12n
0691
(K12n
0691
)
A knot diagram
1
Linearized knot diagam
4 5 8 2 12 10 3 11 5 8 6 9
Solving Sequence
3,7
8
4,10
11 6 12 5 2 1 9
c
7
c
3
c
10
c
6
c
11
c
5
c
2
c
1
c
9
c
4
, c
8
, c
12
Ideals for irreducible components
2
of X
par
I
u
1
= h16394625770u
16
+ 7361888468u
15
+ ··· + 176471185595b + 67083506624,
− 638545424984u
16
+ 494483967338u
15
+ ··· + 176471185595a + 990730965236,
u
17
− u
16
+ ··· − u + 1i
I
u
2
= hu
7
− 2u
5
+ 3u
3
+ b − 2u − 1, −2u
7
− 2u
6
+ 3u
5
+ 4u
4
− 4u
3
− 4u
2
+ a + 3u + 4,
u
8
+ u
7
− u
6
− 2u
5
+ u
4
+ 2u
3
− 2u − 1i
I
u
3
= h2.09794 × 10
14
u
15
− 1.54864 × 10
15
u
14
+ ··· + 1.00649 × 10
18
b − 1.27599 × 10
18
,
3.01917 × 10
14
u
15
− 2.04767 × 10
15
u
14
+ ··· + 2.01298 × 10
18
a − 2.50594 × 10
18
,
u
16
− u
15
+ ··· + 640u + 256i
I
v
1
= ha, 669v
7
+ 1791v
6
+ 1344v
5
− 4076v
4
− 11099v
3
+ 10779v
2
+ 887b + 981v −54,
v
8
+ 2v
7
− 8v
5
− 13v
4
+ 28v
3
− 7v
2
− 3v + 1i
* 4 irreducible components of dim
C
= 0, with total 49 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
= h1.64 × 10
10
u
16
+ 7.36 × 10
9
u
15
+ · · · + 1.76× 10
11
b + 6.71 ×10
10
, −6.39 ×
10
11
u
16
+4.94×10
11
u
15
+· · ·+1.76×10
11
a+9.91×10
11
, u
17
−u
16
+· · ·−u+1i
(i) Arc colorings
a
3
=
0
u
a
7
=
1
0
a
8
=
1
u
2
a
4
=
−u
−u
3
+ u
a
10
=
3.61841u
16
− 2.80207u
15
+ ··· − 2.45782u − 5.61412
−0.0929026u
16
− 0.0417172u
15
+ ··· − 1.35646u − 0.380139
a
11
=
3.73975u
16
− 3.05444u
15
+ ··· − 3.90343u − 6.05033
0.0499193u
16
− 0.188766u
15
+ ··· − 1.60883u − 0.249100
a
6
=
3.51660u
16
− 1.48871u
15
+ ··· + 10.1705u − 1.96079
−0.183505u
16
− 0.0479152u
15
+ ··· − 0.736610u − 1.19077
a
12
=
4.59450u
16
− 5.53078u
15
+ ··· − 7.72513u − 11.9429
−0.302029u
16
− 0.353052u
15
+ ··· − 4.64374u + 0.978839
a
5
=
0.436207u
16
− 0.314873u
15
+ ··· − 2.65787u − 1.88181
−0.318145u
16
+ 0.389552u
15
+ ··· + 0.690292u − 0.0974507
a
2
=
−0.249100u
16
+ 0.199181u
15
+ ··· + 1.65271u + 1.85793
−0.0482596u
16
− 0.0849909u
15
+ ··· + 1.20435u + 0.0738023
a
1
=
−0.118062u
16
− 0.0746790u
15
+ ··· + 1.96758u + 1.97926
−0.175071u
16
+ 0.0850715u
15
+ ··· + 0.615613u + 0.0952905
a
9
=
3.49708u
16
− 2.54969u
15
+ ··· − 1.01221u − 5.17792
−0.164310u
16
+ 0.0417260u
15
+ ··· − 0.940864u − 0.698283
(ii) Obstruction class = −1
(iii) Cusp Shapes
=
