12a
0212
(K12a
0212
)
A knot diagram
1
Linearized knot diagam
3 6 7 9 2 5 11 4 1 12 8 10
Solving Sequence
3,6
2 1 5 7
4,10
9 8 12 11
c
2
c
1
c
5
c
6
c
3
c
9
c
8
c
12
c
10
c
4
, c
7
, c
11
Ideals for irreducible components
2
of X
par
I
u
1
= h13u
74
− 40u
73
+ ··· + 2b + 9, 15u
74
− 62u
73
+ ··· + 4a + 33, u
75
− 4u
74
+ ··· + 2u − 1i
I
u
2
= hb, a
2
− au + 2u
2
+ 3u + 2, u
3
+ u
2
− 1i
I
u
3
= hb, a + 1, u
6
− u
5
+ 2u
2
− 2u + 1i
I
u
4
= hb, a + 1, u + 1i
I
u
5
= hb, a − 1, u
3
+ u
2
− 1i
* 5 irreducible components of dim
C
= 0, with total 91 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
=
h13u
74
−40u
73
+· · ·+2b+9, 15u
74
−62u
73
+· · ·+4a+33, u
75
−4u
74
+· · ·+2u−1i
(i) Arc colorings
a
3
=
1
0
a
6
=
0
u
a
2
=
1
−u
2
a
1
=
−u
2
+ 1
−u
2
a
5
=
u
−u
3
+ u
a
7
=
−u
3
u
5
− u
3
+ u
a
4
=
−u
8
+ u
6
− u
4
+ 1
u
10
− 2u
8
+ 3u
6
− 2u
4
+ u
2
a
10
=
−3.75000u
74
+ 15.5000u
73
+ ··· + 10.2500u − 8.25000
−
13
2
u
74
+ 20u
73
+ ··· +
17
2
u −
9
2
a
9
=
−8u
74
+
115
4
u
73
+ ··· +
57
4
u −
41
4
−
17
2
u
74
+
97
4
u
73
+ ··· +
43
4
u −
9
2
a
8
=
4u
74
−
67
4
u
73
+ ··· −
17
4
u +
17
4
9
2
u
74
−
65
4
u
73
+ ··· −
19
4
u +
9
2
a
12
=
−
1
4
u
72
+
3
4
u
71
+ ··· +
7
2
u +
1
4
u
19
− 3u
17
+ ··· − 4u
2
+ u
a
11
=
9
4
u
73
−
23
4
u
72
+ ··· +
21
2
u
2
−
35
4
u
−
7
2
u
74
+
51
4
u
73
+ ··· +
9
4
u −
7
2
(ii) Obstruction class = −1
(iii) Cusp Shapes =
31
4
u
74
−
3
2
u
73
+ ··· +
3
4
u −
37
2
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
6
u
75
+ 26u
74
+ ··· − 6u + 1
c
2
, c
5
u
75
+ 4u
74
+ ··· + 2u + 1
c
3
u
75
− 4u
74
+ ··· + 3428u + 673
c
4
, c
8
u
75
− 6u
74
+ ··· − 2048u + 512
c
7
, c
11
u
75
− 4u
74
+ ··· + 2u + 1
c
9
, c
10
, c
12
u
75
− 18u
74
+ ··· + 42u − 1
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
6
y
75
+ 50y
74
+ ··· + 338y −1
c
2
, c
5
y
75
− 26y
74
+ ··· − 6y −1
c
3
y
75
− 34y
74
+ ··· + 20450382y −452929
c
4
, c
8
y
75
− 42y
74
+ ··· + 2228224y −262144
c
7
, c
11
y
75
− 18y
74
+ ··· + 42y −1
c
9
, c
10
, c
12
y
75
+ 82y
74
+ ··· + 898y −1
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.701208 + 0.720685I
a = 0.271979 − 0.246067I
b = −0.579346 − 0.610917I
3.38308 − 0.01973I 0
u = 0.701208 − 0.720685I
a = 0.271979 + 0.246067I
b = −0.579346 + 0.610917I
3.38308 + 0.01973I 0
u = 0.627949 + 0.758720I
a = −0.575313 + 1.104250I
b = 0.241056 + 1.106360I
−0.61116 + 1.98602I 0
u = 0.627949 − 0.758720I
a = −0.575313 − 1.104250I
b = 0.241056 − 1.106360I
−0.61116 − 1.98602I 0
u = 0.797274 + 0.636830I
a = 1.023330 + 0.109881I
b = −0.383426 − 0.229792I
−1.24153 − 4.89896I 0
u = 0.797274 − 0.636830I
a = 1.023330 − 0.109881I
