11n
179
(K11n
179
)
A knot diagram
1
Linearized knot diagam
6 11 1 7 1 10 4 11 7 2 8
Solving Sequence
1,4 3,8
7 5 6 11 9 2 10
c
3
c
7
c
4
c
5
c
11
c
8
c
2
c
10
c
1
, c
6
, c
9
Ideals for irreducible components
2
of X
par
I
u
1
= h−30442u
14
+ 342325u
13
+ ··· + 44456b + 31712, −991u
14
+ 44316u
13
+ ··· + 44456a − 908664,
u
15
− 14u
14
+ ··· + 464u − 32i
I
u
2
= h−203u
17
− 446u
16
+ ··· + 16b − 99, −99u
17
a − 1285u
17
+ ··· + 606a − 2283,
u
18
+ 3u
17
+ ··· + 9u + 1i
I
u
3
= h−52u
6
− 135u
5
− 299u
4
− 528u
3
− 706u
2
+ 109b − 172u − 1,
− u
6
− 55u
5
− 142u
4
− 312u
3
− 546u
2
+ 109a − 716u − 174,
u
7
+ 3u
6
+ 7u
5
+ 13u
4
+ 18u
3
+ 10u
2
+ 2u − 1i
I
u
4
= hau + b + u − 1, u
2
a + a
2
− 2au + u
2
+ 2a − 3u + 3, u
3
− 2u
2
+ u + 1i
* 4 irreducible components of dim
C
= 0, with total 64 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−3.04×10
4
u
14
+3.42×10
5
u
13
+· · ·+4.45×10
4
b+3.17×10
4
, −991u
14
+
44316u
13
+ · · · + 44456a − 908664, u
15
− 14u
14
+ · · · + 464u − 32i
(i) Arc colorings
a
1
=
0
u
a
4
=
1
0
a
3
=
1
−u
2
a
8
=
0.0222917u
14
− 0.996851u
13
+ ··· − 194.288u + 20.4396
0.684767u
14
− 7.70031u
13
+ ··· − 10.0963u − 0.713335
a
7
=
0.707059u
14
− 8.69716u
13
+ ··· − 204.384u + 19.7263
0.684767u
14
− 7.70031u
13
+ ··· − 10.0963u − 0.713335
a
5
=
−0.120299u
14
+ 1.65732u
13
+ ··· + 85.8621u − 8.43756
−0.516758u
14
+ 6.69100u
13
+ ··· + 180.708u − 12.6867
a
6
=
−0.120299u
14
+ 1.65732u
13
+ ··· + 85.8621u − 8.43756
−0.692325u
14
+ 8.57538u
13
+ ··· + 172.095u − 11.8272
a
11
=
−0.396459u
14
+ 5.03367u
13
+ ··· + 94.8459u − 3.24915
0.516758u
14
− 6.69100u
13
+ ··· − 179.708u + 12.6867
a
9
=
−2.35699u
14
+ 29.2392u
13
+ ··· + 550.379u − 31.2776
1.87224u
14
− 24.4648u
13
+ ··· − 743.922u + 53.5112
a
2
=
0.442392u
14
− 5.28185u
13
+ ··· − 76.6178u + 5.65350
−0.736076u
14
+ 9.23090u
13
+ ··· + 209.229u − 15.0160
a
10
=
−2.04145u
14
+ 25.4828u
13
+ ··· + 540.956u − 35.1522
1.84779u
14
− 23.4858u
13
+ ··· − 593.170u + 42.6315
a
10
=
−2.04145u
14
+ 25.4828u
13
+ ··· + 540.956u − 35.1522
1.84779u
14
− 23.4858u
13
+ ··· − 593.170u + 42.6315
(ii) Obstruction class = −1
(iii) Cusp Shapes = −
6047
11114
u
14
+
56269
11114
u
13
+ ··· −
448754
5557
u −
32342
5557
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
2
, c
5
c
10
u
15
− 5u
13
+ ··· + 3u + 1
c
3
u
15
− 14u
14
+ ··· + 464u − 32
c
4
, c
7
, c
8
c
11
u
15
− u
14
+ ··· + 4u
2
+ 1
c
6
, c
9
u
15
− 8u
14
+ ··· − 56u + 8
