12a
1257
(K12a
1257
)
A knot diagram
1
Linearized knot diagam
5 7 8 1 11 10 12 4 2 6 3 9
Solving Sequence
4,8 9,12
1 5 3 7 2 10 6 11
c
8
c
12
c
4
c
3
c
7
c
2
c
9
c
6
c
11
c
1
, c
5
, c
10
Ideals for irreducible components
2
of X
par
I
u
1
= h5.69717 × 10
443
u
121
− 1.08046 × 10
443
u
120
+ ··· + 1.39254 × 10
445
b + 1.13421 × 10
446
,
− 1.11587 × 10
444
u
121
+ 9.38471 × 10
444
u
120
+ ··· + 5.98792 × 10
446
a + 3.66043 × 10
447
,
u
122
− u
121
+ ··· + 840u − 344i
I
u
2
= h24839975132u
20
+ 42789429212u
19
+ ··· + 64008861027b − 50213545124,
44188587683u
20
+ 143099664266u
19
+ ··· + 64008861027a − 168032991365,
u
21
− 7u
19
+ ··· − 5u
2
+ 1i
* 2 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
= h5.70 × 10
443
u
121
− 1.08 × 10
443
u
120
+ · · · + 1.39 × 10
445
b + 1.13 ×
10
446
, −1.12 × 10
444
u
121
+ 9.38 × 10
444
u
120
+ · · · + 5.99 × 10
446
a + 3.66 ×
10
447
, u
122
− u
121
+ · · · + 840u − 344i
(i) Arc colorings
a
4
=
0
u
a
8
=
1
0
a
9
=
1
u
2
a
12
=
0.00186353u
121
− 0.0156727u
120
+ ··· + 8.69189u − 6.11302
−0.0409121u
121
+ 0.00775889u
120
+ ··· + 10.8209u − 8.14493
a
1
=
−0.0424622u
121
+ 0.0182287u
120
+ ··· + 7.27198u − 9.50758
−0.0988281u
121
+ 0.0548574u
120
+ ··· + 4.32925u − 11.7309
a
5
=
−0.0333642u
121
+ 0.00722217u
120
+ ··· + 9.88193u − 10.3188
−0.0518144u
121
− 0.0133058u
120
+ ··· + 31.5122u − 17.0446
a
3
=
u
u
a
7
=
0.0249558u
121
+ 0.0248564u
120
+ ··· − 22.7064u + 12.6805
0.0259868u
121
+ 0.0332605u
120
+ ··· − 28.4800u + 14.2995
a
2
=
0.0790093u
121
− 0.0280193u
120
+ ··· + 9.57936u + 9.70489
0.104578u
121
− 0.0400487u
120
+ ··· − 11.8432u + 17.6024
a
10
=
−0.0567863u
121
− 0.0247468u
120
+ ··· + 25.8798u − 21.9604
−0.0657310u
121
− 0.0362288u
120
+ ··· + 51.9703u − 29.6219
a
6
=
−0.0178133u
121
+ 0.0149639u
120
+ ··· + 3.63656u − 4.43187
−0.00460256u
121
+ 0.0149540u
120
+ ··· − 4.51681u + 3.76614
a
11
=
−0.0565800u
121
+ 0.0189299u
120
+ ··· + 10.2260u − 12.7674
−0.0993556u
121
+ 0.0423615u
120
+ ··· + 12.3550u − 14.7993
(ii) Obstruction class = −1
(iii) Cusp Shapes = 0.0488883u
121
+ 0.0908826u
120
+ ··· − 102.646u + 42.5994
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
4
3(3u
122
+ 10u
121
+ ··· + 187864u + 5572)
c
2
3(3u
122
− 4u
121
+ ··· − 1118665u − 446825)
c
3
, c
8
u
122
− u
121
+ ··· + 840u − 344
c
5
, c
6
, c
10
u
122
+ u
121
+ ··· + 8u − 11
c
7
3(3u
122
− 7u
121
+ ··· − 2u + 1)
c
9
u
122
− 2u
121
+ ··· + 950272u − 49152
c
11
u
122
+ 4u
121
+ ··· + 111658u − 20519
c
12
u
122
− 3u
121
+ ··· + 51487u − 8787
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
4
9(9y
122
− 898y
121
+ ··· − 7.94711 × 10
9
y + 3.10472 × 10
7
)
c
2
9(9y
122
− 388y
121
+ ··· − 2.27562 × 10
12
y + 1.99653 × 10
11
)
c
3
, c
8
y
122
− 91y
121
+ ··· − 740000y + 118336
