12a
0869
(K12a
0869
)
A knot diagram
1
Linearized knot diagam
4 6 7 9 10 11 12 1 5 2 3 8
Solving Sequence
7,12
8
1,4
2 9 5 3 11 6 10
c
7
c
12
c
1
c
8
c
4
c
3
c
11
c
6
c
10
c
2
, c
5
, c
9
Ideals for irreducible components
2
of X
par
I
u
1
= h−959u
21
+ 8u
20
+ ··· + 6991b − 10004, 12718u
21
+ 1556u
20
+ ··· + 6991a + 39666,
u
22
− 14u
20
+ ··· + 2u − 1i
I
u
2
= h−1.39235 × 10
140
u
77
+ 6.32801 × 10
139
u
76
+ ··· + 1.95985 × 10
140
b − 2.88234 × 10
142
,
6.63657 × 10
141
u
77
− 2.91804 × 10
141
u
76
+ ··· + 8.42734 × 10
141
a + 1.55560 × 10
144
,
u
78
− 2u
77
+ ··· + 136u − 43i
I
u
3
= h−u
7
+ 4u
5
− 5u
3
− u
2
+ b + u + 1, u
7
− u
6
− 4u
5
+ 4u
4
+ 5u
3
− 4u
2
+ a − u,
u
8
− 5u
6
+ 8u
4
+ u
3
− 3u
2
− 2u − 1i
I
u
4
= h2u
7
− 4u
6
− 5u
5
+ 11u
4
− u
3
− 3u
2
+ b + 5u − 3, −3u
7
+ 6u
6
+ 8u
5
− 18u
4
+ u
3
+ 8u
2
+ a − 8u + 4,
u
8
− 3u
7
− u
6
+ 9u
5
− 5u
4
− 3u
3
+ 4u
2
− 4u + 1i
I
u
5
= h−u
3
+ b + 2u − 2, 2u
3
+ 2u
2
+ a − 3u − 1, u
4
+ 2u
3
− u
2
− 2u + 1i
* 5 irreducible components of dim
C
= 0, with total 120 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−959u
21
+ 8u
20
+ · · · + 6991b − 10004, 12718u
21
+ 1556u
20
+ · · · +
6991a + 39666, u
22
− 14u
20
+ · · · + 2u − 1i
(i) Arc colorings
a
7
=
1
0
a
12
=
0
u
a
8
=
1
−u
2
a
1
=
u
−u
3
+ u
a
4
=
−1.81920u
21
− 0.222572u
20
+ ··· − 0.747533u − 5.67387
0.137176u
21
− 0.00114433u
20
+ ··· + 2.09898u + 1.43098
a
2
=
−1.06737u
21
− 1.55314u
20
+ ··· + 1.34659u − 1.79874
0.447575u
21
+ 0.521814u
20
+ ··· − 0.136890u + 2.47189
a
9
=
−u
2
+ 1
u
4
− 2u
2
a
5
=
−1.81920u
21
− 0.222572u
20
+ ··· + 0.252467u − 5.67387
0.137176u
21
− 0.00114433u
20
+ ··· + 2.09898u + 1.43098
a
3
=
−1.68202u
21
− 0.223716u
20
+ ··· + 1.35145u − 4.24288
0.137176u
21
− 0.00114433u
20
+ ··· + 2.09898u + 1.43098
a
11
=
1.25819u
21
+ 0.476470u
20
+ ··· − 0.714633u + 2.67458
0.733085u
21
− 0.0321842u
20
+ ··· + 1.28394u + 0.746388
a
6
=
2.00458u
21
+ 1.20956u
20
+ ··· − 2.62652u + 5.45129
−0.439565u
21
− 0.405092u
20
+ ··· − 1.95952u − 1.43213
a
10
=
0.222572u
21
− 0.185381u
20
+ ··· + 2.03547u + 2.81920
0.00114433u
21
+ 0.302389u
20
+ ··· − 1.15663u − 0.137176
(ii) Obstruction class = −1
(iii) Cusp Shapes = −
44709
6991
u
21
−
15293
6991
u
20
+ ··· −
71860
6991
u −
27948
6991
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
22
− 18u
21
+ ··· − 1136u + 64
c
2
, c
11
u
22
+ u
21
+ ··· − 5u + 1
c
3
, c
10
u
22
+ u
21
+ ··· − 6u
2
+ 1
c
4
, c
5
, c
7
c
8
, c
9
, c
12
u
22
− 14u
20
+ ··· − 2u − 1
c
6
u
22
− 11u
21
+ ··· − 60u + 8
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
22
+ 94y
20
+ ··· − 435456y + 4096
c
2
, c
11
y
22
− 17y
21
+ ··· − 21y + 1
c
3
, c
10
y
22
+ 3y
21
+ ··· − 12y + 1
c
4
, c
5
, c
7
c
8
, c
9
, c
12
y
22
− 28y
21
+ ··· − 26y + 1
c
6
y
22
− 5y
21
+ ··· − 1168y + 64
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.620777 + 0.699897I
a = −0.444548 − 0.589843I
b = −0.975241 + 0.924812I
