12a
0102
(K12a
0102
)
A knot diagram
1
Linearized knot diagam
3 5 8 2 10 12 4 11 1 7 9 6
Solving Sequence
8,11
9
4,12
3 7 6 1 10 5 2
c
8
c
11
c
3
c
7
c
6
c
12
c
10
c
5
c
2
c
1
, c
4
, c
9
Ideals for irreducible components
2
of X
par
I
u
1
= h−2.86118 × 10
608
u
128
− 9.03918 × 10
608
u
127
+ ··· + 3.04756 × 10
609
b − 2.75259 × 10
610
,
2.19044 × 10
608
u
128
+ 9.28924 × 10
608
u
127
+ ··· + 4.57134 × 10
609
a − 5.57993 × 10
610
,
u
129
+ 4u
128
+ ··· + 810u + 81i
I
u
2
= hb, u
7
+ 2u
6
− 2u
5
− 4u
4
+ 2u
3
+ 2u
2
+ a + 2, u
8
+ u
7
− 3u
6
− 2u
5
+ 3u
4
+ 2u − 1i
I
u
3
= h2b − 3a − 2, 9a
2
+ 6a − 4, u − 1i
* 3 irreducible components of dim
C
= 0, with total 139 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−2.86 × 10
608
u
128
− 9.04 × 10
608
u
127
+ · · · + 3.05 × 10
609
b − 2.75 ×
10
610
, 2.19 × 10
608
u
128
+ 9.29 × 10
608
u
127
+ · · · + 4.57 × 10
609
a − 5.58 ×
10
610
, u
129
+ 4u
128
+ · · · + 810u + 81i
(i) Arc colorings
a
8
=
1
0
a
11
=
0
u
a
9
=
1
u
2
a
4
=
−0.0479167u
128
− 0.203206u
127
+ ··· + 38.5131u + 12.2063
0.0938842u
128
+ 0.296604u
127
+ ··· + 73.2334u + 9.03212
a
12
=
−u
−u
3
+ u
a
3
=
0.0459675u
128
+ 0.0933979u
127
+ ··· + 111.746u + 21.2385
0.0938842u
128
+ 0.296604u
127
+ ··· + 73.2334u + 9.03212
a
7
=
−0.0705351u
128
− 0.229615u
127
+ ··· − 22.0216u − 8.44795
−0.174404u
128
− 0.559025u
127
+ ··· − 129.629u − 14.8100
a
6
=
−0.217094u
128
− 0.708408u
127
+ ··· − 147.263u − 22.5766
−0.108675u
128
− 0.354830u
127
+ ··· − 79.5453u − 9.38430
a
1
=
0.0402884u
128
+ 0.0431499u
127
+ ··· − 3.07411u − 5.90774
0.0971169u
128
+ 0.306541u
127
+ ··· + 72.8538u + 7.09885
a
10
=
0.0935044u
128
+ 0.442842u
127
+ ··· + 39.1713u + 9.65066
0.00292730u
128
+ 0.0528804u
127
+ ··· − 21.8667u − 0.921416
a
5
=
−0.129678u
128
− 0.378848u
127
+ ··· − 146.629u − 20.5705
−0.0423601u
128
− 0.133841u
127
+ ··· − 42.7148u − 5.05621
a
2
=
−0.124068u
128
− 0.463817u
127
+ ··· − 29.7332u + 0.392563
0.0423601u
128
+ 0.133841u
127
+ ··· + 42.7148u + 5.05621
(ii) Obstruction class = −1
(iii) Cusp Shapes = −0.612839u
128
− 1.98956u
127
+ ··· − 336.700u − 48.6406
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
129
+ 68u
128
+ ··· + 31u + 1
c
2
, c
4
u
129
− 10u
128
+ ··· + 5u − 1
c
3
, c
7
u
129
+ 2u
128
+ ··· + 896u + 256
c
5
u
129
− 2u
128
+ ··· − 5940u + 324
c
6
, c
12
u
129
− 3u
128
+ ··· + 3u − 1
c
8
, c
11
u
129
− 4u
128
+ ··· + 810u − 81
c
9
9(9u
129
− 111u
128
+ ··· + 5137u − 257)
c
10
9(9u
129
− 72u
128
+ ··· − 1416882u + 58007)
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
129
− 4y
128
+ ··· + 1563y −1
c
2
, c
4
y
129
− 68y
128
+ ··· + 31y −1
c
3
, c
7
y
129
+ 48y
128
+ ··· − 933888y −65536
c
5
y
129
+ 12y
128
+ ··· + 12906216y −104976
c
6
, c
12
y
