12a
0828
(K12a
0828
)
A knot diagram
1
Linearized knot diagam
4 5 8 2 10 12 3 11 6 1 7 9
Solving Sequence
3,7
8
4,11
9 12 1 6 10 5 2
c
7
c
3
c
8
c
11
c
12
c
6
c
9
c
5
c
2
c
1
, c
4
, c
10
Ideals for irreducible components
2
of X
par
I
u
1
= h1.48295 × 10
68
u
41
+ 7.81857 × 10
68
u
40
+ ··· + 7.16827 × 10
67
b − 2.61630 × 10
70
,
− 1.00081 × 10
69
u
41
− 5.50129 × 10
69
u
40
+ ··· + 5.73462 × 10
68
a + 2.57458 × 10
71
,
u
42
+ 6u
41
+ ··· − 608u − 128i
I
u
2
= h46u
7
a
3
− 35u
7
a
2
+ ··· + 42a − 8, 6u
7
a
3
+ 22u
7
a
2
+ ··· − 74a + 151,
u
8
− 3u
7
+ 3u
6
+ 2u
5
− 8u
4
+ 9u
3
− 3u
2
− 2u + 2i
I
u
3
= h−2543842u
17
− 14606334u
16
+ ··· + 48416059b + 19223447,
− 118380102u
17
− 83676763u
16
+ ··· + 48416059a − 243963069, u
18
+ u
17
+ ··· + u − 1i
I
u
4
= h9.40126 × 10
20
a
7
u
5
− 1.79850 × 10
21
a
6
u
5
+ ··· − 8.65728 × 10
21
a + 3.41117 × 10
21
,
− 2a
7
u
5
− 15a
6
u
5
+ ··· − 17a + 4, u
6
+ u
5
− u
4
− 2u
3
+ u + 1i
I
v
1
= ha, 8v
2
+ b + 26v + 7, 4v
3
+ 14v
2
+ 7v + 1i
I
v
2
= ha, b
4
+ b
3
+ 2b
2
+ 2b + 1, v −1i
* 6 irreducible components of dim
C
= 0, with total 147 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
= h1.48 × 10
68
u
41
+ 7.82 × 10
68
u
40
+ · · · + 7.17 × 10
67
b − 2.62 ×
10
70
, −1.00 × 10
69
u
41
− 5.50 × 10
69
u
40
+ · · · + 5.73 × 10
68
a + 2.57 ×
10
71
, u
42
+ 6u
41
+ · · · − 608u − 128i
(i) Arc colorings
a
3
=
0
u
a
7
=
1
0
a
8
=
1
u
2
a
4
=
−u
−u
3
+ u
a
11
=
1.74520u
41
+ 9.59312u
40
+ ··· − 1224.97u − 448.953
−2.06877u
41
− 10.9072u
40
+ ··· + 1234.36u + 364.984
a
9
=
5.46026u
41
+ 28.9099u
40
+ ··· − 3303.48u − 1037.79
−0.875191u
41
− 4.68441u
40
+ ··· + 555.689u + 190.129
a
12
=
3.81397u
41
+ 20.5003u
40
+ ··· − 2459.34u − 813.937
−2.06877u
41
− 10.9072u
40
+ ··· + 1234.36u + 364.984
a
1
=
−4.29657u
41
− 22.4006u
40
+ ··· + 2436.80u + 697.290
0.303303u
41
+ 1.95238u
40
+ ··· − 355.882u − 170.418
a
6
=
−1.88477u
41
− 9.85936u
40
+ ··· + 1085.97u + 325.842
−1.16502u
41
− 5.92185u
40
+ ··· + 584.581u + 132.111
a
10
=
3.30608u
41
+ 17.3565u
40
+ ··· − 1920.32u − 597.894
−0.0369235u
41
+ 0.105769u
40
+ ··· − 130.892u − 62.0948
a
5
=
−1.33567u
41
− 6.59646u
40
+ ··· + 576.521u + 94.3766
−2.96090u
41
− 15.8041u
40
+ ··· + 1860.27u + 602.914
a
2
=
−3.00789u
41
− 15.7631u
40
+ ··· + 1745.87u + 515.839
−0.0851750u
41
− 0.0145890u
40
+ ··· − 165.539u − 129.080
(ii) Obstruction class = −1
(iii) Cusp Shapes = 50.5421u
41
+ 265.980u
40
+ ··· − 29786.7u − 9077.56
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
2
, c
4
u
42
− 3u
41
+ ··· + 140u + 16
c
3
, c
7
u
42
− 6u
41
+ ··· + 608u − 128
c
5
, c
6
, c
9
c
11
u
42
+ 16u
40
+ ··· + u − 1
c
8
, c
10
u
42
+ 2u
41
+ ··· + 2u + 1
c
12
u
42
+ 39u
41
+ ··· + 24641536u + 1048576
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
2
, c
4
y
42
− 37y
41
+ ··· − 7536y + 256
c
3
, c
7
y
42
− 18y
41
+ ··· − 388096y + 16384
c
5
, c
6
, c
9
c
11
y
42
+ 32y
41
+ ··· − 19y + 1
c
8
, c
10
y
42
− 2y
41
+ ··· − 52y + 1
c
12
y
42
− y
41
+ ··· − 16217796509696y + 1099511627776
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.943550 + 0.455289I
a = −1.34280 + 0.76709I
b = −0.753628 + 0.162890I
−1.59198 − 3.61998I −15.2323 + 5.2048I
u = 0.943550 − 0.455289I
a = −1.34280 − 0.76709I
b = −0.753628 − 0.162890I
−1.59198 + 3.61998I −15.2323 − 5.2048I
u = −0.269584 + 0.910303I
a = 0.762837 + 0.613812I
b = 0.657573 − 0.228220I
−4.18007 − 1.80472I −18.2389 + 0.1966I
u = −0.269584 − 0.910303I
a = 0.762837 − 0.613812I
b = 0.657573 + 0.228220I
−4.18007 + 1.80472I −18.2389 − 0.1966I
u = 0.062598 + 1.055270I
a = −0.046684 + 0.319719I
b = −0.250114 − 1.286520I
7.85485 − 3.56337I −2.67014 + 3.62743I
u = 0.062598 − 1.055270I
a = −0.046684 − 0.319719I
b = −0.250114 + 1.286520I
7.85485 + 3.56337I −2.67014 − 3.62743I
