12a
1255
(K12a
1255
)
A knot diagram
1
Linearized knot diagam
5 7 8 1 10 11 12 4 2 6 3 9
Solving Sequence
5,10
6 11
2,7
3 1 4 9 8 12
c
5
c
10
c
6
c
2
c
1
c
4
c
9
c
8
c
12
c
3
, c
7
, c
11
Ideals for irreducible components
2
of X
par
I
u
1
= h2.19271 × 10
265
u
102
+ 5.65299 × 10
265
u
101
+ ··· + 3.59709 × 10
264
b − 5.56869 × 10
266
,
3.41923 × 10
266
u
102
+ 8.30043 × 10
266
u
101
+ ··· + 7.91361 × 10
265
a − 4.72551 × 10
267
,
u
103
+ 3u
102
+ ··· − 30u − 11i
I
u
2
= hu
13
+ 2u
12
− 8u
11
− 14u
10
+ 25u
9
+ 35u
8
− 31u
7
− 32u
6
− u
5
− 3u
4
+ 24u
3
+ 18u
2
+ b − 3u − 2,
− 6u
13
− 9u
12
+ ··· + a + 17,
u
14
+ u
13
− 9u
12
− 7u
11
+ 30u
10
+ 18u
9
− 41u
8
− 19u
7
+ 10u
6
+ 3u
5
+ 21u
4
+ 7u
3
− 10u
2
− u + 1i
I
u
3
= hb + 1, a
2
+ a − 1, u − 1i
I
u
4
= hb, a + 1, u − 1i
* 4 irreducible components of dim
C
= 0, with total 120 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
= h2.19 × 10
265
u
102
+ 5.65 × 10
265
u
101
+ · · · + 3.60 × 10
264
b − 5.57 ×
10
266
, 3.42 × 10
266
u
102
+ 8.30 × 10
266
u
101
+ · · · + 7.91 × 10
265
a − 4.73 ×
10
267
, u
103
+ 3u
102
+ · · · − 30u − 11i
(i) Arc colorings
a
5
=
1
0
a
10
=
0
u
a
6
=
1
u
2
a
11
=
−u
−u
3
+ u
a
2
=
−4.32069u
102
− 10.4888u
101
+ ··· + 179.840u + 59.7137
−6.09577u
102
− 15.7154u
101
+ ··· + 63.8206u + 154.811
a
7
=
−u
2
+ 1
−u
4
+ 2u
2
a
3
=
−6.71410u
102
− 16.7635u
101
+ ··· + 184.719u + 127.421
−6.80402u
102
− 17.5816u
101
+ ··· + 64.6779u + 175.953
a
1
=
−10.4165u
102
− 26.2042u
101
+ ··· + 243.661u + 214.524
−6.09577u
102
− 15.7154u
101
+ ··· + 63.8206u + 154.811
a
4
=
−9.75655u
102
− 25.0868u
101
+ ··· + 64.3501u + 243.568
0.623874u
102
+ 1.58451u
101
+ ··· − 20.0995u − 19.7696
a
9
=
−4.30255u
102
− 11.7953u
101
+ ··· − 115.645u + 167.369
4.46999u
102
+ 11.4379u
101
+ ··· − 48.0748u − 114.185
a
8
=
−14.1641u
102
− 36.5893u
101
+ ··· + 32.7208u + 379.312
−0.623051u
102
− 1.57175u
101
+ ··· + 2.42488u + 11.4572
a
12
=
3.73375u
102
+ 9.15179u
101
+ ··· − 141.830u − 66.2722
1.12589u
102
+ 2.84348u
101
+ ··· − 12.2490u − 30.2912
(ii) Obstruction class = −1
(iii) Cusp Shapes = 8.97892u
102
+ 21.2749u
101
+ ··· − 439.789u − 159.114
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
4
u
103
+ 5u
102
+ ··· − 140u − 5
c
2
u
103
− 6u
102
+ ··· − 2684u − 1763
c
3
, c
8
u
103
− 3u
102
+ ··· − 340u + 41
c
5
, c
6
, c
10
u
103
− 3u
102
+ ··· − 30u + 11
c
7
u
103
− 6u
102
+ ··· − 120u − 20
c
9
u
103
− 4u
102
+ ··· − 558937u − 115993
c
11
u
103