129
+ 69y
128
+ ··· + 31y −1
c
8
, c
11
y
129
− 82y
128
+ ··· + 92178y −6561
c
9
81(81y
129
+ 1953y
128
+ ··· − 1315317y −66049)
c
10
81(81y
129
− 1926y
128
+ ··· + 4.58236 × 10
11
y −3.36481 × 10
9
)
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −1.00492
a = −0.404669
b = −1.60820
−10.5373 0
u = 0.982713 + 0.038300I
a = 5.27556 − 1.67776I
b = −0.733347 − 0.404998I
−1.87304 + 0.83221I 0
u = 0.982713 − 0.038300I
a = 5.27556 + 1.67776I
b = −0.733347 + 0.404998I
−1.87304 − 0.83221I 0
u = 0.674124 + 0.761026I
a = 0.482223 − 0.849940I
b = −0.501622 + 0.961337I
−1.85468 + 3.08743I 0
u = 0.674124 − 0.761026I
a = 0.482223 + 0.849940I
b = −0.501622 − 0.961337I
−1.85468 − 3.08743I 0
u = 0.980966 + 0.046013I
a = −7.16952 + 1.70964I
b = −0.582621 − 1.073900I
0.04635 − 5.79605I 0
u = 0.980966 − 0.046013I
a = −7.16952 − 1.70964I
b = −0.582621 + 1.073900I
0.04635 + 5.79605I 0
u = −0.982919 + 0.278211I
a = 0.265666 − 1.252800I
b = 0.310620 + 1.117390I
−1.93394 + 3.59448I 0
u = −0.982919 − 0.278211I
a = 0.265666 + 1.252800I
b = 0.310620 − 1.117390I
−1.93394 − 3.59448I 0
u = −0.166599 + 0.952197I
a = −0.018311 − 0.731128I
b = −0.817315 + 0.177510I
3.03000 − 2.69910I 0
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.166599 − 0.952197I
a = −0.018311 + 0.731128I
b = −0.817315 − 0.177510I
3.03000 + 2.69910I 0
u = −1.006390 + 0.296562I
a = 1.261000 + 0.568644I
b = 0.831125 − 1.109170I
0.78134 + 8.18503I 0
u = −1.006390 − 0.296562I
a = 1.261000 − 0.568644I
b = 0.831125 + 1.109170I
0.78134 − 8.18503I 0
u = 0.908132 + 0.527773I
a = −0.630407 + 0.914742I
b = 0.108140 − 0.878237I
−0.309030 − 0.975544I 0
u = 0.908132 − 0.527773I
a = −0.630407 − 0.914742I
b = 0.108140 + 0.878237I
−0.309030 + 0.975544I 0
u = 0.885045 + 0.329182I
a = −0.453167 + 1.264950I
b = 0.666855 − 0.083688I
−1.00084 − 1.88868I 0
u = 0.885045 − 0.329182I
a = −0.453167 − 1.264950I
b = 0.666855 + 0.083688I
−1.00084 + 1.88868I 0
u = −0.581569 + 0.883135I
a = −1.01069 − 1.39213I
b = −0.191368 + 1.227640I
7.90256 + 0.75255I 0
u = −0.581569 − 0.883135I
a = −1.01069 + 1.39213I
b = −0.191368 − 1.227640I
7.90256 − 0.75255I 0
u = 0.132248 + 0.913123I
a = 0.09390 + 1.52207I
b = −0.659661 − 1.130090I
−0.14095 − 8.90764I 0
6
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.132248 − 0.913123I
a = 0.09390 − 1.52207I
b = −0.659661 + 1.130090I
−0.14095 + 8.90764I 0
u = 0.920644 + 0.020580I
a = 4.93732 − 3.68809I
b = 0.354878 + 1.013590I
2.08506 − 0.96748I 0
u = 0.920644 − 0.020580I
a = 4.93732 + 3.68809I
b = 0.354878 − 1.013590I
2.08506 + 0.96748I 0
u = 1.066750 + 0.166485I
a = −1.34067 − 4.93839I
b = −0.193008 + 0.474455I
−2.43184 − 0.84245I 0
u = 1.066750 − 0.166485I
a = −1.34067 + 4.93839I
b = −0.193008 − 0.474455I