u = 0.466056 + 0.981999I
a = −0.048754 − 0.335975I
b = −0.41161 + 1.40369I
8.88785 + 7.82161I −5.25158 − 5.23582I
u = 0.466056 − 0.981999I
a = −0.048754 + 0.335975I
b = −0.41161 − 1.40369I
8.88785 − 7.82161I −5.25158 + 5.23582I
u = −0.786496 + 0.002563I
a = −2.39632 + 0.05081I
b = −0.465074 − 0.281780I
−2.91939 − 0.16667I −21.2268 + 8.1932I
u = −0.786496 − 0.002563I
a = −2.39632 − 0.05081I
b = −0.465074 + 0.281780I
−2.91939 + 0.16667I −21.2268 − 8.1932I
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −1.184420 + 0.429182I
a = 0.697295 + 0.202000I
b = 0.812246 + 0.378376I
−5.91413 + 2.39057I 0
u = −1.184420 − 0.429182I
a = 0.697295 − 0.202000I
b = 0.812246 − 0.378376I
−5.91413 − 2.39057I 0
u = 1.253720 + 0.213033I
a = −1.287820 + 0.268400I
b = −0.606517 − 0.635131I
−9.38202 − 1.73644I 0
u = 1.253720 − 0.213033I
a = −1.287820 − 0.268400I
b = −0.606517 + 0.635131I
−9.38202 + 1.73644I 0
u = −1.171280 + 0.521960I
a = 1.69502 − 0.32871I
b = 0.49391 − 1.37449I
4.28505 + 8.46529I 0
u = −1.171280 − 0.521960I
a = 1.69502 + 0.32871I
b = 0.49391 + 1.37449I
4.28505 − 8.46529I 0
u = −1.183490 + 0.564393I
a = −1.075040 − 0.521185I
b = −0.905363 − 0.213820I
−7.00695 + 7.14218I 0
u = −1.183490 − 0.564393I
a = −1.075040 + 0.521185I
b = −0.905363 + 0.213820I
−7.00695 − 7.14218I 0
u = 0.582949 + 0.315976I
a = 0.876169 − 0.195926I
b = 0.539552 − 0.112152I
−0.538615 − 0.005437I −12.84477 − 0.43346I
u = 0.582949 − 0.315976I
a = 0.876169 + 0.195926I
b = 0.539552 + 0.112152I
−0.538615 + 0.005437I −12.84477 + 0.43346I
6
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.610840 + 1.193460I
a = −0.054193 + 0.342180I
b = −0.52479 − 1.40750I
3.43638 − 11.55830I 0
u = −0.610840 − 1.193460I
a = −0.054193 − 0.342180I
b = −0.52479 + 1.40750I
3.43638 + 11.55830I 0
u = 1.163520 + 0.689411I
a = 1.72107 − 0.08499I
b = 0.52703 + 1.44729I
6.7272 − 13.9058I 0
u = 1.163520 − 0.689411I
a = 1.72107 + 0.08499I
b = 0.52703 − 1.44729I
6.7272 + 13.9058I 0
u = 0.534889 + 1.254550I
a = 0.262606 − 0.299605I
b = −0.206473 + 0.740584I
−1.23399 + 1.54080I 0
u = 0.534889 − 1.254550I
a = 0.262606 + 0.299605I
b = −0.206473 − 0.740584I
−1.23399 − 1.54080I 0
u = −0.535582 + 0.088545I
a = −0.050104 + 0.333280I
b = −0.22875 − 1.51299I
7.50056 − 5.01376I −21.5440 − 1.4253I
u = −0.535582 − 0.088545I
a = −0.050104 − 0.333280I
b = −0.22875 + 1.51299I
7.50056 + 5.01376I −21.5440 + 1.4253I
u = −1.22163 + 0.80316I
a = 1.55023 + 0.27538I
b = 0.56950 − 1.48815I
1.4008 + 18.6869I 0
u = −1.22163 − 0.80316I
a = 1.55023 − 0.27538I
b = 0.56950 + 1.48815I
1.4008 − 18.6869I 0
7
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −1.17869 + 0.90581I
a = −0.942618 − 0.308680I
b = −0.163308 + 1.189210I
−0.91717 + 9.50337I 0
u = −1.17869 − 0.90581I
a = −0.942618 + 0.308680I
b = −0.163308 − 1.189210I
−0.91717 − 9.50337I 0
u = −0.491641
a = −4.91091
b = −0.343981
−2.80521 −47.0160
u = 1.20729 + 0.91942I
a = −0.752800 + 0.170890I
b = −0.065111 − 1.139040I
4.02842 − 4.18037I 0
u = 1.20729 − 0.91942I
a = −0.752800 − 0.170890I
b = −0.065111 + 1.139040I
4.02842 + 4.18037I 0
u = 1.48911 + 0.29406I
a = 0.896680 + 0.297454I
b = 0.617444 + 1.108590I
−6.18728 − 8.08758I 0
u = 1.48911 − 0.29406I
a = 0.896680 − 0.297454I
b = 0.617444 − 1.108590I
−6.18728 + 8.08758I 0
u = −1.50353 + 0.22766I
a = 0.444601 − 0.413741I
b = 0.308344 − 0.976227I
1.53844 + 4.49579I 0
u = −1.50353 − 0.22766I
a = 0.444601 + 0.413741I
b = 0.308344 + 0.976227I
1.53844 − 4.49579I 0
u = −1.01992 + 1.13548I
a = −0.362994 − 0.380675I
b = 0.031656 + 1.071510I
0.04635 − 1.77468I 0
8
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −1.01992 − 1.13548I
a = −0.362994 + 0.380675I
b = 0.031656 − 1.071510I
0.04635 + 1.77468I 0
u = 0.415199
a = 0.943147
b = 0.390970
−0.638593 −15.1720
9
II. I
