12n
0389
(K12n
0389
)
A knot diagram
1
Linearized knot diagam
3 6 7 9 2 12 5 10 4 8 6 7
Solving Sequence
4,9 2,5
6 10 8 11 12 7 3 1
c
4
c
5
c
9
c
8
c
10
c
11
c
7
c
3
c
1
c
2
, c
6
, c
12
Ideals for irreducible components
2
of X
par
I
u
1
= h−u
27
− 2u
26
+ ··· + b − 1, u
27
+ u
26
+ ··· + 2a − 2, u
28
+ 3u
27
+ ··· + 2u + 2i
I
u
2
= h−u
15
a + u
15
+ ··· − a + 3, −2u
15
a + 2u
15
+ ··· − 2a + 2,
u
16
− u
15
+ 3u
14
− 2u
13
+ 7u
12
− 4u
11
+ 10u
10
− 4u
9
+ 11u
8
− 2u
7
+ 8u
6
+ 4u
4
+ 2u
3
+ 2u − 1i
I
u
3
= h−u
2
+ b − u + 1, −u
3
+ 2u
2
+ 2a − u + 4, u
4
+ u
2
+ 2i
I
u
4
= hb + u + 2, a + u + 3, u
2
+ 1i
I
u
5
= hu
3
+ u
2
+ b + 1, a − u − 1, u
4
+ 1i
I
v
1
= ha, b + 1, v + 1i
* 6 irreducible components of dim
C
= 0, with total 71 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−u
27
−2u
26
+· · ·+b−1, u
27
+u
26
+· · ·+2a−2, u
28
+3u
27
+· · ·+2u+2i
(i) Arc colorings
a
4
=
1
0
a
9
=
0
u
a
2
=
−
1
2
u
27
−
1
2
u
26
+ ··· − u + 1
u
27
+ 2u
26
+ ··· + u + 1
a
5
=
1
−u
2
a
6
=
1
2
u
27
+
1
2
u
26
+ ··· +
7
2
u
3
− u
2
−u
26
− u
25
+ ··· + u − 1
a
10
=
u
u
a
8
=
u
3
u
3
+ u
a
11
=
u
5
+ u
u
5
+ u
3
+ u
a
12
=
−
1
2
u
27
−
1
2
u
26
+ ··· −
7
2
u
3
+ u
2
u
27
+ 2u
26
+ ··· + 2u + 1
a
7
=
−u
5
− u
u
7
+ u
5
+ 2u
3
+ u
a
3
=
−u
12
− u
10
− 3u
8
− 2u
6
− 2u
4
− u
2
+ 1
u
14
+ 2u
12
+ 5u
10
+ 6u
8
+ 6u
6
+ 4u
4
+ u
2
a
1
=
5
2
u
27
+
7
2
u
26
+ ··· − u
2
+ 3u
−3u
27
− 6u
26
+ ··· − 5u − 3
(ii) Obstruction class = −1
(iii) Cusp Shapes = 8u
27
+ 18u
26
+ 54u
25
+ 80u
24
+ 176u
23
+ 218u
22
+ 384u
21
+
390u
20
+ 606u
19
+ 500u
18
+ 704u
17
+ 440u
16
+ 614u
15
+ 222u
14
+ 372u
13
− 16u
12
+
148u
11
− 146u
10
+ 30u
9
− 136u
8
− 10u
7
− 92u
6
− 6u
5
− 34u
4
+ 8u
3
+ 8u
2
+ 22u + 4
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
28
+ 7u
27
+ ··· + 8u + 1
c
2
, c
5
, c
6
c
11
, c
12
u
28
+ u
27
+ ··· + 2u + 1
c
3
u
28
− 3u
27
+ ··· − 238u + 50
c
4
, c
9
u
28
− 3u
27
+ ··· − 2u + 2
c
7
u
28
+ 15u
27
+ ··· + 1134u + 158
c
8
, c
10
u
28
+ 9u
27
+ ··· + 20u + 4
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
28
+ 41y
27
+ ··· + 36y + 1
c
2
, c
5
, c
6
c
11
, c
12
y
28
− 7y
27
+ ··· − 8y + 1
c
3
y
28
− 15y
27
+ ··· + 253556y + 2500
c
4
, c
9
y
28
+ 9y
27
+ ··· + 20y + 4
c
7
y
28
− 3y
27
+ ··· + 228948y + 24964
c
8
, c
10
y
28
+ 21y
27
+ ··· + 112y + 16