+ 4u
102
+ ··· − 37150u − 3953
c
12
u
103
+ 3u
102
+ ··· − 3395u + 319
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
4
y
103
− 117y
102
+ ··· + 2440y −25
c
2
y
103
− 20y
102
+ ··· − 30171744y −3108169
c
3
, c
8
y
103
− 89y
102
+ ··· + 19496y −1681
c
5
, c
6
, c
10
y
103
− 115y
102
+ ··· + 10294y −121
c
7
y
103
− 18y
102
+ ··· + 14360y −400
c
9
y
103
+ 42y
102
+ ··· − 65353344557y −13454376049
c
11
y
103
− 48y
102
+ ··· + 1279676770y −15626209
c
12
y
103
+ 21y
102
+ ··· + 6596199y −101761
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −1.02714
a = −0.871216
b = 1.12945
−2.83707 0
u = −0.712753 + 0.660374I
a = 0.12981 − 1.48426I
b = −1.243000 + 0.352054I
−1.53336 + 8.26614I 0
u = −0.712753 − 0.660374I
a = 0.12981 + 1.48426I
b = −1.243000 − 0.352054I
−1.53336 − 8.26614I 0
u = 0.571147 + 0.776168I
a = 0.698957 − 0.445070I
b = 0.043595 + 0.727181I
−2.06014 + 3.60547I 0
u = 0.571147 − 0.776168I
a = 0.698957 + 0.445070I
b = 0.043595 − 0.727181I
−2.06014 − 3.60547I 0
u = 0.922298 + 0.546376I
a = 0.492087 + 0.603509I
b = −1.352480 + 0.129722I
−6.42162 + 1.25693I 0
u = 0.922298 − 0.546376I
a = 0.492087 − 0.603509I
b = −1.352480 − 0.129722I
−6.42162 − 1.25693I 0
u = 0.696204 + 0.862353I
a = 0.393640 + 0.810036I
b = −1.202830 − 0.163141I
−3.80047 − 3.13987I 0
u = 0.696204 − 0.862353I
a = 0.393640 − 0.810036I
b = −1.202830 + 0.163141I
−3.80047 + 3.13987I 0
u = 0.519592 + 0.712577I
a = −0.036788 + 1.108860I
b = −0.297248 − 1.015470I
−1.98401 − 8.53931I 0
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.519592 − 0.712577I
a = −0.036788 − 1.108860I
b = −0.297248 + 1.015470I
−1.98401 + 8.53931I 0
u = −0.263680 + 0.825383I
a = 0.826687 + 0.113153I
b = −1.100060 − 0.204003I
−0.18116 − 3.40409I 0
u = −0.263680 − 0.825383I
a = 0.826687 − 0.113153I
b = −1.100060 + 0.204003I
−0.18116 + 3.40409I 0
u = 0.864517 + 0.038493I
a = −0.737989 − 0.406950I
b = −1.44132 − 0.20978I
−6.85390 − 0.24458I 0
u = 0.864517 − 0.038493I
a = −0.737989 + 0.406950I
b = −1.44132 + 0.20978I
−6.85390 + 0.24458I 0
u = 0.777485 + 0.829059I
a = −0.197802 − 1.189670I
b = 1.42684 + 0.40686I
−7.3811 − 13.5504I 0
u = 0.777485 − 0.829059I
a = −0.197802 + 1.189670I
b = 1.42684 − 0.40686I
−7.3811 + 13.5504I 0
u = 0.833384
a = 2.76816
b = 1.04792
−3.08922 0
u = −0.780557 + 0.878110I
a = −0.287845 + 0.849782I
b = 1.36372 − 0.41744I
−8.07615 + 4.22446I 0
u = −0.780557 − 0.878110I
a = −0.287845 − 0.849782I
b = 1.36372 + 0.41744I
