12a
0071
(K12a
0071
)
A knot diagram
1
Linearized knot diagam
3 5 7 9 2 10 12 1 11 6 4 8
Solving Sequence
7,12
8 1
4,9
5 3 2 11 10 6
c
7
c
12
c
8
c
4
c
3
c
1
c
11
c
9
c
6
c
2
, c
5
, c
10
Ideals for irreducible components
2
of X
par
I
u
1
= h9.06148 × 10
225
u
108
+ 1.05422 × 10
226
u
107
+ ··· + 5.27836 × 10
225
b + 1.18579 × 10
226
,
− 3.01470 × 10
223
u
108
− 3.51077 × 10
223
u
107
+ ··· + 5.38608 × 10
223
a − 7.22964 × 10
223
,
u
109
+ 3u
108
+ ··· + 2u
2
+ 1i
I
u
2
= h21u
2
b + 49b
2
+ 35bu + 10u
2
+ 7b + 19u + 22, a, u
3
+ u
2
− 1i
* 2 irreducible components of dim
C
= 0, with total 115 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
= h9.06 × 10
225
u
108
+ 1.05 × 10
226
u
107
+ · · · + 5.28 × 10
225
b + 1.19 ×
10
226
, −3.01 × 10
223
u
108
− 3.51 × 10
223
u
107
+ · · · + 5.39 × 10
223
a − 7.23 ×
10
223
, u
109
+ 3u
108
+ · · · + 2u
2
+ 1i
(i) Arc colorings
a
7
=
1
0
a
12
=
0
u
a
8
=
1
u
2
a
1
=
−u
−u
3
+ u
a
4
=
0.559721u
108
+ 0.651823u
107
+ ··· − 0.410187u + 1.34228
−1.71672u
108
− 1.99725u
107
+ ··· + 3.05241u − 2.24651
a
9
=
−u
2
+ 1
−u
4
+ 2u
2
a
5
=
0.192858u
108
+ 0.779830u
107
+ ··· + 2.58086u + 0.364839
−0.692306u
108
− 0.275910u
107
+ ··· + 1.29823u − 1.50459
a
3
=
−1.15700u
108
− 1.34542u
107
+ ··· + 2.64222u − 0.904224
−1.71672u
108
− 1.99725u
107
+ ··· + 3.05241u − 2.24651
a
2
=
−4.03867u
108
− 6.47872u
107
+ ··· + 0.850657u − 3.08463
−3.85538u
108
− 6.16675u
107
+ ··· + 6.51846u − 3.48949
a
11
=
0.107568u
108
+ 0.213955u
107
+ ··· + 0.809172u − 0.177700
1.39394u
108
+ 2.20200u
107
+ ··· − 1.98924u + 1.33556
a
10
=
−0.222413u
108
− 0.429613u
107
+ ··· − 0.690353u + 0.836754
1.26981u
108
+ 2.30353u
107
+ ··· + 0.348221u + 1.14552
a
6
=
−1.03789u
108
− 1.77503u
107
+ ··· + 1.07250u − 1.04911
−0.967747u
108
− 1.68509u
107
+ ··· − 0.843787u − 0.111823
(ii) Obstruction class = −1
(iii) Cusp Shapes = 10.5657u
108
+ 18.1769u
107
+ ··· + 8.33675u + 11.3613
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
109
+ 50u
108
+ ··· − 9999u − 2401
c
2
, c
5
u
109
+ 4u
108
+ ··· − 551u − 49
c
3
49(49u
109
+ 42u
108
+ ··· − 1346644u − 153031)
c
4
49(49u
109
+ 154u
108
+ ··· + 1.84924 × 10
7
u + 1398784)
c
6
, c
10
u
109
+ 3u
108
+ ··· + 6u + 1
c
7
, c
8
, c
12
u
109
+ 3u
108
+ ··· + 2u
2
+ 1
c
9
u
109
− 49u
108
+ ··· − 4u + 1
c
11
u
109
− 5u
108
+ ··· + 48608u + 21952
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
109
+ 22y
108
+ ··· + 18653329y −5764801
c
2
, c
5
y
109
+ 50y
108
+ ··· − 9999y −2401
c
3
2401
· (2401y
109
− 163660y
