12n
0438
(K12n
0438
)
A knot diagram
1
Linearized knot diagam
3 6 12 10 2 4 11 3 6 7 8 9
Solving Sequence
3,8 9,11
12 4 1 7 6 2 5 10
c
8
c
11
c
3
c
12
c
7
c
6
c
2
c
5
c
10
c
1
, c
4
, c
9
Ideals for irreducible components
2
of X
par
I
u
1
= h9586u
11
− 3055u
10
+ ··· + 9038b − 18587, −55772u
11
+ 21076u
10
+ ··· + 4519a + 136449,
u
12
+ 9u
10
+ u
9
+ 13u
8
+ 3u
7
− 37u
6
− 8u
5
− u
4
+ 13u
3
+ 7u
2
− 2u − 1i
I
u
2
= h23u
7
− 19u
6
+ 114u
5
− 105u
4
+ 47u
3
− 42u
2
+ 83b − 10u − 77,
67u
7
− 77u
6
+ 379u
5
− 443u
4
+ 422u
3
− 310u
2
+ 83a + 191u − 347, u
8
+ 6u
6
+ 8u
4
+ 3u
3
+ 7u
2
+ u + 1i
I
u
3
= h220741u
11
+ 352170u
10
+ ··· + 4894159b + 8758441,
− 6799412u
11
+ 191458u
10
+ ··· + 4894159a + 38864844,
u
12
+ 13u
10
− u
9
+ 61u
8
− 7u
7
+ 121u
6
− 12u
5
+ 96u
4
− 21u
3
+ 34u
2
− 5u + 1i
I
u
4
= h−u
2
+ b + u − 1, −u
3
+ u
2
+ a − 2u + 2, u
4
− 2u
3
+ 3u
2
− 2u − 1i
I
u
5
= hb, a + u, u
2
+ u + 1i
* 5 irreducible components of dim
C
= 0, with total 38 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
= h9586u
11
− 3055u
10
+ · · · + 9038b − 18587, −55772u
11
+ 21076u
10
+
· · · + 4519a + 136449, u
12
+ 9u
10
+ · · · − 2u − 1i
(i) Arc colorings
a
3
=
0
u
a
8
=
1
0
a
9
=
1
−u
2
a
11
=
12.3417u
11
− 4.66386u
10
+ ··· + 18.7431u − 30.1945
−1.06063u
11
+ 0.338017u
10
+ ··· − 1.12669u + 2.05654
a
12
=
13.4023u
11
− 5.00188u
10
+ ··· + 19.8698u − 32.2511
−1.06063u
11
+ 0.338017u
10
+ ··· − 1.12669u + 2.05654
a
4
=
−7.52003u
11
+ 3.05964u
10
+ ··· − 7.40042u + 16.9010
−3.22129u
11
+ 1.14240u
10
+ ··· − 3.67039u + 7.94722
a
1
=
14.4826u
11
− 5.40407u
10
+ ··· + 22.1416u − 35.1964
−1.23069u
11
+ 0.347201u
10
+ ··· − 1.40263u + 2.45873
a
7
=
6.68843u
11
− 2.59150u
10
+ ··· + 10.4001u − 16.2423
−1.25880u
11
+ 0.629785u
10
+ ··· − 1.01427u + 3.32253
a
6
=
−7.16254u
11
+ 2.94534u
10
+ ··· − 8.99015u + 20.2930
−u
a
2
=
14.4826u
11
− 5.40407u
10
+ ··· + 22.1416u − 35.1964
1.08033u
11
− 0.402191u
10
+ ··· + 2.27185u − 2.94534
a
5
=
10.9114u
11
− 4.21122u
10
+ ··· + 11.3468u − 25.2504
3.39135u
11
− 1.15158u
10
+ ··· + 3.94634u − 8.34941
a
10
=
8.34941u
11
− 3.39135u
10
+ ··· + 12.1990u − 20.6452
0.402191u
11
− 0.170060u
10
+ ··· + 0.784687u − 1.08033
