12a
0557
(K12a
0557
)
A knot diagram
1
Linearized knot diagam
3 7 9 8 11 2 6 4 1 12 5 10
Solving Sequence
5,8
4 9
3,12
11 6 7 2 10 1
c
4
c
8
c
3
c
11
c
5
c
7
c
2
c
10
c
12
c
1
, c
6
, c
9
Ideals for irreducible components
2
of X
par
I
u
1
= h1.49508 × 10
98
u
64
+ 3.45396 × 10
98
u
63
+ ··· + 1.71880 × 10
101
b − 6.24196 × 10
100
,
7.40968 × 10
98
u
64
+ 4.71743 × 10
98
u
63
+ ··· + 1.56255 × 10
100
a + 4.47963 × 10
99
, u
65
+ u
64
+ ··· − 25u − 25i
I
u
2
= h−13687a
5
u − 12349a
4
u + ··· − 16925a + 1043,
a
6
+ 2a
5
u − a
4
u − 4a
4
− 7a
3
u + 6a
3
+ 8a
2
u + 6a
2
− 4au − 11a − u + 6, u
2
+ 1i
* 2 irreducible components of dim
C
= 0, with total 77 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
= h1.50 × 10
98
u
64
+ 3.45 × 10
98
u
63
+ · · · + 1.72 × 10
101
b − 6.24 ×
10
100
, 7.41 × 10
98
u
64
+ 4.72 × 10
98
u
63
+ · · · + 1.56 × 10
100
a + 4.48 ×
10
99
, u
65
+ u
64
+ · · · − 25u − 25i
(i) Arc colorings
a
5
=
1
0
a
8
=
0
u
a
4
=
1
−u
2
a
9
=
−u
u
3
+ u
a
3
=
u
2
+ 1
−u
4
− 2u
2
a
12
=
−0.0474205u
64
− 0.0301906u
63
+ ··· + 7.10316u − 0.286687
−0.000869840u
64
− 0.00200952u
63
+ ··· − 0.135624u + 0.363158
a
11
=
−0.0465507u
64
− 0.0281811u
63
+ ··· + 7.23878u − 0.649845
−0.000869840u
64
− 0.00200952u
63
+ ··· − 0.135624u + 0.363158
a
6
=
0.0150022u
64
+ 0.0129683u
63
+ ··· + 2.59978u − 2.71871
−0.00372994u
64
− 0.00195650u
63
+ ··· + 1.02293u + 0.756420
a
7
=
−0.0176087u
64
− 0.0141154u
63
+ ··· + 6.93497u − 1.17013
−0.00433770u
64
− 0.0109885u
63
+ ··· − 0.534815u + 0.289329
a
2
=
0.0346066u
64
+ 0.0170099u
63
+ ··· − 6.02149u + 0.689262
−0.00352626u
64
− 0.00697665u
63
+ ··· + 1.54019u + 0.392222
a
10
=
−0.0317390u
64
− 0.0250886u
63
+ ··· + 1.23774u − 0.670406
−0.00724756u
64
− 0.0123758u
63
+ ··· + 1.06301u + 0.201180
a
1
=
−0.0299964u
64
− 0.0121632u
63
+ ··· + 3.39288u − 0.548318
0.00192211u
64
− 0.00142328u
63
+ ··· − 1.37640u − 0.164022
(ii) Obstruction class = −1
(iii) Cusp Shapes = 0.0739830u
64
+ 0.0434787u
63
+ ··· + 8.13540u − 8.87805
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
7
u
65
+ 19u
64
+ ··· + 5u + 1
c
2
, c
6
u
65
− u
64
+ ··· + 3u + 1
c
3
, c
4
, c
8
u
65
− u
64
+ ··· − 25u + 25
c
5
, c
11
u
65
+ u
64
+ ··· − 5u + 1
c
9
, c
10
, c
12
u
65
+ 15u
64
+ ··· + 7u − 1
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
7
y
65
+ 61y
64
+ ··· − 107y −1
c
2
, c
6
y
65
− 19y
64
+ ··· + 5y −1
c
3
, c
4
, c
8
y
65
+ 71y
64
+ ··· − 7625y −625
c
5
, c
11
y
65
+ 15y
64
+ ··· + 7y −1
c
9
, c
10
, c
12
y
65
+ 75y
64
+ ··· − 101y −1
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.194939 + 0.985568I
a = 1.136230 − 0.286521I
b = 0.757307 − 0.912410I
4.66678 − 3.00289I −8.00000 + 0.I
