12n
0811
(K12n
0811
)
A knot diagram
1
Linearized knot diagam
4 7 12 7 10 3 1 12 6 8 4 10
Solving Sequence
10,12 1,6
5 9 8 7 4 2 3 11
c
12
c
5
c
9
c
8
c
7
c
4
c
1
c
3
c
11
c
2
, c
6
, c
10
Ideals for irreducible components
2
of X
par
I
u
1
= h−238u
15
+ 537u
14
+ ··· + 1291b + 644, −932u
15
− 273u
14
+ ··· + 1291a + 3661,
u
16
− 4u
14
+ 4u
13
+ 12u
12
− 18u
11
− 13u
10
+ 44u
9
− 6u
8
− 55u
7
+ 38u
6
+ 30u
5
− 42u
4
+ u
3
+ 17u
2
− 6u − 1i
I
u
2
= h1.11360 × 10
68
u
37
− 1.13094 × 10
68
u
36
+ ··· + 3.45683 × 10
69
b − 5.20337 × 10
69
,
− 1.43917 × 10
70
u
37
+ 2.46784 × 10
70
u
36
+ ··· + 2.73089 × 10
71
a + 1.06137 × 10
72
,
u
38
− u
37
+ ··· − 62u − 79i
I
u
3
= h23118092u
15
− 125359960u
14
+ ··· + 12462493b − 54569021,
21062121u
15
− 121014315u
14
+ ··· + 12462493a − 38321689, u
16
− 6u
15
+ ··· − 4u + 1i
I
u
4
= h−u
5
+ u
3
− 2u
2
+ b − u + 1, −u
5
+ 2u
3
− 2u
2
+ a − 2u + 2, u
6
+ u
5
− 2u
4
+ 3u
2
− u − 1i
I
u
5
= hb − 1, a, u − 1i
* 5 irreducible components of dim
C
= 0, with total 77 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−238u
15
+ 537u
14
+ · · · + 1291b + 644, −932u
15
− 273u
14
+ · · · +
1291a + 3661, u
16
− 4u
14
+ · · · − 6u − 1i
(i) Arc colorings
a
10
=
0
u
a
12
=
1
0
a
1
=
1
−u
2
a
6
=
0.721921u
15
+ 0.211464u
14
+ ··· + 4.89388u − 2.83579
0.184353u
15
− 0.415957u
14
+ ··· + 1.94500u − 0.498838
a
5
=
0.721921u
15
+ 0.211464u
14
+ ··· + 4.89388u − 2.83579
−0.367932u
15
− 0.711851u
14
+ ··· − 0.0457010u − 0.710302
a
9
=
−0.0503486u
15
+ 0.344694u
14
+ ··· + 3.12006u − 0.981410
−0.0503486u
15
+ 0.344694u
14
+ ··· + 3.12006u + 0.0185902
a
8
=
−1
−0.0503486u
15
+ 0.344694u
14
+ ··· + 3.12006u + 0.0185902
a
7
=
−0.0503486u
15
+ 0.344694u
14
+ ··· + 3.12006u − 0.981410
−0.0751356u
15
− 0.254841u
14
+ ··· + 1.10225u − 0.326104
a
4
=
0.537568u
15
+ 0.627421u
14
+ ··· + 2.94888u − 2.33695
−0.211464u
15
− 0.552285u
14
+ ··· − 1.49574u − 0.721921
a
2
=
−0.333075u
15
− 0.181255u
14
+ ··· + 0.948102u + 2.43067
0.344694u
15
+ 0.0247870u
14
+ ··· − 1.28350u − 0.0503486
a
3
=
0.326104u
15
+ 0.0751356u
14
+ ··· + 1.45314u − 3.05887
−0.211464u
15
− 0.552285u
14
+ ··· − 1.49574u − 0.721921
a
11
=
u
−0.344694u
15
− 0.0247870u
14
+ ··· + 1.28350u + 0.0503486
(ii) Obstruction class = −1
(iii) Cusp Shapes =
4859
1291
u
15
−
196
1291
u
14
+ ··· +
57432
1291
u −
9123
1291
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
4
u
16
− u
15
+ ··· − 8u + 1
c
2
, c
6
u
16
+ 8u
15
+ ··· + 20u − 8
c
3
, c
5
, c
9
c
11
u
16
+ u
15
+ ··· + 8u + 2
c
7
u
16
− 15u
15
+ ··· + 384u − 64
c
8
u
16
− 23u
15
+ ··· + 2952u − 472
c
10
, c
12
u
16
− 4u
14
+ ··· − 6u − 1
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
4
y
16
− 23y
15
+ ··· − 32y + 1
c
2
, c
6
y
16
+ 8y
15
+ ··· − 1232y + 64
c
3
, c
5
, c
9
c
11
y
16
+ 13y
15
+ ··· + 16y + 4
