![](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 = −0.621935 + 0.782730I
−9.96990 + 2.39006I −4.17438 + 0.I
u = −0.621935 − 0.782730I
−9.96990 − 2.39006I −4.17438 + 0.I
u = 0.438527 + 0.907377I
−1.96094 − 0.80799I −3.24469 + 2.24299I
u = 0.438527 − 0.907377I
−1.96094 + 0.80799I −3.24469 − 2.24299I
u = −0.630886 + 0.761128I
−9.90322 − 7.24194I −3.95069 + 6.24276I
u = −0.630886 − 0.761128I
−9.90322 + 7.24194I −3.95069 − 6.24276I
u = 0.618288 + 0.768075I
−6.12298 + 2.40025I −0.83833 − 3.23354I
u = 0.618288 − 0.768075I
−6.12298 − 2.40025I −0.83833 + 3.23354I
u = −0.473047 + 1.008350I
−0.44679 − 2.73565I 0
u = −0.473047 − 1.008350I
−0.44679 + 2.73565I 0
u = 0.309687 + 1.086540I
−4.07179 + 0.35561I 0
u = 0.309687 − 1.086540I
−4.07179 − 0.35561I 0
u = 0.281866 + 0.810813I
−2.03136 − 0.82581I −5.70235 + 1.89666I
u = 0.281866 − 0.810813I
−2.03136 + 0.82581I −5.70235 − 1.89666I
u = 0.563966 + 0.645928I
−1.23878 + 4.99873I −1.02686 − 8.32445I
u = 0.563966 − 0.645928I
−1.23878 − 4.99873I −1.02686 + 8.32445I
u = −0.274490 + 1.109110I
−6.89845 + 3.68623I 0
u = −0.274490 − 1.109110I
−6.89845 − 3.68623I 0
u = −0.512226 + 1.042810I
0.00316 − 3.27794I 0
u = −0.512226 − 1.042810I
0.00316 + 3.27794I 0
u = 0.795174 + 0.261887I
−12.4090 − 9.0599I −4.87131 + 5.08954I
u = 0.795174 − 0.261887I
−12.4090 + 9.0599I −4.87131 − 5.08954I
u = 0.792169 + 0.247301I
−12.62010 + 0.73676I −5.26880 − 0.86219I
u = 0.792169 − 0.247301I
−12.62010 − 0.73676I −5.26880 + 0.86219I
u = −0.788814 + 0.256117I
−8.63854 + 4.09024I −1.84772 − 2.15081I
u = −0.788814 − 0.256117I
−8.63854 − 4.09024I −1.84772 + 2.15081I
u = −0.335883 + 1.123950I
−7.59429 − 3.78030I 0
u = −0.335883 − 1.123950I
−7.59429 + 3.78030I 0
u = 0.444654 + 1.090310I
−4.15081 + 3.62964I 0
u = 0.444654 − 1.090310I
−4.15081 − 3.62964I 0
5