12n
0705
(K12n
0705
)
A knot diagram
1
Linearized knot diagam
4 11 7 8 11 2 1 12 2 7 9 5
Solving Sequence
2,11 3,7
4 1 6 5 10 9 12 8
c
2
c
3
c
1
c
6
c
5
c
10
c
9
c
11
c
8
c
4
, c
7
, c
12
Ideals for irreducible components
2
of X
par
I
u
1
= h2.19181 × 10
382
u
75
+ 6.42258 × 10
381
u
74
+ ··· + 4.60404 × 10
387
b + 1.33471 × 10
388
,
− 2.21394 × 10
388
u
75
+ 1.64912 × 10
388
u
74
+ ··· + 7.19321 × 10
392
a − 4.98498 × 10
393
,
u
76
− u
75
+ ··· − 23760u + 74007i
I
u
2
= h−149224377175319u
21
+ 98709240274610u
20
+ ··· + 96703178408689b − 82488765402898,
360716486705467u
21
− 113938156490740u
20
+ ··· + 96703178408689a + 729010725759272,
u
22
+ 6u
20
+ ··· + 3u + 1i
* 2 irreducible components of dim
C
= 0, with total 98 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
= h2.19 × 10
382
u
75
+ 6.42 × 10
381
u
74
+ · · · + 4.60 × 10
387
b + 1.33 ×
10
388
, −2.21 × 10
388
u
75
+ 1.65 × 10
388
u
74
+ · · · + 7.19 × 10
392
a − 4.98 ×
10
393
, u
76
− u
75
+ · · · − 23760u + 74007i
(i) Arc colorings
a
2
=
1
0
a
11
=
0
u
a
3
=
1
u
2
a
7
=
0.0000307782u
75
− 0.0000229260u
74
+ ··· + 20.3789u + 6.93012
−4.76062 × 10
−6
u
75
− 1.39499 × 10
−6
u
74
+ ··· − 0.757161u − 2.89899
a
4
=
−7.78630 × 10
−6
u
75
− 1.40375 × 10
−6
u
74
+ ··· + 0.0566661u − 7.56840
−9.12142 × 10
−6
u
75
+ 8.62552 × 10
−6
u
74
+ ··· − 5.37177u + 1.51302
a
1
=
−0.0000221139u
75
+ 0.0000317720u
74
+ ··· − 22.3602u + 6.91672
6.38702 × 10
−6
u
75
− 3.29061 × 10
−6
u
74
+ ··· + 6.79986u + 0.825307
a
6
=
0.0000260176u
75
− 0.0000243210u
74
+ ··· + 19.6217u + 4.03113
−4.76062 × 10
−6
u
75
− 1.39499 × 10
−6
u
74
+ ··· − 0.757161u − 2.89899
a
5
=
0.0000260176u
75
− 0.0000243210u
74
+ ··· + 19.6217u + 4.03113
−6.93011 × 10
−6
u
75
+ 1.21906 × 10
−6
u
74
+ ··· − 2.64233u − 3.02455
a
10
=
−6.72650 × 10
−6
u
75
+ 0.0000218094u
74
+ ··· − 13.5272u + 11.5689
8.76516 × 10
−6
u
75
− 0.0000117617u
74
+ ··· + 10.6096u − 1.69248
a
9
=
2.03866 × 10
−6
u
75
+ 0.0000100477u
74
+ ··· − 2.91766u + 9.87645
8.76516 × 10
−6
u
75
− 0.0000117617u
74
+ ··· + 10.6096u − 1.69248
a
12
=
−0.0000523639u
75
+ 0.0000528643u
74
+ ··· − 39.9625u − 1.49577
8.63617 × 10
−6
u
75
− 3.40978 × 10
−6
u
74
+ ··· + 3.57479u + 4.99056
a
8
=
0.0000265357u
75
− 0.0000320384u
74
+ ··· + 27.2940u − 5.37665
−0.0000162618u
75
+ 0.0000181990u
74
+ ··· − 12.7453u + 0.0118103
(ii) Obstruction class = −1
(iii) Cusp Shapes = 0.0000191588u
75
− 0.0000387698u
74
+ ··· − 0.636809u − 2.73074
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
76
− 10u
75
+ ··· − 221u + 17
c
2
u
76
− u
75
+ ··· − 23760u + 74007
c
3
u
76
+ 2u
75
+ ··· − 19464u + 3677
c
4
u
76
− 2u
75
+ ··· + 549u + 207
c
5
u
76
− u
75
+ ··· + 34842166u + 3425393
c
6
u
76
+ 53u
74
+ ··· + 7437u + 763
c
7
u
76
− 7u
75
+ ··· + 27u + 1
c
8
, c
11
u
76
− 9u
75
+ ··· − 362u + 19
c
9
u
76
− 8u
75
+ ··· + 57253563u + 3204791
c
10
u
76
− 9u
75
+ ··· − 530u + 1279
c
12
u
76
− 6u
75
+ ··· + 78u + 35
