12a
0625
(K12a
0625
)
A knot diagram
1
Linearized knot diagam
3 7 10 8 11 2 1 12 4 6 9 5
Solving Sequence
2,7 3,10
4 1 8 6 11 5 9 12
c
2
c
3
c
1
c
7
c
6
c
10
c
5
c
9
c
12
c
4
, c
8
, c
11
Ideals for irreducible components
2
of X
par
I
u
1
= h−1457u
41
− 15255u
40
+ ··· + 16b − 57360, −3585u
41
− 36521u
40
+ ··· + 32a − 109328,
u
42
+ 11u
41
+ ··· + 336u + 32i
I
u
2
= h3.42256 × 10
57
a
9
u
8
− 3.62814 × 10
57
a
8
u
8
+ ··· + 3.06417 × 10
58
a + 2.10624 × 10
59
,
− a
9
u
8
+ 4a
8
u
8
+ ··· + 163a + 35, u
9
− u
8
− 2u
7
+ 3u
6
+ u
5
− 3u
4
+ 2u
3
− u + 1i
I
u
3
= h−2u
27
− u
26
+ ··· + b − 6, 6u
27
− 2u
26
+ ··· + a − 4, u
28
− 8u
26
+ ··· − 5u
2
+ 1i
* 3 irreducible components of dim
C
= 0, with total 160 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−1457u
41
− 15255u
40
+ · · · + 16b − 57360, −3585u
41
− 36521u
40
+
· · · + 32a − 109328, u
42
+ 11u
41
+ · · · + 336u + 32i
(i) Arc colorings
a
2
=
1
0
a
7
=
0
u
a
3
=
1
u
2
a
10
=
112.031u
41
+ 1141.28u
40
+ ··· + 33519u + 3416.50
91.0625u
41
+ 953.438u
40
+ ··· + 34226u + 3585
a
4
=
−20u
41
− 211u
40
+ ··· −
10527
2
u −
1023
2
−9u
41
−
233
2
u
40
+ ··· −
12415
2
u − 640
a
1
=
−u
2
+ 1
−u
4
a
8
=
u
5
− 2u
3
+ u
u
7
− u
5
+ u
a
6
=
u
u
a
11
=
50.5313u
41
+ 542.531u
40
+ ··· + 19805u + 2046.50
473
16
u
41
+
5675
16
u
40
+ ··· + 20512u + 2215
a
5
=
−
29
2
u
41
− 140u
40
+ ··· −
6575
2
u −
671
2
−
51
2
u
41
−
469
2
u
40
+ ··· −
4687
2
u − 208
a
9
=
455
8
u
41
+
9607
16
u
40
+ ··· + 21813u + 2262
143
16
u
41
+
1979
16
u
40
+ ··· + 11268u + 1222
a
12
=
75
4
u
41
+ 193u
40
+ ··· +
21905
4
u + 553
−
9
4
u
41
−
27
2
u
40
+ ··· + 2904u + 352
(ii) Obstruction class = −1
(iii) Cusp Shapes = −
9
2
u
41
− 114u
40
+ ··· − 16628u − 1806
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
42
+ 21u
41
+ ··· − 256u + 1024
c
2
, c
6
u
42
− 11u
41
+ ··· − 336u + 32
c
3
, c
5
, c
9
c
10
u
42
+ 17u
40
+ ··· − u + 1
c
4
, c
12
u
42
− 3u
40
+ ··· + u + 1
c
7
u
42
− 30u
41
+ ··· − 6179216u + 430496
c
8
, c
11
u
42
− 24u
41
+ ··· − 10752u + 512
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
42
− y
41
+ ··· + 9240576y + 1048576
c
2
, c
6
y
42
− 21y
41
+ ··· + 256y + 1024
c
3
, c
5
, c
9
c
10
y
42
+ 34y
41
+ ··· − 7y + 1
c
4
, c
12
y
42
− 6y
41
+ ··· − 27y + 1
c
7
y
42
+ 20y
41
+ ··· + 1352203186432y + 185326806016
c
8
, c
11
y
42
+ 24y
41
+ ··· + 262144y + 262144
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.674235 + 0.795277I
a = 0.080408 + 1.328660I
b = 1.110860 + 0.831880I
0.40327 − 5.88245I 2.00000 + 4.81824I
u = −0.674235 − 0.795277I
a = 0.080408 − 1.328660I
b = 1.110860 − 0.831880I
0.40327 + 5.88245I 2.00000 − 4.81824I
u = −0.897205 + 0.535743I
a = 1.61355 − 0.35780I
b = 1.25600 − 1.18547I
3.86650 + 2.93954I 6.87204 − 5.52863I
u = −0.897205 − 0.535743I
a = 1.61355 + 0.35780I
b = 1.25600 + 1.18547I
3.86650 − 2.93954I 6.87204 + 5.52863I
u = −0.196032 + 0.924569I
a = −0.899740 + 0.858235I
b = 0.617120 + 1.000110I
−7.95327 − 7.20205I −2.30272 + 4.84345I
u = −0.196032 − 0.924569I
a = −0.899740 − 0.858235I
b = 0.617120 − 1.000110I
−7.95327 + 7.20205I −2.30272 − 4.84345I
u = −0.513181 + 0.939058I
a = 0.000683 − 0.960818I
b = −0.901913 − 0.493715I
−0.94029 + 1.63835I 5.14240 − 3.16816I
u = −0.513181 − 0.939058I
a = 0.000683 + 0.960818I
b = −0.901913 + 0.493715I
