12n
0833
(K12n
0833
)
A knot diagram
1
Linearized knot diagam
4 7 12 9 11 2 10 1 5 7 2 8
Solving Sequence
2,7 3,11
12 4 1 6 5 10 8 9
c
2
c
11
c
3
c
1
c
6
c
5
c
10
c
7
c
9
c
4
, c
8
, c
12
Ideals for irreducible components
2
of X
par
I
u
1
= hb − u, 48548678896552u
20
− 6006433459385u
19
+ ··· + 71783344195601a − 47045556341686,
u
21
+ 14u
19
+ ··· + 2u − 1i
I
u
2
= h−3.76288 × 10
173
u
53
+ 8.45874 × 10
173
u
52
+ ··· + 2.19868 × 10
176
b − 6.84188 × 10
175
,
− 1.56755 × 10
176
u
53
+ 6.60310 × 10
176
u
52
+ ··· + 1.93703 × 10
179
a − 1.61567 × 10
180
,
u
54
− 2u
53
+ ··· + 8u − 881i
I
u
3
= hb + u, −222u
10
− 336u
9
+ ··· + a − 435,
u
11
+ u
10
+ 5u
9
+ 5u
8
+ 8u
7
+ 4u
6
− u
5
− 8u
4
− 5u
3
+ 4u
2
+ 2u − 1i
I
u
4
= h−415u
9
− 3u
8
− 1587u
7
+ 1035u
6
− 446u
5
+ 2078u
4
− 356u
3
− 176u
2
+ 947b − 236u + 990,
− 990u
9
+ 415u
8
− 3957u
7
+ 4557u
6
− 3015u
5
+ 7376u
4
− 5048u
3
+ 356u
2
+ 947a − 814u + 2259,
u
10
+ 4u
8
− 3u
7
+ 2u
6
− 7u
5
+ 3u
4
+ u
2
− 3u − 1i
I
u
5
= hb + 1, a + 1, u
2
+ u + 1i
I
u
6
= hb − a, a
2
− a + 1, u − 1i
I
u
7
= hb + 1, a + 1, u − 1i
* 7 irreducible components of dim
C
= 0, with total 101 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
= hb − u, 4.85 × 10
13
u
20
− 6.01 × 10
12
u
19
+ · · · + 7.18 × 10
13
a − 4.70 ×
10
13
, u
21
+ 14u
19
+ · · · + 2u − 1i
(i) Arc colorings
a
2
=
1
0
a
7
=
0
u
a
3
=
1
u
2
a
11
=
−0.676322u
20
+ 0.0836745u
19
+ ··· − 0.904643u + 0.655383
u
a
12
=
−0.676322u
20
+ 0.0836745u
19
+ ··· − 1.90464u + 0.655383
u
a
4
=
0.278559u
20
+ 0.719791u
19
+ ··· − 0.164650u + 1.12048
−0.135676u
20
+ 0.00165013u
19
+ ··· + 0.646987u − 0.365331
a
1
=
−0.366756u
20
+ 0.375883u
19
+ ··· + 0.868662u − 0.228102
−0.233031u
20
− 0.107091u
19
+ ··· + 0.832055u − 0.0591206
a
6
=
u
u
a
5
=
0.431470u
20
+ 0.0592084u
19
+ ··· − 3.92201u − 0.662751
−0.365331u
20
− 0.135676u
19
+ ··· + 1.84367u − 0.0836745
a
10
=
−0.676322u
20
+ 0.0836745u
19
+ ··· − 0.904643u + 0.655383
0.365331u
20
+ 0.135676u
19
+ ··· + 0.156329u + 0.0836745
a
8
=
−0.0661390u
20
+ 0.0764679u
19
+ ··· + 4.07834u + 0.746425
0.00757019u
20
− 0.0951795u
19
+ ··· − 0.0627460u + 0.160142
a
9
=
−0.0437773u
20
+ 0.585804u
19
+ ··· + 1.76176u + 0.123227
0.501792u
20
+ 0.0290138u
19
+ ··· − 0.808907u + 0.835921
(ii) Obstruction class = −1
(iii) Cusp Shapes
=
93023336471019
71783344195601
u
20
−
12342208661863
71783344195601
u
19
+ ··· −
521990187380724
71783344195601
u +
687807135458680
71783344195601
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
21
− 13u
20
+ ··· − 80u + 16
c
2
, c
6
, c
11
u
21
+ 14u
19
+ ··· + 2u − 1
c
3
u
21
− u
20
+ ··· + 32u − 4
c
4
, c
8
, c
9
c
12
u
21
− 9u
19
+ ··· − 3u − 1
c
5
u
21
− 16u
20
+ ··· − 96u + 16
c
7
, c
10
u
21
+ 12u
20
+ ··· − 48u − 32
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
21
− y
20
+ ··· + 9088y − 256
c
2
, c
6
, c
11
y
21
+ 28y
20
+ ··· − 2y − 1
c
3
y
21
+ 9y
20
+ ··· + 416y − 16
c
4
, c
8
, c
9
c
12
y
21
− 18y
20
+ ··· + 17y − 1
c
5
y
21
− 18y
20
+ ··· + 19840y − 256
c
7
, c
10
y
21
+ 4y
20
+ ··· + 16128y − 1024