c
7
y
16
− y
15
+ ··· − 30720y + 4096
c
8
y
16
− 31y
15
+ ··· − 1605984y + 222784
c
10
, c
12
y
16
− 8y
15
+ ··· − 70y + 1
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.728978 + 0.677201I
a = 0.532336 + 0.060278I
b = −0.100353 − 1.153050I
−2.58048 + 3.00554I −8.10520 − 2.38597I
u = 0.728978 − 0.677201I
a = 0.532336 − 0.060278I
b = −0.100353 + 1.153050I
−2.58048 − 3.00554I −8.10520 + 2.38597I
u = −0.973288 + 0.184794I
a = 0.75785 + 1.37831I
b = 0.04286 + 2.43021I
8.11198 − 4.38794I −0.64562 + 2.92845I
u = −0.973288 − 0.184794I
a = 0.75785 − 1.37831I
b = 0.04286 − 2.43021I
8.11198 + 4.38794I −0.64562 − 2.92845I
u = 0.888929
a = 1.47043
b = 1.55541
−3.37262 −0.442120
u = 0.758242 + 0.439908I
a = −0.459222 − 0.501064I
b = 0.174916 + 0.053608I
1.34319 + 1.06797I 1.49479 − 2.77265I
u = 0.758242 − 0.439908I
a = −0.459222 + 0.501064I
b = 0.174916 − 0.053608I
1.34319 − 1.06797I 1.49479 + 2.77265I
u = −1.184440 + 0.400458I
a = −0.342142 + 1.050790I
b = −0.07013 + 2.63493I
1.19975 − 5.05833I −0.62604 + 3.74336I
u = −1.184440 − 0.400458I
a = −0.342142 − 1.050790I
b = −0.07013 − 2.63493I
1.19975 + 5.05833I −0.62604 − 3.74336I
u = 0.939130 + 0.905743I
a = 0.479797 + 0.632021I
b = −0.395886 + 0.676605I
6.57781 + 4.06178I 0.252631 − 0.871494I
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.939130 − 0.905743I
a = 0.479797 − 0.632021I
b = −0.395886 − 0.676605I
6.57781 − 4.06178I 0.252631 + 0.871494I
u = 0.778111 + 1.047600I
a = −1.027370 − 0.416604I
b = −0.364894 − 0.086454I
1.69590 − 0.28714I −3.98649 + 0.31929I
u = 0.778111 − 1.047600I
a = −1.027370 + 0.416604I
b = −0.364894 + 0.086454I
1.69590 + 0.28714I −3.98649 − 0.31929I
u = −1.42884 + 0.78989I
a = −0.004460 − 1.145420I
b = 0.25947 − 2.48543I
6.3323 − 15.0071I −2.77467 + 7.02006I
u = −1.42884 − 0.78989I
a = −0.004460 + 1.145420I
b = 0.25947 + 2.48543I
6.3323 + 15.0071I −2.77467 − 7.02006I
u = −0.124728
a = −3.34399
b = −0.647391
−0.864939 −12.7770
6
II. I
u
2
= h1.11 × 10
68
u
37
− 1.13 × 10
68
u
36
+ · · · + 3.46 × 10
69
b − 5.20 ×
10
69
, −1.44 × 10
70
u
37
+ 2.47 × 10
70
u
36
+ · · · + 2.73 × 10
71
a + 1.06 ×
10
72
, u
38
− u
37
+ · · · − 62u − 79i
(i) Arc colorings
a
10
=
0
u
a
12
=
1
0
a
1
=
1
−u
2
a
6
=
0.0526998u
37
− 0.0903674u
36
+ ··· + 6.01858u − 3.88653
−0.0322146u
37
+ 0.0327163u
36
+ ··· − 13.6241u + 1.50524
a
5
=
0.0526998u
37
− 0.0903674u
36
+ ··· + 6.01858u − 3.88653
−0.0656788u
37
+ 0.0946351u
36
+ ··· − 15.4520u + 4.48099
a
9
=
−0.0923222u
37
+ 0.172239u
36
+ ··· − 2.83315u + 10.5939
−0.0552169u
37
+ 0.106775u
36
+ ··· − 3.51727u + 1.07664
a
8
=
−0.0371054u
37
+ 0.0654636u
36
+ ··· + 0.684120u + 9.51724
−0.0552169u
37
+ 0.106775u
36
+ ··· − 3.51727u + 1.07664
a
7
=
−0.109138u
37
+ 0.206389u
36
+ ··· − 4.00626u + 12.8342
0.0102538u
37
− 0.0153113u
