12n
0816
(K12n
0816
)
A knot diagram
1
Linearized knot diagam
4 6 12 7 9 2 1 12 5 8 4 10
Solving Sequence
10,12 1,5
9 6 8 7 4 3 2 11
c
12
c
9
c
5
c
8
c
7
c
4
c
3
c
2
c
11
c
1
, c
6
, c
10
Ideals for irreducible components
2
of X
par
I
u
1
= h1.31329 × 10
500
u
97
+ 8.98067 × 10
500
u
96
+ ··· + 8.24393 × 10
497
b + 8.17734 × 10
500
,
9.50553 × 10
500
u
97
+ 6.50354 × 10
501
u
96
+ ··· + 8.24393 × 10
497
a + 5.99735 × 10
501
, u
98
+ 7u
97
+ ··· + 23u + 1i
I
u
2
= h−6.44895 × 10
46
u
35
+ 5.28645 × 10
47
u
34
+ ··· + 1.75776 × 10
44
b + 1.79988 × 10
46
,
− 2.46365 × 10
46
u
35
+ 2.08684 × 10
47
u
34
+ ··· + 1.75776 × 10
44
a + 5.21540 × 10
46
,
u
36
− 9u
35
+ ··· − 14u + 1i
I
u
3
= h−u
3
+ 4u
2
+ 2b − 4u − 3, u
3
− 4u
2
+ a + 5u, u
4
− 3u
3
+ 2u
2
+ 3u + 1i
I
u
4
= hb
2
− b + 1, a, u − 1i
* 4 irreducible components of dim
C
= 0, with total 140 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
= h1.31 × 10
500
u
97
+ 8.98 × 10
500
u
96
+ · · · + 8.24 × 10
497
b + 8.18 ×
10
500
, 9.51 × 10
500
u
97
+ 6.50 × 10
501
u
96
+ · · · + 8.24 × 10
497
a + 6.00 ×
10
501
, u
98
+ 7u
97
+ · · · + 23u + 1i
(i) Arc colorings
a
10
=
0
u
a
12
=
1
0
a
1
=
1
−u
2
a
5
=
−1153.03u
97
− 7888.88u
96
+ ··· − 121463.u − 7274.87
−159.304u
97
− 1089.37u
96
+ ··· − 16618.9u − 991.922
a
9
=
103.914u
97
+ 710.905u
96
+ ··· + 10896.2u + 647.011
−291.954u
97
− 1997.45u
96
+ ··· − 30797.8u − 1846.86
a
6
=
−198.268u
97
− 1356.61u
96
+ ··· − 20919.8u − 1252.01
29.8923u
97
+ 204.433u
96
+ ··· + 3152.92u + 189.763
a
8
=
395.868u
97
+ 2708.36u
96
+ ··· + 41694.0u + 2493.87
−291.954u
97
− 1997.45u
96
+ ··· − 30797.8u − 1846.86
a
7
=
113.875u
97
+ 779.009u
96
+ ··· + 11942.8u + 709.727
−284.872u
97
− 1949.02u
96
+ ··· − 30054.1u − 1802.26
a
4
=
−576.546u
97
− 3943.09u
96
+ ··· − 60413.0u − 3613.27
59.4127u
97
+ 406.296u
96
+ ··· + 6243.88u + 375.722
a
3
=
−517.134u
97
− 3536.80u
96
+ ··· − 54169.1u − 3237.55
59.4127u
97
+ 406.296u
96
+ ··· + 6243.88u + 375.722
a
2
=
−606.313u
97
− 4147.30u
96
+ ··· − 63505.5u − 3796.33
124.345u
97
+ 850.757u
96
+ ··· + 13140.3u + 789.560
a
11
=
535.816u
97
+ 3668.17u
96
+ ··· + 56813.0u + 3403.58
−136.440u
97
− 933.779u
96
+ ··· − 14503.0u − 872.106
(ii) Obstruction class = −1
(iii) Cusp Shapes = −468.986u
97
− 3203.64u
96
+ ··· − 48507.0u − 2901.05
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
98
− 7u
97
+ ··· − 25602u + 2657
c
2
, c
6
u
98
− 3u
97
+ ··· − 216906u + 13157
c
3
, c
11
u
98
+ 2u
97
+ ··· + 26608u + 508
c
4
u
98
− 5u
97
+ ··· − 433u + 23
c
5
, c
9
u
98
+ 42u
96
+ ··· + 140656u + 34228
c
7
u
98
− 7u
97
+ ··· − 2048u + 64
c
8
u
98
+ 20u
96
+ ··· − 26534568u + 43283857
c
10
u
98
+ 12u
97
+ ··· − 2720881u + 1109443
c
12
u
98
+ 7u
97
+ ··· + 23u + 1
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
98
− 55y
97
+ ··· − 751130346y + 7059649
c
2
, c
6
y
98
+ 103y
97
+ ··· − 27972220618y + 173106649
c
3
, c
11
y
98
− 94y
97
+ ··· + 1054871872y + 258064
c
4
y
98
+ 9y
97
+ ··· − 26167y + 529
c
5
, c
9
y
98
+ 84y
97
+ ··· + 44846020736y + 1171555984
c
7
y
98
− 3y
97
+ ··· − 30720y + 4096