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.931812
a = −1.10584
b = −0.931812
−1.23294 −9.61470
u = 0.158069 + 0.768821I
a = 1.54952 + 0.85996I
b = 0.158069 + 0.768821I
3.14578 − 1.78255I 5.78902 + 2.84245I
u = 0.158069 − 0.768821I
a = 1.54952 − 0.85996I
b = 0.158069 − 0.768821I
3.14578 + 1.78255I 5.78902 − 2.84245I
u = 0.368613 + 0.559573I
a = −0.687955 + 1.093130I
b = 0.368613 + 0.559573I
7.34275 + 2.74966I 8.62625 − 1.12631I
u = 0.368613 − 0.559573I
a = −0.687955 − 1.093130I
b = 0.368613 − 0.559573I
7.34275 − 2.74966I 8.62625 + 1.12631I
u = −0.669849
a = −0.412127
b = −0.669849
−1.30942 −8.50190
u = 0.462672 + 0.435720I
a = −1.84142 − 1.00748I
b = 0.462672 + 0.435720I
3.45656 + 7.33502I 6.59710 − 2.57057I
u = 0.462672 − 0.435720I
a = −1.84142 + 1.00748I
b = 0.462672 − 0.435720I
3.45656 − 7.33502I 6.59710 + 2.57057I
u = 0.21115 + 1.51032I
a = 0.507410 + 0.503080I
b = 0.21115 + 1.51032I
3.60338 + 0.39260I 1.59132 − 2.36452I
u = 0.21115 − 1.51032I
a = 0.507410 − 0.503080I
b = 0.21115 − 1.51032I
3.60338 − 0.39260I 1.59132 + 2.36452I
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.207390 + 0.342456I
a = 2.58416 − 1.74247I
b = −0.207390 + 0.342456I
−3.33864 + 1.70008I 4.87006 − 6.64334I
u = −0.207390 − 0.342456I
a = 2.58416 + 1.74247I
b = −0.207390 − 0.342456I
−3.33864 − 1.70008I 4.87006 + 6.64334I
u = 0.355382
a = 1.68281
b = 0.355382
0.901391 11.0500
u = −0.40653 + 1.63380I
a = −0.447826 + 0.505871I
b = −0.40653 + 1.63380I
3.41140 + 5.44166I 0.03097 − 2.59655I
u = −0.40653 − 1.63380I
a = −0.447826 − 0.505871I
b = −0.40653 − 1.63380I
3.41140 − 5.44166I 0.03097 + 2.59655I
u = −0.43942 + 1.74488I
a = −0.453249 + 0.941647I
b = −0.43942 + 1.74488I
7.19102 + 6.99016I 6.70966 − 6.90115I
u = −0.43942 − 1.74488I
a = −0.453249 − 0.941647I
b = −0.43942 − 1.74488I
7.19102 − 6.99016I 6.70966 + 6.90115I
u = −0.03915 + 1.83375I
a = −0.354012 + 0.901091I
b = −0.03915 + 1.83375I
14.3089 − 7.4913I 8.52687 + 5.06459I
u = −0.03915 − 1.83375I
a = −0.354012 − 0.901091I
b = −0.03915 − 1.83375I
14.3089 + 7.4913I 8.52687 − 5.06459I
u = 0.51512 + 1.80013I
a = 0.560954 + 0.682183I
b = 0.51512 + 1.80013I
11.8699 − 16.2021I 6.29206 + 7.56505I
6
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.51512 − 1.80013I
a = 0.560954 − 0.682183I
b = 0.51512 − 1.80013I
11.8699 + 16.2021I 6.29206 − 7.56505I
7
II. I
u
2
= h−3.76 × 10
173
u
53
+ 8.46 × 10
173
u
52
+ · · · + 2.20 × 10
176
b − 6.84 ×
10
175
, −1.57 × 10
176
u
53
+ 6.60 × 10
176
u
52
+ · · · + 1.94 × 10
179
a − 1.62 ×
10
180
, u
54
− 2u
53
+ · · · + 8u − 881i
(i) Arc colorings
a
2
=
1
0
a
7
=
0
u
a
3
=
1
u
2
a
11
=
0.000809251u
53
− 0.00340887u
52
+ ··· − 16.8712u + 8.34097
0.00171143u
53
− 0.00384720u
52
+ ··· − 7.47610u + 0.311182
a
12
=
−0.000902179u
53
+ 0.000438327u
52
+ ··· − 9.39509u + 8.02979
0.00171143u
53
− 0.00384720u
52
+ ··· − 7.47610u + 0.311182
a
4
=
0.000743820u
53
− 0.00251322u
52
+ ··· − 13.5685u − 1.47274
0.00262451u
53
− 0.00732419u
52
+ ··· − 0.123838u + 3.07143
a
1
=
−0.00152046u
53
+ 0.00483363u
52
+ ··· + 18.9650u − 5.02558