0.28538 + 9.52077I 5.54038 − 10.18443I
u = 0.620777 − 0.699897I
a = −0.444548 + 0.589843I
b = −0.975241 − 0.924812I
0.28538 − 9.52077I 5.54038 + 10.18443I
u = −0.543470 + 0.600696I
a = 0.287139 − 0.161144I
b = 0.162955 + 0.882903I
2.06715 − 1.71752I 11.74245 + 5.24817I
u = −0.543470 − 0.600696I
a = 0.287139 + 0.161144I
b = 0.162955 − 0.882903I
2.06715 + 1.71752I 11.74245 − 5.24817I
u = −0.616708 + 0.440990I
a = −1.099990 − 0.644526I
b = 0.481328 − 0.475392I
0.165742 + 1.104130I 7.76898 − 0.48945I
u = −0.616708 − 0.440990I
a = −1.099990 + 0.644526I
b = 0.481328 + 0.475392I
0.165742 − 1.104130I 7.76898 + 0.48945I
u = −0.688001
a = −0.0816056
b = −1.19439
0.164932 13.5940
u = 1.47278 + 0.24907I
a = 0.639561 + 0.759382I
b = −0.461601 − 0.642988I
8.63753 + 2.31951I 6.80409 + 2.73514I
u = 1.47278 − 0.24907I
a = 0.639561 − 0.759382I
b = −0.461601 + 0.642988I
8.63753 − 2.31951I 6.80409 − 2.73514I
u = −0.479173
a = −0.636420
b = −0.286181
0.816563 11.9280
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 1.52797 + 0.02574I
a = −0.26700 + 1.87402I
b = −0.755859 − 1.019260I
14.2021 − 4.2069I 12.43580 + 5.16700I
u = 1.52797 − 0.02574I
a = −0.26700 − 1.87402I
b = −0.755859 + 1.019260I
14.2021 + 4.2069I 12.43580 − 5.16700I
u = 0.357972 + 0.207376I
a = 2.77142 + 1.51494I
b = 0.416028 − 0.835216I
1.27965 + 3.66433I 15.0331 − 10.2324I
u = 0.357972 − 0.207376I
a = 2.77142 − 1.51494I
b = 0.416028 + 0.835216I
1.27965 − 3.66433I 15.0331 + 10.2324I
u = −1.59329 + 0.06074I
a = −0.215693 + 0.896227I
b = 0.973496 − 0.770109I
15.7122 − 0.5131I 13.84357 − 0.14086I
u = −1.59329 − 0.06074I
a = −0.215693 − 0.896227I
b = 0.973496 + 0.770109I
15.7122 + 0.5131I 13.84357 + 0.14086I
u = −1.60156
a = 0.521347
b = 0.540591
15.7785 15.7070
u = 1.63321 + 0.25925I
a = −0.25245 + 1.62291I
b = 1.21002 − 1.23023I
15.4855 + 16.9496I 10.93128 − 7.84709I
u = 1.63321 − 0.25925I
a = −0.25245 − 1.62291I
b = 1.21002 + 1.23023I
15.4855 − 16.9496I 10.93128 + 7.84709I
u = −1.64240 + 0.25438I
a = −0.026921 + 1.355890I
b = −0.57852 − 1.30048I
17.0516 − 8.7183I 13.8836 + 4.8126I
6
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −1.64240 − 0.25438I
a = −0.026921 − 1.355890I
b = −0.57852 + 1.30048I
17.0516 + 8.7183I 13.8836 − 4.8126I
u = 0.335041
a = −2.58634
b = 0.994760
−2.04032 −5.19480
7
II. I
u
2
= h−1.39 × 10
140
u
77
+ 6.33 × 10
139
u
76
+ · · · + 1.96 × 10
140
b − 2.88 ×
10
142
, 6.64 × 10
141
u
77
− 2.92 × 10
141
u
76
+ · · · + 8.43 × 10
141
a + 1.56 ×
10
144
, u
78
− 2u
77
+ · · · + 136u − 43i
(i) Arc colorings
a
7
=
1
0
a
12
=
0
u
a
8
=
1
−u
2
a
1
=
u
−u
3
+ u
a
4
=
−0.787505u
77
+ 0.346259u
76
+ ··· + 138.255u − 184.590
0.710437u
77
− 0.322883u
76
+ ··· − 127.381u + 147.069
a
2
=
−2.36422u
77
+ 3.85705u
76
+ ··· + 112.872u − 279.876
−0.790784u
77
+ 0.595382u
76
+ ··· + 100.423u − 123.684
a
9
=
−u
2
+ 1
u
4
− 2u
2
a
5
=
−0.510367u
77
+ 0.427296u
76
+ ··· + 63.1806u − 113.051
0.677512u
77
− 0.534118u
76