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.357080 + 0.990708I
a = 1.17579 + 1.29712I
b = 0.966655 − 0.502162I
1.10269 − 2.91896I −6.58916 + 1.35621I
u = 0.357080 − 0.990708I
a = 1.17579 − 1.29712I
b = 0.966655 + 0.502162I
1.10269 + 2.91896I −6.58916 − 1.35621I
u = 0.009749 + 1.057290I
a = −2.21816 − 0.73889I
b = −1.78141 − 0.42208I
−5.12130 − 1.42409I −9.75378 + 4.84787I
u = 0.009749 − 1.057290I
a = −2.21816 + 0.73889I
b = −1.78141 + 0.42208I
−5.12130 + 1.42409I −9.75378 − 4.84787I
u = −0.675265 + 0.641850I
a = 0.942832 + 0.025360I
b = −0.656487 + 0.567996I
0.029347 − 0.742942I −2.66483 + 4.11260I
u = −0.675265 − 0.641850I
a = 0.942832 − 0.025360I
b = −0.656487 − 0.567996I
0.029347 + 0.742942I −2.66483 − 4.11260I
u = 0.201680 + 1.066800I
a = 2.93136 + 0.13549I
b = 2.18433 − 0.34282I
0.10693 + 9.35469I −8.40093 − 7.64801I
u = 0.201680 − 1.066800I
a = 2.93136 − 0.13549I
b = 2.18433 + 0.34282I
0.10693 − 9.35469I −8.40093 + 7.64801I
u = −0.851089 + 0.709851I
a = −0.654367 − 0.630430I
b = 2.05001 − 1.47929I
7.15859 + 9.12533I −2.05138 − 4.56575I
u = −0.851089 − 0.709851I
a = −0.654367 + 0.630430I
b = 2.05001 + 1.47929I
7.15859 − 9.12533I −2.05138 + 4.56575I
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.672429 + 0.567673I
a = 0.911611 + 0.160034I
b = −0.71715 − 1.22852I
−0.04567 − 2.37011I −3.07191 + 4.49176I
u = 0.672429 − 0.567673I
a = 0.911611 − 0.160034I
b = −0.71715 + 1.22852I
−0.04567 + 2.37011I −3.07191 − 4.49176I
u = −0.840063 + 0.786573I
a = −0.492673 + 0.823459I
b = −0.087379 + 0.226571I
8.56887 − 4.65353I −0.39876 + 4.46500I
u = −0.840063 − 0.786573I
a = −0.492673 − 0.823459I
b = −0.087379 − 0.226571I
8.56887 + 4.65353I −0.39876 − 4.46500I
u = 0.758184 + 0.875112I
a = 0.635547 + 0.434170I
b = 0.649386 + 0.105970I
4.62333 + 2.86656I 2.11844 − 3.14500I
u = 0.758184 − 0.875112I
a = 0.635547 − 0.434170I
b = 0.649386 − 0.105970I
4.62333 − 2.86656I 2.11844 + 3.14500I
u = 0.638350 + 1.005070I
a = −2.04567 − 0.58767I
b = −1.19550 + 1.80863I
−1.27376 + 7.45615I −5.74748 − 10.04223I
u = 0.638350 − 1.005070I
a = −2.04567 + 0.58767I
b = −1.19550 − 1.80863I
−1.27376 − 7.45615I −5.74748 + 10.04223I
u = −0.660931 + 0.998814I
a = −1.00547 + 1.02454I
b = −1.24984 − 0.99805I
−1.01565 − 4.47891I −4.23563 + 0.76999I
u = −0.660931 − 0.998814I
