12n
0375
(K12n
0375
)
A knot diagram
1
Linearized knot diagam
3 6 8 9 2 11 3 12 5 6 9 7
Solving Sequence
2,6 3,10
11 7 8 1 5 9 4 12
c
2
c
10
c
6
c
7
c
1
c
5
c
9
c
4
c
12
c
3
, c
8
, c
11
Ideals for irreducible components
2
of X
par
I
u
1
= h339u
19
− 3935u
18
+ ··· + 809b + 2456, −1439u
19
+ 6826u
18
+ ··· + 2427a + 13155,
u
20
− 8u
19
+ ··· + 12u − 3i
I
u
2
= h−u
9
a − 9u
9
+ ··· − a − 15, −5u
9
a − u
9
+ ··· − 7a − 3,
u
10
+ 2u
9
+ u
8
− 3u
7
− 2u
6
+ 2u
5
+ 3u
4
− 2u
3
− u
2
+ 2u + 1i
I
u
3
= h2u
10
+ 9u
9
+ 14u
8
+ u
7
− 24u
6
− 23u
5
+ 11u
4
+ 29u
3
+ 7u
2
+ b − 13u − 5,
− 3u
10
− 14u
9
− 22u
8
+ 42u
6
+ 38u
5
− 22u
4
− 50u
3
− 9u
2
+ a + 24u + 7,
u
11
+ 5u
10
+ 9u
9
+ 3u
8
− 13u
7
− 17u
6
+ 2u
5
+ 18u
4
+ 9u
3
− 6u
2
− 5u − 1i
I
u
4
= hb
2
+ b − 1, a + 1, u − 1i
I
v
1
= ha, b + 1, v −1i
* 5 irreducible components of dim
C
= 0, with total 54 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
= h339u
19
− 3935u
18
+ · · · + 809b + 2456, −1439u
19
+ 6826u
18
+ · · · +
2427a + 13155, u
20
− 8u
19
+ · · · + 12u − 3i
(i) Arc colorings
a
2
=
1
0
a
6
=
0
u
a
3
=
1
u
2
a
10
=
0.592913u
19
− 2.81253u
18
+ ··· + 12.5904u − 5.42027
−0.419036u
19
+ 4.86403u
18
+ ··· + 14.5278u − 3.03585
a
11
=
0.592913u
19
− 2.81253u
18
+ ··· + 12.5904u − 5.42027
1.53276u
19
− 10.3375u
18
+ ··· − 6.86279u + 2.75649
a
7
=
−1.20231u
19
+ 7.31685u
18
+ ··· − 4.78451u + 3.02596
−1.03585u
19
+ 7.02967u
18
+ ··· + 3.81211u − 0.846724
a
8
=
−2.01937u
19
+ 15.3379u
18
+ ··· + 15.4157u − 3.03214
2.30161u
19
− 16.5600u
18
+ ··· − 16.4536u + 3.60692
a
1
=
−u
2
+ 1
−u
4
a
5
=
u
u
a
9
=
−0.918830u
19
+ 5.81788u
18
+ ··· + 10.5979u − 4.16316
−1.93078u
19
+ 13.4944u
18
+ ··· + 12.5352u − 1.77874
a
4
=
−0.952616u
19
+ 6.38607u
18
+ ··· + 9.11042u − 2.28307
0.817058u
19
− 8.02101u
18
+ ··· − 20.2002u + 6.05810
a
12
=
0.753605u
19
− 5.80758u
18
+ ··· − 4.77421u + 2.27194
−1.60939u
19
+ 12.5043u
18
+ ··· + 19.8059u − 5.39431
(ii) Obstruction class = −1
(iii) Cusp Shapes = −
277
809
u
19
+
4609
809
u
18
+ ··· +
33642
809
u −
32682
809
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
20
+ 8u
19
+ ··· + 150u + 9
c
2
, c
5
u
20
+ 8u
19
+ ··· − 12u − 3
c
3
, c
7
u
20
− 2u
19
+ ··· + u + 1
c
4
, c
9
u
20
− 8u
18
+ ··· + 3u + 1
c
6
, c
10
u
20
+ 6u
18
+ ··· + 9u + 1
c
8
, c
11
u
20
− 7u
19
+ ··· + 12u − 3
c
12
u
20
+ 21u
19
+ ··· + 6656u + 512
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
20
+ 16y
19
+ ··· − 5202y + 81
c
2
, c
5
y
20
− 8y
19
+ ··· − 150y + 9
c
3
, c
