12a
1212
(K12a
1212
)
A knot diagram
1
Linearized knot diagam
5 6 7 9 10 11 12 1 2 3 4 8
Solving Sequence
7,12
8 1
4,9
3 11 6 2 10 5
c
7
c
12
c
8
c
3
c
11
c
6
c
2
c
10
c
5
c
1
, c
4
, c
9
Ideals for irreducible components
2
of X
par
I
u
1
= h−8237647u
24
− 46666064u
23
+ ··· + 1517168b − 99699472,
50602827u
24
+ 326501622u
23
+ ··· + 3034336a + 1024079008, u
25
+ 8u
24
+ ··· − 32u + 32i
I
u
2
= h91u
12
− 255u
11
+ ··· + 82b + 126, 68u
12
− 191u
11
+ ··· + 164a + 1075,
u
13
− 4u
12
− u
11
+ 24u
10
− 21u
9
− 44u
8
+ 60u
7
+ 23u
6
− 37u
5
− 10u
4
− 15u
3
+ 24u
2
+ 3u − 1i
I
u
3
= h−u
51
a − 375u
51
+ ··· + a + 909, 316u
51
a − 805u
51
+ ··· + 2748a − 4408, u
52
− 6u
51
+ ··· + 18u + 1i
I
u
4
= hb + 1, a, u − 1i
* 4 irreducible components of dim
C
= 0, with total 143 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−8.24 × 10
6
u
24
− 4.67 × 10
7
u
23
+ · · · + 1.52 × 10
6
b − 9.97 × 10
7
, 5.06 ×
10
7
u
24
+3.27×10
8
u
23
+· · ·+3.03×10
6
a+1.02×10
9
, u
25
+8u
24
+· · ·−32u+32i
(i) Arc colorings
a
7
=
1
0
a
12
=
0
u
a
8
=
1
u
2
a
1
=
−u
−u
3
+ u
a
4
=
−16.6767u
24
− 107.602u
23
+ ··· + 549.463u − 337.497
5.42962u
24
+ 30.7587u
23
+ ··· − 86.2463u + 65.7142
a
9
=
−u
2
+ 1
−u
4
+ 2u
2
a
3
=
−11.2471u
24
− 76.8437u
23
+ ··· + 463.217u − 271.783
5.42962u
24
+ 30.7587u
23
+ ··· − 86.2463u + 65.7142
a
11
=
14.2117u
24
+ 90.2914u
23
+ ··· − 434.374u + 271.092
3.50175u
24
+ 25.1620u
23
+ ··· − 177.375u + 100.690
a
6
=
11.8969u
24
+ 71.8441u
23
+ ··· − 240.897u + 176.461
23.6941u
24
+ 153.970u
23
+ ··· − 804.871u + 491.973
a
2
=
−6.67636u
24
− 39.5426u
23
+ ··· + 111.025u − 87.1118
−17.0962u
24
− 108.869u
23
+ ··· + 532.397u − 332.532
a
10
=
−3.98808u
24
− 18.4219u
23
+ ··· − 69.4800u + 9.06809
−19.3622u
24
− 117.721u
23
+ ··· + 440.516u − 303.830
a
5
=
15.1868u
24
+ 104.234u
23
+ ··· − 656.947u + 380.440
1.94010u
24
+ 24.7858u
23
+ ··· − 406.617u + 192.420
(ii) Obstruction class = −1
(iii) Cusp Shapes = −
5240957
94823
u
24
−
67769311
189646
u
23
+ ··· +
187802884
94823
u −
111850042
94823
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
3
u
25
− u
24
+ ··· − 5u + 1
c
2
u
25
− 16u
24
+ ··· + 7168u − 1024
c
4
, c
11
u
25
+ 7u
24
+ ··· + 10u + 2
c
5
, c
10
u
25
+ 4u
24
+ ··· − 3u + 1
c
6
, c
9
u
25
+ 2u
24
+ ··· + 7u − 1
c
7
, c
8
, c
12
u
25
− 8u
24
+ ··· − 32u − 32
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
3
y
25
− 7y
24
+ ··· + 25y −1
c
2
y
25
+ 18y
23
+ ··· − 11010048y −1048576
c
4
, c
11
y
25
− 21y
24
+ ··· − 100y −4
c
5
, c
10
y
25
− 32y
24
+ ··· − 3y −1
c
6
, c
9
y
25
− 2y
24
+ ··· + 15y −1
c
7
, c
8
, c
12
y
25
− 24y
24
+ ··· − 6656y −1024
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.724396 + 0.814795I
a = −0.033461 + 1.260570I
b = −1.18344 − 0.87037I
−0.1080 − 15.3508I −2.78225 + 10.65242I
u = 0.724396 − 0.814795I
a = −0.033461 − 1.260570I
b = −1.18344 + 0.87037I
−0.1080 + 15.3508I −2.78225 − 10.65242I
u = 0.317167 + 1.050900I
a = 0.616196 − 0.409967I
b = −0.827326 + 0.814013I