c
5
, c
6
, c
10
y
122
+ 115y
121
+ ··· − 8600y + 121
c
7
9(9y
122
+ 5y
121
+ ··· − 20y + 1)
c
9
y
122
− 22y
121
+ ··· − 561164320768y + 2415919104
c
11
y
122
− 14y
121
+ ··· − 28711211162y + 421029361
c
12
y
122
+ 53y
121
+ ··· + 2230478219y + 77211369
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.604012 + 0.787190I
a = 1.151760 − 0.060842I
b = −0.862030 + 0.023194I
4.52117 + 4.07559I 0
u = 0.604012 − 0.787190I
a = 1.151760 + 0.060842I
b = −0.862030 − 0.023194I
4.52117 − 4.07559I 0
u = 1.000660 + 0.207886I
a = −0.436527 + 1.299170I
b = −0.235979 + 0.305966I
0.36555 − 2.39525I 0
u = 1.000660 − 0.207886I
a = −0.436527 − 1.299170I
b = −0.235979 − 0.305966I
0.36555 + 2.39525I 0
u = 0.976833 + 0.387500I
a = −0.62050 − 1.97893I
b = 0.354146 − 0.011955I
3.34528 − 8.66044I 0
u = 0.976833 − 0.387500I
a = −0.62050 + 1.97893I
b = 0.354146 + 0.011955I
3.34528 + 8.66044I 0
u = −0.240514 + 0.903459I
a = −0.106658 + 0.239405I
b = 0.937678 + 0.678854I
0.12332 + 4.01287I 0
u = −0.240514 − 0.903459I
a = −0.106658 − 0.239405I
b = 0.937678 − 0.678854I
0.12332 − 4.01287I 0
u = −0.136181 + 0.916927I
a = 0.155274 + 0.361001I
b = 0.930982 − 0.743513I
8.57001 − 7.32077I 0
u = −0.136181 − 0.916927I
a = 0.155274 − 0.361001I
b = 0.930982 + 0.743513I
8.57001 + 7.32077I 0
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.966501 + 0.499176I
a = −0.666110 + 0.332942I
b = −0.423485 + 0.385406I
−1.79362 + 0.74361I 0
u = −0.966501 − 0.499176I
a = −0.666110 − 0.332942I
b = −0.423485 − 0.385406I
−1.79362 − 0.74361I 0
u = −0.867098 + 0.253936I
a = 0.61988 + 1.94729I
b = 0.457387 + 0.092056I
7.08067 + 3.95400I 0
u = −0.867098 − 0.253936I
a = 0.61988 − 1.94729I
b = 0.457387 − 0.092056I
7.08067 − 3.95400I 0
u = −0.088634 + 0.886156I
a = 0.293338 + 0.175849I
b = −0.952380 + 0.636078I
7.63214 − 1.85396I 0
u = −0.088634 − 0.886156I
a = 0.293338 − 0.175849I
b = −0.952380 − 0.636078I
7.63214 + 1.85396I 0
u = 1.084380 + 0.239590I
a = 1.03058 + 1.77666I
b = 0.55960 + 2.00322I
2.71157 + 0.31538I 0
u = 1.084380 − 0.239590I
a = 1.03058 − 1.77666I
b = 0.55960 − 2.00322I
2.71157 − 0.31538I 0
u = 1.122500 + 0.217741I
a = 0.70445 − 1.89025I
b = 1.32380 − 1.19693I
5.88182 − 0.15056I 0
u = 1.122500 − 0.217741I
a = 0.70445 + 1.89025I
b = 1.32380 + 1.19693I
5.88182 + 0.15056I 0
6
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 1.146260 + 0.042855I
a = −0.582703 + 0.076661I
b = −1.88629 − 0.09036I
0.189968 − 1.251570I 0
u = 1.146260 − 0.042855I
a = −0.582703 − 0.076661I
b = −1.88629 + 0.09036I
0.189968 + 1.251570I 0
u = 0.290670 + 1.111480I
a = 0.087173 + 0.145864I
b = −0.903371 + 0.688115I
−1.01392 − 8.75038I 0
u = 0.290670 − 1.111480I
a = 0.087173 − 0.145864I
b = −0.903371 − 0.688115I
−1.01392 + 8.75038I 0
u = −1.14892
