12a
1247
(K12a
1247
)
A knot diagram
1
Linearized knot diagam
5 6 11 9 2 10 12 4 1 3 8 7
Solving Sequence
1,5
2 6
3,10
7 11 9 4 8 12
c
1
c
5
c
2
c
6
c
10
c
9
c
4
c
8
c
12
c
3
, c
7
, c
11
Ideals for irreducible components
2
of X
par
I
u
1
= h−1931u
31
+ 20740u
30
+ ··· + 8b − 23592, −7773u
31
+ 82554u
30
+ ··· + 16a − 89232,
u
32
− 12u
31
+ ··· − 48u − 16i
I
u
2
= h−1.02625 × 10
22
a
7
u
5
+ 8.99106 × 10
21
a
6
u
5
+ ··· − 4.39399 × 10
21
a + 3.98524 × 10
22
,
− a
7
u
5
+ 8a
6
u
5
+ ··· − 489a + 821, u
6
+ u
5
− 3u
4
− 2u
3
+ 2u
2
− u − 1i
I
u
3
= hu
21
+ 2u
20
+ ··· + b + u, 4u
21
+ 8u
20
+ ··· + a + 5, u
22
+ 3u
21
+ ··· + 3u + 1i
* 3 irreducible components of dim
C
= 0, with total 102 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−1931u
31
+ 20740u
30
+ · · · + 8b − 23592, −7773u
31
+ 82554u
30
+
· · · + 16a − 89232, u
32
− 12u
31
+ · · · − 48u − 16i
(i) Arc colorings
a
1
=
1
0
a
5
=
0
u
a
2
=
1
u
2
a
6
=
−u
−u
3
+ u
a
3
=
−u
2
+ 1
−u
4
+ 2u
2
a
10
=
7773
16
u
31
−
41277
8
u
30
+ ··· +
41415
2
u + 5577
1931
8
u
31
−
5185
2
u
30
+ ··· + 11043u + 2949
a
7
=
107
2
u
31
− 546u
30
+ ··· +
3227
2
u +
921
2
143
2
u
31
− 740u
30
+ ··· +
4873
2
u + 680
a
11
=
247
16
u
31
−
1881
8
u
30
+ ··· +
5429
2
u + 656
−
181
8
u
31
+
345
2
u
30
+ ··· + 1311u + 261
a
9
=
3911
16
u
31
−
20537
8
u
30
+ ··· +
19329
2
u + 2628
1931
8
u
31
−
5185
2
u
30
+ ··· + 11043u + 2949
a
4
=
43
2
u
31
−
441
2
u
30
+ ··· + 660u +
377
2
22u
31
− 240u
30
+ ··· +
2169
2
u + 288
a
8
=
2271
8
u
31
−
24371
8
u
30
+ ··· + 13172u +
7009
2
−
1689
8
u
31
+
8795
4
u
30
+ ··· −
14811
2
u − 2064
a
12
=
566u
31
−
23745
4
u
30
+ ··· +
86833
4
u + 5945
355u
31
−
14985
4
u
30
+ ··· + 14324u + 3892
(ii) Obstruction class = −1
(iii) Cusp Shapes =
4311
2
u
31
− 22730u
30
+ ··· + 87134u + 23654
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
2
, c
5
u
32
+ 12u
31
+ ··· + 48u − 16
c
3
, c
4
, c
8
c
10
u
32
− u
31
+ ··· + u
2
+ 1
c
6
, c
9
u
32
+ u
31
+ ··· − 17u − 1
c
7
, c
11
, c
12
u
32
− 14u
31
+ ··· + 736u − 64
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
2
, c
5
y
32
− 32y
31
+ ··· − 1408y + 256
c
3
, c
4
, c
8
c
10
y
32
− 35y
31
+ ··· + 2y + 1
c
6
, c
9
y
32
+ 25y
31
+ ··· − 121y + 1
c
7
, c
11
, c
12
y
32
+ 30y
31
+ ··· − 46080y + 4096
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.680828 + 0.815159I
a = 0.589852 − 0.500904I
b = −0.68125 − 1.37591I
−15.1501 + 11.2353I −10.12137 − 6.63149I
u = −0.680828 − 0.815159I
a = 0.589852 + 0.500904I
b = −0.68125 + 1.37591I
−15.1501 − 11.2353I −10.12137 + 6.63149I
u = −0.494831 + 0.951026I
a = −0.617680 − 0.176687I
b = −0.232561 + 1.197900I
