# Properties

 Label 8.13705853184.12t213.a.a Dimension 8 Group $S_3\wr S_3$ Conductor $2^{8} \cdot 3^{6} \cdot 271^{2}$ Root number 1 Frobenius-Schur indicator 1

# Related objects

## Basic invariants

 Dimension: $8$ Group: $S_3\wr S_3$ Conductor: $13705853184= 2^{8} \cdot 3^{6} \cdot 271^{2}$ Artin number field: Splitting field of 9.3.412698468096.1 defined by $f= x^{9} - 3 x^{8} + 6 x^{7} - 6 x^{6} + 4 x^{5} - 10 x^{3} + 10 x^{2} - 9 x - 3$ over $\Q$ Size of Galois orbit: 1 Smallest containing permutation representation: 12T213 Parity: Even Determinant: 1.1.1t1.a.a Projective image: $S_3\wr S_3$ Projective field: Galois closure of 9.3.412698468096.1

## Galois action

### Roots of defining polynomial

The roots of $f$ are computed in an extension of $\Q_{ 37 }$ to precision 141.
Minimal polynomial of a generator $a$ of $K$ over $\mathbb{Q}_{ 37 }$: $x^{3} + 6 x + 35$
Roots:
 $r_{ 1 }$ $=$ $17 a^{2} + a + 2 + \left(28 a^{2} + 27 a + 30\right)\cdot 37 + \left(17 a^{2} + 6 a + 21\right)\cdot 37^{2} + \left(35 a^{2} + 10 a + 14\right)\cdot 37^{3} + \left(7 a^{2} + 14 a + 14\right)\cdot 37^{4} + \left(8 a^{2} + 6 a + 21\right)\cdot 37^{5} + \left(19 a^{2} + 31 a + 20\right)\cdot 37^{6} + \left(32 a^{2} + 20 a + 34\right)\cdot 37^{7} + \left(2 a^{2} + 2 a + 8\right)\cdot 37^{8} + \left(35 a^{2} + 11 a + 23\right)\cdot 37^{9} + \left(30 a^{2} + 31 a + 30\right)\cdot 37^{10} + \left(24 a^{2} + 35 a + 2\right)\cdot 37^{11} + \left(5 a^{2} + 2 a + 27\right)\cdot 37^{12} + \left(7 a^{2} + 17 a + 26\right)\cdot 37^{13} + \left(34 a + 27\right)\cdot 37^{14} + \left(3 a^{2} + a + 22\right)\cdot 37^{15} + \left(9 a^{2} + 9 a + 7\right)\cdot 37^{16} + \left(21 a^{2} + 33 a + 5\right)\cdot 37^{17} + \left(4 a^{2} + 9 a + 18\right)\cdot 37^{18} + \left(31 a^{2} + 34 a + 12\right)\cdot 37^{19} + \left(15 a^{2} + 27 a + 30\right)\cdot 37^{20} + \left(31 a^{2} + 6 a + 34\right)\cdot 37^{21} + \left(22 a^{2} + 9 a + 15\right)\cdot 37^{22} + \left(12 a^{2} + 18 a\right)\cdot 37^{23} + \left(16 a^{2} + 17 a + 23\right)\cdot 37^{24} + \left(10 a^{2} + 27 a + 30\right)\cdot 37^{25} + \left(3 a^{2} + 34 a + 8\right)\cdot 37^{26} + \left(10 a^{2} + 15 a + 9\right)\cdot 37^{27} + \left(29 a^{2} + 12 a + 19\right)\cdot 37^{28} + \left(4 a^{2} + 7 a + 31\right)\cdot 37^{29} + \left(3 a^{2} + 9 a + 11\right)\cdot 37^{30} + \left(36 a^{2} + 24 a + 11\right)\cdot 37^{31} + \left(34 a^{2} + 17 a + 25\right)\cdot 37^{32} + \left(15 a^{2} + 23 a + 31\right)\cdot 37^{33} + \left(25 a^{2} + 23 a + 5\right)\cdot 37^{34} + \left(27 a^{2} + 31 a + 25\right)\cdot 37^{35} + \left(23 a^{2} + 14 a + 34\right)\cdot 37^{36} + \left(29 a^{2} + 10 a + 14\right)\cdot 37^{37} + \left(14 a^{2} + 33 a + 26\right)\cdot 37^{38} + \left(7 a^{2} + 32 a + 22\right)\cdot 37^{39} + \left(4 a^{2} + 24 a + 6\right)\cdot 37^{40} + \left(13 a^{2} + 30 a + 22\right)\cdot 37^{41} + \left(9 a^{2} + 18\right)\cdot 37^{42} + \left(11 a^{2} + 31 a + 29\right)\cdot 37^{43} + \left(35 a^{2} + 33 a + 16\right)\cdot 37^{44} + \left(16 a^{2} + 19 a + 15\right)\cdot 37^{45} + \left(6 a^{2} + 5\right)\cdot 