a = 0.659162
b = 1.89148
−4.37114 0
u = −1.138110 + 0.195030I
a = −0.15246 + 1.76125I
b = 0.61079 + 1.57952I
−3.14459 + 1.16883I 0
u = −1.138110 − 0.195030I
a = −0.15246 − 1.76125I
b = 0.61079 − 1.57952I
−3.14459 − 1.16883I 0
u = 0.007461 + 0.835751I
a = −0.073744 + 0.397542I
b = −0.890083 − 0.595912I
2.55112 + 4.21322I 0
u = 0.007461 − 0.835751I
a = −0.073744 − 0.397542I
b = −0.890083 + 0.595912I
2.55112 − 4.21322I 0
u = 1.179670 + 0.033463I
a = −0.97750 − 1.76730I
b = 0.740671 − 0.709642I
0.69055 − 7.86145I 0
7
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 1.179670 − 0.033463I
a = −0.97750 + 1.76730I
b = 0.740671 + 0.709642I
0.69055 + 7.86145I 0
u = −1.187310 + 0.055707I
a = 0.57715 + 2.43247I
b = −0.392933 + 0.907576I
−5.78046 − 2.67801I 0
u = −1.187310 − 0.055707I
a = 0.57715 − 2.43247I
b = −0.392933 − 0.907576I
−5.78046 + 2.67801I 0
u = −1.171740 + 0.243574I
a = −0.48719 − 1.83317I
b = −0.100075 − 0.249733I
−4.23137 + 5.27335I 0
u = −1.171740 − 0.243574I
a = −0.48719 + 1.83317I
b = −0.100075 + 0.249733I
−4.23137 − 5.27335I 0
u = 1.208310 + 0.188282I
a = 0.08160 + 2.47331I
b = −0.241048 + 1.103970I
−4.88247 − 3.91427I 0
u = 1.208310 − 0.188282I
a = 0.08160 − 2.47331I
b = −0.241048 − 1.103970I
−4.88247 + 3.91427I 0
u = −0.687999 + 0.359730I
a = 0.848366 − 0.061263I
b = −1.153990 + 0.002434I
7.72907 − 1.13566I 0
u = −0.687999 − 0.359730I
a = 0.848366 + 0.061263I
b = −1.153990 − 0.002434I
7.72907 + 1.13566I 0
u = −0.303172 + 0.711246I
a = −1.059850 − 0.757480I
b = 0.725735 − 0.022937I
−1.45418 − 1.75021I 0
8
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.303172 − 0.711246I
a = −1.059850 + 0.757480I
b = 0.725735 + 0.022937I
−1.45418 + 1.75021I 0
u = 1.194850 + 0.297888I
a = 0.26968 + 1.47503I
b = −0.762477 + 0.986963I
−3.44043 − 4.18263I 0
u = 1.194850 − 0.297888I
a = 0.26968 − 1.47503I
b = −0.762477 − 0.986963I
−3.44043 + 4.18263I 0
u = −1.174990 + 0.399163I
a = −0.64210 + 1.40000I
b = 0.835123 + 0.753703I
2.92338 + 6.99742I 0
u = −1.174990 − 0.399163I
a = −0.64210 − 1.40000I
b = 0.835123 − 0.753703I
2.92338 − 6.99742I 0
u = −1.241760 + 0.061173I
a = −0.76484 + 1.83008I
b = −1.07189 + 1.57808I
−5.21797 − 0.40787I 0
u = −1.241760 − 0.061173I
a = −0.76484 − 1.83008I
b = −1.07189 − 1.57808I
−5.21797 + 0.40787I 0
u = 1.25518
a = 1.40422
b = −0.230257
−6.77287 0
u = −0.236158 + 1.234460I
a = −0.100891 + 0.105992I
b = 0.890900 + 0.723943I
4.87949 + 12.70870I 0
u = −0.236158 − 1.234460I
a = −0.100891 − 0.105992I
b = 0.890900 − 0.723943I
4.87949 − 12.70870I 0
9
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −1.246630 + 0.255267I
a = 0.172527 − 0.247100I
b = 1.051920 − 0.043007I
−3.43189 + 3.95846I 0
u = −1.246630 − 0.255267I
a = 0.172527 + 0.247100I
b = 1.051920 + 0.043007I