−14.5005 − 5.4219I −10.91537 + 2.28879I
u = −0.494831 − 0.951026I
a = −0.617680 + 0.176687I
b = −0.232561 − 1.197900I
−14.5005 + 5.4219I −10.91537 − 2.28879I
u = −1.14307
a = −0.439539
b = −1.07672
−1.32792 −8.36980
u = −0.713057 + 0.906916I
a = −0.473999 + 0.283951I
b = 0.435641 + 1.156230I
−7.22904 + 6.56235I 0
u = −0.713057 − 0.906916I
a = −0.473999 − 0.283951I
b = 0.435641 − 1.156230I
−7.22904 − 6.56235I 0
u = −0.615956 + 1.004530I
a = 0.488535 − 0.045297I
b = −0.108266 − 1.094690I
−6.84872 − 0.16660I 0
u = −0.615956 − 1.004530I
a = 0.488535 + 0.045297I
b = −0.108266 + 1.094690I
−6.84872 + 0.16660I 0
u = 1.157610 + 0.416068I
a = 0.506893 − 0.188759I
b = 0.108022 + 0.275619I
−4.34328 − 2.34802I 0
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 1.157610 − 0.416068I
a = 0.506893 + 0.188759I
b = 0.108022 − 0.275619I
−4.34328 + 2.34802I 0
u = −1.232110 + 0.231185I
a = 0.300965 + 0.165464I
b = 0.944141 + 0.205181I
−4.97841 + 4.31582I 0
u = −1.232110 − 0.231185I
a = 0.300965 − 0.165464I
b = 0.944141 − 0.205181I
−4.97841 − 4.31582I 0
u = 0.739575
a = −0.445134
b = 0.0857344
−0.987038 −12.9270
u = 0.057187 + 0.603926I
a = −0.204724 + 0.701064I
b = 0.460672 − 0.183999I
−1.25850 − 1.44721I −2.35502 + 5.22658I
u = 0.057187 − 0.603926I
a = −0.204724 − 0.701064I
b = 0.460672 + 0.183999I
−1.25850 + 1.44721I −2.35502 − 5.22658I
u = 1.45355 + 0.03396I
a = −0.23567 + 1.66598I
b = −0.262994 + 1.081130I
−4.57485 − 1.68293I 0
u = 1.45355 − 0.03396I
a = −0.23567 − 1.66598I
b = −0.262994 − 1.081130I
−4.57485 + 1.68293I 0
u = 1.50382 + 0.05578I
a = 0.50318 − 1.98250I
b = 0.60170 − 1.43953I
−10.29120 − 4.14932I 0
u = 1.50382 − 0.05578I
a = 0.50318 + 1.98250I
b = 0.60170 + 1.43953I
−10.29120 + 4.14932I 0
6
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.456157 + 0.188264I
a = 0.30670 + 1.62184I
b = 0.776747 + 0.909381I
−3.74818 + 3.21761I 2.70792 − 3.34583I
u = −0.456157 − 0.188264I
a = 0.30670 − 1.62184I
b = 0.776747 − 0.909381I
−3.74818 − 3.21761I 2.70792 + 3.34583I
u = −0.247450 + 0.286515I
a = 0.10986 − 1.41840I
b = −0.582621 − 0.368449I
0.987106 + 0.748744I 5.19413 − 3.21537I
u = −0.247450 − 0.286515I
a = 0.10986 + 1.41840I
b = −0.582621 + 0.368449I
0.987106 − 0.748744I 5.19413 + 3.21537I
u = 1.60347 + 0.26376I
a = 0.08484 + 1.83824I
b = −0.99385 + 1.70026I
16.7864 − 15.2459I 0
u = 1.60347 − 0.26376I
a = 0.08484 − 1.83824I
b = −0.99385 − 1.70026I
16.7864 + 15.2459I 0
u = 1.60023 + 0.36433I
a = −0.567147 − 0.962796I
b = 0.302404 − 1.251650I
18.1780 + 0.4768I 0
u = 1.60023 − 0.36433I
a = −0.567147 + 0.962796I
b = 0.302404 + 1.251650I
18.1780 − 0.4768I 0
u = 1.62632 + 0.27751I
a = −0.07773 − 1.52430I
