12a
0530
(K12a
0530
)
A knot diagram
1
Linearized knot diagam
3 7 8 10 9 11 2 1 12 4 6 5
Solving Sequence
2,8
7 3 4 1
9,11
6 12 5 10
c
7
c
2
c
3
c
1
c
8
c
6
c
11
c
5
c
10
c
4
, c
9
, c
12
Ideals for irreducible components
2
of X
par
I
u
1
= h41u
43
+ 223u
42
+ ··· + 4b + 100, −57u
43
− 353u
42
+ ··· + 8a − 44, u
44
+ 7u
43
+ ··· + 68u + 8i
I
u
2
= h9.53658 × 10
33
a
5
u
14
+ 2.36260 × 10
34
a
4
u
14
+ ··· − 9.99117 × 10
34
a + 8.92448 × 10
34
,
3u
14
a
4
− 10u
14
a
3
+ ··· − 4a − 5,
u
15
− u
14
+ 4u
13
− 3u
12
+ 8u
11
− 6u
10
+ 10u
9
− 7u
8
+ 8u
7
− 6u
6
+ 6u
5
− 4u
4
+ 4u
3
− 2u
2
+ 2u − 1i
I
u
3
= h−3u
25
− u
24
+ ··· + b + 2, u
25
− 2u
24
+ ··· + a − 4, u
26
+ 7u
24
+ ··· + 3u
2
+ 1i
* 3 irreducible components of dim
C
= 0, with total 160 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
= h41u
43
+ 223u
42
+ · · · + 4b + 100, −57u
43
− 353u
42
+ · · · + 8a −
44, u
44
+ 7u
43
+ · · · + 68u + 8i
(i) Arc colorings
a
2
=
0
u
a
8
=
1
0
a
7
=
1
u
2
a
3
=
u
u
3
+ u
a
4
=
−u
3
u
3
+ u
a
1
=
u
3
u
5
+ u
3
+ u
a
9
=
u
8
+ u
6
+ u
4
+ 1
u
10
+ 2u
8
+ 3u
6
+ 2u
4
+ u
2
a
11
=
7.12500u
43
+ 44.1250u
42
+ ··· + 65.2500u + 5.50000
−
41
4
u
43
−
223
4
u
42
+ ··· − 193u − 25
a
6
=
67
8
u
43
+
351
8
u
42
+ ··· −
459
4
u − 16
17
4
u
43
+
161
4
u
42
+ ··· +
1549
2
u + 101
a
12
=
37
8
u
43
+
215
8
u
42
+ ··· +
167
2
u + 12
−4u
43
−
49
2
u
42
+ ··· −
329
2
u − 21
a
5
=
−
59
8
u
43
−
351
8
u
42
+ ··· −
757
4
u − 23
−
3
4
u
43
−
55
4
u
42
+ ··· −
939
2
u − 63
a
10
=
−0.875000u
43
+ 4.12500u
42
+ ··· + 349.250u + 45.5000
−
37
4
u
43
−
239
4
u
42
+ ··· − 463u − 55
(ii) Obstruction class = −1
(iii) Cusp Shapes = −7u
43
− 47u
42
+ ··· − 416u − 62
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
44
+ 21u
43
+ ··· + 112u + 64
c
2
, c
7
u
44
+ 7u
43
+ ··· + 68u + 8
c
3
u
44
− 7u
43
+ ··· − 15900u + 2088
c
4
, c
6
, c
10
c
11
u
44
+ 20u
42
+ ··· + 3u + 1
c
5
, c
12
u
44
− u
43
+ ··· − 2u + 1
c
8
u
44
+ 35u
43
+ ··· + 9095124u + 659432
c
9
u
44
+ 44u
43
+ ··· + 819200u + 32768
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
44
+ 5y
43
+ ··· + 2816y + 4096
c
2
, c
7
y
44
+ 21y
43
+ ··· + 112y + 64
c
3
y
44
− 5y
43
+ ··· − 12038544y + 4359744
c
4
, c
6
, c
10
c
11
y
44
+ 40y
43
+ ··· − 19y + 1
c
5
, c
12
y
44
− 9y
43
+ ··· − 64y
2
+ 1
c
8
y
44
+ 25y
43
+ ··· + 6217463314032y + 434850562624
c
9
y
44
− 6y
43
+ ··· − 6442450944y + 1073741824
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.771961 + 0.602327I
a = 0.784201 + 0.917922I
b = −0.229630 − 0.588406I
11.6828 + 10.3282I 5.41388 − 6.57609I
u = 0.771961 − 0.602327I
a = 0.784201 − 0.917922I
b = −0.229630 + 0.588406I
11.6828 − 10.3282I 5.41388 + 6.57609I
u = −0.878878 + 0.399261I
a = −0.520182 − 0.463224I
b = −0.90418 + 1.33398I
8.51993 + 4.44435I 10.30662 − 5.37023I
u = −0.878878 − 0.399261I
a = −0.520182 + 0.463224I
b = −0.90418 − 1.33398I
8.51993 − 4.44435I 10.30662 + 5.37023I
u = 0.805721 + 0.663985I
a = −0.763958 − 0.526627I
b = 0.296805 + 0.406761I
10.14630 + 0.67163I 10.77089 + 0.I
u = 0.805721 − 0.663985I
a = −0.763958 + 0.526627I
b = 0.296805 − 0.406761I
10.14630 − 0.67163I 10.77089 + 0.I
u = −0.825811 + 0.399312I
a = 0.764760 + 0.689805I
b = 1.38844 − 1.66573I
10.5319 + 13.5470I 4.42171 − 6.43618I
u = −0.825811 − 0.399312I
a = 0.764760 − 0.689805I
