12n
0526
(K12n
0526
)
A knot diagram
1
Linearized knot diagam
3 6 8 7 2 11 10 12 3 4 6 9
Solving Sequence
4,7 5,11
6 12 10 8 3 2 1 9
c
4
c
6
c
11
c
10
c
7
c
3
c
2
c
1
c
9
c
5
, c
8
, c
12
Ideals for irreducible components
2
of X
par
I
u
1
= h509724805881808u
17
+ 62725492089096u
16
+ ··· + 962155230401099b − 2566227709173424,
509724805881808u
17
+ 62725492089096u
16
+ ··· + 962155230401099a − 1604072478772325,
u
18
+ 13u
15
+ ··· − 3u + 1i
I
u
2
= h−2u
3
+ u
2
+ 5b + 7u + 4, −2u
3
+ u
2
+ 5a + 7u + 9, u
4
− u
3
− 2u
2
− 4u + 1i
I
u
3
= h−27u
5
− 100u
4
− 44u
3
+ 97u
2
+ 83b − 149u − 351,
151u
5
+ 341u
4
+ 160u
3
+ 598u
2
+ 1909a + 1153u + 552, u
6
+ 5u
5
+ 7u
4
+ 2u
2
+ 23u + 23i
I
u
4
= h2.26609 × 10
20
u
17
− 1.36596 × 10
21
u
16
+ ··· + 1.11949 × 10
23
b − 1.57690 × 10
23
,
− 2.09433 × 10
24
u
17
+ 1.13703 × 10
25
u
16
+ ··· + 1.33689 × 10
27
a + 3.04454 × 10
27
,
u
18
− 6u
17
+ ··· − 1792u + 448i
I
u
5
= h−u
5
− 2u
4
− 6u
3
− 3u
2
+ 4b − 5u + 5, −u
5
− 2u
4
− 6u
3
− 3u
2
+ 4a − 5u + 5,
u
6
+ u
5
+ 4u
4
+ u
3
+ 2u
2
− 2u + 1i
I
v
1
= ha, 3v
5
− 2v
4
+ 15v
3
− 20v
2
+ 7b + 12v + 3, v
6
− v
5
+ 5v
4
− 9v
3
+ 5v
2
− v + 1i
* 6 irreducible components of dim
C
= 0, with total 58 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
=
h5.10×10
14
u
17
+6.27×10
13
u
16
+· · ·+9.62×10
14
b−2.57×10
15
, 5.10×10
14
u
17
+
6.27 × 10
13
u
16
+ · · · + 9.62 × 10
14
a − 1.60 × 10
15
, u
18
+ 13u
15
+ · · · − 3u + 1i
(i) Arc colorings
a
4
=
1
0
a
7
=
0
u
a
5
=
1
−u
2
a
11
=
−0.529774u
17
− 0.0651927u
16
+ ··· − 10.5792u + 1.66717
−0.529774u
17
− 0.0651927u
16
+ ··· − 10.5792u + 2.66717
a
6
=
0.0770104u
17
+ 0.260613u
16
+ ··· − 4.25101u + 1.18675
0.0118177u
17
+ 0.255567u
16
+ ··· − 3.17317u + 1.71652
a
12
=
−1.25969u
17
+ 0.0649203u
16
+ ··· − 13.8506u + 2.19363
−1.00412u
17
+ 0.0243057u
16
+ ··· − 12.0986u + 3.18181
a
10
=
−1
−0.529774u
17
− 0.0651927u
16
+ ··· − 10.5792u + 2.66717
a
8
=
u
0.0651927u
17
+ 0.00504605u
16
+ ··· − 0.0778441u − 0.529774
a
3
=
−0.00504605u
17
+ 0.0633402u
16
+ ··· + 0.334196u + 1.06519
−0.260613u
17
+ 0.103955u
16
+ ··· − 1.41778u + 0.0770104
a
2
=
0.471649u
17
+ 0.309437u
16
+ ··· + 1.48208u + 1.26622
0.0769485u
17
+ 0.231016u
16
+ ··· − 0.716691u − 0.529509
a
1
=
0.526910u
17
+ 0.0682034u
16
+ ··· + 4.16343u − 0.388870
0.108885u
17
+ 0.0443291u
16
+ ··· + 0.972123u − 0.838062
a
9
=
−0.386278u
17
+ 0.00755787u
16
+ ··· − 9.06550u + 1.82450
−0.335639u
17
− 0.0387286u
16
+ ··· − 9.84582u + 2.34782
(ii) Obstruction class = −1
(iii) Cusp Shapes
= −
10294514371764425
962155230401099
u
17
−
6856664502715686
962155230401099
u
16
+···−
99549238607210006
962155230401099
u−
114009180214742949
962155230401099
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
