12a
0749
(K12a
0749
)
A knot diagram
1
Linearized knot diagam
3 8 10 9 11 12 2 1 4 7 6 5
Solving Sequence
3,10 4,8
2 1 7 11 9 5 12 6
c
3
c
2
c
1
c
7
c
10
c
9
c
4
c
12
c
6
c
5
, c
8
, c
11
Ideals for irreducible components
2
of X
par
I
u
1
= h1.15464 × 10
129
u
82
− 2.12036 × 10
129
u
81
+ ··· + 1.05249 × 10
130
b − 2.56113 × 10
129
,
− 2.50662 × 10
130
u
82
+ 2.53263 × 10
130
u
81
+ ··· + 1.05249 × 10
130
a + 1.83078 × 10
131
,
u
83
− u
82
+ ··· − 16u + 1i
I
u
2
= ha
4
u − a
3
u − 4a
3
− 5a
2
u + 3a
2
+ 2au + b + 2a,
a
6
+ 6a
5
u − a
5
− 5a
4
u − 14a
4
− 16a
3
u + 8a
3
+ 4a
2
u + 10a
2
+ 4au + a + u, u
2
+ 1i
* 2 irreducible components of dim
C
= 0, with total 95 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
= h1.15 × 10
129
u
82
− 2.12 × 10
129
u
81
+ · · · + 1.05 × 10
130
b − 2.56 ×
10
129
, −2.51 × 10
130
u
82
+ 2.53 × 10
130
u
81
+ · · · + 1.05 × 10
130
a + 1.83 ×
10
131
, u
83
− u
82
+ · · · − 16u + 1i
(i) Arc colorings
a
3
=
1
0
a
10
=
0
u
a
4
=
1
−u
2
a
8
=
2.38162u
82
− 2.40633u
81
+ ··· + 211.444u − 17.3948
−0.109706u
82
+ 0.201462u
81
+ ··· − 12.5813u + 0.243341
a
2
=
2.02156u
82
− 1.83927u
81
+ ··· + 180.154u − 20.2709
−0.412232u
82
+ 0.394094u
81
+ ··· − 14.9721u + 0.905614
a
1
=
1.60933u
82
− 1.44517u
81
+ ··· + 165.182u − 19.3652
−0.412232u
82
+ 0.394094u
81
+ ··· − 14.9721u + 0.905614
a
7
=
0.793212u
82
− 0.884660u
81
+ ··· + 82.5878u + 3.62677
−0.0517555u
82
+ 0.217321u
81
+ ··· + 5.93966u − 1.53522
a
11
=
2.60524u
82
− 2.10688u
81
+ ··· + 230.248u − 16.5091
−0.204129u
82
+ 0.0772507u
81
+ ··· − 9.17332u − 0.257104
a
9
=
−u
u
3
+ u
a
5
=
u
2
+ 1
−u
4
− 2u
2
a
12
=
2.04028u
82
− 1.82475u
81
+ ··· + 181.225u − 20.1356
−0.453441u
82
+ 0.484379u
81
+ ··· − 15.0883u + 0.934102
a
6
=
3.21049u
82
− 3.23128u
81
+ ··· + 320.180u − 24.9601
0.0333591u
82
+ 0.0548937u
81
+ ··· − 18.6788u + 0.279037
(ii) Obstruction class = −1
(iii) Cusp Shapes = 0.292915u
82
− 0.00299820u
81
+ ··· − 0.231972u + 11.2199
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
83
+ 43u
82
+ ··· + 210u + 25
c
2
, c
7
u
83
+ u
82
+ ··· + 21u
2
− 5
c
3
, c
4
, c
9
u
83
+ u
82
+ ··· − 16u − 1
c
5
, c
6
, c
11
u
83
+ u
82
+ ··· − 10u − 1
c
8
u
83
+ 3u
82
+ ··· + 21790u − 3655
c
10
, c
12
u
83
− 3u
82
+ ··· + 4852u + 517
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
83
+ y
82
+ ··· + 4550y −625
c
2
, c
7
y
83
− 43y
82
+ ··· + 210y −25
c
3
, c
4
, c
9
y
83
+ 83y
82
+ ··· + 88y −1
c
5
, c
6
, c
11
y
83
− 69y
82
+ ··· + 44y −1
c
8
y
83
+ 41y
82
+ ··· + 762679210y −13359025
c