108
+ ··· − 913616530238y −23418486961)
c
4
2401
· (2401y
109
+ 1666y
108
+ ··· + 9951035523072y −1956596678656)
c
6
, c
10
y
109
+ 49y
108
+ ··· − 4y −1
c
7
, c
8
, c
12
y
109
− 103y
108
+ ··· − 4y −1
c
9
y
109
+ 25y
108
+ ··· + 72y −1
c
11
y
109
+ 35y
108
+ ··· − 3911670784y −481890304
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.489926 + 0.841164I
a = −0.606125 + 1.170680I
b = 1.134530 − 0.822129I
−2.69398 + 8.51191I 0
u = −0.489926 − 0.841164I
a = −0.606125 − 1.170680I
b = 1.134530 + 0.822129I
−2.69398 − 8.51191I 0
u = 0.509943 + 0.826525I
a = 0.50185 + 1.38603I
b = −1.12948 − 1.03666I
−0.5579 − 14.3486I 0
u = 0.509943 − 0.826525I
a = 0.50185 − 1.38603I
b = −1.12948 + 1.03666I
−0.5579 + 14.3486I 0
u = 0.648459 + 0.806149I
a = 1.065950 + 0.105647I
b = −0.773273 + 0.689039I
−0.92733 + 8.91163I 0
u = 0.648459 − 0.806149I
a = 1.065950 − 0.105647I
b = −0.773273 − 0.689039I
−0.92733 − 8.91163I 0
u = −0.705187 + 0.776451I
a = −0.857316 + 0.368561I
b = 0.796547 + 0.451101I
−3.29024 − 3.05508I 0
u = −0.705187 − 0.776451I
a = −0.857316 − 0.368561I
b = 0.796547 − 0.451101I
−3.29024 + 3.05508I 0
u = 0.520207 + 0.931345I
a = 0.253538 + 0.739970I
b = −0.677677 − 0.603783I
3.72190 − 5.56725I 0
u = 0.520207 − 0.931345I
a = 0.253538 − 0.739970I
b = −0.677677 + 0.603783I
3.72190 + 5.56725I 0
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.332705 + 0.846613I
a = −0.994225 + 0.334332I
b = 1.147690 + 0.019200I
−4.05789 + 3.74836I 0
u = −0.332705 − 0.846613I
a = −0.994225 − 0.334332I
b = 1.147690 − 0.019200I
−4.05789 − 3.74836I 0
u = 0.362269 + 0.817846I
a = −0.241246 − 1.015470I
b = 0.522740 + 0.796545I
4.88494 − 0.80424I 0
u = 0.362269 − 0.817846I
a = −0.241246 + 1.015470I
b = 0.522740 − 0.796545I
4.88494 + 0.80424I 0
u = 0.640718 + 0.619636I
a = −1.130640 − 0.166942I
b = 0.673295 − 0.437255I
0.92415 + 4.09684I 0
u = 0.640718 − 0.619636I
a = −1.130640 + 0.166942I
b = 0.673295 + 0.437255I
0.92415 − 4.09684I 0
u = −0.821915 + 0.342724I
a = 0.666369 − 0.371402I
b = −0.172804 − 0.223629I
−1.34681 + 0.71674I 0
u = −0.821915 − 0.342724I
a = 0.666369 + 0.371402I
b = −0.172804 + 0.223629I
−1.34681 − 0.71674I 0
u = 0.438488 + 0.747759I
a = −0.60734 − 1.53057I
b = 0.973424 + 0.926486I
1.56612 − 8.78514I 0
u = 0.438488 − 0.747759I
a = −0.60734 + 1.53057I
b = 0.973424 − 0.926486I
1.56612 + 8.78514I 0
6
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.651090 + 0.533274I
a = −0.28816 + 1.45770I
b = 1.062210 − 0.259698I
−5.38646 + 0.84334I 0
u = −0.651090 − 0.533274I
