12a
0814
(K12a
0814
)
A knot diagram
1
Linearized knot diagam
4 5 7 2 10 3 11 12 6 1 9 8
Solving Sequence
8,12
9
1,4
2 5 11 7 3 6 10
c
8
c
12
c
1
c
4
c
11
c
7
c
3
c
6
c
10
c
2
, c
5
, c
9
Ideals for irreducible components
2
of X
par
I
u
1
= h9.56930 × 10
26
u
91
+ 4.97491 × 10
26
u
90
+ ··· + 1.83397 × 10
27
b + 3.92664 × 10
27
,
− 5.52127 × 10
26
u
91
− 8.62278 × 10
26
u
90
+ ··· + 1.83397 × 10
27
a − 2.61403 × 10
27
, u
92
− 4u
91
+ ··· − 8u
2
+ 1i
I
u
2
= hb − u − 1, u
2
+ a + u + 3, u
3
+ 2u − 1i
I
u
3
= h−u
2
a − u
2
+ b + u − 1, −u
2
a + a
2
+ 2au − u
2
− a + 2u − 3, u
3
− u
2
+ 2u − 1i
I
u
4
= hb − u − 1, −u
3
− u
2
+ a − u − 1, u
4
+ u
3
+ 2u
2
+ 2u + 1i
* 4 irreducible components of dim
C
= 0, with total 105 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
= h9.57 × 10
26
u
91
+ 4.97 × 10
26
u
90
+ · · · + 1.83 × 10
27
b + 3.93 ×
10
27
, −5.52 × 10
26
u
91
− 8.62 × 10
26
u
90
+ · · · + 1.83 × 10
27
a − 2.61 ×
10
27
, u
92
− 4u
91
+ · · · − 8u
2
+ 1i
(i) Arc colorings
a
8
=
1
0
a
12
=
0
u
a
9
=
1
u
2
a
1
=
−u
u
a
4
=
0.301056u
91
+ 0.470171u
90
+ ··· − 2.96443u + 1.42534
−0.521781u
91
− 0.271265u
90
+ ··· − 1.81529u − 2.14106
a
2
=
0.132509u
91
+ 1.28972u
90
+ ··· − 1.42156u + 1.98262
−1.74961u
91
+ 3.41466u
90
+ ··· − 2.45957u − 2.11975
a
5
=
0.499637u
91
− 3.19051u
90
+ ··· − 2.69354u − 1.70145
1.20761u
91
− 2.29856u
90
+ ··· + 2.49070u + 0.858623
a
11
=
u
u
3
+ u
a
7
=
−u
4
− u
2
+ 1
−u
6
− 2u
4
− u
2
a
3
=
0.133234u
91
− 0.329272u
90
+ ··· − 4.03448u − 0.614475
−0.164836u
91
+ 0.0117691u
90
+ ··· − 0.440981u − 0.836998
a
6
=
0.500057u
91
− 1.31833u
90
+ ··· − 1.15620u + 0.817075
−0.663481u
91
+ 0.793381u
90
+ ··· − 0.361576u − 1.01523
a
10
=
u
5
+ 2u
3
+ u
−u
5
− u
3
+ u
(ii) Obstruction class = −1
(iii) Cusp Shapes =
2365091250833776522114268693
916983961196051693206135667
u
91
−
18729853830167391906229939375
1833967922392103386412271334
u
90
+
··· −
1024932205509583481893242009
1833967922392103386412271334
u −
16203344775728881724174542717
1833967922392103386412271334
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
2
, c
4
u
92
− 11u
91
+ ··· + 10u + 1
c
3
, c
6
u
92
+ 4u
91
+ ··· − 576u − 128
c
5
, c
9
u
92
+ 2u
91
+ ··· − 352u − 64
c
7
u
92
+ 4u
91
+ ··· − 228u + 36
c
8
, c
11
, c
12
u
92
− 4u
91
+ ··· − 8u
2
+ 1
c
10
u
92
− 20u
91
+ ··· − 102752u + 13633
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
2
, c
4
y
92
− 89y
91
+ ··· − 208y + 1
c
3
, c
6
y
92
− 54y
91
+ ··· − 716800y + 16384
c
5
, c
9
y
92
+ 42y
91
+ ··· − 25600y + 4096
c
7
y
92
+ 4y
91
+ ··· + 8856y + 1296
c
8
, c
11
, c
12
y
92
+ 84y
91
+ ··· − 16y + 1
c
10
y
92
+ 28y
91
+ ··· + 10518208240y + 185858689
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.142365 + 1.052150I
