12a
0920
(K12a
0920
)
A knot diagram
1
Linearized knot diagam
4 6 9 10 11 3 12 1 2 5 7 8
Solving Sequence
7,12
8 1
3,9
4 6 2 11 5 10
c
7
c
12
c
8
c
3
c
6
c
2
c
11
c
5
c
10
c
1
, c
4
, c
9
Ideals for irreducible components
2
of X
par
I
u
1
= h5.21460 × 10
59
u
68
− 2.30775 × 10
60
u
67
+ ··· + 3.10307 × 10
59
b + 1.14731 × 10
61
,
5.06049 × 10
60
u
68
− 2.13379 × 10
61
u
67
+ ··· + 3.10307 × 10
59
a + 7.69523 × 10
61
, u
69
− 4u
68
+ ··· + 46u + 4i
I
u
2
= h−u
14
+ 10u
12
+ u
11
− 39u
10
− 7u
9
+ 75u
8
+ 17u
7
− 75u
6
− 17u
5
+ 39u
4
+ 9u
3
− 10u
2
+ b − 5u + 1,
u
16
− u
15
+ ··· + a + 5, u
17
− 12u
15
+ ··· + 2u + 1i
I
u
3
= h4a
4
u + 3a
4
− 8a
3
u − 6a
3
+ 24a
2
u + 18a
2
− 32au + 19b − 43a − 2u − 30,
a
5
− 2a
4
+ a
3
u + 6a
3
− 2a
2
u − 10a
2
− 5au − a + 2u − 1, u
2
+ u − 1i
* 3 irreducible components of dim
C
= 0, with total 96 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
=
h5.21×10
59
u
68
−2.31×10
60
u
67
+· · ·+3.10×10
59
b+1.15×10
61
, 5.06×10
60
u
68
−
2.13 × 10
61
u
67
+ · · · + 3.10 × 10
59
a + 7.70 × 10
61
, u
69
− 4u
68
+ · · · + 46u + 4i
(i) Arc colorings
a
7
=
1
0
a
12
=
0
u
a
8
=
1
u
2
a
1
=
−u
−u
3
+ u
a
3
=
−16.3080u
68
+ 68.7640u
67
+ ··· − 1888.29u − 247.988
−1.68047u
68
+ 7.43699u
67
+ ··· − 252.125u − 36.9734
a
9
=
−u
2
+ 1
−u
4
+ 2u
2
a
4
=
−15.0036u
68
+ 65.3287u
67
+ ··· − 1927.12u − 254.936
−0.440613u
68
+ 4.28225u
67
+ ··· − 276.144u − 38.8034
a
6
=
−4.01864u
68
+ 17.3606u
67
+ ··· − 509.348u − 63.6386
3.42123u
68
− 14.2674u
67
+ ··· + 402.460u + 56.0888
a
2
=
−7.35047u
68
+ 32.8090u
67
+ ··· − 855.578u − 94.9110
1.71041u
68
− 5.82409u
67
+ ··· + 94.1801u + 14.7601
a
11
=
u
u
a
5
=
−3.65619u
68
+ 15.7506u
67
+ ··· − 453.155u − 56.1645
3.78369u
68
− 15.8774u
67
+ ··· + 458.653u + 63.5629
a
10
=
11.0584u
68
− 47.9229u
67
+ ··· + 1414.70u + 185.347
−3.29554u
68
+ 12.6333u
67
+ ··· − 282.187u − 38.6325
(ii) Obstruction class = −1
(iii) Cusp Shapes = 30.0615u
68
− 134.302u
67
+ ··· + 4382.18u + 604.662
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
69
− 3u
68
+ ··· + 20777u − 1427
c
2
, c
6
u
69
− 4u
68
+ ··· − 15u − 1
c
3
u
69
− u
68
+ ··· − 231u + 293
c
4
, c
5
, c
10
u
69
+ u
68
+ ··· + 26u − 1
c
7
, c
8
, c
11
c
12
u
69
+ 4u
68
+ ··· + 46u − 4
c
9
u
69
+ 2u
68
+ ··· + 766u − 229
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
69
− 27y
68
+ ··· + 239869243y −2036329
c
2
, c
6
y
69
− 28y
68
+ ··· + 171y −1
c
3
y
69
+ 13y
68
+ ··· − 450599y −85849
