12a
0864
(K12a
0864
)
A knot diagram
1
Linearized knot diagam
4 5 11 9 10 3 12 1 2 6 7 8
Solving Sequence
7,12
8 1
3,9
6 11 4 2 10 5
c
7
c
12
c
8
c
6
c
11
c
3
c
1
c
10
c
5
c
2
, c
4
, c
9
Ideals for irreducible components
2
of X
par
I
u
1
= h−1.21264 × 10
139
u
95
+ 1.73441 × 10
139
u
94
+ ··· + 1.05860 × 10
139
b + 1.91553 × 10
139
,
− 3.04022 × 10
140
u
95
+ 1.79659 × 10
139
u
94
+ ··· + 1.05860 × 10
139
a + 2.01484 × 10
141
,
u
96
− 61u
94
+ ··· − 28u − 1i
I
u
2
= hu
15
− u
14
+ ··· + b + 2, −u
15
+ 2u
14
+ ··· + a − 9, u
16
− 12u
14
+ ··· + 5u + 1i
I
u
3
= hb − 1, a + 2, u + 1i
* 3 irreducible components of dim
C
= 0, with total 113 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−1.21 × 10
139
u
95
+ 1.73 × 10
139
u
94
+ · · · + 1.06 × 10
139
b + 1.92 ×
10
139
, −3.04 × 10
140
u
95
+ 1.80 × 10
139
u
94
+ · · · + 1.06 × 10
139
a + 2.01 ×
10
141
, u
96
− 61u
94
+ · · · − 28u − 1i
(i) Arc colorings
a
7
=
1
0
a
12
=
0
u
a
8
=
1
−u
2
a
1
=
u
−u
3
+ u
a
3
=
28.7194u
95
− 1.69714u
94
+ ··· − 3987.96u − 190.331
1.14552u
95
− 1.63841u
94
+ ··· − 76.6899u − 1.80950
a
9
=
−u
2
+ 1
u
4
− 2u
2
a
6
=
18.9381u
95
− 4.14300u
94
+ ··· − 1887.37u − 59.3130
2.76827u
95
− 0.450564u
94
+ ··· − 370.656u − 18.2747
a
11
=
−u
u
a
4
=
26.6420u
95
− 4.78463u
94
+ ··· − 3924.43u − 186.996
3.22295u
95
+ 1.44908u
94
+ ··· − 140.220u − 5.14505
a
2
=
−3.95609u
95
− 0.462103u
94
+ ··· + 390.837u + 0.542360
3.87936u
95
+ 0.714479u
94
+ ··· − 343.306u − 13.3366
a
10
=
−4.26382u
95
+ 1.69030u
94
+ ··· − 9.12211u − 30.4716
−3.77515u
95
+ 0.646135u
94
+ ··· + 455.415u + 22.4214
a
5
=
31.0772u
95
− 2.97999u
94
+ ··· − 4218.61u − 199.407
1.95541u
95
− 1.75880u
94
+ ··· − 157.514u − 5.53567
(ii) Obstruction class = −1
(iii) Cusp Shapes = −3.53643u
95
+ 0.820615u
94
+ ··· + 864.770u + 50.5047
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
96
+ 5u
95
+ ··· − 4478u + 638
c
2
u
96
− 8u
95
+ ··· + 5u − 1
c
3
u
96
+ 5u
94
+ ··· − 723u − 97
c
4
u
96
+ 2u
95
+ ··· − 5914u − 463
c
5
, c
10
u
96
− 2u
95
+ ··· + 4u + 2
c
6
u
96
− 9u
94
+ ··· − 872u − 79
c
7
, c
8
, c
11
c
12
u
96
− 61u
94
+ ··· + 28u − 1
c
9
u
96
− 3u
95
+ ··· − 1819u + 211
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
96
+ 23y
95
+ ··· − 5697484y + 407044
c
2
y
96
+ 6y
95
+ ··· − 947y + 1
c
3
y
96
+ 10y
95
+ ··· + 487817y + 9409
c
4
y
96
− 32y
95
+ ··· − 43540896y + 214369
c
5
, c
10
y
96
− 74y
95
+ ··· + 592y + 4
c
6
y
96
− 18y
95
+ ··· − 426056y + 6241
