![](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 = −0.384157 + 0.916651I
−0.08016 − 6.28454I 0. + 10.45893I
u = −0.384157 − 0.916651I
−0.08016 + 6.28454I 0. − 10.45893I
u = −0.359432 + 0.963246I
−3.28646 − 6.49921I 0
u = −0.359432 − 0.963246I
−3.28646 + 6.49921I 0
u = 0.181375 + 0.954789I
−8.18742 + 3.05866I −13.52379 − 3.93661I
u = 0.181375 − 0.954789I
−8.18742 − 3.05866I −13.52379 + 3.93661I
u = 0.344445 + 0.969057I
−7.25591 + 2.51870I 0
u = 0.344445 − 0.969057I
−7.25591 − 2.51870I 0
u = 0.151839 + 0.956150I
−7.61091 − 5.67836I −12.50459 + 3.10607I
u = 0.151839 − 0.956150I
−7.61091 + 5.67836I −12.50459 − 3.10607I
u = 0.364368 + 0.973455I
−6.39842 + 11.27770I 0
u = 0.364368 − 0.973455I
−6.39842 − 11.27770I 0
u = 0.387418 + 0.873983I
0.51259 + 2.09295I −1.92214 − 3.70673I
u = 0.387418 − 0.873983I
0.51259 − 2.09295I −1.92214 + 3.70673I
u = −0.162879 + 0.940953I
−4.40542 + 1.03814I −9.57563 + 0.I
u = −0.162879 − 0.940953I
−4.40542 − 1.03814I −9.57563 + 0.I
u = −0.279119 + 0.907947I
−3.80142 − 2.48917I −13.3851 + 5.1983I
u = −0.279119 − 0.907947I
−3.80142 + 2.48917I −13.3851 − 5.1983I
u = −0.735571 + 0.878240I
−2.84182 + 1.57464I 0
u = −0.735571 − 0.878240I
−2.84182 − 1.57464I 0
u = −0.529170 + 0.664612I
−3.03277 + 2.04853I −4.86577 + 0.18647I
u = −0.529170 − 0.664612I
−3.03277 − 2.04853I −4.86577 − 0.18647I
u = −0.099359 + 0.832534I
−1.57015 + 1.62706I −8.90717 − 3.48380I
u = −0.099359 − 0.832534I
−1.57015 − 1.62706I −8.90717 + 3.48380I
u = 0.328773 + 0.768032I
−0.30487 + 1.47590I −2.27756 − 4.79967I
u = 0.328773 − 0.768032I
−0.30487 − 1.47590I −2.27756 + 4.79967I
u = 0.752498 + 0.891905I
0.60818 + 2.85389I 0
u = 0.752498 − 0.891905I
0.60818 − 2.85389I 0
u = −0.743580 + 0.908600I
−2.94895 − 7.20020I 0
u = −0.743580 − 0.908600I
−2.94895 + 7.20020I 0
5