−2.43184 + 0.84245I 0
u = 0.917822
a = −2.96550
b = −0.414891
−2.95218 0
u = −0.774867 + 0.469488I
a = 0.813798 + 1.050750I
b = 0.302427 − 1.316010I
3.08304 + 4.83288I 0
u = −0.774867 − 0.469488I
a = 0.813798 − 1.050750I
b = 0.302427 + 1.316010I
3.08304 − 4.83288I 0
u = −0.871944 + 0.220956I
a = 0.536470 + 0.195240I
b = 1.189990 − 0.367385I
−0.722498 + 0.774565I 0
u = −0.871944 − 0.220956I
a = 0.536470 − 0.195240I
b = 1.189990 + 0.367385I
−0.722498 − 0.774565I 0
7
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −1.033700 + 0.387184I
a = −0.311301 − 0.258206I
b = −1.115560 + 0.163228I
0.43091 + 5.89606I 0
u = −1.033700 − 0.387184I
a = −0.311301 + 0.258206I
b = −1.115560 − 0.163228I
0.43091 − 5.89606I 0
u = −0.077905 + 1.109910I
a = 0.29674 − 1.80543I
b = 0.451396 + 0.833928I
0.59629 − 4.24180I 0
u = −0.077905 − 1.109910I
a = 0.29674 + 1.80543I
b = 0.451396 − 0.833928I
0.59629 + 4.24180I 0
u = −0.823127 + 0.326176I
a = −1.47652 − 0.55961I
b = −0.731170 + 1.053620I
3.98035 + 2.83956I 0
u = −0.823127 − 0.326176I
a = −1.47652 + 0.55961I
b = −0.731170 − 1.053620I
3.98035 − 2.83956I 0
u = −0.471399 + 1.033790I
a = 0.67505 + 1.49811I
b = −0.043017 − 1.232660I
8.20160 − 4.60896I 0
u = −0.471399 − 1.033790I
a = 0.67505 − 1.49811I
b = −0.043017 + 1.232660I
8.20160 + 4.60896I 0
u = 0.650578 + 0.952456I
a = −0.127306 − 1.175360I
b = 0.025470 + 0.914503I
1.88599 − 4.20801I 0
u = 0.650578 − 0.952456I
a = −0.127306 + 1.175360I
b = 0.025470 − 0.914503I
1.88599 + 4.20801I 0
8
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −1.006630 + 0.591665I
a = 0.411815 + 1.236560I
b = 0.000328 − 1.373620I
6.49374 + 4.63447I 0
u = −1.006630 − 0.591665I
a = 0.411815 − 1.236560I
b = 0.000328 + 1.373620I
6.49374 − 4.63447I 0
u = −1.148220 + 0.275689I
a = 0.262420 + 0.214400I
b = 1.081100 + 0.460110I
−3.92344 + 1.90005I 0
u = −1.148220 − 0.275689I
a = 0.262420 − 0.214400I
b = 1.081100 − 0.460110I
−3.92344 − 1.90005I 0
u = −0.120985 + 1.198530I
a = 0.050366 + 0.707725I
b = 0.963931 − 0.522551I
1.25794 − 6.76486I 0
u = −0.120985 − 1.198530I
a = 0.050366 − 0.707725I
b = 0.963931 + 0.522551I
1.25794 + 6.76486I 0
u = 0.035020 + 0.793581I
a = −0.28499 − 1.65893I
b = 0.476647 + 1.106970I
2.20983 − 3.68482I 0
u = 0.035020 − 0.793581I
a = −0.28499 + 1.65893I
b = 0.476647 − 1.106970I
2.20983 + 3.68482I 0
u = 0.305578 + 1.195660I
a = 0.069210 + 0.803414I
b = 0.461373 − 0.896592I
0.818942 − 0.469421I 0
u = 0.305578 − 1.195660I
a = 0.069210 − 0.803414I
b = 0.461373 + 0.896592I
0.818942 + 0.469421I 0
9
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.741171 + 0.116138I
a = 1.154160 + 0.448603I
b = 0.919315 + 0.803419I
−0.19016 + 1.46770I 0
u = −0.741171 − 0.116138I
a = 1.154160 − 0.448603I
