12n
0542
(K12n
0542
)
A knot diagram
1
Linearized knot diagam
3 5 10 8 2 9 5 12 6 4 9 4
Solving Sequence
9,11 4,12
1 8 5 7 6 10 3 2
c
11
c
12
c
8
c
4
c
7
c
6
c
10
c
3
c
2
c
1
, c
5
, c
9
Ideals for irreducible components
2
of X
par
I
u
1
= h974u
18
− 999u
17
+ ··· + 7097b − 1006, −1503u
18
+ 1476u
17
+ ··· + 7097a − 16416,
u
19
+ u
18
+ ··· + 3u − 1i
I
u
2
= h−2.79075 × 10
77
u
61
+ 3.09654 × 10
77
u
60
+ ··· + 3.26293 × 10
76
b − 2.63657 × 10
79
,
− 1.11588 × 10
81
u
61
− 2.33393 × 10
81
u
60
+ ··· + 2.25893 × 10
80
a − 7.73676 × 10
83
,
u
62
− u
61
+ ··· + 219u + 161i
I
u
3
= hu
5
− u
4
+ 3u
3
− 2u
2
+ b + 2u − 1, −u
5
− 3u
3
+ a − 3u + 1, u
6
− u
5
+ 3u
4
− 2u
3
+ 3u
2
− 2u + 1i
I
u
4
= h202u
17
− 333u
16
+ ··· + 67b + 117, 584u
17
− 976u
16
+ ··· + 67a + 122, u
18
− 2u
17
+ ··· − u + 1i
* 4 irreducible components of dim
C
= 0, with total 105 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
= h974u
18
− 999u
17
+ · · · + 7097b − 1006, −1503u
18
+ 1476u
17
+ · · · +
7097a − 16416, u
19
+ u
18
+ · · · + 3u − 1i
(i) Arc colorings
a
9
=
0
u
a
11
=
1
0
a
4
=
0.211780u
18
− 0.207975u
17
+ ··· − 1.45977u + 2.31309
−0.137241u
18
+ 0.140764u
17
+ ··· − 0.499789u + 0.141750
a
12
=
1
−u
2
a
1
=
0.104129u
18
+ 0.448640u
17
+ ··· + 2.49317u + 0.0834155
0.666056u
18
+ 0.178244u
17
+ ··· − 2.10934u + 0.334648
a
8
=
−u
u
3
+ u
a
5
=
0.424968u
18
− 0.0580527u
17
+ ··· − 0.897985u + 2.08468
−0.344089u
18
− 0.398619u
17
+ ··· − 1.46456u + 0.433423
a
7
=
0.123432u
18
+ 0.351839u
17
+ ··· + 0.488516u − 2.03509
−0.378611u
18
− 1.16711u
17
+ ··· − 2.49274u + 1.20008
a
6
=
0.123432u
18
+ 0.351839u
17
+ ··· + 0.488516u − 2.03509
−0.591799u
18
− 1.31704u
17
+ ··· − 3.05453u + 1.42849
a
10
=
0.468367u
18
+ 0.965197u
17
+ ··· + 2.56601u + 0.606594
0.968156u
18
+ 0.911512u
17
+ ··· − 1.08722u − 0.162181
a
3
=
−0.433423u
18
− 0.0893335u
17
+ ··· + 4.76863u + 0.164295
1.80738u
18
+ 1.07538u
17
+ ··· − 4.64703u + 0.722559
a
2
=
0.0495984u
18
+ 0.597999u
17
+ ··· + 3.95886u − 0.260674
1.86191u
18
+ 0.926025u
17
+ ··· − 6.11272u + 1.06665
(ii) Obstruction class = −1
(iii) Cusp Shapes =
29393
7097
u
18
+
35263
7097
u
17
+ ··· +
4731
7097
u +
28953
7097
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
19
+ 9u
18
+ ··· + 3u − 1
c
2
, c
5
, c
8
c
11
u
19
+ u
18
+ ··· + 3u − 1
c
3
, c
10
u
19
− 6u
18
+ ··· + 138u − 20
c
4
, c
6
, c
7
c
9
u
19
− u
18
+ ··· − 2u − 1
c
12
u
19
+ 3u
18
+ ··· + 17u − 1
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
19
+ 9y
18
+ ··· + 83y −1
c
2
, c
5
, c
8
c
11
y
19
+ 9y
18
+ ··· + 3y −1
c
3
, c
10
y
19
− 6y
18
+ ··· + 3644y −400
c
4
, c
6
, c
7
c
9
y
19
+ 11y
18
+ ··· − 16y −1
c
12
y
19
− 9y
18
+ ··· + 185y −1
