12a
0355
(K12a
0355
)
A knot diagram
1
Linearized knot diagam
3 6 9 8 2 11 5 4 12 1 7 10
Solving Sequence
5,8
4 9 3
7,11
12 10 6 2 1
c
4
c
8
c
3
c
7
c
11
c
9
c
6
c
2
c
1
c
5
, c
10
, c
12
Ideals for irreducible components
2
of X
par
I
u
1
= h8.94586 × 10
64
u
73
− 2.69400 × 10
64
u
72
+ ··· + 1.31582 × 10
66
b + 4.80004 × 10
66
,
5.16081 × 10
65
u
73
+ 2.32979 × 10
65
u
72
+ ··· + 1.31582 × 10
66
a − 4.81901 × 10
66
, u
74
+ 2u
73
+ ··· − 20u − 4i
I
u
2
= h2u
4
− 3u
3
+ 8u
2
+ 3b − 7u + 5, 2u
4
− 3u
3
+ 8u
2
+ 3a − 7u + 5, u
5
− u
4
+ 4u
3
− 3u
2
+ 3u − 1i
I
u
3
= h−au + 11b − 8a + 4u − 1, 2a
2
+ au − 2a + 7u + 9, u
2
+ 2i
I
v
1
= ha, b + v + 2, v
2
+ 3v + 1i
* 4 irreducible components of dim
C
= 0, with total 85 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
=
h8.95×10
64
u
73
−2.69×10
64
u
72
+· · ·+1.32×10
66
b+4.80×10
66
, 5.16×10
65
u
73
+
2.33 × 10
65
u
72
+ · · · + 1.32 × 10
66
a − 4.82 × 10
66
, u
74
+ 2u
73
+ · · · − 20u − 4i
(i) Arc colorings
a
5
=
1
0
a
8
=
0
u
a
4
=
1
−u
2
a
9
=
−u
u
3
+ u
a
3
=
u
2
+ 1
−u
4
− 2u
2
a
7
=
u
u
a
11
=
−0.392213u
73
− 0.177060u
72
+ ··· + 27.1492u + 3.66236
−0.0679870u
73
+ 0.0204739u
72
+ ··· − 8.72485u − 3.64795
a
12
=
−0.355590u
73
− 0.176374u
72
+ ··· + 34.8706u + 5.46603
−0.0313639u
73
+ 0.0211600u
72
+ ··· − 1.00340u − 1.84428
a
10
=
−0.852587u
73
− 1.27210u
72
+ ··· + 13.2517u + 3.41225
0.207785u
73
+ 0.612327u
72
+ ··· − 5.79693u − 0.899362
a
6
=
1.17691u
73
+ 1.95949u
72
+ ··· − 19.1812u − 3.66683
−0.0813988u
73
− 0.326325u
72
+ ··· − 7.72533u + 0.765144
a
2
=
1.04202u
73
+ 1.78916u
72
+ ··· − 30.0854u − 4.47897
0.0488339u
73
+ 0.413592u
72
+ ··· + 12.6335u + 1.99163
a
1
=
1.21027u
73
+ 2.52965u
72
+ ··· − 18.7639u − 4.59000
0.149898u
73
+ 0.645216u
72
+ ··· + 0.284782u − 0.278393
(ii) Obstruction class = −1
(iii) Cusp Shapes = 3.89182u
73
+ 7.30859u
72
+ ··· − 106.915u − 60.8282
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
74
+ 36u
73
+ ··· + 9145u + 361
c
2
, c
5
u
74
+ 4u
73
+ ··· + 81u + 19
c
3
, c
4
, c
7
c
8
u
74
− 2u
73
+ ··· + 20u − 4
c
6
, c
11
u
74
− 2u
73
+ ··· + 768u − 288
c
9
, c
10
, c
12
u
74
− 9u
73
+ ··· + 76u + 9
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
74
+ 12y
73
+ ··· − 14397001y + 130321
c
2
, c
5
y
74
− 36y
73
+ ··· − 9145y + 361
c
3
, c
4
, c
7
c
8
y
74
+ 86y
73
+ ··· − 144y + 16
c
6
, c
11
y
74
− 42y
73
+ ··· − 2096640y + 82944
c
9
, c
10
, c
12
y
74
− 71y
73
+ ··· + 578y + 81
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.607505 + 0.741468I
a = −0.183425 − 1.058720I
b = −1.40832 − 0.47940I