b = 0.919315 − 0.803419I
−0.19016 − 1.46770I 0
u = −1.223360 + 0.324904I
a = −1.02985 − 1.24609I
b = −0.575630 + 1.056400I
−6.90472 + 4.00909I 0
u = −1.223360 − 0.324904I
a = −1.02985 + 1.24609I
b = −0.575630 − 1.056400I
−6.90472 − 4.00909I 0
u = −0.645586 + 0.327104I
a = 0.002597 + 0.672417I
b = −0.433681 − 1.273930I
4.44411 + 0.29904I 0
u = −0.645586 − 0.327104I
a = 0.002597 − 0.672417I
b = −0.433681 + 1.273930I
4.44411 − 0.29904I 0
u = −1.115520 + 0.638791I
a = −0.59914 − 1.29559I
b = −0.204658 + 1.363680I
6.10627 + 10.54450I 0
u = −1.115520 − 0.638791I
a = −0.59914 + 1.29559I
b = −0.204658 − 1.363680I
6.10627 − 10.54450I 0
u = −0.202225 + 1.270620I
a = 0.006206 + 1.393810I
b = −0.538338 − 1.124520I
5.71587 − 7.50058I 0
u = −0.202225 − 1.270620I
a = 0.006206 − 1.393810I
b = −0.538338 + 1.124520I
5.71587 + 7.50058I 0
10
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −1.244720 + 0.377582I
a = −0.198296 − 0.258470I
b = −1.099790 − 0.642821I
−6.23959 + 6.98143I 0
u = −1.244720 − 0.377582I
a = −0.198296 + 0.258470I
b = −1.099790 + 0.642821I
−6.23959 − 6.98143I 0
u = −0.456656 + 0.528841I
a = −0.91557 − 1.20900I
b = −0.084954 + 1.241910I
3.87976 − 0.76203I −12.00000 + 0.I
u = −0.456656 − 0.528841I
a = −0.91557 + 1.20900I
b = −0.084954 − 1.241910I
3.87976 + 0.76203I −12.00000 + 0.I
u = 1.245550 + 0.412422I
a = −0.098639 + 0.388820I
b = 0.313701 − 0.441055I
−1.13956 − 1.32806I 0
u = 1.245550 − 0.412422I
a = −0.098639 − 0.388820I
b = 0.313701 + 0.441055I
−1.13956 + 1.32806I 0
u = 0.162155 + 0.668260I
a = 0.248964 − 1.032650I
b = −0.899239 + 0.478152I
−2.15161 − 3.15660I −12.00000 + 4.91890I
u = 0.162155 − 0.668260I
a = 0.248964 + 1.032650I
b = −0.899239 − 0.478152I
−2.15161 + 3.15660I −12.00000 − 4.91890I
u = −1.247090 + 0.447609I
a = 1.02369 + 1.07188I
b = 0.690131 − 1.183640I
−1.58958 + 8.19357I 0
u = −1.247090 − 0.447609I
a = 1.02369 − 1.07188I
b = 0.690131 + 1.183640I
−1.58958 − 8.19357I 0
11
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −1.328620 + 0.228438I
a = 0.175289 − 0.056402I
b = 0.408056 − 0.524170I
−4.20368 + 6.98905I 0
u = −1.328620 − 0.228438I
a = 0.175289 + 0.056402I
b = 0.408056 + 0.524170I
−4.20368 − 6.98905I 0
u = −0.148084 + 1.360490I
a = 0.085023 − 1.239770I
b = 0.693994 + 1.139140I
3.20116 − 12.82290I 0
u = −0.148084 − 1.360490I
a = 0.085023 + 1.239770I
b = 0.693994 − 1.139140I
3.20116 + 12.82290I 0
u = −1.266620 + 0.539126I
a = −0.083766 − 0.279793I
b = −1.021900 − 0.393108I
−0.41432 + 8.09825I 0
u = −1.266620 − 0.539126I
a = −0.083766 + 0.279793I
b = −1.021900 + 0.393108I
−0.41432 − 8.09825I 0
u = 0.622098 + 0.035393I
a = 2.69169 + 2.64059I
b = −0.161584 − 1.002220I
2.76309 − 0.92048I −8.26635 + 0.35450I
u = 0.622098 − 0.035393I
a = 2.69169 − 2.64059I