−3.43189 − 3.95846I 0
u = 1.273820 + 0.112467I
a = 0.57249 + 1.66884I
b = 1.00345 + 1.58304I
−7.11559 − 5.13445I 0
u = 1.273820 − 0.112467I
a = 0.57249 − 1.66884I
b = 1.00345 − 1.58304I
−7.11559 + 5.13445I 0
u = −1.255070 + 0.273667I
a = −0.53404 − 1.58140I
b = −1.29853 − 1.19048I
−1.26423 + 3.63180I 0
u = −1.255070 − 0.273667I
a = −0.53404 + 1.58140I
b = −1.29853 + 1.19048I
−1.26423 − 3.63180I 0
u = −1.275990 + 0.166531I
a = 0.119660 − 0.202339I
b = −0.290527 − 0.199626I
−1.78102 + 0.04002I 0
u = −1.275990 − 0.166531I
a = 0.119660 + 0.202339I
b = −0.290527 + 0.199626I
−1.78102 − 0.04002I 0
u = −1.294610 + 0.150957I
a = −0.56206 + 1.51842I
b = −1.03035 + 1.61105I
−1.27716 + 9.56420I 0
u = −1.294610 − 0.150957I
a = −0.56206 − 1.51842I
b = −1.03035 − 1.61105I
−1.27716 − 9.56420I 0
10
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −1.230320 + 0.437781I
a = −0.13075 − 1.65724I
b = −1.25919 − 1.31101I
5.14389 + 12.14870I 0
u = −1.230320 − 0.437781I
a = −0.13075 + 1.65724I
b = −1.25919 + 1.31101I
5.14389 − 12.14870I 0
u = 1.312370 + 0.071022I
a = −0.133076 − 0.649670I
b = −1.031410 − 0.530995I
−7.22586 − 0.26019I 0
u = 1.312370 − 0.071022I
a = −0.133076 + 0.649670I
b = −1.031410 + 0.530995I
−7.22586 + 0.26019I 0
u = −1.245050 + 0.427250I
a = −0.07700 + 1.74458I
b = 0.934702 + 0.941172I
4.03093 + 6.55649I 0
u = −1.245050 − 0.427250I
a = −0.07700 − 1.74458I
b = 0.934702 − 0.941172I
4.03093 − 6.55649I 0
u = 0.103787 + 1.318050I
a = 0.265587 − 0.229174I
b = −0.550013 − 0.296741I
0.549767 + 1.184870I 0
u = 0.103787 − 1.318050I
a = 0.265587 + 0.229174I
b = −0.550013 + 0.296741I
0.549767 − 1.184870I 0
u = 1.268610 + 0.377816I
a = 0.27334 − 1.56476I
b = 1.24182 − 1.24543I
−1.37091 − 8.56529I 0
u = 1.268610 − 0.377816I
a = 0.27334 + 1.56476I
b = 1.24182 + 1.24543I
−1.37091 + 8.56529I 0
11
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.645612 + 0.061796I
a = 2.74885 + 0.68647I
b = 1.180570 + 0.241608I
2.01963 − 1.05555I −12.10339 + 2.04316I
u = 0.645612 − 0.061796I
a = 2.74885 − 0.68647I
b = 1.180570 − 0.241608I
2.01963 + 1.05555I −12.10339 − 2.04316I
u = −1.352450 + 0.066592I
a = 0.087455 + 0.980535I
b = 1.049130 + 0.936651I
−3.39022 + 2.98405I 0
u = −1.352450 − 0.066592I
a = 0.087455 − 0.980535I
b = 1.049130 − 0.936651I
−3.39022 − 2.98405I 0
u = −0.110309 + 0.572008I
a = 1.229000 − 0.416576I
b = −0.347171 + 0.793115I
5.91854 − 3.13751I 0.76663 + 1.77568I
u = −0.110309 − 0.572008I
a = 1.229000 + 0.416576I
b = −0.347171 − 0.793115I
5.91854 + 3.13751I 0.76663 − 1.77568I
u = 0.068199 + 0.544487I
a = −0.103221 + 0.664665I
b = 1.034830 − 0.343908I
2.70887 − 0.48608I 3.14941 − 1.48071I
u = 0.068199 − 0.544487I
a = −0.103221 − 0.664665I
b = 1.034830 + 0.343908I
2.70887 + 0.48608I 3.14941 + 1.48071I
