12n
0453
(K12n
0453
)
A knot diagram
1
Linearized knot diagam
3 6 9 12 2 10 12 5 1 5 9 7
Solving Sequence
5,12 4,9
3 8 7 1 2 11 10 6
c
4
c
3
c
8
c
7
c
12
c
1
c
11
c
10
c
6
c
2
, c
5
, c
9
Ideals for irreducible components
2
of X
par
I
u
1
= hb − u, −5.24830 × 10
36
u
34
+ 3.76703 × 10
36
u
33
+ ··· + 1.56072 × 10
36
a − 5.62245 × 10
36
,
u
35
− u
34
+ ··· + 3u − 1i
I
u
2
= h2.26126 × 10
120
u
43
− 6.93064 × 10
119
u
42
+ ··· + 1.57860 × 10
123
b − 2.38102 × 10
124
,
− 6.59277 × 10
123
u
43
+ 5.75046 × 10
123
u
42
+ ··· + 1.55634 × 10
127
a + 1.14048 × 10
128
,
u
44
− u
43
+ ··· − 34132u + 9859i
I
u
3
= hb + u, −541775388218u
21
+ 737506675481u
20
+ ··· + 532384024235a − 996909356925,
u
22
− u
21
+ ··· − 13u
3
− 1i
* 3 irreducible components of dim
C
= 0, with total 101 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
= hb − u, −5.25 × 10
36
u
34
+ 3.77 × 10
36
u
33
+ · · · + 1.56 × 10
36
a −
5.62 × 10
36
, u
35
− u
34
+ · · · + 3u − 1i
(i) Arc colorings
a
5
=
1
0
a
12
=
0
u
a
4
=
1
−u
2
a
9
=
3.36274u
34
− 2.41365u
33
+ ··· − 1.77064u + 3.60247
u
a
3
=
−1.50962u
34
+ 0.0976335u
33
+ ··· + 5.85679u − 2.87425
−0.390812u
34
+ 0.123541u
33
+ ··· + 1.97017u − 0.973088
a
8
=
3.36274u
34
− 2.41365u
33
+ ··· − 0.770637u + 3.60247
u
a
7
=
3.36274u
34
− 2.41365u
33
+ ··· − 0.770637u + 3.60247
−0.973088u
34
+ 0.582276u
33
+ ··· + 0.484542u − 0.949096
a
1
=
−2.45768u
34
+ 1.11553u
33
+ ··· + 6.33799u − 4.06168
0.000350385u
34
− 0.0450612u
33
+ ··· − 1.08421u + 0.393051
a
2
=
0.302246u
34
+ 0.208870u
33
+ ··· − 6.15873u + 2.00069
−1.63367u
34
+ 0.497640u
33
+ ··· + 4.44370u − 2.88225
a
11
=
0.511505u
34
+ 0.0490164u
33
+ ··· − 7.36890u + 2.16349
0.973088u
34
− 0.582276u
33
+ ··· + 1.51546u + 0.949096
a
10
=
1.48459u
34
− 0.533259u
33
+ ··· − 5.85345u + 3.11258
0.973088u
34
− 0.582276u
33
+ ··· + 1.51546u + 0.949096
a
6
=
0.778426u
34
+ 0.0389110u
33
+ ··· − 3.48404u + 2.16125
−2.31610u
34
+ 0.760393u
33
+ ··· + 7.17608u − 4.33272
(ii) Obstruction class = −1
(iii) Cusp Shapes = 0.563437u
34
+ 0.739161u
33
+ ··· − 7.54274u − 12.9075
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
35
+ 18u
34
+ ··· + 268u + 16
c
2
, c
5
u
35
+ 8u
34
+ ··· + 42u + 4
c
3
, c
10
u
35
− 3u
33
+ ··· − 2u + 5
c
4
, c
8
u
35
+ u
34
+ ··· + 3u + 1
c
6
, c
9
u
35
− u
34
+ ··· − 2u + 1
c
7
, c
12
u
35
+ 24u
34
+ ··· + 39936u + 2048
c
11
u
35
− 23u
34
+ ··· − 230u + 1300
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
35
+ 2y
34
+ ··· + 40048y −256
c
2
, c
5
y
35
− 18y
34
+ ··· + 268y −16
c
3
, c
10
y
35
− 6y
34
