12n
0719
(K12n
0719
)
A knot diagram
1
Linearized knot diagam
4 6 7 8 12 9 11 2 3 7 6 8
Solving Sequence
8,12 1,6
5 4 2 9 11 7 3 10
c
12
c
5
c
4
c
1
c
8
c
11
c
7
c
3
c
9
c
2
, c
6
, c
10
Ideals for irreducible components
2
of X
par
I
u
1
= h−9.27341 × 10
166
u
43
− 4.43348 × 10
165
u
42
+ ··· + 8.47031 × 10
167
b + 9.37901 × 10
167
,
− 2.43777 × 10
167
u
43
− 6.35520 × 10
166
u
42
+ ··· + 8.47031 × 10
167
a − 2.63451 × 10
168
,
u
44
+ 39u
42
+ ··· − 4u − 1i
I
u
2
= h479931u
10
− 2120739u
9
+ ··· + 70976b − 1189615,
− 238887u
10
+ 992743u
9
+ ··· + 35488a + 973491,
u
11
− 4u
10
+ 6u
9
− 24u
8
+ 41u
7
+ 18u
6
+ 16u
5
− 28u
4
− 73u
3
− 45u
2
− 11u − 1i
I
u
3
= h−7u
5
− 33u
4
− 82u
3
− 73u
2
+ 23b − 11u − 13, 51u
5
+ 247u
4
+ 673u
3
+ 798u
2
+ 23a + 504u + 236,
u
6
+ 5u
5
+ 14u
4
+ 18u
3
+ 13u
2
+ 7u + 1i
* 3 irreducible components of dim
C
= 0, with total 61 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−9.27 × 10
166
u
43
− 4.43 × 10
165
u
42
+ · · · + 8.47 × 10
167
b + 9.38 ×
10
167
, −2.44 × 10
167
u
43
− 6.36 × 10
166
u
42
+ · · · + 8.47 × 10
167
a − 2.63 ×
10
168
, u
44
+ 39u
42
+ · · · − 4u − 1i
(i) Arc colorings
a
8
=
0
u
a
12
=
1
0
a
1
=
1
u
2
a
6
=
0.287802u
43
+ 0.0750292u
42
+ ··· − 75.3078u + 3.11029
0.109481u
43
+ 0.00523414u
42
+ ··· − 7.77140u − 1.10728
a
5
=
0.397283u
43
+ 0.0802633u
42
+ ··· − 83.0792u + 2.00301
0.109481u
43
+ 0.00523414u
42
+ ··· − 7.77140u − 1.10728
a
4
=
0.397283u
43
+ 0.0802633u
42
+ ··· − 83.0792u + 2.00301
0.0983593u
43
+ 0.00483973u
42
+ ··· − 7.05306u − 1.02702
a
2
=
−0.470002u
43
− 0.00424396u
42
+ ··· + 29.0832u − 7.19779
−0.112085u
43
+ 0.000633314u
42
+ ··· + 12.6945u + 0.279509
a
9
=
0.102867u
43
+ 0.129659u
42
+ ··· − 63.4031u − 16.1083
−0.199965u
43
+ 0.0128457u
42
+ ··· + 5.55859u − 0.338500
a
11
=
0.333819u
43
+ 0.00512371u
42
+ ··· − 15.9017u + 9.48154
0.136183u
43
− 0.000879747u
42
+ ··· − 13.1815u − 0.283753
a
7
=
−0.476846u
43
− 0.199627u
42
+ ··· + 108.229u + 16.5533
0.192885u
43
− 0.0142872u
42
+ ··· − 0.0996084u + 0.694413
a
3
=
−1.09702u
43
− 0.168014u
42
+ ··· + 172.835u − 5.26974
−0.161947u
43
− 0.00324765u
42
+ ··· + 21.6795u + 2.19727
a
10
=
−1.65580u
43
− 0.222262u
42
+ ··· + 263.566u − 14.2425
−0.361239u
43
− 0.00429338u
42
+ ··· + 33.9954u + 3.61276
(ii) Obstruction class = −1
(iii) Cusp Shapes = −0.617620u
43
− 0.0398235u
42
+ ··· + 49.7144u − 0.605176
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
5
, c
11
u
44
− u
43
+ ··· − 22u − 1
c
2
u
44
− 2u
43
+ ··· + 544u + 64
c
3
u
44
+ 2u
43
+ ··· + 68u − 52
c
4
u
44
− 32u
42
+ ··· + 6459u + 461
c
6
u
44
− 5u
42