u
2
= h46u
7
a
3
− 35u
7
a
2
+ · · · + 42a − 8, 6u
7
a
3
+ 22u
7
a
2
+ · · · − 74a +
151, u
8
− 3u
7
+ · · · − 2u + 2i
(i) Arc colorings
a
3
=
0
u
a
7
=
1
0
a
8
=
1
u
2
a
4
=
−u
−u
3
+ u
a
11
=
a
−1.58621a
3
u
7
+ 1.20690a
2
u
7
+ ··· − 1.44828a + 0.275862
a
9
=
−0.793103a
3
u
7
+ 0.206897a
2
u
7
+ ··· + 0.275862a − 5.72414
−0.206897a
2
u
7
− 0.896552u
7
+ ··· + 0.551724a
2
− 0.275862
a
12
=
1.58621a
3
u
7
− 1.20690a
2
u
7
+ ··· + 2.44828a − 0.275862
−1.58621a
3
u
7
+ 1.20690a
2
u
7
+ ··· − 1.44828a + 0.275862
a
1
=
3
2
u
7
−
7
2
u
6
+ ··· +
3
2
u − 3
−u
7
+ 2u
6
− u
5
− 3u
4
+ 5u
3
− 3u
2
− u + 1
a
6
=
1.03448a
3
u
7
− 1.17241a
2
u
7
+ ··· − 4.62069a + 5.10345
−0.241379a
3
u
7
+ 0.965517a
2
u
7
+ ··· + 4.34483a + 2.62069
a
10
=
−1.58621a
3
u
7
+ 1.20690a
2
u
7
+ ··· + 3.55172a − 5.72414
0.586207a
3
u
7
− 0.206897a
2
u
7
+ ··· − 4.55172a + 2.72414
a
5
=
1
2
u
7
−
1
2
u
6
+ ··· −
1
2
u
2
+
3
2
u
u
7
− 3u
6
+ 2u
5
+ 3u
4
− 8u
3
+ 6u
2
− 3
a
2
=
1
2
u
7
−
3
2
u
6
+ ··· +
1
2
u − 1
−u
7
+ 2u
6
− 3u
4
+ 4u
3
− 2u
2
+ 1
(ii) Obstruction class = −1
(iii) Cusp Shapes = −
48
29
u
7
a
3
+
92
29
u
7
a
2
+ ··· −
64
29
a −
264
29
10
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
2
, c
4
(u
8
− u
7
− 4u
6
+ 3u
5
+ 5u
4
− u
3
− u
2
− 3u − 1)
4
c
3
, c
7
(u
8
+ 3u
7
+ 3u
6
− 2u
5
− 8u
4
− 9u
3
− 3u
2
+ 2u + 2)
4
c
5
, c
6
, c
9
c
11
u
32
+ u
31
+ ··· − 108u + 19
c
8
, c
10
u
32
− 7u
31
+ ··· − 148u + 13
c
12
(u
2
− u + 1)
16
11
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
2
, c
4
(y
8
− 9y
7
+ 32y
6
− 53y
5
+ 31y
4
+ 15y
3
− 15y
2
− 7y + 1)
4
c
3
, c
7
(y
8
− 3y
7
+ 5y
6
− 4y
5
+ 2y
4
− 13y
3
+ 13y
2
− 16y + 4)
4
c
5
, c
6
, c
9
c
11
y
32
+ 21y
31
+ ··· + 6120y + 361
c
8
, c
10
y
32
+ y
31
+ ··· + 248y + 169
c
12
(y
2
+ y + 1)
16
12
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.821613 + 0.567011I
a = −0.496625 − 0.438250I
b = 0.52992 − 1.64688I
6.41985 − 0.23387I −3.94128 + 1.06967I
u = 0.821613 + 0.567011I
a = 0.26645 − 1.48983I
b = 0.073416 + 1.309500I
6.41985 − 4.29364I −3.94128 + 7.99788I
u = 0.821613 + 0.567011I
a = −2.39394 + 0.27463I
b = −0.73198 − 1.51497I
6.41985 − 4.29364I −3.94128 + 7.99788I
u = 0.821613 + 0.567011I
a = 2.61276 − 0.79661I
b = −0.022697 + 1.179290I
6.41985 − 0.23387I −3.94128 + 1.06967I
u = 0.821613 − 0.567011I
a = −0.496625 + 0.438250I
b = 0.52992 + 1.64688I
6.41985 + 0.23387I −3.94128 − 1.06967I
u = 0.821613 − 0.567011I
a = 0.26645 + 1.48983I
b = 0.073416 − 1.309500I
6.41985 + 4.29364I −3.94128 − 7.99788I
u = 0.821613 − 0.567011I
a = −2.39394 − 0.27463I
b = −0.73198 + 1.51497I
6.41985 + 4.29364I −3.94128 − 7.99788I
u = 0.821613 − 0.567011I
a = 2.61276 + 0.79661I
b = −0.022697 − 1.179290I
6.41985 + 0.23387I −3.94128 − 1.06967I
u = 0.432344 + 1.079150I
a = −0.100401 + 0.617152I
b = −1.201190 + 0.090721I
−1.29038 + 5.58743I −12.52739 − 6.08899I
u = 0.432344 + 1.079150I
a = 0.361262 − 0.454625I
b = −0.207449 + 0.429798I
−1.29038 + 1.52767I −12.52739 + 0.83921I
13
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.432344 + 1.079150I
a = 0.451119 + 0.354898I
b = 0.341939 − 1.164380I
−1.29038 + 5.58743I −12.52739 − 6.08899I
u = 0.432344 + 1.079150I
a = 0.305199 − 0.335131I
b = −0.292741 + 0.851162I
−1.29038 + 1.52767I −12.52739 + 0.83921I
u = 0.432344 − 1.079150I
a = −0.100401 − 0.617152I
b = −1.201190 − 0.090721I
−1.29038 − 5.58743I −12.52739 + 6.08899I
u = 0.432344 − 1.079150I
a = 0.361262 + 0.454625I
b = −0.207449 − 0.429798I
−1.29038 − 1.52767I −12.52739 − 0.83921I
u = 0.432344 − 1.079150I
a = 0.451119 − 0.354898I
b = 0.341939 + 1.164380I
−1.29038 − 5.58743I −12.52739 + 6.08899I
u = 0.432344 − 1.079150I
a = 0.305199 + 0.335131I
b = −0.292741 − 0.851162I
−1.29038 − 1.52767I −12.52739 − 0.83921I
u = −1.38845
a = −0.810223 + 0.602331I
