12a
1141
(K12a
1141
)
A knot diagram
1
Linearized knot diagam
4 8 9 11 10 12 2 3 6 1 7 5
Solving Sequence
2,8
3 9
4,11
5 1 7 12 6 10
c
2
c
8
c
3
c
4
c
1
c
7
c
11
c
6
c
10
c
5
, c
9
, c
12
Ideals for irreducible components
2
of X
par
I
u
1
= h−1.16393 × 10
80
u
98
+ 1.96153 × 10
80
u
97
+ ··· + 1.45806 × 10
80
b − 1.44154 × 10
81
,
2.69483 × 10
80
u
98
+ 2.63977 × 10
81
u
97
+ ··· + 1.02064 × 10
81
a − 2.84283 × 10
82
, u
99
+ u
98
+ ··· − 18u + 7i
I
u
2
= h−u
14
+ u
13
+ 8u
12
− 7u
11
− 24u
10
+ 16u
9
+ 35u
8
− 10u
7
− 31u
6
− 7u
5
+ 21u
4
+ 8u
3
− 6u
2
+ b − 4u + 1,
− 2u
14
+ u
13
+ ··· + a + 1,
u
16
− 10u
14
+ 39u
12
+ u
11
− 74u
10
− 8u
9
+ 71u
8
+ 23u
7
− 38u
6
− 28u
5
+ 18u
4
+ 13u
3
− 4u
2
− 2u + 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
= h−1.16×10
80
u
98
+1.96×10
80
u
97
+· · ·+1.46×10
80
b−1.44×10
81
, 2.69×
10
80
u
98
+2.64×10
81
u
97
+· · ·+1.02×10
81
a−2.84×10
82
, u
99
+u
98
+· · ·−18u+7i
(i) Arc colorings
a
2
=
1
0
a
8
=
0
u
a
3
=
1
u
2
a
9
=
−u
−u
3
+ u
a
4
=
−u
2
+ 1
−u
4
+ 2u
2
a
11
=
−0.264033u
98
− 2.58639u
97
+ ··· − 24.9570u + 27.8534
0.798272u
98
− 1.34530u
97
+ ··· − 18.0941u + 9.88675
a
5
=
0.833020u
98
− 1.92704u
97
+ ··· − 27.1985u + 23.2113
1.31877u
98
− 1.84396u
97
+ ··· − 38.6806u + 21.8148
a
1
=
−u
6
+ 3u
4
− 2u
2
+ 1
−u
8
+ 4u
6
− 4u
4
a
7
=
u
u
a
12
=
−0.00205647u
98
− 2.51782u
97
+ ··· − 29.1751u + 26.6019
1.06025u
98
− 1.27673u
97
+ ··· − 22.3122u + 8.63527
a
6
=
0.514009u
98
+ 1.64940u
97
+ ··· + 14.5324u − 20.0768
−0.502672u
98
+ 1.10075u
97
+ ··· + 15.7291u − 8.88776
a
10
=
0.370327u
98
− 2.17342u
97
+ ··· − 29.7554u + 24.1137
1.00004u
98
− 1.94343u
97
+ ··· − 28.8770u + 14.8644
(ii) Obstruction class = −1
(iii) Cusp Shapes = 4.35878u
98
+ 7.93657u
97
+ ··· + 50.8346u − 78.6235
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
99
− 23u
98
+ ··· + 738442u − 80017
c
2
, c
3
, c
7
c
8
u
99
+ u
98
+ ··· − 18u + 7
c
4
u
99
+ 2u
97
+ ··· + 270u + 25
c
5
, c
9
u
99
+ 2u
98
+ ··· + 1662u + 229
c
6
, c
11
u
99
+ u
98
+ ··· − u + 7
c
10
u
99
+ 13u
98
+ ··· − 4180u − 1361
c
12
u
99
− 5u
98
+ ··· − 3u + 5
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
99
+ 19y
98
+ ··· − 55556666826y −6402720289
c
2
, c
3
, c
7
c
8
y
99
− 113y
98
+ ··· + 954y −49
c
4
y
99
+ 4y
98
+ ··· + 11450y −625
c
5
, c
9
y
99
+ 64y
98
+ ··· + 1987766y −52441
c
6
, c
11
y
99
+ 63y
98
+ ··· − 1595y −49
c
10
y
99
− 25y
98
+ ··· + 92281126y −1852321
c
12
y
99
− 5y
98
+ ··· − 591y −25
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.763291 + 0.609745I
a = −0.310082 − 0.171201I
b = −0.749409 + 0.925641I