1.10917 + 9.40524I 0.04392 − 9.75471I
u = 0.317167 − 1.050900I
a = 0.616196 + 0.409967I
b = −0.827326 − 0.814013I
1.10917 − 9.40524I 0.04392 + 9.75471I
u = 0.664502 + 0.907721I
a = −0.137319 − 0.952600I
b = 1.034870 + 0.744773I
−2.89814 − 6.85193I −7.15013 + 8.59668I
u = 0.664502 − 0.907721I
a = −0.137319 + 0.952600I
b = 1.034870 − 0.744773I
−2.89814 + 6.85193I −7.15013 − 8.59668I
u = 1.20846
a = 1.27084
b = 1.16050
0.266082 −11.4730
u = −1.266140 + 0.080450I
a = −0.243476 − 0.336575I
b = 0.274129 + 1.260920I
−0.76316 + 4.31765I −0.89966 − 6.91445I
u = −1.266140 − 0.080450I
a = −0.243476 + 0.336575I
b = 0.274129 − 1.260920I
−0.76316 − 4.31765I −0.89966 + 6.91445I
u = 0.692428
a = 4.42334
b = 0.311066
0.704588 −85.9750
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −1.379800 + 0.232274I
a = −0.202915 − 0.655047I
b = −0.97116 + 1.06639I
−5.14325 + 3.90529I 0.85581 − 4.51378I
u = −1.379800 − 0.232274I
a = −0.202915 + 0.655047I
b = −0.97116 − 1.06639I
−5.14325 − 3.90529I 0.85581 + 4.51378I
u = 0.068901 + 0.526930I
a = −0.19999 + 1.73646I
b = 0.622226 − 0.843745I
3.21655 − 2.10472I 4.13419 + 3.80054I
u = 0.068901 − 0.526930I
a = −0.19999 − 1.73646I
b = 0.622226 + 0.843745I
3.21655 + 2.10472I 4.13419 − 3.80054I
u = 0.213598 + 0.439117I
a = 0.933169 + 0.905622I
b = −0.321753 − 0.450048I
−0.214830 − 1.179340I −2.40251 + 6.38928I
u = 0.213598 − 0.439117I
a = 0.933169 − 0.905622I
b = −0.321753 + 0.450048I
−0.214830 + 1.179340I −2.40251 − 6.38928I
u = −1.59465 + 0.30004I
a = 0.522691 + 0.816481I
b = 1.39230 − 0.76184I
−10.2598 + 11.2873I −9.23051 − 7.41391I
u = −1.59465 − 0.30004I
a = 0.522691 − 0.816481I
b = 1.39230 + 0.76184I
−10.2598 − 11.2873I −9.23051 + 7.41391I
u = −1.61150 + 0.27184I
a = −0.659558 − 0.892240I
b = −1.42726 + 0.83763I
−7.7900 + 19.4343I −5.59666 − 9.62705I
u = −1.61150 − 0.27184I
a = −0.659558 + 0.892240I
b = −1.42726 − 0.83763I
−7.7900 − 19.4343I −5.59666 + 9.62705I
6
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −1.62950 + 0.21998I
a = 0.325830 + 0.720153I
b = 0.934852 − 0.257112I
−11.48300 + 4.00606I −11.23597 − 3.11051I
u = −1.62950 − 0.21998I
a = 0.325830 − 0.720153I
b = 0.934852 + 0.257112I
−11.48300 − 4.00606I −11.23597 + 3.11051I
u = −1.65218
a = −1.92363
b = −0.377729
−7.34312 37.2350
u = 1.36867 + 1.13663I
a = −0.056444 − 0.143003I
b = 0.425644 − 0.155525I
−2.78022 − 0.18590I −44.6298 + 88.4844I
u = 1.36867 − 1.13663I
a = −0.056444 + 0.143003I
b = 0.425644 + 0.155525I
−2.78022 + 0.18590I −44.6298 − 88.4844I
7
II. I
u
2
= h91u
12
− 255u
11
+ · · · + 82b + 126, 68u
12
− 191u
11
+ · · · + 164a +
1075, u
13
− 4u
12
+ · · · + 3u − 1i
(i) Arc colorings
a
7
=
1
0
a
12
=
0
u
a
8
=
1
u
2
a
1
=
−u
−u
3
+ u
a
4
=
−0.414634u
12
+ 1.16463u
11
+ ··· − 4.85366u − 6.55488
−1.10976u
12
+ 3.10976u
11
+ ··· − 3.40244u − 1.53659
a
9
=
−u
2
+ 1
−u
4
+ 2u
2
a
3
=
−1.52439u
12
+ 4.27439u
11
+ ··· − 8.25610u − 8.09146
−1.10976u
12
+ 3.10976u
11
+ ··· − 3.40244u − 1.53659
a
11
=
−1.41463u