37^{46} + \left(22 a^{2} + 18\right)\cdot 37^{47} + \left(28 a^{2} + 28 a + 23\right)\cdot 37^{48} + \left(28 a^{2} + 18 a + 20\right)\cdot 37^{49} + \left(35 a^{2} + 28 a + 14\right)\cdot 37^{50} + \left(16 a^{2} + 13 a + 14\right)\cdot 37^{51} + \left(20 a^{2} + 5 a + 35\right)\cdot 37^{52} + \left(5 a^{2} + 16 a + 14\right)\cdot 37^{53} + \left(2 a^{2} + 11 a + 7\right)\cdot 37^{54} + \left(34 a^{2} + 6 a + 9\right)\cdot 37^{55} + \left(7 a^{2} + 12 a + 3\right)\cdot 37^{56} + \left(27 a^{2} + 35 a + 4\right)\cdot 37^{57} + \left(12 a^{2} + 6 a + 6\right)\cdot 37^{58} + \left(19 a^{2} + 13 a + 12\right)\cdot 37^{59} + \left(6 a^{2} + 27 a + 27\right)\cdot 37^{60} + \left(22 a^{2} + 7 a + 19\right)\cdot 37^{61} + \left(7 a^{2} + 22 a + 32\right)\cdot 37^{62} + \left(6 a^{2} + 18 a + 1\right)\cdot 37^{63} + \left(6 a^{2} + 3 a + 35\right)\cdot 37^{64} + \left(2 a^{2} + 19 a + 21\right)\cdot 37^{65} + \left(2 a^{2} + 27 a + 2\right)\cdot 37^{66} + \left(32 a^{2} + 23 a + 8\right)\cdot 37^{67} + \left(15 a^{2} + 10 a + 9\right)\cdot 37^{68} + \left(22 a^{2} + 17 a + 1\right)\cdot 37^{69} + \left(16 a^{2} + 7 a + 18\right)\cdot 37^{70} + \left(31 a^{2} + 23 a + 16\right)\cdot 37^{71} + \left(6 a^{2} + 17 a + 19\right)\cdot 37^{72} + \left(23 a^{2} + 4 a + 30\right)\cdot 37^{73} + \left(10 a^{2} + 2 a + 26\right)\cdot 37^{74} + \left(19 a^{2} + 31 a + 17\right)\cdot 37^{75} + \left(35 a^{2} + 13 a + 1\right)\cdot 37^{76} + \left(13 a^{2} + 34 a + 24\right)\cdot 37^{77} + \left(34 a^{2} + 28 a + 36\right)\cdot 37^{78} + \left(5 a^{2} + 12 a + 23\right)\cdot 37^{79} + \left(15 a^{2} + 21 a + 20\right)\cdot 37^{80} + \left(23 a^{2} + 32 a + 36\right)\cdot 37^{81} + \left(21 a^{2} + 26 a + 15\right)\cdot 37^{82} + \left(34 a^{2} + 8 a + 1\right)\cdot 37^{83} + \left(33 a^{2} + 20 a + 14\right)\cdot 37^{84} + \left(6 a^{2} + 23 a + 33\right)\cdot 37^{85} + \left(24 a^{2} + 8 a + 12\right)\cdot 37^{86} + \left(28 a^{2} + 9 a + 20\right)\cdot 37^{87} + \left(20 a^{2} + 22 a + 20\right)\cdot 37^{88} + \left(35 a^{2} + 13 a + 16\right)\cdot 37^{89} + \left(a^{2} + 30 a + 3\right)\cdot 37^{90} + \left(35 a^{2} + 14 a + 8\right)\cdot 37^{91} + \left(2 a^{2} + 29 a + 18\right)\cdot 37^{92} + \left(22 a^{2} + 32 a + 21\right)\cdot 37^{93} + \left(30 a^{2} + 25 a + 17\right)\cdot 37^{94} + \left(29 a^{2} + 28 a + 4\right)\cdot 37^{95} + \left(33 a^{2} + 23 a + 14\right)\cdot 37^{96} + \left(29 a^{2} + 9 a + 23\right)\cdot 37^{97} + \left(35 a^{2} + 24 a + 17\right)\cdot 37^{98} + \left(32 a^{2} + 14 a + 24\right)\cdot 37^{99} + \left(2 a^{2} + 15 a + 29\right)\cdot 37^{100} + \left(19 a^{2} + 21 a + 35\right)\cdot 37^{101} + \left(20 a^{2} + 7 a + 28\right)\cdot 37^{102} + \left(6 a^{2} + 18 a + 22\right)\cdot 37^{103} + \left(28 a^{2} + 7 a + 32\right)\cdot 37^{104} + \left(20 a^{2} + 24 a + 21\right)\cdot 37^{105} + \left(20 a^{2} + 17 a + 27\right)\cdot 37^{106} + \left(18 a^{2} + 29 a + 2\right)\cdot 37^{107} + \left(30 a^{2} + 33 a + 24\right)\cdot 37^{108} + \left(26 a^{2} + 9 a + 34\right)\cdot 37^{109} + \left(8 a^{2} + 2 a + 29\right)\cdot 