18
+ 20u
17
+ ··· + 9u + 1
c
2
, c
5
, c
8
c
12
u
18
− 10u
16
+ ··· + u + 1
c
3
, c
6
, c
11
u
18
+ 4u
16
+ ··· − 5u + 1
c
4
, c
7
u
18
− 13u
15
+ ··· + 3u + 1
c
9
u
18
+ 4u
17
+ ··· + 2u + 49
c
10
u
18
+ 11u
17
+ ··· + 12u + 7
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
18
− 44y
17
+ ··· + 123y + 1
c
2
, c
5
, c
8
c
12
y
18
− 20y
17
+ ··· − 9y + 1
c
3
, c
6
, c
11
y
18
+ 8y
17
+ ··· − 13y + 1
c
4
, c
7
y
18
+ 10y
16
+ ··· + 43y + 1
c
9
y
18
− 38y
17
+ ··· + 23516y + 2401
c
10
y
18
− 7y
17
+ ··· − 578y + 49
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.113980 + 1.055280I
a = −1.44079 − 0.05034I
b = −0.440789 − 0.050343I
0.52334 + 2.87308I −12.86704 − 2.02894I
u = −0.113980 − 1.055280I
a = −1.44079 + 0.05034I
b = −0.440789 + 0.050343I
0.52334 − 2.87308I −12.86704 + 2.02894I
u = 0.954988 + 0.936855I
a = −0.110942 + 0.898533I
b = 0.889058 + 0.898533I
−3.78393 + 7.04028I −11.7360 − 7.9578I
u = 0.954988 − 0.936855I
a = −0.110942 − 0.898533I
b = 0.889058 − 0.898533I
−3.78393 − 7.04028I −11.7360 + 7.9578I
u = −0.058366 + 0.626910I
a = −1.99797 + 0.34561I
b = −0.997971 + 0.345611I
3.21985 − 4.16919I −1.22804 + 6.95897I
u = −0.058366 − 0.626910I
a = −1.99797 − 0.34561I
b = −0.997971 − 0.345611I
3.21985 + 4.16919I −1.22804 − 6.95897I
u = 0.705132 + 1.217160I
a = −0.230297 − 1.183980I
b = 0.769703 − 1.183980I
−18.2643 + 6.2926I −8.79577 − 2.62001I
u = 0.705132 − 1.217160I
a = −0.230297 + 1.183980I
b = 0.769703 + 1.183980I
−18.2643 − 6.2926I −8.79577 + 2.62001I
u = −0.92137 + 1.10060I
a = 0.292045 − 0.754405I
b = 1.29204 − 0.75441I
2.25471 − 6.85293I 2.33518 + 2.51828I
u = −0.92137 − 1.10060I
a = 0.292045 + 0.754405I
b = 1.29204 + 0.75441I
2.25471 + 6.85293I 2.33518 − 2.51828I
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.069851 + 0.514524I
a = −0.761951 + 0.761302I
b = 0.238049 + 0.761302I
−0.860650 − 0.772825I −7.78859 + 5.59560I
u = 0.069851 − 0.514524I
a = −0.761951 − 0.761302I
b = 0.238049 − 0.761302I
−0.860650 + 0.772825I −7.78859 − 5.59560I
u = 0.071122 + 0.227795I
a = 0.79662 − 1.30381I
b = 1.79662 − 1.30381I
−2.88172 + 0.11696I −86.2726 − 33.4077I
u = 0.071122 − 0.227795I
a = 0.79662 + 1.30381I
b = 1.79662 + 1.30381I
−2.88172 − 0.11696I −86.2726 + 33.4077I
u = −2.05408 + 0.03763I
a = −0.195363 + 0.174827I
b = 0.804637 + 0.174827I
5.48543 + 0.72645I −2.62157 − 10.03199I
u = −2.05408 − 0.03763I
a = −0.195363 − 0.174827I
b = 0.804637 − 0.174827I
5.48543 − 0.72645I −2.62157 + 10.03199I
u = 1.34670 + 1.70942I
a = 0.148649 + 0.885147I
b = 1.14865 + 0.88515I
−16.9465 + 13.6621I −7.52555 − 5.67041I
u = 1.34670 − 1.70942I
a = 0.148649 − 0.885147I
b = 1.14865 − 0.88515I
−16.9465 − 13.6621I −7.52555 + 5.67041I
6
II.