u = −0.194939 − 0.985568I
a = 1.136230 + 0.286521I
b = 0.757307 + 0.912410I
4.66678 + 3.00289I −8.00000 + 0.I
u = 0.143383 + 0.948907I
a = −0.264910 − 0.796535I
b = −0.235093 + 0.116598I
1.78080 − 2.10362I 0. + 4.48623I
u = 0.143383 − 0.948907I
a = −0.264910 + 0.796535I
b = −0.235093 − 0.116598I
1.78080 + 2.10362I 0. − 4.48623I
u = 0.221402 + 0.901501I
a = 1.47954 − 0.11084I
b = 0.781778 − 0.855158I
4.84956 − 2.80174I −1.96434 + 4.08273I
u = 0.221402 − 0.901501I
a = 1.47954 + 0.11084I
b = 0.781778 + 0.855158I
4.84956 + 2.80174I −1.96434 − 4.08273I
u = −0.444661 + 0.777234I
a = 0.408200 − 0.203744I
b = −0.506414 + 0.612963I
2.38441 − 2.58306I −3.08948 + 3.45648I
u = −0.444661 − 0.777234I
a = 0.408200 + 0.203744I
b = −0.506414 − 0.612963I
2.38441 + 2.58306I −3.08948 − 3.45648I
u = −0.200493 + 1.105690I
a = 0.077851 − 0.634026I
b = −0.156729 + 0.869731I
−0.456321 + 0.587854I 0
u = −0.200493 − 1.105690I
a = 0.077851 + 0.634026I
b = −0.156729 − 0.869731I
−0.456321 − 0.587854I 0
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.540784 + 0.670619I
a = −0.252084 − 0.024836I
b = 0.558240 + 0.478764I
2.54249 − 2.69464I −2.33919 + 3.35970I
u = 0.540784 − 0.670619I
a = −0.252084 + 0.024836I
b = 0.558240 − 0.478764I
2.54249 + 2.69464I −2.33919 − 3.35970I
u = −0.991125 + 0.561749I
a = −1.220950 + 0.689343I
b = −0.863665 − 0.958398I
9.74563 + 9.54545I 0
u = −0.991125 − 0.561749I
a = −1.220950 − 0.689343I
b = −0.863665 + 0.958398I
9.74563 − 9.54545I 0
u = 0.973757 + 0.615749I
a = −0.383570 − 0.233418I
b = −0.896873 − 0.885529I
9.97887 − 3.03863I 0
u = 0.973757 − 0.615749I
a = −0.383570 + 0.233418I
b = −0.896873 + 0.885529I
9.97887 + 3.03863I 0
u = 0.947294 + 0.674719I
a = 1.243340 + 0.582206I
b = 0.874408 − 0.938153I
10.15870 − 3.31862I 0
u = 0.947294 − 0.674719I
a = 1.243340 − 0.582206I
b = 0.874408 + 0.938153I
10.15870 + 3.31862I 0
u = −0.925321 + 0.731778I
a = 0.465765 − 0.237270I
b = 0.887478 − 0.908982I
10.25190 − 3.19464I 0
u = −0.925321 − 0.731778I
a = 0.465765 + 0.237270I
b = 0.887478 + 0.908982I
10.25190 + 3.19464I 0
6
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.666201 + 0.415426I
a = 0.53075 − 1.62998I
b = 0.470202 + 0.892585I
1.24733 + 6.64277I −7.43550 − 9.53298I
u = −0.666201 − 0.415426I
a = 0.53075 + 1.62998I
b = 0.470202 − 0.892585I
1.24733 − 6.64277I −7.43550 + 9.53298I
u = −0.037730 + 1.240550I
a = −1.51164 − 0.80363I
b = −0.426053 − 0.548434I
2.00616 − 1.49123I 0
u = −0.037730 − 1.240550I
a = −1.51164 + 0.80363I
b = −0.426053 + 0.548434I
2.00616 + 1.49123I 0
u = 0.117997 + 1.274100I
a = 1.40404 − 0.21152I
b = 0.612078 − 0.723737I
4.41355 − 2.28333I 0
u = 0.117997 − 1.274100I
a = 1.40404 + 0.21152I
b = 0.612078 + 0.723737I
