Properties

Label 2.201.16t60.a
Dimension $2$
Group $\SL(2,3):C_2$
Conductor $201$
Indicator $0$

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Basic invariants

Dimension:$2$
Group:16T60
Conductor:\(201\)\(\medspace = 3 \cdot 67 \)
Artin number field: Galois closure of 16.0.2664210032449121601.1
Galois orbit size: $4$
Smallest permutation container: 16T60
Parity: odd
Projective image: $A_4$
Projective field: Galois closure of 4.0.40401.1

Galois action

Roots of defining polynomial

The roots of $f$ are computed in an extension of $\Q_{ 37 }$ to precision 10.
Minimal polynomial of a generator $a$ of $K$ over $\mathbb{Q}_{ 37 }$: \( x^{6} + 35x^{3} + 4x^{2} + 30x + 2 \) Copy content Toggle raw display
Roots:
$r_{ 1 }$ $=$ \( 25 a^{5} + 20 a^{4} + 3 a^{3} + 18 a^{2} + 16 a + 16 + \left(34 a^{5} + 31 a^{4} + 6 a^{3} + 36 a^{2} + 22 a + 10\right)\cdot 37 + \left(26 a^{5} + 13 a^{4} + 25 a^{3} + 25 a^{2} + 18 a\right)\cdot 37^{2} + \left(a^{5} + 11 a^{4} + 35 a^{3} + 8 a^{2} + 29 a + 1\right)\cdot 37^{3} + \left(4 a^{5} + 32 a^{4} + 11 a^{3} + 34 a^{2} + 27 a + 10\right)\cdot 37^{4} + \left(4 a^{5} + 7 a^{4} + 6 a^{3} + 13 a^{2} + 12 a + 28\right)\cdot 37^{5} + \left(24 a^{5} + 28 a^{4} + 27 a^{3} + 35 a^{2} + 23 a + 10\right)\cdot 37^{6} + \left(4 a^{5} + 26 a^{4} + 26 a^{3} + 13 a^{2} + 14 a + 26\right)\cdot 37^{7} + \left(4 a^{5} + 18 a^{4} + 3 a^{3} + 12 a^{2} + 9 a + 28\right)\cdot 37^{8} + \left(12 a^{5} + 4 a^{4} + 7 a^{3} + 23 a^{2} + 3 a + 8\right)\cdot 37^{9} +O(37^{10})\) Copy content Toggle raw display
$r_{ 2 }$ $=$ \( 4 a^{5} + 33 a^{4} + 4 a^{3} + 3 a^{2} + 3 a + 28 + \left(4 a^{5} + 27 a^{4} + 16 a^{3} + 2 a^{2} + 3 a + 7\right)\cdot 37 + \left(24 a^{5} + 10 a^{3} + 33 a^{2} + 6 a + 2\right)\cdot 37^{2} + \left(24 a^{5} + 19 a^{4} + 6 a^{3} + 34 a^{2} + 28 a + 6\right)\cdot 37^{3} + \left(32 a^{5} + 14 a^{4} + 22 a^{3} + 11 a^{2} + 21 a + 35\right)\cdot 37^{4} + \left(34 a^{5} + a^{4} + 15 a^{3} + 11 a^{2} + 8 a + 31\right)\cdot 37^{5} + \left(9 a^{4} + 3 a^{3} + 18 a^{2} + 32 a + 23\right)\cdot 37^{6} + \left(26 a^{5} + a^{4} + 17 a^{3} + 11 a^{2} + 24 a + 12\right)\cdot 37^{7} + \left(9 a^{5} + 10 a^{4} + 36 a^{3} + 33 a^{2} + 30 a + 27\right)\cdot 37^{8} + \left(5 a^{5} + 6 a^{4} + 19 a^{3} + 11 a^{2} + 17 a + 19\right)\cdot 37^{9} +O(37^{10})\) Copy content Toggle raw display
