12a
0339
(K12a
0339
)
A knot diagram
1
Linearized knot diagam
3 6 8 12 11 2 10 1 4 7 5 9
Solving Sequence
2,7
6 3
1,11
5 12 10 8 4 9
c
6
c
2
c
1
c
5
c
11
c
10
c
7
c
3
c
9
c
4
, c
8
, c
12
Ideals for irreducible components
2
of X
par
I
u
1
= h−8.07878 × 10
237
u
106
− 5.69593 × 10
238
u
105
+ ··· + 1.02698 × 10
240
b − 4.14748 × 10
240
,
− 1.16910 × 10
241
u
106
− 1.12816 × 10
239
u
105
+ ··· + 1.95127 × 10
241
a + 9.47218 × 10
241
,
u
107
+ 18u
105
+ ··· − 24u + 19i
I
u
2
= h2130709u
29
+ 9442748u
28
+ ··· + 3960308b − 4255385,
29240837u
29
+ 79392300u
28
+ ··· + 3960308a + 20834703, u
30
+ 3u
29
+ ··· + 3u + 1i
* 2 irreducible components of dim
C
= 0, with total 137 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−8.08 × 10
237
u
106
− 5.70 × 10
238
u
105
+ · · · + 1.03 × 10
240
b − 4.15 ×
10
240
, −1.17 × 10
241
u
106
− 1.13 × 10
239
u
105
+ · · · + 1.95 × 10
241
a + 9.47 ×
10
241
, u
107
+ 18u
105
+ · · · − 24u + 19i
(i) Arc colorings
a
2
=
0
u
a
7
=
1
0
a
6
=
1
u
2
a
3
=
u
u
3
+ u
a
1
=
u
3
u
5
+ u
3
+ u
a
11
=
0.599149u
106
+ 0.00578167u
105
+ ··· + 103.443u − 4.85437
0.00786652u
106
+ 0.0554628u
105
+ ··· + 0.975711u + 4.03851
a
5
=
0.348441u
106
+ 0.156526u
105
+ ··· + 29.4128u + 21.6924
−0.124729u
106
+ 0.120186u
105
+ ··· − 23.9076u + 11.2074
a
12
=
0.639779u
106
+ 0.0436662u
105
+ ··· + 4.19949u + 9.11629
−0.386630u
106
− 0.0480225u
105
+ ··· − 21.3738u − 3.87734
a
10
=
0.607015u
106
+ 0.0612445u
105
+ ··· + 104.419u − 0.815863
0.00786652u
106
+ 0.0554628u
105
+ ··· + 0.975711u + 4.03851
a
8
=
−0.0125601u
106
− 0.317357u
105
+ ··· + 10.5566u − 28.4105
0.0872593u
106
− 0.0226541u
105
+ ··· + 18.7313u − 5.60808
a
4
=
0.871461u
106
+ 0.0699016u
105
+ ··· + 16.2492u + 13.5251
0.0417297u
106
− 0.0636946u
105
+ ··· + 15.8940u − 0.754748
a
9
=
−0.0195297u
106
− 0.335972u
105
+ ··· + 11.9948u − 29.6475
0.0902868u
106
+ 0.0286647u
105
+ ··· + 14.7293u − 1.68637
(ii) Obstruction class = −1
(iii) Cusp Shapes = 1.29735u
106
+ 0.145247u
105
+ ··· + 65.0366u + 28.0789
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
107
+ 36u
106
+ ··· − 16866u − 361
c
2
, c
6
u
107
+ 18u
105
+ ··· − 24u + 19
c
3
u
107
− u
106
+ ··· + 875682u + 270676
c
4
, c
5
, c
11
u
107
+ u
106
+ ··· − 3823u + 653
c
7
, c
10
u
107
− 5u
106
+ ··· − 1215u + 43
c
8
, c
12
u
107
+ 3u
106
+ ··· + 90u + 68
c
9
u
107
+ u
106
+ ··· + 33976041u + 5654997
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
107
+ 84y
106
+ ··· + 71806242y −130321
c
2
, c
6
y
107
+ 36y
106
+ ··· − 16866y −361
c
3
y
107
+ 45y
106
+ ··· − 2480148075396y −73265496976
c
4
, c
5
, c
11
y
107
+ 123y
106