I
u
2
= h−2u
3
+u
2
+5b +7u +4, −2u
3
+u
2
+5a +7u +9, u
4
−u
3
−2u
2
−4u +1i
(i) Arc colorings
a
4
=
1
0
a
7
=
0
u
a
5
=
1
−u
2
a
11
=
2
5
u
3
−
1
5
u
2
−
7
5
u −
9
5
2
5
u
3
−
1
5
u
2
−
7
5
u −
4
5
a
6
=
1
1
5
u
3
−
3
5
u
2
+
4
5
u +
3
5
a
12
=
3
5
u
3
−
4
5
u
2
−
8
5
u −
11
5
1
5
u
3
−
3
5
u
2
−
1
5
u −
7
5
a
10
=
−1
2
5
u
3
−
1
5
u
2
−
7
5
u −
4
5
a
8
=
u
−
1
5
u
3
+
3
5
u
2
+
1
5
u +
2
5
a
3
=
−
2
5
u
3
+
1
5
u
2
+
2
5
u +
4
5
−u
a
2
=
0
2
5
u
3
−
1
5
u
2
−
2
5
u −
4
5
a
1
=
u
3
+ u
2
+ u − 1
u
3
+ u
2
+ u − 1
a
9
=
3
5
u
3
+
1
5
u
2
+
2
5
u −
11
5
2
5
u
3
+
4
5
u
2
−
2
5
u −
4
5
(ii) Obstruction class = 1
(iii) Cusp Shapes =
13
5
u
3
−
29
5
u
2
+
7
5
u −
91
5
7
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
4
− 9u
3
+ 10u
2
− 4u + 1
c
2
, c
8
u
4
+ 3u
3
− 2u − 1
c
3
, c
6
u
4
− u
3
− 2u + 1
c
4
, c
7
u
4
− u
3
− 2u
2
− 4u + 1
c
5
, c
12
u
4
− 3u
3
+ 2u − 1
c
9
u
4
− 5u
3
+ 7u
2
− 7u + 5
c
10
u
4
+ 2u
3
− 3u − 1
c
11
u
4
+ u
3
+ 2u + 1
8
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
4
− 61y
3
+ 30y
2
+ 4y + 1
c
2
, c
5
, c
8
c
12
y
4
− 9y
3
+ 10y
2
− 4y + 1
c
3
, c
6
, c
11
y
4
− y
3
− 2y
2
− 4y + 1
c
4
, c
7
y
4
− 5y
3
− 2y
2
− 20y + 1
c
9
y
4
− 11y
3
− 11y
2
+ 21y + 25
c
10
y
4
− 4y
3
+ 10y
2
− 9y + 1
9
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.826702 + 1.077850I
a = 0.379567 − 0.769480I
b = 1.37957 − 0.76948I
1.92551 − 7.16341I −10.5607 + 14.3354I
u = −0.826702 − 1.077850I
a = 0.379567 + 0.769480I
b = 1.37957 + 0.76948I
1.92551 + 7.16341I −10.5607 − 14.3354I
u = 0.222985
a = −2.11769
b = −1.11769
−2.81853 −18.1470
u = 2.43042
a = −0.641445
b = 0.358555
−14.1920 −11.7310
10
III. I
u
3
= h−27u
5
− 100u
4
+ · · · + 83b − 351, 151u
5
+ 341u
4
+ · · · + 1909a +
552, u
6
+ 5u
5
+ 7u
4
+ 2u
2
+ 23u + 23i
(i) Arc colorings
a
4
=
1
0
a
7
=
0
u
a
5
=
1
−u
2
a
11
=
−0.0790990u
5
− 0.178628u
4
+ ··· − 0.603981u − 0.289157
0.325301u
5
+ 1.20482u
4
+ ··· + 1.79518u + 4.22892
a
6
=
−0.129387u
5
− 0.418020u
4
+ ··· − 1.45155u − 1.63855
0.0843373u
5
+ 0.349398u
4
+ ··· + 0.650602u + 1.09639
a
12
=
−0.0314301u
5
− 0.0246202u
4
+ ··· − 1.27973u − 0.843373
−0.216867u
5
− 0.469880u
4
+ ··· − 1.53012u − 1.81928
a
10
=
−0.404400u
5
− 1.38345u
4
+ ··· − 2.39916u − 4.51807
0.325301u
5
+ 1.20482u
4
+ ··· + 1.79518u + 4.22892
a
8
=
−0.430592u
5
− 1.23730u
4
+ ··· − 1.63227u − 3.55422
0.216867u
5
+ 0.469880u
4
+ ··· + 1.53012u + 0.819277
a
3
=
0.220534u
5
+ 0.789419u
4
+ ··· + 1.86276u + 3.08434
0.204819u
5
+ 0.277108u
4
+ ··· + 1.72289u − 0.337349
a
2
=
0.315872u
5
+ 1.09743u
4
+ ··· + 1.51126u + 3.97590
−0.397590u
5
− 1.36145u
4
+ ··· − 1.63855u − 7.16867
a
1
=
0.358303u
5
+ 1.08067u
4
+ ··· + 0.788895u + 3.61446
