12a
0578
(K12a
0578
)
A knot diagram
1
Linearized knot diagam
3 7 9 10 11 2 12 1 6 5 4 8
Solving Sequence
4,10
5 11 6
8,12
1 7 9 3 2
c
4
c
10
c
5
c
11
c
12
c
7
c
9
c
3
c
2
c
1
, c
6
, c
8
Ideals for irreducible components
2
of X
par
I
u
1
= h−u
58
+ 24u
56
+ ··· + 4b − 4u, u
56
− 23u
54
+ ··· + 4a + 2, u
61
− 2u
60
+ ··· + 2u + 2i
I
u
2
= h474u
7
a
2
+ 726u
7
a + ··· + 845a + 670, 2u
7
a
2
+ 4u
7
a + ··· + 4a + 2, u
8
+ u
7
− 3u
6
− 2u
5
+ 3u
4
+ 2u − 1i
I
u
3
= hb − 1, 2u
3
− 3u
2
+ 3a − 3u + 3, u
4
− 3u
2
+ 3i
I
u
4
= hb + 1, −u
2
+ a + u + 1, u
4
− u
2
− 1i
I
v
1
= ha, b − 1, v −1i
* 5 irreducible components of dim
C
= 0, with total 94 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
=
h−u
58
+24u
56
+· · ·+4b−4u, u
56
−23u
54
+· · ·+4a+2, u
61
−2u
60
+· · ·+2u+2i
(i) Arc colorings
a
4
=
1
0
a
10
=
0
u
a
5
=
1
−u
2
a
11
=
u
−u
3
+ u
a
6
=
−u
2
+ 1
u
4
− 2u
2
a
8
=
−
1
4
u
56
+
23
4
u
54
+ ··· −
3
2
u −
1
2
1
4
u
58
− 6u
56
+ ··· + u
2
+ u
a
12
=
−u
3
+ 2u
−u
3
+ u
a
1
=
−
1
4
u
54
+
23
4
u
52
+ ··· +
5
2
u +
1
2
−
1
4
u
54
+
11
2
u
52
+ ··· − 4u
3
+ u
a
7
=
−
1
2
u
60
+ u
59
+ ··· −
3
2
u −
1
2
−u
60
+ u
59
+ ··· +
5
2
u + 1
a
9
=
−u
5
+ 2u
3
− u
u
7
− 3u
5
+ 2u
3
+ u
a
3
=
−u
12
+ 5u
10
− 9u
8
+ 6u
6
− u
2
+ 1
u
14
− 6u
12
+ 13u
10
− 10u
8
− 2u
6
+ 4u
4
+ u
2
a
2
=
−
1
4
u
57
+ 6u
55
+ ··· + u + 1
−
1
4
u
57
+
23
4
u
55
+ ··· +
1
2
u
2
+
1
2
u
(ii) Obstruction class = −1
(iii) Cusp Shapes = −2u
60
+ 50u
58
+ ··· + 20u + 12
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
61
+ 24u
60
+ ··· + 3579u + 49
c
2
, c
6
u
61
− 2u
60
+ ··· + 31u + 7
c
3
u
61
+ 2u
60
+ ··· − 9398u + 5482
c
4
, c
5
, c
10
u
61
− 2u
60
+ ··· + 2u + 2
c
7
, c
8
, c
12
u
61
+ 2u
60
+ ··· − 69u + 7
c
9
, c
11
u
61
+ 6u
60
+ ··· + 736u + 128
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
61
+ 36y
60
+ ··· + 7535175y −2401
c
2
, c
6
y
61
− 24y
60
+ ··· + 3579y −49
c
3
y
61
− 10y
60
+ ··· − 675769720y −30052324
c
4
, c
5
, c
10
y
61
− 50y
60
+ ··· + 8y −4
c
7
, c
8
, c
12
y
61
− 64y
60
+ ··· + 4075y −49
c
9
, c
11
y
61
+ 38y
60
+ ··· + 115712y −16384
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −1.045080 + 0.313421I
a = 1.89893 − 0.49988I
b = 1.88740 + 0.56009I
6.47668 + 1.81251I 0
u = −1.045080 − 0.313421I
a = 1.89893 + 0.49988I
b = 1.88740 − 0.56009I
6.47668 − 1.81251I 0
u = 1.082430 + 0.367312I
a = −1.87282 − 0.76181I
b = −2.11893 + 0.51520I
4.29961 − 7.38307I 0
u = 1.082430 − 0.367312I
a = −1.87282 + 0.76181I
b = −2.11893 − 0.51520I