b = 0.87969 − 1.48385I
−14.9769 − 10.9327I 0
u = 1.62632 − 0.27751I
a = −0.07773 + 1.52430I
b = 0.87969 + 1.48385I
−14.9769 + 10.9327I 0
7
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 1.63995 + 0.31827I
a = 0.228456 + 1.197060I
b = −0.65199 + 1.30081I
−14.3366 − 4.7680I 0
u = 1.63995 − 0.31827I
a = 0.228456 − 1.197060I
b = −0.65199 − 1.30081I
−14.3366 + 4.7680I 0
8
II. I
u
2
= h−1.03 × 10
22
a
7
u
5
+ 8.99 × 10
21
a
6
u
5
+ · · · − 4.39 × 10
21
a + 3.99 ×
10
22
, −a
7
u
5
+ 8a
6
u
5
+ · · · − 489a + 821, u
6
+ u
5
− 3u
4
− 2u
3
+ 2u
2
− u − 1i
(i) Arc colorings
a
1
=
1
0
a
5
=
0
u
a
2
=
1
u
2
a
6
=
−u
−u
3
+ u
a
3
=
−u
2
+ 1
−u
4
+ 2u
2
a
10
=
a
0.493774a
7
u
5
− 0.432600a
6
u
5
+ ··· + 0.211415a − 1.91748
a
7
=
−0.0990366a
7
u
5
+ 0.0845549a
6
u
5
+ ··· + 0.244699a + 0.622156
0.550411a
7
u
5
− 1.43426a
6
u
5
+ ··· − 0.965495a − 1.46874
a
11
=
−1.24509a
7
u
5
+ 1.54783a
6
u
5
+ ··· + 0.631576a + 0.985297
0.939975a
7
u
5
− 1.15258a
6
u
5
+ ··· − 0.412776a − 2.64976
a
9
=
−0.493774a
7
u
5
+ 0.432600a
6
u
5
+ ··· + 0.788585a + 1.91748
0.493774a
7
u
5
− 0.432600a
6
u
5
+ ··· + 0.211415a − 1.91748
a
4
=
1.15029a
7
u
5
− 1.79608a
6
u
5
+ ··· − 1.16871a − 4.70289
−1.05125a
7
u
5
+ 1.71153a
6
u
5
+ ··· + 0.924014a + 4.08073
a
8
=
0.634934a
7
u
5
− 1.65705a
6
u
5
+ ··· − 2.68099a − 1.05272
−0.970106a
7
u
5
+ 1.96530a
6
u
5
+ ··· + 1.88294a + 3.88034
a
12
=
−0.590593a
7
u
5
+ 1.21867a
6
u
5
+ ··· + 0.288049a + 1.83640
0.520280a
7
u
5
− 0.621535a
6
u
5
+ ··· + 0.504665a − 1.23816
(ii) Obstruction class = −1
(iii) Cusp Shapes =
32386428834844106415168
20783768619782088516773
a
7
u
5
+
23417790588849644990728
20783768619782088516773
a
6
u
5
+ ··· +
45950322676565104630412
20783768619782088516773
a −
306021993643431809155814
20783768619782088516773
9
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
2
, c
5
(u
6
− u
5
− 3u
4
+ 2u
3
+ 2u
2
+ u − 1)
8
c
3
, c
4
, c
8
c
10
u
48
+ u
47
+ ··· − 1444u + 479
c
6
, c
9
u
48
− 7u
47
+ ··· − 40272u + 71579
c
7
, c
11
, c
12
(u
4
+ u
3
+ 3u
2
+ 2u + 1)
12
10
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
2
, c
5
(y
6
− 7y
5
+ 17y
4
− 16y
3
+ 6y
2
− 5y + 1)
8
c
3
, c
4
, c
8
c
10
y
48
− 49y
47
+ ··· + 10146608y + 229441
c
6
, c
9
y
48
+ 23y
47
+ ··· + 117241967100y + 5123553241
c
7
, c
11
, c
12
(y
4
+ 5y
3
+ 7y
2
+ 2y + 1)
12
11
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.493180 + 0.575288I
a = −0.900819 + 0.089225I
b = 0.127208 − 0.784719I
−1.76355 − 0.55731I −4.74899 − 1.22396I
u = 0.493180 + 0.575288I
a = −0.488061 − 1.039120I
b = 0.459656 − 0.638436I
−1.76355 − 3.38752I −4.74899 + 8.59352I
u = 0.493180 + 0.575288I