−0.0963855u
5
− 0.542169u
4
+ ··· − 0.457831u − 5.25301
a
9
=
−0.474070u
5
− 1.45469u
4
+ ··· − 1.71922u − 3.55422
0.132530u
5
+ 0.120482u
4
+ ··· + 0.879518u − 1.27711
(ii) Obstruction class = 1
(iii) Cusp Shapes =
109
83
u
5
+
416
83
u
4
+
193
83
u
3
−
450
83
u
2
+
580
83
u +
1168
83
11
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
6
− u
5
− 8u
4
+ 2u
3
+ 20u
2
+ 8u + 1
c
2
, c
8
u
6
+ 3u
5
+ 4u
4
+ 6u
3
+ 6u
2
+ 2u + 1
c
3
, c
6
u
6
+ 3u
5
+ 4u
4
+ 3u
3
+ 3u
2
+ 2u + 1
c
4
, c
7
u
6
+ 5u
5
+ 7u
4
+ 2u
2
+ 23u + 23
c
5
, c
12
u
6
− 3u
5
+ 4u
4
− 6u
3
+ 6u
2
− 2u + 1
c
9
u
6
+ 2u
5
+ 4u
4
+ 6u
3
+ 4u
2
+ 5u + 5
c
10
(u
3
− u
2
+ 1)
2
c
11
u
6
− 3u
5
+ 4u
4
− 3u
3
+ 3u
2
− 2u + 1
12
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
6
− 17y
5
+ 108y
4
− 306y
3
+ 352y
2
− 24y + 1
c
2
, c
5
, c
8
c
12
y
6
− y
5
− 8y
4
+ 2y
3
+ 20y
2
+ 8y + 1
c
3
, c
6
, c
11
y
6
− y
5
+ 4y
4
+ 5y
3
+ 5y
2
+ 2y + 1
c
4
, c
7
y
6
− 11y
5
+ 53y
4
− 156y
3
+ 326y
2
− 437y + 529
c
9
y
6
+ 4y
5
− 14y
3
− 4y
2
+ 15y + 25
c
10
(y
3
− y
2
+ 2y −1)
2
13
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = 0.988837 + 0.990669I
a = 0.262508 − 1.069710I
b = −0.877439 − 0.744862I
−2.75839 + 5.65624I −7.72484 − 4.28659I
u = 0.988837 − 0.990669I
a = 0.262508 + 1.069710I
b = −0.877439 + 0.744862I
−2.75839 − 5.65624I −7.72484 + 4.28659I
u = −1.44904 + 0.80809I
a = −0.066092 + 0.513653I
b = −0.877439 + 0.744862I
−2.75839 − 5.65624I −7.72484 + 4.28659I
u = −1.44904 − 0.80809I
a = −0.066092 − 0.513653I
b = −0.877439 − 0.744862I
−2.75839 + 5.65624I −7.72484 − 4.28659I
u = −2.03980 + 0.32227I
a = −0.196416 − 0.308287I
b = 0.754878
5.51678 −1.55033 + 0.I
u = −2.03980 − 0.32227I
a = −0.196416 + 0.308287I
b = 0.754878
5.51678 −1.55033 + 0.I
14
IV. I
u
4
= h2.27 × 10
20
u
17
− 1.37 × 10
21
u
16
+ · · · + 1.12 × 10
23
b − 1.58 ×
10
23
, −2.09 × 10
24
u
17
+ 1.14 × 10
25
u
16
+ · · · + 1.34 × 10
27
a + 3.04 ×
10
27
, u
18
− 6u
17
+ · · · − 1792u + 448i
(i) Arc colorings
a
4
=
1
0
a
7
=
0
u
a
5
=
1
−u
2
a
11
=
0.00156657u
17
− 0.00850503u
16
+ ··· + 2.44857u − 2.27733
−0.00202422u
17
+ 0.0122017u
16
+ ··· − 3.29503u + 1.40859
a
6
=
−0.000637368u
17
+ 0.00640601u
16
+ ··· − 5.05787u + 2.59216
0.000789287u
17
− 0.00442185u
16
+ ··· + 1.05475u − 0.409876
a
12
=
0.00561057u
17
− 0.0351617u
16
+ ··· + 10.1022u − 4.69092
−0.00341981u
17
+ 0.0194053u
16
+ ··· − 3.19877u + 1.32313
a
10
=
0.00359079u
17
− 0.0207067u
16
+ ··· + 5.74360u − 3.68591
−0.00202422u
17
+ 0.0122017u
16
+ ··· − 3.29503u + 1.40859
a
8
=
−0.00281027u
17
+ 0.0171228u
16
+ ··· − 3.36307u + 2.95981
0.00138362u
17
− 0.00629498u
16
+ ··· − 0.749549u + 0.0422281
a
3
=
−0.00357012u
17