a = −1.00547 − 1.02454I
b = −1.24984 + 0.99805I
−1.01565 + 4.47891I −4.23563 − 0.76999I
6
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.776659 + 0.972247I
a = −0.490506 − 0.576756I
b = −0.217973 + 0.023439I
7.99447 − 1.37799I −1.229837 + 0.612967I
u = −0.776659 − 0.972247I
a = −0.490506 + 0.576756I
b = −0.217973 − 0.023439I
7.99447 + 1.37799I −1.229837 − 0.612967I
u = −0.747656 + 1.019100I
a = 2.07210 − 1.69147I
b = 2.41123 + 1.53544I
6.2073 − 15.0893I −3.71765 + 9.34150I
u = −0.747656 − 1.019100I
a = 2.07210 + 1.69147I
b = 2.41123 − 1.53544I
6.2073 + 15.0893I −3.71765 − 9.34150I
u = 0.697614 + 0.095875I
a = −0.669180 − 0.749710I
b = 1.260170 − 0.377922I
3.91681 + 6.47583I −1.45394 − 5.09717I
u = 0.697614 − 0.095875I
a = −0.669180 + 0.749710I
b = 1.260170 + 0.377922I
3.91681 − 6.47583I −1.45394 + 5.09717I
u = −0.283422 + 0.542166I
a = 0.906792 − 0.049620I
b = −0.116042 − 0.108742I
−0.175714 − 1.037120I −2.80315 + 6.64420I
u = −0.283422 − 0.542166I
a = 0.906792 + 0.049620I
b = −0.116042 + 0.108742I
−0.175714 + 1.037120I −2.80315 − 6.64420I
7
II. I
u
2
=
h−u
15
a+u
15
+· · ·−a+3, −2u
15
a+2u
15
+· · ·−2a+2, u
16
−u
15
+· · ·+2u−1i
(i) Arc colorings
a
4
=
1
0
a
9
=
0
u
a
2
=
a
1
2
u
15
a −
1
2
u
15
+ ··· +
1
2
a −
3
2
a
5
=
1
−u
2
a
6
=
1
2
u
15
a −
1
2
u
15
+ ··· +
3
2
a −
3
2
u
12
+ 2u
10
+ ··· + 2u + 1
a
10
=
u
u
a
8
=
u
3
u
3
+ u
a
11
=
u
5
+ u
u
5
+ u
3
+ u
a
12
=
−
1
2
u
15
a +
1
2
u
15
+ ··· −
3
2
a +
3
2
−
1
2
u
15
a +
1
2
u
15
+ ··· −
1
2
a +
3
2
a
7
=
−u
5
− u
u
7
+ u
5
+ 2u
3
+ u
a
3
=
−u
12
− u
10
− 3u
8
− 2u
6
− 2u
4
− u
2
+ 1
u
14
+ 2u
12
+ 5u
10
+ 6u
8
+ 6u
6
+ 4u
4
+ u
2
a
1
=
1
2
u
15
a −
1
2
u
15
+ ··· +
3
2
a −
1
2
u
15
a − u
15
+ ··· + a − 2
(ii) Obstruction class = −1
(iii) Cusp Shapes
= 4u
15
+8u
13
+4u
12
+20u
11
+8u
10
+24u
9
+16u
8
+28u
7
+20u
6
+20u
5
+16u
4
+12u
3
+12u
2
−2
8
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
32
+ 13u
31
+ ··· + 2505u + 256
c
2
, c
5
, c
6
c
11
, c
12
u
32
+ u
31
+ ··· − 13u − 16
c
3
(u
16
+ u
15
+ ··· + 2u
2
− 1)
2
c
4
, c
9
(u
16
+ u
15
+ ··· − 2u − 1)
2
c
7
(u
16
− 5u
15
+ ··· + 8u − 7)
2
c
8
, c
10
(u
16
+ 5u
15
+ ··· − 4u + 1)
2
9
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
32
+ 11y
31
+ ··· + 1013295y + 65536
c
2
, c
5
, c
6
c
11
, c
12
y
32
− 13y
31
+ ··· − 2505y + 256
c
3
(y
16
