11n
125
(K11n
125
)
A knot diagram
1
Linearized knot diagam
7 1 9 10 11 2 10 6 4 8 9
Solving Sequence
6,8 9,11
1 5 10 4 3 7 2
c
8
c
11
c
5
c
10
c
4
c
3
c
7
c
1
c
2
, c
6
, c
9
Ideals for irreducible components
2
of X
par
I
u
1
= h3705u
16
− 598u
15
+ ··· + 73291b − 17911, 6307u
16
+ 8497u
15
+ ··· + 73291a − 25307,
u
17
− u
16
+ 8u
13
− 7u
12
+ u
11
+ u
10
+ 15u
9
− 14u
8
− u
7
+ 2u
6
+ 3u
5
+ u
4
− 2u
3
− 2u
2
+ 1i
I
u
2
= h−1.62758 × 10
19
u
23
− 2.19259 × 10
19
u
22
+ ··· + 4.09578 × 10
18
b + 4.17547 × 10
19
,
1.02456 × 10
19
u
23
+ 1.20636 × 10
19
u
22
+ ··· + 1.10459 × 10
18
a − 5.53806 × 10
19
, u
24
+ u
23
+ ··· − 12u + 1i
I
u
3
= h−u
8
− u
7
+ 3u
6
+ 3u
5
− u
4
− 2u
3
− 2u
2
+ b, u
8
+ u
7
− 4u
6
− 4u
5
+ 4u
4
+ 5u
3
+ u
2
+ a − 2u − 1,
u
10
+ u
9
− 4u
8
− 4u
7
+ 4u
6
+ 5u
5
+ u
4
− 2u
3
− 2u
2
+ 1i
* 3 irreducible components of dim
C
= 0, with total 51 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
= h3705u
16
− 598u
15
+ · · · + 73291b − 17911, 6307u
16
+ 8497u
15
+ · · · +
73291a − 25307, u
17
− u
16
+ · · · − 2u
2
+ 1i
(i) Arc colorings
a
6
=
0
u
a
8
=
1
0
a
9
=
1
u
2
a
11
=
−0.0860542u
16
− 0.115935u
15
+ ··· − 0.529669u + 0.345295
−0.0505519u
16
+ 0.00815926u
15
+ ··· + 0.136606u + 0.244382
a
1
=
−0.0233589u
16
− 0.00324733u
15
+ ··· − 0.479117u + 0.387687
0.198278u
16
− 0.0425291u
15
+ ··· + 0.0739108u + 0.0689989
a
5
=
0.654705u
16
− 0.740759u
15
+ ··· − 0.188099u − 0.529669
−0.201989u
16
+ 0.0887421u
15
+ ··· + 0.345295u + 0.0860542
a
10
=
−0.136606u
16
− 0.107776u
15
+ ··· − 0.393063u + 0.589677
−0.0505519u
16
+ 0.00815926u
15
+ ··· + 0.136606u + 0.244382
a
4
=
0.410323u
16
− 0.546929u
15
+ ··· + 0.401577u − 0.393063
−0.244382u
16
+ 0.193830u
15
+ ··· + 0.589677u + 0.136606
a
3
=
0.410323u
16
− 0.546929u
15
+ ··· + 1.40158u − 0.393063
−0.244382u
16
+ 0.193830u
15
+ ··· + 0.589677u + 0.136606
a
7
=
−0.968809u
16
+ 0.0160183u
15
+ ··· + 0.388588u + 1.25569
−0.882755u
16
+ 0.131953u
15
+ ··· + 0.918257u + 0.910398
a
2
=
1.43914u
16
− 0.141054u
15
+ ··· − 4.14755u − 2.06759
2.34525u
16
− 0.269760u
15
+ ··· − 4.58669u − 3.36568
a
2
=
1.43914u
16
− 0.141054u
15
+ ··· − 4.14755u − 2.06759
2.34525u
16
− 0.269760u
15
+ ··· − 4.58669u − 3.36568
(ii) Obstruction class = −1
(iii) Cusp Shapes =
112951
73291
u
16
+
78462
73291
u
15
+ ··· −
754923
73291
u −
768857
73291
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
6
u
17
+ 6u
16
+ ··· + 32u + 8
c
2
u
17
+ 6u
16
+ ··· + 32u − 64
