12n
0101
(K12n
0101
)
A knot diagram
1
Linearized knot diagam
3 5 8 2 9 12 3 11 1 6 8 10
Solving Sequence
3,8 7,12
6 11 9 5 2 1 10 4
c
7
c
6
c
11
c
8
c
5
c
2
c
1
c
9
c
4
c
3
, c
10
, c
12
Ideals for irreducible components
2
of X
par
I
u
1
= h1.59917 × 10
63
u
33
− 4.04815 × 10
63
u
32
+ ··· + 1.01107 × 10
66
b + 7.19589 × 10
65
,
2.84744 × 10
64
u
33
− 3.34343 × 10
64
u
32
+ ··· + 1.61772 × 10
67
a − 7.28658 × 10
66
,
u
34
− 2u
33
+ ··· + 400u − 128i
I
u
2
= h4784545058115u
24
a + 8814443854630u
24
+ ··· − 99015474327346a + 74552531293308,
140691453969588u
24
a + 1943939955417363u
24
+ ··· + 540597466811832a + 15906220085088582,
u
25
− u
24
+ ··· + 4u + 4i
I
u
3
= hb + 1, −4u
2
+ 2a − 2u − 5, u
3
+ u
2
+ 2u + 1i
I
u
4
= h2au + b + a + u − 1, a
2
− 6au + 10a − 29u + 47, u
2
− u − 1i
I
v
1
= ha, −20v
2
+ 13b + 69v −1, 4v
3
− 13v
2
− v −1i
I
v
2
= ha, b
2
− bv −b + v + 1, v
2
+ v + 1i
* 6 irreducible components of dim
C
= 0, with total 98 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
=
h1.60×10
63
u
33
−4.05×10
63
u
32
+· · ·+1.01×10
66
b+7.20×10
65
, 2.85×10
64
u
33
−
3.34 × 10
64
u
32
+ · · · + 1.62 × 10
67
a − 7.29 × 10
66
, u
34
− 2u
33
+ · · · + 400u − 128i
(i) Arc colorings
a
3
=
0
u
a
8
=
1
0
a
7
=
1
−u
2
a
12
=
−0.00176016u
33
+ 0.00206675u
32
+ ··· + 0.145149u + 0.450423
−0.00158165u
33
+ 0.00400381u
32
+ ··· + 2.00876u − 0.711707
a
6
=
−0.000752148u
33
+ 0.00180308u
32
+ ··· − 0.0951497u + 0.841117
0.00232746u
33
− 0.00334332u
32
+ ··· + 0.699372u − 0.556479
a
11
=
−0.000178509u
33
− 0.00193705u
32
+ ··· − 1.86361u + 1.16213
−0.00158165u
33
+ 0.00400381u
32
+ ··· + 2.00876u − 0.711707
a
9
=
−0.000793255u
33
+ 0.000256525u
32
+ ··· + 1.90039u + 0.0186257
−0.00108195u
33
+ 0.00161394u
32
+ ··· − 1.21132u + 0.797112
a
5
=
0.00194472u
33
− 0.00378095u
32
+ ··· − 4.35824u + 0.981712
−0.00233421u
33
+ 0.00660539u
32
+ ··· + 6.08710u − 1.30793
a
2
=
0.000389490u
33
− 0.00282444u
32
+ ··· − 1.72886u + 0.326216
−0.00233421u
33
+ 0.00660539u
32
+ ··· + 6.08710u − 1.30793
a
1
=
0.000389490u
33
− 0.00282444u
32
+ ··· − 1.72886u + 0.326216
−0.00149271u
33
+ 0.00529712u
32
+ ··· + 5.21906u − 1.04611
a
10
=
−0.00250395u
33
+ 0.00347839u
32
+ ··· + 1.84036u + 0.964059
0.00443973u
33
− 0.00740068u
32
+ ··· − 2.07611u − 0.614602
a
4
=
−u
u
(ii) Obstruction class = −1
(iii) Cusp Shapes = −0.0304081u
33
+ 0.0343758u
32
+ ··· + 21.2214u + 3.74656
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
34
+ 19u
33
+ ··· + 24097u + 256
c
2
, c
4
u
34
− 5u
33
+ ··· + 129u + 16
c
3
, c
7
u
34
− 2u
33
+ ··· + 400u − 128
c
5
, c
6
8(8u
34
− 12u
33
+ ··· − 20u − 4)
c
8
, c
9
, c
11
c
12
u
34
− 3u
33
+ ··· − 14u + 1
c
10
u
34
+ 6u
33
+ ··· − 960u − 256
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