− 19y
15
+ ··· − 4y + 1)
2
c
4
, c
9
(y
16
+ 5y
15
+ ··· − 4y + 1)
2
c
7
(y
16
− 7y
15
+ ··· − 344y + 49)
2
c
8
, c
10
(y
16
+ 13y
15
+ ··· − 48y + 1)
2
10
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.254861 + 1.023380I
a = 0.50162 − 1.49362I
b = 0.607139 − 0.301866I
1.40970 − 3.12434I −6.05940 + 3.66013I
u = −0.254861 + 1.023380I
a = 2.28656 + 0.08597I
b = 1.340560 + 0.447711I
1.40970 − 3.12434I −6.05940 + 3.66013I
u = −0.254861 − 1.023380I
a = 0.50162 + 1.49362I
b = 0.607139 + 0.301866I
1.40970 + 3.12434I −6.05940 − 3.66013I
u = −0.254861 − 1.023380I
a = 2.28656 − 0.08597I
b = 1.340560 − 0.447711I
1.40970 + 3.12434I −6.05940 − 3.66013I
u = −0.750689 + 0.759364I
a = 0.956948 − 0.036904I
b = −1.17813 + 1.16703I
0.311107 + 0.489680I −1.64393 − 1.43137I
u = −0.750689 + 0.759364I
a = 0.919406 − 0.682819I
b = 1.233040 + 0.594121I
0.311107 + 0.489680I −1.64393 − 1.43137I
u = −0.750689 − 0.759364I
a = 0.956948 + 0.036904I
b = −1.17813 − 1.16703I
0.311107 − 0.489680I −1.64393 + 1.43137I
u = −0.750689 − 0.759364I
a = 0.919406 + 0.682819I
b = 1.233040 − 0.594121I
0.311107 − 0.489680I −1.64393 + 1.43137I
u = 0.099165 + 0.920214I
a = 0.97209 + 1.30975I
b = 0.277510 + 1.275700I
−5.17692 + 1.52971I −10.72737 − 5.08772I
u = 0.099165 + 0.920214I
a = −3.76471 − 0.60851I
b = −2.03422 + 0.24629I
−5.17692 + 1.52971I −10.72737 − 5.08772I
11
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.099165 − 0.920214I
a = 0.97209 − 1.30975I
b = 0.277510 − 1.275700I
−5.17692 − 1.52971I −10.72737 + 5.08772I
u = 0.099165 − 0.920214I
a = −3.76471 + 0.60851I
b = −2.03422 − 0.24629I
−5.17692 − 1.52971I −10.72737 + 5.08772I
u = 0.665350 + 0.873267I
a = 1.003110 − 0.569330I
b = −1.41970 − 1.66184I
−2.27257 + 2.57669I −7.30756 − 2.71681I
u = 0.665350 + 0.873267I
a = −1.91799 − 2.15716I
b = −1.96956 + 1.27998I
−2.27257 + 2.57669I −7.30756 − 2.71681I
u = 0.665350 − 0.873267I
a = 1.003110 + 0.569330I
b = −1.41970 + 1.66184I
−2.27257 − 2.57669I −7.30756 + 2.71681I
u = 0.665350 − 0.873267I
a = −1.91799 + 2.15716I
b = −1.96956 − 1.27998I
−2.27257 − 2.57669I −7.30756 + 2.71681I
u = 0.847960 + 0.745397I
a = −0.230594 + 0.489998I
b = 1.59945 + 1.15994I
8.61070 − 2.28357I −0.075280 + 0.308256I
u = 0.847960 + 0.745397I
a = −0.198841 − 0.492541I
b = 0.097691 − 0.720809I