a = 0.00718 + 2.51345I
b = 0.224624 − 1.256470I
−1.67872 + 2.40443I 0
u = −0.142365 − 1.052150I
a = 0.00718 − 2.51345I
b = 0.224624 + 1.256470I
−1.67872 − 2.40443I 0
u = −0.031893 + 1.093450I
a = 0.789128 + 0.767645I
b = −1.344780 − 0.179061I
0.0460196 + 0.0531118I 0
u = −0.031893 − 1.093450I
a = 0.789128 − 0.767645I
b = −1.344780 + 0.179061I
0.0460196 − 0.0531118I 0
u = −0.227106 + 1.094750I
a = −0.204440 + 0.030157I
b = 0.889203 + 0.208382I
0.63573 + 4.55193I 0
u = −0.227106 − 1.094750I
a = −0.204440 − 0.030157I
b = 0.889203 − 0.208382I
0.63573 − 4.55193I 0
u = −0.343914 + 1.068750I
a = 0.718999 − 1.078310I
b = −1.331240 − 0.090187I
−5.38660 + 7.98182I 0
u = −0.343914 − 1.068750I
a = 0.718999 + 1.078310I
b = −1.331240 + 0.090187I
−5.38660 − 7.98182I 0
u = 0.448104 + 0.745173I
a = 0.74104 − 1.60583I
b = −0.196534 − 0.021984I
−4.37379 + 8.39720I 0
u = 0.448104 − 0.745173I
a = 0.74104 + 1.60583I
b = −0.196534 + 0.021984I
−4.37379 − 8.39720I 0
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.179563 + 1.129290I
a = −1.30215 − 1.10394I
b = 1.63847 − 0.22558I
−7.32936 − 2.64950I 0
u = 0.179563 − 1.129290I
a = −1.30215 + 1.10394I
b = 1.63847 + 0.22558I
−7.32936 + 2.64950I 0
u = 0.666539 + 0.497806I
a = 0.904957 − 0.193946I
b = 0.316460 − 0.675572I
0.72279 − 2.24152I −17.3233 + 3.8345I
u = 0.666539 − 0.497806I
a = 0.904957 + 0.193946I
b = 0.316460 + 0.675572I
0.72279 + 2.24152I −17.3233 − 3.8345I
u = 0.761685 + 0.298417I
a = 0.456120 + 0.768958I
b = 1.38372 − 1.02861I
−5.88875 − 12.68560I −15.9259 + 8.5530I
u = 0.761685 − 0.298417I
a = 0.456120 − 0.768958I
b = 1.38372 + 1.02861I
−5.88875 + 12.68560I −15.9259 − 8.5530I
u = −0.789964 + 0.118774I
a = −0.661860 − 0.366395I
b = −1.091720 − 0.159682I
−8.30183 − 3.84281I −17.8337 + 2.8735I
u = −0.789964 − 0.118774I
a = −0.661860 + 0.366395I
b = −1.091720 + 0.159682I
−8.30183 + 3.84281I −17.8337 − 2.8735I
u = 0.716560 + 0.297487I
a = 0.002046 − 1.151310I
b = −0.869946 + 0.259215I
−0.00340 − 8.16832I −12.8516 + 8.4123I
u = 0.716560 − 0.297487I
a = 0.002046 + 1.151310I
b = −0.869946 − 0.259215I
−0.00340 + 8.16832I −12.8516 − 8.4123I
6
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.704793 + 0.307944I
a = −0.792982 + 0.830802I
b = −1.05582 − 1.30510I
−7.88429 + 5.84555I −17.7064 − 5.3639I
u = −0.704793 − 0.307944I
a = −0.792982 − 0.830802I
b = −1.05582 + 1.30510I
−7.88429 − 5.84555I −17.7064 + 5.3639I
u = 0.387666 + 0.648093I
a = 0.001726 + 0.890620I
b = 0.716919 + 0.032222I
1.33594 + 4.23494I −9.89163 − 3.43303I
u = 0.387666 − 0.648093I
a = 0.001726 − 0.890620I
b = 0.716919 − 0.032222I
1.33594 − 4.23494I −9.89163 + 3.43303I
u = 0.694128 + 0.276007I
a = −0.208000 − 0.170305I
b = −1.67772 + 0.64980I