34
− 3y
33
+ ··· − 473567809y + 65536
c
2
, c
4
y
34
− 19y
33
+ ··· − 24097y + 256
c
3
, c
7
y
34
+ 12y
33
+ ··· − 83200y + 16384
c
5
, c
6
64(64y
34
− 336y
33
+ ··· − 672y + 16)
c
8
, c
9
, c
11
c
12
y
34
+ 15y
33
+ ··· − 100y + 1
c
10
y
34
+ 22y
33
+ ··· − 872448y + 65536
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.794712 + 0.456011I
a = −0.188293 + 1.208770I
b = −0.240887 − 0.522076I
−1.49824 + 0.24728I 0.14004 − 3.83407I
u = −0.794712 − 0.456011I
a = −0.188293 − 1.208770I
b = −0.240887 + 0.522076I
−1.49824 − 0.24728I 0.14004 + 3.83407I
u = −0.832178 + 0.785945I
a = 0.447308 − 0.208329I
b = −0.408436 + 0.761565I
−1.67003 − 2.80421I 0.86901 + 5.38758I
u = −0.832178 − 0.785945I
a = 0.447308 + 0.208329I
b = −0.408436 − 0.761565I
−1.67003 + 2.80421I 0.86901 − 5.38758I
u = −0.059447 + 1.230540I
a = −1.319320 + 0.166847I
b = −1.210090 + 0.579679I
5.21011 − 1.36737I 3.81985 − 1.34255I
u = −0.059447 − 1.230540I
a = −1.319320 − 0.166847I
b = −1.210090 − 0.579679I
5.21011 + 1.36737I 3.81985 + 1.34255I
u = 0.393005 + 1.221530I
a = −1.127800 − 0.513887I
b = −1.39318 − 0.40476I
4.28492 − 4.01263I −0.30460 + 7.28252I
u = 0.393005 − 1.221530I
a = −1.127800 + 0.513887I
b = −1.39318 + 0.40476I
4.28492 + 4.01263I −0.30460 − 7.28252I
u = 0.720618 + 1.080510I
a = −0.955921 − 0.511219I
b = −0.583998 + 0.942648I
2.44267 − 4.12024I 3.28639 + 5.00197I
u = 0.720618 − 1.080510I
a = −0.955921 + 0.511219I
b = −0.583998 − 0.942648I
2.44267 + 4.12024I 3.28639 − 5.00197I
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.650367 + 0.044010I
a = 1.12796 − 1.09386I
b = −0.930560 + 0.199538I
0.690195 + 0.080524I 8.8969 − 15.6686I
u = 0.650367 − 0.044010I
a = 1.12796 + 1.09386I
b = −0.930560 − 0.199538I
0.690195 − 0.080524I 8.8969 + 15.6686I
u = 0.39356 + 1.36168I
a = 1.203780 − 0.501729I
b = 0.474808 − 1.157210I
−6.44421 − 6.99411I −2.98433 + 6.50573I
u = 0.39356 − 1.36168I
a = 1.203780 + 0.501729I
b = 0.474808 + 1.157210I
−6.44421 + 6.99411I −2.98433 − 6.50573I
u = −0.87961 + 1.15587I
a = −0.913426 + 0.382143I
b = −0.464763 − 1.155720I
−0.80760 + 9.64229I −2.05779 − 8.26691I
u = −0.87961 − 1.15587I
a = −0.913426 − 0.382143I
b = −0.464763 + 1.155720I
−0.80760 − 9.64229I −2.05779 + 8.26691I
u = 1.35864 + 0.52500I
a = 0.193842 − 0.210406I
b = 0.541334 + 1.208100I
−5.25087 + 10.27080I −2.87805 − 7.59115I
u = 1.35864 − 0.52500I
a = 0.193842 + 0.210406I
b = 0.541334 − 1.208100I
−5.25087 − 10.27080I −2.87805 + 7.59115I
u = −1.45769 + 0.28609I
a = 0.190522 + 0.239926I
b = 0.437920 − 1.051280I
−3.76533 − 4.11043I −1.57621 + 5.08065I
u = −1.45769 − 0.28609I
a = 0.190522 − 0.239926I
b = 0.437920 + 1.051280I
−3.76533 + 4.11043I −1.57621 − 5.08065I
6
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.20308 + 1.50476I
