12n
0391
(K12n
0391
)
A knot diagram
1
Linearized knot diagam
3 6 8 10 2 1 11 5 1 4 7 10
Solving Sequence
3,6
2 1 7
5,10
4 9 8 12 11
c
2
c
1
c
6
c
5
c
4
c
9
c
8
c
12
c
11
c
3
, c
7
, c
10
Ideals for irreducible components
2
of X
par
I
u
1
= h3u
32
− 10u
31
+ ··· + 2b + 4, 5u
32
− 31u
31
+ ··· + 2a − 35, u
33
− 6u
32
+ ··· − 10u + 4i
I
u
2
= h−47109570u
10
a
3
− 95144015u
10
a
2
+ ··· − 183653747a − 331708329,
− 2u
10
a
3
− u
10
a
2
+ ··· + 3a
2
− 2a, u
11
+ u
10
− 2u
9
− 3u
8
+ 2u
7
+ 4u
6
− 3u
4
− u
3
+ u
2
− 1i
I
u
3
= h−u
19
− u
18
+ ··· + b − 1,
u
16
+ u
15
− 4u
14
− 5u
13
+ 7u
12
+ 11u
11
− 4u
10
− 12u
9
− 3u
8
+ 5u
7
+ 5u
6
+ 2u
5
− 3u
3
− 3u
2
+ a + u + 1,
u
20
+ u
19
+ ··· + u + 1i
* 3 irreducible components of dim
C
= 0, with total 97 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
32
−10u
31
+· · ·+2b+4 , 5u
32
−31u
31
+· · ·+2a−35, u
33
−6u
32
+· · ·−10u+4i
(i) Arc colorings
a
3
=
1
0
a
6
=
0
u
a
2
=
1
−u
2
a
1
=
−u
2
+ 1
−u
2
a
7
=
u
5
− 2u
3
+ u
u
5
− u
3
+ u
a
5
=
u
−u
3
+ u
a
10
=
−
5
2
u
32
+
31
2
u
31
+ ··· − 27u +
35
2
−
3
2
u
32
+ 5u
31
+ ··· −
1
2
u − 2
a
4
=
−
1
4
u
32
+ 3u
31
+ ··· −
21
4
u + 4
−
5
2
u
32
+ 13u
31
+ ··· −
29
2
u + 7
a
9
=
−5u
32
+
43
2
u
31
+ ··· −
39
2
u +
3
2
9
2
u
32
− 31u
31
+ ··· +
111
2
u − 38
a
8
=
−u
32
+
5
2
u
31
+ ··· −
5
2
u −
9
2
13
2
u
32
− 32u
31
+ ··· +
77
2
u − 24
a
12
=
3
4
u
32
− 6u
31
+ ··· +
39
4
u − 11
13
2
u
32
− 32u
31
+ ··· +
81
2
u − 25
a
11
=
−
13
4
u
32
+ 18u
31
+ ··· −
121
4
u + 19
3
2
u
32
− 8u
31
+ ··· +
21
2
u − 7
(ii) Obstruction class = −1
(iii) Cusp Shapes = 19u
32
− 93u
31
+ 87u
30
+ 399u
29
− 1093u
28
+ 124u
27
+ 3263u
26
−
4355u
25
−2560u
24
+ 11701u
23
−7466u
22
−11755u
21
+ 22346u
20
−4792u
19
−23413u
18
+
26009u
17
+ 2484u
16
−27634u
15
+ 20515u
14
+ 6968u
13
−21858u
12
+ 11815u
11
+ 6157u
10
−
12060u
9
+ 4832u
8
+ 3318u
7
− 4487u
6
+ 1156u
5
+ 1213u
4
− 1111u
3
+ 245u
2
+ 110u − 54
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
33
+ 16u
32
+ ··· + 172u + 16
c
2
, c
5
u
33
+ 6u
32
+ ··· − 10u − 4
c
3
, c
4
, c
10
u
33
+ 9u
31
+ ··· + 2u − 1
c
6
u
33
+ 18u
32
+ ··· − 1198u − 188
c
7
, c
11
u
33
− 24u
32
+ ··· + 26624u − 2048
c
8
u
33
− u
32
+ ··· + 106u − 23
c
9
, c
12
u
33
+ 2u
32
+ ··· − 16u − 1
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
33
+ 4y
32
+ ··· + 9456y −256
c
2
, c
5
y
33
− 16y
32
+ ··· + 172y −16
c
3
, c
4
, c
10
y
33
+ 18y
32
+ ··· − 4y −1
c
6
y
33
+ 8y
32
+ ··· + 252684y −35344
c
7
, c
11
y
33
+ 12y
