12a
1081
(K12a
1081
)
A knot diagram
1
Linearized knot diagam
4 7 10 12 8 11 3 5 1 2 6 9
Solving Sequence
2,7
3
8,11
6 12 5 10 4 1 9
c
2
c
7
c
6
c
11
c
5
c
10
c
3
c
1
c
9
c
4
, c
8
, c
12
Ideals for irreducible components
2
of X
par
I
u
1
= h−6.71552 × 10
713
u
137
+ 1.22208 × 10
714
u
136
+ ··· + 1.77498 × 10
715
b − 8.44541 × 10
717
,
2.38801 × 10
718
u
137
+ 1.12887 × 10
718
u
136
+ ··· + 2.83805 × 10
719
a − 1.43193 × 10
723
,
u
138
− u
137
+ ··· − 38969u + 39973i
I
u
2
= h−1.96664 × 10
19
u
29
+ 4.76700 × 10
18
u
28
+ ··· + 1.93126 × 10
18
b − 2.16039 × 10
19
,
− 1.12071 × 10
18
u
29
− 4.65424 × 10
18
u
28
+ ··· + 7.72503 × 10
17
a + 1.15956 × 10
19
, u
30
− 5u
28
+ ··· + 3u + 1i
* 2 irreducible components of dim
C
= 0, with total 168 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−6.72 × 10
713
u
137
+ 1.22 × 10
714
u
136
+ · · · + 1.77 × 10
715
b − 8.45 ×
10
717
, 2.39 × 10
718
u
137
+ 1.13 × 10
718
u
136
+ · · · + 2.84 × 10
719
a − 1.43 ×
10
723
, u
138
− u
137
+ · · · − 38969u + 39973i
(i) Arc colorings
a
2
=
1
0
a
7
=
0
u
a
3
=
1
−u
2
a
8
=
u
−u
3
+ u
a
11
=
−0.0841427u
137
− 0.0397762u
136
+ ··· − 1556.39u + 5045.49
0.0378343u
137
− 0.0688504u
136
+ ··· − 2935.59u + 475.803
a
6
=
−0.00948334u
137
+ 0.0136277u
136
+ ··· + 823.451u + 2078.34
−0.125302u
137
+ 0.0935960u
136
+ ··· + 3676.61u + 1770.16
a
12
=
0.704121u
137
− 0.0203105u
136
+ ··· − 1419.49u − 28148.0
−0.00997754u
137
− 0.00245078u
136
+ ··· − 58.2883u − 451.123
a
5
=
0.0611026u
137
− 0.0773930u
136
+ ··· − 2719.78u + 2720.21
−0.122978u
137
+ 0.0948035u
136
+ ··· + 3751.24u + 1595.19
a
10
=
−0.121977u
137
+ 0.0290742u
136
+ ··· + 1379.20u + 4569.68
0.0378343u
137
− 0.0688504u
136
+ ··· − 2935.59u + 475.803
a
4
=
−0.0294149u
137
− 0.133869u
136
+ ··· − 5251.86u + 4848.39
0.0378481u
137
+ 0.0929219u
136
+ ··· + 3476.87u − 5619.06
a
1
=
0.232272u
137
− 0.0507081u
136
+ ··· − 1502.79u − 8678.55
0.0517901u
137
− 0.0821151u
136
+ ··· − 3701.95u + 2195.58
a
9
=
0.477195u
137
+ 0.0337432u
136
+ ··· + 367.793u − 21597.4
−0.0262764u
137
+ 0.0591113u
136
+ ··· + 2863.72u − 1195.39
(ii) Obstruction class = −1
(iii) Cusp Shapes = −0.288478u
137
+ 0.0182579u
136
+ ··· + 166.945u + 9522.21
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
5(5u
138
− 70u
137
+ ··· − 54u + 1)
c
2
, c
7
u
138
+ u
137
+ ··· + 38969u + 39973
c
3
u
138
+ u
137
+ ··· + 11328u + 688
c
4
u
138
+ 3u
137
+ ··· + 1824290u + 445340
c
5
, c
8
5(5u
138
+ 20u
137
+ ··· + 566u + 1601)
c
6
, c
11
u
138
− u
137
+ ··· + 3352910u + 356879
c
9
, c
12
u
138
+ 3u
137
+ ··· + 35u + 293
c
10
5(5u
138
− 15u
137
+ ··· − 8.52426 × 10
8
u + 2.04508 × 10
8
)
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
25(25y
138
+ 220y
137
+ ··· − 208y + 1)
c
2
, c
7
y
138
− 81y
137
+ ··· − 16606311865y + 1597840729
c
3
y
138
+ 21y
137
+ ··· + 88302848y + 473344
c
4
y
138
− 45y
137
+ ··· − 10148860553420y + 198327715600
c
5
, c
8
25(25y
138
+ 2770y
137
+ ··· + 9.04133 × 10
8
y + 2563201)
c
6
, c
11
y
138
+ 103y
137
+ ··· + 1941665805688y + 127362620641
c
9
, c
12
y
138
− 109y
137
+ ··· + 451753y + 85849
c
10
25(25y
138
− 1795y
137
+ ··· − 1.65727 × 10
18