0.86700 + 4.61216I 0
u = −0.763291 − 0.609745I
a = −0.310082 + 0.171201I
b = −0.749409 − 0.925641I
0.86700 − 4.61216I 0
u = 0.691941 + 0.585463I
a = 1.024370 − 0.210352I
b = 1.40382 + 1.37236I
0.9782 − 14.1492I 0
u = 0.691941 − 0.585463I
a = 1.024370 + 0.210352I
b = 1.40382 − 1.37236I
0.9782 + 14.1492I 0
u = 0.798193 + 0.428389I
a = −0.247703 − 0.269691I
b = −0.613093 − 0.868425I
−0.09955 − 3.40884I 0
u = 0.798193 − 0.428389I
a = −0.247703 + 0.269691I
b = −0.613093 + 0.868425I
−0.09955 + 3.40884I 0
u = 0.437870 + 0.789230I
a = 0.101251 + 0.317677I
b = −0.503643 − 0.222196I
3.61622 − 2.57236I 0
u = 0.437870 − 0.789230I
a = 0.101251 − 0.317677I
b = −0.503643 + 0.222196I
3.61622 + 2.57236I 0
u = 0.848923 + 0.087013I
a = −0.592659 − 0.955005I
b = −0.231461 + 0.462338I
−5.69841 + 1.85582I 0
u = 0.848923 − 0.087013I
a = −0.592659 + 0.955005I
b = −0.231461 − 0.462338I
−5.69841 − 1.85582I 0
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.649236 + 0.536213I
a = 1.146540 + 0.196143I
b = 1.61665 − 1.19536I
−2.81830 + 7.75472I 0
u = −0.649236 − 0.536213I
a = 1.146540 − 0.196143I
b = 1.61665 + 1.19536I
−2.81830 − 7.75472I 0
u = −1.142900 + 0.201687I
a = −0.506272 + 0.893053I
b = 0.1036290 + 0.0001587I
−2.15673 − 6.65249I 0
u = −1.142900 − 0.201687I
a = −0.506272 − 0.893053I
b = 0.1036290 − 0.0001587I
−2.15673 + 6.65249I 0
u = −0.609435 + 0.533021I
a = −1.47973 + 0.57722I
b = −0.114393 + 1.380160I
4.41559 + 7.48924I 0
u = −0.609435 − 0.533021I
a = −1.47973 − 0.57722I
b = −0.114393 − 1.380160I
4.41559 − 7.48924I 0
u = 0.676022 + 0.428807I
a = −1.39804 + 0.28148I
b = −1.24437 − 1.50203I
−1.43426 − 5.86382I 0
u = 0.676022 − 0.428807I
a = −1.39804 − 0.28148I
b = −1.24437 + 1.50203I
−1.43426 + 5.86382I 0
u = −0.728898 + 0.301402I
a = 0.463149 − 1.182220I
b = −0.714291 − 0.035123I
−2.26210 − 0.32498I 0
u = −0.728898 − 0.301402I
a = 0.463149 + 1.182220I
b = −0.714291 + 0.035123I
−2.26210 + 0.32498I 0
6
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.502985 + 0.582942I
a = 0.746369 − 0.416319I
b = 0.767382 + 0.220139I
3.96912 − 1.96998I 0
u = 0.502985 − 0.582942I
a = 0.746369 + 0.416319I
b = 0.767382 − 0.220139I
3.96912 + 1.96998I 0
u = 0.488561 + 0.594766I
a = 0.188342 − 0.610285I
b = 0.679847 − 0.474605I
4.01500 − 2.06533I 0
u = 0.488561 − 0.594766I
a = 0.188342 + 0.610285I
b = 0.679847 + 0.474605I
4.01500 + 2.06533I 0
u = 0.620258 + 0.414743I
a = −0.983477 − 0.837263I
b = −0.367877 − 1.128180I
0.15736 − 3.84244I 0. + 7.19805I
u = 0.620258 − 0.414743I
a = −0.983477 + 0.837263I
b = −0.367877 + 1.128180I
0.15736 + 3.84244I 0. − 7.19805I
u = 0.250868 + 0.687008I