a = −0.630925 − 0.290654I
b = 0.70939 − 1.58712I
−8.76530 − 5.13637I −8.40246 + 6.24958I
u = 0.493180 + 0.575288I
a = 0.601944 + 0.215661I
b = −0.532273 + 1.115900I
−1.76355 − 3.38752I −4.74899 + 8.59352I
u = 0.493180 + 0.575288I
a = 1.55616 − 0.32740I
b = 0.215809 + 1.064350I
−8.76530 + 1.19155I −8.40246 + 1.11998I
u = 0.493180 + 0.575288I
a = 0.181370 + 0.327241I
b = 0.293994 + 0.548435I
−1.76355 − 0.55731I −4.74899 − 1.22396I
u = 0.493180 + 0.575288I
a = −0.295940 + 0.035805I
b = −0.950173 − 0.904845I
−8.76530 + 1.19155I −8.40246 + 1.11998I
u = 0.493180 + 0.575288I
a = 0.83692 + 1.56767I
b = −0.819030 + 0.843679I
−8.76530 − 5.13637I −8.40246 + 6.24958I
u = 0.493180 − 0.575288I
a = −0.900819 − 0.089225I
b = 0.127208 + 0.784719I
−1.76355 + 0.55731I −4.74899 + 1.22396I
u = 0.493180 − 0.575288I
a = −0.488061 + 1.039120I
b = 0.459656 + 0.638436I
−1.76355 + 3.38752I −4.74899 − 8.59352I
12
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.493180 − 0.575288I
a = −0.630925 + 0.290654I
b = 0.70939 + 1.58712I
−8.76530 + 5.13637I −8.40246 − 6.24958I
u = 0.493180 − 0.575288I
a = 0.601944 − 0.215661I
b = −0.532273 − 1.115900I
−1.76355 + 3.38752I −4.74899 − 8.59352I
u = 0.493180 − 0.575288I
a = 1.55616 + 0.32740I
b = 0.215809 − 1.064350I
−8.76530 − 1.19155I −8.40246 − 1.11998I
u = 0.493180 − 0.575288I
a = 0.181370 − 0.327241I
b = 0.293994 − 0.548435I
−1.76355 + 0.55731I −4.74899 + 1.22396I
u = 0.493180 − 0.575288I
a = −0.295940 − 0.035805I
b = −0.950173 + 0.904845I
−8.76530 − 1.19155I −8.40246 − 1.11998I
u = 0.493180 − 0.575288I
a = 0.83692 − 1.56767I
b = −0.819030 − 0.843679I
−8.76530 + 5.13637I −8.40246 − 6.24958I
u = −0.483672
a = 1.243000 + 0.503165I
b = −1.55666 + 1.20761I
−12.46440 + 3.16396I −17.2435 − 2.5648I
u = −0.483672
a = 1.243000 − 0.503165I
b = −1.55666 − 1.20761I
−12.46440 − 3.16396I −17.2435 + 2.5648I
u = −0.483672
a = −1.68596 + 0.76343I
b = 0.935756 + 0.863246I
−5.46265 − 1.41510I −13.5900 + 4.9087I
u = −0.483672
a = −1.68596 − 0.76343I
b = 0.935756 − 0.863246I
−5.46265 + 1.41510I −13.5900 − 4.9087I
13
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.483672
a = 2.75014 + 1.41553I
b = −0.172089 + 0.700395I
−5.46265 − 1.41510I −13.5900 + 4.9087I
u = −0.483672
a = 2.75014 − 1.41553I
b = −0.172089 − 0.700395I
−5.46265 + 1.41510I −13.5900 − 4.9087I
u = −0.483672
a = −3.81963 + 2.25339I
b = −0.292353 + 0.770523I
−12.46440 + 3.16396I −17.2435 − 2.5648I
u = −0.483672
a = −3.81963 − 2.25339I
b = −0.292353 − 0.770523I
−12.46440 − 3.16396I −17.2435 + 2.5648I
u = −1.52087 + 0.16310I
a = 0.782884 − 1.127760I
b = −0.343085 − 1.002600I
−15.4211 + 1.4282I −12.40788 − 0.64002I
