12n
0738
(K12n
0738
)
A knot diagram
1
Linearized knot diagam
4 7 8 9 11 2 12 2 1 5 7 10
Solving Sequence
7,12 3,8
4 2 9 1 6 11 5 10
c
7
c
3
c
2
c
8
c
1
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
= h−9.79475 × 10
256
u
88
+ 1.43387 × 10
257
u
87
+ ··· + 1.05146 × 10
255
b + 1.97384 × 10
257
,
1.78518 × 10
256
u
88
− 1.84553 × 10
256
u
87
+ ··· + 5.25732 × 10
254
a + 5.76703 × 10
255
, u
89
− 2u
88
+ ··· − 14u + 1i
I
u
2
= h−2542623226711u
21
− 5879535861531u
20
+ ··· + 4155085006409b − 2615410115873,
6655009669836u
21
+ 10389904986854u
20
+ ··· + 4155085006409a + 4757958548853,
u
22
+ 2u
21
+ ··· + u + 1i
I
u
3
= hb + 1, a
3
+ a
2
+ 1, u − 1i
* 3 irreducible components of dim
C
= 0, with total 114 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−9.79 × 10
256
u
88
+ 1.43 × 10
257
u
87
+ · · · + 1.05 × 10
255
b + 1.97 ×
10
257
, 1.79 × 10
256
u
88
− 1.85 × 10
256
u
87
+ · · · + 5.26 × 10
254
a + 5.77 ×
10
255
, u
89
− 2u
88
+ · · · − 14u + 1i
(i) Arc colorings
a
7
=
1
0
a
12
=
0
u
a
3
=
−33.9561u
88
+ 35.1040u
87
+ ··· − 18.7014u − 10.9695
93.1534u
88
− 136.369u
87
+ ··· + 2197.99u − 187.723
a
8
=
1
u
2
a
4
=
81.4663u
88
− 132.400u
87
+ ··· + 2604.65u − 231.500
128.707u
88
− 187.467u
87
+ ··· + 2969.35u − 251.064
a
2
=
59.1974u
88
− 101.265u
87
+ ··· + 2179.29u − 198.692
93.1534u
88
− 136.369u
87
+ ··· + 2197.99u − 187.723
a
9
=
75.1897u
88
− 109.168u
87
+ ··· + 1597.75u − 115.139
−3.66417u
88
+ 10.3005u
87
+ ··· − 159.896u + 11.8154
a
1
=
16.7378u
88
− 44.3957u
87
+ ··· + 1381.92u − 131.287
−16.2704u
88
+ 14.4942u
87
+ ··· + 69.9257u − 18.6626
a
6
=
62.4914u
88
− 86.8598u
87
+ ··· + 1097.29u − 65.6761
18.6435u
88
− 21.1867u
87
+ ··· + 311.334u − 26.3076
a
11
=
u
u
a
5
=
53.5827u
88
− 71.8606u
87
+ ··· + 832.817u − 43.6534
9.73484u
88
− 6.18748u
87
+ ··· + 46.8642u − 4.28488
a
10
=
−50.5975u
88
+ 85.3027u
87
+ ··· − 1981.82u + 202.076
63.8761u
88
− 100.827u
87
+ ··· + 1699.64u − 142.543
(ii) Obstruction class = −1
(iii) Cusp Shapes = 99.2749u
88
− 167.730u
87
+ ··· + 2872.55u − 234.918
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
89
− 2u
88
+ ··· + 3224u − 173
c
2
, c
6
u
89
+ 3u
88
+ ··· + 2143u + 220
c
3
u
89
+ 2u
88
+ ··· + 42280112u + 2904067
c
4
u
89
+ u
88
+ ··· + 76u
2
+ 16
c
5
, c
10
u
89
+ u
88
+ ··· − 1398u + 457
c
7
, c
11
u
89
− 2u
88
+ ··· − 14u + 1
c
8
u
89
+ 3u
88
+ ··· + 37920u + 3361
c
9
, c
12
u
89
+ u
88
+ ··· + 349u + 211
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