−0.00233209u
53
+ 0.00820063u
52
+ ··· + 1.99689u − 4.64813
a
6
=
u
u
a
5
=
0.00275204u
53
− 0.00635627u
52
+ ··· − 36.5154u − 0.446341
0.00127045u
53
− 0.00284976u
52
+ ··· + 4.78832u − 1.13398
a
10
=
0.000809251u
53
− 0.00340887u
52
+ ··· − 16.8712u + 8.34097
0.00116466u
53
− 0.00178627u
52
+ ··· − 6.74883u − 1.26613
a
8
=
−0.00524804u
53
+ 0.0100044u
52
+ ··· + 35.6558u + 4.16462
−0.000245414u
53
− 0.000548473u
52
+ ··· − 5.47921u + 3.28507
a
9
=
−0.00350037u
53
+ 0.00769598u
52
+ ··· + 33.6542u + 5.02678
−0.00147629u
53
+ 0.00489924u
52
+ ··· − 8.61805u − 1.40443
(ii) Obstruction class = −1
(iii) Cusp Shapes = 0.0184310u
53
− 0.0467511u
52
+ ··· − 24.9350u + 14.3006
8
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
(u
27
+ 3u
26
+ ··· + 81u + 31)
2
c
2
, c
6
, c
11
u
54
− 2u
53
+ ··· + 8u − 881
c
3
u
54
+ 5u
53
+ ··· + 653278u + 100003
c
4
, c
8
, c
9
c
12
u
54
+ 2u
53
+ ··· + 150u − 131
c
5
(u
27
+ 7u
26
+ ··· + 4u + 4)
2
c
7
, c
10
(u
27
− 4u
26
+ ··· − 9u + 1)
2
9
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
(y
27
+ 17y
26
+ ··· − 12163y − 961)
2
c
2
, c
6
, c
11
y
54
+ 54y
53
+ ··· + 40772616y + 776161
c
3
y
54
+ 29y
53
+ ··· − 50799866454y + 10000600009
c
4
, c
8
, c
9
c
12
y
54
− 38y
53
+ ··· − 141448y + 17161
c
5
(y
27
− 39y
26
+ ··· + 520y − 16)
2
c
7
, c
10
(y
27
+ 12y
26
+ ··· + 5y − 1)
2
10
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.999576 + 0.200215I
a = 0.056971 − 0.695193I
b = −0.369310 − 0.746851I
−1.89161 + 0.09963I −2.61530 − 0.73623I
u = −0.999576 − 0.200215I
a = 0.056971 + 0.695193I
b = −0.369310 + 0.746851I
−1.89161 − 0.09963I −2.61530 + 0.73623I
u = 0.813130 + 0.646744I
a = 0.722059 + 0.136619I
b = 0.112951 + 0.378161I
1.32145 − 0.50921I 7.89189 + 0.74907I
u = 0.813130 − 0.646744I
a = 0.722059 − 0.136619I
b = 0.112951 − 0.378161I
1.32145 + 0.50921I 7.89189 − 0.74907I
u = −0.859323 + 0.602277I
a = −0.910439 + 0.753077I
b = −0.069617 − 0.196529I
−1.40206 − 1.58564I 1.82793 − 1.68869I
u = −0.859323 − 0.602277I
a = −0.910439 − 0.753077I
b = −0.069617 + 0.196529I
−1.40206 + 1.58564I 1.82793 + 1.68869I
u = 0.107451 + 0.916597I
a = −0.492470 − 0.528025I
b = −1.308180 + 0.112852I
1.02545 − 1.78671I 7.36667 + 4.23667I
u = 0.107451 − 0.916597I
a = −0.492470 + 0.528025I
b = −1.308180 − 0.112852I
1.02545 + 1.78671I 7.36667 − 4.23667I
u = 1.035250 + 0.334870I
a = 0.084787 − 0.942859I
b = −0.049724 − 0.771785I
−0.03561 − 4.27592I 3.10305 + 6.89248I
u = 1.035250 − 0.334870I
a = 0.084787 + 0.942859I
b = −0.049724 + 0.771785I
−0.03561 + 4.27592I 3.10305 − 6.89248I
11
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.369310 + 0.746851I
a = −0.803654 + 0.287281I
b = −0.999576 − 0.200215I
−1.89161 − 0.09963I −2.61530 + 0.73623I
u = −0.369310 − 0.746851I
a = −0.803654 − 0.287281I
b = −0.999576 + 0.200215I
−1.89161 + 0.09963I −2.61530 − 0.73623I
u = −0.263308 + 0.734509I
a = 2.06100 − 0.38717I
b = 0.877552 − 0.994760I
1.99589 + 3.47011I 5.94769 − 2.08047I
u = −0.263308 − 0.734509I
a = 2.06100 + 0.38717I
b = 0.877552 + 0.994760I
1.99589 − 3.47011I 5.94769 + 2.08047I