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.598892 + 0.793130I
a = −0.688695 − 1.114540I
b = 0.584926 + 0.753908I
−4.68072 − 4.53032I 0.23576 + 6.82608I
u = −0.598892 − 0.793130I
a = −0.688695 + 1.114540I
b = 0.584926 − 0.753908I
−4.68072 + 4.53032I 0.23576 − 6.82608I
u = 0.641885 + 0.791191I
a = −0.78268 − 1.74962I
b = −1.19111 + 0.78206I
2.72504 + 2.14853I 5.27491 − 4.89748I
u = 0.641885 − 0.791191I
a = −0.78268 + 1.74962I
b = −1.19111 − 0.78206I
2.72504 − 2.14853I 5.27491 + 4.89748I
u = −0.954552 + 0.529709I
a = 0.788913 − 0.809680I
b = −0.774159 + 0.942461I
4.02799 + 4.33818I 7.30330 − 2.78056I
u = −0.954552 − 0.529709I
a = 0.788913 + 0.809680I
b = −0.774159 − 0.942461I
4.02799 − 4.33818I 7.30330 + 2.78056I
u = 0.703458 + 0.924026I
a = 0.694693 + 0.652223I
b = −0.77405 − 1.50185I
1.92467 + 8.33135I 3.77225 − 7.85485I
u = 0.703458 − 0.924026I
a = 0.694693 − 0.652223I
b = −0.77405 + 1.50185I
1.92467 − 8.33135I 3.77225 + 7.85485I
u = −0.161487 + 0.755198I
a = 0.146971 − 1.177300I
b = 1.88402 + 0.21622I
−9.12584 − 1.43131I −4.00366 + 3.62415I
u = −0.161487 − 0.755198I
a = 0.146971 + 1.177300I
b = 1.88402 − 0.21622I
−9.12584 + 1.43131I −4.00366 − 3.62415I
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.453786 + 0.554000I
a = 0.414166 + 1.161230I
b = 0.334354 − 0.847458I
0.38104 + 1.60999I 2.18079 − 5.36943I
u = 0.453786 − 0.554000I
a = 0.414166 − 1.161230I
b = 0.334354 + 0.847458I
0.38104 − 1.60999I 2.18079 + 5.36943I
u = −0.404171 + 1.249560I
a = −0.428625 + 0.261688I
b = −0.988583 + 0.139575I
−6.67425 − 2.09645I −1.51316 − 1.19213I
u = −0.404171 − 1.249560I
a = −0.428625 − 0.261688I
b = −0.988583 − 0.139575I
−6.67425 + 2.09645I −1.51316 + 1.19213I
u = 0.412299 + 1.282300I
a = −0.913206 − 0.624518I
b = −0.609142 + 0.776738I
−4.85217 + 5.72791I −0.72528 − 2.49727I
u = 0.412299 − 1.282300I
a = −0.913206 + 0.624518I
b = −0.609142 − 0.776738I
−4.85217 − 5.72791I −0.72528 + 2.49727I
u = −0.754119 + 1.179290I
a = −0.44083 + 1.39445I
b = −1.30424 − 1.00552I
0.0879 − 16.9991I 2.43611 + 9.58640I
u = −0.754119 − 1.179290I
a = −0.44083 − 1.39445I
b = −1.30424 + 1.00552I
0.0879 + 16.9991I 2.43611 − 9.58640I
u = 0.323587
a = 2.41860
b = −0.324027
1.11886 7.07800
6
II. I
u
2
= h−2.79 × 10
77
u
61
+ 3.10 × 10
77
u
60
+ · · · + 3.26 × 10
76
b − 2.64 ×
10
79
, −1.12 × 10
81
u
61
− 2.33 × 10
81
u
60
+ · · · + 2.26 × 10
80
a − 7.74 ×
10
83
, u
62
− u
61
+ · · · + 219u + 161i
(i) Arc colorings
a
9
=
0
u
a
11
=
1
0
a
4
=
4.93988u
61
+ 10.3320u
60
+ ··· + 3052.06u + 3424.97
8.55289u
61
− 9.49004u
60
+ ··· + 2109.35u + 808.036
a
12
=
1
−u
2
a
1
=
−14.8092u
61
+ 45.3794u
60
+ ··· − 351.887u + 3904.63
4.35772u
61
+ 0.633217u
60
+ ··· + 1652.87u + 1449.85
a
8
=
−u
u
3