89
+ 26y
88
+ ··· + 2490152y −29929
c
2
, c
6
y
89
+ 63y
88
+ ··· − 2481871y −48400
c
3
y
89
− 56y
88
+ ··· − 83395183689034y −8433605140489
c
4
y
89
+ 3y
88
+ ··· − 2432y −256
c
5
, c
10
y
89
− 43y
88
+ ··· + 3827190y −208849
c
7
, c
11
y
89
− 24y
88
+ ··· + 66y −1
c
8
y
89
− 9y
88
+ ··· + 460345940y −11296321
c
9
, c
12
y
89
+ 55y
88
+ ··· − 1038699y −44521
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.728707 + 0.689660I
a = 1.140920 − 0.798950I
b = −0.106997 + 1.343020I
3.36537 + 3.15246I 0
u = 0.728707 − 0.689660I
a = 1.140920 + 0.798950I
b = −0.106997 − 1.343020I
3.36537 − 3.15246I 0
u = −0.924993 + 0.174397I
a = 1.57826 + 0.33149I
b = 0.991171 − 0.061075I
−3.52619 − 0.12569I 0
u = −0.924993 − 0.174397I
a = 1.57826 − 0.33149I
b = 0.991171 + 0.061075I
−3.52619 + 0.12569I 0
u = 1.116820 + 0.152077I
a = 0.650111 + 0.740802I
b = −0.759825 + 0.290326I
−3.17613 + 0.89707I 0
u = 1.116820 − 0.152077I
a = 0.650111 − 0.740802I
b = −0.759825 − 0.290326I
−3.17613 − 0.89707I 0
u = 0.450061 + 0.744605I
a = 0.607261 − 0.124059I
b = 0.502872 + 0.181456I
3.61994 − 0.64342I 0
u = 0.450061 − 0.744605I
a = 0.607261 + 0.124059I
b = 0.502872 − 0.181456I
3.61994 + 0.64342I 0
u = −0.865942 + 0.013321I
a = −0.377046 + 1.305970I
b = 0.12951 − 1.45777I
−0.82448 − 6.19029I 0
u = −0.865942 − 0.013321I
a = −0.377046 − 1.305970I
b = 0.12951 + 1.45777I
−0.82448 + 6.19029I 0
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.573452 + 0.587260I
a = −0.60537 − 1.48602I
b = −1.077630 + 0.711416I
−0.31660 + 4.57592I 0
u = −0.573452 − 0.587260I
a = −0.60537 + 1.48602I
b = −1.077630 − 0.711416I
−0.31660 − 4.57592I 0
u = −0.809930 + 0.027084I
a = 0.238299 − 0.326731I
b = −1.188020 − 0.459108I
−1.67659 − 1.76730I 0
u = −0.809930 − 0.027084I
a = 0.238299 + 0.326731I
b = −1.188020 + 0.459108I
−1.67659 + 1.76730I 0
u = −1.186060 + 0.122031I
a = 0.473953 − 0.313586I
b = −0.677351 − 0.634263I
−2.10870 − 1.82799I 0
u = −1.186060 − 0.122031I
a = 0.473953 + 0.313586I
b = −0.677351 + 0.634263I
−2.10870 + 1.82799I 0
u = −0.878350 + 0.815051I
a = −0.500476 − 1.315300I
b = −0.76164 + 1.34733I
0.99618 + 5.42464I 0
u = −0.878350 − 0.815051I
a = −0.500476 + 1.315300I
b = −0.76164 − 1.34733I
0.99618 − 5.42464I 0
u = 0.726246 + 0.975893I
a = 0.640522 − 0.768375I
b = 0.351698 + 1.075030I
4.14888 − 0.87827I 0
u = 0.726246 − 0.975893I
a = 0.640522 + 0.768375I
b = 0.351698 − 1.075030I
4.14888 + 0.87827I 0
6