7
y
20
− 28y
19
+ ··· + 7y + 1
c
4
, c
9
y
20
− 16y
19
+ ··· + 5y + 1
c
6
, c
10
y
20
+ 12y
19
+ ··· − 21y + 1
c
8
, c
11
y
20
+ 11y
19
+ ··· − 132y + 9
c
12
y
20
− 9y
19
+ ··· − 2621440y + 262144
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.739766 + 0.810627I
a = −0.332052 − 0.863055I
b = −1.178040 − 0.181845I
−1.201950 + 0.670281I −8.29063 + 0.06466I
u = 0.739766 − 0.810627I
a = −0.332052 + 0.863055I
b = −1.178040 + 0.181845I
−1.201950 − 0.670281I −8.29063 − 0.06466I
u = 0.579374 + 0.935372I
a = −1.121180 − 0.363583I
b = −0.996152 + 0.778841I
6.00051 − 2.90762I −6.41870 + 3.35662I
u = 0.579374 − 0.935372I
a = −1.121180 + 0.363583I
b = −0.996152 − 0.778841I
6.00051 + 2.90762I −6.41870 − 3.35662I
u = 0.725363
a = 0.248162
b = −0.655437
−1.32826 −7.40410
u = −0.641694 + 0.281021I
a = 1.66993 − 0.14677I
b = 0.666818 − 0.229080I
2.15316 + 3.41819I 1.21797 − 1.44999I
u = −0.641694 − 0.281021I
a = 1.66993 + 0.14677I
b = 0.666818 + 0.229080I
2.15316 − 3.41819I 1.21797 + 1.44999I
u = 1.009590 + 0.838851I
a = 1.119650 + 0.309640I
b = 1.50399 − 1.02071I
−1.88231 − 6.91835I −9.67007 + 4.45150I
u = 1.009590 − 0.838851I
a = 1.119650 − 0.309640I
b = 1.50399 + 1.02071I
−1.88231 + 6.91835I −9.67007 − 4.45150I
u = 0.522186 + 0.274434I
a = 0.715817 + 0.493479I
b = 0.035362 − 0.930126I
−0.818282 − 1.020500I −8.50734 + 6.76581I
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.522186 − 0.274434I
a = 0.715817 − 0.493479I
b = 0.035362 + 0.930126I
−0.818282 + 1.020500I −8.50734 − 6.76581I
u = 0.82856 + 1.18903I
a = 0.665734 + 0.836247I
b = 1.275630 + 0.188413I
1.33376 + 6.29384I −5.85142 − 3.79279I
u = 0.82856 − 1.18903I
a = 0.665734 − 0.836247I
b = 1.275630 − 0.188413I
1.33376 − 6.29384I −5.85142 + 3.79279I
u = 1.28182 + 0.74255I
a = 0.465354 + 0.427519I
b = 1.176510 + 0.070724I
3.78911 − 3.43912I −5.47667 + 2.61689I
u = 1.28182 − 0.74255I
a = 0.465354 − 0.427519I
b = 1.176510 − 0.070724I
3.78911 + 3.43912I −5.47667 − 2.61689I
u = 1.14224 + 0.95656I
a = −1.149420 − 0.323355I
b = −1.65497 + 0.80309I
0.28633 − 13.95250I −7.83055 + 7.44247I
u = 1.14224 − 0.95656I
a = −1.149420 + 0.323355I
b = −1.65497 − 0.80309I
0.28633 + 13.95250I −7.83055 − 7.44247I
u = −1.65206 + 0.05162I
a = −0.199755 − 0.409902I
b = −0.127470 − 0.253935I
−9.08165 + 2.30266I −5.04461 + 4.85763I
u = −1.65206 − 0.05162I
a = −0.199755 + 0.409902I
b = −0.127470 + 0.253935I
−9.08165 − 2.30266I −5.04461 − 4.85763I
u = −0.344930
a = −2.91630
b = −0.747935
−1.47402 −6.85190
6
II.