4.29961 + 7.38307I 0
u = 0.026391 + 0.841561I
a = 0.017329 − 0.723163I
b = 0.0358248 + 0.1097390I
−2.59755 − 1.90534I 5.48183 + 3.73036I
u = 0.026391 − 0.841561I
a = 0.017329 + 0.723163I
b = 0.0358248 − 0.1097390I
−2.59755 + 1.90534I 5.48183 − 3.73036I
u = −1.116950 + 0.320702I
a = −0.591762 + 0.486353I
b = −0.901647 − 0.672603I
−1.11946 + 3.33466I 0
u = −1.116950 − 0.320702I
a = −0.591762 − 0.486353I
b = −0.901647 + 0.672603I
−1.11946 − 3.33466I 0
u = 0.148036 + 0.815189I
a = 3.32481 + 2.12115I
b = 2.47279 + 0.61911I
1.44711 + 11.68910I 5.41407 − 7.67902I
u = 0.148036 − 0.815189I
a = 3.32481 − 2.12115I
b = 2.47279 − 0.61911I
1.44711 − 11.68910I 5.41407 + 7.67902I
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.159456 + 0.787209I
a = −3.07363 + 2.55815I
b = −2.30891 + 0.83730I
3.77656 − 5.89886I 8.15888 + 3.94613I
u = −0.159456 − 0.787209I
a = −3.07363 − 2.55815I
b = −2.30891 − 0.83730I
3.77656 + 5.89886I 8.15888 − 3.94613I
u = −0.128661 + 0.790668I
a = 1.20590 − 0.92529I
b = 1.199370 − 0.497535I
−4.10929 − 7.41360I 1.61547 + 7.26505I
u = −0.128661 − 0.790668I
a = 1.20590 + 0.92529I
b = 1.199370 + 0.497535I
−4.10929 + 7.41360I 1.61547 − 7.26505I
u = −0.050353 + 0.793051I
a = 1.03212 − 1.57158I
b = 0.890863 − 0.963022I
−6.44106 − 0.24388I −3.18042 + 0.12157I
u = −0.050353 − 0.793051I
a = 1.03212 + 1.57158I
b = 0.890863 + 0.963022I
−6.44106 + 0.24388I −3.18042 − 0.12157I
u = −0.687219 + 0.308158I
a = 1.43674 − 0.19679I
b = 1.78452 + 0.21827I
7.10517 − 1.78344I 12.35005 + 2.03995I
u = −0.687219 − 0.308158I
a = 1.43674 + 0.19679I
b = 1.78452 − 0.21827I
7.10517 + 1.78344I 12.35005 − 2.03995I
u = 1.25692
a = −0.481060
b = 0.855799
2.32742 0
u = −1.217190 + 0.340958I
a = −1.011960 + 0.019839I
b = −0.688579 − 1.089540I
−2.85750 − 3.85140I 0
6
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −1.217190 − 0.340958I
a = −1.011960 − 0.019839I
b = −0.688579 + 1.089540I
−2.85750 + 3.85140I 0
u = 0.611451 + 0.390031I
a = −1.342980 − 0.209011I
b = −1.75805 + 0.23081I
5.48935 + 7.39656I 9.73203 − 7.29176I
u = 0.611451 − 0.390031I
a = −1.342980 + 0.209011I
b = −1.75805 − 0.23081I
5.48935 − 7.39656I 9.73203 + 7.29176I
u = −1.28941
a = 1.15132
b = −0.131178
5.56027 0
u = −0.235942 + 0.661253I
a = −1.48007 + 2.97320I
b = −1.39466 + 0.87587I
5.54702 − 1.76287I 9.26008 + 3.99131I
u = −0.235942 − 0.661253I
a = −1.48007 − 2.97320I
b = −1.39466 − 0.87587I
5.54702 + 1.76287I 9.26008 − 3.99131I
u = 1.238810 + 0.387315I