b = −0.383426 + 0.229792I
−1.24153 + 4.89896I 0
u = 0.663944 + 0.796185I
a = −0.228762 − 1.369140I
b = −0.75083 − 1.34544I
1.75797 + 5.85887I 0
u = 0.663944 − 0.796185I
a = −0.228762 + 1.369140I
b = −0.75083 + 1.34544I
1.75797 − 5.85887I 0
u = 0.809697 + 0.500286I
a = −1.101780 + 0.206259I
b = 0.331049 + 0.357019I
−1.80504 + 0.21281I 0
u = 0.809697 − 0.500286I
a = −1.101780 − 0.206259I
b = 0.331049 − 0.357019I
−1.80504 − 0.21281I 0
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.746204 + 0.738382I
a = −1.06503 + 1.47927I
b = −1.32562 + 0.86777I
3.84873 − 0.66860I 0
u = −0.746204 − 0.738382I
a = −1.06503 − 1.47927I
b = −1.32562 − 0.86777I
3.84873 + 0.66860I 0
u = −0.628281 + 0.711921I
a = −1.12592 + 3.33671I
b = −1.41795 + 1.94907I
−3.10213 − 3.84461I 0
u = −0.628281 − 0.711921I
a = −1.12592 − 3.33671I
b = −1.41795 − 1.94907I
−3.10213 + 3.84461I 0
u = 0.627365 + 0.846180I
a = −0.14858 + 2.83753I
b = 0.46848 + 2.31286I
−6.70348 + 3.72129I 0
u = 0.627365 − 0.846180I
a = −0.14858 − 2.83753I
b = 0.46848 − 2.31286I
−6.70348 − 3.72129I 0
u = −1.051230 + 0.097083I
a = −0.311756 − 0.810124I
b = 0.066769 + 1.046900I
−4.37588 + 5.64662I 0
u = −1.051230 − 0.097083I
a = −0.311756 + 0.810124I
b = 0.066769 − 1.046900I
−4.37588 − 5.64662I 0
u = −0.812700 + 0.676974I
a = −0.188335 − 1.356770I
b = 0.615066 − 1.037800I
2.12142 + 2.26372I 0
u = −0.812700 − 0.676974I
a = −0.188335 + 1.356770I
b = 0.615066 + 1.037800I
2.12142 − 2.26372I 0
6
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 1.060630 + 0.009927I
a = 0.004661 + 1.039530I
b = 0.20878 − 3.03992I
−8.40746 − 3.15444I 0
u = 1.060630 − 0.009927I
a = 0.004661 − 1.039530I
b = 0.20878 + 3.03992I
−8.40746 + 3.15444I 0
u = 0.638608 + 0.850784I
a = −0.21667 − 2.89559I
b = −0.71638 − 2.35011I
−6.21701 + 10.10530I 0
u = 0.638608 − 0.850784I
a = −0.21667 + 2.89559I
b = −0.71638 + 2.35011I
−6.21701 − 10.10530I 0
u = 0.932954 + 0.071441I
a = −0.193432 + 0.886433I
b = 0.625448 − 1.099660I
−1.44111 − 1.48666I −6.77628 + 4.80712I
u = 0.932954 − 0.071441I
a = −0.193432 − 0.886433I
b = 0.625448 + 1.099660I
−1.44111 + 1.48666I −6.77628 − 4.80712I
u = −1.071330 + 0.046708I
a = 0.314563 + 0.332337I
b = 0.600863 − 0.674517I
−6.34634 + 1.36308I 0
u = −1.071330 − 0.046708I
a = 0.314563 − 0.332337I
b = 0.600863 + 0.674517I
−6.34634 − 1.36308I 0
u = −0.619084 + 0.677506I
a = 0.66146 − 3.38346I
b = 1.12813 − 1.94943I
−3.32990 + 2.33530I −2.00000 − 3.24885I
u = −0.619084 − 0.677506I
a = 0.66146 + 3.38346I
b = 1.12813 + 1.94943I
−3.32990 − 2.33530I −2.00000 + 3.24885I
7
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.911078 + 0.665908I
