12a
1002
(K12a
1002
)
A knot diagram
1
Linearized knot diagam
4 6 12 9 10 11 3 1 5 2 7 8
Solving Sequence
4,9
5 10
2,6
11 1 8 12 3 7
c
4
c
9
c
5
c
10
c
1
c
8
c
12
c
3
c
7
c
2
, c
6
, c
11
Ideals for irreducible components
2
of X
par
I
u
1
= h1.32196 × 10
269
u
109
− 6.64912 × 10
268
u
108
+ ··· + 2.22425 × 10
269
b − 9.95049 × 10
269
,
− 1.97255 × 10
271
u
109
+ 1.64430 × 10
271
u
108
+ ··· + 2.58013 × 10
271
a + 1.37216 × 10
273
,
u
110
− 2u
109
+ ··· + 142u + 29i
I
u
2
= h−9u
16
+ 5u
15
+ ··· + 19b + 25, 172u
16
+ 48u
15
+ ··· + 133a − 178, u
17
− u
16
+ ··· − 2u + 1i
I
u
3
= hb, a − 1, u + 1i
I
u
4
= hb + 1, a
3
− 2a
2
− a + 1, u + 1i
* 4 irreducible components of dim
C
= 0, with total 131 representations.
1
The image of knot diagram is generated by the software “Draw programme” developed by An-
drew Bartholomew(http://www.layer8.co.uk/maths/draw/index.htm#Running-draw), where we modi-
fied some parts for our purpose(https://github.com/CATsTAILs/LinksPainter).
2
All coefficients of polynomials are rational numbers. But the coefficients are sometimes approximated
in decimal forms when there is not enough margin.
1
I. I
u
1
= h1.32 × 10
269
u
109
− 6.65 × 10
268
u
108
+ · · · + 2.22 × 10
269
b − 9.95 ×
10
269
, −1.97 × 10
271
u
109
+ 1.64 × 10
271
u
108
+ · · · + 2.58 × 10
271
a + 1.37 ×
10
273
, u
110
− 2u
109
+ · · · + 142u + 29i
(i) Arc colorings
a
4
=
1
0
a
9
=
0
u
a
5
=
1
−u
2
a
10
=
u
−u
3
+ u
a
2
=
0.764513u
109
− 0.637292u
108
+ ··· − 278.114u − 53.1817
−0.594340u
109
+ 0.298937u
108
+ ··· + 45.4409u + 4.47364
a
6
=
−u
2
+ 1
u
4
− 2u
2
a
11
=
0.797741u
109
− 0.903180u
108
+ ··· − 224.858u − 15.9278
−0.0931427u
109
− 0.0484952u
108
+ ··· − 31.3015u − 2.78574
a
1
=
0.170173u
109
− 0.338354u
108
+ ··· − 232.673u − 48.7081
−0.594340u
109
+ 0.298937u
108
+ ··· + 45.4409u + 4.47364
a
8
=
0.655043u
109
− 1.14852u
108
+ ··· − 381.879u − 32.5792
0.735729u
109
− 0.404328u
108
+ ··· − 126.324u − 20.0634
a
12
=
0.503853u
109
− 0.796458u
108
+ ··· − 126.933u + 0.220543
−0.0221484u
109
+ 0.288965u
108
+ ··· + 100.879u + 14.9464
a
3
=
0.144433u
109
− 0.268865u
108
+ ··· − 245.630u − 49.3323
−0.286770u
109
+ 0.0910355u
108
+ ··· + 14.5909u − 0.821688
a
7
=
0.787523u
109
− 1.66427u
108
+ ··· − 416.345u − 34.1907
−0.0988489u
109
+ 0.179027u
108
+ ··· + 52.5901u + 8.61063
(ii) Obstruction class = −1
(iii) Cusp Shapes = −0.663649u
109
+ 1.82718u
108
+ ··· + 495.499u + 53.9213
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
110
+ 6u
109
+ ··· + 6916672u − 1324600
c
2
u
110
− 8u
108
+ ··· − 1232u − 167
c
3
u
110
− 3u
109
+ ··· − 71u + 1
c
4
, c
5
, c
9
u
110
+ 2u
109
+ ··· − 142u + 29
c
6
, c
11
u
110
− 2u
109
+ ··· + 58u + 1
