12n
0737
(K12n
0737
)
A knot diagram
1
Linearized knot diagam
4 11 7 1 12 2 11 5 2 7 8 9
Solving Sequence
2,11 3,8
12 7 4 1 6 5 10 9
c
2
c
11
c
7
c
3
c
1
c
6
c
5
c
10
c
9
c
4
, c
8
, c
12
Ideals for irreducible components
2
of X
par
I
u
1
= hb + u, −5.39993 × 10
21
u
20
− 1.73558 × 10
22
u
19
+ ··· + 2.47379 × 10
22
a − 8.83120 × 10
22
,
u
21
+ 25u
19
+ ··· + u + 1i
I
u
2
= hb + u, −3035105u
12
+ 837784u
11
+ ··· + 1269257a − 4665416,
u
13
+ 4u
11
− 3u
10
− 14u
9
+ 14u
8
+ 30u
7
− 27u
6
− 9u
5
+ 24u
4
− u
3
− 6u
2
+ 2u + 1i
I
u
3
= h−4.67268 × 10
23
u
17
− 1.17012 × 10
24
u
16
+ ··· + 4.11076 × 10
26
b − 4.67615 × 10
26
,
9.23360 × 10
24
u
17
+ 3.69267 × 10
25
u
16
+ ··· + 1.05852 × 10
28
a + 1.11492 × 10
28
,
u
18
+ u
17
+ ··· + 512u + 206i
I
u
4
= hb − 1, 2a − u + 2, u
2
− 2u + 2i
I
u
5
= hb
2
+ 2b + 2, a − 1, u + 1i
* 5 irreducible components of dim
C
= 0, with total 56 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, −5.40 × 10
21
u
20
− 1.74 × 10
22
u
19
+ · · · + 2.47 × 10
22
a −
8.83 × 10
22
, u
21
+ 25u
19
+ · · · + u + 1i
(i) Arc colorings
a
2
=
1
0
a
11
=
0
u
a
3
=
1
u
2
a
8
=
0.218285u
20
+ 0.701585u
19
+ ··· + 4.16608u + 3.56990
−u
a
12
=
−0.0236086u
20
− 0.454671u
19
+ ··· − 3.43605u − 1.12582
−0.0461919u
20
+ 0.0773359u
19
+ ··· + 1.91987u + 0.701585
a
7
=
0.218285u
20
+ 0.701585u
19
+ ··· + 4.16608u + 3.56990
0.0461919u
20
− 0.0773359u
19
+ ··· − 1.91987u − 0.701585
a
4
=
−0.701585u
20
− 0.0461919u
19
+ ··· − 3.35162u + 1.21829
0.0773359u
20
− 0.0368722u
19
+ ··· + 0.747777u + 0.0461919
a
1
=
−0.344227u
20
+ 0.127290u
19
+ ··· − 2.85190u + 0.707526
0.00198645u
20
− 0.161647u
19
+ ··· + 0.257401u − 0.164162
a
6
=
0.264477u
20
+ 0.624249u
19
+ ··· + 2.24621u + 2.86832
0.0461919u
20
− 0.0773359u
19
+ ··· − 1.91987u − 0.701585
a
5
=
−0.875790u
20
+ 0.451552u
19
+ ··· − 5.00872u + 1.53539
0.266657u
20
− 0.0156100u
19
+ ··· + 0.224114u − 0.576327
a
10
=
0.0236086u
20
+ 0.454671u
19
+ ··· + 3.43605u + 1.12582
0.200090u
20
− 0.189555u
19
+ ··· − 0.398150u − 1.15626
a
9
=
0.223699u
20
+ 0.265116u
19
+ ··· + 3.03790u − 0.0304368
0.200090u
20
− 0.189555u
19
+ ··· − 0.398150u − 1.15626
(ii) Obstruction class = −1
(iii) Cusp Shapes = −
34018566246715620144259
12368961610252189857652
u
20
−
4694223251017745076299
12368961610252189857652
u
19
+ ··· −
153162225510311692592391
6184480805126094928826
u −
44380162749147865603681
12368961610252189857652
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
4
u
21
− 8u
20
+ ··· − 22u + 2
c
2
, c
3
u
21
+ 25u
19
+ ··· + u + 1