a = 0.650989 − 0.156764I
b = 0.450406 − 0.473646I
3.73592 + 1.81982I 0.08831 + 1.82850I
u = −0.20308 − 1.50476I
a = 0.650989 + 0.156764I
b = 0.450406 + 0.473646I
3.73592 − 1.81982I 0.08831 − 1.82850I
u = −0.475511
a = 1.67568
b = −0.0960916
−1.21807 −10.2050
u = 0.81913 + 1.33067I
a = 1.41026 + 0.17074I
b = 0.64527 − 1.33926I
−2.5846 − 17.9258I −1.78648 + 9.71152I
u = 0.81913 − 1.33067I
a = 1.41026 − 0.17074I
b = 0.64527 + 1.33926I
−2.5846 + 17.9258I −1.78648 − 9.71152I
u = 0.042281 + 0.429124I
a = 0.167290 − 0.199986I
b = 0.23202 + 1.50109I
−10.86120 + 5.07702I 13.61431 + 1.23428I
u = 0.042281 − 0.429124I
a = 0.167290 + 0.199986I
b = 0.23202 − 1.50109I
−10.86120 − 5.07702I 13.61431 − 1.23428I
u = −0.68128 + 1.43732I
a = 1.280410 + 0.028747I
b = 0.641425 + 1.240980I
0.15639 + 11.56040I 0.62674 − 6.67003I
u = −0.68128 − 1.43732I
a = 1.280410 − 0.028747I
b = 0.641425 − 1.240980I
0.15639 − 11.56040I 0.62674 + 6.67003I
u = −0.09648 + 1.64631I
a = 0.710357 + 0.202519I
b = 0.514600 + 0.733387I
3.88573 + 4.85584I 1.37960 − 7.57560I
7
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.09648 − 1.64631I
a = 0.710357 − 0.202519I
b = 0.514600 − 0.733387I
3.88573 − 4.85584I 1.37960 + 7.57560I
u = 0.327433
a = 1.02586
b = −0.565142
0.885375 11.5390
u = 1.70092 + 0.16271I
a = 0.068129 − 0.255918I
b = 0.124754 + 0.960782I
−12.03160 + 0.52686I 0. − 14.5498I
u = 1.70092 − 0.16271I
a = 0.068129 + 0.255918I
b = 0.124754 − 0.960782I
−12.03160 − 0.52686I 0. + 14.5498I
8
II.
I
u
2
= h4.78×10
12
au
24
+8.81×10
12
u
24
+· · ·−9.90×10
13
a+7.46×10
13
, 1.41×
10
14
au
24
+1.94×10
15
u
24
+· · ·+5.41×10
14
a+1.59×10
16
, u
25
−u
24
+· · ·+4u+4i
(i) Arc colorings
a
3
=
0
u
a
8
=
1
0
a
7
=
1
−u
2
a
12
=
a
−0.258951au
24
− 0.477058u
24
+ ··· + 5.35894a − 4.03495
a
6
=
−0.124665au
24
− 3.59160u
24
+ ··· + 1.27680a − 26.1250
−0.924644au
24
+ 1.04931u
24
+ ··· + 1.62244a − 2.89924
a
11
=
0.258951au
24
+ 0.477058u
24
+ ··· − 4.35894a + 4.03495
−0.258951au
24
− 0.477058u
24
+ ··· + 5.35894a − 4.03495
a
9
=
−1.08855au
24
+ 0.147616u
24
+ ··· − 0.207055a − 8.18295
1.26334au
24
− 1.09943u
24
+ ··· − 2.69616a + 4.52566
a
5
=
−0.663007u
24
+ 0.208677u
23
+ ··· − 5.67662u − 0.806984
0.644979u
24
− 0.740559u
23
+ ··· + 3.48093u − 1.06790
a
2
=
0.0180278u
24
+ 0.531881u
23
+ ··· + 2.19569u + 1.87488
0.644979u
24
− 0.740559u
23
+ ··· + 3.48093u − 1.06790
a
1
=
0.0180278u
24
+ 0.531881u
23
+ ··· + 2.19569u + 1.87488
0.651848u
24
− 0.230278u
23
+ ··· + 5.75268u + 1.13174
a
10
=
−0.477058au
24
+ 0.192998u
24
+ ··· − 4.03495a − 6.54862
1
a
4
=
−u
u
(ii) Obstruction class = −1
(iii) Cusp Shapes
= −
6062761600965
9238337702138
u
24
−
3225176474347
9238337702138
u
23
+ ··· −
61042729884201
9238337702138
u −
9798007398656
