12a
0391
(K12a
0391
)
A knot diagram
1
Linearized knot diagam
3 6 9 11 2 10 12 4 1 5 7 8
Solving Sequence
2,5
6
3,10
7 11 12 1 4 9 8
c
5
c
2
c
6
c
10
c
11
c
1
c
4
c
9
c
8
c
3
, c
7
, c
12
Ideals for irreducible components
2
of X
par
I
u
1
= h544u
36
+ 6427u
35
+ ··· + 4b + 11548, 1863u
36
+ 20659u
35
+ ··· + 32a + 23056,
u
37
+ 13u
36
+ ··· + 416u + 32i
I
u
2
= h−1.94716 × 10
15
a
9
u
7
− 3.59875 × 10
15
a
8
u
7
+ ··· + 1.27159 × 10
14
a + 2.70520 × 10
14
,
2a
9
u
7
+ 21a
8
u
7
+ ··· − 2134a + 3278, u
8
− u
7
− u
6
+ 2u
5
+ u
4
− 2u
3
+ 2u − 1i
I
u
3
= h−2u
23
+ 2u
22
+ ··· + b − 1, −u
23
+ 2u
22
+ ··· + a − 4, u
24
− 2u
23
+ ··· − 2u + 1i
* 3 irreducible components of dim
C
= 0, with total 141 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
= h544u
36
+ 6427u
35
+ · · · + 4b + 11548, 1863u
36
+ 20659u
35
+ · · · +
32a + 23056, u
37
+ 13u
36
+ · · · + 416u + 32i
(i) Arc colorings
a
2
=
0
u
a
5
=
1
0
a
6
=
1
u
2
a
3
=
−u
−u
3
+ u
a
10
=
−58.2188u
36
− 645.594u
35
+ ··· − 9423u − 720.500
−136u
36
−
6427
4
u
35
+ ··· −
72311
2
u − 2887
a
7
=
205
32
u
36
+
2379
32
u
35
+ ··· + 9u − 19
−
11
16
u
36
−
301
16
u
35
+ ··· − 2628u − 225
a
11
=
77.7813u
36
+ 961.156u
35
+ ··· + 26732.5u + 2166.50
−136u
36
−
6427
4
u
35
+ ··· −
72311
2
u − 2887
a
12
=
−
479
8
u
36
− 599u
35
+ ··· + 11117u + 1067
−
851
8
u
36
−
5439
4
u
35
+ ··· − 50186u − 4130
a
1
=
u
3
u
5
− u
3
+ u
a
4
=
−
541
32
u
36
−
6235
32
u
35
+ ··· − 3157u − 243
−
27
16
u
36
−
509
16
u
35
+ ··· − 3043u − 257
a
9
=
−140.219u
36
− 1723.59u
35
+ ··· − 47943u − 3864.50
147
2
u
36
+ 771u
35
+ ··· −
13221
2
u − 687
a
8
=
30.2500u
36
+ 180.688u
35
+ ··· − 37250.8u − 3265.50
126.313u
36
+ 1576.19u
35
+ ··· + 47332.5u + 3836
(ii) Obstruction class = −1
(iii) Cusp Shapes = 51u
36
+ 733u
35
+ ··· + 41316u + 3454
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
37
+ 11u
36
+ ··· + 26112u + 1024
c
2
, c
5
u
37
+ 13u
36
+ ··· + 416u + 32
c
3
, c
4
, c
8
c
10
u
37
+ 11u
35
+ ··· + 4u + 1
c
6
, c
9
u
37
− u
36
+ ··· + 6u + 1
c
7
, c
11
, c
12
u
37
− 18u
36
+ ··· + 512u + 256
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
37
+ 17y
36
+ ··· + 387842048y −1048576
c
2
, c
5
y
37
− 11y
36
+ ··· + 26112y −1024
c
3
, c
4
, c
8
c
10
y
37
+ 22y
36
+ ··· + 8y −1
c
6
, c
9
y
37
− 9y
36
+ ··· + 10y −1
c
7
, c
11
, c
12
y
37
− 32y
36
+ ··· + 720896y −65536
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.957322 + 0.313722I
a = −1.37747 + 0.35388I
b = −0.371748 − 0.629257I
−2.42925 − 1.37778I −15.2263 + 4.5212I
u = 0.957322 − 0.313722I
a = −1.37747 − 0.35388I
b = −0.371748 + 0.629257I
−2.42925 + 1.37778I −15.2263 − 4.5212I
u = −0.212937 + 1.010140I
a = 0.105717 + 0.341356I
b = 0.417230 − 1.057270I
0.06787 + 6.99887I −9.49176 − 9.04622I
u = −0.212937 − 1.010140I
a = 0.105717 − 0.341356I
b = 0.417230 + 1.057270I
0.06787 − 6.99887I −9.49176 + 9.04622I
u = −0.808608 + 0.468821I
a = 0.794637 + 0.373997I
b = 0.652472 + 0.162568I
−0.382992 + 0.607426I −13.17243 + 1.65752I