+ ··· − 13417961y −426409
c
7
, c
10
y
107
+ 87y
106
+ ··· + 85175y −1849
c
8
, c
12
y
107
+ 85y
106
+ ··· − 46708y −4624
c
9
y
107
+ 57y
106
+ ··· − 1085652345824199y −31978991070009
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.062374 + 1.007540I
a = −0.796736 + 1.058810I
b = 0.457334 − 0.922934I
−1.40043 + 2.59202I 0
u = 0.062374 − 1.007540I
a = −0.796736 − 1.058810I
b = 0.457334 + 0.922934I
−1.40043 − 2.59202I 0
u = −0.539561 + 0.857006I
a = −0.873556 + 1.018200I
b = 1.183120 − 0.066566I
−1.44165 − 2.15650I 0
u = −0.539561 − 0.857006I
a = −0.873556 − 1.018200I
b = 1.183120 + 0.066566I
−1.44165 + 2.15650I 0
u = 0.025107 + 1.017280I
a = 1.248120 − 0.139495I
b = −0.634688 − 0.196469I
−0.98241 + 1.99627I 0
u = 0.025107 − 1.017280I
a = 1.248120 + 0.139495I
b = −0.634688 + 0.196469I
−0.98241 − 1.99627I 0
u = −0.023639 + 0.981626I
a = 0.21172 + 2.86791I
b = −0.262160 − 1.223870I
9.97282 + 1.63565I 0
u = −0.023639 − 0.981626I
a = 0.21172 − 2.86791I
b = −0.262160 + 1.223870I
9.97282 − 1.63565I 0
u = 0.440244 + 0.921461I
a = −1.74646 + 0.37111I
b = 0.722740 − 0.643120I
0.12974 + 4.17616I 0
u = 0.440244 − 0.921461I
a = −1.74646 − 0.37111I
b = 0.722740 + 0.643120I
0.12974 − 4.17616I 0
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.335229 + 0.981009I
a = 0.625167 − 0.886501I
b = 0.128421 + 0.366660I
−0.492891 + 1.302360I 0
u = 0.335229 − 0.981009I
a = 0.625167 + 0.886501I
b = 0.128421 − 0.366660I
−0.492891 − 1.302360I 0
u = −0.740295 + 0.736422I
a = 0.577824 − 0.329961I
b = 0.229242 − 1.359360I
4.06992 + 2.18050I 0
u = −0.740295 − 0.736422I
a = 0.577824 + 0.329961I
b = 0.229242 + 1.359360I
4.06992 − 2.18050I 0
u = −0.183798 + 1.050840I
a = 1.064820 + 0.644412I
b = −0.643115 + 0.334320I
4.91950 − 5.29302I 0
u = −0.183798 − 1.050840I
a = 1.064820 − 0.644412I
b = −0.643115 − 0.334320I
4.91950 + 5.29302I 0
u = 0.717457 + 0.794911I
a = −0.695148 − 0.695475I
b = 0.174245 − 1.299920I
3.27155 + 2.99011I 0
u = 0.717457 − 0.794911I
a = −0.695148 + 0.695475I
b = 0.174245 + 1.299920I
3.27155 − 2.99011I 0
u = −0.754984 + 0.759752I
a = −0.286261 − 0.133543I
b = 0.20941 − 1.47485I
14.9857 + 1.0909I 0
u = −0.754984 − 0.759752I
a = −0.286261 + 0.133543I
b = 0.20941 + 1.47485I
14.9857 − 1.0909I 0
6
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.320021 + 0.864903I
a = 0.772355 − 0.100355I
b = −0.169769 + 0.018359I
−0.51833 + 1.44971I 0
u = 0.320021 − 0.864903I
a = 0.772355 + 0.100355I
b = −0.169769 − 0.018359I
−0.51833 − 1.44971I 0
u = −0.848993 + 0.680119I
a = −1.115690 + 0.835412I
b = 0.477548 − 0.044794I
10.26980 − 3.73972I 0
u = −0.848993 − 0.680119I
a = −1.115690 − 0.835412I