c
7
u
110
+ u
109
+ ··· + 1532u − 40
c
8
, c
12
u
110
+ 2u
109
+ ··· − 455u + 73
c
10
u
110
+ 6u
109
+ ··· + 62u + 5
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
110
+ 54y
109
+ ··· − 68056508021984y + 1754565160000
c
2
y
110
− 16y
109
+ ··· − 1812078y + 27889
c
3
y
110
− 13y
109
+ ··· − 3915y + 1
c
4
, c
5
, c
9
y
110
− 122y
109
+ ··· − 73814y + 841
c
6
, c
11
y
110
− 86y
109
+ ··· − 814y + 1
c
7
y
110
− 5y
109
+ ··· − 2675984y + 1600
c
8
, c
12
y
110
− 90y
109
+ ··· − 177533y + 5329
c
10
y
110
+ 114y
108
+ ··· − 4464y + 25
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.561117 + 0.839392I
a = −0.303990 + 0.131847I
b = −0.421456 − 1.140830I
2.56229 − 4.55331I 0
u = −0.561117 − 0.839392I
a = −0.303990 − 0.131847I
b = −0.421456 + 1.140830I
2.56229 + 4.55331I 0
u = −0.927916 + 0.225382I
a = 0.664044 − 0.078712I
b = 1.003900 + 0.171942I
0.313706 + 0.175524I 0
u = −0.927916 − 0.225382I
a = 0.664044 + 0.078712I
b = 1.003900 − 0.171942I
0.313706 − 0.175524I 0
u = 0.959964 + 0.457834I
a = 1.44411 − 0.00057I
b = −0.378698 − 0.662224I
1.63508 − 0.94549I 0
u = 0.959964 − 0.457834I
a = 1.44411 + 0.00057I
b = −0.378698 + 0.662224I
1.63508 + 0.94549I 0
u = −0.316258 + 1.015460I
a = −0.371801 − 0.517839I
b = 0.327371 − 0.681355I
−1.22848 + 8.07799I 0
u = −0.316258 − 1.015460I
a = −0.371801 + 0.517839I
b = 0.327371 + 0.681355I
−1.22848 − 8.07799I 0
u = 1.06797
a = 0.610464
b = −1.19855
0.377278 0
u = −0.729463 + 0.787079I
a = 0.260649 − 0.445540I
b = 0.91205 + 1.10958I
0.03302 − 13.85620I 0
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.729463 − 0.787079I
a = 0.260649 + 0.445540I
b = 0.91205 − 1.10958I
0.03302 + 13.85620I 0
u = −0.567089 + 0.952408I
a = 0.498975 + 0.089888I
b = 0.239021 + 0.674220I
2.45698 − 1.04644I 0
u = −0.567089 − 0.952408I
a = 0.498975 − 0.089888I
b = 0.239021 − 0.674220I
2.45698 + 1.04644I 0
u = 0.530952 + 0.713864I
a = −0.171699 + 0.282459I
b = 0.927780 + 0.145012I
−4.74837 − 4.09767I 0
u = 0.530952 − 0.713864I
a = −0.171699 − 0.282459I
b = 0.927780 − 0.145012I
−4.74837 + 4.09767I 0
u = 0.773574 + 0.809008I
a = 0.356404 + 0.358372I
b = 0.741088 − 0.968332I
4.96862 + 8.04897I 0
u = 0.773574 − 0.809008I
a = 0.356404 − 0.358372I
b = 0.741088 + 0.968332I
4.96862 − 8.04897I 0
u = 0.513703 + 0.684899I
a = 0.142348 + 1.039150I
b = 0.900529 − 0.488273I
−4.77261 + 8.77139I 0
u = 0.513703 − 0.684899I
a = 0.142348 − 1.039150I
b = 0.900529 + 0.488273I
−4.77261 − 8.77139I 0
u = −0.663764 + 0.503751I
a = 1.221330 + 0.082009I
b = −0.057478 + 0.823623I
2.58165 − 0.03463I 0
6
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.663764 − 0.503751I
a = 1.221330 − 0.082009I
b = −0.057478 − 0.823623I