−4.07736 − 6.36026I 0
u = 0.607505 − 0.741468I
a = −0.183425 + 1.058720I
b = −1.40832 + 0.47940I
−4.07736 + 6.36026I 0
u = −0.667561 + 0.682290I
a = 0.256038 − 1.207670I
b = 1.72165 − 0.74796I
−6.73194 + 12.03370I 0
u = −0.667561 − 0.682290I
a = 0.256038 + 1.207670I
b = 1.72165 + 0.74796I
−6.73194 − 12.03370I 0
u = −0.559459 + 0.669706I
a = −0.35510 + 1.56159I
b = −1.65441 + 0.91662I
−0.91245 + 7.70837I 0
u = −0.559459 − 0.669706I
a = −0.35510 − 1.56159I
b = −1.65441 − 0.91662I
−0.91245 − 7.70837I 0
u = −0.038593 + 0.865679I
a = −0.593774 + 0.924728I
b = 0.028979 + 0.303137I
2.31614 − 1.35523I −12.00000 + 0.I
u = −0.038593 − 0.865679I
a = −0.593774 − 0.924728I
b = 0.028979 − 0.303137I
2.31614 + 1.35523I −12.00000 + 0.I
u = 0.360711 + 0.782136I
a = 0.797293 + 0.395622I
b = 0.224581 − 0.244946I
1.68880 − 3.09277I 0
u = 0.360711 − 0.782136I
a = 0.797293 − 0.395622I
b = 0.224581 + 0.244946I
1.68880 + 3.09277I 0
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.773386 + 0.324218I
a = −0.325616 + 0.996634I
b = −1.43090 − 0.20161I
−7.80941 − 7.24256I −12.00000 + 0.I
u = −0.773386 − 0.324218I
a = −0.325616 − 0.996634I
b = −1.43090 + 0.20161I
−7.80941 + 7.24256I −12.00000 + 0.I
u = 0.410374 + 0.690476I
a = 0.079542 + 1.327180I
b = 1.194690 + 0.654281I
1.22679 − 2.85228I −8.14859 + 5.24888I
u = 0.410374 − 0.690476I
a = 0.079542 − 1.327180I
b = 1.194690 − 0.654281I
1.22679 + 2.85228I −8.14859 − 5.24888I
u = 0.514460 + 0.613164I
a = −1.102640 − 0.882328I
b = −0.253876 + 0.423223I
−3.73773 − 5.34029I −14.6182 + 6.5473I
u = 0.514460 − 0.613164I
a = −1.102640 + 0.882328I
b = −0.253876 − 0.423223I
−3.73773 + 5.34029I −14.6182 − 6.5473I
u = −0.436354 + 0.667310I
a = 0.283686 − 0.895813I
b = 1.52973 + 0.27951I
−9.67609 + 2.66695I −17.4503 − 3.9305I
u = −0.436354 − 0.667310I
a = 0.283686 + 0.895813I
b = 1.52973 − 0.27951I
−9.67609 − 2.66695I −17.4503 + 3.9305I
u = 0.382623 + 1.141660I
a = −0.409174 − 0.900128I
b = −0.604968 − 0.087795I
−1.49710 − 2.18136I 0
u = 0.382623 − 1.141660I
a = −0.409174 + 0.900128I
b = −0.604968 + 0.087795I
−1.49710 + 2.18136I 0
6
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.761356 + 0.203683I
a = −0.133816 + 0.674262I
b = 1.153300 − 0.116691I
−5.69528 + 1.81465I −16.3182 + 0.I
u = 0.761356 − 0.203683I
a = −0.133816 − 0.674262I
b = 1.153300 + 0.116691I
−5.69528 − 1.81465I −16.3182 + 0.I
u = −0.429289 + 0.586607I
a = 0.16786 − 2.19168I
b = 1.30415 − 1.08343I
−2.40757 + 2.56289I −14.9241 − 4.9642I
u = −0.429289 − 0.586607I
a = 0.16786 + 2.19168I
b = 1.30415 + 1.08343I