+ 0.0247277u
16
+ ··· − 10.0442u + 4.09627
0.00217249u
17
− 0.0135804u
16
+ ··· + 3.24713u − 0.842978
a
2
=
−0.00271628u
17
+ 0.0142865u
16
+ ··· − 2.16712u + 2.24397
−0.0000227747u
17
− 0.000799890u
16
+ ··· + 1.37886u − 0.473454
a
1
=
0.00709297u
17
− 0.0701956u
16
+ ··· + 37.8937u − 7.60167
−0.00852875u
17
+ 0.0481617u
16
+ ··· − 1.21841u − 0.548662
a
9
=
−0.00489348u
17
+ 0.0417001u
16
+ ··· − 18.1725u + 3.79994
0.00382063u
17
− 0.0210140u
16
+ ··· − 0.151573u + 0.959736
(ii) Obstruction class = −1
(iii) Cusp Shapes = −
34240253580128948442025
5968267629674793473663576
u
17
+
858353517483104921035359
23873070518699173894654304
u
16
+
··· −
31952090119299828142911655
2984133814837396736831788
u −
315919293533464455836207
746033453709349184207947
15
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
18
+ 45u
17
+ ··· + 2548098u + 35721
c
2
, c
5
, c
8
c
12
u
18
+ u
17
+ ··· − 2016u + 189
c
3
, c
6
, c
11
u
18
+ 2u
17
+ ··· − 140u + 43
c
4
, c
7
u
18
+ 6u
17
+ ··· + 1792u + 448
c
9
u
18
+ 4u
17
+ ··· − 4364u − 2008
c
10
(u
3
− u
2
+ 1)
6
16
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
18
− 193y
17
+ ··· − 6886217865618y + 1275989841
c
2
, c
5
, c
8
c
12
y
18
− 45y
17
+ ··· − 2548098y + 35721
c
3
, c
6
, c
11
y
18
− 12y
17
+ ··· − 25190y + 1849
c
4
, c
7
y
18
+ 12y
17
+ ··· − 1103872y + 200704
c
9
y
18
− 48y
17
+ ··· − 29702960y + 4032064
c
10
(y
3
− y
2
+ 2y −1)
6
17
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
4
√
−1(vol +
√
−1CS) Cusp shape
u = 0.932952
a = 0.372040
b = 0.754878
−1.94142 −2.78240
u = −0.932140 + 0.590672I
a = 0.327877 − 0.904251I
b = 0.754878
3.69835 − 60.266490 + 0.10I
u = −0.932140 − 0.590672I
a = 0.327877 + 0.904251I
b = 0.754878
3.69835 − 60.266490 + 0.10I
u = 0.416621 + 0.787171I
a = 0.712256 − 0.776733I
b = −0.877439 − 0.744862I
−0.43923 + 2.82812I −6.26278 − 2.97945I
u = 0.416621 − 0.787171I
a = 0.712256 + 0.776733I
b = −0.877439 + 0.744862I
−0.43923 − 2.82812I −6.26278 + 2.97945I
u = 0.161200 + 1.140610I
a = 1.11639 + 1.55047I
b = −0.877439 + 0.744862I
−17.3586 − 2.8281I −7.95480 + 2.97945I
u = 0.161200 − 1.140610I
a = 1.11639 − 1.55047I
b = −0.877439 − 0.744862I
−17.3586 + 2.8281I −7.95480 − 2.97945I
u = −0.68739 + 1.23808I
a = −0.248640 + 0.732255I
b = −0.877439 + 0.744862I
−0.43923 − 2.82812I −6.26278 + 2.97945I
u = −0.68739 − 1.23808I
a = −0.248640 − 0.732255I
b = −0.877439 − 0.744862I
−0.43923 + 2.82812I −6.26278 − 2.97945I
u = 0.357169
a = −1.85720
b = 0.754878
−1.94142 −2.78240
18
Solutions to I
u
4
√
−1(vol +
√
−1CS) Cusp shape
u = 1.74158
a = −1.24447
b = 0.754878
−13.2210 −1.42550
u = −0.45245 + 1.70936I
a = 0.320272 + 0.802147I
b = −0.877439 + 0.744862I