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.985705 + 0.750992I
a = 0.782971 + 0.642116I
b = −0.109357 − 1.160930I
0.662776 + 0.539516I 0
u = −0.985705 − 0.750992I
a = 0.782971 − 0.642116I
b = −0.109357 + 1.160930I
0.662776 − 0.539516I 0
u = −0.712728 + 1.015920I
a = 0.499103 + 1.235100I
b = 0.29416 − 1.61372I
9.54462 − 2.29743I 0
u = −0.712728 − 1.015920I
a = 0.499103 − 1.235100I
b = 0.29416 + 1.61372I
9.54462 + 2.29743I 0
u = 0.766930 + 0.993698I
a = 0.401340 − 0.947871I
b = 0.54402 + 1.44826I
4.50282 − 1.08927I 0
u = 0.766930 − 0.993698I
a = 0.401340 + 0.947871I
b = 0.54402 − 1.44826I
4.50282 + 1.08927I 0
u = 1.013200 + 0.753764I
a = −0.646652 + 1.230910I
b = −0.70501 − 1.64006I
2.56199 − 8.83087I 0
u = 1.013200 − 0.753764I
a = −0.646652 − 1.230910I
b = −0.70501 + 1.64006I
2.56199 + 8.83087I 0
u = −0.732612 + 1.030540I
a = 0.156776 + 1.052220I
b = 0.57412 − 1.73131I
6.53176 + 7.27006I 0
u = −0.732612 − 1.030540I
a = 0.156776 − 1.052220I
b = 0.57412 + 1.73131I
6.53176 − 7.27006I 0
7
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.607390 + 0.408610I
a = 0.66595 − 1.34345I
b = −0.190565 + 0.778107I
−1.32281 + 1.49993I −8.00000 + 0.I
u = −0.607390 − 0.408610I
a = 0.66595 + 1.34345I
b = −0.190565 − 0.778107I
−1.32281 − 1.49993I −8.00000 + 0.I
u = 0.581342 + 0.441443I
a = −0.212475 − 0.031319I
b = 1.93552 − 0.28067I
0.71957 − 8.87941I −8.0000 + 13.4036I
u = 0.581342 − 0.441443I
a = −0.212475 + 0.031319I
b = 1.93552 + 0.28067I
0.71957 + 8.87941I −8.0000 − 13.4036I
u = 0.720659 + 0.071260I
a = 2.08430 − 0.32839I
b = 1.001690 − 0.367941I
−0.05018 + 6.72143I −13.2759 − 5.0382I
u = 0.720659 − 0.071260I
a = 2.08430 + 0.32839I
b = 1.001690 + 0.367941I
−0.05018 − 6.72143I −13.2759 + 5.0382I
u = −0.476229 + 0.525739I
a = −0.142712 − 0.221460I
b = 1.48007 + 0.83547I
−1.81194 + 3.10417I −8.00000 − 9.84544I
u = −0.476229 − 0.525739I
a = −0.142712 + 0.221460I
b = 1.48007 − 0.83547I
−1.81194 − 3.10417I −8.00000 + 9.84544I
u = 0.688408 + 0.125680I
a = −0.276936 + 0.559711I
b = −1.53936 + 0.11618I
−2.46249 − 0.67631I −8.00000 + 10.85950I
u = 0.688408 − 0.125680I
a = −0.276936 − 0.559711I
b = −1.53936 − 0.11618I
−2.46249 + 0.67631I −8.00000 − 10.85950I
8
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.644054 + 0.260652I
a = 1.14759 − 1.42214I
b = −0.247479 + 0.278785I
−1.54586 + 1.12108I −11.00706 − 6.04709I
u = −0.644054 − 0.260652I
a = 1.14759 + 1.42214I
b = −0.247479 − 0.278785I
−1.54586 − 1.12108I −11.00706 + 6.04709I
u = 0.620239 + 0.221199I