−0.94029 − 1.63835I 5.14240 + 3.16816I
u = −0.199922 + 0.890800I
a = 1.11885 − 0.92567I
b = −0.600904 − 1.181730I
−4.7341 − 13.6105I 0.87068 + 7.00952I
u = −0.199922 − 0.890800I
a = 1.11885 + 0.92567I
b = −0.600904 + 1.181730I
−4.7341 + 13.6105I 0.87068 − 7.00952I
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 1.032180 + 0.369212I
a = 0.212287 + 0.051646I
b = −0.200051 − 0.131687I
−1.81583 − 1.72148I 0
u = 1.032180 − 0.369212I
a = 0.212287 − 0.051646I
b = −0.200051 + 0.131687I
−1.81583 + 1.72148I 0
u = 1.079330 + 0.256072I
a = −0.186841 + 0.199670I
b = 0.252792 − 0.167664I
−0.789550 + 0.559793I 0
u = 1.079330 − 0.256072I
a = −0.186841 − 0.199670I
b = 0.252792 + 0.167664I
−0.789550 − 0.559793I 0
u = −0.631100 + 0.584325I
a = −1.06958 + 1.01232I
b = −0.083490 + 1.263860I
4.63519 + 1.52738I 8.88253 − 1.45936I
u = −0.631100 − 0.584325I
a = −1.06958 − 1.01232I
b = −0.083490 − 1.263860I
4.63519 − 1.52738I 8.88253 + 1.45936I
u = −0.915481 + 0.700428I
a = 1.43441 + 0.67283I
b = 1.78445 − 0.38874I
−0.32564 + 11.42950I 0
u = −0.915481 − 0.700428I
a = 1.43441 − 0.67283I
b = 1.78445 + 0.38874I
−0.32564 − 11.42950I 0
u = −1.056260 + 0.515954I
a = −0.750294 + 0.590460I
b = −0.487854 + 1.010800I
−0.73191 + 4.82324I 0
u = −1.056260 − 0.515954I
a = −0.750294 − 0.590460I
b = −0.487854 − 1.010800I
−0.73191 − 4.82324I 0
6
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.172613 + 0.773707I
a = 0.706336 + 0.041146I
b = −0.090088 − 0.553599I
0.31212 − 1.94553I 1.90117 − 0.77414I
u = 0.172613 − 0.773707I
a = 0.706336 − 0.041146I
b = −0.090088 + 0.553599I
0.31212 + 1.94553I 1.90117 + 0.77414I
u = −0.328546 + 0.702460I
a = −0.763896 − 0.602422I
b = −0.674152 + 0.338684I
3.37169 − 3.11074I 7.82977 + 0.59012I
u = −0.328546 − 0.702460I
a = −0.763896 + 0.602422I
b = −0.674152 − 0.338684I
3.37169 + 3.11074I 7.82977 − 0.59012I
u = −1.105800 + 0.547612I
a = 0.008344 − 0.999378I
b = −0.538045 − 1.109690I
1.12490 + 7.89388I 0
u = −1.105800 − 0.547612I
a = 0.008344 + 0.999378I
b = −0.538045 + 1.109690I
1.12490 − 7.89388I 0
u = −1.034310 + 0.749961I
a = −1.035710 − 0.489167I
b = −1.43809 + 0.27079I
−2.48081 + 4.43896I 0
u = −1.034310 − 0.749961I
a = −1.035710 + 0.489167I
b = −1.43809 − 0.27079I
−2.48081 − 4.43896I 0
u = 1.273780 + 0.320998I
a = 0.339446 + 0.408725I
b = −0.301180 − 0.629587I
−9.45635 + 9.55250I 0
u = 1.273780 − 0.320998I
a = 0.339446 − 0.408725I
b = −0.301180 + 0.629587I
−9.45635 − 9.55250I 0
7
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.399664 + 0.544104I
a = 0.909536 − 0.090667I
b = 0.314177 − 0.531118I
1.145080 − 0.501768I 8.23694 + 2.15140I
u = −0.399664 − 0.544104I
a = 0.909536 + 0.090667I
b = 0.314177 + 0.531118I
1.145080 + 0.501768I 8.23694 − 2.15140I
u = −1.210730 + 0.556462I
a = −1.97220 + 0.64883I
b = −2.02675 + 1.88302I
−7.7808 + 18.8802I 0
u = −1.210730 − 0.556462I
a = −1.97220 − 0.64883I
b = −2.02675 − 1.88302I
−7.7808 − 18.8802I 0
u = 1.306310 + 0.316617I
a = −0.263807 − 0.388277I
b = 0.221677 + 0.590735I
−12.84150 + 2.96984I 0
u = 1.306310 − 0.316617I
a = −0.263807 + 0.388277I
b = 0.221677 − 0.590735I
−12.84150 − 2.96984I 0
u = −1.223530 + 0.563220I
a = 1.77160 − 0.50494I
b = 1.88321 − 1.61561I
−11.0732 + 12.5871I 0
u = −1.223530 − 0.563220I
a = 1.77160 + 0.50494I