c
4
, c
5
, c
10
y
69
− 79y
68
+ ··· + 462y −1
c
7
, c
8
, c
11
c
12
y
69
− 84y
68
+ ··· + 684y −16
c
9
y
69
+ 14y
68
+ ··· + 8302y −52441
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.858609 + 0.509133I
a = −0.13290 + 1.46749I
b = 1.119670 + 0.509880I
0.11883 + 8.23224I 0
u = −0.858609 − 0.509133I
a = −0.13290 − 1.46749I
b = 1.119670 − 0.509880I
0.11883 − 8.23224I 0
u = 0.922201 + 0.343620I
a = −0.226022 − 0.690778I
b = −0.396644 − 1.154280I
−9.14129 − 5.71438I 0
u = 0.922201 − 0.343620I
a = −0.226022 + 0.690778I
b = −0.396644 + 1.154280I
−9.14129 + 5.71438I 0
u = 0.957142 + 0.344138I
a = 0.346935 − 0.313197I
b = 0.956665 + 0.106533I
−0.408920 + 0.368294I 0
u = 0.957142 − 0.344138I
a = 0.346935 + 0.313197I
b = 0.956665 − 0.106533I
−0.408920 − 0.368294I 0
u = −0.761381 + 0.691428I
a = 0.903514 − 0.730666I
b = −1.019750 − 0.567692I
−6.72025 + 2.21455I 0
u = −0.761381 − 0.691428I
a = 0.903514 + 0.730666I
b = −1.019750 + 0.567692I
−6.72025 − 2.21455I 0
u = 0.875291 + 0.317279I
a = −0.65426 + 1.54098I
b = −0.941128 + 0.295855I
−0.11613 − 2.68304I 0
u = 0.875291 − 0.317279I
a = −0.65426 − 1.54098I
b = −0.941128 − 0.295855I
−0.11613 + 2.68304I 0
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.888247 + 0.623182I
a = 0.428773 + 1.236830I
b = −1.198570 + 0.737599I
−6.69655 − 12.30450I 0
u = 0.888247 − 0.623182I
a = 0.428773 − 1.236830I
b = −1.198570 − 0.737599I
−6.69655 + 12.30450I 0
u = 0.068085 + 0.890261I
a = 0.549835 + 0.167489I
b = −1.014710 − 0.607088I
−4.19382 + 7.32485I 0
u = 0.068085 − 0.890261I
a = 0.549835 − 0.167489I
b = −1.014710 + 0.607088I
−4.19382 − 7.32485I 0
u = 0.627745 + 0.554827I
a = −0.857946 − 0.838190I
b = 0.676355 − 0.302159I
−1.22245 − 1.88994I 0
u = 0.627745 − 0.554827I
a = −0.857946 + 0.838190I
b = 0.676355 + 0.302159I
−1.22245 + 1.88994I 0
u = −0.751462 + 0.303115I
a = 0.418529 − 1.137040I
b = 0.165717 − 0.819333I
−2.66510 + 3.50831I −10.49360 − 7.33854I
u = −0.751462 − 0.303115I
a = 0.418529 + 1.137040I
b = 0.165717 + 0.819333I
−2.66510 − 3.50831I −10.49360 + 7.33854I
u = −1.190400 + 0.048571I
a = 0.888159 − 0.271946I
b = 0.604132 − 0.446757I
−7.88819 + 0.32180I 0
u = −1.190400 − 0.048571I
a = 0.888159 + 0.271946I
b = 0.604132 + 0.446757I
−7.88819 − 0.32180I 0
6
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.747922 + 0.141109I
a = −1.18456 + 1.77018I
b = 1.046390 + 0.542070I
−6.49393 + 4.52204I −12.42024 − 4.96803I
u = −0.747922 − 0.141109I