+ ··· − 97.2276u + 120.573
a
3
=
−0.0770682u
77
+ 0.0233760u
76
+ ··· + 10.8743u − 37.5207
0.710437u
77
− 0.322883u
76
+ ··· − 127.381u + 147.069
a
11
=
−1.01566u
77
+ 2.13882u
76
+ ··· − 56.8939u − 95.6811
1.96720u
77
− 4.01917u
76
+ ··· − 55.8889u + 149.806
a
6
=
4.21314u
77
− 6.18031u
76
+ ··· − 353.473u + 453.881
1.88902u
77
− 0.366972u
76
+ ··· − 387.504u + 407.067
a
10
=
0.555335u
77
− 0.588323u
76
+ ··· − 78.0022u + 39.3661
3.00021u
77
− 6.16888u
76
+ ··· − 82.8724u + 226.957
(ii) Obstruction class = −1
(iii) Cusp Shapes = 15.0721u
77
− 15.2353u
76
+ ··· − 1631.33u + 2376.87
8
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
(u
39
+ 9u
38
+ ··· + 1162u + 266)
2
c
2
, c
11
u
78
− u
77
+ ··· − 7654u + 739
c
3
, c
10
u
78
− 4u
77
+ ··· − 41u − 113
c
4
, c
5
, c
7
c
8
, c
9
, c
12
u
78
+ 2u
77
+ ··· − 136u − 43
c
6
(u
39
+ 6u
38
+ ··· − 3u − 1)
2
9
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
(y
39
+ 31y
38
+ ··· − 924056y −70756)
2
c
2
, c
11
y
78
− 19y
77
+ ··· − 160648484y + 546121
c
3
, c
10
y
78
+ 2y
77
+ ··· + 263643y + 12769
c
4
, c
5
, c
7
c
8
, c
9
, c
12
y
78
− 86y
77
+ ··· − 86350y + 1849
c
6
(y
39
− 8y
38
+ ··· + 11y −1)
2
10
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.878599 + 0.472127I
a = 0.761236 + 0.006801I
b = 0.799415 + 0.070464I
7.26602 − 0.78546I 0
u = 0.878599 − 0.472127I
a = 0.761236 − 0.006801I
b = 0.799415 − 0.070464I
7.26602 + 0.78546I 0
u = 0.400608 + 0.847774I
a = 0.265006 − 0.493852I
b = −0.524818 − 0.571018I
−0.41212 − 4.48592I 0
u = 0.400608 − 0.847774I
a = 0.265006 + 0.493852I
b = −0.524818 + 0.571018I
−0.41212 + 4.48592I 0
u = −0.937174
a = 1.51645
b = −1.58228
1.61912 0
u = −0.499526 + 0.717695I
a = −0.754574 + 0.328335I
b = −0.554095 − 0.691522I
1.72667 − 2.76108I 0
u = −0.499526 − 0.717695I
a = −0.754574 − 0.328335I
b = −0.554095 + 0.691522I
1.72667 + 2.76108I 0
u = −0.783766 + 0.812694I
a = 0.329548 − 0.719810I
b = 0.973644 + 0.916548I
7.4945 − 12.9029I 0
u = −0.783766 − 0.812694I
a = 0.329548 + 0.719810I
b = 0.973644 − 0.916548I
7.4945 + 12.9029I 0
u = −0.620809 + 0.562611I
a = −0.41860 + 1.38503I
b = −0.861580 − 0.980365I
3.93141 − 5.03531I 0
11
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.620809 − 0.562611I
a = −0.41860 − 1.38503I
b = −0.861580 + 0.980365I
3.93141 + 5.03531I 0
u = −0.317001 + 1.163500I
a = −0.118895 − 0.184699I
b = 0.561708 − 0.589908I
5.97998 + 6.68209I 0
u = −0.317001 − 1.163500I
a = −0.118895 + 0.184699I
b = 0.561708 + 0.589908I
5.97998 − 6.68209I 0
u = 0.677706 + 1.009700I
a = 0.401326 + 0.381179I
b = 0.565142 − 0.694366I
8.39691 + 2.42469I 0
u = 0.677706 − 1.009700I
a = 0.401326 − 0.381179I
b = 0.565142 + 0.694366I
8.39691 − 2.42469I 0
u = 0.841597 + 0.916305I
a = −0.126486 − 0.257887I
b = −0.211832 + 0.732575I
8.85565 + 4.48611I 0
u = 0.841597 − 0.916305I
a = −0.126486 + 0.257887I
b = −0.211832 − 0.732575I
8.85565 − 4.48611I 0
u = −0.322712 + 0.643423I
a = 0.350653 + 0.136104I