−6.07901 − 2.82812I −9.31169 + 2.97945I
u = −0.45245 − 1.70936I
a = 0.320272 − 0.802147I
b = −0.877439 − 0.744862I
−6.07901 + 2.82812I −9.31169 − 2.97945I
u = 0.63983 + 2.02141I
a = −0.044419 − 0.705019I
b = −0.877439 − 0.744862I
−6.07901 + 2.82812I −9.31169 − 2.97945I
u = 0.63983 − 2.02141I
a = −0.044419 + 0.705019I
b = −0.877439 + 0.744862I
−6.07901 − 2.82812I −9.31169 + 2.97945I
u = 0.59747 + 2.40404I
a = −0.446280 − 0.570652I
b = −0.877439 − 0.744862I
−17.3586 + 2.8281I −7.95480 − 2.97945I
u = 0.59747 − 2.40404I
a = −0.446280 + 0.570652I
b = −0.877439 + 0.744862I
−17.3586 − 2.8281I −7.95480 + 2.97945I
u = 3.48202
a = 0.254715
b = 0.754878
−13.2210 −1.42550
19
V. I
u
5
= h−u
5
− 2u
4
− 6u
3
− 3u
2
+ 4b − 5u + 5, −u
5
− 2u
4
− 6u
3
− 3u
2
+
4a − 5u + 5, u
6
+ u
5
+ 4u
4
+ u
3
+ 2u
2
− 2u + 1i
(i) Arc colorings
a
4
=
1
0
a
7
=
0
u
a
5
=
1
−u
2
a
11
=
1
4
u
5
+
1
2
u
4
+ ··· +
5
4
u −
5
4
1
4
u
5
+
1
2
u
4
+ ··· +
5
4
u −
5
4
a
6
=
−
1
2
u
4
−
1
2
u
3
−
3
2
u
2
+
1
2
−
1
2
u
4
−
1
2
u
3
−
3
2
u
2
+ u +
1
2
a
12
=
3
4
u
5
+ u
4
+ ··· +
3
4
u −
5
4
u
5
+
1
2
u
4
+ ··· + u −
3
2
a
10
=
0
1
4
u
5
+
1
2
u
4
+ ··· +
5
4
u −
5
4
a
8
=
0
u
a
3
=
1
−u
2
a
2
=
1
2
u
4
+
1
2
u
3
+
3
2
u
2
+
1
2
1
2
u
4
+
1
2
u
3
+
1
2
u
2
− u −
1
2
a
1
=
1
2
u
4
+
1
2
u
3
+
3
2
u
2
−
1
2
1
2
u
4
+
1
2
u
3
+
3
2
u
2
− u −
1
2
a
9
=
1
4
u
5
+
1
2
u
4
+ ··· +
5
4
u −
5
4
u
4
+ u
3
+ 2u
2
+ u − 1
(ii) Obstruction class = 1
(iii) Cusp Shapes =
1
4
u
5
+ u
4
+ 3u
3
+
5
4
u
2
+
13
4
u −
35
4
20
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
2
(u − 1)
6
c
3
, c
4
u
6
+ u
5
+ 4u
4
+ u
3
+ 2u
2
− 2u + 1
c
5
(u + 1)
6
c
6
(u
3
− u
2
+ 2u − 1)
2
c
7
u
6
c
8
(u
3
+ u
2
− 1)
2
c
9
, c
10
, c
12
(u
3
− u
2
+ 1)
2
c
11
(u
3
+ u
2
+ 2u + 1)
2
21
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
2
, c
5
(y −1)
6
c
3
, c
4
y
6
+ 7y
5
+ 18y
4
+ 21y
3
+ 16y
2
+ 1
c
6
, c
11
(y
3
+ 3y
2
+ 2y −1)
2
c
7
y
6
c
8
, c
9
, c
10
c
12
(y
3
− y
2
+ 2y −1)
2
22
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
5
√
−1(vol +
√
−1CS) Cusp shape
u = −0.592519 + 0.986732I
a = −0.877439 + 0.744862I
b = −0.877439 + 0.744862I
1.37919 − 2.82812I −8.07960 + 2.97945I
u = −0.592519 − 0.986732I
a = −0.877439 − 0.744862I
b = −0.877439 − 0.744862I
1.37919 + 2.82812I −8.07960 − 2.97945I
u = 0.377439 + 0.320410I
a = −0.877439 + 0.744862I
b = −0.877439 + 0.744862I
−2.75839 −7.72484 + 1.67231I
u = 0.377439 − 0.320410I
a = −0.877439 − 0.744862I
b = −0.877439 − 0.744862I
−2.75839 −7.72484 − 1.67231I
u = −0.28492 + 1.73159I
a = 0.754878
b = 0.754878
1.37919 + 2.82812I −1.19557 − 1.30714I
u = −0.28492 − 1.73159I
a = 0.754878
b = 0.754878
1.37919 − 2.82812I −1.19557 + 1.30714I
23
VI.