4.41355 + 2.28333I 0
u = 0.574683 + 0.420836I
a = −0.34710 − 1.45942I
b = −0.499917 + 0.810111I
1.75044 − 1.32012I −5.66585 + 3.92029I
u = 0.574683 − 0.420836I
a = −0.34710 + 1.45942I
b = −0.499917 − 0.810111I
1.75044 + 1.32012I −5.66585 − 3.92029I
u = −0.165173 + 1.283860I
a = −1.78999 + 0.19957I
b = −0.424688 − 0.860379I
0.95184 + 4.92361I 0
u = −0.165173 − 1.283860I
a = −1.78999 − 0.19957I
b = −0.424688 + 0.860379I
0.95184 − 4.92361I 0
7
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.572720 + 0.106229I
a = 0.96365 − 1.74351I
b = 0.262020 + 0.873062I
−3.34907 + 2.30473I −16.2162 − 5.9449I
u = −0.572720 − 0.106229I
a = 0.96365 + 1.74351I
b = 0.262020 − 0.873062I
−3.34907 − 2.30473I −16.2162 + 5.9449I
u = −0.437487 + 0.332448I
a = −2.32984 + 0.82322I
b = −0.784409 − 0.913662I
2.66558 + 5.57488I −9.42845 − 7.52087I
u = −0.437487 − 0.332448I
a = −2.32984 − 0.82322I
b = −0.784409 + 0.913662I
2.66558 − 5.57488I −9.42845 + 7.52087I
u = −0.04732 + 1.49280I
a = 0.003876 − 0.697847I
b = −0.024391 + 1.094580I
4.94320 + 3.00427I 0
u = −0.04732 − 1.49280I
a = 0.003876 + 0.697847I
b = −0.024391 − 1.094580I
4.94320 − 3.00427I 0
u = −0.13405 + 1.51695I
a = 2.18073 + 0.49322I
b = 0.859141 + 0.947236I
8.98795 + 7.60409I 0
u = −0.13405 − 1.51695I
a = 2.18073 − 0.49322I
b = 0.859141 − 0.947236I
8.98795 − 7.60409I 0
u = 0.09167 + 1.52042I
a = 1.60247 + 1.13624I
b = 0.883757 + 0.890653I
9.16830 − 1.15187I 0
u = 0.09167 − 1.52042I
a = 1.60247 − 1.13624I
b = 0.883757 − 0.890653I
9.16830 + 1.15187I 0
8
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.353629 + 0.307016I
a = −0.21266 − 1.52151I
b = −0.789122 − 0.859153I
2.82730 + 0.34334I −9.08497 + 2.02539I
u = 0.353629 − 0.307016I
a = −0.21266 + 1.52151I
b = −0.789122 + 0.859153I
2.82730 − 0.34334I −9.08497 − 2.02539I
u = 0.13146 + 1.52657I
a = 1.221890 + 0.412179I
b = 0.516210 − 1.047730I
8.27904 − 3.65206I 0
u = 0.13146 − 1.52657I
a = 1.221890 − 0.412179I
b = 0.516210 + 1.047730I
8.27904 + 3.65206I 0
u = −0.21085 + 1.52413I
a = −1.252790 + 0.515874I
b = −0.473206 − 1.059010I
7.69875 + 9.80033I 0
u = −0.21085 − 1.52413I
a = −1.252790 − 0.515874I
b = −0.473206 + 1.059010I
7.69875 − 9.80033I 0
u = 0.455205
a = −0.0293311
b = 0.404527
−1.07813 −9.13920
u = 0.14198 + 1.58601I
a = −0.829734 − 0.378431I
b = −0.825125 − 0.320393I
10.16130 − 5.11867I 0
u = 0.14198 − 1.58601I
a = −0.829734 + 0.378431I
b = −0.825125 + 0.320393I
10.16130 + 5.11867I 0
u = −0.05580 + 1.59350I
a = 0.883115 − 0.344042I
b = 0.829266 − 0.381772I
10.48610 − 1.22570I 0
9
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.05580 − 1.59350I
a = 0.883115 + 0.344042I
b = 0.829266 + 0.381772I
10.48610 + 1.22570I 0