y + 4.18236 × 10
16
)
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.996983 + 0.016036I
a = −0.196561 + 1.103920I
b = 2.82578 + 0.40806I
−0.433411 − 0.065140I 0
u = −0.996983 − 0.016036I
a = −0.196561 − 1.103920I
b = 2.82578 − 0.40806I
−0.433411 + 0.065140I 0
u = −1.022530 + 0.051510I
a = 0.080646 − 1.132090I
b = −0.76871 − 1.55789I
1.37724 − 0.93730I 0
u = −1.022530 − 0.051510I
a = 0.080646 + 1.132090I
b = −0.76871 + 1.55789I
1.37724 + 0.93730I 0
u = 1.017890 + 0.143350I
a = 0.238571 − 1.029880I
b = −0.02209 − 1.84159I
0.88004 + 4.56519I 0
u = 1.017890 − 0.143350I
a = 0.238571 + 1.029880I
b = −0.02209 + 1.84159I
0.88004 − 4.56519I 0
u = 0.965183 + 0.050981I
a = 1.65426 + 1.36327I
b = −0.558668 − 0.179049I
−2.92758 + 3.55181I 0
u = 0.965183 − 0.050981I
a = 1.65426 − 1.36327I
b = −0.558668 + 0.179049I
−2.92758 − 3.55181I 0
u = 1.018030 + 0.211721I
a = −0.081174 + 1.142740I
b = −0.19084 + 1.95944I
−4.44869 + 10.24780I 0
u = 1.018030 − 0.211721I
a = −0.081174 − 1.142740I
b = −0.19084 − 1.95944I
−4.44869 − 10.24780I 0
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.504413 + 0.811235I
a = −0.062303 − 0.615407I
b = 0.296279 − 0.582273I
−3.47151 + 1.07041I 0
u = 0.504413 − 0.811235I
a = −0.062303 + 0.615407I
b = 0.296279 + 0.582273I
−3.47151 − 1.07041I 0
u = −0.793874 + 0.531232I
a = −0.518585 − 1.140980I
b = 1.104970 − 0.745819I
−6.65052 + 1.68021I 0
u = −0.793874 − 0.531232I
a = −0.518585 + 1.140980I
b = 1.104970 + 0.745819I
−6.65052 − 1.68021I 0
u = −0.987445 + 0.354633I
a = −0.371369 + 1.118390I
b = 0.188524 + 1.020030I
−3.26198 − 2.34672I 0
u = −0.987445 − 0.354633I
a = −0.371369 − 1.118390I
b = 0.188524 − 1.020030I
−3.26198 + 2.34672I 0
u = −0.813351 + 0.666660I
a = 0.814371 + 0.121481I
b = 0.794972 + 1.078600I
−6.70110 − 6.41909I 0
u = −0.813351 − 0.666660I
a = 0.814371 − 0.121481I
b = 0.794972 − 1.078600I
−6.70110 + 6.41909I 0
u = 0.943808 + 0.082756I
a = −0.64334 + 1.61771I
b = −0.177110 + 1.140090I
−2.89503 − 2.86908I 0
u = 0.943808 − 0.082756I
a = −0.64334 − 1.61771I
b = −0.177110 − 1.140090I
−2.89503 + 2.86908I 0
6
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.560468 + 0.902876I
a = −0.161331 + 0.567791I
b = −0.094337 + 0.818976I
−8.01191 + 0.19309I 0
u = 0.560468 − 0.902876I
a = −0.161331 − 0.567791I
b = −0.094337 − 0.818976I
−8.01191 − 0.19309I 0
u = −0.932670 + 0.024684I
a = 0.471310 + 0.914988I
b = −1.47605 − 0.30011I
0.853485 − 0.671174I 0
u = −0.932670 − 0.024684I
a = 0.471310 − 0.914988I
b = −1.47605 + 0.30011I
0.853485 + 0.671174I 0
u = −0.090994 + 0.922516I
a = 1.370980 − 0.008494I
b = 1.055260 + 0.459695I
4.73578 + 2.62567I 0
u = −0.090994 − 0.922516I
a = 1.370980 + 0.008494I
b = 1.055260 − 0.459695I
4.73578 − 2.62567I 0
u = −1.016830 + 0.343231I
a = 1.37765 + 0.82051I
b = −0.808601 + 0.742412I
−0.21336 − 6.06499I 0
u = −1.016830 − 0.343231I
a = 1.37765 − 0.82051I
b = −0.808601 − 0.742412I
−0.21336 + 6.06499I 0
u = 1.056910 + 0.219362I
a = −1.070860 + 0.250455I
b = 0.692913 − 0.169665I
−1.41103 + 3.57036I 0
u = 1.056910 − 0.219362I
a = −1.070860 − 0.250455I
b = 0.692913 + 0.169665I
−1.41103 − 3.57036I 0
7