a = −1.46979 − 0.72717I
b = −0.265473 − 1.359370I
1.81337 + 2.92907I 0
u = −0.911078 − 0.665908I
a = −1.46979 + 0.72717I
b = −0.265473 + 1.359370I
1.81337 − 2.92907I 0
u = −1.126690 + 0.126000I
a = 0.492982 − 0.635491I
b = −0.24597 + 2.58837I
−12.9589 + 9.4189I 0
u = −1.126690 − 0.126000I
a = 0.492982 + 0.635491I
b = −0.24597 − 2.58837I
−12.9589 − 9.4189I 0
u = −1.129400 + 0.113156I
a = −0.413730 + 0.513608I
b = 0.57600 − 2.46752I
−13.35070 + 2.93555I 0
u = −1.129400 − 0.113156I
a = −0.413730 − 0.513608I
b = 0.57600 + 2.46752I
−13.35070 − 2.93555I 0
u = −0.831632 + 0.781731I
a = −0.405448 + 0.090942I
b = −0.717939 + 0.023903I
4.49518 + 3.61543I 0
u = −0.831632 − 0.781731I
a = −0.405448 − 0.090942I
b = −0.717939 − 0.023903I
4.49518 − 3.61543I 0
u = 1.054410 + 0.511172I
a = −2.54504 − 0.47126I
b = −1.17837 + 1.55125I
−10.59020 + 2.33640I 0
u = 1.054410 − 0.511172I
a = −2.54504 + 0.47126I
b = −1.17837 − 1.55125I
−10.59020 − 2.33640I 0
8
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.996108 + 0.618806I
a = 0.657831 + 0.669598I
b = 0.536812 + 0.383150I
−2.90368 − 4.76352I 0
u = 0.996108 − 0.618806I
a = 0.657831 − 0.669598I
b = 0.536812 − 0.383150I
−2.90368 + 4.76352I 0
u = 1.056010 + 0.527223I
a = 2.46210 + 0.75720I
b = 1.41911 − 1.29282I
−10.79530 − 4.15159I 0
u = 1.056010 − 0.527223I
a = 2.46210 − 0.75720I
b = 1.41911 + 1.29282I
−10.79530 + 4.15159I 0
u = −0.959804 + 0.703274I
a = 2.06554 − 0.50300I
b = 1.26162 + 1.12681I
3.20109 + 6.17050I 0
u = −0.959804 − 0.703274I
a = 2.06554 + 0.50300I
b = 1.26162 − 1.12681I
3.20109 − 6.17050I 0
u = −0.915099 + 0.761150I
a = 0.276923 − 0.700562I
b = 0.598686 + 0.067274I
4.24134 + 2.19377I 0
u = −0.915099 − 0.761150I
a = 0.276923 + 0.700562I
b = 0.598686 − 0.067274I
4.24134 − 2.19377I 0
u = 0.292739 + 0.750663I
a = −1.32844 − 2.03101I
b = −0.57813 − 1.46945I
−8.54207 − 0.47640I −5.31082 + 0.38811I
u = 0.292739 − 0.750663I
a = −1.32844 + 2.03101I
b = −0.57813 + 1.46945I
−8.54207 + 0.47640I −5.31082 − 0.38811I
9
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.983291 + 0.679379I
a = 0.326271 + 0.217290I
b = 0.269460 − 0.782508I
2.52825 − 5.35908I 0
u = 0.983291 − 0.679379I
a = 0.326271 − 0.217290I
b = 0.269460 + 0.782508I
2.52825 + 5.35908I 0
u = −1.005430 + 0.652614I
a = −3.71899 − 0.62315I
b = −1.43602 − 2.72402I
−4.45485 + 2.85370I 0
u = −1.005430 − 0.652614I
a = −3.71899 + 0.62315I
b = −1.43602 + 2.72402I
−4.45485 − 2.85370I 0
u = 0.267962 + 0.749469I
a = 0.96458 + 2.24772I
b = 0.33863 + 1.65527I
−8.25339 − 6.87058I −4.66942 + 5.31459I
u = 0.267962 − 0.749469I
a = 0.96458 − 2.24772I
b = 0.33863 − 1.65527I