u = −0.027660 + 0.776154I
a = 0.943960 + 0.930036I
b = 1.46919 + 0.36440I
4.69434 − 8.65979I 7.06084 + 6.43035I
u = −0.027660 − 0.776154I
a = 0.943960 − 0.930036I
b = 1.46919 − 0.36440I
4.69434 + 8.65979I 7.06084 − 6.43035I
u = −0.049724 + 0.771785I
a = 1.189320 − 0.599452I
b = 1.035250 − 0.334870I
−0.03561 + 4.27592I 3.10305 − 6.89248I
u = −0.049724 − 0.771785I
a = 1.189320 + 0.599452I
b = 1.035250 + 0.334870I
−0.03561 − 4.27592I 3.10305 + 6.89248I
u = 0.286573 + 1.197040I
a = 0.012252 − 0.314090I
b = 0.14576 − 1.79863I
9.62723 − 2.79194I 0
u = 0.286573 − 1.197040I
a = 0.012252 + 0.314090I
b = 0.14576 + 1.79863I
9.62723 + 2.79194I 0
12
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −1.308180 + 0.112852I
a = −0.360346 + 0.357343I
b = 0.107451 + 0.916597I
1.02545 − 1.78671I 0
u = −1.308180 − 0.112852I
a = −0.360346 − 0.357343I
b = 0.107451 − 0.916597I
1.02545 + 1.78671I 0
u = 0.877552 + 0.994760I
a = −1.042240 − 0.659781I
b = −0.263308 − 0.734509I
1.99589 − 3.47011I 0
u = 0.877552 − 0.994760I
a = −1.042240 + 0.659781I
b = −0.263308 + 0.734509I
1.99589 + 3.47011I 0
u = −0.323634 + 1.349310I
a = −0.553042 + 0.621426I
b = 0.19309 + 1.92766I
11.74090 + 3.23440I 0
u = −0.323634 − 1.349310I
a = −0.553042 − 0.621426I
b = 0.19309 − 1.92766I
11.74090 − 3.23440I 0
u = −1.44084
a = 0.744869
b = 0.336535
0.903331 0
u = 1.46919 + 0.36440I
a = −0.367164 + 0.572239I
b = −0.027660 + 0.776154I
4.69434 − 8.65979I 0
u = 1.46919 − 0.36440I
a = −0.367164 − 0.572239I
b = −0.027660 − 0.776154I
4.69434 + 8.65979I 0
u = 0.08057 + 1.52846I
a = 0.211067 − 0.658010I
b = 0.02830 − 1.86575I
9.52525 − 3.10529I 0
13
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.08057 − 1.52846I
a = 0.211067 + 0.658010I
b = 0.02830 + 1.86575I
9.52525 + 3.10529I 0
u = 0.112951 + 0.378161I
a = 1.76513 − 0.79172I
b = 0.813130 + 0.646744I
1.32145 − 0.50921I 7.89189 + 0.74907I
u = 0.112951 − 0.378161I
a = 1.76513 + 0.79172I
b = 0.813130 − 0.646744I
1.32145 + 0.50921I 7.89189 − 0.74907I
u = 0.47882 + 1.56299I
a = −0.565280 − 0.793048I
b = −0.25503 − 1.70161I
5.12232 − 4.49310I 0
u = 0.47882 − 1.56299I
a = −0.565280 + 0.793048I
b = −0.25503 + 1.70161I
5.12232 + 4.49310I 0
u = 0.336535
a = −3.18907
b = −1.44084
0.903331 10.7580
u = −0.02444 + 1.69640I
a = 0.551913 + 0.384089I
b = 0.73964 + 1.55006I
11.80540 − 1.90633I 0
u = −0.02444 − 1.69640I
a = 0.551913 − 0.384089I
b = 0.73964 − 1.55006I
11.80540 + 1.90633I 0
u = 0.34221 + 1.67023I
a = −0.621298 − 0.577503I
b = −0.60853 − 1.79153I
6.88193 − 9.55690I 0
u = 0.34221 − 1.67023I
a = −0.621298 + 0.577503I
b = −0.60853 + 1.79153I
6.88193 + 9.55690I 0
14
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.73964 + 1.55006I
a = 0.320300 + 0.581891I
b = −0.02444 + 1.69640I
11.80540 − 1.90633I 0
u = 0.73964 − 1.55006I
a = 0.320300 − 0.581891I
b = −0.02444 − 1.69640I
11.80540 + 1.90633I 0
u = −0.25503 + 1.70161I
a = 0.642616 − 0.665691I
b = 0.47882 − 1.56299I
5.12232 + 4.49310I 0
u = −0.25503 − 1.70161I
a = 0.642616 + 0.665691I
b = 0.47882 + 1.56299I
5.12232 − 4.49310I 0