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.770956 + 0.423785I
a = −1.21398 + 1.30467I
b = −0.297099 + 0.525091I
−3.17629 − 1.83028I 0
u = −0.770956 − 0.423785I
a = −1.21398 − 1.30467I
b = −0.297099 − 0.525091I
−3.17629 + 1.83028I 0
u = 0.092480 + 1.116510I
a = 1.147840 − 0.296204I
b = 1.059000 − 0.502739I
1.41980 − 7.64753I 0
u = 0.092480 − 1.116510I
a = 1.147840 + 0.296204I
b = 1.059000 + 0.502739I
1.41980 + 7.64753I 0
u = 0.821386 + 0.299519I
a = −0.264749 − 0.106864I
b = 0.611123 − 1.044560I
−1.51452 + 2.60208I 0
u = 0.821386 − 0.299519I
a = −0.264749 + 0.106864I
b = 0.611123 + 1.044560I
−1.51452 − 2.60208I 0
u = −1.12788
a = −0.744748
b = 0.811316
2.10767 0
u = 1.060720 + 0.414310I
a = −0.723098 + 0.361918I
b = 0.820123 + 0.152530I
−1.66016 + 3.48939I 0
u = 1.060720 − 0.414310I
a = −0.723098 − 0.361918I
b = 0.820123 − 0.152530I
−1.66016 − 3.48939I 0
u = −1.14037
a = −0.768989
b = 0.831977
2.10732 0
8
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.012209 + 1.140360I
a = −1.116910 − 0.163245I
b = −0.942393 − 0.532548I
0.46890 + 6.76628I 0
u = 0.012209 − 1.140360I
a = −1.116910 + 0.163245I
b = −0.942393 + 0.532548I
0.46890 − 6.76628I 0
u = −1.126750 + 0.187618I
a = 0.157445 − 0.322501I
b = 0.128589 + 0.959329I
−0.269172 + 0.879761I 0
u = −1.126750 − 0.187618I
a = 0.157445 + 0.322501I
b = 0.128589 − 0.959329I
−0.269172 − 0.879761I 0
u = −0.428505 + 0.738242I
a = 0.427428 + 0.902271I
b = 0.731836 + 1.029090I
−7.92339 + 8.13331I 0
u = −0.428505 − 0.738242I
a = 0.427428 − 0.902271I
b = 0.731836 − 1.029090I
−7.92339 − 8.13331I 0
u = 0.413343 + 1.070260I
a = 0.352637 + 0.478381I
b = −0.510469 + 0.482310I
−6.40023 + 2.19729I 0
u = 0.413343 − 1.070260I
a = 0.352637 − 0.478381I
b = −0.510469 − 0.482310I
−6.40023 − 2.19729I 0
u = −1.138890 + 0.216171I
a = 0.938274 − 0.427635I
b = −0.865069 + 0.151451I
0.60557 − 3.31488I 0
u = −1.138890 − 0.216171I
a = 0.938274 + 0.427635I
b = −0.865069 − 0.151451I
0.60557 + 3.31488I 0
9
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 1.159580 + 0.202123I
a = 0.523686 − 0.267001I
b = −1.171280 − 0.588584I
3.49433 + 3.63749I 0
u = 1.159580 − 0.202123I
a = 0.523686 + 0.267001I
b = −1.171280 + 0.588584I
3.49433 − 3.63749I 0
u = 0.520480 + 0.634001I
a = 0.729739 + 1.000500I
b = 1.262870 − 0.523968I
−0.10072 + 2.23441I 0
u = 0.520480 − 0.634001I
a = 0.729739 − 1.000500I
b = 1.262870 + 0.523968I
−0.10072 − 2.23441I 0
u = −0.411925 + 0.705211I
a = −1.26847 + 0.66370I
b = −1.120090 − 0.278044I
1.50408 − 1.69310I 0
u = −0.411925 − 0.705211I
a = −1.26847 − 0.66370I
b = −1.120090 + 0.278044I
1.50408 + 1.69310I 0
u = 0.990132 + 0.648203I
a = 0.469879 − 0.516106I
b = −0.548868 − 0.577042I
−6.59865 + 5.38342I 0
u = 0.990132 − 0.648203I
a = 0.469879 + 0.516106I
b = −0.548868 + 0.577042I
−6.59865 − 5.38342I 0
u = −0.695626 + 0.415796I
a = −0.609051 + 0.662260I
b = −0.589397 − 0.434291I
1.15888 − 1.45618I 0
u = −0.695626 − 0.415796I
a = −0.609051 − 0.662260I
b = −0.589397 + 0.434291I
1.15888 + 1.45618I 0
10
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −1.081540 + 0.505394I
a = −0.180712 + 1.318090I
b = −1.80488 + 0.54914I
3.38089 − 2.95458I 0