(ii) Obstruction class = −1
(iii) Cusp Shapes =
37615
9038
u
11
−
13351
4519
u
10
+
172836
4519
u
9
−
209101
9038
u
8
+
263227
4519
u
7
−
290229
9038
u
6
−
1386017
9038
u
5
+
583207
9038
u
4
−
56976
4519
u
3
+
639833
9038
u
2
−
58931
9038
u −
151555
9038
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
12
+ 37u
11
+ ··· + 6273u + 64
c
2
, c
5
u
12
+ 9u
11
+ ··· − 57u + 8
c
3
, c
6
u
12
− 2u
11
+ ··· − 3u − 1
c
4
, c
8
u
12
+ 9u
10
− u
9
+ 13u
8
− 3u
7
− 37u
6
+ 8u
5
− u
4
− 13u
3
+ 7u
2
+ 2u − 1
c
7
, c
10
, c
11
u
12
+ 6u
11
+ ··· + 7u − 2
c
9
, c
12
u
12
+ u
11
+ ··· + 36u + 1
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
12
− 233y
11
+ ··· − 38719361y + 4096
c
2
, c
5
y
12
− 37y
11
+ ··· − 6273y + 64
c
3
, c
6
y
12
− 6y
11
+ ··· + y + 1
c
4
, c
8
y
12
+ 18y
11
+ ··· − 18y + 1
c
7
, c
10
, c
11
y
12
− 12y
11
+ ··· − 109y + 4
c
9
, c
12
y
12
+ 45y
11
+ ··· − 670y + 1
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 1.04860
a = 3.26000
b = 1.86936
−8.03214 −11.1250
u = −1.19673
a = 0.457184
b = 1.40652
−6.56513 −13.9820
u = 0.785212
a = 0.538255
b = 1.39001
−3.33445 −1.37130
u = −0.237929 + 0.713496I
a = 0.839776 + 0.248914I
b = 0.549193 + 0.617015I
−0.28261 − 1.48442I −3.85780 + 2.07743I
u = −0.237929 − 0.713496I
a = 0.839776 − 0.248914I
b = 0.549193 − 0.617015I
−0.28261 + 1.48442I −3.85780 − 2.07743I
u = 0.413934
a = 1.40772
b = −0.208689
−1.36886 −8.24790
u = −0.398984 + 0.012900I
a = −1.37647 − 2.67835I
b = −0.666632 + 0.239214I
1.97549 − 2.44144I 0.80466 − 1.29895I
u = −0.398984 − 0.012900I
a = −1.37647 + 2.67835I
b = −0.666632 − 0.239214I
1.97549 + 2.44144I 0.80466 + 1.29895I
u = −0.05938 + 2.26410I
a = −1.045270 − 0.699289I
b = −0.85675 − 1.28813I
−15.6479 − 4.2966I −9.24517 + 3.48018I
u = −0.05938 − 2.26410I
a = −1.045270 + 0.699289I
b = −0.85675 + 1.28813I
−15.6479 + 4.2966I −9.24517 − 3.48018I
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.17079 + 2.29628I
a = 2.25039 + 0.29367I
b = 1.74558 − 0.39261I
15.3806 + 10.5658I −8.83901 − 3.88482I
u = 0.17079 − 2.29628I
a = 2.25039 − 0.29367I
b = 1.74558 + 0.39261I
15.3806 − 10.5658I −8.83901 + 3.88482I
6
II. I
u
2
= h23u
7
− 19u
6
+ · · · + 83b − 77, 67u
7
− 77u
6
+ · · · + 83a − 347, u