32
+ ··· + 2097152y −4194304
c
8
y
33
− 31y
32
+ ··· + 16020y −529
c
9
, c
12
y
33
− 42y
32
+ ··· + 54y −1
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.615043 + 0.794458I
a = −0.931151 + 0.481633I
b = −1.158050 + 0.155662I
2.15328 − 7.47057I 6.28978 + 6.05240I
u = 0.615043 − 0.794458I
a = −0.931151 − 0.481633I
b = −1.158050 − 0.155662I
2.15328 + 7.47057I 6.28978 − 6.05240I
u = 0.934351 + 0.256317I
a = 0.138141 − 0.042111I
b = −0.307888 − 0.461843I
−1.58520 − 0.97498I −1.65033 + 1.59039I
u = 0.934351 − 0.256317I
a = 0.138141 + 0.042111I
b = −0.307888 + 0.461843I
−1.58520 + 0.97498I −1.65033 − 1.59039I
u = 0.402264 + 0.852871I
a = −1.58643 − 1.26589I
b = −1.72042 − 0.99064I
0.89438 + 10.98450I 5.23661 − 5.54944I
u = 0.402264 − 0.852871I
a = −1.58643 + 1.26589I
b = −1.72042 + 0.99064I
0.89438 − 10.98450I 5.23661 + 5.54944I
u = −0.927183 + 0.525541I
a = −1.014440 + 0.779993I
b = −0.742899 − 0.107800I
0.18348 + 3.87388I 6.31776 − 7.47791I
u = −0.927183 − 0.525541I
a = −1.014440 − 0.779993I
b = −0.742899 + 0.107800I
0.18348 − 3.87388I 6.31776 + 7.47791I
u = 0.582669 + 0.708437I
a = 0.741361 + 0.151629I
b = 1.178060 + 0.561251I
4.85669 − 0.62382I 7.67399 + 3.72585I
u = 0.582669 − 0.708437I
a = 0.741361 − 0.151629I
b = 1.178060 − 0.561251I
4.85669 + 0.62382I 7.67399 − 3.72585I
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.355906 + 0.802794I
a = 1.57216 + 0.88862I
b = 1.72277 + 0.45864I
3.58955 + 3.24533I 5.20458 − 3.30279I
u = 0.355906 − 0.802794I
a = 1.57216 − 0.88862I
b = 1.72277 − 0.45864I
3.58955 − 3.24533I 5.20458 + 3.30279I
u = 0.050477 + 0.847272I
a = −1.032160 − 0.468103I
b = −0.777802 − 0.129336I
−5.00986 − 1.85205I 6.76082 + 4.03630I
u = 0.050477 − 0.847272I
a = −1.032160 + 0.468103I
b = −0.777802 + 0.129336I
−5.00986 + 1.85205I 6.76082 − 4.03630I
u = 1.010310 + 0.608408I
a = −0.98297 − 1.05108I
b = −0.855242 + 0.984190I
3.58006 − 4.43418I 6.35662 + 2.15933I
u = 1.010310 − 0.608408I
a = −0.98297 + 1.05108I
b = −0.855242 − 0.984190I
3.58006 + 4.43418I 6.35662 − 2.15933I
u = −1.159600 + 0.228047I
a = 0.786672 + 0.851083I
b = −1.034420 + 0.855065I
−1.231110 − 0.428619I −1.25867 + 1.75566I
u = −1.159600 − 0.228047I
a = 0.786672 − 0.851083I
b = −1.034420 − 0.855065I
−1.231110 + 0.428619I −1.25867 − 1.75566I
u = −0.717593 + 0.390417I
a = 1.47547 − 0.34302I
b = 0.464162 + 0.242439I
0.934933 + 0.153832I 10.03665 − 0.30542I
u = −0.717593 − 0.390417I
a = 1.47547 + 0.34302I
b = 0.464162 − 0.242439I