a = −0.28816 − 1.45770I
b = 1.062210 + 0.259698I
−5.38646 − 0.84334I 0
u = −0.416063 + 0.725434I
a = 0.68573 − 1.28827I
b = −0.903118 + 0.735994I
−0.49874 + 3.40197I 0
u = −0.416063 − 0.725434I
a = 0.68573 + 1.28827I
b = −0.903118 − 0.735994I
−0.49874 − 3.40197I 0
u = 0.251562 + 0.774587I
a = 1.165860 − 0.068813I
b = −1.137790 + 0.418799I
−3.07379 + 2.21369I 0
u = 0.251562 − 0.774587I
a = 1.165860 + 0.068813I
b = −1.137790 − 0.418799I
−3.07379 − 2.21369I 0
u = 0.579115 + 0.507577I
a = 0.05747 + 1.87013I
b = −1.137540 − 0.504304I
−4.32288 − 6.26751I 0
u = 0.579115 − 0.507577I
a = 0.05747 − 1.87013I
b = −1.137540 + 0.504304I
−4.32288 + 6.26751I 0
u = 1.013290 + 0.706462I
a = −0.425669 − 0.055355I
b = 0.197913 − 0.411645I
3.19213 − 4.51638I 0
u = 1.013290 − 0.706462I
a = −0.425669 + 0.055355I
b = 0.197913 + 0.411645I
3.19213 + 4.51638I 0
7
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.935705 + 0.861076I
a = 0.293724 + 0.261994I
b = −0.468609 + 0.170672I
2.71396 − 0.69644I 0
u = 0.935705 − 0.861076I
a = 0.293724 − 0.261994I
b = −0.468609 − 0.170672I
2.71396 + 0.69644I 0
u = 1.280350 + 0.018606I
a = −1.43758 + 0.46050I
b = −0.179102 − 0.349982I
−0.30029 − 3.05301I 0
u = 1.280350 − 0.018606I
a = −1.43758 − 0.46050I
b = −0.179102 + 0.349982I
−0.30029 + 3.05301I 0
u = −1.30388
a = 0.888977
b = 0.696510
−2.58592 0
u = −1.303700 + 0.057096I
a = 0.74284 + 1.24535I
b = 0.334669 − 0.980720I
−0.740344 + 0.546849I 0
u = −1.303700 − 0.057096I
a = 0.74284 − 1.24535I
b = 0.334669 + 0.980720I
−0.740344 − 0.546849I 0
u = −0.493875 + 0.488188I
a = 0.884027 − 0.566340I
b = −0.585707 + 0.067307I
−1.18169 + 0.83074I −5.14593 − 2.98967I
u = −0.493875 − 0.488188I
a = 0.884027 + 0.566340I
b = −0.585707 − 0.067307I
−1.18169 − 0.83074I −5.14593 + 2.98967I
u = −1.322990 + 0.037419I
a = 0.419364 − 0.288008I
b = 2.24257 − 0.59888I
−5.13718 + 0.93066I 0
8
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −1.322990 − 0.037419I
a = 0.419364 + 0.288008I
b = 2.24257 + 0.59888I
−5.13718 − 0.93066I 0
u = −1.327760 + 0.089354I
a = −0.08728 + 1.59023I
b = 0.294552 − 1.028630I
−1.54532 + 6.50144I 0
u = −1.327760 − 0.089354I
a = −0.08728 − 1.59023I
b = 0.294552 + 1.028630I
−1.54532 − 6.50144I 0
u = 1.346210 + 0.060339I
a = −0.006328 + 0.929324I
b = −0.225605 − 1.369110I
−3.32385 − 2.89150I 0
u = 1.346210 − 0.060339I
a = −0.006328 − 0.929324I
b = −0.225605 + 1.369110I
−3.32385 + 2.89150I 0
u = 1.364470 + 0.020474I
a = −0.295490 − 0.214355I
b = −4.33439 + 0.52295I
−4.95461 + 3.75362I 0