−8.07615 − 4.22446I 0
6
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.629722 + 0.992893I
a = −0.637158 + 0.631730I
b = 1.283490 + 0.135693I
−7.56113 + 2.31048I 0
u = −0.629722 − 0.992893I
a = −0.637158 − 0.631730I
b = 1.283490 − 0.135693I
−7.56113 − 2.31048I 0
u = 0.300171 + 0.742213I
a = 1.20411 + 1.29920I
b = −1.366820 − 0.263059I
−4.56735 − 5.86087I 0
u = 0.300171 − 0.742213I
a = 1.20411 − 1.29920I
b = −1.366820 + 0.263059I
−4.56735 + 5.86087I 0
u = −0.524235 + 0.540945I
a = 0.320803 + 1.183620I
b = −0.017847 − 0.806346I
2.26250 + 4.10162I 0
u = −0.524235 − 0.540945I
a = 0.320803 − 1.183620I
b = −0.017847 + 0.806346I
2.26250 − 4.10162I 0
u = 0.336627 + 1.200440I
a = −0.602563 + 0.003656I
b = 1.278080 − 0.281645I
−5.92485 + 7.20612I 0
u = 0.336627 − 1.200440I
a = −0.602563 − 0.003656I
b = 1.278080 + 0.281645I
−5.92485 − 7.20612I 0
u = 0.739866 + 0.039993I
a = −1.076040 − 0.142388I
b = 0.274494 − 0.030365I
−1.57618 − 0.01678I 0
u = 0.739866 − 0.039993I
a = −1.076040 + 0.142388I
b = 0.274494 + 0.030365I
−1.57618 + 0.01678I 0
7
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −1.28218
a = 1.40464
b = 0.567004
−0.874990 0
u = −0.471069 + 0.500551I
a = 1.149870 − 0.535713I
b = 0.026305 − 0.383365I
−3.64799 + 4.14125I 0
u = −0.471069 − 0.500551I
a = 1.149870 + 0.535713I
b = 0.026305 + 0.383365I
−3.64799 − 4.14125I 0
u = −0.406822 + 0.472358I
a = −0.96001 − 1.19832I
b = −0.145627 + 0.523403I
2.54202 − 0.51306I 2.93361 + 0.I
u = −0.406822 − 0.472358I
a = −0.96001 + 1.19832I
b = −0.145627 − 0.523403I
2.54202 + 0.51306I 2.93361 + 0.I
u = −1.385410 + 0.083851I
a = 0.148969 + 0.538490I
b = 1.24248 − 0.95308I
−6.64538 + 1.45297I 0
u = −1.385410 − 0.083851I
a = 0.148969 − 0.538490I
b = 1.24248 + 0.95308I
−6.64538 − 1.45297I 0
u = −0.588249 + 0.165010I
a = 0.05567 − 2.04220I
b = −1.42982 + 0.41387I
−8.42839 + 6.91659I −13.4220 − 5.9562I
u = −0.588249 − 0.165010I
a = 0.05567 + 2.04220I
b = −1.42982 − 0.41387I
−8.42839 − 6.91659I −13.4220 + 5.9562I
u = −1.387920 + 0.108419I
a = 0.349460 + 0.849831I
b = 0.321495 − 0.915324I
−4.66943 + 4.64864I 0
8
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −1.387920 − 0.108419I
a = 0.349460 − 0.849831I
b = 0.321495 + 0.915324I
−4.66943 − 4.64864I 0
u = 1.413230 + 0.025821I
a = −0.491532 + 0.637305I
b = −0.164523 − 0.509689I
−3.02206 − 0.88769I 0
u = 1.413230 − 0.025821I
a = −0.491532 − 0.637305I
b = −0.164523 + 0.509689I
−3.02206 + 0.88769I 0
u = 0.202404 + 0.517459I