c
8
y
98
+ 40y
97
+ ··· + 141207617788579830y + 1873492276796449
c
10
y
98
+ 36y
97
+ ··· + 14973133605321y + 1230863770249
c
12
y
98
− 21y
97
+ ··· − 79y + 1
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.297779 + 0.962394I
a = 1.022180 + 0.169332I
b = 1.58919 − 0.84969I
−2.44786 + 2.28046I 0
u = 0.297779 − 0.962394I
a = 1.022180 − 0.169332I
b = 1.58919 + 0.84969I
−2.44786 − 2.28046I 0
u = 1.010880 + 0.161137I
a = −0.213420 − 1.269340I
b = −0.21564 − 1.61424I
−7.52661 + 5.04383I 0
u = 1.010880 − 0.161137I
a = −0.213420 + 1.269340I
b = −0.21564 + 1.61424I
−7.52661 − 5.04383I 0
u = −0.621792 + 0.819445I
a = 0.582418 + 0.765895I
b = 0.344815 + 0.764548I
−8.25028 − 2.12975I 0
u = −0.621792 − 0.819445I
a = 0.582418 − 0.765895I
b = 0.344815 − 0.764548I
−8.25028 + 2.12975I 0
u = −0.896403 + 0.592844I
a = 0.966816 + 0.375746I
b = 0.199042 + 0.683208I
−7.20927 − 3.04632I 0
u = −0.896403 − 0.592844I
a = 0.966816 − 0.375746I
b = 0.199042 − 0.683208I
−7.20927 + 3.04632I 0
u = 0.875671 + 0.627105I
a = 0.247782 + 0.053577I
b = 0.979738 + 0.820171I
−0.46733 + 5.54468I 0
u = 0.875671 − 0.627105I
a = 0.247782 − 0.053577I
b = 0.979738 − 0.820171I
−0.46733 − 5.54468I 0
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.915061 + 0.054031I
a = −0.273898 − 0.828206I
b = 0.034152 − 1.395890I
3.75773 + 1.09085I 0
u = −0.915061 − 0.054031I
a = −0.273898 + 0.828206I
b = 0.034152 + 1.395890I
3.75773 − 1.09085I 0
u = 0.876386 + 0.637072I
a = 0.965490 + 0.211185I
b = 1.312150 − 0.279787I
0.32102 + 5.18997I 0
u = 0.876386 − 0.637072I
a = 0.965490 − 0.211185I
b = 1.312150 + 0.279787I
0.32102 − 5.18997I 0
u = −0.792067 + 0.364533I
a = 1.064860 − 0.751526I
b = 0.849227 − 0.435183I
−1.46403 − 8.46772I 0
u = −0.792067 − 0.364533I
a = 1.064860 + 0.751526I
b = 0.849227 + 0.435183I
−1.46403 + 8.46772I 0
u = −0.672626 + 0.905633I
a = 1.222900 − 0.347747I
b = 2.49118 + 0.26599I
−12.4233 − 7.4999I 0
u = −0.672626 − 0.905633I
a = 1.222900 + 0.347747I
b = 2.49118 − 0.26599I
−12.4233 + 7.4999I 0
u = −0.502964 + 0.672687I
a = −0.112785 + 0.315563I
b = 0.638997 + 0.143982I
−2.47697 + 1.40445I 0
u = −0.502964 − 0.672687I
a = −0.112785 − 0.315563I
b = 0.638997 − 0.143982I
−2.47697 − 1.40445I 0
6
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.902378 + 0.740032I
a = −0.476203 + 1.088780I
b = −1.62606 − 0.36286I
−12.39800 + 2.77753I 0
u = −0.902378 − 0.740032I
a = −0.476203 − 1.088780I
b = −1.62606 + 0.36286I
−12.39800 − 2.77753I 0
u = −0.719806 + 0.334419I
a = 0.839821 − 0.983498I
b = 0.857987 − 0.394289I
−3.32757 − 0.74133I 0
u = −0.719806 − 0.334419I
a = 0.839821 + 0.983498I
b = 0.857987 + 0.394289I
−3.32757 + 0.74133I 0
u = 0.815536 + 0.923671I
a = 0.211361 − 0.892570I
b = −0.292264 + 0.219911I
0.147768 + 0.601523I 0
u = 0.815536 − 0.923671I
a = 0.211361 + 0.892570I
b = −0.292264 − 0.219911I
0.147768 − 0.601523I 0
u = −0.993894 + 0.739046I
a = 0.372429 + 0.295295I
b = 0.168599 − 0.122446I
−1.37363 − 6.86287I 0
u = −0.993894 − 0.739046I
a = 0.372429 − 0.295295I
b = 0.168599 + 0.122446I
−1.37363 + 6.86287I 0
