12a
0312
(K12a
0312
)
A knot diagram
1
Linearized knot diagam
3 6 8 10 12 2 11 1 5 4 7 9
Solving Sequence
5,9
10 4
1,11
8 3 7 12 6 2
c
9
c
4
c
10
c
8
c
3
c
7
c
12
c
5
c
2
c
1
, c
6
, c
11
Ideals for irreducible components
2
of X
par
I
u
1
= h6.51285 × 10
52
u
38
+ 4.25612 × 10
53
u
37
+ ··· + 3.10340 × 10
55
b − 6.72847 × 10
55
,
5.07566 × 10
53
u
38
+ 1.21366 × 10
54
u
37
+ ··· + 8.27573 × 10
55
a + 1.83729 × 10
55
, u
39
+ 3u
38
+ ··· − 96u − 32i
I
u
2
= h−u
25
a − u
25
+ ··· + 6a + 43, −6u
25
a − 35u
25
+ ··· + 15a − 67, u
26
− u
25
+ ··· + u + 1i
I
u
3
= hu
5
+ b + u, −8u
5
+ 4u
4
+ u
3
+ 3u
2
+ 7a − 11u + 9, u
6
+ u
4
+ 2u
2
+ 1i
I
u
4
= hb + 1, 8a
2
− 2au − 8a + u + 1, u
2
+ 2i
I
v
1
= ha, b − 1, 4v
2
+ 2v + 1i
* 5 irreducible components of dim
C
= 0, with total 103 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
=
h6.51×10
52
u
38
+4.26×10
53
u
37
+· · ·+3.10×10
55
b−6.73×10
55
, 5.08×10
53
u
38
+
1.21 × 10
54
u
37
+ · · · + 8.28 × 10
55
a + 1.84 × 10
55
, u
39
+ 3u
38
+ · · · − 96u − 32i
(i) Arc colorings
a
5
=
0
u
a
9
=
1
0
a
10
=
1
u
2
a
4
=
u
u
3
+ u
a
1
=
−0.00613319u
38
− 0.0146653u
37
+ ··· − 1.67950u − 0.222009
−0.00209862u
38
− 0.0137144u
37
+ ··· + 4.11518u + 2.16810
a
11
=
u
2
+ 1
u
4
+ 2u
2
a
8
=
−0.00371852u
38
− 0.00662758u
37
+ ··· − 2.29660u − 0.339906
0.00563183u
38
+ 0.0246725u
37
+ ··· − 4.41659u − 2.14110
a
3
=
0.00147024u
38
+ 0.00779912u
37
+ ··· − 0.146149u − 0.385271
0.0147761u
38
+ 0.0398452u
37
+ ··· − 1.72908u + 0.367860
a
7
=
−0.00248223u
38
+ 0.00407192u
37
+ ··· − 5.63245u − 2.27061
0.00425275u
38
+ 0.0171497u
37
+ ··· − 2.92659u − 1.68001
a
12
=
−0.00823181u
38
− 0.0283797u
37
+ ··· + 2.43568u + 1.94609
−0.00209862u
38
− 0.0137144u
37
+ ··· + 4.11518u + 2.16810
a
6
=
0.0124595u
38
+ 0.0311845u
37
+ ··· − 1.95527u + 0.644702
0.0123050u
38
+ 0.0359587u
37
+ ··· − 2.29733u + 0.0612259
a
2
=
−0.000124004u
38
− 0.00169964u
37
+ ··· + 0.337679u + 0.864298
0.0145344u
38
+ 0.0352525u
37
+ ··· + 0.739324u + 1.46196
(ii) Obstruction class = −1
(iii) Cusp Shapes = 0.240650u
38
+ 0.650895u
37
+ ··· − 36.8708u + 0.708138
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
39
+ 18u
38
+ ··· + 4081u − 576
c
2
, c
6
u
39
− 2u
38
+ ··· − 7u + 24
c
3
, c
5
64(64u
39
− 32u
38
+ ··· + 42u + 7)
c
4
, c
9
, c
10
u
39
− 3u
38
+ ··· − 96u + 32
c
7
, c
8
, c
11
c
12
u
39
− 2u
38
+ ··· − 34u + 3
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
39
+ 10y
38
+ ··· + 63273697y −331776
c
2
, c
6
y
39
+ 18y
38
+ ··· + 4081y −576
c
3
, c
5
4096(4096y
39
+ 134144y
38
+ ··· + 294y −49)
c
4
, c
9
, c
10
y
39
+ 39y
38
+ ··· − 17408y −1024
c
7
, c
8
, c
11
c
12