b = −0.367950 + 0.903689I
−8.50968 + 2.02988I −16.3375 − 3.4641I
u = −1.38845
a = −0.810223 − 0.602331I
b = −0.367950 − 0.903689I
−8.50968 − 2.02988I −16.3375 + 3.4641I
u = −1.38845
a = 1.129680 + 0.049021I
b = 1.122510 − 0.403244I
−8.50968 − 2.02988I −16.3375 + 3.4641I
u = −1.38845
a = 1.129680 − 0.049021I
b = 1.122510 + 0.403244I
−8.50968 + 2.02988I −16.3375 − 3.4641I
14
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 1.215250 + 0.684012I
a = 1.165160 − 0.211690I
b = 0.639095 + 1.148790I
−3.80498 − 7.85312I −13.28252 + 2.60552I
u = 1.215250 + 0.684012I
a = 1.086450 − 0.626118I
b = 1.43070 + 0.15248I
−3.80498 − 11.91290I −13.2825 + 9.5337I
u = 1.215250 + 0.684012I
a = −0.387082 − 0.088325I
b = −0.213058 + 0.253663I
−3.80498 − 7.85312I −13.28252 + 2.60552I
u = 1.215250 + 0.684012I
a = −1.73531 + 0.10229I
b = −0.429159 − 1.222660I
−3.80498 − 11.91290I −13.2825 + 9.5337I
u = 1.215250 − 0.684012I
a = 1.165160 + 0.211690I
b = 0.639095 − 1.148790I
−3.80498 + 7.85312I −13.28252 − 2.60552I
u = 1.215250 − 0.684012I
a = 1.086450 + 0.626118I
b = 1.43070 − 0.15248I
−3.80498 + 11.91290I −13.2825 − 9.5337I
u = 1.215250 − 0.684012I
a = −0.387082 + 0.088325I
b = −0.213058 − 0.253663I
−3.80498 + 7.85312I −13.28252 − 2.60552I
u = 1.215250 − 0.684012I
a = −1.73531 − 0.10229I
b = −0.429159 + 1.222660I
−3.80498 + 11.91290I −13.2825 − 9.5337I
u = −0.549965
a = 2.01507 + 0.46937I
b = 0.255913 + 1.378810I
4.21577 − 2.02988I −12.16015 + 3.46410I
u = −0.549965
a = 2.01507 − 0.46937I
b = 0.255913 − 1.378810I
4.21577 + 2.02988I −12.16015 − 3.46410I
15
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.549965
a = 0.53043 + 4.87830I
b = −0.427270 + 1.082010I
4.21577 + 2.02988I −12.16015 − 3.46410I
u = −0.549965
a = 0.53043 − 4.87830I
b = −0.427270 − 1.082010I
4.21577 − 2.02988I −12.16015 + 3.46410I
16
III.
I
u
3
= h−2.54 × 10
6
u
17
− 1.46 × 10
7
u
16
+ · · · + 4.84 × 10
7
b + 1.92 × 10
7
, −1.18 ×
10
8
u
17
− 8.37 × 10
7
u
16
+ · · · + 4.84 × 10
7
a − 2.44 × 10
8
, u
18
+ u
17
+ · · · + u − 1i
(i) Arc colorings
a
3
=
0
u
a
7
=
1
0
a
8
=
1
u
2
a
4
=
−u
−u
3
+ u
a
11
=
2.44506u
17
+ 1.72829u
16
+ ··· − 2.56183u + 5.03889
0.0525413u
17
+ 0.301684u
16
+ ··· + 0.880761u − 0.397047
a
9
=
0.999862u
17
+ 1.73119u
16
+ ··· − 5.39506u − 5.34506
−0.411438u
17
− 0.578846u
16
+ ··· + 0.180593u + 0.176599
a
12
=
2.39252u
17
+ 1.42660u
16
+ ··· − 3.44259u + 5.43593
0.0525413u
17
+ 0.301684u
16
+ ··· + 0.880761u − 0.397047
a
1
=
0.482663u
17
+ 0.187223u
16
+ ··· − 0.596217u + 0.702631
0.0998597u
17
+ 0.114275u
16
+ ··· + 0.581502u − 0.0462974
a
6
=
3.34248u
17
+ 4.59289u
16
+ ··· − 17.7756u + 0.849286
−0.0239398u
17
− 0.417477u
16
+ ··· + 2.28107u + 0.680274
a
10
=
2.03362u
17
+ 1.14944u
16
+ ··· − 2.38124u + 6.21549
0.0525413u
17
+ 0.301684u
16
+ ··· + 0.880761u − 0.397047
a
5
=
−0.602448u
17
− 0.364456u
16
+ ··· + 0.792818u − 0.951774
0.119785u
17
+ 0.177233u
16
+ ··· − 0.196601u + 0.249142
a
2
=
0.527854u
17
+ 0.454267u
16
+ ··· − 1.43666u + 0.940623
−0.0332079u
17
− 0.113318u
16
+ ··· + 1.24528u − 0.0624363
(ii) Obstruction class = 1
(iii) Cusp Shapes = −
191549447
48416059
u
17
−
183440518
48416059
u
16
+ ··· +
478561907
48416059
u −
255825818
48416059
17
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
2
u
18
+ 3u
17
+ ··· + 3u − 1
c
3
u
18
− u
17
+ ··· − u − 1
c
4
u
18
− 3u
17
+ ··· − 3u − 1
c
5
, c
11
u
18
+ 10u
16
+ ··· − 10u + 1
c
6
, c
9
u
18
+ 10u
16
+ ··· + 10u + 1
c
7
u
18
+ u
17
+ ··· + u − 1
c
8
, c
10
u
18
+ 2u
17
+ ··· − 3u + 1
c
12
u
18
+ 3u
17
+ ··· − 2u + 1
18
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
2
, c
4
y
18
− 17y
17
+ ··· + 7y + 1
c
3
, c
7
y
18
− 9y
17
+ ··· − y + 1
c
5
, c
6
, c
9
c
11
y
18
+ 20y
17
+ ··· − 54y + 1
c
8
, c
10
y
18
+ 2y
17
+ ··· − 3y + 1