c
7
, c
8
, c
11
c
12
y
96
− 122y
95
+ ··· − 208y + 1
c
9
y
96
− 29y
95
+ ··· − 3023067y + 44521
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.848856 + 0.512394I
a = −1.48444 + 0.02987I
b = 1.13304 + 1.13103I
1.79803 + 6.02425I 0
u = 0.848856 − 0.512394I
a = −1.48444 − 0.02987I
b = 1.13304 − 1.13103I
1.79803 − 6.02425I 0
u = −0.762783 + 0.552893I
a = 0.084512 − 0.657058I
b = 0.480853 + 0.094565I
1.63897 − 1.62411I 0
u = −0.762783 − 0.552893I
a = 0.084512 + 0.657058I
b = 0.480853 − 0.094565I
1.63897 + 1.62411I 0
u = −0.872654 + 0.313471I
a = 1.57203 + 0.70936I
b = −0.771400 + 0.941898I
−2.26631 − 4.65369I 0
u = −0.872654 − 0.313471I
a = 1.57203 − 0.70936I
b = −0.771400 − 0.941898I
−2.26631 + 4.65369I 0
u = 0.943151 + 0.542936I
a = 1.046870 − 0.578677I
b = −0.950136 − 0.507528I
4.03768 + 8.33548I 0
u = 0.943151 − 0.542936I
a = 1.046870 + 0.578677I
b = −0.950136 + 0.507528I
4.03768 − 8.33548I 0
u = 0.910484
a = −0.878663
b = −0.378648
−3.16205 0
u = 0.811946 + 0.726956I
a = 0.149340 + 0.747403I
b = 0.505940 − 0.747645I
−2.10344 − 4.68024I 0
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.811946 − 0.726956I
a = 0.149340 − 0.747403I
b = 0.505940 + 0.747645I
−2.10344 + 4.68024I 0
u = −0.951904 + 0.531798I
a = −1.65073 − 0.27863I
b = 1.17052 − 1.03295I
−1.00269 − 14.05450I 0
u = −0.951904 − 0.531798I
a = −1.65073 + 0.27863I
b = 1.17052 + 1.03295I
−1.00269 + 14.05450I 0
u = −0.849730 + 0.148988I
a = 1.28832 − 0.69583I
b = −0.310227 + 0.149527I
1.94088 − 0.58707I 0
u = −0.849730 − 0.148988I
a = 1.28832 + 0.69583I
b = −0.310227 − 0.149527I
1.94088 + 0.58707I 0
u = −0.066590 + 0.860109I
a = 0.044443 + 0.190892I
b = −0.667589 + 0.223840I
0.94601 − 3.74110I 0
u = −0.066590 − 0.860109I
a = 0.044443 − 0.190892I
b = −0.667589 − 0.223840I
0.94601 + 3.74110I 0
u = 0.851105 + 0.131792I
a = 1.01100 + 2.07444I
b = −0.236581 − 0.169350I
0.90358 + 5.68147I 0
u = 0.851105 − 0.131792I
a = 1.01100 − 2.07444I
b = −0.236581 + 0.169350I
0.90358 − 5.68147I 0
u = 0.847214 + 0.071086I
a = −1.54881 + 0.33064I
b = 1.119980 + 0.555179I
4.24776 + 1.77300I 0
6
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.847214 − 0.071086I
a = −1.54881 − 0.33064I
b = 1.119980 − 0.555179I
4.24776 − 1.77300I 0
u = 1.15263
a = −2.79307
b = 1.59079
1.49561 0
u = −1.012410 + 0.563472I
a = 0.915243 + 0.270713I
b = −0.830878 + 0.373538I
3.91381 − 1.35031I 0
u = −1.012410 − 0.563472I
a = 0.915243 − 0.270713I
b = −0.830878 − 0.373538I