+ u
a
5
=
−1.24358u
61
+ 11.5998u
60
+ ··· + 910.505u + 1789.93
6.13216u
61
− 0.902867u
60
+ ··· + 2178.83u + 1651.65
a
7
=
3.30008u
61
− 7.44802u
60
+ ··· + 382.105u − 385.923
21.1575u
61
− 41.4404u
60
+ ··· + 3194.89u − 1232.69
a
6
=
3.30008u
61
− 7.44802u
60
+ ··· + 382.105u − 385.923
20.9712u
61
− 37.5906u
60
+ ··· + 3571.97u − 564.873
a
10
=
5.39314u
61
− 4.87046u
60
+ ··· + 1455.83u + 739.007
9.48677u
61
− 7.50330u
60
+ ··· + 2635.64u + 1534.00
a
3
=
1.01304u
61
+ 11.9845u
60
+ ··· + 1771.40u + 2539.05
−4.85695u
61
+ 5.93802u
60
+ ··· − 1149.76u − 313.552
a
2
=
−2.53436u
61
+ 4.93608u
60
+ ··· − 367.326u + 131.517
−5.55600u
61
+ 18.3449u
60
+ ··· − 49.1658u + 1701.70
(ii) Obstruction class = −1
(iii) Cusp Shapes = −110.094u
61
+ 161.634u
60
+ ··· − 22814.4u − 3810.06
7
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
62
+ 21u
61
+ ··· + 490101u + 25921
c
2
, c
5
, c
8
c
11
u
62
− u
61
+ ··· + 219u + 161
c
3
, c
10
(u
31
+ 3u
30
+ ··· + 8u
2
− 1)
2
c
4
, c
6
, c
7
c
9
u
62
+ 4u
61
+ ··· + 189u + 29
c
12
u
62
+ 5u
61
+ ··· − 20878u + 5329
8
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
62
+ 33y
61
+ ··· + 4781262113y + 671898241
c
2
, c
5
, c
8
c
11
y
62
+ 21y
61
+ ··· + 490101y + 25921
c
3
, c
10
(y
31
− 9y
30
+ ··· + 16y −1)
2
c
4
, c
6
, c
7
c
9
y
62
+ 18y
61
+ ··· + 44435y + 841
c
12
y
62
− 15y
61
+ ··· − 380852972y + 28398241
9
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.880538 + 0.423378I
a = 0.314688 + 0.978587I
b = 0.274664 − 0.986060I
0.11599 + 1.55086I 0
u = 0.880538 − 0.423378I
a = 0.314688 − 0.978587I
b = 0.274664 + 0.986060I
0.11599 − 1.55086I 0
u = −0.555340 + 0.882550I
a = 0.88135 + 1.13257I
b = −0.424965
−5.03919 0
u = −0.555340 − 0.882550I
a = 0.88135 − 1.13257I
b = −0.424965
−5.03919 0
u = −0.704833 + 0.774815I
a = 0.339950 − 0.851399I
b = −0.656234 + 1.058070I
4.12245 − 2.52430I 0
u = −0.704833 − 0.774815I
a = 0.339950 + 0.851399I
b = −0.656234 − 1.058070I
4.12245 + 2.52430I 0
u = −0.761240 + 0.735997I
a = −0.501700 + 0.598901I
b = 1.00918 − 1.06732I
3.03685 + 3.84833I 0
u = −0.761240 − 0.735997I
a = −0.501700 − 0.598901I
b = 1.00918 + 1.06732I
3.03685 − 3.84833I 0
u = −0.322158 + 0.877553I
a = −1.192630 + 0.167789I
b = −1.331560 − 0.055456I
−6.42784 − 4.16920I 2.61762 + 7.23000I
u = −0.322158 − 0.877553I
a = −1.192630 − 0.167789I
b = −1.331560 + 0.055456I
−6.42784 + 4.16920I 2.61762 − 7.23000I
10
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.323211 + 0.872183I
a = 1.11709 − 2.06897I
b = 0.230847 + 0.193317I
1.04832 − 1.42552I −10.45750 − 4.66815I
u = −0.323211 − 0.872183I
a = 1.11709 + 2.06897I
b = 0.230847 − 0.193317I
1.04832 + 1.42552I −10.45750 + 4.66815I
u = 0.321433 + 0.857244I
