12n
0484
(K12n
0484
)
A knot diagram
1
Linearized knot diagam
3 6 12 7 2 10 11 3 6 4 8 9
Solving Sequence
3,8 6,9
10 2 1 12 4 11 7 5
c
8
c
9
c
2
c
1
c
12
c
3
c
11
c
7
c
4
c
5
, c
6
, c
10
Ideals for irreducible components
2
of X
par
I
u
1
= h−2.57724 × 10
98
u
40
+ 8.25670 × 10
97
u
39
+ ··· + 1.32591 × 10
100
b + 2.87003 × 10
100
,
− 1.90566 × 10
100
u
40
+ 7.67451 × 10
99
u
39
+ ··· + 1.84302 × 10
102
a − 3.98069 × 10
102
,
2u
41
+ 59u
39
+ ··· − 792u − 139i
I
u
2
= h183u
10
+ 1583u
9
+ ··· + 3889b − 2353, 2799u
10
+ 10760u
9
+ ··· + 3889a + 223,
u
11
+ 3u
10
+ 7u
9
+ 13u
8
+ 11u
7
+ 19u
6
+ 6u
5
+ 18u
4
+ 6u
2
− 2u + 1i
I
u
3
= hb + 1, a − 1, u + 1i
I
u
4
= h−2u
3
− 2u
2
+ 2b − 3u − 3, −2u
3
+ a − 3u − 2, 2u
4
+ 3u
2
+ 2u + 1i
* 4 irreducible components of dim
C
= 0, with total 57 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−2.58 × 10
98
u
40
+ 8.26 × 10
97
u
39
+ · · · + 1.33 × 10
100
b + 2.87 ×
10
100
, −1.91 × 10
100
u
40
+ 7.67 × 10
99
u
39
+ · · · + 1.84 × 10
102
a − 3.98 ×
10
102
, 2u
41
+ 59u
39
+ · · · − 792u − 139i
(i) Arc colorings
a
3
=
0
u
a
8
=
1
0
a
6
=
0.0103399u
40
− 0.00416410u
39
+ ··· − 1.23241u + 2.15988
0.0194375u
40
− 0.00622719u
39
+ ··· − 11.2533u − 2.16457
a
9
=
1
−u
2
a
10
=
−0.0209471u
40
+ 0.00485889u
39
+ ··· + 19.6703u + 5.53621
−0.00627194u
40
+ 0.00359880u
39
+ ··· + 4.80640u − 0.268658
a
2
=
−0.0223730u
40
+ 0.00212611u
39
+ ··· + 18.5281u + 3.03016
−0.00396870u
40
− 0.00262692u
39
+ ··· + 5.47182u + 1.30806
a
1
=
−0.0223730u
40
+ 0.00212611u
39
+ ··· + 18.5281u + 3.03016
−0.00307852u
40
− 0.00354962u
39
+ ··· + 6.18480u + 1.16029
a
12
=
−0.0184043u
40
+ 0.00475303u
39
+ ··· + 13.0562u + 1.72210
−0.000584007u
40
− 0.00418261u
39
+ ··· + 4.86872u + 0.977723
a
4
=
−0.0191133u
40
+ 0.00882757u
39
+ ··· + 0.506034u − 0.758338
0.00679681u
40
− 0.00471144u
39
+ ··· − 3.46799u − 0.799858
a
11
=
−0.0189883u
40
+ 0.000570424u
39
+ ··· + 17.9250u + 2.69983
−0.000584007u
40
− 0.00418261u
39
+ ··· + 4.86872u + 0.977723
a
7
=
−0.000436229u
40
− 0.00330818u
39
+ ··· + 6.39844u + 2.38333
0.0110725u
40
− 0.0101050u
39
+ ··· − 0.426320u + 1.29385
a
5
=
−0.00336300u
40
+ 0.00725991u
39
+ ··· − 12.4525u − 5.75232
−0.0229539u
40
+ 0.00793740u
39
+ ··· + 12.3051u + 2.17246
(ii) Obstruction class = −1
(iii) Cusp Shapes = 0.0503579u
40
− 0.0337763u
39
+ ··· − 41.9472u − 6.50005