−8.25339 + 6.87058I −4.66942 − 5.31459I
u = −1.009510 + 0.664597I
a = 3.84862 + 0.23046I
b = 1.76093 + 2.58718I
−4.22333 + 9.15433I 0
u = −1.009510 − 0.664597I
a = 3.84862 − 0.23046I
b = 1.76093 − 2.58718I
−4.22333 − 9.15433I 0
u = −0.884174 + 0.827701I
a = 0.858746 − 0.332274I
b = −0.020477 − 0.186379I
−1.61016 + 6.14153I 0
u = −0.884174 − 0.827701I
a = 0.858746 + 0.332274I
b = −0.020477 + 0.186379I
−1.61016 − 6.14153I 0
10
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 1.020350 + 0.680346I
a = −1.026190 + 0.714206I
b = −0.02211 + 1.47609I
−1.77547 − 7.46274I 0
u = 1.020350 − 0.680346I
a = −1.026190 − 0.714206I
b = −0.02211 − 1.47609I
−1.77547 + 7.46274I 0
u = 1.018070 + 0.704584I
a = 1.78244 − 0.14154I
b = 0.63403 − 1.61362I
0.68795 − 11.52010I 0
u = 1.018070 − 0.704584I
a = 1.78244 + 0.14154I
b = 0.63403 + 1.61362I
0.68795 + 11.52010I 0
u = 1.050580 + 0.711144I
a = −2.84228 + 1.32579I
b = −0.58040 + 2.70950I
−7.99110 − 9.53376I 0
u = 1.050580 − 0.711144I
a = −2.84228 − 1.32579I
b = −0.58040 − 2.70950I
−7.99110 + 9.53376I 0
u = 1.048440 + 0.717583I
a = 3.10399 − 1.06144I
b = 0.84917 − 2.69538I
−7.4670 − 15.9552I 0
u = 1.048440 − 0.717583I
a = 3.10399 + 1.06144I
b = 0.84917 + 2.69538I
−7.4670 + 15.9552I 0
u = 0.649139
a = −0.546045
b = 0.341478
−0.884135 −11.8620
u = 0.233494 + 0.573241I
a = 0.058819 + 0.473224I
b = −0.477292 + 0.578592I
−0.29565 − 3.74527I −0.52170 + 7.33925I
11
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.233494 − 0.573241I
a = 0.058819 − 0.473224I
b = −0.477292 − 0.578592I
−0.29565 + 3.74527I −0.52170 − 7.33925I
u = −0.475208 + 0.051931I
a = −0.18074 − 3.75063I
b = 0.015921 − 0.686883I
−3.67022 + 2.91113I 3.44925 − 3.93604I
u = −0.475208 − 0.051931I
a = −0.18074 + 3.75063I
b = 0.015921 + 0.686883I
−3.67022 − 2.91113I 3.44925 + 3.93604I
u = −0.028799 + 0.274080I
a = 0.18442 − 1.93169I
b = −0.520994 − 0.325782I
1.326270 + 0.342139I 6.30252 − 0.67770I
u = −0.028799 − 0.274080I
a = 0.18442 + 1.93169I
b = −0.520994 + 0.325782I
1.326270 − 0.342139I 6.30252 + 0.67770I
12
II. I
u
2
= hb, a
2
− au + 2u
2
+ 3u + 2, u
3
+ u
2
− 1i
(i) Arc colorings
a
3
=
1
0
a
6
=
0
u
a
2
=
1
−u
2
a
1
=
−u
2
+ 1
−u
2
a
5
=
u
u
2
+ u − 1
a
7
=
u
2
− 1
u
2
a
4
=
u
u
2
+ u − 1
a
10
=
a
0
a
9
=
au
u
2
a + au − a
a
8
=
au
u
2
a + au − a
a
12
=
−u
2
a − 2u
2
+ a − 2u
−u
2
a
11
=
−u
2
a − au − u
2
+ a − u
−u
2
a − au + a
(ii) Obstruction class = 1
(iii) Cusp Shapes = −u
2
a − u
2
− 8u − 7
13
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
3
, c
12
(u
3
− u
2
+ 2u − 1)
2
c
2
, c
11
(u
3
+ u
2
− 1)
2
c
4
, c
8
u
6
c
5
, c
7
(u
3
− u
2
+ 1)