b = −0.161584 + 1.002220I
2.76309 + 0.92048I −8.26635 − 0.35450I
u = 1.329090 + 0.374778I
a = −0.977806 + 0.776270I
b = −0.452221 − 0.908343I
−1.30643 − 1.95102I 0
u = 1.329090 − 0.374778I
a = −0.977806 − 0.776270I
b = −0.452221 + 0.908343I
−1.30643 + 1.95102I 0
12
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −1.387680 + 0.119134I
a = −0.099333 − 0.135998I
b = −0.505843 − 0.549552I
−8.55610 − 0.51653I 0
u = −1.387680 − 0.119134I
a = −0.099333 + 0.135998I
b = −0.505843 + 0.549552I
−8.55610 + 0.51653I 0
u = −1.319300 + 0.462663I
a = −1.08523 − 1.01255I
b = −0.793606 + 1.164820I
−4.5214 + 13.8088I 0
u = −1.319300 − 0.462663I
a = −1.08523 + 1.01255I
b = −0.793606 − 1.164820I
−4.5214 − 13.8088I 0
u = −0.175980 + 0.573284I
a = 0.291343 − 1.153700I
b = −0.665378 − 0.313323I
2.70854 − 2.21222I −6.37990 + 3.42963I
u = −0.175980 − 0.573284I
a = 0.291343 + 1.153700I
b = −0.665378 + 0.313323I
2.70854 + 2.21222I −6.37990 − 3.42963I
u = 1.40369 + 0.22869I
a = 0.870467 + 0.145286I
b = 0.748745 − 0.603153I
−5.03711 − 1.30340I 0
u = 1.40369 − 0.22869I
a = 0.870467 − 0.145286I
b = 0.748745 + 0.603153I
−5.03711 + 1.30340I 0
u = 0.262924 + 0.514147I
a = −0.18352 + 2.49956I
b = −0.426177 − 0.694272I
−2.75849 − 0.86457I −15.0728 + 5.8151I
u = 0.262924 − 0.514147I
a = −0.18352 − 2.49956I
b = −0.426177 + 0.694272I
−2.75849 + 0.86457I −15.0728 − 5.8151I
13
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −1.31936 + 0.56356I
a = 1.09944 + 1.48135I
b = 0.541886 − 1.019480I
−3.27476 + 10.10590I 0
u = −1.31936 − 0.56356I
a = 1.09944 − 1.48135I
b = 0.541886 + 1.019480I
−3.27476 − 10.10590I 0
u = 1.38519 + 0.38670I
a = −0.114390 + 0.347369I
b = 0.194051 − 0.668016I
−1.14181 − 1.35551I 0
u = 1.38519 − 0.38670I
a = −0.114390 − 0.347369I
b = 0.194051 + 0.668016I
−1.14181 + 1.35551I 0
u = 1.27027 + 0.69953I
a = −1.09179 + 1.51519I
b = −0.619424 − 0.699430I
−4.15839 − 2.13695I 0
u = 1.27027 − 0.69953I
a = −1.09179 − 1.51519I
b = −0.619424 + 0.699430I
−4.15839 + 2.13695I 0
u = 1.45060 + 0.13256I
a = 1.30633 − 0.70431I
b = 0.693163 + 0.634356I
−5.11123 + 1.06296I 0
u = 1.45060 − 0.13256I
a = 1.30633 + 0.70431I
b = 0.693163 − 0.634356I
−5.11123 − 1.06296I 0
u = −1.40013 + 0.41804I
a = −0.011171 + 0.196830I
b = 0.515312 + 0.615281I
−4.58140 + 5.74757I 0
u = −1.40013 − 0.41804I
a = −0.011171 − 0.196830I
b = 0.515312 − 0.615281I
−4.58140 − 5.74757I 0
14
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −1.33619 + 0.59635I
a = 0.035391 + 0.302029I
b = 1.081690 + 0.612879I
−2.58803 + 12.99720I 0
u = −1.33619 − 0.59635I
a = 0.035391 − 0.302029I
b = 1.081690 − 0.612879I
−2.58803 − 12.99720I 0
u = 1.23165 + 0.79659I
a = −0.164890 − 0.296273I
b = −0.828826 + 0.592006I
−3.89027 − 4.57234I 0