$r_{ 3 }$ $=$ \( 24 a^{5} + 17 a^{4} + 22 a^{3} + 4 a^{2} + 14 a + 11 + \left(16 a^{5} + 11 a^{4} + 4 a^{3} + 14 a^{2} + 34 a + 14\right)\cdot 37 + \left(14 a^{5} + 20 a^{4} + 9 a^{3} + 31 a^{2} + 4 a + 30\right)\cdot 37^{2} + \left(15 a^{5} + 3 a^{4} + 17 a^{3} + 12 a^{2} + 5 a + 23\right)\cdot 37^{3} + \left(4 a^{5} + 29 a^{4} + 2 a^{3} + 14 a^{2} + 25 a + 9\right)\cdot 37^{4} + \left(27 a^{5} + 25 a^{4} + 7 a^{3} + 34 a^{2} + 25 a\right)\cdot 37^{5} + \left(15 a^{5} + 19 a^{4} + 16 a^{3} + 9 a^{2} + 28 a + 35\right)\cdot 37^{6} + \left(28 a^{5} + 23 a^{4} + 32 a^{3} + 14 a^{2} + 19 a + 5\right)\cdot 37^{7} + \left(2 a^{5} + 22 a^{4} + 14 a^{3} + 19 a^{2} + 17 a + 3\right)\cdot 37^{8} + \left(2 a^{4} + 8 a^{3} + 17 a^{2} + 3 a + 29\right)\cdot 37^{9} +O(37^{10})\) Copy content Toggle raw display
$r_{ 4 }$ $=$ \( 28 a^{5} + 34 a^{4} + 28 a^{3} + 21 a^{2} + 30 a + 17 + \left(23 a^{5} + 23 a^{4} + 14 a^{3} + 19 a^{2} + 11 a + 35\right)\cdot 37 + \left(12 a^{5} + 23 a^{4} + 15 a^{3} + 21 a^{2} + 21 a + 9\right)\cdot 37^{2} + \left(20 a^{5} + 15 a^{4} + 8 a^{3} + 16 a^{2} + 2 a + 25\right)\cdot 37^{3} + \left(2 a^{5} + a^{4} + 19 a^{3} + 21 a^{2} + 14 a + 29\right)\cdot 37^{4} + \left(15 a^{5} + 2 a^{4} + 13 a^{3} + 22 a^{2} + 16 a + 11\right)\cdot 37^{5} + \left(21 a^{5} + 23 a^{4} + 12 a^{3} + 23 a^{2} + 17 a + 3\right)\cdot 37^{6} + \left(5 a^{5} + 36 a^{4} + 6 a^{3} + 31 a^{2} + 25 a + 27\right)\cdot 37^{7} + \left(9 a^{5} + 6 a^{4} + 3 a^{3} + 4 a^{2} + 23 a + 14\right)\cdot 37^{8} + \left(8 a^{5} + 3 a^{4} + 35 a^{3} + 18 a^{2} + a + 28\right)\cdot 37^{9} +O(37^{10})\) Copy content Toggle raw display
$r_{ 5 }$ $=$ \( 13 a^{5} + 27 a^{4} + 7 a^{3} + 19 a^{2} + 24 a + 12 + \left(33 a^{5} + 19 a^{4} + 2 a^{3} + 33 a^{2} + 27 a + 23\right)\cdot 37 + \left(31 a^{5} + 15 a^{4} + 23 a^{3} + 28 a^{2} + 9 a + 25\right)\cdot 37^{2} + \left(28 a^{5} + 14 a^{4} + 16 a^{3} + 25 a^{2} + 28 a + 8\right)\cdot 37^{3} + \left(25 a^{5} + 21 a^{4} + 10 a^{3} + 11 a^{2} + 19 a + 9\right)\cdot 37^{4} + \left(29 a^{5} + 14 a^{4} + 32 a^{3} + 36 a + 1\right)\cdot 37^{5} + \left(14 a^{5} + 6 a^{4} + 20 a^{3} + 26 a^{2} + 6 a + 15\right)\cdot 37^{6} + \left(21 a^{5} + 23 a^{4} + 6 a^{3} + 11 a^{2} + 11 a + 36\right)\cdot 37^{7} + \left(14 a^{5} + 15 a^{4} + 35 a^{3} + 15 a^{2} + 5\right)\cdot 37^{8} + \left(17 a^{5} + 3 a^{4} + 35 a^{3} + 2 a^{2} + 21 a + 15\right)\cdot 37^{9} +O(37^{10})\) Copy content Toggle raw display