a = −1.18456 − 1.77018I
b = 1.046390 − 0.542070I
−6.49393 − 4.52204I −12.42024 + 4.96803I
u = −0.278701 + 0.697012I
a = 0.918131 − 0.701090I
b = −0.633259 + 0.581048I
−5.39570 + 2.53481I −8.38084 − 2.80374I
u = −0.278701 − 0.697012I
a = 0.918131 + 0.701090I
b = −0.633259 − 0.581048I
−5.39570 − 2.53481I −8.38084 + 2.80374I
u = −0.034826 + 0.713110I
a = −0.706288 − 0.104021I
b = 1.077410 − 0.310611I
2.61982 − 4.13722I −1.23735 + 6.70183I
u = −0.034826 − 0.713110I
a = −0.706288 + 0.104021I
b = 1.077410 + 0.310611I
2.61982 + 4.13722I −1.23735 − 6.70183I
u = −1.147790 + 0.605056I
a = −0.280564 − 0.113102I
b = −0.707022 + 0.513747I
−7.79544 − 2.18356I 0
u = −1.147790 − 0.605056I
a = −0.280564 + 0.113102I
b = −0.707022 − 0.513747I
−7.79544 + 2.18356I 0
u = 0.549539 + 0.428722I
a = −0.92689 − 1.74841I
b = 1.001700 − 0.945056I
−3.37002 − 4.91183I −5.12008 + 9.10431I
u = 0.549539 − 0.428722I
a = −0.92689 + 1.74841I
b = 1.001700 + 0.945056I
−3.37002 + 4.91183I −5.12008 − 9.10431I
7
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.603111 + 0.317010I
a = −0.06954 − 1.62856I
b = −1.039670 − 0.531907I
1.42958 + 2.33297I −0.70777 − 7.76145I
u = −0.603111 − 0.317010I
a = −0.06954 + 1.62856I
b = −1.039670 + 0.531907I
1.42958 − 2.33297I −0.70777 + 7.76145I
u = −1.36225
a = −0.107589
b = −1.38678
−1.59788 0
u = 0.347963 + 0.505319I
a = 0.188527 − 0.656901I
b = 1.003340 + 0.715218I
−2.79726 + 1.63095I −4.89103 − 0.22167I
u = 0.347963 − 0.505319I
a = 0.188527 + 0.656901I
b = 1.003340 − 0.715218I
−2.79726 − 1.63095I −4.89103 + 0.22167I
u = −1.47026
a = 0.903464
b = 1.02182
−8.11663 0
u = 1.53884 + 0.08382I
a = 0.51726 + 1.39825I
b = −0.030549 + 0.170011I
−11.09110 − 4.38044I 0
u = 1.53884 − 0.08382I
a = 0.51726 − 1.39825I
b = −0.030549 − 0.170011I
−11.09110 + 4.38044I 0
u = 1.54919
a = −1.05617
b = −1.67326
−3.72894 0
u = −1.57061 + 0.09574I
a = 0.29032 + 2.12661I
b = 1.01604 + 1.19413I
−10.56740 + 6.67317I 0
8
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −1.57061 − 0.09574I
a = 0.29032 − 2.12661I
b = 1.01604 − 1.19413I
−10.56740 − 6.67317I 0
u = 1.59295 + 0.06255I
a = −0.65470 + 1.63501I
b = −1.054310 + 0.900547I
−6.11344 − 3.58029I 0
u = 1.59295 − 0.06255I
a = −0.65470 − 1.63501I
b = −1.054310 − 0.900547I
−6.11344 + 3.58029I 0
u = −0.090552 + 0.392237I
a = 0.536976 − 1.059100I
b = −1.143200 + 0.046612I
2.68421 + 0.16764I 2.41572 − 0.19332I
u = −0.090552 − 0.392237I
a = 0.536976 + 1.059100I
b = −1.143200 − 0.046612I