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
41
+ 62u
40
+ ··· + 20980954u + 3066001
c
2
, c
5
u
41
− 2u
40
+ ··· − 994u + 1751
c
3
u
41
− 7u
40
+ ··· − 32u + 2
c
4
u
41
+ 8u
40
+ ··· + 202u + 482
c
6
, c
9
u
41
− 4u
40
+ ··· − 532u − 484
c
7
, c
11
u
41
− 18u
39
+ ··· − 147u − 9
c
8
2(2u
41
+ 59u
39
+ ··· − 792u + 139)
c
10
2(2u
41
+ 4u
40
+ ··· + 12u − 1)
c
12
u
41
+ 50u
39
+ ··· + 3836088u + 323212
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
41
− 174y
40
+ ··· − 176579932485582y −9400362132001
c
2
, c
5
y
41
− 62y
40
+ ··· + 20980954y −3066001
c
3
y
41
− 7y
40
+ ··· + 68y −4
c
4
y
41
+ 26y
40
+ ··· − 2659360y −232324
c
6
, c
9
y
41
+ 50y
39
+ ··· − 1201888y −234256
c
7
, c
11
y
41
− 36y
40
+ ··· + 6831y −81
c
8
4(4y
41
+ 236y
40
+ ··· − 158364y −19321)
c
10
4(4y
41
+ 36y
40
+ ··· + 32y −1)
c
12
y
41
+ 100y
40
+ ··· + 6045979389712y −104465996944
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.659232 + 0.776800I
a = 0.577914 + 0.165637I
b = −0.024468 − 0.254653I
−0.03579 − 2.12702I −2.30724 + 6.34493I
u = −0.659232 − 0.776800I
a = 0.577914 − 0.165637I
b = −0.024468 + 0.254653I
−0.03579 + 2.12702I −2.30724 − 6.34493I
u = 0.393962 + 0.883594I
a = 0.541007 − 0.684990I
b = 1.124350 − 0.835430I
3.52455 − 0.44279I 1.64463 + 0.69069I
u = 0.393962 − 0.883594I
a = 0.541007 + 0.684990I
b = 1.124350 + 0.835430I
3.52455 + 0.44279I 1.64463 − 0.69069I
u = 0.254000 + 1.050130I
a = −1.31930 + 0.64361I
b = −0.809991 + 0.134439I
−5.50368 − 6.18013I −6.07543 + 4.97240I
u = 0.254000 − 1.050130I
a = −1.31930 − 0.64361I
b = −0.809991 − 0.134439I
−5.50368 + 6.18013I −6.07543 − 4.97240I
u = −0.343509 + 0.778339I
a = −1.50036 − 0.93858I
b = −0.597196 − 0.150858I
−5.88104 − 0.44141I −6.92109 + 1.29385I
u = −0.343509 − 0.778339I
a = −1.50036 + 0.93858I
b = −0.597196 + 0.150858I
−5.88104 + 0.44141I −6.92109 − 1.29385I
u = 0.432526 + 0.728373I
a = 0.847277 − 0.498164I
b = −0.263708 − 0.214377I
−1.32932 − 0.71050I −7.34406 + 3.00260I
u = 0.432526 − 0.728373I
a = 0.847277 + 0.498164I
b = −0.263708 + 0.214377I
−1.32932 + 0.71050I −7.34406 − 3.00260I
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.786645
a = 1.52147
b = −0.499922
−2.75131 5.92420
u = 0.572393 + 0.467249I
a = 0.784322 + 0.182815I
b = −0.577015 − 1.030610I
−2.75470 − 0.87273I −3.72912 + 1.33601I
u = 0.572393 − 0.467249I