−2.89176 − 5.69556I −14.8915 + 6.2831I
u = 0.694128 − 0.276007I
a = −0.208000 + 0.170305I
b = −1.67772 − 0.64980I
−2.89176 + 5.69556I −14.8915 − 6.2831I
u = 0.639348 + 0.362879I
a = −0.080883 + 0.391950I
b = 0.796662 − 0.064064I
2.87803 − 3.21226I −7.10916 + 5.15078I
u = 0.639348 − 0.362879I
a = −0.080883 − 0.391950I
b = 0.796662 + 0.064064I
2.87803 + 3.21226I −7.10916 − 5.15078I
u = −0.409671 + 0.598345I
a = −1.35127 − 1.41304I
b = 0.419113 − 0.362791I
−6.70228 − 1.95771I −15.9931 − 0.5196I
u = −0.409671 − 0.598345I
a = −1.35127 + 1.41304I
b = 0.419113 + 0.362791I
−6.70228 + 1.95771I −15.9931 + 0.5196I
7
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.119770 + 1.269710I
a = −0.147331 − 0.963782I
b = 0.148541 + 0.825571I
3.07060 + 1.96014I 0
u = −0.119770 − 1.269710I
a = −0.147331 + 0.963782I
b = 0.148541 − 0.825571I
3.07060 − 1.96014I 0
u = 0.654898 + 0.270175I
a = −0.727352 + 1.149210I
b = −0.045234 + 0.192756I
−1.56617 − 2.78383I −14.9152 + 4.7455I
u = 0.654898 − 0.270175I
a = −0.727352 − 1.149210I
b = −0.045234 − 0.192756I
−1.56617 + 2.78383I −14.9152 − 4.7455I
u = −0.694676 + 0.105876I
a = 0.717960 + 0.636631I
b = −0.237790 + 0.206297I
−2.32258 − 1.07187I −15.2882 + 4.7085I
u = −0.694676 − 0.105876I
a = 0.717960 − 0.636631I
b = −0.237790 − 0.206297I
−2.32258 + 1.07187I −15.2882 − 4.7085I
u = 0.504245 + 0.477251I
a = −0.159414 − 0.994757I
b = −0.156886 + 0.230667I
3.40182 − 0.56518I −5.80669 + 2.57586I
u = 0.504245 − 0.477251I
a = −0.159414 + 0.994757I
b = −0.156886 − 0.230667I
3.40182 + 0.56518I −5.80669 − 2.57586I
u = −0.662313 + 0.175373I
a = −0.022080 − 0.544950I
b = 1.85088 + 0.97936I
−4.18177 + 0.78779I −16.7968 − 0.8436I
u = −0.662313 − 0.175373I
a = −0.022080 + 0.544950I
b = 1.85088 − 0.97936I
−4.18177 − 0.78779I −16.7968 + 0.8436I
8
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.636842 + 0.239791I
a = 0.056662 − 1.355770I
b = 0.795740 + 0.685955I
−1.99118 + 2.67547I −15.2993 − 6.0545I
u = −0.636842 − 0.239791I
a = 0.056662 + 1.355770I
b = 0.795740 − 0.685955I
−1.99118 − 2.67547I −15.2993 + 6.0545I
u = 0.290523 + 0.597652I
a = −0.34550 + 2.29035I
b = −0.306287 − 0.344198I
−1.48070 + 2.06950I −11.57303 − 0.92768I
u = 0.290523 − 0.597652I
a = −0.34550 − 2.29035I
b = −0.306287 + 0.344198I
−1.48070 − 2.06950I −11.57303 + 0.92768I
u = −0.260268 + 1.313650I
a = 0.276935 − 1.203230I
b = −0.47777 + 1.57760I
2.10659 + 2.37333I 0
u = −0.260268 − 1.313650I
a = 0.276935 + 1.203230I
b = −0.47777 − 1.57760I
2.10659 − 2.37333I 0
u = −0.195760 + 1.328170I
a = 2.45199 − 2.17556I
b = −2.43344 + 2.90159I
1.71998 + 2.56116I 0
u = −0.195760 − 1.328170I
a = 2.45199 + 2.17556I
b = −2.43344 − 2.90159I
1.71998 − 2.56116I 0
u = −0.338504 + 1.319110I
a = 0.899677 − 0.362618I