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
2
, c
5
c
10
y
15
− 10y
14
+ ··· + 29y −1
c
3
y
15
+ 4y
14
+ ··· + 67328y −1024
c
4
, c
7
, c
8
c
11
y
15
+ 7y
14
+ ··· − 8y −1
c
6
, c
9
y
15
+ 8y
14
+ ··· + 224y −64
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.441017 + 0.682615I
a = −0.626506 − 0.383690I
b = 0.014387 + 0.596876I
1.16432 + 1.11480I 3.42758 − 4.27035I
u = 0.441017 − 0.682615I
a = −0.626506 + 0.383690I
b = 0.014387 − 0.596876I
1.16432 − 1.11480I 3.42758 + 4.27035I
u = 1.360540 + 0.261249I
a = −0.645886 − 0.354688I
b = 0.786092 + 0.651305I
1.20190 + 2.43151I −0.902369 − 0.814710I
u = 1.360540 − 0.261249I
a = −0.645886 + 0.354688I
b = 0.786092 − 0.651305I
1.20190 − 2.43151I −0.902369 + 0.814710I
u = 0.231740 + 1.386460I
a = −0.727304 + 0.321329I
b = 0.614054 + 0.933909I
7.18561 − 1.74581I 4.31703 + 3.15532I
u = 0.231740 − 1.386460I
a = −0.727304 − 0.321329I
b = 0.614054 − 0.933909I
7.18561 + 1.74581I 4.31703 − 3.15532I
u = 1.38613 + 0.32674I
a = 0.553085 + 0.614738I
b = −0.565792 − 1.032820I
0.37742 − 3.22470I 1.69059 + 1.81692I
u = 1.38613 − 0.32674I
a = 0.553085 − 0.614738I
b = −0.565792 + 1.032820I
0.37742 + 3.22470I 1.69059 − 1.81692I
u = 1.03444 + 1.15733I
a = 0.878543 + 0.103476I
b = −0.789042 − 1.123810I
0.98276 − 7.96105I 1.19655 + 6.90467I
u = 1.03444 − 1.15733I
a = 0.878543 − 0.103476I
b = −0.789042 + 1.123810I
0.98276 + 7.96105I 1.19655 − 6.90467I
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.122764
a = 5.00969
b = −0.615011
−1.24987 −10.6530
u = 1.41089 + 1.28897I
a = −0.730743 − 0.221034I
b = 0.74609 + 1.25376I
4.8601 − 14.7989I 2.41187 + 8.28326I
u = 1.41089 − 1.28897I
a = −0.730743 + 0.221034I
b = 0.74609 − 1.25376I
4.8601 + 14.7989I 2.41187 − 8.28326I
u = 1.07386 + 2.16285I
a = 0.293966 + 0.146746I
b = 0.001713 − 0.793388I
6.23698 + 3.49716I 6.18530 − 1.96585I
u = 1.07386 − 2.16285I
a = 0.293966 − 0.146746I
b = 0.001713 + 0.793388I
6.23698 − 3.49716I 6.18530 + 1.96585I
6
II. I
u
2
= h−203u
17
− 446u
16
+ · · · + 16b − 99, −99u
17
a − 1285u
17
+ · · · +
606a − 2283, u
18
+ 3u
17
+ · · · + 9u + 1i
(i) Arc colorings
a
1
=
0
u
a
4
=
1
0
a
3
=
1
−u
2
a
8
=
a
12.6875u
17
+ 27.8750u
16
+ ··· + 93.5625u + 6.18750
a
7
=
203
16
u
17
+
223
8
u
16
+ ··· + a +
99
16
12.6875u
17
+ 27.8750u
16
+ ··· + 93.5625u + 6.18750
a
5
=
−10.1875au
17
− 49.5625u
17
+ ··· − 12.6875a − 109.375
−10.1875au
17
− 10.8125u
17
+ ··· − 12.6875a − 30.0625
a
6
=