+ ··· − 11u + 1
c
7
, c
10
u
44
+ u
43
+ ··· − 108u − 11
c
8
u
44
+ u
43
+ ··· − 288u + 32
c
9
u
44
− u
43
+ ··· − 46u + 43
c
12
u
44
+ 39u
42
+ ··· + 4u − 1
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
5
, c
11
y
44
+ 59y
43
+ ··· + 50y + 1
c
2
y
44
− 26y
43
+ ··· − 246784y + 4096
c
3
y
44
+ 46y
43
+ ··· − 55168y + 2704
c
4
y
44
− 64y
43
+ ··· − 67584469y + 212521
c
6
y
44
− 10y
43
+ ··· − 41y + 1
c
7
, c
10
y
44
+ 7y
43
+ ··· + 1822y + 121
c
8
y
44
− 3y
43
+ ··· − 139264y + 1024
c
9
y
44
− 39y
43
+ ··· − 62660y + 1849
c
12
y
44
+ 78y
43
+ ··· + 108y + 1
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.653028 + 0.479211I
a = −0.78323 + 1.75591I
b = 0.0581394 − 0.0762256I
0.33032 + 4.70980I −11.3107 − 11.5969I
u = −0.653028 − 0.479211I
a = −0.78323 − 1.75591I
b = 0.0581394 + 0.0762256I
0.33032 − 4.70980I −11.3107 + 11.5969I
u = 0.027724 + 0.750161I
a = 0.567924 + 0.078651I
b = −0.974182 + 0.157306I
3.27845 − 3.12920I −2.75319 + 2.59759I
u = 0.027724 − 0.750161I
a = 0.567924 − 0.078651I
b = −0.974182 − 0.157306I
3.27845 + 3.12920I −2.75319 − 2.59759I
u = 0.670831 + 0.205742I
a = 0.836569 + 0.484990I
b = 0.185017 + 0.160225I
−1.208230 − 0.322851I −9.94677 + 2.27028I
u = 0.670831 − 0.205742I
a = 0.836569 − 0.484990I
b = 0.185017 − 0.160225I
−1.208230 + 0.322851I −9.94677 − 2.27028I
u = 1.31394
a = 0.393355
b = 0.433533
−2.58215 0
u = −1.31681
a = −0.520583
b = 0.478115
−6.41728 0
u = 0.021517 + 0.557538I
a = 1.282020 + 0.262721I
b = 0.233628 + 0.802395I
−0.05460 − 2.35319I −7.41013 + 4.71617I
u = 0.021517 − 0.557538I
a = 1.282020 − 0.262721I
b = 0.233628 − 0.802395I
−0.05460 + 2.35319I −7.41013 − 4.71617I
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.489487 + 0.154722I
a = 1.56149 − 0.49207I
b = 0.215149 + 0.758157I
1.25902 − 2.03144I −0.14682 + 4.37003I
u = −0.489487 − 0.154722I
a = 1.56149 + 0.49207I
b = 0.215149 − 0.758157I
1.25902 + 2.03144I −0.14682 − 4.37003I
u = 0.473973
a = 2.83673
b = −0.506626
−2.36937 1.94390
u = 0.460603
a = 1.26886
b = 0.519451
−1.16126 −8.98030
u = 0.135939 + 0.415909I
a = −2.10897 − 1.43331I
b = 0.300845 + 1.228730I
−2.36079 − 2.76760I −10.42789 + 3.67232I
u = 0.135939 − 0.415909I
a = −2.10897 + 1.43331I
b = 0.300845 − 1.228730I
−2.36079 + 2.76760I −10.42789 − 3.67232I
u = −0.93702 + 1.28948I
a = −0.002221 − 0.962499I
b = 0.328930 + 1.368230I
3.52831 − 3.02493I 0
u = −0.93702 − 1.28948I
a = −0.002221 + 0.962499I
b = 0.328930 − 1.368230I
3.52831 + 3.02493I 0
u = −1.59462 + 0.32915I
a = −0.203262 + 0.245637I
b = −0.113423 − 1.192920I
4.53063 + 4.34162I 0
u = −1.59462 − 0.32915I
a = −0.203262 − 0.245637I