37^{110} + \left(27 a^{2} + 7 a + 2\right)\cdot 37^{111} + \left(11 a^{2} + 32 a + 11\right)\cdot 37^{112} + \left(14 a^{2} + 29 a + 6\right)\cdot 37^{113} + \left(11 a^{2} + 3 a + 28\right)\cdot 37^{114} + \left(27 a^{2} + 19 a + 10\right)\cdot 37^{115} + \left(18 a^{2} + 9 a\right)\cdot 37^{116} + \left(21 a^{2} + a + 16\right)\cdot 37^{117} + \left(11 a^{2} + 7 a + 24\right)\cdot 37^{118} + \left(32 a^{2} + 15 a + 10\right)\cdot 37^{119} + \left(12 a^{2} + 25 a + 36\right)\cdot 37^{120} + \left(21 a^{2} + 16 a + 4\right)\cdot 37^{121} + \left(19 a^{2} + 31\right)\cdot 37^{122} + \left(5 a^{2} + 33 a + 19\right)\cdot 37^{123} + \left(15 a^{2} + 32 a + 8\right)\cdot 37^{124} + \left(19 a^{2} + 17 a + 30\right)\cdot 37^{125} + \left(7 a^{2} + 31 a + 12\right)\cdot 37^{126} + \left(14 a^{2} + 36 a + 6\right)\cdot 37^{127} + \left(10 a^{2} + 13 a + 33\right)\cdot 37^{128} + \left(16 a^{2} + 15 a + 11\right)\cdot 37^{129} + \left(26 a^{2} + 8 a + 35\right)\cdot 37^{130} + \left(18 a^{2} + 26 a + 26\right)\cdot 37^{131} + \left(36 a^{2} + a + 33\right)\cdot 37^{132} + \left(5 a^{2} + 29 a + 16\right)\cdot 37^{133} + \left(4 a^{2} + 3 a + 35\right)\cdot 37^{134} + \left(29 a^{2} + 9 a + 34\right)\cdot 37^{135} + \left(3 a^{2} + 21 a + 7\right)\cdot 37^{136} + \left(21 a^{2} + 16 a + 30\right)\cdot 37^{137} + \left(9 a^{2} + 34 a + 17\right)\cdot 37^{138} + \left(13 a^{2} + 10 a + 15\right)\cdot 37^{139} + \left(12 a^{2} + 27 a + 4\right)\cdot 37^{140} +O\left(37^{ 141 }\right)$ $r_{ 2 }$ $=$ $6 a + 21 + \left(17 a^{2} + 26 a + 8\right)\cdot 37 + \left(27 a + 33\right)\cdot 37^{2} + \left(24 a^{2} + 13 a + 17\right)\cdot 37^{3} + \left(5 a^{2} + 18 a + 9\right)\cdot 37^{4} + \left(3 a^{2} + 30 a + 24\right)\cdot 37^{5} + \left(23 a^{2} + 20 a + 24\right)\cdot 37^{6} + \left(10 a^{2} + 6 a + 22\right)\cdot 37^{7} + \left(32 a^{2} + 36 a\right)\cdot 37^{8} + \left(15 a^{2} + 12 a + 15\right)\cdot 37^{9} + \left(3 a^{2} + 3 a + 29\right)\cdot 37^{10} + \left(13 a^{2} + 17 a + 12\right)\cdot 37^{11} + \left(27 a^{2} + 23\right)\cdot 37^{12} + \left(5 a^{2} + 11 a + 22\right)\cdot 37^{13} + \left(34 a^{2} + 14 a + 30\right)\cdot 37^{14} + \left(16 a + 23\right)\cdot 37^{15} + \left(6 a^{2} + 29 a + 4\right)\cdot 37^{16} + \left(25 a^{2} + 28 a + 25\right)\cdot 37^{17} + \left(28 a^{2} + 14 a + 36\right)\cdot 37^{18} + \left(34 a^{2} + 34 a + 34\right)\cdot 37^{19} + \left(30 a^{2} + 3 a + 28\right)\cdot 37^{20} + \left(3 a^{2} + 35 a + 1\right)\cdot 37^{21} + \left(4 a^{2} + 6 a + 9\right)\cdot 37^{22} + \left(17 a^{2} + 13 a + 17\right)\cdot 37^{23} + \left(18 a^{2} + 3 a + 21\right)\cdot 37^{24} + \left(28 a^{2} + 31 a + 24\right)\cdot 37^{25} + \left(32 a^{2} + 28 a + 28\right)\cdot 37^{26} + \left(24 a^{2} + 5 a + 18\right)\cdot 37^{27} + \left(23 a^{2} + 10 a + 12\right)\cdot 37^{28} + \left(20 a^{2} + 9 a + 21\right)\cdot 37^{29} + \left(22 a^{2} + 35 a + 35\right)\cdot 37^{30} + \left(4 a^{2} + 31 a + 11\right)\cdot 37^{31} + \left(19 a^{2} + 2 a + 32\right)\cdot 37^{32} + \left(16 a^{2} + 16 a + 22\right)\cdot 37^{33} + \left(6 