12
+ 5.66463u
11
+ ··· − 32.3537u − 3.55488
0.390244u
12
− 0.890244u
11
+ ··· − 1.90244u − 1.03659
a
6
=
2.63415u
12
− 9.38415u
11
+ ··· + 42.6585u + 7.62805
−0.0731707u
12
+ 0.0731707u
11
+ ··· + 2.73171u + 1.97561
a
2
=
−1.65854u
12
+ 6.15854u
11
+ ··· − 35.4146u − 7.71951
−1.10976u
12
+ 3.10976u
11
+ ··· − 1.40244u − 2.53659
a
10
=
−2.36585u
12
+ 9.36585u
11
+ ··· − 51.3415u − 11.1220
−0.390244u
12
+ 1.39024u
11
+ ··· − 6.09756u − 2.46341
a
5
=
0.286585u
12
− 0.286585u
11
+ ··· − 11.1159u − 6.48780
0.00609756u
12
+ 0.243902u
11
+ ··· − 5.81098u − 0.664634
(ii) Obstruction class = 1
(iii) Cusp Shapes = −
455
164
u
12
+
1111
164
u
11
+
2107
164
u
10
−
3673
82
u
9
−
727
82
u
8
+
3812
41
u
7
−
1397
82
u
6
−
8187
164
u
5
−
517
41
u
4
−
2515
164
u
3
+
1706
41
u
2
−
2625
164
u +
68
41
8
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
3
u
13
− 2u
12
+ ··· + 12u − 4
c
2
u
13
− u
12
+ ··· − 10u − 2
c
4
, c
11
4(4u
13
+ 4u
12
+ ··· − 8u + 2)
c
5
, c
10
4(4u
13
+ 4u
12
+ ··· + 2u + 1)
c
6
, c
9
u
13
− 3u
12
+ ··· + 8u + 4
c
7
, c
8
u
13
− 4u
12
+ ··· + 3u − 1
c
12
u
13
+ 4u
12
+ ··· + 3u + 1
9
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
3
y
13
− 10y
12
+ ··· + 224y −16
c
2
y
13
− 3y
12
+ ··· + 104y −4
c
4
, c
11
16(16y
13
− 64y
12
+ ··· − 108y −4)
c
5
, c
10
16(16y
13
− 96y
12
+ ··· + 26y −1)
c
6
, c
9
y
13
− 9y
12
+ ··· + 112y −16
c
7
, c
8
, c
12
y
13
− 18y
12
+ ··· + 57y −1
10
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.270141 + 0.676643I
a = −0.93637 + 1.11204I
b = 0.765732 − 0.821657I
−0.48063 + 8.61216I −2.60620 − 9.97787I
u = −0.270141 − 0.676643I
a = −0.93637 − 1.11204I
b = 0.765732 + 0.821657I
−0.48063 − 8.61216I −2.60620 + 9.97787I
u = −1.31514
a = 1.20272
b = 1.39700
0.914772 1.94400
u = 1.329960 + 0.247887I
a = −0.175350 + 0.637473I
b = −1.13244 − 1.15488I
−5.47949 − 3.91166I −23.6039 + 5.6804I
u = 1.329960 − 0.247887I
a = −0.175350 − 0.637473I
b = −1.13244 + 1.15488I
−5.47949 + 3.91166I −23.6039 − 5.6804I
u = −1.46530
a = −1.16965
b = −1.81614
−5.60219 −7.40030
u = 1.51888 + 0.18868I
a = 0.428372 − 1.028980I
b = 1.042110 + 0.953933I
−6.64087 − 11.50500I −6.55247 + 9.76254I
u = 1.51888 − 0.18868I
a = 0.428372 + 1.028980I
b = 1.042110 − 0.953933I
−6.64087 + 11.50500I −6.55247 − 9.76254I
u = −1.63371
a = −0.619363
b = −1.26888
−11.9561 −13.2470
u = −0.251433
a = −4.95375
b = 0.682120
4.61878 8.54690
11
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.157502
a = −7.10717
b = −1.50496
0.0467492 0.0971950
u = 1.67535 + 0.84705I
a = 0.0069550 + 0.1189710I
b = −0.419957 + 0.085891I
−2.79417 − 0.14161I −99.2080 − 53.0661I
u = 1.67535 − 0.84705I
a = 0.0069550 − 0.1189710I
b = −0.419957 − 0.085891I
−2.79417 + 0.14161I −99.2080 + 53.0661I
12
III. I
u
3
= h−u
51
a − 375u
51
+ · · · + a + 909, 316u
51
a − 805u
51
+ · · · + 2748a −
4408, u
52
− 6u
51
+ · · · + 18u + 1i
(i) Arc colorings
a
7
=
1
0
a
12
=
0
u
a
8
=
1
u
2
a
1
=
−u
−u
3
+ u
a
4
=
a
0.0312500au
51
+ 11.7188u
51