8
+
6u
6
+ 8u
4
+ 3u
3
+ 7u
2
+ u + 1i
(i) Arc colorings
a
3
=
0
u
a
8
=
1
0
a
9
=
1
−u
2
a
11
=
−0.807229u
7
+ 0.927711u
6
+ ··· − 2.30120u + 4.18072
−0.277108u
7
+ 0.228916u
6
+ ··· + 0.120482u + 0.927711
a
12
=
−0.530120u
7
+ 0.698795u
6
+ ··· − 2.42169u + 3.25301
−0.277108u
7
+ 0.228916u
6
+ ··· + 0.120482u + 0.927711
a
4
=
−1.74699u
7
− 0.469880u
6
+ ··· − 10.4578u − 3.32530
−0.301205u
7
− 0.0120482u
6
+ ··· − 2.21687u − 0.469880
a
1
=
−0.819277u
7
+ 0.807229u
6
+ ··· − 2.46988u + 3.48193
−0.361446u
7
+ 0.385542u
6
+ ··· − 0.0602410u + 1.03614
a
7
=
0.542169u
7
− 0.578313u
6
+ ··· + 1.59036u − 2.55422
0.0722892u
7
− 0.277108u
6
+ ··· + 0.0120482u − 0.807229
a
6
=
−1.27711u
7
+ 0.228916u
6
+ ··· − 6.87952u + 0.927711
−u
a
2
=
−0.819277u
7
+ 0.807229u
6
+ ··· − 2.46988u + 3.48193
−0.289157u
7
+ 0.108434u
6
+ ··· − 0.0481928u + 0.228916
a
5
=
−1.96386u
7
− 0.638554u
6
+ ··· − 12.4940u − 3.90361
−0.216867u
7
− 0.168675u
6
+ ··· − 2.03614u − 0.578313
a
10
=
−0.578313u
7
+ 0.216867u
6
+ ··· − 2.09639u + 1.45783
−0.108434u
7
− 0.0843373u
6
+ ··· − 0.518072u − 0.289157
(ii) Obstruction class = 1
(iii) Cusp Shapes =
277
83
u
7
+
114
83
u
6
+
1640
83
u
5
+
547
83
u
4
+
2042
83
u
3
+
999
83
u
2
+
2052
83
u −
285
83
7
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
8
− 8u
7
+ 18u
6
− 9u
5
+ 31u
4
+ 18u
3
+ 14u
2
+ 3u + 1
c
2
u
8
+ 6u
7
+ 14u
6
+ 17u
5
+ 13u
4
+ 8u
3
+ 6u
2
+ 3u + 1
c
3
, c
6
u
8
+ 2u
7
+ 2u
6
− 2u
4
− 3u
3
+ 2u + 1
c
4
, c
8
u
8
+ 6u
6
+ 8u
4
+ 3u
3
+ 7u
2
+ u + 1
c
5
u
8
− 6u
7
+ 14u
6
− 17u
5
+ 13u
4
− 8u
3
+ 6u
2
− 3u + 1
c
7
u
8
+ 3u
7
+ u
6
− 3u
5
+ u
3
− 4u
2
− u + 3
c
9
, c
12
u
8
− u
7
+ 8u
6
− u
5
+ 14u
4
+ 5u
3
+ 7u
2
+ 5u + 1
c
10
, c
11
u
8
− 3u
7
+ u
6
+ 3u
5
− u
3
− 4u
2
+ u + 3
8
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
8
− 28y
7
+ 242y
6
+ 1351y
5
+ 1839y
4
+ 634y
3
+ 150y
2
+ 19y + 1
c
2
, c
5
y
8
− 8y
7
+ 18y
6
− 9y
5
+ 31y
4
+ 18y
3
+ 14y
2
+ 3y + 1
c
3
, c
6
y
8
+ 4y
5
− 2y
4
− 5y
3
+ 8y
2
− 4y + 1
c
4
, c
8
y
8
+ 12y
7
+ 52y
6
+ 110y
5
+ 150y
4
+ 115y
3
+ 59y
2
+ 13y + 1
c
7
, c
10
, c
11
y
8
− 7y
7
+ 19y
6
− 23y
5
+ 10y
4
− y
3
+ 18y
2
− 25y + 9
c
9
, c
12
y
8
+ 15y
7
+ 90y
6
+ 247y
5
+ 330y
4
+ 197y
3