2.68421 − 0.16764I 2.41572 + 0.19332I
u = −1.61062 + 0.16002I
a = −0.034132 + 1.263440I
b = 0.891494 + 0.558679I
−8.89500 + 4.54856I 0
u = −1.61062 − 0.16002I
a = −0.034132 − 1.263440I
b = 0.891494 − 0.558679I
−8.89500 − 4.54856I 0
u = 0.070878 + 0.373596I
a = −0.958588 + 0.155139I
b = −0.002941 + 0.459481I
−0.359603 − 1.131530I −5.56898 + 5.13888I
u = 0.070878 − 0.373596I
a = −0.958588 − 0.155139I
b = −0.002941 − 0.459481I
−0.359603 + 1.131530I −5.56898 − 5.13888I
u = 1.62259 + 0.07416I
a = 0.41905 + 1.55527I
b = 0.337200 + 0.935815I
−10.84000 − 4.89494I 0
9
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 1.62259 − 0.07416I
a = 0.41905 − 1.55527I
b = 0.337200 − 0.935815I
−10.84000 + 4.89494I 0
u = 1.64324 + 0.03991I
a = 0.106947 − 1.306450I
b = 1.29168 − 0.59412I
−14.8905 − 5.2157I 0
u = 1.64324 − 0.03991I
a = 0.106947 + 1.306450I
b = 1.29168 + 0.59412I
−14.8905 + 5.2157I 0
u = 1.66632 + 0.14638I
a = 0.46733 − 1.56172I
b = 1.147590 − 0.686553I
−8.56853 − 10.77570I 0
u = 1.66632 − 0.14638I
a = 0.46733 + 1.56172I
b = 1.147590 + 0.686553I
−8.56853 + 10.77570I 0
u = −1.67496 + 0.09834I
a = −0.51698 + 1.53291I
b = −0.50081 + 1.47766I
−18.1559 + 7.4706I 0
u = −1.67496 − 0.09834I
a = −0.51698 − 1.53291I
b = −0.50081 − 1.47766I
−18.1559 − 7.4706I 0
u = 1.66700 + 0.20966I
a = −0.097293 + 1.135820I
b = −1.29837 + 0.61433I
−15.0060 − 5.7097I 0
u = 1.66700 − 0.20966I
a = −0.097293 − 1.135820I
b = −1.29837 − 0.61433I
−15.0060 + 5.7097I 0
u = −1.67919 + 0.09590I
a = −0.70802 − 1.36350I
b = −0.843032 − 0.540808I
−9.07614 + 4.33421I 0
10
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −1.67919 − 0.09590I
a = −0.70802 + 1.36350I
b = −0.843032 + 0.540808I
−9.07614 − 4.33421I 0
u = −1.67662 + 0.18420I
a = −0.33035 − 1.57967I
b = −1.32832 − 0.86095I
−15.4447 + 15.4584I 0
u = −1.67662 − 0.18420I
a = −0.33035 + 1.57967I
b = −1.32832 + 0.86095I
−15.4447 − 15.4584I 0
u = −0.257782 + 0.029613I
a = 3.42531 + 5.22024I
b = 0.515844 − 0.457634I
−4.89351 − 3.67092I −12.31151 − 0.80644I
u = −0.257782 − 0.029613I
a = 3.42531 − 5.22024I
b = 0.515844 + 0.457634I
−4.89351 + 3.67092I −12.31151 + 0.80644I
u = 1.74045 + 0.06218I
a = 0.068694 − 0.932107I
b = −0.032884 − 0.887424I
−18.5613 − 0.1635I 0
u = 1.74045 − 0.06218I
a = 0.068694 + 0.932107I
b = −0.032884 + 0.887424I
−18.5613 + 0.1635I 0
u = −0.222069
a = −1.80233
b = −1.36002
2.83320 10.8910
u = 1.81750
a = 0.292085
b = 0.0660849
−19.0700 0
11
II.