a^{2} + 14 a + 3\right)\cdot 37^{34} + \left(16 a^{2} + 18 a + 28\right)\cdot 37^{35} + \left(12 a^{2} + 18 a + 8\right)\cdot 37^{36} + \left(28 a^{2} + 2 a + 1\right)\cdot 37^{37} + \left(18 a^{2} + 25 a + 4\right)\cdot 37^{38} + \left(22 a + 30\right)\cdot 37^{39} + \left(35 a^{2} + 33 a + 20\right)\cdot 37^{40} + \left(13 a^{2} + 36 a + 4\right)\cdot 37^{41} + \left(30 a^{2} + 21 a + 1\right)\cdot 37^{42} + \left(15 a^{2} + 6 a + 30\right)\cdot 37^{43} + \left(9 a^{2} + 17 a + 7\right)\cdot 37^{44} + \left(29 a^{2} + 7 a + 9\right)\cdot 37^{45} + \left(a^{2} + 26 a + 18\right)\cdot 37^{46} + \left(3 a^{2} + 33 a + 34\right)\cdot 37^{47} + \left(21 a^{2} + 33 a + 29\right)\cdot 37^{48} + \left(27 a^{2} + a + 25\right)\cdot 37^{49} + \left(4 a^{2} + 14 a + 24\right)\cdot 37^{50} + \left(16 a^{2} + 8 a + 14\right)\cdot 37^{51} + \left(25 a^{2} + 34 a + 4\right)\cdot 37^{52} + \left(21 a^{2} + 32 a\right)\cdot 37^{53} + \left(33 a^{2} + 21 a\right)\cdot 37^{54} + \left(31 a^{2} + 7 a + 31\right)\cdot 37^{55} + \left(9 a^{2} + 21 a + 30\right)\cdot 37^{56} + \left(33 a^{2} + 7 a + 27\right)\cdot 37^{57} + \left(22 a^{2} + 6 a + 1\right)\cdot 37^{58} + \left(10 a^{2} + 10 a + 5\right)\cdot 37^{59} + \left(31 a^{2} + 10 a + 25\right)\cdot 37^{60} + \left(8 a^{2} + 27 a + 29\right)\cdot 37^{61} + \left(11 a^{2} + 18 a + 20\right)\cdot 37^{62} + \left(11 a^{2} + 32\right)\cdot 37^{63} + \left(15 a^{2} + 24 a + 30\right)\cdot 37^{64} + \left(21 a^{2} + 25 a + 15\right)\cdot 37^{65} + \left(9 a^{2} + 25 a + 3\right)\cdot 37^{66} + \left(a^{2} + 11 a + 15\right)\cdot 37^{67} + \left(4 a^{2} + 3 a + 35\right)\cdot 37^{68} + \left(19 a^{2} + 2\right)\cdot 37^{69} + \left(10 a^{2} + 27 a + 8\right)\cdot 37^{70} + \left(3 a^{2} + 29 a + 18\right)\cdot 37^{71} + \left(25 a^{2} + 22 a + 9\right)\cdot 37^{72} + \left(14 a^{2} + 4 a + 21\right)\cdot 37^{73} + \left(9 a^{2} + 2 a\right)\cdot 37^{74} + \left(32 a^{2} + 6 a + 4\right)\cdot 37^{75} + \left(31 a^{2} + 16 a + 5\right)\cdot 37^{76} + \left(33 a^{2} + 9 a + 12\right)\cdot 37^{77} + \left(28 a^{2} + 34 a + 18\right)\cdot 37^{78} + \left(2 a^{2} + 25 a + 25\right)\cdot 37^{79} + \left(28 a^{2} + 21 a + 7\right)\cdot 37^{80} + \left(20 a^{2} + 25 a + 19\right)\cdot 37^{81} + \left(20 a^{2} + 11 a + 26\right)\cdot 37^{82} + \left(16 a^{2} + 28 a + 15\right)\cdot 37^{83} + \left(9 a^{2} + 20 a + 13\right)\cdot 37^{84} + \left(2 a^{2} + 24 a + 25\right)\cdot 37^{85} + \left(3 a^{2} + 7 a + 24\right)\cdot 37^{86} + \left(17 a^{2} + 9 a + 11\right)\cdot 37^{87} + \left(9 a^{2} + 24 a + 25\right)\cdot 37^{88} + \left(8 a^{2} + 25 a + 31\right)\cdot 37^{89} + \left(16 a^{2} + 16 a + 22\right)\cdot 37^{90} + \left(19 a^{2} + 15 a + 29\right)\cdot 37^{91} + \left(14 a^{2} + 32 a + 5\right)\cdot 37^{92} + \left(33 a + 30\right)\cdot 37^{93} + \left(34 a^{2} + 14 a + 19\right)\cdot 37^{94} + \left(17 a^{2} + 2 a\right)\cdot 37^{95} + \left(36 a^{2} + 20 a + 21\right)\cdot 37^{96} + \left(32 a^{2} + 3 a + 29\right)\cdot 37^{97} + \left(26 a^{2} + 34 a + 23\right)\cdot 37^{98} + \left(32 a^{2} + 32 a + 