36
+ ··· − 2.09807u − 4.36588
a
4
=
−0.0615144u
37
+ 0.0746738u
36
+ ··· − 6.24915u + 6.93837
−0.0514669u
37
+ 0.116872u
36
+ ··· + 4.44234u + 3.78722
a
2
=
−0.0418893u
37
+ 0.0332093u
36
+ ··· − 18.2103u + 7.21885
−0.0520505u
37
+ 0.129376u
36
+ ··· + 7.63964u + 3.43879
a
3
=
−0.112981u
37
+ 0.191546u
36
+ ··· − 1.80681u + 10.7256
−0.0514669u
37
+ 0.116872u
36
+ ··· + 4.44234u + 3.78722
a
11
=
0.0830893u
37
− 0.117168u
36
+ ··· + 22.3030u − 10.8514
0.0370786u
37
− 0.0992755u
36
+ ··· − 12.0908u − 0.746538
(ii) Obstruction class = −1
(iii) Cusp Shapes = 0.0873374u
37
− 0.323866u
36
+ ··· − 73.1911u − 23.6929
7
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
4
u
38
− 4u
37
+ ··· + 2639u − 353
c
2
, c
6
(u
19
− 3u
18
+ ··· + 65u − 25)
2
c
3
, c
5
, c
9
c
11
u
38
+ 11u
36
+ ··· + 2730u − 2315
c
7
(u
19
+ 6u
18
+ ··· + 10u + 1)
2
c
8
(u
19
+ 12u
18
+ ··· + 1502u + 625)
2
c
10
, c
12
u
38
− u
37
+ ··· − 62u − 79
8
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
4
y
38
− 20y
37
+ ··· + 770615y + 124609
c
2
, c
6
(y
19
+ 17y
18
+ ··· − 5175y −625)
2
c
3
, c
5
, c
9
c
11
y
38
+ 22y
37
+ ··· + 60589580y + 5359225
c
7
(y
19
− 12y
18
+ ··· + 30y −1)
2
c
8
(y
19
− 54y
18
+ ··· − 2158996y −390625)
2
c
10
, c
12
y
38
− 27y
37
+ ··· − 169744y + 6241
9
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.679846 + 0.698404I
a = −0.273776 + 0.556482I
b = −0.473737 + 0.789202I
−2.35949 + 0.16321I −2.70781 − 0.18622I
u = −0.679846 − 0.698404I
a = −0.273776 − 0.556482I
b = −0.473737 − 0.789202I
−2.35949 − 0.16321I −2.70781 + 0.18622I
u = 0.960122 + 0.435314I
a = 0.593065 − 0.764570I
b = −0.438163 − 1.282160I
−1.51388 + 1.79009I −4.72788 − 2.74496I
u = 0.960122 − 0.435314I
a = 0.593065 + 0.764570I
b = −0.438163 + 1.282160I
−1.51388 − 1.79009I −4.72788 + 2.74496I
u = −1.07632
a = 1.52827
b = 1.02377
−7.09286 −34.9180
u = −0.189836 + 0.874146I
a = 0.036583 − 1.409850I
b = −0.274085 − 1.305950I
−2.35949 − 0.16321I −2.70781 + 0.18622I
u = −0.189836 − 0.874146I
a = 0.036583 + 1.409850I
b = −0.274085 + 1.305950I
−2.35949 + 0.16321I −2.70781 − 0.18622I
u = −0.879859 + 0.138648I
a = 1.18883 − 0.97573I
b = 0.737407 − 0.181415I
7.75558 + 3.00592I −1.52759 − 2.83549I
u = −0.879859 − 0.138648I
a = 1.18883 + 0.97573I
b = 0.737407 + 0.181415I
7.75558 − 3.00592I −1.52759 + 2.83549I
u = −1.058720 + 0.361703I
a = 0.182710 + 1.281260I
b = −0.60977 + 2.90746I
10.82200 − 4.29446I −2.82455 + 4.66988I
10
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −1.058720 − 0.361703I
a = 0.182710 − 1.281260I
b = −0.60977 − 2.90746I
10.82200 + 4.29446I −2.82455 − 4.66988I
u = −0.917174 + 0.653292I
a = 0.361519 − 0.436397I
b = 0.077422 + 0.149014I
−1.68798 − 5.37827I 0.03508 + 8.21916I
u = −0.917174 − 0.653292I
a = 0.361519 + 0.436397I
b = 0.077422 − 0.149014I