a = 0.784322 − 0.182815I
b = −0.577015 + 1.030610I
−2.75470 + 0.87273I −3.72912 − 1.33601I
u = −0.416524 + 1.237420I
a = 0.408598 − 0.403112I
b = −0.286242 − 0.497821I
−0.89253 − 2.94273I 0
u = −0.416524 − 1.237420I
a = 0.408598 + 0.403112I
b = −0.286242 + 0.497821I
−0.89253 + 2.94273I 0
u = −0.534052 + 0.272508I
a = 1.35667 + 0.56380I
b = 0.977815 − 0.039583I
2.14913 − 0.81916I 6.43098 + 7.00832I
u = −0.534052 − 0.272508I
a = 1.35667 − 0.56380I
b = 0.977815 + 0.039583I
2.14913 + 0.81916I 6.43098 − 7.00832I
u = 0.171734 + 0.527077I
a = 0.88599 + 1.93343I
b = −0.381893 + 0.315896I
4.54292 + 2.96089I −5.84505 − 9.32253I
u = 0.171734 − 0.527077I
a = 0.88599 − 1.93343I
b = −0.381893 − 0.315896I
4.54292 − 2.96089I −5.84505 + 9.32253I
u = 1.04509 + 1.16303I
a = −0.575660 + 0.408131I
b = 0.336966 + 0.467880I
−4.77375 + 7.71761I 0
6
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 1.04509 − 1.16303I
a = −0.575660 − 0.408131I
b = 0.336966 − 0.467880I
−4.77375 − 7.71761I 0
u = −0.356665 + 0.207131I
a = 1.12852 − 1.40117I
b = −0.933888 + 0.923317I
−1.64023 − 6.11163I −0.87211 + 3.36095I
u = −0.356665 − 0.207131I
a = 1.12852 + 1.40117I
b = −0.933888 − 0.923317I
−1.64023 + 6.11163I −0.87211 − 3.36095I
u = −0.241179 + 0.293581I
a = 1.84296 − 0.32729I
b = 0.998293 − 0.269510I
1.88617 − 0.91020I 6.79810 − 1.89134I
u = −0.241179 − 0.293581I
a = 1.84296 + 0.32729I
b = 0.998293 + 0.269510I
1.88617 + 0.91020I 6.79810 + 1.89134I
u = 0.18824 + 1.62909I
a = −0.155518 + 1.166050I
b = 0.00435 + 2.45451I
−8.69666 + 3.51054I 0
u = 0.18824 − 1.62909I
a = −0.155518 − 1.166050I
b = 0.00435 − 2.45451I
−8.69666 − 3.51054I 0
u = −0.30115 + 1.75023I
a = 0.062139 + 1.105720I
b = 0.52944 + 2.26135I
−14.5520 − 3.8090I 0
u = −0.30115 − 1.75023I
a = 0.062139 − 1.105720I
b = 0.52944 − 2.26135I
−14.5520 + 3.8090I 0
u = −0.24365 + 1.79461I
a = 0.005218 − 1.222810I
b = 0.03876 − 2.26816I
−9.19332 − 6.12722I 0
7
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.24365 − 1.79461I
a = 0.005218 + 1.222810I
b = 0.03876 + 2.26816I
−9.19332 + 6.12722I 0
u = 0.16879 + 1.88364I
a = −0.044736 − 1.118060I
b = 0.35074 − 2.24460I
−16.2241 − 3.4621I 0
u = 0.16879 − 1.88364I
a = −0.044736 + 1.118060I
b = 0.35074 + 2.24460I
−16.2241 + 3.4621I 0
u = 0.32422 + 1.88669I
a = −0.053583 + 0.940689I
b = −0.11454 + 2.30108I