10
, c
12
y
83
+ 63y
82
+ ··· + 14835624y −267289
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.828176 + 0.557418I
a = 0.26185 − 1.69427I
b = −1.155510 + 0.462789I
−2.43646 + 2.58116I 0
u = 0.828176 − 0.557418I
a = 0.26185 + 1.69427I
b = −1.155510 − 0.462789I
−2.43646 − 2.58116I 0
u = −0.880668 + 0.478159I
a = −0.35382 − 1.77762I
b = 1.159560 + 0.498988I
−5.82520 − 6.87062I 0
u = −0.880668 − 0.478159I
a = −0.35382 + 1.77762I
b = 1.159560 − 0.498988I
−5.82520 + 6.87062I 0
u = 0.913983 + 0.416889I
a = 0.42302 − 1.83644I
b = −1.159300 + 0.525076I
−1.42155 + 11.14220I 0
u = 0.913983 − 0.416889I
a = 0.42302 + 1.83644I
b = −1.159300 − 0.525076I
−1.42155 − 11.14220I 0
u = 0.792210 + 0.634260I
a = −0.556105 − 0.320556I
b = 1.160410 + 0.345717I
−2.67272 + 2.90389I 0
u = 0.792210 − 0.634260I
a = −0.556105 + 0.320556I
b = 1.160410 − 0.345717I
−2.67272 − 2.90389I 0
u = −0.084056 + 1.041490I
a = 0.000756 − 1.089570I
b = 0.800253 + 0.494787I
−1.54448 − 2.06060I 0
u = −0.084056 − 1.041490I
a = 0.000756 + 1.089570I
b = 0.800253 − 0.494787I
−1.54448 + 2.06060I 0
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.754065 + 0.726286I
a = 0.524056 − 0.394935I
b = −1.155730 + 0.389682I
−6.60258 + 1.33321I 0
u = −0.754065 − 0.726286I
a = 0.524056 + 0.394935I
b = −1.155730 − 0.389682I
−6.60258 − 1.33321I 0
u = −0.378493 + 1.015650I
a = 0.165756 − 1.219100I
b = 0.970336 + 0.171230I
−0.90265 − 3.43454I 0
u = −0.378493 − 1.015650I
a = 0.165756 + 1.219100I
b = 0.970336 − 0.171230I
−0.90265 + 3.43454I 0
u = 0.720759 + 0.819102I
a = −0.503846 − 0.474505I
b = 1.152480 + 0.431957I
−2.66068 − 5.56325I 0
u = 0.720759 − 0.819102I
a = −0.503846 + 0.474505I
b = 1.152480 − 0.431957I
−2.66068 + 5.56325I 0
u = 0.255809 + 1.067630I
a = −0.155725 − 1.352350I
b = −0.795173 + 0.055550I
−3.85075 + 0.27233I 0
u = 0.255809 − 1.067630I
a = −0.155725 + 1.352350I
b = −0.795173 − 0.055550I
−3.85075 − 0.27233I 0
u = −0.204373 + 1.083280I
a = −0.01086 − 1.54055I
b = 0.683616 − 0.078181I
0.80097 + 3.01593I 0
u = −0.204373 − 1.083280I
a = −0.01086 + 1.54055I
b = 0.683616 + 0.078181I
0.80097 − 3.01593I 0
6
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.782147 + 0.421744I
a = 0.65089 − 1.35866I
b = −0.212910 + 0.749136I
1.33540 − 6.35685I 6.00000 + 5.58288I
u = −0.782147 − 0.421744I
a = 0.65089 + 1.35866I
b = −0.212910 − 0.749136I
1.33540 + 6.35685I 6.00000 − 5.58288I
u = −0.621544 + 0.602167I
a = 0.432472 − 1.247140I
b = −0.056022 + 0.667459I
0.62596 + 1.63981I 6.00000 + 0.I
u = −0.621544 − 0.602167I