b = 0.477548 + 0.044794I
10.26980 + 3.73972I 0
u = −0.264816 + 0.872136I
a = −1.55071 + 0.39752I
b = 0.812011 + 0.520055I
−2.66738 − 2.02745I 0
u = −0.264816 − 0.872136I
a = −1.55071 − 0.39752I
b = 0.812011 − 0.520055I
−2.66738 + 2.02745I 0
u = −0.711644 + 0.568814I
a = 0.301387 − 0.564582I
b = −0.821388 + 0.195331I
4.22158 + 2.73839I 0
u = −0.711644 − 0.568814I
a = 0.301387 + 0.564582I
b = −0.821388 − 0.195331I
4.22158 − 2.73839I 0
u = 0.780037 + 0.764920I
a = −0.051617 + 0.552311I
b = −0.69530 − 1.68565I
15.4381 + 2.3856I 0
u = 0.780037 − 0.764920I
a = −0.051617 − 0.552311I
b = −0.69530 + 1.68565I
15.4381 − 2.3856I 0
7
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.975917 + 0.501487I
a = 0.128420 − 0.091770I
b = −0.125010 + 1.406920I
10.94160 − 0.16306I 0
u = −0.975917 − 0.501487I
a = 0.128420 + 0.091770I
b = −0.125010 − 1.406920I
10.94160 + 0.16306I 0
u = 0.736986 + 0.814530I
a = −1.49735 − 0.88050I
b = −0.007446 − 1.276350I
7.29276 + 0.16570I 0
u = 0.736986 − 0.814530I
a = −1.49735 + 0.88050I
b = −0.007446 + 1.276350I
7.29276 − 0.16570I 0
u = 0.907815 + 0.621230I
a = 0.129498 − 0.217483I
b = 0.45306 + 1.65969I
11.97390 − 4.84056I 0
u = 0.907815 − 0.621230I
a = 0.129498 + 0.217483I
b = 0.45306 − 1.65969I
11.97390 + 4.84056I 0
u = −0.875911 + 0.669880I
a = −0.254070 + 0.531762I
b = −0.277866 + 1.343060I
9.02317 + 6.53228I 0
u = −0.875911 − 0.669880I
a = −0.254070 − 0.531762I
b = −0.277866 − 1.343060I
9.02317 − 6.53228I 0
u = −0.023624 + 0.893109I
a = 1.43160 + 0.33505I
b = −0.427467 − 1.146070I
2.59924 − 1.36437I 0
u = −0.023624 − 0.893109I
a = 1.43160 − 0.33505I
b = −0.427467 + 1.146070I
2.59924 + 1.36437I 0
8
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.764211 + 0.800673I
a = 1.54670 − 0.47986I
b = −0.52662 − 1.32113I
7.48729 − 2.49327I 0
u = −0.764211 − 0.800673I
a = 1.54670 + 0.47986I
b = −0.52662 + 1.32113I
7.48729 + 2.49327I 0
u = 0.806818 + 0.762402I
a = 0.932992 + 1.027070I
b = −1.298740 − 0.344084I
11.37510 − 4.50217I 0
u = 0.806818 − 0.762402I
a = 0.932992 − 1.027070I
b = −1.298740 + 0.344084I
11.37510 + 4.50217I 0
u = −0.703610 + 0.865980I
a = 1.131380 − 0.349386I
b = −0.633257 + 0.178207I
5.57129 − 2.70061I 0
u = −0.703610 − 0.865980I
a = 1.131380 + 0.349386I
b = −0.633257 − 0.178207I
5.57129 + 2.70061I 0
u = 0.726133 + 0.873262I
a = −1.31851 − 1.10584I
b = 1.67613 + 0.13892I
5.43661 + 2.76949I 0
u = 0.726133 − 0.873262I
a = −1.31851 + 1.10584I
b = 1.67613 − 0.13892I
5.43661 − 2.76949I 0
u = 0.688472 + 0.473096I
a = −0.199022 − 0.665762I
b = −0.211697 + 0.099066I
3.72379 + 0.67463I 0
u = 0.688472 − 0.473096I