u = 0.265152 + 0.297533I
a = −1.128460 − 0.499441I
b = −0.222502 + 0.644711I
−0.359965 − 0.971629I −6.26553 + 6.85953I
u = 0.265152 − 0.297533I
a = −1.128460 + 0.499441I
b = −0.222502 − 0.644711I
−0.359965 + 0.971629I −6.26553 − 6.85953I
u = 0.02254 + 1.60792I
a = −1.73396 + 0.67808I
b = −0.893399 + 0.929362I
13.28270 − 3.29649I 0
u = 0.02254 − 1.60792I
a = −1.73396 − 0.67808I
b = −0.893399 − 0.929362I
13.28270 + 3.29649I 0
u = −0.35667 + 1.60371I
a = 1.91240 − 0.16841I
b = 0.857112 + 1.009490I
16.7892 + 14.5383I 0
u = −0.35667 − 1.60371I
a = 1.91240 + 0.16841I
b = 0.857112 − 1.009490I
16.7892 − 14.5383I 0
u = 0.33299 + 1.62729I
a = 0.916394 + 0.913504I
b = 0.942347 + 0.840020I
17.3369 − 7.9187I 0
u = 0.33299 − 1.62729I
a = 0.916394 − 0.913504I
b = 0.942347 − 0.840020I
17.3369 + 7.9187I 0
u = 0.30253 + 1.64433I
a = −1.84849 − 0.02882I
b = −0.872298 + 1.000890I
17.8412 − 8.0089I 0
10
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.30253 − 1.64433I
a = −1.84849 + 0.02882I
b = −0.872298 − 1.000890I
17.8412 + 8.0089I 0
u = −0.27148 + 1.66645I
a = −1.042730 + 0.849827I
b = −0.944098 + 0.861611I
18.2931 + 1.3306I 0
u = −0.27148 − 1.66645I
a = −1.042730 − 0.849827I
b = −0.944098 − 0.861611I
18.2931 − 1.3306I 0
u = −0.176841 + 0.243173I
a = 1.23332 + 4.42124I
b = 0.044375 − 0.853831I
−1.05566 + 2.24342I −14.4833 − 3.3091I
u = −0.176841 − 0.243173I
a = 1.23332 − 4.42124I
b = 0.044375 + 0.853831I
−1.05566 − 2.24342I −14.4833 + 3.3091I
11
II. I
u
2
=
h−13687a
5
u−12349a
4
u+· · ·−16925a+1043, 2a
5
u−a
4
u+· · ·−11a+6, u
2
+1i
(i) Arc colorings
a
5
=
1
0
a
8
=
0
u
a
4
=
1
1
a
9
=
−u
0
a
3
=
0
1
a
12
=
a
0.184498a
5
u + 0.166462a
4
u + ··· + 0.228146a − 0.0140594
a
11
=
−0.184498a
5
u − 0.166462a
4
u + ··· + 0.771854a + 0.0140594
0.184498a
5
u + 0.166462a
4
u + ··· + 0.228146a − 0.0140594
a
6
=
0.0408978a
5
u + 0.129177a
4
u + ··· + 0.154613a + 0.806484
−0.167972a
5
u − 0.213143a
4
u + ··· + 0.380805a + 0.496178
a
7
=
0.0408978a
5
u + 0.129177a
4
u + ··· + 0.154613a + 0.806484
−0.182126a
5
u − 0.0785469a
4
u + ··· + 0.763025a − 0.786224
a
2
=
0.0179551a
5
u − 0.0164589a
4
u + ··· + 0.0922693a + 0.329676
−0.0874301a
5
u + 0.282847a
4
u + ··· + 1.08674a − 1.08730
a
10
=
−0.182126a
5
u − 0.0785469a
4
u + ··· + 0.763025a − 0.786224
0.0791130a
5
u + 0.465768a
4
u + ··· + 1.22262a − 1.43103
a
1
=
0.0179551a
5
u − 0.0164589a
4
u + ··· + 0.0922693a + 0.329676
−0.105385a
5
u + 0.299306a
4
u + ··· + 0.994473a − 1.41697
(ii) Obstruction class = 1
(iii) Cusp Shapes =
11172
74185
a
5
u −
66884
74185
a
5
−
88436
74185
a
4
u −
87728
74185
a
4
−
10956
14837
a
3
u +
31104
14837
a
3
+
61696
14837
a
2
u −
7576
14837
a
2
+
22716
14837