I
u
2
= h−u
9
a−9u
9
+· · ·−a−15, −5u
9
a−u
9
+· · ·−7a−3, u
10
+ 2 u
9
+· · ·+2u+1i
(i) Arc colorings
a
2
=
1
0
a
6
=
0
u
a
3
=
1
u
2
a
10
=
a
1
2
u
9
a +
9
2
u
9
+ ··· +
1
2
a +
15
2
a
11
=
a
1
2
u
9
a +
9
2
u
9
+ ··· +
1
2
a +
15
2
a
7
=
3u
9
a + u
9
+ ··· + 5a + 1
−
1
2
u
9
a +
1
2
u
9
+ ··· −
1
2
a −
1
2
a
8
=
9
2
u
9
a +
1
2
u
9
+ ··· +
15
2
a +
3
2
−1
a
1
=
−u
2
+ 1
−u
4
a
5
=
u
u
a
9
=
−
1
2
u
9
a −
3
2
u
9
+ ··· +
1
2
a −
5
2
3u
9
+ 4u
8
− 9u
6
+ u
5
+ 7u
4
+ 4u
3
+ au − 10u
2
+ 3u + 5
a
4
=
6u
9
a + u
9
+ ··· + 10a + 2
3
2
u
9
a −
1
2
u
9
+ ··· +
5
2
a +
1
2
a
12
=
3u
9
a + u
9
+ ··· + 5a + 2
−
1
2
u
9
a +
1
2
u
9
+ ··· −
1
2
a −
1
2
(ii) Obstruction class = −1
(iii) Cusp Shapes = −11u
9
− 17u
8
+ 37u
6
+ 3u
5
− 35u
4
− 20u
3
+ 38u
2
− 3u − 35
7
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
(u
10
+ 2u
9
+ 9u
8
+ 15u
7
+ 28u
6
+ 36u
5
+ 35u
4
+ 22u
3
+ 15u
2
+ 6u + 1)
2
c
2
, c
5
(u
10
− 2u
9
+ u
8
+ 3u
7
− 2u
6
− 2u
5
+ 3u
4
+ 2u
3
− u
2
− 2u + 1)
2
c
3
, c
7
u
20
+ 2u
19
+ ··· − 19u + 61
c
4
, c
9
u
20
− 6u
18
+ ··· − 15u + 85
c
6
, c
10
u
20
− 3u
19
+ ··· − 108u + 59
c
8
, c
11
(u
10
+ 3u
9
+ 6u
8
+ 7u
7
+ 9u
6
+ 9u
5
+ 10u
4
+ 6u
3
+ 5u
2
+ 3u + 2)
2
c
12
(u − 1)
20
8
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
(y
10
+ 14y
9
+ ··· − 6y + 1)
2
c
2
, c
5
(y
10
− 2y
9
+ 9y
8
− 15y
7
+ 28y
6
− 36y
5
+ 35y
4
− 22y
3
+ 15y
2
− 6y + 1)
2
c
3
, c
7
y
20
− 12y
19
+ ··· − 40987y + 3721
c
4
, c
9
y
20
− 12y
19
+ ··· − 97975y + 7225
c
6
, c
10
y
20
+ 13y
19
+ ··· + 76246y + 3481
c
8
, c
11
(y
10
+ 3y
9
+ ··· + 11y + 4)
2
c
12
(y −1)
20
9
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.975430 + 0.320615I
a = −1.065150 + 0.247050I
b = −1.63832 + 0.24814I
−3.87176 + 0.60085I −13.31849 − 3.40041I
u = 0.975430 + 0.320615I
a = 0.880921 − 0.910530I
b = −0.559442 − 0.182706I
−3.87176 + 0.60085I −13.31849 − 3.40041I
u = 0.975430 − 0.320615I
a = −1.065150 − 0.247050I
b = −1.63832 − 0.24814I
−3.87176 − 0.60085I −13.31849 + 3.40041I
u = 0.975430 − 0.320615I
a = 0.880921 + 0.910530I
b = −0.559442 + 0.182706I
−3.87176 − 0.60085I −13.31849 + 3.40041I
u = 0.541733 + 0.670646I
a = 1.294850 − 0.350726I
b = 1.70668 − 0.48449I
−2.20007 − 4.58635I −7.79322 + 7.42430I
u = 0.541733 + 0.670646I
a = −0.49398 + 2.09684I
b = 0.312809 + 0.203725I