a = −1.06970 − 2.54323I
b = −0.075257 − 0.139231I
−3.44636 − 3.28123I −20.2992 + 8.3870I
u = 0.620239 − 0.221199I
a = −1.06970 + 2.54323I
b = −0.075257 + 0.139231I
−3.44636 + 3.28123I −20.2992 − 8.3870I
u = −0.445574 + 0.477651I
a = −2.96309 + 1.38824I
b = 0.116212 + 0.104340I
1.10496 + 8.28971I −4.3178 − 14.5248I
u = −0.445574 − 0.477651I
a = −2.96309 − 1.38824I
b = 0.116212 − 0.104340I
1.10496 − 8.28971I −4.3178 + 14.5248I
u = 0.855189 + 1.043680I
a = −0.407496 + 0.805868I
b = 0.24636 − 1.41483I
7.31163 − 1.88418I 0
u = 0.855189 − 1.043680I
a = −0.407496 − 0.805868I
b = 0.24636 + 1.41483I
7.31163 + 1.88418I 0
u = 0.429882 + 0.485314I
a = 0.85439 + 2.04202I
b = −0.483871 − 1.087000I
−0.54805 − 3.51803I −5.26955 + 4.96976I
u = 0.429882 − 0.485314I
a = 0.85439 − 2.04202I
b = −0.483871 + 1.087000I
−0.54805 + 3.51803I −5.26955 − 4.96976I
9
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.780322 + 1.124850I
a = 0.879309 + 0.837722I
b = 0.042420 − 1.053150I
5.37297 + 0.17301I 0
u = −0.780322 − 1.124850I
a = 0.879309 − 0.837722I
b = 0.042420 + 1.053150I
5.37297 − 0.17301I 0
u = −0.810003 + 1.147870I
a = −0.579327 − 0.691089I
b = 0.19153 + 1.41504I
2.04685 − 4.05320I 0
u = −0.810003 − 1.147870I
a = −0.579327 + 0.691089I
b = 0.19153 − 1.41504I
2.04685 + 4.05320I 0
u = 1.122200 + 0.854316I
a = −0.583374 + 0.657925I
b = −0.33959 − 1.41890I
3.37656 − 5.71824I 0
u = 1.122200 − 0.854316I
a = −0.583374 − 0.657925I
b = −0.33959 + 1.41890I
3.37656 + 5.71824I 0
u = −1.150330 + 0.818490I
a = −0.863157 − 0.795066I
b = −0.22259 + 1.57983I
8.14222 + 9.05246I 0
u = −1.150330 − 0.818490I
a = −0.863157 + 0.795066I
b = −0.22259 − 1.57983I
8.14222 − 9.05246I 0
u = 1.12526 + 0.86285I
a = −0.357076 + 0.892757I
b = −0.47716 − 1.43875I
2.91341 − 5.91259I 0
u = 1.12526 − 0.86285I
a = −0.357076 − 0.892757I
b = −0.47716 + 1.43875I
2.91341 + 5.91259I 0
10
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 1.08481 + 0.92394I
a = 0.665171 − 0.977161I
b = 0.73889 + 1.21253I
6.57099 − 5.29222I 0
u = 1.08481 − 0.92394I
a = 0.665171 + 0.977161I
b = 0.73889 − 1.21253I
6.57099 + 5.29222I 0
u = 0.76985 + 1.20914I
a = −0.249525 + 1.327490I
b = −0.388594 − 1.129600I
6.48905 − 4.72393I 0
u = 0.76985 − 1.20914I
a = −0.249525 − 1.327490I
b = −0.388594 + 1.129600I
6.48905 + 4.72393I 0
u = 0.81489 + 1.19005I
a = −0.679307 + 0.759719I
b = 0.229063 − 1.393780I
6.15465 + 10.11680I 0
u = 0.81489 − 1.19005I
a = −0.679307 − 0.759719I