u = −1.52087 + 0.16310I
a = −0.200569 + 1.374100I
b = 0.675225 + 1.150860I
−8.41938 + 3.17702I −8.75440 + 1.70392I
u = −1.52087 + 0.16310I
a = 0.439631 − 1.327350I
b = 0.265769 − 1.130460I
−8.41938 + 3.17702I −8.75440 + 1.70392I
u = −1.52087 + 0.16310I
a = −1.15986 + 1.16720I
b = −1.06617 + 1.40127I
−15.4211 + 1.4282I −12.40788 − 0.64002I
u = −1.52087 + 0.16310I
a = −0.04775 + 1.70162I
b = 0.327173 + 1.006110I
−8.41938 + 6.00723I −8.75440 − 8.11356I
u = −1.52087 + 0.16310I
a = −0.06236 − 1.91890I
b = −0.88964 − 1.76077I
−8.41938 + 6.00723I −8.75440 − 8.11356I
14
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −1.52087 + 0.16310I
a = −0.07791 − 2.08226I
b = −0.593633 − 1.010750I
−15.4211 + 7.7561I −12.40788 − 5.76962I
u = −1.52087 + 0.16310I
a = 0.14267 + 2.45572I
b = 1.08638 + 2.38993I
−15.4211 + 7.7561I −12.40788 − 5.76962I
u = −1.52087 − 0.16310I
a = 0.782884 + 1.127760I
b = −0.343085 + 1.002600I
−15.4211 − 1.4282I −12.40788 + 0.64002I
u = −1.52087 − 0.16310I
a = −0.200569 − 1.374100I
b = 0.675225 − 1.150860I
−8.41938 − 3.17702I −8.75440 − 1.70392I
u = −1.52087 − 0.16310I
a = 0.439631 + 1.327350I
b = 0.265769 + 1.130460I
−8.41938 − 3.17702I −8.75440 − 1.70392I
u = −1.52087 − 0.16310I
a = −1.15986 − 1.16720I
b = −1.06617 − 1.40127I
−15.4211 − 1.4282I −12.40788 + 0.64002I
u = −1.52087 − 0.16310I
a = −0.04775 − 1.70162I
b = 0.327173 − 1.006110I
−8.41938 − 6.00723I −8.75440 + 8.11356I
u = −1.52087 − 0.16310I
a = −0.06236 + 1.91890I
b = −0.88964 + 1.76077I
−8.41938 − 6.00723I −8.75440 + 8.11356I
u = −1.52087 − 0.16310I
a = −0.07791 + 2.08226I
b = −0.593633 + 1.010750I
−15.4211 − 7.7561I −12.40788 + 5.76962I
u = −1.52087 − 0.16310I
a = 0.14267 − 2.45572I
b = 1.08638 − 2.38993I
−15.4211 − 7.7561I −12.40788 + 5.76962I
15
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 1.53904
a = 0.244560 + 1.155160I
b = −0.847287 + 0.822406I
−12.38390 − 1.41510I −12.44276 + 4.90874I
u = 1.53904
a = 0.244560 − 1.155160I
b = −0.847287 − 0.822406I
−12.38390 + 1.41510I −12.44276 − 4.90874I
u = 1.53904
a = 0.92692 + 1.24349I
b = 1.81916 + 1.16754I
−12.38390 − 1.41510I −12.44276 + 4.90874I
u = 1.53904
a = 0.92692 − 1.24349I
b = 1.81916 − 1.16754I
−12.38390 + 1.41510I −12.44276 − 4.90874I
u = 1.53904
a = −1.03576 + 1.39658I
b = 0.317947 + 0.787184I
−19.3856 + 3.1640I −16.0962 − 2.5648I
u = 1.53904
a = −1.03576 − 1.39658I
b = 0.317947 − 0.787184I
−19.3856 − 3.1640I −16.0962 + 2.5648I
u = 1.53904
a = −1.80066 + 1.63792I
b = −2.67107 + 1.73026I
−19.3856 + 3.1640I −16.0962 − 2.5648I
u = 1.53904
a = −1.80066 − 1.63792I
b = −2.67107 − 1.73026I
−19.3856 − 3.1640I −16.0962 + 2.5648I
16
III.