2048919230872
176471185595
u
16
−
1391303845096
176471185595
u
15
+ ··· −
3163149744064
176471185595
u −
6932356318654
176471185595
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
2
, c
4
c
8
, c
10
u
17
− 7u
16
+ ··· − 5u − 1
c
3
, c
7
, c
9
u
17
− u
16
+ ··· − u + 1
c
5
, c
11
u
17
− u
16
+ ··· + 3u − 1
c
6
u
17
+ u
16
+ ··· − 699u + 199
c
12
u
17
+ 3u
16
+ ··· − 263u − 83
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
2
, c
4
c
8
, c
10
y
17
− 13y
16
+ ··· + 21y −1
c
3
, c
7
, c
9
y
17
+ 15y
16
+ ··· + 13y −1
c
5
, c
11
y
17
+ 11y
16
+ ··· + 25y −1
c
6
y
17
+ 27y
16
+ ··· + 947097y −39601
c
12
y
17
+ 7y
16
+ ··· + 91413y −6889
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.764077 + 0.442209I
a = 0.346619 + 0.162821I
b = −0.958812 + 0.033588I
−4.55533 + 6.93072I −21.1582 − 11.9778I
u = −0.764077 − 0.442209I
a = 0.346619 − 0.162821I
b = −0.958812 − 0.033588I
−4.55533 − 6.93072I −21.1582 + 11.9778I
u = 0.791671
a = 0.322502
b = −1.02671
−8.70952 −30.7710
u = −0.753921 + 0.115715I
a = 1.18926 − 1.58502I
b = 1.125680 − 0.771688I
−0.77832 − 2.01331I −15.1488 + 1.3786I
u = −0.753921 − 0.115715I
a = 1.18926 + 1.58502I
b = 1.125680 + 0.771688I
−0.77832 + 2.01331I −15.1488 − 1.3786I
u = 0.502094 + 0.490826I
a = 1.152440 + 0.058194I
b = −0.008463 + 0.987921I
2.49540 − 2.02523I −6.20824 + 3.33819I
u = 0.502094 − 0.490826I
a = 1.152440 − 0.058194I
b = −0.008463 − 0.987921I
2.49540 + 2.02523I −6.20824 − 3.33819I
u = 0.291694 + 0.477697I
a = 7.34853 + 5.73057I
b = −1.56713 + 1.11619I
−2.45442 + 0.76114I −1.7282 + 15.9915I
u = 0.291694 − 0.477697I
a = 7.34853 − 5.73057I
b = −1.56713 − 1.11619I
−2.45442 − 0.76114I −1.7282 − 15.9915I
u = −0.439135
a = 0.949461
b = 0.384048
−0.644803 −15.2830
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.432752
a = −6.06938
b = −0.248275
−2.91990 −47.5300
u = 0.78485 + 1.87131I
a = 0.345543 − 0.823882I
b = 0.13775 + 2.40985I
11.20130 − 3.50827I −11.32341 + 1.79574I
u = 0.78485 − 1.87131I
a = 0.345543 + 0.823882I
b = 0.13775 − 2.40985I
11.20130 + 3.50827I −11.32341 − 1.79574I
u = −0.93651 + 1.91501I
a = 0.272274 + 0.835217I
b = 0.86840 − 2.32205I
6.80306 + 8.74093I −14.7558 − 4.0661I
u = −0.93651 − 1.91501I
a = 0.272274 − 0.835217I
b = 0.86840 + 2.32205I
6.80306 − 8.74093I −14.7558 + 4.0661I