c
3
, c
4
, c
8
c
9
u
17
− u
16
+ ··· − 2u
2
+ 1
c
5
u
17
+ u
16
+ ··· − 22u
2
+ 1
c
7
, c
10
u
17
− 7u
16
+ ··· − 80u + 16
c
11
u
17
+ 3u
16
+ ··· + 4u + 1
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
6
y
17
+ 6y
16
+ ··· + 32y −64
c
2
y
17
+ 10y
16
+ ··· + 33280y −4096
c
3
, c
4
, c
8
c
9
y
17
− y
16
+ ··· + 4y −1
c
5
y
17
− 13y
16
+ ··· + 44y −1
c
7
, c
10
y
17
− 7y
16
+ ··· − 128y −256
c
11
y
17
− 27y
16
+ ··· − 24y −1
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.724405 + 0.548318I
a = −0.75306 + 1.73640I
b = −1.210220 − 0.484731I
−4.29085 − 6.01779I −7.18678 + 9.97359I
u = 0.724405 − 0.548318I
a = −0.75306 − 1.73640I
b = −1.210220 + 0.484731I
−4.29085 + 6.01779I −7.18678 − 9.97359I
u = −0.126925 + 0.721173I
a = 0.84923 − 1.76296I
b = −0.778224 + 0.460398I
1.34232 + 1.94872I 2.56083 − 3.14210I
u = −0.126925 − 0.721173I
a = 0.84923 + 1.76296I
b = −0.778224 − 0.460398I
1.34232 − 1.94872I 2.56083 + 3.14210I
u = 0.725128 + 0.055021I
a = 0.394130 − 0.065047I
b = 1.46996 + 0.40764I
−4.56765 − 3.93288I −12.22005 + 0.69203I
u = 0.725128 − 0.055021I
a = 0.394130 + 0.065047I
b = 1.46996 − 0.40764I
−4.56765 + 3.93288I −12.22005 − 0.69203I
u = 0.746984 + 1.046150I
a = 0.322934 − 0.862372I
b = −0.619169 + 1.016980I
6.33629 − 0.97017I −0.559057 + 0.284542I
u = 0.746984 − 1.046150I
a = 0.322934 + 0.862372I
b = −0.619169 − 1.016980I
6.33629 + 0.97017I −0.559057 − 0.284542I
u = −0.909916 + 0.943922I
a = 0.275853 + 0.793772I
b = −0.609367 − 1.124050I
5.27663 + 7.20759I −2.52796 − 5.51575I
u = −0.909916 − 0.943922I
a = 0.275853 − 0.793772I
b = −0.609367 + 1.124050I
5.27663 − 7.20759I −2.52796 + 5.51575I
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.512854 + 0.417660I
a = 0.640794 + 0.460951I
b = 0.028408 − 0.739779I
−0.81159 + 1.48098I −4.11600 − 4.97481I
u = −0.512854 − 0.417660I
a = 0.640794 − 0.460951I
b = 0.028408 + 0.739779I
−0.81159 − 1.48098I −4.11600 + 4.97481I
u = −0.641391
a = 0.489889
b = 1.04128
−1.52652 −7.18720
u = −1.05004 + 1.03914I
a = −0.221763 − 1.275910I
b = −1.132230 + 0.760774I
4.69624 + 7.43319I −2.80359 − 4.35460I
u = −1.05004 − 1.03914I
a = −0.221763 + 1.275910I
b = −1.132230 − 0.760774I
4.69624 − 7.43319I −2.80359 + 4.35460I
u = 1.22392 + 0.97901I
a = −0.253054 + 1.194280I
b = −1.16979 − 0.80134I
3.4739 − 14.0835I −4.55379 + 8.21992I
u = 1.22392 − 0.97901I
a = −0.253054 − 1.194280I
b = −1.16979 + 0.80134I
3.4739 + 14.0835I −4.55379 − 8.21992I
6
II.