b = 1.88321 + 1.61561I
−11.0732 − 12.5871I 0
u = 1.342730 + 0.165815I
a = 0.065422 + 0.397087I
b = −0.022002 − 0.544029I
−7.39787 − 4.96712I 0
u = 1.342730 − 0.165815I
a = 0.065422 − 0.397087I
b = −0.022002 + 0.544029I
−7.39787 + 4.96712I 0
8
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −1.32094 + 0.50553I
a = −1.068810 + 0.664801I
b = −1.07576 + 1.41848I
−4.11032 + 6.77393I 0
u = −1.32094 − 0.50553I
a = −1.068810 − 0.664801I
b = −1.07576 − 1.41848I
−4.11032 − 6.77393I 0
9
II. I
u
2
= h3.42 × 10
57
a
9
u
8
− 3.63 × 10
57
a
8
u
8
+ · · · + 3.06 × 10
58
a + 2.11 ×
10
59
, −a
9
u
8
+4a
8
u
8
+· · ·+163a+ 35, u
9
−u
8
−2u
7
+3u
6
+u
5
−3u
4
+2u
3
−u+1i
(i) Arc colorings
a
2
=
1
0
a
7
=
0
u
a
3
=
1
u
2
a
10
=
a
−0.0712580a
9
u
8
+ 0.0755383a
8
u
8
+ ··· − 0.637963a − 4.38520
a
4
=
0.0584008a
9
u
8
− 0.0300572a
8
u
8
+ ··· − 5.51490a + 0.377013
0.0549383a
9
u
8
− 0.0452833a
8
u
8
+ ··· − 7.58208a − 1.17835
a
1
=
−u
2
+ 1
−u
4
a
8
=
u
5
− 2u
3
+ u
u
7
− u
5
+ u
a
6
=
u
u
a
11
=
0.00108894a
9
u
8
+ 0.0965666a
8
u
8
+ ··· − 2.75887a − 0.950595
−0.0701691a
9
u
8
+ 0.172105a
8
u
8
+ ··· − 4.39683a − 5.33580
a
5
=
−0.109055a
9
u
8
+ 0.108963a
8
u
8
+ ··· − 2.14889a − 1.68427
0.0310586a
9
u
8
+ 0.0638539a
8
u
8
+ ··· − 5.80623a − 0.240168
a
9
=
0.00526858a
9
u
8
+ 0.00207832a
8
u
8
+ ··· + 4.33867a + 4.07290
−0.000848598a
9
u
8
− 0.0162695a
8
u
8
+ ··· + 16.4296a + 6.90589
a
12
=
−0.120100a
9
u
8
+ 0.0400133a
8
u
8
+ ··· − 0.561264a − 1.82874
−0.0635614a
9
u
8
+ 0.00692470a
8
u
8
+ ··· − 9.08400a − 5.46049
(ii) Obstruction class = −1
(iii) Cusp Shapes = −0.0987063a
9
u
8
+ 0.116009a
8
u
8
+ ··· − 19.0748a − 6.36312
10
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
(u
9
+ 5u
8
+ 12u
7
+ 15u
6
+ 9u
5
− u
4
− 4u
3
− 2u
2
+ u + 1)
10
c
2
, c
6
(u
9
+ u
8
− 2u
7
− 3u
6
+ u
5
+ 3u
4
+ 2u
3
− u − 1)
10
c
3
, c
5
, c
9
c
10
u
90
+ u
89
+ ··· + 7431322u + 1174423
c
4
, c
12
u
90
− 5u
89
+ ··· + 46u + 7
c
7
(u
9
+ 3u
8
+ 8u
7
+ 13u
6
+ 17u
5
+ 17u
4
+ 12u
3
+ 6u
2
+ u − 1)
10
c
8
, c
11
(u
5
+ u
4
+ 2u
3
+ u
2
+ u + 1)
18
11
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
(y
9
− y
8
+ 12y
7
− 7y
6
+ 37y
5
+ y
4
− 10y
2
+ 5y −1)
10
c
2
, c
6
(y
9
− 5y
8
+ 12y
7
− 15y
6
+ 9y
5
+ y
4
− 4y
3
+ 2y
2
+ y −1)
10
c
3
, c
5
, c
9
c
10
y
90
+ 75y
89
+ ··· + 22867447038168y + 1379269382929
c
4
, c
12
y
90
+ 15y
89
+ ··· + 3680y + 49
c
7
(y
9
+ 7y
8
+ 20y
7
+ 25y
6
+ 5y
5
− 15y
4
+ 22y
2
+ 13y −1)
10
c
8
, c
11
(y
5
+ 3y
4
+ 4y
3
+ y
2
− y −1)
18
12
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.772920 + 0.510351I
a = 0.522149 + 0.844231I
b = 0.17636 + 1.65146I
2.72120 + 2.30746I 5.25931 + 0.66425I
u = 0.772920 + 0.510351I
a = 1.114750 + 0.143726I
b = 0.522706 + 0.092356I
−0.75029 − 2.09337I 1.99613 + 4.16283I
u = 0.772920 + 0.510351I
a = 1.317910 + 0.023336I
b = 1.42189 + 1.32751I
2.72120 − 6.49421I 5.25931 + 7.66142I
u = 0.772920 + 0.510351I
a = −0.525892 + 0.227752I
b = −0.788261 − 0.680002I
−0.75029 − 2.09337I 1.99613 + 4.16283I
u = 0.772920 + 0.510351I
a = −1.14137 − 1.38302I
b = 0.027275 − 0.919003I
2.72120 + 2.30746I 5.25931 + 0.66425I
u = 0.772920 + 0.510351I
a = 1.17889 − 1.64289I
b = 1.94743 − 0.93765I
−2.82227 − 0.56279I 1.030106 − 0.267817I
u = 0.772920 + 0.510351I
a = −1.41315 + 1.50457I
b = −2.19306 + 0.41207I