a = −0.45415 − 1.77758I
b = 0.185959 + 0.653658I
0.35181 − 2.51428I −0.26813 + 6.54682I
u = 0.202404 − 0.517459I
a = −0.45415 + 1.77758I
b = 0.185959 − 0.653658I
0.35181 + 2.51428I −0.26813 − 6.54682I
u = 0.524734 + 0.179457I
a = −0.34303 − 3.63364I
b = 1.095430 + 0.095403I
−2.66135 − 0.55125I −11.0570 − 24.4501I
u = 0.524734 − 0.179457I
a = −0.34303 + 3.63364I
b = 1.095430 − 0.095403I
−2.66135 + 0.55125I −11.0570 + 24.4501I
u = −0.378270 + 0.402322I
a = −0.18660 + 2.77093I
b = 1.250900 − 0.146970I
−1.55030 + 1.74305I −1.47413 − 7.39084I
u = −0.378270 − 0.402322I
a = −0.18660 − 2.77093I
b = 1.250900 + 0.146970I
−1.55030 − 1.74305I −1.47413 + 7.39084I
u = 1.47222
a = 0.396859
b = 2.75375
−8.32712 0
9
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 1.47249 + 0.01020I
a = 0.358466 + 0.126650I
b = 2.66884 − 0.76302I
−8.32828 − 0.00094I 0
u = 1.47249 − 0.01020I
a = 0.358466 − 0.126650I
b = 2.66884 + 0.76302I
−8.32828 + 0.00094I 0
u = −1.46126 + 0.20951I
a = −0.46855 − 1.36304I
b = −1.44279 + 0.35405I
−10.27290 + 9.16958I 0
u = −1.46126 − 0.20951I
a = −0.46855 + 1.36304I
b = −1.44279 − 0.35405I
−10.27290 − 9.16958I 0
u = 0.324874 + 0.404930I
a = −0.696250 − 0.864255I
b = 0.059592 + 0.327808I
−0.327590 − 1.145130I −4.44806 + 5.32602I
u = 0.324874 − 0.404930I
a = −0.696250 + 0.864255I
b = 0.059592 − 0.327808I
−0.327590 + 1.145130I −4.44806 − 5.32602I
u = −1.47822 + 0.11344I
a = −0.090198 + 0.729338I
b = 0.124953 − 0.868255I
−6.30597 + 2.96568I 0
u = −1.47822 − 0.11344I
a = −0.090198 − 0.729338I
b = 0.124953 + 0.868255I
−6.30597 − 2.96568I 0
u = −0.257883 + 0.431811I
a = 0.322742 − 0.847082I
b = −0.190119 + 1.297650I
−3.19960 − 1.12337I −10.6824 − 10.5618I
u = −0.257883 − 0.431811I
a = 0.322742 + 0.847082I
b = −0.190119 − 1.297650I
−3.19960 + 1.12337I −10.6824 + 10.5618I
10
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −1.49764
a = −0.874802
b = −2.05907
−10.4823 0
u = 1.50436 + 0.11483I
a = 1.04288 − 1.31009I
b = 1.360600 + 0.207898I
−7.87558 − 3.55965I 0
u = 1.50436 − 0.11483I
a = 1.04288 + 1.31009I
b = 1.360600 − 0.207898I
−7.87558 + 3.55965I 0
u = 1.52443 + 0.16772I
a = 0.374823 + 0.893625I
b = −0.0391754 − 0.0967406I
−10.28230 − 6.62865I 0
u = 1.52443 − 0.16772I
a = 0.374823 − 0.893625I
b = −0.0391754 + 0.0967406I
−10.28230 + 6.62865I 0
u = 1.53416 + 0.00571I
a = −1.08498 − 1.19461I
b = −1.330510 + 0.027870I
−14.5673 − 6.1962I 0
u = 1.53416 − 0.00571I
a = −1.08498 + 1.19461I
