![](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 = 0.173491 + 1.180500I
2.34143 + 0.79685I −9.60388 + 0.I
u = 0.173491 − 1.180500I
2.34143 − 0.79685I −9.60388 + 0.I
u = −0.684801 + 0.378128I
3.75424 + 9.27677I −8.25553 − 7.97070I
u = −0.684801 − 0.378128I
3.75424 − 9.27677I −8.25553 + 7.97070I
u = 0.621068 + 0.446082I
8.22635 − 2.04073I −3.94848 + 3.44114I
u = 0.621068 − 0.446082I
8.22635 + 2.04073I −3.94848 − 3.44114I
u = −0.201180 + 1.222030I
−1.22666 + 3.11008I −13.45910 − 3.92090I
u = −0.201180 − 1.222030I
−1.22666 − 3.11008I −13.45910 + 3.92090I
u = 0.668653 + 0.360931I
−1.01882 − 5.34555I −13.0771 + 6.6770I
u = 0.668653 − 0.360931I
−1.01882 + 5.34555I −13.0771 − 6.6770I
u = −0.531587 + 0.532708I
4.39098 − 5.19546I −6.57369 + 1.97435I
u = −0.531587 − 0.532708I
4.39098 + 5.19546I −6.57369 − 1.97435I
u = 0.221809 + 1.250810I
2.95833 − 7.06778I 0
u = 0.221809 − 1.250810I
2.95833 + 7.06778I 0
u = −0.628212 + 0.325456I
1.70221 + 1.51503I −10.15673 − 3.08750I
u = −0.628212 − 0.325456I
1.70221 − 1.51503I −10.15673 + 3.08750I
u = 0.051758 + 1.295040I
3.37520 − 1.28237I 0
u = 0.051758 − 1.295040I
3.37520 + 1.28237I 0
u = 0.491173 + 0.503611I
−0.35195 + 1.46105I −11.42087 − 0.49778I
u = 0.491173 − 0.503611I
−0.35195 − 1.46105I −11.42087 + 0.49778I
u = −0.558081 + 0.379170I
1.91831 + 1.74747I −7.74964 − 4.82540I
u = −0.558081 − 0.379170I
1.91831 − 1.74747I −7.74964 + 4.82540I
u = 0.651243 + 0.045491I
−1.01454 − 3.87980I −14.3154 + 4.0831I
u = 0.651243 − 0.045491I
−1.01454 + 3.87980I −14.3154 − 4.0831I
u = −0.645744
−4.92194 −19.0830
u = −0.075458 + 1.385010I
8.25893 + 3.09453I 0
u = −0.075458 − 1.385010I
8.25893 − 3.09453I 0
u = −0.314368 + 0.485643I
2.57671 + 1.81798I −7.01819 − 3.75999I
u = −0.314368 − 0.485643I
2.57671 − 1.81798I −7.01819 + 3.75999I
u = −0.23908 + 1.43322I
7.36078 + 4.69095I 0
5