−2.82227 − 3.62395I 1.03011 + 8.59348I
u = 0.772920 + 0.510351I
a = −2.07084 − 0.35016I
b = −1.006730 − 0.690634I
2.72120 − 6.49421I 5.25931 + 7.66142I
u = 0.772920 + 0.510351I
a = −1.19678 + 2.00335I
b = −1.74964 + 0.66817I
−2.82227 − 0.56279I 1.030106 − 0.267817I
u = 0.772920 + 0.510351I
a = 1.73076 − 1.67594I
b = 1.86011 − 0.44171I
−2.82227 − 3.62395I 1.03011 + 8.59348I
13
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.772920 − 0.510351I
a = 0.522149 − 0.844231I
b = 0.17636 − 1.65146I
2.72120 − 2.30746I 5.25931 − 0.66425I
u = 0.772920 − 0.510351I
a = 1.114750 − 0.143726I
b = 0.522706 − 0.092356I
−0.75029 + 2.09337I 1.99613 − 4.16283I
u = 0.772920 − 0.510351I
a = 1.317910 − 0.023336I
b = 1.42189 − 1.32751I
2.72120 + 6.49421I 5.25931 − 7.66142I
u = 0.772920 − 0.510351I
a = −0.525892 − 0.227752I
b = −0.788261 + 0.680002I
−0.75029 + 2.09337I 1.99613 − 4.16283I
u = 0.772920 − 0.510351I
a = −1.14137 + 1.38302I
b = 0.027275 + 0.919003I
2.72120 − 2.30746I 5.25931 − 0.66425I
u = 0.772920 − 0.510351I
a = 1.17889 + 1.64289I
b = 1.94743 + 0.93765I
−2.82227 + 0.56279I 1.030106 + 0.267817I
u = 0.772920 − 0.510351I
a = −1.41315 − 1.50457I
b = −2.19306 − 0.41207I
−2.82227 + 3.62395I 1.03011 − 8.59348I
u = 0.772920 − 0.510351I
a = −2.07084 + 0.35016I
b = −1.006730 + 0.690634I
2.72120 + 6.49421I 5.25931 − 7.66142I
u = 0.772920 − 0.510351I
a = −1.19678 − 2.00335I
b = −1.74964 − 0.66817I
−2.82227 + 0.56279I 1.030106 + 0.267817I
u = 0.772920 − 0.510351I
a = 1.73076 + 1.67594I
b = 1.86011 + 0.44171I
−2.82227 + 3.62395I 1.03011 − 8.59348I
14
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.825933
a = −0.476007 + 0.067634I
b = −0.51907 − 1.67449I
−5.80415 + 1.53058I −8.13723 − 4.43065I
u = −0.825933
a = −0.476007 − 0.067634I
b = −0.51907 + 1.67449I
−5.80415 − 1.53058I −8.13723 + 4.43065I
u = −0.825933
a = −0.62847 + 2.02740I
b = −0.393149 − 0.055861I
−5.80415 − 1.53058I −8.13723 + 4.43065I
u = −0.825933
a = −0.62847 − 2.02740I
b = −0.393149 + 0.055861I
−5.80415 + 1.53058I −8.13723 − 4.43065I
u = −0.825933
a = 2.19158 + 0.04238I
b = 2.36602 − 0.68010I
−0.26068 − 4.40083I −3.90804 + 3.49859I
u = −0.825933
a = 2.19158 − 0.04238I
b = 2.36602 + 0.68010I
−0.26068 + 4.40083I −3.90804 − 3.49859I
u = −0.825933
a = −2.16987 + 0.54772I
b = −1.79217 − 0.45238I
−3.73217 −7.17121 + 0.I
u = −0.825933
a = −2.16987 − 0.54772I
b = −1.79217 + 0.45238I
−3.73217 −7.17121 + 0.I
u = −0.825933
a = 2.86466 + 0.82344I
b = 1.81010 − 0.03500I
−0.26068 + 4.40083I −3.90804 − 3.49859I
u = −0.825933
a = 2.86466 − 0.82344I
b = 1.81010 + 0.03500I
−0.26068 − 4.40083I −3.90804 + 3.49859I
15
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −1.173910 + 0.391555I
a = 0.180120 − 1.006390I
b = −0.882145 + 0.065167I
−8.97705 − 0.19441I −6.76898 + 3.72890I
u = −1.173910 + 0.391555I
a = 1.004320 − 0.370378I
b = 0.532694 + 0.531817I
−8.97705 + 2.86675I −6.76898 − 5.13240I
u = −1.173910 + 0.391555I
a = 0.462278 − 0.785629I
b = 0.75098 − 1.81026I
−6.90507 + 1.33617I −5.80295 − 0.70175I
u = −1.173910 + 0.391555I
a = −0.301740 + 1.190390I
b = −0.73634 + 2.05646I
−3.43359 − 3.06466I −2.53978 + 2.79684I
u = −1.173910 + 0.391555I
a = −0.692888 − 0.175598I
b = −0.182613 − 1.251940I
−8.97705 − 0.19441I −6.76898 + 3.72890I
u = −1.173910 + 0.391555I