u = 0.98322 + 2.02620I
a = 0.244045 − 0.883210I
b = 1.34803 + 2.71046I
10.6972 − 14.1953I −12.00000 + 6.60789I
u = 0.98322 − 2.02620I
a = 0.244045 + 0.883210I
b = 1.34803 − 2.71046I
10.6972 + 14.1953I −12.00000 − 6.60789I
6
II. I
u
2
= hu
7
− 2u
5
+ 3u
3
+ b − 2u − 1, −2u
7
− 2u
6
+ · · · + a + 4, u
8
+ u
7
−
u
6
− 2u
5
+ u
4
+ 2u
3
− 2u − 1i
(i) Arc colorings
a
3
=
0
u
a
7
=
1
0
a
8
=
1
u
2
a
4
=
−u
−u
3
+ u
a
10
=
2u
7
+ 2u
6
− 3u
5
− 4u
4
+ 4u
3
+ 4u
2
− 3u − 4
−u
7
+ 2u
5
− 3u
3
+ 2u + 1
a
11
=
2u
7
+ 2u
6
− 3u
5
− 4u
4
+ 4u
3
+ 4u
2
− 3u − 5
−u
7
+ 2u
5
− 3u
3
− u
2
+ 2u + 1
a
6
=
2u
7
+ 2u
6
− 4u
5
− 4u
4
+ 5u
3
+ 4u
2
− 4u − 1
−u
7
+ u
5
− u
3
+ 2u
2
− 1
a
12
=
2u
6
− 4u
4
+ 7u
2
− u − 5
−2u
7
− u
6
+ 4u
5
+ 3u
4
− 5u
3
− 4u
2
+ 3u + 2
a
5
=
u
4
− u
2
+ 1
−u
4
a
2
=
u
6
− u
4
+ 2u
2
− 1
−u
7
− u
6
+ 2u
5
+ u
4
− 2u
3
− 2u
2
+ 2u + 1
a
1
=
u
2
− 1
−u
2
a
9
=
2u
7
+ 2u
6
− 3u
5
− 4u
4
+ 4u
3
+ 4u
2
− 3u − 4
−u
7
+ 2u
5
− 3u
3
+ 2u + 1
(ii) Obstruction class = 1
(iii) Cusp Shapes = −u
7
− 4u
6
+ 2u
5
+ 5u
4
− 3u
3
− 5u
2
+ 5u − 10
7
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
2
u
8
+ u
7
− 3u
6
− 2u
5
+ 3u
4
+ 2u − 1
c
3
u
8
− u
7
− u
6
+ 2u
5
+ u
4
− 2u
3
+ 2u − 1
c
4
u
8
− u
7
− 3u
6
+ 2u
5
+ 3u
4
− 2u − 1
c
5
u
8
+ 3u
7
+ 7u
6
+ 10u
5
+ 11u
4
+ 10u
3
+ 6u
2
+ 4u + 1
c
6
u
8
− 2u
7
− u
6
+ 5u
5
+ 4u
4
− 17u
3
+ 17u
2
− 7u + 1
c
7
u
8
+ u
7
− u
6
− 2u
5
+ u
4
+ 2u
3
− 2u − 1
c
8
(u − 1)
8
c
9
u
8
c
10
(u + 1)
8
c
11
u
8
− 3u
7
+ 7u
6
− 10u
5
+ 11u
4
− 10u
3
+ 6u
2
− 4u + 1
c
12
u
8
+ 3u
7
+ 6u
6
+ 7u
5
+ 13u
4
+ 11u
3
+ 4u
2
+ 3u + 1
8
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
2
, c
4
y
8
− 7y
7
+ 19y
6
− 22y
5
+ 3y
4
+ 14y
3
− 6y
2
− 4y + 1
c
3
, c
7
y
8
− 3y
7
+ 7y
6
− 10y
5
+ 11y
4
− 10y
3
+ 6y
2
− 4y + 1
c
5
, c
11
y
8
+ 5y
7
+ 11y
6
+ 6y
5
− 17y
4
− 34y
3
− 22y
2
− 4y + 1
c
6
y
8
− 6y
7
+ 29y
6
− 67y
5
+ 126y
4
− 85y
3
+ 59y
2
− 15y + 1
c
8
, c
10
(y −1)
8
c
9
y
8
c
12
y
8
+ 3y
7
+ 20y
6
+ 49y
5
+ 47y
4
− 47y
3
− 24y
2
− y + 1
9
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.570868 + 0.730671I
a = 1.72219 − 2.56817I
b = −1.50065 − 0.90255I
−2.68559 − 1.13123I −18.1377 + 5.3065I
u = −0.570868 − 0.730671I
a = 1.72219 + 2.56817I
b = −1.50065 + 0.90255I
−2.68559 + 1.13123I −18.1377 − 5.3065I