b = 1.38844 + 1.66573I
10.5319 − 13.5470I 4.42171 + 6.43618I
u = −0.251030 + 1.084220I
a = 1.178010 + 0.266520I
b = −0.503510 − 0.887089I
−3.62681 + 1.22923I −9.94128 + 0.I
u = −0.251030 − 1.084220I
a = 1.178010 − 0.266520I
b = −0.503510 + 0.887089I
−3.62681 − 1.22923I −9.94128 + 0.I
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.528484 + 0.991235I
a = 0.049966 + 0.348359I
b = 0.077091 − 0.202845I
0.42486 + 2.54152I 0
u = 0.528484 − 0.991235I
a = 0.049966 − 0.348359I
b = 0.077091 + 0.202845I
0.42486 − 2.54152I 0
u = −0.353895 + 1.083280I
a = −1.36755 + 0.92675I
b = 1.44320 + 0.38079I
−4.55447 − 1.96039I −10.29608 + 0.I
u = −0.353895 − 1.083280I
a = −1.36755 − 0.92675I
b = 1.44320 − 0.38079I
−4.55447 + 1.96039I −10.29608 + 0.I
u = 0.604521 + 0.571054I
a = 0.260116 − 0.443639I
b = −0.203569 + 0.147021I
1.65990 + 1.95709I −0.58811 − 2.61893I
u = 0.604521 − 0.571054I
a = 0.260116 + 0.443639I
b = −0.203569 − 0.147021I
1.65990 − 1.95709I −0.58811 + 2.61893I
u = −0.132961 + 1.170640I
a = −1.16316 + 1.55025I
b = 1.54309 − 0.27524I
5.21956 + 11.00520I 0
u = −0.132961 − 1.170640I
a = −1.16316 − 1.55025I
b = 1.54309 + 0.27524I
5.21956 − 11.00520I 0
u = −0.813214 + 0.089482I
a = −0.277438 + 0.262138I
b = −0.38381 + 1.45806I
3.95344 + 5.94910I 3.39079 − 6.28501I
u = −0.813214 − 0.089482I
a = −0.277438 − 0.262138I
b = −0.38381 − 1.45806I
3.95344 − 5.94910I 3.39079 + 6.28501I
6
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.704448 + 0.960389I
a = −0.845199 − 0.047081I
b = 0.457004 + 0.238192I
9.25750 + 4.95114I 0
u = 0.704448 − 0.960389I
a = −0.845199 + 0.047081I
b = 0.457004 − 0.238192I
9.25750 − 4.95114I 0
u = −0.494271 + 1.091860I
a = −1.83138 + 0.39862I
b = 1.49231 + 1.12163I
−3.61088 − 5.26891I 0
u = −0.494271 − 1.091860I
a = −1.83138 − 0.39862I
b = 1.49231 − 1.12163I
−3.61088 + 5.26891I 0
u = 0.660554 + 1.000590I
a = 0.961092 − 0.250231I
b = −0.603096 − 0.116175I
10.49750 − 4.93338I 0
u = 0.660554 − 1.000590I
a = 0.961092 + 0.250231I
b = −0.603096 + 0.116175I
10.49750 + 4.93338I 0
u = −0.716710 + 0.346180I
a = −0.020035 − 0.488746I
b = −0.853904 − 0.168551I
0.62836 + 3.74210I −3.41810 − 3.14319I
u = −0.716710 − 0.346180I
a = −0.020035 + 0.488746I
b = −0.853904 + 0.168551I
0.62836 − 3.74210I −3.41810 + 3.14319I
u = 0.240552 + 0.734610I
a = 0.708960 + 0.258355I
b = −0.194536 − 0.354720I
−0.292714 + 1.270550I −2.89377 − 5.36729I
u = 0.240552 − 0.734610I
a = 0.708960 − 0.258355I
b = −0.194536 + 0.354720I
−0.292714 − 1.270550I −2.89377 + 5.36729I
7
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.557436 + 1.108860I
a = 0.625340 − 1.061380I
b = −1.256840 + 0.245380I
−1.59229 − 8.61061I 0
u = −0.557436 − 1.108860I
a = 0.625340 + 1.061380I
b = −1.256840 − 0.245380I
−1.59229 + 8.61061I 0
u = −0.366767 + 1.214540I
a = −0.31007 − 1.60906I
b = −0.83625 + 1.26669I
−0.06974 + 1.87494I 0
u = −0.366767 − 1.214540I
a = −0.31007 + 1.60906I
b = −0.83625 − 1.26669I
−0.06974 − 1.87494I 0
u = −0.477226 + 1.182400I
a = 1.61627 + 1.09507I
b = −0.33602 − 1.89598I
0.69334 − 10.58120I 0
u = −0.477226 − 1.182400I
a = 1.61627 − 1.09507I
b = −0.33602 + 1.89598I
0.69334 + 10.58120I 0
u = −0.131279 + 1.268580I
a = 0.420628 − 1.134570I
b = −0.874900 + 0.491913I
2.77015 + 1.49845I 0
u = −0.131279 − 1.268580I