au −
73396
14837
a +
235144
74185
u −
192528
74185
12
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
(u
2
− u + 1)
6
c
2
, c
6
(u
4
− u
2
+ 1)
3
c
3
, c
4
, c
8
(u
2
+ 1)
6
c
5
, c
11
(u
6
+ u
4
+ 2u
2
+ 1)
2
c
7
(u
2
+ u + 1)
6
c
9
, c
10
(u
3
− u
2
+ 2u − 1)
4
c
12
(u
3
+ u
2
+ 2u + 1)
4
13
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
7
(y
2
+ y + 1)
6
c
2
, c
6
(y
2
− y + 1)
6
c
3
, c
4
, c
8
(y + 1)
12
c
5
, c
11
(y
3
+ y
2
+ 2y + 1)
4
c
9
, c
10
, c
12
(y
3
+ 3y
2
+ 2y −1)
4
14
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 1.000000I
a = 0.662359 + 0.577399I
b = 0.754878I
0.53148 − 2.02988I −9.01951 + 3.46410I
u = 1.000000I
a = 0.489013 − 0.507560I
b = 0.744862 − 0.877439I
4.66906 − 4.85801I −2.49024 + 6.44355I
u = 1.000000I
a = −1.15137 − 1.06984I
b = −0.744862 − 0.877439I
4.66906 + 0.79824I −2.49024 + 0.48465I
u = 1.000000I
a = 1.46291 + 0.63968I
b = 0.744862 − 0.877439I
4.66906 − 0.79824I −2.49024 − 0.48465I
u = 1.000000I
a = 0.66236 − 1.71708I
b = 0.754878I
0.53148 + 2.02988I −9.01951 − 3.46410I
u = 1.000000I
a = −2.12527 + 0.07740I
b = −0.744862 − 0.877439I
4.66906 + 4.85801I −2.49024 − 6.44355I
u = − 1.000000I
a = 0.662359 − 0.577399I
b = − 0.754878I
0.53148 + 2.02988I −9.01951 − 3.46410I
u = − 1.000000I
a = 0.489013 + 0.507560I
b = 0.744862 + 0.877439I
4.66906 + 4.85801I −2.49024 − 6.44355I
u = − 1.000000I
a = −1.15137 + 1.06984I
b = −0.744862 + 0.877439I
4.66906 − 0.79824I −2.49024 − 0.48465I
u = − 1.000000I
a = 1.46291 − 0.63968I
b = 0.744862 + 0.877439I
4.66906 + 0.79824I −2.49024 + 0.48465I
15
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = − 1.000000I
a = 0.66236 + 1.71708I
b = − 0.754878I
0.53148 − 2.02988I −9.01951 + 3.46410I
u = − 1.000000I
a = −2.12527 − 0.07740I
b = −0.744862 + 0.877439I
4.66906 − 4.85801I −2.49024 + 6.44355I
16
III. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
((u
2
− u + 1)
6
)(u
65
+ 19u
64
+ ··· + 5u + 1)
c
2
, c
6
((u
4
− u
2
+ 1)
3
)(u
65
− u
64
+ ··· + 3u + 1)
c
3
, c
4
, c
8
((u
2
+ 1)
6
)(u
65
− u
64
+ ··· − 25u + 25)
c
5
, c
11
((u
6
+ u
4
+ 2u
2
+ 1)
2
)(u
65
+ u
64
+ ··· − 5u + 1)
c
7
((u
2
+ u + 1)
6
)(u
65
+ 19u
64
+ ··· + 5u + 1)
c
9
, c
10
((u
3
− u
2
+ 2u − 1)
4
)(u
65
+ 15u
64
+ ··· + 7u − 1)
c
12
((u
3
+ u
2
+ 2u + 1)
4
)(u
65
+ 15u
64
+ ··· + 7u − 1)
17
IV. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
, c
7
((y
2
+ y + 1)
6
)(y
65
+ 61y
64
+ ··· − 107y −1)
c
2
, c
6
((y
2
− y + 1)
6
)(y
65
− 19y
64
+ ··· + 5y −1)
c
3
, c
4
, c
8
((y + 1)
12
)(y
65
+ 71y
64
+ ··· − 7625y −625)
c
5
, c
11
((y
3
+ y
2
+ 2y + 1)
4
)(y
65
+ 15y
64
+ ··· + 7y −1)
c
9
, c
10
, c
12
((y
3
+ 3y
2
+ 2y −1)
4
)(y
65
+ 75y
64
+ ··· − 101y −1)
18