a = 0.432472 + 1.247140I
b = −0.056022 − 0.667459I
0.62596 − 1.63981I 6.00000 + 0.I
u = 0.710823 + 0.487393I
a = −0.57026 − 1.29476I
b = 0.155215 + 0.709269I
−2.94696 + 2.31361I 3.43042 − 3.33064I
u = 0.710823 − 0.487393I
a = −0.57026 + 1.29476I
b = 0.155215 − 0.709269I
−2.94696 − 2.31361I 3.43042 + 3.33064I
u = −0.287984 + 1.116130I
a = 0.259716 − 0.868717I
b = −0.993147 + 0.583252I
1.74339 + 2.15963I 0
u = −0.287984 − 1.116130I
a = 0.259716 + 0.868717I
b = −0.993147 − 0.583252I
1.74339 − 2.15963I 0
u = 0.279482 + 1.139960I
a = 0.020964 − 1.246390I
b = −0.565039 + 0.608087I
2.98511 + 2.56133I 0
u = 0.279482 − 1.139960I
a = 0.020964 + 1.246390I
b = −0.565039 − 0.608087I
2.98511 − 2.56133I 0
7
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.176144 + 1.296320I
a = 0.611233 − 0.029819I
b = −0.248951 − 0.649703I
1.94452 + 3.81460I 0
u = 0.176144 − 1.296320I
a = 0.611233 + 0.029819I
b = −0.248951 + 0.649703I
1.94452 − 3.81460I 0
u = 0.649068 + 0.077548I
a = −1.19948 − 1.21441I
b = 0.465751 + 0.631327I
6.17107 + 0.86345I 14.3969 − 0.7384I
u = 0.649068 − 0.077548I
a = −1.19948 + 1.21441I
b = 0.465751 − 0.631327I
6.17107 − 0.86345I 14.3969 + 0.7384I
u = −0.610090 + 0.179998I
a = −0.14723 − 2.51696I
b = 1.030630 + 0.544608I
4.53717 − 5.47882I 11.04158 + 6.52708I
u = −0.610090 − 0.179998I
a = −0.14723 + 2.51696I
b = 1.030630 − 0.544608I
4.53717 + 5.47882I 11.04158 − 6.52708I
u = 0.477840 + 0.410372I
a = −0.36614 − 1.97770I
b = −1.023630 + 0.465904I
−0.86580 + 4.07227I 5.56865 − 9.23249I
u = 0.477840 − 0.410372I
a = −0.36614 + 1.97770I
b = −1.023630 − 0.465904I
−0.86580 − 4.07227I 5.56865 + 9.23249I
u = −0.067862 + 1.384400I
a = −0.196273 + 0.154900I
b = 0.083261 − 0.720975I
−3.97118 − 1.82061I 0
u = −0.067862 − 1.384400I
a = −0.196273 − 0.154900I
b = 0.083261 + 0.720975I
−3.97118 + 1.82061I 0
8
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.001191 + 1.386730I
a = 1.57028 + 0.32567I
b = 1.114940 − 0.388135I
−1.50250 − 0.63171I 0
u = 0.001191 − 1.386730I
a = 1.57028 − 0.32567I
b = 1.114940 + 0.388135I
−1.50250 + 0.63171I 0
u = 0.028734 + 1.407100I
a = −0.278899 − 1.167510I
b = 0.869859 + 0.754641I
−1.95541 + 1.26508I 0
u = 0.028734 − 1.407100I
a = −0.278899 + 1.167510I
b = 0.869859 − 0.754641I
−1.95541 − 1.26508I 0
u = 0.045458 + 1.407770I
a = 0.248108 − 1.206250I
b = −0.824993 + 0.766512I
−5.76997 + 2.85289I 0
u = 0.045458 − 1.407770I
a = 0.248108 + 1.206250I
b = −0.824993 − 0.766512I
−5.76997 − 2.85289I 0
u = −0.586055
a = 0.708998
b = −0.913508
1.91063 6.04100