b = −0.829719 + 0.618378I
3.04287 + 0.97727I 4.00000 + 0.I
u = −0.322712 − 0.643423I
a = 0.350653 − 0.136104I
b = −0.829719 − 0.618378I
3.04287 − 0.97727I 4.00000 + 0.I
u = 0.292751 + 0.656074I
a = 1.13118 + 1.51679I
b = 0.587768 − 0.046192I
5.50541 + 4.90955I 4.00000 − 6.21885I
12
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.292751 − 0.656074I
a = 1.13118 − 1.51679I
b = 0.587768 + 0.046192I
5.50541 − 4.90955I 4.00000 + 6.21885I
u = 0.697366 + 0.077892I
a = 1.98372 − 0.61577I
b = −0.080857 + 0.333280I
7.69383 − 0.20004I 14.04950 − 0.81267I
u = 0.697366 − 0.077892I
a = 1.98372 + 0.61577I
b = −0.080857 − 0.333280I
7.69383 + 0.20004I 14.04950 + 0.81267I
u = 1.30141
a = −0.0545808
b = 1.31020
1.61912 0
u = −0.687585 + 0.025628I
a = −0.0831851 + 0.0374082I
b = −1.193040 − 0.025967I
0.164937 13.54531 + 0.I
u = −0.687585 − 0.025628I
a = −0.0831851 − 0.0374082I
b = −1.193040 + 0.025967I
0.164937 13.54531 + 0.I
u = 0.524261 + 0.441733I
a = 0.306573 + 1.053310I
b = 0.976668 − 0.787130I
−1.42813 + 2.90883I −0.86909 − 8.81897I
u = 0.524261 − 0.441733I
a = 0.306573 − 1.053310I
b = 0.976668 + 0.787130I
−1.42813 − 2.90883I −0.86909 + 8.81897I
u = −0.619957 + 0.241745I
a = 0.599856 + 0.984205I
b = 0.607492 − 1.169200I
8.47744 − 6.16342I 12.6402 + 6.3717I
u = −0.619957 − 0.241745I
a = 0.599856 − 0.984205I
b = 0.607492 + 1.169200I
8.47744 + 6.16342I 12.6402 − 6.3717I
13
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.416423 + 0.505098I
a = 0.692855 − 0.298181I
b = 0.998092 + 0.980397I
−0.41212 − 4.48592I 4.00000 + 9.50012I
u = −0.416423 − 0.505098I
a = 0.692855 + 0.298181I
b = 0.998092 − 0.980397I
−0.41212 + 4.48592I 4.00000 − 9.50012I
u = −1.386030 + 0.009998I
a = −0.447622 + 1.236780I
b = 0.223101 − 0.511859I
3.04287 + 0.97727I 0
u = −1.386030 − 0.009998I
a = −0.447622 − 1.236780I
b = 0.223101 + 0.511859I
3.04287 − 0.97727I 0
u = −0.250999 + 0.528179I
a = −0.64407 + 1.62571I
b = −0.650925 − 0.017019I
−1.42813 − 2.90883I −0.86909 + 8.81897I
u = −0.250999 − 0.528179I
a = −0.64407 − 1.62571I
b = −0.650925 + 0.017019I
−1.42813 + 2.90883I −0.86909 − 8.81897I
u = 1.42440 + 0.11009I
a = 0.21108 − 1.52515I
b = −0.212514 + 0.389730I
3.93141 + 5.03531I 0
u = 1.42440 − 0.11009I
a = 0.21108 + 1.52515I
b = −0.212514 − 0.389730I
3.93141 − 5.03531I 0
u = −1.47071 + 0.16976I
a = 0.02924 − 1.73933I
b = 0.208151 + 0.324331I
11.26620 − 7.70313I 0
u = −1.47071 − 0.16976I
a = 0.02924 + 1.73933I
b = 0.208151 − 0.324331I
11.26620 + 7.70313I 0
14
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −1.50105 + 0.07381I
a = 0.16363 − 1.73769I
b = 0.831975 + 1.040000I
7.57373 − 4.71354I 0
u = −1.50105 − 0.07381I
a = 0.16363 + 1.73769I
b = 0.831975 − 1.040000I
7.57373 + 4.71354I 0
u = 1.50689 + 0.13292I
a = −0.57785 + 1.84820I
b = 1.43408 − 1.52823I
5.97998 + 6.68209I 0
u = 1.50689 − 0.13292I
a = −0.57785 − 1.84820I
b = 1.43408 + 1.52823I
5.97998 − 6.68209I 0
u = −1.52031 + 0.02429I