2
c
6
, c
9
, c
10
(u
3
+ u
2
+ 2u + 1)
2
14
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
3
, c
6
c
9
, c
10
, c
12
(y
3
+ 3y
2
+ 2y −1)
2
c
2
, c
5
, c
7
c
11
(y
3
− y
2
+ 2y −1)
2
c
4
, c
8
y
6
15
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.877439 + 0.744862I
a = −0.947279 + 0.320410I
b = 0
5.65624I −0.41065 − 5.95889I
u = −0.877439 + 0.744862I
a = 0.069840 + 0.424452I
b = 0
4.13758 + 2.82812I −0.76541 − 4.65175I
u = −0.877439 − 0.744862I
a = −0.947279 − 0.320410I
b = 0
− 5.65624I −0.41065 + 5.95889I
u = −0.877439 − 0.744862I
a = 0.069840 − 0.424452I
b = 0
4.13758 − 2.82812I −0.76541 + 4.65175I
u = 0.754878
a = 0.37744 + 2.29387I
b = 0
−4.13758 + 2.82812I −13.82394 − 1.30714I
u = 0.754878
a = 0.37744 − 2.29387I
b = 0
−4.13758 − 2.82812I −13.82394 + 1.30714I
16
III. I
u
3
= hb, a + 1, u
6
− u
5
+ 2u
2
− 2u + 1i
(i) Arc colorings
a
3
=
1
0
a
6
=
0
u
a
2
=
1
−u
2
a
1
=
−u
2
+ 1
−u
2
a
5
=
u
−u
3
+ u
a
7
=
−u
3
u
5
− u
3
+ u
a
4
=
u
4
− u
2
+ u + 1
u
4
− u
3
+ u
a
10
=
−1
0
a
9
=
−u
4
+ u
2
− 1
−u
4
a
8
=
u
−u
3
+ u
a
12
=
1
−u
2
a
11
=
−u
2
− 1
u
4
(ii) Obstruction class = −1
(iii) Cusp Shapes = −6
17
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
6
u
6
+ u
5
+ 4u
4
+ 2u
3
+ 4u
2
+ 1
c
2
, c
5
, c
7
c
11
u
6
+ u
5
+ 2u
2
+ 2u + 1
c
3
u
6
+ u
5
+ 4u
4
+ 2u
3
− 2u
2
+ 1
c
4
, c
8
(u + 1)
6
c
9
, c
10
, c
12
u
6
− u
5
+ 4u
4
− 2u
3
+ 4u
2
+ 1
18
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
6
, c
9
c
10
, c
12
y
6
+ 7y
5
+ 20y
4
+ 30y
3
+ 24y
2
+ 8y + 1
c
2
, c
5
, c
7
c
11
y
6
− y
5
+ 4y
4
− 2y
3
+ 4y
2
+ 1
c
3
y
6
+ 7y
5
+ 8y
4
− 18y
3
+ 12y
2
− 4y + 1
c
4
, c
8
(y −1)
6
19
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = 0.929638 + 0.614235I
a = −1.00000
b = 0
−1.64493 −6.00000
u = 0.929638 − 0.614235I
a = −1.00000
b = 0
−1.64493 −6.00000
u = −0.895432 + 0.823751I
a = −1.00000
b = 0
−1.64493 −6.00000
u = −0.895432 − 0.823751I
a = −1.00000
b = 0
−1.64493 −6.00000
u = 0.465794 + 0.571960I
a = −1.00000
b = 0
−1.64493 −6.00000
u = 0.465794 − 0.571960I
a = −1.00000
b = 0
−1.64493 −6.00000
20
IV. I
u
4
= hb, a + 1, u + 1i
(i) Arc colorings
a
3
=
1
0
a
6
=
0
−1
a
2
=
1
−1
a
1
=
0
−1
a
5
=
−1
0
a
7
=
1
−1
a
4
=
0
1
a
10
=
−1
0
a
9
=
−1
−1
a
8
=
−1
0
a
12
=
1
−1
a
11
=
−2
1
(ii) Obstruction class = −1
(iii) Cusp Shapes = −6
21
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
4
, c
6
c
8
u + 1
c
2
, c
3
, c
5
c
7
, c
9
, c
10
c
11
, c
12
u − 1
22
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
2
, c
3
c
4
, c
5
, c
6
c
7
, c
8
, c
9
c
10
, c
11
, c
12
y −1
23
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
