![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAtMAAAMECAIAAADy2j5FAAAACXBIWXMAABYlAAAWJQFJUiTwAAALsklEQVR42u3ZMW4CUAxEwWyUkvvflHrpUltyFBJr5gAUlg0P/bT9ABaSuCOsFgx9GQH8zZ+cH/y0w79ez+fz8XgYFPyn7zeXBv6YYrXg13waAQCgPAAA5QEAoDwAAOUBAKA8AADlAQAoDwAA5QEAKA8AAOUBACgPAEB5AAAoDwBAeQAAKA8AQHkAAMoDAEB5AADKAwBAeQAAAAB8S1tTgNUVxR1htWDKawsAoDwAAOUBAKA8AADlAQCgPAAA5QEAKA8AAOUBACgPAADlAQAoDwBAeQAAKA8AQHkAACgPAEB5AADKAwBAeQAAygMAQHkAAMoDAEB5AAAAALelrSnA6orijrBaMOW1BQBQHgCA8gAAUB4AgPIAAFAeAIDyAACUBwCA8gAAlAcAgPIAAJQHAKA8AACUBwCgPAAAlAcAoDwAAOUBAKA8AADlAQCgPAAA5QEAoDwAAACA29LWFGB1RXFHWC2Y8toCACgPAEB5AAAoDwBAeQAAKA8AQHkAAMoDAEB5AADKAwBAeQAAygMAUB4AAMoDAFAeAADKAwBQHgCA8gAAUB4AgPIAAFAeAIDyAABQHgAAAMBtaWsKsLqiuCOsFkx5bQEAlAcAoDwAAJQHAKA8AACUBwCgPAAA5QEAoDwAAOUBAKA8AADlAQAoDwAA5QEAKA8AAOUBACgPAEB5AAAoDwBAeQAAKA8AQHkAACgPAAAA4La0NQVYXVHcEVYLpry2AADKAwBQHgAAygMAUB4AAMoDAFAeAIDyAABQHgCA8gAAUB4AgPIAAJQHAIDyAACUBwCA8gAAlAcAoDwAAJQHAKA8AACUBwCgPAAAlAcAAABwW9qaAqyuKO4IqwVTXlsAAOUBACgPAADlAQAoDwAA5QEAKA8AQHkAACgPAEB5AAAoDwBAeQAAygMAQHkAAMoDAEB5AADKAwBQHgAAygMAUB4AAMoDAFAeAADKAwAAALgtbU0BVlcUd4TVgimvLQCA8gAAlAcAgPIAAJQHAIDyAACUBwCgPAAAlAcAoDwAAJQHAKA8AADlAQCgPAAA5QEAoDwAAOUBACgPAADlAQAoDwAA5QEAKA8AAOUBAAAA3Ja2pgCrK4o7wmrBlNcWAEB5AADKAwBAeQAAygMAQHkAAMoDAFAeAADKAwBQHgAAygMAUB4AgPIAAFAeAIDyAABQHgCA8gAAlAcAgPIAAJQHAIDyAACUBwAAAMA7pK0pwOqK4o6wWjDltQUAUB4AgPIAAFAeAIDyAABQHgCA8gAAlAcAgPIAAJQHAIDyAACUBwCgPAAAlAcAoDwAAJQHAKA8AADlAQCgPAAA5QEAoDwAAOUBAKA8AAAAgNvS1hRgdUVxR1gtmPLaAgAoDwBAeQAAKA8AQHkAACgPAEB5AADKAwBAeQAAygMAQHkAAMoDAFAeAADKAwBQHgAAygMAUB4AgPIAAFAeAIDyAABQHgCA8gAAUB4AAADAbWlrCrC6orgjrBZMeW0BAJQHAKA8AACUBwCgPAAAlAcAoDwAAOUBAKA8AADlAQCgPAAA5QEAKA8AAOUBACgPAADlAQAoDwBAeQAAKA8AQHkAACgPAEB5AAAoDwAAAOC2tDUFWF1R3BFWC6a8tgAAygMAUB4AAMoDAFAeAADKAwBQHgCA8gAAUB4AgPIAAFAeAIDyAACUBwCA8gAAlAcAgPIAAJQHAKA8AACUBwCgPAAAlAcAoDwAAJQHAAAAcFvamgKsrijuCKsFU15bAADlAQAoDwAA5QEAKA8AAOUBACgPAEB5AAAoDwBAeQAAKA8AQHkAAMoDAEB5AADKAwBAeQAAygMAUB4AAMoDAFAeAADKAwBQHgAAygMAAAC4LW1NAVZXFHeE1YIpry0AgPIAAJQHAIDyAACUBwCA8gAAlAcAoDwAAJQHAKA8AACUBwCgPAAA5QEAoDwAAOUBAKA8AADlAQAoDwAA5QEAKA8AAOUBACgPAADlAQAAANyWtqYAqyuKO8JqwZTXFgBAeQAAygMAQHkAAMoDAEB5AADKAwBQHgAAygMAUB4AAMoDAFAeAIDyAABQHgCA8gAAUB4AgPIAAJQHAIDyAACUBwCA8gAAlAcAgPIAAAAAbktbU4DVFcUdYbVgymsLAKA8AADlAQCgPAAA5QEAoDwAAOUBACgPAADlAQAoDwAA5QEAKA8AQHkAACgPAEB5AAAoDwBAeQAAygMAQHkAAMoDAEB5AADKAwBAeQAAAAC3pa0pwOqK4o6wWjDltQUAUB4AgPIAAFAeAIDyAABQHgCA8gAAlAcAgPIAAJQHAIDyAACUBwCgPAAAlAcAoDwAAJQHAKA8AADlAQCgPAAA5QEAoDwAAOUBAKA8AAAAgNvS1hRgdUVxR1gtmPLaAgAoDwBAeQAAKA8AQHkAACgPAEB5AADKAwBAeQAAygMAQHkAAMoDAFAeAADKAwBQHgAAygMAUB4AgPIAAFAeAIDyAABQHgCA8gAAUB4AAADAbWlrCrC6orgjrBZMeW0BAJQHAKA8AACUBwCgPAAAlAcAoDwAAOUBAKA8AADlAQCgPAAA5QEAKA8AAOUBACgPAADlAQAoDwBAeQAAKA8AQHkAACgPAEB5AAAAALxD2poCrK4o7girBVNeWwAA5QEAKA8AAOUBACgPAADlAQAoDwBAeQAAKA8AQHkAACgPAEB5AADKAwBAeQAAygMAQHkAAMoDAFAeAADKAwBQHgAAygMAUB4AAMoDAAAAuC1tTQFWVxR3hNWCKa8tAIDyAACUBwCA8gAAlAcAgPIAAJQHAKA8AACUBwCgPAAAlAcAoDwAAOUBAKA8AADlAQCgPAAA5QEAKA8AAOUBACgPAADlAQAoDwAA5QEAAADclramAKsrijvCasGU1xYAQHkAAMoDAEB5AADKAwBAeQAAygMAUB4AAMoDAFAeAADKAwBQHgCA8gAAUB4AgPIAAFAeAIDyAACUBwCA8gAAlAcAgPIAAJQHAIDyAAAAAG5LW1OA1RXFHWG1YMprCwCgPAAA5QEAoDwAAOUBAKA8AADlAQAoDwAA5QEAKA8AAOUBACgPAEB5AAAoDwBAeQAAKA8AQHkAAMoDAEB5AADKAwBAeQAAygMAQHkAAAAAt6WtKcDqiuKOsFow5bUFAFAeAIDyAABQHgCA8gAAUB4AgPIAAJQHAIDyAACUBwCA8gAAlAcAoDwAAJQHAKA8AACUBwCgPAAA5QEAoDwAAOUBAKA8AADlAQCgPAAAAIDb0tYUYHVFcUdYLZjy2gIAKA8AQHkAACgPAEB5AAAoDwBAeQAAygMAQHkAAMoDAEB5AADKAwBQHgAAygMAUB4AAMoDAFAeAIDyAABQHgCA8gAAUB4AgPIAAFAeAAAAwG1pawqwuqK4I6wWTHltAQCUBwCgPAAAlAcAoDwAAJQHAKA8AADlAQCgPAAA5QEAoDwAAOUBACgPAADlAQAoDwAA5QEAKA8AQHkAACgPAEB5AAAoDwBAeQAAKA8AAADgtrQ1BVhdUdwRVgumvLYAAMoDAFAeAADKAwBQHgAAygMAUB4AgPIAAFAeAIDyAABQHgCA8gAAlAcAgPIAAJQHAIDyAACUBwCgPAAAlAcAoDwAAJQHAKA8AACUBwAAAHBb2poCrK4o7girBVNeWwAA5QEAKA8AAOUBACgPAADlAQAoDwBAeQAAKA8AQHkAACgPAEB5AADKAwBAeQAAygMAQHkAAMoDAFAeAADKAwBQHgAAygMAUB4AAMoDAAAAuC1tTQFWVxR3hNWCKa8tAIDyAACUBwCA8gAAlAcAgPIAAJQHAKA8AACUBwCgPAAAlAcAoDwAAOUBAKA8AADlAQCgPAAA5QEAKA8AAOUBACgPAADlAQAoDwAA5QEAAADclramAKsrijvCasGU1xYAQHkAAMoDAEB5AADKAwBAeQAAygMAUB4AAMoDAFAeAADKAwBQHgCA8gAAUB4AgPIAAFAeAIDyAACUBwCA8gAAlAcAgPIAAJQHAAAAwDu8ALuaLlwB18wVAAAAAElFTkSuQmCC)