4619168851069
9
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
(u
25
+ 11u
24
+ ··· − 2u + 1)
2
c
2
, c
4
(u
25
− 3u
24
+ ··· − 4u + 1)
2
c
3
, c
7
(u
25
− u
24
+ ··· + 4u + 4)
2
c
5
, c
6
u
50
− 4u
49
+ ··· + 9832u + 2407
c
8
, c
9
, c
11
c
12
u
50
+ 8u
49
+ ··· + 434u + 49
c
10
(u
25
− 2u
24
+ ··· + 3u − 1)
2
10
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
(y
25
+ 9y
24
+ ··· − 2y −1)
2
c
2
, c
4
(y
25
− 11y
24
+ ··· − 2y −1)
2
c
3
, c
7
(y
25
+ 15y
24
+ ··· − 88y −16)
2
c
5
, c
6
y
50
+ 18y
49
+ ··· + 211966944y + 5793649
c
8
, c
9
, c
11
c
12
y
50
+ 30y
49
+ ··· + 4704y + 2401
c
10
(y
25
+ 8y
24
+ ··· + 11y −1)
2
11
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.111975 + 0.962557I
a = 1.72008 − 0.26684I
b = 0.665176 + 0.113324I
−3.49154 − 2.66172I 1.28523 + 3.57661I
u = 0.111975 + 0.962557I
a = −1.13128 + 1.66859I
b = −0.381710 + 1.094260I
−3.49154 − 2.66172I 1.28523 + 3.57661I
u = 0.111975 − 0.962557I
a = 1.72008 + 0.26684I
b = 0.665176 − 0.113324I
−3.49154 + 2.66172I 1.28523 − 3.57661I
u = 0.111975 − 0.962557I
a = −1.13128 − 1.66859I
b = −0.381710 − 1.094260I
−3.49154 + 2.66172I 1.28523 − 3.57661I
u = −1.061780 + 0.135314I
a = 0.240534 + 0.826928I
b = 0.394082 − 0.313244I
−1.76494 + 0.43356I 0.911962 + 0.045065I
u = −1.061780 + 0.135314I
a = 0.157939 + 0.550535I
b = −0.287348 − 0.868580I
−1.76494 + 0.43356I 0.911962 + 0.045065I
u = −1.061780 − 0.135314I
a = 0.240534 − 0.826928I
b = 0.394082 + 0.313244I
−1.76494 − 0.43356I 0.911962 − 0.045065I
u = −1.061780 − 0.135314I
a = 0.157939 − 0.550535I
b = −0.287348 + 0.868580I
−1.76494 − 0.43356I 0.911962 − 0.045065I
u = 0.465035 + 1.033020I
a = 1.48303 − 0.11082I
b = 0.86062 − 1.16851I
−5.20581 − 5.41987I −3.35697 + 6.54919I
u = 0.465035 + 1.033020I
a = 0.034490 + 0.179256I
b = 0.30041 + 1.61643I
−5.20581 − 5.41987I −3.35697 + 6.54919I
12
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.465035 − 1.033020I
a = 1.48303 + 0.11082I
b = 0.86062 + 1.16851I
−5.20581 + 5.41987I −3.35697 − 6.54919I
u = 0.465035 − 1.033020I
a = 0.034490 − 0.179256I
b = 0.30041 − 1.61643I
−5.20581 + 5.41987I −3.35697 − 6.54919I
u = 1.096160 + 0.296196I
a = 0.424515 + 0.723296I
b = 0.877631 − 0.175572I
−2.14901 + 5.11531I −0.18255 − 5.48464I
u = 1.096160 + 0.296196I
a = 0.133523 + 0.354909I
b = −0.531250 − 1.162460I
−2.14901 + 5.11531I −0.18255 − 5.48464I
u = 1.096160 − 0.296196I
a = 0.424515 − 0.723296I
b = 0.877631 + 0.175572I
−2.14901 − 5.11531I −0.18255 + 5.48464I
u = 1.096160 − 0.296196I
a = 0.133523 − 0.354909I
b = −0.531250 + 1.162460I
−2.14901 − 5.11531I −0.18255 + 5.48464I
u = −0.202658 + 1.122680I
a = −1.19686 + 1.38943I
b = −0.194773 − 1.170190I
−1.18805 + 2.44039I 3.83401 − 3.61173I
u = −0.202658 + 1.122680I
a = −1.88921 − 0.26546I