$r_{ 6 }$ $=$ \( 28 a^{5} + 5 a^{4} + 33 a^{3} + 6 a^{2} + 11 a + 5 + \left(26 a^{5} + 30 a^{4} + 12 a^{3} + 3 a^{2} + 25 a + 17\right)\cdot 37 + \left(10 a^{5} + 12 a^{4} + 12 a^{3} + 4 a^{2} + 34 a + 15\right)\cdot 37^{2} + \left(25 a^{5} + 31 a^{4} + 18 a^{3} + 9 a^{2} + 16 a + 22\right)\cdot 37^{3} + \left(22 a^{5} + 36 a^{4} + 20 a^{3} + a^{2} + 2 a + 24\right)\cdot 37^{4} + \left(20 a^{5} + 18 a^{4} + 32 a^{3} + 17 a^{2} + 31 a + 30\right)\cdot 37^{5} + \left(8 a^{5} + 5 a^{4} + 5 a^{3} + 7 a^{2} + 11 a + 5\right)\cdot 37^{6} + \left(22 a^{5} + 2 a^{4} + 16 a^{3} + 7 a^{2} + 19 a + 1\right)\cdot 37^{7} + \left(27 a^{5} + 14 a^{4} + 14 a^{3} + 27 a^{2} + 3 a + 21\right)\cdot 37^{8} + \left(20 a^{5} + 33 a^{4} + 25 a^{3} + 15 a^{2} + 6 a + 7\right)\cdot 37^{9} +O(37^{10})\) Copy content Toggle raw display
$r_{ 7 }$ $=$ \( 2 a^{5} + 10 a^{4} + 14 a^{3} + 23 a^{2} + 6 a + 20 + \left(5 a^{5} + 4 a^{4} + 5 a^{3} + 7 a^{2} + 31 a + 23\right)\cdot 37 + \left(8 a^{5} + 4 a^{4} + 14 a^{3} + 32 a^{2} + a + 20\right)\cdot 37^{2} + \left(11 a^{5} + 30 a^{4} + 25 a^{3} + 14 a^{2} + 5 a + 15\right)\cdot 37^{3} + \left(28 a^{5} + 29 a^{4} + 9 a^{3} + 15 a^{2} + 17 a + 33\right)\cdot 37^{4} + \left(8 a^{5} + 29 a^{4} + 6 a^{3} + 10 a^{2} + 2 a + 10\right)\cdot 37^{5} + \left(13 a^{5} + 14 a^{4} + 7 a^{3} + 20 a^{2} + 15 a + 25\right)\cdot 37^{6} + \left(4 a^{5} + 3 a^{4} + a^{3} + 29 a^{2} + 26 a + 27\right)\cdot 37^{7} + \left(9 a^{5} + 20 a^{4} + 4 a^{3} + 35 a^{2} + 13 a + 20\right)\cdot 37^{8} + \left(32 a^{5} + 28 a^{4} + 33 a^{3} + 11 a^{2} + 13 a + 1\right)\cdot 37^{9} +O(37^{10})\) Copy content Toggle raw display
$r_{ 8 }$ $=$ \( a^{5} + 20 a^{4} + 21 a^{3} + 24 a^{2} + 7 a + 28 + \left(33 a^{5} + 9 a^{4} + 14 a^{3} + 12 a^{2} + 27 a + 21\right)\cdot 37 + \left(24 a^{5} + 24 a^{4} + 4 a^{3} + 28 a^{2} + 12 a\right)\cdot 37^{2} + \left(15 a^{5} + 32 a^{4} + 29 a^{3} + 36 a^{2} + 33 a + 36\right)\cdot 37^{3} + \left(34 a^{5} + 10 a^{4} + 21 a^{3} + 6 a^{2} + 29 a + 