a = 0.420628 + 1.134570I
b = −0.874900 − 0.491913I
2.77015 − 1.49845I 0
u = −0.611031 + 1.124960I
a = −2.67560 + 0.20316I
b = 2.10236 + 1.97702I
8.3623 − 18.9020I 0
u = −0.611031 − 1.124960I
a = −2.67560 − 0.20316I
b = 2.10236 − 1.97702I
8.3623 + 18.9020I 0
8
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.632273 + 1.140160I
a = 1.91318 − 0.02296I
b = −1.44122 − 1.50281I
6.28900 − 10.01230I 0
u = −0.632273 − 1.140160I
a = 1.91318 + 0.02296I
b = −1.44122 + 1.50281I
6.28900 + 10.01230I 0
u = −0.573459 + 0.202063I
a = 0.742047 + 0.156983I
b = 0.821175 − 0.529483I
−1.22290 + 1.05754I −4.87264 − 3.36875I
u = −0.573459 − 0.202063I
a = 0.742047 − 0.156983I
b = 0.821175 + 0.529483I
−1.22290 − 1.05754I −4.87264 + 3.36875I
9
II. I
u
2
= h9.54 × 10
33
a
5
u
14
+ 2.36 × 10
34
a
4
u
14
+ · · · − 9.99 × 10
34
a + 8.92 ×
10
34
, 3u
14
a
4
− 10u
14
a
3
+ · · · − 4a − 5, u
15
− u
14
+ · · · + 2u − 1i
(i) Arc colorings
a
2
=
0
u
a
8
=
1
0
a
7
=
1
u
2
a
3
=
u
u
3
+ u
a
4
=
−u
3
u
3
+ u
a
1
=
u
3
u
5
+ u
3
+ u
a
9
=
u
8
+ u
6
+ u
4
+ 1
u
10
+ 2u
8
+ 3u
6
+ 2u
4
+ u
2
a
11
=
a
−0.0854987a
5
u
14
− 0.211815a
4
u
14
+ ··· + 0.895743a − 0.800111
a
6
=
0.209507a
5
u
14
+ 0.276316a
4
u
14
+ ··· − 0.462222a − 2.00165
−0.146946a
5
u
14
− 0.572407a
4
u
14
+ ··· + 2.04664a − 0.429965
a
12
=
−0.0840752a
5
u
14
+ 0.390687a
4
u
14
+ ··· − 3.11449a + 4.18804
0.676411a
5
u
14
+ 1.24879a
4
u
14
+ ··· − 0.707745a − 1.12050
a
5
=
−0.0277234a
5
u
14
− 0.151646a
4
u
14
+ ··· − 3.44125a − 1.92141
−0.150719a
5
u
14
− 0.395079a
4
u
14
+ ··· + 2.67683a + 0.0983859
a
10
=
−0.0946863a
5
u
14
− 0.100970a
4
u
14
+ ··· + 1.69746a + 0.622719
−0.126657a
5
u
14
− 0.357588a
4
u
14
+ ··· + 1.45430a − 0.523499
(ii) Obstruction class = −1
(iii) Cusp Shapes = 0.256222a
5
u
14
− 0.295492a
4
u
14
+ ··· − 7.25786a − 2.41631
10
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
(u
15
+ 7u
14
+ ··· + 4u
2
− 1)
6
c
2
, c
7
(u
15
− u
14
+ ··· + 2u − 1)
6
c
3
(u
15
+ u
14
+ ··· − 4u − 1)
6
c
4
, c
6
, c
10
c
11
u
90
− u
89
+ ··· + 462430u + 196657
c
5
, c
12
u
90
− 3u
89
+ ··· − 78508u + 9713
c
8
(u
15
− 5u
14
+ ··· + 12u
3
− 1)
6
c
9
(u
3
− u
2
+ 1)
30
11
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
(y
15
+ 3y
14
+ ··· + 8y −1)
6
c
2
, c
7
(y
15
+ 7y
14
+ ··· + 4y
2
− 1)
6
c
3
(y
15
− y
14
+ ··· + 16y −1)
6
c
4
, c
6
, c
10
c
11
y
90
+ 75y
89
+ ··· − 18280277704y + 38673975649
c
5
, c
12
y
90
− 25y
89
+ ··· − 3696637176y + 94342369
c
8
(y
15
+ 11y
14
+ ··· − 84y
2
− 1)
6
c
9
(y
3
− y
2
+ 2y −1)
30
12
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.385605 + 0.867795I
a = 1.39356 − 0.27234I
b = −0.39588 − 1.73424I
1.55950 + 1.16728I 2.00066 + 0.98460I
u = −0.385605 + 0.867795I
a = −1.11988 − 1.14279I
b = −0.00931 + 2.32258I
1.55950 − 4.48897I 2.00066 + 6.94350I
u = −0.385605 + 0.867795I
a = −1.40402 − 1.01795I
b = 0.035932 − 0.206750I
5.69708 − 1.66084I 8.52993 + 3.96405I
u = −0.385605 + 0.867795I
a = 1.80466 − 0.76880I
b = −1.59033 + 0.71496I
5.69708 − 1.66084I 8.52993 + 3.96405I
u = −0.385605 + 0.867795I
a = −2.82748 − 0.45062I
b = 0.58840 + 1.43483I
1.55950 − 4.48897I 2.00066 + 6.94350I
u = −0.385605 + 0.867795I
a = 2.85623 + 0.51697I
b = −1.35659 − 1.63953I
1.55950 + 1.16728I 2.00066 + 0.98460I
u = −0.385605 − 0.867795I