u = 0.855237 + 0.665892I
a = −0.658590 − 0.551963I
b = 1.43900 − 0.90910I
0.51448 − 2.57849I −10.11893 + 3.45077I
u = 0.855237 − 0.665892I
a = −0.658590 + 0.551963I
b = 1.43900 + 0.90910I
0.51448 + 2.57849I −10.11893 − 3.45077I
u = 1.09818
a = −0.421763
b = 0.491355
−8.14766 −12.9880
u = −1.031810 + 0.655470I
a = −0.420504 − 0.057447I
b = 0.655281 + 0.532312I
−4.02461 + 6.44354I −10.82984 − 2.68172I
u = −1.031810 − 0.655470I
a = −0.420504 + 0.057447I
b = 0.655281 − 0.532312I
−4.02461 − 6.44354I −10.82984 + 2.68172I
u = −0.603304
a = −1.86442
b = 0.321397
−2.48997 −13.8390
10
III. I
u
3
=
h2.10×10
14
u
15
−1.55×10
15
u
14
+· · ·+1.01×10
18
b−1.28×10
18
, 3.02×10
14
u
15
−
2.05 × 10
15
u
14
+ · · · + 2.01 × 10
18
a − 2.51 × 10
18
, u
16
− u
15
+ · · · + 640u + 256i
(i) Arc colorings
a
3
=
0
u
a
7
=
1
0
a
8
=
1
u
2
a
4
=
−u
−u
3
+ u
a
10
=
−0.000149985u
15
+ 0.00101723u
14
+ ··· + 0.522231u + 1.24489
−0.000208441u
15
+ 0.00153866u
14
+ ··· + 0.527819u + 1.26776
a
11
=
0.000149985u
15
− 0.00101723u
14
+ ··· − 0.522231u − 0.244888
−0.000391498u
15
+ 0.00253027u
14
+ ··· + 1.56110u + 1.71179
a
6
=
0.0000210778u
15
− 0.00137312u
14
+ ··· − 1.23583u − 0.524902
0.000823010u
15
− 0.00190398u
14
+ ··· − 1.08393u − 1.43592
a
12
=
−0.000987334u
15
+ 0.000332252u
14
+ ··· − 1.64360u − 0.285638
−0.00263050u
15
+ 0.00407270u
14
+ ··· − 2.52850u + 0.754844
a
5
=
−0.000548337u
15
− 0.000148181u
14
+ ··· − 1.41913u − 0.208839
0.00209134u
15
− 0.00192142u
14
+ ··· + 1.92702u + 0.216705
a
2
=
−0.000318911u
15
+ 0.000923900u
14
+ ··· + 0.0782544u + 0.170443
0.0000474371u
15
+ 0.00190210u
14
+ ··· + 1.03533u − 0.116481
a
1
=
−0.00154300u
15
+ 0.00206961u
14
+ ··· − 0.507891u − 0.00786525
0.00175647u
15
+ 0.00275194u
14
+ ··· + 1.98501u + 0.0818943
a
9
=
−0.000675440u
15
+ 0.000547485u
14
+ ··· − 1.09374u + 0.615472
0.00211859u
15
− 0.000320222u
14
+ ··· + 3.48674u + 2.29159
(ii) Obstruction class = −1
(iii) Cusp Shapes =
4129940980039711
1006491371550221696
u
15
−
3800282985571637
1006491371550221696
u
14
+ ···+
45304359399533900
7863213840236107
u −
73541352487366340
7863213840236107
11
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
2
, c
4
c
8
, c
10
u
16
− 3u
15
+ ··· − 8u + 1
c
3
, c
7
, c
9
u
16
− u
15
+ ··· + 640u + 256
c
5
, c
11
(u
8
− u
7
+ 3u