+ ··· − 0.0312500a − 28.4063
a
9
=
−u
2
+ 1
−u
4
+ 2u
2
a
3
=
0.0312500au
51
+ 11.7188u
51
+ ··· + 0.968750a − 28.4063
0.0312500au
51
+ 11.7188u
51
+ ··· − 0.0312500a − 28.4063
a
11
=
20.0625au
51
− 41.6250u
51
+ ··· − 19.7500a + 50.3125
95.1563au
51
+ 30.0313u
51
+ ··· − 60.0938a − 21.5313
a
6
=
−39.6563au
51
+ 40.9063u
51
+ ··· − 76.2188a + 136.719
−156.906au
51
+ 24.2188u
51
+ ··· + 98.9063a − 16.2813
a
2
=
−167.281au
51
− 65.6563u
51
+ ··· + 123.719a + 12.5313
−146.594au
51
− 64.6563u
51
+ ··· + 92.9688a + 27.5313
a
10
=
494.219au
51
+ 95.1563u
51
+ ··· − 336.594a − 117.531
395.313au
51
+ 111.438u
51
+ ··· − 261.500a − 167.375
a
5
=
−
1335
16
u
51
+
2831
8
u
50
+ ··· + a +
507
16
0.0312500au
51
− 143.844u
51
+ ··· − 0.0312500a + 66.9063
(ii) Obstruction class = −1
(iii) Cusp Shapes = 36u
51
+
195
4
u
50
+ ··· − 8010u − 2630
13
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
3
u
104
+ 5u
103
+ ··· − 552520u + 36268
c
2
(u
52
+ 12u
51
+ ··· − 64u
2
+ 1)
2
c
4
, c
11
4(4u
104
+ 52u
103
+ ··· − 20472u + 2183)
c
5
, c
10
4(4u
104
+ 52u
103
+ ··· − 114u + 1)
c
6
, c
9
u
104
+ 15u
103
+ ··· − 1504u − 2908
c
7
, c
8
, c
12
(u
52
+ 6u
51
+ ··· − 18u + 1)
2
14
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
3
y
104
− 113y
103
+ ··· − 119319983280y + 1315367824
c
2
(y
52
− 12y
51
+ ··· − 128y + 1)
2
c
4
, c
11
16(16y
104
− 928y
103
+ ··· − 2.19441 × 10
8
y + 4765489)
c
5
, c
10
16(16y
104
− 1440y
103
+ ··· − 4076y + 1)
c
6
, c
9
y
104
− 97y
103
+ ··· − 959773360y + 8456464
c
7
, c
8
, c
12
(y
52
− 58y
51
+ ··· − 278y + 1)
2
15
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = −0.666943 + 0.765381I
a = −0.411358 + 0.852975I
b = 0.753598 + 0.019420I
−2.60454 + 7.14131I 0
u = −0.666943 + 0.765381I
a = 0.047648 − 1.142430I
b = −1.12596 + 0.94335I
−2.60454 + 7.14131I 0
u = −0.666943 − 0.765381I
a = −0.411358 − 0.852975I
b = 0.753598 − 0.019420I
−2.60454 − 7.14131I 0
u = −0.666943 − 0.765381I
a = 0.047648 + 1.142430I
b = −1.12596 − 0.94335I
−2.60454 − 7.14131I 0
u = −0.930311
a = −1.35080
b = 0.295990
3.18882 2.51350
u = −0.930311
a = 1.46851
b = 1.37728
3.18882 2.51350
u = −0.451134 + 0.971186I
a = 0.653621 − 0.050648I
b = −0.608265 − 0.548442I
−1.79010 − 1.53599I 0
u = −0.451134 + 0.971186I
a = −0.217119 + 0.512197I
b = 0.806048 − 0.774083I
−1.79010 − 1.53599I 0
u = −0.451134 − 0.971186I
a = 0.653621 + 0.050648I
b = −0.608265 + 0.548442I
−1.79010 + 1.53599I 0
u = −0.451134 − 0.971186I
a = −0.217119 − 0.512197I
b = 0.806048 + 0.774083I
−1.79010 + 1.53599I 0
16
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = −0.616816 + 0.640019I
a = −0.18999 − 1.45500I
b = −0.636561 + 0.935758I
2.51626 + 7.46030I 0. − 8.58345I
u = −0.616816 + 0.640019I
a = 0.05358 + 1.63243I
b = 1.027170 − 0.731584I
2.51626 + 7.46030I 0. − 8.58345I
u = −0.616816 − 0.640019I
a = −0.18999 + 1.45500I
b = −0.636561 − 0.935758I
2.51626 − 7.46030I 0. + 8.58345I
u = −0.616816 − 0.640019I
a = 0.05358 − 1.63243I
b = 1.027170 + 0.731584I