8.61070 − 2.28357I −0.075280 + 0.308256I
u = 0.847960 − 0.745397I
a = −0.230594 − 0.489998I
b = 1.59945 − 1.15994I
8.61070 + 2.28357I −0.075280 − 0.308256I
u = 0.847960 − 0.745397I
a = −0.198841 + 0.492541I
b = 0.097691 + 0.720809I
8.61070 + 2.28357I −0.075280 − 0.308256I
12
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.716556 + 0.957138I
a = 0.113653 − 1.335050I
b = 1.35141 − 0.89567I
−0.28749 − 6.07197I −3.38425 + 7.02814I
u = −0.716556 + 0.957138I
a = −1.51453 + 1.63636I
b = −1.57634 − 1.36115I
−0.28749 − 6.07197I −3.38425 + 7.02814I
u = −0.716556 − 0.957138I
a = 0.113653 + 1.335050I
b = 1.35141 + 0.89567I
−0.28749 + 6.07197I −3.38425 − 7.02814I
u = −0.716556 − 0.957138I
a = −1.51453 − 1.63636I
b = −1.57634 + 1.36115I
−0.28749 + 6.07197I −3.38425 − 7.02814I
u = 0.761782 + 1.000110I
a = −0.879278 + 0.655399I
b = −0.021538 + 0.554655I
7.82454 + 8.28859I −1.42292 − 5.27135I
u = 0.761782 + 1.000110I
a = 1.69603 + 1.36600I
b = 1.82121 − 1.08166I
7.82454 + 8.28859I −1.42292 − 5.27135I
u = 0.761782 − 1.000110I
a = −0.879278 − 0.655399I
b = −0.021538 − 0.554655I
7.82454 − 8.28859I −1.42292 + 5.27135I
u = 0.761782 − 1.000110I
a = 1.69603 − 1.36600I
b = 1.82121 + 1.08166I
7.82454 − 8.28859I −1.42292 + 5.27135I
u = −0.689113
a = −0.213554 + 0.496575I
b = 0.887810 + 0.688994I
4.71670 0.147800
u = −0.689113
a = −0.213554 − 0.496575I
b = 0.887810 − 0.688994I
4.71670 0.147800
13
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.384812
a = 1.07569
b = −1.31135
−2.52578 1.09360
u = 0.384812
a = 2.46446
b = 0.278658
−2.52578 1.09360
14
III. I
u
3
= h−u
2
+ b − u + 1, −u
3
+ 2u
2
+ 2a − u + 4, u
4
+ u
2
+ 2i
(i) Arc colorings
a
4
=
1
0
a
9
=
0
u
a
2
=
1
2
u
3
− u
2
+
1
2
u − 2
u
2
+ u − 1
a
5
=
1
−u
2
a
6
=
1
2
u
3
− u
2
+
1
2
u − 1
u − 1
a
10
=
u
u
a
8
=
u
3
u
3
+ u
a
11
=
−u
3
− u
−u
a
12
=
−
1
2
u
3
− u
2
−
1
2
u − 1
−1
a
7
=
u
3
+ u
u
a
3
=
−1
u
2
a
1
=
1
2
u
3
− u
2
+
1
2
u − 1
u − 1
(ii) Obstruction class = 1
(iii) Cusp Shapes = −4u
2
− 12
15
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
5
, c
11
c
12
(u − 1)
4
c
2
, c
6
(u + 1)
4
c
3
, c
4
, c
7
c
9
u
4
+ u
2
+ 2
c
8
(u
2
− u + 2)
2
c
10
(u
2
+ u + 2)
2
16
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
2
, c
5
c
6
, c
11
, c
12
(y −1)
4
c
3
, c
4
, c
7
c
9
(y
2
+ y + 2)
2
c
8
, c
10
(y
2
+ 3y + 4)
2
17
