Properties

 Label 1.108.18t1.a.a Dimension $1$ Group $C_{18}$ Conductor $108$ Root number not computed Indicator $0$

Related objects

Basic invariants

 Dimension: $1$ Group: $C_{18}$ Conductor: $$108$$$$\medspace = 2^{2} \cdot 3^{3}$$ Artin field: Galois closure of 18.0.258151783382020583032356864.7 Galois orbit size: $6$ Smallest permutation container: $C_{18}$ Parity: odd Dirichlet character: $$\chi_{108}(103,\cdot)$$ Projective image: $C_1$ Projective field: Galois closure of $$\Q$$

Defining polynomial

 $f(x)$ $=$ $$x^{18} + 18x^{16} + 135x^{14} + 546x^{12} + 1287x^{10} + 1782x^{8} + 1386x^{6} + 540x^{4} + 81x^{2} + 1$$ x^18 + 18*x^16 + 135*x^14 + 546*x^12 + 1287*x^10 + 1782*x^8 + 1386*x^6 + 540*x^4 + 81*x^2 + 1 .

The roots of $f$ are computed in an extension of $\Q_{ 29 }$ to precision 7.

Minimal polynomial of a generator $a$ of $K$ over $\mathbb{Q}_{ 29 }$: $$x^{9} + 4x^{3} + 22x^{2} + 22x + 27$$

Roots:
 $r_{ 1 }$ $=$ $$6 a^{8} + 10 a^{6} + 10 a^{5} + 6 a^{4} + 13 a^{3} + 5 a^{2} + 28 + \left(20 a^{8} + 6 a^{7} + 16 a^{6} + 4 a^{5} + 6 a^{4} + 5 a^{3} + 23 a^{2} + 14 a + 12\right)\cdot 29 + \left(25 a^{8} + 20 a^{7} + 4 a^{6} + 27 a^{4} + a^{3} + 6 a^{2} + 26 a + 19\right)\cdot 29^{2} + \left(18 a^{8} + 11 a^{7} + 21 a^{6} + 14 a^{5} + 7 a^{4} + 14 a^{3} + 24 a^{2} + 11 a + 13\right)\cdot 29^{3} + \left(a^{8} + 24 a^{7} + 13 a^{6} + 23 a^{5} + 7 a^{4} + 5 a^{3} + a^{2} + 16 a + 22\right)\cdot 29^{4} + \left(7 a^{8} + 10 a^{7} + 24 a^{6} + 23 a^{5} + 27 a^{4} + 18 a^{3} + 26 a^{2} + 11 a + 11\right)\cdot 29^{5} + \left(22 a^{8} + 8 a^{7} + 8 a^{6} + 3 a^{5} + 25 a^{4} + 5 a^{3} + 22 a^{2} + a + 15\right)\cdot 29^{6} +O(29^{7})$$ 6*a^8 + 10*a^6 + 10*a^5 + 6*a^4 + 13*a^3 + 5*a^2 + 28 + (20*a^8 + 6*a^7 + 16*a^6 + 4*a^5 + 6*a^4 + 5*a^3 + 23*a^2 + 14*a + 12)*29 + (25*a^8 + 20*a^7 + 4*a^6 + 27*a^4 + a^3 + 6*a^2 + 26*a + 19)*29^2 + (18*a^8 + 11*a^7 + 21*a^6 + 14*a^5 + 7*a^4 + 14*a^3 + 24*a^2 + 11*a + 13)*29^3 + (a^8 + 24*a^7 + 13*a^6 + 23*a^5 + 7*a^4 + 5*a^3 + a^2 + 16*a + 22)*29^4 + (7*a^8 + 10*a^7 + 24*a^6 + 23*a^5 + 27*a^4 + 18*a^3 + 26*a^2 + 11*a + 11)*29^5 + (22*a^8 + 8*a^7 + 8*a^6 + 3*a^5 + 25*a^4 + 5*a^3 + 22*a^2 + a + 15)*29^6+O(29^7) $r_{ 2 }$ $=$ $$16 a^{8} + 20 a^{7} + 28 a^{6} + 11 a^{5} + 28 a^{4} + 18 a^{3} + a^{2} + 5 a + 8 + \left(9 a^{8} + 27 a^{7} + 4 a^{6} + 25 a^{5} + 21 a^{4} + 10 a^{2} + 26 a + 13\right)\cdot 29 + \left(6 a^{8} + 21 a^{7} + 3 a^{5} + 27 a^{4} + 17 a^{3} + 9 a^{2} + 25 a\right)\cdot 29^{2} + \left(23 a^{8} + 27 a^{7} + 2 a^{6} + 9 a^{5} + 2 a^{4} + 9 a^{3} + 19 a^{2} + 16\right)\cdot 29^{3} + \left(26 a^{7} + 27 a^{6} + 26 a^{5} + 22 a^{4} + 16 a^{3} + 4 a^{2} + 12 a + 4\right)\cdot 29^{4} + \left(28 a^{8} + 3 a^{7} + 9 a^{6} + 13 a^{5} + 22 a^{4} + 14 a^{3} + 14 a + 23\right)\cdot 29^{5} + \left(21 a^{8} + 7 a^{7} + 23 a^{6} + 17 a^{5} + 12 a^{4} + 18 a^{3} + 22 a^{2} + 11 a + 17\right)\cdot 29^{6} +O(29^{7})$$ 16*a^8 + 20*a^7 + 28*a^6 + 11*a^5 + 28*a^4 + 18*a^3 + a^2 + 5*a + 8 + (9*a^8 + 27*a^7 + 4*a^6 + 25*a^5 + 21*a^4 + 10*a^2 + 26*a + 13)*29 + (6*a^8 + 21*a^7 + 3*a^5 + 27*a^4 + 17*a^3 + 9*a^2 + 25*a)*29^2 + (23*a^8 + 27*a^7 + 2*a^6 + 9*a^5 + 2*a^4 + 9*a^3 + 19*a^2 + 16)*29^3 + (26*a^7 + 27*a^6 + 