![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAr4AAAMECAIAAADWw7GFAAAACXBIWXMAABYlAAAWJQFJUiTwAAAMCUlEQVR42u3ZwY1cMQxEwaHh4+Yfae+5nYIMGTBWrArgHwgS8waath/gwsy4I2wme/w2Avhxvr+/v76+/tXX3v51mZl/+DW/xPD5fDQp+G+HzYS/8MsIAADpAABIBwBAOgAA0gEAkA4AgHQwAgBAOgAA0gEAkA4AgHQAAKQDACAdjAAAkA4AgHQAAKQDACAdAADpAABIByMAAKQDACAdAID/LokhAACHpq0pwNUVjTvCZrKIBwsAQDoAANIBAJAOAIB0AACkAwCAdAAApAMAIB0AAOkAAEgHAEA6AABIBwBAOgAA0gEAkA4AgHQAAKQDAIB0AACkAwAgHQAA6QAASAcA4FVJDAEAODRtTQGurmjcETaTRTxYAADSAQCQDgCAdAAApAMAIB0AAKQDACAdAADpAABIBwBAOgAA0gEAQDoAANIBAJAOAIB0AACkAwAgHQAApAMAIB0AAOkAAEgHAEA6AACvSmIIAMChaWsKcHVF446wmSziwQIAkA4AgHQAAKQDACAdAADpAAAgHQAA6QAASAcAQDoAANIBAJAOAADSAQCQDgCAdAAApAMAIB0AAOkAACAdAADpAABIBwBAOgAA0gEAeFUSQwAADk1bU4CrKxp3hM1kEQ8WAIB0AACkAwAgHQAA6QAASAcAAOkAAEgHAEA6AADSAQCQDgCAdAAAkA4AgHQAAKQDACAdAADpAABIBwAA6QAASAcAQDoAANIBAJAOAMCrkhgCAHBo2poCXF3RuCNsJot4sAAApAMAIB0AAOkAAEgHAEA6AABIBwBAOgAA0gEAkA4AgHQAAKQDAIB0AACkAwAgHQAA6QAASAcAQDoAAEgHAEA6AADSAQCQDgCAdAAAXpXEEACAQ9PWFODqisYdYTNZxIMFACAdAADpAABIBwBAOgAA0gEAQDoAANIBAJAOAIB0AACkAwAgHQAApAMAIB0AAOkAAEgHAEA6AADSAQBAOgAA0gEAkA4AgHQAAKQDAPCqJIYAAByatqYAV1c07gibySIeLAAA6QAASAcAQDoAANIBAJAOAADSAQCQDgCAdAAApAMAIB0AAOkAACAdAADpAABIBwBAOgAA0gEAkA4AANIBAJAOAIB0AACkAwAgHQCAVyUxBADg0LQ1Bbi6onFH2EwW8WABAEgHAEA6AADSAQCQDgCAdAAAkA4AgHQAAKQDACAdAADpAABIBwAA6QAASAcAQDoAANIBAJAOAIB0AACQDgCAdAAApAMAIB0AgB8liSEAAIemrSnA1RWNO8JmsogHCwBAOgAA0gEAkA4AgHQAAKQDAIB0AACkAwAgHQAA6QAASAcAQDoAAEgHAEA6AADSAQCQDgCAdAAApAMAgHQAAKQDACAdAADpAABIBwDgVUkMAQA4NG1NAa6uaNwRNpNFPFgAANIBAJAOAIB0AACkAwAgHQAApAMAIB0AAOkAAEgHAEA6AADSAQBAOgAA0gEAkA4AgHQAAKQDACAdAACkAwAgHQAA6QAASAcAQDoAAK9KYggAwKFpawpwdUXjjrCZLOLBAgCQDgCAdAAApAMAIB0AAOkAACAdAADpAABIBwBAOgAA0gEAkA4AANIBAJAOAIB0AACkAwAgHQAA6QAAIB0AAOkAAEgHAEA6AADSAQB4VRJDAAAOTVtTgKsrGneEzWQRDxYAgHQAAKQDACAdAADpAABIBwAA6QAASAcAQDoAANIBAJAOAIB0AACQDgCAdAAApAMAIB0AAOkAAEgHAADpAABIBwBAOgAA0gEAkA4AwKuSGAIAcGjamgJcXdG4I2wmi3iwAACkAwAgHQAA6QAASAcAQDoAAEgHAEA6AADSAQCQDgCAdAAApAMAgHQAAKQDACAdAADpAABIBwBAOgAASAcAQDoAANIBAJAOAIB0AABelcQQAIBD09YU4OqKxh1hM1nEgwUAIB0AAOkAAEgHAEA6AADSAQBAOgAA0gEAkA4AgHQAAKQDACAdAACkAwAgHQAA6QAASAcAQDoAANIBAEA6AADSAQCQDgCAdAAApAMA8KokhgAAHJq2pgBXVzTuCJvJIh4sAADpAABIBwBAOgAA0gEAkA4AANIBAJAOAIB0AACkAwAgHQAA6QAAIB0AAOkAAEgHAEA6AADSAQCQDgAA0gEAkA4AgHQAAKQDACAdAIBXJTEEAODQtDUFuLqicUfYTBbxYAEASAcAQDoAANIBAJAOAIB0AACQDgCAdAAApAMAIB0AAOkAAEgHAADpAABIBwBAOgAA0gEAkA4AgHQAAJAOAIB0AACkAwAgHQAA6QAAvCqJIQAAh6atKcDVFY07wmayiAcLAEA6AADSAQCQDgCAdAAApAMAgHQAAKQDACAdAADpAABIBwBAOgAASAcAQDoAANIBAJAOAIB0AACkAwCAdAAApAMAIB0AAOkAAEgHAOBVSQwBADg0bU0Brq5o3BE2k0U8WAAA0gEAkA4AgHQAAKQDACAdAACkAwAgHQAA6QAASAcAQDoAANIBAEA6AADSAQCQDgCAdAAApAMAIB0AAKQDACAdAADpAABIBwBAOgAAr0piCADAoWlrCnB1ReOOsJks4sECAJAOAIB0AACkAwAgHQAA6QAAIB0AAOkAAEgHAEA6AADSAQCQDgAA0gEAkA4AgHQAAKQDACAdAADpAAAgHQAA6QAASAcAQDoAAD9KEkMAAA5NW1OAqysad4TNZBEPFgCAdAAApAMAIB0AAOkAAEgHAADpAABIBwBAOgAA0gEAkA4AgHQAAJAOAIB0AACkAwAgHQAA6QAASAcAAOkAAEgHAEA6AADSAQCQDgDAq5IYAgBwaNqaAlxd0bgjbCaLeLAAAKQDACAdAADpAABIBwBAOgAASAcAQDoAANIBAJAOAIB0AACkAwCAdAAApAMAIB0AAOkAAEgHAEA6AABIBwBAOgAA0gEAkA4AgHQAAF6VxBAAgEPT1hTg6orGHWEzWcSDBQAgHQAA6QAASAcAQDoAANIBAEA6AADSAQCQDgCAdAAApAMAIB0AAKQDACAdAADpAABIBwBAOgAA0gEAQDoAANIBAJAOAIB0AACkAwDwqiSGAAAcmramAFdXNO4Im8kiHiwAAOkAAEgHAEA6AADSAQCQDgAA0gEAkA4AgHQAAKQDACAdAADpAAAgHQAA6QAASAcAQDoAANIBAJAOAADSAQCQDgCAdAAApAMAIB0AgFclMQQA4NC0NQW4uqJxR9hMFvFgAQBIBwBAOgAA0gEAkA4AgHQAAJAOAIB0AACkAwAgHQAA6QAASAcAAOkAAEgHAEA6AADSAQCQDgCAdAAAkA4AgHQAAKQDACAdAADpAAC8KokhAACHpq0pwNUVjTvCZrKIBwsAQDoAANIBAJAOAIB0AACkAwCAdAAApAMAIB0AAOkAAEgHAEA6AABIBwBAOgAA0gEAkA4AgHQAAKQDAIB0AACkAwAgHQAA6QAASAcA4FVJDAEAODRtTQGurmjcETaTRTxYAADSAQCQDgCAdAAApAMAIB0AAKQDACAdAADpAABIBwBAOgAA0gEAQDoAANIBAJAOAIB0AACkAwAgHQAApAMAIB0AAOkAAEgHAEA6AACvSmIIAMChaWsKcHVF446wmSziwQIAkA4AgHQAAKQDACAdAADpAAAgHQAA6QAASAcAQDoAANIBAJAOAADSAQCQDgCAdAAApAMAIB0AAOkAACAdAADpAABIBwBAOgAA0gEAeFUSQwAADk1bU4CrKxp3hM1kEQ8WAIB0AACkAwAgHQAA6QAASAcAAOkAAEgHAEA6AADSAQCQDgCAdAAAkA4AgHQAAKQDACAdAADpAABIBwAA6QAASAcAQDoAANIBAJAOAMCrkhgCAHBo2poCXF3RuCNsJot4sAAApAMAIB0AAOkAAEgHAEA6AABIBwBAOgAA0gEAkA4AgHQAAKQDAIB0AACkAwAgHQAA6QAASAcAQDoAAEgHAEA6AADSAQCQDgCAdAAAXpXEEACAQ9PWFODqisYdYTNZxIMFACAdAADpAABIBwBAOgAA0gEAQDoAANIBAJAOAIB0AACkAwAgHQAApAMAIB0AAOkAAEgHAEA6AADSAQBAOgAA0gEAkA4AgHQAAH6UJIYAABz6A4r5hwCgLPvSAAAAAElFTkSuQmCC)