I
u
2
= h−u
14
+10u
12
+· · ·+b+1, u
16
−u
15
+· · ·+a+5, u
17
−12u
15
+· · ·+2u+1i
(i) Arc colorings
a
7
=
1
0
a
12
=
0
u
a
8
=
1
u
2
a
1
=
−u
−u
3
+ u
a
3
=
−u
16
+ u
15
+ ··· + 2u − 5
u
14
− 10u
12
+ ··· + 5u − 1
a
9
=
−u
2
+ 1
−u
4
+ 2u
2
a
4
=
−u
16
+ u
15
+ ··· + 5u − 5
2u
14
− 19u
12
+ ··· + 6u − 1
a
6
=
2u
16
− 2u
15
+ ··· − 5u + 8
−u
15
− u
14
+ ··· + u + 4
a
2
=
u
16
− 2u
15
+ ··· − 10u + 7
−u
15
− 3u
14
+ ··· − 5u + 3
a
11
=
u
u
a
5
=
2u
16
− u
15
+ ··· − 5u + 7
u
12
− u
11
+ ··· + u + 3
a
10
=
−3u
16
+ 34u
14
+ ··· + 12u − 8
−2u
16
+ 22u
14
+ ··· + 2u − 4
(ii) Obstruction class = 1
(iii) Cusp Shapes = 6u
16
− 2u
15
− 73u
14
+ 15u
13
+ 361u
12
− 34u
11
− 928u
10
+ 8u
9
+
1320u
8
+ 54u
7
− 1027u
6
− 59u
5
+ 406u
4
+ 53u
3
− 66u
2
− 38u − 4
12
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
17
− 6u
15
+ ··· + 3u − 1
c
2
u
17
− 3u
16
+ ··· − 3u + 1
c
3
u
17
− 2u
14
+ ··· + u + 1
c
4
, c
5
u
17
− 10u
15
+ ··· + 2u − 1
c
6
u
17
+ 3u
16
+ ··· − 3u − 1
c
7
, c
8
u
17
− 12u
15
+ ··· + 2u + 1
c
9
u
17
+ u
16
+ ··· − 2u
3
+ 1
c
10
u
17
− 10u
15
+ ··· + 2u + 1
c
11
, c
12
u
17
− 12u
15
+ ··· + 2u − 1
13
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
17
− 12y
16
+ ··· + 21y −1
c
2
, c
6
y
17
− 17y
16
+ ··· + 17y −1
c
3
y
17
− 6y
15
+ ··· + 3y −1
c
4
, c
5
, c
10
y
17
− 20y
16
+ ··· + 16y −1
c
7
, c
8
, c
11
c
12
y
17
− 24y
16
+ ··· + 24y −1
c
9
y
17
− 3y
16
+ ··· + 6y
2
− 1
14
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 1.09578
a = 0.547612
b = 1.14178
0.341936 0.875270
u = −1.123960 + 0.382204I
a = −0.478136 − 0.578939I
b = −0.617479 + 0.293759I
−7.13101 − 1.62524I −6.68084 + 0.62023I
u = −1.123960 − 0.382204I
a = −0.478136 + 0.578939I
b = −0.617479 − 0.293759I
−7.13101 + 1.62524I −6.68084 − 0.62023I
u = −1.18833
a = 0.0332715
b = −1.43147
−3.07503 −11.9270
u = 0.667353 + 0.370935I
a = −0.47830 − 1.61454I
b = 0.724488 − 0.164054I
−0.59938 − 1.32532I −5.05705 + 2.80405I
u = 0.667353 − 0.370935I
a = −0.47830 + 1.61454I
b = 0.724488 + 0.164054I
−0.59938 + 1.32532I −5.05705 − 2.80405I
u = −0.369667 + 0.360033I
a = 2.85434 − 1.27851I
b = −0.773403 − 0.575136I
−4.67731 + 4.33112I −8.36560 − 8.69813I
u = −0.369667 − 0.360033I
a = 2.85434 + 1.27851I
b = −0.773403 + 0.575136I
−4.67731 − 4.33112I −8.36560 + 8.69813I
u = 1.53432
a = −1.73698
b = −1.84039
−6.74002 −3.61890
u = −1.55322
a = 0.672900
b = 1.56084
−4.27815 −13.1180
15