c
12
y
18
− 3y
17
+ ··· + 2y + 1
19
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = −0.667124 + 0.619286I
a = 1.01984 + 1.11236I
b = 0.212619 − 1.347020I
5.76963 + 2.84768I −5.80039 − 3.08267I
u = −0.667124 − 0.619286I
a = 1.01984 − 1.11236I
b = 0.212619 + 1.347020I
5.76963 − 2.84768I −5.80039 + 3.08267I
u = −1.055780 + 0.337935I
a = 0.752306 + 0.462739I
b = 0.52727 + 1.35411I
0.149777 + 0.573147I −11.90162 − 1.71738I
u = −1.055780 − 0.337935I
a = 0.752306 − 0.462739I
b = 0.52727 − 1.35411I
0.149777 − 0.573147I −11.90162 + 1.71738I
u = 1.033920 + 0.533161I
a = 1.072240 − 0.558681I
b = 0.25310 + 1.50609I
1.35611 − 6.05440I −11.20100 + 4.57946I
u = 1.033920 − 0.533161I
a = 1.072240 + 0.558681I
b = 0.25310 − 1.50609I
1.35611 + 6.05440I −11.20100 − 4.57946I
u = 1.29032
a = −1.10366
b = −0.542837
−9.23099 −17.8620
u = 0.558729 + 0.320333I
a = 0.56850 − 2.05955I
b = 0.410236 − 1.270600I
4.90710 + 1.43926I −3.61056 + 2.10868I
u = 0.558729 − 0.320333I
a = 0.56850 + 2.05955I
b = 0.410236 + 1.270600I
4.90710 − 1.43926I −3.61056 − 2.10868I
u = −0.620039
a = −2.97714
b = −0.128138
−2.58277 0.576260
20
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = 1.31870 + 0.61305I
a = −0.711353 − 0.204327I
b = −0.313099 − 0.878541I
2.11412 − 4.59078I −5.85313 + 11.31334I
u = 1.31870 − 0.61305I
a = −0.711353 + 0.204327I
b = −0.313099 + 0.878541I
2.11412 + 4.59078I −5.85313 − 11.31334I
u = −1.25726 + 0.73302I
a = −0.981696 − 0.076103I
b = −0.547277 + 0.825974I
−3.59976 + 9.26853I −12.3886 − 8.3976I
u = −1.25726 − 0.73302I
a = −0.981696 + 0.076103I
b = −0.547277 − 0.825974I
−3.59976 − 9.26853I −12.3886 + 8.3976I
u = 0.154725 + 0.410246I
a = 6.48299 − 9.35699I
b = −0.334159 + 1.303000I
3.14889 + 2.15923I −0.71378 + 11.60791I
u = 0.154725 − 0.410246I
a = 6.48299 + 9.35699I
b = −0.334159 − 1.303000I
3.14889 − 2.15923I −0.71378 − 11.60791I
u = −0.92104 + 1.30056I
a = −0.162423 − 0.197229I
b = 0.126798 + 0.744120I
−1.35926 − 1.84701I −25.8879 + 15.8048I
u = −0.92104 − 1.30056I
a = −0.162423 + 0.197229I
b = 0.126798 − 0.744120I
−1.35926 + 1.84701I −25.8879 − 15.8048I
21
IV. I
u
4
= h9.40 × 10
20
a
7
u
5
− 1.80 × 10
21
a
6
u
5
+ · · · − 8.66 × 10
21
a + 3.41 ×
10
21
, −2a
7
u
5
− 15a
6
u
5
+ · · · − 17a + 4, u
6
+ u
5
− u
4
− 2u
3
+ u + 1i
(i) Arc colorings
a
3
=
0
u
a
7
=
1
0
a
8
=
1
u
2
a
4
=
−u
−u
3
+ u
a
11
=
a
−0.619077a
7
u
5
+ 1.18432a
6
u
5
+ ··· + 5.70086a − 2.24627
a
9
=
−0.144354a
7
u
5
− 0.0472911a
6
u
5
+ ··· + 2.04271a + 1.04864
−0.432105a
7
u
5
− 0.470608a
6
u
5
+ ··· + 6.51432a + 0.283008
a
12
=
0.619077a
7
u
5
− 1.18432a
6
u
5
+ ··· − 4.70086a + 2.24627
−0.619077a
7
u
5
+ 1.18432a
6
u
5
+ ··· + 5.70086a − 2.24627
a
1
=
0.504551a
7
u
5
− 1.18691a
6
u
5
+ ··· − 6.01844a + 2.02586
−0.324435a
7
u
5
− 0.258046a
6
u
5
+ ··· + 6.15154a + 0.0467776
a
6
=
−0.548791a
7
u
5
− 0.215845a
6
u
5
+ ··· + 10.3830a + 0.685023
0.693145a
7
u
5
+ 0.263136a
6
u
5
+ ··· − 12.4257a + 0.266333
a
10
=
0.365245a
7
u
5
− 2.17240a
6
u
5
+ ··· − 2.92393a + 3.61311
−1.24989a
7
u
5
+ 1.93322a
6
u
5
+ ··· + 15.2852a − 3.25253
a
5
=
0.178710a
7
u
5
+ 0.628134a
6
u
5
+ ··· − 3.07508a − 1.50634
0.325841a
7
u
5
− 1.81504a
6
u
5
+ ··· − 2.94336a + 3.53220
a
2
=
0.109496a
7
u
5
− 1.15664a
6
u
5
+ ··· + 0.510002a + 2.23395
−0.236751a
7
u
5
+ 1.06982a
6
u
5
+ ··· + 3.70555a − 2.28804
(ii) Obstruction class = −1
(iii) Cusp Shapes =
19685370949816372
64944255491057667
a
7
u
5
−
2890452071925236
64944255491057667
a
6
u
5
+···−
318855097360929472
64944255491057667
a−
635548858610032834
64944255491057667
22
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
2
, c
4
(u
12
− u
11
− 4u
10
+ 2u
9
+ 7u
8
+ u
7
− 5u
6
− 5u
5
− u
4
+ 3u
3
+ 2u
2
+ 1)
4
c
3
, c
7
(u
6
− u
5
− u
4
+ 2u
3
− u + 1)
8
c
5
, c
6
, c
9
c
11
u
