![](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 = 0.184893 + 0.994464I
−1.51339 − 0.94191I −13.19182 + 4.87111I
u = 0.184893 − 0.994464I
−1.51339 + 0.94191I −13.19182 − 4.87111I
u = −0.326237 + 0.909164I
−0.68099 − 1.40662I −7.42529 + 4.24722I
u = −0.326237 − 0.909164I
−0.68099 + 1.40662I −7.42529 − 4.24722I
u = −0.704783 + 0.594687I
−11.28020 − 3.60891I −10.18311 + 3.00606I
u = −0.704783 − 0.594687I
−11.28020 + 3.60891I −10.18311 − 3.00606I
u = −0.178198 + 1.087930I
−6.59012 + 2.77027I −17.1418 − 2.7652I
u = −0.178198 − 1.087930I
−6.59012 − 2.77027I −17.1418 + 2.7652I
u = 0.416484 + 1.021060I
−2.94716 + 3.14297I −16.2536 − 6.2768I
u = 0.416484 − 1.021060I
−2.94716 − 3.14297I −16.2536 + 6.2768I
u = 0.682369 + 0.551619I
−1.05424 + 2.63533I −9.41238 − 3.91934I
u = 0.682369 − 0.551619I
−1.05424 − 2.63533I −9.41238 + 3.91934I
u = 0.782799 + 0.379135I
−12.41790 − 6.21468I −11.22155 + 2.89024I
u = 0.782799 − 0.379135I
−12.41790 + 6.21468I −11.22155 − 2.89024I
u = 0.176585 + 1.127330I
−17.3002 − 3.7251I −17.4761 + 1.6666I
u = 0.176585 − 1.127330I
−17.3002 + 3.7251I −17.4761 − 1.6666I
u = −0.755772 + 0.394629I
−1.86778 + 5.03167I −10.41788 − 4.02250I
u = −0.755772 − 0.394629I
−1.86778 − 5.03167I −10.41788 + 4.02250I
u = −0.606936 + 0.980785I
−12.42340 − 1.42472I −12.03958 + 2.60670I
u = −0.606936 − 0.980785I
−12.42340 + 1.42472I −12.03958 − 2.60670I
u = −0.695732 + 0.480590I
3.22968 − 0.39612I −4.26312 + 3.61739I
u = −0.695732 − 0.480590I
3.22968 + 0.39612I −4.26312 − 3.61739I
u = 0.722948 + 0.432712I
2.97485 − 2.70484I −5.59126 + 4.77948I
u = 0.722948 − 0.432712I
2.97485 + 2.70484I −5.59126 − 4.77948I
u = 0.575889 + 1.009940I
−2.41083 + 2.23503I −11.92132 − 1.73873I
u = 0.575889 − 1.009940I
−2.41083 − 2.23503I −11.92132 + 1.73873I
u = −0.421289 + 1.102850I
−8.91985 − 3.72236I −18.4297 + 4.1960I
u = −0.421289 − 1.102850I
−8.91985 + 3.72236I −18.4297 − 4.1960I
u = −0.578382 + 1.056610I
1.52744 − 4.51839I −7.10529 + 1.88338I
u = −0.578382 − 1.056610I
1.52744 + 4.51839I −7.10529 − 1.88338I
5