u = −0.11242 + 1.41303I
a = −0.224623 − 1.243150I
b = 0.783760 + 0.782633I
−1.69873 − 6.98576I 0
u = −0.11242 − 1.41303I
a = −0.224623 + 1.243150I
b = 0.783760 − 0.782633I
−1.69873 + 6.98576I 0
u = −0.20015 + 1.40506I
a = −1.30473 + 1.45890I
b = −1.132050 − 0.511264I
−0.59248 − 8.34419I 0
9
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.20015 − 1.40506I
a = −1.30473 − 1.45890I
b = −1.132050 + 0.511264I
−0.59248 + 8.34419I 0
u = −0.04676 + 1.47166I
a = −1.166650 + 0.648335I
b = −1.170280 − 0.419278I
−7.49627 − 2.14085I 0
u = −0.04676 − 1.47166I
a = −1.166650 − 0.648335I
b = −1.170280 + 0.419278I
−7.49627 + 2.14085I 0
u = 0.13948 + 1.47980I
a = 1.09205 + 1.05374I
b = 1.173810 − 0.475339I
−7.09658 + 6.25907I 0
u = 0.13948 − 1.47980I
a = 1.09205 − 1.05374I
b = 1.173810 + 0.475339I
−7.09658 − 6.25907I 0
u = −0.29281 + 1.49818I
a = −0.618256 + 0.621581I
b = 0.275741 − 0.898548I
−4.88602 − 10.29530I 0
u = −0.29281 − 1.49818I
a = −0.618256 − 0.621581I
b = 0.275741 + 0.898548I
−4.88602 + 10.29530I 0
u = −0.444092 + 0.145528I
a = 0.978477 − 0.640428I
b = −0.408435 + 0.412605I
0.852672 − 0.232931I 12.03073 + 2.51602I
u = −0.444092 − 0.145528I
a = 0.978477 + 0.640428I
b = −0.408435 − 0.412605I
0.852672 + 0.232931I 12.03073 − 2.51602I
u = −0.20380 + 1.52010I
a = −0.431672 + 0.572184I
b = 0.193463 − 0.891300I
−6.27329 − 1.34438I 0
10
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.20380 − 1.52010I
a = −0.431672 − 0.572184I
b = 0.193463 + 0.891300I
−6.27329 + 1.34438I 0
u = 0.25612 + 1.51278I
a = 0.537026 + 0.607048I
b = −0.240717 − 0.899184I
−9.45956 + 5.87960I 0
u = 0.25612 − 1.51278I
a = 0.537026 − 0.607048I
b = −0.240717 + 0.899184I
−9.45956 − 5.87960I 0
u = 0.34667 + 1.51698I
a = 0.59504 + 1.62681I
b = 1.193840 − 0.587206I
−7.6640 + 15.7308I 0
u = 0.34667 − 1.51698I
a = 0.59504 − 1.62681I
b = 1.193840 + 0.587206I
−7.6640 − 15.7308I 0
u = 0.023429 + 0.440080I
a = 0.993538 − 0.407074I
b = 0.936093 + 0.425987I
−1.28387 − 1.68323I 3.77150 − 0.35257I
u = 0.023429 − 0.440080I
a = 0.993538 + 0.407074I
b = 0.936093 − 0.425987I
−1.28387 + 1.68323I 3.77150 + 0.35257I
u = −0.399913 + 0.171939I
a = 2.65180 + 1.24043I
b = −0.711891 − 0.566818I
3.50631 − 5.22844I 11.78714 + 6.73129I
u = −0.399913 − 0.171939I
a = 2.65180 − 1.24043I
b = −0.711891 + 0.566818I
3.50631 + 5.22844I 11.78714 − 6.73129I
u = −0.31801 + 1.53692I
a = −0.61042 + 1.52370I
b = −1.204090 − 0.572653I
−12.3754 − 11.2511I 0
11
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.31801 − 1.53692I
a = −0.61042 − 1.52370I