u = −1.081540 − 0.505394I
a = −0.180712 − 1.318090I
b = −1.80488 − 0.54914I
3.38089 + 2.95458I 0
u = 1.162870 + 0.276034I
a = 0.096834 + 1.367440I
b = 0.980530 + 0.470691I
8.55444 + 1.64656I 0
u = 1.162870 − 0.276034I
a = 0.096834 − 1.367440I
b = 0.980530 − 0.470691I
8.55444 − 1.64656I 0
u = −1.113260 + 0.456514I
a = −0.982564 − 0.655815I
b = 1.038310 − 0.681708I
−5.74217 − 12.64610I 0
u = −1.113260 − 0.456514I
a = −0.982564 + 0.655815I
b = 1.038310 + 0.681708I
−5.74217 + 12.64610I 0
u = 0.008076 + 0.790874I
a = 0.260982 − 0.671054I
b = 0.478744 − 0.871301I
−4.04280 − 4.31437I 0
u = 0.008076 − 0.790874I
a = 0.260982 + 0.671054I
b = 0.478744 + 0.871301I
−4.04280 + 4.31437I 0
u = 1.166460 + 0.431597I
a = 0.29623 − 1.39948I
b = −1.44889 − 1.13303I
3.17025 + 5.90259I 0
u = 1.166460 − 0.431597I
a = 0.29623 + 1.39948I
b = −1.44889 + 1.13303I
3.17025 − 5.90259I 0
11
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 1.209910 + 0.311574I
a = 0.088859 + 0.869332I
b = 1.83190 + 1.37499I
1.38856 + 0.65407I 0
u = 1.209910 − 0.311574I
a = 0.088859 − 0.869332I
b = 1.83190 − 1.37499I
1.38856 − 0.65407I 0
u = 1.146150 + 0.539747I
a = 0.606393 − 0.247136I
b = −1.127740 − 0.159710I
−4.00738 + 3.41898I 0
u = 1.146150 − 0.539747I
a = 0.606393 + 0.247136I
b = −1.127740 + 0.159710I
−4.00738 − 3.41898I 0
u = −1.129130 + 0.582961I
a = −0.445496 + 0.901056I
b = −1.285570 + 0.184924I
2.40065 − 2.15460I 0
u = −1.129130 − 0.582961I
a = −0.445496 − 0.901056I
b = −1.285570 − 0.184924I
2.40065 + 2.15460I 0
u = 1.030820 + 0.753682I
a = −0.756733 − 1.147380I
b = −1.43686 − 0.31488I
2.14575 + 3.01232I 0
u = 1.030820 − 0.753682I
a = −0.756733 + 1.147380I
b = −1.43686 + 0.31488I
2.14575 − 3.01232I 0
u = 0.634624 + 0.312550I
a = 1.59810 + 0.77415I
b = −0.579748 − 0.769653I
−5.55250 − 7.98043I 0
u = 0.634624 − 0.312550I
a = 1.59810 − 0.77415I
b = −0.579748 + 0.769653I
−5.55250 + 7.98043I 0
12
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 1.256390 + 0.320487I
a = −0.513825 + 0.288479I
b = 1.080400 + 0.615837I
−0.04047 + 8.34936I 0
u = 1.256390 − 0.320487I
a = −0.513825 − 0.288479I
b = 1.080400 − 0.615837I
−0.04047 − 8.34936I 0
u = 0.189025 + 1.313350I
a = −1.009440 + 0.156140I
b = −1.072560 + 0.500228I
−4.01940 − 12.59110I 0
u = 0.189025 − 1.313350I
a = −1.009440 − 0.156140I
b = −1.072560 − 0.500228I
−4.01940 + 12.59110I 0
u = 1.237780 + 0.542430I
a = 0.373747 + 1.064420I
b = 0.982098 + 0.406502I
8.60909 + 2.05167I 0
u = 1.237780 − 0.542430I
a = 0.373747 − 1.064420I
b = 0.982098 − 0.406502I
8.60909 − 2.05167I 0
u = −1.324450 + 0.269204I
a = −0.188429 − 1.262470I
b = 0.787991 − 0.440040I
5.38983 − 5.08115I 0
u = −1.324450 − 0.269204I
a = −0.188429 + 1.262470I
b = 0.787991 + 0.440040I
5.38983 + 5.08115I 0
u = −0.197399 + 1.343800I
a = −0.857178 − 0.030179I
b = −0.781340 − 0.073537I
−1.13873 + 1.54484I 0
u = −0.197399 − 1.343800I
a = −0.857178 + 0.030179I
b = −0.781340 + 0.073537I
−1.13873 − 1.54484I 0
13
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.430877 + 0.462874I
a = −0.74939 − 1.49100I
b = −0.525108 − 0.989918I
−1.87250 + 2.69080I −2.88096 − 3.36538I
u = −0.430877 − 0.462874I
a = −0.74939 + 1.49100I