6
− 2u
5
+ 3u
4
− 2u
3
− 1)
2
c
6
u
16
+ 3u
15
+ ··· + 2169u + 361
c
12
u
16
− 4u
15
+ ··· − 189u + 297
12
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
2
, c
4
c
8
, c
10
y
16
+ 9y
15
+ ··· + 4y + 1
c
3
, c
7
, c
9
y
16
+ 33y
15
+ ··· + 606208y + 65536
c
5
, c
11
(y
8
+ 5y
7
+ 11y
6
+ 10y
5
− y
4
− 10y
3
− 6y
2
+ 1)
2
c
6
y
16
+ 31y
15
+ ··· − 741503y + 130321
c
12
y
16
+ 32y
15
+ ··· + 78327y + 88209
13
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = −0.928106 + 0.575657I
a = 0.600905 + 0.372711I
b = 0.918546 + 0.300867I
−0.290648 −13.26997 + 0.I
u = −0.928106 − 0.575657I
a = 0.600905 − 0.372711I
b = 0.918546 − 0.300867I
−0.290648 −13.26997 + 0.I
u = −0.684023 + 0.882805I
a = 0.433643 − 0.063937I
b = −0.344993 − 0.631679I
−1.15366 − 1.27532I −10.53127 + 1.72199I
u = −0.684023 − 0.882805I
a = 0.433643 + 0.063937I
b = −0.344993 + 0.631679I
−1.15366 + 1.27532I −10.53127 − 1.72199I
u = 0.577755 + 0.986475I
a = 0.638361 − 0.648733I
b = 0.608076 − 0.155053I
2.70026 + 3.63283I −9.34305 − 4.59352I
u = 0.577755 − 0.986475I
a = 0.638361 + 0.648733I
b = 0.608076 + 0.155053I
2.70026 − 3.63283I −9.34305 + 4.59352I
u = −0.153757 + 0.400659I
a = 1.128490 + 0.166387I
b = 1.123000 + 0.170958I
−1.15366 − 1.27532I −10.53127 + 1.72199I
u = −0.153757 − 0.400659I
a = 1.128490 − 0.166387I
b = 1.123000 − 0.170958I
−1.15366 + 1.27532I −10.53127 − 1.72199I
u = 1.61868 + 0.98339I
a = 0.385316 − 0.391577I
b = 1.65420 − 0.20376I
2.70026 − 3.63283I −9.34305 + 4.59352I
u = 1.61868 − 0.98339I
a = 0.385316 + 0.391577I
b = 1.65420 + 0.20376I
2.70026 + 3.63283I −9.34305 − 4.59352I
14
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = 0.05666 + 2.24811I
a = 0.010165 + 0.766423I
b = −1.22626 − 2.33561I
12.42750 − 4.93524I −10.31351 + 3.19667I
u = 0.05666 − 2.24811I
a = 0.010165 − 0.766423I
b = −1.22626 + 2.33561I
12.42750 + 4.93524I −10.31351 − 3.19667I
u = 0.14941 + 2.37106I
a = 0.044468 − 0.705707I
b = −0.66007 + 2.57178I
8.53095 −13.35437 + 0.I
u = 0.14941 − 2.37106I
a = 0.044468 + 0.705707I
b = −0.66007 − 2.57178I
8.53095 −13.35437 + 0.I
u = −0.13661 + 2.63887I
a = 0.008651 + 0.652267I
b = −0.57250 − 3.23168I
12.42750 + 4.93524I −10.31351 − 3.19667I
u = −0.13661 − 2.63887I
a = 0.008651 − 0.652267I
b = −0.57250 + 3.23168I
12.42750 − 4.93524I −10.31351 + 3.19667I