26*a^5 + 22*a^4 + 16*a^3 + 4*a^2 + 12*a + 4)*29^4 + (28*a^8 + 3*a^7 + 9*a^6 + 13*a^5 + 22*a^4 + 14*a^3 + 14*a + 23)*29^5 + (21*a^8 + 7*a^7 + 23*a^6 + 17*a^5 + 12*a^4 + 18*a^3 + 22*a^2 + 11*a + 17)*29^6+O(29^7) $r_{ 3 }$ $=$ $$4 a^{8} + 19 a^{7} + 13 a^{6} + 10 a^{5} + 10 a^{4} + 15 a^{3} + 7 a^{2} + 20 a + 3 + \left(2 a^{8} + a^{7} + 6 a^{6} + 6 a^{5} + 4 a^{4} + 24 a^{3} + 5 a^{2} + 13 a + 26\right)\cdot 29 + \left(6 a^{8} + 22 a^{7} + 18 a^{6} + 4 a^{5} + 16 a^{4} + 4 a^{3} + 23 a^{2} + 3 a + 9\right)\cdot 29^{2} + \left(13 a^{8} + 24 a^{7} + 8 a^{6} + 24 a^{5} + 23 a^{4} + 10 a^{3} + 9 a^{2} + 9 a + 28\right)\cdot 29^{3} + \left(6 a^{7} + a^{6} + 9 a^{5} + 14 a^{4} + 3 a^{3} + 21 a^{2} + 22 a + 3\right)\cdot 29^{4} + \left(10 a^{8} + 4 a^{7} + 14 a^{6} + 16 a^{5} + 26 a^{4} + 12 a^{3} + a^{2} + 28 a + 6\right)\cdot 29^{5} + \left(24 a^{8} + 23 a^{7} + 5 a^{6} + 16 a^{5} + 9 a^{4} + 20 a^{3} + a^{2} + 23\right)\cdot 29^{6} +O(29^{7})$$ 4*a^8 + 19*a^7 + 13*a^6 + 10*a^5 + 10*a^4 + 15*a^3 + 7*a^2 + 20*a + 3 + (2*a^8 + a^7 + 6*a^6 + 6*a^5 + 4*a^4 + 24*a^3 + 5*a^2 + 13*a + 26)*29 + (6*a^8 + 22*a^7 + 18*a^6 + 4*a^5 + 16*a^4 + 4*a^3 + 23*a^2 + 3*a + 9)*29^2 + (13*a^8 + 24*a^7 + 8*a^6 + 24*a^5 + 23*a^4 + 10*a^3 + 9*a^2 + 9*a + 28)*29^3 + (6*a^7 + a^6 + 9*a^5 + 14*a^4 + 3*a^3 + 21*a^2 + 22*a + 3)*29^4 + (10*a^8 + 4*a^7 + 14*a^6 + 16*a^5 + 26*a^4 + 12*a^3 + a^2 + 28*a + 6)*29^5 + (24*a^8 + 23*a^7 + 5*a^6 + 16*a^5 + 9*a^4 + 20*a^3 + a^2 + 23)*29^6+O(29^7) $r_{ 4 }$ $=$ $$10 a^{8} + 19 a^{7} + 14 a^{6} + 23 a^{5} + 18 a^{4} + 5 a^{3} + 15 a^{2} + 16 a + 7 + \left(16 a^{8} + 24 a^{7} + 4 a^{6} + 18 a^{5} + 6 a^{4} + 27 a^{3} + 13 a^{2} + 4 a + 25\right)\cdot 29 + \left(5 a^{8} + 24 a^{7} + 19 a^{6} + 9 a^{5} + 3 a^{4} + 24 a^{3} + 24 a^{2} + 16 a + 1\right)\cdot 29^{2} + \left(7 a^{7} + 25 a^{6} + 25 a^{5} + 9 a^{4} + 28 a^{3} + 17 a^{2} + 18 a + 10\right)\cdot 29^{3} + \left(27 a^{8} + 26 a^{7} + 16 a^{6} + 19 a^{5} + 24 a^{4} + 15 a^{3} + a^{2} + 3 a + 17\right)\cdot 29^{4} + \left(13 a^{8} + 27 a^{7} + 15 a^{6} + 28 a^{5} + 23 a^{3} + 12 a^{2} + 23 a + 24\right)\cdot 29^{5} + \left(22 a^{7} + 9 a^{6} + 4 a^{5} + 5 a^{4} + 6 a^{3} + 13 a^{2} + 8\right)\cdot 29^{6} +O(29^{7})$$ 10*a^8 + 19*a^7 + 14*a^6 + 23*a^5 + 18*a^4 + 5*a^3 + 15*a^2 + 16*a + 7 + (16*a^8 + 24*a^7 + 4*a^6 + 18*a^5 + 6*a^4 + 27*a^3 + 13*a^2 + 4*a + 25)*29 + (5*a^8 + 24*a^7 + 19*a^6 + 9*a^5 + 3*a^4 + 24*a^3 + 24*a^2 + 16*a + 1)*29^2 + (7*a^7 + 25*a^6 + 25*a^5 + 9*a^4 + 28*a^3 + 17*a^2 + 18*a + 10)*29^3 + (27*a^8 + 26*a^7 + 16*a^6 + 19*a^5 + 24*a^4 + 15*a^3 + a^2 + 3*a + 17)*29^4 + (13*a^8 + 27*a^7 + 15*a^6 + 28*a^5 + 23*a^3 + 12*a^2 + 23*a + 24)*29^5 + (22*a^7 + 9*a^6 + 4*a^5 + 5*a^4 + 6*a^3 + 13*a^2 + 8)*29^6+O(29^7) $r_{ 5 }$ $=$ $$23 a^{8} + 7 a^{7} + 28 a^{6} + 9 a^{5} + 10 a^{4} + a^{3} + 9 a^{2} + 3 a + 3 + \left(7 a^{8} + 8 a^{7} + 28 a^{6} + 27 a^{5} + 18 a^{4} + 17 a^{3} + 15 a^{2} + 13 a\right)\cdot 29 + \left(19 a^{8} + 7 a^{7} + 12 a^{6} + 5 a^{5} + 20 a^{4} + 2 a^{3} + 27 a^{2} + 28 a + 27\right)\cdot 29^{2} + \left(28 a^{8} + 12 a^{7} + 19 a^{6} + 23 a^{5} + 22 a^{4} + 21 a^{3} + 3 a^{2} + 15 a + 22\right)\cdot 29^{3} + \left(12 a^{8} + 2 a^{7} + 25 a^{6} + 12 a^{5} + 27 a^{4} + 