12a
0411
(K12a
0411
)
A knot diagram
1
Linearized knot diagam
3 6 9 12 2 10 11 1 5 7 8 4
Solving Sequence
6,10
7 11 8
3,12
2 1 5 4 9
c
6
c
10
c
7
c
11
c
2
c
1
c
5
c
4
c
9
c
3
, c
8
, c
12
Ideals for irreducible components
2
of X
par
I
u
1
= h−6.05318 × 10
105
u
79
− 2.71139 × 10
106
u
78
+ ··· + 6.14360 × 10
104
b + 1.09875 × 10
106
,
1.04172 × 10
107
u
79
+ 4.58247 × 10
107
u
78
+ ··· + 3.07180 × 10
104
a − 1.70407 × 10
107
, u
80
+ 5u
79
+ ··· − 6u − 1i
I
u
2
= ha
2
+ 6b + 4a + 4, a
4
+ 2a
3
+ 6a
2
− 4a + 4, u + 1i
* 2 irreducible components of dim
C
= 0, with total 84 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−6.05 × 10
105
u
79
− 2.71 × 10
106
u
78
+ · · · + 6.14 × 10
104
b + 1.10 ×
10
106
, 1.04 × 10
107
u
79
+ 4.58 × 10
107
u
78
+ · · · + 3.07 × 10
104
a − 1.70 ×
10
107
, u
80
+ 5u
79
+ · · · − 6u − 1i
(i) Arc colorings
a
6
=
1
0
a
10
=
0
u
a
7
=
1
−u
2
a
11
=
u
−u
3
+ u
a
8
=
−u
2
+ 1
u
4
− 2u
2
a
3
=
−339.123u
79
− 1491.79u
78
+ ··· + 2436.78u + 554.746
9.85281u
79
+ 44.1335u
78
+ ··· − 72.3996u − 17.8844
a
12
=
−u
3
+ 2u
u
5
− 3u
3
+ u
a
2
=
−329.270u
79
− 1447.65u
78
+ ··· + 2364.38u + 536.861
9.85281u
79
+ 44.1335u
78
+ ··· − 72.3996u − 17.8844
a
1
=
−405.884u
79
− 1783.77u
78
+ ··· + 2936.77u + 667.230
−9.50049u
79
− 43.5798u
78
+ ··· + 69.1784u + 16.0314
a
5
=
142.976u
79
+ 628.242u
78
+ ··· − 1036.69u − 240.087
−19.2570u
79
− 82.9318u
78
+ ··· + 136.175u + 30.0287
a
4
=
164.052u
79
+ 719.781u
78
+ ··· − 1187.59u − 274.887
−18.4406u
79
− 79.7156u
78
+ ··· + 130.155u + 28.5642
a
9
=
−3509.05u
79
− 15418.0u
78
+ ··· + 25205.3u + 5785.93
176.743u
79
+ 775.971u
78
+ ··· − 1267.41u − 292.353
(ii) Obstruction class = −1
(iii) Cusp Shapes = −219.391u
79
− 967.071u
78
+ ··· + 1569.64u + 365.051
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
80
+ 29u
79
+ ··· + 13u + 4
c
2
, c
5
u
80
+ 5u
79
+ ··· − 5u + 2
c
3
u
80
− u
79
+ ··· − 10u − 1
c
4
, c
12
u
80
+ 5u
79
+ ··· + 14u + 1
c
6
, c
7
, c
10
c
11
u
80
− 5u
79
+ ··· + 6u − 1
c
8
u
80
+ 7u
79
+ ··· − 616u − 121
c
9
u
80
+ 15u
79
+ ··· − 497268u − 29873
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
80
+ 47y
79
+ ··· − 19809y + 16
c
2
, c
5
y
80
− 29y
79
+ ··· − 13y + 4
c
3
y
80
+ 9y
79
+ ··· − 98y + 1
c
4
, c
12
y
80
+ 45y
79
+ ··· − 134y + 1
c
6
, c
7
, c
10
c
11
y
80
− 95y
79
+ ··· − 50y + 1
c
8
y
80
+ 299y
79
+ ··· − 532400y + 14641
c
9
y
80
− 321y
79
+ ··· − 110926727384y + 892396129
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.982239 + 0.110037I
a = 0.60518 + 1.80389I
b = −0.832671 − 0.498946I
1.69931 − 2.04874I 0
u = −0.982239 − 0.110037I
a = 0.60518 − 1.80389I
b = −0.832671 + 0.498946I
1.69931 + 2.04874I 0