0.934933 − 0.153832I 10.03665 + 0.30542I
6
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.998884 + 0.676093I
a = 0.251045 + 1.284470I
b = 0.779513 − 0.138727I
1.00418 + 1.96266I 5.00130 − 1.18904I
u = 0.998884 − 0.676093I
a = 0.251045 − 1.284470I
b = 0.779513 + 0.138727I
1.00418 − 1.96266I 5.00130 + 1.18904I
u = −1.206650 + 0.128661I
a = −0.777551 − 0.265371I
b = 1.07673 − 1.12681I
−4.62253 − 8.29061I −0.38123 + 5.10542I
u = −1.206650 − 0.128661I
a = −0.777551 + 0.265371I
b = 1.07673 + 1.12681I
−4.62253 + 8.29061I −0.38123 − 5.10542I
u = 1.137250 + 0.591003I
a = −1.26745 − 1.33966I
b = −1.96175 + 0.78277I
1.26915 − 8.46714I 2.03049 + 6.90183I
u = 1.137250 − 0.591003I
a = −1.26745 + 1.33966I
b = −1.96175 − 0.78277I
1.26915 + 8.46714I 2.03049 − 6.90183I
u = 1.134040 + 0.622957I
a = 1.85392 + 1.17676I
b = 1.88230 − 1.28411I
−1.3038 − 16.4563I 2.44177 + 9.38335I
u = 1.134040 − 0.622957I
a = 1.85392 − 1.17676I
b = 1.88230 + 1.28411I
−1.3038 + 16.4563I 2.44177 − 9.38335I
u = −1.235010 + 0.421827I
a = 0.063782 − 0.847588I
b = 0.792204 − 0.461041I
−8.92302 + 6.29912I 2.49834 − 8.51829I
u = −1.235010 − 0.421827I
a = 0.063782 + 0.847588I
b = 0.792204 + 0.461041I
−8.92302 − 6.29912I 2.49834 + 8.51829I
7
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 1.223850 + 0.478588I
a = 0.363356 + 0.518472I
b = 1.022240 − 0.038770I
−8.52990 − 2.90559I 5.04684 − 0.50243I
u = 1.223850 − 0.478588I
a = 0.363356 − 0.518472I
b = 1.022240 + 0.038770I
−8.52990 + 2.90559I 5.04684 + 0.50243I
u = −0.398026
a = 1.69246
b = 0.281003
0.805352 12.7890
8
II. I
u
2
= h−4.71 × 10
7
a
3
u
10
− 9.51 × 10
7
a
2
u
10
+ · · · − 1.84 × 10
8
a − 3.32 ×
10
8
, −2u
10
a
3
− u
10
a
2
+ · · · + 3a
2
− 2a, u
11
+ u
10
+ · · · + u
2
− 1i
(i) Arc colorings
a
3
=
1
0
a
6
=
0
u
a
2
=
1
−u
2
a
1
=
−u
2
+ 1
−u
2
a
7
=
u
5
− 2u
3
+ u
u
5
− u
3
+ u
a
5
=
u
−u
3
+ u
a
10
=
a
0.292477a
3
u
10
+ 0.590697a
2
u
10
+ ··· + 1.14021a + 2.05940
a
4
=
0.326323a
3
u
10
+ 0.238038a
2
u
10
+ ··· + 1.88296a + 1.75190
−0.276430a
3
u
10
− 0.0714295a
2
u
10
+ ··· − 0.0211672a + 0.331551
a
9
=
−0.00330395a
3
u
10
+ 0.297508a
2
u
10
+ ··· + 0.696558a − 0.975173
0.424962a
3
u
10
+ 0.642654a
2
u
10
+ ··· + 2.04544a + 2.56376
a
8
=
−0.249089a
3
u
10
− 0.636279a
2
u
10
+ ··· + 1.04188a − 2.44185
0.224244a
3
u
10
+ 0.754589a
2
u
10
+ ··· + 0.602927a + 1.16330
a
12
=
0.0482423a
3
u
10
+ 0.442391a
2
u
10
+ ··· − 0.454053a + 3.19168
−0.00902801a
3
u
10
− 0.883875a
2
u
10
+ ··· + 0.0444369a − 1.60853