b = −1.330510 − 0.027870I
−14.5673 + 6.1962I 0
u = −1.52421 + 0.22221I
a = −0.333823 − 0.630700I
b = −0.579117 + 1.196210I
−8.6740 + 11.9101I 0
u = −1.52421 − 0.22221I
a = −0.333823 + 0.630700I
b = −0.579117 − 1.196210I
−8.6740 − 11.9101I 0
u = 1.53334 + 0.16126I
a = 0.282129 − 0.634196I
b = 0.134070 + 0.995707I
−4.57553 − 6.63598I 0
11
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 1.53334 − 0.16126I
a = 0.282129 + 0.634196I
b = 0.134070 − 0.995707I
−4.57553 + 6.63598I 0
u = −1.54554 + 0.03526I
a = 0.52814 + 1.42258I
b = 1.212190 − 0.310410I
−9.71175 + 1.24822I 0
u = −1.54554 − 0.03526I
a = 0.52814 − 1.42258I
b = 1.212190 + 0.310410I
−9.71175 − 1.24822I 0
u = 1.56057 + 0.05597I
a = −0.579035 + 0.883979I
b = −1.60931 − 0.51198I
−15.7506 − 7.7744I 0
u = 1.56057 − 0.05597I
a = −0.579035 − 0.883979I
b = −1.60931 + 0.51198I
−15.7506 + 7.7744I 0
u = −0.432528 + 0.029442I
a = −1.52258 − 3.52704I
b = −1.298650 − 0.172110I
−7.78808 − 6.20487I −13.9822 + 5.6630I
u = −0.432528 − 0.029442I
a = −1.52258 + 3.52704I
b = −1.298650 + 0.172110I
−7.78808 + 6.20487I −13.9822 − 5.6630I
u = 1.54984 + 0.33274I
a = −0.243993 + 0.508809I
b = −1.134800 − 0.184103I
−5.73052 − 1.37854I 0
u = 1.54984 − 0.33274I
a = −0.243993 − 0.508809I
b = −1.134800 + 0.184103I
−5.73052 + 1.37854I 0
u = −1.60792 + 0.04446I
a = −0.715503 − 0.664078I
b = −1.386150 + 0.038694I
−15.3821 + 0.1306I 0
12
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −1.60792 − 0.04446I
a = −0.715503 + 0.664078I
b = −1.386150 − 0.038694I
−15.3821 − 0.1306I 0
u = −1.59236 + 0.26987I
a = −0.386964 − 0.928357I
b = −1.39050 + 0.32925I
−11.28290 + 7.25392I 0
u = −1.59236 − 0.26987I
a = −0.386964 + 0.928357I
b = −1.39050 − 0.32925I
−11.28290 − 7.25392I 0
u = 1.60706 + 0.20908I
a = −0.621581 + 1.155290I
b = −1.36323 − 0.40356I
−9.2872 − 11.5369I 0
u = 1.60706 − 0.20908I
a = −0.621581 − 1.155290I
b = −1.36323 + 0.40356I
−9.2872 + 11.5369I 0
u = −1.62705
a = −0.818615
b = 0.496694
−9.75984 0
u = −0.371286 + 0.021894I
a = 0.526117 + 0.437761I
b = 1.338920 − 0.088809I
−2.18166 + 0.01143I −10.62209 + 3.29150I
u = −0.371286 − 0.021894I
a = 0.526117 − 0.437761I
b = 1.338920 + 0.088809I
−2.18166 − 0.01143I −10.62209 − 3.29150I
u = 1.62612 + 0.25559I
a = 0.518267 − 0.841793I
b = 1.61663 + 0.47724I
−16.0242 − 8.3524I 0
u = 1.62612 − 0.25559I
a = 0.518267 + 0.841793I
b = 1.61663 − 0.47724I
−16.0242 + 8.3524I 0
13
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 1.61871 + 0.32164I