u = −0.808608 − 0.468821I
a = 0.794637 − 0.373997I
b = 0.652472 − 0.162568I
−0.382992 − 0.607426I −13.17243 − 1.65752I
u = 0.930819 + 0.078146I
a = 2.43124 − 0.30243I
b = 0.561271 + 0.218932I
−10.40420 − 0.06262I −27.5972 + 8.6345I
u = 0.930819 − 0.078146I
a = 2.43124 + 0.30243I
b = 0.561271 − 0.218932I
−10.40420 + 0.06262I −27.5972 − 8.6345I
u = −0.926437 + 0.557113I
a = −1.031580 − 0.740190I
b = −0.770583 − 0.153074I
−0.87598 + 3.63195I −14.6770 − 6.3220I
u = −0.926437 − 0.557113I
a = −1.031580 + 0.740190I
b = −0.770583 + 0.153074I
−0.87598 − 3.63195I −14.6770 + 6.3220I
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.614591 + 0.927505I
a = 0.101554 − 0.338395I
b = 0.59999 + 1.38292I
2.35753 − 12.00730I −10.01703 + 5.56781I
u = −0.614591 − 0.927505I
a = 0.101554 + 0.338395I
b = 0.59999 − 1.38292I
2.35753 + 12.00730I −10.01703 − 5.56781I
u = −0.630557 + 0.967163I
a = −0.048373 + 0.373479I
b = −0.405525 − 1.330510I
8.47416 − 7.17337I 0
u = −0.630557 − 0.967163I
a = −0.048373 − 0.373479I
b = −0.405525 + 1.330510I
8.47416 + 7.17337I 0
u = −0.990193 + 0.597141I
a = 1.12308 + 1.13131I
b = 0.981847 + 0.092937I
−7.29602 + 5.47264I −18.3738 + 0.I
u = −0.990193 − 0.597141I
a = 1.12308 − 1.13131I
b = 0.981847 − 0.092937I
−7.29602 − 5.47264I −18.3738 + 0.I
u = −0.536542 + 0.602236I
a = −0.573017 − 0.130584I
b = −0.886654 + 0.014064I
−6.05184 − 0.72046I −16.3757 − 0.2379I
u = −0.536542 − 0.602236I
a = −0.573017 + 0.130584I
b = −0.886654 − 0.014064I
−6.05184 + 0.72046I −16.3757 + 0.2379I
u = 1.221810 + 0.174233I
a = −1.37712 − 0.86239I
b = −0.670944 − 1.153860I
−5.18126 − 10.69840I 0
u = 1.221810 − 0.174233I
a = −1.37712 + 0.86239I
b = −0.670944 + 1.153860I
−5.18126 + 10.69840I 0
6
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.215278 + 1.228850I
a = 0.054876 − 0.356628I
b = −0.149731 + 0.905170I
4.52184 + 0.80776I 0
u = 0.215278 − 1.228850I
a = 0.054876 + 0.356628I
b = −0.149731 − 0.905170I
4.52184 − 0.80776I 0
u = −0.694901 + 1.046620I
a = −0.055254 − 0.424345I
b = 0.200354 + 1.178170I
7.14912 − 0.88155I 0
u = −0.694901 − 1.046620I
a = −0.055254 + 0.424345I
b = 0.200354 − 1.178170I
7.14912 + 0.88155I 0
u = 1.226760 + 0.280486I
a = 1.109360 + 0.476558I
b = 0.460985 + 1.013230I
0.19290 − 5.94150I 0
u = 1.226760 − 0.280486I
a = 1.109360 − 0.476558I
b = 0.460985 − 1.013230I
0.19290 + 5.94150I 0
u = −1.257750 + 0.369372I
a = 0.003296 − 0.634264I
b = −0.379654 − 0.721501I
−3.74392 − 1.77689I 0
u = −1.257750 − 0.369372I
a = 0.003296 + 0.634264I
b = −0.379654 + 0.721501I
−3.74392 + 1.77689I 0
u = −1.087090 + 0.734376I
a = −1.92634 − 0.43812I
b = −0.66863 + 1.42209I
0.8899 + 18.1180I 0
u = −1.087090 − 0.734376I
a = −1.92634 + 0.43812I
b = −0.66863 − 1.42209I
0.8899 − 18.1180I 0
7
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −1.095130 + 0.752809I
a = 1.70277 + 0.33196I
b = 0.48754 − 1.36862I
7.0104 + 13.4550I 0
u = −1.095130 − 0.752809I
a = 1.70277 − 0.33196I