+ ··· + 434y −25
c
4
, c
8
y
35
− 47y
34
+ ··· + 13y −1
c
6
, c
9
y
35
+ 3y
34
+ ··· − 2y −1
c
7
, c
12
y
35
+ 16y
34
+ ··· + 47185920y −4194304
c
11
y
35
− 23y
34
+ ··· + 9249100y −1690000
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.955967 + 0.450664I
a = −0.277341 + 1.028180I
b = 0.955967 + 0.450664I
0.32153 + 2.91618I −4.71539 − 0.02368I
u = 0.955967 − 0.450664I
a = −0.277341 − 1.028180I
b = 0.955967 − 0.450664I
0.32153 − 2.91618I −4.71539 + 0.02368I
u = −0.603532 + 0.339224I
a = −0.087049 − 1.096610I
b = −0.603532 + 0.339224I
−1.37493 − 3.82893I −14.7554 + 5.1588I
u = −0.603532 − 0.339224I
a = −0.087049 + 1.096610I
b = −0.603532 − 0.339224I
−1.37493 + 3.82893I −14.7554 − 5.1588I
u = 0.505207 + 0.466803I
a = −1.53217 − 2.19035I
b = 0.505207 + 0.466803I
3.54205 + 7.35026I −11.99203 − 4.50938I
u = 0.505207 − 0.466803I
a = −1.53217 + 2.19035I
b = 0.505207 − 0.466803I
3.54205 − 7.35026I −11.99203 + 4.50938I
u = −0.639207 + 0.204758I
a = −0.14927 + 1.74146I
b = −0.639207 + 0.204758I
3.60027 + 1.54452I −7.64624 − 4.60913I
u = −0.639207 − 0.204758I
a = −0.14927 − 1.74146I
b = −0.639207 − 0.204758I
3.60027 − 1.54452I −7.64624 + 4.60913I
u = 0.373896 + 0.520116I
a = 1.270260 + 0.311437I
b = 0.373896 + 0.520116I
0.95580 − 4.75953I −9.19791 + 7.90177I
u = 0.373896 − 0.520116I
a = 1.270260 − 0.311437I
b = 0.373896 − 0.520116I
0.95580 + 4.75953I −9.19791 − 7.90177I
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.558191 + 0.285053I
a = 1.18752 − 2.42194I
b = −0.558191 + 0.285053I
4.88354 − 2.69019I −10.47730 + 0.12447I
u = −0.558191 − 0.285053I
a = 1.18752 + 2.42194I
b = −0.558191 − 0.285053I
4.88354 + 2.69019I −10.47730 − 0.12447I
u = 0.605489 + 0.009295I
a = 0.206739 + 0.573796I
b = 0.605489 + 0.009295I
−0.426536 + 0.312778I −12.16336 + 0.78895I
u = 0.605489 − 0.009295I
a = 0.206739 − 0.573796I
b = 0.605489 − 0.009295I
−0.426536 − 0.312778I −12.16336 − 0.78895I
u = −0.177738 + 0.486118I
a = −0.17737 − 1.74965I
b = −0.177738 + 0.486118I
−2.39864 + 1.51734I −15.0669 − 4.1108I
u = −0.177738 − 0.486118I
a = −0.17737 + 1.74965I
b = −0.177738 − 0.486118I
−2.39864 − 1.51734I −15.0669 + 4.1108I
u = 0.057585 + 0.464773I
a = −2.70671 − 1.34166I
b = 0.057585 + 0.464773I
1.72575 + 1.86389I −7.37932 + 5.72849I
u = 0.057585 − 0.464773I
a = −2.70671 + 1.34166I
b = 0.057585 − 0.464773I
1.72575 − 1.86389I −7.37932 − 5.72849I
u = 1.54010 + 0.38619I
a = −0.729617 + 0.149966I
b = 1.54010 + 0.38619I
−1.11453 − 0.96016I 0
u = 1.54010 − 0.38619I
a = −0.729617 − 0.149966I
b = 1.54010 − 0.38619I
−1.11453 + 0.96016I 0