y
39
+ 28y
38
+ ··· − 32y −9
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.284805 + 0.928305I
a = −0.13683 − 1.42324I
b = −0.452196 + 0.700666I
−0.54297 + 5.03875I −8.25655 − 9.28786I
u = −0.284805 − 0.928305I
a = −0.13683 + 1.42324I
b = −0.452196 − 0.700666I
−0.54297 − 5.03875I −8.25655 + 9.28786I
u = 0.484749 + 0.961063I
a = 0.477652 − 0.888292I
b = −0.265156 + 0.743897I
−0.68459 − 2.11963I −9.46610 − 1.15998I
u = 0.484749 − 0.961063I
a = 0.477652 + 0.888292I
b = −0.265156 − 0.743897I
−0.68459 + 2.11963I −9.46610 + 1.15998I
u = −0.850562 + 0.700092I
a = −0.913679 − 0.827942I
b = −0.43681 + 1.39469I
7.9219 + 13.0672I −2.83281 − 8.70370I
u = −0.850562 − 0.700092I
a = −0.913679 + 0.827942I
b = −0.43681 − 1.39469I
7.9219 − 13.0672I −2.83281 + 8.70370I
u = 0.021011 + 1.113620I
a = 0.113149 + 0.982543I
b = −0.417378 − 0.585720I
2.61415 − 1.46386I −3.75938 + 4.77609I
u = 0.021011 − 1.113620I
a = 0.113149 − 0.982543I
b = −0.417378 + 0.585720I
2.61415 + 1.46386I −3.75938 − 4.77609I
u = −1.024080 + 0.504017I
a = −0.340192 − 0.350015I
b = 0.242441 + 1.346780I
7.21089 − 6.95675I −1.57897 + 4.70182I
u = −1.024080 − 0.504017I
a = −0.340192 + 0.350015I
b = 0.242441 − 1.346780I
7.21089 + 6.95675I −1.57897 − 4.70182I
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.899466 + 0.710929I
a = −0.806485 + 0.746074I
b = −0.31980 − 1.40480I
9.60981 − 6.62935I −0.44294 + 4.43297I
u = 0.899466 − 0.710929I
a = −0.806485 − 0.746074I
b = −0.31980 + 1.40480I
9.60981 + 6.62935I −0.44294 − 4.43297I
u = 1.046090 + 0.585321I
a = −0.447106 + 0.457880I
b = 0.097717 − 1.375450I
9.08947 + 0.21395I 1.186596 + 0.413950I
u = 1.046090 − 0.585321I
a = −0.447106 − 0.457880I
b = 0.097717 + 1.375450I
9.08947 − 0.21395I 1.186596 − 0.413950I
u = −1.088540 + 0.802120I
a = −0.469791 − 0.757971I
b = −0.104038 + 1.220040I
1.35178 + 3.70831I 0. − 5.50700I
u = −1.088540 − 0.802120I
a = −0.469791 + 0.757971I
b = −0.104038 − 1.220040I
1.35178 − 3.70831I 0. + 5.50700I
u = 0.024809 + 1.389690I
a = −0.682113 + 0.285569I
b = −0.128700 − 0.137181I
4.95731 − 2.14817I 0. + 4.01911I
u = 0.024809 − 1.389690I
a = −0.682113 − 0.285569I
b = −0.128700 + 0.137181I
4.95731 + 2.14817I 0. − 4.01911I
u = −0.087825 + 1.410570I
a = 0.565414 + 0.372983I
b = −0.993287 − 0.445251I
2.42149 − 0.42416I −8.00000 + 0.I
u = −0.087825 − 1.410570I
a = 0.565414 − 0.372983I
b = −0.993287 + 0.445251I
2.42149 + 0.42416I −8.00000 + 0.I
6
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.475767 + 0.181696I
a = 0.383979 − 0.039197I
b = 0.773750 + 0.480261I
−2.68424 − 2.19929I −15.6702 + 1.3086I
u = −0.475767 − 0.181696I
a = 0.383979 + 0.039197I