a = −0.199022 + 0.665762I
b = −0.211697 − 0.099066I
3.72379 − 0.67463I 0
9
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.719491 + 0.924050I
a = 0.804282 + 0.829297I
b = −0.117343 + 1.380920I
6.95460 + 5.38684I 0
u = 0.719491 − 0.924050I
a = 0.804282 − 0.829297I
b = −0.117343 − 1.380920I
6.95460 − 5.38684I 0
u = 0.704822 + 0.935335I
a = 1.285040 + 0.272947I
b = −0.065644 + 1.227300I
2.83607 + 2.46285I 0
u = 0.704822 − 0.935335I
a = 1.285040 − 0.272947I
b = −0.065644 − 1.227300I
2.83607 − 2.46285I 0
u = −0.627669 + 1.016570I
a = 0.957118 − 0.642842I
b = −0.925935 − 0.125369I
2.89976 − 7.88337I 0
u = −0.627669 − 1.016570I
a = 0.957118 + 0.642842I
b = −0.925935 + 0.125369I
2.89976 + 7.88337I 0
u = 1.078200 + 0.516103I
a = 0.312864 + 0.366963I
b = −0.127842 + 1.201690I
7.45884 + 1.96382I 0
u = 1.078200 − 0.516103I
a = 0.312864 − 0.366963I
b = −0.127842 − 1.201690I
7.45884 − 1.96382I 0
u = −0.708192 + 0.970538I
a = −1.55393 + 0.30428I
b = 0.42556 + 1.41768I
3.36549 − 7.71269I 0
u = −0.708192 − 0.970538I
a = −1.55393 − 0.30428I
b = 0.42556 − 1.41768I
3.36549 + 7.71269I 0
10
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.743599 + 0.944448I
a = −0.409508 − 0.163918I
b = −0.30345 + 1.38705I
7.04718 − 3.21757I 0
u = −0.743599 − 0.944448I
a = −0.409508 + 0.163918I
b = −0.30345 − 1.38705I
7.04718 + 3.21757I 0
u = −0.713232 + 0.971192I
a = −2.14749 − 0.16533I
b = 0.265095 + 1.319150I
14.3327 − 6.6828I 0
u = −0.713232 − 0.971192I
a = −2.14749 + 0.16533I
b = 0.265095 − 1.319150I
14.3327 + 6.6828I 0
u = 0.587429 + 1.064290I
a = 0.006483 + 0.463539I
b = −0.0760179 + 0.1019750I
1.99866 + 4.27946I 0
u = 0.587429 − 1.064290I
a = 0.006483 − 0.463539I
b = −0.0760179 − 0.1019750I
1.99866 − 4.27946I 0
u = 0.730979 + 0.973848I
a = 2.16693 − 0.00922I
b = −0.82519 + 1.51811I
14.7938 + 3.3348I 0
u = 0.730979 − 0.973848I
a = 2.16693 + 0.00922I
b = −0.82519 − 1.51811I
14.7938 − 3.3348I 0
u = 0.749141 + 0.979656I
a = 1.37421 + 0.69699I
b = −1.41804 + 0.13113I
10.7084 + 10.3555I 0
u = 0.749141 − 0.979656I
a = 1.37421 − 0.69699I
b = −1.41804 − 0.13113I
10.7084 − 10.3555I 0
11
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.048608 + 0.750751I
a = −1.38279 − 1.56458I
b = 0.779034 − 0.538606I
1.68546 + 0.16765I −8.00000 + 0.I
u = 0.048608 − 0.750751I
a = −1.38279 + 1.56458I
b = 0.779034 + 0.538606I
1.68546 − 0.16765I −8.00000 + 0.I
u = 0.233771 + 1.227040I
a = 0.899341 − 0.630264I
b = −0.357995 + 1.042710I
1.45365 + 5.80199I 0
u = 0.233771 − 1.227040I
a = 0.899341 + 0.630264I
b = −0.357995 − 1.042710I
1.45365 − 5.80199I 0
u = 1.055390 + 0.671932I
a = 0.016625 + 0.154982I