I
u
2
= h−1.63×10
19
u
23
−2.19×10
19
u
22
+· · ·+4.10×10
18
b+4.18×10
19
, 1.02×
10
19
u
23
+1.21×10
19
u
22
+· · ·+1.10×10
18
a−5.54×10
19
, u
24
+u
23
+· · ·−12u+1i
(i) Arc colorings
a
6
=
0
u
a
8
=
1
0
a
9
=
1
u
2
a
11
=
−9.27552u
23
− 10.9214u
22
+ ··· − 365.606u + 50.1368
3.97380u
23
+ 5.35329u
22
+ ··· + 100.403u − 10.1946
a
1
=
−4.82541u
23
− 4.75510u
22
+ ··· − 254.728u + 38.2964
4.74826u
23
+ 6.65968u
22
+ ··· + 116.547u − 11.9107
a
5
=
11.3054u
23
+ 12.3377u
22
+ ··· + 440.071u − 45.2263
6.36090u
23
+ 7.80155u
22
+ ··· + 204.414u − 23.9970
a
10
=
−5.30172u
23
− 5.56808u
22
+ ··· − 265.203u + 39.9422
3.97380u
23
+ 5.35329u
22
+ ··· + 100.403u − 10.1946
a
4
=
14.7955u
23
+ 17.5151u
22
+ ··· + 528.748u − 61.5891
−0.682634u
23
− 1.19757u
22
+ ··· − 4.09647u − 0.631997
a
3
=
13.8574u
23
+ 16.1229u
22
+ ··· + 506.811u − 59.5014
−0.936526u
23
− 1.63331u
22
+ ··· − 8.60722u − 0.177923
a
7
=
17.3035u
23
+ 22.0294u
22
+ ··· + 507.574u − 57.5598
−6.69344u
23
− 8.32845u
22
+ ··· − 216.360u + 25.9901
a
2
=
−7.27158u
23
− 9.66160u
22
+ ··· − 203.491u + 24.3547
2.43276u
23
+ 3.92231u
22
+ ··· + 34.3850u − 0.488514
a
2
=
−7.27158u
23
− 9.66160u
22
+ ··· − 203.491u + 24.3547
2.43276u
23
+ 3.92231u
22
+ ··· + 34.3850u − 0.488514
(ii) Obstruction class = −1
(iii) Cusp Shapes = −
5816969908025562256904
462822645525235397669
u
23
−
6619395108009854597496
462822645525235397669
u
22
+ ··· −
12260288530768323150784
27224861501484435157
u +
21994338350330534399466
462822645525235397669
7
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
6
(u
4
− u
3
+ u
2
+ 1)
6
c
2
(u
4
+ u
3
+ 3u
2
+ 2u + 1)
6
c
3
, c
4
, c
8
c
9
u
24
+ u
23
+ ··· − 12u + 1
c
5
u
24
+ 3u
23
+ ··· + 54u + 107
c
7
, c
10
(u
3
+ u
2
− 1)
8
c
11
u
24
+ 3u
23
+ ··· + 846u + 347
8
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
6
(y
4
+ y
3
+ 3y
2
+ 2y + 1)
6
c
2
(y
4
+ 5y
3
+ 7y
2
+ 2y + 1)
6
c
3
, c
4
, c
8
c
9
y
24
− 9y
23
+ ··· − 40y + 1
c
5
y
24
+ 3y
23
+ ··· + 23192y + 11449
c
7
, c
10
(y
3
− y
2
+ 2y −1)
8
c
11
y
24
− 9y
23