48
+ u
47
+ ··· − 6u + 67
c
8
, c
10
u
48
− 15u
47
+ ··· − 1598u + 181
c
12
(u
2
− u + 1)
24
23
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
2
, c
4
(y
12
− 9y
11
+ ··· + 4y + 1)
4
c
3
, c
7
(y
6
− 3y
5
+ 5y
4
− 4y
3
+ 2y
2
− y + 1)
8
c
5
, c
6
, c
9
c
11
y
48
+ 45y
47
+ ··· + 147096y + 4489
c
8
, c
10
y
48
+ 21y
47
+ ··· + 890464y + 32761
c
12
(y
2
+ y + 1)
24
24
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
4
√
−1(vol +
√
−1CS) Cusp shape
u = 1.002190 + 0.295542I
a = 0.775552 − 0.660384I
b = 0.509589 + 0.258929I
−0.245672 + 1.105580I −13.71672 − 2.66988I
u = 1.002190 + 0.295542I
a = −0.707173 + 0.866335I
b = −1.13881 + 0.88777I
−0.245672 + 1.105580I −13.71672 − 2.66988I
u = 1.002190 + 0.295542I
a = 0.567084 + 0.568800I
b = 0.23682 − 1.40073I
−0.245672 + 1.105580I −13.71672 − 2.66988I
u = 1.002190 + 0.295542I
a = 1.059310 − 0.667850I
b = 0.034695 − 0.596516I
−0.24567 − 2.95419I −13.7167 + 4.2583I
u = 1.002190 + 0.295542I
a = 0.617928 + 1.137550I
b = 0.031020 + 0.957172I
−0.245672 + 1.105580I −13.71672 − 2.66988I
u = 1.002190 + 0.295542I
a = 0.253602 + 0.071603I
b = −0.02794 + 1.63414I
−0.24567 − 2.95419I −13.7167 + 4.2583I
u = 1.002190 + 0.295542I
a = 1.74575 − 0.31336I
b = 1.068290 + 0.063919I
−0.24567 − 2.95419I −13.7167 + 4.2583I
u = 1.002190 + 0.295542I
a = −2.02925 − 1.13201I
b = −0.285419 − 1.140150I
−0.24567 − 2.95419I −13.7167 + 4.2583I
u = 1.002190 − 0.295542I
a = 0.775552 + 0.660384I
b = 0.509589 − 0.258929I
−0.245672 − 1.105580I −13.71672 + 2.66988I
u = 1.002190 − 0.295542I
a = −0.707173 − 0.866335I
b = −1.13881 − 0.88777I
−0.245672 − 1.105580I −13.71672 + 2.66988I
25
Solutions to I
u
4
√
−1(vol +
√
−1CS) Cusp shape
u = 1.002190 − 0.295542I
a = 0.567084 − 0.568800I
b = 0.23682 + 1.40073I
−0.245672 − 1.105580I −13.71672 + 2.66988I
u = 1.002190 − 0.295542I
a = 1.059310 + 0.667850I
b = 0.034695 + 0.596516I
−0.24567 + 2.95419I −13.7167 − 4.2583I
u = 1.002190 − 0.295542I
a = 0.617928 − 1.137550I
b = 0.031020 − 0.957172I
−0.245672 − 1.105580I −13.71672 + 2.66988I
u = 1.002190 − 0.295542I
a = 0.253602 − 0.071603I
b = −0.02794 − 1.63414I
−0.24567 + 2.95419I −13.7167 − 4.2583I
u = 1.002190 − 0.295542I
a = 1.74575 + 0.31336I
b = 1.068290 − 0.063919I
−0.24567 + 2.95419I −13.7167 − 4.2583I
u = 1.002190 − 0.295542I
a = −2.02925 + 1.13201I
b = −0.285419 + 1.140150I
−0.24567 + 2.95419I −13.7167 − 4.2583I
u = −0.428243 + 0.664531I
a = 0.424006 + 0.749679I
b = −0.347802 + 0.145509I
3.53554 + 1.10558I −6.28328 − 2.66988I
u = −0.428243 + 0.664531I
a = −0.109037 − 0.835332I
b = −0.980418 − 0.347385I
3.53554 − 2.95419I −6.28328 + 4.25833I
u = −0.428243 + 0.664531I
a = 0.514379 − 0.344758I
b = 0.236687 + 1.251690I
3.53554 − 2.95419I −6.28328 + 4.25833I
u = −0.428243 + 0.664531I
a = −1.51339 + 0.24563I
b = 0.63729 + 1.39949I
3.53554 − 2.95419I −6.28328 + 4.25833I
26
Solutions to I
u
4
√
−1(vol +
√
−1CS) Cusp shape
u = −0.428243 + 0.664531I
a = 0.395311 + 0.191403I
b = −0.063487 − 1.241750I
3.53554 + 1.10558I −6.28328 − 2.66988I
u = −0.428243 + 0.664531I
a = −0.51608 + 2.28821I
b = 0.118211 − 1.155270I
3.53554 + 1.10558I −6.28328 − 2.66988I
u = −0.428243 + 0.664531I
a = −3.30609 − 2.45775I
b = −0.46396 + 1.53136I
3.53554 + 1.10558I −6.28328 − 2.66988I
u = −0.428243 + 0.664531I
a = 3.27764 + 3.14924I
b = −0.138713 − 1.288100I
3.53554 − 2.95419I −6.28328 + 4.25833I
u = −0.428243 − 0.664531I
a = 0.424006 − 0.749679I
b = −0.347802 − 0.145509I
3.53554 − 1.10558I −6.28328 + 2.66988I
u = −0.428243 − 0.664531I
a = −0.109037 + 0.835332I
b = −0.980418 + 0.347385I
3.53554 + 2.95419I −6.28328 − 4.25833I
u = −0.428243 − 0.664531I
a = 0.514379 + 0.344758I
b = 0.236687 − 1.251690I
3.53554 + 2.95419I −6.28328 − 4.25833I
u = −0.428243 − 0.664531I
a = −1.51339 − 0.24563I