15
IV. I
v
1
=
ha, 669v
7
+1791v
6
+· · ·+887b −54, v
8
+2v
7
−8v
5
−13v
4
+28v
3
−7v
2
−3v +1i
(i) Arc colorings
a
3
=
v
0
a
7
=
1
0
a
8
=
1
0
a
4
=
v
0
a
10
=
0
−0.754228v
7
− 2.01917v
6
+ ··· − 1.10598v + 0.0608794
a
11
=
0.754228v
7
+ 2.01917v
6
+ ··· + 1.10598v −0.0608794
−0.754228v
7
− 2.01917v
6
+ ··· − 1.10598v + 0.0608794
a
6
=
1
−1.32244v
7
− 3.19504v
6
+ ··· − 1.54904v + 1.44307
a
12
=
−0.872604v
7
− 1.55581v
6
+ ··· − 0.0732807v + 3.76550
3.44419v
7
+ 7.94701v
6
+ ··· + 1.00113v −9.59639
a
5
=
−0.510710v
7
− 1.51522v
6
+ ··· − 3.20180v + 0.754228
−v
7
− 2v
6
+ 8v
4
+ 13v
3
− 28v
2
+ 7v + 3
a
2
=
0.510710v
7
+ 1.51522v
6
+ ··· + 4.20180v −0.754228
v
7
+ 2v
6
− 8v
4
− 13v
3
+ 28v
2
− 7v −3
a
1
=
0.510710v
7
+ 1.51522v
6
+ ··· + 3.20180v −0.754228
v
7
+ 2v
6
− 8v
4
− 13v
3
+ 28v
2
− 7v −3
a
9
=
−1.32244v
7
− 3.19504v
6
+ ··· − 1.54904v + 2.44307
1.32244v
7
+ 3.19504v
6
+ ··· + 1.54904v −1.44307
(ii) Obstruction class = 1
(iii) Cusp Shapes
=
2247
887
v
7
+
4687
887
v
6
−
426
887
v
5
−
21184
887
v
4
−
35807
887
v
3
+
61378
887
v
2
+
5411
887
v −
17810
887
16
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
2
(u − 1)
8
c
3
, c
7
u
8
c
4
(u + 1)
8
c
5
u
8
− 3u
7
+ 7u
6
− 10u
5
+ 11u
4
− 10u
3
+ 6u
2
− 4u + 1
c
6
, c
8
u
8
+ u
7
− 3u
6
− 2u
5
+ 3u
4
+ 2u − 1
c
9
, c
12
u
8
+ u
7
− u
6
− 2u
5
+ u
4
+ 2u
3
− 2u − 1
c
10
u
8
− u
7
− 3u
6
+ 2u
5
+ 3u
4
− 2u − 1
c
11
u
8
+ 3u
7
+ 7u
6
+ 10u
5
+ 11u
4
+ 10u
3
+ 6u
2
+ 4u + 1
17
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
2
, c
4
(y −1)
8
c
3
, c
7
y
8
c
5
, c
11
y
8
+ 5y
7
+ 11y
6
+ 6y
5
− 17y
4
− 34y
3
− 22y
2
− 4y + 1
c
6
, c
8
, c
10
y
8
− 7y
7
+ 19y
6
− 22y
5
+ 3y
4
+ 14y
3
− 6y
2
− 4y + 1
c
9
, c
12
y
8
− 3y
7
+ 7y
6
− 10y
5
+ 11y
4
− 10y
3
+ 6y
2
− 4y + 1
18
(vi) Complex Volumes and Cusp Shapes
Solutions to I
v
1
√
−1(vol +
√
−1CS) Cusp shape
v = 1.230330 + 0.083902I
a = 0
b = 0.108090 − 0.747508I
0.51448 + 2.57849I −10.11893 − 3.45077I
v = 1.230330 − 0.083902I
a = 0
b = 0.108090 + 0.747508I
0.51448 − 2.57849I −10.11893 + 3.45077I
v = 0.370895 + 0.073482I
a = 0
b = −1.334530 − 0.318930I
−4.02461 − 6.44354I −10.82984 + 2.68172I
v = 0.370895 − 0.073482I
a = 0
b = −1.334530 + 0.318930I
−4.02461 + 6.44354I −10.82984 − 2.68172I
v = −0.337834
a = 0