3.91381 + 1.35031I 0
u = 0.776553 + 0.310353I
a = −0.378054 + 0.041126I
b = 0.132735 + 0.970644I
1.05313 + 4.13427I 0
u = 0.776553 − 0.310353I
a = −0.378054 − 0.041126I
b = 0.132735 − 0.970644I
1.05313 − 4.13427I 0
u = −1.140350 + 0.241058I
a = 0.287971 + 0.490780I
b = −0.752610 − 0.354976I
−0.561295 + 0.360803I 0
u = −1.140350 − 0.241058I
a = 0.287971 − 0.490780I
b = −0.752610 + 0.354976I
−0.561295 − 0.360803I 0
u = 0.094602 + 0.804581I
a = −0.126983 + 0.252363I
b = 0.872343 + 0.988761I
−4.18034 + 9.61860I 0
u = 0.094602 − 0.804581I
a = −0.126983 − 0.252363I
b = 0.872343 − 0.988761I
−4.18034 − 9.61860I 0
7
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.793794 + 0.085736I
a = 1.86729 − 0.01780I
b = −1.14389 + 1.32461I
0.16910 − 5.24105I 0
u = −0.793794 − 0.085736I
a = 1.86729 + 0.01780I
b = −1.14389 − 1.32461I
0.16910 + 5.24105I 0
u = 0.695579 + 0.387592I
a = 1.59202 − 1.13315I
b = −0.963161 − 0.805203I
−3.16653 + 6.53955I 0
u = 0.695579 − 0.387592I
a = 1.59202 + 1.13315I
b = −0.963161 + 0.805203I
−3.16653 − 6.53955I 0
u = −0.737621 + 0.059931I
a = −2.65688 + 1.12940I
b = 0.868841 + 0.104292I
2.70279 − 1.66171I 0
u = −0.737621 − 0.059931I
a = −2.65688 − 1.12940I
b = 0.868841 − 0.104292I
2.70279 + 1.66171I 0
u = 1.29643
a = −2.87389
b = 1.91941
1.51634 0
u = −0.594053 + 0.361218I
a = 0.08272 − 1.62751I
b = 0.57340 + 1.63096I
−2.48411 − 5.40065I 0. + 7.91391I
u = −0.594053 − 0.361218I
a = 0.08272 + 1.62751I
b = 0.57340 − 1.63096I
−2.48411 + 5.40065I 0. − 7.91391I
u = −1.33022
a = 1.56693
b = −1.00223
2.87442 0
8
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.043672 + 0.662877I
a = 0.494388 + 0.045800I
b = 0.511933 − 0.907807I
−0.60901 − 2.02374I 4.31550 + 2.89349I
u = 0.043672 − 0.662877I
a = 0.494388 − 0.045800I
b = 0.511933 + 0.907807I
−0.60901 + 2.02374I 4.31550 − 2.89349I
u = 0.551928 + 0.251478I
a = −0.186747 − 0.541257I
b = −0.881756 + 0.722362I
−3.43641 + 0.55635I 0.02779 − 2.86592I
u = 0.551928 − 0.251478I
a = −0.186747 + 0.541257I
b = −0.881756 − 0.722362I
−3.43641 − 0.55635I 0.02779 + 2.86592I
u = −0.295504 + 0.529164I
a = −1.52202 − 0.43687I
b = 1.22688 − 1.09252I
−3.35245 + 2.24266I −2.14064 − 1.00817I
u = −0.295504 − 0.529164I
a = −1.52202 + 0.43687I
b = 1.22688 + 1.09252I
−3.35245 − 2.24266I −2.14064 + 1.00817I
u = −0.497027 + 0.346630I
a = 0.012234 − 1.062080I
b = 0.622420 − 0.341049I
0.85142 − 1.38736I 0.21088 + 3.87321I
u = −0.497027 − 0.346630I
a = 0.012234 + 1.062080I
