12a
1137
(K12a
1137
)
A knot diagram
1
Linearized knot diagam
4 8 9 10 11 1 12 3 2 6 5 7
Solving Sequence
2,8
3 9 4 10 5
1,12
7 6 11
c
2
c
8
c
3
c
9
c
4
c
1
c
7
c
6
c
11
c
5
, c
10
, c
12
Ideals for irreducible components
2
of X
par
I
u
1
= h3u
29
− 5u
28
+ ··· + b − 3, −u
29
+ u
28
+ ··· + 2a − 1, u
30
− 3u
29
+ ··· + 3u + 2i
I
u
2
= hu
22
a − u
22
+ ··· + b − 1, u
22
− 11u
20
+ ··· + a
2
+ u, u
23
+ u
22
+ ··· − 2u
3
+ 1i
I
u
3
= hu
3
+ b − u − 1, −u
4
+ 2u
2
+ a − 1, u
6
− 3u
4
+ 2u
2
+ 1i
* 3 irreducible components of dim
C
= 0, with total 82 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
= h3u
29
−5u
28
+· · ·+b−3, −u
29
+u
28
+· · ·+2a−1, u
30
−3u
29
+· · ·+3u+2i
(i) Arc colorings
a
2
=
1
0
a
8
=
0
u
a
3
=
1
−u
2
a
9
=
u
−u
3
+ u
a
4
=
−u
2
+ 1
u
4
− 2u
2
a
10
=
−u
3
+ 2u
−u
3
+ u
a
5
=
−u
10
+ 5u
8
− 8u
6
+ 3u
4
+ u
2
+ 1
−u
10
+ 4u
8
− 5u
6
+ 2u
4
− u
2
a
1
=
u
6
− 3u
4
+ 2u
2
+ 1
−u
8
+ 4u
6
− 4u
4
a
12
=
1
2
u
29
−
1
2
u
28
+ ··· − u +
1
2
−3u
29
+ 5u
28
+ ··· + 6u + 3
a
7
=
1
2
u
29
−
1
2
u
28
+ ··· − 3u −
3
2
2u
29
− 3u
28
+ ··· − 6u − 3
a
6
=
3
2
u
29
−
3
2
u
28
+ ··· − 9u −
9
2
5u
29
− 7u
28
+ ··· − 16u − 7
a
11
=
1
2
u
29
−
1
2
u
28
+ ··· − 2u
2
−
1
2
−u
29
+ 2u
28
+ ··· + 3u + 1
(ii) Obstruction class = −1
(iii) Cusp Shapes
= 4u
29
− 6u
28
− 44u
27
+ 58u
26
+ 214u
25
− 222u
24
− 596u
23
+ 376u
22
+ 1006u
21
−
58u
20
− 920u
19
− 828u
18
+ 88u
17
+ 1268u
16
+ 752u
15
− 520u
14
− 658u
13
− 320u
12
+
76u
11
+ 234u
10
− 14u
9
− 2u
8
+ 148u
7
+ 92u
6
+ 38u
5
− 30u
4
− 80u
3
− 44u
2
− 24u − 18
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
30
− 7u
29
+ ··· − 415u + 136
c
2
, c
3
, c
8
u
30
− 3u
29
+ ··· + 3u + 2
c
4
u
30
+ 3u
29
+ ··· + 320u + 128
c
5
, c
6
, c
7
c
10
, c
11
, c
12
u
30
+ 16u
28
+ ··· + u + 1
c
9
u
30
+ 9u
29
+ ··· + 93u + 6
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
30
+ 5y
29
+ ··· + 17087y + 18496
c
2
, c
3
, c
8
y
30
− 27y
29
+ ··· + 15y + 4
c
4
y
30
− 5y
29
+ ··· + 323584y + 16384
c
5
, c
6
, c
7
c
10
, c
11
, c
12
y
30
+ 32y
29
+ ··· + 9y + 1
c
9
y
30
+ y
29
+ ··· − 2433y + 36
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.930902
a = 0.756247
b = −1.08322
−1.46218 −7.28610
u = −1.089660 + 0.308662I
a = 0.099048 − 1.205780I
b = 1.65581 + 0.20452I
6.92010 − 7.02665I 2.40937 + 6.27539I
u = −1.089660 − 0.308662I
a = 0.099048 + 1.205780I
b = 1.65581 − 0.20452I
6.92010 + 7.02665I 2.40937 − 6.27539I
u = −0.704410 + 0.436123I
a = −1.21026 + 1.24528I
b = 0.040668 − 0.499528I
7.95280 + 7.12520I 2.76356 − 2.96102I
u = −0.704410 − 0.436123I
a = −1.21026 − 1.24528I
b = 0.040668 + 0.499528I
7.95280 − 7.12520I 2.76356 + 2.96102I
u = −0.304786 + 0.743959I
a = −1.46293 + 1.06283I
b = −1.36076 + 1.49177I
6.54937 − 11.30350I 0.19641 + 8.01251I
u = −0.304786 − 0.743959I