a = 0.227540 − 0.957922I
b = 1.356680 + 0.038936I
−14.9433 − 7.1365I 0
u = 1.61871 − 0.32164I
a = 0.227540 + 0.957922I
b = 1.356680 − 0.038936I
−14.9433 + 7.1365I 0
u = −1.63081 + 0.26666I
a = 0.573248 + 1.045090I
b = 1.55881 − 0.43597I
−15.3224 + 17.6791I 0
u = −1.63081 − 0.26666I
a = 0.573248 − 1.045090I
b = 1.55881 + 0.43597I
−15.3224 − 17.6791I 0
u = −1.65863 + 0.11860I
a = 0.034513 − 0.340879I
b = 0.207696 + 0.018879I
−10.04670 + 0.23980I 0
u = −1.65863 − 0.11860I
a = 0.034513 + 0.340879I
b = 0.207696 − 0.018879I
−10.04670 − 0.23980I 0
u = −1.68743
a = −0.792765
b = −1.44820
−16.0198 0
u = 0.258505
a = −2.15575
b = −1.92945
−4.36674 7.82600
u = −0.258232
a = −5.52541
b = 0.0746109
2.71902 22.6240
u = 0.192817 + 0.141272I
a = −3.14244 − 0.71357I
b = 1.005980 + 0.329602I
−1.79614 − 0.74156I −0.145145 + 1.121615I
14
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.192817 − 0.141272I
a = −3.14244 + 0.71357I
b = 1.005980 − 0.329602I
−1.79614 + 0.74156I −0.145145 − 1.121615I
u = −1.91993 + 0.23729I
a = 0.482015 + 0.321775I
b = 1.271850 + 0.009500I
−13.53340 + 0.19028I 0
u = −1.91993 − 0.23729I
a = 0.482015 − 0.321775I
b = 1.271850 − 0.009500I
−13.53340 − 0.19028I 0
15
II.
I
u
2
= hu
13
+2u
12
+· · ·+b−2, −6u
13
−9u
12
+· · ·+a+17, u
14
+u
13
+· · ·−u+1i
(i) Arc colorings
a
5
=
1
0
a
10
=
0
u
a
6
=
1
u
2
a
11
=
−u
−u
3
+ u
a
2
=
6u
13
+ 9u
12
+ ··· − 14u − 17
−u
13
− 2u
12
+ ··· + 3u + 2
a
7
=
−u
2
+ 1
−u
4
+ 2u
2
a
3
=
4u
13
+ 5u
12
+ ··· − 9u − 11
−2u
13
− 3u
12
+ ··· + 6u + 4
a
1
=
5u
13
+ 7u
12
+ ··· − 11u − 15
−u
13
− 2u
12
+ ··· + 3u + 2
a
4
=
7u
13
+ 6u
12
+ ··· − 20u − 11
−4u
12
+ 34u
10
+ ··· + 4u + 7
a
9
=
−2u
13
− 4u
12
+ ··· + 3u + 12
3u
13
+ 4u
12
+ ··· − 11u − 7
a
8
=
2u
12
− u
11
+ ··· − 10u + 1
−2u
13
+ 17u
11
+ ··· + 4u + 2
a
12
=
3u
13
+ 3u
12
+ ··· − 17u − 4
−u
13
− 2u
12
+ ··· + 3u + 1
(ii) Obstruction class = 1
(iii) Cusp Shapes = −47u
13
− 3u
12
+ 392u
11
− 44u
10
− 1096u
9
+ 177u
8
+ 1045u
7
−
20u
6
+ 126u
5
− 250u
4
− 555u
3
+ 62u
2
+ 97u − 26
16
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
14
− 2u
13
+ ··· − u − 1
c
2
u
14
+ 7u
13
+ ··· − 3u
2
+ 1
c
3
u
14
− 8u
12
+ ··· − 2u − 1
c
4
u
14
+ 2u
13
+ ··· + u − 1
c
5
, c
6
u
14
+ u
13
+ ··· − u + 1
c
7
u
14
− 5u
13
+ ··· − 12u − 5
c
8
u
14
− 8u
12
+ ··· + 2u − 1
c
9
u
14
− u
13
+ ··· − 3u − 1
c
10
u
14
− u
13
+ ··· + u + 1
c
11
u
14
+ 3u
13
+ ··· + 2u − 1
c
12
u
14
+ 5u
13
+ ··· − 8u − 1
17