b = 0.622420 + 0.341049I
0.85142 + 1.38736I 0.21088 − 3.87321I
u = 0.188695 + 0.570976I
a = −0.707038 + 0.414108I
b = −0.825190 + 0.720729I
−4.67936 − 3.24452I −3.85119 + 2.80796I
u = 0.188695 − 0.570976I
a = −0.707038 − 0.414108I
b = −0.825190 − 0.720729I
−4.67936 + 3.24452I −3.85119 − 2.80796I
9
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.601266
a = 3.64462
b = −1.64639
−3.91831 2.29380
u = 0.057784 + 0.492981I
a = −0.40481 − 1.64013I
b = −0.666921 − 0.779900I
−5.07392 + 1.88167I −6.82321 − 4.06316I
u = 0.057784 − 0.492981I
a = −0.40481 + 1.64013I
b = −0.666921 + 0.779900I
−5.07392 − 1.88167I −6.82321 + 4.06316I
u = 0.091019 + 0.471956I
a = 1.089190 − 0.659128I
b = −0.116040 − 0.648601I
−0.98522 − 1.39774I −2.89275 + 1.25458I
u = 0.091019 − 0.471956I
a = 1.089190 + 0.659128I
b = −0.116040 + 0.648601I
−0.98522 + 1.39774I −2.89275 − 1.25458I
u = −1.54294 + 0.01252I
a = 0.742691 − 1.008020I
b = −0.757567 + 1.181720I
3.43603 + 1.18460I 0
u = −1.54294 − 0.01252I
a = 0.742691 + 1.008020I
b = −0.757567 − 1.181720I
3.43603 − 1.18460I 0
u = 1.60158 + 0.06458I
a = −1.052070 + 0.237578I
b = 0.812605 + 0.692601I
8.25434 + 2.62646I 0
u = 1.60158 − 0.06458I
a = −1.052070 − 0.237578I
b = 0.812605 − 0.692601I
8.25434 − 2.62646I 0
u = 1.60934 + 0.07157I
a = −0.29325 + 2.18032I
b = 0.33233 − 2.28003I
5.17458 + 6.78996I 0
10
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 1.60934 − 0.07157I
a = −0.29325 − 2.18032I
b = 0.33233 + 2.28003I
5.17458 − 6.78996I 0
u = −1.61881
a = 2.97964
b = −2.07397
3.94904 0
u = −1.62599 + 0.08701I
a = 2.00071 + 0.13636I
b = −1.136690 + 0.824125I
4.85829 − 8.19264I 0
u = −1.62599 − 0.08701I
a = 2.00071 − 0.13636I
b = −1.136690 − 0.824125I
4.85829 + 8.19264I 0
u = 1.64739 + 0.01618I
a = −2.07833 − 0.43318I
b = 1.037310 − 0.320280I
11.12640 + 1.94775I 0
u = 1.64739 − 0.01618I
a = −2.07833 + 0.43318I
b = 1.037310 + 0.320280I
11.12640 − 1.94775I 0
u = −1.65486 + 0.07324I
a = −0.427785 + 0.471354I
b = 0.238957 − 1.184620I
9.56125 − 5.52496I 0
u = −1.65486 − 0.07324I
a = −0.427785 − 0.471354I
b = 0.238957 + 1.184620I
9.56125 + 5.52496I 0
u = 1.65791 + 0.02566I
a = 2.04402 + 0.77118I
b = −1.48917 − 1.43556I
8.81525 + 5.68308I 0
u = 1.65791 − 0.02566I
a = 2.04402 − 0.77118I
b = −1.48917 + 1.43556I
8.81525 − 5.68308I 0
11
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 1.66776 + 0.02292I
a = 1.210920 + 0.397812I
b = −0.554963 + 0.218840I
10.80050 + 1.14005I 0