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
76
+ 18y
75
+ ··· − 2227y + 289
c
2
y
76
+ 93y
75
+ ··· + 236846070036y + 5477036049
c
3
y
76
+ 20y
75
+ ··· + 475032998y + 13520329
c
4
y
76
− 14y
75
+ ··· − 1120293y + 42849
c
5
y
76
− 57y
75
+ ··· − 439239317966814y + 11733317204449
c
6
y
76
+ 106y
75
+ ··· + 5285439y + 582169
c
7
y
76
+ 15y
75
+ ··· − 7y + 1
c
8
, c
11
y
76
+ 63y
75
+ ··· + 208y + 361
c
9
y
76
+ 128y
75
+ ··· + 7840289593898607y + 10270685353681
c
10
y
76
− 105y
75
+ ··· − 4524622y + 1635841
c
12
y
76
− 8y
75
+ ··· − 58374y + 1225
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 1.009200 + 0.019949I
a = −0.755402 + 0.769566I
b = −0.141359 − 0.446045I
0.24108 − 3.09498I −7.87234 + 7.34515I
u = 1.009200 − 0.019949I
a = −0.755402 − 0.769566I
b = −0.141359 + 0.446045I
0.24108 + 3.09498I −7.87234 − 7.34515I
u = −0.165558 + 0.962769I
a = −0.682721 + 0.385052I
b = −0.846371 − 0.090077I
−1.18877 + 0.93128I −6.34635 − 7.99915I
u = −0.165558 − 0.962769I
a = −0.682721 − 0.385052I
b = −0.846371 + 0.090077I
−1.18877 − 0.93128I −6.34635 + 7.99915I
u = −0.895115 + 0.388201I
a = −0.560008 + 0.114830I
b = −0.259160 + 0.201495I
−1.46389 + 0.73897I −3.77155 + 0.I
u = −0.895115 − 0.388201I
a = −0.560008 − 0.114830I
b = −0.259160 − 0.201495I
−1.46389 − 0.73897I −3.77155 + 0.I
u = 0.810100 + 0.696527I
a = −0.338242 + 0.436580I
b = 0.218121 + 0.101852I
4.06725 − 2.79115I 0
u = 0.810100 − 0.696527I
a = −0.338242 − 0.436580I
b = 0.218121 − 0.101852I
4.06725 + 2.79115I 0
u = 0.564725 + 0.948830I
a = −0.645295 − 0.262477I
b = 0.150567 − 0.619486I
3.85710 − 3.89576I 0
u = 0.564725 − 0.948830I
a = −0.645295 + 0.262477I
b = 0.150567 + 0.619486I
3.85710 + 3.89576I 0
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.046617 + 1.142370I
a = −0.63482 + 2.26238I
b = 0.79960 − 2.66733I
4.62267 + 0.14372I 0
u = 0.046617 − 1.142370I
a = −0.63482 − 2.26238I
b = 0.79960 + 2.66733I
4.62267 − 0.14372I 0
u = 1.150780 + 0.219130I
a = 0.522685 + 0.399011I
b = −0.094055 − 0.540195I
−0.65964 − 4.41450I 0
u = 1.150780 − 0.219130I
a = 0.522685 − 0.399011I
b = −0.094055 + 0.540195I
−0.65964 + 4.41450I 0
u = −0.592031 + 0.568502I
a = 1.33340 − 0.84287I
b = −0.193442 + 0.277813I
−1.42596 − 3.59118I −1.75527 + 3.21770I
u = −0.592031 − 0.568502I
a = 1.33340 + 0.84287I
b = −0.193442 − 0.277813I
−1.42596 + 3.59118I −1.75527 − 3.21770I
u = 1.164960 + 0.183393I
a = −0.472076 + 0.327161I
b = −1.356770 + 0.193388I
0.967603 − 0.985142I 0
u = 1.164960 − 0.183393I
a = −0.472076 − 0.327161I
b = −1.356770 − 0.193388I
0.967603 + 0.985142I 0
u = −0.520526 + 0.633146I
a = −0.375631 + 0.423504I
b = 1.47986 + 0.80086I
2.52872 − 8.60121I 1.83866 + 3.84455I
u = −0.520526 − 0.633146I
a = −0.375631 − 0.423504I
b = 1.47986 − 0.80086I
2.52872 + 8.60121I 1.83866 − 3.84455I
6
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.294916 + 0.746389I
a = 1.98912 − 0.26808I
b = −0.433848 − 0.020928I