b = 0.48754 + 1.36862I
7.0104 − 13.4550I 0
u = −0.983113 + 0.905356I
a = 0.658309 + 0.731201I
b = 0.068498 − 0.917485I
−3.94428 + 3.41322I 0
u = −0.983113 − 0.905356I
a = 0.658309 − 0.731201I
b = 0.068498 + 0.917485I
−3.94428 − 3.41322I 0
u = −1.100530 + 0.794275I
a = −1.344770 − 0.325865I
b = −0.298478 + 1.225560I
5.79816 + 7.52421I 0
u = −1.100530 − 0.794275I
a = −1.344770 + 0.325865I
b = −0.298478 − 1.225560I
5.79816 − 7.52421I 0
u = −0.227221
a = 1.29817
b = 0.343523
−0.528764 −18.5960
8
II. I
u
2
= h−1.95 × 10
15
a
9
u
7
− 3.60 × 10
15
a
8
u
7
+ · · · + 1.27 × 10
14
a + 2.71 ×
10
14
, 2a
9
u
7
+21a
8
u
7
+· · ·−2134a+3278, u
8
−u
7
−u
6
+2u
5
+u
4
−2u
3
+2u−1i
(i) Arc colorings
a
2
=
0
u
a
5
=
1
0
a
6
=
1
u
2
a
3
=
−u
−u
3
+ u
a
10
=
a
11.1056a
9
u
7
+ 20.5255a
8
u
7
+ ··· − 0.725251a − 1.54291
a
7
=
3.98131a
9
u
7
− 2.65272a
8
u
7
+ ··· − 0.325728a − 0.746886
1.02326a
2
u
7
− 0.511628u
7
+ ··· + 0.139535a
2
− 1.06977
a
11
=
−11.1056a
9
u
7
− 20.5255a
8
u
7
+ ··· + 1.72525a + 1.54291
11.1056a
9
u
7
+ 20.5255a
8
u
7
+ ··· − 0.725251a − 1.54291
a
12
=
−20.1671a
9
u
7
− 27.8400a
8
u
7
+ ··· + 1.73758a − 0.272610
11.1859a
9
u
7
+ 29.1048a
8
u
7
+ ··· − 0.552681a + 1.07179
a
1
=
u
3
u
5
− u
3
+ u
a
4
=
−1.02730a
9
u
7
+ 3.91889a
8
u
7
+ ··· + 0.758648a + 1.50660
−2.95401a
9
u
7
− 1.26617a
8
u
7
+ ··· − 0.432919a + 1.24029
a
9
=
−0.906309a
9
u
7
+ 1.79884a
8
u
7
+ ··· + 2.18676a + 1.25107
9.35107a
9
u
7
+ 13.2623a
8
u
7
+ ··· + 0.466900a − 1.73564
a
8
=
−8.72539a
9
u
7
− 15.3608a
8
u
7
+ ··· + 1.00957a − 1.08501
2.09106a
9
u
7
+ 10.0259a
8
u
7
+ ··· + 0.977705a − 0.181873
(ii) Obstruction class = −1
(iii) Cusp Shapes
= −
3312696866563328
175330710141469
a
9
u
7
−
10860915930820932
175330710141469
a
8
u
7
+ ···−
524784750398904
175330710141469
a −
3778793332341578
175330710141469
9
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
(u
8
+ 3u
7
+ 7u
6
+ 10u
5
+ 11u
4
+ 10u
3
+ 6u
2
+ 4u + 1)
10
c
2
, c
5
(u
8
− u
7
− u
6
+ 2u
5
+ u
4
− 2u
3
+ 2u − 1)
10
c
3
, c
4
, c
8
c
10
u
80
− u
79
+ ··· + 3548u + 1579
c
6
, c
9
u
80
+ 9u
79
+ ··· + 6422u + 569
c
7
, c
11
, c
12
(u
5
+ u
4
− 2u
3
− u
2
+ u − 1)
16
10
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
(y
8
+ 5y
7
+ 11y
6
+ 6y
5
− 17y
4
− 34y
3
− 22y
2
− 4y + 1)
10
c
2
, c
5
(y
8
− 3y
7
+ 7y
6
− 10y
5
+ 11y
4
− 10y
3
+ 6y
2
− 4y + 1)
10
c
3
, c
4
, c
8
c
10
y
80
+ 63y
79
+ ··· + 269522152y + 2493241
c
6
, c
9
y
80
+ 27y
79
+ ··· + 120888776y + 323761
c
7
, c
11
, c
12
(y
5
− 5y
4
+ 8y
3
− 3y
2
− y −1)
16
11
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.570868 + 0.730671I
a = 0.317717 − 0.891415I
b = 1.305780 − 0.021800I
−1.97842 + 5.53207I −12.15954 − 4.00938I
u = 0.570868 + 0.730671I
a = −0.372527 + 0.813712I
b = 0.473970 − 0.367837I
−1.97842 − 3.26960I −12.15954 + 2.98779I
u = 0.570868 + 0.730671I
a = −0.472750 − 0.641845I
b = −0.445650 + 1.315720I
−1.97842 + 5.53207I −12.15954 − 4.00938I
u = 0.570868 + 0.730671I
a = 0.453598 − 0.633400I