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.827985 + 0.442924I
−0.41301 − 6.75076I −7.52201 + 10.31083I
u = 0.827985 − 0.442924I
−0.41301 + 6.75076I −7.52201 − 10.31083I
u = −0.819369 + 0.722392I
3.00560 + 2.68433I −6.38966 − 3.26103I
u = −0.819369 − 0.722392I
3.00560 − 2.68433I −6.38966 + 3.26103I
u = −0.748025 + 0.473052I
1.37372 + 2.37460I −2.95509 − 5.64025I
u = −0.748025 − 0.473052I
1.37372 − 2.37460I −2.95509 + 5.64025I
u = −0.781691 + 0.815109I
6.78620 − 3.64652I −2.24620 + 2.51117I
u = −0.781691 − 0.815109I
6.78620 + 3.64652I −2.24620 − 2.51117I
u = 0.812484 + 0.804258I
8.37825 − 1.52833I 0.15922 + 2.57141I
u = 0.812484 − 0.804258I
8.37825 + 1.52833I 0.15922 − 2.57141I
u = 0.876029 + 0.769070I
8.16101 − 4.25998I −0.39518 + 3.37976I
u = 0.876029 − 0.769070I
8.16101 + 4.25998I −0.39518 − 3.37976I
u = −0.899548 + 0.751693I
6.38574 + 9.40965I −3.35814 − 8.21027I
u = −0.899548 − 0.751693I
6.38574 − 9.40965I −3.35814 + 8.21027I
u = 0.764387 + 0.291862I
−2.05998 − 0.57416I −12.32788 + 4.08784I
u = 0.764387 − 0.291862I
−2.05998 + 0.57416I −12.32788 − 4.08784I
u = −0.796033 + 0.081424I
−3.02472 + 3.09558I −15.0272 − 5.6835I
u = −0.796033 − 0.081424I
−3.02472 − 3.09558I −15.0272 + 5.6835I
u = −0.569720 + 0.552671I
1.96860 + 1.39447I −0.18894 − 3.96327I
u = −0.569720 − 0.552671I
1.96860 − 1.39447I −0.18894 + 3.96327I
u = 0.446314 + 0.583151I
0.82978 + 3.00776I −2.26446 − 2.93479I
u = 0.446314 − 0.583151I
0.82978 − 3.00776I −2.26446 + 2.93479I
u = 0.954730 + 0.937736I
13.9541 − 3.4440I −5.66125 + 2.21477I
u = 0.954730 − 0.937736I
13.9541 + 3.4440I −5.66125 − 2.21477I
u = 0.947637 + 0.954402I
18.2191 + 3.9502I −2.24732 − 2.32186I
u = 0.947637 − 0.954402I
18.2191 − 3.9502I −2.24732 + 2.32186I
u = −0.953750 + 0.951945I
−19.4865 + 1.6085I 0. − 2.11449I
u = −0.953750 − 0.951945I
−19.4865 − 1.6085I 0. + 2.11449I
u = −0.967443 + 0.943280I
−19.5330 + 5.3455I 0. − 2.28570I
u = −0.967443 − 0.943280I
−19.5330 − 5.3455I 0. + 2.28570I
5