+ 27y
2
− 11y + 1
9
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.452128 + 0.754240I
a = 0.281547 + 0.149763I
b = 0.364928 + 0.928632I
−0.91626 − 2.11958I −9.09548 + 6.29610I
u = −0.452128 − 0.754240I
a = 0.281547 − 0.149763I
b = 0.364928 − 0.928632I
−0.91626 + 2.11958I −9.09548 − 6.29610I
u = 0.588231 + 1.086850I
a = −1.70900 − 0.76306I
b = −1.56785 + 0.26923I
−7.73259 + 6.48719I −6.82312 − 5.90005I
u = 0.588231 − 1.086850I
a = −1.70900 + 0.76306I
b = −1.56785 − 0.26923I
−7.73259 − 6.48719I −6.82312 + 5.90005I
u = −0.051535 + 0.424185I
a = 3.68516 − 0.74169I
b = 0.862997 + 0.073353I
1.63676 − 2.95067I −6.12574 + 8.48868I
u = −0.051535 − 0.424185I
a = 3.68516 + 0.74169I
b = 0.862997 − 0.073353I
1.63676 + 2.95067I −6.12574 − 8.48868I
u = −0.08457 + 2.15179I
a = −1.257710 − 0.086043I
b = −1.160080 − 0.491572I
−14.3720 − 2.0722I −9.45567 + 2.68473I
u = −0.08457 − 2.15179I
a = −1.257710 + 0.086043I
b = −1.160080 + 0.491572I
−14.3720 + 2.0722I −9.45567 − 2.68473I
10
III.
I
u
3
= h2.21 × 10
5
u
11
+ 3.52 × 10
5
u
10
+ · · · + 4.89 × 10
6
b + 8.76 × 10
6
, −6.80 ×
10
6
u
11
+1.91×10
5
u
10
+· · ·+4.89×10
6
a+3.89×10
7
, u
12
+13u
10
+· · ·−5u+1i
(i) Arc colorings
a
3
=
0
u
a
8
=
1
0
a
9
=
1
−u
2
a
11
=
1.38929u
11
− 0.0391197u
10
+ ··· + 43.9779u − 7.94107
−0.0451029u
11
− 0.0719572u
10
+ ··· − 0.177550u − 1.78957
a
12
=
1.43439u
11
+ 0.0328375u
10
+ ··· + 44.1554u − 6.15150
−0.0451029u
11
− 0.0719572u
10
+ ··· − 0.177550u − 1.78957
a
4
=
1.86149u
11
+ 0.0277566u
10
+ ··· + 56.7778u − 7.54448
−0.0255782u
11
− 0.108973u
10
+ ··· + 1.02646u − 2.23971
a
1
=
1.35518u
11
− 0.0779405u
10
+ ··· + 42.7077u − 7.97390
−0.0413761u
11
− 0.131233u
10
+ ··· + 0.297122u − 1.90035
a
7
=
2.16779u
11
− 0.0984377u
10
+ ··· + 66.0594u − 12.7530
−0.0719229u
11
− 0.0728595u
10
+ ··· − 2.91466u − 2.58092
a
6
=
0.740548u
11
+ 0.241490u
10
+ ··· + 20.0889u + 4.36298
0.434394u
11
+ 0.0328375u
10
+ ··· + 11.1554u − 1.15150
a
2
=
1.35518u
11
− 0.0779405u
10
+ ··· + 42.7077u − 7.97390
−0.0792181u
11
− 0.110778u
10
+ ··· − 1.44776u − 1.82241
a
5
=
2.02148u
11
+ 0.591926u
10
+ ··· + 56.7443u + 8.63238
0.902855u
11
+ 0.0689238u
10
+ ··· + 24.8073u − 2.82600
a
10
=
−1.74447u
11