b = −1.041090 − 0.688240I
−3.80390 + 0.22278I 0
u = −0.338504 − 1.319110I
a = 0.899677 + 0.362618I
b = −1.041090 + 0.688240I
−3.80390 − 0.22278I 0
9
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.618274 + 0.124073I
a = 1.250510 − 0.537485I
b = 1.251080 − 0.087774I
−10.31260 − 0.38606I −19.6066 + 9.7099I
u = 0.618274 − 0.124073I
a = 1.250510 + 0.537485I
b = 1.251080 + 0.087774I
−10.31260 + 0.38606I −19.6066 − 9.7099I
u = 0.230538 + 1.357000I
a = −1.213770 − 0.237388I
b = 1.37325 − 0.97206I
−5.59686 − 3.43534I 0
u = 0.230538 − 1.357000I
a = −1.213770 + 0.237388I
b = 1.37325 + 0.97206I
−5.59686 + 3.43534I 0
u = −0.255344 + 1.366370I
a = −3.38633 + 0.53751I
b = 3.62963 + 0.34549I
0.70883 + 4.11092I 0
u = −0.255344 − 1.366370I
a = −3.38633 − 0.53751I
b = 3.62963 − 0.34549I
0.70883 − 4.11092I 0
u = −0.177622 + 1.386400I
a = 1.86610 − 0.97129I
b = −2.19074 + 1.06368I
4.32545 + 2.08315I 0
u = −0.177622 − 1.386400I
a = 1.86610 + 0.97129I
b = −2.19074 − 1.06368I
4.32545 − 2.08315I 0
u = −0.25033 + 1.39564I
a = −2.35899 + 0.08339I
b = 2.87723 + 0.04231I
3.23137 + 5.92026I 0
u = −0.25033 − 1.39564I
a = −2.35899 − 0.08339I
b = 2.87723 − 0.04231I
3.23137 − 5.92026I 0
10
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.15781 + 1.41089I
a = 2.15833 − 0.39554I
b = −2.63802 + 1.10324I
5.23253 − 2.39068I 0
u = 0.15781 − 1.41089I
a = 2.15833 + 0.39554I
b = −2.63802 − 1.10324I
5.23253 + 2.39068I 0
u = 0.12683 + 1.41487I
a = −0.729131 − 0.110038I
b = 0.861769 + 1.075790I
4.56630 + 0.56531I 0
u = 0.12683 − 1.41487I
a = −0.729131 + 0.110038I
b = 0.861769 − 1.075790I
4.56630 − 0.56531I 0
u = 0.25775 + 1.40739I
a = −0.554080 − 0.855524I
b = 0.93444 + 1.57819I
3.79344 − 6.12228I 0
u = 0.25775 − 1.40739I
a = −0.554080 + 0.855524I
b = 0.93444 − 1.57819I
3.79344 + 6.12228I 0
u = 0.27288 + 1.41137I
a = 2.55359 + 0.49150I
b = −2.89375 + 0.48625I
2.49560 − 9.21773I 0
u = 0.27288 − 1.41137I
a = 2.55359 − 0.49150I
b = −2.89375 − 0.48625I
2.49560 + 9.21773I 0
u = 0.11384 + 1.44409I
a = −1.88011 − 0.47011I
b = 2.46388 + 0.65654I
7.85404 + 2.62441I 0
u = 0.11384 − 1.44409I
a = −1.88011 + 0.47011I
b = 2.46388 − 0.65654I
7.85404 − 2.62441I 0
11
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.28096 + 1.42230I
a = 2.01261 + 0.55638I
b = −2.69665 − 0.44481I
5.49300 − 11.79800I 0
u = 0.28096 − 1.42230I
a = 2.01261 − 0.55638I
b = −2.69665 + 0.44481I
5.49300 + 11.79800I 0
u = −0.27578 + 1.42573I
a = 2.79313 + 0.98533I
b = −3.16091 − 1.91717I
−2.33948 + 9.41935I 0
u = −0.27578 − 1.42573I
a = 2.79313 − 0.98533I
b = −3.16091 + 1.91717I
−2.33948 − 9.41935I 0
u = 0.17968 + 1.44599I
a = 1.255330 − 0.089450I
b = −1.69161 − 0.12091I
9.52465 − 3.04531I 0
u = 0.17968 − 1.44599I
a = 1.255330 + 0.089450I