b = −0.45093 − 1.53503I
17.4631 − 10.5485I 0
u = 1.055390 − 0.671932I
a = 0.016625 − 0.154982I
b = −0.45093 + 1.53503I
17.4631 + 10.5485I 0
u = 0.294195 + 0.676992I
a = −1.22935 − 1.04561I
b = 0.652001 + 0.964062I
1.07815 − 1.00344I 0
u = 0.294195 − 0.676992I
a = −1.22935 + 1.04561I
b = 0.652001 − 0.964062I
1.07815 + 1.00344I 0
u = −0.749047 + 1.044310I
a = 1.53319 − 0.33817I
b = −0.38115 − 1.41268I
7.8840 − 12.5635I 0
u = −0.749047 − 1.044310I
a = 1.53319 + 0.33817I
b = −0.38115 + 1.41268I
7.8840 + 12.5635I 0
12
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.120559 + 1.279760I
a = −0.47126 − 1.61592I
b = 0.237383 + 1.271990I
4.59560 − 3.27389I 0
u = −0.120559 − 1.279760I
a = −0.47126 + 1.61592I
b = 0.237383 − 1.271990I
4.59560 + 3.27389I 0
u = −0.774879 + 1.033690I
a = −0.876089 + 0.146350I
b = 0.735854 − 0.243311I
9.21759 − 2.32867I 0
u = −0.774879 − 1.033690I
a = −0.876089 − 0.146350I
b = 0.735854 + 0.243311I
9.21759 + 2.32867I 0
u = 0.743217 + 1.078610I
a = −1.91151 + 0.20399I
b = 0.63523 − 1.61393I
10.5811 + 10.9341I 0
u = 0.743217 − 1.078610I
a = −1.91151 − 0.20399I
b = 0.63523 + 1.61393I
10.5811 − 10.9341I 0
u = 0.809651 + 1.122980I
a = 1.72454 − 0.09217I
b = −0.57794 + 1.52854I
16.0137 + 17.2862I 0
u = 0.809651 − 1.122980I
a = 1.72454 + 0.09217I
b = −0.57794 − 1.52854I
16.0137 − 17.2862I 0
u = −0.776522 + 1.151580I
a = 1.44249 + 0.27410I
b = −0.303897 − 1.263650I
9.01377 − 6.21436I 0
u = −0.776522 − 1.151580I
a = 1.44249 − 0.27410I
b = −0.303897 + 1.263650I
9.01377 + 6.21436I 0
13
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.86831 + 1.12947I
a = −0.811002 + 0.025216I
b = 0.107445 − 1.239510I
5.68735 + 4.99956I 0
u = 0.86831 − 1.12947I
a = −0.811002 − 0.025216I
b = 0.107445 + 1.239510I
5.68735 − 4.99956I 0
u = 0.042049 + 0.502770I
a = −0.45019 − 3.58868I
b = −0.331026 + 0.797513I
4.10173 + 1.38508I −6.99846 − 5.18657I
u = 0.042049 − 0.502770I
a = −0.45019 + 3.58868I
b = −0.331026 − 0.797513I
4.10173 − 1.38508I −6.99846 + 5.18657I
u = −1.42970 + 0.45260I
a = −0.0289961 + 0.1132680I
b = 0.082748 − 1.309140I
14.6083 − 2.0661I 0
u = −1.42970 − 0.45260I
a = −0.0289961 − 0.1132680I
b = 0.082748 + 1.309140I
14.6083 + 2.0661I 0
u = −0.33951 + 1.47842I
a = 0.669897 + 1.011210I
b = −0.222808 − 1.242850I
7.88132 − 8.25912I 0
u = −0.33951 − 1.47842I
a = 0.669897 − 1.011210I
b = −0.222808 + 1.242850I
7.88132 + 8.25912I 0
u = −0.051433 + 0.438790I
a = 1.291860 + 0.130913I
b = −0.13751 + 1.66263I
12.14830 − 1.91198I −9.81121 + 4.85503I
u = −0.051433 − 0.438790I
a = 1.291860 − 0.130913I
b = −0.13751 − 1.66263I
12.14830 + 1.91198I −9.81121 − 4.85503I
14