b = −1.37100
−8.14766 −12.9880
v = −1.21928 + 2.03110I
a = 0
b = 1.180120 − 0.268597I
−2.68559 + 1.13123I −18.1377 − 5.3065I
v = −1.21928 − 2.03110I
a = 0
b = 1.180120 + 0.268597I
−2.68559 − 1.13123I −18.1377 + 5.3065I
v = −2.42604
a = 0
b = 0.463640
−2.48997 −13.8390
19
V. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
, c
2
, c
8
((u − 1)
8
)(u
8
+ u
7
+ ··· + 2u − 1)(u
16
− 3u
15
+ ··· − 8u + 1)
· (u
17
− 7u
16
+ ··· − 5u − 1)
c
3
u
8
(u
8
− u
7
+ ··· + 2u − 1)(u
16
− u
15
+ ··· + 640u + 256)
· (u
17
− u
16
+ ··· − u + 1)
c
4
, c
10
((u + 1)
8
)(u
8
− u
7
+ ··· − 2u − 1)(u
16
− 3u
15
+ ··· − 8u + 1)
· (u
17
− 7u
16
+ ··· − 5u − 1)
c
5
, c
11
(u
8
− 3u
7
+ 7u
6
− 10u
5
+ 11u
4
− 10u
3
+ 6u
2
− 4u + 1)
· (u
8
− u
7
+ 3u
6
− 2u
5
+ 3u
4
− 2u
3
− 1)
2
· (u
8
+ 3u
7
+ 7u
6
+ 10u
5
+ 11u
4
+ 10u
3
+ 6u
2
+ 4u + 1)
· (u
17
− u
16
+ ··· + 3u − 1)
c
6
(u
8
− 2u
7
− u
6
+ 5u
5
+ 4u
4
− 17u
3
+ 17u
2
− 7u + 1)
· (u
8
+ u
7
− 3u
6
− 2u
5
+ 3u
4
+ 2u − 1)(u
16
+ 3u
15
+ ··· + 2169u + 361)
· (u
17
+ u
16
+ ··· − 699u + 199)
c
7
, c
9
u
8
(u
8
+ u
7
+ ··· − 2u − 1)(u
16
− u
15
+ ··· + 640u + 256)
· (u
17
− u
16
+ ··· − u + 1)
c
12
(u
8
+ u
7
− u
6
− 2u
5
+ u
4
+ 2u
3
− 2u − 1)
· (u
8
+ 3u
7
+ 6u
6
+ 7u
5
+ 13u
4
+ 11u
3
+ 4u
2
+ 3u + 1)
· (u
16
− 4u
15
+ ··· − 189u + 297)(u
17
+ 3u
16
+ ··· − 263u − 83)
20
VI. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
, c
2
, c
4
c
8
, c
10
(y −1)
8
(y
8
− 7y
7
+ 19y
6
− 22y
5
+ 3y
4
+ 14y
3
− 6y
2
− 4y + 1)
· (y
16
+ 9y
15
+ ··· + 4y + 1)(y
17
− 13y
16
+ ··· + 21y −1)
c
3
, c
7
, c
9
y
8
(y
8
− 3y
7
+ 7y
6
− 10y
5
+ 11y
4
− 10y
3
+ 6y
2
− 4y + 1)
· (y
16
+ 33y
15
+ ··· + 606208y + 65536)(y
17
+ 15y
16
+ ··· + 13y −1)
c
5
, c
11
(y
8
+ 5y
7
+ 11y
6
+ 6y
5
− 17y
4
− 34y
3
− 22y
2
− 4y + 1)
2
· (y
8
+ 5y
7
+ 11y
6
+ 10y
5
− y
4
− 10y
3
− 6y
2
+ 1)
2
· (y
17
+ 11y
16
+ ··· + 25y −1)
c
6
(y
8
− 7y
7
+ 19y
6
− 22y
5
+ 3y
4
+ 14y
3
− 6y
2
− 4y + 1)
· (y
8
− 6y
7
+ 29y
6
− 67y
5
+ 126y
4
− 85y
3
+ 59y
2
− 15y + 1)
· (y
16
+ 31y
15
+ ··· − 741503y + 130321)
· (y
17
+ 27y
16
+ ··· + 947097y −39601)
c
12
(y
8
− 3y
7
+ 7y
6
− 10y
5
+ 11y
4
− 10y
3
+ 6y
2
− 4y + 1)
· (y
8
+ 3y
7
+ 20y
6
+ 49y
5
+ 47y
4
− 47y
3
− 24y
2
− y + 1)
· (y
16
+ 32y
15
+ ··· + 78327y + 88209)
· (y
17
+ 7y
16
+ ··· + 91413y −6889)
21