b = 0.773750 − 0.480261I
−2.68424 + 2.19929I −15.6702 − 1.3086I
u = −0.01764 + 1.52619I
a = 0.955880 + 0.065318I
b = −1.64994 − 0.11450I
5.17213 + 2.58745I 0
u = −0.01764 − 1.52619I
a = 0.955880 − 0.065318I
b = −1.64994 + 0.11450I
5.17213 − 2.58745I 0
u = 0.071403 + 0.441330I
a = 1.51732 − 0.80229I
b = −0.338553 + 0.229132I
−0.54939 − 1.65860I −4.21380 + 1.79570I
u = 0.071403 − 0.441330I
a = 1.51732 + 0.80229I
b = −0.338553 − 0.229132I
−0.54939 + 1.65860I −4.21380 − 1.79570I
u = −0.094781 + 0.360218I
a = 0.544712 + 0.036408I
b = 1.215470 + 0.103619I
−1.37228 + 2.24874I 4.40609 − 10.02980I
u = −0.094781 − 0.360218I
a = 0.544712 − 0.036408I
b = 1.215470 − 0.103619I
−1.37228 − 2.24874I 4.40609 + 10.02980I
u = 0.372322
a = 0.597491
b = 0.434285
−0.672199 −14.5900
u = −0.27857 + 1.61370I
a = 0.62986 + 1.83200I
b = 0.56880 − 1.49325I
15.5418 + 17.2782I 0
7
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.27857 − 1.61370I
a = 0.62986 − 1.83200I
b = 0.56880 + 1.49325I
15.5418 − 17.2782I 0
u = 0.28827 + 1.62593I
a = 0.62219 − 1.76672I
b = 0.48592 + 1.51538I
17.3108 − 11.0467I 0
u = 0.28827 − 1.62593I
a = 0.62219 + 1.76672I
b = 0.48592 − 1.51538I
17.3108 + 11.0467I 0
u = −0.27452 + 1.67561I
a = 0.45265 + 1.68686I
b = 0.351061 − 1.346420I
9.74081 + 8.64375I 0
u = −0.27452 − 1.67561I
a = 0.45265 − 1.68686I
b = 0.351061 + 1.346420I
9.74081 − 8.64375I 0
u = 0.34143 + 1.66879I
a = 0.56308 − 1.50519I
b = 0.14914 + 1.47169I
16.5682 − 5.0648I 0
u = 0.34143 − 1.66879I
a = 0.56308 + 1.50519I
b = 0.14914 − 1.47169I
16.5682 + 5.0648I 0
u = −0.38631 + 1.66978I
a = 0.54657 + 1.37900I
b = 0.00441 − 1.41697I
14.2718 − 1.5060I 0
u = −0.38631 − 1.66978I
a = 0.54657 − 1.37900I
b = 0.00441 + 1.41697I
14.2718 + 1.5060I 0
8
II. I
u
2
= h−u
25
a − u
25
+ · · · + 6a + 43, −6u
25
a − 35u
25
+ · · · + 15a −
67, u
26
− u
25
+ · · · + u + 1i
(i) Arc colorings
a
5
=
0
u
a
9
=
1
0
a
10
=
1
u
2
a
4
=
u
u
3
+ u
a
1
=
a
0.0270270au
25
+ 0.0270270u
25
+ ··· − 0.162162a − 1.16216
a
11
=
u
2
+ 1
u
4
+ 2u
2
a
8
=
0.0270270au
25
+ 1.36036u
25
+ ··· − 1.16216a − 0.495495
0.0270270au
25
+ 0.0270270u
25
+ ··· − 0.162162a + 0.837838
a
3
=
0.990991au
25
− 0.453453u
25
+ ··· + 1.38739a + 2.16517
0.486486au
25
− 0.846847u
25
+ ··· + 0.0810811a − 0.585586
a
7
=
0.0270270au
25
+ 1.36036u
25
+ ··· − 1.16216a − 1.49550
1
a
12
=
0.0270270au
25
+ 0.0270270u
25
+ ··· + 0.837838a − 1.16216
0.0270270au
25
+ 0.0270270u
25
+ ··· − 0.162162a − 1.16216
a
6
=
0.846847au
25
− 1.04204u
25
+ ··· + 0.585586a + 1.14114
−0.324324au
25
− 0.990991u
25
+ ··· − 0.0540541a − 1.38739
a
2
=
−0.774775au
25
− 0.330330u
25
+ ··· + 2.31532a − 1.46246