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.400661 + 0.105641I
a = 1.027140 − 0.099097I
b = 0.220831 − 0.806135I
1.84584 + 1.50741I −1.79883 − 5.24379I
u = 0.400661 − 0.105641I
a = 1.027140 + 0.099097I
b = 0.220831 + 0.806135I
1.84584 − 1.50741I −1.79883 + 5.24379I
u = −0.98850 + 1.27967I
a = −1.046920 − 0.110585I
b = 0.329701 + 1.201370I
12.16570 − 6.23367I 0
u = −0.98850 − 1.27967I
a = −1.046920 + 0.110585I
b = 0.329701 − 1.201370I
12.16570 + 6.23367I 0
u = −0.041896 + 0.274421I
a = 3.93536 + 6.99260I
b = −0.346022 + 0.707510I
8.17527 + 4.24698I 1.66879 − 8.52198I
u = −0.041896 − 0.274421I
a = 3.93536 − 6.99260I
b = −0.346022 − 0.707510I
8.17527 − 4.24698I 1.66879 + 8.52198I
u = −0.273724
a = 0.993855
b = 0.418225
−0.715457 −13.8390
15
II. I
u
2
= h2.13 × 10
6
u
29
+ 9.44 × 10
6
u
28
+ · · · + 3.96 × 10
6
b − 4.26 × 10
6
, 2.92 ×
10
7
u
29
+7.94×10
7
u
28
+· · · +3.96×10
6
a+2.08×10
7
, u
30
+3u
29
+· · · +3u +1i
(i) Arc colorings
a
2
=
0
u
a
7
=
1
0
a
6
=
1
u
2
a
3
=
u
u
3
+ u
a
1
=
u
3
u
5
+ u
3
+ u
a
11
=
−7.38348u
29
− 20.0470u
28
+ ··· − 25.6615u − 5.26088
−0.538016u
29
− 2.38435u
28
+ ··· + 1.52402u + 1.07451
a
5
=
−1.41047u
29
+ 4.08168u
28
+ ··· + 38.5120u + 19.1518
−1.03955u
29
− 5.77094u
28
+ ··· − 13.5288u − 4.31310
a
12
=
11.1058u
29
+ 26.5222u
28
+ ··· + 9.04210u − 5.67327
−3.56537u
29
− 8.19367u
28
+ ··· + 0.640742u + 1.45368
a
10
=
−7.92149u
29
− 22.4313u
28
+ ··· − 24.1374u − 4.18637
−0.538016u
29
− 2.38435u
28
+ ··· + 1.52402u + 1.07451
a
8
=
1.10526u
29
+ 8.76852u
28
+ ··· + 18.3986u + 7.64244
−2.73707u
29
− 6.13105u
28
+ ··· − 0.431273u + 0.940510
a
4
=
−12.2492u
29
− 31.8845u
28
+ ··· − 18.7182u + 0.618818
0.621245u
29
− 0.0800342u
28
+ ··· − 11.3400u − 3.86308
a
9
=
2.08569u
29
+ 12.3698u
28
+ ··· + 26.6734u + 9.94719
−3.61317u
29
− 10.4115u
28
+ ··· − 9.74404u − 2.56995
(ii) Obstruction class = 1
(iii) Cusp Shapes =
5159705
990077
u
29
+
22034949
990077
u
28
+ ··· +
61479057
990077
u +
8886923
990077
16
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
30
− 13u
29
+ ··· − 13u + 1
c
2
u
30
− 3u
29
+ ··· − 3u + 1
c
3
u
30
+ 5u
28
+ ··· + 2u + 1
c
4
, c
5
u
30
+ 18u
28
+ ··· + 4u + 1
c
6
u
30
+ 3u
29
+ ··· + 3u + 1
c
7
u
30
− 4u
29
+ ··· − 4u + 1
c
8
u
30
+ 2u
29
+ ··· + 6u + 4
c
9
u
30
+ 5u
28
+ ··· + 8u + 1
c
10
u
30
+ 4u
29
+ ··· + 4u + 1
c
11
u
30
+ 18u
28
+ ··· − 4u + 1
c
12
u
30
− 2u
29
+ ··· − 6u + 4
17
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
30
+ 21y
29
+ ··· + 13y + 1
c
2
, c
6
y
30
+ 13y
29
+ ··· + 13y + 1
c
3
y
30
+ 10y
29
+ ··· + 14y + 1
c
4
, c
5
, c
11
y
30
+ 36y
29
+ ··· + 20y + 1
c
7
, c
10
y