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
4
y
14
− 40y
13
+ ··· − 61y + 1
c
2
y
14
− 35y
13
+ ··· − 6y + 1
c
3
, c
8
y
14
− 16y
13
+ ··· − 14y + 1
c
5
, c
6
, c
10
y
14
− 19y
13
+ ··· − 21y + 1
c
7
y
14
− 27y
13
+ ··· − 164y + 25
c
9
y
14
+ 3y
13
+ ··· − 13y + 1
c
11
y
14
− 11y
13
+ ··· − 4y + 1
c
12
y
14
− 7y
13
+ ··· − 34y + 1
18
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.041995 + 0.809993I
a = −1.344060 + 0.026852I
b = 1.264380 − 0.271420I
−6.26906 + 6.17855I −9.91494 − 4.69414I
u = −0.041995 − 0.809993I
a = −1.344060 − 0.026852I
b = 1.264380 + 0.271420I
−6.26906 − 6.17855I −9.91494 + 4.69414I
u = −0.809847
a = −0.605793
b = 1.48781
−5.03348 −9.02450
u = −1.22502
a = 1.34057
b = 0.162959
−0.336250 4.57820
u = −1.45185
a = −0.212486
b = −5.02868
−8.30808 458.040
u = 1.45372 + 0.20790I
a = −0.329363 + 0.632179I
b = −1.132490 − 0.288555I
−5.25130 − 1.24855I −3.88671 − 0.79369I
u = 1.45372 − 0.20790I
a = −0.329363 − 0.632179I
b = −1.132490 + 0.288555I
−5.25130 + 1.24855I −3.88671 + 0.79369I
u = 1.48805 + 0.23094I
a = 0.127982 − 1.175550I
b = 1.327500 + 0.419823I
−11.7013 − 9.6047I −13.0076 + 8.0736I
u = 1.48805 − 0.23094I
a = 0.127982 + 1.175550I
b = 1.327500 − 0.419823I
−11.7013 + 9.6047I −13.0076 − 8.0736I
u = 0.405276 + 0.018783I
a = 0.68516 + 2.08226I
b = −1.069550 − 0.376548I
−2.21239 − 0.64026I −17.0015 − 2.7974I
19
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.405276 − 0.018783I
a = 0.68516 − 2.08226I
b = −1.069550 + 0.376548I
−2.21239 + 0.64026I −17.0015 + 2.7974I
u = −0.379798
a = −3.82894
b = −0.316150
2.56739 −30.6950
u = −1.64496
a = 0.649623
b = −0.358139
−9.69171 39.2320
u = −2.09863
a = 0.377591
b = 1.27250
−13.8663 −28.5140
20
III. I
u
3
= hb + 1, a
2
+ a − 1, u − 1i
(i) Arc colorings
a
5
=
1
0
a
10
=
0
1
a
6
=
1
1
a
11
=
−1
0
a
2
=
a
−1
a
7
=
0
1
a
3
=
a
−a − 1
a
1
=
a − 1
−1
a
4
=
a
−1
a
9
=
a − 1
a + 1
a
8
=
0
1
a
12
=
0
−a − 2
(ii) Obstruction class = 1
(iii) Cusp Shapes = −17
21
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
5
, c
6
(u − 1)
2
c
2
, c
3
u
2
+ u − 1
c
4
, c
10
, c
12
(u + 1)
2
c
7
u
2
c
8
, c
9
, c
11
u
2
− u − 1
22
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
4
, c
5
c
6
, c
10
, c
12
(y −1)
2
c
2
, c
3
, c
8
c
9
, c
11
y
2
− 3y + 1
c
7
y
2
23
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = 1.00000
a = 0.618034
b = −1.00000
−3.28987 −17.0000
u = 1.00000
a = −1.61803
b = −1.00000
−3.28987 −17.0000
24
IV. I
u
4
= hb, a + 1, u − 1i
