12a
0944
(K12a
0944
)
A knot diagram
1
Linearized knot diagam
4 6 10 2 9 11 12 3 5 1 7 8
Solving Sequence
8,12 1,4
2 5 7 11 6 10 3 9
c
12
c
1
c
4
c
7
c
11
c
6
c
10
c
3
c
9
c
2
, c
5
, c
8
Ideals for irreducible components
2
of X
par
I
u
1
= h−5.89366 × 10
43
u
82
− 4.02871 × 10
43
u
81
+ ··· + 5.84962 × 10
43
b − 9.28047 × 10
43
,
− 4.02033 × 10
43
u
82
− 6.96508 × 10
43
u
81
+ ··· + 5.84962 × 10
43
a + 9.14712 × 10
42
, u
83
+ 2u
82
+ ··· + 2u + 1i
I
u
2
= h2b − 3, 2a + 1, u − 1i
* 2 irreducible components of dim
C
= 0, with total 84 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−5.89×10
43
u
82
−4.03×10
43
u
81
+· · ·+5.85×10
43
b−9.28×10
43
, −4.02×
10
43
u
82
−6.97×10
43
u
81
+· · ·+5.85×10
43
a+9.15×10
42
, u
83
+2u
82
+· · ·+2u+1i
(i) Arc colorings
a
8
=
0
u
a
12
=
1
0
a
1
=
1
−u
2
a
4
=
0.687280u
82
+ 1.19069u
81
+ ··· − 4.55423u − 0.156371
1.00753u
82
+ 0.688714u
81
+ ··· + 2.17242u + 1.58651
a
2
=
0.595958u
82
+ 0.451262u
81
+ ··· − 3.44105u + 1.45422
0.130801u
82
+ 0.302832u
81
+ ··· + 0.730664u + 0.811722
a
5
=
0.485737u
82
+ 1.80641u
81
+ ··· − 1.46200u − 1.94018
1.01774u
82
+ 0.0762026u
81
+ ··· + 2.45408u + 1.22439
a
7
=
−u
u
a
11
=
−u
2
+ 1
u
2
a
6
=
u
3
− 2u
−u
3
+ u
a
10
=
u
4
− 3u
2
+ 1
−u
6
+ 2u
4
+ u
2
a
3
=
−0.0563813u
82
− 0.557025u
81
+ ··· − 0.575560u + 2.07556
1.78385u
82
+ 1.83521u
81
+ ··· + 0.274886u + 1.23971
a
9
=
0.389463u
82
+ 0.804666u
81
+ ··· − 2.31500u + 0.480446
0.263809u
82
− 0.0637110u
81
+ ··· − 2.47071u − 0.459997
(ii) Obstruction class = −1
(iii) Cusp Shapes = 0.357481u
82
− 3.48793u
81
+ ··· + 11.5669u − 5.41910
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
4
u
83
− 2u
82
+ ··· − 35u + 4
c
2
2(2u
83
− 13u
82
+ ··· + 3u + 1)
c
3
2(2u
83
− 11u
82
+ ··· + 4480u + 352)
c
5
, c
9
u
83
+ 2u
82
+ ··· + 4u + 1
c
6
, c
7
, c
11
c
12
u
83
+ 2u
82
+ ··· + 2u + 1
c
8
u
83
+ u
82
+ ··· − 2u + 8
c
10
u
83
+ 16u
82
+ ··· − 11522u − 2671
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
4
y
83
− 52y
82
+ ··· − 479y −16
c
2
4(4y
83
+ 523y
82
+ ··· − 117y −1)
c
3
4(4y
83
− 517y
82
+ ··· + 6829568y −123904)
c
5
, c
9
y
83
+ 48y
82
+ ··· + 12y −1
c
6
, c
7
, c
11
c
12
y
83
− 92y
82
+ ··· + 12y −1
c
8
y
83
+ 9y
82
+ ··· + 2164y −64
c
10
y
83
+ 28y
82
+ ··· + 65725068y −7134241
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −1.011980 + 0.179958I
a = 0.609871 − 0.498601I
b = −1.54206 + 0.26964I
3.08858 − 7.00447I 0
u = −1.011980 − 0.179958I
a = 0.609871 + 0.498601I
b = −1.54206 − 0.26964I
3.08858 + 7.00447I 0
u = 0.808275 + 0.494108I
a = 0.668900 + 0.762033I