a
11
=
0.171496a
3
u
10
+ 0.454263a
2
u
10
+ ··· − 0.0937667a + 4.72095
−0.0960514a
3
u
10
− 0.897715a
2
u
10
+ ··· + 0.429026a − 0.906337
(ii) Obstruction class = −1
(iii) Cusp Shapes =
3600864
23010109
u
10
a
3
−
14406376
23010109
u
10
a
2
+ ··· −
22413624
23010109
a −
195703918
23010109
9
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
(u
11
+ 5u
10
+ ··· + 2u + 1)
4
c
2
, c
5
(u
11
− u
10
− 2u
9
+ 3u
8
+ 2u
7
− 4u
6
+ 3u
4
− u
3
− u
2
+ 1)
4
c
3
, c
4
, c
10
u
44
+ u
43
+ ··· + 6594u + 4921
c
6
(u
11
− 3u
10
+ 4u
9
− u
8
+ 2u
7
− 8u
6
+ 8u
5
+ 5u
4
− 3u
3
− u
2
+ 4u − 1)
4
c
7
, c
11
(u
2
+ u + 1)
22
c
8
u
44
− u
43
+ ··· + 472696u + 34447
c
9
, c
12
u
44
+ 9u
43
+ ··· + 1718u + 241
10
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
(y
11
+ 3y
10
+ ··· − 10y −1)
4
c
2
, c
5
(y
11
− 5y
10
+ ··· + 2y −1)
4
c
3
, c
4
, c
10
y
44
+ 27y
43
+ ··· + 362915028y + 24216241
c
6
(y
11
− y
10
+ ··· + 14y −1)
4
c
7
, c
11
(y
2
+ y + 1)
22
c
8
y
44
+ 3y
43
+ ··· + 16852909668y + 1186595809
c
9
, c
12
y
44
− 13y
43
+ ··· + 3475464y + 58081
11
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.959860 + 0.351396I
a = −1.046440 + 0.210475I
b = −0.487010 + 0.928193I
−6.57107 + 3.30529I −3.47945 − 4.26507I
u = −0.959860 + 0.351396I
a = −0.08726 − 1.76989I
b = 1.74145 − 1.57969I
−6.57107 − 0.75447I −3.47945 + 2.66314I
u = −0.959860 + 0.351396I
a = 1.13540 − 1.43177I
b = 0.09037 + 1.50821I
−6.57107 − 0.75447I −3.47945 + 2.66314I
u = −0.959860 + 0.351396I
a = −2.25035 + 0.48264I
b = −0.49081 − 2.47885I
−6.57107 + 3.30529I −3.47945 − 4.26507I
u = −0.959860 − 0.351396I
a = −1.046440 − 0.210475I
b = −0.487010 − 0.928193I
−6.57107 − 3.30529I −3.47945 + 4.26507I
u = −0.959860 − 0.351396I
a = −0.08726 + 1.76989I
b = 1.74145 + 1.57969I
−6.57107 + 0.75447I −3.47945 − 2.66314I
u = −0.959860 − 0.351396I
a = 1.13540 + 1.43177I
b = 0.09037 − 1.50821I
−6.57107 + 0.75447I −3.47945 − 2.66314I
u = −0.959860 − 0.351396I
a = −2.25035 − 0.48264I
b = −0.49081 + 2.47885I
−6.57107 − 3.30529I −3.47945 + 4.26507I
u = −0.488025 + 0.800566I
a = −0.562669 − 0.387878I
b = −0.938604 − 0.140148I
4.10386 + 0.38395I 6.04988 − 3.21929I
u = −0.488025 + 0.800566I
a = 1.339240 + 0.110888I
b = 1.391310 − 0.247736I
4.10386 − 3.67581I 6.04988 + 3.70891I
12
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.488025 + 0.800566I
a = −0.98893 + 1.37600I
b = −1.31716 + 1.07528I
4.10386 − 3.67581I 6.04988 + 3.70891I
u = −0.488025 + 0.800566I