−1.68798 + 5.37827I 0.03508 − 8.21916I
u = 1.114930 + 0.331378I
a = −0.097416 − 1.249650I
b = −0.20466 − 2.97495I
2.34940 + 5.26338I −1.37964 − 4.11831I
u = 1.114930 − 0.331378I
a = −0.097416 + 1.249650I
b = −0.20466 + 2.97495I
2.34940 − 5.26338I −1.37964 + 4.11831I
u = −0.772346 + 0.321245I
a = 1.182060 − 0.764049I
b = 0.507053 + 0.918255I
9.66886 + 1.37924I −3.48192 + 4.90124I
u = −0.772346 − 0.321245I
a = 1.182060 + 0.764049I
b = 0.507053 − 0.918255I
9.66886 − 1.37924I −3.48192 − 4.90124I
u = 0.637865 + 0.264901I
a = 1.10480 + 1.21426I
b = −0.357558 − 0.149777I
0.57050 − 2.67427I 0.072556 − 0.682395I
u = 0.637865 − 0.264901I
a = 1.10480 − 1.21426I
b = −0.357558 + 0.149777I
0.57050 + 2.67427I 0.072556 + 0.682395I
u = 1.048900 + 0.822943I
a = 0.305122 + 0.894638I
b = 0.586337 + 1.200440I
2.61541 + 7.05508I −3.99946 − 5.58788I
11
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 1.048900 − 0.822943I
a = 0.305122 − 0.894638I
b = 0.586337 − 1.200440I
2.61541 − 7.05508I −3.99946 + 5.58788I
u = −0.407834 + 0.346492I
a = 1.26494 − 1.09438I
b = −1.010750 − 0.253529I
−1.51388 + 1.79009I −4.72788 − 2.74496I
u = −0.407834 − 0.346492I
a = 1.26494 + 1.09438I
b = −1.010750 + 0.253529I
−1.51388 − 1.79009I −4.72788 + 2.74496I
u = 1.27274 + 0.74326I
a = −0.483706 − 0.727031I
b = −0.12463 − 2.06088I
7.75558 + 3.00592I −1.52759 − 2.83549I
u = 1.27274 − 0.74326I
a = −0.483706 + 0.727031I
b = −0.12463 + 2.06088I
7.75558 − 3.00592I −1.52759 + 2.83549I
u = 0.87992 + 1.24235I
a = −0.116819 + 0.798464I
b = 0.65914 + 2.10587I
−1.68798 + 5.37827I 0. − 8.21916I
u = 0.87992 − 1.24235I
a = −0.116819 − 0.798464I
b = 0.65914 − 2.10587I
−1.68798 − 5.37827I 0. + 8.21916I
u = −0.25188 + 1.54807I
a = −1.122660 − 0.209177I
b = 0.206822 − 0.294680I
2.61541 + 7.05508I −6.00000 − 5.58788I
u = −0.25188 − 1.54807I
a = −1.122660 + 0.209177I
b = 0.206822 + 0.294680I
2.61541 − 7.05508I −6.00000 + 5.58788I
u = −1.52147 + 0.50416I
a = −1.238570 − 0.121447I
b = −0.791063 − 0.291030I
2.34940 − 5.26338I 0
12
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −1.52147 − 0.50416I
a = −1.238570 + 0.121447I
b = −0.791063 + 0.291030I
2.34940 + 5.26338I 0
u = 1.45976 + 0.75358I
a = −0.605323 − 0.131479I
b = 0.968053 − 0.061001I
0.57050 + 2.67427I 0
u = 1.45976 − 0.75358I
a = −0.605323 + 0.131479I
b = 0.968053 + 0.061001I
0.57050 − 2.67427I 0
u = 0.265268
a = 2.21133
b = −5.15791
−7.09286 −34.9180
u = −1.76625 + 0.22968I
a = −0.073141 − 1.196270I
b = −0.02502 − 2.32333I
10.82200 − 4.29446I 0
u = −1.76625 − 0.22968I
a = −0.073141 + 1.196270I
b = −0.02502 + 2.32333I
10.82200 + 4.29446I 0
u = 1.97650 + 0.49731I
a = 0.099205 + 0.900550I
b = 0.13426 + 2.15608I
9.66886 + 1.37924I 0
u = 1.97650 − 0.49731I
a = 0.099205 − 0.900550I
b = 0.13426 − 2.15608I
9.66886 − 1.37924I 0
13
III.