b = −1.69161 + 0.12091I
9.52465 + 3.04531I 0
u = −0.13242 + 1.45194I
a = −0.68894 + 1.87780I
b = 0.70885 − 2.81549I
−0.261764 − 0.086646I 0
u = −0.13242 − 1.45194I
a = −0.68894 − 1.87780I
b = 0.70885 + 2.81549I
−0.261764 + 0.086646I 0
u = 0.24084 + 1.43911I
a = −1.43804 − 0.52544I
b = 1.83565 + 0.29596I
8.65874 − 6.43078I 0
u = 0.24084 − 1.43911I
a = −1.43804 + 0.52544I
b = 1.83565 − 0.29596I
8.65874 + 6.43078I 0
12
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.30135 + 1.42773I
a = −2.83705 + 0.26025I
b = 3.29716 − 1.20217I
−0.3747 − 16.5437I 0
u = 0.30135 − 1.42773I
a = −2.83705 − 0.26025I
b = 3.29716 + 1.20217I
−0.3747 + 16.5437I 0
u = 0.07972 + 1.47696I
a = 1.09343 + 1.10864I
b = −1.27233 − 2.06372I
2.77556 + 6.92698I 0
u = 0.07972 − 1.47696I
a = 1.09343 − 1.10864I
b = −1.27233 + 2.06372I
2.77556 − 6.92698I 0
u = −0.517611
a = 4.21782
b = −2.35556
−2.53998 −87.3520
u = 0.323090 + 0.404159I
a = −0.870583 + 0.503536I
b = −0.938911 + 0.326913I
−0.442132 − 0.425306I −11.54885 + 1.57345I
u = 0.323090 − 0.404159I
a = −0.870583 − 0.503536I
b = −0.938911 − 0.326913I
−0.442132 + 0.425306I −11.54885 − 1.57345I
u = 0.22336 + 1.49048I
a = −0.84405 + 1.24122I
b = 1.00216 − 2.02573I
7.17979 − 5.45280I 0
u = 0.22336 − 1.49048I
a = −0.84405 − 1.24122I
b = 1.00216 + 2.02573I
7.17979 + 5.45280I 0
u = −0.391886
a = 0.753572
b = −0.538627
−0.730054 −13.0620
13
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.246092 + 0.167191I
a = 1.31115 + 1.05386I
b = −0.719211 + 0.058991I
−0.764396 − 0.029182I −11.62093 − 0.70639I
u = −0.246092 − 0.167191I
a = 1.31115 − 1.05386I
b = −0.719211 − 0.058991I
−0.764396 + 0.029182I −11.62093 + 0.70639I
14
II. I
u
2
= hb − u − 1, u
2
+ a + u + 3, u
3
+ 2u − 1i
(i) Arc colorings
a
8
=
1
0
a
12
=
0
u
a
9
=
1
u
2
a
1
=
−u
u
a
4
=
−u
2
− u − 3
u + 1
a
2
=
−u
2
− 2u − 3
2u + 1
a
5
=
u
−u
a
11
=
u
−u + 1
a
7
=
u
2
− u + 1
−u
2
+ 2u − 1
a
3
=
−u
2
− u − 3
u + 1
a
6
=
u
2
− u + 1
−u
2
+ 2u − 1
a
10
=
u
2
+ u
−u
2
− u + 1
(ii) Obstruction class = 1
(iii) Cusp Shapes = 3u
2
+ u + 2
15
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
2
(u − 1)
3
c
3
, c
6
u
3
c
4
(u + 1)
3
c
5
, c
8
, c
10
u
3
+ 2u − 1
c
7
u
3
− 3u
2
+ 5u − 2
c
9
, c
11
, c
12
u
3
+ 2u + 1
16
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
2
, c
4
(y −1)
3
c
3
, c
6
y
3
c
5
, c
8
, c
9
c
10
, c
11
, c
12
y
3
+ 4y
2
+ 4y −1
c
7
y
3
+ y
2
+ 13y −4
17
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.22670 + 1.46771I
a = −0.670516 − 0.802255I
b = 0.77330 + 1.46771I
7.79580 + 5.13794I −4.53505 − 0.52866I
u = −0.22670 − 1.46771I
a = −0.670516 + 0.802255I
b = 0.77330 − 1.46771I
7.79580 − 5.13794I −4.53505 + 0.52866I
u = 0.453398
a = −3.65897
b = 1.45340
−2.43213 3.07010
18
III.