+ ··· + 602884y + 120409
9
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 1.008370 + 0.230741I
a = 0.324592 − 1.318030I
b = 0.877439 + 0.744862I
−2.12168 − 4.24323I −6.31698 + 7.88819I
u = 1.008370 − 0.230741I
a = 0.324592 + 1.318030I
b = 0.877439 − 0.744862I
−2.12168 + 4.24323I −6.31698 − 7.88819I
u = −0.430835 + 0.856235I
a = −0.577262 + 0.850887I
b = 0.877439 − 0.744862I
−2.12168 + 4.24323I −6.31698 − 7.88819I
u = −0.430835 − 0.856235I
a = −0.577262 − 0.850887I
b = 0.877439 + 0.744862I
−2.12168 − 4.24323I −6.31698 + 7.88819I
u = −0.324811 + 1.039220I
a = 1.271110 − 0.441707I
b = −0.754878
0.74248 + 3.16396I −9.19277 − 2.56480I
u = −0.324811 − 1.039220I
a = 1.271110 + 0.441707I
b = −0.754878
0.74248 − 3.16396I −9.19277 + 2.56480I
u = −1.003940 + 0.452899I
a = 0.012479 + 0.854104I
b = 0.877439 − 0.744862I
−2.12168 + 1.41302I −6.31698 + 1.92930I
u = −1.003940 − 0.452899I
a = 0.012479 − 0.854104I
b = 0.877439 + 0.744862I
−2.12168 − 1.41302I −6.31698 − 1.92930I
u = 1.382990 + 0.000366I
a = −0.948443 − 0.485387I
b = −0.754878
−6.25926 − 1.41510I −12.84625 + 4.90874I
u = 1.382990 − 0.000366I
a = −0.948443 + 0.485387I
b = −0.754878
−6.25926 + 1.41510I −12.84625 − 4.90874I
10
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −1.043140 + 0.911052I
a = 0.738284 + 1.097470I
b = 0.877439 − 0.744862I
4.88007 − 0.33584I −2.66351 − 0.41465I
u = −1.043140 − 0.911052I
a = 0.738284 − 1.097470I
b = 0.877439 + 0.744862I
4.88007 + 0.33584I −2.66351 + 0.41465I
u = 1.19721 + 0.83587I
a = 0.694157 − 1.132290I
b = 0.877439 + 0.744862I
4.88007 − 5.99209I −2.66351 + 5.54425I
u = 1.19721 − 0.83587I
a = 0.694157 + 1.132290I
b = 0.877439 − 0.744862I
4.88007 + 5.99209I −2.66351 − 5.54425I
u = −1.00875 + 1.10787I
a = −0.390615 − 0.422077I
b = 0.877439 + 0.744862I
4.88007 + 0.33584I −2.66351 + 0.41465I
u = −1.00875 − 1.10787I
a = −0.390615 + 0.422077I
b = 0.877439 − 0.744862I
4.88007 − 0.33584I −2.66351 − 0.41465I
u = 0.80956 + 1.30687I
a = −0.428288 + 0.453956I
b = 0.877439 − 0.744862I
4.88007 + 5.99209I −2.66351 − 5.54425I