u = −0.759367 + 0.618307I
a = −0.344166 + 0.141148I
b = 0.830140 − 0.649151I
2.36183 + 0.48997I 0
u = −0.759367 − 0.618307I
a = −0.344166 − 0.141148I
b = 0.830140 + 0.649151I
2.36183 − 0.48997I 0
u = 0.874853 + 0.530372I
a = 0.802361 + 0.585193I
b = −0.571602 − 0.856402I
1.75059 + 7.74311I 0
u = 0.874853 − 0.530372I
a = 0.802361 − 0.585193I
b = −0.571602 + 0.856402I
1.75059 − 7.74311I 0
u = 0.873797 + 0.412672I
a = 0.39497 + 1.86274I
b = 1.069280 − 0.698680I
3.64655 + 8.02514I 0
u = 0.873797 − 0.412672I
a = 0.39497 − 1.86274I
b = 1.069280 + 0.698680I
3.64655 − 8.02514I 0
u = −0.655250 + 0.692019I
a = 0.86289 − 1.33749I
b = 0.869750 + 0.660212I
2.24057 − 4.60261I 0
u = −0.655250 − 0.692019I
a = 0.86289 + 1.33749I
b = 0.869750 − 0.660212I
2.24057 + 4.60261I 0
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.862986 + 0.606936I
a = −0.60152 − 1.82721I
b = −1.072300 + 0.693311I
0.23574 + 13.50530I 0
u = 0.862986 − 0.606936I
a = −0.60152 + 1.82721I
b = −1.072300 − 0.693311I
0.23574 − 13.50530I 0
u = 0.890674 + 0.278765I
a = −0.775206 − 0.805171I
b = 0.569460 + 0.870192I
5.15281 + 2.22250I 0
u = 0.890674 − 0.278765I
a = −0.775206 + 0.805171I
b = 0.569460 − 0.870192I
5.15281 − 2.22250I 0
u = −1.001950 + 0.553061I
a = −0.32963 + 1.53584I
b = −0.763637 − 0.645618I
2.03589 − 1.14374I 0
u = −1.001950 − 0.553061I
a = −0.32963 − 1.53584I
b = −0.763637 + 0.645618I
2.03589 + 1.14374I 0
u = 0.086726 + 0.850018I
a = −0.681133 + 0.501362I
b = −1.019290 − 0.654420I
−2.13020 − 8.69514I 0
u = 0.086726 − 0.850018I
a = −0.681133 − 0.501362I
b = −1.019290 + 0.654420I
−2.13020 + 8.69514I 0
u = 0.673885 + 0.494383I
a = 0.633666 + 0.692030I
b = 1.176500 − 0.080914I
−4.82659 + 6.36458I 0
u = 0.673885 − 0.494383I
a = 0.633666 − 0.692030I
b = 1.176500 + 0.080914I
−4.82659 − 6.36458I 0
6
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.731433 + 0.268270I
a = 0.380165 + 0.677378I
b = 0.017151 + 0.232479I
0.144692 − 0.492251I 0
u = −0.731433 − 0.268270I
a = 0.380165 − 0.677378I
b = 0.017151 − 0.232479I
0.144692 + 0.492251I 0
u = 0.000926 + 0.775832I
a = −0.416848 − 0.459903I
b = −0.600120 + 0.713934I
−0.90150 − 3.42282I 0
u = 0.000926 − 0.775832I
a = −0.416848 + 0.459903I
b = −0.600120 − 0.713934I
−0.90150 + 3.42282I 0
u = −1.127500 + 0.540430I
a = 0.446319 − 0.595511I
b = −0.930935 + 0.641996I
1.51642 + 3.88958I 0
u = −1.127500 − 0.540430I
a = 0.446319 + 0.595511I
b = −0.930935 − 0.641996I
1.51642 − 3.88958I 0
u = 0.705170 + 0.221551I
a = 0.143659 − 1.137600I
b = −0.379959 + 0.898795I
0.71940 + 3.75775I 6.00000 − 11.49284I
u = 0.705170 − 0.221551I
a = 0.143659 + 1.137600I
b = −0.379959 − 0.898795I