I
u
3
= h2.31 × 10
7
u
15
− 1.25 × 10
8
u
14
+ · · · + 1.25 × 10
7
b − 5.46 × 10
7
, 2.11 ×
10
7
u
15
−1.21×10
8
u
14
+· · ·+1.25×10
7
a−3.83×10
7
, u
16
−6u
15
+· · · −4u +1i
(i) Arc colorings
a
10
=
0
u
a
12
=
1
0
a
1
=
1
−u
2
a
6
=
−1.69004u
15
+ 9.71028u
14
+ ··· − 11.2665u + 3.07496
−1.85501u
15
+ 10.0590u
14
+ ··· − 7.38636u + 4.37866
a
5
=
−1.69004u
15
+ 9.71028u
14
+ ··· − 11.2665u + 3.07496
−1.71227u
15
+ 9.23673u
14
+ ··· − 7.35655u + 3.94870
a
9
=
−0.376986u
15
+ 1.70048u
14
+ ··· − 2.72215u − 1.41104
−0.848481u
15
+ 4.83411u
14
+ ··· − 1.79540u + 2.41738
a
8
=
0.471494u
15
− 3.13362u
14
+ ··· − 0.926749u − 3.82841
−0.848481u
15
+ 4.83411u
14
+ ··· − 1.79540u + 2.41738
a
7
=
−0.288189u
15
+ 1.18161u
14
+ ··· − 4.41227u − 1.10638
−0.864013u
15
+ 4.90405u
14
+ ··· − 1.58362u + 2.17451
a
4
=
−1.60776u
15
+ 8.55089u
14
+ ··· − 11.0989u + 0.0562033
0.926120u
15
− 4.93366u
14
+ ··· + 6.43429u − 1.93874
a
2
=
−0.0288059u
15
− 0.202607u
14
+ ··· + 1.24805u − 4.58211
−0.605617u
15
+ 3.36139u
14
+ ··· − 2.47870u + 2.65769
a
3
=
−0.681644u
15
+ 3.61723u
14
+ ··· − 4.66458u − 1.88253
0.926120u
15
− 4.93366u
14
+ ··· + 6.43429u − 1.93874
a
11
=
0.566156u
15
− 2.60910u
14
+ ··· + 13.8955u + 1.50899
0.952811u
15
− 5.42292u
14
+ ··· − 0.106500u − 1.86985
(ii) Obstruction class = 1
(iii) Cusp Shapes = −
124023768
12462493
u
15
+
710614222
12462493
u
14
+ ··· −
606563351
12462493
u +
272307501
12462493
14
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
4
u
16
− 7u
15
+ ··· − 29u − 53
c
2
(u
8
+ u
7
+ u
6
− 4u
4
+ 2u
3
+ 2u − 1)
2
c
3
, c
9
u
16
+ u
15
+ ··· − 12u − 2
c
5
, c
11
u
16
− u
15
+ ··· + 12u − 2
c
6
(u
8
− u
7
+ u
6
− 4u
4
− 2u
3
− 2u − 1)
2
c
7
(u
8
− 4u
6
+ 7u
5
+ u
4
− 5u
3
+ 5u − 4)
2
c
8
(u
8
− 2u
7
− 9u
6
+ 25u
5
+ 3u
4
− 43u
3
+ 9u
2
+ 25u − 1)
2
c
10
, c
12
u
16
− 6u
15
+ ··· − 4u + 1
15
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
4
y
16
− 17y
15
+ ··· − 37835y + 2809
c
2
, c
6
(y
8
+ y
7
− 7y
6
− 12y
5
+ 10y
4
− 6y
3
− 4y + 1)
2
c
3
, c
5
, c
9
c
11
y
16
+ 3y
15
+ ··· − 28y + 4
c
7
(y
8
− 8y
7
+ 18y
6
− 57y
5
+ 63y
4
− 63y
3
+ 42y
2
− 25y + 16)
2
c
8
(y
8
− 22y
7
+ ··· − 643y + 1)
2
c
10
, c
12
y
16
− 12y
15
+ ··· − 6y + 1
16
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = −0.530066 + 0.765157I