a = 1.39356 + 0.27234I
b = −0.39588 + 1.73424I
1.55950 − 1.16728I 2.00066 − 0.98460I
u = −0.385605 − 0.867795I
a = −1.11988 + 1.14279I
b = −0.00931 − 2.32258I
1.55950 + 4.48897I 2.00066 − 6.94350I
u = −0.385605 − 0.867795I
a = −1.40402 + 1.01795I
b = 0.035932 + 0.206750I
5.69708 + 1.66084I 8.52993 − 3.96405I
u = −0.385605 − 0.867795I
a = 1.80466 + 0.76880I
b = −1.59033 − 0.71496I
5.69708 + 1.66084I 8.52993 − 3.96405I
13
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.385605 − 0.867795I
a = −2.82748 + 0.45062I
b = 0.58840 − 1.43483I
1.55950 + 4.48897I 2.00066 − 6.94350I
u = −0.385605 − 0.867795I
a = 2.85623 − 0.51697I
b = −1.35659 + 1.63953I
1.55950 − 1.16728I 2.00066 − 0.98460I
u = 0.146928 + 1.062740I
a = 0.845731 + 0.455155I
b = −0.758939 + 1.001010I
0.08992 − 4.90214I −3.33798 + 5.65067I
u = 0.146928 + 1.062740I
a = 0.244032 − 0.733403I
b = 0.082293 − 0.199938I
0.089924 + 0.754105I −3.33798 − 0.30823I
u = 0.146928 + 1.062740I
a = 1.213950 + 0.311169I
b = −1.039850 − 0.209665I
0.089924 + 0.754105I −3.33798 − 0.30823I
u = 0.146928 + 1.062740I
a = 1.46969 + 1.40857I
b = −1.92743 + 0.11527I
4.22751 − 2.07402I 3.19129 + 2.67122I
u = 0.146928 + 1.062740I
a = −2.36213 − 0.52233I
b = 1.53477 − 0.30619I
0.08992 − 4.90214I −3.33798 + 5.65067I
u = 0.146928 + 1.062740I
a = −1.54708 − 2.05690I
b = 1.68670 + 0.26256I
4.22751 − 2.07402I 3.19129 + 2.67122I
u = 0.146928 − 1.062740I
a = 0.845731 − 0.455155I
b = −0.758939 − 1.001010I
0.08992 + 4.90214I −3.33798 − 5.65067I
u = 0.146928 − 1.062740I
a = 0.244032 + 0.733403I
b = 0.082293 + 0.199938I
0.089924 − 0.754105I −3.33798 + 0.30823I
14
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.146928 − 1.062740I
a = 1.213950 − 0.311169I
b = −1.039850 + 0.209665I
0.089924 − 0.754105I −3.33798 + 0.30823I
u = 0.146928 − 1.062740I
a = 1.46969 − 1.40857I
b = −1.92743 − 0.11527I
4.22751 + 2.07402I 3.19129 − 2.67122I
u = 0.146928 − 1.062740I
a = −2.36213 + 0.52233I
b = 1.53477 + 0.30619I
0.08992 + 4.90214I −3.33798 − 5.65067I
u = 0.146928 − 1.062740I
a = −1.54708 + 2.05690I
b = 1.68670 − 0.26256I
4.22751 + 2.07402I 3.19129 − 2.67122I
u = −0.715401 + 0.518352I
a = 0.506703 − 1.023280I
b = −0.007263 + 1.157640I
9.58164 − 1.50523I 11.17084 + 2.74048I
u = −0.715401 + 0.518352I
a = −0.786437 − 0.319557I
b = −0.932520 + 0.393953I
5.44406 + 1.32289I 4.64158 − 0.23897I
u = −0.715401 + 0.518352I
a = 0.074786 − 1.202470I
b = −1.19118 + 0.94425I
5.44406 + 1.32289I 4.64158 − 0.23897I
u = −0.715401 + 0.518352I
a = 0.268686 − 0.125191I
b = 1.293500 + 0.181955I
5.44406 − 4.33335I 4.64158 + 5.71992I
u = −0.715401 + 0.518352I
a = −1.20243 + 1.21904I
b = 0.426945 − 0.162765I
9.58164 − 1.50523I 11.17084 + 2.74048I
u = −0.715401 + 0.518352I
a = −0.08222 + 1.79499I
b = 1.147010 − 0.769151I
5.44406 − 4.33335I 4.64158 + 5.71992I
15
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.715401 − 0.518352I
a = 0.506703 + 1.023280I
b = −0.007263 − 1.157640I
9.58164 + 1.50523I 11.17084 − 2.74048I
u = −0.715401 − 0.518352I
a = −0.786437 + 0.319557I
b = −0.932520 − 0.393953I
5.44406 − 1.32289I 4.64158 + 0.23897I
u = −0.715401 − 0.518352I
a = 0.074786 + 1.202470I
b = −1.19118 − 0.94425I
5.44406 − 1.32289I 4.64158 + 0.23897I
u = −0.715401 − 0.518352I
a = 0.268686 + 0.125191I