a = 0.41183 + 1.96209I
b = −0.92775 − 1.82852I
8.39691 + 2.42469I 0
u = −1.52031 − 0.02429I
a = 0.41183 − 1.96209I
b = −0.92775 + 1.82852I
8.39691 − 2.42469I 0
u = −1.52220 + 0.00111I
a = 1.033490 + 0.891914I
b = −2.01729 − 0.75252I
13.10170 + 0.51825I 0
u = −1.52220 − 0.00111I
a = 1.033490 − 0.891914I
b = −2.01729 + 0.75252I
13.10170 − 0.51825I 0
u = 1.52470 + 0.17283I
a = 0.17190 + 1.67399I
b = 0.42027 − 1.57556I
8.85565 + 4.48611I 0
u = 1.52470 − 0.17283I
a = 0.17190 − 1.67399I
b = 0.42027 + 1.57556I
8.85565 − 4.48611I 0
15
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 1.53498 + 0.05067I
a = 0.031004 − 0.599115I
b = −0.664705 + 0.481914I
7.69383 + 0.20004I 0
u = 1.53498 − 0.05067I
a = 0.031004 + 0.599115I
b = −0.664705 − 0.481914I
7.69383 − 0.20004I 0
u = 0.456519 + 0.068241I
a = −0.935816 − 0.494654I
b = −0.349780 + 1.220370I
1.72667 − 2.76108I 13.6219 + 4.5455I
u = 0.456519 − 0.068241I
a = −0.935816 + 0.494654I
b = −0.349780 − 1.220370I
1.72667 + 2.76108I 13.6219 − 4.5455I
u = 0.299577 + 0.344619I
a = −0.66963 + 1.35775I
b = 0.815822 + 0.126759I
−1.89357 −2.70742 + 0.I
u = 0.299577 − 0.344619I
a = −0.66963 − 1.35775I
b = 0.815822 − 0.126759I
−1.89357 −2.70742 + 0.I
u = 1.54424 + 0.05173I
a = 0.99834 − 1.20923I
b = −1.54824 + 0.97543I
7.26602 + 0.78546I 0
u = 1.54424 − 0.05173I
a = 0.99834 + 1.20923I
b = −1.54824 − 0.97543I
7.26602 − 0.78546I 0
u = −1.54178 + 0.12147I
a = −0.53568 − 1.87198I
b = 1.09374 + 1.36438I
5.50541 − 4.90955I 0
u = −1.54178 − 0.12147I
a = −0.53568 + 1.87198I
b = 1.09374 − 1.36438I
5.50541 + 4.90955I 0
16
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 1.53887 + 0.22306I
a = −0.02826 − 1.42027I
b = −0.950908 + 1.004730I
8.47744 + 6.16342I 0
u = 1.53887 − 0.22306I
a = −0.02826 + 1.42027I
b = −0.950908 − 1.004730I
8.47744 − 6.16342I 0
u = 1.57176 + 0.06808I
a = −0.67201 − 1.65866I
b = 1.13908 + 1.58816I
15.9502 + 7.3009I 0
u = 1.57176 − 0.06808I
a = −0.67201 + 1.65866I
b = 1.13908 − 1.58816I
15.9502 − 7.3009I 0
u = −1.56399 + 0.22067I
a = 0.33159 + 1.70584I
b = −1.25296 − 1.32410I
7.4945 − 12.9029I 0
u = −1.56399 − 0.22067I
a = 0.33159 − 1.70584I
b = −1.25296 + 1.32410I
7.4945 + 12.9029I 0
u = 1.57094 + 0.16644I
a = 0.20882 − 2.09117I
b = −0.79192 + 1.34950I
11.26620 + 7.70313I 0
u = 1.57094 − 0.16644I
a = 0.20882 + 2.09117I
b = −0.79192 − 1.34950I
11.26620 − 7.70313I 0
u = −0.390732 + 0.140644I
a = −1.45524 − 4.29333I
b = −0.234921 + 0.913111I
7.57373 + 4.71354I 14.3655 − 4.2774I
u = −0.390732 − 0.140644I
a = −1.45524 + 4.29333I
b = −0.234921 − 0.913111I
7.57373 − 4.71354I 14.3655 + 4.2774I
17
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.380331 + 0.011403I
a = −2.25231 + 1.00243I
b = −1.252690 − 0.561132I
6.53510 + 0.50706I 14.0625 − 11.2444I
u = 0.380331 − 0.011403I
a = −2.25231 − 1.00243I
b = −1.252690 + 0.561132I
6.53510 − 0.50706I 14.0625 + 11.2444I
u = −1.62932 + 0.32096I
a = 0.007896 − 1.263720I