u = 0.344938 + 0.638925I
a = 0.274724 + 0.765846I
b = 0.163839 − 0.856175I
−0.21248 + 1.79826I 0
u = 0.344938 − 0.638925I
a = 0.274724 − 0.765846I
b = 0.163839 + 0.856175I
−0.21248 − 1.79826I 0
7
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.374511 + 1.218040I
a = −1.127910 − 0.152756I
b = −1.63102 + 0.44266I
−5.94774 + 6.35238I 0
u = 0.374511 − 1.218040I
a = −1.127910 + 0.152756I
b = −1.63102 − 0.44266I
−5.94774 − 6.35238I 0
u = 0.664993 + 1.095230I
a = −1.046210 − 0.547420I
b = −1.88449 + 0.56737I
−8.39095 − 0.53811I 0
u = 0.664993 − 1.095230I
a = −1.046210 + 0.547420I
b = −1.88449 − 0.56737I
−8.39095 + 0.53811I 0
u = −0.936379 + 0.874958I
a = 1.094090 − 0.548079I
b = 2.20657 + 0.71506I
−12.4049 − 8.9977I 0
u = −0.936379 − 0.874958I
a = 1.094090 + 0.548079I
b = 2.20657 − 0.71506I
−12.4049 + 8.9977I 0
u = −0.744621 + 1.043820I
a = −1.022590 + 0.676287I
b = −1.68981 − 0.63987I
−7.71494 − 4.90990I 0
u = −0.744621 − 1.043820I
a = −1.022590 − 0.676287I
b = −1.68981 + 0.63987I
−7.71494 + 4.90990I 0
u = −1.175390 + 0.516378I
a = −0.622936 − 0.849858I
b = −1.34008 − 0.54188I
−6.12476 + 3.89475I 0
u = −1.175390 − 0.516378I
a = −0.622936 + 0.849858I
b = −1.34008 + 0.54188I
−6.12476 − 3.89475I 0
8
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.328261 + 1.249000I
a = 1.25659 − 0.83325I
b = 1.299970 + 0.167085I
−13.11780 − 1.97601I 0
u = −0.328261 − 1.249000I
a = 1.25659 + 0.83325I
b = 1.299970 − 0.167085I
−13.11780 + 1.97601I 0
u = −0.601045 + 0.319523I
a = −1.47869 + 0.84409I
b = −1.006790 + 0.230868I
0.46988 − 3.49771I 0
u = −0.601045 − 0.319523I
a = −1.47869 − 0.84409I
b = −1.006790 − 0.230868I
0.46988 + 3.49771I 0
u = 0.678764 + 0.023481I
a = 1.165110 + 0.262883I
b = −0.202309 + 0.037094I
1.49876 + 0.09907I 0
u = 0.678764 − 0.023481I
a = 1.165110 − 0.262883I
b = −0.202309 − 0.037094I
1.49876 − 0.09907I 0
u = −0.202651 + 0.646746I
a = 0.504766 + 1.251150I
b = 0.402736 − 0.412523I
−0.38569 + 2.12879I 0
u = −0.202651 − 0.646746I
a = 0.504766 − 1.251150I
b = 0.402736 + 0.412523I
−0.38569 − 2.12879I 0
u = −0.863600 + 1.019240I
a = −0.767920 − 0.879189I
b = −0.346321 − 0.321968I
−7.46331 − 10.46160I 0
u = −0.863600 − 1.019240I
a = −0.767920 + 0.879189I
b = −0.346321 + 0.321968I
−7.46331 + 10.46160I 0
9
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 1.217230 + 0.669504I
a = −0.112972 + 0.543057I
b = −0.167988 − 0.464929I
2.32202 + 2.06905I 0
u = 1.217230 − 0.669504I
a = −0.112972 − 0.543057I
b = −0.167988 + 0.464929I
2.32202 − 2.06905I 0
u = 0.557808 + 0.223218I
a = 1.03702 + 1.07809I
b = 0.56620 + 1.88391I
−2.54420 + 3.14291I 2.00000 − 10.38283I
u = 0.557808 − 0.223218I
a = 1.03702 − 1.07809I
b = 0.56620 − 1.88391I
−2.54420 − 3.14291I 2.00000 + 10.38283I
u = 1.304760 + 0.530697I
a = 0.136175 − 0.830160I
b = −0.0066614 + 0.0625832I
0.489098 + 0.388700I 0
u = 1.304760 − 0.530697I
a = 0.136175 + 0.830160I
b = −0.0066614 − 0.0625832I
0.489098 − 0.388700I 0
u = 0.376700 + 0.454340I
a = −3.06674 − 1.14555I
b = −0.932034 + 0.551422I
−10.42540 + 6.06568I −1.8335 − 15.3637I
u = 0.376700 − 0.454340I