u = −0.069617 + 0.196529I
a = 4.87818 − 3.40103I
b = −0.859323 − 0.602277I
−1.40206 + 1.58564I 1.82793 + 1.68869I
u = −0.069617 − 0.196529I
a = 4.87818 + 3.40103I
b = −0.859323 + 0.602277I
−1.40206 − 1.58564I 1.82793 − 1.68869I
u = 0.14576 + 1.79863I
a = 0.058603 − 0.206239I
b = 0.286573 − 1.197040I
9.62723 + 2.79194I 0
u = 0.14576 − 1.79863I
a = 0.058603 + 0.206239I
b = 0.286573 + 1.197040I
9.62723 − 2.79194I 0
u = 0.02830 + 1.86575I
a = −0.136152 − 0.550235I
b = 0.08057 − 1.52846I
9.52525 + 3.10529I 0
u = 0.02830 − 1.86575I
a = −0.136152 + 0.550235I
b = 0.08057 + 1.52846I
9.52525 − 3.10529I 0
15
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.60853 + 1.79153I
a = 0.490396 − 0.586300I
b = 0.34221 − 1.67023I
6.88193 + 9.55690I 0
u = −0.60853 − 1.79153I
a = 0.490396 + 0.586300I
b = 0.34221 + 1.67023I
6.88193 − 9.55690I 0
u = 0.19309 + 1.92766I
a = −0.520491 + 0.289994I
b = −0.323634 + 1.349310I
11.74090 + 3.23440I 0
u = 0.19309 − 1.92766I
a = −0.520491 − 0.289994I
b = −0.323634 − 1.349310I
11.74090 − 3.23440I 0
16
III. I
u
3
= hb + u, −222u
10
− 336u
9
+ · · · + a − 435, u
11
+ u
10
+ · · · + 2u − 1i
(i) Arc colorings
a
2
=
1
0
a
7
=
0
u
a
3
=
1
u
2
a
11
=
222u
10
+ 336u
9
+ ··· − 21u + 435
−u
a
12
=
222u
10
+ 336u
9
+ ··· − 20u + 435
−u
a
4
=
−200u
10
− 302u
9
+ ··· + 18u − 386
30u
10
+ 45u
9
+ ··· − 2u + 58
a
1
=
71u
10
+ 108u
9
+ ··· − 8u + 137
−38u
10
− 57u
9
+ ··· + u − 72
a
6
=
u
u
a
5
=
−107u
10
− 163u
9
+ ··· + 19u − 207
58u
10
+ 88u
9
+ ··· − 5u + 114
a
10
=
222u
10
+ 336u
9
+ ··· − 21u + 435
58u
10
+ 88u
9
+ ··· − 7u + 114
a
8
=
49u
10
+ 75u
9
+ ··· − 12u + 93
−44u
10
− 67u
9
+ ··· + 4u − 88
a
9
=
70u
10
+ 106u
9
+ ··· − 8u + 132
−11u
10
− 16u
9
+ ··· − u − 21
(ii) Obstruction class = 1
(iii) Cusp Shapes
= 52u
10
+ 80u
9
+ 306u
8
+ 428u
7
+ 662u
6
+ 580u
5
+ 289u
4
− 248u
3
− 387u
2
− 24u + 83
17
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
11
− 2u
10
+ ··· + 16u − 5
c
2
, c
11
u
11
+ u
10
+ 5u
9
+ 5u
8
+ 8u
7
+ 4u
6
− u
5
− 8u
4
− 5u
3
+ 4u
2
+ 2u − 1
c
3
u
11
+ 3u
9
− 2u
8
+ 6u
7
+ u
6
− 4u
5
+ 2u
4
+ 2u
3
− 4u
2
− 4u + 4
c
4
, c
8
u
11
− u
10
− 4u
9
+ 4u
8
+ 7u
7
− 8u
6
− 3u
5
+ 6u
4
− 3u
2
+ u + 1
c
5
u
11
− 7u
10
+ ··· − 18u + 9
c
6
u
11
− u
10
+ 5u
9
− 5u
8
+ 8u
7
− 4u
6
− u
5
+ 8u
4
− 5u
3
− 4u
2
+ 2u + 1
c
7
u
11
+ 2u
10
+ ··· + 7u + 1
c
9
, c
12
u
11
+ u
10
− 4u
9
− 4u
8
+ 7u
7
+ 8u
6
− 3u
5
− 6u
4
+ 3u
2
+ u − 1
c
10
u
11
− 2u
10
+ ··· + 7u − 1
18
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
11
+ 8y
10
+ ··· + 46y − 25
c
2
, c
6
, c
11
y
11
+ 9y
10
+ ··· + 12y − 1
c
3
y
11
+ 6y
10
+ ··· + 48y − 16
c
4
, c
8
, c
9
c
12
y
11
− 9y
10
+ ··· + 7y − 1
c
5
y
11
− 9y
10
+ ··· + 216y − 81
c
7
, c
10
y
11
+ 12y
10
+ ··· + 15y − 1
19
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = −0.764733 + 0.907103I
a = 1.32980 − 0.80414I
b = 0.764733 − 0.907103I
1.14680 + 4.22750I −1.36621 − 8.43394I
u = −0.764733 − 0.907103I
a = 1.32980 + 0.80414I
b = 0.764733 + 0.907103I
1.14680 − 4.22750I −1.36621 + 8.43394I
u = −0.733496 + 0.174852I