12 a^{3} + 25 a^{2} + 13 a + 28\right)\cdot 29^{4} + \left(16 a^{8} + 23 a^{7} + 18 a^{6} + 26 a^{5} + 17 a^{4} + 14 a^{3} + 25 a^{2} + 4 a + 12\right)\cdot 29^{5} + \left(15 a^{8} + 21 a^{7} + 5 a^{6} + 16 a^{4} + 7 a^{3} + 28 a^{2} + 2 a + 25\right)\cdot 29^{6} +O(29^{7})$$ 23*a^8 + 7*a^7 + 28*a^6 + 9*a^5 + 10*a^4 + a^3 + 9*a^2 + 3*a + 3 + (7*a^8 + 8*a^7 + 28*a^6 + 27*a^5 + 18*a^4 + 17*a^3 + 15*a^2 + 13*a)*29 + (19*a^8 + 7*a^7 + 12*a^6 + 5*a^5 + 20*a^4 + 2*a^3 + 27*a^2 + 28*a + 27)*29^2 + (28*a^8 + 12*a^7 + 19*a^6 + 23*a^5 + 22*a^4 + 21*a^3 + 3*a^2 + 15*a + 22)*29^3 + (12*a^8 + 2*a^7 + 25*a^6 + 12*a^5 + 27*a^4 + 12*a^3 + 25*a^2 + 13*a + 28)*29^4 + (16*a^8 + 23*a^7 + 18*a^6 + 26*a^5 + 17*a^4 + 14*a^3 + 25*a^2 + 4*a + 12)*29^5 + (15*a^8 + 21*a^7 + 5*a^6 + 16*a^4 + 7*a^3 + 28*a^2 + 2*a + 25)*29^6+O(29^7) $r_{ 6 }$ $=$ $$25 a^{8} + 9 a^{7} + 28 a^{6} + 27 a^{5} + 21 a^{4} + 21 a^{3} + 25 a^{2} + 12 a + 28 + \left(19 a^{8} + 17 a^{7} + 5 a^{6} + 14 a^{5} + 26 a^{4} + 28 a^{3} + 27 a^{2} + 6 a + 10\right)\cdot 29 + \left(7 a^{8} + 24 a^{7} + 10 a^{6} + 16 a^{5} + 5 a^{4} + 17 a^{3} + 4 a^{2} + 20 a + 18\right)\cdot 29^{2} + \left(21 a^{8} + 10 a^{7} + 23 a^{6} + 27 a^{5} + 27 a^{4} + 19 a^{3} + 17 a^{2} + 22 a + 9\right)\cdot 29^{3} + \left(16 a^{7} + 3 a^{6} + 18 a^{5} + 4 a^{4} + 13 a^{3} + 11 a^{2} + 12 a + 24\right)\cdot 29^{4} + \left(10 a^{8} + 17 a^{7} + a^{6} + 22 a^{5} + 10 a^{3} + 8 a^{2} + 24 a + 9\right)\cdot 29^{5} + \left(a^{8} + 5 a^{7} + 15 a^{6} + 7 a^{5} + 4 a^{4} + 9 a^{3} + 25 a^{2} + 26 a + 17\right)\cdot 29^{6} +O(29^{7})$$ 25*a^8 + 9*a^7 + 28*a^6 + 27*a^5 + 21*a^4 + 21*a^3 + 25*a^2 + 12*a + 28 + (19*a^8 + 17*a^7 + 5*a^6 + 14*a^5 + 26*a^4 + 28*a^3 + 27*a^2 + 6*a + 10)*29 + (7*a^8 + 24*a^7 + 10*a^6 + 16*a^5 + 5*a^4 + 17*a^3 + 4*a^2 + 20*a + 18)*29^2 + (21*a^8 + 10*a^7 + 23*a^6 + 27*a^5 + 27*a^4 + 19*a^3 + 17*a^2 + 22*a + 9)*29^3 + (16*a^7 + 3*a^6 + 18*a^5 + 4*a^4 + 13*a^3 + 11*a^2 + 12*a + 24)*29^4 + (10*a^8 + 17*a^7 + a^6 + 22*a^5 + 10*a^3 + 8*a^2 + 24*a + 9)*29^5 + (a^8 + 5*a^7 + 15*a^6 + 7*a^5 + 4*a^4 + 9*a^3 + 25*a^2 + 26*a + 17)*29^6+O(29^7) $r_{ 7 }$ $=$ $$22 a^{8} + 13 a^{7} + 2 a^{5} + 18 a^{4} + 17 a^{3} + 21 a^{2} + 2 a + 5 + \left(a^{8} + 19 a^{7} + 5 a^{6} + 27 a^{5} + 3 a^{4} + 12 a^{3} + 23 a^{2} + 13 a + 13\right)\cdot 29 + \left(16 a^{8} + 14 a^{7} + 16 a^{6} + 26 a^{5} + 7 a^{4} + 14 a^{3} + 10 a^{2} + 26 a + 2\right)\cdot 29^{2} + \left(23 a^{8} + 15 a^{7} + 11 a^{6} + 14 a^{5} + 9 a^{4} + 17 a^{3} + 15 a^{2} + 13 a + 22\right)\cdot 29^{3} + \left(16 a^{8} + 24 a^{7} + a^{6} + 13 a^{5} + 23 a^{4} + 3 a^{3} + 8 a^{2} + 27 a + 4\right)\cdot 29^{4} + \left(11 a^{8} + 9 a^{7} + 20 a^{6} + 16 a^{5} + 4 a^{4} + 3 a^{2} + 9 a + 10\right)\cdot 29^{5} + \left(6 a^{8} + 14 a^{7} + 17 a^{6} + 16 a^{5} + 25 a^{4} + 11 a^{3} + 22 a^{2} + 9 a + 21\right)\cdot 29^{6} +O(29^{7})$$ 22*a^8 + 13*a^7 + 2*a^5 + 18*a^4 + 17*a^3 + 21*a^2 + 2*a + 5 + (a^8 + 19*a^7 + 5*a^6 + 27*a^5 + 3*a^4 + 12*a^3 + 23*a^2 + 13*a + 13)*29 + (16*a^8 + 14*a^7 + 16*a^6 + 26*a^5 + 7*a^4 + 14*a^3 + 10*a^2 + 26*a + 2)*29^2 + (23*a^8 + 15*a^7 + 11*a^6 + 14*a^5 + 9*a^4 + 17*a^3 + 15*a^2 + 13*a + 22)*29^3 + (16*a^8 + 24*a^7 + a^6 + 13*a^5 + 23*a^4 + 3*a^3 + 