u = 1.23165 − 0.79659I
a = −0.164890 + 0.296273I
b = −0.828826 − 0.592006I
−3.89027 + 4.57234I 0
u = 1.15795 + 0.91147I
a = 0.60365 − 1.33882I
b = 0.513844 + 0.972227I
0.08922 − 5.31573I 0
u = 1.15795 − 0.91147I
a = 0.60365 + 1.33882I
b = 0.513844 − 0.972227I
0.08922 + 5.31573I 0
u = −1.34044 + 0.64173I
a = −1.04124 − 1.26118I
b = −0.659884 + 1.184340I
2.0610 + 14.1160I 0
u = −1.34044 − 0.64173I
a = −1.04124 + 1.26118I
b = −0.659884 − 1.184340I
2.0610 − 14.1160I 0
u = −0.392930 + 0.316930I
a = −0.258243 − 0.154711I
b = 0.601075 + 1.204190I
2.43301 − 5.31759I −7.07742 + 1.86035I
u = −0.392930 − 0.316930I
a = −0.258243 + 0.154711I
b = 0.601075 − 1.204190I
2.43301 + 5.31759I −7.07742 − 1.86035I
15
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 1.51286 + 0.02516I
a = −0.483067 + 0.335421I
b = −0.423058 − 0.813762I
−1.62544 − 1.74532I 0
u = 1.51286 − 0.02516I
a = −0.483067 − 0.335421I
b = −0.423058 + 0.813762I
−1.62544 + 1.74532I 0
u = −1.38800 + 0.64909I
a = 1.11088 + 1.18127I
b = 0.776955 − 1.167520I
−0.7851 + 19.7119I 0
u = −1.38800 − 0.64909I
a = 1.11088 − 1.18127I
b = 0.776955 + 1.167520I
−0.7851 − 19.7119I 0
u = 1.48468 + 0.41784I
a = 0.982445 − 0.628255I
b = 0.637709 + 1.032430I
−3.72158 − 6.59471I 0
u = 1.48468 − 0.41784I
a = 0.982445 + 0.628255I
b = 0.637709 − 1.032430I
−3.72158 + 6.59471I 0
u = 1.28130 + 0.98074I
a = −0.691242 + 1.149970I
b = −0.666782 − 1.057980I
−2.44628 − 10.17080I 0
u = 1.28130 − 0.98074I
a = −0.691242 − 1.149970I
b = −0.666782 + 1.057980I
−2.44628 + 10.17080I 0
u = 0.350067 + 0.094915I
a = −2.84369 + 3.18211I
b = 0.494219 − 1.032940I
1.26936 + 5.44661I −9.63617 − 6.98566I
u = 0.350067 − 0.094915I
a = −2.84369 − 3.18211I
b = 0.494219 + 1.032940I
1.26936 − 5.44661I −9.63617 + 6.98566I
16
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 1.65304 + 0.08274I
a = 0.505877 + 0.143652I
b = 0.616968 − 0.997278I
−4.00569 + 6.12775I 0
u = 1.65304 − 0.08274I
a = 0.505877 − 0.143652I
b = 0.616968 + 0.997278I
−4.00569 − 6.12775I 0
u = 1.51841 + 0.66229I
a = 0.021514 − 0.214805I
b = −0.586562 + 0.959572I
−3.34466 + 2.62448I 0
u = 1.51841 − 0.66229I
a = 0.021514 + 0.214805I
b = −0.586562 − 0.959572I
−3.34466 − 2.62448I 0
u = 0.264288
a = −1.49188
b = 0.395152
−0.675214 −14.6290
u = −0.075513 + 0.203086I
a = 0.44466 + 2.46621I
b = 0.736606 + 0.101583I
−0.839116 + 0.254597I −10.56987 + 0.84875I
u = −0.075513 − 0.203086I
a = 0.44466 − 2.46621I
b = 0.736606 − 0.101583I
−0.839116 − 0.254597I −10.56987 − 0.84875I
u = −0.130513 + 0.154925I
a = 6.57809 + 1.35839I
b = 0.628497 − 0.648119I
−0.107532 − 1.168680I −10.33746 − 0.59013I
u = −0.130513 − 0.154925I
a = 6.57809 − 1.35839I
b = 0.628497 + 0.648119I
−0.107532 + 1.168680I −10.33746 + 0.59013I
17
II.