29\right)\cdot 37^{99} + \left(26 a^{2} + a + 13\right)\cdot 37^{100} + \left(27 a^{2} + 32 a + 28\right)\cdot 37^{101} + \left(2 a^{2} + 2 a + 26\right)\cdot 37^{102} + \left(33 a^{2} + 2 a\right)\cdot 37^{103} + \left(23 a^{2} + 4 a + 36\right)\cdot 37^{104} + \left(8 a^{2} + 16 a + 3\right)\cdot 37^{105} + \left(32 a^{2} + 3 a + 23\right)\cdot 37^{106} + \left(6 a^{2} + 7\right)\cdot 37^{107} + \left(21 a^{2} + 10 a + 14\right)\cdot 37^{108} + \left(4 a^{2} + 36 a + 3\right)\cdot 37^{109} + \left(2 a^{2} + 9 a + 35\right)\cdot 37^{110} + \left(11 a^{2} + 2 a + 9\right)\cdot 37^{111} + \left(27 a^{2} + 15 a + 9\right)\cdot 37^{112} + \left(22 a^{2} + 20 a + 1\right)\cdot 37^{113} + \left(31 a^{2} + 16 a + 6\right)\cdot 37^{114} + \left(25 a^{2} + 5 a + 11\right)\cdot 37^{115} + \left(5 a^{2} + 30 a + 14\right)\cdot 37^{116} + \left(21 a^{2} + 29 a + 5\right)\cdot 37^{117} + \left(28 a^{2} + 10 a + 8\right)\cdot 37^{118} + \left(22 a^{2} + 27 a + 34\right)\cdot 37^{119} + \left(11 a^{2} + 5 a\right)\cdot 37^{120} + \left(36 a^{2} + 13 a + 23\right)\cdot 37^{121} + \left(34 a + 12\right)\cdot 37^{122} + \left(20 a^{2} + 21 a + 7\right)\cdot 37^{123} + \left(24 a^{2} + 7 a + 35\right)\cdot 37^{124} + \left(a^{2} + 6 a + 11\right)\cdot 37^{125} + \left(29 a^{2} + 5 a + 28\right)\cdot 37^{126} + \left(18 a^{2} + 11 a + 23\right)\cdot 37^{127} + \left(15 a^{2} + 2 a + 19\right)\cdot 37^{128} + \left(36 a^{2} + 30 a + 22\right)\cdot 37^{129} + \left(31 a^{2} + 15 a + 19\right)\cdot 37^{130} + \left(27 a^{2} + 5 a + 35\right)\cdot 37^{131} + \left(29 a^{2} + 7 a + 27\right)\cdot 37^{132} + \left(a^{2} + 9 a + 1\right)\cdot 37^{133} + \left(19 a + 13\right)\cdot 37^{134} + \left(25 a^{2} + 25 a + 14\right)\cdot 37^{135} + \left(31 a^{2} + a + 3\right)\cdot 37^{136} + \left(16 a^{2} + 8 a + 24\right)\cdot 37^{137} + \left(28 a^{2} + 13 a + 7\right)\cdot 37^{138} + \left(2 a^{2} + 9 a + 12\right)\cdot 37^{139} + \left(14 a^{2} + 17 a + 13\right)\cdot 37^{140} +O\left(37^{ 141 }\right)$ $r_{ 3 }$ $=$ $30 a^{2} + 14 a + 18 + \left(36 a^{2} + 31 a + 36\right)\cdot 37 + \left(33 a^{2} + 22 a + 1\right)\cdot 37^{2} + \left(6 a + 13\right)\cdot 37^{3} + \left(14 a^{2} + 36 a + 24\right)\cdot 37^{4} + \left(29 a^{2} + 25 a + 27\right)\cdot 37^{5} + \left(33 a^{2} + 35 a + 19\right)\cdot 37^{6} + \left(19 a^{2} + 29 a + 34\right)\cdot 37^{7} + \left(35 a^{2} + 18 a + 11\right)\cdot 37^{8} + \left(22 a^{2} + 25 a + 19\right)\cdot 37^{9} + \left(36 a^{2} + a + 10\right)\cdot 37^{10} + \left(29 a^{2} + 3 a + 8\right)\cdot 37^{11} + \left(26 a^{2} + 3 a + 9\right)\cdot 37^{12} + \left(35 a^{2} + 14 a + 23\right)\cdot 37^{13} + \left(26 a^{2} + 9 a + 5\right)\cdot 37^{14} + \left(28 a^{2} + 20 a + 18\right)\cdot 37^{15} + \left(26 a^{2} + 24 a + 35\right)\cdot 37^{16} + \left(8 a^{2} + 4 a + 4\right)\cdot 37^{17} + \left(27 a^{2} + 35 a + 8\right)\cdot 37^{18} + \left(23 a^{2} + 8 a + 12\right)\cdot 37^{19} + \left(11 a^{2} + 20 a + 32\right)\cdot 37^{20} + \left(10 a^{2} + 7 a + 17\right)\cdot 37^{21} + \left(19 a^{2} + 12 a + 19\right)\cdot 