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.635381 + 0.544778I
4.89318 + 8.99255I 2.54683 − 8.05726I
u = 0.635381 − 0.544778I
4.89318 − 8.99255I 2.54683 + 8.05726I
u = −0.637190 + 0.525254I
6.72503 − 3.70347I 5.40296 + 3.46584I
u = −0.637190 − 0.525254I
6.72503 + 3.70347I 5.40296 − 3.46584I
u = −0.646186 + 0.476105I
6.87083 − 0.63435I 5.86902 + 2.86167I
u = −0.646186 − 0.476105I
6.87083 + 0.63435I 5.86902 − 2.86167I
u = 0.651941 + 0.454511I
5.16060 − 4.64389I 3.40172 + 1.99685I
u = 0.651941 − 0.454511I
5.16060 + 4.64389I 3.40172 − 1.99685I
u = 0.587799 + 0.498634I
1.34506 + 2.00929I −0.48209 − 3.49556I
u = 0.587799 − 0.498634I
1.34506 − 2.00929I −0.48209 + 3.49556I
u = −0.330816 + 0.636061I
−2.01726 − 5.47617I −3.09870 + 9.17486I
u = −0.330816 − 0.636061I
−2.01726 + 5.47617I −3.09870 − 9.17486I
u = −0.144727 + 0.660329I
−3.03329 + 1.00909I −7.12564 + 0.28235I
u = −0.144727 − 0.660329I
−3.03329 − 1.00909I −7.12564 − 0.28235I
u = 0.301795 + 0.520951I
−0.018847 + 1.384110I 1.16696 − 5.74622I
u = 0.301795 − 0.520951I
−0.018847 − 1.384110I 1.16696 + 5.74622I
u = 0.03046 + 1.45212I
−4.91125 + 2.21769I 0
u = 0.03046 − 1.45212I
−4.91125 − 2.21769I 0
u = 0.19314 + 1.48235I
−1.12742 − 1.62626I 0
u = 0.19314 − 1.48235I
−1.12742 + 1.62626I 0
u = −0.19488 + 1.49761I
0.43075 − 3.64794I 0
u = −0.19488 − 1.49761I
0.43075 + 3.64794I 0
u = 0.379571 + 0.296373I
0.630271 + 1.053360I 5.17597 − 5.21367I
u = 0.379571 − 0.296373I
0.630271 − 1.053360I 5.17597 + 5.21367I
u = 0.17234 + 1.52286I
−5.33654 + 4.72378I 0
u = 0.17234 − 1.52286I
−5.33654 − 4.72378I 0
u = −0.448691 + 0.124937I
−0.48331 + 2.76150I 3.31371 − 3.04166I
u = −0.448691 − 0.124937I
−0.48331 − 2.76150I 3.31371 + 3.04166I
u = 0.06806 + 1.53625I
−6.95274 + 2.61432I 0
u = 0.06806 − 1.53625I
−6.95274 − 2.61432I 0
5