3.01635 + 9.32304I 3.19894 − 5.62741I
u = 0.294916 − 0.746389I
a = 1.98912 + 0.26808I
b = −0.433848 + 0.020928I
3.01635 − 9.32304I 3.19894 + 5.62741I
u = −0.771153 + 0.130660I
a = −1.040020 − 0.437054I
b = −0.083499 − 0.951857I
4.69688 − 2.57649I 1.57467 + 2.30402I
u = −0.771153 − 0.130660I
a = −1.040020 + 0.437054I
b = −0.083499 + 0.951857I
4.69688 + 2.57649I 1.57467 − 2.30402I
u = 0.131578 + 0.739838I
a = −1.68627 − 0.52919I
b = 1.321970 − 0.419785I
4.44676 + 0.47633I 7.82049 − 1.23300I
u = 0.131578 − 0.739838I
a = −1.68627 + 0.52919I
b = 1.321970 + 0.419785I
4.44676 − 0.47633I 7.82049 + 1.23300I
u = −0.365970 + 0.650492I
a = −0.923300 + 0.352826I
b = −0.405458 + 0.239034I
−1.30459 + 1.15321I −3.91266 − 5.89962I
u = −0.365970 − 0.650492I
a = −0.923300 − 0.352826I
b = −0.405458 − 0.239034I
−1.30459 − 1.15321I −3.91266 + 5.89962I
u = 0.027626 + 1.265550I
a = −0.18747 + 1.64404I
b = 0.41367 − 2.13372I
4.64117 + 0.14396I 0
u = 0.027626 − 1.265550I
a = −0.18747 − 1.64404I
b = 0.41367 + 2.13372I
4.64117 − 0.14396I 0
7
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −1.050630 + 0.743716I
a = −0.260234 − 0.008456I
b = −1.151120 − 0.614051I
−0.025364 − 0.694709I 0
u = −1.050630 − 0.743716I
a = −0.260234 + 0.008456I
b = −1.151120 + 0.614051I
−0.025364 + 0.694709I 0
u = 0.966250 + 0.854364I
a = 0.030557 + 0.171811I
b = 0.284472 − 0.438444I
4.18587 − 3.26120I 0
u = 0.966250 − 0.854364I
a = 0.030557 − 0.171811I
b = 0.284472 + 0.438444I
4.18587 + 3.26120I 0
u = −0.030321 + 0.608824I
a = −0.377141 − 0.458763I
b = 1.236080 − 0.334684I
−1.19917 + 5.41165I 1.34156 − 7.26392I
u = −0.030321 − 0.608824I
a = −0.377141 + 0.458763I
b = 1.236080 + 0.334684I
−1.19917 − 5.41165I 1.34156 + 7.26392I
u = 0.356043 + 0.423213I
a = −2.08467 − 0.32556I
b = −0.069706 + 0.303853I
0.24691 + 2.62762I 0.32414 − 5.86582I
u = 0.356043 − 0.423213I
a = −2.08467 + 0.32556I
b = −0.069706 − 0.303853I
0.24691 − 2.62762I 0.32414 + 5.86582I
u = −0.24387 + 1.47515I
a = 0.017377 − 1.220120I
b = 0.44822 + 1.78089I
11.22230 + 0.28649I 0
u = −0.24387 − 1.47515I
a = 0.017377 + 1.220120I
b = 0.44822 − 1.78089I
11.22230 − 0.28649I 0
8
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.327271 + 0.358349I
a = −0.886714 − 0.274566I
b = −1.045100 + 0.416367I
−1.90605 + 1.11051I 2.44459 + 0.53234I
u = −0.327271 − 0.358349I
a = −0.886714 + 0.274566I
b = −1.045100 − 0.416367I
−1.90605 − 1.11051I 2.44459 − 0.53234I
u = −1.42583 + 0.57546I
a = 0.498504 + 0.022033I
b = 0.479276 + 0.563280I
4.46008 + 9.11025I 0
u = −1.42583 − 0.57546I
a = 0.498504 − 0.022033I
b = 0.479276 − 0.563280I
4.46008 − 9.11025I 0
u = 0.250236 + 0.342228I
a = −1.226160 + 0.462405I
b = 0.309303 + 0.470318I
1.39381 + 0.89309I 4.09738 − 0.87482I
u = 0.250236 − 0.342228I
a = −1.226160 − 0.462405I
b = 0.309303 − 0.470318I
1.39381 − 0.89309I 4.09738 + 0.87482I
u = −0.30462 + 1.58289I
a = −0.159862 − 0.920028I
b = −0.20723 + 1.71520I
3.23935 + 3.92724I 0