b = −0.506716 − 0.978105I
1.080250 + 0.304022I 0
u = 0.808275 − 0.494108I
a = 0.668900 − 0.762033I
b = −0.506716 + 0.978105I
1.080250 − 0.304022I 0
u = −0.651779 + 0.604556I
a = 1.96345 − 1.28262I
b = −0.373780 + 1.237280I
−4.75200 − 7.90588I 0
u = −0.651779 − 0.604556I
a = 1.96345 + 1.28262I
b = −0.373780 − 1.237280I
−4.75200 + 7.90588I 0
u = 0.651416 + 0.587957I
a = 2.25811 + 1.40134I
b = −0.455813 − 1.238970I
−1.07019 + 13.90660I 0
u = 0.651416 − 0.587957I
a = 2.25811 − 1.40134I
b = −0.455813 + 1.238970I
−1.07019 − 13.90660I 0
u = 0.549669 + 0.652540I
a = 1.77757 + 0.60916I
b = −0.166242 − 1.069510I
1.14584 + 2.23192I 0
u = 0.549669 − 0.652540I
a = 1.77757 − 0.60916I
b = −0.166242 + 1.069510I
1.14584 − 2.23192I 0
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.621208 + 0.516711I
a = −1.122620 + 0.653975I
b = 0.442519 − 0.591802I
2.87214 + 7.55799I 0. − 9.17056I
u = 0.621208 − 0.516711I
a = −1.122620 − 0.653975I
b = 0.442519 + 0.591802I
2.87214 − 7.55799I 0. + 9.17056I
u = −0.794140 + 0.067445I
a = 0.828496 − 0.746859I
b = −0.754413 − 0.297712I
5.68714 + 2.25774I 7.48178 − 1.40093I
u = −0.794140 − 0.067445I
a = 0.828496 + 0.746859I
b = −0.754413 + 0.297712I
5.68714 − 2.25774I 7.48178 + 1.40093I
u = −0.603519 + 0.480975I
a = −0.693273 + 0.188096I
b = 0.158367 + 0.299299I
−0.49436 − 3.88362I −2.00000 + 7.10699I
u = −0.603519 − 0.480975I
a = −0.693273 − 0.188096I
b = 0.158367 − 0.299299I
−0.49436 + 3.88362I −2.00000 − 7.10699I
u = −0.311368 + 0.686203I
a = 2.05458 − 0.49843I
b = −0.259155 + 0.996903I
−5.76402 + 3.56956I −7.33230 − 3.19643I
u = −0.311368 − 0.686203I
a = 2.05458 + 0.49843I
b = −0.259155 − 0.996903I
−5.76402 − 3.56956I −7.33230 + 3.19643I
u = −0.540900 + 0.513654I
a = −2.36141 + 1.14016I
b = 0.686576 − 0.514783I
−2.34688 − 5.23319I −4.54446 + 9.84503I
u = −0.540900 − 0.513654I
a = −2.36141 − 1.14016I
b = 0.686576 + 0.514783I
−2.34688 + 5.23319I −4.54446 − 9.84503I
6
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.302357 + 0.661044I
a = 2.15568 + 0.69658I
b = −0.305424 − 1.170910I
−2.10269 − 9.69142I −3.57256 + 4.73391I
u = 0.302357 − 0.661044I
a = 2.15568 − 0.69658I
b = −0.305424 + 1.170910I
−2.10269 + 9.69142I −3.57256 − 4.73391I
u = 0.176369 + 0.694417I
a = 1.79640 − 0.14808I
b = −0.244225 − 0.252132I
−0.84399 + 3.83418I −2.64069 − 10.16954I
u = 0.176369 − 0.694417I
a = 1.79640 + 0.14808I
b = −0.244225 + 0.252132I
−0.84399 − 3.83418I −2.64069 + 10.16954I
u = 0.659821 + 0.267940I
a = 0.761044 + 0.351679I
b = −0.382761 − 0.240353I
1.22968 + 0.74629I 5.11191 − 1.69537I