−10.1875au
17
− 49.5625u
17
+ ··· − 12.6875a − 109.375
−6u
17
a − u
17
+ ··· −
95
16
a − 8
a
11
=
−12.6875au
17
− 38.7500u
17
+ ··· − 6.18750a − 80.3125
17.6875u
17
+ 45.1875u
16
+ ··· + 269.438u + 38.7500
a
9
=
−10.8125au
17
+ 102.938u
17
+ ··· − 29.0625a + 256.750
−7.87500au
17
+ 12.6875u
17
+ ··· − 17.6875a + 6.18750
a
2
=
−29.6875au
17
− 4.12500u
17
+ ··· − 64.6250a + 32.9375
−7u
17
a −
109
8
u
17
+ ··· −
119
8
a −
611
16
a
10
=
−8.43750au
17
+ 100.625u
17
+ ··· − 10.3750a + 254.688
−3.50000au
17
+ 10.3750u
17
+ ··· − 15.6875a + 4.12500
a
10
=
−8.43750au
17
+ 100.625u
17
+ ··· − 10.3750a + 254.688
−3.50000au
17
+ 10.3750u
17
+ ··· − 15.6875a + 4.12500
(ii) Obstruction class = −1
(iii) Cusp Shapes
=
371
4
u
17
+ 247u
16
+
41
4
u
15
−
3345
4
u
14
−
4809
4
u
13
−1271u
12
+
1677
4
u
11
+
23513
4
u
10
+ 6462u
9
−
13723
2
u
8
−
21065
2
u
7
+
13659
2
u
6
+
38345
4
u
5
−
6133
2
u
4
−
13047
4
u
3
+
7575
4
u
2
+ 1672u +
585
2
7
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
2
, c
5
c
10
u
36
− 10u
34
+ ··· + 503u + 161
c
3
(u
18
+ 3u
17
+ ··· + 9u + 1)
2
c
4
, c
7
, c
8
c
11
u
36
− 2u
35
+ ··· − 151u + 47
c
6
, c
9
(u
18
+ 3u
17
+ ··· + 4u + 5)
2
8
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
2
, c
5
c
10
y
36
− 20y
35
+ ··· − 295835y + 25921
c
3
(y
18
− 7y
17
+ ··· − 31y + 1)
2
c
4
, c
7
, c
8
c
11
y
36
+ 16y
35
+ ··· + 18277y + 2209
c
6
, c
9
(y
18
+ 11y
17
+ ··· + 174y + 25)
2
9
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.894501 + 0.439989I
a = −1.068970 − 0.589062I
b = 1.172180 − 0.401841I
2.21070 − 8.01702I 0.26506 + 6.04046I
u = 0.894501 + 0.439989I
a = −0.877218 + 0.880723I
b = 0.697017 + 0.997253I
2.21070 − 8.01702I 0.26506 + 6.04046I
u = 0.894501 − 0.439989I
a = −1.068970 + 0.589062I
b = 1.172180 + 0.401841I
2.21070 + 8.01702I 0.26506 − 6.04046I
u = 0.894501 − 0.439989I
a = −0.877218 − 0.880723I
b = 0.697017 − 0.997253I
2.21070 + 8.01702I 0.26506 − 6.04046I
u = −0.950537 + 0.162221I
a = −0.971317 + 0.562568I
b = 0.732831 + 0.297516I
−1.79766 + 2.11512I −3.46832 − 4.22083I
u = −0.950537 + 0.162221I
a = 0.697241 + 0.431990I
b = −0.832013 + 0.692310I
−1.79766 + 2.11512I −3.46832 − 4.22083I
u = −0.950537 − 0.162221I
a = −0.971317 − 0.562568I
b = 0.732831 − 0.297516I
−1.79766 − 2.11512I −3.46832 + 4.22083I
u = −0.950537 − 0.162221I
a = 0.697241 − 0.431990I
b = −0.832013 − 0.692310I
−1.79766 − 2.11512I −3.46832 + 4.22083I
u = 0.550574 + 0.534542I
a = 1.151550 + 0.184083I