b = 0.973599 + 0.972165I
15.9502 − 7.3009I 0
u = −1.62932 − 0.32096I
a = 0.007896 + 1.263720I
b = 0.973599 − 0.972165I
15.9502 + 7.3009I 0
u = −1.69553 + 0.23371I
a = −0.089709 − 0.529312I
b = 0.469851 + 0.558658I
6.53510 − 0.50706I 0
u = −1.69553 − 0.23371I
a = −0.089709 + 0.529312I
b = 0.469851 − 0.558658I
6.53510 + 0.50706I 0
u = 1.89223 + 0.33820I
a = 0.123352 − 0.452574I
b = −0.432999 + 0.540506I
13.10170 + 0.51825I 0
u = 1.89223 − 0.33820I
a = 0.123352 + 0.452574I
b = −0.432999 − 0.540506I
13.10170 − 0.51825I 0
18
III. I
u
3
= h−u
7
+ 4u
5
− 5u
3
− u
2
+ b + u + 1, u
7
− u
6
− 4u
5
+ 4u
4
+ 5u
3
−
4u
2
+ a − u, u
8
− 5u
6
+ 8u
4
+ u
3
− 3u
2
− 2u − 1i
(i) Arc colorings
a
7
=
1
0
a
12
=
0
u
a
8
=
1
−u
2
a
1
=
u
−u
3
+ u
a
4
=
−u
7
+ u
6
+ 4u
5
− 4u
4
− 5u
3
+ 4u
2
+ u
u
7
− 4u
5
+ 5u
3
+ u
2
− u − 1
a
2
=
u
2
− u
u
7
− 4u
5
+ 4u
3
+ u
a
9
=
−u
2
+ 1
u
4
− 2u
2
a
5
=
−u
7
+ u
6
+ 4u
5
− 4u
4
− 4u
3
+ 4u
2
u
7
− 5u
5
+ 7u
3
+ u
2
− u − 1
a
3
=
u
6
− 4u
4
+ 5u
2
− 1
u
7
− 4u
5
+ 5u
3
+ u
2
− u − 1
a
11
=
−u
5
+ u
4
+ 3u
3
− 3u
2
− 2u + 1
−u
6
+ 4u
4
− 4u
2
a
6
=
−u
4
+ u
3
+ 3u
2
− 2u − 1
u
7
− 5u
5
+ 7u
3
− 2u − 1
a
10
=
u
7
− u
6
− 4u
5
+ 4u
4
+ 5u
3
− 4u
2
− 2u
u + 1
(ii) Obstruction class = 1
(iii) Cusp Shapes = −u
7
− 3u
6
+ 7u
5
+ 7u
4
− 16u
3
+ 11u + 8
19
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
8
− 5u
7
+ 17u
6
− 36u
5
+ 46u
4
− 42u
3
+ 28u
2
− 13u + 5
c
2
, c
11
u
8
− u
7
+ u
6
+ 3u
5
− u
4
− 4u
3
+ 3u − 1
c
3
, c
10
u
8
+ u
7
+ u
6
+ u
5
− u
4
+ u
3
− 2u
2
− 1
c
4
, c
5
, c
7
c
8
u
8
− 5u
6
+ 8u
4
+ u
3
− 3u
2
− 2u − 1
c
6
u
8
− 4u
7
+ 6u
6
− u
5
− 7u
4
+ 9u
3
− 3u
2
− u + 1
c
9
, c
12
u
8
− 5u
6
+ 8u
4
− u
3
− 3u
2
+ 2u − 1
20
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
8
+ 9y
7
+ 21y
6
− 96y
5
− 76y
4
+ 46y
3
+ 152y
2
+ 111y + 25
c
2
, c
11
y
8
+ y
7
+ 5y
6
− 19y
5
+ 29y
4
− 36y
3
+ 26y
2
− 9y + 1
c
3
, c
10
y
8
+ y
7
− 3y
6
− 9y
5
− 7y
4
+ y
3
+ 6y
2
+ 4y + 1
c
4
, c
5
, c
7
c
8
, c
9
, c
12
y
8
− 10y
7
+ 41y
6
− 86y
5
+ 92y
4
− 39y
3
− 3y
2
+ 2y + 1
c
6
y
8
− 4y
7
+ 14y
6
− 19y
5
+ 25y
4
− 29y
3
+ 13y
2
− 7y + 1
21
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = 1.20754
a = −0.642094
b = 1.52836
2.74185 12.9220
u = −0.707725
a = 1.56906
b = −0.942535
−1.25808 6.11200
u = 1.43029 + 0.31228I
a = −0.724269 − 0.732499I
b = 0.205718 + 0.735138I
9.18866 + 2.66551I 17.8547 − 3.7342I
u = 1.43029 − 0.31228I
a = −0.724269 + 0.732499I
b = 0.205718 − 0.735138I
9.18866 − 2.66551I 17.8547 + 3.7342I
u = −0.170510 + 0.455537I
a = −1.52393 − 0.15367I
b = −0.391872 − 0.855920I
0.63948 − 3.35759I 4.34775 + 6.26225I
u = −0.170510 − 0.455537I
a = −1.52393 + 0.15367I
b = −0.391872 + 0.855920I
0.63948 + 3.35759I 4.34775 − 6.26225I
u = −1.50969 + 0.16872I
a = 0.28471 − 2.07483I
b = 0.393243 + 1.090700I
12.4590 − 7.8594I 14.2808 + 7.0452I
u = −1.50969 − 0.16872I
a = 0.28471 + 2.07483I
b = 0.393243 − 1.090700I
12.4590 + 7.8594I 14.2808 − 7.0452I
22
IV.