8*a^2 + 27*a + 4)*29^4 + (11*a^8 + 9*a^7 + 20*a^6 + 16*a^5 + 4*a^4 + 3*a^2 + 9*a + 10)*29^5 + (6*a^8 + 14*a^7 + 17*a^6 + 16*a^5 + 25*a^4 + 11*a^3 + 22*a^2 + 9*a + 21)*29^6+O(29^7) $r_{ 8 }$ $=$ $$6 a^{8} + 28 a^{7} + 13 a^{6} + 21 a^{5} + 10 a^{4} + 26 a^{3} + 11 a^{2} + 28 a + 6 + \left(7 a^{8} + 12 a^{7} + 10 a^{6} + 4 a^{5} + 4 a^{4} + 26 a^{3} + 12 a^{2} + 10 a + 7\right)\cdot 29 + \left(13 a^{8} + 20 a^{7} + 26 a^{5} + 9 a^{4} + 13 a^{3} + 7 a + 20\right)\cdot 29^{2} + \left(21 a^{8} + 18 a^{7} + 20 a^{6} + 23 a^{5} + 7 a^{4} + 19 a^{3} + 6 a^{2} + 12 a + 19\right)\cdot 29^{3} + \left(27 a^{8} + 13 a^{7} + 20 a^{6} + 9 a^{5} + 13 a^{2} + 16 a + 12\right)\cdot 29^{4} + \left(23 a^{8} + 16 a^{7} + 16 a^{6} + 22 a^{5} + a^{4} + 5 a^{3} + 20 a^{2} + 18 a + 5\right)\cdot 29^{5} + \left(a^{8} + 28 a^{7} + 24 a^{6} + 12 a^{5} + 9 a^{4} + 16 a^{3} + 9 a^{2} + 27 a + 26\right)\cdot 29^{6} +O(29^{7})$$ 6*a^8 + 28*a^7 + 13*a^6 + 21*a^5 + 10*a^4 + 26*a^3 + 11*a^2 + 28*a + 6 + (7*a^8 + 12*a^7 + 10*a^6 + 4*a^5 + 4*a^4 + 26*a^3 + 12*a^2 + 10*a + 7)*29 + (13*a^8 + 20*a^7 + 26*a^5 + 9*a^4 + 13*a^3 + 7*a + 20)*29^2 + (21*a^8 + 18*a^7 + 20*a^6 + 23*a^5 + 7*a^4 + 19*a^3 + 6*a^2 + 12*a + 19)*29^3 + (27*a^8 + 13*a^7 + 20*a^6 + 9*a^5 + 13*a^2 + 16*a + 12)*29^4 + (23*a^8 + 16*a^7 + 16*a^6 + 22*a^5 + a^4 + 5*a^3 + 20*a^2 + 18*a + 5)*29^5 + (a^8 + 28*a^7 + 24*a^6 + 12*a^5 + 9*a^4 + 16*a^3 + 9*a^2 + 27*a + 26)*29^6+O(29^7) $r_{ 9 }$ $=$ $$27 a^{8} + 19 a^{7} + 3 a^{6} + 4 a^{4} + 2 a^{3} + 2 a^{2} + 20 a + 4 + \left(10 a^{8} + 24 a^{7} + 19 a^{6} + 2 a^{5} + 27 a^{4} + 19 a^{3} + 11 a^{2} + 28 a + 13\right)\cdot 29 + \left(9 a^{8} + a^{7} + 13 a^{6} + 4 a^{5} + 17 a^{4} + 3 a^{3} + 16 a^{2} + 5 a + 19\right)\cdot 29^{2} + \left(23 a^{8} + 13 a^{7} + 16 a^{6} + 10 a^{5} + 15 a^{4} + 25 a^{3} + 14 a^{2} + 26 a + 14\right)\cdot 29^{3} + \left(27 a^{8} + 11 a^{7} + 16 a^{6} + 15 a^{5} + 7 a^{4} + 26 a^{3} + 19 a^{2} + 5 a + 10\right)\cdot 29^{4} + \left(2 a^{8} + 22 a^{7} + 18 a^{6} + 21 a^{5} + 28 a^{4} + 22 a^{3} + 4 a^{2} + 17 a + 23\right)\cdot 29^{5} + \left(2 a^{8} + 14 a^{7} + 25 a^{6} + 12 a^{5} + 12 a^{4} + 14 a^{3} + 7 a^{2} + 28 a + 7\right)\cdot 29^{6} +O(29^{7})$$ 27*a^8 + 19*a^7 + 3*a^6 + 4*a^4 + 2*a^3 + 2*a^2 + 20*a + 4 + (10*a^8 + 24*a^7 + 19*a^6 + 2*a^5 + 27*a^4 + 19*a^3 + 11*a^2 + 28*a + 13)*29 + (9*a^8 + a^7 + 13*a^6 + 4*a^5 + 17*a^4 + 3*a^3 + 16*a^2 + 5*a + 19)*29^2 + (23*a^8 + 13*a^7 + 16*a^6 + 10*a^5 + 15*a^4 + 25*a^3 + 14*a^2 + 26*a + 14)*29^3 + (27*a^8 + 11*a^7 + 16*a^6 + 15*a^5 + 7*a^4 + 26*a^3 + 19*a^2 + 5*a + 10)*29^4 + (2*a^8 + 22*a^7 + 18*a^6 + 21*a^5 + 28*a^4 + 22*a^3 + 4*a^2 + 17*a + 23)*29^5 + (2*a^8 + 14*a^7 + 25*a^6 + 12*a^5 + 12*a^4 + 14*a^3 + 7*a^2 + 28*a + 7)*29^6+O(29^7) $r_{ 10 }$ $=$ $$23 a^{8} + 19 a^{6} + 19 a^{5} + 23 a^{4} + 16 a^{3} + 24 a^{2} + 1 + \left(8 a^{8} + 23 a^{7} + 12 a^{6} + 24 a^{5} + 22 a^{4} + 23 a^{3} + 5 a^{2} + 15 a + 16\right)\cdot 29 + \left(3 a^{8} + 8 a^{7} + 24 a^{6} + 28 a^{5} + a^{4} + 27 a^{3} + 22 a^{2} + 2 a + 9\right)\cdot 29^{2} + \left(10 a^{8} + 17 a^{7} + 7 a^{6} + 14 a^{5} + 21 a^{4} + 14 a^{3} + 4 a^{2} + 17 a + 15\right)\cdot 29^{3} + \left(27 a^{8} + 4 a^{7} + 15 a^{6} + 5 a^{5} + 21 a^{4} + 