a = 0.69671 + 1.45294I
b = 0.274664 − 0.986060I
0.11599 + 1.55086I 0. − 2.83247I
u = 0.321433 − 0.857244I
a = 0.69671 − 1.45294I
b = 0.274664 + 0.986060I
0.11599 − 1.55086I 0. + 2.83247I
u = 0.738364 + 0.803627I
a = 0.91857 + 1.41297I
b = 1.02061 − 1.10114I
2.30077 − 2.83428I 0
u = 0.738364 − 0.803627I
a = 0.91857 − 1.41297I
b = 1.02061 + 1.10114I
2.30077 + 2.83428I 0
u = −0.161867 + 0.874417I
a = −1.03396 + 1.39536I
b = −1.60582
−9.62704 −6.32419 + 0.I
u = −0.161867 − 0.874417I
a = −1.03396 − 1.39536I
b = −1.60582
−9.62704 −6.32419 + 0.I
u = 0.632047 + 0.924598I
a = −0.690760 − 0.442538I
b = 1.02061 + 1.10114I
2.30077 + 2.83428I 0
u = 0.632047 − 0.924598I
a = −0.690760 + 0.442538I
b = 1.02061 − 1.10114I
2.30077 − 2.83428I 0
11
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.738797 + 0.844402I
a = −0.616959 − 1.028670I
b = 1.43788 + 0.39387I
−6.06260 − 1.36069I 0
u = −0.738797 − 0.844402I
a = −0.616959 + 1.028670I
b = 1.43788 − 0.39387I
−6.06260 + 1.36069I 0
u = −0.333024 + 0.787088I
a = 0.612484 − 0.040784I
b = 1.43788 − 0.39387I
−6.06260 + 1.36069I 3.05496 + 3.58665I
u = −0.333024 − 0.787088I
a = 0.612484 + 0.040784I
b = 1.43788 + 0.39387I
−6.06260 − 1.36069I 3.05496 − 3.58665I
u = −0.668918 + 0.938345I
a = 0.99125 − 1.25893I
b = 0.923139 + 0.712544I
3.61426 − 2.76516I 0
u = −0.668918 − 0.938345I
a = 0.99125 + 1.25893I
b = 0.923139 − 0.712544I
3.61426 + 2.76516I 0
u = −0.043664 + 0.838028I
a = −1.01464 + 2.65763I
b = −0.293987 + 0.302045I
−1.92162 + 5.04186I −1.96742 − 5.03142I
u = −0.043664 − 0.838028I
a = −1.01464 − 2.65763I
b = −0.293987 − 0.302045I
−1.92162 − 5.04186I −1.96742 + 5.03142I
u = −0.688297 + 0.942130I
a = 0.450937 + 1.314910I
b = −1.331560 − 0.055456I
−6.42784 − 4.16920I 0
u = −0.688297 − 0.942130I
a = 0.450937 − 1.314910I
b = −1.331560 + 0.055456I
−6.42784 + 4.16920I 0
12
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.819017 + 0.053471I
a = −0.091379 + 0.684673I
b = 0.854298 − 0.246502I
−2.76144 + 2.29121I 1.38772 − 4.30711I
u = −0.819017 − 0.053471I
a = −0.091379 − 0.684673I
b = 0.854298 + 0.246502I
−2.76144 − 2.29121I 1.38772 + 4.30711I
u = 0.008722 + 1.184200I
a = 0.234534 + 0.024290I
b = 0.854298 − 0.246502I
−2.76144 + 2.29121I 0
u = 0.008722 − 1.184200I
a = 0.234534 − 0.024290I
b = 0.854298 + 0.246502I
−2.76144 − 2.29121I 0
u = 0.128103 + 0.797173I
a = −0.45608 − 2.09717I
b = 0.303847 + 1.172310I
−1.67295 − 4.62397I −2.07779 + 1.32263I
u = 0.128103 − 0.797173I
a = −0.45608 + 2.09717I
b = 0.303847 − 1.172310I
−1.67295 + 4.62397I −2.07779 − 1.32263I
u = −0.702406 + 0.967738I
a = −0.86851 + 1.43021I
b = −1.21644 − 0.81414I
2.32939 − 9.40399I 0
u = −0.702406 − 0.967738I
a = −0.86851 − 1.43021I
b = −1.21644 + 0.81414I