2.58165 + 0.03463I 0
u = −1.18213
a = 1.50672
b = −1.65419
−2.89730 0
u = 0.586598 + 0.524605I
a = −0.292439 − 0.789688I
b = −0.91004 + 1.31036I
−2.19521 + 5.10239I 0
u = 0.586598 − 0.524605I
a = −0.292439 + 0.789688I
b = −0.91004 − 1.31036I
−2.19521 − 5.10239I 0
u = −0.467339 + 0.592282I
a = −0.569458 + 0.168185I
b = −0.665733 − 1.241350I
2.02732 − 3.98332I 0
u = −0.467339 − 0.592282I
a = −0.569458 − 0.168185I
b = −0.665733 + 1.241350I
2.02732 + 3.98332I 0
u = −0.388667 + 0.644207I
a = 0.609698 − 0.868649I
b = 0.610278 + 0.381243I
0.34111 − 3.17260I 0
u = −0.388667 − 0.644207I
a = 0.609698 + 0.868649I
b = 0.610278 − 0.381243I
0.34111 + 3.17260I 0
u = −1.259520 + 0.213847I
a = 0.457879 − 0.631771I
b = 0.247105 + 0.397332I
1.79921 − 0.26763I 0
u = −1.259520 − 0.213847I
a = 0.457879 + 0.631771I
b = 0.247105 − 0.397332I
1.79921 + 0.26763I 0
7
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.705578
a = 0.686211
b = −1.81071
−4.29507 0
u = 0.197875 + 0.654372I
a = −0.167494 + 0.382578I
b = −0.76633 + 1.33681I
−0.64558 + 4.99505I 0
u = 0.197875 − 0.654372I
a = −0.167494 − 0.382578I
b = −0.76633 − 1.33681I
−0.64558 − 4.99505I 0
u = −0.522290 + 0.434471I
a = 0.191918 + 0.244207I
b = 0.240332 − 0.360798I
1.176650 − 0.617251I 0
u = −0.522290 − 0.434471I
a = 0.191918 − 0.244207I
b = 0.240332 + 0.360798I
1.176650 + 0.617251I 0
u = −0.553619 + 0.372557I
a = 0.96752 + 1.55292I
b = −1.005840 − 0.395070I
−3.87784 − 1.19491I 0. + 3.34499I
u = −0.553619 − 0.372557I
a = 0.96752 − 1.55292I
b = −1.005840 + 0.395070I
−3.87784 + 1.19491I 0. − 3.34499I
u = −0.609765 + 0.259275I
a = −1.74801 + 1.21596I
b = −0.304239 − 1.351150I
2.09953 − 6.85443I 6.48042 + 7.99330I
u = −0.609765 − 0.259275I
a = −1.74801 − 1.21596I
b = −0.304239 + 1.351150I
2.09953 + 6.85443I 6.48042 − 7.99330I
u = 1.345720 + 0.087315I
a = 0.62240 − 1.65565I
b = −0.800525 + 1.105590I
−0.36834 + 3.75700I 0
8
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 1.345720 − 0.087315I
a = 0.62240 + 1.65565I
b = −0.800525 − 1.105590I
−0.36834 − 3.75700I 0
u = 0.338412 + 0.532311I
a = 1.049160 − 0.832600I
b = −0.652477 − 0.520997I
−2.89784 − 1.43811I −1.19470 + 1.30013I
u = 0.338412 − 0.532311I
a = 1.049160 + 0.832600I
b = −0.652477 + 0.520997I
−2.89784 + 1.43811I −1.19470 − 1.30013I
u = 0.384390 + 0.472117I
a = −0.057955 − 0.709801I
b = −0.072193 + 1.060730I
−1.80335 + 4.26864I 0. − 8.46446I
u = 0.384390 − 0.472117I
a = −0.057955 + 0.709801I
b = −0.072193 − 1.060730I
−1.80335 − 4.26864I 0. + 8.46446I
u = −1.43088 + 0.15235I
a = 0.25860 + 2.38251I
b = −1.22902 − 2.26534I
4.56457 − 7.63869I 0
u = −1.43088 − 0.15235I
a = 0.25860 − 2.38251I
b = −1.22902 + 2.26534I