b = −0.525108 + 0.989918I
−1.87250 − 2.69080I −2.88096 + 3.36538I
u = 1.358020 + 0.265113I
a = 0.084193 − 1.061350I
b = −1.129230 − 0.560877I
7.00962 + 4.90136I 0
u = 1.358020 − 0.265113I
a = 0.084193 + 1.061350I
b = −1.129230 + 0.560877I
7.00962 − 4.90136I 0
u = −1.287330 + 0.522829I
a = 0.101630 − 1.029570I
b = 1.68143 − 0.76937I
8.40357 − 7.89822I 0
u = −1.287330 − 0.522829I
a = 0.101630 + 1.029570I
b = 1.68143 + 0.76937I
8.40357 + 7.89822I 0
u = −0.285947 + 0.538897I
a = −1.53356 − 0.32358I
b = 0.659564 − 0.112720I
−5.11736 − 1.24300I −1.70455 + 2.55035I
u = −0.285947 − 0.538897I
a = −1.53356 + 0.32358I
b = 0.659564 + 0.112720I
−5.11736 + 1.24300I −1.70455 − 2.55035I
u = −0.362457 + 1.343170I
a = 0.865960 − 0.059347I
b = 0.532963 + 0.185245I
−5.04634 + 2.90316I 0
u = −0.362457 − 1.343170I
a = 0.865960 + 0.059347I
b = 0.532963 − 0.185245I
−5.04634 − 2.90316I 0
14
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.010838 + 0.579003I
a = −1.76510 + 0.96046I
b = −0.838793 + 0.502080I
−0.01717 − 1.98636I 2.78651 + 4.49302I
u = 0.010838 − 0.579003I
a = −1.76510 − 0.96046I
b = −0.838793 − 0.502080I
−0.01717 + 1.98636I 2.78651 − 4.49302I
u = 0.566220 + 0.086865I
a = −0.978966 + 0.126970I
b = 0.981078 + 0.088750I
−2.00025 − 0.00344I −6.94218 − 0.61335I
u = 0.566220 − 0.086865I
a = −0.978966 − 0.126970I
b = 0.981078 − 0.088750I
−2.00025 + 0.00344I −6.94218 + 0.61335I
u = 1.38859 + 0.38666I
a = −0.012945 − 0.765406I
b = −1.31049 − 0.76680I
4.68075 + 3.92363I 0
u = 1.38859 − 0.38666I
a = −0.012945 + 0.765406I
b = −1.31049 + 0.76680I
4.68075 − 3.92363I 0
u = 0.525541 + 0.164085I
a = −1.69473 − 0.88728I
b = 0.295736 + 0.960287I
−0.45907 − 2.93054I 0. − 1.91622I
u = 0.525541 − 0.164085I
a = −1.69473 + 0.88728I
b = 0.295736 − 0.960287I
−0.45907 + 2.93054I 0. + 1.91622I
u = 1.33594 + 0.57325I
a = 0.019626 + 1.132410I
b = 1.51970 + 0.86519I
5.3209 + 13.6138I 0
u = 1.33594 − 0.57325I
a = 0.019626 − 1.132410I
b = 1.51970 − 0.86519I
5.3209 − 13.6138I 0
15
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −1.36480 + 0.54080I
a = −0.094028 + 0.965375I
b = −1.62793 + 0.90934I
4.78648 − 12.63490I 0
u = −1.36480 − 0.54080I
a = −0.094028 − 0.965375I
b = −1.62793 − 0.90934I
4.78648 + 12.63490I 0
u = −1.34700 + 0.61996I
a = 0.171636 − 0.968001I
b = 1.06851 − 1.00429I
−1.46014 − 9.68701I 0
u = −1.34700 − 0.61996I
a = 0.171636 + 0.968001I
b = 1.06851 + 1.00429I
−1.46014 + 9.68701I 0
u = −1.45806 + 0.40964I
a = 0.201591 − 0.773749I
b = 1.042010 − 0.296088I
6.55050 + 2.02054I 0
u = −1.45806 − 0.40964I
a = 0.201591 + 0.773749I
b = 1.042010 + 0.296088I
6.55050 − 2.02054I 0
u = 0.82795 + 1.27576I
a = −0.495265 − 0.477064I
b = −1.166930 − 0.026150I
−4.59262 + 4.27321I 0
u = 0.82795 − 1.27576I
a = −0.495265 + 0.477064I
b = −1.166930 + 0.026150I
−4.59262 − 4.27321I 0
u = 1.38279 + 0.64774I
a = −0.086681 − 1.060280I
b = −1.54040 − 0.84654I
−0.1511 + 19.4140I 0
u = 1.38279 − 0.64774I
a = −0.086681 + 1.060280I
b = −1.54040 + 0.84654I
−0.1511 − 19.4140I 0
16
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −1.42623 + 0.59463I
a = −0.096708 + 0.938802I
b = −1.174820 + 0.735466I
3.13111 − 8.34888I 0