a = 0.12549 + 1.45658I
b = 0.733496 − 0.174852I
2.59459 + 8.35550I 1.41259 − 6.78712I
u = −0.733496 − 0.174852I
a = 0.12549 − 1.45658I
b = 0.733496 + 0.174852I
2.59459 − 8.35550I 1.41259 + 6.78712I
u = 0.599843
a = 0.370877
b = −0.599843
−0.711473 7.33160
u = 0.511585 + 0.003373I
a = 0.17657 − 2.30312I
b = −0.511585 − 0.003373I
−3.83973 − 1.32944I −6.18276 − 0.13949I
u = 0.511585 − 0.003373I
a = 0.17657 + 2.30312I
b = −0.511585 + 0.003373I
−3.83973 + 1.32944I −6.18276 + 0.13949I
u = −0.23085 + 1.58674I
a = 0.228794 − 0.236470I
b = 0.23085 − 1.58674I
11.32230 − 0.31593I 7.05420 + 0.54035I
u = −0.23085 − 1.58674I
a = 0.228794 + 0.236470I
b = 0.23085 + 1.58674I
11.32230 + 0.31593I 7.05420 − 0.54035I
u = 0.41757 + 1.70908I
a = −0.546090 − 0.778511I
b = −0.41757 − 1.70908I
5.58114 − 6.07222I 4.91640 + 5.82146I
20
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = 0.41757 − 1.70908I
a = −0.546090 + 0.778511I
b = −0.41757 + 1.70908I
5.58114 + 6.07222I 4.91640 − 5.82146I
21
IV. I
u
4
= h−415u
9
− 3u
8
+ · · · + 947b + 990, −990u
9
+ 415u
8
+ · · · + 947a +
2259, u
10
+ 4u
8
+ · · · − 3u − 1i
(i) Arc colorings
a
2
=
1
0
a
7
=
0
u
a
3
=
1
u
2
a
11
=
1.04541u
9
− 0.438226u
8
+ ··· + 0.859556u − 2.38543
0.438226u
9
+ 0.00316790u
8
+ ··· + 0.249208u − 1.04541
a
12
=
0.607181u
9
− 0.441394u
8
+ ··· + 0.610348u − 1.34002
0.438226u
9
+ 0.00316790u
8
+ ··· + 0.249208u − 1.04541
a
4
=
−0.456177u
9
+ 0.100317u
8
+ ··· + 1.22492u + 2.89546
−0.0443506u
9
+ 0.0791975u
8
+ ··· − 0.769799u + 0.864836
a
1
=
0.165787u
9
− 0.367476u
8
+ ··· + 1.09187u − 1.73284
0.409715u
9
− 0.303062u
8
+ ··· + 0.825766u − 0.989440
a
6
=
u
u
a
5
=
0.0105597u
9
+ 0.409715u
8
+ ··· − 0.102429u + 0.794087
−0.483633u
9
+ 0.435058u
8
+ ··· + 0.891235u + 0.430834
a
10
=
1.04541u
9
− 0.438226u
8
+ ··· + 0.859556u − 2.38543
0.435058u
9
+ 0.0802534u
8
+ ··· − 0.0200634u − 1.48363
a
8
=
0.472017u
9
− 0.485744u
8
+ ··· + 1.12144u − 1.70433
0.635692u
9
− 0.135164u
8
+ ··· + 0.0337909u − 1.39599
a
9
=
0.795143u
9
− 0.348469u
8
+ ··· + 1.58712u − 1.00528
0.635692u
9
− 0.135164u
8
+ ··· − 0.966209u − 1.39599
(ii) Obstruction class = 1
(iii) Cusp Shapes
=
727
947
u
9
+
934
947
u
8
+
2593
947
u
7
+
1644
947
u
6
−
1617
947
u
5
−
1728
947
u
4
−
4068
947
u
3
+
3341
947
u
2
−
4495
947
u +
2396
947
22
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
(u
5
− u
2
− 1)
2
c
2
, c
11
u
10
+ 4u
8
− 3u
7
+ 2u
6
− 7u
5
+ 3u
4
+ u
2
− 3u − 1
c
3
u
10
− 5u
9
+ 14u
8
− 21u
7
+ 13u
6
+ 17u
5
− 29u
4
+ 5u
3
+ 2u
2
+ 3u + 1
c
4
, c
8
u
10
− 4u
8
+ u
7
+ 4u
6
+ u
5
+ u
4
− 8u
3
+ u
2
+ 5u − 1
c
5
(u
5
+ 3u
4
+ 3u
3
+ 5u
2
+ 8u + 3)
2
c
6
u
10
+ 4u
8
+ 3u
7
+ 2u
6
+ 7u
5
+ 3u
4
+ u
2
+ 3u − 1
c
7
(u
5
+ u
3
+ 1)
2
c
9
, c
12
u
10
− 4u
8
− u
7
+ 4u
6
− u
5
+ u
4
+ 8u
3
+ u
2
− 5u − 1
c
10
(u
5
+ u
3
− 1)
2
23
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
(y
5
− y
2
− 2y − 1)
2
c
2
, c
6
, c
11
y
10
+ 8y
9
+ ··· − 11y + 1
c
3
y
10
+ 3y
9
+ ··· − 5y + 1
c
4
, c
8
, c
9
c
12
y
10
− 8y
9
+ ··· − 27y + 1
c
5
(y
5
− 3y
4
− 5y
3
+ 5y
2
+ 34y − 9)
2
c
7
, c
10