4.56457 + 7.63869I 0
u = −0.191657 + 0.512923I
a = −0.046361 + 0.638848I
b = −1.112870 − 0.427835I
−5.06856 − 1.65720I −7.16569 + 4.46058I
u = −0.191657 − 0.512923I
a = −0.046361 − 0.638848I
b = −1.112870 + 0.427835I
−5.06856 + 1.65720I −7.16569 − 4.46058I
u = 1.46115 + 0.08625I
a = −0.37508 + 1.49521I
b = −0.279736 − 0.529528I
3.59759 + 4.20792I 0
9
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 1.46115 − 0.08625I
a = −0.37508 − 1.49521I
b = −0.279736 + 0.529528I
3.59759 − 4.20792I 0
u = 1.46767
a = 0.691382
b = −1.86135
4.07909 0
u = −1.46887 + 0.01504I
a = 0.25445 − 1.71637I
b = −0.311834 + 0.911854I
4.77660 + 1.78089I 0
u = −1.46887 − 0.01504I
a = 0.25445 + 1.71637I
b = −0.311834 − 0.911854I
4.77660 − 1.78089I 0
u = 1.48030 + 0.19076I
a = −0.00626 + 1.52329I
b = 0.500378 − 0.750683I
6.44612 + 6.13114I 0
u = 1.48030 − 0.19076I
a = −0.00626 − 1.52329I
b = 0.500378 + 0.750683I
6.44612 − 6.13114I 0
u = 0.498224 + 0.071301I
a = 1.59392 + 0.46947I
b = 0.764381 − 1.087900I
4.99636 − 2.04697I 13.62932 + 3.40547I
u = 0.498224 − 0.071301I
a = 1.59392 − 0.46947I
b = 0.764381 + 1.087900I
4.99636 + 2.04697I 13.62932 − 3.40547I
u = −1.49656 + 0.05118I
a = 0.44142 + 1.68291I
b = −0.376738 − 1.055420I
4.71699 − 2.04167I 0
u = −1.49656 − 0.05118I
a = 0.44142 − 1.68291I
b = −0.376738 + 1.055420I
4.71699 + 2.04167I 0
10
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −1.49200 + 0.15868I
a = −0.31177 + 1.83486I
b = 0.11957 − 1.60278I
4.41842 − 6.58737I 0
u = −1.49200 − 0.15868I
a = −0.31177 − 1.83486I
b = 0.11957 + 1.60278I
4.41842 + 6.58737I 0
u = 1.51008 + 0.00548I
a = −0.76849 + 2.42077I
b = 1.57911 − 2.38327I
7.37201 − 5.32957I 0
u = 1.51008 − 0.00548I
a = −0.76849 − 2.42077I
b = 1.57911 + 2.38327I
7.37201 + 5.32957I 0
u = −1.52187 + 0.03609I
a = −0.105944 + 1.408030I
b = −0.98553 − 1.09051I
11.45720 − 3.34903I 0
u = −1.52187 − 0.03609I
a = −0.105944 − 1.408030I
b = −0.98553 + 1.09051I
11.45720 + 3.34903I 0
u = 1.51607 + 0.14680I
a = −0.307512 − 1.226570I
b = 0.284687 + 1.072820I
7.84229 + 2.83049I 0
u = 1.51607 − 0.14680I
a = −0.307512 + 1.226570I
b = 0.284687 − 1.072820I
7.84229 − 2.83049I 0
u = 1.52317 + 0.16202I
a = 0.19102 − 2.07830I
b = −1.06013 + 1.93180I
8.63374 + 6.61963I 0
u = 1.52317 − 0.16202I
a = 0.19102 + 2.07830I
b = −1.06013 − 1.93180I
8.63374 − 6.61963I 0
11
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −1.52037 + 0.21522I
a = −0.32083 − 1.59097I
b = 0.669087 + 0.872290I
1.89051 − 12.02380I 0
u = −1.52037 − 0.21522I
a = −0.32083 + 1.59097I
b = 0.669087 − 0.872290I
1.89051 + 12.02380I 0
u = −1.53845 + 0.01503I
a = −0.77655 − 1.50959I
b = 1.62064 + 1.47082I
11.94240 + 1.77338I 0
u = −1.53845 − 0.01503I