a = −1.180340 − 0.709707I
b = 0.716050 − 0.942890I
2.28768 + 9.87518I −2.00000 − 5.33704I
u = 0.250868 − 0.687008I
a = −1.180340 + 0.709707I
b = 0.716050 + 0.942890I
2.28768 − 9.87518I −2.00000 + 5.33704I
u = −0.114104 + 0.710742I
a = 1.021980 + 0.034819I
b = −0.272551 − 0.242795I
2.77279 − 0.19088I 4.76195 − 1.33883I
u = −0.114104 − 0.710742I
a = 1.021980 − 0.034819I
b = −0.272551 + 0.242795I
2.77279 + 0.19088I 4.76195 + 1.33883I
7
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.574003 + 0.422917I
a = −0.98239 − 1.03631I
b = −1.56531 + 0.74752I
−2.25497 + 2.06352I −5.88569 − 4.07985I
u = −0.574003 − 0.422917I
a = −0.98239 + 1.03631I
b = −1.56531 − 0.74752I
−2.25497 − 2.06352I −5.88569 + 4.07985I
u = −0.551944 + 0.442603I
a = 0.142792 − 0.247167I
b = 0.69382 − 1.76142I
1.87885 + 5.04729I 0. − 8.53052I
u = −0.551944 − 0.442603I
a = 0.142792 + 0.247167I
b = 0.69382 + 1.76142I
1.87885 − 5.04729I 0. + 8.53052I
u = −1.297430 + 0.245162I
a = −0.724683 − 0.405345I
b = −0.553294 + 0.342994I
−1.84376 + 6.35965I 0
u = −1.297430 − 0.245162I
a = −0.724683 + 0.405345I
b = −0.553294 − 0.342994I
−1.84376 − 6.35965I 0
u = −0.330304 + 0.573316I
a = 0.761223 + 0.313103I
b = 0.33905 − 1.40088I
5.23430 − 3.68890I 2.98854 + 1.79364I
u = −0.330304 − 0.573316I
a = 0.761223 − 0.313103I
b = 0.33905 + 1.40088I
5.23430 + 3.68890I 2.98854 − 1.79364I
u = −0.270684 + 0.587647I
a = −1.15217 + 1.17890I
b = 0.638102 + 0.968916I
−1.71656 − 3.90788I −3.38936 + 3.68440I
u = −0.270684 − 0.587647I
a = −1.15217 − 1.17890I
b = 0.638102 − 0.968916I
−1.71656 + 3.90788I −3.38936 − 3.68440I
8
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.521611 + 0.357512I
a = 0.69052 + 1.77803I
b = −1.005600 − 0.390867I
−2.87449 − 1.28088I −2.04294 + 6.38847I
u = 0.521611 − 0.357512I
a = 0.69052 − 1.77803I
b = −1.005600 + 0.390867I
−2.87449 + 1.28088I −2.04294 − 6.38847I
u = −0.569395 + 0.213633I
a = 0.815353 − 0.538900I
b = −0.037666 − 0.231193I
−1.071210 + 0.471534I −7.90805 − 1.67970I
u = −0.569395 − 0.213633I
a = 0.815353 + 0.538900I
b = −0.037666 + 0.231193I
−1.071210 − 0.471534I −7.90805 + 1.67970I
u = −0.419265 + 0.424814I
a = −2.13162 + 1.24115I
b = −0.358198 + 0.662173I
2.28522 − 1.94327I 3.21298 − 1.03946I
u = −0.419265 − 0.424814I
a = −2.13162 − 1.24115I
b = −0.358198 − 0.662173I
2.28522 + 1.94327I 3.21298 + 1.03946I
u = 0.517050 + 0.296886I
a = 0.934378 + 0.341756I
b = 1.56636 + 1.33611I
0.87417 + 1.73334I −4.33449 + 2.25502I
u = 0.517050 − 0.296886I
a = 0.934378 − 0.341756I
b = 1.56636 − 1.33611I
0.87417 − 1.73334I −4.33449 − 2.25502I
u = 1.42400 + 0.08728I