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 1.55960 + 0.10540I
a = 0.20362 + 1.87120I
b = −0.891995 + 0.798543I
−11.47150 − 5.99192I −13.12352 + 4.84870I
u = 1.55960 − 0.10540I
a = 0.20362 − 1.87120I
b = −0.891995 − 0.798543I
−11.47150 + 5.99192I −13.12352 − 4.84870I
u = 0.389234
a = −0.308648
b = 1.38986
2.56515 −19.7450
u = −1.63154 + 0.11334I
a = 0.255071 + 1.300460I
b = 0.681332 + 0.453515I
−8.67576 + 3.16393I −7.87236 − 0.20715I
u = −1.63154 − 0.11334I
a = 0.255071 − 1.300460I
b = 0.681332 − 0.453515I
−8.67576 − 3.16393I −7.87236 + 0.20715I
u = −0.315662
a = −3.47084
b = −1.66703
−0.212009 3.05600
u = 1.83431
a = −0.450508
b = −0.399475
−18.8982 15.6760
16
III. I
u
3
= h4a
4
u − 8a
3
u + · · · − 43a − 30, a
3
u − 2a
2
u + · · · − a − 1, u
2
+ u − 1i
(i) Arc colorings
a
7
=
1
0
a
12
=
0
u
a
8
=
1
−u + 1
a
1
=
−u
−u + 1
a
3
=
a
−0.210526a
4
u + 0.421053a
3
u + ··· + 2.26316a + 1.57895
a
9
=
u
u
a
4
=
−0.263158a
4
u + 0.526316a
3
u + ··· + 0.578947a + 1.47368
−0.473684a
4
u + 0.947368a
3
u + ··· + 1.84211a + 3.05263
a
6
=
−0.0526316a
3
u − 0.315789a
2
u + ··· + 0.368421a + 1.26316
−0.421053a
4
u + 0.526316a
3
u + ··· + 4.73684a + 2.73684
a
2
=
0.526316a
4
u − 0.421053a
3
u + ··· − 1.57895a − 2.10526
0.947368a
4
u − a
3
u + ··· − 5.94737a − 3.57895
a
11
=
u
u
a
5
=
−0.526316a
4
u + 0.421053a
3
u + ··· + 1.57895a + 2.10526
−0.947368a
4
u + a
3
u + ··· + 5.94737a + 3.57895
a
10
=
−0.473684a
4
u + 0.315789a
3
u + ··· − 5.73684a + 0.210526
−0.315789a
4
u + 0.315789a
2
u + ··· − 9.68421a − 1.47368
(ii) Obstruction class = −1
(iii) Cusp Shapes = −10
17
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
10
− 4u
9
+ 2u
8
+ 8u
7
− 5u
6
− 11u
5
+ 8u
4
+ 7u
3
− 5u
2
− 3u + 1
c
2
, c
6
u
10
+ 4u
9
+ 2u
8
− 8u
7
− 5u
6
+ 11u
5
+ 8u
4
− 7u
3
− 5u
2
+ 3u + 1
c
3
u
10
+ 2u
8
− 4u
7
+ 5u
6
− 7u
5
− 12u
4
+ 9u
3
− 5u
2
− u + 1
c
4
, c
5
, c
9
c
10
u
10
− 2u
8
− u
6
+ u
5
+ 2u
4
− u
3
+ u
2
− u − 1
c
7
, c
8
, c
11
c
12
(u
2
− u − 1)
5
18
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
2
, c
6
y
10
− 12y
9
+ ··· − 19y + 1
c
3
y
10
+ 4y
9
+ ··· − 11y + 1
c
4
, c
5
, c
9
c
10
y
10
− 4y
9
+ 2y
8
+ 8y
7
− 5y
6
− 11y
5
+ 8y
4
+ 7y
3
− 5y
2
− 3y + 1
c
7
, c
8
, c
11
c
12
(y
2
− 3y + 1)
5
19
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = 0.618034
a = −0.345749
b = 0.267133
−0.986960 −10.0000
u = 0.618034
a = 0.0508281
b = 1.80755
−0.986960 −10.0000
u = 0.618034
a = 1.99880
b = 1.34705
−0.986960 −10.0000