a = −1.46293 − 1.06283I
b = −1.36076 − 1.49177I
6.54937 + 11.30350I 0.19641 − 8.01251I
u = −0.103486 + 0.765219I
a = 1.73841 + 0.04408I
b = 1.54138 + 0.39049I
3.91072 + 3.07613I −0.68680 − 2.45527I
u = −0.103486 − 0.765219I
a = 1.73841 − 0.04408I
b = 1.54138 − 0.39049I
3.91072 − 3.07613I −0.68680 + 2.45527I
u = 0.463501 + 0.614076I
a = −1.51718 − 1.19039I
b = −0.727847 − 0.567986I
11.82910 + 2.06121I 4.42340 − 3.33690I
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.463501 − 0.614076I
a = −1.51718 + 1.19039I
b = −0.727847 + 0.567986I
11.82910 − 2.06121I 4.42340 + 3.33690I
u = −0.229240 + 0.685867I
a = −0.139869 − 1.010570I
b = −0.032234 − 1.383400I
−3.39097 − 3.33199I −9.55544 + 5.59326I
u = −0.229240 − 0.685867I
a = −0.139869 + 1.010570I
b = −0.032234 + 1.383400I
−3.39097 + 3.33199I −9.55544 − 5.59326I
u = −0.680122
a = 0.965666
b = −0.665414
−1.48461 −6.75330
u = 1.307540 + 0.319637I
a = 0.353413 + 0.920897I
b = 1.132810 − 0.600648I
8.31617 + 0.83782I 4.44779 + 0.17762I
u = 1.307540 − 0.319637I
a = 0.353413 − 0.920897I
b = 1.132810 + 0.600648I
8.31617 − 0.83782I 4.44779 − 0.17762I
u = 1.352520 + 0.135874I
a = 0.381110 + 0.172911I
b = −0.383620 + 0.193018I
3.75541 + 0.77985I −2.27872 + 2.76052I
u = 1.352520 − 0.135874I
a = 0.381110 − 0.172911I
b = −0.383620 − 0.193018I
3.75541 − 0.77985I −2.27872 − 2.76052I
u = −1.350210 + 0.200800I
a = −0.056070 − 0.361065I
b = 0.555528 − 0.782092I
4.51414 − 3.42768I −0.15581 + 5.80126I
u = −1.350210 − 0.200800I
a = −0.056070 + 0.361065I
b = 0.555528 + 0.782092I
4.51414 + 3.42768I −0.15581 − 5.80126I
6
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 1.38985 + 0.27006I
a = −0.489440 + 0.230842I
b = 1.07204 + 1.56270I
1.76191 + 6.80641I −4.17068 − 6.44926I
u = 1.38985 − 0.27006I
a = −0.489440 − 0.230842I
b = 1.07204 − 1.56270I
1.76191 − 6.80641I −4.17068 + 6.44926I
u = 1.42853 + 0.29221I
a = 0.046116 − 1.008880I
b = −2.90289 − 1.59266I
12.0906 + 15.0680I 4.25091 − 8.34423I
u = 1.42853 − 0.29221I
a = 0.046116 + 1.008880I
b = −2.90289 + 1.59266I
12.0906 − 15.0680I 4.25091 + 8.34423I
u = 1.46604 + 0.09649I
a = −0.257035 − 0.974980I
b = 0.50288 − 1.41355I
14.8637 − 5.5424I 6.83012 + 3.12730I
u = 1.46604 − 0.09649I
a = −0.257035 + 0.974980I
b = 0.50288 + 1.41355I
14.8637 + 5.5424I 6.83012 − 3.12730I
u = −1.46325 + 0.21014I
a = −0.110662 + 1.025770I
b = −1.28614 + 1.87885I
18.0378 − 5.0287I 7.86103 + 3.20489I
u = −1.46325 − 0.21014I
a = −0.110662 − 1.025770I
b = −1.28614 − 1.87885I
18.0378 + 5.0287I 7.86103 − 3.20489I
u = 0.142590 + 0.468477I
a = 0.514389 + 0.535305I
b = 0.066704 + 0.337976I
−0.231238 + 0.878798I −5.31548 − 7.61341I
u = 0.142590 − 0.468477I
a = 0.514389 − 0.535305I
b = 0.066704 − 0.337976I
−0.231238 − 0.878798I −5.31548 + 7.61341I
7
II.