+ 0.117060u
10
+ ··· − 53.6856u + 13.9150
0.286593u
11
+ 0.0646620u
10
+ ··· + 8.24327u + 2.04902
(ii) Obstruction class = −1
(iii) Cusp Shapes =
1038229
4894159
u
11
−
453029
4894159
u
10
+ ··· +
62859079
4894159
u −
46129032
4894159
11
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
(u
6
+ 8u
5
− 53u
3
+ 58u
2
− 15u + 9)
2
c
2
, c
5
(u
6
− 4u
5
+ 4u
4
− 3u
3
+ 4u
2
+ 3u + 3)
2
c
3
, c
6
u
12
− 4u
11
+ ··· + u + 1
c
4
, c
8
u
12
+ 13u
10
+ ··· + 5u + 1
c
7
, c
10
, c
11
(u
6
− u
5
− 4u
4
+ 3u
3
+ 4u
2
− 2)
2
c
9
, c
12
u
12
− 3u
11
+ ··· − 8u + 173
12
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
(y
6
− 64y
5
+ 964y
4
− 2551y
3
+ 1774y
2
+ 819y + 81)
2
c
2
, c
5
(y
6
− 8y
5
+ 53y
3
+ 58y
2
+ 15y + 9)
2
c
3
, c
6
y
12
− 2y
11
+ ··· + 23y + 1
c
4
, c
8
y
12
+ 26y
11
+ ··· + 43y + 1
c
7
, c
10
, c
11
(y
6
− 9y
5
+ 30y
4
− 45y
3
+ 32y
2
− 16y + 4)
2
c
9
, c
12
y
12
+ 29y
11
+ ··· + 170514y + 29929
13
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = −0.374731 + 0.890342I
a = 1.185720 − 0.141464I
b = 0.629305 + 0.469465I
−0.31318 − 1.57342I −5.93222 + 3.43140I
u = −0.374731 − 0.890342I
a = 1.185720 + 0.141464I
b = 0.629305 − 0.469465I
−0.31318 + 1.57342I −5.93222 − 3.43140I
u = 0.219901 + 0.674731I
a = 0.347492 + 0.244157I
b = 0.629305 + 0.469465I
−0.31318 − 1.57342I −5.93222 + 3.43140I
u = 0.219901 − 0.674731I
a = 0.347492 − 0.244157I
b = 0.629305 − 0.469465I
−0.31318 + 1.57342I −5.93222 − 3.43140I
u = 0.32643 + 1.59597I
a = −2.15982 − 0.63392I
b = −1.63022 + 0.19616I
−8.12771 + 4.22943I −8.28340 − 1.79030I
u = 0.32643 − 1.59597I
a = −2.15982 + 0.63392I
b = −1.63022 − 0.19616I
−8.12771 − 4.22943I −8.28340 + 1.79030I
u = 0.080159 + 0.164473I
a = −4.43127 + 6.14837I
b = −1.63022 − 0.19616I
−8.12771 − 4.22943I −8.28340 + 1.79030I
u = 0.080159 − 0.164473I
a = −4.43127 − 6.14837I
b = −1.63022 + 0.19616I
−8.12771 + 4.22943I −8.28340 − 1.79030I
u = −0.37385 + 2.16844I
a = 2.53178 + 0.44785I
b = 1.70687
16.3722 −8.87611 + 0.I
u = −0.37385 − 2.16844I
a = 2.53178 − 0.44785I
b = 1.70687
16.3722 −8.87611 + 0.I
14
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = 0.12209 + 2.22085I
a = −0.973901 + 0.448921I
b = −0.705047
−14.2948 −8.69265 + 0.I