u = 1.40814 + 0.41089I
a = −0.18904 + 1.63083I
b = −1.09729 + 1.16633I
−5.04061 − 8.77658I 0
u = 1.40814 − 0.41089I
a = −0.18904 − 1.63083I
b = −1.09729 − 1.16633I
−5.04061 + 8.77658I 0
12
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.285251 + 0.447657I
a = −0.469896 + 0.646478I
b = −1.316700 − 0.502443I
8.41814 − 2.55121I 4.33699 + 5.44008I
u = 0.285251 − 0.447657I
a = −0.469896 − 0.646478I
b = −1.316700 + 0.502443I
8.41814 + 2.55121I 4.33699 − 5.44008I
u = 0.351099 + 0.371932I
a = 2.26061 − 0.65659I
b = 0.452952 + 0.854468I
1.94986 − 1.37190I −3.76005 − 3.82007I
u = 0.351099 − 0.371932I
a = 2.26061 + 0.65659I
b = 0.452952 − 0.854468I
1.94986 + 1.37190I −3.76005 + 3.82007I
u = −1.43663 + 0.39328I
a = −0.018429 − 1.154060I
b = −0.290989 − 0.943659I
−5.43258 + 4.56786I 0
u = −1.43663 − 0.39328I
a = −0.018429 + 1.154060I
b = −0.290989 + 0.943659I
−5.43258 − 4.56786I 0
u = 1.09205 + 1.01974I
a = −0.0585516 + 0.0289578I
b = 0.309304 − 0.236222I
2.12157 − 3.07632I 0
u = 1.09205 − 1.01974I
a = −0.0585516 − 0.0289578I
b = 0.309304 + 0.236222I
2.12157 + 3.07632I 0
u = −1.45256 + 0.46650I
a = 0.15761 + 1.49423I
b = 1.17247 + 1.14441I
−6.4453 + 14.3034I 0
u = −1.45256 − 0.46650I
a = 0.15761 − 1.49423I
b = 1.17247 − 1.14441I
−6.4453 − 14.3034I 0
13
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.460293
a = −1.25249
b = 1.12792
2.71449 20.9140
u = 1.46911 + 0.47244I
a = −0.044461 − 1.145230I
b = 0.573742 − 1.119100I
−8.49065 − 7.01308I 0
u = 1.46911 − 0.47244I
a = −0.044461 + 1.145230I
b = 0.573742 + 1.119100I
−8.49065 + 7.01308I 0
u = 1.46222 + 0.51383I
a = −0.09764 + 1.43786I
b = −1.21014 + 1.12528I
−0.4189 − 18.7740I 0
u = 1.46222 − 0.51383I
a = −0.09764 − 1.43786I
b = −1.21014 − 1.12528I
−0.4189 + 18.7740I 0
u = 1.42202 + 0.62487I
a = −0.178198 − 1.086890I
b = 0.925255 − 0.701304I
−3.61881 − 7.97481I 0
u = 1.42202 − 0.62487I
a = −0.178198 + 1.086890I
b = 0.925255 + 0.701304I
−3.61881 + 7.97481I 0
u = −1.47952 + 0.50088I
a = 0.061725 − 1.161990I
b = −0.68737 − 1.27852I
−3.83299 + 9.60532I 0
u = −1.47952 − 0.50088I
a = 0.061725 + 1.161990I
b = −0.68737 + 1.27852I
−3.83299 − 9.60532I 0
u = −1.47125 + 0.55335I
a = 0.087489 − 1.084120I
b = −0.882401 − 0.878137I
−7.81978 + 6.19714I 0
14
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −1.47125 − 0.55335I
a = 0.087489 + 1.084120I
b = −0.882401 + 0.878137I
−7.81978 − 6.19714I 0
u = 0.049547 + 0.424919I
a = −0.718020 − 0.593551I
b = 0.187791 + 0.579194I
−0.255044 + 1.126440I −3.57834 − 5.49956I
u = 0.049547 − 0.424919I
a = −0.718020 + 0.593551I
b = 0.187791 − 0.579194I
−0.255044 − 1.126440I −3.57834 + 5.49956I
u = 1.53383 + 0.51429I
a = −0.015778 − 1.032470I
b = 0.969673 − 0.986951I
−3.60645 − 4.16463I 0
u = 1.53383 − 0.51429I
a = −0.015778 + 1.032470I