a = 0.113664 − 0.741618I
b = 0.115647 + 0.168942I
1.14891 + 6.31724I 0
u = 1.238810 − 0.387315I
a = 0.113664 + 0.741618I
b = 0.115647 − 0.168942I
1.14891 − 6.31724I 0
u = −1.280270 + 0.275839I
a = −0.249437 − 0.922926I
b = 0.613860 + 0.196052I
2.59552 − 4.85268I 0
u = −1.280270 − 0.275839I
a = −0.249437 + 0.922926I
b = 0.613860 − 0.196052I
2.59552 + 4.85268I 0
7
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.302742 + 0.600452I
a = 0.95957 + 2.68395I
b = 1.173020 + 0.631568I
4.47511 − 3.82165I 8.02527 + 1.02116I
u = 0.302742 − 0.600452I
a = 0.95957 − 2.68395I
b = 1.173020 − 0.631568I
4.47511 + 3.82165I 8.02527 − 1.02116I
u = −1.284030 + 0.381487I
a = −0.134033 − 0.700730I
b = −0.157554 + 0.062498I
1.47922 − 2.48565I 0
u = −1.284030 − 0.381487I
a = −0.134033 + 0.700730I
b = −0.157554 − 0.062498I
1.47922 + 2.48565I 0
u = 1.299870 + 0.344849I
a = 0.463664 − 1.207460I
b = −1.040970 − 0.847148I
−2.22544 + 4.34429I 0
u = 1.299870 − 0.344849I
a = 0.463664 + 1.207460I
b = −1.040970 + 0.847148I
−2.22544 − 4.34429I 0
u = 1.318970 + 0.274899I
a = 0.178307 − 0.453100I
b = 0.367203 − 0.307219I
2.88323 + 1.86161I 0
u = 1.318970 − 0.274899I
a = 0.178307 + 0.453100I
b = 0.367203 + 0.307219I
2.88323 − 1.86161I 0
u = −0.010977 + 0.647106I
a = −0.368429 − 0.667382I
b = −0.488496 + 0.022625I
−1.39623 + 1.46553I 4.80729 − 4.40781I
u = −0.010977 − 0.647106I
a = −0.368429 + 0.667382I
b = −0.488496 − 0.022625I
−1.39623 − 1.46553I 4.80729 + 4.40781I
8
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 1.383270 + 0.045423I
a = −0.445627 − 0.436211I
b = 0.630719 − 0.251341I
5.65281 + 4.80409I 0
u = 1.383270 − 0.045423I
a = −0.445627 + 0.436211I
b = 0.630719 + 0.251341I
5.65281 − 4.80409I 0
u = −1.368750 + 0.233531I
a = 1.10473 + 1.86272I
b = −1.17608 + 1.32230I
9.69673 + 0.83184I 0
u = −1.368750 − 0.233531I
a = 1.10473 − 1.86272I
b = −1.17608 − 1.32230I
9.69673 − 0.83184I 0
u = 1.346800 + 0.339601I
a = 0.168072 − 1.073780I
b = −1.370380 − 0.345312I
0.53517 + 11.49560I 0
u = 1.346800 − 0.339601I
a = 0.168072 + 1.073780I
b = −1.370380 + 0.345312I
0.53517 − 11.49560I 0
u = 1.368020 + 0.269439I
a = −0.92620 + 2.29059I
b = 1.61066 + 1.41688I
10.58940 + 5.14714I 0
u = 1.368020 − 0.269439I
a = −0.92620 − 2.29059I
b = 1.61066 − 1.41688I
10.58940 − 5.14714I 0
u = −0.536071 + 0.277726I
a = 0.182357 − 0.605325I
b = −0.358021 + 0.249835I
−0.27372 − 3.92540I 6.34246 + 7.90863I
u = −0.536071 − 0.277726I
a = 0.182357 + 0.605325I
b = −0.358021 − 0.249835I