2.51626 − 7.46030I 0. + 8.58345I
u = 0.872813 + 0.698635I
a = −0.645062 + 0.662035I
b = −1.10805 − 0.95668I
0.44754 + 2.99101I 0
u = 0.872813 + 0.698635I
a = −0.605533 − 0.090182I
b = 0.832738 − 0.497105I
0.44754 + 2.99101I 0
u = 0.872813 − 0.698635I
a = −0.645062 − 0.662035I
b = −1.10805 + 0.95668I
0.44754 − 2.99101I 0
u = 0.872813 − 0.698635I
a = −0.605533 + 0.090182I
b = 0.832738 + 0.497105I
0.44754 − 2.99101I 0
u = 0.329397 + 0.733690I
a = 0.355573 − 0.859717I
b = −0.476590 + 1.311850I
1.93142 − 7.86817I 1.54415 + 8.03498I
u = 0.329397 + 0.733690I
a = −0.55839 − 1.54194I
b = 1.046220 + 0.703764I
1.93142 − 7.86817I 1.54415 + 8.03498I
17
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = 0.329397 − 0.733690I
a = 0.355573 + 0.859717I
b = −0.476590 − 1.311850I
1.93142 + 7.86817I 1.54415 − 8.03498I
u = 0.329397 − 0.733690I
a = −0.55839 + 1.54194I
b = 1.046220 − 0.703764I
1.93142 + 7.86817I 1.54415 − 8.03498I
u = −0.383886 + 0.683449I
a = −1.005650 − 0.435411I
b = 0.832036 + 0.618946I
3.20645 − 3.00363I 2.68384 + 4.04752I
u = −0.383886 + 0.683449I
a = 0.947761 + 0.795250I
b = −0.318481 − 0.754888I
3.20645 − 3.00363I 2.68384 + 4.04752I
u = −0.383886 − 0.683449I
a = −1.005650 + 0.435411I
b = 0.832036 − 0.618946I
3.20645 + 3.00363I 2.68384 − 4.04752I
u = −0.383886 − 0.683449I
a = 0.947761 − 0.795250I
b = −0.318481 + 0.754888I
3.20645 + 3.00363I 2.68384 − 4.04752I
u = 0.713698 + 0.208798I
a = 0.510056 + 1.009760I
b = −0.941920 − 0.046805I
−2.92201 − 1.86532I −8.84509 + 5.50281I
u = 0.713698 + 0.208798I
a = 1.052470 + 0.698068I
b = 0.616268 + 0.472651I
−2.92201 − 1.86532I −8.84509 + 5.50281I
u = 0.713698 − 0.208798I
a = 0.510056 − 1.009760I
b = −0.941920 + 0.046805I
−2.92201 + 1.86532I −8.84509 − 5.50281I
u = 0.713698 − 0.208798I
a = 1.052470 − 0.698068I
b = 0.616268 − 0.472651I
−2.92201 + 1.86532I −8.84509 − 5.50281I
18
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = −0.419761 + 0.482531I
a = −0.735342 − 0.873272I
b = 0.679260 + 0.823186I
3.56510 + 1.61688I 3.53854 − 5.28642I
u = −0.419761 + 0.482531I
a = 0.54033 + 1.94819I
b = 0.674298 − 0.619590I
3.56510 + 1.61688I 3.53854 − 5.28642I
u = −0.419761 − 0.482531I
a = −0.735342 + 0.873272I
b = 0.679260 − 0.823186I
3.56510 − 1.61688I 3.53854 + 5.28642I
u = −0.419761 − 0.482531I
a = 0.54033 − 1.94819I
b = 0.674298 + 0.619590I
3.56510 − 1.61688I 3.53854 + 5.28642I
u = 0.045922 + 0.614097I
a = 0.388372 + 0.865568I
b = −0.178151 − 1.294950I
−0.596311 − 0.798278I −1.05944 + 5.87715I
u = 0.045922 + 0.614097I
a = 1.70122 + 0.38926I
b = −0.756307 − 0.292721I
−0.596311 − 0.798278I −1.05944 + 5.87715I
u = 0.045922 − 0.614097I
a = 0.388372 − 0.865568I
b = −0.178151 + 1.294950I
−0.596311 + 0.798278I −1.05944 − 5.87715I
u = 0.045922 − 0.614097I
a = 1.70122 − 0.38926I
b = −0.756307 + 0.292721I
−0.596311 + 0.798278I −1.05944 − 5.87715I
u = −1.384960 + 0.212125I
a = −0.301792 − 0.760811I
b = −1.08419 + 0.98460I
−5.13846 + 3.88504I 0
u = −1.384960 + 0.212125I