b = 0.969673 + 0.986951I
−3.60645 + 4.16463I 0
u = 1.61469 + 0.13966I
a = 0.069315 + 0.398022I
b = 0.283938 + 0.541467I
2.43291 − 2.68890I 0
u = 1.61469 − 0.13966I
a = 0.069315 − 0.398022I
b = 0.283938 − 0.541467I
2.43291 + 2.68890I 0
u = 0.033396 + 0.372902I
a = −1.05313 + 1.25297I
b = 0.571256 + 1.023590I
−1.39848 + 1.69419I 5.40238 + 3.22646I
u = 0.033396 − 0.372902I
a = −1.05313 − 1.25297I
b = 0.571256 − 1.023590I
−1.39848 − 1.69419I 5.40238 − 3.22646I
u = −0.322077 + 0.005347I
a = −3.93287 + 0.12149I
b = −0.697814 + 0.167206I
−2.19840 + 0.01517I −11.05542 + 3.71706I
15
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.322077 − 0.005347I
a = −3.93287 − 0.12149I
b = −0.697814 − 0.167206I
−2.19840 − 0.01517I −11.05542 − 3.71706I
u = 0.244987 + 0.197622I
a = −4.14152 − 0.10127I
b = 0.128878 + 0.864098I
3.39289 − 7.96178I −2.64222 + 4.65082I
u = 0.244987 − 0.197622I
a = −4.14152 + 0.10127I
b = 0.128878 − 0.864098I
3.39289 + 7.96178I −2.64222 − 4.65082I
u = −0.144108 + 0.266850I
a = 2.88110 + 1.43551I
b = −0.259595 + 0.980782I
−2.80629 + 3.70003I −5.46472 − 7.08880I
u = −0.144108 − 0.266850I
a = 2.88110 − 1.43551I
b = −0.259595 − 0.980782I
−2.80629 − 3.70003I −5.46472 + 7.08880I
u = 0.12591 + 1.74655I
a = −0.0520078 − 0.0988769I
b = 0.229755 − 0.247671I
−2.69265 + 0.62772I 0
u = 0.12591 − 1.74655I
a = −0.0520078 + 0.0988769I
b = 0.229755 + 0.247671I
−2.69265 − 0.62772I 0
u = 0.32303 + 1.90836I
a = 0.0514929 − 0.0037415I
b = −0.022781 − 0.353229I
1.95055 − 3.13857I 0
u = 0.32303 − 1.90836I
a = 0.0514929 + 0.0037415I
b = −0.022781 + 0.353229I
1.95055 + 3.13857I 0
u = −1.95815 + 0.18847I
a = 0.308717 + 0.266503I
b = 0.501721 + 0.402916I
0.74141 − 3.88564I 0
16
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −1.95815 − 0.18847I
a = 0.308717 − 0.266503I
b = 0.501721 − 0.402916I
0.74141 + 3.88564I 0
u = 2.05667
a = −0.320631
b = −0.499157
−3.51656 0
17
II. I
u
2
=
h2.48×10
10
u
20
+4.28×10
10
u
19
+· · ·+6.40×10
10
b−5.02×10
10
, 4.42×10
10
u
20
+
1.43 × 10
11
u
19
+ · · · + 6.40 × 10
10
a − 1.68 × 10
11
, u
21
− 7u
19
+ · · · − 5u
2
+ 1i
(i) Arc colorings
a
4
=
0
u
a
8
=
1
0
a
9
=
1
u
2
a
12
=
−0.690351u
20
− 2.23562u
19
+ ··· + 1.01142u + 2.62515
−0.388071u
20
− 0.668492u
19
+ ··· + 3.51184u + 0.784478
a
1
=
−1.63561u
20
− 0.900464u
19
+ ··· + 3.83291u + 1.17401
−1.27762u
20
+ 0.796704u
19
+ ··· + 4.45710u − 0.550681
a
5
=
1.96739u
20
+ 0.741300u
19
+ ··· − 0.738960u − 0.132507
1.49248u
20
+ 1.26446u
19
+ ··· − 3.14590u − 2.19244
a
3
=
u
u
a
7
=
−0.705270u
20
− 2.67361u
19
+ ··· + 2.59865u + 3.79884
0.468738u
20
− 2.03800u
19
+ ··· + 2.93390u + 3.96593
a
2
=
−0.415493u
20
+ 1.70473u
19
+ ··· + 5.96094u + 0.740078
0.240138u
20
+ 2.11931u
19
+ ··· + 3.21820u − 1.97827
a
10
=