u = −0.30462 − 1.58289I
a = −0.159862 + 0.920028I
b = −0.20723 − 1.71520I
3.23935 − 3.92724I 0
u = 0.44818 + 1.58154I
a = 0.414772 − 0.918491I
b = 0.52106 + 1.85961I
11.27930 − 1.44429I 0
u = 0.44818 − 1.58154I
a = 0.414772 + 0.918491I
b = 0.52106 − 1.85961I
11.27930 + 1.44429I 0
9
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.017872 + 0.303347I
a = 3.82605 + 1.87714I
b = −1.132580 + 0.363636I
3.42718 − 1.06387I 2.11989 − 0.34485I
u = −0.017872 − 0.303347I
a = 3.82605 − 1.87714I
b = −1.132580 − 0.363636I
3.42718 + 1.06387I 2.11989 + 0.34485I
u = 0.25994 + 1.72565I
a = 0.109906 + 1.123310I
b = −0.39160 − 2.11059I
12.4056 − 6.9129I 0
u = 0.25994 − 1.72565I
a = 0.109906 − 1.123310I
b = −0.39160 + 2.11059I
12.4056 + 6.9129I 0
u = 0.27832 + 1.76522I
a = 0.022137 − 1.136350I
b = 0.43502 + 1.99701I
13.3454 − 7.9741I 0
u = 0.27832 − 1.76522I
a = 0.022137 + 1.136350I
b = 0.43502 − 1.99701I
13.3454 + 7.9741I 0
u = 0.54424 + 1.73484I
a = −0.126901 + 1.035400I
b = −0.05331 − 1.76815I
6.10244 − 3.92680I 0
u = 0.54424 − 1.73484I
a = −0.126901 − 1.035400I
b = −0.05331 + 1.76815I
6.10244 + 3.92680I 0
u = −0.08745 + 1.81957I
a = 0.183051 − 0.960988I
b = −0.02671 + 1.86706I
8.17378 + 5.03717I 0
u = −0.08745 − 1.81957I
a = 0.183051 + 0.960988I
b = −0.02671 − 1.86706I
8.17378 − 5.03717I 0
10
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.44832 + 1.79678I
a = 0.011918 − 1.072770I
b = 0.23871 + 1.75816I
6.36319 − 10.94220I 0
u = 0.44832 − 1.79678I
a = 0.011918 + 1.072770I
b = 0.23871 − 1.75816I
6.36319 + 10.94220I 0
u = 0.33240 + 1.86146I
a = −0.052763 + 0.804686I
b = −0.52702 − 2.08999I
8.73089 − 7.50113I 0
u = 0.33240 − 1.86146I
a = −0.052763 − 0.804686I
b = −0.52702 + 2.08999I
8.73089 + 7.50113I 0
u = −0.48571 + 1.83508I
a = −0.079389 + 1.054680I
b = −0.17441 − 1.45972I
8.82884 + 2.54421I 0
u = −0.48571 − 1.83508I
a = −0.079389 − 1.054680I
b = −0.17441 + 1.45972I
8.82884 − 2.54421I 0
u = −0.12198 + 1.91973I
a = −0.088250 + 1.035080I
b = 0.07581 − 1.61679I
8.04212 + 1.07975I 0
u = −0.12198 − 1.91973I
a = −0.088250 − 1.035080I
b = 0.07581 + 1.61679I
8.04212 − 1.07975I 0
u = −0.53576 + 1.86215I
a = 0.079592 + 1.028730I
b = 0.39767 − 2.06815I
12.2627 + 16.8504I 0
u = −0.53576 − 1.86215I
a = 0.079592 − 1.028730I
b = 0.39767 + 2.06815I
12.2627 − 16.8504I 0
11
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.12813 + 2.03521I
a = −0.082429 − 0.921487I
b = −0.36312 + 1.77545I
13.2288 + 5.7083I 0
u = 0.12813 − 2.03521I
a = −0.082429 + 0.921487I
b = −0.36312 − 1.77545I
13.2288 − 5.7083I 0
u = −0.17018 + 2.10478I
a = 0.177794 + 0.752992I
b = 0.49529 − 1.96195I
12.29870 − 3.68520I 0
u = −0.17018 − 2.10478I
a = 0.177794 − 0.752992I
b = 0.49529 + 1.96195I
12.29870 + 3.68520I 0
u = −0.60072 + 2.06916I
a = −0.125600 − 0.868073I
b = −0.34884 + 2.04283I
9.43831 + 8.00299I 0
u = −0.60072 − 2.06916I
a = −0.125600 + 0.868073I
b = −0.34884 − 2.04283I
9.43831 − 8.00299I 0
12
II.
