 − 8.05284I
u = −1.097340 − 0.604979I
3.87224 − 11.00000I 1.31825 + 8.05284I
u = 0.143789 + 0.548880I
0.05596 + 1.77225I 0.01088 − 4.04184I
u = 0.143789 − 0.548880I
0.05596 − 1.77225I 0.01088 + 4.04184I
5