−0.334901u
20
+ 0.532403u
19
+ ··· − 2.76763u − 0.291504
−2.19802u
20
− 0.352779u
19
+ ··· + 2.57696u + 0.620270
a
6
=
2.29196u
20
+ 0.506276u
19
+ ··· + 2.04133u + 0.278852
5.05533u
20
+ 1.17230u
19
+ ··· − 12.5850u − 6.06332
a
11
=
−0.691332u
20
− 1.03050u
19
+ ··· + 0.709138u + 1.05802
−0.389051u
20
+ 0.536629u
19
+ ··· + 3.20956u − 0.782652
(ii) Obstruction class = 1
(iii) Cusp Shapes
= −
19253119502519
1728239247729
u
20
+
2253298001296
1728239247729
u
19
+ ··· +
67555449295790
1728239247729
u −
12666145653124
1728239247729
18
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
3(3u
21
+ 5u
20
+ ··· + 72u − 16)
c
2
3(3u
21
+ 13u
20
+ ··· − 6u + 1)
c
3
u
21
− 7u
19
+ ··· + 5u
2
− 1
c
4
3(3u
21
− 5u
20
+ ··· + 72u + 16)
c
5
, c
6
u
21
+ 2u
20
+ ··· − u + 1
c
7
3(3u
21
− 10u
20
+ ··· + 3u + 1)
c
8
u
21
− 7u
19
+ ··· − 5u
2
+ 1
c
9
u
21
− u
20
+ ··· + 10u + 3
c
10
u
21
− 2u
20
+ ··· − u − 1
c
11
u
21
+ 3u
20
+ ··· − 11u + 1
c
12
u
21
+ 11u
19
+ ··· − 16u − 3
19
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
4
9(9y
21
− 241y
20
+ ··· + 4800y − 256)
c
2
9(9y
21
− 55y
20
+ ··· + 14y − 1)
c
3
, c
8
y
21
− 14y
20
+ ··· + 10y − 1
c
5
, c
6
, c
10
y
21
+ 20y
20
+ ··· + 9y − 1
c
7
9(9y
21
− 22y
20
+ ··· − 31y − 1)
c
9
y
21
+ 7y
20
+ ··· − 38y − 9
c
11
y
21
+ 3y
20
+ ··· + 27y − 1
c
12
y
21
+ 22y
20
+ ··· − 98y − 9
20
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −1.020200 + 0.329581I
a = 1.26224 − 2.11915I
b = −0.401136 − 0.780145I
2.52476 + 9.09814I −5.99965 − 10.70332I
u = −1.020200 − 0.329581I
a = 1.26224 + 2.11915I
b = −0.401136 + 0.780145I
2.52476 − 9.09814I −5.99965 + 10.70332I
u = −0.797353 + 0.725488I
a = −0.715029 − 0.018354I
b = −0.362489 + 0.468408I
−2.23815 + 0.64309I −16.7302 + 2.7247I
u = −0.797353 − 0.725488I
a = −0.715029 + 0.018354I
b = −0.362489 − 0.468408I
−2.23815 − 0.64309I −16.7302 − 2.7247I
u = 1.164760 + 0.165737I
a = −0.18412 − 2.54738I
b = −0.078863 − 1.020960I
−5.08783 − 4.68052I −10.26822 + 8.30783I
u = 1.164760 − 0.165737I
a = −0.18412 + 2.54738I
b = −0.078863 + 1.020960I
−5.08783 + 4.68052I −10.26822 − 8.30783I
u = −1.207670 + 0.016287I
a = 0.36660 − 1.77644I
b = 1.12812 − 1.21332I
−5.03951 − 1.18769I −6.11414 + 3.27926I
u = −1.207670 − 0.016287I
a = 0.36660 + 1.77644I
b = 1.12812 + 1.21332I
−5.03951 + 1.18769I −6.11414 − 3.27926I
u = 0.668402 + 0.300520I
a = 2.19057 − 0.50439I
b = 1.38280 + 0.47163I
2.31013 + 0.76215I −3.00672 + 7.16992I
u = 0.668402 − 0.300520I
a = 2.19057 + 0.50439I
b = 1.38280 − 0.47163I
2.31013 − 0.76215I −3.00672 − 7.16992I
21
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.531064 + 0.126324I
a = −0.82675 − 1.19106I
b = 1.195870 − 0.278600I
7.49754 + 1.98939I −1.66955 − 3.30703I
u = 0.531064 − 0.126324I
a = −0.82675 + 1.19106I