b = −0.113423 + 1.192920I
4.53063 − 4.34162I 0
6
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.221192 + 0.259639I
a = 1.096330 − 0.751243I
b = 0.691688 + 0.860912I
−0.63985 − 2.51667I −0.25112 + 12.13395I
u = 0.221192 − 0.259639I
a = 1.096330 + 0.751243I
b = 0.691688 − 0.860912I
−0.63985 + 2.51667I −0.25112 − 12.13395I
u = 1.79427 + 0.24600I
a = −0.388449 + 0.834790I
b = 0.170782 − 1.110490I
3.71457 − 3.73003I 0
u = 1.79427 − 0.24600I
a = −0.388449 − 0.834790I
b = 0.170782 + 1.110490I
3.71457 + 3.73003I 0
u = −0.132537 + 0.054215I
a = 7.14008 + 4.56284I
b = −0.667537 − 0.943356I
6.59035 − 2.00605I −1.41219 + 2.45712I
u = −0.132537 − 0.054215I
a = 7.14008 − 4.56284I
b = −0.667537 + 0.943356I
6.59035 + 2.00605I −1.41219 − 2.45712I
u = 0.0147871 + 0.1034350I
a = 3.52739 − 9.95970I
b = −0.846924 − 0.960944I
5.56957 − 9.21803I −3.16193 + 6.85768I
u = 0.0147871 − 0.1034350I
a = 3.52739 + 9.95970I
b = −0.846924 + 0.960944I
5.56957 + 9.21803I −3.16193 − 6.85768I
u = 1.12598 + 1.82301I
a = 0.258801 − 0.517356I
b = −0.280939 + 1.357240I
2.17978 + 2.84039I 0
u = 1.12598 − 1.82301I
a = 0.258801 + 0.517356I
b = −0.280939 − 1.357240I
2.17978 − 2.84039I 0
7
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.02621 + 2.20554I
a = −0.367494 + 0.963515I
b = 0.01860 − 1.79839I
14.6659 − 2.9427I 0
u = −0.02621 − 2.20554I
a = −0.367494 − 0.963515I
b = 0.01860 + 1.79839I
14.6659 + 2.9427I 0
u = 0.19526 + 2.30945I
a = −0.025151 − 0.822816I
b = 0.15012 + 1.78556I
9.15531 − 5.87106I 0
u = 0.19526 − 2.30945I
a = −0.025151 + 0.822816I
b = 0.15012 − 1.78556I
9.15531 + 5.87106I 0
u = 0.07782 + 2.32588I
a = −0.276416 − 0.894062I
b = 0.00497 + 1.82063I
16.0678 − 3.9170I 0
u = 0.07782 − 2.32588I
a = −0.276416 + 0.894062I
b = 0.00497 − 1.82063I
16.0678 + 3.9170I 0
u = −0.38957 + 2.32401I
a = 0.028999 + 0.969270I
b = 0.02619 − 1.71994I
8.96812 + 2.93237I 0
u = −0.38957 − 2.32401I
a = 0.028999 − 0.969270I
b = 0.02619 + 1.71994I
8.96812 − 2.93237I 0
u = −0.12922 + 2.71476I
a = 0.127432 − 0.901567I
b = −0.27414 + 1.75440I
14.7550 + 13.7953I 0
u = −0.12922 − 2.71476I
a = 0.127432 + 0.901567I
b = −0.27414 − 1.75440I
14.7550 − 13.7953I 0
8
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.07164 + 2.78151I
a = 0.159925 + 0.862115I
b = −0.25526 − 1.71524I
15.5530 − 5.8620I 0
u = −0.07164 − 2.78151I
a = 0.159925 − 0.862115I
b = −0.25526 + 1.71524I
15.5530 + 5.8620I 0
u = −0.32784 + 2.77330I
a = 0.079049 + 0.854859I
b = 0.06611 − 1.66236I
9.77050 + 3.12424I 0
u = −0.32784 − 2.77330I
a = 0.079049 − 0.854859I
b = 0.06611 + 1.66236I
9.77050 − 3.12424I 0
9
II.