a = 1.67519 − 0.65894I
b = 1.61820 − 0.33784I
4.10386 + 0.38395I 6.04988 − 3.21929I
u = −0.488025 − 0.800566I
a = −0.562669 + 0.387878I
b = −0.938604 + 0.140148I
4.10386 − 0.38395I 6.04988 + 3.21929I
u = −0.488025 − 0.800566I
a = 1.339240 − 0.110888I
b = 1.391310 + 0.247736I
4.10386 + 3.67581I 6.04988 − 3.70891I
u = −0.488025 − 0.800566I
a = −0.98893 − 1.37600I
b = −1.31716 − 1.07528I
4.10386 + 3.67581I 6.04988 − 3.70891I
u = −0.488025 − 0.800566I
a = 1.67519 + 0.65894I
b = 1.61820 + 0.33784I
4.10386 − 0.38395I 6.04988 + 3.21929I
u = 1.11640
a = −0.674977 + 0.221102I
b = 0.442711 − 0.889819I
−1.55223 − 2.02988I 0.18572 + 3.46410I
u = 1.11640
a = −0.674977 − 0.221102I
b = 0.442711 + 0.889819I
−1.55223 + 2.02988I 0.18572 − 3.46410I
u = 1.11640
a = 0.601217 + 0.348857I
b = −1.078060 + 0.210631I
−1.55223 + 2.02988I 0.18572 − 3.46410I
u = 1.11640
a = 0.601217 − 0.348857I
b = −1.078060 − 0.210631I
−1.55223 − 2.02988I 0.18572 + 3.46410I
13
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 1.031510 + 0.521913I
a = −0.908426 + 0.370296I
b = −0.539113 − 0.133729I
−5.31149 − 2.72042I 0.64109 + 3.31280I
u = 1.031510 + 0.521913I
a = 1.24853 + 1.39026I
b = 2.15369 + 0.09233I
−5.31149 − 6.78019I 0.64109 + 10.24101I
u = 1.031510 + 0.521913I
a = −2.33476 − 0.10037I
b = −0.285235 + 1.312870I
−5.31149 − 6.78019I 0.64109 + 10.24101I
u = 1.031510 + 0.521913I
a = 2.56862 − 0.07454I
b = 0.82183 − 2.18700I
−5.31149 − 2.72042I 0.64109 + 3.31280I
u = 1.031510 − 0.521913I
a = −0.908426 − 0.370296I
b = −0.539113 + 0.133729I
−5.31149 + 2.72042I 0.64109 − 3.31280I
u = 1.031510 − 0.521913I
a = 1.24853 − 1.39026I
b = 2.15369 − 0.09233I
−5.31149 + 6.78019I 0.64109 − 10.24101I
u = 1.031510 − 0.521913I
a = −2.33476 + 0.10037I
b = −0.285235 − 1.312870I
−5.31149 + 6.78019I 0.64109 − 10.24101I
u = 1.031510 − 0.521913I
a = 2.56862 + 0.07454I
b = 0.82183 + 2.18700I
−5.31149 + 2.72042I 0.64109 − 3.31280I
u = −1.081080 + 0.631709I
a = 0.087716 − 0.913307I
b = 0.687058 + 0.202804I
2.33004 + 4.99231I 3.50054 − 1.42209I
u = −1.081080 + 0.631709I
a = −0.87402 + 1.56312I
b = −1.238220 − 0.460596I
2.33004 + 9.05208I 3.50054 − 8.35029I
14
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −1.081080 + 0.631709I
a = −1.37993 + 1.31396I
b = −1.64849 − 0.60404I
2.33004 + 4.99231I 3.50054 − 1.42209I
u = −1.081080 + 0.631709I
a = 1.86710 − 0.64436I
b = 1.37146 + 1.49384I
2.33004 + 9.05208I 3.50054 − 8.35029I
u = −1.081080 − 0.631709I
a = 0.087716 + 0.913307I