0.71940 − 3.75775I 6.00000 + 11.49284I
u = −1.272480 + 0.232109I
a = −0.077573 − 1.327820I
b = 0.862974 + 0.150904I
−1.44152 − 0.51003I 0
u = −1.272480 − 0.232109I
a = −0.077573 + 1.327820I
b = 0.862974 − 0.150904I
−1.44152 + 0.51003I 0
7
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.243048 + 0.629200I
a = 1.17488 + 1.11461I
b = 1.061150 − 0.014230I
−6.12935 − 2.55225I −1.74573 + 1.31196I
u = 0.243048 − 0.629200I
a = 1.17488 − 1.11461I
b = 1.061150 + 0.014230I
−6.12935 + 2.55225I −1.74573 − 1.31196I
u = −0.111177 + 0.623613I
a = 1.101240 − 0.355446I
b = 0.975206 + 0.620136I
0.69805 − 4.57533I 7.44408 + 5.23824I
u = −0.111177 − 0.623613I
a = 1.101240 + 0.355446I
b = 0.975206 − 0.620136I
0.69805 + 4.57533I 7.44408 − 5.23824I
u = −0.310855 + 0.540574I
a = 0.484610 − 0.177259I
b = 0.699014 − 0.609698I
1.56224 + 0.31078I 10.32905 − 0.04232I
u = −0.310855 − 0.540574I
a = 0.484610 + 0.177259I
b = 0.699014 + 0.609698I
1.56224 − 0.31078I 10.32905 + 0.04232I
u = −0.604081 + 0.001377I
a = 13.5746 − 17.1139I
b = 0.877405 + 0.507465I
−0.68319 − 2.03117I 157.990 − 13.051I
u = −0.604081 − 0.001377I
a = 13.5746 + 17.1139I
b = 0.877405 − 0.507465I
−0.68319 + 2.03117I 157.990 + 13.051I
u = 0.540486 + 0.177581I
a = 0.36709 − 2.47230I
b = −1.008760 + 0.761264I
−1.52216 + 3.07297I −0.13001 − 12.94551I
u = 0.540486 − 0.177581I
a = 0.36709 + 2.47230I
b = −1.008760 − 0.761264I
−1.52216 − 3.07297I −0.13001 + 12.94551I
8
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.452044
a = 0.820522
b = 0.201146
0.707924 14.1880
u = 1.54810 + 0.07689I
a = −0.806628 + 0.115866I
b = −0.972871 + 0.136497I
5.02760 + 3.22521I 0
u = 1.54810 − 0.07689I
a = −0.806628 − 0.115866I
b = −0.972871 − 0.136497I
5.02760 − 3.22521I 0
u = 0.357453 + 0.272374I
a = −0.28354 − 1.47622I
b = −1.082900 + 0.195290I
−1.99021 + 1.12837I −0.61556 − 4.33419I
u = 0.357453 − 0.272374I
a = −0.28354 + 1.47622I
b = −1.082900 − 0.195290I
−1.99021 − 1.12837I −0.61556 + 4.33419I
u = 1.57162
a = 0.420961
b = 0.775180
7.67792 0
u = −1.57728 + 0.00721I
a = 0.560042 + 0.801944I
b = −1.37891 − 0.39634I
4.86129 − 1.42349I 0
u = −1.57728 − 0.00721I
a = 0.560042 − 0.801944I
b = −1.37891 + 0.39634I
4.86129 + 1.42349I 0
u = −1.59511 + 0.02885I
a = 0.80382 + 1.88339I
b = −1.05746 − 0.93966I
5.96830 − 3.68106I 0
u = −1.59511 − 0.02885I
a = 0.80382 − 1.88339I
b = −1.05746 + 0.93966I
5.96830 + 3.68106I 0
9
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.209332 + 0.339332I
a = −0.70138 − 2.09676I
b = −0.567508 − 0.324974I
−1.43343 − 2.05795I 2.20961 + 4.63586I
u = −0.209332 − 0.339332I
a = −0.70138 + 2.09676I
b = −0.567508 + 0.324974I
−1.43343 + 2.05795I 2.20961 − 4.63586I