23 a^{3} + 27 a^{2} + 12 a + 6\right)\cdot 29^{4} + \left(21 a^{8} + 18 a^{7} + 4 a^{6} + 5 a^{5} + a^{4} + 10 a^{3} + 2 a^{2} + 17 a + 17\right)\cdot 29^{5} + \left(6 a^{8} + 20 a^{7} + 20 a^{6} + 25 a^{5} + 3 a^{4} + 23 a^{3} + 6 a^{2} + 27 a + 13\right)\cdot 29^{6} +O(29^{7})$$ 23*a^8 + 19*a^6 + 19*a^5 + 23*a^4 + 16*a^3 + 24*a^2 + 1 + (8*a^8 + 23*a^7 + 12*a^6 + 24*a^5 + 22*a^4 + 23*a^3 + 5*a^2 + 15*a + 16)*29 + (3*a^8 + 8*a^7 + 24*a^6 + 28*a^5 + a^4 + 27*a^3 + 22*a^2 + 2*a + 9)*29^2 + (10*a^8 + 17*a^7 + 7*a^6 + 14*a^5 + 21*a^4 + 14*a^3 + 4*a^2 + 17*a + 15)*29^3 + (27*a^8 + 4*a^7 + 15*a^6 + 5*a^5 + 21*a^4 + 23*a^3 + 27*a^2 + 12*a + 6)*29^4 + (21*a^8 + 18*a^7 + 4*a^6 + 5*a^5 + a^4 + 10*a^3 + 2*a^2 + 17*a + 17)*29^5 + (6*a^8 + 20*a^7 + 20*a^6 + 25*a^5 + 3*a^4 + 23*a^3 + 6*a^2 + 27*a + 13)*29^6+O(29^7) $r_{ 11 }$ $=$ $$13 a^{8} + 9 a^{7} + a^{6} + 18 a^{5} + a^{4} + 11 a^{3} + 28 a^{2} + 24 a + 21 + \left(19 a^{8} + a^{7} + 24 a^{6} + 3 a^{5} + 7 a^{4} + 28 a^{3} + 18 a^{2} + 2 a + 15\right)\cdot 29 + \left(22 a^{8} + 7 a^{7} + 28 a^{6} + 25 a^{5} + a^{4} + 11 a^{3} + 19 a^{2} + 3 a + 28\right)\cdot 29^{2} + \left(5 a^{8} + a^{7} + 26 a^{6} + 19 a^{5} + 26 a^{4} + 19 a^{3} + 9 a^{2} + 28 a + 12\right)\cdot 29^{3} + \left(28 a^{8} + 2 a^{7} + a^{6} + 2 a^{5} + 6 a^{4} + 12 a^{3} + 24 a^{2} + 16 a + 24\right)\cdot 29^{4} + \left(25 a^{7} + 19 a^{6} + 15 a^{5} + 6 a^{4} + 14 a^{3} + 28 a^{2} + 14 a + 5\right)\cdot 29^{5} + \left(7 a^{8} + 21 a^{7} + 5 a^{6} + 11 a^{5} + 16 a^{4} + 10 a^{3} + 6 a^{2} + 17 a + 11\right)\cdot 29^{6} +O(29^{7})$$ 13*a^8 + 9*a^7 + a^6 + 18*a^5 + a^4 + 11*a^3 + 28*a^2 + 24*a + 21 + (19*a^8 + a^7 + 24*a^6 + 3*a^5 + 7*a^4 + 28*a^3 + 18*a^2 + 2*a + 15)*29 + (22*a^8 + 7*a^7 + 28*a^6 + 25*a^5 + a^4 + 11*a^3 + 19*a^2 + 3*a + 28)*29^2 + (5*a^8 + a^7 + 26*a^6 + 19*a^5 + 26*a^4 + 19*a^3 + 9*a^2 + 28*a + 12)*29^3 + (28*a^8 + 2*a^7 + a^6 + 2*a^5 + 6*a^4 + 12*a^3 + 24*a^2 + 16*a + 24)*29^4 + (25*a^7 + 19*a^6 + 15*a^5 + 6*a^4 + 14*a^3 + 28*a^2 + 14*a + 5)*29^5 + (7*a^8 + 21*a^7 + 5*a^6 + 11*a^5 + 16*a^4 + 10*a^3 + 6*a^2 + 17*a + 11)*29^6+O(29^7) $r_{ 12 }$ $=$ $$25 a^{8} + 10 a^{7} + 16 a^{6} + 19 a^{5} + 19 a^{4} + 14 a^{3} + 22 a^{2} + 9 a + 26 + \left(26 a^{8} + 27 a^{7} + 22 a^{6} + 22 a^{5} + 24 a^{4} + 4 a^{3} + 23 a^{2} + 15 a + 2\right)\cdot 29 + \left(22 a^{8} + 6 a^{7} + 10 a^{6} + 24 a^{5} + 12 a^{4} + 24 a^{3} + 5 a^{2} + 25 a + 19\right)\cdot 29^{2} + \left(15 a^{8} + 4 a^{7} + 20 a^{6} + 4 a^{5} + 5 a^{4} + 18 a^{3} + 19 a^{2} + 19 a\right)\cdot 29^{3} + \left(28 a^{8} + 22 a^{7} + 27 a^{6} + 19 a^{5} + 14 a^{4} + 25 a^{3} + 7 a^{2} + 6 a + 25\right)\cdot 29^{4} + \left(18 a^{8} + 24 a^{7} + 14 a^{6} + 12 a^{5} + 2 a^{4} + 16 a^{3} + 27 a^{2} + 22\right)\cdot 29^{5} + \left(4 a^{8} + 5 a^{7} + 23 a^{6} + 12 a^{5} + 19 a^{4} + 8 a^{3} + 27 a^{2} + 28 a + 5\right)\cdot 29^{6} +O(29^{7})$$ 25*a^8 + 10*a^7 + 16*a^6 + 19*a^5 + 19*a^4 + 14*a^3 + 22*a^2 + 9*a + 26 + (26*a^8 + 27*a^7 + 22*a^6 + 22*a^5 + 24*a^4 + 4*a^3 + 23*a^2 + 15*a + 2)*29 + (22*a^8 + 6*a^7 + 10*a^6 + 24*a^5 + 12*a^4 + 24*a^3 + 5*a^2 + 25*a + 19)*29^2 + (15*a^8 + 4*a^7 + 20*a^6 + 4*a^5 + 5*a^4 + 18*a^3 + 19*a^2 + 19*a)*29^3 + (28*a^8 + 22*a^7 + 27*a^6 + 19*a^5 + 14*a^4 + 25*a^3 + 7*a^2 + 6*a + 25)*29^4 + (18*a^8 + 24*a^7 + 14*a^6 + 12*a^5 + 2*a^4 + 16*a^3 + 27*a^2 + 22)*29^5 + (4*a^8 + 5*a^7 + 23*a^6 + 12*a^5 + 19*a^4 + 8*a^3 + 27*a^2 + 28*a + 5)*29^6+O(29^7) $r_{ 13 }$ $=$ $$19 a^{8} + 10 a^{7} + 15 a^{6} + 6 a^{5} + 11 a^{4} + 24 a^{3} + 14 a^{2} + 13 a + 22 + \left(12 a^{8} + 4 a^{7} + 24 a^{6} + 10 a^{5} + 22 a^{4} + a^{3} + 15 a^{2} + 24 a + 3\right)\cdot 29 + \left(23 a^{8} + 4 a^{7} + 9 a^{6} + 19 a^{5} + 25 a^{4} + 4 a^{3} + 4 a^{2} + 12 a + 27\right)\cdot 29^{2} + \left(28 a^{8} + 21 a^{7} + 3 a^{6} + 3 a^{5} + 19 a^{4} + 11 a^{2} + 10 a + 18\right)\cdot 29^{3} + \left(a^{8} + 2 a^{7} + 12 a^{6} + 9 a^{5} + 4 a^{4} + 13 a^{3} + 27 a^{2} + 25 a + 11\right)\cdot 29^{4} + \left(15 a^{8} + a^{7} + 13 a^{6} + 28 a^{4} + 5 a^{3} + 16 a^{2} + 5 a + 4\right)\cdot 29^{5} + \left(28 a^{8} + 6 a^{7} + 19 a^{6} + 24 a^{5} + 23 a^{4} + 22 a^{3} + 15 a^{2} + 28 a + 20\right)\cdot 29^{6} +O(29^{7})$$ 19*a^8 + 10*a^7 + 15*a^6 + 6*a^5 + 11*a^4 + 24*a^3 + 14*a^2 + 13*a + 22 + (12*a^8 + 4*a^7 + 24*a^6 + 10*a^5 + 22*a^4 + a^3 + 15*a^2 + 24*a + 3)*29 + (23*a^8 + 4*a^7 + 9*a^6 + 19*a^5 + 25*a^4 + 4*a^3 + 4*a^2 + 12*a + 27)*29^2 + (28*a^8 + 21*a^7 + 3*a^6 + 3*a^5 + 19*a^4 + 11*a^2 + 10*a + 18)*29^3 + (a^8 + 2*a^7 + 12*a^6 + 9*a^5 + 4*a^4 + 13*a^3 + 27*a^2 + 25*a + 11)*29^4 + (15*a^8 + a^7 + 13*a^6 + 28*a^4 + 5*a^3 + 16*a^2 + 5*a + 4)*29^5 + (28*a^8 + 6*a^7 + 19*a^6 + 24*a^5 + 23*a^4 + 22*a^3 + 15*a^2 + 28*a + 20)*29^6+O(29^7) $r_{ 14 }$ $=$ $$6 a^{8} + 22 a^{7} + a^{6} + 20 a^{5} + 19 a^{4} + 28 a^{3} + 20 a^{2} + 26 a + 26 + \left(21 a^{8} + 20 a^{7} + a^{5} + 10 a^{4} + 11 a^{3} + 13 a^{2} + 15 a + 28\right)\cdot 29 + \left(9 a^{8} + 21 a^{7} + 16 a^{6} + 23 a^{5} + 8 a^{4} + 26 a^{3} + a^{2} + 1\right)\cdot 29^{2} + \left(16 a^{7} + 9 a^{6} + 5 a^{5} + 6 a^{4} + 7 a^{3} + 25 a^{2} + 13 a + 6\right)\cdot 29^{3} + \left(16 a^{8} + 26 a^{7} + 3 a^{6} + 16 a^{5} + a^{4} + 16 a^{3} + 3 a^{2} + 15 a\right)\cdot 29^{4} + \left(12 a^{8} + 5 a^{7} + 10 a^{6} + 2 a^{5} + 11 a^{4} + 14 a^{3} + 3 a^{2} + 24 a + 16\right)\cdot 29^{5} + \left(13 a^{8} + 7 a^{7} + 23 a^{6} + 28 a^{5} + 12 a^{4} + 21 a^{3} + 26 a + 3\right)\cdot 29^{6} +O(29^{7})$$ 6*a^8 + 22*a^7 + a^6 + 20*a^5 + 19*a^4 + 28*a^3 + 20*a^2 + 26*a + 26 + (21*a^8 + 20*a^7 + a^5 + 10*a^4 + 11*a^3 + 13*a^2 + 15*a + 28)*29 + (9*a^8 + 21*a^7 + 16*a^6 + 23*a^5 + 8*a^4 + 26*a^3 + a^2 + 1)*29^2 + (16*a^7 + 9*a^6 + 5*a^5 + 6*a^4 + 7*a^3 + 25*a^2 + 13*a + 6)*29^3 + (16*a^8 + 26*a^7 + 3*a^6 + 16*a^5 + a^4 + 16*a^3 + 3*a^2 + 15*a)*29^4 + (12*a^8 + 5*a^7 + 10*a^6 + 2*a^5 + 11*a^4 + 14*a^3 + 3*a^2 + 24*a + 16)*29^5 + (13*a^8 + 7*a^7 + 23*a^6 + 28*a^5 + 12*a^4 + 21*a^3 + 26*a + 3)*29^6+O(29^7) $r_{ 15 }$ $=$ $$4 a^{8} + 20 a^{7} + a^{6} + 2 a^{5} + 8 a^{4} + 8 a^{3} + 4 a^{2} + 17 a + 1 + \left(9 a^{8} + 11 a^{7} + 23 a^{6} + 14 a^{5} + 2 a^{4} + a^{2} + 22 a + 18\right)\cdot 29 + \left(21 a^{8} + 4 a^{7} + 18 a^{6} + 12 a^{5} + 23 a^{4} + 11 a^{3} + 24 a^{2} + 8 a + 10\right)\cdot 29^{2} + \left(7 a^{8} + 18 a^{7} + 5 a^{6} + a^{5} + a^{4} + 9 a^{3} + 11 a^{2} + 6 a + 19\right)\cdot 29^{3} + \left(28 a^{8} + 12 a^{7} + 25 a^{6} + 10 a^{5} + 24 a^{4} + 15 a^{3} + 17 a^{2} + 16 