b = 1.293500 − 0.181955I
5.44406 + 4.33335I 4.64158 − 5.71992I
u = −0.715401 − 0.518352I
a = −1.20243 − 1.21904I
b = 0.426945 + 0.162765I
9.58164 + 1.50523I 11.17084 − 2.74048I
u = −0.715401 − 0.518352I
a = −0.08222 − 1.79499I
b = 1.147010 + 0.769151I
5.44406 + 4.33335I 4.64158 − 5.71992I
u = 0.758945 + 0.422629I
a = 0.246369 − 1.004030I
b = 0.611721 + 1.055930I
4.92757 − 1.26387I 3.53451 + 0.17150I
u = 0.758945 + 0.422629I
a = 0.735819 − 0.752840I
b = 1.54405 + 1.84732I
9.06515 − 4.09199I 10.06378 + 3.15094I
u = 0.758945 + 0.422629I
a = −0.577307 − 0.317344I
b = −0.629308 − 0.402043I
4.92757 − 1.26387I 3.53451 + 0.17150I
u = 0.758945 + 0.422629I
a = −1.31979 + 0.80102I
b = −1.26774 − 1.79419I
9.06515 − 4.09199I 10.06378 + 3.15094I
16
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.758945 + 0.422629I
a = −0.45532 + 1.53780I
b = −1.42772 − 1.00598I
4.92757 − 6.92011I 3.53451 + 6.13039I
u = 0.758945 + 0.422629I
a = 0.345436 − 0.180063I
b = 1.65389 + 0.39221I
4.92757 − 6.92011I 3.53451 + 6.13039I
u = 0.758945 − 0.422629I
a = 0.246369 + 1.004030I
b = 0.611721 − 1.055930I
4.92757 + 1.26387I 3.53451 − 0.17150I
u = 0.758945 − 0.422629I
a = 0.735819 + 0.752840I
b = 1.54405 − 1.84732I
9.06515 + 4.09199I 10.06378 − 3.15094I
u = 0.758945 − 0.422629I
a = −0.577307 + 0.317344I
b = −0.629308 + 0.402043I
4.92757 + 1.26387I 3.53451 − 0.17150I
u = 0.758945 − 0.422629I
a = −1.31979 − 0.80102I
b = −1.26774 + 1.79419I
9.06515 + 4.09199I 10.06378 − 3.15094I
u = 0.758945 − 0.422629I
a = −0.45532 − 1.53780I
b = −1.42772 + 1.00598I
4.92757 + 6.92011I 3.53451 − 6.13039I
u = 0.758945 − 0.422629I
a = 0.345436 + 0.180063I
b = 1.65389 − 0.39221I
4.92757 + 6.92011I 3.53451 − 6.13039I
u = 0.426893 + 1.085670I
a = −0.360764 − 1.264230I
b = 1.012290 − 0.008853I
−2.29749 + 0.77528I −5.67348 − 1.49727I
u = 0.426893 + 1.085670I
a = 1.43808 + 0.24695I
b = −0.78296 + 1.34819I
−2.29749 + 6.43153I −5.67348 − 7.45617I
17
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.426893 + 1.085670I
a = 1.34979 + 0.97420I
b = −1.66027 − 0.16387I
−2.29749 + 0.77528I −5.67348 − 1.49727I
u = 0.426893 + 1.085670I
a = −2.28204 + 0.34468I
b = 1.45212 − 1.39219I
−2.29749 + 6.43153I −5.67348 − 7.45617I
u = 0.426893 + 1.085670I
a = 1.56592 − 1.89697I
b = 0.61352 + 2.21467I
1.84009 + 3.60340I 0.85579 − 4.47672I
u = 0.426893 + 1.085670I
a = −1.37375 + 2.29651I
b = −0.58547 − 2.50177I
1.84009 + 3.60340I 0.85579 − 4.47672I
u = 0.426893 − 1.085670I
a = −0.360764 + 1.264230I
b = 1.012290 + 0.008853I
−2.29749 − 0.77528I −5.67348 + 1.49727I
u = 0.426893 − 1.085670I
a = 1.43808 − 0.24695I
b = −0.78296 − 1.34819I
−2.29749 − 6.43153I −5.67348 + 7.45617I
u = 0.426893 − 1.085670I
a = 1.34979 − 0.97420I
b = −1.66027 + 0.16387I
−2.29749 − 0.77528I −5.67348 + 1.49727I
u = 0.426893 − 1.085670I
a = −2.28204 − 0.34468I
b = 1.45212 + 1.39219I
−2.29749 − 6.43153I −5.67348 + 7.45617I
u = 0.426893 − 1.085670I
a = 1.56592 + 1.89697I
b = 0.61352 − 2.21467I
1.84009 − 3.60340I 0.85579 + 4.47672I
u = 0.426893 − 1.085670I
a = −1.37375 − 2.29651I
b = −0.58547 + 2.50177I
1.84009 − 3.60340I 0.85579 + 4.47672I
18
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.594997 + 1.040830I
a = 0.957853 − 0.988756I
b = −1.43936 − 0.69293I
3.89372 − 6.34664I 2.20327 + 5.56972I