I
u
2
= h−1.49×10
14
u
21
+9.87×10
13
u
20
+· · ·+9.67×10
13
b−8.25×10
13
, 3.61×
10
14
u
21
−1.14×10
14
u
20
+· · ·+9.67×10
13
a+7.29×10
14
, u
22
+6u
20
+· · ·+3u+1i
(i) Arc colorings
a
2
=
1
0
a
11
=
0
u
a
3
=
1
u
2
a
7
=
−3.73014u
21
+ 1.17823u
20
+ ··· − 5.77790u − 7.53864
1.54312u
21
− 1.02074u
20
+ ··· + 3.61870u + 0.853010
a
4
=
2.80559u
21
− 0.613746u
20
+ ··· + 3.94605u + 7.99627
−1.59401u
21
+ 0.617282u
20
+ ··· − 2.45622u − 2.03309
a
1
=
2.43638u
21
− 1.64663u
20
+ ··· + 4.38963u + 0.101156
2.86235u
21
− 1.16568u
20
+ ··· + 4.78482u + 5.72462
a
6
=
−2.18702u
21
+ 0.157481u
20
+ ··· − 2.15920u − 6.68563
1.54312u
21
− 1.02074u
20
+ ··· + 3.61870u + 0.853010
a
5
=
−2.18702u
21
+ 0.157481u
20
+ ··· − 2.15920u − 6.68563
1.66941u
21
− 1.23031u
20
+ ··· + 5.33328u + 0.695529
a
10
=
2.78514u
21
− 1.62442u
20
+ ··· + 9.90008u + 3.76942
1.36682u
21
− 0.449827u
20
+ ··· + 4.50861u + 4.43001
a
9
=
4.15196u
21
− 2.07424u
20
+ ··· + 14.4087u + 8.19943
1.36682u
21
− 0.449827u
20
+ ··· + 4.50861u + 4.43001
a
12
=
−4.30959u
21
+ 1.04490u
20
+ ··· − 9.47528u − 13.1314
0.804486u
21
− 0.868380u
20
+ ··· + 3.26438u − 1.10562
a
8
=
−0.963368u
21
+ 1.38410u
20
+ ··· − 2.10831u + 3.97684
−3.61664u
21
+ 1.69124u
20
+ ··· − 7.01111u − 5.08948
(ii) Obstruction class = 1
(iii) Cusp Shapes
= −
1686035164509931
96703178408689
u
21
+
901461064070090
96703178408689
u
20
+ ··· −
76450416088126
2358614107529
u −
3061925079195016
96703178408689
13
(iv) u-Polynomials at the component
14
Crossings u-Polynomials at each crossing
c
1
u
22
− 9u
21
+ ··· − 10u + 1
c
2
u
22
+ 6u
20
+ ··· + 3u + 1
c
3
u
22
+ u
21
+ ··· − 41u + 5
c
4
u
22
− 5u
21
+ ··· − 2u + 3
c
5
u
22
− 7u
20
+ ··· − 17u + 5
c
6
u
22
+ 9u
21
+ ··· − 2u + 1
c
7
u
22
+ 4u
21
+ ··· + 4u + 1
c
8
u
22
− 4u
21
+ ··· − 59u + 7
c
9
u
22
+ 31u
21
+ ··· − 6u + 1
c
10
u
22
− 8u
21
+ ··· − 13u + 3
c
11
u
22
+ 4u
21
+ ··· + 59u + 7
c
12
u
22
− 7u
21
+ ··· + 9u + 1
15
16
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
22
− 3y
21
+ ··· + 26y + 1
c
2
y
22
+ 12y
21
+ ··· − 15y + 1
c
3
y
22
− 5y
21
+ ··· + 119y + 25
c
4
y
22
+ y
21
+ ··· + 8y + 9
c
5
y
22
− 14y
21
+ ··· − 449y + 25
c
6
y
22
+ 13y
21
+ ··· + 224y + 1
c
7
y
22
+ 14y
21
+ ··· + 14y + 1
c
8
, c
11
y
22
+ 18y
21
+ ··· − 51y + 49
c
9
y
22
− 421y
21
+ ··· − 16y + 1