c
5
u
21
− 19u
20
+ ··· − 1856u + 256
c
6
u
21
+ u
20
+ ··· + 5u + 2
c
7
, c
10
, c
11
u
21
− 8u
20
+ ··· − 26u + 10
c
8
, c
12
u
21
+ u
20
+ ··· + 6u + 1
c
9
u
21
− u
20
+ ··· + 66u + 76
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
4
y
21
+ 16y
20
+ ··· + 56y −4
c
2
, c
3
y
21
+ 50y
20
+ ··· − 19y −1
c
5
y
21
− 7y
20
+ ··· + 348160y −65536
c
6
y
21
+ 43y
20
+ ··· − 179y −4
c
7
, c
10
, c
11
y
21
− 32y
20
+ ··· + 1776y −100
c
8
, c
12
y
21
+ 11y
20
+ ··· + 38y −1
c
9
y
21
+ 29y
20
+ ··· + 6636y −5776
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.591384 + 0.684501I
a = 0.986086 − 0.952196I
b = −0.591384 − 0.684501I
2.90718 + 0.62164I −0.21352 − 2.05306I
u = 0.591384 − 0.684501I
a = 0.986086 + 0.952196I
b = −0.591384 + 0.684501I
2.90718 − 0.62164I −0.21352 + 2.05306I
u = 0.633459 + 0.554243I
a = 0.225131 − 0.559868I
b = −0.633459 − 0.554243I
3.13654 − 0.77238I −1.08315 + 3.79652I
u = 0.633459 − 0.554243I
a = 0.225131 + 0.559868I
b = −0.633459 + 0.554243I
3.13654 + 0.77238I −1.08315 − 3.79652I
u = −0.411221 + 0.734008I
a = −1.125200 − 0.068544I
b = 0.411221 − 0.734008I
3.06565 − 2.80817I −0.13665 + 3.60000I
u = −0.411221 − 0.734008I
a = −1.125200 + 0.068544I
b = 0.411221 + 0.734008I
3.06565 + 2.80817I −0.13665 − 3.60000I
u = 0.433795 + 0.519955I
a = −1.39067 + 1.14375I
b = −0.433795 − 0.519955I
8.38211 − 0.33360I 5.43964 + 0.18682I
u = 0.433795 − 0.519955I
a = −1.39067 − 1.14375I
b = −0.433795 + 0.519955I
8.38211 + 0.33360I 5.43964 − 0.18682I
u = −0.449539 + 0.447984I
a = 2.36305 + 0.92529I
b = 0.449539 − 0.447984I
9.25551 − 8.18754I 2.61786 + 4.84295I
u = −0.449539 − 0.447984I
a = 2.36305 − 0.92529I
b = 0.449539 + 0.447984I
9.25551 + 8.18754I 2.61786 − 4.84295I
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.610649
a = 0.463396
b = 0.610649
−1.19744 −2.54880
u = 0.064145 + 0.480475I
a = −0.97482 + 2.36314I
b = −0.064145 − 0.480475I
4.25500 + 4.70062I 0.78101 − 5.95257I
u = 0.064145 − 0.480475I
a = −0.97482 − 2.36314I
b = −0.064145 + 0.480475I
4.25500 − 4.70062I 0.78101 + 5.95257I
u = −0.118660 + 0.375406I
a = 1.27547 − 0.90971I
b = 0.118660 − 0.375406I
−0.104584 + 1.401550I −1.22515 − 5.35896I
u = −0.118660 − 0.375406I
a = 1.27547 + 0.90971I
b = 0.118660 + 0.375406I
−0.104584 − 1.401550I −1.22515 + 5.35896I
u = −0.02275 + 2.82542I
a = 0.063198 − 0.686482I
b = 0.02275 − 2.82542I
−17.8874 + 12.7180I 0
u = −0.02275 − 2.82542I
a = 0.063198 + 0.686482I
b = 0.02275 + 2.82542I
−17.8874 − 12.7180I 0
u = −0.62719 + 2.81445I
a = −0.180831 − 0.609250I
b = 0.62719 − 2.81445I