u = −0.594997 + 1.040830I
a = −0.536209 + 0.198387I
b = 0.806559 − 0.874865I
8.03130 − 3.51852I 8.73253 + 2.59027I
u = −0.594997 + 1.040830I
a = 1.51064 + 0.90579I
b = −0.543239 − 0.683890I
8.03130 − 3.51852I 8.73253 + 2.59027I
u = −0.594997 + 1.040830I
a = −1.59885 + 0.80930I
b = 2.27503 + 0.14919I
3.89372 − 0.69040I 2.20327 − 0.38918I
u = −0.594997 + 1.040830I
a = −0.56621 + 1.84268I
b = 1.399940 − 0.133497I
3.89372 − 0.69040I 2.20327 − 0.38918I
u = −0.594997 + 1.040830I
a = 1.94278 − 0.82970I
b = −2.03684 − 0.49943I
3.89372 − 6.34664I 2.20327 + 5.56972I
u = −0.594997 − 1.040830I
a = 0.957853 + 0.988756I
b = −1.43936 + 0.69293I
3.89372 + 6.34664I 2.20327 − 5.56972I
u = −0.594997 − 1.040830I
a = −0.536209 − 0.198387I
b = 0.806559 + 0.874865I
8.03130 + 3.51852I 8.73253 − 2.59027I
u = −0.594997 − 1.040830I
a = 1.51064 − 0.90579I
b = −0.543239 + 0.683890I
8.03130 + 3.51852I 8.73253 − 2.59027I
u = −0.594997 − 1.040830I
a = −1.59885 − 0.80930I
b = 2.27503 − 0.14919I
3.89372 + 0.69040I 2.20327 + 0.38918I
19
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.594997 − 1.040830I
a = −0.56621 − 1.84268I
b = 1.399940 + 0.133497I
3.89372 + 0.69040I 2.20327 + 0.38918I
u = −0.594997 − 1.040830I
a = 1.94278 + 0.82970I
b = −2.03684 + 0.49943I
3.89372 + 6.34664I 2.20327 − 5.56972I
u = 0.594032 + 1.095620I
a = 0.824511 + 0.540339I
b = −0.741965 + 0.769330I
2.93698 + 6.38968I 0.34485 − 4.41190I
u = 0.594032 + 1.095620I
a = −1.64476 + 0.05084I
b = 1.38586 − 0.86842I
2.93698 + 6.38968I 0.34485 − 4.41190I
u = 0.594032 + 1.095620I
a = −1.59275 − 1.59922I
b = 1.98971 − 0.52935I
2.93698 + 12.04590I 0.34485 − 10.37079I
u = 0.594032 + 1.095620I
a = 2.18034 + 0.77640I
b = −2.56791 + 0.82953I
2.93698 + 12.04590I 0.34485 − 10.37079I
u = 0.594032 + 1.095620I
a = 2.79694 + 0.07274I
b = −2.21149 + 2.34261I
7.07456 + 9.21780I 6.87411 − 7.39135I
u = 0.594032 + 1.095620I
a = −3.10516 − 0.37961I
b = 2.29852 − 2.07623I
7.07456 + 9.21780I 6.87411 − 7.39135I
u = 0.594032 − 1.095620I
a = 0.824511 − 0.540339I
b = −0.741965 − 0.769330I
2.93698 − 6.38968I 0.34485 + 4.41190I
u = 0.594032 − 1.095620I
a = −1.64476 − 0.05084I
b = 1.38586 + 0.86842I
2.93698 − 6.38968I 0.34485 + 4.41190I
20
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.594032 − 1.095620I
a = −1.59275 + 1.59922I
b = 1.98971 + 0.52935I
2.93698 − 12.04590I 0.34485 + 10.37079I
u = 0.594032 − 1.095620I
a = 2.18034 − 0.77640I
b = −2.56791 − 0.82953I
2.93698 − 12.04590I 0.34485 + 10.37079I
u = 0.594032 − 1.095620I
a = 2.79694 − 0.07274I
b = −2.21149 − 2.34261I
7.07456 − 9.21780I 6.87411 + 7.39135I
u = 0.594032 − 1.095620I
a = −3.10516 + 0.37961I
b = 2.29852 + 2.07623I
7.07456 − 9.21780I 6.87411 + 7.39135I
u = 0.538411
a = 0.749650 + 0.385618I
b = 0.655215 − 0.882369I
0.48639 + 2.82812I −2.07315 − 2.97945I
u = 0.538411
a = 0.749650 − 0.385618I
b = 0.655215 + 0.882369I
0.48639 − 2.82812I −2.07315 + 2.97945I
u = 0.538411
a = −0.46055 + 1.37138I
b = −0.756394 + 0.267456I
0.48639 + 2.82812I −2.07315 − 2.97945I
u = 0.538411
a = −0.46055 − 1.37138I
b = −0.756394 − 0.267456I
0.48639 − 2.82812I −2.07315 + 2.97945I
u = 0.538411
a = 0.38298 + 1.40881I
b = −0.13403 + 1.64328I
4.62398 4.45612 + 0.I
u = 0.538411
a = 0.38298 − 1.40881I
b = −0.13403 − 1.64328I
4.62398 4.45612 + 0.I
21
III.