6
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −1.58422 + 0.48939I
a = 0.844245 + 0.075878I
b = −1.58422 + 0.48939I
−0.30923 + 6.97118I 0
u = −1.58422 − 0.48939I
a = 0.844245 − 0.075878I
b = −1.58422 − 0.48939I
−0.30923 − 6.97118I 0
u = 0.339571
a = 0.730904
b = 0.339571
−0.605268 −16.1480
u = 1.72430 + 0.03737I
a = −0.913428 − 0.274991I
b = 1.72430 + 0.03737I
−5.06642 − 3.71082I 0
u = 1.72430 − 0.03737I
a = −0.913428 + 0.274991I
b = 1.72430 − 0.03737I
−5.06642 + 3.71082I 0
u = −1.75744 + 0.08760I
a = 0.995064 − 0.291635I
b = −1.75744 + 0.08760I
−7.51086 + 9.54692I 0
u = −1.75744 − 0.08760I
a = 0.995064 + 0.291635I
b = −1.75744 − 0.08760I
−7.51086 − 9.54692I 0
u = 1.70176 + 0.47815I
a = −1.051060 + 0.162856I
b = 1.70176 + 0.47815I
−7.79536 − 8.25620I 0
u = 1.70176 − 0.47815I
a = −1.051060 − 0.162856I
b = 1.70176 − 0.47815I
−7.79536 + 8.25620I 0
u = −1.71391 + 0.54641I
a = 1.082860 + 0.037259I
b = −1.71391 + 0.54641I
−1.90251 + 11.15310I 0
7
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −1.71391 − 0.54641I
a = 1.082860 − 0.037259I
b = −1.71391 − 0.54641I
−1.90251 − 11.15310I 0
u = 1.74961 + 0.55030I
a = −1.143750 + 0.033525I
b = 1.74961 + 0.55030I
−4.1343 − 16.7869I 0
u = 1.74961 − 0.55030I
a = −1.143750 − 0.033525I
b = 1.74961 − 0.55030I
−4.1343 + 16.7869I 0
u = −1.84947 + 0.03525I
a = 0.815630 + 0.068482I
b = −1.84947 + 0.03525I
−11.47940 − 0.02354I 0
u = −1.84947 − 0.03525I
a = 0.815630 − 0.068482I
b = −1.84947 − 0.03525I
−11.47940 + 0.02354I 0
8
II. I
u
2
= h2.26 × 10
120
u
43
− 6.93 × 10
119
u
42
+ · · · + 1.58 × 10
123
b − 2.38 ×
10
124
, −6.59 × 10
123
u
43
+ 5.75 × 10
123
u
42
+ · · · + 1.56 × 10
127
a + 1.14 ×
10
128
, u
44
− u
43
+ · · · − 34132u + 9859i
(i) Arc colorings
a
5
=
1
0
a
12
=
0
u
a
4
=
1
−u
2
a
9
=
0.000423608u
43
− 0.000369486u
42
+ ··· + 1.13379u − 7.32800
−0.00143245u
43
+ 0.000439038u
42
+ ··· − 35.5630u + 15.0831
a
3
=
−0.000366681u
43
+ 6.86484 × 10
−6
u
42
+ ··· + 0.722864u + 4.29414
−0.000979566u
43
+ 0.000158000u
42
+ ··· − 38.9308u + 18.6302
a
8
=
−0.00100884u
43
+ 0.0000695518u
42
+ ··· − 34.4292u + 7.75514
−0.00143245u
43
+ 0.000439038u
42
+ ··· − 35.5630u + 15.0831
a
7
=
−0.00100884u
43
+ 0.0000695518u
42
+ ··· − 34.4292u + 7.75514
−0.000519378u
43
+ 0.000227604u
42
+ ··· − 13.4493u + 5.82268
a
1
=
−0.00111027u
43
+ 0.000170982u
42
+ ··· − 24.7199u + 11.2172
0.0000227599u
43
+ 0.0000793547u
42
+ ··· + 7.51625u + 0.662428
a
2
=
−0.00106771u
43
+ 0.000531820u
42
+ ··· − 15.1776u + 15.0692
−0.00135172u
43
+ 0.000249506u
42