30
+ 20y
29
+ ··· + 12y + 1
c
8
, c
12
y
30
+ 22y
29
+ ··· + 164y + 16
c
9
y
30
+ 10y
29
+ ··· + 50y + 1
18
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.195308 + 0.957964I
a = −1.07212 + 1.33653I
b = 0.414320 − 0.801375I
−0.37236 + 2.52004I −5.45651 − 4.22445I
u = 0.195308 − 0.957964I
a = −1.07212 − 1.33653I
b = 0.414320 + 0.801375I
−0.37236 − 2.52004I −5.45651 + 4.22445I
u = 0.466434 + 0.845804I
a = −0.892880 − 0.832983I
b = 0.967848 − 0.062813I
−1.70840 + 1.91345I −13.43138 + 2.91957I
u = 0.466434 − 0.845804I
a = −0.892880 + 0.832983I
b = 0.967848 + 0.062813I
−1.70840 − 1.91345I −13.43138 − 2.91957I
u = −0.901262 + 0.507417I
a = 0.093250 − 0.369620I
b = −0.276345 + 1.366110I
13.25460 − 1.69916I 0.47422 + 2.17666I
u = −0.901262 − 0.507417I
a = 0.093250 + 0.369620I
b = −0.276345 − 1.366110I
13.25460 + 1.69916I 0.47422 − 2.17666I
u = −0.309838 + 0.904507I
a = 0.25293 + 1.39391I
b = 0.565566 + 0.136116I
1.80347 − 1.32517I −4.12560 + 4.83226I
u = −0.309838 − 0.904507I
a = 0.25293 − 1.39391I
b = 0.565566 − 0.136116I
1.80347 + 1.32517I −4.12560 − 4.83226I
u = 0.770041 + 0.706619I
a = 0.992277 + 0.928887I
b = −0.227353 + 1.210060I
5.95829 + 1.96683I −2.61215 − 2.76487I
u = 0.770041 − 0.706619I
a = 0.992277 − 0.928887I
b = −0.227353 − 1.210060I
5.95829 − 1.96683I −2.61215 + 2.76487I
19
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.687218 + 0.874757I
a = −1.31408 + 0.74628I
b = 1.226180 − 0.137254I
4.33803 − 2.64785I −7.28108 + 2.55575I
u = −0.687218 − 0.874757I
a = −1.31408 − 0.74628I
b = 1.226180 + 0.137254I
4.33803 + 2.64785I −7.28108 − 2.55575I
u = 0.524353 + 1.102340I
a = 0.567747 − 0.631453I
b = −0.163922 + 0.746611I
2.69473 + 4.61399I 0.43393 − 4.98963I
u = 0.524353 − 1.102340I
a = 0.567747 + 0.631453I
b = −0.163922 − 0.746611I
2.69473 − 4.61399I 0.43393 + 4.98963I
u = 0.052618 + 0.767054I
a = −1.40487 − 0.23613I
b = 0.567244 + 0.991173I
0.38855 − 1.43362I −10.77096 + 3.19735I
u = 0.052618 − 0.767054I
a = −1.40487 + 0.23613I
b = 0.567244 − 0.991173I
0.38855 + 1.43362I −10.77096 − 3.19735I
u = −0.416790 + 1.166540I
a = −0.317453 − 0.359239I
b = −0.127732 − 0.573484I
5.77733 − 6.51784I −2.42963 + 6.50104I
u = −0.416790 − 1.166540I
a = −0.317453 + 0.359239I
b = −0.127732 + 0.573484I
5.77733 + 6.51784I −2.42963 − 6.50104I
u = 0.787799 + 0.972770I
a = −0.707630 − 0.266604I
b = 0.027929 − 1.285710I
5.15442 + 3.95870I −2.90292 − 2.36325I
u = 0.787799 − 0.972770I
a = −0.707630 + 0.266604I
b = 0.027929 + 1.285710I
5.15442 − 3.95870I −2.90292 + 2.36325I
20
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.400683 + 0.601968I
a = −0.01171 + 2.07238I