u = 1.66776 − 0.02292I
a = 1.210920 − 0.397812I
b = −0.554963 − 0.218840I
10.80050 − 1.14005I 0
u = −1.66827 + 0.01675I
a = −1.84161 + 0.17726I
b = 1.36616 − 0.72640I
13.11230 − 2.09984I 0
u = −1.66827 − 0.01675I
a = −1.84161 − 0.17726I
b = 1.36616 + 0.72640I
13.11230 + 2.09984I 0
u = −1.66940 + 0.03737I
a = 0.692148 − 1.011590I
b = −0.276753 − 0.247517I
9.78135 − 6.34874I 0
u = −1.66940 − 0.03737I
a = 0.692148 + 1.011590I
b = −0.276753 + 0.247517I
9.78135 + 6.34874I 0
u = −1.66635 + 0.14890I
a = −2.17840 + 0.50376I
b = 1.57381 − 1.13285I
10.45570 − 8.59652I 0
u = −1.66635 − 0.14890I
a = −2.17840 − 0.50376I
b = 1.57381 + 1.13285I
10.45570 + 8.59652I 0
u = 1.66512 + 0.17047I
a = −0.729902 + 0.338360I
b = 0.691944 + 0.302616I
10.03660 + 4.49493I 0
u = 1.66512 − 0.17047I
a = −0.729902 − 0.338360I
b = 0.691944 − 0.302616I
10.03660 − 4.49493I 0
12
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 1.67885 + 0.07865I
a = 1.60585 + 0.06324I
b = −0.872569 − 1.059720I
6.68731 + 6.14608I 0
u = 1.67885 − 0.07865I
a = 1.60585 − 0.06324I
b = −0.872569 + 1.059720I
6.68731 − 6.14608I 0
u = −1.69202 + 0.15408I
a = 1.60685 + 0.16379I
b = −1.166170 + 0.647670I
13.1227 − 11.0928I 0
u = −1.69202 − 0.15408I
a = 1.60685 − 0.16379I
b = −1.166170 − 0.647670I
13.1227 + 11.0928I 0
u = 1.69608 + 0.15323I
a = −2.10270 − 0.25181I
b = 1.39715 + 1.04056I
8.1438 + 16.7871I 0
u = 1.69608 − 0.15323I
a = −2.10270 + 0.25181I
b = 1.39715 − 1.04056I
8.1438 − 16.7871I 0
u = −1.71128
a = −2.50112
b = 1.27351
11.3997 0
u = 1.70574 + 0.14595I
a = 1.59733 − 0.07514I
b = −1.160380 − 0.528430I
13.29620 + 4.11407I 0
u = 1.70574 − 0.14595I
a = 1.59733 + 0.07514I
b = −1.160380 + 0.528430I
13.29620 − 4.11407I 0
u = 1.71898
a = 1.36314
b = −1.21199
9.74779 0
13
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.196123 + 0.005228I
a = 0.82450 − 3.34814I
b = 0.762236 − 0.307912I
1.21956 − 1.26043I 6.74350 − 0.63516I
u = −0.196123 − 0.005228I
a = 0.82450 + 3.34814I
b = 0.762236 + 0.307912I
1.21956 + 1.26043I 6.74350 + 0.63516I
u = −1.86286 + 0.10282I
a = −0.595381 − 0.156590I
b = 0.351069 − 0.006997I
7.23091 − 0.06693I 0
u = −1.86286 − 0.10282I
a = −0.595381 + 0.156590I
b = 0.351069 + 0.006997I
7.23091 + 0.06693I 0
u = −0.0883854 + 0.0407157I
a = 3.34955 − 11.61160I
b = −0.487062 + 0.970812I
−1.92017 − 4.82828I −0.55587 + 7.49185I
u = −0.0883854 − 0.0407157I
a = 3.34955 + 11.61160I
b = −0.487062 − 0.970812I
−1.92017 + 4.82828I −0.55587 − 7.49185I
14
II.