u = 1.364470 − 0.020474I
a = −0.295490 + 0.214355I
b = −4.33439 − 0.52295I
−4.95461 − 3.75362I 0
u = 1.373840 + 0.099861I
a = 0.819714 + 0.934876I
b = 0.250264 − 0.590954I
−2.88115 − 3.30978I 0
u = 1.373840 − 0.099861I
a = 0.819714 − 0.934876I
b = 0.250264 + 0.590954I
−2.88115 + 3.30978I 0
u = 1.405360 + 0.131951I
a = 1.51446 + 0.37423I
b = 0.346042 + 0.380484I
−4.85566 − 8.88179I 0
9
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 1.405360 − 0.131951I
a = 1.51446 − 0.37423I
b = 0.346042 − 0.380484I
−4.85566 + 8.88179I 0
u = −1.42243 + 0.11797I
a = −1.192690 + 0.117412I
b = −0.762736 + 0.416056I
−6.25207 + 4.41292I 0
u = −1.42243 − 0.11797I
a = −1.192690 − 0.117412I
b = −0.762736 − 0.416056I
−6.25207 − 4.41292I 0
u = 1.44211 + 0.02977I
a = 0.303260 − 0.075434I
b = 4.14471 + 2.85875I
−5.17776 + 0.09499I 0
u = 1.44211 − 0.02977I
a = 0.303260 + 0.075434I
b = 4.14471 − 2.85875I
−5.17776 − 0.09499I 0
u = −1.44737 + 0.07794I
a = −0.658075 − 0.070611I
b = −1.61466 + 0.78393I
−6.17975 + 3.74343I 0
u = −1.44737 − 0.07794I
a = −0.658075 + 0.070611I
b = −1.61466 − 0.78393I
−6.17975 − 3.74343I 0
u = −1.45325 + 0.17426I
a = −0.022009 + 0.560798I
b = 1.191190 − 0.354754I
−5.88811 − 1.65848I 0
u = −1.45325 − 0.17426I
a = −0.022009 − 0.560798I
b = 1.191190 + 0.354754I
−5.88811 + 1.65848I 0
u = 1.46074 + 0.22397I
a = −0.087044 + 0.735866I
b = −1.246400 − 0.536367I
−7.30379 − 3.60572I 0
10
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 1.46074 − 0.22397I
a = −0.087044 − 0.735866I
b = −1.246400 + 0.536367I
−7.30379 + 3.60572I 0
u = 0.517939 + 0.030277I
a = −1.257170 − 0.613936I
b = 0.585738 + 0.551331I
0.80173 + 2.83553I −4.73944 − 4.73337I
u = 0.517939 − 0.030277I
a = −1.257170 + 0.613936I
b = 0.585738 − 0.551331I
0.80173 − 2.83553I −4.73944 + 4.73337I
u = −0.268706 + 0.441472I
a = 2.76472 + 1.19560I
b = 0.174119 − 0.914672I
0.49351 + 6.83165I 0.30272 − 12.02369I
u = −0.268706 − 0.441472I
a = 2.76472 − 1.19560I
b = 0.174119 + 0.914672I
0.49351 − 6.83165I 0.30272 + 12.02369I
u = −1.46682 + 0.28160I
a = 0.432061 + 0.746282I
b = 0.980677 − 0.924511I
−1.01642 + 4.71566I 0
u = −1.46682 − 0.28160I
a = 0.432061 − 0.746282I
b = 0.980677 + 0.924511I
−1.01642 − 4.71566I 0
u = 0.316309 + 0.384190I
a = −1.93029 + 1.27801I
b = −0.506253 − 0.870148I
−0.67357 − 2.60087I −3.21300 + 6.51215I
u = 0.316309 − 0.384190I
a = −1.93029 − 1.27801I
b = −0.506253 + 0.870148I
−0.67357 + 2.60087I −3.21300 − 6.51215I
u = −1.46418 + 0.35096I
a = 0.061766 − 0.696071I
b = −1.204820 − 0.108656I