u = 0.80956 − 1.30687I
a = −0.428288 − 0.453956I
b = 0.877439 + 0.744862I
4.88007 − 5.99209I −2.66351 + 5.54425I
u = −1.60815 + 0.28919I
a = −0.181824 − 0.347739I
b = −0.754878
−6.25926 + 1.41510I −12.84625 − 4.90874I
u = −1.60815 − 0.28919I
a = −0.181824 + 0.347739I
b = −0.754878
−6.25926 − 1.41510I −12.84625 + 4.90874I
11
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.265048 + 0.154544I
a = −4.33744 − 5.56259I
b = −0.754878
0.74248 − 3.16396I −9.19277 + 2.56480I
u = 0.265048 − 0.154544I
a = −4.33744 + 5.56259I
b = −0.754878
0.74248 + 3.16396I −9.19277 − 2.56480I
u = 0.256438 + 0.045429I
a = −0.67675 − 3.40086I
b = 0.877439 + 0.744862I
−2.12168 − 1.41302I −6.31698 − 1.92930I
u = 0.256438 − 0.045429I
a = −0.67675 + 3.40086I
b = 0.877439 − 0.744862I
−2.12168 + 1.41302I −6.31698 + 1.92930I
12
III. I
u
3
= h−u
8
− u
7
+ 3u
6
+ 3u
5
− u
4
− 2u
3
− 2u
2
+ b, u
8
+ u
7
+ · · · + a −
1, u
10
+ u
9
+ · · · − 2u
2
+ 1i
(i) Arc colorings
a
6
=
0
u
a
8
=
1
0
a
9
=
1
u
2
a
11
=
−u
8
− u
7
+ 4u
6
+ 4u
5
− 4u
4
− 5u
3
− u
2
+ 2u + 1
u
8
+ u
7
− 3u
6
− 3u
5
+ u
4
+ 2u
3
+ 2u
2
a
1
=
u
6
+ u
5
− 3u
4
− 3u
3
+ 2u
2
+ 2u
2u
8
+ 2u
7
− 6u
6
− 6u
5
+ 3u
4
+ 4u
3
+ 3u
2
− 1
a
5
=
u
7
+ u
6
− 4u
5
− 4u
4
+ 4u
3
+ 5u
2
− 2
u
9
+ u
8
− 4u
7
− 4u
6
+ 4u
5
+ 5u
4
+ u
3
− 2u
2
− u
a
10
=
u
6
+ u
5
− 3u
4
− 3u
3
+ u
2
+ 2u + 1
u
8
+ u
7
− 3u
6
− 3u
5
+ u
4
+ 2u
3
+ 2u
2
a
4
=
−u
5
− u
4
+ 3u
3
+ 3u
2
− u − 2
−u
7
− u
6
+ 3u
5
+ 3u
4
− u
3
− 2u
2
− u
a
3
=
−u
5
− u
4
+ 3u
3
+ 3u
2
− 2u − 2
−u
7
− u
6
+ 3u
5
+ 3u
4
− 2u
3
− 2u
2
− u
a
7
=
u
4
+ u
3
− 2u
2
− 2u
−u
8
− u
7
+ 4u
6
+ 4u
5
− 3u
4
− 4u
3
− 3u
2
+ 1
a
2
=
u
9
+ 2u
8
− 3u
7
− 7u
6
+ u
5
+ 6u
4
+ 3u
3
+ u
2
− u − 1
u
9
+ 3u
8
− 2u
7
− 10u
6
− 2u
5
+ 8u
4
+ 6u
3
+ 2u
2
− 3u − 2
a
2
=
u
9
+ 2u
8
− 3u
7
− 7u
6
+ u
5
+ 6u
4
+ 3u
3
+ u
2
− u − 1
u
9
+ 3u
8
− 2u
7
− 10u
6
− 2u
5
+ 8u
4
+ 6u
3
+ 2u
2
− 3u − 2
(ii) Obstruction class = 1
(iii) Cusp Shapes = −u
9
+ 4u
8
+ 10u
7
−18u
6
−30u
5
+ 17u
4
+ 30u
3
+ 10u
2
−8u − 15
13