a = −3.06674 + 1.14555I
b = −0.932034 − 0.551422I
−10.42540 − 6.06568I −1.8335 + 15.3637I
u = 0.554881 + 0.140141I
a = 0.27046 + 1.79547I
b = 0.453971 − 0.844268I
−0.06150 + 2.48943I 3.17370 − 4.01834I
u = 0.554881 − 0.140141I
a = 0.27046 − 1.79547I
b = 0.453971 + 0.844268I
−0.06150 − 2.48943I 3.17370 + 4.01834I
10
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 1.19386 + 0.86245I
a = −0.501291 − 0.565693I
b = −1.50989 + 0.01628I
−1.87185 + 3.47822I 0
u = 1.19386 − 0.86245I
a = −0.501291 + 0.565693I
b = −1.50989 − 0.01628I
−1.87185 − 3.47822I 0
u = 1.24300 + 0.89145I
a = 0.681143 + 0.699008I
b = 1.98865 − 0.52084I
−6.59645 + 7.81675I 0
u = 1.24300 − 0.89145I
a = 0.681143 − 0.699008I
b = 1.98865 + 0.52084I
−6.59645 − 7.81675I 0
u = −0.099402 + 0.428459I
a = −2.36898 + 2.26274I
b = −1.39345 − 0.42785I
−11.61500 + 2.97623I −4.67472 − 1.54835I
u = −0.099402 − 0.428459I
a = −2.36898 − 2.26274I
b = −1.39345 + 0.42785I
−11.61500 − 2.97623I −4.67472 + 1.54835I
u = −0.416159 + 0.139948I
a = −2.18643 + 1.00702I
b = −0.590900 + 0.023581I
1.41101 − 1.64765I 4.38403 + 7.71230I
u = −0.416159 − 0.139948I
a = −2.18643 − 1.00702I
b = −0.590900 − 0.023581I
1.41101 + 1.64765I 4.38403 − 7.71230I
u = −1.27052 + 0.92169I
a = 0.688840 − 0.639863I
b = 1.87760 + 0.38054I
−6.07607 − 2.31012I 0
u = −1.27052 − 0.92169I
a = 0.688840 + 0.639863I
b = 1.87760 − 0.38054I
−6.07607 + 2.31012I 0
11
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.367068 + 0.160217I
a = −2.60294 + 2.27563I
b = −0.617257 − 0.732831I
1.75773 − 1.88898I 19.6084 − 9.7659I
u = −0.367068 − 0.160217I
a = −2.60294 − 2.27563I
b = −0.617257 + 0.732831I
1.75773 + 1.88898I 19.6084 + 9.7659I
u = −1.20084 + 1.07188I
a = −0.946736 + 0.444946I
b = −2.20732 − 0.57872I
−12.4887 − 18.1031I 0
u = −1.20084 − 1.07188I
a = −0.946736 − 0.444946I
b = −2.20732 + 0.57872I
−12.4887 + 18.1031I 0
u = 1.16072 + 1.12461I
a = −0.742562 − 0.133966I
b = −2.28470 + 0.61290I
1.57710 + 7.14701I 0
u = 1.16072 − 1.12461I
a = −0.742562 + 0.133966I
b = −2.28470 − 0.61290I
1.57710 − 7.14701I 0
u = −1.19450 + 1.10023I
a = 0.712857 − 0.499549I
b = 2.11446 + 0.79329I
−5.99457 − 10.31610I 0
u = −1.19450 − 1.10023I
a = 0.712857 + 0.499549I
b = 2.11446 − 0.79329I
−5.99457 + 10.31610I 0
u = 0.191209 + 0.306647I
a = 1.43023 + 0.62187I
b = −0.30448 − 3.78683I
−4.46447 + 5.23065I −15.8390 + 3.5168I
u = 0.191209 − 0.306647I
a = 1.43023 − 0.62187I
b = −0.30448 + 3.78683I
−4.46447 − 5.23065I −15.8390 − 3.5168I
12
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.90440 + 1.40261I
a = −0.661781 + 0.425974I
b = −2.11701 − 0.67980I
−6.96776 + 1.62024I 0
u = −0.90440 − 1.40261I
a = −0.661781 − 0.425974I
b = −2.11701 + 0.67980I
−6.96776 − 1.62024I 0
u = 1.04890 + 1.34938I
a = 0.698921 + 0.255621I
b = 1.92274 − 0.86568I
−2.66284 + 5.40803I 0
u = 1.04890 − 1.34938I
a = 0.698921 − 0.255621I
b = 1.92274 + 0.86568I
−2.66284 − 5.40803I 0
u = −1.03230 + 1.39080I
a = 0.601176 − 0.727613I
b = 1.59571 + 0.41095I
−13.3115 + 9.4190I 0
u = −1.03230 − 1.39080I
a = 0.601176 + 0.727613I
b = 1.59571 − 0.41095I