b = −1.137440 + 0.607496I
−0.695457 − 1.211150I 2.01684 + 5.97065I
u = 0.550574 + 0.534542I
a = 0.51202 − 1.60050I
b = −0.535612 − 0.716902I
−0.695457 − 1.211150I 2.01684 + 5.97065I
10
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.550574 − 0.534542I
a = 1.151550 − 0.184083I
b = −1.137440 − 0.607496I
−0.695457 + 1.211150I 2.01684 − 5.97065I
u = 0.550574 − 0.534542I
a = 0.51202 + 1.60050I
b = −0.535612 + 0.716902I
−0.695457 + 1.211150I 2.01684 − 5.97065I
u = −0.559442 + 0.038809I
a = −1.60100 + 1.20636I
b = 0.620068 + 1.024030I
0.388234 − 1.127970I 1.85464 + 1.58148I
u = −0.559442 + 0.038809I
a = 0.97669 + 1.89819I
b = −0.848848 + 0.737023I
0.388234 − 1.127970I 1.85464 + 1.58148I
u = −0.559442 − 0.038809I
a = −1.60100 − 1.20636I
b = 0.620068 − 1.024030I
0.388234 + 1.127970I 1.85464 − 1.58148I
u = −0.559442 − 0.038809I
a = 0.97669 − 1.89819I
b = −0.848848 − 0.737023I
0.388234 + 1.127970I 1.85464 − 1.58148I
u = −1.20149 + 0.95062I
a = −0.794303 + 0.267048I
b = 0.590660 − 0.737715I
−0.58133 + 3.63224I −1.22357 − 0.72654I
u = −1.20149 + 0.95062I
a = 0.601110 − 0.138403I
b = −0.700489 + 1.075930I
−0.58133 + 3.63224I −1.22357 − 0.72654I
u = −1.20149 − 0.95062I
a = −0.794303 − 0.267048I
b = 0.590660 + 0.737715I
−0.58133 − 3.63224I −1.22357 + 0.72654I
u = −1.20149 − 0.95062I
a = 0.601110 + 0.138403I
b = −0.700489 − 1.075930I
−0.58133 − 3.63224I −1.22357 + 0.72654I
11
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 1.57847 + 0.07406I
a = −0.056442 − 0.945021I
b = 0.253884 + 0.746014I
8.78344 + 0.53962I 4.04425 + 2.43806I
u = 1.57847 + 0.07406I
a = −0.182614 − 0.464051I
b = 0.01910 + 1.49587I
8.78344 + 0.53962I 4.04425 + 2.43806I
u = 1.57847 − 0.07406I
a = −0.056442 + 0.945021I
b = 0.253884 − 0.746014I
8.78344 − 0.53962I 4.04425 − 2.43806I
u = 1.57847 − 0.07406I
a = −0.182614 + 0.464051I
b = 0.01910 − 1.49587I
8.78344 − 0.53962I 4.04425 − 2.43806I
u = −0.305821 + 0.029607I
a = 0.52691 + 2.98749I
b = 0.20657 − 1.64071I
9.40827 − 2.73362I 5.19032 + 6.28765I
u = −0.305821 + 0.029607I
a = 1.18377 − 5.25035I
b = 0.249590 + 0.898036I
9.40827 − 2.73362I 5.19032 + 6.28765I
u = −0.305821 − 0.029607I
a = 0.52691 − 2.98749I
b = 0.20657 + 1.64071I
9.40827 + 2.73362I 5.19032 − 6.28765I
u = −0.305821 − 0.029607I
a = 1.18377 + 5.25035I
b = 0.249590 − 0.898036I
9.40827 + 2.73362I 5.19032 − 6.28765I
u = 0.08820 + 1.71388I
a = 0.440400 + 0.416925I
b = 0.047819 + 0.888995I