30\right)\cdot 37^{4} + \left(4 a^{5} + 10 a^{4} + 17 a^{3} + 8 a^{2} + 11 a\right)\cdot 37^{5} + \left(22 a^{5} + 15 a^{4} + 33 a^{3} + 4 a^{2} + 30 a + 11\right)\cdot 37^{6} + \left(9 a^{5} + 21 a^{4} + 33 a^{3} + 19 a^{2} + 28 a + 35\right)\cdot 37^{7} + \left(13 a^{5} + 11 a^{4} + 18 a^{3} + 22 a^{2} + 35 a + 1\right)\cdot 37^{8} + \left(5 a^{5} + 5 a^{4} + 17 a^{3} + 6 a^{2} + 14 a + 19\right)\cdot 37^{9} +O(37^{10})\) Copy content Toggle raw display
$r_{ 9 }$ $=$ \( 14 a^{5} + 14 a^{4} + 8 a^{3} + 18 a^{2} + a + 16 + \left(33 a^{5} + 22 a^{4} + 34 a^{2} + 30 a + 17\right)\cdot 37 + \left(36 a^{5} + 31 a^{4} + 6 a^{3} + 20 a^{2} + 32 a + 35\right)\cdot 37^{2} + \left(7 a^{5} + 23 a^{4} + 15 a^{3} + 26 a^{2} + 20 a + 16\right)\cdot 37^{3} + \left(36 a^{5} + 2 a^{4} + 23 a^{3} + 9 a^{2} + 25 a + 10\right)\cdot 37^{4} + \left(19 a^{5} + 30 a^{4} + 8 a^{3} + 7 a^{2} + 22 a + 31\right)\cdot 37^{5} + \left(30 a^{5} + 28 a^{4} + 9 a^{3} + 34 a^{2} + 36 a + 31\right)\cdot 37^{6} + \left(29 a^{5} + 29 a^{4} + 14 a^{3} + 9 a^{2} + 3 a + 25\right)\cdot 37^{7} + \left(a^{5} + 6 a^{4} + 2 a^{3} + 6 a^{2} + 35 a + 32\right)\cdot 37^{8} + \left(a^{5} + 26 a^{4} + 28 a^{3} + 22 a^{2} + 34 a + 8\right)\cdot 37^{9} +O(37^{10})\) Copy content Toggle raw display
$r_{ 10 }$ $=$ \( 17 a^{5} + 32 a^{3} + 15 a^{2} + 7 a + 15 + \left(15 a^{5} + 16 a^{4} + 36 a^{3} + 29 a^{2} + 36 a + 6\right)\cdot 37 + \left(31 a^{5} + 14 a^{4} + 13 a^{3} + 20 a^{2} + 29 a + 6\right)\cdot 37^{2} + \left(21 a^{5} + a^{4} + 7 a^{3} + 16 a^{2} + 35 a + 19\right)\cdot 37^{3} + \left(7 a^{5} + 13 a^{4} + 36 a^{3} + 21 a^{2} + 8 a + 7\right)\cdot 37^{4} + \left(a^{5} + 6 a^{4} + 8 a^{3} + 32 a + 6\right)\cdot 37^{5} + \left(9 a^{5} + 33 a^{4} + 21 a^{3} + 35 a^{2} + 22 a + 4\right)\cdot 37^{6} + \left(33 a^{5} + 27 a^{4} + 29 a^{3} + 2 a^{2} + a + 20\right)\cdot 37^{7} + \left(31 a^{5} + 8 a^{4} + 34 a^{3} + 32 a^{2} + 15 a + 25\right)\cdot 37^{8} + \left(13 a^{5} + a^{4} + 22 a^{3} + 2 a^{2} + 19 a + 1\right)\cdot 37^{9} +O(37^{10})\) Copy content Toggle raw display