a + 4\right)\cdot 29^{4} + \left(18 a^{8} + 11 a^{7} + 27 a^{6} + 6 a^{5} + 28 a^{4} + 18 a^{3} + 20 a^{2} + 4 a + 19\right)\cdot 29^{5} + \left(27 a^{8} + 23 a^{7} + 13 a^{6} + 21 a^{5} + 24 a^{4} + 19 a^{3} + 3 a^{2} + 2 a + 11\right)\cdot 29^{6} +O(29^{7})$$ 4*a^8 + 20*a^7 + a^6 + 2*a^5 + 8*a^4 + 8*a^3 + 4*a^2 + 17*a + 1 + (9*a^8 + 11*a^7 + 23*a^6 + 14*a^5 + 2*a^4 + a^2 + 22*a + 18)*29 + (21*a^8 + 4*a^7 + 18*a^6 + 12*a^5 + 23*a^4 + 11*a^3 + 24*a^2 + 8*a + 10)*29^2 + (7*a^8 + 18*a^7 + 5*a^6 + a^5 + a^4 + 9*a^3 + 11*a^2 + 6*a + 19)*29^3 + (28*a^8 + 12*a^7 + 25*a^6 + 10*a^5 + 24*a^4 + 15*a^3 + 17*a^2 + 16*a + 4)*29^4 + (18*a^8 + 11*a^7 + 27*a^6 + 6*a^5 + 28*a^4 + 18*a^3 + 20*a^2 + 4*a + 19)*29^5 + (27*a^8 + 23*a^7 + 13*a^6 + 21*a^5 + 24*a^4 + 19*a^3 + 3*a^2 + 2*a + 11)*29^6+O(29^7) $r_{ 16 }$ $=$ $$7 a^{8} + 16 a^{7} + 27 a^{5} + 11 a^{4} + 12 a^{3} + 8 a^{2} + 27 a + 24 + \left(27 a^{8} + 9 a^{7} + 24 a^{6} + a^{5} + 25 a^{4} + 16 a^{3} + 5 a^{2} + 15 a + 15\right)\cdot 29 + \left(12 a^{8} + 14 a^{7} + 12 a^{6} + 2 a^{5} + 21 a^{4} + 14 a^{3} + 18 a^{2} + 2 a + 26\right)\cdot 29^{2} + \left(5 a^{8} + 13 a^{7} + 17 a^{6} + 14 a^{5} + 19 a^{4} + 11 a^{3} + 13 a^{2} + 15 a + 6\right)\cdot 29^{3} + \left(12 a^{8} + 4 a^{7} + 27 a^{6} + 15 a^{5} + 5 a^{4} + 25 a^{3} + 20 a^{2} + a + 24\right)\cdot 29^{4} + \left(17 a^{8} + 19 a^{7} + 8 a^{6} + 12 a^{5} + 24 a^{4} + 28 a^{3} + 25 a^{2} + 19 a + 18\right)\cdot 29^{5} + \left(22 a^{8} + 14 a^{7} + 11 a^{6} + 12 a^{5} + 3 a^{4} + 17 a^{3} + 6 a^{2} + 19 a + 7\right)\cdot 29^{6} +O(29^{7})$$ 7*a^8 + 16*a^7 + 27*a^5 + 11*a^4 + 12*a^3 + 8*a^2 + 27*a + 24 + (27*a^8 + 9*a^7 + 24*a^6 + a^5 + 25*a^4 + 16*a^3 + 5*a^2 + 15*a + 15)*29 + (12*a^8 + 14*a^7 + 12*a^6 + 2*a^5 + 21*a^4 + 14*a^3 + 18*a^2 + 2*a + 26)*29^2 + (5*a^8 + 13*a^7 + 17*a^6 + 14*a^5 + 19*a^4 + 11*a^3 + 13*a^2 + 15*a + 6)*29^3 + (12*a^8 + 4*a^7 + 27*a^6 + 15*a^5 + 5*a^4 + 25*a^3 + 20*a^2 + a + 24)*29^4 + (17*a^8 + 19*a^7 + 8*a^6 + 12*a^5 + 24*a^4 + 28*a^3 + 25*a^2 + 19*a + 18)*29^5 + (22*a^8 + 14*a^7 + 11*a^6 + 12*a^5 + 3*a^4 + 17*a^3 + 6*a^2 + 19*a + 7)*29^6+O(29^7) $r_{ 17 }$ $=$ $$23 a^{8} + a^{7} + 16 a^{6} + 8 a^{5} + 19 a^{4} + 3 a^{3} + 18 a^{2} + a + 23 + \left(21 a^{8} + 16 a^{7} + 18 a^{6} + 24 a^{5} + 24 a^{4} + 2 a^{3} + 16 a^{2} + 18 a + 21\right)\cdot 29 + \left(15 a^{8} + 8 a^{7} + 28 a^{6} + 2 a^{5} + 19 a^{4} + 15 a^{3} + 28 a^{2} + 21 a + 8\right)\cdot 29^{2} + \left(7 a^{8} + 10 a^{7} + 8 a^{6} + 5 a^{5} + 21 a^{4} + 9 a^{3} + 22 a^{2} + 16 a + 9\right)\cdot 29^{3} + \left(a^{8} + 15 a^{7} + 8 a^{6} + 19 a^{5} + 28 a^{4} + 28 a^{3} + 15 a^{2} + 12 a + 16\right)\cdot 29^{4} + \left(5 a^{8} + 12 a^{7} + 12 a^{6} + 6 a^{5} + 27 a^{4} + 23 a^{3} + 8 a^{2} + 10 a + 23\right)\cdot 29^{5} + \left(27 a^{8} + 4 a^{6} + 16 a^{5} + 19 a^{4} + 12 a^{3} + 19 a^{2} + a + 2\right)\cdot 29^{6} +O(29^{7})$$ 23*a^8 + a^7 + 16*a^6 + 8*a^5 + 19*a^4 + 3*a^3 + 18*a^2 + a + 23 + (21*a^8 + 16*a^7 + 18*a^6 + 24*a^5 + 24*a^4 + 2*a^3 + 16*a^2 + 18*a + 21)*29 + (15*a^8 + 8*a^7 + 28*a^6 + 2*a^5 + 19*a^4 + 15*a^3 + 28*a^2 + 21*a + 8)*29^2 + (7*a^8 + 10*a^7 + 8*a^6 + 5*a^5 + 21*a^4 + 9*a^3 + 22*a^2 + 16*a + 9)*29^3 + (a^8 + 15*a^7 + 8*a^6 + 19*a^5 + 28*a^4 + 