I
u
2
= h4.80 × 10
5
u
10
− 2.12 × 10
6
u
9
+ · · · + 7.10 × 10
4
b − 1.19 × 10
6
, −2.39 ×
10
5
u
10
+9.93×10
5
u
9
+· · ·+3.55×10
4
a+9.73×10
5
, u
11
−4u
10
+· · ·−11u−1i
(i) Arc colorings
a
8
=
0
u
a
12
=
1
0
a
1
=
1
u
2
a
6
=
6.73149u
10
− 27.9740u
9
+ ··· − 221.023u − 27.4316
−6.76188u
10
+ 29.8797u
9
+ ··· + 142.163u + 16.7608
a
5
=
−0.0303906u
10
+ 1.90562u
9
+ ··· − 78.8596u − 10.6707
−6.76188u
10
+ 29.8797u
9
+ ··· + 142.163u + 16.7608
a
4
=
−0.0303906u
10
+ 1.90562u
9
+ ··· − 78.8596u − 10.6707
−8.06267u
10
+ 35.7716u
9
+ ··· + 161.757u + 18.5449
a
2
=
−11.1264u
10
+ 48.7428u
9
+ ··· + 260.727u + 35.5197
−7.45591u
10
+ 33.4040u
9
+ ··· + 137.150u + 15.0996
a
9
=
−5.52166u
10
+ 23.6000u
9
+ ··· + 159.059u + 22.6573
1.66821u
10
− 7.26548u
9
+ ··· − 38.1666u − 4.78324
a
11
=
5.52166u
10
− 23.6000u
9
+ ··· − 159.059u − 22.6573
5.60475u
10
− 25.1429u
9
+ ··· − 101.667u − 10.8624
a
7
=
0.691854u
10
− 2.26038u
9
+ ··· − 49.0295u − 6.10828
−4.45455u
10
+ 19.7759u
9
+ ··· + 90.5815u + 10.4505
a
3
=
−0.722019u
10
+ 5.76214u
9
+ ··· − 106.881u − 20.0806
−9.39040u
10
+ 41.6118u
9
+ ··· + 192.292u + 23.0600
a
10
=
2.25640u
10
− 8.91251u
9
+ ··· − 104.377u − 18.8743
3.11448u
10
− 14.0435u
9
+ ··· − 53.7697u − 5.09808
(ii) Obstruction class = 1
(iii) Cusp Shapes =
337445
17744
u
10
−
1511195
17744
u
9
+
2742643
17744
u
8
−
9383585
17744
u
7
+
4567969
4436
u
6
−
1254329
8872
u
5
+
3112763
8872
u
4
−
6155547
8872
u
3
−
18822875
17744
u
2
−
366794
1109
u −
635379
17744
10
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
11
u
11
+ 7u
9
+ 18u
7
+ u
6
+ 22u
5
+ 5u
4
+ 14u
3
+ 6u
2
+ 4u + 1
c
2
u
11
− 3u
10
+ ··· − 47u + 101
c
3
u
11
− u
10
+ ··· + 22u + 4
c
4
u
11
− u
10
+ u
9
− 6u
8
+ 3u
7
+ 3u
6
+ 29u
5
+ 27u
4
+ 28u
3
− u
2
− 6u − 7
c
5
u
11
+ 7u
9
+ 18u
7
− u
6
+ 22u
5
− 5u
4
+ 14u
3
− 6u
2
+ 4u − 1
c
6
u
11
− 2u
10
+ 7u
8
− 7u
7
− 5u
6
+ 15u
5
− 7u
4
− 7u
3
+ 10u
2
− 5u + 1
c
7
u
11
+ 6u
10
+ ··· + 2u + 1
c
8
u
11
− 3u
9
− u
8
+ 3u
7
+ 2u
6
− 2u
5
+ u
3
− u
2
+ 1
c
9
u
11
− u
9
− u
8
+ 2u
6
+ 2u
5
− 3u
4
− u
3
+ 3u
2
− 1
c
10
u
11
− 6u
10
+ ··· + 2u − 1
c
12
u
11
− 4u
10
+ ··· − 11u − 1