−2.40757 − 2.56289I −14.9241 + 4.9642I
u = −0.638318 + 0.268989I
a = 0.405828 − 1.016150I
b = 1.49765 + 0.09427I
−2.09894 − 3.64746I −14.7101 + 4.2800I
u = −0.638318 − 0.268989I
a = 0.405828 + 1.016150I
b = 1.49765 − 0.09427I
−2.09894 + 3.64746I −14.7101 − 4.2800I
u = −0.083637 + 1.344550I
a = −0.77219 + 1.92354I
b = −0.62622 + 1.38019I
2.73777 − 1.04981I 0
u = −0.083637 − 1.344550I
a = −0.77219 − 1.92354I
b = −0.62622 − 1.38019I
2.73777 + 1.04981I 0
u = −0.312075 + 1.325480I
a = 0.811130 − 1.137160I
b = 0.722128 − 0.253750I
−2.60689 − 3.35324I 0
u = −0.312075 − 1.325480I
a = 0.811130 + 1.137160I
b = 0.722128 + 0.253750I
−2.60689 + 3.35324I 0
7
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.545002 + 0.321138I
a = −0.082844 − 0.488685I
b = 0.990683 + 0.671822I
−4.59270 + 1.67311I −16.9582 + 0.3985I
u = 0.545002 − 0.321138I
a = −0.082844 + 0.488685I
b = 0.990683 − 0.671822I
−4.59270 − 1.67311I −16.9582 − 0.3985I
u = −0.325449 + 0.532358I
a = 0.59075 − 1.40862I
b = −0.224777 − 0.237458I
−1.49527 + 1.17529I −9.83671 − 1.84843I
u = −0.325449 − 0.532358I
a = 0.59075 + 1.40862I
b = −0.224777 + 0.237458I
−1.49527 − 1.17529I −9.83671 + 1.84843I
u = 0.044226 + 0.581685I
a = 0.42124 − 2.21522I
b = −0.434104 − 1.036480I
−0.913331 + 0.906579I −10.85003 − 0.71233I
u = 0.044226 − 0.581685I
a = 0.42124 + 2.21522I
b = −0.434104 + 1.036480I
−0.913331 − 0.906579I −10.85003 + 0.71233I
u = 0.08277 + 1.44936I
a = −2.31320 − 0.95840I
b = −2.80340 − 1.07180I
1.013510 − 0.325527I 0
u = 0.08277 − 1.44936I
a = −2.31320 + 0.95840I
b = −2.80340 + 1.07180I
1.013510 + 0.325527I 0
u = −0.382429 + 0.362260I
a = −0.434039 + 0.798270I
b = −1.72137 − 0.26154I
−3.09747 + 0.40995I −17.3230 − 6.9039I
u = −0.382429 − 0.362260I
a = −0.434039 − 0.798270I
b = −1.72137 + 0.26154I
−3.09747 − 0.40995I −17.3230 + 6.9039I
8
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.501836 + 0.000176I
a = 0.258344 + 0.412671I
b = −0.700497 − 0.288592I
−0.628535 + 0.108862I −11.90695 + 0.35188I
u = 0.501836 − 0.000176I
a = 0.258344 − 0.412671I
b = −0.700497 + 0.288592I
−0.628535 − 0.108862I −11.90695 − 0.35188I
u = −0.06225 + 1.50268I
a = 0.35254 − 2.42780I
b = 0.292023 − 1.218950I
−4.75549 + 1.52900I 0
u = −0.06225 − 1.50268I
a = 0.35254 + 2.42780I
b = 0.292023 + 1.218950I
−4.75549 − 1.52900I 0
u = −0.07068 + 1.52465I
a = 1.88422 − 0.82743I
b = 2.17873 − 0.30315I
3.33353 + 1.76863I 0
u = −0.07068 − 1.52465I
a = 1.88422 + 0.82743I
b = 2.17873 + 0.30315I
3.33353 − 1.76863I 0
u = −0.362675 + 0.286458I
a = 1.62379 + 2.91989I
b = −0.876997 + 0.508032I