c
10
y
22
− 18y
21
+ ··· + 35y + 9
c
12
y
22
− y
21
+ ··· − 5y + 1
17
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.951034 + 0.134444I
a = 0.605350 + 1.006750I
b = −0.107028 − 0.680421I
0.79970 + 2.99966I 6.51980 − 4.32864I
u = −0.951034 − 0.134444I
a = 0.605350 − 1.006750I
b = −0.107028 + 0.680421I
0.79970 − 2.99966I 6.51980 + 4.32864I
u = 0.054801 + 1.050180I
a = −2.33429 + 2.96337I
b = 2.37282 − 3.26912I
4.72694 + 0.15173I 81.0248 + 14.3588I
u = 0.054801 − 1.050180I
a = −2.33429 − 2.96337I
b = 2.37282 + 3.26912I
4.72694 − 0.15173I 81.0248 − 14.3588I
u = 0.394378 + 1.036170I
a = 0.529717 + 0.484241I
b = 0.891472 − 0.443374I
−1.121450 − 0.412393I −3.86761 − 5.50321I
u = 0.394378 − 1.036170I
a = 0.529717 − 0.484241I
b = 0.891472 + 0.443374I
−1.121450 + 0.412393I −3.86761 + 5.50321I
u = −0.705719 + 0.514320I
a = 1.141760 − 0.226080I
b = 0.820094 − 0.039020I
−0.58337 − 2.20721I −7.14382 + 5.39648I
u = −0.705719 − 0.514320I
a = 1.141760 + 0.226080I
b = 0.820094 + 0.039020I
−0.58337 + 2.20721I −7.14382 − 5.39648I
u = 1.150040 + 0.122620I
a = 0.501064 − 0.269186I
b = 1.38047 − 0.53268I
1.142400 − 0.428165I −0.33704 − 3.69823I
u = 1.150040 − 0.122620I
a = 0.501064 + 0.269186I
b = 1.38047 + 0.53268I
1.142400 + 0.428165I −0.33704 + 3.69823I
18
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.769922 + 0.872233I
a = 0.393736 + 0.406091I
b = −0.0213916 + 0.0853977I
3.60622 − 3.26427I −6.14063 + 0.76896I
u = 0.769922 − 0.872233I
a = 0.393736 − 0.406091I
b = −0.0213916 − 0.0853977I
3.60622 + 3.26427I −6.14063 − 0.76896I
u = −0.706428 + 0.363074I
a = 0.393152 − 0.102422I
b = 0.929325 − 0.401157I
−2.32161 + 1.24252I −16.7069 − 5.8630I
u = −0.706428 − 0.363074I
a = 0.393152 + 0.102422I
b = 0.929325 + 0.401157I
−2.32161 − 1.24252I −16.7069 + 5.8630I
u = 0.530753 + 0.117442I
a = 0.11104 − 1.74126I
b = −0.779379 + 0.428668I
−2.25567 + 4.82318I −6.03196 − 5.94405I
u = 0.530753 − 0.117442I
a = 0.11104 + 1.74126I
b = −0.779379 − 0.428668I
−2.25567 − 4.82318I −6.03196 + 5.94405I
u = −0.449674 + 0.157084I
a = −0.20238 − 2.18846I
b = −1.157300 + 0.217672I
1.54910 + 9.74946I −3.15022 − 8.05150I
u = −0.449674 − 0.157084I
a = −0.20238 + 2.18846I
b = −1.157300 − 0.217672I
1.54910 − 9.74946I −3.15022 + 8.05150I
u = −0.34131 + 1.81217I
a = −0.115503 + 1.041120I