−8.55069 + 2.04352I 0
11
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −1.46418 − 0.35096I
a = 0.061766 + 0.696071I
b = −1.204820 + 0.108656I
−8.55069 − 2.04352I 0
u = 1.48529 + 0.26251I
a = −0.349746 + 0.983137I
b = −1.32341 − 0.99961I
−6.67106 − 7.00396I 0
u = 1.48529 − 0.26251I
a = −0.349746 − 0.983137I
b = −1.32341 + 0.99961I
−6.67106 + 7.00396I 0
u = 0.027486 + 0.487190I
a = −0.96250 − 2.69226I
b = 0.177661 + 0.847878I
3.12289 + 1.30549I 8.69976 − 1.36522I
u = 0.027486 − 0.487190I
a = −0.96250 + 2.69226I
b = 0.177661 − 0.847878I
3.12289 − 1.30549I 8.69976 + 1.36522I
u = −1.49169 + 0.26804I
a = 0.449384 + 1.049550I
b = 1.33215 − 1.16283I
−4.69085 + 12.48030I 0
u = −1.49169 − 0.26804I
a = 0.449384 − 1.049550I
b = 1.33215 + 1.16283I
−4.69085 − 12.48030I 0
u = −1.50759 + 0.17219I
a = −0.617594 − 1.177080I
b = −1.17609 + 0.78971I
−11.1073 + 8.7748I 0
u = −1.50759 − 0.17219I
a = −0.617594 + 1.177080I
b = −1.17609 − 0.78971I
−11.1073 − 8.7748I 0
u = 0.086000 + 0.474332I
a = −2.43919 − 1.92635I
b = 0.367378 + 0.456437I
2.74605 − 4.56330I 6.84455 + 8.54463I
12
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.086000 − 0.474332I
a = −2.43919 + 1.92635I
b = 0.367378 − 0.456437I
2.74605 + 4.56330I 6.84455 − 8.54463I
u = 1.49415 + 0.33116I
a = 0.076295 − 0.792286I
b = 1.375540 + 0.230057I
−9.99282 − 8.09149I 0
u = 1.49415 − 0.33116I
a = 0.076295 + 0.792286I
b = 1.375540 − 0.230057I
−9.99282 + 8.09149I 0
u = 1.52357 + 0.17118I
a = 0.421306 − 1.094450I
b = 1.124160 + 0.649554I
−12.44990 − 3.40335I 0
u = 1.52357 − 0.17118I
a = 0.421306 + 1.094450I
b = 1.124160 − 0.649554I
−12.44990 + 3.40335I 0
u = −0.160251 + 0.432564I
a = 2.74408 − 0.38939I
b = −0.076446 − 0.185049I
1.93549 + 1.48976I 4.80637 − 4.55092I
u = −0.160251 − 0.432564I
a = 2.74408 + 0.38939I
b = −0.076446 + 0.185049I
1.93549 − 1.48976I 4.80637 + 4.55092I
u = −1.54980 + 0.09230I
a = −0.363553 − 0.522923I
b = −0.543928 + 0.839192I
−6.36585 + 3.09614I 0
u = −1.54980 − 0.09230I
a = −0.363553 + 0.522923I
b = −0.543928 − 0.839192I
−6.36585 − 3.09614I 0
u = 1.52512 + 0.30119I
a = 0.381361 − 0.948118I
b = 1.52384 + 0.96207I
−9.2312 − 12.6732I 0
13
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 1.52512 − 0.30119I
a = 0.381361 + 0.948118I
b = 1.52384 − 0.96207I
−9.2312 + 12.6732I 0
u = −1.53021 + 0.29511I
a = −0.473162 − 0.979653I
b = −1.52026 + 1.16960I
−7.1817 + 18.4464I 0
u = −1.53021 − 0.29511I
a = −0.473162 + 0.979653I
b = −1.52026 − 1.16960I
−7.1817 − 18.4464I 0
u = −0.028029 + 0.432349I
