![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAArQAAAMECAIAAADB4SFMAAAACXBIWXMAABYlAAAWJQFJUiTwAAAL5ElEQVR42u3ZMWqdQQyFUSuk9P5Xel3fdANJYQbGRRDnLOAvhMT7HjNtP4AHM+OOsF1s8tsI4D/09fX1+fn5U1/b/esyMz/4Nb/E8PHxoUnBfztsF/zllxEAAOIAABAHAIA4AADEAQAgDgAAcQAAiAMAQBwAAOIAABAHAIA4AADEAQAgDgAAcQAAiAMAQBwAAOIAABAHAIA4AAAQBwDAP5IYAgBwTFtTgKcrGneE7WIVzwoAgDgAAMQBACAOAABxAACIAwBAHAAA4gAAEAcAgDgAAMQBACAOAABxAACIAwBAHAAA4gAAEAcAgDgAAMQBACAOAADEAQAgDgAAcQAA3EtiCADAMW1NAZ6uaNwRtotVPCsAAOIAABAHAIA4AADEAQAgDgAAcQAAiAMAQBwAAOIAABAHAIA4AADEAQAgDgAAcQAAiAMAQBwAAOIAABAHAIA4AAAQBwCAOAAAxAEAcC+JIQAAx7Q1BXi6onFH2C5W8awAAIgDAEAcAADiAAAQBwCAOAAAxAEAIA4AAHEAAIgDAEAcAADiAAAQBwCAOAAAxAEAIA4AAHEAAIgDAEAcAADiAABAHAAA4gAAEAcAwL0khgAAHNPWFODpisYdYbtYxbMCACAOAABxAACIAwBAHAAA4gAAEAcAgDgAAMQBACAOAABxAACIAwBAHAAA4gAAEAcAgDgAAMQBACAOAABxAACIAwAAcQAAiAMAQBwAAPeSGAIAcExbU4CnKxp3hO1iFc8KAIA4AADEAQAgDgAAcQAAiAMAQBwAAOIAABAHAIA4AADEAQAgDgAAcQAAiAMAQBwAAOIAABAHAIA4AADEAQAgDgAAxAEAIA4AAHEAANxLYggAwDFtTQGermjcEbaLVTwrAADiAAAQBwCAOAAAxAEAIA4AAHEAAIgDAEAcAADiAAAQBwCAOAAAxAEAIA4AAHEAAIgDAEAcAADiAAAQBwCAOAAAEAcAgDgAAMQBAHAviSEAAMe0NQV4uqJxR9guVvGsAACIAwBAHAAA4gAAEAcAgDgAAMQBACAOAABxAACIAwBAHAAA4gAAEAcAgDgAAMQBACAOAABxAACIAwBAHAAA4gAAQBwAAOIAABAHAMC9JIYAABzT1hTg6YrGHWG7WMWzAgAgDgAAcQAAiAMAQBwAAOIAABAHAIA4AADEAQAgDgAAcQAAiAMAQBwAAOIAABAHAIA4AADEAQAgDgAAcQAAiAMAAHEAAIgDAOBbSQwBADimrSnA0xWNO8J2sYpnBQBAHAAA4gAAEAcAgDgAAMQBACAOAABxAACIAwBAHAAA4gAAEAcAgDgAAMQBACAOAABxAACIAwBAHAAA4gAAEAcAAOIAABAHAIA4AADuJTEEAOCYtqYAT1c07gjbxSqeFQAAcQAAiAMAQBwAAOIAABAHAIA4AADEAQAgDgAAcQAAiAMAQBwAAOIAABAHAIA4AADEAQAgDgAAcQAAiAMAQBwAAIgDAEAcAADiAAC4l8QQAIBj2poCPF3RuCNsF6t4VgAAxAEAIA4AAHEAAIgDAEAcAADiAAAQBwCAOAAAxAEAIA4AAHEAAIgDAEAcAADiAAAQBwCAOAAAxAEAIA4AAHEAACAOAABxAACIAwDgXhJDAACOaWsK8HRF446wXaziWQEAEAcAgDgAAMQBACAOAABxAACIAwBAHAAA4gAAEAcAgDgAAMQBACAOAABxAACIAwBAHAAA4gAAEAcAgDgAAMQBAIA4AADEAQAgDgCAe0kMAQA4pq0pwNMVjTvCdrGKZwUAQBwAAOIAABAHAIA4AADEAQAgDgAAcQAAiAMAQBwAAOIAABAHAIA4AADEAQAgDgAAcQAAiAMAQBwAAOIAABAHAADiAAAQBwCAOAAA7iUxBADgmLamAE9XNO4I28UqnhUAAHEAAIgDAEAcAADiAAAQBwCAOAAAxAEAIA4AAHEAAIgDAEAcAADiAAAQBwCAOAAAxAEAIA4AAHEAAIgDAEAcAACIAwBAHAAA4gAAuJfEEACAY9qaAjxd0bgjbBereFYAAMQBACAOAABxAACIAwBAHAAA4gAAEAcAgDgAAMQBACAOAABxAACIAwBAHAAA4gAAEAcAgDgAAMQBACAOAABxAAAgDgAAcQAAiAMA4F4SQwAAjmlrCvB0ReOOsF2s4lkBABAHAIA4AADEAQAgDgAAcQAAiAMAQBwAAOIAABAHAIA4AADEAQAgDgAAcQAAiAMAQBwAAOIAABAHAIA4AADEAQCAOAAAxAEAIA4AgHtJDAEAOKatKcDTFY07wnaximcFAEAcAADiAAAQBwCAOAAAxAEAIA4AAHEAAIgDAEAcAADiAAAQBwCAOAAAxAEAIA4AAHEAAIgDAEAcAADiAAAQBwAA4gAAEAcAgDgAAO4lMQQA4Ji2pgBPVzTuCNvFKp4VAABxAACIAwBAHAAA4gAAEAcAgDgAAMQBACAOAABxAACIAwBAHAAA4gAAEAcAgDgAAMQBACAOAABxAACIAwBAHAAAiAMAQBwAAOIAALiXxBAAgGPamgI8XdG4I2wXq3hWAADEAQAgDgAAcQAAiAMAQBwAAOIAABAHAIA4AADEAQAgDgAAcQAAiAMAQBwAAOIAABAHAIA4AADEAQAgDgAAcQAAIA4AAHEAAHwriSEAAMe0NQV4uqJxR9guVvGsAACIAwBAHAAA4gAAEAcAgDgAAMQBACAOAABxAACIAwBAHAAA4gAAEAcAgDgAAMQBACAOAABxAACIAwBAHAAA4gAAQBwAAOIAABAHAMC9JIYAABzT1hTg6YrGHWG7WMWzAgAgDgAAcQAAiAMAQBwAAOIAABAHAIA4AADEAQAgDgAAcQAAiAMAQBwAAOIAABAHAIA4AADEAQAgDgAAcQAAiAMAAHEAAIgDAEAcAAD3khgCAHBMW1OApysad4TtYhXPCgCAOAAAxAEAIA4AAHEAAIgDAEAcAADiAAAQBwCAOAAAxAEAIA4AAHEAAIgDAEAcAADiAAAQBwCAOAAAxAEAIA4AAMQBACAOAABxAADcS2IIAMAxbU0Bnq5o3BG2i1U8KwAA4gAAEAcAgDgAAMQBACAOAABxAACIAwBAHAAA4gAAEAcAgDgAAMQBACAOAABxAACIAwBAHAAA4gAAEAcAgDgAABAHAIA4AADEAQBwL4khAADHtDUFeLqicUfYLlbxrAAAiAMAQBwAAOIAABAHAIA4AADEAQAgDgAAcQAAiAMAQBwAAOIAABAHAIA4AADEAQAgDgAAcQAAiAMAQBwAAOIAAEAcAADiAAAQBwDAvSSGAAAc09YU4OmKxh1hu1jFswIAIA4AAHEAAIgDAEAcAADiAAAQBwCAOAAAxAEAIA4AAHEAAIgDAEAcAADiAAAQBwCAOAAAxAEAIA4AAHEAAIgDAABxAACIAwBAHAAA95IYAgBwTFtTgKcrGneE7WIVzwoAgDgAAMQBACAOAABxAACIAwBAHAAA4gAAEAcAgDgAAMQBACAOAABxAACIAwBAHAAA4gAAEAcAgDgAAMQBACAOAADEAQAgDgAAcQAA3EtiCADAMW1NAZ6uaNwRtotVPCsAAOIAABAHAIA4AADEAQAgDgAAcQAAiAMAQBwAAOIAABAHAIA4AADEAQAgDgAAcQAAiAMAQBwAAOIAABAHAIA4AAAQBwCAOAAAxAEAcC+JIQAAx7Q1BXi6onFH2C5W8awAAIgDAEAcAADiAAAQBwCAOAAAxAEAIA4AAHEAAIgDAEAcAADiAAAQBwCAOAAAxAEAIA4AAHEAAIgDAEAcAADiAABAHAAA4gAAEAcAwL0khgAAHNPWFODpisYdYbtYxbMCACAOAABxAACIAwBAHAAA4gAAEAcAgDgAAMQBACAOAABxAACIAwBAHAAA4gAAEAcAgDgAAMQBACAOAABxAACIAwAAcQAAiAMAQBwAAPeSGAIAcExbU4CnKxp3hO1iFc8KAIA4AADEAQAgDgAAcQAAiAMAQBwAAOIAABAHAIA4AADEAQAgDgAAcQAAiAMAQBwAAOIAABAHAIA4AADEAQAgDgAAxAEAIA4AgG8lMQQA4PgDdByHANJxJ8sAAAAASUVORK5CYII=)