b = −0.18866 − 1.53705I
8.66862 + 2.29552I −0.26375 + 5.19421I
u = −0.34131 − 1.81217I
a = −0.115503 − 1.041120I
b = −0.18866 + 1.53705I
8.66862 − 2.29552I −0.26375 − 5.19421I
19
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.25428 + 1.98779I
a = −0.023650 − 0.890837I
b = 0.35958 + 2.02401I
10.46310 − 7.23363I 3.59733 + 5.30923I
u = 0.25428 − 1.98779I
a = −0.023650 + 0.890837I
b = 0.35958 − 2.02401I
10.46310 + 7.23363I 3.59733 − 5.30923I
20
III. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
(u
22
− 9u
21
+ ··· − 10u + 1)(u
76
− 10u
75
+ ··· − 221u + 17)
c
2
(u
22
+ 6u
20
+ ··· + 3u + 1)(u
76
− u
75
+ ··· − 23760u + 74007)
c
3
(u
22
+ u
21
+ ··· − 41u + 5)(u
76
+ 2u
75
+ ··· − 19464u + 3677)
c
4
(u
22
− 5u
21
+ ··· − 2u + 3)(u
76
− 2u
75
+ ··· + 549u + 207)
c
5
(u
22
− 7u
20
+ ··· − 17u + 5)(u
76
− u
75
+ ··· + 3.48422 × 10
7
u + 3425393)
c
6
(u
22
+ 9u
21
+ ··· − 2u + 1)(u
76
+ 53u
74
+ ··· + 7437u + 763)
c
7
(u
22
+ 4u
21
+ ··· + 4u + 1)(u
76
− 7u
75
+ ··· + 27u + 1)
c
8
(u
22
− 4u
21
+ ··· − 59u + 7)(u
76
− 9u
75
+ ··· − 362u + 19)
c
9
(u
22
+ 31u
21
+ ··· − 6u + 1)
· (u
76
− 8u
75
+ ··· + 57253563u + 3204791)
c
10
(u
22
− 8u
21
+ ··· − 13u + 3)(u
76
− 9u
75
+ ··· − 530u + 1279)
c
11
(u
22
+ 4u
21
+ ··· + 59u + 7)(u
76
− 9u
75
+ ··· − 362u + 19)
c
12
(u
22
− 7u
21
+ ··· + 9u + 1)(u
76
− 6u
75
+ ··· + 78u + 35)
21
IV. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
(y
22
− 3y
21
+ ··· + 26y + 1)(y
76
+ 18y
75
+ ··· − 2227y + 289)
c
2
(y
22
+ 12y
21
+ ··· − 15y + 1)
· (y
76
+ 93y
75
+ ··· + 236846070036y + 5477036049)
c
3
(y
22
− 5y
21
+ ··· + 119y + 25)
· (y
76
+ 20y
75
+ ··· + 475032998y + 13520329)
c
4
(y
22
+ y
21
+ ··· + 8y + 9)(y
76
− 14y
75
+ ··· − 1120293y + 42849)
c
5
(y
22
− 14y
21
+ ··· − 449y + 25)
· (y
76
− 57y
75
+ ··· − 439239317966814y + 11733317204449)
c
6
(y
22
+ 13y
21
+ ··· + 224y + 1)
· (y
76
+ 106y
75
+ ··· + 5285439y + 582169)
c
7
(y
22
+ 14y
21
+ ··· + 14y + 1)(y
76
+ 15y
75
+ ··· − 7y + 1)
c
8
, c
11
(y
22
+ 18y
21
+ ··· − 51y + 49)(y
76
+ 63y
75
+ ··· + 208y + 361)
c
9
(y
22
− 421y
21
+ ··· − 16y + 1)
· (y
76
+ 128y
75
+ ··· + 7840289593898607y + 10270685353681)
c
10
(y
22
− 18y
21
+ ··· + 35y + 9)
· (y
76
− 105y
75
+ ··· − 4524622y + 1635841)
c
12
(y
22
− y
21
+ ··· − 5y + 1)(y
76
− 8y
75
+ ··· − 58374y + 1225)
22