−0.27372 + 3.92540I 6.34246 − 7.90863I
9
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 1.361620 + 0.334725I
a = 0.07582 + 2.89140I
b = 2.60850 + 0.92122I
8.57491 + 9.95414I 0
u = 1.361620 − 0.334725I
a = 0.07582 − 2.89140I
b = 2.60850 − 0.92122I
8.57491 − 9.95414I 0
u = −1.359900 + 0.350372I
a = −0.40622 + 2.83427I
b = −2.72449 + 0.62392I
6.2004 − 15.8925I 0
u = −1.359900 − 0.350372I
a = −0.40622 − 2.83427I
b = −2.72449 − 0.62392I
6.2004 + 15.8925I 0
u = 1.41422 + 0.03842I
a = 1.006490 − 0.306439I
b = −2.60422 + 0.34117I
13.60740 + 2.58481I 0
u = 1.41422 − 0.03842I
a = 1.006490 + 0.306439I
b = −2.60422 − 0.34117I
13.60740 − 2.58481I 0
u = −1.41341 + 0.06611I
a = −0.898179 − 0.480612I
b = 2.43333 + 0.51052I
11.8693 − 8.6563I 0
u = −1.41341 − 0.06611I
a = −0.898179 + 0.480612I
b = 2.43333 − 0.51052I
11.8693 + 8.6563I 0
u = −0.170322 + 0.434793I
a = −0.067068 − 0.388822I
b = −0.294850 + 0.289305I
−1.34960 + 1.22997I 1.31252 − 1.31517I
u = −0.170322 − 0.434793I
a = −0.067068 + 0.388822I
b = −0.294850 − 0.289305I
−1.34960 − 1.22997I 1.31252 + 1.31517I
10
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.356420
a = −1.27045
b = 0.399618
0.765127 14.4300
11
II. I
u
2
= h474u
7
a
2
+ 726u
7
a + · · · + 845a + 670, 2u
7
a
2
+ 4u
7
a + · · · + 4a +
2, u
8
+ u
7
− 3u
6
− 2u
5
+ 3u
4
+ 2u − 1i
(i) Arc colorings
a
4
=
1
0
a
10
=
0
u
a
5
=
1
−u
2
a
11
=
u
−u
3
+ u
a
6
=
−u
2
+ 1
u
4
− 2u
2
a
8
=
a
−1.15892a
2
u
7
− 1.77506au
7
+ ··· − 2.06601a − 1.63814
a
12
=
−u
3
+ 2u
−u
3
+ u
a
1
=
−1.15892a
2
u
7
− 1.77506au
7
+ ··· − 3.06601a − 1.63814
−0.205379a
2
u
7
− 1.12469au
7
+ ··· − 1.66993a − 1.80929
a
7
=
0.256724a
2
u
7
+ 0.405868au
7
+ ··· + 3.33741a + 1.26161
−1.08802a
2
u
7
− 2.76773au
7
+ ··· − 0.144254a − 1.06112
a
9
=
−u
5
+ 2u
3
− u
u
7
− 3u
5
+ 2u
3
+ u
a
3
=
−u
3
+ 2u
−u
3
+ u
a
2
=
−0.513447a
2
u
7
− 1.81174au
7
+ ··· − 2.67482a − 2.52323
−0.398533a
2
u
7
− 0.420538au
7
+ ··· − 2.18093a − 2.41565
(ii) Obstruction class = −1
(iii) Cusp Shapes = 4u
6
− 12u
4
+ 4u
3
+ 8u
2
− 8u + 14
12
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
24
+ 16u
23
+ ··· + 4u + 1
c
2
, c
6
, c
7
c
8
, c
12
u
24
− 8u
22
+ ··· + 2u − 1
c
3
(u
8
− u
7
− u
6
+ 2u
5
+ u
4
− 2u
3
+ 2u − 1)
3
c
4
, c
5
, c
10
(u
8
+ u
7
− 3u
6
− 2u
5
+ 3u
4
+ 2u − 1)
3
c
9
, c
11
(u
8
− 3u
7
+ 7u
6
− 10u
5
+ 11u
4
− 10u
3
+ 6u
2
− 4u + 1)
3
13
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
24
− 16y
23
+ ··· + 12y + 1
c
2
, c
6
, c
7
c
8
, c
12
y
24
− 16y
23