b = 0.687058 − 0.202804I
2.33004 − 4.99231I 3.50054 + 1.42209I
u = −1.081080 − 0.631709I
a = −0.87402 − 1.56312I
b = −1.238220 + 0.460596I
2.33004 − 9.05208I 3.50054 + 8.35029I
u = −1.081080 − 0.631709I
a = −1.37993 − 1.31396I
b = −1.64849 + 0.60404I
2.33004 − 4.99231I 3.50054 + 1.42209I
u = −1.081080 − 0.631709I
a = 1.86710 + 0.64436I
b = 1.37146 − 1.49384I
2.33004 − 9.05208I 3.50054 + 8.35029I
u = 0.439259 + 0.522038I
a = 0.62115 + 1.61415I
b = −0.087698 − 0.114607I
−3.64484 − 1.57512I 5.19508 + 2.09453I
u = 0.439259 + 0.522038I
a = 0.90086 + 1.58512I
b = 0.000049 + 1.243830I
−3.64484 + 2.48465I 5.19508 − 4.83368I
u = 0.439259 + 0.522038I
a = 0.06157 − 2.48781I
b = −0.47411 − 1.63416I
−3.64484 − 1.57512I 5.19508 + 2.09453I
u = 0.439259 + 0.522038I
a = −1.99884 − 1.73954I
b = −1.233620 + 0.117096I
−3.64484 + 2.48465I 5.19508 − 4.83368I
15
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.439259 − 0.522038I
a = 0.62115 − 1.61415I
b = −0.087698 + 0.114607I
−3.64484 + 1.57512I 5.19508 − 2.09453I
u = 0.439259 − 0.522038I
a = 0.90086 − 1.58512I
b = 0.000049 − 1.243830I
−3.64484 − 2.48465I 5.19508 + 4.83368I
u = 0.439259 − 0.522038I
a = 0.06157 + 2.48781I
b = −0.47411 + 1.63416I
−3.64484 + 1.57512I 5.19508 − 2.09453I
u = 0.439259 − 0.522038I
a = −1.99884 + 1.73954I
b = −1.233620 − 0.117096I
−3.64484 − 2.48465I 5.19508 + 4.83368I
16
III.
I
u
3
= h−u
19
− u
18
+ · · · + b − 1, u
16
+ u
15
+ · · · + a + 1, u
20
+ u
19
+ · · · + u + 1i
(i) Arc colorings
a
3
=
1
0
a
6
=
0
u
a
2
=
1
−u
2
a
1
=
−u
2
+ 1
−u
2
a
7
=
u
5
− 2u
3
+ u
u
5
− u
3
+ u
a
5
=
u
−u
3
+ u
a
10
=
−u
16
− u
15
+ ··· − u − 1
u
19
+ u
18
+ ··· − u + 1
a
4
=
u
17
+ u
16
+ ··· + u
2
+ 3u
−u
19
+ 6u
17
+ ··· − 2u
3
+ 3u
2
a
9
=
−u
19
+ 5u
17
+ ··· − u − 1
u
19
+ u
18
+ ··· − u + 2
a
8
=
−u
19
+ 5u
17
+ ··· − u − 2
u
19
+ u
18
+ ··· − u + 1
a
12
=
u
19
− 6u
17
+ ··· − u + 2
−u
18
+ u
17
+ ··· + u − 2
a
11
=
u
19
− 6u
17
+ ··· − u + 2
−u
18
+ 5u
16
+ ··· + u − 1
(ii) Obstruction class = 1
(iii) Cusp Shapes = −4u
19
+ 21u
17
+ 3u
16
−57u
15
−14u
14
+ 89u
13
+ 34u
12
−86u
11
−
45u
10
+ 43u
9
+ 36u
8
− 8u
7
− 7u
6
− 3u
5
− 8u
4
− u
3
+ 13u
2
− 2u − 3
17
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
20
− 11u
19
+ ··· − 5u + 1
c
2
u
20
+ u
19
+ ··· + u + 1
c
3
, c
10
u
20
+ 9u
18
+ ··· − 3u + 1
c
4
u
20
+ 9u
18
+ ··· + 3u + 1
c
5
u
20
− u
19
+ ··· − u + 1
c
6
u
20
− 3u
19
+ ··· − 3u + 1
c
7
u
20
− u
19
+ ··· + 2u + 1
c
8
u
20
+ u
19
+ ··· + u + 101
c
9
u
20
+ 2u