−0.135135au
25
− 0.801802u
25
+ ··· + 0.810811a − 1.52252
(ii) Obstruction class = −1
(iii) Cusp Shapes = 4u
24
− 4u
23
+ 56u
22
− 52u
21
+ 332u
20
− 284u
19
+ 1080u
18
−
844u
17
+ 2096u
16
− 1484u
15
+ 2508u
14
− 1596u
13
+ 1940u
12
− 1096u
11
+ 1112u
10
−
540u
9
+ 504u
8
− 212u
7
+ 132u
6
− 60u
5
+ 48u
4
− 12u
3
+ 16u
2
− 12u − 6
9
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
(u
26
+ 9u
25
+ ··· + 5u + 1)
2
c
2
, c
6
(u
26
− u
25
+ ··· − u + 1)
2
c
3
, c
5
9(9u
52
− 87u
51
+ ··· − 3.27654 × 10
7
u + 6443297)
c
4
, c
9
, c
10
(u
26
+ u
25
+ ··· − u + 1)
2
c
7
, c
8
, c
11
c
12
u
52
+ 5u
51
+ ··· + 548u + 125
10
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
(y
26
+ 17y
25
+ ··· + 29y + 1)
2
c
2
, c
6
(y
26
+ 9y
25
+ ··· + 5y + 1)
2
c
3
, c
5
81
· (81y
52
+ 2835y
51
+ ··· + 516271175779380y + 41516076230209)
c
4
, c
9
, c
10
(y
26
+ 29y
25
+ ··· + 5y + 1)
2
c
7
, c
8
, c
11
c
12
y
52
+ 39y
51
+ ··· + 151696y + 15625
11
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.557205 + 0.605601I
a = 0.908515 − 0.786612I
b = 0.44461 + 1.37915I
3.14131 − 7.92757I −5.52051 + 8.33110I
u = 0.557205 + 0.605601I
a = −0.546617 + 0.149415I
b = −1.009470 − 0.105339I
3.14131 − 7.92757I −5.52051 + 8.33110I
u = 0.557205 − 0.605601I
a = 0.908515 + 0.786612I
b = 0.44461 − 1.37915I
3.14131 + 7.92757I −5.52051 − 8.33110I
u = 0.557205 − 0.605601I
a = −0.546617 − 0.149415I
b = −1.009470 + 0.105339I
3.14131 + 7.92757I −5.52051 − 8.33110I
u = −0.063283 + 0.808616I
a = −0.774190 + 0.526907I
b = −0.406074 − 1.296320I
7.01322 + 2.64715I 0.54618 − 3.67555I
u = −0.063283 + 0.808616I
a = −1.113660 − 0.448597I
b = −0.481799 + 1.224650I
7.01322 + 2.64715I 0.54618 − 3.67555I
u = −0.063283 − 0.808616I
a = −0.774190 − 0.526907I
b = −0.406074 + 1.296320I
7.01322 − 2.64715I 0.54618 + 3.67555I
u = −0.063283 − 0.808616I
a = −1.113660 + 0.448597I
b = −0.481799 − 1.224650I
7.01322 − 2.64715I 0.54618 + 3.67555I
u = −0.506771 + 0.602442I
a = 0.845502 + 0.826551I
b = 0.283417 − 1.369520I
4.26499 + 2.50037I −3.37218 − 3.68649I
u = −0.506771 + 0.602442I
a = −0.706203 − 0.001643I
b = −0.857226 + 0.277909I
4.26499 + 2.50037I −3.37218 − 3.68649I
12
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.506771 − 0.602442I
a = 0.845502 − 0.826551I
b = 0.283417 + 1.369520I
4.26499 − 2.50037I −3.37218 + 3.68649I
u = −0.506771 − 0.602442I
a = −0.706203 + 0.001643I
b = −0.857226 − 0.277909I
4.26499 − 2.50037I −3.37218 + 3.68649I
u = 0.565256 + 0.486664I
a = 0.876953 − 0.806174I
b = 0.315896 + 0.901619I
−1.29717 − 1.94179I −11.39486 + 3.84898I
u = 0.565256 + 0.486664I
a = 0.023979 − 0.302536I
b = −0.446412 + 0.289709I