a = −0.086570 − 0.550152I
b = −0.690758 + 1.137670I
−5.13846 + 3.88504I 0
19
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = −1.384960 − 0.212125I
a = −0.301792 + 0.760811I
b = −1.08419 − 0.98460I
−5.13846 − 3.88504I 0
u = −1.384960 − 0.212125I
a = −0.086570 + 0.550152I
b = −0.690758 − 1.137670I
−5.13846 − 3.88504I 0
u = 1.42229 + 0.08245I
a = −0.0081558 − 0.1341870I
b = −0.11523 + 2.58075I
−4.85666 − 0.84505I 0
u = 1.42229 + 0.08245I
a = −0.44566 + 1.85120I
b = −0.911624 − 0.228098I
−4.85666 − 0.84505I 0
u = 1.42229 − 0.08245I
a = −0.0081558 + 0.1341870I
b = −0.11523 − 2.58075I
−4.85666 + 0.84505I 0
u = 1.42229 − 0.08245I
a = −0.44566 − 1.85120I
b = −0.911624 + 0.228098I
−4.85666 + 0.84505I 0
u = 1.43082 + 0.19034I
a = 0.203101 − 0.215510I
b = 0.580757 + 0.091897I
−2.57458 − 0.10242I 0
u = 1.43082 + 0.19034I
a = 0.255686 + 0.054319I
b = 0.153310 − 0.085568I
−2.57458 − 0.10242I 0
u = 1.43082 − 0.19034I
a = 0.203101 + 0.215510I
b = 0.580757 − 0.091897I
−2.57458 + 0.10242I 0
u = 1.43082 − 0.19034I
a = 0.255686 − 0.054319I
b = 0.153310 + 0.085568I
−2.57458 + 0.10242I 0
20
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = −1.45251
a = 0.438958
b = 4.04061
−5.33005 0
u = −1.45251
a = −3.01723
b = −1.20431
−5.33005 0
u = −1.44587 + 0.20732I
a = 0.719613 + 1.113810I
b = 1.27041 − 0.72613I
−3.76396 + 11.13930I 0
u = −1.44587 + 0.20732I
a = 0.181699 + 0.251896I
b = 0.00148 − 1.67493I
−3.76396 + 11.13930I 0
u = −1.44587 − 0.20732I
a = 0.719613 − 1.113810I
b = 1.27041 + 0.72613I
−3.76396 − 11.13930I 0
u = −1.44587 − 0.20732I
a = 0.181699 − 0.251896I
b = 0.00148 + 1.67493I
−3.76396 − 11.13930I 0
u = −1.48820 + 0.02121I
a = 0.367795 − 0.819327I
b = 0.66690 + 1.37814I
−6.00418 + 1.14263I 0
u = −1.48820 + 0.02121I
a = −0.55078 − 1.40100I
b = −0.852406 + 0.492909I
−6.00418 + 1.14263I 0
u = −1.48820 − 0.02121I
a = 0.367795 + 0.819327I
b = 0.66690 − 1.37814I
−6.00418 − 1.14263I 0
u = −1.48820 − 0.02121I
a = −0.55078 + 1.40100I
b = −0.852406 − 0.492909I
−6.00418 − 1.14263I 0
21
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = 1.48325 + 0.13019I
a = 0.880572 − 0.865612I
b = 0.891996 + 0.603870I
−2.66236 − 3.76069I 0
u = 1.48325 + 0.13019I
a = −0.099166 + 0.326301I
b = 0.543218 − 1.173170I
−2.66236 − 3.76069I 0
u = 1.48325 − 0.13019I
a = 0.880572 + 0.865612I
b = 0.891996 − 0.603870I
−2.66236 + 3.76069I 0
u = 1.48325 − 0.13019I
a = −0.099166 − 0.326301I
b = 0.543218 + 1.173170I
−2.66236 + 3.76069I 0
u = −0.486302 + 0.122804I
a = 0.58416 + 2.33590I
b = 1.107410 − 0.847322I
−2.15302 + 8.44584I −8.09837 − 8.04505I
u = −0.486302 + 0.122804I
a = 1.23147 − 2.51030I
b = 0.724727 − 0.354156I
−2.15302 + 8.44584I −8.09837 − 8.04505I
u = −0.486302 − 0.122804I
a = 0.58416 − 2.33590I
b = 1.107410 + 0.847322I
−2.15302 − 8.44584I −8.09837 + 8.04505I
u = −0.486302 − 0.122804I
a = 1.23147 + 2.51030I
b = 0.724727 + 0.354156I
−2.15302 − 8.44584I −8.09837 + 8.04505I
u = 1.51223 + 0.05669I
a = −0.724214 + 0.595511I