a = −0.77655 + 1.50959I
b = 1.62064 − 1.47082I
11.94240 − 1.77338I 0
u = 0.439368 + 0.125267I
a = −2.91173 − 0.94485I
b = −0.296311 + 0.914392I
4.78298 + 2.77580I 10.74262 − 4.23324I
u = 0.439368 − 0.125267I
a = −2.91173 + 0.94485I
b = −0.296311 − 0.914392I
4.78298 − 2.77580I 10.74262 + 4.23324I
u = 1.54191 + 0.10236I
a = 0.82257 − 1.60996I
b = −0.538138 + 1.028000I
3.13802 + 2.89810I 0
u = 1.54191 − 0.10236I
a = 0.82257 + 1.60996I
b = −0.538138 − 1.028000I
3.13802 − 2.89810I 0
u = −1.55010
a = 0.515231
b = −0.188672
2.86877 0
u = 0.314782 + 0.316499I
a = 0.04286 − 1.45370I
b = −0.719949 + 0.376921I
−1.29001 + 0.97335I −5.23681 − 1.57208I
12
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.314782 − 0.316499I
a = 0.04286 + 1.45370I
b = −0.719949 − 0.376921I
−1.29001 − 0.97335I −5.23681 + 1.57208I
u = 1.55565 + 0.07957I
a = −0.13471 − 1.87630I
b = −0.81156 + 1.54843I
9.40554 + 8.12188I 0
u = 1.55565 − 0.07957I
a = −0.13471 + 1.87630I
b = −0.81156 − 1.54843I
9.40554 − 8.12188I 0
u = 1.55716 + 0.08388I
a = 0.079050 + 1.135280I
b = 0.812119 − 1.044250I
10.06430 + 1.82526I 0
u = 1.55716 − 0.08388I
a = 0.079050 − 1.135280I
b = 0.812119 + 1.044250I
10.06430 − 1.82526I 0
u = 0.417614 + 0.127707I
a = 1.22900 + 2.26831I
b = −0.244550 − 0.614686I
−1.42070 − 2.02385I 5.86521 + 0.25795I
u = 0.417614 − 0.127707I
a = 1.22900 − 2.26831I
b = −0.244550 + 0.614686I
−1.42070 + 2.02385I 5.86521 − 0.25795I
u = −0.188293 + 0.392923I
a = 0.53118 − 3.05353I
b = 0.240285 − 0.019161I
−1.97408 − 2.72746I −13.6098 + 7.1286I
u = −0.188293 − 0.392923I
a = 0.53118 + 3.05353I
b = 0.240285 + 0.019161I
−1.97408 + 2.72746I −13.6098 − 7.1286I
u = −1.56070 + 0.15405I
a = 0.36566 + 2.37618I
b = −1.08051 − 2.20286I
4.99912 − 7.57034I 0
13
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −1.56070 − 0.15405I
a = 0.36566 − 2.37618I
b = −1.08051 + 2.20286I
4.99912 + 7.57034I 0
u = 1.57068 + 0.29738I
a = −0.14027 − 1.56575I
b = −0.71535 + 1.61442I
9.53813 + 8.77828I 0
u = 1.57068 − 0.29738I
a = −0.14027 + 1.56575I
b = −0.71535 − 1.61442I
9.53813 − 8.77828I 0
u = 1.60561
a = −1.37001
b = 2.25122
8.86339 0
u = 0.99962 + 1.25672I
a = −0.151543 + 0.000614I
b = −0.235450 + 0.608818I
3.59740 − 1.02869I 0
u = 0.99962 − 1.25672I
a = −0.151543 − 0.000614I
b = −0.235450 − 0.608818I
3.59740 + 1.02869I 0
u = 1.59888 + 0.26921I
a = −0.033918 + 1.188430I
b = 1.01703 − 1.06081I
9.89750 + 5.36352I 0
u = 1.59888 − 0.26921I
a = −0.033918 − 1.188430I
b = 1.01703 + 1.06081I
9.89750 − 5.36352I 0
u = −1.63257
a = 0.100653
b = 0.830742
10.9931 0
u = 1.61310 + 0.25881I
a = −0.30620 + 1.75307I
b = 1.26003 − 1.61640I
7.7665 + 17.7910I 0
14