19.4705 − 1.7019I 0
u = −0.62719 − 2.81445I
a = −0.180831 + 0.609250I
b = 0.62719 + 2.81445I
19.4705 + 1.7019I 0
u = 0.21191 + 2.98201I
a = 0.026904 − 0.620788I
b = −0.21191 − 2.98201I
15.8213 − 6.2554I 0
6
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.21191 − 2.98201I
a = 0.026904 + 0.620788I
b = −0.21191 + 2.98201I
15.8213 + 6.2554I 0
7
II. I
u
2
= hb + u, −3.04 × 10
6
u
12
+ 8.38 × 10
5
u
11
+ · · · + 1.27 × 10
6
a − 4.67 ×
10
6
, u
13
+ 4u
11
+ · · · + 2u + 1i
(i) Arc colorings
a
2
=
1
0
a
11
=
0
u
a
3
=
1
u
2
a
8
=
2.39125u
12
− 0.660059u
11
+ ··· − 9.61560u + 3.67571
−u
a
12
=
−2.96162u
12
+ 1.00248u
11
+ ··· + 12.9399u − 5.17648
−0.0312159u
12
+ 0.392917u
11
+ ··· + 2.07113u − 0.660059
a
7
=
2.39125u
12
− 0.660059u
11
+ ··· − 9.61560u + 3.67571
0.0312159u
12
− 0.392917u
11
+ ··· − 2.07113u + 0.660059
a
4
=
0.660059u
12
− 0.0312159u
11
+ ··· + 1.10678u + 3.39125
0.392917u
12
+ 0.0508833u
11
+ ··· − 0.597627u + 0.0312159
a
1
=
−1.65839u
12
− 0.257842u
11
+ ··· + 2.91119u + 0.964264
−0.424133u
12
+ 0.342034u
11
+ ··· + 2.66876u + 0.308725
a
6
=
2.42246u
12
− 1.05298u
11
+ ··· − 11.6867u + 4.33576
0.0312159u
12
− 0.392917u
11
+ ··· − 2.07113u + 0.660059
a
5
=
1.26999u
12
− 1.05851u
11
+ ··· − 6.41247u + 2.32712
0.166291u
12
− 0.668395u
11
+ ··· + 0.612283u + 1.34966
a
10
=
2.96162u
12
− 1.00248u
11
+ ··· − 12.9399u + 5.17648
−0.0266959u
12
− 0.872552u
11
+ ··· − 1.02779u + 1.66254
a
9
=
2.93493u
12
− 1.87504u
11
+ ··· − 13.9677u + 6.83902
−0.0266959u
12
− 0.872552u
11
+ ··· − 1.02779u + 1.66254
(ii) Obstruction class = 1
(iii) Cusp Shapes = −
11098661
1269257
u
12
+
5890928
1269257
u
11
+ ··· +
9880480
1269257
u −
16615848
1269257
8
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
13
− 5u
12
+ ··· + 27u − 4
c
2
u
13
+ 4u
11
+ ··· + 2u + 1
c
3
u
13
+ 4u
11
+ ··· + 2u − 1
c
4
u
13
+ 5u
12
+ ··· + 27u + 4
c
5
u
13
+ 6u
12
+ ··· + u − 1
c
6
u
13
− u
12
+ ··· − u + 1
c
7
u
13
− 5u
12
+ ··· + 3u + 2
c
8
, c
12
u
13
− u
12
+ u
11
+ u
10
+ 2u
9
− 3u
8
+ u
7
+ 3u
6
− u
5
− 2u
4
+ 2u
3
− u − 1
c
9
u
13
− u
12
+ 6u
11
+ u
10
+ 12u
9
+ 10u
8
+ 9u
7
+ 7u
6
+ 6u
4
+ 3u
3
− 3u
2
+ 1
c
10
, c
11
u
13
+ 5u
12
+ ··· + 3u − 2
9
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
4
y
13
+ 9y
12
+ ··· + 97y − 16
c
2
, c
3
y
13
+ 8y
12
+ ··· + 16y − 1
c
5
y
13
− 6y
12
+ ··· + 7y − 1
c
6
y
13
+ 9y
12
+ ··· + 11y − 1
c
7
, c
10
, c
11
y
13
− 19y
12
+ ··· − 11y − 4
c
8
, c
12
y
13
+ y
12
+ ··· + y − 1
c
9
y
13
+ 11y
12
+ ··· + 6y − 1
10
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.584682 + 0.557508I