b = 0.63729 − 1.39949I
3.53554 + 2.95419I −6.28328 − 4.25833I
u = −0.428243 − 0.664531I
a = 0.395311 − 0.191403I
b = −0.063487 + 1.241750I
3.53554 − 1.10558I −6.28328 + 2.66988I
u = −0.428243 − 0.664531I
a = −0.51608 − 2.28821I
b = 0.118211 + 1.155270I
3.53554 − 1.10558I −6.28328 + 2.66988I
27
Solutions to I
u
4
√
−1(vol +
√
−1CS) Cusp shape
u = −0.428243 − 0.664531I
a = −3.30609 + 2.45775I
b = −0.46396 − 1.53136I
3.53554 − 1.10558I −6.28328 + 2.66988I
u = −0.428243 − 0.664531I
a = 3.27764 − 3.14924I
b = −0.138713 + 1.288100I
3.53554 + 2.95419I −6.28328 − 4.25833I
u = −1.073950 + 0.558752I
a = 0.243335 + 1.147080I
b = 0.049252 − 1.384420I
1.64493 + 7.72290I −10.00000 − 8.97467I
u = −1.073950 + 0.558752I
a = 1.243930 − 0.068036I
b = 0.422756 − 1.046490I
1.64493 + 3.66314I −10.0000 − 2.04647I
u = −1.073950 + 0.558752I
a = 1.33854 + 0.68306I
b = 1.276570 − 0.165471I
1.64493 + 7.72290I −10.00000 − 8.97467I
u = −1.073950 + 0.558752I
a = −0.276943 + 0.247722I
b = 0.48789 + 1.80331I
1.64493 + 3.66314I −10.00000 − 2.04647I
u = −1.073950 + 0.558752I
a = −0.135569 + 0.287270I
b = 0.021435 − 0.262960I
1.64493 + 3.66314I −10.00000 − 2.04647I
u = −1.073950 + 0.558752I
a = −1.71509 − 0.08243I
b = −0.90809 + 1.55445I
1.64493 + 7.72290I −10.0000 − 8.97467I
u = −1.073950 + 0.558752I
a = 1.93484 + 0.49453I
b = 0.088785 − 1.144550I
1.64493 + 3.66314I −10.0000 − 2.04647I
u = −1.073950 + 0.558752I
a = −2.08258 + 0.16719I
b = −0.364647 + 1.204880I
1.64493 + 7.72290I −10.0000 − 8.97467I
28
Solutions to I
u
4
√
−1(vol +
√
−1CS) Cusp shape
u = −1.073950 − 0.558752I
a = 0.243335 − 1.147080I
b = 0.049252 + 1.384420I
1.64493 − 7.72290I −10.00000 + 8.97467I
u = −1.073950 − 0.558752I
a = 1.243930 + 0.068036I
b = 0.422756 + 1.046490I
1.64493 − 3.66314I −10.0000 + 2.04647I
u = −1.073950 − 0.558752I
a = 1.33854 − 0.68306I
b = 1.276570 + 0.165471I
1.64493 − 7.72290I −10.00000 + 8.97467I
u = −1.073950 − 0.558752I
a = −0.276943 − 0.247722I
b = 0.48789 − 1.80331I
1.64493 − 3.66314I −10.00000 + 2.04647I
u = −1.073950 − 0.558752I
a = −0.135569 − 0.287270I
b = 0.021435 + 0.262960I
1.64493 − 3.66314I −10.00000 + 2.04647I
u = −1.073950 − 0.558752I
a = −1.71509 + 0.08243I
b = −0.90809 − 1.55445I
1.64493 − 7.72290I −10.0000 + 8.97467I
u = −1.073950 − 0.558752I
a = 1.93484 − 0.49453I
b = 0.088785 + 1.144550I
1.64493 − 3.66314I −10.0000 + 2.04647I
u = −1.073950 − 0.558752I
a = −2.08258 − 0.16719I
b = −0.364647 − 1.204880I
1.64493 − 7.72290I −10.0000 + 8.97467I
29
V. I
v
1
= ha, 8v
2
+ b + 26v + 7, 4v
3
+ 14v
2
+ 7v + 1i
(i) Arc colorings
a
3
=
v
0
a
7
=
1
0
a
8
=
1
0
a
4
=
v
0
a
11
=
0
−8v
2
− 26v − 7
a
9
=
1
4v
2
+ 12v + 1
a
12
=
8v
2
+ 26v + 7
−8v
2
− 26v − 7
a
1
=
−1
4v
2
+ 14v + 7
a
6
=
4v
2
+ 12v + 2
−4v
2
− 12v − 1
a
10
=
−8v
2
− 26v − 7
20v
2
+ 64v + 16
a
5
=
1
−4v
2
− 14v − 7
a
2
=
v − 1
4v
2
+ 14v + 7
(ii) Obstruction class = 1
(iii) Cusp Shapes = 45v
2
+ 150v + 41
30
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
2
(u − 1)
3
c
3
, c
7
u
3
c
4
(u + 1)
3
c
5
, c
6
, c
8
c
10
u
3
+ 2u − 1
c
9
, c
11
u
3
+ 2u + 1
c
12
u
3
+ 3u
2
+ 5u + 2
31
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
2
, c
4
(y − 1)
3
c
3
, c
7
y
3
c
5
, c
6
, c
8
c
9
, c
10
, c
11
y
3
+ 4y
2
+ 4y − 1
c
12
y
3
+ y
2
+ 13y − 4
32
(vi) Complex Volumes and Cusp Shapes
Solutions to I
v
1
√
−1(vol +
√
−1CS) Cusp shape
v = −0.283866 + 0.068399I
a = 0
b = −0.22670 − 1.46771I
7.79580 − 5.13794I 1.83568 + 8.51237I
v = −0.283866 − 0.068399I
a = 0
b = −0.22670 + 1.46771I
7.79580 + 5.13794I 1.83568 − 8.51237I
v = −2.93227
a = 0
b = 0.453398
−2.43213 −11.9210
33
VI. I
v
2
= ha, b
4
+ b
3
+ 2b
2
+ 2b + 1, v − 1i
(i) Arc colorings
a
3
=
1
0
a
7
=
1
0
a
8
=
1
0
a
4
=
1
0
a
11
=
0
b
a
9
=
1
b
2
a
12
=
−b
b
a
1
=
−b
3
− 2b
−1
a
6
=
b
2
+ 1
−b
2
a
10