19
+ ··· − u + 1
c
11
u
20
+ u
19
+ ··· − 2u + 1
c
12
u
20
− 2u
19
+ ··· + u + 1
18
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
20
+ y
19
+ ··· − y + 1
c
2
, c
5
y
20
− 11y
19
+ ··· − 5y + 1
c
3
, c
4
, c
10
y
20
+ 18y
19
+ ··· + y + 1
c
6
y
20
+ 9y
19
+ ··· + 5y + 1
c
7
, c
11
y
20
+ 11y
19
+ ··· − 2y + 1
c
8
y
20
+ 5y
19
+ ··· − 7071y + 10201
c
9
, c
12
y
20
− 2y
19
+ ··· + 11y + 1
19
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = −0.986798 + 0.418262I
a = 0.916722 + 0.179386I
b = −0.72653 + 1.86571I
−6.22972 + 0.44184I −0.71189 − 3.55840I
u = −0.986798 − 0.418262I
a = 0.916722 − 0.179386I
b = −0.72653 − 1.86571I
−6.22972 − 0.44184I −0.71189 + 3.55840I
u = 1.056360 + 0.185688I
a = 0.920530 − 0.435659I
b = −0.539001 − 0.524223I
−0.333887 − 0.354532I 3.85326 + 1.48197I
u = 1.056360 − 0.185688I
a = 0.920530 + 0.435659I
b = −0.539001 + 0.524223I
−0.333887 + 0.354532I 3.85326 − 1.48197I
u = −0.463700 + 0.776372I
a = 1.094600 − 0.505689I
b = 1.34865 − 0.43580I
4.58119 − 1.46415I 7.52882 + 0.72109I
u = −0.463700 − 0.776372I
a = 1.094600 + 0.505689I
b = 1.34865 + 0.43580I
4.58119 + 1.46415I 7.52882 − 0.72109I
u = 0.998878 + 0.504762I
a = −2.38196 − 0.40426I
b = −1.20506 + 1.03770I
−5.62654 − 5.35911I −0.67945 + 5.04575I
u = 0.998878 − 0.504762I
a = −2.38196 + 0.40426I
b = −1.20506 − 1.03770I
−5.62654 + 5.35911I −0.67945 − 5.04575I
u = 0.619770 + 0.457053I
a = 0.74949 + 2.56110I
b = 0.645794 + 0.713320I
−4.41314 + 1.30187I 1.37797 + 0.73682I
u = 0.619770 − 0.457053I
a = 0.74949 − 2.56110I
b = 0.645794 − 0.713320I
−4.41314 − 1.30187I 1.37797 − 0.73682I
20
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = −0.696477 + 0.280022I
a = 0.431012 − 0.388308I
b = 0.11010 + 1.65096I
−5.12204 + 2.74361I 2.78554 − 4.12363I
u = −0.696477 − 0.280022I
a = 0.431012 + 0.388308I
b = 0.11010 − 1.65096I
−5.12204 − 2.74361I 2.78554 + 4.12363I
u = −1.090000 + 0.616356I
a = −1.08636 + 1.09305I
b = −1.32363 − 0.76947I
2.71510 + 6.72791I 4.63472 − 5.67234I
u = −1.090000 − 0.616356I
a = −1.08636 − 1.09305I
b = −1.32363 + 0.76947I
2.71510 − 6.72791I 4.63472 + 5.67234I
u = −1.187500 + 0.437992I
a = −0.266528 − 0.704783I
b = 0.904799 − 1.025460I
−9.61313 + 5.54516I −3.77106 − 2.99593I
u = −1.187500 − 0.437992I
a = −0.266528 + 0.704783I
b = 0.904799 + 1.025460I
−9.61313 − 5.54516I −3.77106 + 2.99593I
u = 0.060744 + 0.729831I
a = −1.29396 − 0.92044I
b = −0.566056 − 0.737960I
−6.10698 − 1.39664I −0.706411 + 0.849051I
u = 0.060744 − 0.729831I