−13.3115 − 9.4190I 0
u = −0.117543 + 0.220736I
a = −0.98093 + 4.64440I
b = 0.282949 − 0.016428I
−0.48485 − 2.96998I −5.78061 − 2.76336I
u = −0.117543 − 0.220736I
a = −0.98093 − 4.64440I
b = 0.282949 + 0.016428I
−0.48485 + 2.96998I −5.78061 + 2.76336I
u = 1.75469 + 0.35098I
a = −0.078590 − 0.419650I
b = −0.97885 + 1.47115I
3.11758 + 3.82652I 0
u = 1.75469 − 0.35098I
a = −0.078590 + 0.419650I
b = −0.97885 − 1.47115I
3.11758 − 3.82652I 0
13
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.158595 + 0.000579I
a = −0.27132 − 5.75775I
b = 1.64593 − 0.78163I
−2.70884 − 1.02332I 1.77227 − 2.30546I
u = −0.158595 − 0.000579I
a = −0.27132 + 5.75775I
b = 1.64593 + 0.78163I
−2.70884 + 1.02332I 1.77227 + 2.30546I
u = −1.40148 + 1.37678I
a = −0.884947 + 0.442312I
b = −1.91337 − 0.27619I
−8.74306 − 7.50542I 0
u = −1.40148 − 1.37678I
a = −0.884947 − 0.442312I
b = −1.91337 + 0.27619I
−8.74306 + 7.50542I 0
u = −1.87585 + 0.68624I
a = −0.099794 + 0.580457I
b = −1.19365 − 1.50047I
−9.37416 + 1.26969I 0
u = −1.87585 − 0.68624I
a = −0.099794 − 0.580457I
b = −1.19365 + 1.50047I
−9.37416 − 1.26969I 0
u = 1.86439 + 1.30631I
a = 0.100434 + 0.639423I
b = 0.465943 − 0.834397I
1.74223 + 2.15763I 0
u = 1.86439 − 1.30631I
a = 0.100434 − 0.639423I
b = 0.465943 + 0.834397I
1.74223 − 2.15763I 0
14
II. I
u
2
= h−6.45 × 10
46
u
35
+ 5.29 × 10
47
u
34
+ · · · + 1.76 × 10
44
b + 1.80 ×
10
46
, −2.46 × 10
46
u
35
+ 2.09 × 10
47
u
34
+ · · · + 1.76 × 10
44
a + 5.22 ×
10
46
, u
36
− 9u
35
+ · · · − 14u + 1i
(i) Arc colorings
a
10
=
0
u
a
12
=
1
0
a
1
=
1
−u
2
a
5
=
140.158u
35
− 1187.21u
34
+ ··· + 3524.39u − 296.706
366.884u
35
− 3007.49u
34
+ ··· + 2539.57u − 102.396
a
9
=
238.295u
35
− 1927.86u
34
+ ··· + 1235.01u − 44.4770
328.269u
35
− 2833.09u
34
+ ··· + 8330.09u − 666.273
a
6
=
563.553u
35
− 4811.95u
34
+ ··· + 12684.8u − 991.409
295.393u
35
− 2429.91u
34
+ ··· + 2251.27u − 98.4593
a
8
=
−89.9730u
35
+ 905.235u
34
+ ··· − 7095.08u + 621.796
328.269u
35
− 2833.09u
34
+ ··· + 8330.09u − 666.273
a
7
=
348.754u
35
− 2849.01u
34
+ ··· + 2661.67u − 139.954
266.407u
35
− 2283.23u
34
+ ··· + 6048.60u − 471.972
a
4
=
541.938u
35
− 4736.15u
34
+ ··· + 16865.3u − 1387.65
−221.527u
35
+ 1946.78u
34
+ ··· − 7346.51u + 620.328
a
3
=
320.411u
35
− 2789.37u
34
+ ··· + 9518.75u − 767.324
−221.527u
35
+ 1946.78u
34
+ ··· − 7346.51u + 620.328
a
2
=
647.693u
35
− 5541.90u
34
+ ··· + 13860.9u − 1062.14
254.012u
35
− 2185.29u
34
+ ··· + 6133.90u − 488.778
a
11
=
493.207u
35
− 4306.08u
34
+ ··· + 13158.1u − 1047.25
−227.149u
35
+ 2008.25u
34
+ ··· − 7499.57u + 621.554
(ii) Obstruction class = 1
(iii) Cusp Shapes = 1583.96u
35
− 13530.4u
34
+ ··· + 35840.2u − 2796.67
15
(iv) u-Polynomials at the component
16
Crossings u-Polynomials at each crossing
c
1
u
36
− 14u
35
+ ··· − 4u + 1
c
2
u
36
− 3u
35
+ ··· + 9u + 1
c
3
u
36
+ u
35
+ ··· + 24u + 4
c
4
u
36
− 7u
35
+ ··· + 23u
2
+ 1
c
5
u
36
− u
35
+ ··· + 24u + 4
c
6
u
36
+ 3u
35
+ ··· − 9u + 1
c
7
u
36
+ 2u
35
+ ··· + 112u + 784
c
8
u
36
− u
35
+ ··· + 98u + 13
c
9
u
36
+ u
35
+ ··· − 24u + 4
c