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.583032 + 0.813066I
3.26959 − 8.77818I −0.47164 + 8.68429I
u = −0.583032 − 0.813066I
3.26959 + 8.77818I −0.47164 − 8.68429I
u = 0.580211 + 0.794129I
5.10030 + 3.64576I 2.63542 − 3.97208I
u = 0.580211 − 0.794129I
5.10030 − 3.64576I 2.63542 + 3.97208I
u = 0.105740 + 0.954737I
−3.61435 − 0.81482I −11.81807 + 0.39125I
u = 0.105740 − 0.954737I
−3.61435 + 0.81482I −11.81807 − 0.39125I
u = 0.583734 + 0.745935I
5.23854 + 0.95699I 3.16051 − 3.05625I
u = 0.583734 − 0.745935I
5.23854 − 0.95699I 3.16051 + 3.05625I
u = −0.513490 + 0.784053I
0.12062 − 2.09029I −3.61559 + 4.04072I
u = −0.513490 − 0.784053I
0.12062 + 2.09029I −3.61559 − 4.04072I
u = 0.267008 + 1.029790I
−2.27337 + 5.68828I −7.21814 − 7.12378I
u = 0.267008 − 1.029790I
−2.27337 − 5.68828I −7.21814 + 7.12378I
u = −0.590577 + 0.723804I
3.52494 + 4.14809I 0.42761 − 2.02743I
u = −0.590577 − 0.723804I
3.52494 − 4.14809I 0.42761 + 2.02743I
u = −0.277374 + 0.855227I
−0.47179 − 1.53127I −3.18476 + 4.49987I
u = −0.277374 − 0.855227I
−0.47179 + 1.53127I −3.18476 − 4.49987I
u = 0.402583 + 1.057810I
−2.16744 + 5.71812I −4.90219 − 7.50071I
u = 0.402583 − 1.057810I
−2.16744 − 5.71812I −4.90219 + 7.50071I
u = −0.343840 + 1.124430I
−0.89986 − 1.11007I 0
u = −0.343840 − 1.124430I
−0.89986 + 1.11007I 0
u = 0.791530 + 0.188709I
0.29452 − 9.84540I −2.45493 + 7.04615I
u = 0.791530 − 0.188709I
0.29452 + 9.84540I −2.45493 − 7.04615I
u = −0.776617 + 0.194322I
2.34089 + 4.71915I 0.72234 − 2.89887I
u = −0.776617 − 0.194322I
2.34089 − 4.71915I 0.72234 + 2.89887I
u = 0.760501 + 0.155795I
−2.48885 − 2.55680I −6.01367 + 2.15869I
u = 0.760501 − 0.155795I
−2.48885 + 2.55680I −6.01367 − 2.15869I
u = −0.345622 + 1.179020I
−1.76168 + 1.10867I 0
u = −0.345622 − 1.179020I
−1.76168 − 1.10867I 0
u = −0.734385 + 0.223140I
3.02131 + 2.16148I 1.92228 − 2.64869I
u = −0.734385 − 0.223140I
3.02131 − 2.16148I 1.92228 + 2.64869I
5