a = −0.975268 + 0.845917I
b = −0.85954 + 1.84219I
−3.43359 + 5.73700I −2.53978 − 4.20034I
u = −1.173910 + 0.391555I
a = 0.272368 + 0.543878I
b = 1.033960 − 0.828037I
−8.97705 + 2.86675I −6.76898 − 5.13240I
u = −1.173910 + 0.391555I
a = 1.03854 − 1.19568I
b = 0.235057 − 1.103270I
−6.90507 + 1.33617I −5.80295 − 0.70175I
u = −1.173910 + 0.391555I
a = −1.12992 + 1.19239I
b = −0.81366 + 1.37490I
−3.43359 + 5.73700I −2.53978 − 4.20034I
u = −1.173910 + 0.391555I
a = −1.09027 + 1.38815I
b = 0.11189 + 1.51556I
−3.43359 − 3.06466I −2.53978 + 2.79684I
16
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −1.173910 − 0.391555I
a = 0.180120 + 1.006390I
b = −0.882145 − 0.065167I
−8.97705 + 0.19441I −6.76898 − 3.72890I
u = −1.173910 − 0.391555I
a = 1.004320 + 0.370378I
b = 0.532694 − 0.531817I
−8.97705 − 2.86675I −6.76898 + 5.13240I
u = −1.173910 − 0.391555I
a = 0.462278 + 0.785629I
b = 0.75098 + 1.81026I
−6.90507 − 1.33617I −5.80295 + 0.70175I
u = −1.173910 − 0.391555I
a = −0.301740 − 1.190390I
b = −0.73634 − 2.05646I
−3.43359 + 3.06466I −2.53978 − 2.79684I
u = −1.173910 − 0.391555I
a = −0.692888 + 0.175598I
b = −0.182613 + 1.251940I
−8.97705 + 0.19441I −6.76898 − 3.72890I
u = −1.173910 − 0.391555I
a = −0.975268 − 0.845917I
b = −0.85954 − 1.84219I
−3.43359 − 5.73700I −2.53978 + 4.20034I
u = −1.173910 − 0.391555I
a = 0.272368 − 0.543878I
b = 1.033960 + 0.828037I
−8.97705 − 2.86675I −6.76898 + 5.13240I
u = −1.173910 − 0.391555I
a = 1.03854 + 1.19568I
b = 0.235057 + 1.103270I
−6.90507 − 1.33617I −5.80295 + 0.70175I
u = −1.173910 − 0.391555I
a = −1.12992 − 1.19239I
b = −0.81366 − 1.37490I
−3.43359 − 5.73700I −2.53978 + 4.20034I
u = −1.173910 − 0.391555I
a = −1.09027 − 1.38815I
b = 0.11189 − 1.51556I
−3.43359 + 3.06466I −2.53978 − 2.79684I
17
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.141484 + 0.739668I
a = 0.833321 + 0.197836I
b = −0.148096 − 0.486452I
0.32082 − 1.94642I 2.41639 + 0.58561I
u = 0.141484 + 0.739668I
a = 0.671396 − 0.071794I
b = 0.028431 − 0.644371I
0.32082 − 1.94642I 2.41639 + 0.58561I
u = 0.141484 + 0.739668I
a = −0.568678 + 0.319831I
b = −0.08989 − 1.48960I
0.32082 + 6.85525I 2.41639 − 6.41156I
u = 0.141484 + 0.739668I
a = 1.41403 + 0.59823I
b = −0.68925 + 1.35493I
−5.22264 + 3.98500I −1.81281 − 7.34362I
u = 0.141484 + 0.739668I
a = 0.342864 + 0.158229I
b = −0.114649 + 1.239450I
−3.15066 + 2.45442I −0.84678 − 2.91298I
u = 0.141484 + 0.739668I
a = −1.58794 − 0.45874I
b = 0.068527 − 0.275993I
−3.15066 + 2.45442I −0.84678 − 2.91298I
u = 0.141484 + 0.739668I
a = 1.07862 + 1.32292I
b = −0.402567 + 1.251020I
−5.22264 + 0.92384I −1.81281 + 1.51767I
u = 0.141484 + 0.739668I
a = −1.53120 − 0.83714I
b = 0.825911 − 0.984993I
−5.22264 + 0.92384I −1.81281 + 1.51767I
u = 0.141484 + 0.739668I
a = 1.96522 + 0.25438I
b = 0.317028 + 0.375382I
0.32082 + 6.85525I 2.41639 − 6.41156I
u = 0.141484 + 0.739668I
a = −1.59520 − 1.23697I
b = 0.242430 − 1.130550I
−5.22264 + 3.98500I −1.81281 − 7.34362I
18
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.141484 − 0.739668I
a = 0.833321 − 0.197836I
b = −0.148096 + 0.486452I
0.32082 + 1.94642I 2.41639 − 0.58561I
u = 0.141484 − 0.739668I
a = 0.671396 + 0.071794I
b = 0.028431 + 0.644371I
0.32082 + 1.94642I 2.41639 − 0.58561I
u = 0.141484 − 0.739668I