I
u
2
= hu
15
−u
14
+· · ·+b+2, −u
15
+2u
14
+· · ·+a−9, u
16
−12u
14
+· · ·+5u+1i
(i) Arc colorings
a
7
=
1
0
a
12
=
0
u
a
8
=
1
−u
2
a
1
=
u
−u
3
+ u
a
3
=
u
15
− 2u
14
+ ··· − 2u + 9
−u
15
+ u
14
+ ··· − 2u − 2
a
9
=
−u
2
+ 1
u
4
− 2u
2
a
6
=
2u
13
− 21u
11
+ ··· + 14u − 9
−u
13
− u
12
+ ··· − 6u + 1
a
11
=
−u
u
a
4
=
2u
15
− u
14
+ ··· − 7u + 8
−2u
15
+ 21u
13
+ ··· + 3u − 1
a
2
=
2u
15
− u
14
+ ··· − 10u + 11
−u
15
+ u
14
+ ··· − 5u − 3
a
10
=
−3u
15
+ u
14
+ ··· + 13u − 13
u
13
+ u
12
+ ··· + 3u + 3
a
5
=
u
15
− u
14
+ ··· − 7u + 7
−2u
15
+ 2u
14
+ ··· − 2u − 2
(ii) Obstruction class = 1
(iii) Cusp Shapes = −11u
15
+ 11u
14
+ 122u
13
− 122u
12
− 505u
11
+ 506u
10
+ 952u
9
−
974u
8
− 789u
7
+ 894u
6
+ 252u
5
− 417u
4
− 67u
3
+ 135u
2
− 6u − 13
15
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
16
− 8u
15
+ ··· − 12u + 2
c
2
u
16
+ 8u
15
+ ··· + 2u − 1
c
3
u
16
+ 2u
15
+ ··· − 4u − 1
c
4
u
16
+ 2u
15
+ ··· − u − 1
c
5
u
16
+ u
15
+ ··· − 10u − 2
c
6
u
16
+ 4u
15
+ ··· + u + 1
c
7
, c
8
u
16
− 12u
14
+ ··· + 5u + 1
c
9
u
16
− u
15
+ ··· + 2u − 1
c
10
u
16
− u
15
+ ··· + 10u − 2
c
11
, c
12
u
16
− 12u
14
+ ··· − 5u + 1
16
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
16
+ 8y
15
+ ··· − 84y + 4
c
2
y
16
+ 8y
15
+ ··· − 22y + 1
c
3
y
16
+ 4y
15
+ ··· − 14y + 1
c
4
y
16
− 6y
15
+ ··· − 11y + 1
c
5
, c
10
y
16
− 17y
15
+ ··· − 88y + 4
c
6
y
16
− 4y
15
+ ··· − 11y + 1
c
7
, c
8
, c
11
c
12
y
16
− 24y
15
+ ··· − 51y + 1
c
9
y
16
− 11y
15
+ ··· − 6y + 1
17
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −1.19636
a = −1.77658
b = 1.10535
3.32897 13.9120
u = −1.22692
a = −0.0953975
b = −0.556654
−1.15723 −3.31060
u = 0.730798 + 0.226517I
a = 0.905085 − 0.455462I
b = −0.64601 − 1.27305I
−0.84370 + 5.86905I 2.90360 − 9.44604I
u = 0.730798 − 0.226517I
a = 0.905085 + 0.455462I
b = −0.64601 + 1.27305I
−0.84370 − 5.86905I 2.90360 + 9.44604I
u = 0.526726 + 0.434145I
a = −0.60415 − 1.41349I
b = −0.321537 + 0.919054I
−1.59369 − 3.77560I 3.21977 + 1.38171I
u = 0.526726 − 0.434145I
a = −0.60415 + 1.41349I
b = −0.321537 − 0.919054I
−1.59369 + 3.77560I 3.21977 − 1.38171I
u = −0.546876 + 0.396366I
a = 0.459891 − 0.407083I
b = 0.513445 − 0.275172I
1.24652 − 2.20120I 3.77391 + 9.48109I
u = −0.546876 − 0.396366I
a = 0.459891 + 0.407083I
b = 0.513445 + 0.275172I
1.24652 + 2.20120I 3.77391 − 9.48109I
u = 1.44929
a = 3.12675
b = −2.35102
0.798829 −5.03330
u = 1.64226 + 0.10055I
a = −0.465382 + 0.144697I
b = 0.463753 + 0.629045I
9.13670 + 4.01794I 4.05125 − 2.49021I
18
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 1.64226 − 0.10055I