−10.43640 + 3.80935I 0
u = 0.32422 − 1.88669I
a = −0.053583 − 0.940689I
b = −0.11454 − 2.30108I
−10.43640 − 3.80935I 0
u = 0.32406 + 1.92161I
a = −0.072428 − 1.055780I
b = −0.14431 − 2.43176I
−15.2118 + 13.8525I 0
u = 0.32406 − 1.92161I
a = −0.072428 + 1.055780I
b = −0.14431 + 2.43176I
−15.2118 − 13.8525I 0
u = −0.17851 + 2.01135I
a = −0.115497 + 0.968666I
b = −0.18704 + 2.37176I
−16.2944 − 5.5634I 0
u = −0.17851 − 2.01135I
a = −0.115497 − 0.968666I
b = −0.18704 − 2.37176I
−16.2944 + 5.5634I 0
u = −0.99386 + 1.82091I
a = −0.349882 − 0.371487I
b = 0.70955 − 1.54548I
−3.40570 + 0.32734I 0
8
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.99386 − 1.82091I
a = −0.349882 + 0.371487I
b = 0.70955 + 1.54548I
−3.40570 − 0.32734I 0
9
II. I
u
2
= h183u
10
+ 1583u
9
+ · · · + 3889b − 2353, 2799u
10
+ 10760u
9
+ · · · +
3889a + 223, u
11
+ 3u
10
+ · · · − 2u + 1i
(i) Arc colorings
a
3
=
0
u
a
8
=
1
0
a
6
=
−0.719722u
10
− 2.76678u
9
+ ··· − 5.35485u − 0.0573412
−0.0470558u
10
− 0.407046u
9
+ ··· − 0.206480u + 0.605040
a
9
=
1
−u
2
a
10
=
0.582926u
10
+ 2.36488u
9
+ ··· + 6.37208u + 1.15505
−0.136796u
10
− 0.401903u
9
+ ··· + 1.01723u − 0.902289
a
2
=
−0.622011u
10
− 2.33685u
9
+ ··· − 4.65287u − 2.26999
−0.556956u
10
− 1.85060u
9
+ ··· − 0.00128568u + 0.112111
a
1
=
−0.622011u
10
− 2.33685u
9
+ ··· − 4.65287u − 2.26999
−0.497814u
10
− 1.59038u
9
+ ··· + 0.318334u − 0.358704
a
12
=
−0.0650553u
10
− 0.486243u
9
+ ··· − 4.65158u − 2.38210
−0.349447u
10
− 1.13757u
9
+ ··· + 0.515814u − 0.178966
a
4
=
−2.03626u
10
− 6.55953u
9
+ ··· − 8.33942u + 3.59733
0.212651u
10
+ 0.735665u
9
+ ··· + 1.50141u + 0.276678
a
11
=
−0.414502u
10
− 1.62381u
9
+ ··· − 4.13577u − 2.56107
−0.349447u
10
− 1.13757u
9
+ ··· + 0.515814u − 0.178966
a
7
=
−0.0105426u
10
− 0.446387u
9
+ ··· + 1.58215u + 1.43610
0.266135u
10
+ 0.170995u
9
+ ··· + 1.93829u − 0.618668
a
5
=
−1.32142u
10
− 4.41425u
9
+ ··· − 3.51967u + 3.51530
0.286192u
10
+ 0.459244u
9
+ ··· + 2.97711u − 0.204423
(ii) Obstruction class = 1
(iii) Cusp Shapes = −
9564
3889
u
10
−
28859
3889
u
9
−
63016
3889
u
8
−
109107
3889
u
7
−
66615
3889
u
6
−
107750
3889
u
5
+
13439
3889
u
4
−
81002
3889
u
3
+
23490
3889
u
2
+
22170
3889
u +
11276
3889
10
(iv) u-Polynomials at the component
11
Crossings u-Polynomials at each crossing
c
1
u
11
− 8u
10
+ ··· − 16u
2
− 1
c
2
u
11
+ 6u
10