11
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
5
, c
11
y
11
+ 14y
10
+ ··· + 4y − 1
c
2
y
11
− 5y
10
+ ··· − 1427y − 10201
c
3
y
11
+ 13y
10
+ ··· + 156y − 16
c
4
y
11
+ y
10
+ ··· + 22y − 49
c
6
y
11
− 4y
10
+ ··· + 5y − 1
c
7
, c
10
y
11
− 6y
10
+ ··· + 2y − 1
c
8
y
11
− 6y
10
+ ··· + 2y − 1
c
9
y
11
− 2y
10
+ ··· + 6y − 1
c
12
y
11
− 4y
10
+ ··· + 31y − 1
12
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.220751 + 1.034860I
a = 1.083470 − 0.902408I
b = −0.146555 + 1.398110I
−1.22111 + 1.62586I −4.59364 − 0.34038I
u = −0.220751 − 1.034860I
a = 1.083470 + 0.902408I
b = −0.146555 − 1.398110I
−1.22111 − 1.62586I −4.59364 + 0.34038I
u = 1.51215
a = 0.674582
b = −0.287899
−6.03089 0.409510
u = −0.460304 + 0.019735I
a = 0.349750 + 0.389318I
b = 0.585282 + 0.924323I
−0.87162 − 2.16835I −10.04732 − 2.60427I
u = −0.460304 − 0.019735I
a = 0.349750 − 0.389318I
b = 0.585282 − 0.924323I
−0.87162 + 2.16835I −10.04732 + 2.60427I
u = −0.224917 + 0.097237I
a = 4.05209 − 4.10027I
b = −0.209535 + 0.545606I
0.76129 − 4.28079I −1.91886 + 3.11496I
u = −0.224917 − 0.097237I
a = 4.05209 + 4.10027I
b = −0.209535 − 0.545606I
0.76129 + 4.28079I −1.91886 − 3.11496I
u = −0.55730 + 2.45122I
a = 0.097167 + 0.873801I
b = 0.02440 − 1.69392I
9.41812 + 3.72319I −2.84715 − 8.70383I
u = −0.55730 − 2.45122I
a = 0.097167 − 0.873801I
b = 0.02440 + 1.69392I
9.41812 − 3.72319I −2.84715 + 8.70383I
u = 2.70719 + 0.06892I
a = 0.080229 + 0.646110I
b = −0.109646 − 1.218970I
3.15344 − 5.47871I −5.29777 + 8.13210I
13
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 2.70719 − 0.06892I
a = 0.080229 − 0.646110I
b = −0.109646 + 1.218970I
3.15344 + 5.47871I −5.29777 − 8.13210I
14
III. I
u
3
= h−7u
5
− 33u
4
+ · · · + 23b − 13, 51u
5
+ 247u
4
+ · · · + 23a +
236, u
6
+ 5u
5
+ 14u
4
+ 18u
3
+ 13u
2
+ 7u + 1i
(i) Arc colorings
a
8
=
0
u
a
12
=
1
0
a
1
=
1
u
2
a
6
=
−2.21739u
5
− 10.7391u
4
+ ··· − 21.9130u − 10.2609
0.304348u
5
+ 1.43478u
4
+ ··· + 0.478261u + 0.565217
a
5
=
−1.91304u
5
− 9.30435u
4
+ ··· − 21.4348u − 9.69565
0.304348u
5
+ 1.43478u
4
+ ··· + 0.478261u + 0.565217
a
4
=
−1.91304u
5
− 9.30435u
4