u = −1.59909 + 0.12620I
a = −0.154490 − 0.604773I
b = 1.277360 + 0.151788I
2.88077 − 8.60117I 0
u = −1.59909 − 0.12620I
a = −0.154490 + 0.604773I
b = 1.277360 − 0.151788I
2.88077 + 8.60117I 0
u = 1.60983 + 0.00290I
a = 1.69153 + 4.69097I
b = 0.914469 − 0.540849I
7.10700 + 2.05661I 0
u = 1.60983 − 0.00290I
a = 1.69153 − 4.69097I
b = 0.914469 + 0.540849I
7.10700 − 2.05661I 0
u = −1.62146 + 0.05130I
a = 0.25483 + 1.52795I
b = −0.314660 − 1.105270I
8.79176 − 4.72449I 0
u = −1.62146 − 0.05130I
a = 0.25483 − 1.52795I
b = −0.314660 + 1.105270I
8.79176 + 4.72449I 0
u = 0.331464 + 0.167817I
a = 0.790108 + 0.421831I
b = −1.086350 − 0.487000I
−2.01483 − 1.42900I −2.63503 − 2.24034I
u = 0.331464 − 0.167817I
a = 0.790108 − 0.421831I
b = −1.086350 + 0.487000I
−2.01483 + 1.42900I −2.63503 + 2.24034I
10
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 1.63729 + 0.04142I
a = −0.121690 + 0.165881I
b = 0.186036 − 0.459060I
8.44312 + 1.45094I 0
u = 1.63729 − 0.04142I
a = −0.121690 − 0.165881I
b = 0.186036 + 0.459060I
8.44312 − 1.45094I 0
u = 1.63038 + 0.22067I
a = 0.09225 + 1.74343I
b = 0.968177 − 0.699422I
9.99013 + 8.08376I 0
u = 1.63038 − 0.22067I
a = 0.09225 − 1.74343I
b = 0.968177 + 0.699422I
9.99013 − 8.08376I 0
u = −1.66412 + 0.07716I
a = −0.82132 + 1.36692I
b = 0.609910 − 1.021180I
14.0285 − 3.6133I 0
u = −1.66412 − 0.07716I
a = −0.82132 − 1.36692I
b = 0.609910 + 1.021180I
14.0285 + 3.6133I 0
u = −1.66410 + 0.11541I
a = −0.28155 − 1.88460I
b = 1.119640 + 0.766021I
12.4183 − 10.0748I 0
u = −1.66410 − 0.11541I
a = −0.28155 + 1.88460I
b = 1.119640 − 0.766021I
12.4183 + 10.0748I 0
u = 1.66377 + 0.17561I
a = −0.762447 − 0.909794I
b = 0.720008 + 0.743870I
10.73520 + 2.58534I 0
u = 1.66377 − 0.17561I
a = −0.762447 + 0.909794I
b = 0.720008 − 0.743870I
10.73520 − 2.58534I 0
11
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −1.66760 + 0.15263I
a = 0.93902 − 1.16501I
b = −0.587447 + 0.950346I
10.4735 − 10.3982I 0
u = −1.66760 − 0.15263I
a = 0.93902 + 1.16501I
b = −0.587447 − 0.950346I
10.4735 + 10.3982I 0
u = −1.66703 + 0.17926I
a = 0.08049 + 1.99128I
b = −1.106230 − 0.731601I
8.8607 − 16.5566I 0
u = −1.66703 − 0.17926I
a = 0.08049 − 1.99128I
b = −1.106230 + 0.731601I
8.8607 + 16.5566I 0
u = 1.69474 + 0.10689I
a = 0.26077 − 1.84251I
b = −0.912299 + 0.690710I
11.56300 + 3.48604I 0
u = 1.69474 − 0.10689I
a = 0.26077 + 1.84251I
b = −0.912299 − 0.690710I
11.56300 − 3.48604I 0
u = 1.72076 + 0.06241I
a = 0.83025 + 1.28263I
b = −0.796402 − 0.710069I
11.91770 − 1.88395I 0
u = 1.72076 − 0.06241I
a = 0.83025 − 1.28263I
b = −0.796402 + 0.710069I
11.91770 + 1.88395I 0
u = −0.184682 + 0.116658I
a = −1.73641 − 5.49293I