I
u
2
= hu
22
a−u
22
+· · ·+b−1, u
22
−11u
20
+· · ·+a
2
+u, u
23
+u
22
+· · ·−2u
3
+1i
(i) Arc colorings
a
2
=
1
0
a
8
=
0
u
a
3
=
1
−u
2
a
9
=
u
−u
3
+ u
a
4
=
−u
2
+ 1
u
4
− 2u
2
a
10
=
−u
3
+ 2u
−u
3
+ u
a
5
=
−u
10
+ 5u
8
− 8u
6
+ 3u
4
+ u
2
+ 1
−u
10
+ 4u
8
− 5u
6
+ 2u
4
− u
2
a
1
=
u
6
− 3u
4
+ 2u
2
+ 1
−u
8
+ 4u
6
− 4u
4
a
12
=
a
−u
22
a + u
22
+ ··· − u + 1
a
7
=
u
22
+ u
21
+ ··· − u
2
+ 1
−u
22
a + u
21
+ ··· − a + u
a
6
=
u
22
+ u
21
+ ··· + au + 1
−u
22
a + u
21
+ ··· − a + u
a
11
=
u
17
− 8u
15
+ ··· + a + 1
−u
22
a + u
22
+ ··· − u
2
a + 1
(ii) Obstruction class = −1
(iii) Cusp Shapes = −4u
20
+ 36u
18
− 4u
17
− 132u
16
+ 32u
15
+ 244u
14
− 100u
13
−
220u
12
+ 144u
11
+ 60u
10
− 80u
9
+ 24u
8
+ 4u
6
− 12u
5
− 8u
4
+ 20u
3
− 4u
2
− 2
8
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
(u
23
− 5u
22
+ ··· + 32u − 7)
2
c
2
, c
3
, c
8
(u
23
+ u
22
+ ··· − 2u
3
+ 1)
2
c
4
(u
23
− u
22
+ ··· − 8u + 5)
2
c
5
, c
6
, c
7
c
10
, c
11
, c
12
u
46
− u
45
+ ··· − 18u + 5
c
9
(u
23
− 3u
22
+ ··· + 4u − 1)
2
9
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
(y
23
+ 7y
22
+ ··· − 404y −49)
2
c
2
, c
3
, c
8
(y
23
− 21y
22
+ ··· − 6y
2
− 1)
2
c
4
(y
23
− 5y
22
+ ··· + 264y −25)
2
c
5
, c
6
, c
7
c
10
, c
11
, c
12
y
46
+ 35y
45
+ ··· − 264y + 25
c
9
(y
23
− y
22
+ ··· + 4y −1)
2
10
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 1.070060 + 0.182203I
a = −0.070084 + 1.156430I
b = 1.59533 − 0.13562I
2.26450 + 3.60580I −2.88555 − 4.48858I
u = 1.070060 + 0.182203I
a = 0.603866 − 0.224449I
b = −1.405470 − 0.026465I
2.26450 + 3.60580I −2.88555 − 4.48858I
u = 1.070060 − 0.182203I
a = −0.070084 − 1.156430I
b = 1.59533 + 0.13562I
2.26450 − 3.60580I −2.88555 + 4.48858I
u = 1.070060 − 0.182203I
a = 0.603866 + 0.224449I
b = −1.405470 + 0.026465I
2.26450 − 3.60580I −2.88555 + 4.48858I
u = −1.15018
a = −0.261144 + 0.980051I
b = 1.95558 − 0.15361I
5.24303 1.52610
u = −1.15018
a = −0.261144 − 0.980051I
b = 1.95558 + 0.15361I
5.24303 1.52610
u = 0.285113 + 0.703745I
a = −0.120117 + 1.147110I
b = 0.22592 + 1.52660I
1.28846 + 7.02777I −3.56401 − 7.34039I
u = 0.285113 + 0.703745I
a = −1.49794 − 1.02732I
b = −1.14402 − 1.60438I
1.28846 + 7.02777I −3.56401 − 7.34039I
u = 0.285113 − 0.703745I
a = −0.120117 − 1.147110I
b = 0.22592 − 1.52660I
1.28846 − 7.02777I −3.56401 + 7.34039I
u = 0.285113 − 0.703745I