I
u
3
= hu
21
+2u
20
+· · ·+b+u, 4u
21
+8u
20
+· · ·+a+5, u
22
+3u
21
+· · ·+3u+1i
(i) Arc colorings
a
1
=
1
0
a
5
=
0
u
a
2
=
1
u
2
a
6
=
−u
−u
3
+ u
a
3
=
−u
2
+ 1
−u
4
+ 2u
2
a
10
=
−4u
21
− 8u
20
+ ··· − 17u − 5
−u
21
− 2u
20
+ ··· − 10u
2
− u
a
7
=
−7u
21
− 13u
20
+ ··· − 23u − 4
−3u
21
− 5u
20
+ ··· + u − 1
a
11
=
−u
21
− 3u
20
+ ··· − 12u − 4
−2u
21
− 3u
20
+ ··· − 12u
2
− u
a
9
=
−3u
21
− 6u
20
+ ··· − 16u − 5
−u
21
− 2u
20
+ ··· − 10u
2
− u
a
4
=
−3u
20
− 4u
19
+ ··· − 20u − 3
4u
21
+ 7u
20
+ ··· + 10u + 4
a
8
=
4u
21
+ 9u
20
+ ··· + 26u + 1
3u
21
+ 4u
20
+ ··· + 19u
2
+ 2
a
12
=
6u
21
+ 11u
20
+ ··· + 16u + 11
2u
21
+ 2u
20
+ ··· + 17u
2
+ 6u
(ii) Obstruction class = 1
(iii) Cusp Shapes
= −5u
21
−12u
20
+41u
19
+109u
18
−134u
17
−397u
16
+250u
15
+753u
14
−378u
13
−815u
12
+
539u
11
+ 500u
10
− 577u
9
− 125u
8
+ 397u
7
− 16u
6
− 155u
5
+ 15u
4
+ 39u
3
− 7u
2
− u − 7
17
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
2
u
22
+ 3u
21
+ ··· + 3u + 1
c
3
, c
8
u
22
+ u
21
+ ··· + u − 1
c
4
, c
10
u
22
− u
21
+ ··· − u − 1
c
5
u
22
− 3u
21
+ ··· − 3u + 1
c
6
, c
9
u
22
+ u
21
+ ··· − 5u
2
− 1
c
7
u
22
− u
21
+ ··· + 2u − 1
c
11
, c
12
u
22
+ u
21
+ ··· − 2u − 1
18
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
2
, c
5
y
22
− 25y
21
+ ··· + 3y + 1
c
3
, c
4
, c
8
c
10
y
22
− 25y
21
+ ··· − 39y + 1
c
6
, c
9
y
22
+ 7y
21
+ ··· + 10y + 1
c
7
, c
11
, c
12
y
22
+ 25y
21
+ ··· + 8y + 1
19
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = 0.830041 + 0.372143I
a = 0.018859 + 0.570003I
b = −0.538229 + 0.805569I
−4.33333 − 3.17748I −11.15222 + 4.56629I
u = 0.830041 − 0.372143I
a = 0.018859 − 0.570003I
b = −0.538229 − 0.805569I
−4.33333 + 3.17748I −11.15222 − 4.56629I
u = 0.856682 + 0.292394I
a = −0.110513 + 0.558228I
b = −0.609214 + 0.752506I
−4.33137 − 3.17736I −10.79809 + 3.65508I
u = 0.856682 − 0.292394I
a = −0.110513 − 0.558228I
b = −0.609214 − 0.752506I
−4.33137 + 3.17736I −10.79809 − 3.65508I
u = 0.903347
a = 0.392353
b = 0.674604
−0.339311 2.40450
u = 0.366487 + 0.738621I
a = −0.651754 − 0.018325I
b = 0.052630 − 0.833432I
−2.73349 − 1.32865I −11.07966 + 3.39512I
u = 0.366487 − 0.738621I
a = −0.651754 + 0.018325I
b = 0.052630 + 0.833432I
−2.73349 + 1.32865I −11.07966 − 3.39512I
u = −1.133040 + 0.450430I
a = −0.837685 + 0.173018I
b = 0.142357 + 0.468689I
−6.73763 + 4.05980I −12.29979 − 3.84797I
u = −1.133040 − 0.450430I
a = −0.837685 − 0.173018I
b = 0.142357 − 0.468689I
−6.73763 − 4.05980I −12.29979 + 3.84797I
u = −0.556044 + 0.401150I
a = 1.062440 + 0.854118I
b = −0.394837 − 0.396064I
−4.73125 − 0.60844I −6.34000 − 1.21463I
20
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = −0.556044 − 0.401150I
a = 1.062440 − 0.854118I