+ ··· − 22.2369u + 10.6788
a
11
=
−0.00104245u
43
+ 0.000171126u
42
+ ··· − 18.5615u + 10.9112
0.00126241u
43
− 0.0000513188u
42
+ ··· + 29.6839u − 12.2055
a
10
=
0.000219960u
43
+ 0.000119807u
42
+ ··· + 11.1224u − 1.29427
0.00126241u
43
− 0.0000513188u
42
+ ··· + 29.6839u − 12.2055
a
6
=
0.000928242u
43
− 0.000395266u
42
+ ··· + 6.92574u − 13.5888
0.00136897u
43
− 0.000507756u
42
+ ··· + 27.5784u − 15.4736
(ii) Obstruction class = −1
(iii) Cusp Shapes = 0.00924417u
43
− 0.00117823u
42
+ ··· + 253.150u − 126.267
9
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
(u
11
+ 5u
10
+ ··· + 2u + 1)
4
c
2
, c
5
(u
11
− u
10
− 2u
9
+ 3u
8
+ 2u
7
− 4u
6
+ 3u
4
− u
3
− u
2
+ 1)
4
c
3
, c
10
u
44
− u
43
+ ··· + 910u + 19909
c
4
, c
8
u
44
+ u
43
+ ··· + 34132u + 9859
c
6
, c
9
u
44
+ 9u
43
+ ··· + 332u + 43
c
7
, c
12
(u
2
− u + 1)
22
c
11
(u
11
+ 9u
10
+ ··· + 10u − 1)
4
10
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
(y
11
+ 3y
10
+ ··· − 10y −1)
4
c
2
, c
5
(y
11
− 5y
10
+ ··· + 2y −1)
4
c
3
, c
10
y
44
− 21y
43
+ ··· − 17790568y + 396368281
c
4
, c
8
y
44
− 45y
43
+ ··· − 3052479256y + 97199881
c
6
, c
9
y
44
+ 11y
43
+ ··· + 25828y + 1849
c
7
, c
12
(y
2
+ y + 1)
22
c
11
(y
11
− 21y
10
+ ··· + 66y −1)
4
11
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.146600 + 1.027860I
a = 0.0175660 + 0.1231610I
b = 0.876184 + 0.235814I
−1.55223 + 2.02988I −15.8143 − 3.4641I
u = −0.146600 − 1.027860I
a = 0.0175660 − 0.1231610I
b = 0.876184 − 0.235814I
−1.55223 − 2.02988I −15.8143 + 3.4641I
u = 0.876184 + 0.235814I
a = −0.137463 + 0.036996I
b = −0.146600 + 1.027860I
−1.55223 + 2.02988I −15.8143 − 3.4641I
u = 0.876184 − 0.235814I
a = −0.137463 − 0.036996I
b = −0.146600 − 1.027860I
−1.55223 − 2.02988I −15.8143 + 3.4641I
u = 0.834580 + 0.096635I
a = −0.552333 + 0.589324I
b = −0.15741 − 1.54482I
2.33004 − 9.05208I −12.4995 + 8.3503I
u = 0.834580 − 0.096635I
a = −0.552333 − 0.589324I
b = −0.15741 + 1.54482I
2.33004 + 9.05208I −12.4995 − 8.3503I
u = 1.177290 + 0.201858I
a = 1.38770 − 0.77626I
b = −1.92280 + 0.13240I
−5.31149 + 2.72042I −15.3589 − 3.3128I
u = 1.177290 − 0.201858I
a = 1.38770 + 0.77626I
b = −1.92280 − 0.13240I
−5.31149 − 2.72042I −15.3589 + 3.3128I
u = −0.757902 + 0.040013I
a = 0.692319 + 0.354490I
b = 0.02572 − 1.45924I
4.10386 + 3.67581I −9.95012 − 3.70891I
u = −0.757902 − 0.040013I
a = 0.692319 − 0.354490I
b = 0.02572 + 1.45924I
4.10386 − 3.67581I −9.95012 + 3.70891I
12
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −1.204130 + 0.383857I
a = −1.143760 − 0.610482I
b = 1.72881 + 0.07778I