a = 0.467799 + 0.459309I
b = −0.584682 − 0.557508I
1.87818 − 5.16888I −5.45109 + 5.60438I
u = 0.584682 − 0.557508I
a = 0.467799 − 0.459309I
b = −0.584682 + 0.557508I
1.87818 + 5.16888I −5.45109 − 5.60438I
u = −0.646836 + 0.067688I
a = 0.529126 − 0.404517I
b = 0.646836 − 0.067688I
−1.42512 − 0.47239I −7.52545 + 9.55816I
u = −0.646836 − 0.067688I
a = 0.529126 + 0.404517I
b = 0.646836 + 0.067688I
−1.42512 + 0.47239I −7.52545 − 9.55816I
u = 0.498804 + 0.404257I
a = −2.04698 + 0.60897I
b = −0.498804 − 0.404257I
6.09438 − 1.34909I 0.36538 + 1.86326I
u = 0.498804 − 0.404257I
a = −2.04698 − 0.60897I
b = −0.498804 + 0.404257I
6.09438 + 1.34909I 0.36538 − 1.86326I
u = −1.254250 + 0.588394I
a = −0.840675 − 0.538825I
b = 1.254250 − 0.588394I
6.40935 + 7.59409I 1.22194 − 5.34686I
u = −1.254250 − 0.588394I
a = −0.840675 + 0.538825I
b = 1.254250 + 0.588394I
6.40935 − 7.59409I 1.22194 + 5.34686I
u = 1.245380 + 0.642473I
a = 0.984992 − 0.368357I
b = −1.245380 − 0.642473I
4.54418 + 2.44460I 2.99018 − 2.95945I
u = 1.245380 − 0.642473I
a = 0.984992 + 0.368357I
b = −1.245380 + 0.642473I
4.54418 − 2.44460I 2.99018 + 2.95945I
11
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.328910
a = 4.07049
b = 0.328910
1.84881 −6.67710
u = −0.26332 + 2.64930I
a = −0.129510 − 0.704018I
b = 0.26332 − 2.64930I
17.7632 − 2.2039I 0.237574 + 0.419872I
u = −0.26332 − 2.64930I
a = −0.129510 + 0.704018I
b = 0.26332 + 2.64930I
17.7632 + 2.2039I 0.237574 − 0.419872I
12
III. I
u
3
= h−4.67 × 10
23
u
17
− 1.17 × 10
24
u
16
+ · · · + 4.11 × 10
26
b − 4.68 ×
10
26
, 9.23 × 10
24
u
17
+ 3.69 × 10
25
u
16
+ · · · + 1.06 × 10
28
a + 1.11 ×
10
28
, u
18
+ u
17
+ · · · + 512u + 206i
(i) Arc colorings
a
2
=
1
0
a
11
=
0
u
a
3
=
1
u
2
a
8
=
−0.000872310u
17
− 0.00348851u
16
+ ··· − 0.911938u − 1.05328
0.00113669u
17
+ 0.00284649u
16
+ ··· + 0.0571899u + 1.13754
a
12
=
−0.00619818u
17
− 0.00659840u
16
+ ··· − 3.79065u − 2.55336
−0.000735882u
17
+ 0.00238650u
16
+ ··· + 0.849826u + 0.901098
a
7
=
−0.000872310u
17
− 0.00348851u
16
+ ··· − 0.911938u − 1.05328
0.00337890u
17
+ 0.00352881u
16
+ ··· + 1.57638u + 1.67648
a
4
=
−0.00437426u
17
− 0.00511014u
16
+ ··· − 3.81879u − 1.38980
0.00392577u
17
+ 0.00295684u
16
+ ··· + 1.78231u + 1.86297
a
1
=
0.00326686u
17
− 0.00265625u
16
+ ··· + 2.02077u − 1.22406
−0.00672287u
17
− 0.00269067u
16
+ ··· − 2.56234u − 1.01072
a
6
=
0.00250659u
17
+ 0.0000402959u
16
+ ··· + 0.664442u + 0.623194
0.00337890u
17
+ 0.00352881u
16
+ ··· + 1.57638u + 1.67648
a
5
=