2.32939 + 9.40399I 0
u = 0.958116 + 0.721272I
a = 0.779508 + 0.543823I
b = −0.656234 − 1.058070I
4.12245 + 2.52430I 0
u = 0.958116 − 0.721272I
a = 0.779508 − 0.543823I
b = −0.656234 + 1.058070I
4.12245 − 2.52430I 0
13
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −1.082620 + 0.533747I
a = −0.800331 + 0.606904I
b = 1.03536 − 0.98869I
2.12962 + 10.40970I 0
u = −1.082620 − 0.533747I
a = −0.800331 − 0.606904I
b = 1.03536 + 0.98869I
2.12962 − 10.40970I 0
u = 1.039630 + 0.699325I
a = −0.720564 − 0.293050I
b = 0.923139 + 0.712544I
3.61426 − 2.76516I 0
u = 1.039630 − 0.699325I
a = −0.720564 + 0.293050I
b = 0.923139 − 0.712544I
3.61426 + 2.76516I 0
u = −0.479366 + 1.198710I
a = −0.83274 + 1.30196I
b = −0.811516 − 0.370609I
−6.15144 − 6.93633I 0
u = −0.479366 − 1.198710I
a = −0.83274 − 1.30196I
b = −0.811516 + 0.370609I
−6.15144 + 6.93633I 0
u = 0.782667 + 1.056430I
a = 0.378022 + 1.278080I
b = 1.00918 − 1.06732I
3.03685 + 3.84833I 0
u = 0.782667 − 1.056430I
a = 0.378022 − 1.278080I
b = 1.00918 + 1.06732I
3.03685 − 3.84833I 0
u = −0.702326 + 1.138380I
a = 0.51785 − 1.41136I
b = 1.03536 + 0.98869I
2.12962 − 10.40970I 0
u = −0.702326 − 1.138380I
a = 0.51785 + 1.41136I
b = 1.03536 − 0.98869I
2.12962 + 10.40970I 0
14
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.782473 + 1.095100I
a = 0.358659 + 0.761459I
b = 0.303847 − 1.172310I
−1.67295 + 4.62397I 0
u = 0.782473 − 1.095100I
a = 0.358659 − 0.761459I
b = 0.303847 + 1.172310I
−1.67295 − 4.62397I 0
u = 0.801657 + 1.089810I
a = −0.187234 − 1.326080I
b = −1.21644 + 0.81414I
2.32939 + 9.40399I 0
u = 0.801657 − 1.089810I
a = −0.187234 + 1.326080I
b = −1.21644 − 0.81414I
2.32939 − 9.40399I 0
u = 1.331690 + 0.249393I
a = −0.0878421 − 0.0786949I
b = 0.230847 − 0.193317I
1.04832 + 1.42552I 0
u = 1.331690 − 0.249393I
a = −0.0878421 + 0.0786949I
b = 0.230847 + 0.193317I
1.04832 − 1.42552I 0
u = 0.719158 + 1.164620I
a = −0.052952 − 0.721865I
b = −0.293987 + 0.302045I
−1.92162 + 5.04186I 0
u = 0.719158 − 1.164620I
a = −0.052952 + 0.721865I
b = −0.293987 − 0.302045I
−1.92162 − 5.04186I 0
u = 0.331198 + 0.511142I
a = 0.61237 − 2.04841I
b = −0.529398
0.947764 − 60.736645 + 0.10I
u = 0.331198 − 0.511142I
a = 0.61237 + 2.04841I
b = −0.529398
0.947764 − 60.736645 + 0.10I
15
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.13128 + 1.50361I
a = −0.176799 + 0.132893I
b = −0.811516 + 0.370609I
−6.15144 + 6.93633I 0
u = 0.13128 − 1.50361I
a = −0.176799 − 0.132893I
b = −0.811516 − 0.370609I
−6.15144 − 6.93633I 0
16
III. I
u
3
= hu
5
− u
4
+ 3u
3
− 2u
2
+ b + 2u − 1, −u
5
− 3u
3
+ a − 3u + 1, u
6
−
u
5
+ 3u
4
− 2u
3
+ 3u
2
− 2u + 1i
(i) Arc colorings
a
9
=
0
u
a
11
=
1
0
a
4
=
u
5
+ 3u
3
+ 3u − 1
−u
5
+ u