b = −0.388672 − 0.875053I
4.56827 − 0.65664I −0.38201 − 1.75672I
u = 0.400683 − 0.601968I
a = −0.01171 − 2.07238I
b = −0.388672 + 0.875053I
4.56827 + 0.65664I −0.38201 + 1.75672I
u = −0.236150 + 0.675236I
a = −1.37606 − 3.52580I
b = −0.330690 + 0.524370I
7.84227 + 3.73571I −5.77697 + 1.81841I
u = −0.236150 − 0.675236I
a = −1.37606 + 3.52580I
b = −0.330690 − 0.524370I
7.84227 − 3.73571I −5.77697 − 1.81841I
u = −0.903508 + 1.019370I
a = 1.41787 − 0.13373I
b = −0.410945 − 1.028460I
11.87230 − 5.04347I 0.53474 + 2.19290I
u = −0.903508 − 1.019370I
a = 1.41787 + 0.13373I
b = −0.410945 + 1.028460I
11.87230 + 5.04347I 0.53474 − 2.19290I
u = −0.500831 + 0.362084I
a = −0.462531 − 0.517164I
b = −0.06917 − 1.58008I
12.66780 + 1.57160I 2.37536 + 1.96173I
u = −0.500831 − 0.362084I
a = −0.462531 + 0.517164I
b = −0.06917 + 1.58008I
12.66780 − 1.57160I 2.37536 − 1.96173I
u = −0.74164 + 1.24998I
a = −1.264740 − 0.447593I
b = 0.225746 + 1.334070I
9.65227 − 7.08993I 0. + 6.61887I
u = −0.74164 − 1.24998I
a = −1.264740 + 0.447593I
b = 0.225746 − 1.334070I
9.65227 + 7.08993I 0. − 6.61887I
21
III. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
(u
30
− 13u
29
+ ··· − 13u + 1)(u
107
+ 36u
106
+ ··· − 16866u − 361)
c
2
(u
30
− 3u
29
+ ··· − 3u + 1)(u
107
+ 18u
105
+ ··· − 24u + 19)
c
3
(u
30
+ 5u
28
+ ··· + 2u + 1)(u
107
− u
106
+ ··· + 875682u + 270676)
c
4
, c
5
(u
30
+ 18u
28
+ ··· + 4u + 1)(u
107
+ u
106
+ ··· − 3823u + 653)
c
6
(u
30
+ 3u
29
+ ··· + 3u + 1)(u
107
+ 18u
105
+ ··· − 24u + 19)
c
7
(u
30
− 4u
29
+ ··· − 4u + 1)(u
107
− 5u
106
+ ··· − 1215u + 43)
c
8
(u
30
+ 2u
29
+ ··· + 6u + 4)(u
107
+ 3u
106
+ ··· + 90u + 68)
c
9
(u
30
+ 5u
28
+ ··· + 8u + 1)(u
107
+ u
106
+ ··· + 3.39760 × 10
7
u + 5654997)
c
10
(u
30
+ 4u
29
+ ··· + 4u + 1)(u
107
− 5u
106
+ ··· − 1215u + 43)
c
11
(u
30
+ 18u
28
+ ··· − 4u + 1)(u
107
+ u
106
+ ··· − 3823u + 653)
c
12
(u
30
− 2u
29
+ ··· − 6u + 4)(u
107
+ 3u
106
+ ··· + 90u + 68)
22
IV. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
(y
30
+ 21y
29
+ ··· + 13y + 1)
· (y
107
+ 84y
106
+ ··· + 71806242y −130321)
c
2
, c
6
(y
30
+ 13y
29
+ ··· + 13y + 1)(y
107
+ 36y
106
+ ··· − 16866y −361)
c
3
(y
30
+ 10y
29
+ ··· + 14y + 1)
· (y
107
+ 45y
106
+ ··· − 2480148075396y −73265496976)
c
4
, c
5
, c
11
(y
30
+ 36y
29
+ ··· + 20y + 1)
· (y
107
+ 123y
106
+ ··· − 13417961y −426409)
c
7
, c
10
(y
30
+ 20y
29
+ ··· + 12y + 1)(y
107
+ 87y
106
+ ··· + 85175y −1849)
c
8
, c
12
(y
30
+ 22y
29
+ ··· + 164y + 16)(y
107
+ 85y
106
+ ··· − 46708y −4624)
c
9
(y
30
+ 10y
29
+ ··· + 50y + 1)
· (y
107
+ 57y
106
+ ··· − 1085652345824199y −31978991070009)
23