b = 0.229063 + 1.393780I
6.15465 − 10.11680I 0
u = 0.548991 + 0.053107I
a = −0.61886 − 1.53164I
b = −0.19159 + 1.61911I
−3.16683 + 2.11548I −19.9398 + 0.6159I
u = 0.548991 − 0.053107I
a = −0.61886 + 1.53164I
b = −0.19159 − 1.61911I
−3.16683 − 2.11548I −19.9398 − 0.6159I
u = 0.320160 + 0.435342I
a = −0.30304 − 1.39831I
b = −0.168673 − 0.492183I
2.82976 − 3.05132I −6.01961 + 4.35621I
u = 0.320160 − 0.435342I
a = −0.30304 + 1.39831I
b = −0.168673 + 0.492183I
2.82976 + 3.05132I −6.01961 − 4.35621I
11
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −1.12958 + 0.94056I
a = 0.487277 + 1.033280I
b = 0.83552 − 1.47021I
1.00959 + 11.54230I 0
u = −1.12958 − 0.94056I
a = 0.487277 − 1.033280I
b = 0.83552 + 1.47021I
1.00959 − 11.54230I 0
u = 1.15144 + 0.94647I
a = 0.474981 − 1.113650I
b = 0.78479 + 1.56197I
5.0305 − 17.7489I 0
u = 1.15144 − 0.94647I
a = 0.474981 + 1.113650I
b = 0.78479 − 1.56197I
5.0305 + 17.7489I 0
u = −1.20389 + 0.87932I
a = −0.720920 − 0.365436I
b = −0.272531 + 1.294200I
5.08544 − 0.24142I 0
u = −1.20389 − 0.87932I
a = −0.720920 + 0.365436I
b = −0.272531 − 1.294200I
5.08544 + 0.24142I 0
u = −1.14972 + 0.98487I
a = −0.240161 − 1.118220I
b = −0.47345 + 1.46567I
4.23168 + 7.42784I 0
u = −1.14972 − 0.98487I
a = −0.240161 + 1.118220I
b = −0.47345 − 1.46567I
4.23168 − 7.42784I 0
u = −0.471056
a = 0.731915
b = −0.314436
−0.833811 −11.9600
u = 1.14245 + 1.06741I
a = 0.522645 − 0.840930I
b = −0.004729 + 1.016560I
5.36861 − 3.34549I 0
12
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 1.14245 − 1.06741I
a = 0.522645 + 0.840930I
b = −0.004729 − 1.016560I
5.36861 + 3.34549I 0
u = 0.339291 + 0.239137I
a = −1.56566 + 1.14010I
b = −1.189080 + 0.093441I
−1.76767 − 0.26940I −7.85955 + 0.15438I
u = 0.339291 − 0.239137I
a = −1.56566 − 1.14010I
b = −1.189080 − 0.093441I
−1.76767 + 0.26940I −7.85955 − 0.15438I
u = 1.60629 + 0.04073I
a = −0.209632 − 0.044831I
b = −0.400984 − 0.348661I
−7.65923 + 0.42868I 0
u = 1.60629 − 0.04073I
a = −0.209632 + 0.044831I
b = −0.400984 + 0.348661I
−7.65923 − 0.42868I 0
u = −1.65953 + 0.11879I
a = −0.170689 + 0.140332I
b = −0.108870 − 0.439743I
−4.40554 + 6.24970I 0
u = −1.65953 − 0.11879I
a = −0.170689 − 0.140332I
b = −0.108870 + 0.439743I
−4.40554 − 6.24970I 0
u = 0.238593 + 0.068203I
a = 4.52558 + 0.58023I
b = −0.172188 + 0.904850I
2.91692 + 2.97937I −6.43690 − 3.41848I
u = 0.238593 − 0.068203I
a = 4.52558 − 0.58023I
b = −0.172188 − 0.904850I
2.91692 − 2.97937I −6.43690 + 3.41848I
13
II.