37^{22} + \left(29 a^{2} + 25 a + 10\right)\cdot 37^{23} + \left(28 a^{2} + 28 a + 24\right)\cdot 37^{24} + \left(7 a^{2} + 3 a + 31\right)\cdot 37^{25} + \left(34 a^{2} + 34 a + 31\right)\cdot 37^{26} + \left(14 a^{2} + 5 a + 22\right)\cdot 37^{27} + \left(35 a^{2} + 26 a + 19\right)\cdot 37^{28} + \left(22 a^{2} + 14 a + 32\right)\cdot 37^{29} + \left(27 a^{2} + 27 a + 16\right)\cdot 37^{30} + \left(12 a^{2} + 36 a + 14\right)\cdot 37^{31} + \left(24 a^{2} + 15 a + 23\right)\cdot 37^{32} + \left(7 a^{2} + 30 a + 32\right)\cdot 37^{33} + \left(20 a^{2} + 2 a + 17\right)\cdot 37^{34} + \left(23 a^{2} + 13 a + 24\right)\cdot 37^{35} + \left(29 a^{2} + 13 a + 10\right)\cdot 37^{36} + \left(26 a^{2} + 25 a + 17\right)\cdot 37^{37} + \left(8 a^{2} + 35 a + 36\right)\cdot 37^{38} + \left(3 a^{2} + 4 a + 2\right)\cdot 37^{39} + \left(6 a + 18\right)\cdot 37^{40} + \left(12 a^{2} + 16 a + 2\right)\cdot 37^{41} + \left(25 a^{2} + 30 a + 20\right)\cdot 37^{42} + \left(28 a^{2} + 20 a + 12\right)\cdot 37^{43} + \left(6 a^{2} + 26 a + 17\right)\cdot 37^{44} + \left(19 a^{2} + 20 a + 31\right)\cdot 37^{45} + \left(27 a^{2} + 25 a + 33\right)\cdot 37^{46} + \left(12 a^{2} + 16 a + 21\right)\cdot 37^{47} + \left(15 a^{2} + 7 a + 34\right)\cdot 37^{48} + \left(18 a^{2} + 34 a + 6\right)\cdot 37^{49} + \left(15 a^{2} + 13 a + 30\right)\cdot 37^{50} + \left(a^{2} + 11 a + 28\right)\cdot 37^{51} + \left(6 a^{2} + 18 a + 15\right)\cdot 37^{52} + \left(27 a^{2} + 28 a + 22\right)\cdot 37^{53} + \left(20 a^{2} + 36 a + 22\right)\cdot 37^{54} + \left(11 a^{2} + 25 a + 20\right)\cdot 37^{55} + \left(34 a^{2} + 33 a + 14\right)\cdot 37^{56} + \left(27 a^{2} + 31 a + 30\right)\cdot 37^{57} + \left(6 a^{2} + 18 a + 4\right)\cdot 37^{58} + \left(13 a^{2} + 33 a + 24\right)\cdot 37^{59} + \left(7 a^{2} + 2 a + 4\right)\cdot 37^{60} + \left(13 a^{2} + 15 a + 33\right)\cdot 37^{61} + \left(27 a^{2} + 2 a + 13\right)\cdot 37^{62} + \left(13 a^{2} + 19 a + 23\right)\cdot 37^{63} + \left(7 a^{2} + 22 a + 8\right)\cdot 37^{64} + \left(17 a^{2} + 2 a + 25\right)\cdot 37^{65} + \left(31 a^{2} + 36 a + 32\right)\cdot 37^{66} + \left(36 a^{2} + 32 a + 5\right)\cdot 37^{67} + \left(8 a^{2} + 36 a + 23\right)\cdot 37^{68} + \left(32 a^{2} + 32 a + 1\right)\cdot 37^{69} + \left(10 a^{2} + 24 a + 25\right)\cdot 37^{70} + \left(34 a^{2} + 21 a + 17\right)\cdot 37^{71} + \left(36 a^{2} + 4 a + 30\right)\cdot 37^{72} + \left(25 a^{2} + 28 a + 8\right)\cdot 37^{73} + \left(28 a^{2} + 3 a + 25\right)\cdot 37^{74} + \left(9 a^{2} + 27 a + 33\right)\cdot 37^{75} + \left(5 a^{2} + 33 a + 3\right)\cdot 37^{76} + \left(27 a^{2} + 35 a + 22\right)\cdot 37^{77} + \left(24 a^{2} + 17 a + 20\right)\cdot 37^{78} + \left(26 a^{2} + 6 a + 32\right)\cdot 37^{79} + \left(3 a^{2} + 24 a + 4\right)\cdot 37^{80} + \left(11 a^{2} + 11 a + 5\right)\cdot 37^{81} + \left(36 a^{2} + 8 a + 35\right)\cdot 37^{82} + \left(7 a^{2} + 27 a + 26\right)\cdot 37^{83} + \left(7 a^{2} + 26 a + 10\right)\cdot 37^{84} + \left(10 a^{2} + 9 a + 9\right)\cdot 37^{85} + \left(12 a^{2} + 25 a + 30\right)\cdot 37^{86} + \left(a^{2} + 