a = 1.61066 + 0.70366I
b = 0.96811 + 1.12630I
−0.26486 + 1.46630I 0
u = 1.42400 − 0.08728I
a = 1.61066 − 0.70366I
b = 0.96811 − 1.12630I
−0.26486 − 1.46630I 0
9
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 1.44232 + 0.02930I
a = −1.03789 − 1.40791I
b = −0.879871 − 0.773001I
−6.73733 + 2.03033I 0
u = 1.44232 − 0.02930I
a = −1.03789 + 1.40791I
b = −0.879871 + 0.773001I
−6.73733 − 2.03033I 0
u = −0.303479 + 0.431708I
a = 0.86305 − 1.28776I
b = −0.986240 − 0.387244I
−1.52675 + 0.96711I −4.03573 − 4.34958I
u = −0.303479 − 0.431708I
a = 0.86305 + 1.28776I
b = −0.986240 + 0.387244I
−1.52675 − 0.96711I −4.03573 + 4.34958I
u = −1.48799
a = 2.09639
b = 1.68145
−4.04626 0
u = 0.494977 + 0.033800I
a = 1.76169 − 1.98879I
b = 0.439062 − 0.955413I
0.87319 − 3.26894I −5.13325 + 7.07926I
u = 0.494977 − 0.033800I
a = 1.76169 + 1.98879I
b = 0.439062 + 0.955413I
0.87319 + 3.26894I −5.13325 − 7.07926I
u = 0.220361 + 0.439245I
a = 0.959569 − 0.061026I
b = 0.380950 + 0.742407I
1.31423 + 0.82561I 3.50137 − 0.32849I
u = 0.220361 − 0.439245I
a = 0.959569 + 0.061026I
b = 0.380950 − 0.742407I
1.31423 − 0.82561I 3.50137 + 0.32849I
u = −1.51425 + 0.17065I
a = 0.527100 + 1.191720I
b = 0.597586 + 0.935450I
−2.57936 + 4.78942I 0
10
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −1.51425 − 0.17065I
a = 0.527100 − 1.191720I
b = 0.597586 − 0.935450I
−2.57936 − 4.78942I 0
u = 0.101860 + 0.460295I
a = 1.84322 − 0.11187I
b = −0.595286 + 0.892959I
0.12875 + 2.77820I −1.87617 − 4.60612I
u = 0.101860 − 0.460295I
a = 1.84322 + 0.11187I
b = −0.595286 − 0.892959I
0.12875 − 2.77820I −1.87617 + 4.60612I
u = 1.52610 + 0.09330I
a = −1.80851 − 0.49814I
b = −1.356600 + 0.129572I
−4.27161 + 0.25928I 0
u = 1.52610 − 0.09330I
a = −1.80851 + 0.49814I
b = −1.356600 − 0.129572I
−4.27161 − 0.25928I 0
u = −1.52712 + 0.15738I
a = 1.48245 + 0.37484I
b = 1.130290 + 0.082284I
−2.74425 + 4.58226I 0
u = −1.52712 − 0.15738I
a = 1.48245 − 0.37484I
b = 1.130290 − 0.082284I
−2.74425 − 4.58226I 0
u = −1.55819 + 0.03781I
a = 1.51013 − 1.40745I
b = 0.796484 − 1.079400I
−6.20517 − 2.93963I 0
u = −1.55819 − 0.03781I
a = 1.51013 + 1.40745I
b = 0.796484 + 1.079400I
−6.20517 + 2.93963I 0
u = −1.55895 + 0.08512I
a = 2.84299 − 1.47477I
b = 2.79322 − 2.03600I
−6.23677 − 0.35234I 0
11
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −1.55895 − 0.08512I
a = 2.84299 + 1.47477I
b = 2.79322 + 2.03600I
−6.23677 + 0.35234I 0
u = −1.56027 + 0.09761I
a = −0.825260 − 0.038446I
b = −1.04023 + 1.11745I
−9.98972 + 2.89332I 0
u = −1.56027 − 0.09761I
a = −0.825260 + 0.038446I
b = −1.04023 − 1.11745I