4
− 3u
3
+ 2u
2
− 2u + 1
a
12
=
1
−u
2
a
1
=
u
5
− u
4
+ 2u
3
− 2u
2
+ 2u − 1
u
4
− u
3
+ u
2
− u + 1
a
8
=
−u
u
3
+ u
a
5
=
u
5
− u
4
+ 4u
3
− 2u
2
+ 4u − 2
−u
5
+ u
4
− 3u
3
+ 2u
2
− u + 1
a
7
=
u
5
+ 2u
3
+ 2u − 1
u
4
− u
3
+ 3u
2
− 2u + 2
a
6
=
u
5
+ 2u
3
+ 2u − 1
u
2
− u + 1
a
10
=
−u
5
− 2u
3
− u
2
− u
u
4
− u
3
+ 2u
2
a
3
=
u
5
+ 2u
3
+ u
2
+ u − 1
−u
4
+ u
3
− u
2
+ 1
a
2
=
u
5
− u
4
+ 2u
3
+ u
−u
4
+ u
3
− 3u
2
+ u
(ii) Obstruction class = 1
(iii) Cusp Shapes = −7u
5
+ 10u
4
− 19u
3
+ 13u
2
− 14u + 11
17
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
6
− 5u
5
+ 11u
4
− 12u
3
+ 7u
2
− 2u + 1
c
2
, c
8
u
6
+ u
5
+ 3u
4
+ 2u
3
+ 3u
2
+ 2u + 1
c
3
u
6
− 3u
5
+ 2u
4
+ u
2
− u + 1
c
4
, c
6
u
6
+ u
5
+ 2u
4
+ 2u
3
+ u
2
+ u + 1
c
5
, c
11
u
6
− u
5
+ 3u
4
− 2u
3
+ 3u
2
− 2u + 1
c
7
, c
9
u
6
− u
5
+ 2u
4
− 2u
3
+ u
2
− u + 1
c
10
u
6
+ 3u
5
+ 2u
4
+ u
2
+ u + 1
c
12
u
6
− u
5
− 2u
4
+ 2u
2
+ 2u + 1
18
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
6
− 3y
5
+ 15y
4
− 8y
3
+ 23y
2
+ 10y + 1
c
2
, c
5
, c
8
c
11
y
6
+ 5y
5
+ 11y
4
+ 12y
3
+ 7y
2
+ 2y + 1
c
3
, c
10
y
6
− 5y
5
+ 6y
4
+ 5y
2
+ y + 1
c
4
, c
6
, c
7
c
9
y
6
+ 3y
5
+ 2y
4
+ y
2
+ y + 1
c
12
y
6
− 5y
5
+ 8y
4
− 2y
3
+ 1
19
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = −0.368622 + 1.044700I
a = −0.290865 + 0.782701I
b = −1.66898 + 0.19346I
−9.91965 − 2.91185I −3.45428 + 5.11141I
u = −0.368622 − 1.044700I
a = −0.290865 − 0.782701I
b = −1.66898 − 0.19346I
−9.91965 + 2.91185I −3.45428 − 5.11141I
u = 0.474902 + 0.458521I
a = −0.24864 + 1.93653I
b = 0.564694 − 0.593680I
1.33814 + 0.90202I 6.98442 − 4.12364I
u = 0.474902 − 0.458521I
a = −0.24864 − 1.93653I
b = 0.564694 + 0.593680I
1.33814 − 0.90202I 6.98442 + 4.12364I
u = 0.393720 + 1.309500I
a = −0.960493 − 0.454104I
b = −0.395713 + 0.609164I
−4.57797 + 6.62522I 2.96986 − 9.69037I
u = 0.393720 − 1.309500I
a = −0.960493 + 0.454104I
b = −0.395713 − 0.609164I
−4.57797 − 6.62522I 2.96986 + 9.69037I
20
IV. I
u
4
= h202u
17
− 333u
16
+ · · · + 67b + 117, 584u
17
− 976u
16
+ · · · + 67a +
122, u
18
− 2u
17
+ · · · − u + 1i
(i) Arc colorings
a
9
=
0
u
a
11
=
1
0
a
4
=
−8.71642u
17
+ 14.5672u
16
+ ··· − 24.1343u − 1.82090
−3.01493u
17
+ 4.97015u
16
+ ··· + 1.05970u − 1.74627
a
12
=
1
−u
2
a
1
=
2.16418u
17
− 19.6716u
16
+ ··· + 32.3433u − 35.7910
8.05970u
17
− 14.8806u
16
+ ··· + 6.76119u + 2.98507
a
8
=
−u
u
3
+ u
a
5
=
−3.82090u
17
+ 7.35821u
16
+ ··· − 16.7164u + 0.955224
−6.23881u
17
+ 10.5224u
16
+ ··· − 4.04478u − 1.94030
a
7
=
9.05970u
17
− 16.8806u
16
+ ··· + 13.7612u + 1.98507
0.835821u
17
− 10.3284u
16
+ ··· + 8.65672u − 12.2090
a
6
=
9.05970u
17
− 16.8806u
16
+ ··· + 13.7612u + 1.98507
−4.20896u
17
− 1.41791u