−3.64484 + 1.57512I −10.80492 − 2.09453I
u = −1.204130 − 0.383857I
a = −1.143760 + 0.610482I
b = 1.72881 − 0.07778I
−3.64484 − 1.57512I −10.80492 + 2.09453I
u = −0.390583 + 1.224810I
a = −0.051222 + 0.456318I
b = −0.472418 + 0.118896I
4.10386 − 0.38395I −9.95012 + 3.21929I
u = −0.390583 − 1.224810I
a = −0.051222 − 0.456318I
b = −0.472418 − 0.118896I
4.10386 + 0.38395I −9.95012 − 3.21929I
u = 0.625013 + 1.170720I
a = 0.107660 + 0.499867I
b = 0.290566 + 0.139821I
2.33004 − 4.99231I −12.49946 + 1.42209I
u = 0.625013 − 1.170720I
a = 0.107660 − 0.499867I
b = 0.290566 − 0.139821I
2.33004 + 4.99231I −12.49946 − 1.42209I
u = 1.401580 + 0.160493I
a = 1.54394 − 0.34544I
b = −1.96590 − 0.22413I
−6.57107 − 3.30529I −19.4794 + 4.2651I
u = 1.401580 − 0.160493I
a = 1.54394 + 0.34544I
b = −1.96590 + 0.22413I
−6.57107 + 3.30529I −19.4794 − 4.2651I
u = 0.02572 + 1.45924I
a = 0.158572 + 0.372092I
b = −0.757902 − 0.040013I
4.10386 − 3.67581I −9.95012 + 3.70891I
u = 0.02572 − 1.45924I
a = 0.158572 − 0.372092I
b = −0.757902 + 0.040013I
4.10386 + 3.67581I −9.95012 − 3.70891I
13
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −1.49934 + 0.09123I
a = −1.215360 + 0.348743I
b = 1.58262 − 0.90400I
−5.31149 + 6.78019I −12.0000 − 10.2410I
u = −1.49934 − 0.09123I
a = −1.215360 − 0.348743I
b = 1.58262 + 0.90400I
−5.31149 − 6.78019I −12.0000 + 10.2410I
u = −0.472418 + 0.118896I
a = 0.952038 + 0.749677I
b = −0.390583 + 1.224810I
4.10386 − 0.38395I −9.95012 + 3.21929I
u = −0.472418 − 0.118896I
a = 0.952038 − 0.749677I
b = −0.390583 − 1.224810I
4.10386 + 0.38395I −9.95012 − 3.21929I
u = −1.51036 + 0.12279I
a = −1.47245 + 0.03680I
b = 1.84763 − 0.57968I
−6.57107 + 0.75447I −12.00000 + 0.I
u = −1.51036 − 0.12279I
a = −1.47245 − 0.03680I
b = 1.84763 + 0.57968I
−6.57107 − 0.75447I −12.00000 + 0.I
u = 1.53293 + 0.03815I
a = 1.055460 + 0.166867I
b = −1.39548 − 0.72335I
−3.64484 − 2.48465I 0
u = 1.53293 − 0.03815I
a = 1.055460 − 0.166867I
b = −1.39548 + 0.72335I
−3.64484 + 2.48465I 0
u = −0.15741 + 1.54482I
a = −0.247102 + 0.360437I
b = 0.834580 − 0.096635I
2.33004 + 9.05208I 0
u = −0.15741 − 1.54482I
a = −0.247102 − 0.360437I
b = 0.834580 + 0.096635I
2.33004 − 9.05208I 0
14
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −1.39548 + 0.72335I
a = −0.996952 − 0.304617I
b = 1.53293 − 0.03815I
−3.64484 + 2.48465I 0
u = −1.39548 − 0.72335I
a = −0.996952 + 0.304617I
b = 1.53293 + 0.03815I
−3.64484 − 2.48465I 0
u = 0.290566 + 0.139821I
a = −0.85770 + 1.92172I
b = 0.625013 + 1.170720I
2.33004 − 4.99231I −12.49946 + 1.42209I