a = −1.49794 + 1.02732I
b = −1.14402 + 1.60438I
1.28846 − 7.02777I −3.56401 + 7.34039I
11
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.625021 + 0.336059I
a = 1.106610 − 0.179524I
b = −0.474160 − 0.683912I
2.66992 − 3.26242I −0.80376 + 2.26815I
u = 0.625021 + 0.336059I
a = −1.18555 − 1.45591I
b = 0.343202 + 0.182577I
2.66992 − 3.26242I −0.80376 + 2.26815I
u = 0.625021 − 0.336059I
a = 1.106610 + 0.179524I
b = −0.474160 + 0.683912I
2.66992 + 3.26242I −0.80376 − 2.26815I
u = 0.625021 − 0.336059I
a = −1.18555 + 1.45591I
b = 0.343202 − 0.182577I
2.66992 + 3.26242I −0.80376 − 2.26815I
u = −0.284234 + 0.630366I
a = 1.56548 + 0.06970I
b = 0.841978 + 0.781651I
3.51028 − 2.29224I −0.17333 + 3.81893I
u = −0.284234 + 0.630366I
a = −1.60090 + 1.02304I
b = −0.68342 + 1.61231I
3.51028 − 2.29224I −0.17333 + 3.81893I
u = −0.284234 − 0.630366I
a = 1.56548 − 0.06970I
b = 0.841978 − 0.781651I
3.51028 + 2.29224I −0.17333 − 3.81893I
u = −0.284234 − 0.630366I
a = −1.60090 − 1.02304I
b = −0.68342 − 1.61231I
3.51028 + 2.29224I −0.17333 − 3.81893I
u = 0.143415 + 0.670993I
a = −0.229021 + 0.764912I
b = −0.467867 + 1.159790I
−0.452611 − 0.303352I −7.41146 − 0.40480I
u = 0.143415 + 0.670993I
a = 1.68536 − 0.02244I
b = 1.182440 − 0.435170I
−0.452611 − 0.303352I −7.41146 − 0.40480I
12
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.143415 − 0.670993I
a = −0.229021 − 0.764912I
b = −0.467867 − 1.159790I
−0.452611 + 0.303352I −7.41146 + 0.40480I
u = 0.143415 − 0.670993I
a = 1.68536 + 0.02244I
b = 1.182440 + 0.435170I
−0.452611 + 0.303352I −7.41146 + 0.40480I
u = −1.347540 + 0.251864I
a = 0.317756 − 0.706992I
b = 0.719514 + 0.327199I
4.24683 − 3.02476I −2.12213 + 2.21609I
u = −1.347540 + 0.251864I
a = −0.312944 − 0.116370I
b = 0.63476 − 1.57084I
4.24683 − 3.02476I −2.12213 + 2.21609I
u = −1.347540 − 0.251864I
a = 0.317756 + 0.706992I
b = 0.719514 − 0.327199I
4.24683 + 3.02476I −2.12213 − 2.21609I
u = −1.347540 − 0.251864I
a = −0.312944 + 0.116370I
b = 0.63476 + 1.57084I
4.24683 + 3.02476I −2.12213 − 2.21609I
u = −0.405548 + 0.414027I
a = 0.39267 − 1.50726I
b = 0.861333 − 0.590644I
4.30391 − 0.94673I 2.43633 + 4.33310I
u = −0.405548 + 0.414027I
a = −1.66459 + 1.46493I
b = 0.245747 + 0.579180I
4.30391 − 0.94673I 2.43633 + 4.33310I
u = −0.405548 − 0.414027I
a = 0.39267 + 1.50726I
b = 0.861333 + 0.590644I