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
10
+ u
9
+ 3u
8
+ 2u
7
+ 5u
6
+ 2u
5
+ 5u
4
+ 3u
2
+ 1
c
2
u
10
+ 5u
9
+ ··· + 6u + 1
c
3
, c
4
, c
8
u
10
+ u
9
− 4u
8
− 4u
7
+ 4u
6
+ 5u
5
+ u
4
− 2u
3
− 2u
2
+ 1
c
5
u
10
+ u
9
+ 4u
8
+ 5u
7
+ 2u
6
− u
3
− 2u
2
+ 1
c
6
u
10
− u
9
+ 3u
8
− 2u
7
+ 5u
6
− 2u
5
+ 5u
4
+ 3u
2
+ 1
c
7
u
10
− 2u
9
− u
8
+ 6u
7
− 2u
6
− 7u
5
+ 6u
4
+ 4u
3
− 4u
2
− u + 1
c
9
u
10
− u
9
− 4u
8
+ 4u
7
+ 4u
6
− 5u
5
+ u
4
+ 2u
3
− 2u
2
+ 1
c
10
u
10
+ 2u
9
− u
8
− 6u
7
− 2u
6
+ 7u
5
+ 6u
4
− 4u
3
− 4u
2
+ u + 1
c
11
u
10
+ u
9
+ 3u
8
+ u
6
− 2u
5
+ 3u
4
+ u
3
+ 2u
2
+ 1
14
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
6
y
10
+ 5y
9
+ ··· + 6y + 1
c
2
y
10
+ 5y
9
+ ··· + 2y + 1
c
3
, c
4
, c
8
c
9
y
10
− 9y
9
+ 32y
8
− 56y
7
+ 48y
6
− 15y
5
− 3y
4
+ 6y
2
− 4y + 1
c
5
y
10
+ 7y
9
+ 10y
8
− 9y
7
+ 2y
6
− 4y
5
+ 3y
3
+ 4y
2
− 4y + 1
c
7
, c
10
y
10
− 6y
9
+ ··· − 9y + 1
c
11
y
10
+ 5y
9
+ ··· + 4y + 1
15
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = −0.782055 + 0.380490I
a = −0.184015 + 1.040230I
b = 0.835101 − 0.932160I
−2.47371 + 2.31326I −10.56078 − 6.69278I
u = −0.782055 − 0.380490I
a = −0.184015 − 1.040230I
b = 0.835101 + 0.932160I
−2.47371 − 2.31326I −10.56078 + 6.69278I
u = −0.231765 + 0.745305I
a = −2.35204 + 0.93089I
b = 0.632416 − 0.145483I
1.41924 + 3.41496I 4.16112 − 7.56429I
u = −0.231765 − 0.745305I
a = −2.35204 − 0.93089I
b = 0.632416 + 0.145483I
1.41924 − 3.41496I 4.16112 + 7.56429I
u = 0.669161 + 0.228612I
a = 0.581803 − 1.223630I
b = 1.31693 + 0.66655I
−4.21796 − 4.66670I −8.97137 + 7.61170I
u = 0.669161 − 0.228612I
a = 0.581803 + 1.223630I
b = 1.31693 − 0.66655I
−4.21796 + 4.66670I −8.97137 − 7.61170I
u = 1.363390 + 0.095887I
a = −0.469948 − 0.074927I
b = −1.075150 + 0.330855I
−7.15848 + 3.23765I −10.59891 − 4.72266I
u = 1.363390 − 0.095887I
a = −0.469948 + 0.074927I
b = −1.075150 − 0.330855I
−7.15848 − 3.23765I −10.59891 + 4.72266I
u = −1.51873 + 0.12956I
a = −0.575804 + 0.072905I
b = −0.709299 − 0.216421I
−5.66336 + 0.80372I −4.03005 + 2.76686I