+ ··· − 21.4348u − 9.69565
0.0869565u
5
+ 0.695652u
4
+ ··· + 0.565217u + 0.304348
a
2
=
−0.608696u
5
− 2.86957u
4
+ ··· − 8.95652u − 4.13043
−0.0869565u
5
+ 0.304348u
4
+ ··· + 3.43478u + 0.695652
a
9
=
−0.391304u
5
− 1.13043u
4
+ ··· + 3.95652u + 2.13043
−1.17391u
5
− 5.39130u
4
+ ··· − 9.13043u − 1.60870
a
11
=
u
5
+ 5u
4
+ 14u
3
+ 18u
2
+ 13u + 7
−0.391304u
5
− 2.13043u
4
+ ··· − 4.04348u − 0.869565
a
7
=
−u
5
− 5u
4
− 14u
3
− 18u
2
− 13u − 7
0.391304u
5
+ 2.13043u
4
+ ··· + 5.04348u + 0.869565
a
3
=
−0.608696u
5
− 2.86957u
4
+ ··· − 8.95652u − 4.13043
−0.0869565u
5
+ 0.304348u
4
+ ··· + 3.43478u + 0.695652
a
10
=
0
u
(ii) Obstruction class = 1
(iii) Cusp Shapes =
16
23
u
5
−
33
23
u
4
−
220
23
u
3
−
809
23
u
2
−
563
23
u −
542
23
15
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
11
(u
3
− u
2
+ 2u − 1)
2
c
2
u
6
c
3
(u
3
+ u
2
− 1)
2
c
4
u
6
+ 2u
5
− 2u
3
+ 2u
2
− 3u − 7
c
5
(u
3
+ u
2
+ 2u + 1)
2
c
6
u
6
− 3u
5
+ 2u
4
+ u
3
+ u
2
− 2u − 1
c
7
(u − 1)
6
c
8
, c
9
u
6
− 4u
4
− u
3
+ 4u
2
− 1
c
10
(u + 1)
6
c
12
u
6
+ 5u
5
+ 14u
4
+ 18u
3
+ 13u
2
+ 7u + 1
16
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
5
, c
11
(y
3
+ 3y
2
+ 2y − 1)
2
c
2
y
6
c
3
(y
3
− y
2
+ 2y − 1)
2
c
4
y
6
− 4y
5
+ 12y
4
− 6y
3
− 8y
2
− 37y + 49
c
6
y
6
− 5y
5
+ 12y
4
− 11y
3
+ y
2
− 6y + 1
c
7
, c
10
(y − 1)
6
c
8
, c
9
y
6
− 8y
5
+ 24y
4
− 35y
3
+ 24y
2
− 8y + 1
c
12
y
6
+ 3y
5
+ 42y
4
− 28y
3
− 55y
2
− 23y + 1
17
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = −0.211786 + 0.750504I
a = 0.999155 + 0.334189I
b = 0.215080 − 1.307140I
1.37919 + 2.82812I −3.91642 − 4.54590I
u = −0.211786 − 0.750504I
a = 0.999155 − 0.334189I
b = 0.215080 + 1.307140I
1.37919 − 2.82812I −3.91642 + 4.54590I
u = −1.23104
a = 0.329355
b = 0.569840
−2.75839 −34.1530
u = −0.199118
a = −7.05839
b = 0.569840
−2.75839 −20.0130
u = −1.57313 + 2.05765I
a = −0.134639 − 0.607788I
b = 0.215080 + 1.307140I
1.37919 − 2.82812I −11.50056 + 1.38392I
u = −1.57313 − 2.05765I
a = −0.134639 + 0.607788I
b = 0.215080 − 1.307140I
1.37919 + 2.82812I −11.50056 − 1.38392I
18
IV. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
, c