b = 0.0442048 − 0.1093490I
3.56505 − 0.39935I −7.93034 + 3.91986I
u = 0.570868 + 0.730671I
a = −0.242021 + 0.721707I
b = −0.914022 + 0.321383I
3.56505 + 2.66181I −7.93034 − 4.94144I
u = 0.570868 + 0.730671I
a = −0.701722 + 0.223215I
b = 0.118471 + 0.985556I
1.49307 + 1.13123I −8.89637 − 0.51079I
u = 0.570868 + 0.730671I
a = −0.529151 + 0.436048I
b = −0.258551 − 1.170880I
−1.97842 − 3.26960I −12.15954 + 2.98779I
u = 0.570868 + 0.730671I
a = 0.379390 + 0.337276I
b = 0.292944 − 1.200800I
3.56505 + 2.66181I −7.93034 − 4.94144I
u = 0.570868 + 0.730671I
a = −0.187370 − 0.461746I
b = 0.78647 − 1.19152I
1.49307 + 1.13123I −8.89637 − 0.51079I
u = 0.570868 + 0.730671I
a = 0.195391 − 0.214615I
b = −0.223507 + 1.170930I
3.56505 − 0.39935I −7.93034 + 3.91986I
12
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.570868 − 0.730671I
a = 0.317717 + 0.891415I
b = 1.305780 + 0.021800I
−1.97842 − 5.53207I −12.15954 + 4.00938I
u = 0.570868 − 0.730671I
a = −0.372527 − 0.813712I
b = 0.473970 + 0.367837I
−1.97842 + 3.26960I −12.15954 − 2.98779I
u = 0.570868 − 0.730671I
a = −0.472750 + 0.641845I
b = −0.445650 − 1.315720I
−1.97842 − 5.53207I −12.15954 + 4.00938I
u = 0.570868 − 0.730671I
a = 0.453598 + 0.633400I
b = 0.0442048 + 0.1093490I
3.56505 + 0.39935I −7.93034 − 3.91986I
u = 0.570868 − 0.730671I
a = −0.242021 − 0.721707I
b = −0.914022 − 0.321383I
3.56505 − 2.66181I −7.93034 + 4.94144I
u = 0.570868 − 0.730671I
a = −0.701722 − 0.223215I
b = 0.118471 − 0.985556I
1.49307 − 1.13123I −8.89637 + 0.51079I
u = 0.570868 − 0.730671I
a = −0.529151 − 0.436048I
b = −0.258551 + 1.170880I
−1.97842 + 3.26960I −12.15954 − 2.98779I
u = 0.570868 − 0.730671I
a = 0.379390 − 0.337276I
b = 0.292944 + 1.200800I
3.56505 − 2.66181I −7.93034 + 4.94144I
u = 0.570868 − 0.730671I
a = −0.187370 + 0.461746I
b = 0.78647 + 1.19152I
1.49307 − 1.13123I −8.89637 + 0.51079I
u = 0.570868 − 0.730671I
a = 0.195391 + 0.214615I
b = −0.223507 − 1.170930I
3.56505 + 0.39935I −7.93034 − 3.91986I
13
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.855237 + 0.665892I
a = 0.184288 + 1.123720I
b = −0.049819 − 1.318620I
6.76512 + 4.10907I −4.79219 − 7.99861I
u = −0.855237 + 0.665892I
a = −0.000369 − 0.558136I
b = −0.89941 − 1.42516I
1.22165 − 1.82234I −9.02139 − 0.06937I
u = −0.855237 + 0.665892I
a = 0.55671 − 1.37754I
b = −0.094640 + 1.087870I
1.22165 + 6.97933I −9.02139 − 7.06654I
u = −0.855237 + 0.665892I
a = −0.461095 + 0.026790I
b = 0.46574 + 1.57218I
6.76512 + 1.04791I −4.79219 + 0.86269I
u = −0.855237 + 0.665892I
a = 1.67042 − 0.02563I
b = 0.09310 − 2.08054I
4.69313 + 2.57849I −5.75822 − 3.56796I
u = −0.855237 + 0.665892I
a = −2.07727 − 0.57527I
b = −0.60157 + 1.48322I
6.76512 + 4.10907I −4.79219 − 7.99861I
u = −0.855237 + 0.665892I
a = −1.48542 − 1.66320I
b = −0.01022 + 1.50733I
4.69313 + 2.57849I −5.75822 − 3.56796I
u = −0.855237 + 0.665892I
a = 2.19641 + 0.66346I
b = 1.04102 − 1.29878I
1.22165 + 6.97933I −9.02139 − 7.06654I