4.30391 + 0.94673I 2.43633 − 4.33310I
u = −0.405548 − 0.414027I
a = −1.66459 − 1.46493I
b = 0.245747 − 0.579180I
4.30391 + 0.94673I 2.43633 − 4.33310I
13
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 1.41968 + 0.16903I
a = −0.155020 − 0.948878I
b = −0.25191 − 2.81816I
10.07070 + 3.16234I 5.66460 − 3.46689I
u = 1.41968 + 0.16903I
a = −0.365183 + 0.593904I
b = 1.25657 + 0.90144I
10.07070 + 3.16234I 5.66460 − 3.46689I
u = 1.41968 − 0.16903I
a = −0.155020 + 0.948878I
b = −0.25191 + 2.81816I
10.07070 − 3.16234I 5.66460 + 3.46689I
u = 1.41968 − 0.16903I
a = −0.365183 − 0.593904I
b = 1.25657 − 0.90144I
10.07070 − 3.16234I 5.66460 + 3.46689I
u = −1.42608 + 0.11950I
a = −0.215286 + 0.943925I
b = 0.61581 + 2.08277I
8.93108 + 1.73636I 3.79313 − 2.46590I
u = −1.42608 + 0.11950I
a = 0.567183 − 0.228717I
b = −0.479254 + 0.173931I
8.93108 + 1.73636I 3.79313 − 2.46590I
u = −1.42608 − 0.11950I
a = −0.215286 − 0.943925I
b = 0.61581 − 2.08277I
8.93108 − 1.73636I 3.79313 + 2.46590I
u = −1.42608 − 0.11950I
a = 0.567183 + 0.228717I
b = −0.479254 − 0.173931I
8.93108 − 1.73636I 3.79313 + 2.46590I
u = 1.41107 + 0.24900I
a = −0.025103 − 0.955027I
b = −2.65658 − 2.58973I
8.92938 + 5.52406I 4.27222 − 3.52157I
u = 1.41107 + 0.24900I
a = 0.505997 + 0.609997I
b = 0.287249 − 0.596485I
8.92938 + 5.52406I 4.27222 − 3.52157I
14
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 1.41107 − 0.24900I
a = −0.025103 + 0.955027I
b = −2.65658 + 2.58973I
8.92938 − 5.52406I 4.27222 + 3.52157I
u = 1.41107 − 0.24900I
a = 0.505997 − 0.609997I
b = 0.287249 + 0.596485I
8.92938 − 5.52406I 4.27222 + 3.52157I
u = −1.41586 + 0.27635I
a = 0.023737 + 0.976168I
b = −2.96691 + 1.96056I
6.72129 − 10.59580I 1.03092 + 7.47788I
u = −1.41586 + 0.27635I
a = −0.565778 − 0.293599I
b = 1.26416 − 1.54071I
6.72129 − 10.59580I 1.03092 + 7.47788I
u = −1.41586 − 0.27635I
a = 0.023737 − 0.976168I
b = −2.96691 − 1.96056I
6.72129 + 10.59580I 1.03092 − 7.47788I
u = −1.41586 − 0.27635I
a = −0.565778 + 0.293599I
b = 1.26416 + 1.54071I
6.72129 + 10.59580I 1.03092 − 7.47788I
15
III. I
u
3
= hu
3
+ b − u − 1, −u
4
+ 2u
2
+ a − 1, u
6
− 3u
4
+ 2u
2
+ 1i
(i) Arc colorings
a
2
=
1
0
a
8
=
0
u
a
3
=
1
−u
2
a
9
=
u
−u
3
+ u
a
4
=
−u
2
+ 1
u
4
− 2u
2
a
10
=
−u
3
+ 2u
−u
3
+ u
a
5
=
−u
2
+ 1
u
4
− 2u
2
a
1
=
0
u
4
− u
2
− 1
a
12
=
u
4
− 2u
2
+ 1
−u
3
+ u + 1