a = −0.145854 − 1.019240I
b = 0.100679 − 0.942977I
−3.54970 −10.93452 + 0.I
u = −0.530066 − 0.765157I
a = −0.145854 + 1.019240I
b = 0.100679 + 0.942977I
−3.54970 −10.93452 + 0.I
u = −0.964408 + 0.610229I
a = −0.510934 + 0.031145I
b = −0.521192 − 0.566442I
−2.38347 − 5.06224I −9.20231 + 4.42667I
u = −0.964408 − 0.610229I
a = −0.510934 − 0.031145I
b = −0.521192 + 0.566442I
−2.38347 + 5.06224I −9.20231 − 4.42667I
u = 1.14978
a = −1.51833
b = −1.08522
−6.94401 19.2240
u = −0.765359 + 0.097139I
a = 0.937764 − 1.042880I
b = 0.962499 + 0.741172I
9.91734 + 2.03431I 1.49914 − 4.94059I
u = −0.765359 − 0.097139I
a = 0.937764 + 1.042880I
b = 0.962499 − 0.741172I
9.91734 − 2.03431I 1.49914 + 4.94059I
u = 0.930008 + 1.034990I
a = −0.016590 + 0.832356I
b = 0.64870 + 2.33325I
−2.38347 + 5.06224I −9.20231 − 4.42667I
u = 0.930008 − 1.034990I
a = −0.016590 − 0.832356I
b = 0.64870 − 2.33325I
−2.38347 − 5.06224I −9.20231 + 4.42667I
u = 0.452649
a = 1.05539
b = 5.42502
−6.94401 19.2240
17
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = 1.38729 + 0.79942I
a = 0.639330 − 0.166225I
b = −0.600710 − 0.519283I
0.18039 + 3.47753I −3.44178 − 6.27230I
u = 1.38729 − 0.79942I
a = 0.639330 + 0.166225I
b = −0.600710 + 0.519283I
0.18039 − 3.47753I −3.44178 + 6.27230I
u = 0.234382 + 0.304234I
a = −1.95550 − 2.23470I
b = 0.291354 + 0.555465I
0.18039 + 3.47753I −3.44178 − 6.27230I
u = 0.234382 − 0.304234I
a = −1.95550 + 2.23470I
b = 0.291354 − 0.555465I
0.18039 − 3.47753I −3.44178 + 6.27230I
u = 1.90694 + 0.52056I
a = −0.216748 − 0.899742I
b = −0.05123 − 2.14476I
9.91734 + 2.03431I 1.49914 − 4.94059I
u = 1.90694 − 0.52056I
a = −0.216748 + 0.899742I
b = −0.05123 + 2.14476I
9.91734 − 2.03431I 1.49914 + 4.94059I
18
IV. I
u
4
=
h−u
5
+u
3
−2u
2
+b−u+1, −u
5
+2u
3
−2u
2
+a−2u+2, u
6
+u
5
−2u
4
+3u
2
−u−1i
(i) Arc colorings
a
10
=
0
u
a
12
=
1
0
a
1
=
1
−u
2
a
6
=
u
5
− 2u
3
+ 2u
2
+ 2u − 2
u
5
− u
3
+ 2u
2
+ u − 1
a
5
=
u
5
− 2u
3
+ 2u
2
+ 2u − 2
u
a
9
=
u
5
+ u
4
− 2u
3
+ u
2
+ 2u − 2
u
5
+ u
4
− 2u
3
+ u
2
+ 2u − 1
a
8
=
−1
u
5
+ u
4
− 2u
3
+ u
2
+ 2u − 1
a
7
=
u
5
+ u
4
− 2u
3
+ 2u − 2
u
5
+ u
4
− u
3
+ u
2
+ u − 1
a
4
=
u
3
− u + 1
−u
5
+ 2u
3
− u
2
− u + 1
a
2
=
−u
5
+ 2u
3
− 2u
2
− u + 3
−u
2
− u + 1
a
3
=
−u
5
+ 3u
3
− u