−10.87560 + 0.29586I −20.8413 − 9.3211I
u = −0.362675 − 0.286458I
a = 1.62379 − 2.91989I
b = −0.876997 − 0.508032I
−10.87560 − 0.29586I −20.8413 + 9.3211I
u = −0.09170 + 1.56641I
a = 0.106439 + 0.604211I
b = 0.786542 + 0.160086I
5.71104 + 2.67349I 0
u = −0.09170 − 1.56641I
a = 0.106439 − 0.604211I
b = 0.786542 − 0.160086I
5.71104 − 2.67349I 0
9
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.04751 + 1.56902I
a = 0.61041 + 2.24346I
b = 0.99106 + 1.54336I
6.42184 + 0.33972I 0
u = 0.04751 − 1.56902I
a = 0.61041 − 2.24346I
b = 0.99106 − 1.54336I
6.42184 − 0.33972I 0
u = −0.11939 + 1.57046I
a = −0.79528 + 2.64599I
b = −1.06004 + 1.80892I
4.90324 + 4.54099I 0
u = −0.11939 − 1.57046I
a = −0.79528 − 2.64599I
b = −1.06004 − 1.80892I
4.90324 − 4.54099I 0
u = 0.14833 + 1.57361I
a = 0.473364 − 0.025225I
b = −0.351936 − 0.410786I
3.62172 − 7.75592I 0
u = 0.14833 − 1.57361I
a = 0.473364 + 0.025225I
b = −0.351936 + 0.410786I
3.62172 + 7.75592I 0
u = −0.16764 + 1.59281I
a = 1.15342 − 2.36244I
b = 1.61348 − 1.60654I
6.70349 + 10.40740I 0
u = −0.16764 − 1.59281I
a = 1.15342 + 2.36244I
b = 1.61348 + 1.60654I
6.70349 − 10.40740I 0
u = 0.12065 + 1.59882I
a = −0.96141 − 1.83317I
b = −1.43763 − 1.18663I
9.01239 − 4.83964I 0
u = 0.12065 − 1.59882I
a = −0.96141 + 1.83317I
b = −1.43763 + 1.18663I
9.01239 + 4.83964I 0
10
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.13360 + 1.59895I
a = −1.44072 + 0.67557I
b = −1.80299 − 0.01955I
−1.95351 + 4.80687I 0
u = −0.13360 − 1.59895I
a = −1.44072 − 0.67557I
b = −1.80299 + 0.01955I
−1.95351 − 4.80687I 0
u = −0.21190 + 1.59846I
a = −1.20844 + 2.04050I
b = −1.81241 + 1.29307I
0.8816 + 15.3259I 0
u = −0.21190 − 1.59846I
a = −1.20844 − 2.04050I
b = −1.81241 − 1.29307I
0.8816 − 15.3259I 0
u = 0.18569 + 1.61660I
a = 1.01642 + 1.53262I
b = 1.55579 + 0.86892I
3.86130 − 9.35513I 0
u = 0.18569 − 1.61660I
a = 1.01642 − 1.53262I
b = 1.55579 − 0.86892I
3.86130 + 9.35513I 0
u = −0.02145 + 1.62935I
a = 0.039433 − 0.379694I
b = −0.521747 − 0.073738I
10.84750 − 1.02517I 0
u = −0.02145 − 1.62935I
a = 0.039433 + 0.379694I
b = −0.521747 + 0.073738I
10.84750 + 1.02517I 0
u = 0.08779 + 1.62994I
a = −0.272775 + 0.123691I
b = 0.280139 + 0.277553I
9.99358 − 4.73908I 0
u = 0.08779 − 1.62994I
a = −0.272775 − 0.123691I
b = 0.280139 − 0.277553I
9.99358 + 4.73908I 0
11
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.355126
a = 0.787893
b = −0.561465
−0.670068 −14.5670
u = −0.273544
a = −0.903552
b = −2.51009
−2.88449 −51.7460
u = 0.04621 + 1.72842I
a = 0.110542 + 0.138918I
b = 0.197044 − 0.248926I
8.82291 − 3.58672I 0