−9.98972 − 2.89332I 0
u = 1.55972 + 0.12130I
a = 1.70559 + 2.08880I
b = 1.57167 + 2.85062I
−5.26165 − 7.05580I 0
u = 1.55972 − 0.12130I
a = 1.70559 − 2.08880I
b = 1.57167 − 2.85062I
−5.26165 + 7.05580I 0
u = 1.56570 + 0.07807I
a = 0.749210 + 0.562591I
b = 0.286823 + 0.284697I
−8.34824 − 1.63671I 0
u = 1.56570 − 0.07807I
a = 0.749210 − 0.562591I
b = 0.286823 − 0.284697I
−8.34824 + 1.63671I 0
u = 1.56598 + 0.11409I
a = −2.55571 − 0.12395I
b = −2.26156 − 1.03244I
−9.50202 − 3.97617I 0
u = 1.56598 − 0.11409I
a = −2.55571 + 0.12395I
b = −2.26156 + 1.03244I
−9.50202 + 3.97617I 0
u = 1.57047 + 0.15448I
a = −1.42059 − 1.23113I
b = −0.545692 − 1.202280I
−2.90241 − 9.99401I 0
12
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 1.57047 − 0.15448I
a = −1.42059 + 1.23113I
b = −0.545692 + 1.202280I
−2.90241 + 9.99401I 0
u = −1.57507 + 0.11656I
a = −1.61810 + 1.13603I
b = −1.18957 + 1.06359I
−7.26990 + 5.77422I 0
u = −1.57507 − 0.11656I
a = −1.61810 − 1.13603I
b = −1.18957 − 1.06359I
−7.26990 − 5.77422I 0
u = 1.58482 + 0.15976I
a = 2.79031 + 0.46182I
b = 2.55704 + 1.24136I
−10.3375 − 10.3262I 0
u = 1.58482 − 0.15976I
a = 2.79031 − 0.46182I
b = 2.55704 − 1.24136I
−10.3375 + 10.3262I 0
u = −1.59587 + 0.12411I
a = −2.45389 + 1.03531I
b = −1.93276 + 1.84915I
−9.15520 + 7.91610I 0
u = −1.59587 − 0.12411I
a = −2.45389 − 1.03531I
b = −1.93276 − 1.84915I
−9.15520 − 7.91610I 0
u = 1.60647 + 0.08510I
a = −0.542163 + 0.210261I
b = −0.890760 − 0.619723I
−10.24050 − 1.11922I 0
u = 1.60647 − 0.08510I
a = −0.542163 − 0.210261I
b = −0.890760 + 0.619723I
−10.24050 + 1.11922I 0
u = −1.60022 + 0.17865I
a = 2.45649 − 0.73425I
b = 2.13417 − 1.63116I
−6.7302 + 17.0060I 0
13
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −1.60022 − 0.17865I
a = 2.45649 + 0.73425I
b = 2.13417 + 1.63116I
−6.7302 − 17.0060I 0
u = −1.62129 + 0.02269I
a = −0.422405 − 0.828882I
b = −0.28613 − 1.67040I
−14.1221 − 1.4415I 0
u = −1.62129 − 0.02269I
a = −0.422405 + 0.828882I
b = −0.28613 + 1.67040I
−14.1221 + 1.4415I 0
u = 1.61475 + 0.19360I
a = −1.46104 − 0.59865I
b = −1.35349 − 1.38366I
−7.10456 − 7.68717I 0
u = 1.61475 − 0.19360I
a = −1.46104 + 0.59865I
b = −1.35349 + 1.38366I
−7.10456 + 7.68717I 0
u = −1.62392 + 0.13743I
a = −1.56203 + 0.90007I
b = −1.47911 + 1.38232I
−8.31409 + 5.62806I 0
u = −1.62392 − 0.13743I
a = −1.56203 − 0.90007I
b = −1.47911 − 1.38232I
−8.31409 − 5.62806I 0
u = 1.67170 + 0.00590I
a = −0.075885 − 0.586017I
b = 0.107620 − 1.333890I
−11.85680 − 6.44606I 0
u = 1.67170 − 0.00590I
a = −0.075885 + 0.586017I
b = 0.107620 + 1.333890I
−11.85680 + 6.44606I 0
14
II.