+ ··· − 4y + 1
c
3
(y
8
− 3y
7
+ 7y
6
− 10y
5
+ 11y
4
− 10y
3
+ 6y
2
− 4y + 1)
3
c
4
, c
5
, c
10
(y
8
− 7y
7
+ 19y
6
− 22y
5
+ 3y
4
+ 14y
3
− 6y
2
− 4y + 1)
3
c
9
, c
11
(y
8
+ 5y
7
+ 11y
6
+ 6y
5
− 17y
4
− 34y
3
− 22y
2
− 4y + 1)
3
14
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 1.180120 + 0.268597I
a = 0.076281 − 0.895533I
b = −0.077043 + 0.520180I
1.04066 + 1.13123I 7.41522 − 0.51079I
u = 1.180120 + 0.268597I
a = 0.459141 + 0.156574I
b = 0.701428 − 0.662460I
1.04066 + 1.13123I 7.41522 − 0.51079I
u = 1.180120 + 0.268597I
a = −2.78777 − 0.16222I
b = −1.76612 + 1.60362I
1.04066 + 1.13123I 7.41522 − 0.51079I
u = 1.180120 − 0.268597I
a = 0.076281 + 0.895533I
b = −0.077043 − 0.520180I
1.04066 − 1.13123I 7.41522 + 0.51079I
u = 1.180120 − 0.268597I
a = 0.459141 − 0.156574I
b = 0.701428 + 0.662460I
1.04066 − 1.13123I 7.41522 + 0.51079I
u = 1.180120 − 0.268597I
a = −2.78777 + 0.16222I
b = −1.76612 − 1.60362I
1.04066 − 1.13123I 7.41522 + 0.51079I
u = 0.108090 + 0.747508I
a = 0.113638 − 0.691981I
b = 0.212333 + 0.099676I
−2.15941 + 2.57849I 4.27708 − 3.56796I
u = 0.108090 + 0.747508I
a = −0.963002 − 0.938902I
b = −0.991467 − 0.421518I
−2.15941 + 2.57849I 4.27708 − 3.56796I
u = 0.108090 + 0.747508I
a = 3.56457 + 3.92845I
b = 2.48961 + 1.65363I
−2.15941 + 2.57849I 4.27708 − 3.56796I
u = 0.108090 − 0.747508I
a = 0.113638 + 0.691981I
b = 0.212333 − 0.099676I
−2.15941 − 2.57849I 4.27708 + 3.56796I
15
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.108090 − 0.747508I
a = −0.963002 + 0.938902I
b = −0.991467 + 0.421518I
−2.15941 − 2.57849I 4.27708 + 3.56796I
u = 0.108090 − 0.747508I
a = 3.56457 − 3.92845I
b = 2.48961 − 1.65363I
−2.15941 − 2.57849I 4.27708 + 3.56796I
u = −1.37100
a = 0.636845 + 0.458999I
b = −0.572115 + 0.288256I
6.50273 13.8640
u = −1.37100
a = 0.636845 − 0.458999I
b = −0.572115 − 0.288256I
6.50273 13.8640
u = −1.37100
a = −1.57420
b = 3.34059
6.50273 13.8640
u = −1.334530 + 0.318930I
a = −0.244708 − 1.025470I
b = 1.179160 − 0.265563I
2.37968 − 6.44354I 9.42845 + 5.29417I
u = −1.334530 + 0.318930I
a = −0.156204 − 0.575525I
b = −0.287346 − 0.164227I
2.37968 − 6.44354I 9.42845 + 5.29417I
u = −1.334530 + 0.318930I
a = 0.46011 + 3.64228I
b = −2.95543 + 1.74073I
2.37968 − 6.44354I 9.42845 + 5.29417I
u = −1.334530 − 0.318930I
a = −0.244708 + 1.025470I
b = 1.179160 + 0.265563I
2.37968 + 6.44354I 9.42845 − 5.29417I
u = −1.334530 − 0.318930I
a = −0.156204 + 0.575525I
b = −0.287346 + 0.164227I
2.37968 + 6.44354I 9.42845 − 5.29417I