a = 1.28487 − 1.33272I
b = −0.012099 + 0.713001I
0.85731 + 1.39747I 1.09021 − 4.04698I
u = −0.028029 − 0.432349I
a = 1.28487 + 1.33272I
b = −0.012099 − 0.713001I
0.85731 − 1.39747I 1.09021 + 4.04698I
u = −1.53867 + 0.32025I
a = −0.373328 − 0.730198I
b = −1.096350 + 0.805215I
−2.93916 + 10.06180I 0
u = −1.53867 − 0.32025I
a = −0.373328 + 0.730198I
b = −1.096350 − 0.805215I
−2.93916 − 10.06180I 0
u = −0.404504 + 0.057065I
a = 0.83922 − 1.30855I
b = −0.19631 + 1.74420I
0.671600 + 0.217161I −12.32084 + 0.43118I
u = −0.404504 − 0.057065I
a = 0.83922 + 1.30855I
b = −0.19631 − 1.74420I
0.671600 − 0.217161I −12.32084 − 0.43118I
u = 1.58565 + 0.17300I
a = 0.029475 − 0.750207I
b = 0.775362 + 0.263203I
−11.13310 − 0.27637I 0
14
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 1.58565 − 0.17300I
a = 0.029475 + 0.750207I
b = 0.775362 − 0.263203I
−11.13310 + 0.27637I 0
u = 0.317229 + 0.245819I
a = −1.24995 + 0.85292I
b = −0.738382 − 0.858373I
−0.37551 − 2.54693I 1.38986 + 6.91010I
u = 0.317229 − 0.245819I
a = −1.24995 − 0.85292I
b = −0.738382 + 0.858373I
−0.37551 + 2.54693I 1.38986 − 6.91010I
u = 0.214125 + 0.331266I
a = 0.79698 − 1.33459I
b = −0.08689 + 2.01105I
−0.555437 + 0.437836I 4.35743 + 8.19634I
u = 0.214125 − 0.331266I
a = 0.79698 + 1.33459I
b = −0.08689 − 2.01105I
−0.555437 − 0.437836I 4.35743 − 8.19634I
u = −0.295460 + 0.242991I
a = −0.28861 − 1.62323I
b = −0.03817 + 2.38617I
0.03496 − 4.63924I −4.02680 − 10.12172I
u = −0.295460 − 0.242991I
a = −0.28861 + 1.62323I
b = −0.03817 − 2.38617I
0.03496 + 4.63924I −4.02680 + 10.12172I
u = −1.61960 + 0.20021I
a = 0.142144 − 0.608389I
b = −0.637498 + 0.018740I
−8.65273 − 5.12333I 0
u = −1.61960 − 0.20021I
a = 0.142144 + 0.608389I
b = −0.637498 − 0.018740I
−8.65273 + 5.12333I 0
15
II. I
u
2
= h21u
2
b + 10u
2
+ · · · + 7b + 22, a, u
3
+ u
2
− 1i
(i) Arc colorings
a
7
=
1
0
a
12
=
0
u
a
8
=
1
u
2
a
1
=
−u
u
2
+ u − 1
a
4
=
0
b
a
9
=
−u
2
+ 1
u
2
− u + 1
a
5
=
−u
2
b + bu
−2u
2
b − 2bu + 4b
a
3
=
b
b
a
2
=
3
7
u
2
+ b −
2
7
u +
1
7
10
7
u
2
+ b +
12
7
u −
6
7
a
11
=
0
u
a
10
=
−u
2
+ 1
u
2
a
6
=
u
−u
2
− u + 1
(ii) Obstruction class = 1
(iii) Cusp Shapes =
82
7
u
2
b −
71
7
bu +
19
49
u
2
−
17
7
b −
155
49
u −
262
49
16
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
5
(u
2
− u + 1)
3
c
2
(u
2
+ u + 1)
3
c
3
49(49u
6
− 7u
5
+ 29u
4
+ 18u
3
+ 15u
2
+ 4u + 1)
c
4
49(49u
6
+ 7u
5
− 6u
4
+ 15u
3
+ 2u
2
− u + 1)
c
6
(u
3
− u
2
+ 2u − 1)
2
c
7
, c
8
(u
3
+ u
2
− 1)
2
c
9
(u
3
+ 3u
2
+ 2u − 1)
2
c
10
(u
3
+ u
2