u = −1.51873 − 0.12956I
a = −0.575804 − 0.072905I
b = −0.709299 + 0.216421I
−5.66336 − 0.80372I −4.03005 − 2.76686I
16
IV. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
(u
4
− u
3
+ u
2
+ 1)
6
(u
10
+ u
9
+ 3u
8
+ 2u
7
+ 5u
6
+ 2u
5
+ 5u
4
+ 3u
2
+ 1)
· (u
17
+ 6u
16
+ ··· + 32u + 8)
c
2
((u
4
+ u
3
+ 3u
2
+ 2u + 1)
6
)(u
10
+ 5u
9
+ ··· + 6u + 1)
· (u
17
+ 6u
16
+ ··· + 32u − 64)
c
3
, c
4
, c
8
(u
10
+ u
9
− 4u
8
− 4u
7
+ 4u
6
+ 5u
5
+ u
4
− 2u
3
− 2u
2
+ 1)
· (u
17
− u
16
+ ··· − 2u
2
+ 1)(u
24
+ u
23
+ ··· − 12u + 1)
c
5
(u
10
+ u
9
+ ··· − 2u
2
+ 1)(u
17
+ u
16
+ ··· − 22u
2
+ 1)
· (u
24
+ 3u
23
+ ··· + 54u + 107)
c
6
(u
4
− u
3
+ u
2
+ 1)
6
(u
10
− u
9
+ 3u
8
− 2u
7
+ 5u
6
− 2u
5
+ 5u
4
+ 3u
2
+ 1)
· (u
17
+ 6u
16
+ ··· + 32u + 8)
c
7
(u
3
+ u
2
− 1)
8
· (u
10
− 2u
9
− u
8
+ 6u
7
− 2u
6
− 7u
5
+ 6u
4
+ 4u
3
− 4u
2
− u + 1)
· (u
17
− 7u
16
+ ··· − 80u + 16)
c
9
(u
10
− u
9
− 4u
8
+ 4u
7
+ 4u
6
− 5u
5
+ u
4
+ 2u
3
− 2u
2
+ 1)
· (u
17
− u
16
+ ··· − 2u
2
+ 1)(u
24
+ u
23
+ ··· − 12u + 1)
c
10
(u
3
+ u
2
− 1)
8
· (u
10
+ 2u
9
− u
8
− 6u
7
− 2u
6
+ 7u
5
+ 6u
4
− 4u
3
− 4u
2
+ u + 1)
· (u
17
− 7u
16
+ ··· − 80u + 16)
c
11
(u
10
+ u
9
+ 3u
8
+ u
6
− 2u
5
+ 3u
4
+ u
3
+ 2u
2
+ 1)
· (u
17
+ 3u
16
+ ··· + 4u + 1)(u
24
+ 3u
23
+ ··· + 846u + 347)
17
V. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
, c
6
((y
4
+ y
3
+ 3y
2
+ 2y + 1)
6
)(y
10
+ 5y
9
+ ··· + 6y + 1)
· (y
17
+ 6y
16
+ ··· + 32y −64)
c
2
((y
4
+ 5y
3
+ 7y
2
+ 2y + 1)
6
)(y
10
+ 5y
9
+ ··· + 2y + 1)
· (y
17
+ 10y
16
+ ··· + 33280y −4096)
c
3
, c
4
, c
8
c
9
(y
10
− 9y
9
+ 32y
8
− 56y
7
+ 48y
6
− 15y
5
− 3y
4
+ 6y
2
− 4y + 1)
· (y
17
− y
16
+ ··· + 4y −1)(y
24
− 9y
23
+ ··· − 40y + 1)
c
5
(y
10
+ 7y
9
+ 10y
8
− 9y
7
+ 2y
6
− 4y
5
+ 3y
3
+ 4y
2
− 4y + 1)
· (y
17
− 13y
16
+ ··· + 44y −1)(y
24
+ 3y
23
+ ··· + 23192y + 11449)
c
7
, c
10
((y
3
− y
2
+ 2y −1)
8
)(y
10
− 6y
9
+ ··· − 9y + 1)
· (y
17
− 7y
16
+ ··· − 128y −256)
c
11
(y
10
+ 5y
9
+ ··· + 4y + 1)(y
17
− 27y
16
+ ··· − 24y −1)
· (y
24
− 9y
23
+ ··· + 602884y + 120409)
18