u = 0.659821 − 0.267940I
a = 0.761044 − 0.351679I
b = −0.382761 + 0.240353I
1.22968 − 0.74629I 5.11191 + 1.69537I
u = 0.501968 + 0.498745I
a = −2.65030 − 1.61037I
b = 0.629147 + 1.068660I
−3.50723 + 1.89136I −6.82387 − 2.66530I
u = 0.501968 − 0.498745I
a = −2.65030 + 1.61037I
b = 0.629147 − 1.068660I
−3.50723 − 1.89136I −6.82387 + 2.66530I
u = 1.289970 + 0.207695I
a = 0.815121 + 0.281289I
b = −2.32584 − 1.05852I
−0.716216 − 0.352949I 0
u = 1.289970 − 0.207695I
a = 0.815121 − 0.281289I
b = −2.32584 + 1.05852I
−0.716216 + 0.352949I 0
7
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −1.305710 + 0.116254I
a = 0.821552 − 0.148933I
b = −2.60864 + 0.95083I
2.88394 + 6.80535I 0
u = −1.305710 − 0.116254I
a = 0.821552 + 0.148933I
b = −2.60864 − 0.95083I
2.88394 − 6.80535I 0
u = 0.465968 + 0.499477I
a = −2.48917 − 1.39113I
b = 0.76305 + 1.24356I
−3.61323 + 1.60159I −7.16367 − 5.67884I
u = 0.465968 − 0.499477I
a = −2.48917 + 1.39113I
b = 0.76305 − 1.24356I
−3.61323 − 1.60159I −7.16367 + 5.67884I
u = −0.533295 + 0.405202I
a = 3.22952 + 9.36950I
b = −3.45923 + 0.25484I
−0.168100 − 1.376260I −60.2145 + 47.3401I
u = −0.533295 − 0.405202I
a = 3.22952 − 9.36950I
b = −3.45923 − 0.25484I
−0.168100 + 1.376260I −60.2145 − 47.3401I
u = −0.413981 + 0.510073I
a = −1.43503 + 1.37204I
b = 0.607418 − 1.178460I
−2.71843 + 1.65955I −6.37148 − 1.99257I
u = −0.413981 − 0.510073I
a = −1.43503 − 1.37204I
b = 0.607418 + 1.178460I
−2.71843 − 1.65955I −6.37148 + 1.99257I
u = 0.411973 + 0.454512I
a = 1.168770 + 0.361760I
b = 0.160378 − 0.591800I
1.38976 + 1.62588I 0.70067 − 4.03519I
u = 0.411973 − 0.454512I
a = 1.168770 − 0.361760I
b = 0.160378 + 0.591800I
1.38976 − 1.62588I 0.70067 + 4.03519I
8
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.288666 + 0.539586I
a = 0.86073 − 1.17268I
b = −0.218842 + 0.593876I
1.92020 − 3.90128I −1.03104 + 3.05326I
u = 0.288666 − 0.539586I
a = 0.86073 + 1.17268I
b = −0.218842 − 0.593876I
1.92020 + 3.90128I −1.03104 − 3.05326I
u = 0.547852 + 0.128586I
a = 1.91306 − 0.32470I
b = 0.175410 − 0.576033I
1.05027 + 2.14204I 3.95885 − 3.96047I
u = 0.547852 − 0.128586I
a = 1.91306 + 0.32470I
b = 0.175410 + 0.576033I
1.05027 − 2.14204I 3.95885 + 3.96047I
u = −0.315876 + 0.453421I
a = 0.296378 + 0.378985I
b = 0.274103 − 0.402505I
−1.32179 + 0.54535I −6.25461 − 0.32765I
u = −0.315876 − 0.453421I
a = 0.296378 − 0.378985I
b = 0.274103 + 0.402505I
−1.32179 − 0.54535I −6.25461 + 0.32765I
u = −1.49785 + 0.04527I
a = 0.737149 − 0.181176I
b = −1.256150 − 0.488763I
7.43791 + 2.40793I 0
u = −1.49785 − 0.04527I