u = −0.855237 + 0.665892I
a = 2.19046 + 0.91845I
b = 0.112336 − 1.229800I
6.76512 + 1.04791I −4.79219 + 0.86269I
u = −0.855237 + 0.665892I
a = −2.53287 − 0.73501I
b = 0.051544 + 0.954798I
1.22165 − 1.82234I −9.02139 − 0.06937I
14
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.855237 − 0.665892I
a = 0.184288 − 1.123720I
b = −0.049819 + 1.318620I
6.76512 − 4.10907I −4.79219 + 7.99861I
u = −0.855237 − 0.665892I
a = −0.000369 + 0.558136I
b = −0.89941 + 1.42516I
1.22165 + 1.82234I −9.02139 + 0.06937I
u = −0.855237 − 0.665892I
a = 0.55671 + 1.37754I
b = −0.094640 − 1.087870I
1.22165 − 6.97933I −9.02139 + 7.06654I
u = −0.855237 − 0.665892I
a = −0.461095 − 0.026790I
b = 0.46574 − 1.57218I
6.76512 − 1.04791I −4.79219 − 0.86269I
u = −0.855237 − 0.665892I
a = 1.67042 + 0.02563I
b = 0.09310 + 2.08054I
4.69313 − 2.57849I −5.75822 + 3.56796I
u = −0.855237 − 0.665892I
a = −2.07727 + 0.57527I
b = −0.60157 − 1.48322I
6.76512 − 4.10907I −4.79219 + 7.99861I
u = −0.855237 − 0.665892I
a = −1.48542 + 1.66320I
b = −0.01022 − 1.50733I
4.69313 − 2.57849I −5.75822 + 3.56796I
u = −0.855237 − 0.665892I
a = 2.19641 − 0.66346I
b = 1.04102 + 1.29878I
1.22165 − 6.97933I −9.02139 + 7.06654I
u = −0.855237 − 0.665892I
a = 2.19046 − 0.91845I
b = 0.112336 + 1.229800I
6.76512 − 1.04791I −4.79219 − 0.86269I
u = −0.855237 − 0.665892I
a = −2.53287 + 0.73501I
b = 0.051544 − 0.954798I
1.22165 + 1.82234I −9.02139 + 0.06937I
15
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −1.09818
a = 1.213950 + 0.060472I
b = 0.743281 − 0.274344I
−1.89703 − 1.53058I −14.3792 + 4.4306I
u = −1.09818
a = 1.213950 − 0.060472I
b = 0.743281 + 0.274344I
−1.89703 + 1.53058I −14.3792 − 4.4306I
u = −1.09818
a = −0.794603 + 1.077430I
b = −0.278360 + 0.853134I
−1.89703 + 1.53058I −14.3792 − 4.4306I
u = −1.09818
a = −0.794603 − 1.077430I
b = −0.278360 − 0.853134I
−1.89703 − 1.53058I −14.3792 + 4.4306I
u = −1.09818
a = −0.474135 + 1.292280I
b = −0.525660 + 0.657310I
−3.96901 −15.3452 + 0.I
u = −1.09818
a = −0.474135 − 1.292280I
b = −0.525660 − 0.657310I
−3.96901 −15.3452 + 0.I
u = −1.09818
a = −1.87939 + 0.04068I
b = −1.125010 + 0.465951I
−7.44049 − 4.40083I −18.6084 + 3.4986I
u = −1.09818
a = −1.87939 − 0.04068I
b = −1.125010 − 0.465951I
−7.44049 + 4.40083I −18.6084 − 3.4986I
u = −1.09818
a = 1.31587 + 1.44345I
b = 0.500246 + 1.179460I
−7.44049 − 4.40083I −18.6084 + 3.4986I
u = −1.09818
a = 1.31587 − 1.44345I
b = 0.500246 − 1.179460I
−7.44049 + 4.40083I −18.6084 − 3.4986I
16
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 1.031810 + 0.655470I
a = −0.999846 + 0.759611I
b = −0.518695 − 0.817196I
−3.31744 − 2.04270I −14.1728 + 1.7956I
u = 1.031810 + 0.655470I
a = 1.117550 − 0.688666I
b = 1.127550 + 0.190536I
2.22602 − 7.97412I −9.94356 + 9.72482I
u = 1.031810 + 0.655470I
a = −0.452863 − 0.411616I
b = 0.293319 − 0.929775I
−3.31744 − 2.04270I −14.1728 + 1.7956I
u = 1.031810 + 0.655470I
a = −0.523882 − 0.058026I
b = −0.298543 + 0.084388I