I
v
1
= ha, 3v
5
−2v
4
+15v
3
−20v
2
+7b+12v +3, v
6
−v
5
+5v
4
−9v
3
+5v
2
−v +1i
(i) Arc colorings
a
4
=
1
0
a
7
=
v
0
a
5
=
1
0
a
11
=
0
−
3
7
v
5
+
2
7
v
4
+ ··· −
12
7
v −
3
7
a
6
=
v
−
2
7
v
5
−
1
7
v
4
+ ··· −
1
7
v +
5
7
a
12
=
1
7
v
5
+
2
7
v
4
+ ··· −
2
7
v −
1
7
−
6
7
v
5
+
2
7
v
4
+ ··· −
9
7
v −
1
7
a
10
=
3
7
v
5
−
2
7
v
4
+ ··· +
12
7
v +
3
7
−
3
7
v
5
+
2
7
v
4
+ ··· −
12
7
v −
3
7
a
8
=
2
7
v
5
+
1
7
v
4
+ ··· +
8
7
v −
5
7
−
2
7
v
5
−
1
7
v
4
+ ··· −
1
7
v +
5
7
a
3
=
5
7
v
5
−
2
7
v
4
+ ··· −
4
7
v +
4
7
−
2
7
v
5
+
2
7
v
4
+ ··· +
1
7
v +
1
7
a
2
=
2
7
v
5
+ v
3
−
6
7
v
2
−
9
7
v +
8
7
−
4
7
v
5
+
1
7
v
4
+ ··· + 3v
2
−
1
7
a
1
=
−
2
7
v
5
−
1
7
v
4
+ ··· −
8
7
v +
5
7
2
7
v
5
+
1
7
v
4
+ ··· +
1
7
v −
5
7
a
9
=
3
7
v
5
+
3
7
v
4
+ ··· +
6
7
v −
6
7
−
8
7
v
5
+
1
7
v
4
+ ··· −
10
7
v +
4
7
(ii) Obstruction class = 1
(iii) Cusp Shapes = −
9
7
v
5
+
4
7
v
4
−
44
7
v
3
+ 7v
2
− 4v −
46
7
24
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
3
(u
3
− u
2
+ 2u − 1)
2
c
2
(u
3
+ u
2
− 1)
2
c
4
u
6
c
5
, c
10
(u
3
− u
2
+ 1)
2
c
6
, c
7
u
6
+ u
5
+ 4u
4
+ u
3
+ 2u
2
− 2u + 1
c
8
(u − 1)
6
c
9
u
6
− 4u
5
+ 7u
4
− 9u
3
+ 14u
2
− 16u + 8
c
11
u
6
− u
5
+ 4u
4
− u
3
+ 2u
2
+ 2u + 1
c
12
(u + 1)
6
25
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
3
(y
3
+ 3y
2
+ 2y −1)
2
c
2
, c
5
, c
10
(y
3
− y
2
+ 2y −1)
2
c
4
y
6
c
6
, c
7
, c
11
y
6
+ 7y
5
+ 18y
4
+ 21y
3
+ 16y
2
+ 1
c
8
, c
12
(y −1)
6
c
9
y
6
− 2y
5
+ 5y
4
+ 3y
3
+ 20y
2
− 32y + 64
26
(vi) Complex Volumes and Cusp Shapes
Solutions to I
v
1
√
−1(vol +
√
−1CS) Cusp shape
v = 0.947279 + 0.320410I
a = 0
b = −0.877439 − 0.744862I
1.37919 + 2.82812I −8.07960 − 2.97945I
v = 0.947279 − 0.320410I
a = 0
b = −0.877439 + 0.744862I
1.37919 − 2.82812I −8.07960 + 2.97945I
v = −0.069840 + 0.424452I
a = 0
b = −0.877439 − 0.744862I
−2.75839 −7.72484 − 1.67231I
v = −0.069840 − 0.424452I
a = 0
b = −0.877439 + 0.744862I
−2.75839 −7.72484 + 1.67231I
v = −0.37744 + 2.29387I
a = 0
b = 0.754878
1.37919 + 2.82812I −1.19557 − 1.30714I
v = −0.37744 − 2.29387I
a = 0
b = 0.754878
1.37919 − 2.82812I −1.19557 + 1.30714I
27
VII. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
(u − 1)
6
(u
3
− u
2
+ 2u − 1)
2
(u
4
− 9u
3
+ 10u
2
− 4u + 1)
· (u
6
− u
5
+ ··· + 8u + 1)(u
18
+ 20u
17
+ ··· + 9u + 1)
· (u
18
+ 45u
17
+ ··· + 2548098u + 35721)
c
2
, c
8
(u − 1)
6
(u