I
u
3
= h−u
2
a−u
2
+b+u−1, −u
2
a+a
2
+2au−u
2
−a+2u−3, u
3
−u
2
+2u−1i
(i) Arc colorings
a
8
=
1
0
a
12
=
0
u
a
9
=
1
u
2
a
1
=
−u
u
a
4
=
a
u
2
a + u
2
− u + 1
a
2
=
−au − 2u
2
− u − 1
−u
2
a + au − a + 3u − 2
a
5
=
−u
2
− a − u − 1
−u
2
a − u
2
+ 3u − 2
a
11
=
u
u
2
− u + 1
a
7
=
u
−u
a
3
=
−au − u
2
+ 2a + u
u
2
a + au + 2u
2
− a − 2u + 1
a
6
=
−u
2
− a − u − 1
−u
2
a − u
2
+ 3u − 2
a
10
=
1
u
2
(ii) Obstruction class = 1
(iii) Cusp Shapes = 3u
2
a + 3au + 4u
2
+ u − 15
19
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
2
, c
3
(u
2
+ u − 1)
3
c
4
, c
6
(u
2
− u − 1)
3
c
5
, c
9
u
6
c
7
, c
10
(u
3
+ u
2
− 1)
2
c
8
(u
3
− u
2
+ 2u − 1)
2
c
11
, c
12
(u
3
+ u
2
+ 2u + 1)
2
20
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
2
, c
3
c
4
, c
6
(y
2
− 3y + 1)
3
c
5
, c
9
y
6
c
7
, c
10
(y
3
− y
2
+ 2y −1)
2
c
8
, c
11
, c
12
(y
3
+ 3y
2
+ 2y −1)
2
21
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = 0.215080 + 1.307140I
a = −1.286800 − 0.397354I
b = 1.48511 − 0.80786I
−5.85852 − 2.82812I −13.61882 − 1.93520I
u = 0.215080 + 1.307140I
a = 0.19428 − 1.65465I
b = −0.27003 + 2.11500I
2.03717 − 2.82812I −12.9982 + 11.8301I
u = 0.215080 − 1.307140I
a = −1.286800 + 0.397354I
b = 1.48511 + 0.80786I
−5.85852 + 2.82812I −13.61882 + 1.93520I
u = 0.215080 − 1.307140I
a = 0.19428 + 1.65465I
b = −0.27003 − 2.11500I
2.03717 + 2.82812I −12.9982 − 11.8301I
u = 0.569840
a = −1.38856
b = 0.303987
−2.10041 −16.8580
u = 0.569840
a = 1.57360
b = 1.26585
−9.99610 −8.90830
22
IV. I
u
4
= hb − u − 1, −u
3
− u
2
+ a − u − 1, u
4
+ u
3
+ 2u
2
+ 2u + 1i
(i) Arc colorings
a
8
=
1
0
a
12
=
0
u
a
9
=
1
u
2
a
1
=
−u
u
a
4
=
u
3
+ u
2
+ u + 1
u + 1
a
2
=
u
3
+ u
2
+ 1
2u + 1
a
5
=
u
−u
a
11
=
u
u
3
+ u
a
7
=
u
3
+ u
2
+ 2u + 2
u
3
+ u + 1
a
3
=
u
3
+ u
2
+ u + 1
u + 1
a
6
=
u
3
+ u
2
+ 2u + 2
u
3
+ u + 1
a
10
=
u
3
+ 2u + 1
−1
(ii) Obstruction class = 1
(iii) Cusp Shapes = −u
3
+ 3u
2
− u − 10
23
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
2
(u − 1)
4
c
3
, c
6
u
4
c
4
(u + 1)
4
c
5
, c
8
, c
10
u
4
+ u
3
+ 2u
2
+ 2u + 1
c
7
(u
2
+ u + 1)
2
c
9
, c
11
, c
12
u
4
− u
3
+ 2u
2
− 2u + 1
24
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
2
, c