10
u
36
+ u
34
+ ··· − 2u + 1
c
11
u
36
− u
35
+ ··· − 24u + 4
c
12
u
36
− 9u
35
+ ··· − 14u + 1
17
18
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
36
− 20y
35
+ ··· + 14y + 1
c
2
, c
6
y
36
+ 39y
35
+ ··· + 11y + 1
c
3
, c
11
y
36
− 17y
35
+ ··· + 192y + 16
c
4
y
36
+ 5y
35
+ ··· + 46y + 1
c
5
, c
9
y
36
+ 25y
35
+ ··· + 384y + 16
c
7
y
36
+ 12y
35
+ ··· + 3543680y + 614656
c
8
y
36
− 23y
35
+ ··· − 504y + 169
c
10
y
36
+ 2y
35
+ ··· + 12y + 1
c
12
y
36
− 15y
35
+ ··· − 8y + 1
19
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.783910 + 0.567549I
a = −1.031160 − 0.365602I
b = −1.42007 − 0.16561I
1.11632 + 4.34442I 4.96433 − 5.45878I
u = 0.783910 − 0.567549I
a = −1.031160 + 0.365602I
b = −1.42007 + 0.16561I
1.11632 − 4.34442I 4.96433 + 5.45878I
u = 0.923228 + 0.255717I
a = 0.818859 + 0.911702I
b = 0.842409 + 0.343380I
−1.13046 + 8.19995I 6.40697 − 2.11842I
u = 0.923228 − 0.255717I
a = 0.818859 − 0.911702I
b = 0.842409 − 0.343380I
−1.13046 − 8.19995I 6.40697 + 2.11842I
u = −0.933033 + 0.152736I
a = 0.092399 + 0.911581I
b = −0.49503 + 1.40427I
3.45740 + 0.33361I 2.00000 + 2.78678I
u = −0.933033 − 0.152736I
a = 0.092399 − 0.911581I
b = −0.49503 − 1.40427I
3.45740 − 0.33361I 2.00000 − 2.78678I
u = 0.072178 + 0.847312I
a = −1.061610 + 0.083248I
b = −1.22132 + 1.06933I
−3.42025 + 2.44760I −7.56538 − 4.04607I
u = 0.072178 − 0.847312I
a = −1.061610 − 0.083248I
b = −1.22132 − 1.06933I
−3.42025 − 2.44760I −7.56538 + 4.04607I
u = 0.654359 + 0.525832I
a = 0.720318 + 0.799120I
b = 1.34910 + 1.19327I
−3.02633 + 1.86473I −3.68534 − 5.03423I
u = 0.654359 − 0.525832I
a = 0.720318 − 0.799120I
b = 1.34910 − 1.19327I
−3.02633 − 1.86473I −3.68534 + 5.03423I
20
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.769338 + 0.869206I
a = −0.136041 + 0.730713I
b = 0.426769 − 0.758158I
0.74417 + 1.94304I 0
u = 0.769338 − 0.869206I
a = −0.136041 − 0.730713I
b = 0.426769 + 0.758158I
0.74417 − 1.94304I 0
u = −0.955066 + 0.661677I
a = 0.358015 − 0.189666I
b = 0.614046 − 0.444675I
−2.09816 − 6.94123I 0
u = −0.955066 − 0.661677I
a = 0.358015 + 0.189666I
b = 0.614046 + 0.444675I
−2.09816 + 6.94123I 0
u = −0.736685 + 0.307532I
a = 0.158477 + 1.146740I
b = 0.815660 + 0.537024I
−2.83927 + 2.26358I −1.13362 − 4.65512I
u = −0.736685 − 0.307532I
a = 0.158477 − 1.146740I
b = 0.815660 − 0.537024I
−2.83927 − 2.26358I −1.13362 + 4.65512I
u = 0.477491 + 0.168394I
a = −1.22747 + 1.77822I
b = 0.057881 + 0.200524I
1.61441 − 0.99906I 7.88978 + 0.68592I
u = 0.477491 − 0.168394I
a = −1.22747 − 1.77822I
b = 0.057881 − 0.200524I
1.61441 + 0.99906I 7.88978 − 0.68592I
u = 0.436590 + 0.243522I
a = −0.845760 − 0.680243I
b = −0.60906 − 3.74778I
−4.25937 + 5.36577I 11.6445 − 14.0471I
u = 0.436590 − 0.243522I
a = −0.845760 + 0.680243I
b = −0.60906 + 3.74778I
−4.25937 − 5.36577I 11.6445 + 14.0471I
21
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.393209 + 0.289851I
a = 0.15719 − 2.70525I
b = −0.144531 + 0.494841I
−0.28530 + 3.27162I 6.0438 − 17.3787I
u = 0.393209 − 0.289851I
a = 0.15719 + 2.70525I
b = −0.144531 − 0.494841I