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = 0.676097 + 0.978318I
a = −1.97807 − 0.63110I
b = −0.82390 + 2.30119I
−2.46740 + 5.33349I −10.00000 − 5.29150I
u = 0.676097 − 0.978318I
a = −1.97807 + 0.63110I
b = −0.82390 − 2.30119I
−2.46740 − 5.33349I −10.00000 + 5.29150I
u = −0.676097 + 0.978318I
a = −1.02193 + 2.01465I
b = −2.17610 − 0.34456I
−2.46740 − 5.33349I −10.00000 + 5.29150I
u = −0.676097 − 0.978318I
a = −1.02193 − 2.01465I
b = −2.17610 + 0.34456I
−2.46740 + 5.33349I −10.00000 − 5.29150I
18
IV. I
u
4
= hb + u + 2, a + u + 3, u
2
+ 1i
(i) Arc colorings
a
4
=
1
0
a
9
=
0
u
a
2
=
−u − 3
−u − 2
a
5
=
1
1
a
6
=
−u − 2
−u − 1
a
10
=
u
u
a
8
=
−u
0
a
11
=
2u
u
a
12
=
u − 2
−1
a
7
=
−2u
−u
a
3
=
−1
−1
a
1
=
−u − 2
−u − 1
(ii) Obstruction class = 1
(iii) Cusp Shapes = −16
19
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
5
, c
8
c
11
, c
12
(u − 1)
2
c
2
, c
6
, c
10
(u + 1)
2
c
3
, c
4
, c
7
c
9
u
2
+ 1
20
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
2
, c
5
c
6
, c
8
, c
10
c
11
, c
12
(y −1)
2
c
3
, c
4
, c
7
c
9
(y + 1)
2
21
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
4
√
−1(vol +
√
−1CS) Cusp shape
u = 1.000000I
a = −3.00000 − 1.00000I
b = −2.00000 − 1.00000I
−6.57974 −16.0000
u = − 1.000000I
a = −3.00000 + 1.00000I
b = −2.00000 + 1.00000I
−6.57974 −16.0000
22
V. I
u
5
= hu
3
+ u
2
+ b + 1, a − u − 1, u
4
+ 1i
(i) Arc colorings
a
4
=
1
0
a
9
=
0
u
a
2
=
u + 1
−u
3
− u
2
− 1
a
5
=
1
−u
2
a
6
=
−u
u
3
+ 1
a
10
=
u
u
a
8
=
u
3
u
3
+ u
a
11
=
0
u
3
a
12
=
u
−1
a
7
=
0
u
3
a
3
=
1
−u
2
a
1
=
u
−u
3
− 1
(ii) Obstruction class = 1
(iii) Cusp Shapes = −8
23
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
2
, c
6
(u − 1)
4
c
3
, c
4
, c
7
c
9
u
4
+ 1
c
5
, c
11
, c
12
(u + 1)
4
c
8
, c
10
(u
2
+ 1)
2
24
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
2
, c
5
c
6
, c
11
, c
12
(y −1)
4
c
3
, c
4
, c
7
c
9
(y
2
+ 1)
2
c
8
, c
10
(y + 1)
4
25
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
5
√
−1(vol +
√
−1CS) Cusp shape
u = 0.707107 + 0.707107I
a = 1.70711 + 0.70711I
b = −0.29289 − 1.70711I
−1.64493 −8.00000
u = 0.707107 − 0.707107I
a = 1.70711 − 0.70711I
b = −0.29289 + 1.70711I
−1.64493 −8.00000
u = −0.707107 + 0.707107I
a = 0.292893 + 0.707107I
b = −1.70711 + 0.29289I
−1.64493 −8.00000
u = −0.707107 − 0.707107I