(i) Arc colorings
a
5
=
1
0
a
10
=
0
1
a
6
=
1
1
a
11
=
−1
0
a
2
=
−1
0
a
7
=
0
1
a
3
=
−1
1
a
1
=
−1
0
a
4
=
1
0
a
9
=
−1
1
a
8
=
0
1
a
12
=
0
−1
(ii) Obstruction class = −1
(iii) Cusp Shapes = −6
25
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
4
, c
7
u
c
2
, c
3
, c
5
c
6
, c
8
, c
9
c
10
, c
12
u + 1
c
11
u − 1
26
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
4
, c
7
y
c
2
, c
3
, c
5
c
6
, c
8
, c
9
c
10
, c
11
, c
12
y −1
27
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
4
√
−1(vol +
√
−1CS) Cusp shape
u = 1.00000
a = −1.00000
b = 0
−1.64493 −6.00000
28
V. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
u(u − 1)
2
(u
14
− 2u
13
+ ··· − u − 1)(u
103
+ 5u
102
+ ··· − 140u − 5)
c
2
(u + 1)(u
2
+ u − 1)(u
14
+ 7u
13
+ ··· − 3u
2
+ 1)
· (u
103
− 6u
102
+ ··· − 2684u − 1763)
c
3
(u + 1)(u
2
+ u − 1)(u
14
− 8u
12
+ ··· − 2u − 1)
· (u
103
− 3u
102
+ ··· − 340u + 41)
c
4
u(u + 1)
2
(u
14
+ 2u
13
+ ··· + u − 1)(u
103
+ 5u
102
+ ··· − 140u − 5)
c
5
, c
6
((u − 1)
2
)(u + 1)(u
14
+ u
13
+ ··· − u + 1)(u
103
− 3u
102
+ ··· − 30u + 11)
c
7
u
3
(u
14
− 5u
13
+ ··· − 12u − 5)(u
103
− 6u
102
+ ··· − 120u − 20)
c
8
(u + 1)(u
2
− u − 1)(u
14
− 8u
12
+ ··· + 2u − 1)
· (u
103
− 3u
102
+ ··· − 340u + 41)
c
9
(u + 1)(u
2
− u − 1)(u
14
− u
13
+ ··· − 3u − 1)
· (u
103
− 4u
102
+ ··· − 558937u − 115993)
c
10
((u + 1)
3
)(u
14
− u
13
+ ··· + u + 1)(u
103
− 3u
102
+ ··· − 30u + 11)
c
11
(u − 1)(u
2
− u − 1)(u
14
+ 3u
13
+ ··· + 2u − 1)
· (u
103
+ 4u
102
+ ··· − 37150u − 3953)
c
12
((u + 1)
3
)(u
14
+ 5u
13
+ ··· − 8u − 1)(u
103
+ 3u
102
+ ··· − 3395u + 319)
29
VI. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
, c
4
y(y −1)
2
(y
14
− 40y
13
+ ··· − 61y + 1)
· (y
103
− 117y
102
+ ··· + 2440y −25)
c
2
(y −1)(y
2
− 3y + 1)(y
14
− 35y
13
+ ··· − 6y + 1)
· (y
103
− 20y
102
+ ··· − 30171744y −3108169)
c
3
, c
8
(y −1)(y
2
− 3y + 1)(y
14
− 16y
13
+ ··· − 14y + 1)
· (y
103
− 89y
102
+ ··· + 19496y −1681)
c
5
, c
6
, c
10
((y −1)
3
)(y
14
− 19y
13
+ ··· − 21y + 1)
· (y
103
− 115y
102
+ ··· + 10294y −121)
c
7
y
3
(y
14
− 27y
13
+ ··· − 164y + 25)(y
103
− 18y
102
+ ··· + 14360y −400)
c
9
(y −1)(y
2
− 3y + 1)(y
14
+ 3y
13
+ ··· − 13y + 1)
· (y
103
+ 42y
102
+ ··· − 65353344557y −13454376049)
c
11
(y −1)(y
2
− 3y + 1)(y
14
− 11y
13
+ ··· − 4y + 1)
· (y
103
− 48y
102
+ ··· + 1279676770y −15626209)
c
12
((y −1)
3
)(y
14
− 7y
13
+ ··· − 34y + 1)
· (y
103
+ 21y
102
+ ··· + 6596199y −101761)
30