b = −0.315193 + 0.999419I
−1.18805 + 2.44039I 3.83401 − 3.61173I
u = −0.202658 − 1.122680I
a = −1.19686 − 1.38943I
b = −0.194773 + 1.170190I
−1.18805 − 2.44039I 3.83401 + 3.61173I
u = −0.202658 − 1.122680I
a = −1.88921 + 0.26546I
b = −0.315193 − 0.999419I
−1.18805 − 2.44039I 3.83401 + 3.61173I
13
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.641188 + 0.544744I
a = −0.583198 + 1.057510I
b = 0.440569 + 1.132290I
−6.75523 + 1.05922I −7.39395 − 0.37058I
u = 0.641188 + 0.544744I
a = 3.42198 + 0.62987I
b = 0.321269 − 1.257010I
−6.75523 + 1.05922I −7.39395 − 0.37058I
u = 0.641188 − 0.544744I
a = −0.583198 − 1.057510I
b = 0.440569 − 1.132290I
−6.75523 − 1.05922I −7.39395 + 0.37058I
u = 0.641188 − 0.544744I
a = 3.42198 − 0.62987I
b = 0.321269 + 1.257010I
−6.75523 − 1.05922I −7.39395 + 0.37058I
u = 0.082989 + 0.805818I
a = 1.048640 + 0.674364I
b = 0.914155 + 0.667714I
−3.91328 + 1.39976I 0.957222 − 0.060617I
u = 0.082989 + 0.805818I
a = 0.258734 + 0.032072I
b = −0.07533 − 1.53307I
−3.91328 + 1.39976I 0.957222 − 0.060617I
u = 0.082989 − 0.805818I
a = 1.048640 − 0.674364I
b = 0.914155 − 0.667714I
−3.91328 − 1.39976I 0.957222 + 0.060617I
u = 0.082989 − 0.805818I
a = 0.258734 − 0.032072I
b = −0.07533 + 1.53307I
−3.91328 − 1.39976I 0.957222 + 0.060617I
u = −0.340493 + 0.559321I
a = 0.708209 − 0.192820I
b = 0.071939 − 1.290900I
−3.62565 + 1.50728I 1.02072 − 4.31266I
u = −0.340493 + 0.559321I
a = 1.57740 + 1.43813I
b = 0.478126 + 0.780931I
−3.62565 + 1.50728I 1.02072 − 4.31266I
14
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.340493 − 0.559321I
a = 0.708209 + 0.192820I
b = 0.071939 + 1.290900I
−3.62565 − 1.50728I 1.02072 + 4.31266I
u = −0.340493 − 0.559321I
a = 1.57740 − 1.43813I
b = 0.478126 − 0.780931I
−3.62565 − 1.50728I 1.02072 + 4.31266I
u = 0.291960 + 1.368920I
a = 1.040950 + 0.164703I
b = 0.535319 − 0.817834I
3.63887 + 0.59688I 4.46758 − 1.80507I
u = 0.291960 + 1.368920I
a = −0.439291 − 0.194912I
b = −0.625618 − 0.508372I
3.63887 + 0.59688I 4.46758 − 1.80507I
u = 0.291960 − 1.368920I
a = 1.040950 − 0.164703I
b = 0.535319 + 0.817834I
3.63887 − 0.59688I 4.46758 + 1.80507I
u = 0.291960 − 1.368920I
a = −0.439291 + 0.194912I
b = −0.625618 + 0.508372I
3.63887 − 0.59688I 4.46758 + 1.80507I
u = −0.414621 + 1.342760I
a = 1.111960 − 0.253905I
b = 1.076060 − 0.322023I
3.05811 + 5.44271I 3.50171 − 3.51350I
u = −0.414621 + 1.342760I
a = −1.225620 − 0.254682I
b = −0.730267 − 1.190880I
3.05811 + 5.44271I 3.50171 − 3.51350I
u = −0.414621 − 1.342760I
a = 1.111960 + 0.253905I
b = 1.076060 + 0.322023I
3.05811 − 5.44271I 3.50171 + 3.51350I
u = −0.414621 − 1.342760I
a = −1.225620 + 0.254682I
b = −0.730267 + 1.190880I
3.05811 − 5.44271I 3.50171 + 3.51350I
15