a = 0.737149 + 0.181176I
b = −1.256150 + 0.488763I
7.43791 − 2.40793I 0
u = 1.50844 + 0.10984I
a = −0.366290 − 0.424061I
b = 2.14759 + 1.67044I
3.62477 + 0.37465I 0
u = 1.50844 − 0.10984I
a = −0.366290 + 0.424061I
b = 2.14759 − 1.67044I
3.62477 − 0.37465I 0
9
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 1.51764 + 0.07703I
a = 0.309031 + 0.420314I
b = 0.118516 − 0.411587I
4.86678 + 0.90172I 0
u = 1.51764 − 0.07703I
a = 0.309031 − 0.420314I
b = 0.118516 + 0.411587I
4.86678 − 0.90172I 0
u = −1.52317 + 0.12412I
a = −1.002440 + 0.955249I
b = 3.54266 − 2.61988I
3.00779 − 3.73916I 0
u = −1.52317 − 0.12412I
a = −1.002440 − 0.955249I
b = 3.54266 + 2.61988I
3.00779 + 3.73916I 0
u = −1.53604 + 0.13173I
a = −1.14572 + 1.42417I
b = 3.52474 − 3.40314I
3.30531 − 4.09518I 0
u = −1.53604 − 0.13173I
a = −1.14572 − 1.42417I
b = 3.52474 + 3.40314I
3.30531 + 4.09518I 0
u = −1.54259 + 0.07842I
a = 1.25091 − 0.75446I
b = −2.33633 + 2.11548I
7.91717 − 3.07456I 0
u = −1.54259 − 0.07842I
a = 1.25091 + 0.75446I
b = −2.33633 − 2.11548I
7.91717 + 3.07456I 0
u = 1.54528 + 0.14306I
a = −1.00062 − 1.36700I
b = 2.99004 + 2.73171I
4.62683 + 7.57614I 0
u = 1.54528 − 0.14306I
a = −1.00062 + 1.36700I
b = 2.99004 − 2.73171I
4.62683 − 7.57614I 0
10
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 1.55353 + 0.11383I
a = −0.62588 − 6.02561I
b = 0.3272 + 14.6513I
6.89620 + 3.23942I 0
u = 1.55353 − 0.11383I
a = −0.62588 + 6.02561I
b = 0.3272 − 14.6513I
6.89620 − 3.23942I 0
u = −1.55820 + 0.19721I
a = 1.143280 − 0.793518I
b = −3.16223 + 2.29837I
8.17592 − 5.31400I 0
u = −1.55820 − 0.19721I
a = 1.143280 + 0.793518I
b = −3.16223 − 2.29837I
8.17592 + 5.31400I 0
u = 1.57099 + 0.13986I
a = −0.404004 − 0.556034I
b = 0.836754 + 0.686893I
6.83837 + 6.14929I 0
u = 1.57099 − 0.13986I
a = −0.404004 + 0.556034I
b = 0.836754 − 0.686893I
6.83837 − 6.14929I 0
u = −1.57388 + 0.15206I
a = −0.843712 + 0.254247I
b = 1.77781 + 0.28661I
10.2522 − 10.0098I 0
u = −1.57388 − 0.15206I
a = −0.843712 − 0.254247I
b = 1.77781 − 0.28661I
10.2522 + 10.0098I 0
u = 1.58337 + 0.18572I
a = 1.01285 + 1.28924I
b = −3.02981 − 3.33050I
2.72408 + 10.83480I 0
u = 1.58337 − 0.18572I
a = 1.01285 − 1.28924I
b = −3.02981 + 3.33050I
2.72408 − 10.83480I 0
11
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −1.58408 + 0.17957I
a = 1.15293 − 1.49962I
b = −3.36712 + 3.72673I
6.4197 − 16.7505I 0
u = −1.58408 − 0.17957I
a = 1.15293 + 1.49962I
b = −3.36712 − 3.72673I
6.4197 + 16.7505I 0
u = 1.60360 + 0.01774I
a = 0.453485 + 0.946776I
b = −1.62552 − 1.50801I
13.83160 − 1.94519I 0