16
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −1.334530 − 0.318930I
a = 0.46011 − 3.64228I
b = −2.95543 − 1.74073I
2.37968 + 6.44354I 9.42845 − 5.29417I
u = 0.463640
a = −0.636726 + 0.745558I
b = 0.458330 − 0.091081I
0.845036 11.8940
u = 0.463640
a = −0.636726 − 0.745558I
b = 0.458330 + 0.091081I
0.845036 11.8940
u = 0.463640
a = −1.47016
b = −2.12327
0.845036 11.8940
17
III. I
u
3
= hb − 1, 2u
3
− 3u
2
+ 3a − 3u + 3, u
4
− 3u
2
+ 3i
(i) Arc colorings
a
4
=
1
0
a
10
=
0
u
a
5
=
1
−u
2
a
11
=
u
−u
3
+ u
a
6
=
−u
2
+ 1
u
2
− 3
a
8
=
−
2
3
u
3
+ u
2
+ u − 1
1
a
12
=
−u
3
+ 2u
−u
3
+ u
a
1
=
−
1
3
u
3
− u
2
+ u + 1
−u
3
+ u − 1
a
7
=
1
3
u
3
+ u
2
− u − 1
u
3
− u + 1
a
9
=
−u
3
+ 2u
−u
3
+ u
a
3
=
−u
2
+ 1
u
2
− 3
a
2
=
−
1
3
u
3
− 2u
2
+ u + 2
−u
3
+ u
2
+ u − 4
(ii) Obstruction class = 1
(iii) Cusp Shapes = −4u
2
+ 12
18
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
2
, c
12
(u − 1)
4
c
3
, c
9
, c
11
u
4
+ 3u
2
+ 3
c
4
, c
5
, c
10
u
4
− 3u
2
+ 3
c
6
, c
7
, c
8
(u + 1)
4
19
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
2
, c
6
c
7
, c
8
, c
12
(y − 1)
4
c
3
, c
9
, c
11
(y
2
+ 3y + 3)
2
c
4
, c
5
, c
10
(y
2
− 3y + 3)
2
20
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = 1.271230 + 0.340625I
a = 0.696660 + 0.132080I
b = 1.00000
4.05977I 6.00000 − 3.46410I
u = 1.271230 − 0.340625I
a = 0.696660 − 0.132080I
b = 1.00000
− 4.05977I 6.00000 + 3.46410I
u = −1.271230 + 0.340625I
a = 0.30334 − 1.59997I
b = 1.00000
− 4.05977I 6.00000 + 3.46410I
u = −1.271230 − 0.340625I
a = 0.30334 + 1.59997I
b = 1.00000
4.05977I 6.00000 − 3.46410I
21
IV. I
u
4
= hb + 1, −u
2
+ a + u + 1, u
4
− u
2
− 1i
(i) Arc colorings
a
4
=
1
0
a
10
=
0
u
a
5
=
1
−u
2
a
11
=
u
−u
3
+ u
a
6
=
−u
2
+ 1
−u
2
+ 1
a
8
=
u
2
− u − 1
−1
a
12
=
−u
3
+ 2u
−u
3
+ u
a
1
=
−u
3
+ u
2
+ u − 1
−u
3
+ u − 1
a
7
=
−u
3
+ u
2
+ u − 1
−u
3
+ u − 1
a
9
=
u
3
− 2u
u
3
− u
a
3
=
u
2
− 1
u
2
− 1
a
2
=
−u
3
+ 2u
2
+ u − 2
−u
3
+ u
2
+ u − 2
(ii) Obstruction class = 1
(iii) Cusp Shapes = 4u
2
+ 4
22
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
6
, c
7
c
8
(u − 1)
4
c
2
, c
12
(u + 1)
4
c
3
, c
9
, c
11
u
4
+ u
2
− 1
c
4
, c
5
, c
10
u
4
− u
2
− 1
23
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
2
, c
6
c
7
, c
8
, c
12
(y − 1)
4
c
3
, c
9
, c
11
(y
2
+ y − 1)
2
c
4
, c
5
, c
10
(y
2
− y − 1)
2
24
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
4
√
−1(vol +
√
−1CS) Cusp shape
u = 0.786151I
a = −1.61803 − 0.78615I