u = 0.04621 − 1.72842I
a = 0.110542 − 0.138918I
b = 0.197044 + 0.248926I
8.82291 + 3.58672I 0
12
II. I
u
2
= h2u
4
− 3u
3
+ 8u
2
+ 3b − 7u + 5, 2u
4
− 3u
3
+ 8u
2
+ 3a − 7u +
5, u
5
− u
4
+ 4u
3
− 3u
2
+ 3u − 1i
(i) Arc colorings
a
5
=
1
0
a
8
=
0
u
a
4
=
1
−u
2
a
9
=
−u
u
3
+ u
a
3
=
u
2
+ 1
−u
4
− 2u
2
a
7
=
u
u
a
11
=
−
2
3
u
4
+ u
3
−
8
3
u
2
+
7
3
u −
5
3
−
2
3
u
4
+ u
3
−
8
3
u
2
+
7
3
u −
5
3
a
12
=
−
2
3
u
4
+ u
3
−
8
3
u
2
+
7
3
u −
5
3
−
2
3
u
4
+ u
3
−
8
3
u
2
+
7
3
u −
5
3
a
10
=
−
2
3
u
4
+ u
3
−
8
3
u
2
+
4
3
u −
5
3
−
2
3
u
4
+ 2u
3
+ ··· +
10
3
u −
5
3
a
6
=
u
u
a
2
=
u
3
+ 2u
−u
4
+ u
3
− 3u
2
+ 2u − 1
a
1
=
u
−u
3
− u
(ii) Obstruction class = 1
(iii) Cusp Shapes = −
14
9
u
4
+
11
3
u
3
−
77
9
u
2
+
88
9
u −
137
9
13
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
3
, c
4
u
5
− u
4
+ 4u
3
− 3u
2
+ 3u − 1
c
2
u
5
− u
4
+ u
2
+ u − 1
c
5
u
5
+ u
4
− u
2
+ u + 1
c
6
, c
11
u
5
c
7
, c
8
u
5
+ u
4
+ 4u
3
+ 3u
2
+ 3u + 1
c
9
, c
10
(u − 1)
5
c
12
(u + 1)
5
14
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
3
, c
4
c
7
, c
8
y
5
+ 7y
4
+ 16y
3
+ 13y
2
+ 3y −1
c
2
, c
5
y
5
− y
4
+ 4y
3
− 3y
2
+ 3y −1
c
6
, c
11
y
5
c
9
, c
10
, c
12
(y −1)
5
15
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.233677 + 0.885557I
a = 0.046507 + 0.815869I
b = 0.046507 + 0.815869I
0.17487 − 2.21397I −9.22580 + 4.04289I
u = 0.233677 − 0.885557I
a = 0.046507 − 0.815869I
b = 0.046507 − 0.815869I
0.17487 + 2.21397I −9.22580 − 4.04289I
u = 0.416284
a = −1.10533
b = −1.10533
−2.52712 −12.4170
u = 0.05818 + 1.69128I
a = 0.172825 − 0.649395I
b = 0.172825 − 0.649395I
9.31336 − 3.33174I −4.67696 − 1.07305I
u = 0.05818 − 1.69128I
a = 0.172825 + 0.649395I
b = 0.172825 + 0.649395I
9.31336 + 3.33174I −4.67696 + 1.07305I
16
III. I
u
3
= h−au + 11b − 8a + 4u − 1, 2a
2
+ au − 2a + 7u + 9, u
2
+ 2i
(i) Arc colorings
a
5
=
1
0
a
8
=
0
u
a
4
=
1
2
a
9
=
−u
−u
a
3
=
−1
0
a
7
=
u
u
a
11
=
a
0.0909091au + 0.727273a − 0.363636u + 0.0909091
a
12
=
0.181818au + 0.454545a − 0.727273u + 0.181818
0.272727au + 0.181818a − 1.09091u + 0.272727
a
10
=
−0.0909091au + 0.272727a − 1.13636u + 0.909091
−0.181818au + 0.545455a − 0.272727u + 0.818182
a
6
=
0.0909091au − 0.272727a − 0.863636u + 1.09091
1
a
2
=
0.0909091au − 0.272727a − 0.863636u + 0.0909091
1
a
1
=
0.0909091au − 0.272727a − 0.863636u + 1.09091
1
(ii) Obstruction class = 1
(iii) Cusp Shapes = −16
17
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
5
(u − 1)
4
c
2
(u + 1)
4
c
3
, c
4
, c
7
c
8
(u
2
+ 2)
2
c
6
, c
12
(u
2
− u − 1)
2
c
9
, c
10
, c
11
(u
2
+ u − 1)