4
√
−1(vol +
√
−1CS) Cusp shape
u = −1.00000
a = −1.00000
b = 0
−1.64493 −6.00000
24
V. I
u
5
= hb, a − 1, u
3
+ u
2
− 1i
(i) Arc colorings
a
3
=
1
0
a
6
=
0
u
a
2
=
1
−u
2
a
1
=
−u
2
+ 1
−u
2
a
5
=
u
u
2
+ u − 1
a
7
=
u
2
− 1
u
2
a
4
=
u
u
2
+ u − 1
a
10
=
1
0
a
9
=
u
u
2
+ u − 1
a
8
=
u
u
2
+ u − 1
a
12
=
1
−u
2
a
11
=
u
2
+ 1
−u
2
− u + 1
(ii) Obstruction class = 1
(iii) Cusp Shapes = 0
25
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
3
, c
12
u
3
− u
2
+ 2u − 1
c
2
, c
11
u
3
+ u
2
− 1
c
4
, c
8
u
3
c
5
, c
7
u
3
− u
2
+ 1
c
6
, c
9
, c
10
u
3
+ u
2
+ 2u + 1
26
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
3
, c
6
c
9
, c
10
, c
12
y
3
+ 3y
2
+ 2y −1
c
2
, c
5
, c
7
c
11
y
3
− y
2
+ 2y −1
c
4
, c
8
y
3
27
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
5
√
−1(vol +
√
−1CS) Cusp shape
u = −0.877439 + 0.744862I
a = 1.00000
b = 0
0 0
u = −0.877439 − 0.744862I
a = 1.00000
b = 0
0 0
u = 0.754878
a = 1.00000
b = 0
0 0
28
VI. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
(u + 1)(u
3
− u
2
+ 2u − 1)
3
(u
6
+ u
5
+ 4u
4
+ 2u
3
+ 4u
2
+ 1)
· (u
75
+ 26u
74
+ ··· − 6u + 1)
c
2
(u − 1)(u
3
+ u
2
− 1)
3
(u
6
+ u
5
+ ··· + 2u + 1)(u
75
+ 4u
74
+ ··· + 2u + 1)
c
3
(u − 1)(u
3
− u
2
+ 2u − 1)
3
(u
6
+ u
5
+ 4u
4
+ 2u
3
− 2u
2
+ 1)
· (u
75
− 4u
74
+ ··· + 3428u + 673)
c
4
, c
8
u
9
(u + 1)
7
(u
75
− 6u
74
+ ··· − 2048u + 512)
c
5
(u − 1)(u
3
− u
2
+ 1)
3
(u
6
+ u
5
+ ··· + 2u + 1)(u
75
+ 4u
74
+ ··· + 2u + 1)
c
6
(u + 1)(u
3
+ u
2
+ 2u + 1)
3
(u
6
+ u
5
+ 4u
4
+ 2u
3
+ 4u
2
+ 1)
· (u
75
+ 26u
74
+ ··· − 6u + 1)
c
7
(u − 1)(u
3
− u
2
+ 1)
3
(u
6
+ u
5
+ ··· + 2u + 1)(u
75
− 4u
74
+ ··· + 2u + 1)
c
9
, c
10
(u − 1)(u
3
+ u
2
+ 2u + 1)
3
(u
6
− u
5
+ 4u
4
− 2u
3
+ 4u
2
+ 1)
· (u
75
− 18u
74
+ ··· + 42u − 1)
c
11
(u − 1)(u
3
+ u
2
− 1)
3
(u
6
+ u
5
+ ··· + 2u + 1)(u
75
− 4u
74
+ ··· + 2u + 1)
c
12
(u − 1)(u
3
− u
2
+ 2u − 1)
3
(u
6
− u
5
+ 4u
4
− 2u
3
+ 4u
2
+ 1)
· (u
75
− 18u
74
+ ··· + 42u − 1)
29
VII. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
, c
6
(y −1)(y
3
+ 3y
2
+ 2y −1)
3
(y
6
+ 7y
5
+ ··· + 8y + 1)
· (y
75
+ 50y
74
+ ··· + 338y −1)
c
2
, c
5
(y −1)(y
3
− y
2
+ 2y −1)
3
(y
6
− y
5
+ 4y
4
− 2y
3
+ 4y
2
+ 1)
· (y
75
− 26y
74
+ ··· − 6y −1)
c
3
(y −1)(y
3
+ 3y
2
+ 2y −1)
3
(y
6
+ 7y
5
+ ··· − 4y + 1)
· (y
75
− 34y
74
+ ··· + 20450382y −452929)
c
4
, c
8
y
9
(y −1)
7
(y
75
− 42y
74
+ ··· + 2228224y −262144)
c
7
, c
11
(y −1)(y
3
− y
2
+ 2y −1)
3
(y
6
− y
5
+ 4y
4
− 2y
3
+ 4y
2
+ 1)
· (y
75
− 18y
74
+ ··· + 42y −1)
c
9
, c
10
, c
12
(y −1)(y
3
+ 3y
2
+ 2y −1)
3
(y
6
+ 7y
5
+ ··· + 8y + 1)
· (y
75
+ 82y
74
+ ··· + 898y −1)
30