−0.28530 − 3.27162I 6.0438 + 17.3787I
u = 1.11443 + 1.08695I
a = 0.751887 + 0.057142I
b = 2.33283 − 0.57703I
1.14131 + 7.52068I 0
u = 1.11443 − 1.08695I
a = 0.751887 − 0.057142I
b = 2.33283 + 0.57703I
1.14131 − 7.52068I 0
u = 0.055007 + 0.419156I
a = 3.94903 − 0.68109I
b = 1.102340 − 0.556965I
−10.40340 + 5.53544I −1.71980 + 0.01244I
u = 0.055007 − 0.419156I
a = 3.94903 + 0.68109I
b = 1.102340 + 0.556965I
−10.40340 − 5.53544I −1.71980 − 0.01244I
u = −1.10224 + 1.29509I
a = −0.954080 + 0.431686I
b = −1.94135 − 0.32574I
−8.98347 − 7.10070I 0
u = −1.10224 − 1.29509I
a = −0.954080 − 0.431686I
b = −1.94135 + 0.32574I
−8.98347 + 7.10070I 0
u = 1.72237 + 0.31033I
a = −0.216278 − 0.476815I
b = −0.80304 + 1.44936I
3.03372 + 4.42529I 0
u = 1.72237 − 0.31033I
a = −0.216278 + 0.476815I
b = −0.80304 − 1.44936I
3.03372 − 4.42529I 0
22
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 1.16482 + 1.31553I
a = −0.649968 − 0.324635I
b = −1.85409 + 0.89277I
−2.34572 + 5.63950I 0
u = 1.16482 − 1.31553I
a = −0.649968 + 0.324635I
b = −1.85409 − 0.89277I
−2.34572 − 5.63950I 0
u = −1.74432 + 0.60395I
a = 0.079442 − 0.631620I
b = 1.13819 + 1.39043I
−9.27344 + 1.23026I 0
u = −1.74432 − 0.60395I
a = 0.079442 + 0.631620I
b = 1.13819 − 1.39043I
−9.27344 − 1.23026I 0
u = 1.40441 + 1.26419I
a = 0.036762 − 0.836323I
b = −0.190721 + 0.293793I
0.769313 + 0.940904I 0
u = 1.40441 − 1.26419I
a = 0.036762 + 0.836323I
b = −0.190721 − 0.293793I
0.769313 − 0.940904I 0
23
III.
I
u
3
= h−u
3
+ 4u
2
+ 2b − 4u − 3, u
3
− 4u
2
+ a + 5u, u
4
− 3u
3
+ 2u
2
+ 3u + 1i
(i) Arc colorings
a
10
=
0
u
a
12
=
1
0
a
1
=
1
−u
2
a
5
=
−u
3
+ 4u
2
− 5u
1
2
u
3
− 2u
2
+ 2u +
3
2
a
9
=
−3u
3
+ 10u
2
− 9u − 6
1
a
6
=
−2u
3
+ 6u
2
− 4u − 6
−
1
2
u
3
+ u
2
− u +
1
2
a
8
=
−3u
3
+ 10u
2
− 9u − 7
1
a
7
=
−3u
3
+ 10u
2
− 9u − 7
1
a
4
=
3
2
u
3
− 6u
2
+ 9u −
5
2
−u
3
+ 3u
2
− 3u − 1
a
3
=
1
2
u
3
− 3u
2
+ 6u −
7
2
−u
3
+ 3u
2
− 3u − 1
a
2
=
−
1
2
u
3
+ u
2
−
5
2
−u
a
11
=
−7u
3
+ 24u
2
− 24u − 12
u
3
− 3u
2
+ 3u + 3
(ii) Obstruction class = 1
(iii) Cusp Shapes = 17u
3
− 53u
2
+ 53u + 19
24
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
10
u
4
+ 3u
3
+ 2u
2
− 3u + 1
c
2
(u
2
+ u + 1)
2
c
3
, c
5
(u
2
+ u + 2)
2
c
4
u
4
+ 5u
2
+ 1
c
6
(u
2
− u + 1)
2
c
7
u
4
c
8
(u + 1)
4
c
9
, c
11
(u
2
− u + 2)
2
c
12
u
4
− 3u
3
+ 2u
2
+ 3u + 1
25
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
10
, c
12
y
4
− 5y
3
+ 24y
2
− 5y + 1
c
2
, c
6
(y
2
+ y + 1)
2
c
3
, c
5
, c
9
c
11
(y
2
+ 3y + 4)
2
c
4
(y
2
+ 5y + 1)
2
c
7
y
4
c
8
(y −1)
4
26
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = −0.395644 + 0.228425I
a = 2.39564 − 1.96048I
b = 0.500000 + 0.866025I
1.64493 − 2.02988I −7.5000 + 23.3072I
u = −0.395644 − 0.228425I
a = 2.39564 + 1.96048I
b = 0.500000 − 0.866025I
1.64493 + 2.02988I −7.5000 − 23.3072I
u = 1.89564 + 1.09445I
a = 0.104356 + 0.637600I
b = 0.500000 − 0.866025I
1.64493 + 2.02988I −7.5000 + 16.3790I
u = 1.89564 − 1.09445I
a = 0.104356 − 0.637600I
b = 0.500000 + 0.866025I
1.64493 − 2.02988I −7.5000 − 16.3790I
27
IV. I
u
4
= hb
2
− b + 1, a, u − 1i