u = 0.290566 − 0.139821I
a = −0.85770 − 1.92172I
b = 0.625013 − 1.170720I
2.33004 + 4.99231I −12.49946 − 1.42209I
u = 1.72881 + 0.07778I
a = 0.937991 + 0.129053I
b = −1.204130 + 0.383857I
−3.64484 + 1.57512I 0
u = 1.72881 − 0.07778I
a = 0.937991 − 0.129053I
b = −1.204130 − 0.383857I
−3.64484 − 1.57512I 0
u = 1.58262 + 0.90400I
a = 1.025460 − 0.185291I
b = −1.49934 − 0.09123I
−5.31149 − 6.78019I 0
u = 1.58262 − 0.90400I
a = 1.025460 + 0.185291I
b = −1.49934 + 0.09123I
−5.31149 + 6.78019I 0
u = −1.92280 + 0.13240I
a = −0.949343 + 0.264236I
b = 1.177290 + 0.201858I
−5.31149 + 2.72042I 0
u = −1.92280 − 0.13240I
a = −0.949343 − 0.264236I
b = 1.177290 − 0.201858I
−5.31149 − 2.72042I 0
15
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 1.84763 + 0.57968I
a = 1.130110 − 0.226634I
b = −1.51036 − 0.12279I
−6.57107 − 0.75447I 0
u = 1.84763 − 0.57968I
a = 1.130110 + 0.226634I
b = −1.51036 + 0.12279I
−6.57107 + 0.75447I 0
u = −1.96590 + 0.22413I
a = −1.100930 − 0.245753I
b = 1.401580 − 0.160493I
−6.57107 + 3.30529I 0
u = −1.96590 − 0.22413I
a = −1.100930 + 0.245753I
b = 1.401580 + 0.160493I
−6.57107 − 3.30529I 0
16
III. I
u
3
= hb + u, −5.42 × 10
11
u
21
+ 7.38 × 10
11
u
20
+ · · · + 5.32 × 10
11
a −
9.97 × 10
11
, u
22
− u
21
+ · · · − 13u
3
− 1i
(i) Arc colorings
a
5
=
1
0
a
12
=
0
u
a
4
=
1
−u
2
a
9
=
1.01764u
21
− 1.38529u
20
+ ··· + 4.76849u + 1.87254
−u
a
3
=
−0.0255060u
21
− 0.569625u
20
+ ··· + 3.04415u + 3.41674
0.0203918u
21
+ 0.140321u
20
+ ··· − 0.367651u − 0.341643
a
8
=
1.01764u
21
− 1.38529u
20
+ ··· + 3.76849u + 1.87254
−u
a
7
=
1.01764u
21
− 1.38529u
20
+ ··· + 3.76849u + 1.87254
0.341643u
21
− 0.362035u
20
+ ··· − 2.01764u + 0.367651
a
1
=
0.715811u
21
− 0.332883u
20
+ ··· − 4.20735u + 0.436308
−0.409581u
21
+ 0.405462u
20
+ ··· + 1.30183u − 0.750579
a
2
=
0.323078u
21
+ 0.207966u
20
+ ··· − 2.39576u + 1.94745
−0.154747u
21
+ 0.0396708u
20
+ ··· + 0.632801u − 0.675730
a
11
=
−1.39910u
21
+ 1.05695u
20
+ ··· + 6.24263u − 1.17161
0.341643u
21
− 0.362035u
20
+ ··· − 0.0176402u + 0.367651
a
10
=
−1.05745u
21
+ 0.694918u
20
+ ··· + 6.22499u − 0.803959
0.341643u
21
− 0.362035u
20
+ ··· − 0.0176402u + 0.367651
a
6
=
−1.83352u
21
+ 1.54719u
20
+ ··· + 6.31772u − 1.17672
0.0666835u
21
− 0.0438075u
20
+ ··· − 0.525767u + 0.674367
(ii) Obstruction class = 1
(iii) Cusp Shapes
= −
7686198297006
2661920121175
u
21
+
1900522941334
2661920121175
u
20
+ ··· +
41695789261051
2661920121175
u −
29133516690588
2661920121175
17
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
22
− 13u
21
+ ··· − 70u + 9
