![](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 = 0.655099 + 0.751397I
10.47210 + 2.42057I 5.00512 − 3.50428I
u = 0.655099 − 0.751397I
10.47210 − 2.42057I 5.00512 + 3.50428I
u = 0.457290 + 0.880807I
−1.50378 + 2.68816I −5.95162 − 3.22752I
u = 0.457290 − 0.880807I
−1.50378 − 2.68816I −5.95162 + 3.22752I
u = −0.495314 + 0.905747I
−0.91674 − 6.42453I −3.67057 + 9.87108I
u = −0.495314 − 0.905747I
−0.91674 + 6.42453I −3.67057 − 9.87108I
u = −0.379628 + 0.881690I
4.48646 − 0.62493I −2.71495 + 3.55329I
u = −0.379628 − 0.881690I
4.48646 + 0.62493I −2.71495 − 3.55329I
u = 0.520660 + 0.926121I
6.20074 + 8.92581I −0.06506 − 8.28337I
u = 0.520660 − 0.926121I
6.20074 − 8.92581I −0.06506 + 8.28337I
u = −0.075736 + 0.916828I
2.88611 − 4.18901I −5.84139 + 3.97616I
u = −0.075736 − 0.916828I
2.88611 + 4.18901I −5.84139 − 3.97616I
u = −0.558233 + 0.724774I
2.78376 − 2.11026I 4.66535 + 4.95546I
u = −0.558233 − 0.724774I
2.78376 + 2.11026I 4.66535 − 4.95546I
u = 0.027533 + 0.895789I
−3.76094 + 1.84552I −10.24133 − 4.26971I
u = 0.027533 − 0.895789I
−3.76094 − 1.84552I −10.24133 + 4.26971I
u = 0.672800 + 0.488934I
7.59840 − 4.48618I 3.71469 + 2.30966I
u = 0.672800 − 0.488934I
7.59840 + 4.48618I 3.71469 − 2.30966I
u = −0.608827 + 0.473439I
0.43015 + 2.25708I 0.48990 − 3.95946I
u = −0.608827 − 0.473439I
0.43015 − 2.25708I 0.48990 + 3.95946I
u = 0.855723 + 0.916416I
11.73180 + 3.17974I 1.84300 − 2.50377I
u = 0.855723 − 0.916416I
11.73180 − 3.17974I 1.84300 + 2.50377I
u = −0.888935 + 0.892951I
6.98756 − 1.09197I −1.86937 + 2.51379I
u = −0.888935 − 0.892951I
6.98756 + 1.09197I −1.86937 − 2.51379I
u = 0.902652 + 0.887567I
8.07252 − 2.80136I 0. + 3.37397I
u = 0.902652 − 0.887567I
8.07252 + 2.80136I 0. − 3.37397I
u = −0.913567 + 0.886340I
15.5582 + 5.3967I 3.71419 − 2.08485I
u = −0.913567 − 0.886340I
15.5582 − 5.3967I 3.71419 + 2.08485I
u = 0.885790 + 0.925568I
11.28050 + 3.27174I 4.41927 − 2.54057I
u = 0.885790 − 0.925568I
11.28050 − 3.27174I 4.41927 + 2.54057I
5