2.22602 − 4.91296I −9.94356 + 0.86352I
u = 1.031810 + 0.655470I
a = −1.00804 + 1.15213I
b = −1.49599 + 0.11672I
−3.31744 − 10.84440I −14.1728 + 8.7928I
u = 1.031810 + 0.655470I
a = 1.52330 − 0.21142I
b = 0.488814 + 1.121250I
2.22602 − 4.91296I −9.94356 + 0.86352I
u = 1.031810 + 0.655470I
a = 1.64924 + 0.59159I
b = −0.002912 + 0.837279I
0.15404 − 6.44354I −10.90959 + 5.29417I
u = 1.031810 + 0.655470I
a = −1.76293 + 0.29343I
b = −1.02044 − 1.08184I
0.15404 − 6.44354I −10.90959 + 5.29417I
u = 1.031810 + 0.655470I
a = −2.01641 + 0.17535I
b = −0.412717 − 1.179870I
2.22602 − 7.97412I −9.94356 + 9.72482I
u = 1.031810 + 0.655470I
a = 2.32562 − 0.44824I
b = 0.50508 + 1.33958I
−3.31744 − 10.84440I −14.1728 + 8.7928I
17
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 1.031810 − 0.655470I
a = −0.999846 − 0.759611I
b = −0.518695 + 0.817196I
−3.31744 + 2.04270I −14.1728 − 1.7956I
u = 1.031810 − 0.655470I
a = 1.117550 + 0.688666I
b = 1.127550 − 0.190536I
2.22602 + 7.97412I −9.94356 − 9.72482I
u = 1.031810 − 0.655470I
a = −0.452863 + 0.411616I
b = 0.293319 + 0.929775I
−3.31744 + 2.04270I −14.1728 − 1.7956I
u = 1.031810 − 0.655470I
a = −0.523882 + 0.058026I
b = −0.298543 − 0.084388I
2.22602 + 4.91296I −9.94356 − 0.86352I
u = 1.031810 − 0.655470I
a = −1.00804 − 1.15213I
b = −1.49599 − 0.11672I
−3.31744 + 10.84440I −14.1728 − 8.7928I
u = 1.031810 − 0.655470I
a = 1.52330 + 0.21142I
b = 0.488814 − 1.121250I
2.22602 + 4.91296I −9.94356 − 0.86352I
u = 1.031810 − 0.655470I
a = 1.64924 − 0.59159I
b = −0.002912 − 0.837279I
0.15404 + 6.44354I −10.90959 − 5.29417I
u = 1.031810 − 0.655470I
a = −1.76293 − 0.29343I
b = −1.02044 + 1.08184I
0.15404 + 6.44354I −10.90959 − 5.29417I
u = 1.031810 − 0.655470I
a = −2.01641 − 0.17535I
b = −0.412717 + 1.179870I
2.22602 + 7.97412I −9.94356 − 9.72482I
u = 1.031810 − 0.655470I
a = 2.32562 + 0.44824I
b = 0.50508 − 1.33958I
−3.31744 + 10.84440I −14.1728 − 8.7928I
18
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.603304
a = 0.955688 + 0.192007I
b = 0.152198 + 1.333960I
3.76067 − 1.53058I −12.40958 + 4.43065I
u = 0.603304
a = 0.955688 − 0.192007I
b = 0.152198 − 1.333960I
3.76067 + 1.53058I −12.40958 − 4.43065I
u = 0.603304
a = −1.62568 + 0.77113I
b = −0.436213 − 1.233300I
−1.78280 − 4.40083I −16.6388 + 3.4986I
u = 0.603304
a = −1.62568 − 0.77113I
b = −0.436213 + 1.233300I
−1.78280 + 4.40083I −16.6388 − 3.4986I
u = 0.603304
a = −1.39197 + 2.25490I
b = 0.17777 + 1.53018I
1.68869 −13.37561 + 0.I
u = 0.603304
a = −1.39197 − 2.25490I
b = 0.17777 − 1.53018I
1.68869 −13.37561 + 0.I
u = 0.603304
a = 0.27544 + 3.17761I
b = −0.309423 + 0.952672I
3.76067 + 1.53058I −12.40958 − 4.43065I
u = 0.603304
a = 0.27544 − 3.17761I
b = −0.309423 − 0.952672I
3.76067 − 1.53058I −12.40958 + 4.43065I
u = 0.603304
a = −0.02871 + 3.58598I
b = 0.647493 + 0.676864I
−1.78280 − 4.40083I −16.6388 + 3.4986I
u = 0.603304
a = −0.02871 − 3.58598I
b = 0.647493 − 0.676864I
−1.78280 + 4.40083I −16.6388 − 3.4986I
19
III.