−1.29717 − 1.94179I −11.39486 + 3.84898I
u = 0.565256 − 0.486664I
a = 0.876953 + 0.806174I
b = 0.315896 − 0.901619I
−1.29717 + 1.94179I −11.39486 − 3.84898I
u = 0.565256 − 0.486664I
a = 0.023979 + 0.302536I
b = −0.446412 − 0.289709I
−1.29717 + 1.94179I −11.39486 − 3.84898I
u = 0.588033 + 0.339866I
a = 1.354340 + 0.197426I
b = −0.190825 + 1.201440I
2.36739 + 4.00629I −7.77829 − 2.28167I
u = 0.588033 + 0.339866I
a = 0.52368 − 1.59827I
b = 0.544635 − 0.217951I
2.36739 + 4.00629I −7.77829 − 2.28167I
u = 0.588033 − 0.339866I
a = 1.354340 − 0.197426I
b = −0.190825 − 1.201440I
2.36739 − 4.00629I −7.77829 + 2.28167I
u = 0.588033 − 0.339866I
a = 0.52368 + 1.59827I
b = 0.544635 + 0.217951I
2.36739 − 4.00629I −7.77829 + 2.28167I
13
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.489623 + 0.284759I
a = 2.18275 + 0.11119I
b = −0.014701 − 1.195450I
3.40411 + 1.00551I −6.42231 − 3.62739I
u = −0.489623 + 0.284759I
a = 0.06160 + 2.26036I
b = 0.279398 + 0.549276I
3.40411 + 1.00551I −6.42231 − 3.62739I
u = −0.489623 − 0.284759I
a = 2.18275 − 0.11119I
b = −0.014701 + 1.195450I
3.40411 − 1.00551I −6.42231 + 3.62739I
u = −0.489623 − 0.284759I
a = 0.06160 − 2.26036I
b = 0.279398 − 0.549276I
3.40411 − 1.00551I −6.42231 + 3.62739I
u = 0.08778 + 1.44888I
a = 1.36031 + 0.96993I
b = 0.123022 + 0.607999I
7.95687 + 1.77746I −4.37085 − 2.67865I
u = 0.08778 + 1.44888I
a = −1.67018 + 2.70770I
b = 0.003774 − 1.163280I
7.95687 + 1.77746I −4.37085 − 2.67865I
u = 0.08778 − 1.44888I
a = 1.36031 − 0.96993I
b = 0.123022 − 0.607999I
7.95687 − 1.77746I −4.37085 + 2.67865I
u = 0.08778 − 1.44888I
a = −1.67018 − 2.70770I
b = 0.003774 + 1.163280I
7.95687 − 1.77746I −4.37085 + 2.67865I
u = −0.304550 + 0.390095I
a = −2.14676 + 1.48082I
b = −0.147408 + 0.712500I
3.22784 + 0.99254I −5.03716 − 6.67512I
u = −0.304550 + 0.390095I
a = 1.58906 + 2.18030I
b = −0.024365 − 1.159480I
3.22784 + 0.99254I −5.03716 − 6.67512I
14
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.304550 − 0.390095I
a = −2.14676 − 1.48082I
b = −0.147408 − 0.712500I
3.22784 − 0.99254I −5.03716 + 6.67512I
u = −0.304550 − 0.390095I
a = 1.58906 − 2.18030I
b = −0.024365 + 1.159480I
3.22784 − 0.99254I −5.03716 + 6.67512I
u = 0.15393 + 1.51610I
a = −0.244659 + 0.073372I
b = 0.781532 + 0.034297I
5.31067 − 4.47678I −7.30340 + 3.58620I
u = 0.15393 + 1.51610I
a = −0.51526 + 1.89761I
b = −0.374114 − 1.224410I
5.31067 − 4.47678I −7.30340 + 3.58620I
u = 0.15393 − 1.51610I
a = −0.244659 − 0.073372I
b = 0.781532 − 0.034297I
5.31067 + 4.47678I −7.30340 − 3.58620I
u = 0.15393 − 1.51610I
a = −0.51526 − 1.89761I
b = −0.374114 + 1.224410I
5.31067 + 4.47678I −7.30340 − 3.58620I