−2.20007 − 4.58635I −7.79322 + 7.42430I
u = 0.541733 − 0.670646I
a = 1.294850 + 0.350726I
b = 1.70668 + 0.48449I
−2.20007 + 4.58635I −7.79322 − 7.42430I
u = 0.541733 − 0.670646I
a = −0.49398 − 2.09684I
b = 0.312809 − 0.203725I
−2.20007 + 4.58635I −7.79322 − 7.42430I
u = −0.876556 + 1.026090I
a = −0.533352 + 0.614318I
b = −1.129040 − 0.385187I
6.17677 + 1.75340I −6.60526 + 0.85033I
u = −0.876556 + 1.026090I
a = 1.221340 − 0.556605I
b = 1.54773 + 0.26490I
6.17677 + 1.75340I −6.60526 + 0.85033I
10
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.876556 − 1.026090I
a = −0.533352 − 0.614318I
b = −1.129040 + 0.385187I
6.17677 − 1.75340I −6.60526 − 0.85033I
u = −0.876556 − 1.026090I
a = 1.221340 + 0.556605I
b = 1.54773 − 0.26490I
6.17677 − 1.75340I −6.60526 − 0.85033I
u = −0.580680 + 0.133301I
a = −0.062064 + 0.507460I
b = 0.18768 + 2.50740I
−4.85763 + 3.93250I −20.2791 − 6.7139I
u = −0.580680 + 0.133301I
a = −1.04621 + 3.04432I
b = −0.411614 − 1.128030I
−4.85763 + 3.93250I −20.2791 − 6.7139I
u = −0.580680 − 0.133301I
a = −0.062064 − 0.507460I
b = 0.18768 − 2.50740I
−4.85763 − 3.93250I −20.2791 + 6.7139I
u = −0.580680 − 0.133301I
a = −1.04621 − 3.04432I
b = −0.411614 + 1.128030I
−4.85763 − 3.93250I −20.2791 + 6.7139I
u = −1.059930 + 0.922349I
a = 0.797570 − 0.248575I
b = 1.51824 + 0.58719I
5.57516 + 5.36397I −8.50388 − 6.50559I
u = −1.059930 + 0.922349I
a = −0.993922 + 0.803452I
b = −1.53472 − 0.22114I
5.57516 + 5.36397I −8.50388 − 6.50559I
u = −1.059930 − 0.922349I
a = 0.797570 + 0.248575I
b = 1.51824 − 0.58719I
5.57516 − 5.36397I −8.50388 + 6.50559I
u = −1.059930 − 0.922349I
a = −0.993922 − 0.803452I
b = −1.53472 + 0.22114I
5.57516 − 5.36397I −8.50388 + 6.50559I
11
III.
I
u
3
= h2u
10
+9u
9
+· · ·+b−5, −3u
10
−14u
9
+· · ·+a+7, u
11
+5u
10
+· · ·−5u−1i
(i) Arc colorings
a
2
=
1
0
a
6
=
0
u
a
3
=
1
u
2
a
10
=
3u
10
+ 14u
9
+ 22u
8
− 42u
6
− 38u
5
+ 22u
4
+ 50u
3
+ 9u
2
− 24u − 7
−2u
10
− 9u
9
+ ··· + 13u + 5
a
11
=
3u
10
+ 14u
9
+ 22u
8
− 42u
6
− 38u
5
+ 22u
4
+ 50u
3
+ 9u
2
− 24u − 7
−2u
10
− 9u
9
+ ··· + 11u + 4
a
7
=
u
10
+ 5u
9
+ 9u
8
+ 3u
7
− 13u
6
− 17u
5
+ 2u
4
+ 18u
3
+ 9u
2
− 7u − 6
u
10
+ 4u
9
+ 5u
8
− 2u
7
− 11u
6
− 6u
5
+ 8u
4
+ 9u
3
− 2u
2
− 4u
a
8
=
u
9
+ 4u
8
+ 5u
7
− 2u
6
− 11u
5
− 6u
4
+ 8u
3
+ 10u
2
− 2u − 6
−u
3
− u
2
+ 1
a
1
=
−u
2
+ 1
−u
4
a
5
=
u
u
a
9
=
4u
10