+ 14u
9
+ 16u
8
+ 8u
7
− u
6
− 3u
5
− 4u
4
− 7u
3
− 8u
2
− 4u − 1
c
3
u
11
+ 3u
10
+ ··· + 5u + 1
c
4
u
11
+ 2u
10
+ ··· + 2u − 1
c
5
u
11
− 6u
10
+ 14u
9
− 16u
8
+ 8u
7
+ u
6
− 3u
5
+ 4u
4
− 7u
3
+ 8u
2
− 4u + 1
c
6
u
11
− 3u
10
+ u
9
+ 7u
8
− 8u
7
− 5u
6
+ 12u
5
+ 2u
4
− 10u
3
+ 5u − 1
c
7
u
11
− 3u
9
− 4u
8
+ 2u
7
+ 11u
6
+ 12u
5
− 5u
4
− 11u
3
− 10u
2
+ 7u − 1
c
8
u
11
+ 3u
10
+ 7u
9
+ 13u
8
+ 11u
7
+ 19u
6
+ 6u
5
+ 18u
4
+ 6u
2
− 2u + 1
c
9
u
11
+ 3u
10
+ u
9
− 7u
8
− 8u
7
+ 5u
6
+ 12u
5
− 2u
4
− 10u
3
+ 5u + 1
c
10
u
11
+ 3u
10
+ 4u
9
+ 7u
8
+ 6u
7
+ 8u
6
+ u
5
+ 6u
4
+ 2u
3
+ 2u
2
+ 1
c
11
u
11
− 3u
9
+ 4u
8
+ 2u
7
− 11u
6
+ 12u
5
+ 5u
4
− 11u
3
+ 10u
2
+ 7u + 1
c
12
u
11
− u
10
+ 11u
9
+ 26u
7
+ 29u
6
+ 35u
5
+ 42u
4
+ 37u
3
+ 14u
2
+ 4u − 1
12
13
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
11
− 24y
10
+ ··· − 32y −1
c
2
, c
5
y
11
− 8y
10
+ ··· − 16y
2
− 1
c
3
y
11
+ y
10
+ ··· + 7y −1
c
4
y
11
+ 2y
10
+ ··· − 2y −1
c
6
, c
9
y
11
− 7y
10
+ ··· + 25y −1
c
7
, c
11
y
11
− 6y
10
+ ··· + 29y −1
c
8
y
11
+ 5y
10
+ ··· − 8y −1
c
10
y
11
− y
10
+ ··· − 4y −1
c
12
y
11
+ 21y
10
+ ··· + 44y −1
14
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.480135 + 0.881380I
a = −0.153776 − 0.485356I
b = −1.41525 − 0.50524I
−2.33883 + 7.37149I −3.11706 − 6.99331I
u = 0.480135 − 0.881380I
a = −0.153776 + 0.485356I
b = −1.41525 + 0.50524I
−2.33883 − 7.37149I −3.11706 + 6.99331I
u = −0.264154 + 0.702912I
a = 1.116630 + 0.190741I
b = 1.138780 − 0.052004I
1.51158 − 1.27486I −4.85663 + 8.07328I
u = −0.264154 − 0.702912I
a = 1.116630 − 0.190741I
b = 1.138780 + 0.052004I
1.51158 + 1.27486I −4.85663 − 8.07328I
u = −0.484263 + 1.208900I
a = 0.410507 − 0.693136I
b = −0.113275 − 0.961423I
−1.13538 − 3.62559I −3.13967 + 10.18749I
u = −0.484263 − 1.208900I
a = 0.410507 + 0.693136I
b = −0.113275 + 0.961423I
−1.13538 + 3.62559I −3.13967 − 10.18749I
u = 0.241024 + 0.302729I
a = 0.11240 − 3.01728I
b = 0.661755 − 0.219226I
4.85889 + 2.59846I 5.06519 + 2.32360I
u = 0.241024 − 0.302729I
a = 0.11240 + 3.01728I
b = 0.661755 + 0.219226I
4.85889 − 2.59846I 5.06519 − 2.32360I
u = −0.34106 + 1.71658I
a = −0.189096 − 1.101710I
b = −0.12085 − 2.27707I
−9.52186 − 4.70907I −4.95123 + 4.90980I
u = −0.34106 − 1.71658I
a = −0.189096 + 1.101710I
b = −0.12085 + 2.27707I
−9.52186 + 4.70907I −4.95123 − 4.90980I
15