(y
5
+ 2y
4
+ y
3
− 1)
2
24
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
4
√
−1(vol +
√
−1CS) Cusp shape
u = 0.708454 + 0.548065I
a = 0.989557 + 0.881651I
b = 0.490601 − 0.618886I
−1.28683 + 2.49842I 2.82575 − 5.47824I
u = 0.708454 − 0.548065I
a = 0.989557 − 0.881651I
b = 0.490601 + 0.618886I
−1.28683 − 2.49842I 2.82575 + 5.47824I
u = 1.12964
a = 0.741495
b = 0.292016
−0.487604 4.31500
u = −0.490601 + 0.618886I
a = 0.98657 − 1.13408I
b = −0.708454 − 0.548065I
−1.28683 + 2.49842I 2.82575 − 5.47824I
u = −0.490601 − 0.618886I
a = 0.98657 + 1.13408I
b = −0.708454 + 0.548065I
−1.28683 − 2.49842I 2.82575 + 5.47824I
u = −0.484903 + 1.213150I
a = −0.291566 + 0.641344I
b = 0.15176 + 1.87785I
9.75531 + 3.69319I 5.51677 − 7.22620I
u = −0.484903 − 1.213150I
a = −0.291566 − 0.641344I
b = 0.15176 − 1.87785I
9.75531 − 3.69319I 5.51677 + 7.22620I
u = −0.292016
a = −2.86840
b = −1.12964
−0.487604 4.31500
u = −0.15176 + 1.87785I
a = 0.378895 + 0.308418I
b = 0.484903 + 1.213150I
9.75531 − 3.69319I 5.51677 + 7.22620I
u = −0.15176 − 1.87785I
a = 0.378895 − 0.308418I
b = 0.484903 − 1.213150I
9.75531 + 3.69319I 5.51677 − 7.22620I
25
V. I
u
5
= hb + 1, a + 1, u
2
+ u + 1i
(i) Arc colorings
a
2
=
1
0
a
7
=
0
u
a
3
=
1
−u − 1
a
11
=
−1
−1
a
12
=
0
−1
a
4
=
1
−u
a
1
=
u + 1
u + 1
a
6
=
u
u
a
5
=
u
u
a
10
=
−1
u
a
8
=
u
2u + 1
a
9
=
u − 1
2u
(ii) Obstruction class = 1
(iii) Cusp Shapes = 3
26
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
6
, c
8
c
10
u
2
− u + 1
c
2
, c
7
, c
12
u
2
+ u + 1
c
3
, c
4
(u + 1)
2
c
5
u
2
c
9
, c
11
(u − 1)
2
27
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
2
, c
6
c
7
, c
8
, c
10
c
12
y
2
+ y + 1
c
3
, c
4
, c
9
c
11
(y − 1)
2
c
5
y
2
28
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
5
√
−1(vol +
√
−1CS) Cusp shape
u = −0.500000 + 0.866025I
a = −1.00000
b = −1.00000
0 3.00000
u = −0.500000 − 0.866025I
a = −1.00000
b = −1.00000
0 3.00000
29
VI. I
u
6
= hb − a, a
2
− a + 1, u − 1i
(i) Arc colorings
a
2
=
1
0
a
7
=
0
1
a
3
=
1
1
a
11
=
a
a
a
12
=
0
a
a
4
=
1
a
a
1
=
−a + 1
−a + 1
a
6
=
1
1
a
5
=
1
1
a
10
=
a
2a
a
8
=
a − 1
2a − 1
a
9
=
0
a
(ii) Obstruction class = 1
(iii) Cusp Shapes = 3
30
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
3
, c
4
c
10
u
2
− u + 1
c
2
, c
12
(u − 1)
2
c
5
u
2
c
6
, c
8
(u + 1)
2
c
7
, c
9
, c
11
u
2
+ u + 1
31
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
3
, c
4
c
7
, c
9
, c
10
c
11
y
2
+ y + 1
c
2
, c
6
, c
8
c
12
(y − 1)
2
c
5
y
2
32
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
6
√
−1(vol +
√
−1CS) Cusp shape
u = 1.00000
a = 0.500000 + 0.866025I
b = 0.500000 + 0.866025I
0 3.00000
u = 1.00000
a = 0.500000 − 0.866025I
b = 0.500000 − 0.866025I
0 3.00000
33
VII. I
u
7
= hb + 1, a + 1, u − 1i
(i) Arc colorings
a
2
=
1
0
a
7
=
0
1
a
3
=
1
1
a
11
=
−1
−1
a
12
=
0
−1
a
4
=
1
2
a
1
=
−1
−4
a
6
=
1
1
a
5
=
1
1
a
10
=
−1
−2
a
8
=
1
3
a
9
=
0
−1
(ii) Obstruction class = 1
(iii) Cusp Shapes = 0
34
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u − 2
c
2
, c
7
, c
9
c
11
, c
12
u − 1
c
3
, c
4
, c