+ 18u
9
+ ··· − 29u − 9
−u
10
− 5u
9
− 9u
8
− 3u
7
+ 13u
6
+ 16u
5
− 4u
4
− 18u
3
− 6u
2
+ 8u + 3
a
4
=
−u
10
− 4u
9
− 4u
8
+ 5u
7
+ 13u
6
+ 2u
5
− 15u
4
− 9u
3
+ 8u
2
+ 8u − 4
u
10
+ 4u
9
+ 5u
8
− 2u
7
− 11u
6
− 6u
5
+ 8u
4
+ 10u
3
− u
2
− 5u
a
12
=
−u
10
− 5u
9
− 9u
8
− 3u
7
+ 13u
6
+ 17u
5
− 3u
4
− 20u
3
− 10u
2
+ 8u + 7
−u
10
− 4u
9
− 5u
8
+ 2u
7
+ 10u
6
+ 4u
5
− 9u
4
− 8u
3
+ 3u
2
+ 4u
(ii) Obstruction class = 1
(iii) Cusp Shapes
= u
10
+ 6u
9
+ 10u
8
− u
7
− 24u
6
− 21u
5
+ 17u
4
+ 35u
3
+ 5u
2
− 26u − 14
12
(iv) u-Polynomials at the component
13
Crossings u-Polynomials at each crossing
c
1
u
11
− 7u
10
+ ··· + 13u − 1
c
2
u
11
+ 5u
10
+ ··· − 5u − 1
c
3
u
11
− u
10
+ ··· + 6u − 1
c
4
u
11
+ u
10
− u
9
− 2u
8
− 5u
7
+ 4u
6
+ 12u
5
− 4u
4
+ u
3
+ 5u
2
− 1
c
5
u
11
− 5u
10
+ ··· − 5u + 1
c
6
u
11
+ u
10
+ 5u
9
+ 5u
8
+ 9u
7
+ 8u
6
+ 6u
5
− u
3
− 6u
2
− 2u − 1
c
7
u
11
+ u
10
+ ··· + 6u + 1
c
8
u
11
− 4u
10
+ ··· + 15u − 5
c
9
u
11
− u
10
− u
9
+ 2u
8
− 5u
7
− 4u
6
+ 12u
5
+ 4u
4
+ u
3
− 5u
2
+ 1
c
10
u
11
− u
10
+ 5u
9
− 5u
8
+ 9u
7
− 8u
6
+ 6u
5
− u
3
+ 6u
2
− 2u + 1
c
11
u
11
+ 4u
10
+ ··· + 15u + 5
c
12
u
11
− 3u
10
− u
8
+ 8u
7
+ 8u
6
+ 10u
5
− 13u
4
− 17u
3
− 8u
2
+ 11u + 5
14
15
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
11
+ y
10
+ ··· − 11y −1
c
2
, c
5
y
11
− 7y
10
+ ··· + 13y −1
c
3
, c
7
y
11
− 7y
10
+ ··· + 8y −1
c
4
, c
9
y
11
− 3y
10
+ ··· + 10y −1
c
6
, c
10
y
11
+ 9y
10
+ ··· − 8y −1
c
8
, c
11
y
11
+ 8y
10
+ ··· − 65y −25
c
12
y
11
− 9y
10
+ ··· + 201y −25
16
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = 0.888248 + 0.348807I
a = 1.094700 + 0.166339I
b = 0.518352 + 0.184714I
1.62880 − 3.55605I −13.8351 + 4.8849I
u = 0.888248 − 0.348807I
a = 1.094700 − 0.166339I
b = 0.518352 − 0.184714I
1.62880 + 3.55605I −13.8351 − 4.8849I
u = 0.865988
a = −0.906257
b = −0.420586
−2.51061 −16.1470
u = −0.794068 + 1.051540I
a = −1.013640 + 0.571990I
b = −1.35569 − 0.45895I
7.94404 + 2.78344I −1.36367 − 2.55365I
u = −0.794068 − 1.051540I
a = −1.013640 − 0.571990I
b = −1.35569 + 0.45895I
7.94404 − 2.78344I −1.36367 + 2.55365I
u = −1.12350 + 0.92492I
a = 0.823218 − 0.546732I
b = 1.52074 + 0.25018I
6.92380 + 4.41989I −2.52937 − 2.98344I
u = −1.12350 − 0.92492I
a = 0.823218 + 0.546732I
b = 1.52074 − 0.25018I
6.92380 − 4.41989I −2.52937 + 2.98344I