=
2b
3
+ b
2
+ 3b + 3
−b
3
− b − 1
a
5
=
b
3
+ 2b
1
a
2
=
−b
3
− 2b + 1
−1
(ii) Obstruction class = 1
(iii) Cusp Shapes = −4b
3
− 4b − 12
34
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
2
(u − 1)
4
c
3
, c
7
u
4
c
4
(u + 1)
4
c
5
, c
6
, c
8
c
10
u
4
+ u
3
+ 2u
2
+ 2u + 1
c
9
, c
11
u
4
− u
3
+ 2u
2
− 2u + 1
c
12
(u
2
− u + 1)
2
35
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
2
, c
4
(y − 1)
4
c
3
, c
7
y
4
c
5
, c
6
, c
8
c
9
, c
10
, c
11
y
4
+ 3y
3
+ 2y
2
+ 1
c
12
(y
2
+ y + 1)
2
36
(vi) Complex Volumes and Cusp Shapes
Solutions to I
v
2
√
−1(vol +
√
−1CS) Cusp shape
v = 1.00000
a = 0
b = −0.621744 + 0.440597I
1.64493 + 2.02988I −10.00000 − 3.46410I
v = 1.00000
a = 0
b = −0.621744 − 0.440597I
1.64493 − 2.02988I −10.00000 + 3.46410I
v = 1.00000
a = 0
b = 0.121744 + 1.306620I
1.64493 − 2.02988I −10.00000 + 3.46410I
v = 1.00000
a = 0
b = 0.121744 − 1.306620I
1.64493 + 2.02988I −10.00000 − 3.46410I
37
VII. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
, c
2
(u − 1)
7
(u
8
− u
7
− 4u
6
+ 3u
5
+ 5u
4
− u
3
− u
2
− 3u − 1)
4
· (u
12
− u
11
− 4u
10
+ 2u
9
+ 7u
8
+ u
7
− 5u
6
− 5u
5
− u
4
+ 3u
3
+ 2u
2
+ 1)
4
· (u
18
+ 3u
17
+ ··· + 3u − 1)(u
42
− 3u
41
+ ··· + 140u + 16)
c
3
u
7
(u
6
− u
5
− u
4
+ 2u
3
− u + 1)
8
· (u
8
+ 3u
7
+ 3u
6
− 2u
5
− 8u
4
− 9u
3
− 3u
2
+ 2u + 2)
4
· (u
18
− u
17
+ ··· − u − 1)(u
42
− 6u
41
+ ··· + 608u − 128)
c
4
(u + 1)
7
(u
8
− u
7
− 4u
6
+ 3u
5
+ 5u
4
− u
3
− u
2
− 3u − 1)
4
· (u
12
− u
11
− 4u
10
+ 2u
9
+ 7u
8
+ u
7
− 5u
6
− 5u
5
− u
4
+ 3u
3
+ 2u
2
+ 1)
4
· (u
18
− 3u
17
+ ··· − 3u − 1)(u
42
− 3u
41
+ ··· + 140u + 16)
c
5
(u
3
+ 2u − 1)(u
4
+ u
3
+ 2u
2
+ 2u + 1)(u
18
+ 10u
16
+ ··· − 10u + 1)
· (u
32
+ u
31
+ ··· − 108u + 19)(u
42
+ 16u
40
+ ··· + u − 1)
· (u
48
+ u
47
+ ··· − 6u + 67)
c
6
(u
3
+ 2u − 1)(u
4
+ u
3
+ 2u
2
+ 2u + 1)(u
18
+ 10u
16
+ ··· + 10u + 1)
· (u
32
+ u
31
+ ··· − 108u + 19)(u
42
+ 16u
40
+ ··· + u − 1)
· (u
48
+ u
47
+ ··· − 6u + 67)
c
7
u
7
(u
6
− u
5
− u
4
+ 2u
3
− u + 1)
8
· (u
8
+ 3u
7
+ 3u
6
− 2u
5
− 8u
4
− 9u
3
− 3u
2
+ 2u + 2)
4
· (u
18
+ u
17
+ ··· + u − 1)(u
42
− 6u
41
+ ··· + 608u − 128)
c
8
, c
10
(u
3
+ 2u − 1)(u
4
+ u
3
+ 2u
2
+ 2u + 1)(u
18
+ 2u
17
+ ··· − 3u + 1)
· (u
32
− 7u
31
+ ··· − 148u + 13)(u
42
+ 2u
41
+ ··· + 2u + 1)
· (u
48
− 15u
47
+ ··· − 1598u + 181)
c
9
(u
3
+ 2u + 1)(u
4
− u
3
+ 2u
2
− 2u + 1)(u
18
+ 10u
16
+ ··· + 10u + 1)
· (u
32
+ u
31
+ ··· − 108u + 19)(u
42
+ 16u
40
+ ··· + u − 1)
· (u
48
+ u
47
+ ··· − 6u + 67)
c
11
(u
3
+ 2u + 1)(u
4
− u
3
+ 2u
2
− 2u + 1)(u
18
+ 10u
16
+ ··· − 10u + 1)
· (u
32
+ u
31
+ ··· − 108u + 19)(u
42
+ 16u
40
+ ··· + u − 1)
· (u
48
+ u
47
+ ··· − 6u + 67)
c
12
((u
2
− u + 1)
42
)(u
3
+ 3u
2
+ 5u + 2)(u
18
+ 3u
17
+ ··· − 2u + 1)
· (u
42
+ 39u
41
+ ··· + 24641536u + 1048576)
38
VIII. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
, c
2
, c
4
(y − 1)
7
(y
8
− 9y
7
+ 32y
6
− 53y
5
+ 31y
4
+ 15y
3
− 15y
2
− 7y + 1)
4
· ((y
12
− 9y
11
+ ··· + 4y + 1)
4
)(y
18
− 17y
17
+ ··· + 7y + 1)
· (y
42
− 37y
41
+ ··· − 7536y + 256)
c
3
, c
7
y
7
(y
6
− 3y
5
+ 5y
4
− 4y
3
+ 2y
2
− y + 1)
8
· (y
8
− 3y
7
+ 5y
6
− 4y
5
+ 2y
4
− 13y
3
+ 13y
2
− 16y + 4)
4
· (y
18
− 9y
17
+ ··· − y + 1)(y
42
− 18y
41
+ ··· − 388096y + 16384)
c
5
, c
6
, c
9
c
11
(y
3
+ 4y
2
+ 4y − 1)(y
4
+ 3y
3
+ 2y
2
+ 1)(y
18
+ 20y
17
+ ··· − 54y + 1)
· (y
32
+ 21y
31
+ ··· + 6120y + 361)(y
42
+ 32y
41
+ ··· − 19y + 1)
· (y
48
+ 45y
47
+ ··· + 147096y + 4489)
c
8
, c
10
(y
3
+ 4y
2
+ 4y − 1)(y
4
+ 3y
3
+ 2y
2
+ 1)(y
18
+ 2y
17
+ ··· − 3y + 1)
· (y
32
+ y
31
+ ··· + 248y + 169)(y
42
− 2y
41
+ ··· − 52y + 1)
· (y
48
+ 21y
47
+ ··· + 890464y + 32761)
c
12
((y
2
+ y + 1)
42
)(y
3
+ y
2
+ 13y − 4)(y
18
− 3y
17
+ ··· + 2y + 1)
· (y
42
− y
41
+ ··· − 16217796509696y + 1099511627776)
39