I
u
2
= h−u
14
+u
13
+· · ·+b+1, −2u
14
+u
13
+· · ·+a+1, u
16
−10u
14
+· · ·−2u+1i
(i) Arc colorings
a
2
=
1
0
a
8
=
0
u
a
3
=
1
u
2
a
9
=
−u
−u
3
+ u
a
4
=
−u
2
+ 1
−u
4
+ 2u
2
a
11
=
2u
14
− u
13
+ ··· + 8u − 1
u
14
− u
13
+ ··· + 4u − 1
a
5
=
−u
15
+ 9u
13
+ ··· − 3u − 1
u
12
− 7u
10
+ 17u
8
+ u
7
− 16u
6
− 5u
5
+ 5u
4
+ 7u
3
− 2u
2
− 3u
a
1
=
−u
6
+ 3u
4
− 2u
2
+ 1
−u
8
+ 4u
6
− 4u
4
a
7
=
u
u
a
12
=
u
14
− u
13
+ ··· + 10u
2
+ 6u
−u
13
+ 7u
11
− 17u
9
− 2u
8
+ 16u
7
+ 9u
6
− 5u
5
− 11u
4
+ u
3
+ 2u
2
+ 2u
a
6
=
−u
15
+ u
14
+ ··· + 2u + 1
u
15
+ u
14
+ ··· − 2u + 1
a
10
=
2u
14
− u
13
+ ··· + 6u − 1
u
14
− u
13
+ ··· + 4u − 1
(ii) Obstruction class = 1
(iii) Cusp Shapes = u
15
−3u
13
−u
12
−18u
11
+ 7u
10
+ 94u
9
−11u
8
−143u
7
−19u
6
+
84u
5
+ 58u
4
− 38u
3
− 33u
2
+ 11u − 1
15
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
16
+ 4u
15
+ ··· − 2u + 1
c
2
, c
3
u
16
− 10u
14
+ ··· − 2u + 1
c
4
u
16
+ u
15
+ ··· + 2u
3
+ 1
c
5
u
16
+ u
15
+ ··· + 8u
2
+ 1
c
6
u
16
+ 8u
14
+ ··· − u + 1
c
7
, c
8
u
16
− 10u
14
+ ··· + 2u + 1
c
9
u
16
− u
15
+ ··· + 8u
2
+ 1
c
10
u
16
− 4u
14
+ ··· + 8u + 1
c
11
u
16
+ 8u
14
+ ··· + u + 1
c
12
u
16
− 2u
13
− 2u
12
+ u
11
+ u
9
+ 3u
8
− 2u
7
+ u
6
+ u
5
− u
4
+ u
3
− u
2
− u + 1
16
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
16
+ 4y
15
+ ··· + 12y + 1
c
2
, c
3
, c
7
c
8
y
16
− 20y
15
+ ··· − 12y + 1
c
4
y
16
− 3y
15
+ ··· − 4y
2
+ 1
c
5
, c
9
y
16
+ 13y
15
+ ··· + 16y + 1
c
6
, c
11
y
16
+ 16y
15
+ ··· + 13y + 1
c
10
y
16
− 8y
15
+ ··· − 8y + 1
c
12
y
16
− 4y
14
+ ··· − 3y + 1
17
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.749888 + 0.412737I
a = −0.482981 − 0.157116I
b = −0.57933 − 1.35783I
−0.31642 − 4.80216I −4.28190 + 8.53963I
u = 0.749888 − 0.412737I
a = −0.482981 + 0.157116I
b = −0.57933 + 1.35783I
−0.31642 + 4.80216I −4.28190 − 8.53963I
u = −0.441315 + 0.700895I
a = 0.028510 − 0.642080I
b = −0.644596 − 0.091812I
3.29668 + 2.36445I −7.72275 − 1.32048I
u = −0.441315 − 0.700895I
a = 0.028510 + 0.642080I
b = −0.644596 + 0.091812I
3.29668 − 2.36445I −7.72275 + 1.32048I
u = −0.569717 + 0.232049I
a = −0.10645 − 2.03638I
b = −1.200940 + 0.301920I
−3.44134 + 0.81986I −12.20354 + 0.25953I
u = −0.569717 − 0.232049I
a = −0.10645 + 2.03638I
b = −1.200940 − 0.301920I
−3.44134 − 0.81986I −12.20354 − 0.25953I
u = 1.48473 + 0.16212I
a = −0.320775 + 1.110710I
b = −0.230819 + 0.697084I
−2.82368 − 5.27538I −7.16301 + 8.89431I
u = 1.48473 − 0.16212I