a = −1.29396 + 0.92044I
b = −0.566056 + 0.737960I
−6.10698 + 1.39664I −0.706411 − 0.849051I
u = 1.188720 + 0.477485I
a = 0.916450 + 0.427522I
b = 0.850927 − 0.434222I
−9.32928 − 3.08388I −5.31149 + 2.51247I
u = 1.188720 − 0.477485I
a = 0.916450 − 0.427522I
b = 0.850927 + 0.434222I
−9.32928 + 3.08388I −5.31149 − 2.51247I
21
IV. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
((u
11
+ 5u
10
+ ··· + 2u + 1)
4
)(u
20
− 11u
19
+ ··· − 5u + 1)
· (u
33
+ 16u
32
+ ··· + 172u + 16)
c
2
(u
11
− u
10
− 2u
9
+ 3u
8
+ 2u
7
− 4u
6
+ 3u
4
− u
3
− u
2
+ 1)
4
· (u
20
+ u
19
+ ··· + u + 1)(u
33
+ 6u
32
+ ··· − 10u − 4)
c
3
, c
10
(u
20
+ 9u
18
+ ··· − 3u + 1)(u
33
+ 9u
31
+ ··· + 2u − 1)
· (u
44
+ u
43
+ ··· + 6594u + 4921)
c
4
(u
20
+ 9u
18
+ ··· + 3u + 1)(u
33
+ 9u
31
+ ··· + 2u − 1)
· (u
44
+ u
43
+ ··· + 6594u + 4921)
c
5
(u
11
− u
10
− 2u
9
+ 3u
8
+ 2u
7
− 4u
6
+ 3u
4
− u
3
− u
2
+ 1)
4
· (u
20
− u
19
+ ··· − u + 1)(u
33
+ 6u
32
+ ··· − 10u − 4)
c
6
(u
11
− 3u
10
+ 4u
9
− u
8
+ 2u
7
− 8u
6
+ 8u
5
+ 5u
4
− 3u
3
− u
2
+ 4u − 1)
4
· (u
20
− 3u
19
+ ··· − 3u + 1)(u
33
+ 18u
32
+ ··· − 1198u − 188)
c
7
((u
2
+ u + 1)
22
)(u
20
− u
19
+ ··· + 2u + 1)
· (u
33
− 24u
32
+ ··· + 26624u − 2048)
c
8
(u
20
+ u
19
+ ··· + u + 101)(u
33
− u
32
+ ··· + 106u − 23)
· (u
44
− u
43
+ ··· + 472696u + 34447)
c
9
(u
20
+ 2u
19
+ ··· − u + 1)(u
33
+ 2u
32
+ ··· − 16u − 1)
· (u
44
+ 9u
43
+ ··· + 1718u + 241)
c
11
((u
2
+ u + 1)
22
)(u
20
+ u
19
+ ··· − 2u + 1)
· (u
33
− 24u
32
+ ··· + 26624u − 2048)
c
12
(u
20
− 2u
19
+ ··· + u + 1)(u
33
+ 2u
32
+ ··· − 16u − 1)
· (u
44
+ 9u
43
+ ··· + 1718u + 241)
22
V. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
((y
11
+ 3y
10
+ ··· − 10y −1)
4
)(y
20
+ y
19
+ ··· − y + 1)
· (y
33
+ 4y
32
+ ··· + 9456y −256)
c
2
, c
5
((y
11
− 5y
10
+ ··· + 2y −1)
4
)(y
20
− 11y
19
+ ··· − 5y + 1)
· (y
33
− 16y
32
+ ··· + 172y −16)
c
3
, c
4
, c
10
(y
20
+ 18y
19
+ ··· + y + 1)(y
33
+ 18y
32
+ ··· − 4y −1)
· (y
44
+ 27y
43
+ ··· + 362915028y + 24216241)
c
6
((y
11
− y
10
+ ··· + 14y −1)
4
)(y
20
+ 9y
19
+ ··· + 5y + 1)
· (y
33
+ 8y
32
+ ··· + 252684y −35344)
c
7
, c
11
((y
2
+ y + 1)
22
)(y
20
+ 11y
19
+ ··· − 2y + 1)
· (y
33
+ 12y
32
+ ··· + 2097152y −4194304)
c
8
(y
20
+ 5y
19
+ ··· − 7071y + 10201)
· (y
33
− 31y
32
+ ··· + 16020y −529)
· (y
44
+ 3y
43
+ ··· + 16852909668y + 1186595809)
c
9
, c
12
(y
20
− 2y
19
+ ··· + 11y + 1)(y
33
− 42y
32
+ ··· + 54y −1)
· (y
44
− 13y
43
+ ··· + 3475464y + 58081)
23