u = −1.42623 − 0.59463I
a = −0.096708 − 0.938802I
b = −1.174820 − 0.735466I
3.13111 + 8.34888I 0
u = −0.066144 + 0.444811I
a = −0.735825 + 0.869045I
b = −0.384960 + 0.628250I
−0.131886 − 1.180470I −1.41889 + 5.75274I
u = −0.066144 − 0.444811I
a = −0.735825 − 0.869045I
b = −0.384960 − 0.628250I
−0.131886 + 1.180470I −1.41889 − 5.75274I
u = −1.53238 + 0.36627I
a = 0.131082 + 0.957577I
b = −1.035590 + 0.465784I
3.13151 − 9.72521I 0
u = −1.53238 − 0.36627I
a = 0.131082 − 0.957577I
b = −1.035590 − 0.465784I
3.13151 + 9.72521I 0
u = 1.51131 + 0.47546I
a = −0.213994 − 0.849356I
b = −0.710119 − 0.431194I
5.27507 − 0.55882I 0
u = 1.51131 − 0.47546I
a = −0.213994 + 0.849356I
b = −0.710119 + 0.431194I
5.27507 + 0.55882I 0
u = 1.55411 + 0.52753I
a = 0.044115 + 0.616806I
b = 1.257950 + 0.547846I
1.03904 + 7.82712I 0
u = 1.55411 − 0.52753I
a = 0.044115 − 0.616806I
b = 1.257950 − 0.547846I
1.03904 − 7.82712I 0
17
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −1.62989 + 0.23691I
a = −0.085618 + 0.720439I
b = −0.903124 + 0.325023I
2.62833 + 6.36462I 0
u = −1.62989 − 0.23691I
a = −0.085618 − 0.720439I
b = −0.903124 − 0.325023I
2.62833 − 6.36462I 0
u = −0.07786 + 1.68194I
a = 0.661690 + 0.070230I
b = 0.923050 + 0.073229I
−4.80730 − 0.10343I 0
u = −0.07786 − 1.68194I
a = 0.661690 − 0.070230I
b = 0.923050 − 0.073229I
−4.80730 + 0.10343I 0
u = −1.54875 + 0.71855I
a = 0.098530 − 0.817622I
b = 1.276700 − 0.587261I
0.08562 − 8.14481I 0
u = −1.54875 − 0.71855I
a = 0.098530 + 0.817622I
b = 1.276700 + 0.587261I
0.08562 + 8.14481I 0
u = −0.115504 + 0.256129I
a = 2.36631 − 2.30608I
b = −0.286364 − 1.026140I
−2.22352 + 1.22343I −2.79696 + 0.76631I
u = −0.115504 − 0.256129I
a = 2.36631 + 2.30608I
b = −0.286364 + 1.026140I
−2.22352 − 1.22343I −2.79696 − 0.76631I
18
II.
I
u
2
= h−1.97×10
19
u
29
+4.77×10
18
u
28
+· · ·+1.93×10
18
b−2.16×10
19
, −1.12×
10
18
u
29
−4.65×10
18
u
28
+· · ·+7.73×10
17
a+1.16×10
19
, u
30
−5u
28
+· · ·+3u+1i
(i) Arc colorings
a
2
=
1
0
a
7
=
0
u
a
3
=
1
−u
2
a
8
=
u
−u
3
+ u
a
11
=
1.45075u
29
+ 6.02489u
28
+ ··· − 40.5117u − 15.0104
10.1832u
29
− 2.46834u
28
+ ··· + 2.35971u + 11.1864
a
6
=
21.4770u
29
+ 7.08737u
28
+ ··· − 85.5345u − 12.9536
−2.05857u
29
+ 5.35184u
28
+ ··· − 32.9400u − 14.6400
a
12
=
12.5193u
29
+ 23.9450u
28
+ ··· − 190.390u − 58.0777
15.3254u
29
− 1.21118u
28
+ ··· − 13.6164u + 10.6001
a
5
=
27.2689u
29
+ 6.92862u
28
+ ··· − 91.9989u − 10.6800
1.30925u
29
+ 4.88824u
28
+ ··· − 34.0887u − 12.5251
a
10
=
−8.73246u
29
+ 8.49323u
28
+ ··· − 42.8714u − 26.1969
10.1832u
29
− 2.46834u
28
+ ··· + 2.35971u + 11.1864
a
4
=
−10.5836u
29
− 8.70196u
28
+ ··· + 78.4154u + 15.8292
−5.79193u
29
+ 0.158751u
28
+ ··· + 6.46435u − 1.27361
a
1
=
5.61843u
29
+ 6.98725u
28
+ ··· − 52.6134u − 9.52046
4.75041u
29
+ 0.290080u
28
+ ··· − 6.18947u − 0.0702685
a
9
=
−1.14518u
29
+ 2.00028u
28
+ ··· − 21.8170u − 2.60160
7.22275u
29
− 4.29895u
28
+ ··· + 15.4686u + 10.4007
(ii) Obstruction class = 1
(iii) Cusp Shapes = −
812989079024551444058
9656289974668587475
u
29
+
583091651501789816809
19312579949337174950
u
28
+ ··· −
754014162184226002028
9656289974668587475