a = −0.320775 − 1.110710I
b = −0.230819 − 0.697084I
−2.82368 + 5.27538I −7.16301 − 8.89431I
u = −1.52213 + 0.04939I
a = 2.32971 − 1.33467I
b = 1.97084 − 0.94365I
−5.10540 − 1.62333I −2.28629 + 4.04054I
u = −1.52213 − 0.04939I
a = 2.32971 + 1.33467I
b = 1.97084 + 0.94365I
−5.10540 + 1.62333I −2.28629 − 4.04054I
18
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 1.58491 + 0.07036I
a = −1.102130 + 0.179111I
b = −1.25975 − 0.84936I
−10.91500 − 1.94360I −11.86525 + 1.00527I
u = 1.58491 − 0.07036I
a = −1.102130 − 0.179111I
b = −1.25975 + 0.84936I
−10.91500 + 1.94360I −11.86525 − 1.00527I
u = 0.324777 + 0.221310I
a = 2.90404 + 1.73077I
b = 0.936104 + 0.903034I
1.32598 + 2.48939I −0.39288 − 3.29934I
u = 0.324777 − 0.221310I
a = 2.90404 − 1.73077I
b = 0.936104 − 0.903034I
1.32598 − 2.48939I −0.39288 + 3.29934I
u = −1.61115 + 0.13456I
a = −1.74992 + 1.16607I
b = −1.49151 + 1.86069I
−8.33978 + 6.95567I −6.08440 − 5.77311I
u = −1.61115 − 0.13456I
a = −1.74992 − 1.16607I
b = −1.49151 − 1.86069I
−8.33978 − 6.95567I −6.08440 + 5.77311I
19
III. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
(u
16
+ 4u
15
+ ··· − 2u + 1)(u
99
− 23u
98
+ ··· + 738442u − 80017)
c
2
, c
3
(u
16
− 10u
14
+ ··· − 2u + 1)(u
99
+ u
98
+ ··· − 18u + 7)
c
4
(u
16
+ u
15
+ ··· + 2u
3
+ 1)(u
99
+ 2u
97
+ ··· + 270u + 25)
c
5
(u
16
+ u
15
+ ··· + 8u
2
+ 1)(u
99
+ 2u
98
+ ··· + 1662u + 229)
c
6
(u
16
+ 8u
14
+ ··· − u + 1)(u
99
+ u
98
+ ··· − u + 7)
c
7
, c
8
(u
16
− 10u
14
+ ··· + 2u + 1)(u
99
+ u
98
+ ··· − 18u + 7)
c
9
(u
16
− u
15
+ ··· + 8u
2
+ 1)(u
99
+ 2u
98
+ ··· + 1662u + 229)
c
10
(u
16
− 4u
14
+ ··· + 8u + 1)(u
99
+ 13u
98
+ ··· − 4180u − 1361)
c
11
(u
16
+ 8u
14
+ ··· + u + 1)(u
99
+ u
98
+ ··· − u + 7)
c
12
(u
16
− 2u
13
− 2u
12
+ u
11
+ u
9
+ 3u
8
− 2u
7
+ u
6
+ u
5
− u
4
+ u
3
− u
2
− u + 1)
· (u
99
− 5u
98
+ ··· − 3u + 5)
20
IV. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
(y
16
+ 4y
15
+ ··· + 12y + 1)
· (y
99
+ 19y
98
+ ··· − 55556666826y −6402720289)
c
2
, c
3
, c
7
c
8
(y
16
− 20y
15
+ ··· − 12y + 1)(y
99
− 113y
98
+ ··· + 954y −49)
c
4
(y
16
− 3y
15
+ ··· − 4y
2
+ 1)(y
99
+ 4y
98
+ ··· + 11450y −625)
c
5
, c
9
(y
16
+ 13y
15
+ ··· + 16y + 1)(y
99
+ 64y
98
+ ··· + 1987766y −52441)
c
6
, c
11
(y
16
+ 16y
15
+ ··· + 13y + 1)(y
99
+ 63y
98
+ ··· − 1595y −49)
c
10
(y
16
− 8y
15
+ ··· − 8y + 1)
· (y
99
− 25y
98
+ ··· + 92281126y −1852321)
c
12
(y
16
− 4y
14
+ ··· − 3y + 1)(y
99
− 5y
98
+ ··· − 591y −25)
21