0.00870477u
17
+ 0.00663870u
16
+ ··· + 4.45509u + 3.17656
0.00411478u
17
+ 0.00114230u
16
+ ··· + 0.726555u + 0.775377
a
10
=
0.00619818u
17
+ 0.00659840u
16
+ ··· + 3.79065u + 2.55336
−0.00116233u
17
− 0.00210654u
16
+ ··· − 0.331565u − 0.983544
a
9
=
0.00503585u
17
+ 0.00449186u
16
+ ··· + 3.45908u + 1.56982
−0.00116233u
17
− 0.00210654u
16
+ ··· − 0.331565u − 0.983544
(ii) Obstruction class = −1
(iii) Cusp Shapes = −
2356314796722538609456367
205538248502201329427999196
u
17
−
197356226700656101872041
102769124251100664713999598
u
16
+
··· −
644603608722482183906910875
102769124251100664713999598
u +
7790438242139030196174041
102769124251100664713999598
13
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
4
(u
9
+ u
8
+ 5u
7
+ 4u
6
+ 8u
5
+ 5u
4
+ 2u
3
+ u
2
− 4u − 1)
2
c
2
, c
3
u
18
+ u
17
+ ··· + 512u + 206
c
5
(u + 1)
18
c
6
u
18
− u
17
+ ··· − 532u + 401
c
7
, c
10
, c
11
(u
9
+ 3u
8
− 3u
7
− 12u
6
+ 6u
5
+ 21u
4
− 2u
3
− 11u
2
− 6u − 1)
2
c
8
, c
12
u
18
+ 3u
17
+ ··· + 8u + 2
c
9
u
18
− u
17
+ ··· + 3168u + 1504
14
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
4
(y
9
+ 9y
8
+ 33y
7
+ 58y
6
+ 34y
5
− 39y
4
− 62y
3
− 7y
2
+ 18y − 1)
2
c
2
, c
3
y
18
+ 37y
17
+ ··· − 103112y + 42436
c
5
(y − 1)
18
c
6
y
18
+ 39y
17
+ ··· + 109154y + 160801
c
7
, c
10
, c
11
(y
9
− 15y
8
+ ··· + 14y − 1)
2
c
8
, c
12
y
18
+ y
17
+ ··· + 72y + 4
c
9
y
18
+ 25y
17
+ ··· − 7100416y + 2262016
15
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = 0.886434 + 0.371388I
a = 1.096950 − 0.459588I
b = −0.886434 + 0.371388I
3.15999 −1.78243 + 0.I
u = 0.886434 − 0.371388I
a = 1.096950 + 0.459588I
b = −0.886434 − 0.371388I
3.15999 −1.78243 + 0.I
u = 0.205642 + 0.879714I
a = 0.257101 + 0.425056I
b = −1.095690 + 0.759227I
2.95021 + 4.83805I 3.38372 − 2.81539I
u = 0.205642 − 0.879714I
a = 0.257101 − 0.425056I
b = −1.095690 − 0.759227I
2.95021 − 4.83805I 3.38372 + 2.81539I
u = −0.653145 + 0.189006I
a = 0.414794 + 0.120032I
b = 0.653145 + 0.189006I
−1.18935 −6 − 0.171800 + 0.10I
u = −0.653145 − 0.189006I
a = 0.414794 − 0.120032I
b = 0.653145 − 0.189006I
−1.18935 −6 − 0.171800 + 0.10I
u = 1.095690 + 0.759227I
a = −0.331949 − 0.056184I
b = −0.205642 + 0.879714I
2.95021 − 4.83805I 3.38372 + 2.81539I
u = 1.095690 − 0.759227I
a = −0.331949 + 0.056184I
b = −0.205642 − 0.879714I
2.95021 + 4.83805I 3.38372 − 2.81539I
u = −0.419711 + 0.477941I
a = −0.60540 − 2.16213I
b = 1.40135 + 0.64766I
7.78134 − 1.20594I 6.24179 + 1.20422I
u = −0.419711 − 0.477941I
a = −0.60540 + 2.16213I
b = 1.40135 − 0.64766I