b = −1.204090 + 0.572653I
−12.3754 + 11.2511I 0
u = 0.27270 + 1.55039I
a = 0.66002 + 1.38973I
b = 1.211490 − 0.549265I
−9.35289 + 6.58290I 0
u = 0.27270 − 1.55039I
a = 0.66002 − 1.38973I
b = 1.211490 + 0.549265I
−9.35289 − 6.58290I 0
u = 0.23240 + 1.57121I
a = −0.456742 − 0.075976I
b = −1.267760 − 0.252241I
−9.99924 + 6.60552I 0
u = 0.23240 − 1.57121I
a = −0.456742 + 0.075976I
b = −1.267760 + 0.252241I
−9.99924 − 6.60552I 0
u = −0.18866 + 1.59001I
a = 0.490949 + 0.040309I
b = 1.270750 − 0.282944I
−14.4041 − 2.0103I 0
u = −0.18866 − 1.59001I
a = 0.490949 − 0.040309I
b = 1.270750 + 0.282944I
−14.4041 + 2.0103I 0
u = 0.13358 + 1.59807I
a = −0.552059 + 0.174631I
b = −1.266410 − 0.318036I
−10.97300 − 2.69837I 0
u = 0.13358 − 1.59807I
a = −0.552059 − 0.174631I
b = −1.266410 + 0.318036I
−10.97300 + 2.69837I 0
u = 0.301350 + 0.041219I
a = −2.81466 − 0.24393I
b = 0.742127 − 0.477090I
−0.90760 + 1.95680I 5.79568 − 4.89911I
12
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.301350 − 0.041219I
a = −2.81466 + 0.24393I
b = 0.742127 + 0.477090I
−0.90760 − 1.95680I 5.79568 + 4.89911I
u = 0.0855141 + 0.0580346I
a = 1.99596 + 11.61360I
b = −0.878605 − 0.525027I
3.03134 + 0.82073I 11.47240 + 0.34762I
u = 0.0855141 − 0.0580346I
a = 1.99596 − 11.61360I
b = −0.878605 + 0.525027I
3.03134 − 0.82073I 11.47240 − 0.34762I
13
II. I
u
2
=
ha
4
u−a
3
u−4a
3
−5a
2
u+3a
2
+2au+b+2a, 6a
5
u−5a
4
u+· · ·+10a
2
+a, u
2
+1i
(i) Arc colorings
a
3
=
1
0
a
10
=
0
u
a
4
=
1
1
a
8
=
a
−a
4
u + a
3
u + 4a
3
+ 5a
2
u − 3a
2
− 2au − 2a
a
2
=
a
5
u − a
4
u − 4a
4
− 5a
3
u + 3a
3
+ 2a
2
u + 2a
2
+ 1
−a
4
− 4a
3
u + a
3
+ 3a
2
u + 5a
2
+ 2au − 2a − 1
a
1
=
a
5
u − a
4
u − 5a
4
− 9a
3
u + 4a
3
+ 5a
2
u + 7a
2
+ 2au − 2a
−a
4
− 4a
3
u + a
3
+ 3a
2
u + 5a
2
+ 2au − 2a − 1
a
7
=
−a
5
− 5a
4
u + a
4
+ 4a
3
u + 9a
3
+ 7a
2
u − 5a
2
− 2au − 2a
−a
4
u + a
3
u + 4a
3
+ 5a
2
u − 3a
2
− 2au − 2a − u
a
11
=
−a
3
u + 3a
2
+ 3au + u − 1
a + 2u
a
9
=
−u
0
a
5
=
0
1
a
12
=
a
5
u − a
4
u − 5a
4
− 9a
3
u + 4a
3
+ 5a
2
u + 7a
2
+ 2au − 2a
a
5
u − a
4
u − 6a
4
− 13a
3
u + 5a
3
+ 8a
2
u + 12a
2
+ 4au − 4a − 1
a
6
=
−a
5
− 5a
4
u + a
4
+ 4a
3
u + 10a
3
+ 10a
2
u − 5a
2
− 2au − 5a − u
−a
4
u + 5a
3
+ 9a
2
u + au − 7a − 2u − 1
(ii) Obstruction class = 1
(iii) Cusp Shapes = −4a
5
− 20a
4
u + 8a
4
+ 32a
3
u + 32a
3
+ 16a
2
u − 40a
2
− 16au + 4
14
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
(u
2
− u + 1)
6
c
2
, c
7
, c
8
(u
4
− u
2
+ 1)
3
c
3
, c
4
, c
9
(u
2
+ 1)
6
c
5
, c
6
, c
11
(u
6
− 3u
4
+ 2u
2
+ 1)
2
c
10
, c