b = −1.61518 − 0.65585I
−9.94685 − 2.82043I 0
u = 1.51223 + 0.05669I
a = −0.854976 − 0.740454I
b = −1.016630 + 0.155554I
−9.94685 − 2.82043I 0
22
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = 1.51223 − 0.05669I
a = −0.724214 − 0.595511I
b = −1.61518 + 0.65585I
−9.94685 + 2.82043I 0
u = 1.51223 − 0.05669I
a = −0.854976 + 0.740454I
b = −1.016630 − 0.155554I
−9.94685 + 2.82043I 0
u = 1.52714 + 0.05481I
a = 0.652836 − 0.809744I
b = 1.45810 + 0.96153I
−8.98085 − 9.19273I 0
u = 1.52714 + 0.05481I
a = 0.654078 + 1.174640I
b = 0.737950 − 0.124608I
−8.98085 − 9.19273I 0
u = 1.52714 − 0.05481I
a = 0.652836 + 0.809744I
b = 1.45810 − 0.96153I
−8.98085 + 9.19273I 0
u = 1.52714 − 0.05481I
a = 0.654078 − 1.174640I
b = 0.737950 + 0.124608I
−8.98085 + 9.19273I 0
u = −0.446869 + 0.150367I
a = −0.59796 − 1.67547I
b = −1.267440 + 0.621768I
−3.34579 + 1.99954I −9.53386 − 5.76530I
u = −0.446869 + 0.150367I
a = −1.63764 + 1.19484I
b = −0.940989 + 0.288189I
−3.34579 + 1.99954I −9.53386 − 5.76530I
u = −0.446869 − 0.150367I
a = −0.59796 + 1.67547I
b = −1.267440 − 0.621768I
−3.34579 − 1.99954I −9.53386 + 5.76530I
u = −0.446869 − 0.150367I
a = −1.63764 − 1.19484I
b = −0.940989 − 0.288189I
−3.34579 − 1.99954I −9.53386 + 5.76530I
23
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = −1.56443 + 0.02584I
a = 0.670758 − 0.787254I
b = 0.737244 + 0.082736I
−10.56320 + 2.54580I 0
u = −1.56443 + 0.02584I
a = −0.326491 − 0.690903I
b = −1.086970 + 0.336405I
−10.56320 + 2.54580I 0
u = −1.56443 − 0.02584I
a = 0.670758 + 0.787254I
b = 0.737244 − 0.082736I
−10.56320 − 2.54580I 0
u = −1.56443 − 0.02584I
a = −0.326491 + 0.690903I
b = −1.086970 − 0.336405I
−10.56320 − 2.54580I 0
u = 1.57281 + 0.20541I
a = −0.594745 + 0.855793I
b = −0.908037 − 1.003660I
−4.77180 − 10.59140I 0
u = 1.57281 + 0.20541I
a = 0.697890 − 1.021960I
b = 1.19777 + 0.76508I
−4.77180 − 10.59140I 0
u = 1.57281 − 0.20541I
a = −0.594745 − 0.855793I
b = −0.908037 + 1.003660I
−4.77180 + 10.59140I 0
u = 1.57281 − 0.20541I
a = 0.697890 + 1.021960I
b = 1.19777 − 0.76508I
−4.77180 + 10.59140I 0
u = 1.58464 + 0.25100I
a = 0.232902 − 0.974487I
b = 0.973307 + 0.270389I
−10.0157 − 10.9120I 0
u = 1.58464 + 0.25100I
a = −0.607967 + 0.778820I
b = −1.51183 − 0.91314I
−10.0157 − 10.9120I 0
24
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = 1.58464 − 0.25100I
a = 0.232902 + 0.974487I
b = 0.973307 − 0.270389I
−10.0157 + 10.9120I 0
u = 1.58464 − 0.25100I
a = −0.607967 − 0.778820I
b = −1.51183 + 0.91314I
−10.0157 + 10.9120I 0
u = 0.347781 + 0.161481I
a = 1.12566 + 2.31078I
b = −0.101270 − 0.960129I
0.159547 − 0.651334I −2.56530 + 10.53331I
u = 0.347781 + 0.161481I
a = 1.55949 + 3.68489I
b = −0.513031 − 0.014829I
0.159547 − 0.651334I −2.56530 + 10.53331I
u = 0.347781 − 0.161481I
a = 1.12566 − 2.31078I
b = −0.101270 + 0.960129I
0.159547 + 0.651334I −2.56530 − 10.53331I
u = 0.347781 − 0.161481I
a = 1.55949 − 3.68489I
b = −0.513031 + 0.014829I
0.159547 + 0.651334I −2.56530 − 10.53331I