I
u
3
= h−2u
23
+2u
22
+· · ·+b−1, −u
23
+2u
22
+· · ·+a−4, u
24
−2u
23
+· · ·−2u+1i
(i) Arc colorings
a
2
=
0
u
a
5
=
1
0
a
6
=
1
u
2
a
3
=
−u
−u
3
+ u
a
10
=
u
23
− 2u
22
+ ··· − 3u + 4
2u
23
− 2u
22
+ ··· + 3u + 1
a
7
=
−4u
23
+ 7u
22
+ ··· + 3u − 1
−2u
23
+ 2u
22
+ ··· − 3u + 1
a
11
=
−u
23
+ 6u
21
+ ··· − 6u + 3
2u
23
− 2u
22
+ ··· + 3u + 1
a
12
=
−u
23
+ 5u
22
+ ··· + 5u + 1
3u
23
− 2u
22
+ ··· + 2u + 2
a
1
=
u
3
u
5
− u
3
+ u
a
4
=
−u
20
+ u
19
+ ··· + 3u + 1
−u
22
+ 4u
20
+ ··· + 4u
2
+ u
a
9
=
u
23
− 3u
21
+ ··· − u + 4
u
23
− u
22
+ ··· + 4u − 1
a
8
=
2u
23
− 4u
22
+ ··· + 2u
2
− 2u
−2u
23
+ 3u
22
+ ··· − 3u
2
− 3u
(ii) Obstruction class = 1
(iii) Cusp Shapes = 22u
23
− 38u
22
− 42u
21
+ 159u
20
+ 11u
19
− 320u
18
+ 155u
17
+
435u
16
− 413u
15
− 315u
14
+ 694u
13
− 11u
12
− 699u
11
+ 324u
10
+ 595u
9
− 454u
8
−
311u
7
+ 354u
6
+ 145u
5
− 165u
4
− 58u
3
+ 75u
2
+ 2u − 16
20
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
24
− 8u
23
+ ··· − 8u + 1
c
2
u
24
+ 2u
23
+ ··· + 2u + 1
c
3
, c
10
u
24
+ 13u
22
+ ··· − u − 1
c
4
, c
8
u
24
+ 13u
22
+ ··· + u − 1
c
5
u
24
− 2u
23
+ ··· − 2u + 1
c
6
, c
9
u
24
− u
23
+ ··· + 9u − 3
c
7
u
24
− u
23
+ ··· − u − 1
c
11
, c
12
u
24
+ u
23
+ ··· + u − 1
21
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
24
+ 12y
23
+ ··· + 16y + 1
c
2
, c
5
y
24
− 8y
23
+ ··· − 8y + 1
c
3
, c
4
, c
8
c
10
y
24
+ 26y
23
+ ··· − 21y + 1
c
6
, c
9
y
24
+ 3y
23
+ ··· + 69y + 9
c
7
, c
11
, c
12
y
24
− 27y
23
+ ··· − 9y + 1
22
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = −0.859104 + 0.619061I
a = −1.77700 − 0.81550I
b = −0.05224 + 1.79614I
3.64574 + 2.43004I −15.3160 − 2.5325I
u = −0.859104 − 0.619061I
a = −1.77700 + 0.81550I
b = −0.05224 − 1.79614I
3.64574 − 2.43004I −15.3160 + 2.5325I
u = −0.921806
a = −1.13142
b = −0.238208
−2.48108 −16.6080
u = 0.274672 + 1.053350I
a = −0.186811 + 0.192436I
b = 0.163662 − 0.961355I
4.89050 + 0.67182I −0.331093 − 0.291966I
u = 0.274672 − 1.053350I
a = −0.186811 − 0.192436I
b = 0.163662 + 0.961355I
4.89050 − 0.67182I −0.331093 + 0.291966I
u = −0.847989 + 0.693024I
a = 1.23905 + 0.72068I
b = 0.06183 − 1.51814I
6.81902 + 2.66285I −3.87424 − 2.89541I
u = −0.847989 − 0.693024I
a = 1.23905 − 0.72068I
b = 0.06183 + 1.51814I
6.81902 − 2.66285I −3.87424 + 2.89541I
u = 0.694510 + 0.572688I
a = −0.830889 + 1.076290I
b = −0.698566 + 1.033420I
−0.25743 + 3.41207I −11.71453 − 2.05195I
u = 0.694510 − 0.572688I
a = −0.830889 − 1.076290I
b = −0.698566 − 1.033420I
−0.25743 − 3.41207I −11.71453 + 2.05195I
u = 0.998881 + 0.595015I
a = 1.82392 + 0.25160I
b = 0.776391 + 0.880199I
−1.25649 − 8.10140I −14.1033 + 8.4780I
23
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = 0.998881 − 0.595015I
a = 1.82392 − 0.25160I
b = 0.776391 − 0.880199I
−1.25649 + 8.10140I −14.1033 − 8.4780I
u = −0.829372
a = 2.78344
b = 0.236926
−10.1589 5.82770
u = 0.772444 + 0.266120I
a = 0.21598 + 1.86268I
b = −0.13292 + 1.53643I
1.73546 − 1.04679I −12.7704 + 7.1412I