$r_{ 11 }$ $=$ \( 35 a^{5} + 24 a^{4} + 25 a^{3} + 22 a^{2} + 25 a + 18 + \left(33 a^{5} + 36 a^{3} + 5 a^{2} + 11 a + 23\right)\cdot 37 + \left(22 a^{5} + 17 a^{4} + 11 a^{3} + 25 a^{2} + 32 a + 30\right)\cdot 37^{2} + \left(34 a^{5} + 35 a^{4} + 18 a^{3} + 34 a^{2} + 30 a + 28\right)\cdot 37^{3} + \left(a^{5} + 15 a^{4} + 23 a^{3} + 19 a^{2} + 28 a + 27\right)\cdot 37^{4} + \left(3 a^{5} + 35 a^{4} + 20 a^{3} + 21 a + 31\right)\cdot 37^{5} + \left(23 a^{5} + 25 a^{4} + 21 a^{3} + 29 a^{2} + 24 a + 14\right)\cdot 37^{6} + \left(13 a^{5} + 26 a^{4} + 34 a^{3} + 34 a^{2} + 3 a + 33\right)\cdot 37^{7} + \left(22 a^{5} + 36 a^{3} + 29 a^{2} + 17 a + 12\right)\cdot 37^{8} + \left(35 a^{5} + 16 a^{4} + 20 a^{3} + 28 a^{2} + a + 20\right)\cdot 37^{9} +O(37^{10})\) Copy content Toggle raw display
$r_{ 12 }$ $=$ \( 32 a^{5} + 3 a^{4} + 25 a^{3} + 12 a^{2} + 16 a + 25 + \left(26 a^{5} + 18 a^{4} + 6 a^{3} + 10 a^{2} + 20 a + 11\right)\cdot 37 + \left(29 a^{5} + 12 a^{4} + 26 a^{3} + 8 a^{2} + 3 a + 16\right)\cdot 37^{2} + \left(28 a^{5} + 29 a^{4} + 17 a^{3} + 31 a^{2} + 35 a + 10\right)\cdot 37^{3} + \left(32 a^{5} + 20 a^{4} + 16 a^{3} + 15 a^{2} + 26 a + 24\right)\cdot 37^{4} + \left(13 a^{5} + 16 a^{4} + 26 a^{3} + 35 a^{2} + 33 a + 6\right)\cdot 37^{5} + \left(20 a^{5} + 2 a^{4} + 22 a^{3} + 32 a^{2} + 9 a + 11\right)\cdot 37^{6} + \left(4 a^{5} + 27 a^{4} + 16 a^{3} + 35 a^{2} + 24 a + 26\right)\cdot 37^{7} + \left(36 a^{5} + 26 a^{4} + 10 a^{3} + 26 a^{2} + 20 a + 5\right)\cdot 37^{8} + \left(13 a^{5} + 23 a^{4} + 22 a^{3} + 20 a^{2} + 29 a + 33\right)\cdot 37^{9} +O(37^{10})\) Copy content Toggle raw display
$r_{ 13 }$ $=$ \( 18 a^{5} + 10 a^{4} + 21 a^{3} + 11 a^{2} + a + 16 + \left(7 a^{5} + 35 a^{4} + 14 a^{3} + 26 a^{2} + 35 a + 29\right)\cdot 37 + \left(23 a^{5} + 5 a^{4} + 5 a^{3} + 8 a^{2} + 27 a + 3\right)\cdot 37^{2} + \left(22 a^{5} + 8 a^{3} + 23 a^{2} + 19 a + 24\right)\cdot 37^{3} + \left(a^{5} + 17 a^{4} + 16 a^{3} + 31 a^{2} + 6 a + 24\right)\cdot 37^{4} + \left(15 a^{5} + 27 a^{4} + 26 a^{3} + 26 a^{2} + 23 a + 35\right)\cdot 37^{5} + \left(10 a^{5} + 16 a^{4} + 27 a^{3} + 29 a^{2} + 32 a + 33\right)\cdot 37^{6} + \left(25 a^{5} + 8 a^{4} + 27 a^{3} + 35 a^{2} + 12 a + 20\right)\cdot 37^{7} + \left(29 a^{5} + 16 a^{4} + 26 a^{3} + 17 a^{2} + 30 a + 9\right)\cdot 37^{8} + \left(a^{5} + 7 a^{4} + 2 a^{3} + 10 a^{2} + 10 a + 4\right)\cdot 37^{9} +O(37^{10})\) Copy content Toggle raw display