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −2.26337
a = 0.406666
b = −2.30231
−3.19814 −36.0010
16
III. I
u
3
= hb + 1, a − 1, u + 1i
(i) Arc colorings
a
3
=
0
−1
a
8
=
1
0
a
6
=
1
−1
a
9
=
1
−1
a
10
=
1
−1
a
2
=
−1
0
a
1
=
−1
1
a
12
=
−1
1
a
4
=
1
−2
a
11
=
0
1
a
7
=
1
−1
a
5
=
0
−1
(ii) Obstruction class = 1
(iii) Cusp Shapes = −12
17
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
2
, c
4
c
7
u − 1
c
3
, c
5
, c
8
c
10
, c
11
u + 1
c
6
, c
9
, c
12
u
18
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
2
, c
3
c
4
, c
5
, c
7
c
8
, c
10
, c
11
y −1
c
6
, c
9
, c
12
y
19
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = −1.00000
a = 1.00000
b = −1.00000
−3.28987 −12.0000
20
IV. I
u
4
= h−2u
3
− 2u
2
+ 2b − 3u − 3, −2u
3
+ a − 3u − 2, 2u
4
+ 3u
2
+ 2u + 1i
(i) Arc colorings
a
3
=
0
u
a
8
=
1
0
a
6
=
2u
3
+ 3u + 2
u
3
+ u
2
+
3
2
u +
3
2
a
9
=
1
−u
2
a
10
=
−3u
3
+ u
2
−
7
2
u −
3
2
−u
3
−
1
2
u −
3
2
a
2
=
−2u
3
− 3u − 2
−u
3
− u
2
−
1
2
u −
3
2
a
1
=
−2u
3
− 3u − 2
−u
3
− u
2
−
3
2
u −
3
2
a
12
=
−u
3
+ u
2
−
5
2
u −
1
2
−1
a
4
=
−2u
2
− 1
u
3
− u
2
+
3
2
u +
1
2
a
11
=
−u
3
+ u
2
−
5
2
u −
3
2
−1
a
7
=
−u
3
+ u
2
−
5
2
u −
1
2
−1
a
5
=
0
u
(ii) Obstruction class = 1
(iii) Cusp Shapes = −4
21
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
2
, c
11
(u − 1)
4
c
3
, c
4
u
4
+ 2u
3
+ 5u
2
+ 4u + 2
c
5
, c
7
(u + 1)
4
c
6
, c
9
, c
12
(u
2
− 2)
2
c
8
2(2u
4
+ 3u
2
+ 2u + 1)
c
10
2(2u
4
+ 3u
2
− 2u + 1)
22
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
2
, c
5
c
7
, c
11
(y −1)
4
c
3
, c
4
y
4
+ 6y
3
+ 13y
2
+ 4y + 4
c
6
, c
9
, c
12
(y −2)
4
c
8
, c
10
4(4y
4
+ 12y
3
+ 13y
2
+ 2y + 1)
23
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
4
√
−1(vol +
√
−1CS) Cusp shape
u = 0.353553 + 1.257820I
a = −0.207107 + 0.736813I
b = −1.06066 + 1.25782I
1.64493 −4.00000
u = 0.353553 − 1.257820I
a = −0.207107 − 0.736813I
b = −1.06066 − 1.25782I
1.64493 −4.00000
u = −0.353553 + 0.409748I
a = 1.20711 + 1.39897I
b = 1.060660 + 0.409748I
1.64493 −4.00000
u = −0.353553 − 0.409748I
a = 1.20711 − 1.39897I
b = 1.060660 − 0.409748I
1.64493 −4.00000
24
V. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
((u − 1)
5
)(u
11
− 8u
10
+ ··· − 16u
2
− 1)
· (u
41
+ 62u
40
+ ··· + 20980954u + 3066001)
c
2
(u − 1)
5
· (u
11
+ 6u
10
+ 14u
9
+ 16u
8
+ 8u
7
− u
6
− 3u
5
− 4u
4
− 7u
3