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.55118 + 1.32473I
a = 1.144470 − 0.278607I
b = 0.393415 + 1.053730I
2.03395 + 5.36637I 2.46678 − 3.05337I
u = −0.55118 + 1.32473I
a = −0.537601 − 0.047197I
b = −0.643930 + 0.168348I
2.03395 + 5.36637I 2.46678 − 3.05337I
u = −0.55118 − 1.32473I
a = 1.144470 + 0.278607I
b = 0.393415 − 1.053730I
2.03395 − 5.36637I 2.46678 + 3.05337I
u = −0.55118 − 1.32473I
a = −0.537601 + 0.047197I
b = −0.643930 − 0.168348I
2.03395 − 5.36637I 2.46678 + 3.05337I
u = 0.64072 + 1.29917I
a = 1.012980 + 0.450455I
b = 1.221550 + 0.193871I
1.04287 − 11.39030I 0.71017 + 7.76664I
u = 0.64072 + 1.29917I
a = −1.376020 − 0.045093I
b = −0.73317 + 1.35425I
1.04287 − 11.39030I 0.71017 + 7.76664I
u = 0.64072 − 1.29917I
a = 1.012980 − 0.450455I
b = 1.221550 − 0.193871I
1.04287 + 11.39030I 0.71017 − 7.76664I
u = 0.64072 − 1.29917I
a = −1.376020 + 0.045093I
b = −0.73317 − 1.35425I
1.04287 + 11.39030I 0.71017 − 7.76664I
u = −0.518583
a = −15.1403 + 19.4448I
b = −0.031733 − 1.001510I
−4.48394 −4.44380
u = −0.518583
a = −15.1403 − 19.4448I
b = −0.031733 + 1.001510I
−4.48394 −4.44380
16
III. I
u
3
= hb + 1, −4u
2
+ 2a − 2u − 5, u
3
+ u
2
+ 2u + 1i
(i) Arc colorings
a
3
=
0
u
a
8
=
1
0
a
7
=
1
−u
2
a
12
=
2u
2
+ u +
5
2
−1
a
6
=
1
4
u
2
+
1
2
−
1
2
u
2
a
11
=
2u
2
+ u +
7
2
−1
a
9
=
2u
2
+ u +
9
2
−1
a
5
=
u
2
+ 1
−u
2
a
2
=
−1
−u
2
a
1
=
−1
0
a
10
=
2u
2
+ u +
7
2
−1
a
4
=
−u
u
(ii) Obstruction class = 1
(iii) Cusp Shapes = −
95
4
u
2
−
49
4
u −
153
4
17
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
3
u
3
− u
2
+ 2u − 1
c
2
u
3
+ u
2
− 1
c
4
u
3
− u
2
+ 1
c
5
8(8u
3
+ 12u
2
+ 4u − 1)
c
6
8(8u
3
− 12u
2
+ 4u + 1)
c
7
u
3
+ u
2
+ 2u + 1
c
8
, c
9
(u + 1)
3
c
10
u
3
c
11
, c
12
(u − 1)
3
18
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
3
, c
7
y
3
+ 3y
2
+ 2y −1
c
2
, c
4
y
3
− y
2
+ 2y −1
c
5
, c
6
64(64y
3
− 80y
2
+ 40y −1)
c
8
, c
9
, c
11
c
12
(y −1)
3
c
10
y
3
19
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = −0.215080 + 1.307140I
a = −1.039800 + 0.182582I
b = −1.00000
4.66906 + 2.82812I 3.86575 − 2.65834I
u = −0.215080 − 1.307140I
a = −1.039800 − 0.182582I
b = −1.00000
4.66906 − 2.82812I 3.86575 + 2.65834I
u = −0.569840
a = 2.57960
b = −1.00000
0.531480 −38.9820
20
IV. I
u
4
= h2au + b + a + u − 1, a
2
− 6au + 10a − 29u + 47, u
2
− u − 1i
(i) Arc colorings
a
3
=
0
u
a
8
=
1
0
a
7
=
1
−u − 1
a
12
=
a
−2au − a − u + 1
a
6
=
3au − 5a + 18u − 28
au + 2u − 6
a
11
=
2au + 2a + u − 1
−2au − a − u + 1
a
9
=
−au + a − 7u + 11
1
a
5
=
1
−u − 1
a
2
=
u
−u − 1
a
1
=
u
−3u − 2
a
10
=
−4au − a − 7u + 10
13au + 8a + 2u + 2
a
4
=
−u
u
(ii) Obstruction class = 1
(iii) Cusp Shapes = −8
21
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
(u
2
− 3u + 1)
2
c
2
, c
3
(u
2
+ u − 1)
2
c
4
, c
7
(u
2