a = 0.292893 − 0.707107I
b = −1.70711 − 0.29289I
−1.64493 −8.00000
26
VI. I
v
1
= ha, b + 1, v + 1i
(i) Arc colorings
a
4
=
1
0
a
9
=
−1
0
a
2
=
0
−1
a
5
=
1
0
a
6
=
1
1
a
10
=
−1
0
a
8
=
−1
0
a
11
=
−1
0
a
12
=
−2
−1
a
7
=
−1
0
a
3
=
1
0
a
1
=
−1
−1
(ii) Obstruction class = 1
(iii) Cusp Shapes = −12
27
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
2
, c
6
u − 1
c
3
, c
4
, c
7
c
8
, c
9
, c
10
u
c
5
, c
11
, c
12
u + 1
28
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
2
, c
5
c
6
, c
11
, c
12
y −1
c
3
, c
4
, c
7
c
8
, c
9
, c
10
y
29
(vi) Complex Volumes and Cusp Shapes
Solutions to I
v
1
√
−1(vol +
√
−1CS) Cusp shape
v = −1.00000
a = 0
b = −1.00000
−3.28987 −12.0000
30
VII. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
((u − 1)
11
)(u
28
+ 7u
27
+ ··· + 8u + 1)(u
32
+ 13u
31
+ ··· + 2505u + 256)
c
2
, c
6
((u − 1)
5
)(u + 1)
6
(u
28
+ u
27
+ ··· + 2u + 1)(u
32
+ u
31
+ ··· − 13u − 16)
c
3
u(u
2
+ 1)(u
4
+ 1)(u
4
+ u
2
+ 2)(u
16
+ u
15
+ ··· + 2u
2
− 1)
2
· (u
28
− 3u
27
+ ··· − 238u + 50)
c
4
, c
9
u(u
2
+ 1)(u
4
+ 1)(u
4
+ u
2
+ 2)(u
16
+ u
15
+ ··· − 2u − 1)
2
· (u
28
− 3u
27
+ ··· − 2u + 2)
c
5
, c
11
, c
12
((u − 1)
6
)(u + 1)
5
(u
28
+ u
27
+ ··· + 2u + 1)(u
32
+ u
31
+ ··· − 13u − 16)
c
7
u(u
2
+ 1)(u
4
+ 1)(u
4
+ u
2
+ 2)(u
16
− 5u
15
+ ··· + 8u − 7)
2
· (u
28
+ 15u
27
+ ··· + 1134u + 158)
c
8
u(u − 1)
2
(u
2
+ 1)
2
(u
2
− u + 2)
2
(u
16
+ 5u
15
+ ··· − 4u + 1)
2
· (u
28
+ 9u
27
+ ··· + 20u + 4)
c
10
u(u + 1)
2
(u
2
+ 1)
2
(u
2
+ u + 2)
2
(u
16
+ 5u
15
+ ··· − 4u + 1)
2
· (u
28
+ 9u
27
+ ··· + 20u + 4)
31
VIII. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
((y −1)
11
)(y
28
+ 41y
27
+ ··· + 36y + 1)
· (y
32
+ 11y
31
+ ··· + 1013295y + 65536)
c
2
, c
5
, c
6
c
11
, c
12
((y −1)
11
)(y
28
− 7y
27
+ ··· − 8y + 1)(y
32
− 13y
31
+ ··· − 2505y + 256)
c
3
y(y + 1)
2
(y
2
+ 1)
2
(y
2
+ y + 2)
2
(y
16
− 19y
15
+ ··· − 4y + 1)
2
· (y
28
− 15y
27
+ ··· + 253556y + 2500)
c
4
, c
9
y(y + 1)
2
(y
2
+ 1)
2
(y
2
+ y + 2)
2
(y
16
+ 5y
15
+ ··· − 4y + 1)
2
· (y
28
+ 9y
27
+ ··· + 20y + 4)
c
7
y(y + 1)
2
(y
2
+ 1)
2
(y
2
+ y + 2)
2
(y
16
− 7y
15
+ ··· − 344y + 49)
2
· (y
28
− 3y
27
+ ··· + 228948y + 24964)
c
8
, c
10
y(y −1)
2
(y + 1)
4
(y
2
+ 3y + 4)
2
(y
16
+ 13y
15
+ ··· − 48y + 1)
2
· (y
28
+ 21y
27
+ ··· + 112y + 16)
32