7.78134 + 1.20594I 6.24179 − 1.20422I
16
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = −1.40135 + 0.64766I
a = −0.925008 + 0.013582I
b = 0.419711 + 0.477941I
7.78134 + 1.20594I 6.24179 − 1.20422I
u = −1.40135 − 0.64766I
a = −0.925008 − 0.013582I
b = 0.419711 − 0.477941I
7.78134 − 1.20594I 6.24179 + 1.20422I
u = −0.22580 + 2.48577I
a = 0.159711 + 0.767946I
b = 0.15187 + 2.78180I
19.3983 − 3.3753I 4.74375 + 2.72891I
u = −0.22580 − 2.48577I
a = 0.159711 − 0.767946I
b = 0.15187 − 2.78180I
19.3983 + 3.3753I 4.74375 − 2.72891I
u = 0.16411 + 2.66586I
a = −0.043531 + 0.707136I
b = −0.16411 + 2.66586I
15.0815 −6 − 0.784284 + 0.10I
u = 0.16411 − 2.66586I
a = −0.043531 − 0.707136I
b = −0.16411 − 2.66586I
15.0815 −6 − 0.784284 + 0.10I
u = −0.15187 + 2.78180I
a = −0.042083 + 0.701486I
b = 0.22580 + 2.48577I
19.3983 + 3.3753I 4.74375 − 2.72891I
u = −0.15187 − 2.78180I
a = −0.042083 − 0.701486I
b = 0.22580 − 2.48577I
19.3983 − 3.3753I 4.74375 + 2.72891I
17
IV. I
u
4
= hb − 1, 2a − u + 2, u
2
− 2u + 2i
(i) Arc colorings
a
2
=
1
0
a
11
=
0
u
a
3
=
1
2u − 2
a
8
=
1
2
u − 1
1
a
12
=
−
1
2
u + 1
u − 1
a
7
=
1
2
u − 1
−u + 1
a
4
=
1
2
u
u − 1
a
1
=
−
1
2
u + 2
1
a
6
=
−
1
2
u
−u + 1
a
5
=
−u + 1
0
a
10
=
1
2
u − 1
1
a
9
=
1
2
u
1
(ii) Obstruction class = 1
(iii) Cusp Shapes = 4
18
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
4
, c
6
c
8
u
2
+ 1
c
2
, c
12
u
2
− 2u + 2
c
3
, c
5
, c
10
c
11
(u − 1)
2
c
7
, c
9
(u + 1)
2
19
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
4
, c
6
c
8
(y + 1)
2
c
2
, c
12
y
2
+ 4
c
3
, c
5
, c
7
c
9
, c
10
, c
11
(y − 1)
2
20
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
4
√
−1(vol +
√
−1CS) Cusp shape
u = 1.00000 + 1.00000I
a = −0.500000 + 0.500000I
b = 1.00000
4.93480 4.00000
u = 1.00000 − 1.00000I
a = −0.500000 − 0.500000I
b = 1.00000
4.93480 4.00000
21
V. I
u
5
= hb
2
+ 2b + 2, a − 1, u + 1i
(i) Arc colorings
a
2
=
1
0
a
11
=
0
−1
a
3
=
1
1
a
8
=
1
b
a
12
=
−1
−b − 1
a
7
=
1
b + 1
a
4
=
b + 1
−b − 1
a
1
=
0
1
a
6
=
b + 2
b + 1
a
5
=
b + 1
0
a
10
=
1
b
a
9
=
b + 1
b
(ii) Obstruction class = 1
(iii) Cusp Shapes = 4
22
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
4
, c
6
c
12
u
2
+ 1
c
2
, c
7
(u + 1)
2
c
3
u
2
+ 2u + 2
c
5
, c
10
, c
11
(u − 1)
2
c
8
, c
9
u
2
− 2u + 2
23
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
4
, c
6
c
12
(y + 1)
2
c
2
, c
5
, c
7
c
10
, c
11
(y − 1)
2
c
3
, c
8
, c
9
y
2
+ 4
24
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
5
√
−1(vol +
√
−1CS) Cusp shape
u = −1.00000
a = 1.00000