a = −0.568678 − 0.319831I
b = −0.08989 + 1.48960I
0.32082 − 6.85525I 2.41639 + 6.41156I
u = 0.141484 − 0.739668I
a = 1.41403 − 0.59823I
b = −0.68925 − 1.35493I
−5.22264 − 3.98500I −1.81281 + 7.34362I
u = 0.141484 − 0.739668I
a = 0.342864 − 0.158229I
b = −0.114649 − 1.239450I
−3.15066 − 2.45442I −0.84678 + 2.91298I
u = 0.141484 − 0.739668I
a = −1.58794 + 0.45874I
b = 0.068527 + 0.275993I
−3.15066 − 2.45442I −0.84678 + 2.91298I
u = 0.141484 − 0.739668I
a = 1.07862 − 1.32292I
b = −0.402567 − 1.251020I
−5.22264 − 0.92384I −1.81281 − 1.51767I
u = 0.141484 − 0.739668I
a = −1.53120 + 0.83714I
b = 0.825911 + 0.984993I
−5.22264 − 0.92384I −1.81281 − 1.51767I
u = 0.141484 − 0.739668I
a = 1.96522 − 0.25438I
b = 0.317028 − 0.375382I
0.32082 − 6.85525I 2.41639 + 6.41156I
u = 0.141484 − 0.739668I
a = −1.59520 + 1.23697I
b = 0.242430 + 1.130550I
−5.22264 − 3.98500I −1.81281 + 7.34362I
19
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 1.172470 + 0.500383I
a = 0.792012 + 0.503592I
b = 0.162057 + 0.387615I
−2.66037 − 2.68409I −0.83249 + 2.41476I
u = 1.172470 + 0.500383I
a = 0.945073 + 0.712591I
b = 1.26045 + 1.74402I
−6.13185 − 7.08493I −4.09566 + 5.91335I
u = 1.172470 + 0.500383I
a = −0.80474 − 1.26876I
b = −0.98004 − 2.30622I
−2.66037 − 11.48580I −0.83249 + 9.41193I
u = 1.172470 + 0.500383I
a = −0.236274 − 0.229760I
b = −0.676624 − 0.986758I
−2.66037 − 2.68409I −0.83249 + 2.41476I
u = 1.172470 + 0.500383I
a = −1.44640 − 0.87018I
b = −0.75150 − 1.30839I
−6.13185 − 7.08493I −4.09566 + 5.91335I
u = 1.172470 + 0.500383I
a = 1.41720 + 1.36214I
b = 0.30867 + 1.89027I
−2.66037 − 11.48580I −0.83249 + 9.41193I
u = 1.172470 + 0.500383I
a = 2.12983 + 0.34060I
b = 2.25954 + 1.80577I
−8.20383 − 5.55435I −5.06169 + 1.48270I
u = 1.172470 + 0.500383I
a = 2.07246 + 0.88521I
b = 2.31320 + 1.95595I
−8.20383 − 8.61551I −5.06169 + 10.34400I
u = 1.172470 + 0.500383I
a = −2.18626 − 0.60710I
b = −2.32674 − 1.46507I
−8.20383 − 5.55435I −5.06169 + 1.48270I
u = 1.172470 + 0.500383I
a = −2.27121 − 0.69892I
b = −1.98696 − 2.07491I
−8.20383 − 8.61551I −5.06169 + 10.34400I
20
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 1.172470 − 0.500383I
a = 0.792012 − 0.503592I
b = 0.162057 − 0.387615I
−2.66037 + 2.68409I −0.83249 − 2.41476I
u = 1.172470 − 0.500383I
a = 0.945073 − 0.712591I
b = 1.26045 − 1.74402I
−6.13185 + 7.08493I −4.09566 − 5.91335I
u = 1.172470 − 0.500383I
a = −0.80474 + 1.26876I
b = −0.98004 + 2.30622I
−2.66037 + 11.48580I −0.83249 − 9.41193I
u = 1.172470 − 0.500383I
a = −0.236274 + 0.229760I
b = −0.676624 + 0.986758I
−2.66037 + 2.68409I −0.83249 − 2.41476I
u = 1.172470 − 0.500383I
a = −1.44640 + 0.87018I
b = −0.75150 + 1.30839I
−6.13185 + 7.08493I −4.09566 − 5.91335I
u = 1.172470 − 0.500383I
a = 1.41720 − 1.36214I
b = 0.30867 − 1.89027I
−2.66037 + 11.48580I −0.83249 − 9.41193I
u = 1.172470 − 0.500383I
a = 2.12983 − 0.34060I
b = 2.25954 − 1.80577I
−8.20383 + 5.55435I −5.06169 − 1.48270I
u = 1.172470 − 0.500383I
a = 2.07246 − 0.88521I
b = 2.31320 − 1.95595I
−8.20383 + 8.61551I −5.06169 − 10.34400I
u = 1.172470 − 0.500383I
a = −2.18626 + 0.60710I
b = −2.32674 + 1.46507I
−8.20383 + 5.55435I −5.06169 − 1.48270I
u = 1.172470 − 0.500383I
a = −2.27121 + 0.69892I
b = −1.98696 + 2.07491I
−8.20383 + 8.61551I −5.06169 − 10.34400I
21
III.