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 1.61310 − 0.25881I
a = −0.30620 − 1.75307I
b = 1.26003 + 1.61640I
7.7665 − 17.7910I 0
u = −1.61784 + 0.25740I
a = −0.18698 − 1.54451I
b = 1.15091 + 1.41429I
12.8283 − 12.0395I 0
u = −1.61784 − 0.25740I
a = −0.18698 + 1.54451I
b = 1.15091 − 1.41429I
12.8283 + 12.0395I 0
u = −0.341173 + 0.081513I
a = 2.56530 − 0.70164I
b = 0.63053 + 1.90328I
0.98612 + 5.53424I 9.21361 − 3.89205I
u = −0.341173 − 0.081513I
a = 2.56530 + 0.70164I
b = 0.63053 − 1.90328I
0.98612 − 5.53424I 9.21361 + 3.89205I
u = −1.66219 + 0.28544I
a = 0.105978 + 1.138680I
b = −0.87100 − 1.21409I
11.98830 − 4.05097I 0
u = −1.66219 − 0.28544I
a = 0.105978 − 1.138680I
b = −0.87100 + 1.21409I
11.98830 + 4.05097I 0
u = 1.83473
a = 0.791840
b = −1.43197
5.03924 0
u = −0.159152
a = −8.05301
b = −1.10930
−1.59084 −6.53800
u = −2.00901
a = −0.107919
b = 0.383709
2.58600 0
15
II. I
u
2
= h−9u
16
+ 5u
15
+ · · · + 19b + 25, 172u
16
+ 48u
15
+ · · · + 133a −
178, u
17
− u
16
+ · · · − 2u + 1i
(i) Arc colorings
a
4
=
1
0
a
9
=
0
u
a
5
=
1
−u
2
a
10
=
u
−u
3
+ u
a
2
=
−1.29323u
16
− 0.360902u
15
+ ··· + 5.40602u + 1.33835
0.473684u
16
− 0.263158u
15
+ ··· − 0.578947u − 1.31579
a
6
=
−u
2
+ 1
u
4
− 2u
2
a
11
=
−0.924812u
16
− 0.676692u
15
+ ··· + 5.51128u − 3.24060
0.263158u
16
+ 0.631579u
15
+ ··· + 0.789474u + 1.15789
a
1
=
−0.819549u
16
− 0.624060u
15
+ ··· + 4.82707u + 0.0225564
0.473684u
16
− 0.263158u
15
+ ··· − 0.578947u − 1.31579
a
8
=
−0.120301u
16
+ 0.0827068u
15
+ ··· + 4.78195u − 2.01504
−0.390977u
16
− 0.481203u
15
+ ··· + 0.541353u + 0.451128
a
12
=
−0.353383u
16
− 0.819549u
15
+ ··· + 3.79699u + 1.33083
0.112782u
16
− 0.0150376u
15
+ ··· − 1.23308u − 0.360902
a
3
=
−0.819549u
16
− 0.624060u
15
+ ··· + 4.82707u + 1.02256
−0.0751880u
16
− 0.323308u
15
+ ··· − 0.511278u − 0.759398
a
7
=
8
7
u
16
+
5
7
u
15
+ ··· +
46
7
u −
34
7
−1.65414u
16
− 0.112782u
15
+ ··· − 0.248120u + 3.29323
(ii) Obstruction class = 1
(iii) Cusp Shapes =
47
19
u
16
−
81
19
u
15
+ ··· −
49
19
u −
63
19
16
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
17
− 6u
16
+ ··· − 44u + 8
c
2
u
17
− 2u
16
+ ··· − 8u + 1
c
3
u
17
− 2u
15
+ ··· − 4u − 1
c
4
, c
5
u
17
− u
16
+ ··· − 2u + 1
c
6
u
17
+ u
16
+ ··· − 13u + 1
c
7
u
17
+ 2u
15
+ ··· + 56u − 49
c
8
u
17
− u
16
+ ··· + 4u + 1
c
9
u
17
+ u
16
+ ··· − 2u − 1
c
10
u
17
+ 2u
16
+ ··· + 10u + 1
c
11
u
17
− u
16
+ ··· − 13u − 1
c
12
u
17
+ u
16
+ ··· + 4u − 1
17
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
17
+ 18y
16
+ ··· − 368y −64
c
2
y
17
+ 2y
16
+ ··· + 36y −1
c
3
y
17
− 4y
16
+ ··· − 22y
2
− 1
c
4
, c
5
, c
9
y
17
− 23y
16
+ ··· + 2y −1
c
6
, c
11
y
17
− 17y
16
+ ··· + 139y −1
c
7
y
17
+ 4y
16