a = −0.465382 − 0.144697I
b = 0.463753 − 0.629045I
9.13670 − 4.01794I 4.05125 + 2.49021I
u = −1.65755 + 0.06178I
a = 1.243350 − 0.432612I
b = −0.80550 + 1.39626I
7.62680 − 6.95712I 4.96915 + 7.75044I
u = −1.65755 − 0.06178I
a = 1.243350 + 0.432612I
b = −0.80550 − 1.39626I
7.62680 + 6.95712I 4.96915 − 7.75044I
u = 1.68754
a = −2.22031
b = 1.17434
12.5960 13.1870
u = −0.154144
a = 8.34734
b = −1.36621
−4.74106 −8.86620
u = −1.95010
a = 0.540609
b = −0.414098
7.37732 47.2750
19
III. I
u
3
= hb − 1, a + 2, u + 1i
(i) Arc colorings
a
7
=
1
0
a
12
=
0
−1
a
8
=
1
−1
a
1
=
−1
0
a
3
=
−2
1
a
9
=
0
−1
a
6
=
−1
1
a
11
=
1
−1
a
4
=
−1
0
a
2
=
−1
0
a
10
=
1
−1
a
5
=
−1
1
(ii) Obstruction class = 1
(iii) Cusp Shapes = 12
20
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
5
, c
10
u
c
2
, c
7
, c
8
c
9
u + 1
c
3
, c
4
, c
6
c
11
, c
12
u − 1
21
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
5
, c
10
y
c
2
, c
3
, c
4
c
6
, c
7
, c
8
c
9
, c
11
, c
12
y −1
22
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = −1.00000
a = −2.00000
b = 1.00000
3.28987 12.0000
23
IV. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
u(u
16
− 8u
15
+ ··· − 12u + 2)(u
96
+ 5u
95
+ ··· − 4478u + 638)
c
2
(u + 1)(u
16
+ 8u
15
+ ··· + 2u − 1)(u
96
− 8u
95
+ ··· + 5u − 1)
c
3
(u − 1)(u
16
+ 2u
15
+ ··· − 4u − 1)(u
96
+ 5u
94
+ ··· − 723u − 97)
c
4
(u − 1)(u
16
+ 2u
15
+ ··· − u − 1)(u
96
+ 2u
95
+ ··· − 5914u − 463)
c
5
u(u
16
+ u
15
+ ··· − 10u − 2)(u
96
− 2u
95
+ ··· + 4u + 2)
c
6
(u − 1)(u
16
+ 4u
15
+ ··· + u + 1)(u
96
− 9u
94
+ ··· − 872u − 79)
c
7
, c
8
(u + 1)(u
16
− 12u
14
+ ··· + 5u + 1)(u
96
− 61u
94
+ ··· + 28u − 1)
c
9
(u + 1)(u
16
− u
15
+ ··· + 2u − 1)(u
96
− 3u
95
+ ··· − 1819u + 211)
c
10
u(u
16
− u
15
+ ··· + 10u − 2)(u
96
− 2u
95
+ ··· + 4u + 2)
c
11
, c
12
(u − 1)(u
16
− 12u
14
+ ··· − 5u + 1)(u
96
− 61u
94
+ ··· + 28u − 1)
24
V. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
y(y
16
+ 8y
15
+ ··· − 84y + 4)
· (y
96
+ 23y
95
+ ··· − 5697484y + 407044)
c
2
(y −1)(y
16
+ 8y
15
+ ··· − 22y + 1)(y
96
+ 6y
95
+ ··· − 947y + 1)
c
3
(y −1)(y
16
+ 4y
15
+ ··· − 14y + 1)
· (y
96
+ 10y
95
+ ··· + 487817y + 9409)
c
4
(y −1)(y
16
− 6y
15
+ ··· − 11y + 1)
· (y
96
− 32y
95
+ ··· − 43540896y + 214369)
c
5
, c
10
y(y
16
− 17y
15
+ ··· − 88y + 4)(y
96
− 74y
95
+ ··· + 592y + 4)
c
6
(y −1)(y
16
− 4y
15
+ ··· − 11y + 1)
· (y
96
− 18y
95
+ ··· − 426056y + 6241)
c
7
, c
8
, c
11
c
12
(y −1)(y
16
− 24y
15
+ ··· − 51y + 1)(y
96
− 122y
95
+ ··· − 208y + 1)
c
9
(y −1)(y
16
− 11y
15
+ ··· − 6y + 1)
· (y
96
− 29y
95
+ ··· − 3023067y + 44521)
25