I
u
3
= h−2u
27
−u
26
+· · ·+b−6, 6u
27
−2u
26
+· · ·+a−4, u
28
−8u
26
+· · ·−5u
2
+1i
(i) Arc colorings
a
2
=
1
0
a
7
=
0
u
a
3
=
1
u
2
a
10
=
−6u
27
+ 2u
26
+ ··· + 17u + 4
2u
27
+ u
26
+ ··· + 4u + 6
a
4
=
2u
27
+ 3u
26
+ ··· − 4u − 8
3u
27
+ u
26
+ ··· − 9u − 2
a
1
=
−u
2
+ 1
−u
4
a
8
=
u
5
− 2u
3
+ u
u
7
− u
5
+ u
a
6
=
u
u
a
11
=
−2u
27
+ u
26
+ ··· + 9u + 5
6u
27
− 42u
25
+ ··· − 4u + 7
a
5
=
2u
27
+ 3u
26
+ ··· − 4u − 7
3u
27
+ u
26
+ ··· + 3u
2
− 9u
a
9
=
−4u
27
− 2u
26
+ ··· + 12u + 8
−7u
27
+ 3u
26
+ ··· + 17u − 1
a
12
=
−5u
27
− u
26
+ ··· + 5u + 1
3u
27
− 4u
26
+ ··· − 8u + 9
(ii) Obstruction class = 1
(iii) Cusp Shapes
= 15u
27
+ 19u
26
− 106u
25
− 149u
24
+ 360u
23
+ 584u
22
− 700u
21
− 1413u
20
+ 765u
19
+
2322u
18
− 199u
17
− 2661u
16
− 746u
15
+ 2165u
14
+ 1354u
13
− 1227u
12
− 1167u
11
+
506u
10
+ 538u
9
− 188u
8
− 29u
7
+ 148u
6
− 106u
5
− 123u
4
+ 66u
3
+ 77u
2
− 14u − 14
22
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
28
− 16u
27
+ ··· − 10u + 1
c
2
u
28
− 8u
26
+ ··· − 5u
2
+ 1
c
3
, c
10
u
28
+ 14u
26
+ ··· + u + 1
c
4
, c
12
u
28
+ 2u
26
+ ··· + 3u + 1
c
5
, c
9
u
28
+ 14u
26
+ ··· − u + 1
c
6
u
28
− 8u
26
+ ··· − 5u
2
+ 1
c
7
u
28
− 3u
27
+ ··· − 9u
2
+ 1
c
8
u
28
− 7u
27
+ ··· − 3u + 1
c
11
u
28
+ 7u
27
+ ··· + 3u + 1
23
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
28
+ 32y
26
+ ··· − 6y + 1
c
2
, c
6
y
28
− 16y
27
+ ··· − 10y + 1
c
3
, c
5
, c
9
c
10
y
28
+ 28y
27
+ ··· + 17y + 1
c
4
, c
12
y
28
+ 4y
27
+ ··· + y + 1
c
7
y
28
+ 13y
27
+ ··· − 18y + 1
c
8
, c
11
y
28
+ 21y
27
+ ··· + 21y + 1
24
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = 0.909624 + 0.399283I
a = −1.35681 + 1.21818I
b = −1.72058 + 0.56633I
−3.24975 − 1.66982I −4.52503 + 3.50835I
u = 0.909624 − 0.399283I
a = −1.35681 − 1.21818I
b = −1.72058 − 0.56633I
−3.24975 + 1.66982I −4.52503 − 3.50835I
u = −0.381271 + 0.904184I
a = 0.465172 − 0.049713I
b = −0.132407 + 0.439556I
0.60188 + 2.20318I 19.4970 − 11.9673I
u = −0.381271 − 0.904184I
a = 0.465172 + 0.049713I
b = −0.132407 − 0.439556I
0.60188 − 2.20318I 19.4970 + 11.9673I
u = 1.024400 + 0.383160I
a = 0.61006 − 1.65384I
b = 1.25863 − 1.46043I
−0.83437 + 2.19030I 0.51959 − 1.67301I
u = 1.024400 − 0.383160I
a = 0.61006 + 1.65384I
b = 1.25863 + 1.46043I
−0.83437 − 2.19030I 0.51959 + 1.67301I
u = 0.716573 + 0.538278I
a = −1.14819 + 1.73127I
b = −1.75466 + 0.62254I
−3.06915 − 2.17150I −0.43947 + 3.55816I
u = 0.716573 − 0.538278I
a = −1.14819 − 1.73127I
b = −1.75466 − 0.62254I
−3.06915 + 2.17150I −0.43947 − 3.55816I
u = −1.113090 + 0.299686I
a = 0.273509 − 0.536051I
b = −0.143794 + 0.678642I
−7.04737 + 3.15969I −2.79688 − 5.16503I
u = −1.113090 − 0.299686I
a = 0.273509 + 0.536051I
b = −0.143794 − 0.678642I
−7.04737 − 3.15969I −2.79688 + 5.16503I
25
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = −1.052520 + 0.535447I
a = 0.019621 + 0.244212I
b = −0.151414 − 0.246532I
0.29369 + 8.62276I −1.09109 − 8.86228I
u = −1.052520 − 0.535447I
a = 0.019621 − 0.244212I
b = −0.151414 + 0.246532I
0.29369 − 8.62276I −1.09109 + 8.86228I
u = −1.155670 + 0.401281I
a = −0.434187 + 0.437982I
b = 0.326024 − 0.680396I
−8.44495 + 0.86552I −1.99597 − 3.31819I
u = −1.155670 − 0.401281I
a = −0.434187 − 0.437982I
b = 0.326024 + 0.680396I
−8.44495 − 0.86552I −1.99597 + 3.31819I
u = −1.054750 + 0.632515I
a = 0.202172 − 0.143686I
b = −0.122357 + 0.279430I
−1.26603 + 3.39888I 3.29789 − 7.55521I
u = −1.054750 − 0.632515I
a = 0.202172 + 0.143686I
b = −0.122357 − 0.279430I