28*a^3 + 15*a^2 + 12*a + 16)*29^4 + (5*a^8 + 12*a^7 + 12*a^6 + 6*a^5 + 27*a^4 + 23*a^3 + 8*a^2 + 10*a + 23)*29^5 + (27*a^8 + 4*a^6 + 16*a^5 + 19*a^4 + 12*a^3 + 19*a^2 + a + 2)*29^6+O(29^7) $r_{ 18 }$ $=$ $$2 a^{8} + 10 a^{7} + 26 a^{6} + 25 a^{4} + 27 a^{3} + 27 a^{2} + 9 a + 25 + \left(18 a^{8} + 4 a^{7} + 9 a^{6} + 27 a^{5} + a^{4} + 9 a^{3} + 17 a^{2} + 15\right)\cdot 29 + \left(19 a^{8} + 27 a^{7} + 15 a^{6} + 24 a^{5} + 11 a^{4} + 25 a^{3} + 12 a^{2} + 23 a + 9\right)\cdot 29^{2} + \left(5 a^{8} + 15 a^{7} + 12 a^{6} + 18 a^{5} + 13 a^{4} + 3 a^{3} + 14 a^{2} + 2 a + 14\right)\cdot 29^{3} + \left(a^{8} + 17 a^{7} + 12 a^{6} + 13 a^{5} + 21 a^{4} + 2 a^{3} + 9 a^{2} + 23 a + 18\right)\cdot 29^{4} + \left(26 a^{8} + 6 a^{7} + 10 a^{6} + 7 a^{5} + 6 a^{3} + 24 a^{2} + 11 a + 5\right)\cdot 29^{5} + \left(26 a^{8} + 14 a^{7} + 3 a^{6} + 16 a^{5} + 16 a^{4} + 14 a^{3} + 21 a^{2} + 21\right)\cdot 29^{6} +O(29^{7})$$ 2*a^8 + 10*a^7 + 26*a^6 + 25*a^4 + 27*a^3 + 27*a^2 + 9*a + 25 + (18*a^8 + 4*a^7 + 9*a^6 + 27*a^5 + a^4 + 9*a^3 + 17*a^2 + 15)*29 + (19*a^8 + 27*a^7 + 15*a^6 + 24*a^5 + 11*a^4 + 25*a^3 + 12*a^2 + 23*a + 9)*29^2 + (5*a^8 + 15*a^7 + 12*a^6 + 18*a^5 + 13*a^4 + 3*a^3 + 14*a^2 + 2*a + 14)*29^3 + (a^8 + 17*a^7 + 12*a^6 + 13*a^5 + 21*a^4 + 2*a^3 + 9*a^2 + 23*a + 18)*29^4 + (26*a^8 + 6*a^7 + 10*a^6 + 7*a^5 + 6*a^3 + 24*a^2 + 11*a + 5)*29^5 + (26*a^8 + 14*a^7 + 3*a^6 + 16*a^5 + 16*a^4 + 14*a^3 + 21*a^2 + 21)*29^6+O(29^7)

Generators of the action on the roots $r_1, \ldots, r_{ 18 }$

 Cycle notation $(1,9,12)(2,16,14)(3,10,18)(4,17,6)(5,11,7)(8,15,13)$ $(1,16,6,9,14,4,12,2,17)(3,11,8,10,7,15,18,5,13)$ $(1,10)(2,11)(3,12)(4,13)(5,14)(6,15)(7,16)(8,17)(9,18)$

Character values on conjugacy classes

 Size Order Action on $r_1, \ldots, r_{ 18 }$ Character value $1$ $1$ $()$ $1$ $1$ $2$ $(1,10)(2,11)(3,12)(4,13)(5,14)(6,15)(7,16)(8,17)(9,18)$ $-1$ $1$ $3$ $(1,9,12)(2,16,14)(3,10,18)(4,17,6)(5,11,7)(8,15,13)$ $\zeta_{9}^{3}$ $1$ $3$ $(1,12,9)(2,14,16)(3,18,10)(4,6,17)(5,7,11)(8,13,15)$ $-\zeta_{9}^{3} - 1$ $1$ $6$ $(1,18,12,10,9,3)(2,7,14,11,16,5)(4,8,6,13,17,15)$ $-\zeta_{9}^{3}$ $1$ $6$ $(1,3,9,10,12,18)(2,5,16,11,14,7)(4,15,17,13,6,8)$ $\zeta_{9}^{3} + 1$ $1$ $9$ $(1,16,6,9,14,4,12,2,17)(3,11,8,10,7,15,18,5,13)$ $\zeta_{9}$ $1$ $9$ $(1,6,14,12,17,16,9,4,2)(3,8,7,18,13,11,10,15,5)$ $\zeta_{9}^{2}$ $1$ $9$ $(1,14,17,9,2,6,12,16,4)(3,7,13,10,5,8,18,11,15)$ $\zeta_{9}^{4}$ $1$ $9$ $(1,4,16,12,6,2,9,17,14)(3,15,11,18,8,5,10,13,7)$ $\zeta_{9}^{5}$ $1$ $9$ $(1,2,4,9,16,17,12,14,6)(3,5,15,10,11,13,18,7,8)$ $-\zeta_{9}^{4} - \zeta_{9}$ $1$ $9$ $(1,17,2,12,4,14,9,6,16)(3,13,5,18,15,7,10,8,11)$ $-\zeta_{9}^{5} - \zeta_{9}^{2}$ $1$ $18$ $(1,7,6,18,14,13,12,11,17,10,16,15,9,5,4,3,2,8)$ $-\zeta_{9}$ $1$ $18$ $(1,13,16,3,6,11,9,8,14,10,4,7,12,15,2,18,17,5)$ $-\zeta_{9}^{5}$ $1$ $18$ $(1,11,4,18,16,8,12,5,6,10,2,13,9,7,17,3,14,15)$ $\zeta_{9}^{4} + \zeta_{9}$ $1$ $18$ $(1,15,14,3,17,7,9,13,2,10,6,5,12,8,16,18,4,11)$ $-\zeta_{9}^{2}$ $1$ $18$ $(1,5,17,18,2,15,12,7,4,10,14,8,9,11,6,3,16,13)$ $-\zeta_{9}^{4}$ $1$ $18$ $(1,8,2,3,4,5,9,15,16,10,17,11,12,13,14,18,6,7)$ $\zeta_{9}^{5} + \zeta_{9}^{2}$

The blue line marks the conjugacy class containing complex conjugation.