u = 0.772444 − 0.266120I
a = 0.21598 − 1.86268I
b = −0.13292 − 1.53643I
1.73546 + 1.04679I −12.7704 − 7.1412I
u = −1.196510 + 0.259459I
a = −0.231267 + 0.835819I
b = 0.318802 + 0.654164I
−3.32815 − 1.41217I −8.36483 + 0.95661I
u = −1.196510 − 0.259459I
a = −0.231267 − 0.835819I
b = 0.318802 − 0.654164I
−3.32815 + 1.41217I −8.36483 − 0.95661I
u = −0.535643 + 0.545861I
a = −0.12086 − 1.74579I
b = −0.401964 + 1.059050I
−0.55694 + 5.07983I −9.81409 − 5.66090I
u = −0.535643 − 0.545861I
a = −0.12086 + 1.74579I
b = −0.401964 − 1.059050I
−0.55694 − 5.07983I −9.81409 + 5.66090I
u = 1.069460 + 0.653928I
a = −1.328700 − 0.042768I
b = −0.478932 − 0.857563I
2.77511 − 6.09098I −6.24923 + 6.46782I
u = 1.069460 − 0.653928I
a = −1.328700 + 0.042768I
b = −0.478932 + 0.857563I
2.77511 + 6.09098I −6.24923 − 6.46782I
24
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = 0.510957 + 0.450721I
a = −0.220431 − 1.219110I
b = 0.326073 − 1.173880I
4.69210 + 1.06045I −2.95845 − 0.15547I
u = 0.510957 − 0.450721I
a = −0.220431 + 1.219110I
b = 0.326073 + 1.173880I
4.69210 − 1.06045I −2.95845 + 0.15547I
u = 0.993906 + 0.876026I
a = 0.591000 − 0.624229I
b = 0.118504 + 0.699899I
−4.61425 − 3.36496I −21.1138 + 3.8610I
u = 0.993906 − 0.876026I
a = 0.591000 + 0.624229I
b = 0.118504 − 0.699899I
−4.61425 + 3.36496I −21.1138 − 3.8610I
25
IV. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
(u
8
+ 3u
7
+ 7u
6
+ 10u
5
+ 11u
4
+ 10u
3
+ 6u
2
+ 4u + 1)
10
· (u
24
− 8u
23
+ ··· − 8u + 1)(u
37
+ 11u
36
+ ··· + 26112u + 1024)
c
2
((u
8
− u
7
+ ··· + 2u − 1)
10
)(u
24
+ 2u
23
+ ··· + 2u + 1)
· (u
37
+ 13u
36
+ ··· + 416u + 32)
c
3
, c
10
(u
24
+ 13u
22
+ ··· − u − 1)(u
37
+ 11u
35
+ ··· + 4u + 1)
· (u
80
− u
79
+ ··· + 3548u + 1579)
c
4
, c
8
(u
24
+ 13u
22
+ ··· + u − 1)(u
37
+ 11u
35
+ ··· + 4u + 1)
· (u
80
− u
79
+ ··· + 3548u + 1579)
c
5
((u
8
− u
7
+ ··· + 2u − 1)
10
)(u
24
− 2u
23
+ ··· − 2u + 1)
· (u
37
+ 13u
36
+ ··· + 416u + 32)
c
6
, c
9
(u
24
− u
23
+ ··· + 9u − 3)(u
37
− u
36
+ ··· + 6u + 1)
· (u
80
+ 9u
79
+ ··· + 6422u + 569)
c
7
((u
5
+ u
4
− 2u
3
− u
2
+ u − 1)
16
)(u
24
− u
23
+ ··· − u − 1)
· (u
37
− 18u
36
+ ··· + 512u + 256)
c
11
, c
12
((u
5
+ u
4
− 2u
3
− u
2
+ u − 1)
16
)(u
24
+ u
23
+ ··· + u − 1)
· (u
37
− 18u
36
+ ··· + 512u + 256)
26
V. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
(y
8
+ 5y
7
+ 11y
6
+ 6y
5
− 17y
4
− 34y
3
− 22y
2
− 4y + 1)
10
· (y
24
+ 12y
23
+ ··· + 16y + 1)
· (y
37
+ 17y
36
+ ··· + 387842048y −1048576)
c
2
, c
5
(y
8
− 3y
7
+ 7y
6
− 10y
5
+ 11y
4
− 10y
3
+ 6y
2
− 4y + 1)
10
· (y
24
− 8y
23
+ ··· − 8y + 1)(y
37
− 11y
36
+ ··· + 26112y −1024)
c
3
, c
4
, c
8
c
10
(y
24
+ 26y
23
+ ··· − 21y + 1)(y
37
+ 22y
36
+ ··· + 8y −1)
· (y
80
+ 63y
79
+ ··· + 269522152y + 2493241)
c
6
, c
9
(y
24
+ 3y
23
+ ··· + 69y + 9)(y
37
− 9y
36
+ ··· + 10y −1)
· (y
80
+ 27y
79
+ ··· + 120888776y + 323761)
c
7
, c
11
, c
12
((y
5
− 5y
4
+ 8y
3
− 3y
2
− y −1)
16
)(y
24
− 27y
23
+ ··· − 9y + 1)
· (y
37
− 32y
36
+ ··· + 720896y −65536)
27