I
u
2
= hb, u
7
+2u
6
−2u
5
−4u
4
+2u
3
+2u
2
+a+2, u
8
+u
7
−3u
6
−2u
5
+3u
4
+2u−1i
(i) Arc colorings
a
8
=
1
0
a
11
=
0
u
a
9
=
1
u
2
a
4
=
−u
7
− 2u
6
+ 2u
5
+ 4u
4
− 2u
3
− 2u
2
− 2
0
a
12
=
−u
−u
3
+ u
a
3
=
−u
7
− 2u
6
+ 2u
5
+ 4u
4
− 2u
3
− 2u
2
− 2
0
a
7
=
1
0
a
6
=
−u
4
+ u
2
+ 1
−u
6
+ 2u
4
− u
2
a
1
=
−u
7
+ 2u
5
− 2u
−u
7
+ u
6
+ 2u
5
− 3u
4
+ 2u
2
− 2u + 1
a
10
=
u
u
a
5
=
u
7
− 2u
5
+ 2u
u
7
− u
6
− 2u
5
+ 3u
4
− 2u
2
+ 2u − 1
a
2
=
−2u
7
− 2u
6
+ 4u
5
+ 4u
4
− 2u
3
− 2u
2
− 2u − 2
−u
7
+ u
6
+ 2u
5
− 3u
4
+ 2u
2
− 2u + 1
(ii) Obstruction class = 1
(iii) Cusp Shapes = u
7
+ u
6
+ u
5
+ 2u
4
− 5u
3
− 4u
2
+ 3u − 14
18
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
2
(u − 1)
8
c
3
, c
7
u
8
c
4
(u + 1)
8
c
5
, c
9
u
8
− u
7
− u
6
+ 2u
5
+ u
4
− 2u
3
+ 2u − 1
c
6
u
8
− 3u
7
+ 7u
6
− 10u
5
+ 11u
4
− 10u
3
+ 6u
2
− 4u + 1
c
8
u
8
+ u
7
− 3u
6
− 2u
5
+ 3u
4
+ 2u − 1
c
10
, c
11
u
8
− u
7
− 3u
6
+ 2u
5
+ 3u
4
− 2u − 1
c
12
u
8
+ 3u
7
+ 7u
6
+ 10u
5
+ 11u
4
+ 10u
3
+ 6u
2
+ 4u + 1
19
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
2
, c
4
(y −1)
8
c
3
, c
7
y
8
c
5
, c
9
y
8
− 3y
7
+ 7y
6
− 10y
5
+ 11y
4
− 10y
3
+ 6y
2
− 4y + 1
c
6
, c
12
y
8
+ 5y
7
+ 11y
6
+ 6y
5
− 17y
4
− 34y
3
− 22y
2
− 4y + 1
c
8
, c
10
, c
11
y
8
− 7y
7
+ 19y
6
− 22y
5
+ 3y
4
+ 14y
3
− 6y
2
− 4y + 1
20
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 1.180120 + 0.268597I
a = −1.21928 − 2.03110I
b = 0
−2.68559 − 1.13123I −18.1377 + 5.3065I
u = 1.180120 − 0.268597I
a = −1.21928 + 2.03110I
b = 0
−2.68559 + 1.13123I −18.1377 − 5.3065I
u = 0.108090 + 0.747508I
a = 1.230330 − 0.083902I
b = 0
0.51448 − 2.57849I −10.11893 + 3.45077I
u = 0.108090 − 0.747508I
a = 1.230330 + 0.083902I
b = 0
0.51448 + 2.57849I −10.11893 − 3.45077I
u = −1.37100
a = −0.337834
b = 0
−8.14766 −12.9880
u = −1.334530 + 0.318930I
a = 0.370895 − 0.073482I
b = 0
−4.02461 + 6.44354I −10.82984 − 2.68172I
u = −1.334530 − 0.318930I
a = 0.370895 + 0.073482I
b = 0
−4.02461 − 6.44354I −10.82984 + 2.68172I
u = 0.463640
a = −2.42604
b = 0
−2.48997 −13.8390
21
III. I
u
3
= h2b − 3a − 2, 9a
2
+ 6a − 4, u − 1i
(i) Arc colorings
a
8
=
1
0
a
11
=
0
1
a
9
=
1
1
a
4
=
a
3
2
a + 1
a
12
=
−1
0
a
3
=
5
2
a + 1
3
2
a + 1
a
7
=
0.333333
−
3
2
a − 2
a
6
=
−
3
2
a −
5
3
−
3
2
a − 2
a
1
=
−4a −
16
3
−
9
2
a − 5
a
10
=
0.111111
−
1
2
a +
1
3
a
5
=
−
3
2
a −
5
3
−
3
2
a − 2
a
2
=
−1.66667
−
3
2
a − 2
(ii) Obstruction class = 1
(iii) Cusp Shapes = 280a +
2605
9
22