+ ··· − 490y −2401
c
8
, c
12
y
17
− 13y
16
+ ··· + 18y −1
c
10
y
17
+ 18y
15
+ ··· + 10y −1
18
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.775884 + 0.786019I
a = 0.565091 − 0.244403I
b = 0.099687 − 0.637521I
3.52883 − 1.34033I 6.22025 + 4.59101I
u = 0.775884 − 0.786019I
a = 0.565091 + 0.244403I
b = 0.099687 + 0.637521I
3.52883 + 1.34033I 6.22025 − 4.59101I
u = 1.19074
a = 1.13854
b = −1.68727
−2.29823 7.51380
u = 0.188468 + 0.483306I
a = −1.106310 + 0.252673I
b = −0.13780 + 1.74335I
0.30417 + 5.98476I 0.88458 − 9.18662I
u = 0.188468 − 0.483306I
a = −1.106310 − 0.252673I
b = −0.13780 − 1.74335I
0.30417 − 5.98476I 0.88458 + 9.18662I
u = 1.49754 + 0.07202I
a = 0.36875 − 1.82402I
b = 0.082526 + 1.150800I
4.39708 + 3.90435I 6.82804 − 3.81833I
u = 1.49754 − 0.07202I
a = 0.36875 + 1.82402I
b = 0.082526 − 1.150800I
4.39708 − 3.90435I 6.82804 + 3.81833I
u = −1.50371 + 0.14008I
a = −0.13517 + 2.72302I
b = −0.68266 − 2.58485I
6.23453 − 8.10814I 7.34439 + 7.84548I
u = −1.50371 − 0.14008I
a = −0.13517 − 2.72302I
b = −0.68266 + 2.58485I
6.23453 + 8.10814I 7.34439 − 7.84548I
u = 1.50540 + 0.20269I
a = −0.16005 − 1.61021I
b = −0.72949 + 1.40654I
8.53803 + 5.44346I 7.21039 − 3.12363I
19
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 1.50540 − 0.20269I
a = −0.16005 + 1.61021I
b = −0.72949 − 1.40654I
8.53803 − 5.44346I 7.21039 + 3.12363I
u = −1.59626
a = −0.363429
b = 1.27870
12.1374 13.4350
u = 0.381978
a = 2.53018
b = −1.53551
−4.99201 −9.55970
u = −0.213418 + 0.264891I
a = −0.41873 + 3.65151I
b = −0.168737 − 0.514234I
−1.60221 − 2.77869I 7.58534 + 9.18091I
u = −0.213418 − 0.264891I
a = −0.41873 − 3.65151I
b = −0.168737 + 0.514234I
−1.60221 + 2.77869I 7.58534 − 9.18091I
u = −1.73839 + 0.20848I
a = 0.233778 + 0.276480I
b = −0.491484 − 0.171737I
2.49494 − 0.04707I −1.7675 + 22.1407I
u = −1.73839 − 0.20848I
a = 0.233778 − 0.276480I
b = −0.491484 + 0.171737I
2.49494 + 0.04707I −1.7675 − 22.1407I
20
III. I
u
3
= hb, a − 1, u + 1i
(i) Arc colorings
a
4
=
1
0
a
9
=
0
−1
a
5
=
1
−1
a
10
=
−1
0
a
2
=
1
0
a
6
=
0
−1
a
11
=
−1
0
a
1
=
1
0
a
8
=
1
−1
a
12
=
0
1
a
3
=
1
−1
a
7
=
1
−1
(ii) Obstruction class = −1
(iii) Cusp Shapes = 6
21
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
7
, c
10
u
c
2
, c
3
, c
4
c
5
, c
6
, c
8
c
9
, c
11
, c
12
u − 1
22
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
7
, c
10
y
c
2
, c
3
, c
4
c
5
, c
6
, c
8
c
9
, c
11
, c
12
y −1
23
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = −1.00000
a = 1.00000
b = 0
1.64493 6.00000
24
IV. I
u
4
= hb + 1, a
3
− 2a
2
− a + 1, u + 1i
(i) Arc colorings
a
4
=
1
0
a
9
=
0
−1
a
5
=
1
−1
a
10
=
−1
0
a
2
=
a
−1
a
6
=
0
−1
a
11
=
a − 1
−1
a
1
=
a − 1