$r_{ 14 }$ $=$ \( 9 a^{5} + 32 a^{4} + 4 a^{3} + 31 a^{2} + 26 a + 1 + \left(10 a^{5} + 6 a^{4} + 24 a^{3} + 33 a^{2} + 11 a + 16\right)\cdot 37 + \left(26 a^{5} + 24 a^{4} + 24 a^{3} + 32 a^{2} + 2 a + 2\right)\cdot 37^{2} + \left(11 a^{5} + 5 a^{4} + 18 a^{3} + 27 a^{2} + 20 a + 21\right)\cdot 37^{3} + \left(14 a^{5} + 16 a^{3} + 35 a^{2} + 34 a + 11\right)\cdot 37^{4} + \left(16 a^{5} + 18 a^{4} + 4 a^{3} + 19 a^{2} + 5 a + 16\right)\cdot 37^{5} + \left(28 a^{5} + 31 a^{4} + 31 a^{3} + 29 a^{2} + 25 a + 33\right)\cdot 37^{6} + \left(14 a^{5} + 34 a^{4} + 20 a^{3} + 29 a^{2} + 17 a + 26\right)\cdot 37^{7} + \left(9 a^{5} + 22 a^{4} + 22 a^{3} + 9 a^{2} + 33 a + 21\right)\cdot 37^{8} + \left(16 a^{5} + 3 a^{4} + 11 a^{3} + 21 a^{2} + 30 a + 12\right)\cdot 37^{9} +O(37^{10})\) Copy content Toggle raw display
$r_{ 15 }$ $=$ \( 10 a^{5} + 30 a^{4} + 33 a^{3} + 19 a^{2} + 5 a + 20 + \left(24 a^{5} + 10 a^{4} + 3 a^{3} + 2 a^{2} + 32 a + 20\right)\cdot 37 + \left(33 a^{5} + 25 a^{4} + 24 a^{3} + 2 a^{2} + 32 a + 7\right)\cdot 37^{2} + \left(3 a^{5} + 8 a^{3} + 13 a^{2} + 17 a + 4\right)\cdot 37^{3} + \left(7 a^{5} + 24 a^{4} + 30 a^{3} + 14 a^{2} + 36 a + 14\right)\cdot 37^{4} + \left(12 a^{5} + 24 a^{4} + 12 a^{3} + 21 a^{2} + 22 a + 6\right)\cdot 37^{5} + \left(a^{5} + 13 a^{4} + 32 a^{3} + a^{2} + 8 a + 17\right)\cdot 37^{6} + \left(25 a^{5} + 24 a^{4} + 8 a^{3} + 27 a^{2} + 16 a + 13\right)\cdot 37^{7} + \left(13 a^{5} + 31 a^{4} + 13 a^{3} + 24 a^{2} + 8 a + 18\right)\cdot 37^{8} + \left(6 a^{5} + 24 a^{4} + 22 a^{3} + 14 a^{2} + 28 a + 1\right)\cdot 37^{9} +O(37^{10})\) Copy content Toggle raw display
$r_{ 16 }$ $=$ \( 36 a^{5} + 17 a^{4} + 16 a^{3} + 13 a^{2} + 30 a + 12 + \left(3 a^{5} + 27 a^{4} + 22 a^{3} + 24 a^{2} + 9 a + 17\right)\cdot 37 + \left(12 a^{5} + 12 a^{4} + 32 a^{3} + 8 a^{2} + 24 a + 14\right)\cdot 37^{2} + \left(21 a^{5} + 4 a^{4} + 7 a^{3} + 3 a + 32\right)\cdot 37^{3} + \left(2 a^{5} + 26 a^{4} + 15 a^{3} + 30 a^{2} + 7 a + 29\right)\cdot 37^{4} + \left(32 a^{5} + 26 a^{4} + 19 a^{3} + 28 a^{2} + 25 a + 8\right)\cdot 37^{5} + \left(14 a^{5} + 21 a^{4} + 3 a^{3} + 32 a^{2} + 6 a + 19\right)\cdot 37^{6} + \left(27 a^{5} + 15 a^{4} + 3 a^{3} + 17 a^{2} + 8 a + 30\right)\cdot 37^{7} + \left(23 a^{5} + 25 a^{4} + 18 a^{3} + 14 a^{2} + a + 8\right)\cdot 37^{8} + \left(31 a^{5} + 31 a^{4} + 19 a^{3} + 30 a^{2} + 22 a + 10\right)\cdot 37^{9} +O(37^{10})\) Copy content Toggle raw display