− 8u
2
− 4u − 1)
· (u
41
− 2u
40
+ ··· − 994u + 1751)
c
3
(u + 1)(u
4
+ 2u
3
+ ··· + 4u + 2)(u
11
+ 3u
10
+ ··· + 5u + 1)
· (u
41
− 7u
40
+ ··· − 32u + 2)
c
4
(u − 1)(u
4
+ 2u
3
+ ··· + 4u + 2)(u
11
+ 2u
10
+ ··· + 2u − 1)
· (u
41
+ 8u
40
+ ··· + 202u + 482)
c
5
(u + 1)
5
· (u
11
− 6u
10
+ 14u
9
− 16u
8
+ 8u
7
+ u
6
− 3u
5
+ 4u
4
− 7u
3
+ 8u
2
− 4u + 1)
· (u
41
− 2u
40
+ ··· − 994u + 1751)
c
6
u(u
2
− 2)
2
· (u
11
− 3u
10
+ u
9
+ 7u
8
− 8u
7
− 5u
6
+ 12u
5
+ 2u
4
− 10u
3
+ 5u − 1)
· (u
41
− 4u
40
+ ··· − 532u − 484)
c
7
(u − 1)(u + 1)
4
· (u
11
− 3u
9
− 4u
8
+ 2u
7
+ 11u
6
+ 12u
5
− 5u
4
− 11u
3
− 10u
2
+ 7u − 1)
· (u
41
− 18u
39
+ ··· − 147u − 9)
c
8
4(u + 1)(2u
4
+ 3u
2
+ 2u + 1)
· (u
11
+ 3u
10
+ 7u
9
+ 13u
8
+ 11u
7
+ 19u
6
+ 6u
5
+ 18u
4
+ 6u
2
− 2u + 1)
· (2u
41
+ 59u
39
+ ··· − 792u + 139)
c
9
u(u
2
− 2)
2
· (u
11
+ 3u
10
+ u
9
− 7u
8
− 8u
7
+ 5u
6
+ 12u
5
− 2u
4
− 10u
3
+ 5u + 1)
· (u
41
− 4u
40
+ ··· − 532u − 484)
c
10
4(u + 1)(2u
4
+ 3u
2
− 2u + 1)
· (u
11
+ 3u
10
+ 4u
9
+ 7u
8
+ 6u
7
+ 8u
6
+ u
5
+ 6u
4
+ 2u
3
+ 2u
2
+ 1)
· (2u
41
+ 4u
40
+ ··· + 12u − 1)
c
11
(u − 1)
4
(u + 1)
· (u
11
− 3u
9
+ 4u
8
+ 2u
7
− 11u
6
+ 12u
5
+ 5u
4
− 11u
3
+ 10u
2
+ 7u + 1)
· (u
41
− 18u
39
+ ··· − 147u − 9)
c
12
u(u
2
− 2)
2
· (u
11
− u
10
+ 11u
9
+ 26u
7
+ 29u
6
+ 35u
5
+ 42u
4
+ 37u
3
+ 14u
2
+ 4u − 1)
· (u
41
+ 50u
39
+ ··· + 3836088u + 323212)
25
VI. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
((y −1)
5
)(y
11
− 24y
10
+ ··· − 32y −1)
· (y
41
− 174y
40
+ ··· − 176579932485582y −9400362132001)
c
2
, c
5
((y −1)
5
)(y
11
− 8y
10
+ ··· − 16y
2
− 1)
· (y
41
− 62y
40
+ ··· + 20980954y −3066001)
c
3
(y −1)(y
4
+ 6y
3
+ ··· + 4y + 4)(y
11
+ y
10
+ ··· + 7y −1)
· (y
41
− 7y
40
+ ··· + 68y −4)
c
4
(y −1)(y
4
+ 6y
3
+ ··· + 4y + 4)(y
11
+ 2y
10
+ ··· − 2y −1)
· (y
41
+ 26y
40
+ ··· − 2659360y −232324)
c
6
, c
9
y(y −2)
4
(y
11
− 7y
10
+ ··· + 25y −1)
· (y
41
+ 50y
39
+ ··· − 1201888y −234256)
c
7
, c
11
((y −1)
5
)(y
11
− 6y
10
+ ··· + 29y −1)(y
41
− 36y
40
+ ··· + 6831y −81)
c
8
16(y −1)(4y
4
+ 12y
3
+ ··· + 2y + 1)(y
11
+ 5y
10
+ ··· − 8y −1)
· (4y
41
+ 236y
40
+ ··· − 158364y −19321)
c
10
16(y −1)(4y
4
+ 12y
3
+ ··· + 2y + 1)(y
11
− y
10
+ ··· − 4y −1)
· (4y
41
+ 36y
40
+ ··· + 32y −1)
c
12
y(y −2)
4
(y
11
+ 21y
10
+ ··· + 44y −1)
· (y
41
+ 100y
40
+ ··· + 6045979389712y −104465996944)
26