(i) Arc colorings
a
10
=
0
1
a
12
=
1
0
a
1
=
1
−1
a
5
=
0
b
a
9
=
0
1
a
6
=
0
b
a
8
=
−1
1
a
7
=
−1
1
a
4
=
b
0
a
3
=
b
0
a
2
=
b
−1
a
11
=
1
0
(ii) Obstruction class = 1
(iii) Cusp Shapes = 4b + 4
28
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
4
, c
6
u
2
− u + 1
c
2
u
2
+ u + 1
c
3
, c
5
, c
7
c
9
, c
11
u
2
c
8
(u + 1)
2
c
10
, c
12
(u − 1)
2
29
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
2
, c
4
c
6
y
2
+ y + 1
c
3
, c
5
, c
7
c
9
, c
11
y
2
c
8
, c
10
, c
12
(y −1)
2
30
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
4
√
−1(vol +
√
−1CS) Cusp shape
u = 1.00000
a = 0
b = 0.500000 + 0.866025I
1.64493 − 2.02988I 6.00000 + 3.46410I
u = 1.00000
a = 0
b = 0.500000 − 0.866025I
1.64493 + 2.02988I 6.00000 − 3.46410I
31
V. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
(u
2
− u + 1)(u
4
+ 3u
3
+ ··· − 3u + 1)(u
36
− 14u
35
+ ··· − 4u + 1)
· (u
98
− 7u
97
+ ··· − 25602u + 2657)
c
2
((u
2
+ u + 1)
3
)(u
36
− 3u
35
+ ··· + 9u + 1)
· (u
98
− 3u
97
+ ··· − 216906u + 13157)
c
3
u
2
(u
2
+ u + 2)
2
(u
36
+ u
35
+ ··· + 24u + 4)
· (u
98
+ 2u
97
+ ··· + 26608u + 508)
c
4
(u
2
− u + 1)(u
4
+ 5u
2
+ 1)(u
36
− 7u
35
+ ··· + 23u
2
+ 1)
· (u
98
− 5u
97
+ ··· − 433u + 23)
c
5
u
2
(u
2
+ u + 2)
2
(u
36
− u
35
+ ··· + 24u + 4)
· (u
98
+ 42u
96
+ ··· + 140656u + 34228)
c
6
((u
2
− u + 1)
3
)(u
36
+ 3u
35
+ ··· − 9u + 1)
· (u
98
− 3u
97
+ ··· − 216906u + 13157)
c
7
u
6
(u
36
+ 2u
35
+ ··· + 112u + 784)(u
98
− 7u
97
+ ··· − 2048u + 64)
c
8
((u + 1)
6
)(u
36
− u
35
+ ··· + 98u + 13)
· (u
98
+ 20u
96
+ ··· − 26534568u + 43283857)
c
9
u
2
(u
2
− u + 2)
2
(u
36
+ u
35
+ ··· − 24u + 4)
· (u
98
+ 42u
96
+ ··· + 140656u + 34228)
c
10
((u − 1)
2
)(u
4
+ 3u
3
+ ··· − 3u + 1)(u
36
+ u
34
+ ··· − 2u + 1)
· (u
98
+ 12u
97
+ ··· − 2720881u + 1109443)
c
11
u
2
(u
2
− u + 2)
2
(u
36
− u
35
+ ··· − 24u + 4)
· (u
98
+ 2u
97
+ ··· + 26608u + 508)
c
12
((u − 1)
2
)(u
4
− 3u
3
+ ··· + 3u + 1)(u
36
− 9u
35
+ ··· − 14u + 1)
· (u
98
+ 7u
97
+ ··· + 23u + 1)
32
VI. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
(y
2
+ y + 1)(y
4
− 5y
3
+ ··· − 5y + 1)(y
36
− 20y
35
+ ··· + 14y + 1)
· (y
98
− 55y
97
+ ··· − 751130346y + 7059649)
c
2
, c
6
((y
2
+ y + 1)
3
)(y
36
+ 39y
35
+ ··· + 11y + 1)
· (y
98
+ 103y
97
+ ··· − 27972220618y + 173106649)
c
3
, c
11
y
2
(y
2
+ 3y + 4)
2
(y
36
− 17y
35
+ ··· + 192y + 16)
· (y
98
− 94y
97
+ ··· + 1054871872y + 258064)
c
4
(y
2
+ y + 1)(y
2
+ 5y + 1)
2
(y
36
+ 5y
35
+ ··· + 46y + 1)
· (y
98
+ 9y
97
+ ··· − 26167y + 529)
c
5
, c
9
y
2
(y
2
+ 3y + 4)
2
(y
36
+ 25y
35
+ ··· + 384y + 16)
· (y
98
+ 84y
97
+ ··· + 44846020736y + 1171555984)
c
7
y
6
(y
36
+ 12y
35
+ ··· + 3543680y + 614656)
· (y
98
− 3y
97
+ ··· − 30720y + 4096)
c
8
((y −1)
6
)(y
36
− 23y
35
+ ··· − 504y + 169)
· (y
98
+ 40y
97
+ ··· + 141207617788579830y + 1873492276796449)
c
10
((y −1)
2
)(y
4
− 5y
3
+ ··· − 5y + 1)(y
36
+ 2y
35
+ ··· + 12y + 1)
· (y
98
+ 36y
97
+ ··· + 14973133605321y + 1230863770249)
c
12
((y −1)
2
)(y
4
− 5y
3
+ ··· − 5y + 1)(y
36
− 15y
35
+ ··· − 8y + 1)
· (y
98
− 21y
97
+ ··· − 79y + 1)
33