c
2
u
22
+ 3u
21
+ ··· − 4u − 3
c
3
, c
10
u
22
− 7u
20
+ ··· − 21u + 5
c
4
, c
8
u
22
− u
21
+ ··· − 13u
3
− 1
c
5
u
22
− 3u
21
+ ··· + 4u − 3
c
6
, c
9
u
22
− u
21
+ ··· − 7u + 1
c
7
u
22
+ u
21
+ ··· − u − 5
c
11
u
22
+ 18u
21
+ ··· + 42u + 7
c
12
u
22
− u
21
+ ··· + u − 5
18
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
22
− y
21
+ ··· + 374y + 81
c
2
, c
5
y
22
− 13y
21
+ ··· − 70y + 9
c
3
, c
10
y
22
− 14y
21
+ ··· − 1081y + 25
c
4
, c
8
y
22
− 19y
21
+ ··· + 16y
2
+ 1
c
6
, c
9
y
22
+ 7y
21
+ ··· − 33y + 1
c
7
, c
12
y
22
+ 15y
21
+ ··· + 159y + 25
c
11
y
22
− 22y
21
+ ··· + 4536y + 49
19
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = −0.462364 + 0.864470I
a = 0.141220 − 0.066021I
b = 0.462364 − 0.864470I
3.13797 + 5.67407I −4.97107 − 7.09540I
u = −0.462364 − 0.864470I
a = 0.141220 + 0.066021I
b = 0.462364 + 0.864470I
3.13797 − 5.67407I −4.97107 + 7.09540I
u = 0.400384 + 0.812221I
a = −0.480146 − 0.219236I
b = −0.400384 − 0.812221I
5.18891 − 0.00823I −1.60029 + 0.02294I
u = 0.400384 − 0.812221I
a = −0.480146 + 0.219236I
b = −0.400384 + 0.812221I
5.18891 + 0.00823I −1.60029 − 0.02294I
u = −0.688652 + 0.496345I
a = 0.053910 − 1.209490I
b = 0.688652 − 0.496345I
−0.09221 − 3.34290I −14.2348 + 8.5592I
u = −0.688652 − 0.496345I
a = 0.053910 + 1.209490I
b = 0.688652 + 0.496345I
−0.09221 + 3.34290I −14.2348 − 8.5592I
u = 0.120422 + 0.762961I
a = 1.68075 + 0.72584I
b = −0.120422 − 0.762961I
4.48540 − 8.38571I −7.24473 + 7.59410I
u = 0.120422 − 0.762961I
a = 1.68075 − 0.72584I
b = −0.120422 + 0.762961I
4.48540 + 8.38571I −7.24473 − 7.59410I
u = 0.024400 + 0.736221I
a = −1.57859 + 0.33368I
b = −0.024400 − 0.736221I
6.06599 + 3.18341I −3.75646 − 2.30234I
u = 0.024400 − 0.736221I
a = −1.57859 − 0.33368I
b = −0.024400 + 0.736221I
6.06599 − 3.18341I −3.75646 + 2.30234I
20
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = −1.46656 + 0.25570I
a = −1.094500 − 0.034003I
b = 1.46656 − 0.25570I
−3.72903 + 0.96569I −10.94638 + 1.02718I
u = −1.46656 − 0.25570I
a = −1.094500 + 0.034003I
b = 1.46656 + 0.25570I
−3.72903 − 0.96569I −10.94638 − 1.02718I
u = 1.52896 + 0.38298I
a = 1.221380 + 0.007638I
b = −1.52896 − 0.38298I
−4.94288 − 5.39591I −12.40328 + 4.41457I
u = 1.52896 − 0.38298I
a = 1.221380 − 0.007638I
b = −1.52896 + 0.38298I
−4.94288 + 5.39591I −12.40328 − 4.41457I
u = −0.411408
a = −1.51545
b = 0.411408
−2.45749 −16.5320
u = 0.280393 + 0.291523I
a = 2.88851 + 2.16258I
b = −0.280393 − 0.291523I
1.47540 − 2.33440I −14.8004 + 7.0340I
u = 0.280393 − 0.291523I
a = 2.88851 − 2.16258I