I
u
4
= h2u
7
− 4u
6
+ · · · + b − 3, −3u
7
+ 6u
6
+ · · · + a + 4, u
8
− 3u
7
+ · · · − 4u + 1i
(i) Arc colorings
a
7
=
1
0
a
12
=
0
u
a
8
=
1
−u
2
a
1
=
u
−u
3
+ u
a
4
=
3u
7
− 6u
6
− 8u
5
+ 18u
4
− u
3
− 8u
2
+ 8u − 4
−2u
7
+ 4u
6
+ 5u
5
− 11u
4
+ u
3
+ 3u
2
− 5u + 3
a
2
=
u
7
− 2u
6
− 3u
5
+ 7u
4
+ u
3
− 5u
2
+ u − 2
−2u
7
+ 4u
6
+ 5u
5
− 12u
4
+ u
3
+ 5u
2
− 4u + 3
a
9
=
−u
2
+ 1
u
4
− 2u
2
a
5
=
u
7
− 2u
6
− 3u
5
+ 6u
4
− 2u
2
+ 3u − 2
−u
7
+ 3u
6
+ 2u
5
− 9u
4
+ 2u
3
+ 4u
2
− 3u + 2
a
3
=
u
7
− 2u
6
− 3u
5
+ 7u
4
− 5u
2
+ 3u − 1
−2u
7
+ 4u
6
+ 5u
5
− 11u
4
+ u
3
+ 3u
2
− 5u + 3
a
11
=
u
7
− u
6
− 4u
5
+ 2u
4
+ 4u
3
+ u
2
− u
−u
7
+ 2u
6
+ 3u
5
− 6u
4
− u
3
+ 3u
2
− 2u + 1
a
6
=
u
6
− u
5
− 4u
4
+ 3u
3
+ 3u
2
− u + 1
−u
7
+ u
6
+ 4u
5
− 3u
4
− 3u
3
+ u
2
− u
a
10
=
u
6
− u
5
− 3u
4
+ 2u
3
+ u
2
+ 2
−u
7
+ u
6
+ 3u
5
− 2u
4
− u
3
− 2u − 1
(ii) Obstruction class = 1
(iii) Cusp Shapes = 13u
7
− 24u
6
− 41u
5
+ 79u
4
+ 10u
3
− 42u
2
+ 31u − 15
23
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
(u
4
+ u
2
− 3)
2
c
2
, c
11
u
8
− 2u
7
+ 2u
5
− u
4
+ 3u
3
− 11u
2
+ 8u − 1
c
3
, c
10
u
8
+ u
7
− 2u
6
+ 4u
5
+ 4u
4
− 7u
3
− 3u + 1
c
4
, c
5
, c
7
c
8
u
8
− 3u
7
− u
6
+ 9u
5
− 5u
4
− 3u
3
+ 4u
2
− 4u + 1
c
6
(u
4
− u
3
− u
2
− u + 1)
2
c
9
, c
12
u
8
+ 3u
7
− u
6
− 9u
5
− 5u
4
+ 3u
3
+ 4u
2
+ 4u + 1
24
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
(y
2
+ y −3)
4
c
2
, c
11
y
8
− 4y
7
+ 6y
6
− 14y
5
+ 19y
4
− 19y
3
+ 75y
2
− 42y + 1
c
3
, c
10
y
8
− 5y
7
+ 4y
6
− 18y
5
+ 80y
4
− 29y
3
− 34y
2
− 9y + 1
c
4
, c
5
, c
7
c
8
, c
9
, c
12
y
8
− 11y
7
+ 45y
6
− 81y
5
+ 49y
4
+ 21y
3
− 18y
2
− 8y + 1
c
6
(y
4
− 3y
3
+ y
2
− 3y + 1)
2
25
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
4
√
−1(vol +
√
−1CS) Cusp shape
u = −1.04482
a = −0.422860
b = −1.05367
−0.204105 −8.34250
u = 0.148948 + 0.646816I
a = 1.70704 + 0.17509I
b = 0.189142 − 0.597506I
6.57974 + 5.19078I 8.80278 − 6.62004I
u = 0.148948 − 0.646816I
a = 1.70704 − 0.17509I
b = 0.189142 + 0.597506I
6.57974 − 5.19078I 8.80278 + 6.62004I
u = 1.50244 + 0.11193I
a = 0.09573 − 1.92231I
b = −0.84053 + 1.35625I
6.57974 + 5.19078I 8.80278 − 6.62004I
u = 1.50244 − 0.11193I
a = 0.09573 + 1.92231I
b = −0.84053 − 1.35625I
6.57974 − 5.19078I 8.80278 + 6.62004I
u = −1.52514
a = −0.952048
b = 2.01086
13.3636 18.7370
u = 0.322737
a = −2.12340
b = 1.63436
−0.204105 −8.34250
u = 1.94445
a = −0.107239
b = −0.288778
13.3636 18.7370
26
V. I
u
5
= h−u
3
+ b + 2u − 2, 2u
3
+ 2u
2
+ a − 3u − 1, u
4
+ 2u
3
− u
2
− 2u + 1i
(i) Arc colorings
a
7
=
1
0
a
12
=
0
u
a
8
=
1
−u
2
a
1
=
u
−u
3
+ u
a
4
=
−2u
3
− 2u
2
+ 3u + 1
u
3
− 2u + 2
a
2
=
u
2
+ 2u − 1
u
2
a
9
=
−u
2
+ 1
−2u
3
− u
2
+ 2u − 1
a
5
=
−2u
3
− 3u
2
+ 2u + 3
u
3
− u
2
− 3u + 2
a
3
=
−u
3
− 2u
2
+ u + 3
u
3
− 2u + 2
a
11
=
u
3
+ 2u
2
− 2u − 4
u
3
+ u
2
− u − 1
a
6
=
2u
3
+ 5u
2
− u − 5
2u
3
+ 2u
2
− 2u − 1
a
10
=
2u
3
+ 4u
2
− u − 5
2u