6.66136 + 3.28569I 5.54170 − 2.88739I
u = 0.08820 + 1.71388I
a = −0.518764 + 0.001204I
b = 0.675718 − 0.791567I
6.66136 + 3.28569I 5.54170 − 2.88739I
12
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.08820 − 1.71388I
a = 0.440400 − 0.416925I
b = 0.047819 − 0.888995I
6.66136 − 3.28569I 5.54170 + 2.88739I
u = 0.08820 − 1.71388I
a = −0.518764 − 0.001204I
b = 0.675718 + 0.791567I
6.66136 − 3.28569I 5.54170 + 2.88739I
u = −1.59445 + 1.02172I
a = 0.595268 − 0.396932I
b = −0.754617 + 0.978635I
1.11892 + 7.08645I 2.27907 − 7.07165I
u = −1.59445 + 1.02172I
a = −0.614327 + 0.220117I
b = 0.543574 − 1.241090I
1.11892 + 7.08645I 2.27907 − 7.07165I
u = −1.59445 − 1.02172I
a = 0.595268 + 0.396932I
b = −0.754617 − 0.978635I
1.11892 − 7.08645I 2.27907 + 7.07165I
u = −1.59445 − 1.02172I
a = −0.614327 − 0.220117I
b = 0.543574 + 1.241090I
1.11892 − 7.08645I 2.27907 + 7.07165I
13
III. I
u
3
= h−52u
6
− 135u
5
+ · · · + 109b − 1, −u
6
− 55u
5
+ · · · + 109a −
174, u
7
+ 3u
6
+ 7u
5
+ 13u
4
+ 18u
3
+ 10u
2
+ 2u − 1i
(i) Arc colorings
a
1
=
0
u
a
4
=
1
0
a
3
=
1
−u
2
a
8
=
0.00917431u
6
+ 0.504587u
5
+ ··· + 6.56881u + 1.59633
0.477064u
6
+ 1.23853u
5
+ ··· + 1.57798u + 0.00917431
a
7
=
0.486239u
6
+ 1.74312u
5
+ ··· + 8.14679u + 1.60550
0.477064u
6
+ 1.23853u
5
+ ··· + 1.57798u + 0.00917431
a
5
=
−0.339450u
6
− 0.669725u
5
+ ··· + 2.95413u + 2.93578
0.100917u
6
+ 0.550459u
5
+ ··· + 3.25688u − 0.440367
a
6
=
−0.339450u
6
− 0.669725u
5
+ ··· + 2.95413u + 2.93578
−0.0275229u
6
+ 0.486239u
5
+ ··· + 4.29358u − 0.788991
a
11
=
−0.440367u
6
− 1.22018u
5
+ ··· − 0.302752u + 2.37615
0.100917u
6
+ 0.550459u
5
+ ··· + 4.25688u − 0.440367
a
9
=
0.899083u
6
+ 2.44954u
5
+ ··· + 6.74312u + 2.44037
−0.440367u
6
− 1.22018u
5
+ ··· − 0.302752u + 1.37615
a
2
=
1.33945u
6
+ 3.66972u
5
+ ··· + 7.04587u + 0.0642202
−0.220183u
6
− 1.11009u
5
+ ··· − 4.65138u + 1.68807
a
10
=
0.889908u
6
+ 1.94495u
5
+ ··· + 0.174312u − 0.155963
−0.788991u
6
− 2.39450u
5
+ ··· − 3.91743u + 1.71560
a
10
=
0.889908u
6
+ 1.94495u
5
+ ··· + 0.174312u − 0.155963
−0.788991u
6
− 2.39450u
5
+ ··· − 3.91743u + 1.71560
(ii) Obstruction class = 1
(iii) Cusp Shapes = −
56
109
u
6
−
246
109
u
5
−
431
109
u
4
−
904
109
u
3
−
1146
109
u
2
−
856
109
u +
611
109
14
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
10
u
7
− 2u
5
− 2u
4
+ u
3
+ 2u
2
+ 2u + 1
c
2
, c
5
u
7
− 2u
5
+ 2u
4
+ u
3
− 2u
2
+ 2u − 1
c
3
u
7
+ 3u
6
+ 7u
5
+ 13u
4
+ 18u
3
+ 10u
2
+ 2u − 1
c