11
(u
3
− u
2
+ 2u − 1)
2
· (u
11
+ 7u
9
+ 18u
7
+ u
6
+ 22u
5
+ 5u
4
+ 14u
3
+ 6u
2
+ 4u + 1)
· (u
44
− u
43
+ ··· − 22u − 1)
c
2
u
6
(u
11
− 3u
10
+ ··· − 47u + 101)(u
44
− 2u
43
+ ··· + 544u + 64)
c
3
((u
3
+ u
2
− 1)
2
)(u
11
− u
10
+ ··· + 22u + 4)(u
44
+ 2u
43
+ ··· + 68u − 52)
c
4
(u
6
+ 2u
5
− 2u
3
+ 2u
2
− 3u − 7)
· (u
11
− u
10
+ u
9
− 6u
8
+ 3u
7
+ 3u
6
+ 29u
5
+ 27u
4
+ 28u
3
− u
2
− 6u − 7)
· (u
44
− 32u
42
+ ··· + 6459u + 461)
c
5
(u
3
+ u
2
+ 2u + 1)
2
· (u
11
+ 7u
9
+ 18u
7
− u
6
+ 22u
5
− 5u
4
+ 14u
3
− 6u
2
+ 4u − 1)
· (u
44
− u
43
+ ··· − 22u − 1)
c
6
(u
6
− 3u
5
+ 2u
4
+ u
3
+ u
2
− 2u − 1)
· (u
11
− 2u
10
+ 7u
8
− 7u
7
− 5u
6
+ 15u
5
− 7u
4
− 7u
3
+ 10u
2
− 5u + 1)
· (u
44
− 5u
42
+ ··· − 11u + 1)
c
7
((u − 1)
6
)(u
11
+ 6u
10
+ ··· + 2u + 1)(u
44
+ u
43
+ ··· − 108u − 11)
c
8
(u
6
− 4u
4
− u
3
+ 4u
2
− 1)(u
11
− 3u
9
+ ··· − u
2
+ 1)
· (u
44
+ u
43
+ ··· − 288u + 32)
c
9
(u
6
− 4u
4
− u
3
+ 4u
2
− 1)(u
11
− u
9
+ ··· + 3u
2
− 1)
· (u
44
− u
43
+ ··· − 46u + 43)
c
10
((u + 1)
6
)(u
11
− 6u
10
+ ··· + 2u − 1)(u
44
+ u
43
+ ··· − 108u − 11)
c
12
(u
6
+ 5u
5
+ ··· + 7u + 1)(u
11
− 4u
10
+ ··· − 11u − 1)
· (u
44
+ 39u
42
+ ··· + 4u − 1)
19
V. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
, c
5
, c
11
((y
3
+ 3y
2
+ 2y − 1)
2
)(y
11
+ 14y
10
+ ··· + 4y − 1)
· (y
44
+ 59y
43
+ ··· + 50y + 1)
c
2
y
6
(y
11
− 5y
10
+ ··· − 1427y − 10201)
· (y
44
− 26y
43
+ ··· − 246784y + 4096)
c
3
((y
3
− y
2
+ 2y − 1)
2
)(y
11
+ 13y
10
+ ··· + 156y − 16)
· (y
44
+ 46y
43
+ ··· − 55168y + 2704)
c
4
(y
6
− 4y
5
+ ··· − 37y + 49)(y
11
+ y
10
+ ··· + 22y − 49)
· (y
44
− 64y
43
+ ··· − 67584469y + 212521)
c
6
(y
6
− 5y
5
+ ··· − 6y + 1)(y
11
− 4y
10
+ ··· + 5y − 1)
· (y
44
− 10y
43
+ ··· − 41y + 1)
c
7
, c
10
((y − 1)
6
)(y
11
− 6y
10
+ ··· + 2y − 1)(y
44
+ 7y
43
+ ··· + 1822y + 121)
c
8
(y
6
− 8y
5
+ ··· − 8y + 1)(y
11
− 6y
10
+ ··· + 2y − 1)
· (y
44
− 3y
43
+ ··· − 139264y + 1024)
c
9
(y
6
− 8y
5
+ ··· − 8y + 1)(y
11
− 2y
10
+ ··· + 6y − 1)
· (y
44
− 39y
43
+ ··· − 62660y + 1849)
c
12
(y
6
+ 3y
5
+ ··· − 23y + 1)(y
11
− 4y
10
+ ··· + 31y − 1)
· (y
44
+ 78y
43
+ ··· + 108y + 1)
20