I
u
3
= h−3u
25
−u
24
+· · ·+b+2, u
25
−2u
24
+· · ·+a−4, u
26
+7u
24
+· · ·+3u
2
+1i
(i) Arc colorings
a
2
=
0
u
a
8
=
1
0
a
7
=
1
u
2
a
3
=
u
u
3
+ u
a
4
=
−u
3
u
3
+ u
a
1
=
u
3
u
5
+ u
3
+ u
a
9
=
u
8
+ u
6
+ u
4
+ 1
u
10
+ 2u
8
+ 3u
6
+ 2u
4
+ u
2
a
11
=
−u
25
+ 2u
24
+ ··· + 2u + 4
3u
25
+ u
24
+ ··· + 2u − 2
a
6
=
−2u
25
− u
24
+ ··· − 5u + 1
u
24
+ u
23
+ ··· + 2u + 2
a
12
=
−u
25
+ 3u
24
+ ··· + u + 3
2u
25
+ 13u
23
+ ··· + u − 2
a
5
=
−u
24
− 2u
23
+ ··· − 2u
2
− 4u
−u
25
+ u
24
+ ··· + u + 2
a
10
=
−u
25
+ u
24
+ ··· + 2u + 3
3u
25
+ u
24
+ ··· + 2u − 1
(ii) Obstruction class = 1
(iii) Cusp Shapes = 8u
25
+ 8u
24
+ 52u
23
+ 45u
22
+ 171u
21
+ 130u
20
+ 355u
19
+
230u
18
+ 507u
17
+ 270u
16
+ 524u
15
+ 228u
14
+ 428u
13
+ 174u
12
+ 316u
11
+ 159u
10
+
232u
9
+ 132u
8
+ 133u
7
+ 70u
6
+ 52u
5
+ 20u
4
+ 8u
3
+ 9u
2
+ 6u + 1
22
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
26
− 14u
25
+ ··· − 6u + 1
c
2
u
26
+ 7u
24
+ ··· + 3u
2
+ 1
c
3
u
26
− 2u
24
+ ··· − 2u + 1
c
4
, c
11
u
26
+ 13u
24
+ ··· − u + 1
c
5
, c
12
u
26
− u
25
+ ··· + 2u + 1
c
6
, c
10
u
26
+ 13u
24
+ ··· + u + 1
c
7
u
26
+ 7u
24
+ ··· + 3u
2
+ 1
c
8
u
26
+ 7u
24
+ ··· + 3u
2
+ 1
c
9
u
26
+ 7u
25
+ ··· − 4u
2
+ 1
23
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
26
+ 2y
25
+ ··· + 10y + 1
c
2
, c
7
y
26
+ 14y
25
+ ··· + 6y + 1
c
3
y
26
− 4y
25
+ ··· + 6y + 1
c
4
, c
6
, c
10
c
11
y
26
+ 26y
25
+ ··· + 19y + 1
c
5
, c
12
y
26
− 7y
25
+ ··· − 2y + 1
c
8
y
26
+ 14y
25
+ ··· + 6y + 1
c
9
y
26
− 5y
25
+ ··· − 8y + 1
24
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = −0.359440 + 0.910887I
a = 1.56618 + 0.26862I
b = −0.862450 + 0.400507I
5.10436 − 1.47433I −7.05374 − 0.92833I
u = −0.359440 − 0.910887I
a = 1.56618 − 0.26862I
b = −0.862450 − 0.400507I
5.10436 + 1.47433I −7.05374 + 0.92833I
u = 0.402070 + 1.012970I
a = −2.19445 + 1.70140I
b = 0.00051 − 2.57273I
0.19383 + 5.11284I −4.31585 − 8.46349I
u = 0.402070 − 1.012970I
a = −2.19445 − 1.70140I
b = 0.00051 + 2.57273I
0.19383 − 5.11284I −4.31585 + 8.46349I
u = 0.789971 + 0.415474I
a = −0.781487 + 0.606884I
b = −1.13923 − 1.51688I
7.57489 − 3.71076I 3.24837 + 0.96954I
u = 0.789971 − 0.415474I
a = −0.781487 − 0.606884I
b = −1.13923 + 1.51688I
7.57489 + 3.71076I 3.24837 − 0.96954I
u = −0.699594 + 0.550884I
a = −0.907068 + 0.915280I
b = 0.266153 − 0.584489I
8.41284 − 1.01125I 3.87939 − 0.08794I
u = −0.699594 − 0.550884I
a = −0.907068 − 0.915280I
b = 0.266153 + 0.584489I
8.41284 + 1.01125I 3.87939 + 0.08794I
u = 0.510275 + 1.047840I
a = 0.60513 − 2.04696I
b = 1.21970 + 1.77160I
1.00464 + 1.24764I −0.638665 − 0.006398I
u = 0.510275 − 1.047840I
a = 0.60513 + 2.04696I
b = 1.21970 − 1.77160I
1.00464 − 1.24764I −0.638665 + 0.006398I
25
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = −0.339378 + 1.125810I
a = 0.376376 + 0.395893I
b = −0.357297 − 0.084276I
−1.72686 + 0.90484I −3.78242 − 2.96504I
u = −0.339378 − 1.125810I
a = 0.376376 − 0.395893I
b = −0.357297 + 0.084276I
−1.72686 − 0.90484I −3.78242 + 2.96504I
u = −0.585961 + 1.027330I
a = −1.005760 − 0.272668I
b = 0.637491 − 0.137812I
6.98807 − 3.93735I 0.51867 + 6.15974I
u = −0.585961 − 1.027330I
a = −1.005760 + 0.272668I
b = 0.637491 + 0.137812I
6.98807 + 3.93735I 0.51867 − 6.15974I
u = 0.131481 + 1.188190I
a = 0.66452 + 1.27426I