16
+ ··· + 0.835821u − 13.4478
a
10
=
−u
16
+ 2u
15
+ ··· + 7u − 6
8.05970u
17
− 14.8806u
16
+ ··· + 7.76119u + 1.98507
a
3
=
−12.7910u
17
+ 26.4179u
16
+ ··· − 38.8358u + 0.447761
8.80597u
17
− 20.3881u
16
+ ··· + 17.7761u − 4.70149
a
2
=
−3.07463u
17
+ 10.8507u
16
+ ··· − 20.7015u + 9.26866
1.62687u
17
− 9.74627u
16
+ ··· + 6.49254u − 9.65672
(ii) Obstruction class = 1
(iii) Cusp Shapes =
3631
67
u
17
−
5066
67
u
16
+ ··· +
6179
67
u +
1789
67
21
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
18
− 6u
17
+ ··· − 13u + 1
c
2
, c
8
u
18
+ 2u
17
+ ··· + u + 1
c
3
(u
9
+ 3u
8
+ u
7
− 4u
6
− 5u
5
− 3u
4
+ u
3
+ 4u
2
+ 2u + 1)
2
c
4
, c
6
u
18
+ u
17
+ ··· + u + 1
c
5
, c
11
u
18
− 2u
17
+ ··· − u + 1
c
7
, c
9
u
18
− u
17
+ ··· − u + 1
c
10
(u
9
− 3u
8
+ u
7
+ 4u
6
− 5u
5
+ 3u
4
+ u
3
− 4u
2
+ 2u − 1)
2
c
12
u
18
+ 5u
16
+ ··· + 22u + 1
22
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
18
+ 6y
17
+ ··· − 15y + 1
c
2
, c
5
, c
8
c
11
y
18
+ 6y
17
+ ··· + 13y + 1
c
3
, c
10
(y
9
− 7y
8
+ 15y
7
− 6y
6
− 17y
5
+ 11y
4
+ 13y
3
− 6y
2
− 4y −1)
2
c
4
, c
6
, c
7
c
9
y
18
+ 15y
17
+ ··· + 11y + 1
c
12
y
18
+ 10y
17
+ ··· − 44y + 1
23
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
4
√
−1(vol +
√
−1CS) Cusp shape
u = 0.342912 + 0.833148I
a = 1.15322 + 2.05111I
b = 0.211261 − 0.513789I
1.30441 + 1.54301I 16.6608 − 7.1430I
u = 0.342912 − 0.833148I
a = 1.15322 − 2.05111I
b = 0.211261 + 0.513789I
1.30441 − 1.54301I 16.6608 + 7.1430I
u = −0.796545 + 0.768764I
a = −0.788205 − 0.913578I
b = 1.272940 + 0.355082I
−6.40959 − 2.04751I −2.57470 + 5.29814I
u = −0.796545 − 0.768764I
a = −0.788205 + 0.913578I
b = 1.272940 − 0.355082I
−6.40959 + 2.04751I −2.57470 − 5.29814I
u = 0.260259 + 1.085480I
a = −0.868381 + 0.394106I
b = −1.102310 + 0.083847I
−7.62664 + 3.85565I −5.05044 − 4.04682I
u = 0.260259 − 1.085480I
a = −0.868381 − 0.394106I
b = −1.102310 − 0.083847I
−7.62664 − 3.85565I −5.05044 + 4.04682I
u = 0.164659 + 0.798207I
a = 1.065200 − 0.773127I
b = 1.272940 + 0.355082I
−6.40959 − 2.04751I −2.57470 + 5.29814I
u = 0.164659 − 0.798207I
a = 1.065200 + 0.773127I
b = 1.272940 − 0.355082I
−6.40959 + 2.04751I −2.57470 − 5.29814I
u = −0.303814 + 0.709388I
a = 0.345523 − 1.282220I
b = 1.87686
−8.62045 1.96292 + 0.I
u = −0.303814 − 0.709388I
a = 0.345523 + 1.282220I
b = 1.87686
−8.62045 1.96292 + 0.I
24
Solutions to I
u
4
√
−1(vol +
√
−1CS) Cusp shape
u = 1.231780 + 0.251859I
a = −0.013021 + 0.389564I
b = 0.211261 − 0.513789I
1.30441 + 1.54301I 16.6608 − 7.1430I
u = 1.231780 − 0.251859I
a = −0.013021 − 0.389564I
b = 0.211261 + 0.513789I
1.30441 − 1.54301I 16.6608 + 7.1430I
u = −0.687312 + 1.135150I
a = 0.193398 + 1.026570I
b = −1.102310 − 0.083847I