u = −1.56100 + 0.06449I
a = −0.120564 + 0.249710I
b = −0.383171 + 0.664642I
−9.38029 − 2.74226I −13.9541 + 7.1206I
u = −1.56100 − 0.06449I
a = −0.120564 − 0.249710I
b = −0.383171 − 0.664642I
−9.38029 + 2.74226I −13.9541 − 7.1206I
u = −0.342676 + 0.154468I
a = 1.16941 − 2.73498I
b = 0.41006 + 1.60424I
−4.21611 + 3.79963I −5.24446 − 3.20279I
17
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = −0.342676 − 0.154468I
a = 1.16941 + 2.73498I
b = 0.41006 − 1.60424I
−4.21611 − 3.79963I −5.24446 + 3.20279I
18
IV. I
u
4
= hb
2
+ b − 1, a + 1, u − 1i
(i) Arc colorings
a
2
=
1
0
a
6
=
0
1
a
3
=
1
1
a
10
=
−1
b
a
11
=
−1
b − 1
a
7
=
−1
b
a
8
=
−b − 2
−1
a
1
=
0
−1
a
5
=
1
1
a
9
=
−b − 2
−1
a
4
=
−2b − 2
−b
a
12
=
−1
b − 1
(ii) Obstruction class = 1
(iii) Cusp Shapes = −7
19
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
2
, c
6
(u − 1)
2
c
3
, c
4
u
2
− u − 1
c
5
, c
10
, c
12
(u + 1)
2
c
7
, c
9
u
2
+ u − 1
c
8
, c
11
u
2
20
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
2
, c
5
c
6
, c
10
, c
12
(y − 1)
2
c
3
, c
4
, c
7
c
9
y
2
− 3y + 1
c
8
, c
11
y
2
21
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
4
√
−1(vol +
√
−1CS) Cusp shape
u = 1.00000
a = −1.00000
b = 0.618034
−3.28987 −7.00000
u = 1.00000
a = −1.00000
b = −1.61803
−3.28987 −7.00000
22
V. I
v
1
= ha, b + 1, v − 1i
(i) Arc colorings
a
2
=
1
0
a
6
=
1
0
a
3
=
1
0
a
10
=
0
−1
a
11
=
1
−1
a
7
=
0
1
a
8
=
−1
1
a
1
=
1
0
a
5
=
1
0
a
9
=
1
−1
a
4
=
0
1
a
12
=
1
−1
(ii) Obstruction class = −1
(iii) Cusp Shapes = −6
23
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
2
, c
5
c
8
, c
11
u
c
3
, c
4
, c
6
c
7
, c
9
, c
10
c
12
u + 1
24
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
2
, c
5
c
8
, c
11
y
c
3
, c
4
, c
6
c
7
, c
9
, c
10
c
12
y − 1
25
(vi) Complex Volumes and Cusp Shapes
Solutions to I
v
1
√
−1(vol +
√
−1CS) Cusp shape
v = 1.00000
a = 0
b = −1.00000
−1.64493 −6.00000
26
VI. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
u(u − 1)
2
· (u
10
+ 2u
9
+ 9u
8
+ 15u
7
+ 28u
6
+ 36u
5
+ 35u
4
+ 22u
3
+ 15u
2
+ 6u + 1)
2
· (u
11
− 7u
10
+ ··· + 13u − 1)(u
20
+ 8u
19
+ ··· + 150u + 9)
c
2
u(u − 1)
2
· (u
10
− 2u
9
+ u
8
+ 3u
7
− 2u
6
− 2u
5
+ 3u
4
+ 2u
3
− u
2
− 2u + 1)
2
· (u
11
+ 5u
10
+ ··· − 5u − 1)(u
20
+ 8u
19
+ ··· − 12u − 3)
c
3
(u + 1)(u
2
− u − 1)(u
11
− u
10