I
u
2
= h−2.54×10
12
u
21
−5.88×10
12
u
20
+· · ·+4.16×10
12
b−2.62×10
12
, 6.66×
10
12
u
21
+1.04×10
13
u
20
+· · ·+4.16×10
12
a+4.76×10
12
, u
22
+2u
21
+· · ·+u+1i
(i) Arc colorings
a
7
=
1
0
a
12
=
0
u
a
3
=
−1.60165u
21
− 2.50053u
20
+ ··· + 2.81817u − 1.14509
0.611930u
21
+ 1.41502u
20
+ ··· − 0.982911u + 0.629448
a
8
=
1
u
2
a
4
=
−0.521525u
21
− 0.227058u
20
+ ··· + 0.936384u + 0.187136
1.03584u
21
+ 2.36411u
20
+ ··· − 2.17625u + 0.516237
a
2
=
−0.989724u
21
− 1.08551u
20
+ ··· + 1.83526u − 0.515645
0.611930u
21
+ 1.41502u
20
+ ··· − 0.982911u + 0.629448
a
9
=
0.712784u
21
+ 1.59340u
20
+ ··· − 4.81578u − 4.56029
0.420560u
21
+ 1.30356u
20
+ ··· − 4.86085u − 1.77823
a
1
=
−1.17981u
21
− 2.41220u
20
+ ··· + 3.22411u + 2.57632
−0.845661u
21
− 2.05422u
20
+ ··· + 3.70732u + 0.457794
a
6
=
−0.166253u
21
− 0.520197u
20
+ ··· − 2.22843u − 2.74819
0.657520u
21
+ 1.59914u
20
+ ··· − 4.50691u − 1.59053
a
11
=
u
u
a
5
=
0.0455890u
21
+ 0.184121u
20
+ ··· − 3.52400u − 3.21998
0.869362u
21
+ 2.30346u
20
+ ··· − 5.80247u − 2.06233
a
10
=
0.595136u
21
+ 1.39636u
20
+ ··· + 2.92959u − 2.00034
1.12554u
21
+ 2.04526u
20
+ ··· − 0.383547u − 0.835575
(ii) Obstruction class = 1
(iii) Cusp Shapes
= −
14644014353596
4155085006409
u
21
−
19925641665362
4155085006409
u
20
+ ··· −
251442070714
4155085006409
u −
90897297812916
4155085006409
14
(iv) u-Polynomials at the component
15
Crossings u-Polynomials at each crossing
c
1
u
22
− 8u
21
+ ··· − 2u + 1
c
2
u
22
− 3u
21
+ ··· + 6u + 1
c
3
u
22
+ u
21
+ ··· − 397u + 73
c
4
u
22
− 2u
21
+ ··· − 61u + 31
c
5
u
22
+ 2u
21
+ ··· − 7u + 1
c
6
u
22
+ 3u
21
+ ··· − 6u + 1
c
7
u
22
+ 2u
21
+ ··· + u + 1
c
8
u
22
+ u
21
+ ··· + 6u + 1
c
9
u
22
− u
21
+ ··· − 7u + 1
c
10
u
22
− 2u
21
+ ··· + 7u + 1
c
11
u
22
− 2u
21
+ ··· − u + 1
c
12
u
22
+ u
21
+ ··· + 7u + 1
16
17
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
22
+ 10y
21
+ ··· + 6y + 1
c
2
, c
6
y
22
+ 9y
21
+ ··· − 10y + 1
c
3
y
22
− 7y
21
+ ··· + 9707y + 5329
c
4
y
22
− 6y
21
+ ··· − 11409y + 961
c
5
, c
10
y
22
− 22y
21
+ ··· − 21y + 1
c
7
, c
11
y
22
− 14y
21
+ ··· − 15y + 1
c
8
y
22
+ 3y
21
+ ··· − 6y + 1
c
9
, c
12
y
22
+ 15y
21
+ ··· − 3y + 1
18
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −1.069910 + 0.150673I
a = 0.577013 − 0.784503I
b = −0.838504 − 0.683407I
−2.93463 − 1.89534I −16.0134 + 7.0646I
u = −1.069910 − 0.150673I
a = 0.577013 + 0.784503I
b = −0.838504 + 0.683407I
−2.93463 + 1.89534I −16.0134 − 7.0646I
u = 0.895310 + 0.875198I
a = 0.899910 − 0.506349I
b = 0.259337 + 1.161090I
3.98677 + 0.79058I −7.82878 − 2.57835I