4
(y −1)
4
c
3
, c
6
y
4
c
5
, c
8
, c
9
c
10
, c
11
, c
12
y
4
+ 3y
3
+ 2y
2
+ 1
c
7
(y
2
+ y + 1)
2
25
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
4
√
−1(vol +
√
−1CS) Cusp shape
u = −0.621744 + 0.440597I
a = 0.692440 + 0.318148I
b = 0.378256 + 0.440597I
1.64493 + 2.02988I −8.92268 − 2.50966I
u = −0.621744 − 0.440597I
a = 0.692440 − 0.318148I
b = 0.378256 − 0.440597I
1.64493 − 2.02988I −8.92268 + 2.50966I
u = 0.121744 + 1.306620I
a = −1.192440 − 0.547877I
b = 1.12174 + 1.30662I
1.64493 − 2.02988I −14.5773 + 1.8205I
u = 0.121744 − 1.306620I
a = −1.192440 + 0.547877I
b = 1.12174 − 1.30662I
1.64493 + 2.02988I −14.5773 − 1.8205I
26
V. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
, c
2
((u − 1)
7
)(u
2
+ u − 1)
3
(u
92
− 11u
91
+ ··· + 10u + 1)
c
3
u
7
(u
2
+ u − 1)
3
(u
92
+ 4u
91
+ ··· − 576u − 128)
c
4
((u + 1)
7
)(u
2
− u − 1)
3
(u
92
− 11u
91
+ ··· + 10u + 1)
c
5
u
6
(u
3
+ 2u − 1)(u
4
+ u
3
+ ··· + 2u + 1)(u
92
+ 2u
91
+ ··· − 352u − 64)
c
6
u
7
(u
2
− u − 1)
3
(u
92
+ 4u
91
+ ··· − 576u − 128)
c
7
(u
2
+ u + 1)
2
(u
3
− 3u
2
+ 5u − 2)(u
3
+ u
2
− 1)
2
· (u
92
+ 4u
91
+ ··· − 228u + 36)
c
8
(u
3
+ 2u − 1)(u
3
− u
2
+ 2u − 1)
2
(u
4
+ u
3
+ 2u
2
+ 2u + 1)
· (u
92
− 4u
91
+ ··· − 8u
2
+ 1)
c
9
u
6
(u
3
+ 2u + 1)(u
4
− u
3
+ ··· − 2u + 1)(u
92
+ 2u
91
+ ··· − 352u − 64)
c
10
(u
3
+ 2u − 1)(u
3
+ u
2
− 1)
2
(u
4
+ u
3
+ 2u
2
+ 2u + 1)
· (u
92
− 20u
91
+ ··· − 102752u + 13633)
c
11
, c
12
(u
3
+ 2u + 1)(u
3
+ u
2
+ 2u + 1)
2
(u
4
− u
3
+ 2u
2
− 2u + 1)
· (u
92
− 4u
91
+ ··· − 8u
2
+ 1)
27
VI. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
, c
2
, c
4
((y −1)
7
)(y
2
− 3y + 1)
3
(y
92
− 89y
91
+ ··· − 208y + 1)
c
3
, c
6
y
7
(y
2
− 3y + 1)
3
(y
92
− 54y
91
+ ··· − 716800y + 16384)
c
5
, c
9
y
6
(y
3
+ 4y
2
+ 4y −1)(y
4
+ 3y
3
+ 2y
2
+ 1)
· (y
92
+ 42y
91
+ ··· − 25600y + 4096)
c
7
(y
2
+ y + 1)
2
(y
3
− y
2
+ 2y −1)
2
(y
3
+ y
2
+ 13y −4)
· (y
92
+ 4y
91
+ ··· + 8856y + 1296)
c
8
, c
11
, c
12
(y
3
+ 3y
2
+ 2y −1)
2
(y
3
+ 4y
2
+ 4y −1)(y
4
+ 3y
3
+ 2y
2
+ 1)
· (y
92
+ 84y
91
+ ··· − 16y + 1)
c
10
(y
3
− y
2
+ 2y −1)
2
(y
3
+ 4y
2
+ 4y −1)(y
4
+ 3y
3
+ 2y
2
+ 1)
· (y
92
+ 28y
91
+ ··· + 10518208240y + 185858689)
28