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
12
u
2
− 3u + 1
c
2
, c
3
u
2
+ u − 1
c
4
, c
7
u
2
− u − 1
c
5
u
2
c
6
u
2
+ 3u + 1
c
8
(u − 1)
2
c
9
9(9u
2
− 9u + 1)
c
10
9(3u + 1)
2
c
11
(u + 1)
2
23
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
6
, c
12
y
2
− 7y + 1
c
2
, c
3
, c
4
c
7
y
2
− 3y + 1
c
5
y
2
c
8
, c
11
(y −1)
2
c
9
81(81y
2
− 63y + 1)
c
10
81(9y −1)
2
24
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = 1.00000
a = −1.07869
b = −0.618034
−2.63189 −12.5890
u = 1.00000
a = 0.412023
b = 1.61803
−10.5276 404.810
25
IV. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
((u − 1)
8
)(u
2
− 3u + 1)(u
129
+ 68u
128
+ ··· + 31u + 1)
c
2
((u − 1)
8
)(u
2
+ u − 1)(u
129
− 10u
128
+ ··· + 5u − 1)
c
3
u
8
(u
2
+ u − 1)(u
129
+ 2u
128
+ ··· + 896u + 256)
c
4
((u + 1)
8
)(u
2
− u − 1)(u
129
− 10u
128
+ ··· + 5u − 1)
c
5
u
2
(u
8
− u
7
− u
6
+ 2u
5
+ u
4
− 2u
3
+ 2u − 1)
· (u
129
− 2u
128
+ ··· − 5940u + 324)
c
6
(u
2
+ 3u + 1)(u
8
− 3u
7
+ 7u
6
− 10u
5
+ 11u
4
− 10u
3
+ 6u
2
− 4u + 1)
· (u
129
− 3u
128
+ ··· + 3u − 1)
c
7
u
8
(u
2
− u − 1)(u
129
+ 2u
128
+ ··· + 896u + 256)
c
8
(u − 1)
2
(u
8
+ u
7
− 3u
6
− 2u
5
+ 3u
4
+ 2u − 1)
· (u
129
− 4u
128
+ ··· + 810u − 81)
c
9
81(9u
2
− 9u + 1)(u
8
− u
7
− u
6
+ 2u
5
+ u
4
− 2u
3
+ 2u − 1)
· (9u
129
− 111u
128
+ ··· + 5137u − 257)
c
10
81(3u + 1)
2
(u
8
− u
7
− 3u
6
+ 2u
5
+ 3u
4
− 2u − 1)
· (9u
129
− 72u
128
+ ··· − 1416882u + 58007)
c
11
(u + 1)
2
(u
8
− u
7
− 3u
6
+ 2u
5
+ 3u
4
− 2u − 1)
· (u
129
− 4u
128
+ ··· + 810u − 81)
c
12
(u
2
− 3u + 1)(u
8
+ 3u
7
+ 7u
6
+ 10u
5
+ 11u
4
+ 10u
3
+ 6u
2
+ 4u + 1)
· (u
129
− 3u
128
+ ··· + 3u − 1)
26
V. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
((y −1)
8
)(y
2
− 7y + 1)(y
129
− 4y
128
+ ··· + 1563y −1)
c
2
, c
4
((y −1)
8
)(y
2
− 3y + 1)(y
129
− 68y
128
+ ··· + 31y −1)
c
3
, c
7
y
8
(y
2
− 3y + 1)(y
129
+ 48y
128
+ ··· − 933888y −65536)
c
5
y
2
(y
8
− 3y
7
+ 7y
6
− 10y
5
+ 11y
4
− 10y
3
+ 6y
2
− 4y + 1)
· (y
129
+ 12y
128
+ ··· + 12906216y −104976)
c
6
, c
12
(y
2
− 7y + 1)(y
8
+ 5y
7
+ ··· − 4y + 1)
· (y
129
+ 69y
128
+ ··· + 31y −1)
c
8
, c
11
(y −1)
2
(y
8
− 7y
7
+ 19y
6
− 22y
5
+ 3y
4
+ 14y
3
− 6y
2
− 4y + 1)
· (y
129
− 82y
128
+ ··· + 92178y −6561)
c
9
6561(81y
2
− 63y + 1)
· (y
8
− 3y
7
+ 7y
6
− 10y
5
+ 11y
4
− 10y
3
+ 6y
2
− 4y + 1)
· (81y
129
+ 1953y
128
+ ··· − 1315317y −66049)
c
10
6561(9y −1)
2
(y
8
− 7y
7
+ ··· − 4y + 1)
· (81y
129
− 1926y
128
+ ··· + 458235777734y −3364812049)
27