u = −0.09394 + 1.52190I
a = 0.460645 + 0.452308I
b = 0.665565 − 0.626074I
9.71769 + 2.46970I −0.41193 − 2.77943I
u = −0.09394 + 1.52190I
a = −0.45078 − 2.30789I
b = −0.038145 + 1.373730I
9.71769 + 2.46970I −0.41193 − 2.77943I
u = −0.09394 − 1.52190I
a = 0.460645 − 0.452308I
b = 0.665565 + 0.626074I
9.71769 − 2.46970I −0.41193 + 2.77943I
u = −0.09394 − 1.52190I
a = −0.45078 + 2.30789I
b = −0.038145 − 1.373730I
9.71769 − 2.46970I −0.41193 + 2.77943I
15
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.14965 + 1.56671I
a = −0.427513 + 0.464073I
b = 1.286740 − 0.289716I
11.55040 + 4.90123I −0.29851 − 2.20839I
u = −0.14965 + 1.56671I
a = −0.33833 − 2.00964I
b = −0.45547 + 1.63285I
11.55040 + 4.90123I −0.29851 − 2.20839I
u = −0.14965 − 1.56671I
a = −0.427513 − 0.464073I
b = 1.286740 + 0.289716I
11.55040 − 4.90123I −0.29851 + 2.20839I
u = −0.14965 − 1.56671I
a = −0.33833 + 2.00964I
b = −0.45547 − 1.63285I
11.55040 − 4.90123I −0.29851 + 2.20839I
u = 0.16684 + 1.56649I
a = −0.567065 − 0.388686I
b = 1.367540 + 0.115693I
10.4089 − 10.5785I −2.23924 + 6.94484I
u = 0.16684 + 1.56649I
a = −0.31601 + 1.97598I
b = −0.60715 − 1.60654I
10.4089 − 10.5785I −2.23924 + 6.94484I
u = 0.16684 − 1.56649I
a = −0.567065 + 0.388686I
b = 1.367540 − 0.115693I
10.4089 + 10.5785I −2.23924 − 6.94484I
u = 0.16684 − 1.56649I
a = −0.31601 − 1.97598I
b = −0.60715 + 1.60654I
10.4089 + 10.5785I −2.23924 − 6.94484I
u = −0.01123 + 1.60251I
a = −0.09006 + 1.65768I
b = 0.80517 − 1.55246I
15.1804 + 2.8815I 1.60306 − 2.87824I
u = −0.01123 + 1.60251I
a = −0.11338 − 1.79936I
b = 0.65186 + 1.66532I
15.1804 + 2.8815I 1.60306 − 2.87824I
16
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.01123 − 1.60251I
a = −0.09006 − 1.65768I
b = 0.80517 + 1.55246I
15.1804 − 2.8815I 1.60306 + 2.87824I
u = −0.01123 − 1.60251I
a = −0.11338 + 1.79936I
b = 0.65186 − 1.66532I
15.1804 − 2.8815I 1.60306 + 2.87824I
17
III.
I
u
3
= hu
5
+ b + u, −8u
5
+ 4u
4
+ u
3
+ 3u
2
+ 7a − 11u + 9, u
6
+ u
4
+ 2u
2
+ 1i
(i) Arc colorings
a
5
=
0
u
a
9
=
1
0
a
10
=
1
u
2
a
4
=
u
u
3
+ u
a
1
=
8
7
u
5
−
4
7
u
4
+ ··· +
11
7
u −
9
7
−u
5
− u
a
11
=
u
2
+ 1
u
4
+ 2u
2
a
8
=
−
6
7
u
5
−
3
7
u
4
+ ··· −
10
7
u −
5
7
1
a
3
=
−
29
49
u
4
−
6
49
u
2
+ u −
60
49
−
4
7
u
5
+
2
7
u
4
+ ··· −
2
7
u +
1
7
a
7
=
−
6
7
u
5
−
3
7
u
4
+ ··· −
10
7
u −
5
7
2u
5
+ u
3
+ u + 1
a
12
=
1
7
u
5
−
4
7
u
4
+ ··· +
4
7
u −
9
7
−u
5
− u
a
6
=
−
4
7
u
5
−
20
49
u
4
+ ··· −
9
7
u −
38
49
−
3
7
u
5
+
5
7
u
4
+ ··· +
2
7
u +
6
7
a
2
=
1
7
u
5
−
3
49
u
4
+ ··· +
11
7
u −
40
49
−
5
7
u
5
−
1
7
u
4
+ ··· +
1
7
u −
4
7
(ii) Obstruction class = 1
(iii) Cusp Shapes = 4u
4
+ 4u
2