a
7
=
u
5
− 3u
3
+ 2u
u
5
− u
4
− 2u
3
+ 2u
2
+ 2u
a
6
=
u
5
− 3u
3
+ 2u
u
5
− u
4
− 2u
3
+ 2u
2
+ u
a
11
=
u
4
− u
3
− 2u
2
+ 2u + 1
−2u
3
+ 2u + 1
(ii) Obstruction class = 1
(iii) Cusp Shapes = −4u
4
+ 8u
2
16
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
(u
3
+ u
2
− 1)
2
c
2
, c
3
, c
8
u
6
− 3u
4
+ 2u
2
+ 1
c
4
u
6
c
5
, c
6
, c
7
c
10
, c
11
, c
12
(u
2
+ 1)
3
c
9
u
6
+ u
4
+ 2u
2
+ 1
17
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
(y
3
− y
2
+ 2y −1)
2
c
2
, c
3
, c
8
(y
3
− 3y
2
+ 2y + 1)
2
c
4
y
6
c
5
, c
6
, c
7
c
10
, c
11
, c
12
(y + 1)
6
c
9
(y
3
+ y
2
+ 2y + 1)
2
18
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = 1.307140 + 0.215080I
a = 0.122561 + 0.744862I
b = 0.255138 − 0.877439I
6.31400 + 2.82812I 3.50976 − 2.97945I
u = 1.307140 − 0.215080I
a = 0.122561 − 0.744862I
b = 0.255138 + 0.877439I
6.31400 − 2.82812I 3.50976 + 2.97945I
u = −1.307140 + 0.215080I
a = 0.122561 − 0.744862I
b = 1.74486 − 0.87744I
6.31400 − 2.82812I 3.50976 + 2.97945I
u = −1.307140 − 0.215080I
a = 0.122561 + 0.744862I
b = 1.74486 + 0.87744I
6.31400 + 2.82812I 3.50976 − 2.97945I
u = 0.569840I
a = 1.75488
b = 1.000000 + 0.754878I
2.17641 −3.01950
u = − 0.569840I
a = 1.75488
b = 1.000000 − 0.754878I
2.17641 −3.01950
19
IV. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
((u
3
+ u
2
− 1)
2
)(u
23
− 5u
22
+ ··· + 32u − 7)
2
· (u
30
− 7u
29
+ ··· − 415u + 136)
c
2
, c
3
, c
8
(u
6
− 3u
4
+ 2u
2
+ 1)(u
23
+ u
22
+ ··· − 2u
3
+ 1)
2
· (u
30
− 3u
29
+ ··· + 3u + 2)
c
4
u
6
(u
23
− u
22
+ ··· − 8u + 5)
2
(u
30
+ 3u
29
+ ··· + 320u + 128)
c
5
, c
6
, c
7
c
10
, c
11
, c
12
((u
2
+ 1)
3
)(u
30
+ 16u
28
+ ··· + u + 1)(u
46
− u
45
+ ··· − 18u + 5)
c
9
(u
6
+ u
4
+ 2u
2
+ 1)(u
23
− 3u
22
+ ··· + 4u − 1)
2
· (u
30
+ 9u
29
+ ··· + 93u + 6)
20
V. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
((y
3
− y
2
+ 2y −1)
2
)(y
23
+ 7y
22
+ ··· − 404y −49)
2
· (y
30
+ 5y
29
+ ··· + 17087y + 18496)
c
2
, c
3
, c
8
((y
3
− 3y
2
+ 2y + 1)
2
)(y
23
− 21y
22
+ ··· − 6y
2
− 1)
2
· (y
30
− 27y
29
+ ··· + 15y + 4)
c
4
y
6
(y
23
− 5y
22
+ ··· + 264y −25)
2
· (y
30
− 5y
29
+ ··· + 323584y + 16384)
c
5
, c
6
, c
7
c
10
, c
11
, c
12
((y + 1)
6
)(y
30
+ 32y
29
+ ··· + 9y + 1)(y
46
+ 35y
45
+ ··· − 264y + 25)
c
9
((y
3
+ y
2
+ 2y + 1)
2
)(y
23
− y
22
+ ··· + 4y −1)
2
· (y
30
+ y
29
+ ··· − 2433y + 36)
21