b = −0.280393 + 0.291523I
1.47540 + 2.33440I −14.8004 − 7.0340I
u = −1.63485 + 0.24302I
a = −1.279140 − 0.301141I
b = 1.63485 − 0.24302I
−5.42396 + 3.27804I −10.07598 − 4.81247I
u = −1.63485 − 0.24302I
a = −1.279140 + 0.301141I
b = 1.63485 + 0.24302I
−5.42396 − 3.27804I −10.07598 + 4.81247I
u = 1.65513 + 0.30479I
a = 1.342160 − 0.171780I
b = −1.65513 − 0.30479I
−5.86273 − 0.02756I −11.53859 − 3.91620I
21
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = 1.65513 − 0.30479I
a = 1.342160 + 0.171780I
b = −1.65513 + 0.30479I
−5.86273 + 0.02756I −11.53859 + 3.91620I
u = 1.89690
a = 0.724335
b = −1.89690
−11.3077 19.6760
22
IV. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
((u
11
+ 5u
10
+ ··· + 2u + 1)
4
)(u
22
− 13u
21
+ ··· − 70u + 9)
· (u
35
+ 18u
34
+ ··· + 268u + 16)
c
2
(u
11
− u
10
− 2u
9
+ 3u
8
+ 2u
7
− 4u
6
+ 3u
4
− u
3
− u
2
+ 1)
4
· (u
22
+ 3u
21
+ ··· − 4u − 3)(u
35
+ 8u
34
+ ··· + 42u + 4)
c
3
, c
10
(u
22
− 7u
20
+ ··· − 21u + 5)(u
35
− 3u
33
+ ··· − 2u + 5)
· (u
44
− u
43
+ ··· + 910u + 19909)
c
4
, c
8
(u
22
− u
21
+ ··· − 13u
3
− 1)(u
35
+ u
34
+ ··· + 3u + 1)
· (u
44
+ u
43
+ ··· + 34132u + 9859)
c
5
(u
11
− u
10
− 2u
9
+ 3u
8
+ 2u
7
− 4u
6
+ 3u
4
− u
3
− u
2
+ 1)
4
· (u
22
− 3u
21
+ ··· + 4u − 3)(u
35
+ 8u
34
+ ··· + 42u + 4)
c
6
, c
9
(u
22
− u
21
+ ··· − 7u + 1)(u
35
− u
34
+ ··· − 2u + 1)
· (u
44
+ 9u
43
+ ··· + 332u + 43)
c
7
((u
2
− u + 1)
22
)(u
22
+ u
21
+ ··· − u − 5)
· (u
35
+ 24u
34
+ ··· + 39936u + 2048)
c
11
((u
11
+ 9u
10
+ ··· + 10u − 1)
4
)(u
22
+ 18u
21
+ ··· + 42u + 7)
· (u
35
− 23u
34
+ ··· − 230u + 1300)
c
12
((u
2
− u + 1)
22
)(u
22
− u
21
+ ··· + u − 5)
· (u
35
+ 24u
34
+ ··· + 39936u + 2048)
23
V. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
((y
11
+ 3y
10
+ ··· − 10y −1)
4
)(y
22
− y
21
+ ··· + 374y + 81)
· (y
35
+ 2y
34
+ ··· + 40048y −256)
c
2
, c
5
((y
11
− 5y
10
+ ··· + 2y −1)
4
)(y
22
− 13y
21
+ ··· − 70y + 9)
· (y
35
− 18y
34
+ ··· + 268y −16)
c
3
, c
10
(y
22
− 14y
21
+ ··· − 1081y + 25)(y
35
− 6y
34
+ ··· + 434y −25)
· (y
44
− 21y
43
+ ··· − 17790568y + 396368281)
c
4
, c
8
(y
22
− 19y
21
+ ··· + 16y
2
+ 1)(y
35
− 47y
34
+ ··· + 13y −1)
· (y
44
− 45y
43
+ ··· − 3052479256y + 97199881)
c
6
, c
9
(y
22
+ 7y
21
+ ··· − 33y + 1)(y
35
+ 3y
34
+ ··· − 2y −1)
· (y
44
+ 11y
43
+ ··· + 25828y + 1849)
c
7
, c
12
((y
2
+ y + 1)
22
)(y
22
+ 15y
21
+ ··· + 159y + 25)
· (y
35
+ 16y
34
+ ··· + 47185920y −4194304)
c
11
((y
11
− 21y
10
+ ··· + 66y −1)
4
)(y
22
− 22y
21
+ ··· + 4536y + 49)
· (y
35
− 23y
34
+ ··· + 9249100y −1690000)
24
