![](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 = −0.902903 + 0.325577I
−5.89300 − 4.56154I −5.05236 + 4.07430I
u = −0.902903 − 0.325577I
−5.89300 + 4.56154I −5.05236 − 4.07430I
u = 0.880468 + 0.335436I
−9.82971 − 0.24622I −8.39004 − 1.01660I
u = 0.880468 − 0.335436I
−9.82971 + 0.24622I −8.39004 + 1.01660I
u = −1.06813
−1.03647 −8.72440
u = −0.856904 + 0.340697I
−5.78926 + 5.03648I −4.83082 − 1.94671I
u = −0.856904 − 0.340697I
−5.78926 − 5.03648I −4.83082 + 1.94671I
u = 1.124900 + 0.134876I
2.48134 + 3.32280I −4.00000 − 4.36423I
u = 1.124900 − 0.134876I
2.48134 − 3.32280I −4.00000 + 4.36423I
u = −0.235766 + 0.759825I
−7.79875 − 9.11345I −7.48289 + 6.59020I
u = −0.235766 − 0.759825I
−7.79875 + 9.11345I −7.48289 − 6.59020I
u = 0.226258 + 0.761773I
−11.92180 + 4.31858I −11.15925 − 3.68436I
u = 0.226258 − 0.761773I
−11.92180 − 4.31858I −11.15925 + 3.68436I
u = −0.215763 + 0.760894I
−8.06841 + 0.51576I −8.00781 + 0.53421I
u = −0.215763 − 0.760894I
−8.06841 − 0.51576I −8.00781 − 0.53421I
u = 0.257995 + 0.660448I
1.16289 + 6.09519I −4.37920 − 8.32748I
u = 0.257995 − 0.660448I
1.16289 − 6.09519I −4.37920 + 8.32748I
u = −0.206282 + 0.659987I
−3.14927 − 2.95888I −11.20613 + 6.09343I
u = −0.206282 − 0.659987I
−3.14927 + 2.95888I −11.20613 − 6.09343I
u = 0.131114 + 0.652792I
−0.354349 − 0.264714I −8.41042 − 0.51951I
u = 0.131114 − 0.652792I
−0.354349 + 0.264714I −8.41042 + 0.51951I
u = 1.339110 + 0.139421I
3.66804 + 0.85390I 0
u = 1.339110 − 0.139421I
3.66804 − 0.85390I 0
u = −1.341180 + 0.248138I
4.28060 − 2.99425I 0
u = −1.341180 − 0.248138I
4.28060 + 2.99425I 0
u = −1.354380 + 0.201765I
4.54456 − 3.46632I 0
u = −1.354380 − 0.201765I
4.54456 + 3.46632I 0
u = −1.390510 + 0.124734I
8.28822 + 1.34028I 0
u = −1.390510 − 0.124734I
8.28822 − 1.34028I 0
u = 1.375440 + 0.261240I
1.86998 + 6.31343I 0
5