b = −0.749491 − 0.451267I
−1.42133 − 2.10255I 1.91167 + 3.48130I
u = −0.184682 − 0.116658I
a = −1.73641 + 5.49293I
b = −0.749491 + 0.451267I
−1.42133 + 2.10255I 1.91167 − 3.48130I
12
II. I
u
2
= ha
2
+ 6b + 4a + 4, a
4
+ 2a
3
+ 6a
2
− 4a + 4, u + 1i
(i) Arc colorings
a
6
=
1
0
a
10
=
0
−1
a
7
=
1
−1
a
11
=
−1
0
a
8
=
0
−1
a
3
=
a
−
1
6
a
2
−
2
3
a −
2
3
a
12
=
−1
1
a
2
=
−
1
6
a
2
+
1
3
a −
2
3
−
1
6
a
2
−
2
3
a −
2
3
a
1
=
−
1
6
a
3
−
1
6
a
2
−
2
3
a
1
6
a
3
+
1
6
a
2
+
2
3
a − 1
a
5
=
1
6
a
2
−
1
3
a +
2
3
−
1
6
a
3
−
1
2
a
2
− a −
1
3
a
4
=
1
6
a
3
+
1
2
a
2
+ a +
1
3
−
1
3
a
3
−
5
6
a
2
−
7
3
a
a
9
=
−
1
6
a
3
+
1
6
a
2
−
1
3
a +
1
3
−
1
3
a
2
−
1
3
a −
4
3
(ii) Obstruction class = 1
(iii) Cusp Shapes =
2
3
a
3
+ 2a
2
+ 4a +
16
3
13
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
(u
2
− u + 1)
2
c
2
, c
5
u
4
− u
2
+ 1
c
3
, c
4
, c
12
(u
2
+ 1)
2
c
6
, c
7
(u + 1)
4
c
8
u
4
+ 4u
3
+ 5u
2
+ 2u + 1
c
9
u
4
− 2u
3
+ 5u
2
− 4u + 1
c
10
, c
11
(u − 1)
4
14
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
(y
2
+ y + 1)
2
c
2
, c
5
(y
2
− y + 1)
2
c
3
, c
4
, c
12
(y + 1)
4
c
6
, c
7
, c
10
c
11
(y −1)
4
c
8
y
4
− 6y
3
+ 11y
2
+ 6y + 1
c
9
y
4
+ 6y
3
+ 11y
2
− 6y + 1
15
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −1.00000
a = 0.366025 + 0.633975I
b = −0.866025 − 0.500000I
− 2.02988I 6.00000 + 3.46410I
u = −1.00000
a = 0.366025 − 0.633975I
b = −0.866025 + 0.500000I
2.02988I 6.00000 − 3.46410I
u = −1.00000
a = −1.36603 + 2.36603I
b = 0.866025 − 0.500000I
2.02988I 6.00000 − 3.46410I
u = −1.00000
a = −1.36603 − 2.36603I
b = 0.866025 + 0.500000I
− 2.02988I 6.00000 + 3.46410I
16
III. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
((u
2
− u + 1)
2
)(u
80
+ 29u
79
+ ··· + 13u + 4)
c
2
, c
5
(u
4
− u
2
+ 1)(u
80
+ 5u
79
+ ··· − 5u + 2)
c
3
((u
2
+ 1)
2
)(u
80
− u
79
+ ··· − 10u − 1)
c
4
, c
12
((u
2
+ 1)
2
)(u
80
+ 5u
79
+ ··· + 14u + 1)
c
6
, c
7
((u + 1)
4
)(u
80
− 5u
79
+ ··· + 6u − 1)
c
8
(u
4
+ 4u
3
+ 5u
2
+ 2u + 1)(u
80
+ 7u
79
+ ··· − 616u − 121)
c
9
(u
4
− 2u
3
+ 5u
2
− 4u + 1)(u
80
+ 15u
79
+ ··· − 497268u − 29873)
c
10
, c
11
((u − 1)
4
)(u
80
− 5u
79
+ ··· + 6u − 1)
17
IV. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
((y
2
+ y + 1)
2
)(y
80
+ 47y
79
+ ··· − 19809y + 16)
c
2
, c
5
((y
2
− y + 1)
2
)(y
80
− 29y
79
+ ··· − 13y + 4)
c
3
((y + 1)
4
)(y
80
+ 9y
79
+ ··· − 98y + 1)
c
4
, c
12
((y + 1)
4
)(y
80
+ 45y
79
+ ··· − 134y + 1)
c
6
, c
7
, c
10
c
11
((y −1)
4
)(y
80
− 95y
79
+ ··· − 50y + 1)
c
8
(y
4
− 6y
3
+ 11y
2
+ 6y + 1)(y
80
+ 299y
79
+ ··· − 532400y + 14641)
c
9
(y
4
+ 6y
3
+ 11y
2
− 6y + 1)
· (y
80
− 321y
79
+ ··· − 110926727384y + 892396129)
18