2
− 2u + 2
−u
5
+ 2u
3
− u
2
− u + 1
a
11
=
u
−u
3
+ u
2
+ u − 1
(ii) Obstruction class = 1
(iii) Cusp Shapes = 6u
5
+ 5u
4
− 10u
3
+ 2u
2
+ 9u − 8
19
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
4
u
6
− 2u
3
− 2u
2
+ u + 1
c
2
u
6
+ 3u
4
− u
3
+ 4u
2
− 7u + 1
c
3
, c
9
u
6
− u
5
+ 3u
4
+ 2u
3
− u
2
+ 4u + 1
c
5
, c
11
u
6
+ u
5
+ 3u
4
− 2u
3
− u
2
− 4u + 1
c
6
u
6
+ 3u
4
+ u
3
+ 4u
2
+ 7u + 1
c
7
u
6
− u
3
− 4u
2
− 4u − 1
c
8
u
6
+ 5u
5
+ 4u
4
− 14u
3
− 11u
2
+ 3u − 1
c
10
, c
12
u
6
+ u
5
− 2u
4
+ 3u
2
− u − 1
20
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
4
y
6
− 4y
4
− 2y
3
+ 8y
2
− 5y + 1
c
2
, c
6
y
6
+ 6y
5
+ 17y
4
+ 25y
3
+ 8y
2
− 41y + 1
c
3
, c
5
, c
9
c
11
y
6
+ 5y
5
+ 11y
4
− 9y
2
− 18y + 1
c
7
y
6
− 8y
4
− 3y
3
+ 8y
2
− 8y + 1
c
8
y
6
− 17y
5
+ 134y
4
− 316y
3
+ 197y
2
+ 13y + 1
c
10
, c
12
y
6
− 5y
5
+ 10y
4
− 12y
3
+ 13y
2
− 7y + 1
21
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
4
√
−1(vol +
√
−1CS) Cusp shape
u = 0.772562 + 0.775063I
a = 0.298956 + 0.982149I
b = −0.404786 + 1.129280I
5.91845 + 4.87319I −5.51837 − 6.60993I
u = 0.772562 − 0.775063I
a = 0.298956 − 0.982149I
b = −0.404786 − 1.129280I
5.91845 − 4.87319I −5.51837 + 6.60993I
u = 0.827970
a = 0.280915
b = 1.02055
0.0306709 −0.168770
u = −1.45553 + 0.25337I
a = 0.221038 + 1.185900I
b = −0.12674 + 2.52662I
12.64200 − 3.59018I 1.92451 + 1.76671I
u = −1.45553 − 0.25337I
a = 0.221038 − 1.185900I
b = −0.12674 − 2.52662I
12.64200 + 3.59018I 1.92451 − 1.76671I
u = −0.462038
a = −2.32090
b = −0.957501
−4.25280 −10.6440
22
V. I
u
5
= hb − 1, a, u − 1i
(i) Arc colorings
a
10
=
0
1
a
12
=
1
0
a
1
=
1
−1
a
6
=
0
1
a
5
=
0
1
a
9
=
0
1
a
8
=
−1
1
a
7
=
−1
1
a
4
=
1
0
a
2
=
2
−1
a
3
=
1
0
a
11
=
1
0
(ii) Obstruction class = 1
(iii) Cusp Shapes = 0
23
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
2
, c
4
c
10
, c
12
u − 1
c
3
, c
5
, c
7
c
9
, c
11
u
c
6
, c
8
u + 1
24
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
2
, c
4
c
6
, c
8
, c
10
c
12
y −1
c
3
, c
5
, c
7
c
9
, c
11
y
25
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
5
√
−1(vol +
√
−1CS) Cusp shape
u = 1.00000
a = 0
b = 1.00000
0 0
26
VI. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
, c
4
(u − 1)(u
6
− 2u
3
− 2u
2
+ u + 1)(u
16
− 7u
15