4
, c
8
u
7
− u
6
+ 3u
5
− 2u
4
+ 3u
3
− u
2
+ u − 1
c
6
u
7
− u
6
+ 3u
5
− 2u
4
+ u
3
− u
2
− u − 1
c
7
, c
11
u
7
+ u
6
+ 3u
5
+ 2u
4
+ 3u
3
+ u
2
+ u + 1
c
9
u
7
+ u
6
+ 3u
5
+ 2u
4
+ u
3
+ u
2
− u + 1
15
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
2
, c
5
c
10
y
7
− 4y
6
+ 6y
5
− 4y
4
+ y
3
+ 4y
2
− 1
c
3
y
7
+ 5y
6
+ 7y
5
+ 27y
4
+ 98y
3
− 2y
2
+ 24y −1
c
4
, c
7
, c
8
c
11
y
7
+ 5y
6
+ 11y
5
+ 14y
4
+ 9y
3
+ y
2
− y −1
c
6
, c
9
y
7
+ 5y
6
+ 7y
5
− 2y
4
− 11y
3
− 7y
2
− y −1
16
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = −0.508137 + 0.486029I
a = −1.22583 + 1.38607I
b = −0.050784 − 1.300110I
11.34660 + 1.05141I 8.13453 − 0.52743I
u = −0.508137 − 0.486029I
a = −1.22583 − 1.38607I
b = −0.050784 + 1.300110I
11.34660 − 1.05141I 8.13453 + 0.52743I
u = −1.35766 + 0.93784I
a = −0.676700 + 0.313046I
b = 0.625140 − 1.059640I
−0.00156 + 5.16496I 0.90846 − 5.47109I
u = −1.35766 − 0.93784I
a = −0.676700 − 0.313046I
b = 0.625140 + 1.059640I
−0.00156 − 5.16496I 0.90846 + 5.47109I
u = 0.203752
a = 3.16933
b = 0.645755
−0.607992 3.49110
u = 0.26392 + 1.89105I
a = 0.317866 + 0.254422I
b = −0.397234 + 0.668248I
5.40832 + 4.21557I −0.78856 − 7.31442I
u = 0.26392 − 1.89105I
a = 0.317866 − 0.254422I
b = −0.397234 − 0.668248I
5.40832 − 4.21557I −0.78856 + 7.31442I
17
IV. I
u
4
= hau + b + u − 1, u
2
a + a
2
− 2au + u
2
+ 2a − 3u + 3, u
3
− 2u
2
+ u + 1i
(i) Arc colorings
a
1
=
0
u
a
4
=
1
0
a
3
=
1
−u
2
a
8
=
a
−au − u + 1
a
7
=
−au + a − u + 1
−au − u + 1
a
5
=
u
2
a − au
u
2
a − au + u
2
− 2u
a
6
=
u
2
a − au
au + u
2
+ a − 2u
a
11
=
−au + u
2
+ a − 2u + 1
u + 1
a
9
=
u
2
a − 2au + u
2
+ a − 2u + 2
u
2
a − u + 1
a
2
=
u
2
a − au + 1
−2u
2
a + 3au − u
2
+ 2a + u + 1
a
10
=
u
2
a − 2au + u
2
− 2u + 1
2u
2
a − au − a − u
a
10
=
u
2
a − 2au + u
2
− 2u + 1
2u
2
a − au − a − u
(ii) Obstruction class = 1
(iii) Cusp Shapes = −4u
2
+ 6u + 1
18
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
10
u
6
+ 3u
5
+ u
4
− 3u
3
− u
2
+ u + 1
c
2
, c
5
u
6
− 3u
5
+ u
4
+ 3u
3
− u
2
− u + 1
c
3
(u
3
− 2u
2
+ u + 1)
2
c
4
, c
8
u
6
− u
5
+ 3u
4
− 3u
3
+ 3u
2
− u + 1
c
6
(u
3
+ u − 1)
2
c
7
, c
11
u
6
+ u
5
+ 3u
4
+ 3u
3
+ 3u
2
+ u + 1
c
9
(u
3
+ u + 1)
2
19
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
2
, c
5
c
10
y
6
− 7y
5
+ 17y
4
− 15y
3
+ 9y
2
− 3y + 1
c
3
(y
3
− 2y
2
+ 5y −1)
2
c
4
, c
7
, c
8
c
11
y
6
+ 5y
5
+ 9y
4
+ 9y
3
+ 9y
2
+ 5y + 1
c
6
, c
9
(y
3
+ 2y
2
+ y −1)
2
20