b = −0.394837 + 0.396064I
−4.73125 + 0.60844I −6.34000 + 1.21463I
u = −1.404820 + 0.132257I
a = 1.38773 − 1.60582I
b = 0.380589 − 1.217270I
−16.0996 + 4.5307I −12.95570 − 3.19344I
u = −1.404820 − 0.132257I
a = 1.38773 + 1.60582I
b = 0.380589 + 1.217270I
−16.0996 − 4.5307I −12.95570 + 3.19344I
u = −1.50090 + 0.18006I
a = −0.45664 + 1.58550I
b = 0.243005 + 1.305180I
−8.89437 + 4.43912I −12.33495 − 4.11395I
u = −1.50090 − 0.18006I
a = −0.45664 − 1.58550I
b = 0.243005 − 1.305180I
−8.89437 − 4.43912I −12.33495 + 4.11395I
u = 1.51916 + 0.06554I
a = 0.358638 − 0.126439I
b = 1.40443 − 0.38841I
−17.6475 + 1.8704I −12.10898 − 0.36759I
u = 1.51916 − 0.06554I
a = 0.358638 + 0.126439I
b = 1.40443 + 0.38841I
−17.6475 − 1.8704I −12.10898 + 0.36759I
u = 1.55580
a = −0.343399
b = −1.36546
−12.3748 −12.4960
u = −1.56422 + 0.13165I
a = −0.14890 − 1.88832I
b = −0.65795 − 1.59210I
−11.90160 + 5.17271I −12.89162 − 3.86694I
u = −1.56422 − 0.13165I
a = −0.14890 + 1.88832I
b = −0.65795 + 1.59210I
−11.90160 − 5.17271I −12.89162 + 3.86694I
21
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = −0.142925 + 0.254512I
a = −0.14665 − 4.37491I
b = 0.822645 + 0.792653I
−11.63890 − 3.03242I −5.49334 + 0.66440I
u = −0.142925 − 0.254512I
a = −0.14665 + 4.37491I
b = 0.822645 − 0.792653I
−11.63890 + 3.03242I −5.49334 − 0.66440I
22
IV. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
, c
2
((u
6
− u
5
− 3u
4
+ 2u
3
+ 2u
2
+ u − 1)
8
)(u
22
+ 3u
21
+ ··· + 3u + 1)
· (u
32
+ 12u
31
+ ··· + 48u − 16)
c
3
, c
8
(u
22
+ u
21
+ ··· + u − 1)(u
32
− u
31
+ ··· + u
2
+ 1)
· (u
48
+ u
47
+ ··· − 1444u + 479)
c
4
, c
10
(u
22
− u
21
+ ··· − u − 1)(u
32
− u
31
+ ··· + u
2
+ 1)
· (u
48
+ u
47
+ ··· − 1444u + 479)
c
5
((u
6
− u
5
− 3u
4
+ 2u
3
+ 2u
2
+ u − 1)
8
)(u
22
− 3u
21
+ ··· − 3u + 1)
· (u
32
+ 12u
31
+ ··· + 48u − 16)
c
6
, c
9
(u
22
+ u
21
+ ··· − 5u
2
− 1)(u
32
+ u
31
+ ··· − 17u − 1)
· (u
48
− 7u
47
+ ··· − 40272u + 71579)
c
7
((u
4
+ u
3
+ 3u
2
+ 2u + 1)
12
)(u
22
− u
21
+ ··· + 2u − 1)
· (u
32
− 14u
31
+ ··· + 736u − 64)
c
11
, c
12
((u
4
+ u
3
+ 3u
2
+ 2u + 1)
12
)(u
22
+ u
21
+ ··· − 2u − 1)
· (u
32
− 14u
31
+ ··· + 736u − 64)
23
V. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
, c
2
, c
5
((y
6
− 7y
5
+ ··· − 5y + 1)
8
)(y
22
− 25y
21
+ ··· + 3y + 1)
· (y
32
− 32y
31
+ ··· − 1408y + 256)
c
3
, c
4
, c
8
c
10
(y
22
− 25y
21
+ ··· − 39y + 1)(y
32
− 35y
31
+ ··· + 2y + 1)
· (y
48
− 49y
47
+ ··· + 10146608y + 229441)
c
6
, c
9
(y
22
+ 7y
21
+ ··· + 10y + 1)(y
32
+ 25y
31
+ ··· − 121y + 1)
· (y
48
+ 23y
47
+ ··· + 117241967100y + 5123553241)
c
7
, c
11
, c
12
((y
4
+ 5y
3
+ 7y
2
+ 2y + 1)
12
)(y
22
+ 25y
21
+ ··· + 8y + 1)
· (y
32
+ 30y
31
+ ··· − 46080y + 4096)
24