+ ··· − 29u − 53)
· (u
16
− u
15
+ ··· − 8u + 1)(u
38
− 4u
37
+ ··· + 2639u − 353)
c
2
(u − 1)(u
6
+ 3u
4
− u
3
+ 4u
2
− 7u + 1)
· ((u
8
+ u
7
+ u
6
− 4u
4
+ 2u
3
+ 2u − 1)
2
)(u
16
+ 8u
15
+ ··· + 20u − 8)
· (u
19
− 3u
18
+ ··· + 65u − 25)
2
c
3
, c
9
u(u
6
− u
5
+ ··· + 4u + 1)(u
16
+ u
15
+ ··· − 12u − 2)
· (u
16
+ u
15
+ ··· + 8u + 2)(u
38
+ 11u
36
+ ··· + 2730u − 2315)
c
5
, c
11
u(u
6
+ u
5
+ ··· − 4u + 1)(u
16
− u
15
+ ··· + 12u − 2)
· (u
16
+ u
15
+ ··· + 8u + 2)(u
38
+ 11u
36
+ ··· + 2730u − 2315)
c
6
(u + 1)(u
6
+ 3u
4
+ u
3
+ 4u
2
+ 7u + 1)
· ((u
8
− u
7
+ u
6
− 4u
4
− 2u
3
− 2u − 1)
2
)(u
16
+ 8u
15
+ ··· + 20u − 8)
· (u
19
− 3u
18
+ ··· + 65u − 25)
2
c
7
u(u
6
− u
3
− 4u
2
− 4u − 1)(u
8
− 4u
6
+ 7u
5
+ u
4
− 5u
3
+ 5u − 4)
2
· (u
16
− 15u
15
+ ··· + 384u − 64)(u
19
+ 6u
18
+ ··· + 10u + 1)
2
c
8
(u + 1)(u
6
+ 5u
5
+ 4u
4
− 14u
3
− 11u
2
+ 3u − 1)
· (u
8
− 2u
7
− 9u
6
+ 25u
5
+ 3u
4
− 43u
3
+ 9u
2
+ 25u − 1)
2
· (u
16
− 23u
15
+ ··· + 2952u − 472)
· (u
19
+ 12u
18
+ ··· + 1502u + 625)
2
c
10
, c
12
(u − 1)(u
6
+ u
5
+ ··· − u − 1)(u
16
− 4u
14
+ ··· − 6u − 1)
· (u
16
− 6u
15
+ ··· − 4u + 1)(u
38
− u
37
+ ··· − 62u − 79)
27
VII. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
, c
4
(y −1)(y
6
− 4y
4
+ ··· − 5y + 1)(y
16
− 23y
15
+ ··· − 32y + 1)
· (y
16
− 17y
15
+ ··· − 37835y + 2809)
· (y
38
− 20y
37
+ ··· + 770615y + 124609)
c
2
, c
6
(y −1)(y
6
+ 6y
5
+ 17y
4
+ 25y
3
+ 8y
2
− 41y + 1)
· (y
8
+ y
7
− 7y
6
− 12y
5
+ 10y
4
− 6y
3
− 4y + 1)
2
· (y
16
+ 8y
15
+ ··· − 1232y + 64)(y
19
+ 17y
18
+ ··· − 5175y −625)
2
c
3
, c
5
, c
9
c
11
y(y
6
+ 5y
5
+ ··· − 18y + 1)(y
16
+ 3y
15
+ ··· − 28y + 4)
· (y
16
+ 13y
15
+ ··· + 16y + 4)
· (y
38
+ 22y
37
+ ··· + 60589580y + 5359225)
c
7
y(y
6
− 8y
4
− 3y
3
+ 8y
2
− 8y + 1)
· (y
8
− 8y
7
+ 18y
6
− 57y
5
+ 63y
4
− 63y
3
+ 42y
2
− 25y + 16)
2
· (y
16
− y
15
+ ··· − 30720y + 4096)(y
19
− 12y
18
+ ··· + 30y −1)
2
c
8
(y −1)(y
6
− 17y
5
+ 134y
4
− 316y
3
+ 197y
2
+ 13y + 1)
· (y
8
− 22y
7
+ ··· − 643y + 1)
2
· (y
16
− 31y
15
+ ··· − 1605984y + 222784)
· (y
19
− 54y
18
+ ··· − 2158996y −390625)
2
c
10
, c
12
(y −1)(y
6
− 5y
5
+ 10y
4
− 12y
3
+ 13y
2
− 7y + 1)
· (y
16
− 12y
15
+ ··· − 6y + 1)(y
16
− 8y
15
+ ··· − 70y + 1)
· (y
38
− 27y
37
+ ··· − 169744y + 6241)
28