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
4
√
−1(vol +
√
−1CS) Cusp shape
u = 1.23279 + 0.79255I
a = −0.632657 − 0.782837I
b = −0.073295 + 0.673932I
8.79110 + 1.58317I 4.83023 − 3.06106I
u = 1.23279 + 0.79255I
a = 0.206606 + 0.413848I
b = −0.15949 − 1.46648I
8.79110 + 1.58317I 4.83023 − 3.06106I
u = 1.23279 − 0.79255I
a = −0.632657 + 0.782837I
b = −0.073295 − 0.673932I
8.79110 − 1.58317I 4.83023 + 3.06106I
u = 1.23279 − 0.79255I
a = 0.206606 − 0.413848I
b = −0.15949 + 1.46648I
8.79110 − 1.58317I 4.83023 + 3.06106I
u = −0.465571
a = −1.57395 + 1.46156I
b = 0.732786 + 0.680460I
−1.13287 −2.66050
u = −0.465571
a = −1.57395 − 1.46156I
b = 0.732786 − 0.680460I
−1.13287 −2.66050
21
V. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
, c
10
(u
6
+ 3u
5
+ u
4
− 3u
3
− u
2
+ u + 1)(u
7
− 2u
5
− 2u
4
+ u
3
+ 2u
2
+ 2u + 1)
· (u
15
− 5u
13
+ ··· + 3u + 1)(u
36
− 10u
34
+ ··· + 503u + 161)
c
2
, c
5
(u
6
− 3u
5
+ u
4
+ 3u
3
− u
2
− u + 1)(u
7
− 2u
5
+ 2u
4
+ u
3
− 2u
2
+ 2u − 1)
· (u
15
− 5u
13
+ ··· + 3u + 1)(u
36
− 10u
34
+ ··· + 503u + 161)
c
3
(u
3
− 2u
2
+ u + 1)
2
(u
7
+ 3u
6
+ 7u
5
+ 13u
4
+ 18u
3
+ 10u
2
+ 2u − 1)
· (u
15
− 14u
14
+ ··· + 464u − 32)(u
18
+ 3u
17
+ ··· + 9u + 1)
2
c
4
, c
8
(u
6
− u
5
+ 3u
4
− 3u
3
+ 3u
2
− u + 1)
· (u
7
− u
6
+ ··· + u − 1)(u
15
− u
14
+ ··· + 4u
2
+ 1)
· (u
36
− 2u
35
+ ··· − 151u + 47)
c
6
(u
3
+ u − 1)
2
(u
7
− u
6
+ 3u
5
− 2u
4
+ u
3
− u
2
− u − 1)
· (u
15
− 8u
14
+ ··· − 56u + 8)(u
18
+ 3u
17
+ ··· + 4u + 5)
2
c
7
, c
11
(u
6
+ u
5
+ 3u
4
+ 3u
3
+ 3u
2
+ u + 1)
· (u
7
+ u
6
+ ··· + u + 1)(u
15
− u
14
+ ··· + 4u
2
+ 1)
· (u
36
− 2u
35
+ ··· − 151u + 47)
c
9
(u
3
+ u + 1)
2
(u
7
+ u
6
+ 3u
5
+ 2u
4
+ u
3
+ u
2
− u + 1)
· (u
15
− 8u
14
+ ··· − 56u + 8)(u
18
+ 3u
17
+ ··· + 4u + 5)
2
22
VI. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
, c
2
, c
5
c
10
(y
6
− 7y
5
+ 17y
4
− 15y
3
+ 9y
2
− 3y + 1)
· (y
7
− 4y
6
+ ··· + 4y
2
− 1)(y
15
− 10y
14
+ ··· + 29y −1)
· (y
36
− 20y
35
+ ··· − 295835y + 25921)
c
3
((y
3
− 2y
2
+ 5y −1)
2
)(y
7
+ 5y
6
+ ··· + 24y −1)
· (y
15
+ 4y
14
+ ··· + 67328y −1024)(y
18
− 7y
17
+ ··· − 31y + 1)
2
c
4
, c
7
, c
8
c
11
(y
6
+ 5y
5
+ 9y
4
+ 9y
3
+ 9y
2
+ 5y + 1)
· (y
7
+ 5y
6
+ ··· − y −1)(y
15
+ 7y
14
+ ··· − 8y −1)
· (y
36
+ 16y
35
+ ··· + 18277y + 2209)
c
6
, c
9
(y
3
+ 2y
2
+ y −1)
2
(y
7
+ 5y
6
+ 7y
5
− 2y
4
− 11y
3
− 7y
2
− y −1)
· (y
15
+ 8y
14
+ ··· + 224y −64)(y
18
+ 11y
17
+ ··· + 174y + 25)
2
23