u = 0.895310 − 0.875198I
a = 0.899910 + 0.506349I
b = 0.259337 − 1.161090I
3.98677 − 0.79058I −7.82878 + 2.57835I
u = −0.666787 + 0.261360I
a = −0.25275 − 1.66366I
b = −0.831001 + 1.015850I
−1.52733 + 3.60865I −15.1313 − 6.6117I
u = −0.666787 − 0.261360I
a = −0.25275 + 1.66366I
b = −0.831001 − 1.015850I
−1.52733 − 3.60865I −15.1313 + 6.6117I
u = 0.708422 + 0.007961I
a = −0.502117 − 0.222546I
b = −1.186880 + 0.108689I
−2.70850 − 0.00901I −17.4901 − 0.4015I
u = 0.708422 − 0.007961I
a = −0.502117 + 0.222546I
b = −1.186880 − 0.108689I
−2.70850 + 0.00901I −17.4901 + 0.4015I
u = 1.066780 + 0.843600I
a = −0.345137 + 1.079520I
b = −0.50641 − 1.57274I
3.31029 − 7.19107I −8.47997 + 7.24995I
u = 1.066780 − 0.843600I
a = −0.345137 − 1.079520I
b = −0.50641 + 1.57274I
3.31029 + 7.19107I −8.47997 − 7.24995I
19
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.997024 + 0.998501I
a = −0.494715 − 1.148990I
b = −0.514008 + 1.127450I
5.51088 + 5.10187I −8.67511 − 6.86093I
u = −0.997024 − 0.998501I
a = −0.494715 + 1.148990I
b = −0.514008 − 1.127450I
5.51088 − 5.10187I −8.67511 + 6.86093I
u = −0.95941 + 1.19557I
a = 0.447477 + 0.817898I
b = −0.033772 − 1.076920I
5.70839 + 2.72360I −2.20784 + 0.67124I
u = −0.95941 − 1.19557I
a = 0.447477 − 0.817898I
b = −0.033772 + 1.076920I
5.70839 − 2.72360I −2.20784 − 0.67124I
u = 0.358330 + 0.266127I
a = 2.95918 + 0.87373I
b = 0.963513 − 0.225172I
0.60336 − 7.79834I −11.52931 + 5.72788I
u = 0.358330 − 0.266127I
a = 2.95918 − 0.87373I
b = 0.963513 + 0.225172I
0.60336 + 7.79834I −11.52931 − 5.72788I
u = −0.343418 + 0.283245I
a = 1.39869 − 1.74155I
b = 0.438864 + 1.183790I
−2.67905 + 2.65765I −12.41068 − 5.25421I
u = −0.343418 − 0.283245I
a = 1.39869 + 1.74155I
b = 0.438864 − 1.183790I
−2.67905 − 2.65765I −12.41068 + 5.25421I
u = −1.57250 + 0.12187I
a = 0.260238 − 0.205227I
b = 0.404374 − 0.170638I
−7.78467 − 0.66795I −17.6587 + 13.6602I
u = −1.57250 − 0.12187I
a = 0.260238 + 0.205227I
b = 0.404374 + 0.170638I
−7.78467 + 0.66795I −17.6587 − 13.6602I
20
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 1.58021 + 0.02080I
a = 0.052206 − 0.352538I
b = 0.344492 + 0.223654I
−4.77539 − 6.53518I −16.0749 + 9.4216I
u = 1.58021 − 0.02080I
a = 0.052206 + 0.352538I
b = 0.344492 − 0.223654I
−4.77539 + 6.53518I −16.0749 − 9.4216I
21
III. I
u
3
= hb + 1, a
3
+ a
2
+ 1, u − 1i
(i) Arc colorings
a
7
=
1
0
a
12
=
0
1
a
3
=
a
−1
a
8
=
1
1
a
4
=
−1
−a − 2
a
2
=
a − 1
−1
a
9
=
a
2
− a + 1
−a + 1
a
1
=
−a
2
−2a
2
− a + 2
a
6
=
a
−1
a
11
=
1
1
a
5
=
−1
−a − 2
a
10
=
−a
−a
2
− 3a − 1
(ii) Obstruction class = 1
(iii) Cusp Shapes = 9a