u = 1.62109 + 0.33591I
a = 0.555168 − 0.573504I
b = 1.60200 + 0.70870I
−8.69767 − 3.49825I 0
u = 1.62109 + 0.33591I
a = −0.047708 + 0.657048I
b = −0.729629 − 0.022515I
−8.69767 − 3.49825I 0
u = 1.62109 − 0.33591I
a = 0.555168 + 0.573504I
b = 1.60200 − 0.70870I
−8.69767 + 3.49825I 0
u = 1.62109 − 0.33591I
a = −0.047708 − 0.657048I
b = −0.729629 + 0.022515I
−8.69767 + 3.49825I 0
25
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = −1.77146
a = −0.755855
b = −1.41414
−9.81056 0
u = −1.77146
a = 0.182973
b = 0.931880
−9.81056 0
u = −0.0631759
a = 1.69572
b = −8.85412
0.00212035 −2056.70
u = −0.0631759
a = −139.805
b = −1.01065
0.00212035 −2056.70
26
IV. I
u
4
= hb + 1, a, u − 1i
(i) Arc colorings
a
7
=
1
0
a
12
=
0
1
a
8
=
1
1
a
1
=
−1
0
a
4
=
0
−1
a
9
=
0
1
a
3
=
−1
−1
a
11
=
0
1
a
6
=
1
1
a
2
=
−1
−1
a
10
=
1
2
a
5
=
0
−1
(ii) Obstruction class = 1
(iii) Cusp Shapes = −12
27
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
3
, c
5
c
6
, c
7
, c
8
c
9
, c
10
u − 1
c
2
, c
4
, c
11
u
c
12
u + 1
28
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
3
, c
5
c
6
, c
7
, c
8
c
9
, c
10
, c
12
y −1
c
2
, c
4
, c
11
y
29
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
4
√
−1(vol +
√
−1CS) Cusp shape
u = 1.00000
a = 0
b = −1.00000
−3.28987 −12.0000
30
V. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
, c
3
(u − 1)(u
13
− 2u
12
+ ··· + 12u − 4)(u
25
− u
24
+ ··· − 5u + 1)
· (u
104
+ 5u
103
+ ··· − 552520u + 36268)
c
2
u(u
13
− u
12
+ ··· − 10u − 2)(u
25
− 16u
24
+ ··· + 7168u − 1024)
· (u
52
+ 12u
51
+ ··· − 64u
2
+ 1)
2
c
4
, c
11
16(u)(4u
13
+ 4u
12
+ ··· − 8u + 2)(u
25
+ 7u
24
+ ··· + 10u + 2)
· (4u
104
+ 52u
103
+ ··· − 20472u + 2183)
c
5
, c
10
16(u − 1)(4u
13
+ 4u
12
+ ··· + 2u + 1)(u
25
+ 4u
24
+ ··· − 3u + 1)
· (4u
104
+ 52u
103
+ ··· − 114u + 1)
c
6
, c
9
(u − 1)(u
13
− 3u
12
+ ··· + 8u + 4)(u
25
+ 2u
24
+ ··· + 7u − 1)
· (u
104
+ 15u
103
+ ··· − 1504u − 2908)
c
7
, c
8
(u − 1)(u
13
− 4u
12
+ ··· + 3u − 1)(u
25
− 8u
24
+ ··· − 32u − 32)
· (u
52
+ 6u
51
+ ··· − 18u + 1)
2
c
12
(u + 1)(u
13
+ 4u
12
+ ··· + 3u + 1)(u
25
− 8u
24
+ ··· − 32u − 32)
· (u
52
+ 6u
51
+ ··· − 18u + 1)
2
31
VI. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
, c
3
(y −1)(y
13
− 10y
12
+ ··· + 224y −16)(y
25
− 7y
24
+ ··· + 25y −1)
· (y
104
− 113y
103
+ ··· − 119319983280y + 1315367824)
c
2
y(y
13
− 3y
12
+ ··· + 104y −4)
· (y
25
+ 18y
23
+ ··· − 11010048y −1048576)
· (y
52
− 12y
51
+ ··· − 128y + 1)
2
c
4
, c
11
256(y)(16y
13
− 64y
12
+ ··· − 108y −4)(y
25
− 21y
24
+ ··· − 100y −4)
· (16y
104
− 928y
103
+ ··· − 219441238y + 4765489)
c
5
, c
10
256(y −1)(16y
13
− 96y
12
+ ··· + 26y −1)(y
25
− 32y
24
+ ··· − 3y −1)
· (16y
104
− 1440y
103
+ ··· − 4076y + 1)
c
6
, c
9
(y −1)(y
13
− 9y
12
+ ··· + 112y −16)(y
25
− 2y
24
+ ··· + 15y −1)
· (y
104
− 97y
103
+ ··· − 959773360y + 8456464)
c
7
, c
8
, c
12
(y −1)(y
13
− 18y
12
+ ··· + 57y −1)(y
25
− 24y
24
+ ··· − 6656y −1024)
· (y
52
− 58y
51
+ ··· − 278y + 1)
2
32