u = 0.12209 − 2.22085I
a = −0.973901 − 0.448921I
b = −0.705047
−14.2948 −8.69265 + 0.I
15
IV. I
u
4
= h−u
2
+ b + u − 1, −u
3
+ u
2
+ a − 2u + 2, u
4
− 2u
3
+ 3u
2
− 2u − 1i
(i) Arc colorings
a
3
=
0
u
a
8
=
1
0
a
9
=
1
−u
2
a
11
=
u
3
− u
2
+ 2u − 2
u
2
− u + 1
a
12
=
u
3
− 2u
2
+ 3u − 3
u
2
− u + 1
a
4
=
−u
3
+ 2u
2
− 4u + 4
u
3
− 2u
2
+ 3u − 1
a
1
=
u
3
− 2u
2
+ 3u − 2
−u + 1
a
7
=
−u
3
+ 3u
2
− 5u + 3
−2
a
6
=
−u
3
+ 2u
2
− 3u + 2
u − 1
a
2
=
u
3
− 2u
2
+ 3u − 2
1
a
5
=
0
u
a
10
=
−u
3
+ 2u
2
− 3u + 3
−u
2
+ u − 1
(ii) Obstruction class = 1
(iii) Cusp Shapes = −8
16
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
2
(u − 1)
4
c
3
, c
6
u
4
+ 2u
3
+ 3u
2
+ 2u − 1
c
4
, c
8
u
4
− 2u
3
+ 3u
2
− 2u − 1
c
5
, c
9
, c
12
(u + 1)
4
c
7
, c
10
, c
11
(u
2
− 2)
2
17
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
2
, c
5
c
9
, c
12
(y − 1)
4
c
3
, c
4
, c
6
c
8
y
4
+ 2y
3
− y
2
− 10y + 1
c
7
, c
10
, c
11
(y − 2)
4
18
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
4
√
−1(vol +
√
−1CS) Cusp shape
u = 1.31499
a = 1.17467
b = 1.41421
−4.93480 −8.00000
u = 0.50000 + 1.47113I
a = −2.20711 − 0.60936I
b = −1.41421
−4.93480 −8.00000
u = 0.50000 − 1.47113I
a = −2.20711 + 0.60936I
b = −1.41421
−4.93480 −8.00000
u = −0.314993
a = −2.76046
b = 1.41421
−4.93480 −8.00000
19
V. I
u
5
= hb, a + u, u
2
+ u + 1i
(i) Arc colorings
a
3
=
0
u
a
8
=
1
0
a
9
=
1
u + 1
a
11
=
−u
0
a
12
=
−u
0
a
4
=
−1
u
a
1
=
−u − 1
−u − 1
a
7
=
1
0
a
6
=
u + 1
u + 1
a
2
=
−u − 1
−1
a
5
=
0
u
a
10
=
−u
0
(ii) Obstruction class = 1
(iii) Cusp Shapes = −6
20
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
2
, c
9
c
12
(u − 1)
2
c
3
, c
4
, c
6
c
8
u
2
+ u + 1
c
5
(u + 1)
2
c
7
, c
10
, c
11
u
2
21
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
2
, c
5
c
9
, c
12
(y − 1)
2
c
3
, c
4
, c
6
c
8
y
2
+ y + 1
c
7
, c
10
, c
11
y
2
22
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
5
√
−1(vol +
√
−1CS) Cusp shape
u = −0.500000 + 0.866025I
a = 0.500000 − 0.866025I
b = 0
0 −6.00000
u = −0.500000 − 0.866025I
a = 0.500000 + 0.866025I
b = 0
0 −6.00000
23
VI. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
(u − 1)
6
(u
6
+ 8u
5
− 53u
3
+ 58u
2
− 15u + 9)
2
· (u
8
− 8u
7
+ 18u