+ 2u + 1)
2
c
11
u
6
c
12
(u
3
− u
2
+ 1)
2
17
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
2
, c
5
(y
2
+ y + 1)
3
c
3
2401(2401y
6
+ 2793y
5
+ 2563y
4
+ 700y
3
+ 139y
2
+ 14y + 1)
c
4
2401(2401y
6
− 637y
5
+ 22y
4
− 137y
3
+ 22y
2
+ 3y + 1)
c
6
, c
10
(y
3
+ 3y
2
+ 2y −1)
2
c
7
, c
8
, c
12
(y
3
− y
2
+ 2y −1)
2
c
9
(y
3
− 5y
2
+ 10y −1)
2
c
11
y
6
18
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.877439 + 0.744862I
a = 0
b = 0.171467 + 0.353309I
3.02413 + 4.85801I −7.94313 − 10.82265I
u = −0.877439 + 0.744862I
a = 0
b = 0.220241 − 0.325149I
3.02413 + 0.79824I 7.13283 − 3.60755I
u = −0.877439 − 0.744862I
a = 0
b = 0.171467 − 0.353309I
3.02413 − 4.85801I −7.94313 + 10.82265I
u = −0.877439 − 0.744862I
a = 0
b = 0.220241 + 0.325149I
3.02413 − 0.79824I 7.13283 + 3.60755I
u = 0.754878
a = 0
b = −0.463136 + 0.802176I
−1.11345 + 2.02988I −5.93460 − 2.73535I
u = 0.754878
a = 0
b = −0.463136 − 0.802176I
−1.11345 − 2.02988I −5.93460 + 2.73535I
19
III. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
((u
2
− u + 1)
3
)(u
109
+ 50u
108
+ ··· − 9999u − 2401)
c
2
((u
2
+ u + 1)
3
)(u
109
+ 4u
108
+ ··· − 551u − 49)
c
3
2401(49u
6
− 7u
5
+ 29u
4
+ 18u
3
+ 15u
2
+ 4u + 1)
· (49u
109
+ 42u
108
+ ··· − 1346644u − 153031)
c
4
2401(49u
6
+ 7u
5
− 6u
4
+ 15u
3
+ 2u
2
− u + 1)
· (49u
109
+ 154u
108
+ ··· + 18492416u + 1398784)
c
5
((u
2
− u + 1)
3
)(u
109
+ 4u
108
+ ··· − 551u − 49)
c
6
((u
3
− u
2
+ 2u − 1)
2
)(u
109
+ 3u
108
+ ··· + 6u + 1)
c
7
, c
8
((u
3
+ u
2
− 1)
2
)(u
109
+ 3u
108
+ ··· + 2u
2
+ 1)
c
9
((u
3
+ 3u
2
+ 2u − 1)
2
)(u
109
− 49u
108
+ ··· − 4u + 1)
c
10
((u
3
+ u
2
+ 2u + 1)
2
)(u
109
+ 3u
108
+ ··· + 6u + 1)
c
11
u
6
(u
109
− 5u
108
+ ··· + 48608u + 21952)
c
12
((u
3
− u
2
+ 1)
2
)(u
109
+ 3u
108
+ ··· + 2u
2
+ 1)
20
IV. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
((y
2
+ y + 1)
3
)(y
109
+ 22y
108
+ ··· + 1.86533 × 10
7
y −5764801)
c
2
, c
5
((y
2
+ y + 1)
3
)(y
109
+ 50y
108
+ ··· − 9999y −2401)
c
3
5764801(2401y
6
+ 2793y
5
+ 2563y
4
+ 700y
3
+ 139y
2
+ 14y + 1)
· (2401y
109
− 163660y
108
+ ··· − 913616530238y −23418486961)
c
4
5764801(2401y
6
− 637y
5
+ 22y
4
− 137y
3
+ 22y
2
+ 3y + 1)
· (2401y
109
+ 1666y
108
+ ··· + 9951035523072y −1956596678656)
c
6
, c
10
((y
3
+ 3y
2
+ 2y −1)
2
)(y
109
+ 49y
108
+ ··· − 4y −1)
c
7
, c
8
, c
12
((y
3
− y
2
+ 2y −1)
2
)(y
109
− 103y
108
+ ··· − 4y −1)
c
9
((y
3
− 5y
2
+ 10y −1)
2
)(y
109
+ 25y
108
+ ··· + 72y −1)
c
11
y
6
(y
109
+ 35y
108
+ ··· − 3.91167 × 10
9
y −4.81890 × 10
8
)
21