+ 4
18
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
(u
3
− 3u
2
+ 2u + 1)
2
c
2
(u
3
+ u
2
+ 2u + 1)
2
c
3
49(49u
6
− 14u
5
+ 72u
4
− 32u
3
+ 47u
2
− 26u + 5)
c
4
, c
9
, c
10
u
6
+ u
4
+ 2u
2
+ 1
c
5
49(49u
6
+ 14u
5
+ 72u
4
+ 32u
3
+ 47u
2
+ 26u + 5)
c
6
(u
3
− u
2
+ 2u − 1)
2
c
7
, c
8
, c
11
c
12
(u
2
+ 1)
3
19
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
(y
3
− 5y
2
+ 10y −1)
2
c
2
, c
6
(y
3
+ 3y
2
+ 2y −1)
2
c
3
, c
5
2401(2401y
6
+ 6860y
5
+ ··· − 206y + 25)
c
4
, c
9
, c
10
(y
3
+ y
2
+ 2y + 1)
2
c
7
, c
8
, c
11
c
12
(y + 1)
6
20
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = 0.744862 + 0.877439I
a = 0.262343 − 1.117840I
b = 1.000000I
0.26574 − 2.82812I −3.50976 + 2.97945I
u = 0.744862 − 0.877439I
a = 0.262343 + 1.117840I
b = − 1.000000I
0.26574 + 2.82812I −3.50976 − 2.97945I
u = −0.744862 + 0.877439I
a = −0.749579 − 0.640043I
b = 1.000000I
0.26574 + 2.82812I −3.50976 − 2.97945I
u = −0.744862 − 0.877439I
a = −0.749579 + 0.640043I
b = − 1.000000I
0.26574 − 2.82812I −3.50976 + 2.97945I
u = 0.754878I
a = −1.22705 + 1.52783I
b = − 1.000000I
4.40332 3.01950
u = − 0.754878I
a = −1.22705 − 1.52783I
b = 1.000000I
4.40332 3.01950
21
IV. I
u
4
= hb + 1, 8a
2
− 2au − 8a + u + 1, u
2
+ 2i
(i) Arc colorings
a
5
=
0
u
a
9
=
1
0
a
10
=
1
−2
a
4
=
u
−u
a
1
=
a
−1
a
11
=
−1
0
a
8
=
a + 1
−1
a
3
=
−2au +
1
2
a +
9
8
u −
1
4
au − u
a
7
=
a
−1
a
12
=
a − 1
−1
a
6
=
au +
1
2
a −
7
8
u −
1
4
au
a
2
=
−2au + 2a +
7
8
u −
3
2
au − 2a −
1
2
u +
1
2
(ii) Obstruction class = 1
(iii) Cusp Shapes = −8au + 4u − 8
22
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
2
(u
2
− u + 1)
2
c
3
16(16u
4
+ 16u
3
+ 28u
2
+ 12u + 3)
c
4
, c
9
, c
10
(u
2
+ 2)
2
c
5
16(16u
4
− 16u
3
+ 28u
2
− 12u + 3)
c
6
(u
2
+ u + 1)
2
c
7
, c
8
(u + 1)
4
c
11
, c
12
(u − 1)
4
23
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
2
, c
6
(y
2
+ y + 1)
2
c
3
, c
5
256(256y
4
+ 640y
3
+ 496y
2
+ 24y + 9)
c
4
, c
9
, c
10
(y + 2)
4
c
7
, c
8
, c
11
c
12
(y −1)
4
24
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
4
√
−1(vol +
√
−1CS) Cusp shape
u = 1.414210I
a = 0.806186 + 0.176777I
b = −1.00000
3.28987 + 2.02988I −6.00000 − 3.46410I
u = 1.414210I
a = 0.193814 + 0.176777I
b = −1.00000
3.28987 − 2.02988I −6.00000 + 3.46410I
u = − 1.414210I
a = 0.806186 − 0.176777I
b = −1.00000
3.28987 − 2.02988I −6.00000 + 3.46410I
u = − 1.414210I
a = 0.193814 − 0.176777I
b = −1.00000
3.28987 + 2.02988I −6.00000 − 3.46410I
25
V. I
v
1
= ha, b − 1, 4v
2
+ 2v + 1i
(i) Arc colorings
a
5
=
v
0
a
9
=
1
0
a
10
=
1
0
a
4
=
v
0
a
1
=
0
1
a
11
=
1
0
a
8
=
1
−1
a
3
=
2v
−v
a
7
=
0
−1
a
12
=
1
1
a
6
=
2v
v
a
2
=