6
− 9u
5
+ 31u
4
+ 18u
3
+ 14u
2
+ 3u + 1)
· (u
12
+ 37u
11
+ ··· + 6273u + 64)
c
2
(u − 1)
6
(u
6
− 4u
5
+ 4u
4
− 3u
3
+ 4u
2
+ 3u + 3)
2
· (u
8
+ 6u
7
+ 14u
6
+ 17u
5
+ 13u
4
+ 8u
3
+ 6u
2
+ 3u + 1)
· (u
12
+ 9u
11
+ ··· − 57u + 8)
c
3
, c
6
(u
2
+ u + 1)(u
4
+ 2u
3
+ ··· + 2u − 1)(u
8
+ 2u
7
+ ··· + 2u + 1)
· (u
12
− 4u
11
+ ··· + u + 1)(u
12
− 2u
11
+ ··· − 3u − 1)
c
4
, c
8
(u
2
+ u + 1)(u
4
− 2u
3
+ ··· − 2u − 1)(u
8
+ 6u
6
+ ··· + u + 1)
· (u
12
+ 9u
10
− u
9
+ 13u
8
− 3u
7
− 37u
6
+ 8u
5
− u
4
− 13u
3
+ 7u
2
+ 2u − 1)
· (u
12
+ 13u
10
+ ··· + 5u + 1)
c
5
(u + 1)
6
(u
6
− 4u
5
+ 4u
4
− 3u
3
+ 4u
2
+ 3u + 3)
2
· (u
8
− 6u
7
+ 14u
6
− 17u
5
+ 13u
4
− 8u
3
+ 6u
2
− 3u + 1)
· (u
12
+ 9u
11
+ ··· − 57u + 8)
c
7
u
2
(u
2
− 2)
2
(u
6
− u
5
− 4u
4
+ 3u
3
+ 4u
2
− 2)
2
· (u
8
+ 3u
7
+ ··· − u + 3)(u
12
+ 6u
11
+ ··· + 7u − 2)
c
9
, c
12
(u − 1)
2
(u + 1)
4
(u
8
− u
7
+ 8u
6
− u
5
+ 14u
4
+ 5u
3
+ 7u
2
+ 5u + 1)
· (u
12
− 3u
11
+ ··· − 8u + 173)(u
12
+ u
11
+ ··· + 36u + 1)
c
10
, c
11
u
2
(u
2
− 2)
2
(u
6
− u
5
− 4u
4
+ 3u
3
+ 4u
2
− 2)
2
· (u
8
− 3u
7
+ ··· + u + 3)(u
12
+ 6u
11
+ ··· + 7u − 2)
24
VII. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
(y − 1)
6
(y
6
− 64y
5
+ 964y
4
− 2551y
3
+ 1774y
2
+ 819y + 81)
2
· (y
8
− 28y
7
+ 242y
6
+ 1351y
5
+ 1839y
4
+ 634y
3
+ 150y
2
+ 19y + 1)
· (y
12
− 233y
11
+ ··· − 38719361y + 4096)
c
2
, c
5
(y − 1)
6
(y
6
− 8y
5
+ 53y
3
+ 58y
2
+ 15y + 9)
2
· (y
8
− 8y
7
+ 18y
6
− 9y
5
+ 31y
4
+ 18y
3
+ 14y
2
+ 3y + 1)
· (y
12
− 37y
11
+ ··· − 6273y + 64)
c
3
, c
6
(y
2
+ y + 1)(y
4
+ 2y
3
+ ··· − 10y + 1)(y
8
+ 4y
5
+ ··· − 4y + 1)
· (y
12
− 6y
11
+ ··· + y + 1)(y
12
− 2y
11
+ ··· + 23y + 1)
c
4
, c
8
(y
2
+ y + 1)(y
4
+ 2y
3
− y
2
− 10y + 1)
· (y
8
+ 12y
7
+ 52y
6
+ 110y
5
+ 150y
4
+ 115y
3
+ 59y
2
+ 13y + 1)
· (y
12
+ 18y
11
+ ··· − 18y + 1)(y
12
+ 26y
11
+ ··· + 43y + 1)
c
7
, c
10
, c
11
y
2
(y − 2)
4
(y
6
− 9y
5
+ 30y
4
− 45y
3
+ 32y
2
− 16y + 4)
2
· (y
8
− 7y
7
+ 19y
6
− 23y
5
+ 10y
4
− y
3
+ 18y
2
− 25y + 9)
· (y
12
− 12y
11
+ ··· − 109y + 4)
c
9
, c
12
(y − 1)
6
· (y
8
+ 15y
7
+ 90y
6
+ 247y
5
+ 330y
4
+ 197y
3
+ 27y
2
− 11y + 1)
· (y
12
+ 29y
11
+ ··· + 170514y + 29929)(y
12
+ 45y
11
+ ··· − 670y + 1)
25