u = 0.618034
a = 0.14806 + 2.58817I
b = −0.710869 + 0.286205I
−0.986960 −10.0000
u = 0.618034
a = 0.14806 − 2.58817I
b = −0.710869 − 0.286205I
−0.986960 −10.0000
u = −1.61803
a = 1.12160
b = 2.04335
−8.88264 −10.0000
u = −1.61803
a = 0.687673 + 0.972900I
b = 0.880270 + 0.618196I
−8.88264 −10.0000
u = −1.61803
a = 0.687673 − 0.972900I
b = 0.880270 − 0.618196I
−8.88264 −10.0000
u = −1.61803
a = −0.24847 + 1.61216I
b = −0.901944 + 0.542076I
−8.88264 −10.0000
u = −1.61803
a = −0.24847 − 1.61216I
b = −0.901944 − 0.542076I
−8.88264 −10.0000
20
IV. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
(u
10
− 4u
9
+ 2u
8
+ 8u
7
− 5u
6
− 11u
5
+ 8u
4
+ 7u
3
− 5u
2
− 3u + 1)
· (u
17
− 6u
15
+ ··· + 3u − 1)(u
69
− 3u
68
+ ··· + 20777u − 1427)
c
2
(u
10
+ 4u
9
+ 2u
8
− 8u
7
− 5u
6
+ 11u
5
+ 8u
4
− 7u
3
− 5u
2
+ 3u + 1)
· (u
17
− 3u
16
+ ··· − 3u + 1)(u
69
− 4u
68
+ ··· − 15u − 1)
c
3
(u
10
+ 2u
8
− 4u
7
+ 5u
6
− 7u
5
− 12u
4
+ 9u
3
− 5u
2
− u + 1)
· (u
17
− 2u
14
+ ··· + u + 1)(u
69
− u
68
+ ··· − 231u + 293)
c
4
, c
5
(u
10
− 2u
8
+ ··· − u − 1)(u
17
− 10u
15
+ ··· + 2u − 1)
· (u
69
+ u
68
+ ··· + 26u − 1)
c
6
(u
10
+ 4u
9
+ 2u
8
− 8u
7
− 5u
6
+ 11u
5
+ 8u
4
− 7u
3
− 5u
2
+ 3u + 1)
· (u
17
+ 3u
16
+ ··· − 3u − 1)(u
69
− 4u
68
+ ··· − 15u − 1)
c
7
, c
8
((u
2
− u − 1)
5
)(u
17
− 12u
15
+ ··· + 2u + 1)(u
69
+ 4u
68
+ ··· + 46u − 4)
c
9
(u
10
− 2u
8
+ ··· − u − 1)(u
17
+ u
16
+ ··· − 2u
3
+ 1)
· (u
69
+ 2u
68
+ ··· + 766u − 229)
c
10
(u
10
− 2u
8
+ ··· − u − 1)(u
17
− 10u
15
+ ··· + 2u + 1)
· (u
69
+ u
68
+ ··· + 26u − 1)
c
11
, c
12
((u
2
− u − 1)
5
)(u
17
− 12u
15
+ ··· + 2u − 1)(u
69
+ 4u
68
+ ··· + 46u − 4)
21
V. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
(y
10
− 12y
9
+ ··· − 19y + 1)(y
17
− 12y
16
+ ··· + 21y −1)
· (y
69
− 27y
68
+ ··· + 239869243y −2036329)
c
2
, c
6
(y
10
− 12y
9
+ ··· − 19y + 1)(y
17
− 17y
16
+ ··· + 17y −1)
· (y
69
− 28y
68
+ ··· + 171y −1)
c
3
(y
10
+ 4y
9
+ ··· − 11y + 1)(y
17
− 6y
15
+ ··· + 3y −1)
· (y
69
+ 13y
68
+ ··· − 450599y −85849)
c
4
, c
5
, c
10
(y
10
− 4y
9
+ 2y
8
+ 8y
7
− 5y
6
− 11y
5
+ 8y
4
+ 7y
3
− 5y
2
− 3y + 1)
· (y
17
− 20y
16
+ ··· + 16y −1)(y
69
− 79y
68
+ ··· + 462y −1)
c
7
, c
8
, c
11
c
12
((y
2
− 3y + 1)
5
)(y
17
− 24y
16
+ ··· + 24y −1)
· (y
69
− 84y
68
+ ··· + 684y −16)
c
9
(y
10
− 4y
9
+ 2y
8
+ 8y
7
− 5y
6
− 11y
5
+ 8y
4
+ 7y
3
− 5y
2
− 3y + 1)
· (y
17
− 3y
16
+ ··· + 6y
2
− 1)(y
69
+ 14y
68
+ ··· + 8302y −52441)
22