− u − 1)
2
c
5
u
4
− 6u
3
+ 18u
2
− 12u + 4
c
6
u
4
+ 6u
3
+ 18u
2
+ 12u + 4
c
8
, c
9
, c
11
c
12
(u
2
+ 1)
2
c
10
u
4
+ 7u
2
+ 1
22
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
(y
2
− 7y + 1)
2
c
2
, c
3
, c
4
c
7
(y
2
− 3y + 1)
2
c
5
, c
6
y
4
+ 188y
2
+ 16
c
8
, c
9
, c
11
c
12
(y + 1)
4
c
10
(y
2
+ 7y + 1)
2
23
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
4
√
−1(vol +
√
−1CS) Cusp shape
u = −0.618034
a = −6.85410 + 4.23607I
b = 1.000000I
−4.27683 −8.00000
u = −0.618034
a = −6.85410 − 4.23607I
b = − 1.000000I
−4.27683 −8.00000
u = 1.61803
a = −0.145898 + 0.236068I
b = − 1.000000I
−12.1725 −8.00000
u = 1.61803
a = −0.145898 − 0.236068I
b = 1.000000I
−12.1725 −8.00000
24
V. I
v
1
= ha, −20v
2
+ 13b + 69v − 1, 4v
3
− 13v
2
− v − 1i
(i) Arc colorings
a
3
=
v
0
a
8
=
1
0
a
7
=
1
0
a
12
=
0
20
13
v
2
−
69
13
v +
1
13
a
6
=
1
12
13
v
2
−
31
13
v −
28
13
a
11
=
−
20
13
v
2
+
69
13
v −
1
13
20
13
v
2
−
69
13
v +
1
13
a
9
=
12
13
v
2
−
31
13
v −
15
13
−
12
13
v
2
+
31
13
v +
28
13
a
5
=
−
20
13
v
2
+
69
13
v −
1
13
4v
2
− 13v − 1
a
2
=
20
13
v
2
−
56
13
v +
1
13
−4v
2
+ 13v + 1
a
1
=
20
13
v
2
−
69
13
v +
1
13
−4v
2
+ 13v + 1
a
10
=
1
−
8
13
v
2
+
38
13
v −
42
13
a
4
=
v
0
(ii) Obstruction class = 1
(iii) Cusp Shapes = −
71
13
v
2
+
373
13
v −
246
13
25
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
2
(u − 1)
3
c
3
, c
7
u
3
c
4
(u + 1)
3
c
5
, c
6
, c
8
c
9
u
3
+ 2u + 1
c
10
u
3
− 3u
2
+ 5u − 2
c
11
, c
12
u
3
+ 2u − 1
26
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
2
, c
4
(y − 1)
3
c
3
, c
7
y
3
c
5
, c
6
, c
8
c
9
, c
11
, c
12
y
3
+ 4y
2
+ 4y − 1
c
10
y
3
+ y
2
+ 13y − 4
27
(vi) Complex Volumes and Cusp Shapes
Solutions to I
v
1
√
−1(vol +
√
−1CS) Cusp shape
v = −0.048505 + 0.268962I
a = 0
b = 0.22670 − 1.46771I
−11.08570 − 5.13794I −19.9326 + 7.8597I
v = −0.048505 − 0.268962I
a = 0
b = 0.22670 + 1.46771I
−11.08570 + 5.13794I −19.9326 − 7.8597I
v = 3.34701
a = 0
b = −0.453398
−0.857735 15.9280
28
VI. I
v
2
= ha, b
2
− bv − b + v + 1, v
2
+ v + 1i
(i) Arc colorings
a
3
=
v
0
a
8
=
1
0
a
7
=
1
0
a
12
=
0
b
a
6
=
1
bv + b − v − 1
a
11
=
−b
b
a
9
=
bv + b − v
−bv − b + v + 1
a
5
=
bv + v + 2
−v − 1
a
2
=
−bv − 2
v + 1
a
1
=
−bv − v − 2
v + 1
a
10
=
−b + v
1
a
4
=
v
0
(ii) Obstruction class = 1
(iii) Cusp Shapes = 4v − 3
29
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
2
(u − 1)
4
c
3
, c
7
u
4
c
4
(u + 1)
4
c
5
, c
6
, c
8
c
9
u
4
− u
3
+ 2u
2
− 2u + 1
c
10
(u
2
+ u + 1)
2
c
11
, c
12
u
4
+ u
3
+ 2u
2
+ 2u + 1
30
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
2
, c
4
(y − 1)
4
c
3
, c
7
y
4
c
5
, c
6
, c
8
c
9
, c
11
, c
12
y
4
+ 3y
3
+ 2y
2
+ 1
c
10
(y
2
+ y + 1)
2
31
(vi) Complex Volumes and Cusp Shapes
Solutions to I
v
2
√
−1(vol +
√