u −
1912243179715117561229
19312579949337174950
19
(iv) u-Polynomials at the component
20
Crossings u-Polynomials at each crossing
c
1
5(5u
30
− 25u
29
+ ··· − 2u + 1)
c
2
u
30
− 5u
28
+ ··· + 3u + 1
c
3
u
30
+ 2u
28
+ ··· + 8u + 4
c
4
u
30
− 2u
29
+ ··· + 50u + 20
c
5
5(5u
30
+ 35u
29
+ ··· − 12u + 1)
c
6
u
30
+ 11u
28
+ ··· − 2u + 1
c
7
u
30
− 5u
28
+ ··· − 3u + 1
c
8
5(5u
30
− 35u
29
+ ··· + 12u + 1)
c
9
u
30
− 13u
28
+ ··· + 59u + 7
c
10
5(5u
30
+ 20u
29
+ ··· + 12u + 1)
c
11
u
30
+ 11u
28
+ ··· + 2u + 1
c
12
u
30
− 13u
28
+ ··· − 59u + 7
21
22
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
25(25y
30
− 285y
29
+ ··· + 18y + 1)
c
2
, c
7
y
30
− 10y
29
+ ··· − 19y + 1
c
3
y
30
+ 4y
29
+ ··· + 128y + 16
c
4
y
30
− 18y
29
+ ··· − 1260y + 400
c
5
, c
8
25(25y
30
+ 465y
29
+ ··· + 48y + 1)
c
6
, c
11
y
30
+ 22y
29
+ ··· + 50y + 1
c
9
, c
12
y
30
− 26y
29
+ ··· − 1129y + 49
c
10
25(25y
30
− 40y
29
+ ··· − 70y + 1)
23
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −1.038440 + 0.086994I
a = −0.006233 − 0.561359I
b = 0.009243 + 1.246340I
−0.137606 + 0.577838I 3.60094 + 10.09804I
u = −1.038440 − 0.086994I
a = −0.006233 + 0.561359I
b = 0.009243 − 1.246340I
−0.137606 − 0.577838I 3.60094 − 10.09804I
u = −0.058619 + 1.041750I
a = 1.011210 + 0.210339I
b = 0.604712 − 0.044034I
−1.64156 + 1.21048I −4.65835 + 0.93429I
u = −0.058619 − 1.041750I
a = 1.011210 − 0.210339I
b = 0.604712 + 0.044034I
−1.64156 − 1.21048I −4.65835 − 0.93429I
u = −0.804050 + 0.309012I
a = 0.614185 − 0.530918I
b = −0.262953 − 0.875664I
−1.04080 − 2.28652I 3.84381 + 0.62186I
u = −0.804050 − 0.309012I
a = 0.614185 + 0.530918I
b = −0.262953 + 0.875664I
−1.04080 + 2.28652I 3.84381 − 0.62186I
u = 0.037142 + 1.141930I
a = −0.624241 − 0.266305I
b = 0.172749 + 0.023131I
−6.08778 − 0.51937I −8.26764 − 0.60398I
u = 0.037142 − 1.141930I
a = −0.624241 + 0.266305I
b = 0.172749 − 0.023131I
−6.08778 + 0.51937I −8.26764 + 0.60398I
u = 1.031060 + 0.553226I
a = 0.521597 + 1.281310I
b = 1.63956 + 0.31351I
3.52797 + 2.32196I 9.63228 + 2.66947I
u = 1.031060 − 0.553226I
a = 0.521597 − 1.281310I
b = 1.63956 − 0.31351I
3.52797 − 2.32196I 9.63228 − 2.66947I
24
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 1.132580 + 0.433372I
a = −0.351000 − 1.287120I
b = −0.937170 − 0.455634I
8.16172 + 1.94892I −6.48394 − 4.05910I
u = 1.132580 − 0.433372I
a = −0.351000 + 1.287120I
b = −0.937170 + 0.455634I
8.16172 − 1.94892I −6.48394 + 4.05910I
u = 1.190290 + 0.287703I
a = −1.092900 − 0.078542I
b = 0.766835 + 0.186620I
−1.20250 + 4.51634I 1.10088 − 8.64099I
u = 1.190290 − 0.287703I
a = −1.092900 + 0.078542I
b = 0.766835 − 0.186620I
−1.20250 − 4.51634I 1.10088 + 8.64099I
u = 0.651568 + 0.345268I
a = 0.451434 + 0.990608I
b = 1.25390 − 1.29041I
−0.35004 + 1.45842I −0.30403 + 2.53979I
u = 0.651568 − 0.345268I
a = 0.451434 − 0.990608I
b = 1.25390 + 1.29041I
−0.35004 − 1.45842I −0.30403 − 2.53979I
u = 0.903556 + 0.918690I
a = 0.133890 + 0.140174I
b = −0.737154 + 0.223538I
−5.92952 + 3.36777I −7.06092 − 4.63947I
u = 0.903556 − 0.918690I
a = 0.133890 − 0.140174I
b = −0.737154 − 0.223538I
−5.92952 − 3.36777I −7.06092 + 4.63947I