3
+ u
2
− 1)
2
(u
4
+ 3u
3
− 2u − 1)
· (u
6
+ 3u
5
+ ··· + 2u + 1)(u
18
− 10u
16
+ ··· + u + 1)
· (u
18
+ u
17
+ ··· − 2016u + 189)
c
3
, c
6
((u
3
− u
2
+ 2u − 1)
2
)(u
4
− u
3
− 2u + 1)(u
6
+ u
5
+ ··· − 2u + 1)
· (u
6
+ 3u
5
+ ··· + 2u + 1)(u
18
+ 4u
16
+ ··· − 5u + 1)
· (u
18
+ 2u
17
+ ··· − 140u + 43)
c
4
, c
7
u
6
(u
4
− u
3
− 2u
2
− 4u + 1)(u
6
+ u
5
+ 4u
4
+ u
3
+ 2u
2
− 2u + 1)
· (u
6
+ 5u
5
+ 7u
4
+ 2u
2
+ 23u + 23)(u
18
− 13u
15
+ ··· + 3u + 1)
· (u
18
+ 6u
17
+ ··· + 1792u + 448)
c
5
, c
12
(u + 1)
6
(u
3
− u
2
+ 1)
2
(u
4
− 3u
3
+ 2u − 1)
· (u
6
− 3u
5
+ ··· − 2u + 1)(u
18
− 10u
16
+ ··· + u + 1)
· (u
18
+ u
17
+ ··· − 2016u + 189)
c
9
(u
3
− u
2
+ 1)
2
(u
4
− 5u
3
+ 7u
2
− 7u + 5)
· (u
6
− 4u
5
+ 7u
4
− 9u
3
+ 14u
2
− 16u + 8)
· (u
6
+ 2u
5
+ ··· + 5u + 5)(u
18
+ 4u
17
+ ··· − 4364u − 2008)
· (u
18
+ 4u
17
+ ··· + 2u + 49)
c
10
((u
3
− u
2
+ 1)
12
)(u
4
+ 2u
3
− 3u − 1)(u
18
+ 11u
17
+ ··· + 12u + 7)
c
11
(u
3
+ u
2
+ 2u + 1)
2
(u
4
+ u
3
+ 2u + 1)
· (u
6
− 3u
5
+ ··· − 2u + 1)(u
6
− u
5
+ 4u
4
− u
3
+ 2u
2
+ 2u + 1)
· (u
18
+ 4u
16
+ ··· − 5u + 1)(u
18
+ 2u
17
+ ··· − 140u + 43)
28
VIII. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
(y −1)
6
(y
3
+ 3y
2
+ 2y −1)
2
(y
4
− 61y
3
+ 30y
2
+ 4y + 1)
· (y
6
− 17y
5
+ 108y
4
− 306y
3
+ 352y
2
− 24y + 1)
· (y
18
− 193y
17
+ ··· − 6886217865618y + 1275989841)
· (y
18
− 44y
17
+ ··· + 123y + 1)
c
2
, c
5
, c
8
c
12
(y −1)
6
(y
3
− y
2
+ 2y −1)
2
(y
4
− 9y
3
+ 10y
2
− 4y + 1)
· (y
6
− y
5
− 8y
4
+ 2y
3
+ 20y
2
+ 8y + 1)
· (y
18
− 45y
17
+ ··· − 2548098y + 35721)(y
18
− 20y
17
+ ··· − 9y + 1)
c
3
, c
6
, c
11
(y
3
+ 3y
2
+ 2y −1)
2
(y
4
− y
3
− 2y
2
− 4y + 1)
· (y
6
− y
5
+ 4y
4
+ 5y
3
+ 5y
2
+ 2y + 1)(y
6
+ 7y
5
+ 18y
4
+ 21y
3
+ 16y
2
+ 1)
· (y
18
− 12y
17
+ ··· − 25190y + 1849)(y
18
+ 8y
17
+ ··· − 13y + 1)
c
4
, c
7
y
6
(y
4
− 5y
3
− 2y
2
− 20y + 1)
· (y
6
− 11y
5
+ 53y
4
− 156y
3
+ 326y
2
− 437y + 529)
· (y
6
+ 7y
5
+ 18y
4
+ 21y
3
+ 16y
2
+ 1)(y
18
+ 10y
16
+ ··· + 43y + 1)
· (y
18
+ 12y
17
+ ··· − 1103872y + 200704)
c
9
(y
3
− y
2
+ 2y −1)
2
(y
4
− 11y
3
− 11y
2
+ 21y + 25)
· (y
6
− 2y
5
+ 5y
4
+ 3y
3
+ 20y
2
− 32y + 64)
· (y
6
+ 4y
5
− 14y
3
− 4y
2
+ 15y + 25)
· (y
18
− 48y
17
+ ··· − 29702960y + 4032064)
· (y
18
− 38y
17
+ ··· + 23516y + 2401)
c
10
(y
3
− y
2
+ 2y −1)
12
(y
4
− 4y
3
+ 10y
2
− 9y + 1)
· (y
18
− 7y
17
+ ··· − 578y + 49)
29