−1
a
8
=
a
2
− 2a + 1
−a
a
12
=
a
2
− 3a + 1
a
2
− a − 1
a
3
=
a
−a − 1
a
7
=
a
2
− 2a + 1
−a
(ii) Obstruction class = 1
(iii) Cusp Shapes = −a
2
+ 6a − 9
25
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
9
, c
10
(u − 1)
3
c
2
u
3
+ 2u
2
− u − 1
c
3
, c
11
, c
12
u
3
− u
2
− 2u + 1
c
4
, c
5
(u + 1)
3
c
6
, c
8
u
3
+ u
2
− 2u − 1
c
7
u
3
26
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
4
, c
5
c
9
, c
10
(y −1)
3
c
2
y
3
− 6y
2
+ 5y −1
c
3
, c
6
, c
8
c
11
, c
12
y
3
− 5y
2
+ 6y −1
c
7
y
3
27
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
4
√
−1(vol +
√
−1CS) Cusp shape
u = −1.00000
a = −0.801938
b = −1.00000
0 −14.4550
u = −1.00000
a = 0.554958
b = −1.00000
0 −5.97820
u = −1.00000
a = 2.24698
b = −1.00000
0 −0.567040
28
V. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
u(u − 1)
3
(u
17
− 6u
16
+ ··· − 44u + 8)
· (u
110
+ 6u
109
+ ··· + 6916672u − 1324600)
c
2
(u − 1)(u
3
+ 2u
2
− u − 1)(u
17
− 2u
16
+ ··· − 8u + 1)
· (u
110
− 8u
108
+ ··· − 1232u − 167)
c
3
(u − 1)(u
3
− u
2
− 2u + 1)(u
17
− 2u
15
+ ··· − 4u − 1)
· (u
110
− 3u
109
+ ··· − 71u + 1)
c
4
, c
5
(u − 1)(u + 1)
3
(u
17
− u
16
+ ··· − 2u + 1)(u
110
+ 2u
109
+ ··· − 142u + 29)
c
6
(u − 1)(u
3
+ u
2
− 2u − 1)(u
17
+ u
16
+ ··· − 13u + 1)
· (u
110
− 2u
109
+ ··· + 58u + 1)
c
7
u
4
(u
17
+ 2u
15
+ ··· + 56u − 49)(u
110
+ u
109
+ ··· + 1532u − 40)
c
8
(u − 1)(u
3
+ u
2
− 2u − 1)(u
17
− u
16
+ ··· + 4u + 1)
· (u
110
+ 2u
109
+ ··· − 455u + 73)
c
9
((u − 1)
4
)(u
17
+ u
16
+ ··· − 2u − 1)(u
110
+ 2u
109
+ ··· − 142u + 29)
c
10
u(u − 1)
3
(u
17
+ 2u
16
+ ··· + 10u + 1)(u
110
+ 6u
109
+ ··· + 62u + 5)
c
11
(u − 1)(u
3
− u
2
− 2u + 1)(u
17
− u
16
+ ··· − 13u − 1)
· (u
110
− 2u
109
+ ··· + 58u + 1)
c
12
(u − 1)(u
3
− u
2
− 2u + 1)(u
17
+ u
16
+ ··· + 4u − 1)
· (u
110
+ 2u
109
+ ··· − 455u + 73)
29
VI. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
y(y −1)
3
(y
17
+ 18y
16
+ ··· − 368y −64)
· (y
110
+ 54y
109
+ ··· − 68056508021984y + 1754565160000)
c
2
(y −1)(y
3
− 6y
2
+ 5y −1)(y
17
+ 2y
16
+ ··· + 36y −1)
· (y
110
− 16y
109
+ ··· − 1812078y + 27889)
c
3
(y −1)(y
3
− 5y
2
+ 6y −1)(y
17
− 4y
16
+ ··· − 22y
2
− 1)
· (y
110
− 13y
109
+ ··· − 3915y + 1)
c
4
, c
5
, c
9
((y −1)
4
)(y
17
− 23y
16
+ ··· + 2y −1)
· (y
110
− 122y
109
+ ··· − 73814y + 841)
c
6
, c
11
(y −1)(y
3
− 5y
2
+ 6y −1)(y
17
− 17y
16
+ ··· + 139y −1)
· (y
110
− 86y
109
+ ··· − 814y + 1)
c
7
y
4
(y
17
+ 4y
16
+ ··· − 490y −2401)
· (y
110
− 5y
109
+ ··· − 2675984y + 1600)
c
8
, c
12
(y −1)(y
3
− 5y
2
+ 6y −1)(y
17
− 13y
16
+ ··· + 18y −1)
· (y
110
− 90y
109
+ ··· − 177533y + 5329)
c
10
y(y −1)
3
(y
17
+ 18y
15
+ ··· + 10y −1)
· (y
110
+ 114y
108
+ ··· − 4464y + 25)
30