2
− 12
22
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
3
− 3u
2
+ 4u − 1
c
2
, c
7
(u − 1)
3
c
3
, c
5
u
3
− 2u
2
+ u + 1
c
4
u
3
c
6
, c
11
(u + 1)
3
c
8
, c
9
u
3
− u
2
− 1
c
10
u
3
+ 2u
2
+ u − 1
c
12
u
3
+ u
2
+ 1
23
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
3
− y
2
+ 10y −1
c
2
, c
6
, c
7
c
11
(y −1)
3
c
3
, c
5
, c
10
y
3
− 2y
2
+ 5y −1
c
4
y
3
c
8
, c
9
, c
12
y
3
− y
2
− 2y −1
24
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = 1.00000
a = 0.232786 + 0.792552I
b = −1.00000
−3.28987 −17.1655 + 3.3209I
u = 1.00000
a = 0.232786 − 0.792552I
b = −1.00000
−3.28987 −17.1655 − 3.3209I
u = 1.00000
a = −1.46557
b = −1.00000
−3.28987 7.33110
25
IV. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
(u
3
− 3u
2
+ 4u − 1)(u
22
− 8u
21
+ ··· − 2u + 1)
· (u
89
− 2u
88
+ ··· + 3224u − 173)
c
2
((u − 1)
3
)(u
22
− 3u
21
+ ··· + 6u + 1)(u
89
+ 3u
88
+ ··· + 2143u + 220)
c
3
(u
3
− 2u
2
+ u + 1)(u
22
+ u
21
+ ··· − 397u + 73)
· (u
89
+ 2u
88
+ ··· + 42280112u + 2904067)
c
4
u
3
(u
22
− 2u
21
+ ··· − 61u + 31)(u
89
+ u
88
+ ··· + 76u
2
+ 16)
c
5
(u
3
− 2u
2
+ u + 1)(u
22
+ 2u
21
+ ··· − 7u + 1)
· (u
89
+ u
88
+ ··· − 1398u + 457)
c
6
((u + 1)
3
)(u
22
+ 3u
21
+ ··· − 6u + 1)(u
89
+ 3u
88
+ ··· + 2143u + 220)
c
7
((u − 1)
3
)(u
22
+ 2u
21
+ ··· + u + 1)(u
89
− 2u
88
+ ··· − 14u + 1)
c
8
(u
3
− u
2
− 1)(u
22
+ u
21
+ ··· + 6u + 1)
· (u
89
+ 3u
88
+ ··· + 37920u + 3361)
c
9
(u
3
− u
2
− 1)(u
22
− u
21
+ ··· − 7u + 1)(u
89
+ u
88
+ ··· + 349u + 211)
c
10
(u
3
+ 2u
2
+ u − 1)(u
22
− 2u
21
+ ··· + 7u + 1)
· (u
89
+ u
88
+ ··· − 1398u + 457)
c
11
((u + 1)
3
)(u
22
− 2u
21
+ ··· − u + 1)(u
89
− 2u
88
+ ··· − 14u + 1)
c
12
(u
3
+ u
2
+ 1)(u
22
+ u
21
+ ··· + 7u + 1)(u
89
+ u
88
+ ··· + 349u + 211)
26
V. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
(y
3
− y
2
+ 10y −1)(y
22
+ 10y
21
+ ··· + 6y + 1)
· (y
89
+ 26y
88
+ ··· + 2490152y −29929)
c
2
, c
6
((y −1)
3
)(y
22
+ 9y
21
+ ··· − 10y + 1)
· (y
89
+ 63y
88
+ ··· − 2481871y −48400)
c
3
(y
3
− 2y
2
+ 5y −1)(y
22
− 7y
21
+ ··· + 9707y + 5329)
· (y
89
− 56y
88
+ ··· − 83395183689034y −8433605140489)
c
4
y
3
(y
22
− 6y
21
+ ··· − 11409y + 961)(y
89
+ 3y
88
+ ··· − 2432y −256)
c
5
, c
10
(y
3
− 2y
2
+ 5y −1)(y
22
− 22y
21
+ ··· − 21y + 1)
· (y
89
− 43y
88
+ ··· + 3827190y −208849)
c
7
, c
11
((y −1)
3
)(y
22
− 14y
21
+ ··· − 15y + 1)(y
89
− 24y
88
+ ··· + 66y −1)
c
8
(y
3
− y
2
− 2y −1)(y
22
+ 3y
21
+ ··· − 6y + 1)
· (y
89
− 9y
88
+ ··· + 460345940y −11296321)
c
9
, c
12
(y
3
− y
2
− 2y −1)(y
22
+ 15y
21
+ ··· − 3y + 1)
· (y
89
+ 55y
88
+ ··· − 1038699y −44521)
27