Generators of the action on the roots $r_1, \ldots, r_{ 16 }$

Cycle notation
$(1,7,4)(2,13,11)(3,10,5)(9,15,12)$
$(1,9)(2,10)(3,11)(4,12)(5,13)(6,14)(7,15)(8,16)$
$(1,3,9,11)(2,7,10,15)(4,5,12,13)(6,16,14,8)$
$(1,16,9,8)(2,13,10,5)(3,14,11,6)(4,15,12,7)$
$(1,12,9,4)(2,6,10,14)(3,13,11,5)(7,16,15,8)$

Character values on conjugacy classes

SizeOrderAction on $r_1, \ldots, r_{ 16 }$ Character values
$c1$ $c2$ $c3$ $c4$
$1$ $1$ $()$ $2$ $2$ $2$ $2$
$1$ $2$ $(1,9)(2,10)(3,11)(4,12)(5,13)(6,14)(7,15)(8,16)$ $-2$ $-2$ $-2$ $-2$
$6$ $2$ $(1,14)(2,4)(3,8)(5,7)(6,9)(10,12)(11,16)(13,15)$ $0$ $0$ $0$ $0$
$4$ $3$ $(1,16,12)(3,14,13)(4,9,8)(5,11,6)$ $\zeta_{12}^{2}$ $-\zeta_{12}^{2} + 1$ $-\zeta_{12}^{2} + 1$ $\zeta_{12}^{2}$
$4$ $3$ $(1,12,16)(3,13,14)(4,8,9)(5,6,11)$ $-\zeta_{12}^{2} + 1$ $\zeta_{12}^{2}$ $\zeta_{12}^{2}$ $-\zeta_{12}^{2} + 1$
$1$ $4$ $(1,3,9,11)(2,7,10,15)(4,5,12,13)(6,16,14,8)$ $2 \zeta_{12}^{3}$ $-2 \zeta_{12}^{3}$ $2 \zeta_{12}^{3}$ $-2 \zeta_{12}^{3}$
$1$ $4$ $(1,11,9,3)(2,15,10,7)(4,13,12,5)(6,8,14,16)$ $-2 \zeta_{12}^{3}$ $2 \zeta_{12}^{3}$ $-2 \zeta_{12}^{3}$ $2 \zeta_{12}^{3}$
$6$ $4$ $(1,16,9,8)(2,13,10,5)(3,14,11,6)(4,15,12,7)$ $0$ $0$ $0$ $0$
$4$ $6$ $(1,4,16,9,12,8)(2,10)(3,5,14,11,13,6)(7,15)$ $\zeta_{12}^{2} - 1$ $-\zeta_{12}^{2}$ $-\zeta_{12}^{2}$ $\zeta_{12}^{2} - 1$
$4$ $6$ $(1,8,12,9,16,4)(2,10)(3,6,13,11,14,5)(7,15)$ $-\zeta_{12}^{2}$ $\zeta_{12}^{2} - 1$ $\zeta_{12}^{2} - 1$ $-\zeta_{12}^{2}$
$4$ $12$ $(1,14,4,11,16,13,9,6,12,3,8,5)(2,7,10,15)$ $\zeta_{12}^{3} - \zeta_{12}$ $-\zeta_{12}$ $\zeta_{12}$ $-\zeta_{12}^{3} + \zeta_{12}$
$4$ $12$ $(1,13,8,11,12,14,9,5,16,3,4,6)(2,7,10,15)$ $\zeta_{12}$ $-\zeta_{12}^{3} + \zeta_{12}$ $\zeta_{12}^{3} - \zeta_{12}$ $-\zeta_{12}$
$4$ $12$ $(1,6,4,3,16,5,9,14,12,11,8,13)(2,15,10,7)$ $-\zeta_{12}^{3} + \zeta_{12}$ $\zeta_{12}$ $-\zeta_{12}$ $\zeta_{12}^{3} - \zeta_{12}$
$4$ $12$ $(1,5,8,3,12,6,9,13,16,11,4,14)(2,15,10,7)$ $-\zeta_{12}$ $\zeta_{12}^{3} - \zeta_{12}$ $-\zeta_{12}^{3} + \zeta_{12}$ $\zeta_{12}$
The blue line marks the conjugacy class containing complex conjugation.