b = −1.00000
−3.94784 1.52790
u = − 0.786151I
a = −1.61803 + 0.78615I
b = −1.00000
−3.94784 1.52790
u = 1.27202
a = −0.653986
b = −1.00000
3.94784 10.4720
u = −1.27202
a = 1.89005
b = −1.00000
3.94784 10.4720
25
V. I
v
1
= ha, b − 1, v − 1i
(i) Arc colorings
a
4
=
1
0
a
10
=
1
0
a
5
=
1
0
a
11
=
1
0
a
6
=
1
0
a
8
=
0
1
a
12
=
1
0
a
1
=
1
−1
a
7
=
−1
1
a
9
=
1
0
a
3
=
1
0
a
2
=
2
−1
(ii) Obstruction class = 1
(iii) Cusp Shapes = 0
26
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
2
, c
12
u − 1
c
3
, c
4
, c
5
c
9
, c
10
, c
11
u
c
6
, c
7
, c
8
u + 1
27
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
2
, c
6
c
7
, c
8
, c
12
y − 1
c
3
, c
4
, c
5
c
9
, c
10
, c
11
y
28
(vi) Complex Volumes and Cusp Shapes
Solutions to I
v
1
√
−1(vol +
√
−1CS) Cusp shape
v = 1.00000
a = 0
b = 1.00000
0 0
29
VI. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
((u − 1)
9
)(u
24
+ 16u
23
+ ··· + 4u + 1)(u
61
+ 24u
60
+ ··· + 3579u + 49)
c
2
((u − 1)
5
)(u + 1)
4
(u
24
− 8u
22
+ ··· + 2u − 1)
· (u
61
− 2u
60
+ ··· + 31u + 7)
c
3
u(u
4
+ u
2
− 1)(u
4
+ 3u
2
+ 3)(u
8
− u
7
+ ··· + 2u − 1)
3
· (u
61
+ 2u
60
+ ··· − 9398u + 5482)
c
4
, c
5
, c
10
u(u
4
− 3u
2
+ 3)(u
4
− u
2
− 1)(u
8
+ u
7
− 3u
6
− 2u
5
+ 3u
4
+ 2u − 1)
3
· (u
61
− 2u
60
+ ··· + 2u + 2)
c
6
((u − 1)
4
)(u + 1)
5
(u
24
− 8u
22
+ ··· + 2u − 1)
· (u
61
− 2u
60
+ ··· + 31u + 7)
c
7
, c
8
((u − 1)
4
)(u + 1)
5
(u
24
− 8u
22
+ ··· + 2u − 1)
· (u
61
+ 2u
60
+ ··· − 69u + 7)
c
9
, c
11
u(u
4
+ u
2
− 1)(u
4
+ 3u
2
+ 3)
· (u
8
− 3u
7
+ 7u
6
− 10u
5
+ 11u
4
− 10u
3
+ 6u
2
− 4u + 1)
3
· (u
61
+ 6u
60
+ ··· + 736u + 128)
c
12
((u − 1)
5
)(u + 1)
4
(u
24
− 8u
22
+ ··· + 2u − 1)
· (u
61
+ 2u
60
+ ··· − 69u + 7)
30
VII. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
((y − 1)
9
)(y
24
− 16y
23
+ ··· + 12y + 1)
· (y
61
+ 36y
60
+ ··· + 7535175y − 2401)
c
2
, c
6
((y − 1)
9
)(y
24
− 16y
23
+ ··· − 4y + 1)(y
61
− 24y
60
+ ··· + 3579y − 49)
c
3
y(y
2
+ y − 1)
2
(y
2
+ 3y + 3)
2
· (y
8
− 3y
7
+ 7y
6
− 10y
5
+ 11y
4
− 10y
3
+ 6y
2
− 4y + 1)
3
· (y
61
− 10y
60
+ ··· − 675769720y − 30052324)
c
4
, c
5
, c
10
y(y
2
− 3y + 3)
2
(y
2
− y − 1)
2
· (y
8
− 7y
7
+ 19y
6
− 22y
5
+ 3y
4
+ 14y
3
− 6y
2
− 4y + 1)
3
· (y
61
− 50y
60
+ ··· + 8y − 4)
c
7
, c
8
, c
12
((y − 1)
9
)(y
24
− 16y
23
+ ··· − 4y + 1)(y
61
− 64y
60
+ ··· + 4075y − 49)
c
9
, c
11
y(y
2
+ y − 1)
2
(y
2
+ 3y + 3)
2
· (y
8
+ 5y
7
+ 11y
6
+ 6y
5
− 17y
4
− 34y
3
− 22y
2
− 4y + 1)
3
· (y
61
+ 38y
60
+ ··· + 115712y − 16384)
31