b = −1.00000 + 1.00000I
4.93480 4.00000
u = −1.00000
a = 1.00000
b = −1.00000 − 1.00000I
4.93480 4.00000
25
VI. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
(u
2
+ 1)
2
(u
9
+ u
8
+ 5u
7
+ 4u
6
+ 8u
5
+ 5u
4
+ 2u
3
+ u
2
− 4u − 1)
2
· (u
13
− 5u
12
+ ··· + 27u − 4)(u
21
− 8u
20
+ ··· − 22u + 2)
c
2
((u + 1)
2
)(u
2
− 2u + 2)(u
13
+ 4u
11
+ ··· + 2u + 1)
· (u
18
+ u
17
+ ··· + 512u + 206)(u
21
+ 25u
19
+ ··· + u + 1)
c
3
((u − 1)
2
)(u
2
+ 2u + 2)(u
13
+ 4u
11
+ ··· + 2u − 1)
· (u
18
+ u
17
+ ··· + 512u + 206)(u
21
+ 25u
19
+ ··· + u + 1)
c
4
(u
2
+ 1)
2
(u
9
+ u
8
+ 5u
7
+ 4u
6
+ 8u
5
+ 5u
4
+ 2u
3
+ u
2
− 4u − 1)
2
· (u
13
+ 5u
12
+ ··· + 27u + 4)(u
21
− 8u
20
+ ··· − 22u + 2)
c
5
((u − 1)
4
)(u + 1)
18
(u
13
+ 6u
12
+ ··· + u − 1)
· (u
21
− 19u
20
+ ··· − 1856u + 256)
c
6
((u
2
+ 1)
2
)(u
13
− u
12
+ ··· − u + 1)(u
18
− u
17
+ ··· − 532u + 401)
· (u
21
+ u
20
+ ··· + 5u + 2)
c
7
(u + 1)
4
· (u
9
+ 3u
8
− 3u
7
− 12u
6
+ 6u
5
+ 21u
4
− 2u
3
− 11u
2
− 6u − 1)
2
· (u
13
− 5u
12
+ ··· + 3u + 2)(u
21
− 8u
20
+ ··· − 26u + 10)
c
8
, c
12
(u
2
+ 1)(u
2
− 2u + 2)
· (u
13
− u
12
+ u
11
+ u
10
+ 2u
9
− 3u
8
+ u
7
+ 3u
6
− u
5
− 2u
4
+ 2u
3
− u − 1)
· (u
18
+ 3u
17
+ ··· + 8u + 2)(u
21
+ u
20
+ ··· + 6u + 1)
c
9
(u + 1)
2
(u
2
− 2u + 2)
· (u
13
− u
12
+ 6u
11
+ u
10
+ 12u
9
+ 10u
8
+ 9u
7
+ 7u
6
+ 6u
4
+ 3u
3
− 3u
2
+ 1)
· (u
18
− u
17
+ ··· + 3168u + 1504)(u
21
− u
20
+ ··· + 66u + 76)
c
10
, c
11
(u − 1)
4
· (u
9
+ 3u
8
− 3u
7
− 12u
6
+ 6u
5
+ 21u
4
− 2u
3
− 11u
2
− 6u − 1)
2
· (u
13
+ 5u
12
+ ··· + 3u − 2)(u
21
− 8u
20
+ ··· − 26u + 10)
26
VII. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
, c
4
(y + 1)
4
· (y
9
+ 9y
8
+ 33y
7
+ 58y
6
+ 34y
5
− 39y
4
− 62y
3
− 7y
2
+ 18y − 1)
2
· (y
13
+ 9y
12
+ ··· + 97y − 16)(y
21
+ 16y
20
+ ··· + 56y − 4)
c
2
, c
3
((y − 1)
2
)(y
2
+ 4)(y
13
+ 8y
12
+ ··· + 16y − 1)
· (y
18
+ 37y
17
+ ··· − 103112y + 42436)(y
21
+ 50y
20
+ ··· − 19y − 1)
c
5
((y − 1)
22
)(y
13
− 6y
12
+ ··· + 7y − 1)
· (y
21
− 7y
20
+ ··· + 348160y − 65536)
c
6
((y + 1)
4
)(y
13
+ 9y
12
+ ··· + 11y − 1)
· (y
18
+ 39y
17
+ ··· + 109154y + 160801)
· (y
21
+ 43y
20
+ ··· − 179y − 4)
c
7
, c
10
, c
11
((y − 1)
4
)(y
9
− 15y
8
+ ··· + 14y − 1)
2
(y
13
− 19y
12
+ ··· − 11y − 4)
· (y
21
− 32y
20
+ ··· + 1776y − 100)
c
8
, c
12
((y + 1)
2
)(y
2
+ 4)(y
13
+ y
12
+ ··· + y − 1)(y
18
+ y
17
+ ··· + 72y + 4)
· (y
21
+ 11y
20
+ ··· + 38y − 1)
c
9
((y − 1)
2
)(y
2
+ 4)(y
13
+ 11y
12
+ ··· + 6y − 1)
· (y
18
+ 25y
17
+ ··· − 7100416y + 2262016)
· (y
21
+ 29y
20
+ ··· + 6636y − 5776)
27