2
+ u − 2
(ii) Obstruction class = 1
(iii) Cusp Shapes = −18u
3
− 18u
2
+ 18u + 8
27
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
4
c
2
, c
4
, c
5
c
7
, c
8
, c
11
(u
2
+ u − 1)
2
c
3
, c
6
, c
10
(u + 1)
4
c
9
, c
12
(u
2
− u − 1)
2
28
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
4
c
2
, c
4
, c
5
c
7
, c
8
, c
9
c
11
, c
12
(y
2
− 3y + 1)
2
c
3
, c
6
, c
10
(y − 1)
4
29
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
5
√
−1(vol +
√
−1CS) Cusp shape
u = 0.618034
a = 1.61803
b = 1.00000
6.57974 8.00000
u = 0.618034
a = 1.61803
b = 1.00000
6.57974 8.00000
u = −1.61803
a = −0.618034
b = 1.00000
6.57974 8.00000
u = −1.61803
a = −0.618034
b = 1.00000
6.57974 8.00000
30
VI. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
u
4
(u
4
+ u
2
− 3)
2
· (u
8
− 5u
7
+ 17u
6
− 36u
5
+ 46u
4
− 42u
3
+ 28u
2
− 13u + 5)
· (u
22
− 18u
21
+ ··· − 1136u + 64)(u
39
+ 9u
38
+ ··· + 1162u + 266)
2
c
2
, c
11
(u
2
+ u − 1)
2
(u
8
− 2u
7
+ 2u
5
− u
4
+ 3u
3
− 11u
2
+ 8u − 1)
· (u
8
− u
7
+ ··· + 3u − 1)(u
22
+ u
21
+ ··· − 5u + 1)
· (u
78
− u
77
+ ··· − 7654u + 739)
c
3
, c
10
(u + 1)
4
(u
8
+ u
7
− 2u
6
+ 4u
5
+ 4u
4
− 7u
3
− 3u + 1)
· (u
8
+ u
7
+ ··· − 2u
2
− 1)(u
22
+ u
21
+ ··· − 6u
2
+ 1)
· (u
78
− 4u
77
+ ··· − 41u − 113)
c
4
, c
5
, c
7
c
8
(u
2
+ u − 1)
2
(u
8
− 5u
6
+ 8u
4
+ u
3
− 3u
2
− 2u − 1)
· (u
8
− 3u
7
− u
6
+ 9u
5
− 5u
4
− 3u
3
+ 4u
2
− 4u + 1)
· (u
22
− 14u
20
+ ··· − 2u − 1)(u
78
+ 2u
77
+ ··· − 136u − 43)
c
6
(u + 1)
4
(u
4
− u
3
− u
2
− u + 1)
2
· (u
8
− 4u
7
+ 6u
6
− u
5
− 7u
4
+ 9u
3
− 3u
2
− u + 1)
· (u
22
− 11u
21
+ ··· − 60u + 8)(u
39
+ 6u
38
+ ··· − 3u − 1)
2
c
9
, c
12
(u
2
− u − 1)
2
(u
8
− 5u
6
+ 8u
4
− u
3
− 3u
2
+ 2u − 1)
· (u
8
+ 3u
7
− u
6
− 9u
5
− 5u
4
+ 3u
3
+ 4u
2
+ 4u + 1)
· (u
22
− 14u
20
+ ··· − 2u − 1)(u
78
+ 2u
77
+ ··· − 136u − 43)
31
VII. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
y
4
(y
2
+ y − 3)
4
· (y
8
+ 9y
7
+ 21y
6
− 96y
5
− 76y
4
+ 46y
3
+ 152y
2
+ 111y + 25)
· (y
22
+ 94y
20
+ ··· − 435456y + 4096)
· (y
39
+ 31y
38
+ ··· − 924056y − 70756)
2
c
2
, c
11
((y
2
− 3y + 1)
2
)(y
8
− 4y
7
+ ··· − 42y + 1)
· (y
8
+ y
7
+ 5y
6
− 19y
5
+ 29y
4
− 36y
3
+ 26y
2
− 9y + 1)
· (y
22
− 17y
21
+ ··· − 21y + 1)
· (y
78
− 19y
77
+ ··· − 160648484y + 546121)
c
3
, c
10
(y − 1)
4
(y
8
− 5y
7
+ 4y
6
− 18y
5
+ 80y
4
− 29y
3
− 34y
2
− 9y + 1)
· (y
8
+ y
7
− 3y
6
− 9y
5
− 7y
4
+ y
3
+ 6y
2
+ 4y + 1)
· (y
22
+ 3y
21
+ ··· − 12y + 1)(y
78
+ 2y
77
+ ··· + 263643y + 12769)
c
4
, c
5
, c
7
c
8
, c
9
, c
12
(y
2
− 3y + 1)
2
· (y
8
− 11y
7
+ 45y
6
− 81y
5
+ 49y
4
+ 21y
3
− 18y
2
− 8y + 1)
· (y
8
− 10y
7
+ 41y
6
− 86y
5
+ 92y
4
− 39y
3
− 3y
2
+ 2y + 1)
· (y
22
− 28y
21
+ ··· − 26y + 1)(y
78
− 86y
77
+ ··· − 86350y + 1849)
c
6
(y − 1)
4
(y
4
− 3y
3
+ y
2
− 3y + 1)
2
· (y
8
− 4y
7
+ 14y
6
− 19y
5
+ 25y
4
− 29y
3
+ 13y
2
− 7y + 1)
· (y
22
− 5y
21
+ ··· − 1168y + 64)(y
39
− 8y
38
+ ··· + 11y − 1)
2
32