2
18
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
2
, c
5
(y −1)
4
c
3
, c
4
, c
7
c
8
(y + 2)
4
c
6
, c
9
, c
10
c
11
, c
12
(y
2
− 3y + 1)
2
19
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = 1.414210I
a = −0.61803 + 2.01815I
b = −0.618034 + 0.874032I
−5.59278 −16.0000
u = 1.414210I
a = 1.61803 − 2.72526I
b = 1.61803 − 2.28825I
2.30291 −16.0000
u = − 1.414210I
a = −0.61803 − 2.01815I
b = −0.618034 − 0.874032I
−5.59278 −16.0000
u = − 1.414210I
a = 1.61803 + 2.72526I
b = 1.61803 + 2.28825I
2.30291 −16.0000
20
IV. I
v
1
= ha, b + v + 2, v
2
+ 3v + 1i
(i) Arc colorings
a
5
=
1
0
a
8
=
v
0
a
4
=
1
0
a
9
=
v
0
a
3
=
1
0
a
7
=
v
0
a
11
=
0
−v − 2
a
12
=
2v + 1
−v − 2
a
10
=
−2v − 1
−1
a
6
=
v
1
a
2
=
−v + 1
−1
a
1
=
−v
−1
(ii) Obstruction class = 1
(iii) Cusp Shapes = −6
21
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
2
(u − 1)
2
c
3
, c
4
, c
7
c
8
u
2
c
5
(u + 1)
2
c
6
, c
9
, c
10
u
2
+ u − 1
c
11
, c
12
u
2
− u − 1
22
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
2
, c
5
(y − 1)
2
c
3
, c
4
, c
7
c
8
y
2
c
6
, c
9
, c
10
c
11
, c
12
y
2
− 3y + 1
23
(vi) Complex Volumes and Cusp Shapes
Solutions to I
v
1
√
−1(vol +
√
−1CS) Cusp shape
v = −0.381966
a = 0
b = −1.61803
−2.63189 −6.00000
v = −2.61803
a = 0
b = 0.618034
−10.5276 −6.00000
24
V. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
(u − 1)
6
(u
5
− u
4
+ 4u
3
− 3u
2
+ 3u − 1)
· (u
74
+ 36u
73
+ ··· + 9145u + 361)
c
2
((u − 1)
2
)(u + 1)
4
(u
5
− u
4
+ ··· + u − 1)(u
74
+ 4u
73
+ ··· + 81u + 19)
c
3
, c
4
u
2
(u
2
+ 2)
2
(u
5
− u
4
+ ··· + 3u − 1)(u
74
− 2u
73
+ ··· + 20u − 4)
c
5
((u − 1)
4
)(u + 1)
2
(u
5
+ u
4
+ ··· + u + 1)(u
74
+ 4u
73
+ ··· + 81u + 19)
c
6
u
5
(u
2
− u − 1)
2
(u
2
+ u − 1)(u
74
− 2u
73
+ ··· + 768u − 288)
c
7
, c
8
u
2
(u
2
+ 2)
2
(u
5
+ u
4
+ ··· + 3u + 1)(u
74
− 2u
73
+ ··· + 20u − 4)
c
9
, c
10
((u − 1)
5
)(u
2
+ u − 1)
3
(u
74
− 9u
73
+ ··· + 76u + 9)
c
11
u
5
(u
2
− u − 1)(u
2
+ u − 1)
2
(u
74
− 2u
73
+ ··· + 768u − 288)
c
12
((u + 1)
5
)(u
2
− u − 1)
3
(u
74
− 9u
73
+ ··· + 76u + 9)
25
VI. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
(y − 1)
6
(y
5
+ 7y
4
+ 16y
3
+ 13y
2
+ 3y − 1)
· (y
74
+ 12y
73
+ ··· − 14397001y + 130321)
c
2
, c
5
(y − 1)
6
(y
5
− y
4
+ 4y
3
− 3y
2
+ 3y − 1)
· (y
74
− 36y
73
+ ··· − 9145y + 361)
c
3
, c
4
, c
7
c
8
y
2
(y + 2)
4
(y
5
+ 7y
4
+ 16y
3
+ 13y
2
+ 3y − 1)
· (y
74
+ 86y
73
+ ··· − 144y + 16)
c
6
, c
11
y
5
(y
2
− 3y + 1)
3
(y
74
− 42y
73
+ ··· − 2096640y + 82944)
c
9
, c
10
, c
12
((y − 1)
5
)(y
2
− 3y + 1)
3
(y
74
− 71y
73
+ ··· + 578y + 81)
26