b = −1.097050 − 0.398827I
2.33267 − 1.32676I −4.14910 − 0.80898I
u = 0.131481 − 1.188190I
a = 0.66452 − 1.27426I
b = −1.097050 + 0.398827I
2.33267 + 1.32676I −4.14910 + 0.80898I
u = 0.212681 + 0.768560I
a = 2.44540 + 0.16272I
b = −0.95827 + 1.49565I
1.38754 − 2.26974I −0.04281 + 6.48249I
u = 0.212681 − 0.768560I
a = 2.44540 − 0.16272I
b = −0.95827 − 1.49565I
1.38754 + 2.26974I −0.04281 − 6.48249I
u = −0.528659 + 1.117570I
a = −0.407474 + 0.070848I
b = 0.211681 − 0.167641I
−0.40252 − 8.55446I 0.18681 + 7.57743I
u = −0.528659 − 1.117570I
a = −0.407474 − 0.070848I
b = 0.211681 + 0.167641I
−0.40252 + 8.55446I 0.18681 − 7.57743I
26
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = 0.605745 + 1.102710I
a = 2.38383 + 0.24010I
b = −1.89158 + 1.74570I
5.54067 + 8.95210I 0.55413 − 5.52648I
u = 0.605745 − 1.102710I
a = 2.38383 − 0.24010I
b = −1.89158 − 1.74570I
5.54067 − 8.95210I 0.55413 + 5.52648I
u = −0.650503 + 0.273818I
a = −0.647303 + 0.420209I
b = 0.224517 − 0.235754I
1.99064 + 3.95173I 4.07496 − 4.85079I
u = −0.650503 − 0.273818I
a = −0.647303 − 0.420209I
b = 0.224517 + 0.235754I
1.99064 − 3.95173I 4.07496 + 4.85079I
u = 0.511312 + 0.470800I
a = −1.097890 − 0.795276I
b = 0.745837 − 1.171260I
2.72258 + 2.99412I 4.52024 − 3.90167I
u = 0.511312 − 0.470800I
a = −1.097890 + 0.795276I
b = 0.745837 + 1.171260I
2.72258 − 2.99412I 4.52024 + 3.90167I
27
IV. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
((u
15
+ 7u
14
+ ··· + 4u
2
− 1)
6
)(u
26
− 14u
25
+ ··· − 6u + 1)
· (u
44
+ 21u
43
+ ··· + 112u + 64)
c
2
((u
15
− u
14
+ ··· + 2u − 1)
6
)(u
26
+ 7u
24
+ ··· + 3u
2
+ 1)
· (u
44
+ 7u
43
+ ··· + 68u + 8)
c
3
((u
15
+ u
14
+ ··· − 4u − 1)
6
)(u
26
− 2u
24
+ ··· − 2u + 1)
· (u
44
− 7u
43
+ ··· − 15900u + 2088)
c
4
, c
11
(u
26
+ 13u
24
+ ··· − u + 1)(u
44
+ 20u
42
+ ··· + 3u + 1)
· (u
90
− u
89
+ ··· + 462430u + 196657)
c
5
, c
12
(u
26
− u
25
+ ··· + 2u + 1)(u
44
− u
43
+ ··· − 2u + 1)
· (u
90
− 3u
89
+ ··· − 78508u + 9713)
c
6
, c
10
(u
26
+ 13u
24
+ ··· + u + 1)(u
44
+ 20u
42
+ ··· + 3u + 1)
· (u
90
− u
89
+ ··· + 462430u + 196657)
c
7
((u
15
− u
14
+ ··· + 2u − 1)
6
)(u
26
+ 7u
24
+ ··· + 3u
2
+ 1)
· (u
44
+ 7u
43
+ ··· + 68u + 8)
c
8
((u
15
− 5u
14
+ ··· + 12u
3
− 1)
6
)(u
26
+ 7u
24
+ ··· + 3u
2
+ 1)
· (u
44
+ 35u
43
+ ··· + 9095124u + 659432)
c
9
((u
3
− u
2
+ 1)
30
)(u
26
+ 7u
25
+ ··· − 4u
2
+ 1)
· (u
44
+ 44u
43
+ ··· + 819200u + 32768)
28
V. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
((y
15
+ 3y
14
+ ··· + 8y −1)
6
)(y
26
+ 2y
25
+ ··· + 10y + 1)
· (y
44
+ 5y
43
+ ··· + 2816y + 4096)
c
2
, c
7
((y
15
+ 7y
14
+ ··· + 4y
2
− 1)
6
)(y
26
+ 14y
25
+ ··· + 6y + 1)
· (y
44
+ 21y
43
+ ··· + 112y + 64)
c
3
((y
15
− y
14
+ ··· + 16y −1)
6
)(y
26
− 4y
25
+ ··· + 6y + 1)
· (y
44
− 5y
43
+ ··· − 12038544y + 4359744)
c
4
, c
6
, c
10
c
11
(y
26
+ 26y
25
+ ··· + 19y + 1)(y
44
+ 40y
43
+ ··· − 19y + 1)
· (y
90
+ 75y
89
+ ··· − 18280277704y + 38673975649)
c
5
, c
12
(y
26
− 7y
25
+ ··· − 2y + 1)(y
44
− 9y
43
+ ··· − 64y
2
+ 1)
· (y
90
− 25y
89
+ ··· − 3696637176y + 94342369)
c
8
((y
15
+ 11y
14
+ ··· − 84y
2
− 1)
6
)(y
26
+ 14y
25
+ ··· + 6y + 1)
· (y
44
+ 25y
43
+ ··· + 6217463314032y + 434850562624)
c
9
((y
3
− y
2
+ 2y −1)
30
)(y
26
− 5y
25
+ ··· − 8y + 1)
· (y
44
− 6y
43
+ ··· − 6442450944y + 1073741824)
29