−7.62664 − 3.85565I −5.05044 + 4.04682I
u = −0.687312 − 1.135150I
a = 0.193398 − 1.026570I
b = −1.102310 + 0.083847I
−7.62664 + 3.85565I −5.05044 − 4.04682I
u = 0.802633 + 1.107250I
a = 0.223663 + 0.630139I
b = 0.179684 − 0.881245I
−1.05223 + 5.01504I 9.48288 − 6.97143I
u = 0.802633 − 1.107250I
a = 0.223663 − 0.630139I
b = 0.179684 + 0.881245I
−1.05223 − 5.01504I 9.48288 + 6.97143I
u = −0.014569 + 0.625748I
a = −1.31140 − 3.11852I
b = 0.179684 + 0.881245I
−1.05223 − 5.01504I 9.48288 + 6.97143I
u = −0.014569 − 0.625748I
a = −1.31140 + 3.11852I
b = 0.179684 − 0.881245I
−1.05223 + 5.01504I 9.48288 − 6.97143I
25
V. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
(u
6
− 5u
5
+ ··· − 2u + 1)(u
18
− 6u
17
+ ··· − 13u + 1)
· (u
19
+ 9u
18
+ ··· + 3u − 1)(u
62
+ 21u
61
+ ··· + 490101u + 25921)
c
2
, c
8
(u
6
+ u
5
+ 3u
4
+ 2u
3
+ 3u
2
+ 2u + 1)(u
18
+ 2u
17
+ ··· + u + 1)
· (u
19
+ u
18
+ ··· + 3u − 1)(u
62
− u
61
+ ··· + 219u + 161)
c
3
(u
6
− 3u
5
+ 2u
4
+ u
2
− u + 1)
· (u
9
+ 3u
8
+ u
7
− 4u
6
− 5u
5
− 3u
4
+ u
3
+ 4u
2
+ 2u + 1)
2
· (u
19
− 6u
18
+ ··· + 138u − 20)(u
31
+ 3u
30
+ ··· + 8u
2
− 1)
2
c
4
, c
6
(u
6
+ u
5
+ 2u
4
+ 2u
3
+ u
2
+ u + 1)(u
18
+ u
17
+ ··· + u + 1)
· (u
19
− u
18
+ ··· − 2u − 1)(u
62
+ 4u
61
+ ··· + 189u + 29)
c
5
, c
11
(u
6
− u
5
+ 3u
4
− 2u
3
+ 3u
2
− 2u + 1)(u
18
− 2u
17
+ ··· − u + 1)
· (u
19
+ u
18
+ ··· + 3u − 1)(u
62
− u
61
+ ··· + 219u + 161)
c
7
, c
9
(u
6
− u
5
+ 2u
4
− 2u
3
+ u
2
− u + 1)(u
18
− u
17
+ ··· − u + 1)
· (u
19
− u
18
+ ··· − 2u − 1)(u
62
+ 4u
61
+ ··· + 189u + 29)
c
10
(u
6
+ 3u
5
+ 2u
4
+ u
2
+ u + 1)
· (u
9
− 3u
8
+ u
7
+ 4u
6
− 5u
5
+ 3u
4
+ u
3
− 4u
2
+ 2u − 1)
2
· (u
19
− 6u
18
+ ··· + 138u − 20)(u
31
+ 3u
30
+ ··· + 8u
2
− 1)
2
c
12
(u
6
− u
5
− 2u
4
+ 2u
2
+ 2u + 1)(u
18
+ 5u
16
+ ··· + 22u + 1)
· (u
19
+ 3u
18
+ ··· + 17u − 1)(u
62
+ 5u
61
+ ··· − 20878u + 5329)
26
VI. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
(y
6
− 3y
5
+ ··· + 10y + 1)(y
18
+ 6y
17
+ ··· − 15y + 1)
· (y
19
+ 9y
18
+ ··· + 83y −1)
· (y
62
+ 33y
61
+ ··· + 4781262113y + 671898241)
c
2
, c
5
, c
8
c
11
(y
6
+ 5y
5
+ ··· + 2y + 1)(y
18
+ 6y
17
+ ··· + 13y + 1)
· (y
19
+ 9y
18
+ ··· + 3y −1)(y
62
+ 21y
61
+ ··· + 490101y + 25921)
c
3
, c
10
(y
6
− 5y
5
+ 6y
4
+ 5y
2
+ y + 1)
· (y
9
− 7y
8
+ 15y
7
− 6y
6
− 17y
5
+ 11y
4
+ 13y
3
− 6y
2
− 4y −1)
2
· (y
19
− 6y
18
+ ··· + 3644y −400)(y
31
− 9y
30
+ ··· + 16y −1)
2
c
4
, c
6
, c
7
c
9
(y
6
+ 3y
5
+ 2y
4
+ y
2
+ y + 1)(y
18
+ 15y
17
+ ··· + 11y + 1)
· (y
19
+ 11y
18
+ ··· − 16y −1)(y
62
+ 18y
61
+ ··· + 44435y + 841)
c
12
(y
6
− 5y
5
+ 8y
4
− 2y
3
+ 1)(y
18
+ 10y
17
+ ··· − 44y + 1)
· (y
19
− 9y
18
+ ··· + 185y −1)
· (y
62
− 15y
61
+ ··· − 380852972y + 28398241)
27