−1.26603 − 3.39888I 3.29789 + 7.55521I
u = −0.500430 + 0.579905I
a = −0.501513 − 0.182933I
b = 0.357056 − 0.199285I
1.96468 − 4.13139I 3.07949 + 3.75164I
u = −0.500430 − 0.579905I
a = −0.501513 + 0.182933I
b = 0.357056 + 0.199285I
1.96468 + 4.13139I 3.07949 − 3.75164I
u = 0.719513 + 0.210138I
a = 3.01137 − 1.26584I
b = 2.43272 − 0.27799I
0.49510 − 4.96252I 5.23060 + 9.28386I
u = 0.719513 − 0.210138I
a = 3.01137 + 1.26584I
b = 2.43272 + 0.27799I
0.49510 + 4.96252I 5.23060 − 9.28386I
26
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = 1.158930 + 0.497770I
a = 2.26263 + 0.62418I
b = 2.31152 + 1.84965I
−7.74631 − 7.32565I −1.47863 + 4.71350I
u = 1.158930 − 0.497770I
a = 2.26263 − 0.62418I
b = 2.31152 − 1.84965I
−7.74631 + 7.32565I −1.47863 − 4.71350I
u = −0.721884 + 0.081239I
a = 0.293190 − 1.240550I
b = −0.110868 + 0.919351I
−5.21361 − 1.26266I 6.29853 − 1.62701I
u = −0.721884 − 0.081239I
a = 0.293190 + 1.240550I
b = −0.110868 − 0.919351I
−5.21361 + 1.26266I 6.29853 + 1.62701I
u = 0.155553 + 0.691734I
a = −1.57108 − 1.11636I
b = 0.527840 − 1.260420I
−4.88233 + 2.80056I 1.208918 − 0.721960I
u = 0.155553 − 0.691734I
a = −1.57108 + 1.11636I
b = 0.527840 + 1.260420I
−4.88233 − 2.80056I 1.208918 + 0.721960I
u = 1.295040 + 0.446899I
a = −1.125940 − 0.851291I
b = −1.07770 − 1.60564I
−4.36975 − 6.65598I −14.8049 + 6.5840I
u = 1.295040 − 0.446899I
a = −1.125940 + 0.851291I
b = −1.07770 + 1.60564I
−4.36975 + 6.65598I −14.8049 − 6.5840I
27
IV. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
(u
9
+ 5u
8
+ 12u
7
+ 15u
6
+ 9u
5
− u
4
− 4u
3
− 2u
2
+ u + 1)
10
· (u
28
− 16u
27
+ ··· − 10u + 1)(u
42
+ 21u
41
+ ··· − 256u + 1024)
c
2
(u
9
+ u
8
− 2u
7
− 3u
6
+ u
5
+ 3u
4
+ 2u
3
− u − 1)
10
· (u
28
− 8u
26
+ ··· − 5u
2
+ 1)(u
42
− 11u
41
+ ··· − 336u + 32)
c
3
, c
10
(u
28
+ 14u
26
+ ··· + u + 1)(u
42
+ 17u
40
+ ··· − u + 1)
· (u
90
+ u
89
+ ··· + 7431322u + 1174423)
c
4
, c
12
(u
28
+ 2u
26
+ ··· + 3u + 1)(u
42
− 3u
40
+ ··· + u + 1)
· (u
90
− 5u
89
+ ··· + 46u + 7)
c
5
, c
9
(u
28
+ 14u
26
+ ··· − u + 1)(u
42
+ 17u
40
+ ··· − u + 1)
· (u
90
+ u
89
+ ··· + 7431322u + 1174423)
c
6
(u
9
+ u
8
− 2u
7
− 3u
6
+ u
5
+ 3u
4
+ 2u
3
− u − 1)
10
· (u
28
− 8u
26
+ ··· − 5u
2
+ 1)(u
42
− 11u
41
+ ··· − 336u + 32)
c
7
(u
9
+ 3u
8
+ 8u
7
+ 13u
6
+ 17u
5
+ 17u
4
+ 12u
3
+ 6u
2
+ u − 1)
10
· (u
28
− 3u
27
+ ··· − 9u
2
+ 1)(u
42
− 30u
41
+ ··· − 6179216u + 430496)
c
8
((u
5
+ u
4
+ 2u
3
+ u
2
+ u + 1)
18
)(u
28
− 7u
27
+ ··· − 3u + 1)
· (u
42
− 24u
41
+ ··· − 10752u + 512)
c
11
((u
5
+ u
4
+ 2u
3
+ u
2
+ u + 1)
18
)(u
28
+ 7u
27
+ ··· + 3u + 1)
· (u
42
− 24u
41
+ ··· − 10752u + 512)
28
V. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
(y
9
− y
8
+ 12y
7
− 7y
6
+ 37y
5
+ y
4
− 10y
2
+ 5y −1)
10
· (y
28
+ 32y
26
+ ··· − 6y + 1)(y
42
− y
41
+ ··· + 9240576y + 1048576)
c
2
, c
6
(y
9
− 5y
8
+ 12y
7
− 15y
6
+ 9y
5
+ y
4
− 4y
3
+ 2y
2
+ y −1)
10
· (y
28
− 16y
27
+ ··· − 10y + 1)(y
42
− 21y
41
+ ··· + 256y + 1024)
c
3
, c
5
, c
9
c
10
(y
28
+ 28y
27
+ ··· + 17y + 1)(y
42
+ 34y
41
+ ··· − 7y + 1)
· (y
90
+ 75y
89
+ ··· + 22867447038168y + 1379269382929)
c
4
, c
12
(y
28
+ 4y
27
+ ··· + y + 1)(y
42
− 6y
41
+ ··· − 27y + 1)
· (y
90
+ 15y
89
+ ··· + 3680y + 49)
c
7
(y
9
+ 7y
8
+ 20y
7
+ 25y
6
+ 5y
5
− 15y
4
+ 22y
2
+ 13y −1)
10
· (y
28
+ 13y
27
+ ··· − 18y + 1)
· (y
42
+ 20y
41
+ ··· + 1352203186432y + 185326806016)
c
8
, c
11
((y
5
+ 3y
4
+ 4y
3
+ y
2
− y −1)
18
)(y
28
+ 21y
27
+ ··· + 21y + 1)
· (y
42
+ 24y
41
+ ··· + 262144y + 262144)
29