6
c
8
, c
10
u + 1
c
5
u
35
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y − 4
c
2
, c
3
, c
4
c
6
, c
7
, c
8
c
9
, c
10
, c
11
c
12
y − 1
c
5
y
36
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
7
√
−1(vol +
√
−1CS) Cusp shape
u = 1.00000
a = −1.00000
b = −1.00000
0 0
37
VIII. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
(u − 2)(u
2
− u + 1)
2
(u
5
− u
2
− 1)
2
(u
11
− 2u
10
+ ··· + 16u − 5)
· (u
21
− 13u
20
+ ··· − 80u + 16)(u
27
+ 3u
26
+ ··· + 81u + 31)
2
c
2
, c
11
((u − 1)
3
)(u
2
+ u + 1)(u
10
+ 4u
8
+ ··· − 3u − 1)
· (u
11
+ u
10
+ 5u
9
+ 5u
8
+ 8u
7
+ 4u
6
− u
5
− 8u
4
− 5u
3
+ 4u
2
+ 2u − 1)
· (u
21
+ 14u
19
+ ··· + 2u − 1)(u
54
− 2u
53
+ ··· + 8u − 881)
c
3
(u + 1)
3
(u
2
− u + 1)
· (u
10
− 5u
9
+ 14u
8
− 21u
7
+ 13u
6
+ 17u
5
− 29u
4
+ 5u
3
+ 2u
2
+ 3u + 1)
· (u
11
+ 3u
9
− 2u
8
+ 6u
7
+ u
6
− 4u
5
+ 2u
4
+ 2u
3
− 4u
2
− 4u + 4)
· (u
21
− u
20
+ ··· + 32u − 4)(u
54
+ 5u
53
+ ··· + 653278u + 100003)
c
4
, c
8
((u + 1)
3
)(u
2
− u + 1)(u
10
− 4u
8
+ ··· + 5u − 1)
· (u
11
− u
10
− 4u
9
+ 4u
8
+ 7u
7
− 8u
6
− 3u
5
+ 6u
4
− 3u
2
+ u + 1)
· (u
21
− 9u
19
+ ··· − 3u − 1)(u
54
+ 2u
53
+ ··· + 150u − 131)
c
5
u
5
(u
5
+ 3u
4
+ ··· + 8u + 3)
2
(u
11
− 7u
10
+ ··· − 18u + 9)
· (u
21
− 16u
20
+ ··· − 96u + 16)(u
27
+ 7u
26
+ ··· + 4u + 4)
2
c
6
((u + 1)
3
)(u
2
− u + 1)(u
10
+ 4u
8
+ ··· + 3u − 1)
· (u
11
− u
10
+ 5u
9
− 5u
8
+ 8u
7
− 4u
6
− u
5
+ 8u
4
− 5u
3
− 4u
2
+ 2u + 1)
· (u
21
+ 14u
19
+ ··· + 2u − 1)(u
54
− 2u
53
+ ··· + 8u − 881)
c
7
(u − 1)(u
2
+ u + 1)
2
(u
5
+ u
3
+ 1)
2
(u
11
+ 2u
10
+ ··· + 7u + 1)
· (u
21
+ 12u
20
+ ··· − 48u − 32)(u
27
− 4u
26
+ ··· − 9u + 1)
2
c
9
, c
12
((u − 1)
3
)(u
2
+ u + 1)(u
10
− 4u
8
+ ··· − 5u − 1)
· (u
11
+ u
10
− 4u
9
− 4u
8
+ 7u
7
+ 8u
6
− 3u
5
− 6u
4
+ 3u
2
+ u − 1)
· (u
21
− 9u
19
+ ··· − 3u − 1)(u
54
+ 2u
53
+ ··· + 150u − 131)
c
10
(u + 1)(u
2
− u + 1)
2
(u
5
+ u
3
− 1)
2
(u
11
− 2u
10
+ ··· + 7u − 1)
· (u
21
+ 12u
20
+ ··· − 48u − 32)(u
27
− 4u
26
+ ··· − 9u + 1)
2
38
IX. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
(y − 4)(y
2
+ y + 1)
2
(y
5
− y
2
− 2y − 1)
2
(y
11
+ 8y
10
+ ··· + 46y − 25)
· (y
21
− y
20
+ ··· + 9088y − 256)(y
27
+ 17y
26
+ ··· − 12163y − 961)
2
c
2
, c
6
, c
11
((y − 1)
3
)(y
2
+ y + 1)(y
10
+ 8y
9
+ ··· − 11y + 1)
· (y
11
+ 9y
10
+ ··· + 12y − 1)(y
21
+ 28y
20
+ ··· − 2y − 1)
· (y
54
+ 54y
53
+ ··· + 40772616y + 776161)
c
3
((y − 1)
3
)(y
2
+ y + 1)(y
10
+ 3y
9
+ ··· − 5y + 1)
· (y
11
+ 6y
10
+ ··· + 48y − 16)(y
21
+ 9y
20
+ ··· + 416y − 16)
· (y
54
+ 29y
53
+ ··· − 50799866454y + 10000600009)
c
4
, c
8
, c
9
c
12
((y − 1)
3
)(y
2
+ y + 1)(y
10
− 8y
9
+ ··· − 27y + 1)
· (y
11
− 9y
10
+ ··· + 7y − 1)(y
21
− 18y
20
+ ··· + 17y − 1)
· (y
54
− 38y
53
+ ··· − 141448y + 17161)
c
5
y
5
(y
5
− 3y
4
+ ··· + 34y − 9)
2
(y
11
− 9y
10
+ ··· + 216y − 81)
· (y
21
− 18y
20
+ ··· + 19840y − 256)(y
27
− 39y
26
+ ··· + 520y − 16)
2
c
7
, c
10
(y − 1)(y
2
+ y + 1)
2
(y
5
+ 2y
4
+ y
3
− 1)
2
(y
11
+ 12y
10
+ ··· + 15y − 1)
· (y
21
+ 4y
20
+ ··· + 16128y − 1024)(y
27
+ 12y
26
+ ··· + 5y − 1)
2
39