b = 1.195870 + 0.278600I
7.49754 − 1.98939I −1.66955 + 3.30703I
u = −0.525884
a = 0.781585
b = −1.20616
2.54622 −27.2940
u = 1.40648 + 0.45133I
a = −0.040383 − 1.323510I
b = 0.750823 − 0.978670I
−6.58291 − 6.20833I −6.71892 + 5.20796I
u = 1.40648 − 0.45133I
a = −0.040383 + 1.323510I
b = 0.750823 + 0.978670I
−6.58291 + 6.20833I −6.71892 − 5.20796I
u = −0.166137 + 0.398513I
a = −0.48203 − 1.38068I
b = −0.557499 − 0.764154I
−1.87170 + 1.94044I −8.89437 − 4.60282I
u = −0.166137 − 0.398513I
a = −0.48203 + 1.38068I
b = −0.557499 + 0.764154I
−1.87170 − 1.94044I −8.89437 + 4.60282I
u = −1.51731 + 0.61410I
a = 0.071459 − 0.891436I
b = −0.750662 − 0.778246I
−4.62418 + 6.67061I −6.64164 − 5.35255I
u = −1.51731 − 0.61410I
a = 0.071459 + 0.891436I
b = −0.750662 + 0.778246I
−4.62418 − 6.67061I −6.64164 + 5.35255I
u = 1.20090 + 1.61257I
a = 0.1333140 + 0.0080635I
b = −0.037216 + 0.260866I
1.96912 − 3.00198I −36.4146 − 28.7310I
22
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 1.20090 − 1.61257I
a = 0.1333140 − 0.0080635I
b = −0.037216 − 0.260866I
1.96912 + 3.00198I −36.4146 + 28.7310I
23
III. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
9(3u
21
+ 5u
20
+ ··· + 72u − 16)
· (3u
122
+ 10u
121
+ ··· + 187864u + 5572)
c
2
9(3u
21
+ 13u
20
+ ··· − 6u + 1)
· (3u
122
− 4u
121
+ ··· − 1118665u − 446825)
c
3
(u
21
− 7u
19
+ ··· + 5u
2
− 1)(u
122
− u
121
+ ··· + 840u − 344)
c
4
9(3u
21
− 5u
20
+ ··· + 72u + 16)
· (3u
122
+ 10u
121
+ ··· + 187864u + 5572)
c
5
, c
6
(u
21
+ 2u
20
+ ··· − u + 1)(u
122
+ u
121
+ ··· + 8u − 11)
c
7
9(3u
21
− 10u
20
+ ··· + 3u + 1)(3u
122
− 7u
121
+ ··· − 2u + 1)
c
8
(u
21
− 7u
19
+ ··· − 5u
2
+ 1)(u
122
− u
121
+ ··· + 840u − 344)
c
9
(u
21
− u
20
+ ··· + 10u + 3)(u
122
− 2u
121
+ ··· + 950272u − 49152)
c
10
(u
21
− 2u
20
+ ··· − u − 1)(u
122
+ u
121
+ ··· + 8u − 11)
c
11
(u
21
+ 3u
20
+ ··· − 11u + 1)(u
122
+ 4u
121
+ ··· + 111658u − 20519)
c
12
(u
21
+ 11u
19
+ ··· − 16u − 3)(u
122
− 3u
121
+ ··· + 51487u − 8787)
24
IV. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
, c
4
81(9y
21
− 241y
20
+ ··· + 4800y − 256)
· (9y
122
− 898y
121
+ ··· − 7947111232y + 31047184)
c
2
81(9y
21
− 55y
20
+ ··· + 14y − 1)
· (9y
122
− 388y
121
+ ··· − 2275616498025y + 199652580625)
c
3
, c
8
(y
21
− 14y
20
+ ··· + 10y − 1)
· (y
122
− 91y
121
+ ··· − 740000y + 118336)
c
5
, c
6
, c
10
(y
21
+ 20y
20
+ ··· + 9y − 1)(y
122
+ 115y
121
+ ··· − 8600y + 121)
c
7
81(9y
21
− 22y
20
+ ··· − 31y − 1)(9y
122
+ 5y
121
+ ··· − 20y + 1)
c
9
(y
21
+ 7y
20
+ ··· − 38y − 9)
· (y
122
− 22y
121
+ ··· − 561164320768y + 2415919104)
c
11
(y
21
+ 3y
20
+ ··· + 27y − 1)
· (y
122
− 14y
121
+ ··· − 28711211162y + 421029361)
c
12
(y
21
+ 22y
20
+ ··· − 98y − 9)
· (y
122
+ 53y
121
+ ··· + 2230478219y + 77211369)
25