u = −1.224650 + 0.411509I
a = −0.244223 − 1.222500I
b = 1.25788 − 1.04548I
2.85308 − 5.73028I −5.21981 + 3.10172I
u = −1.224650 − 0.411509I
a = −0.244223 + 1.222500I
b = 1.25788 + 1.04548I
2.85308 + 5.73028I −5.21981 − 3.10172I
25
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.706557 + 0.027268I
a = 1.88379 + 2.03206I
b = 0.091158 + 0.734308I
−3.77992 + 3.28664I −10.70122 − 5.75697I
u = 0.706557 − 0.027268I
a = 1.88379 − 2.03206I
b = 0.091158 − 0.734308I
−3.77992 − 3.28664I −10.70122 + 5.75697I
u = −0.565179 + 0.036789I
a = 1.39085 − 0.74467I
b = 0.042033 + 1.273390I
−0.41343 + 3.46874I 1.40033 − 12.33534I
u = −0.565179 − 0.036789I
a = 1.39085 + 0.74467I
b = 0.042033 − 1.273390I
−0.41343 − 3.46874I 1.40033 + 12.33534I
u = 0.00052 + 1.50689I
a = −0.767316 − 0.102364I
b = −0.859874 + 0.140663I
−4.43610 + 2.14473I 0
u = 0.00052 − 1.50689I
a = −0.767316 + 0.102364I
b = −0.859874 − 0.140663I
−4.43610 − 2.14473I 0
u = −0.334932 + 0.261625I
a = 0.07649 − 2.21765I
b = 0.031293 + 1.154740I
−5.91856 − 9.19911I −3.19756 + 7.31318I
u = −0.334932 − 0.261625I
a = 0.07649 + 2.21765I
b = 0.031293 − 1.154740I
−5.91856 + 9.19911I −3.19756 − 7.31318I
u = −1.62740 + 0.51917I
a = 0.002467 + 0.783515I
b = −1.072220 + 0.657131I
1.59062 − 9.80549I 0
u = −1.62740 − 0.51917I
a = 0.002467 − 0.783515I
b = −1.072220 − 0.657131I
1.59062 + 9.80549I 0
26
III. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
25(5u
30
− 25u
29
+ ··· − 2u + 1)(5u
138
− 70u
137
+ ··· − 54u + 1)
c
2
(u
30
− 5u
28
+ ··· + 3u + 1)(u
138
+ u
137
+ ··· + 38969u + 39973)
c
3
(u
30
+ 2u
28
+ ··· + 8u + 4)(u
138
+ u
137
+ ··· + 11328u + 688)
c
4
(u
30
− 2u
29
+ ··· + 50u + 20)
· (u
138
+ 3u
137
+ ··· + 1824290u + 445340)
c
5
25(5u
30
+ 35u
29
+ ··· − 12u + 1)(5u
138
+ 20u
137
+ ··· + 566u + 1601)
c
6
(u
30
+ 11u
28
+ ··· − 2u + 1)(u
138
− u
137
+ ··· + 3352910u + 356879)
c
7
(u
30
− 5u
28
+ ··· − 3u + 1)(u
138
+ u
137
+ ··· + 38969u + 39973)
c
8
25(5u
30
− 35u
29
+ ··· + 12u + 1)(5u
138
+ 20u
137
+ ··· + 566u + 1601)
c
9
(u
30
− 13u
28
+ ··· + 59u + 7)(u
138
+ 3u
137
+ ··· + 35u + 293)
c
10
25(5u
30
+ 20u
29
+ ··· + 12u + 1)
· (5u
138
− 15u
137
+ ··· − 852426176u + 204508079)
c
11
(u
30
+ 11u
28
+ ··· + 2u + 1)(u
138
− u
137
+ ··· + 3352910u + 356879)
c
12
(u
30
− 13u
28
+ ··· − 59u + 7)(u
138
+ 3u
137
+ ··· + 35u + 293)
27
IV. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
625(25y
30
− 285y
29
+ ··· + 18y + 1)
· (25y
138
+ 220y
137
+ ··· − 208y + 1)
c
2
, c
7
(y
30
− 10y
29
+ ··· − 19y + 1)
· (y
138
− 81y
137
+ ··· − 16606311865y + 1597840729)
c
3
(y
30
+ 4y
29
+ ··· + 128y + 16)
· (y
138
+ 21y
137
+ ··· + 88302848y + 473344)
c
4
(y
30
− 18y
29
+ ··· − 1260y + 400)
· (y
138
− 45y
137
+ ··· − 10148860553420y + 198327715600)
c
5
, c
8
625(25y
30
+ 465y
29
+ ··· + 48y + 1)
· (25y
138
+ 2770y
137
+ ··· + 904132574y + 2563201)
c
6
, c
11
(y
30
+ 22y
29
+ ··· + 50y + 1)
· (y
138
+ 103y
137
+ ··· + 1941665805688y + 127362620641)
c
9
, c
12
(y
30
− 26y
29
+ ··· − 1129y + 49)
· (y
138
− 109y
137
+ ··· + 451753y + 85849)
c
10
625(25y
30
− 40y
29
+ ··· − 70y + 1)
· (25y
138
− 1795y
137
+ ··· − 1.66 × 10
18
y + 4.18 × 10
16
)
28