u = 1.60360 − 0.01774I
a = 0.453485 − 0.946776I
b = −1.62552 + 1.50801I
13.83160 + 1.94519I 0
u = −1.60301 + 0.12387I
a = 0.125633 − 0.183458I
b = −0.769235 + 0.803186I
9.21058 − 2.41580I 0
u = −1.60301 − 0.12387I
a = 0.125633 + 0.183458I
b = −0.769235 − 0.803186I
9.21058 + 2.41580I 0
u = −1.61558 + 0.05199I
a = 0.324769 − 0.551870I
b = −1.36648 + 1.04218I
9.23692 − 1.94054I 0
u = −1.61558 − 0.05199I
a = 0.324769 + 0.551870I
b = −1.36648 − 1.04218I
9.23692 + 1.94054I 0
u = 1.63808 + 0.02486I
a = −0.038093 + 0.657170I
b = −0.91055 − 1.15054I
12.0271 + 7.5660I 0
u = 1.63808 − 0.02486I
a = −0.038093 − 0.657170I
b = −0.91055 + 1.15054I
12.0271 − 7.5660I 0
12
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.323079
a = 1.36070
b = 0.686867
−1.16036 −10.6000
u = −0.117959 + 0.274951I
a = 0.758936 − 0.289574I
b = 1.170840 + 0.220885I
−0.892197 − 0.937335I −1.14664 − 2.00945I
u = −0.117959 − 0.274951I
a = 0.758936 + 0.289574I
b = 1.170840 − 0.220885I
−0.892197 + 0.937335I −1.14664 + 2.00945I
13
II. I
u
2
= h2b − 3, 2a + 1, u − 1i
(i) Arc colorings
a
8
=
0
1
a
12
=
1
0
a
1
=
1
−1
a
4
=
−0.5
1.5
a
2
=
0.5
0.5
a
5
=
−1
1
a
7
=
−1
1
a
11
=
0
1
a
6
=
−1
0
a
10
=
−1
2
a
3
=
0
0.5
a
9
=
0
1
(ii) Obstruction class = 1
(iii) Cusp Shapes = 2.25
14
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
9
, c
11
c
12
u − 1
c
2
, c
3
2(2u − 1)
c
4
, c
5
, c
6
c
7
, c
10
u + 1
c
8
u
15
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
4
, c
5
c
6
, c
7
, c
9
c
10
, c
11
, c
12
y −1
c
2
, c
3
4(4y −1)
c
8
y
16
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 1.00000
a = −0.500000
b = 1.50000
0 2.25000
17
III. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
(u − 1)(u
83
− 2u
82
+ ··· − 35u + 4)
c
2
4(2u − 1)(2u
83
− 13u
82
+ ··· + 3u + 1)
c
3
4(2u − 1)(2u
83
− 11u
82
+ ··· + 4480u + 352)
c
4
(u + 1)(u
83
− 2u
82
+ ··· − 35u + 4)
c
5
(u + 1)(u
83
+ 2u
82
+ ··· + 4u + 1)
c
6
, c
7
(u + 1)(u
83
+ 2u
82
+ ··· + 2u + 1)
c
8
u(u
83
+ u
82
+ ··· − 2u + 8)
c
9
(u − 1)(u
83
+ 2u
82
+ ··· + 4u + 1)
c
10
(u + 1)(u
83
+ 16u
82
+ ··· − 11522u − 2671)
c
11
, c
12
(u − 1)(u
83
+ 2u
82
+ ··· + 2u + 1)
18
IV. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
, c
4
(y −1)(y
83
− 52y
82
+ ··· − 479y −16)
c
2
16(4y −1)(4y
83
+ 523y
82
+ ··· − 117y −1)
c
3
16(4y −1)(4y
83
− 517y
82
+ ··· + 6829568y −123904)
c
5
, c
9
(y −1)(y
83
+ 48y
82
+ ··· + 12y −1)
c
6
, c
7
, c
11
c
12
(y −1)(y
83
− 92y
82
+ ··· + 12y −1)
c
8
y(y
83
+ 9y
82
+ ··· + 2164y −64)
c
10
(y −1)(y
83
+ 28y
82
+ ··· + 6.57251 × 10
7
y −7134241)
19