12
(u
6
+ u
4
+ 2u
2
+ 1)
2
15
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
(y
2
+ y + 1)
6
c
2
, c
7
, c
8
(y
2
− y + 1)
6
c
3
, c
4
, c
9
(y + 1)
12
c
5
, c
6
, c
11
(y
3
− 3y
2
+ 2y + 1)
4
c
10
, c
12
(y
3
+ y
2
+ 2y + 1)
4
16
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 1.000000I
a = 1.083790 − 0.612547I
b = 0.866025 + 0.500000I
1.37919 + 0.79824I 5.50976 + 0.48465I
u = 1.000000I
a = −0.377439 − 0.346257I
b = −0.866025 + 0.500000I
−2.75839 + 2.02988I −1.01951 − 3.46410I
u = 1.000000I
a = −0.37744 − 1.65374I
b = 0.866025 + 0.500000I
−2.75839 − 2.02988I −1.01951 + 3.46410I
u = 1.000000I
a = −0.206350 + 0.132315I
b = 0.866025 + 0.500000I
1.37919 − 4.85801I 5.50976 + 6.44355I
u = 1.000000I
a = 1.08379 − 1.38745I
b = −0.866025 + 0.500000I
1.37919 − 0.79824I 5.50976 − 0.48465I
u = 1.000000I
a = −0.20635 − 2.13232I
b = −0.866025 + 0.500000I
1.37919 + 4.85801I 5.50976 − 6.44355I
u = − 1.000000I
a = 1.083790 + 0.612547I
b = 0.866025 − 0.500000I
1.37919 − 0.79824I 5.50976 − 0.48465I
u = − 1.000000I
a = −0.377439 + 0.346257I
b = −0.866025 − 0.500000I
−2.75839 − 2.02988I −1.01951 + 3.46410I
u = − 1.000000I
a = −0.37744 + 1.65374I
b = 0.866025 − 0.500000I
−2.75839 + 2.02988I −1.01951 − 3.46410I
u = − 1.000000I
a = −0.206350 − 0.132315I
b = 0.866025 − 0.500000I
1.37919 + 4.85801I 5.50976 − 6.44355I
17
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = − 1.000000I
a = 1.08379 + 1.38745I
b = −0.866025 − 0.500000I
1.37919 + 0.79824I 5.50976 + 0.48465I
u = − 1.000000I
a = −0.20635 + 2.13232I
b = −0.866025 − 0.500000I
1.37919 − 4.85801I 5.50976 + 6.44355I
18
III. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
((u
2
− u + 1)
6
)(u
83
+ 43u
82
+ ··· + 210u + 25)
c
2
, c
7
((u
4
− u
2
+ 1)
3
)(u
83
+ u
82
+ ··· + 21u
2
− 5)
c
3
, c
4
, c
9
((u
2
+ 1)
6
)(u
83
+ u
82
+ ··· − 16u − 1)
c
5
, c
6
, c
11
((u
6
− 3u
4
+ 2u
2
+ 1)
2
)(u
83
+ u
82
+ ··· − 10u − 1)
c
8
((u
4
− u
2
+ 1)
3
)(u
83
+ 3u
82
+ ··· + 21790u − 3655)
c
10
, c
12
((u
6
+ u
4
+ 2u
2
+ 1)
2
)(u
83
− 3u
82
+ ··· + 4852u + 517)
19
IV. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
((y
2
+ y + 1)
6
)(y
83
+ y
82
+ ··· + 4550y −625)
c
2
, c
7
((y
2
− y + 1)
6
)(y
83
− 43y
82
+ ··· + 210y −25)
c
3
, c
4
, c
9
((y + 1)
12
)(y
83
+ 83y
82
+ ··· + 88y −1)
c
5
, c
6
, c
11
((y
3
− 3y
2
+ 2y + 1)
4
)(y
83
− 69y
82
+ ··· + 44y −1)
c
8
((y
2
− y + 1)
6
)(y
83
+ 41y
82
+ ··· + 7.62679 × 10
8
y −1.33590 × 10
7
)
c
10
, c
12
((y
3
+ y
2
+ 2y + 1)
4
)(y
83
+ 63y
82
+ ··· + 1.48356 × 10
7
y −267289)
20