2v + 1
−v +
1
2
(ii) Obstruction class = 1
(iii) Cusp Shapes = 7v −
25
2
26
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
6
u
2
− u + 1
c
2
u
2
+ u + 1
c
3
4(4u
2
− 2u + 1)
c
4
, c
9
, c
10
u
2
c
5
4(4u
2
+ 2u + 1)
c
7
, c
8
(u − 1)
2
c
11
, c
12
(u + 1)
2
27
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
2
, c
6
y
2
+ y + 1
c
3
, c
5
16(16y
2
+ 4y + 1)
c
4
, c
9
, c
10
y
2
c
7
, c
8
, c
11
c
12
(y − 1)
2
28
(vi) Complex Volumes and Cusp Shapes
Solutions to I
v
1
√
−1(vol +
√
−1CS) Cusp shape
v = −0.250000 + 0.433013I
a = 0
b = 1.00000
−1.64493 + 2.02988I −14.2500 + 3.0311I
v = −0.250000 − 0.433013I
a = 0
b = 1.00000
−1.64493 − 2.02988I −14.2500 − 3.0311I
29
VI. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
((u
2
− u + 1)
3
)(u
3
− 3u
2
+ 2u + 1)
2
(u
26
+ 9u
25
+ ··· + 5u + 1)
2
· (u
39
+ 18u
38
+ ··· + 4081u − 576)
c
2
((u
2
− u + 1)
2
)(u
2
+ u + 1)(u
3
+ u
2
+ 2u + 1)
2
(u
26
− u
25
+ ··· − u + 1)
2
· (u
39
− 2u
38
+ ··· − 7u + 24)
c
3
1806336(4u
2
− 2u + 1)(16u
4
+ 16u
3
+ 28u
2
+ 12u + 3)
· (49u
6
− 14u
5
+ 72u
4
− 32u
3
+ 47u
2
− 26u + 5)
· (64u
39
− 32u
38
+ ··· + 42u + 7)
· (9u
52
− 87u
51
+ ··· − 32765418u + 6443297)
c
4
, c
9
, c
10
u
2
(u
2
+ 2)
2
(u
6
+ u
4
+ 2u
2
+ 1)(u
26
+ u
25
+ ··· − u + 1)
2
· (u
39
− 3u
38
+ ··· − 96u + 32)
c
5
1806336(4u
2
+ 2u + 1)(16u
4
− 16u
3
+ 28u
2
− 12u + 3)
· (49u
6
+ 14u
5
+ 72u
4
+ 32u
3
+ 47u
2
+ 26u + 5)
· (64u
39
− 32u
38
+ ··· + 42u + 7)
· (9u
52
− 87u
51
+ ··· − 32765418u + 6443297)
c
6
(u
2
− u + 1)(u
2
+ u + 1)
2
(u
3
− u
2
+ 2u − 1)
2
(u
26
− u
25
+ ··· − u + 1)
2
· (u
39
− 2u
38
+ ··· − 7u + 24)
c
7
, c
8
((u − 1)
2
)(u + 1)
4
(u
2
+ 1)
3
(u
39
− 2u
38
+ ··· − 34u + 3)
· (u
52
+ 5u
51
+ ··· + 548u + 125)
c
11
, c
12
((u − 1)
4
)(u + 1)
2
(u
2
+ 1)
3
(u
39
− 2u
38
+ ··· − 34u + 3)
· (u
52
+ 5u
51
+ ··· + 548u + 125)
30
VII. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
((y
2
+ y + 1)
3
)(y
3
− 5y
2
+ 10y − 1)
2
(y
26
+ 17y
25
+ ··· + 29y + 1)
2
· (y
39
+ 10y
38
+ ··· + 63273697y − 331776)
c
2
, c
6
((y
2
+ y + 1)
3
)(y
3
+ 3y
2
+ 2y − 1)
2
(y
26
+ 9y
25
+ ··· + 5y + 1)
2
· (y
39
+ 18y
38
+ ··· + 4081y − 576)
c
3
, c
5
3262849744896(16y
2
+ 4y + 1)(256y
4
+ 640y
3
+ ··· + 24y + 9)
· (2401y
6
+ 6860y
5
+ 8894y
4
+ 5506y
3
+ 1265y
2
− 206y + 25)
· (4096y
39
+ 134144y
38
+ ··· + 294y − 49)
· (81y
52
+ 2835y
51
+ ··· + 516271175779380y + 41516076230209)
c
4
, c
9
, c
10
y
2
(y + 2)
4
(y
3
+ y
2
+ 2y + 1)
2
(y
26
+ 29y
25
+ ··· + 5y + 1)
2
· (y
39
+ 39y
38
+ ··· − 17408y − 1024)
c
7
, c
8
, c
11
c
12
((y − 1)
6
)(y + 1)
6
(y
39
+ 28y
38
+ ··· − 32y − 9)
· (y
52
+ 39y
51
+ ··· + 151696y + 15625)
31