+ ··· + 6u − 1)(u
20
− 2u
19
+ ··· + u + 1)
· (u
20
+ 2u
19
+ ··· − 19u + 61)
c
4
(u + 1)(u
2
− u − 1)
· (u
11
+ u
10
− u
9
− 2u
8
− 5u
7
+ 4u
6
+ 12u
5
− 4u
4
+ u
3
+ 5u
2
− 1)
· (u
20
− 8u
18
+ ··· + 3u + 1)(u
20
− 6u
18
+ ··· − 15u + 85)
c
5
u(u + 1)
2
· (u
10
− 2u
9
+ u
8
+ 3u
7
− 2u
6
− 2u
5
+ 3u
4
+ 2u
3
− u
2
− 2u + 1)
2
· (u
11
− 5u
10
+ ··· − 5u + 1)(u
20
+ 8u
19
+ ··· − 12u − 3)
c
6
(u − 1)
2
(u + 1)
· (u
11
+ u
10
+ 5u
9
+ 5u
8
+ 9u
7
+ 8u
6
+ 6u
5
− u
3
− 6u
2
− 2u − 1)
· (u
20
+ 6u
18
+ ··· + 9u + 1)(u
20
− 3u
19
+ ··· − 108u + 59)
c
7
(u + 1)(u
2
+ u − 1)(u
11
+ u
10
+ ··· + 6u + 1)(u
20
− 2u
19
+ ··· + u + 1)
· (u
20
+ 2u
19
+ ··· − 19u + 61)
c
8
u
3
(u
10
+ 3u
9
+ 6u
8
+ 7u
7
+ 9u
6
+ 9u
5
+ 10u
4
+ 6u
3
+ 5u
2
+ 3u + 2)
2
· (u
11
− 4u
10
+ ··· + 15u − 5)(u
20
− 7u
19
+ ··· + 12u − 3)
c
9
(u + 1)(u
2
+ u − 1)
· (u
11
− u
10
− u
9
+ 2u
8
− 5u
7
− 4u
6
+ 12u
5
+ 4u
4
+ u
3
− 5u
2
+ 1)
· (u
20
− 8u
18
+ ··· + 3u + 1)(u
20
− 6u
18
+ ··· − 15u + 85)
c
10
((u + 1)
3
)(u
11
− u
10
+ ··· − 2u + 1)
· (u
20
+ 6u
18
+ ··· + 9u + 1)(u
20
− 3u
19
+ ··· − 108u + 59)
c
11
u
3
(u
10
+ 3u
9
+ 6u
8
+ 7u
7
+ 9u
6
+ 9u
5
+ 10u
4
+ 6u
3
+ 5u
2
+ 3u + 2)
2
· (u
11
+ 4u
10
+ ··· + 15u + 5)(u
20
− 7u
19
+ ··· + 12u − 3)
c
12
(u − 1)
20
(u + 1)
3
· (u
11
− 3u
10
− u
8
+ 8u
7
+ 8u
6
+ 10u
5
− 13u
4
− 17u
3
− 8u
2
+ 11u + 5)
· (u
20
+ 21u
19
+ ··· + 6656u + 512)
27
VII. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
y(y − 1)
2
(y
10
+ 14y
9
+ ··· − 6y + 1)
2
(y
11
+ y
10
+ ··· − 11y − 1)
· (y
20
+ 16y
19
+ ··· − 5202y + 81)
c
2
, c
5
y(y − 1)
2
· (y
10
− 2y
9
+ 9y
8
− 15y
7
+ 28y
6
− 36y
5
+ 35y
4
− 22y
3
+ 15y
2
− 6y + 1)
2
· (y
11
− 7y
10
+ ··· + 13y − 1)(y
20
− 8y
19
+ ··· − 150y + 9)
c
3
, c
7
(y − 1)(y
2
− 3y + 1)(y
11
− 7y
10
+ ··· + 8y − 1)(y
20
− 28y
19
+ ··· + 7y + 1)
· (y
20
− 12y
19
+ ··· − 40987y + 3721)
c
4
, c
9
(y − 1)(y
2
− 3y + 1)(y
11
− 3y
10
+ ··· + 10y − 1)
· (y
20
− 16y
19
+ ··· + 5y + 1)(y
20
− 12y
19
+ ··· − 97975y + 7225)
c
6
, c
10
((y − 1)
3
)(y
11
+ 9y
10
+ ··· − 8y − 1)(y
20
+ 12y
19
+ ··· − 21y + 1)
· (y
20
+ 13y
19
+ ··· + 76246y + 3481)
c
8
, c
11
y
3
(y
10
+ 3y
9
+ ··· + 11y + 4)
2
(y
11
+ 8y
10
+ ··· − 65y − 25)
· (y
20
+ 11y
19
+ ··· − 132y + 9)
c
12
((y − 1)
23
)(y
11
− 9y
10
+ ··· + 201y − 25)
· (y
20
− 9y
19
+ ··· − 2621440y + 262144)
28