−1CS) Cusp shape
v = −0.500000 + 0.866025I
a = 0
b = 0.621744 − 0.440597I
−4.93480 − 2.02988I −5.00000 + 3.46410I
v = −0.500000 + 0.866025I
a = 0
b = −0.121744 + 1.306620I
−4.93480 − 2.02988I −5.00000 + 3.46410I
v = −0.500000 − 0.866025I
a = 0
b = 0.621744 + 0.440597I
−4.93480 + 2.02988I −5.00000 − 3.46410I
v = −0.500000 − 0.866025I
a = 0
b = −0.121744 − 1.306620I
−4.93480 + 2.02988I −5.00000 − 3.46410I
32
VII. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
(u − 1)
7
(u
2
− 3u + 1)
2
(u
3
− u
2
+ 2u − 1)
· ((u
25
+ 11u
24
+ ··· − 2u + 1)
2
)(u
34
+ 19u
33
+ ··· + 24097u + 256)
c
2
((u − 1)
7
)(u
2
+ u − 1)
2
(u
3
+ u
2
− 1)(u
25
− 3u
24
+ ··· − 4u + 1)
2
· (u
34
− 5u
33
+ ··· + 129u + 16)
c
3
u
7
(u
2
+ u − 1)
2
(u
3
− u
2
+ 2u − 1)(u
25
− u
24
+ ··· + 4u + 4)
2
· (u
34
− 2u
33
+ ··· + 400u − 128)
c
4
((u + 1)
7
)(u
2
− u − 1)
2
(u
3
− u
2
+ 1)(u
25
− 3u
24
+ ··· − 4u + 1)
2
· (u
34
− 5u
33
+ ··· + 129u + 16)
c
5
64(u
3
+ 2u + 1)(8u
3
+ 12u
2
+ 4u − 1)(u
4
− 6u
3
+ ··· − 12u + 4)
· (u
4
− u
3
+ 2u
2
− 2u + 1)(8u
34
− 12u
33
+ ··· − 20u − 4)
· (u
50
− 4u
49
+ ··· + 9832u + 2407)
c
6
64(u
3
+ 2u + 1)(8u
3
− 12u
2
+ 4u + 1)(u
4
− u
3
+ 2u
2
− 2u + 1)
· (u
4
+ 6u
3
+ 18u
2
+ 12u + 4)(8u
34
− 12u
33
+ ··· − 20u − 4)
· (u
50
− 4u
49
+ ··· + 9832u + 2407)
c
7
u
7
(u
2
− u − 1)
2
(u
3
+ u
2
+ 2u + 1)(u
25
− u
24
+ ··· + 4u + 4)
2
· (u
34
− 2u
33
+ ··· + 400u − 128)
c
8
, c
9
(u + 1)
3
(u
2
+ 1)
2
(u
3
+ 2u + 1)(u
4
− u
3
+ 2u
2
− 2u + 1)
· (u
34
− 3u
33
+ ··· − 14u + 1)(u
50
+ 8u
49
+ ··· + 434u + 49)
c
10
u
3
(u
2
+ u + 1)
2
(u
3
− 3u
2
+ 5u − 2)(u
4
+ 7u
2
+ 1)
· ((u
25
− 2u
24
+ ··· + 3u − 1)
2
)(u
34
+ 6u
33
+ ··· − 960u − 256)
c
11
, c
12
(u − 1)
3
(u
2
+ 1)
2
(u
3
+ 2u − 1)(u
4
+ u
3
+ 2u
2
+ 2u + 1)
· (u
34
− 3u
33
+ ··· − 14u + 1)(u
50
+ 8u
49
+ ··· + 434u + 49)
33
VIII. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
(y − 1)
7
(y
2
− 7y + 1)
2
(y
3
+ 3y
2
+ 2y − 1)
· (y
25
+ 9y
24
+ ··· − 2y − 1)
2
· (y
34
− 3y
33
+ ··· − 473567809y + 65536)
c
2
, c
4
(y − 1)
7
(y
2
− 3y + 1)
2
(y
3
− y
2
+ 2y − 1)
· ((y
25
− 11y
24
+ ··· − 2y − 1)
2
)(y
34
− 19y
33
+ ··· − 24097y + 256)
c
3
, c
7
y
7
(y
2
− 3y + 1)
2
(y
3
+ 3y
2
+ 2y − 1)(y
25
+ 15y
24
+ ··· − 88y − 16)
2
· (y
34
+ 12y
33
+ ··· − 83200y + 16384)
c
5
, c
6
4096(y
3
+ 4y
2
+ 4y − 1)(64y
3
− 80y
2
+ 40y − 1)(y
4
+ 188y
2
+ 16)
· (y
4
+ 3y
3
+ 2y
2
+ 1)(64y
34
− 336y
33
+ ··· − 672y + 16)
· (y
50
+ 18y
49
+ ··· + 211966944y + 5793649)
c
8
, c
9
, c
11
c
12
(y − 1)
3
(y + 1)
4
(y
3
+ 4y
2
+ 4y − 1)(y
4
+ 3y
3
+ 2y
2
+ 1)
· (y
34
+ 15y
33
+ ··· − 100y + 1)(y
50
+ 30y
49
+ ··· + 4704y + 2401)
c
10
y
3
(y
2
+ y + 1)
2
(y
2
+ 7y + 1)
2
(y
3
+ y
2
+ 13y − 4)
· ((y
25
+ 8y
24
+ ··· + 11y − 1)
2
)(y
34
+ 22y
33
+ ··· − 872448y + 65536)
34