8 a + 18\right)\cdot 37^{87} + \left(13 a^{2} + 29 a + 17\right)\cdot 37^{88} + \left(24 a^{2} + 20 a + 29\right)\cdot 37^{89} + \left(23 a^{2} + 35 a + 2\right)\cdot 37^{90} + \left(21 a^{2} + 5 a + 1\right)\cdot 37^{91} + \left(a^{2} + 32 a + 25\right)\cdot 37^{92} + \left(36 a^{2} + 29 a + 15\right)\cdot 37^{93} + \left(17 a^{2} + 32 a + 29\right)\cdot 37^{94} + \left(20 a^{2} + 25 a + 15\right)\cdot 37^{95} + \left(14 a^{2} + 5 a + 34\right)\cdot 37^{96} + \left(25 a^{2} + 7 a + 18\right)\cdot 37^{97} + \left(17 a^{2} + 33 a + 23\right)\cdot 37^{98} + \left(36 a^{2} + 17 a + 28\right)\cdot 37^{99} + \left(15 a^{2} + 32 a + 29\right)\cdot 37^{100} + \left(10 a^{2} + 36 a + 6\right)\cdot 37^{101} + \left(30 a^{2} + 33 a + 31\right)\cdot 37^{102} + \left(25 a^{2} + 17 a + 19\right)\cdot 37^{103} + \left(34 a^{2} + 19 a + 31\right)\cdot 37^{104} + \left(27 a^{2} + 26 a + 17\right)\cdot 37^{105} + \left(31 a^{2} + 3 a + 35\right)\cdot 37^{106} + \left(19 a^{2} + 27 a + 6\right)\cdot 37^{107} + \left(26 a^{2} + 12 a + 36\right)\cdot 37^{108} + \left(6 a^{2} + 22 a + 8\right)\cdot 37^{109} + \left(24 a^{2} + 5 a + 8\right)\cdot 37^{110} + \left(12 a^{2} + 10 a + 20\right)\cdot 37^{111} + \left(10 a^{2} + 3 a + 16\right)\cdot 37^{112} + \left(30 a^{2} + 8 a + 10\right)\cdot 37^{113} + \left(6 a^{2} + 5 a + 3\right)\cdot 37^{114} + \left(35 a^{2} + 12 a + 8\right)\cdot 37^{115} + \left(35 a^{2} + 34 a + 27\right)\cdot 37^{116} + \left(25 a^{2} + 27 a + 26\right)\cdot 37^{117} + \left(22 a^{2} + 4 a + 17\right)\cdot 37^{118} + \left(36 a^{2} + 22 a + 14\right)\cdot 37^{119} + \left(27 a^{2} + 8 a + 31\right)\cdot 37^{120} + \left(25 a^{2} + 22 a + 3\right)\cdot 37^{121} + \left(31 a^{2} + 19 a + 11\right)\cdot 37^{122} + \left(10 a^{2} + 26 a + 19\right)\cdot 37^{123} + \left(a^{2} + 30 a + 6\right)\cdot 37^{124} + \left(22 a^{2} + 34 a + 22\right)\cdot 37^{125} + \left(18 a^{2} + 4 a + 18\right)\cdot 37^{126} + \left(a^{2} + 6 a + 11\right)\cdot 37^{127} + \left(15 a^{2} + 35 a + 23\right)\cdot 37^{128} + \left(29 a^{2} + 24 a + 9\right)\cdot 37^{129} + \left(19 a^{2} + 7 a + 32\right)\cdot 37^{130} + \left(28 a^{2} + 23 a + 24\right)\cdot 37^{131} + \left(3 a^{2} + 33\right)\cdot 37^{132} + \left(17 a^{2} + 24 a + 6\right)\cdot 37^{133} + \left(20 a^{2} + 24 a + 13\right)\cdot 37^{134} + \left(36 a^{2} + 25 a + 17\right)\cdot 37^{135} + \left(27 a^{2} + 7 a + 20\right)\cdot 37^{136} + \left(15 a^{2} + 7 a + 12\right)\cdot 37^{137} + \left(31 a^{2} + 5 a + 30\right)\cdot 37^{138} + \left(16 a^{2} + 19 a + 29\right)\cdot 37^{139} + \left(28 a^{2} + 19 a + 16\right)\cdot 37^{140} +O\left(37^{ 141 }\right)$ $r_{ 4 }$ $=$ $5 a^{2} + 18 a + 4 + \left(18 a^{2} + 33 a + 30\right)\cdot 37 + \left(17 a^{2} + 8 a + 5\right)\cdot 37^{2} + \left(23 a^{2} + 10\right)\cdot 37^{3} + \left(36 a^{2} + 33 a + 26\right)\cdot 37^{4} + \left(29 a^{2} + 19 a + 14\right)\cdot 37^{5} + \left(23 a^{2} + 27 a + 36\right)\cdot 37^{6} + \left(11 a^{2} + 13 a + 31\right)\cdot 37^{7} + \left(21 a^{2} + 21 a + 17\right)\cdot 37^{8} + \left(34 a^{2} + 26 a + 27\right)\cdot 37^{9} + \left(6 a^{2} + 29 a + 21\right)\cdot 37^{10} + \left(22 a^{2} + 27 a + 26\right)\cdot 37^{11} + \left(21 a^{2} + 9 a + 13\right)\cdot 37^{12} + \left(19 a^{2} + 20 a + 14\right)\cdot 37^{13} + \left(36 a^{2} + 36 a + 29\right)\cdot 37^{14} + \left(7 a^{2} + 34 a + 7\right)\cdot 37^{15} + \left(3 a^{2} + 34 a + 10\right)\cdot 37^{16} + \left(14 a^{2} + 35 a + 36\right)\cdot 37^{17} + \left(11 a^{2} + 25 a + 31\right)\cdot 37^{18} + \left(21 a^{2} + 29 a + 9\right)\cdot 37^{19} + \left(36 a^{2} + 5 a + 16\right)\cdot 37^{20} + \left(30 a^{2} + 18 a + 28\right)\cdot 37^{21} + \left(27 a^{2} + 15 a + 21\right)\cdot 37^{22} + \left(35 a^{2} + 30 a + 18\right)\cdot 37^{23} + \left(6 a^{2} + 32 a + 11\right)\cdot 37^{24} + \left(34 a^{2} + 24 a + 21\right)\cdot 37^{25} + \left(5 a^{2} + 30 a + 14\right)\cdot 37^{26} + \left(9 a^{2} + 22 a + 29\right)\cdot 37^{27} + \left(5 a^{2} + 8 a + 7\right)\cdot 37^{28} + \left(15 a^{2} + 20 a + 7\right)\cdot 37^{29} + \left(19 a^{2} + 21 a + 36\right)\cdot 37^{30} + \left(29 a^{2} + 22 a + 18\right)\cdot 37^{31} + \left(32 a^{2} + 25 a + 36\right)\cdot 37^{32} + \left(18 a^{2} + 20 a + 15\right)\cdot 37^{33} + \left(a^{2} + 34 a + 5\right)\cdot 37^{34} + \left(8 a + 34\right)\cdot 37^{35} + \left(7 a^{2} + 7 a + 31\right)\cdot 37^{36} + \left(35 a^{2} + 17 a + 21\right)\cdot 37^{37} + \left(5 a^{2} + 35 a + 7\right)\cdot 37^{38} + \left(23 a^{2} + 32 a + 19\right)\cdot 37^{39} + \left(32 a^{2} + 26 a + 30\right)\cdot 37^{40} + \left(7 a^{2} + 12 a + 1\right)\cdot 37^{41} + \left(32 a^{2} + 27 a + 5\right)\cdot 37^{42} + \left(25 a^{2} + 33 a + 22\right)\cdot 37^{43} + \left(18 a^{2} + 10 a + 25\right)\cdot 37^{44} + \left(17 a^{2} + 25 a + 9\right)\cdot 37^{45} + \left(21 a^{2} + 15 a + 7\right)\cdot 37^{46} + \left(31 a^{2} + 13 a + 36\right)\cdot 37^{47} + \left(17 a^{2} + 20 a + 15\right)\cdot 37^{48} + \left(20 a^{2} + 21 a + 26\right)\cdot 37^{49} + \left(23 a^{2} + 35 a + 15\right)\cdot 37^{50} + \left(36 a^{2} + 13 a\right)\cdot 37^{51} + \left(14 a^{2} + a + 1\right)\cdot 37^{52} + \left(21 a^{2} + 3 a + 17\right)\cdot 37^{53} + \left(9 a^{2} + 6 a + 32\right)\cdot 37^{54} + \left(9 a^{2} + 32 a + 21\right)\cdot 37^{55} + \left(17 a^{2} + 33 a + 4\right)\cdot 37^{56} + \left(13 a^{2} + 17 a\right)\cdot 37^{57} + 17 a^{2}37^{58} + \left(18 a + 12\right)\cdot 37^{59} + \left(2 a^{2} + 25 a + 27\right)\cdot 37^{60} + \left(20 a^{2} + 33 a + 1\right)\cdot 37^{61} + \left(12 a^{2} + 3 a + 17\right)\cdot 37^{62} + \left(21 a^{2} + 19 a + 7\right)\cdot 37^{63} + \left(24 a^{2} + 26 a + 17\right)\cdot 37^{64} + \left(12 a^{2} + 25 a + 9\right)\cdot 37^{65} + \left(29 a^{2} + 2 a + 10\right)\cdot 37^{66} + \left(32 a^{2} + 13 a + 7\right)\cdot 37^{67} + \left(10 a^{2} + 22 a\right)\cdot 37^{68} + \left(28 a^{2} + 28 a + 21\right)\cdot 37^{69} + \left(29 a^{2} + 22 a + 32\right)\cdot 37^{70} + \left(31 a^{2} + 11 a + 7\right)\cdot 37^{71} + \left(19 a^{2} + 27 a + 36\right)\cdot 37^{72} + \left(33 a^{2} + 30 a + 31\right)\cdot 37^{73} + \left(28 a^{2} + 24 a + 36\right)\cdot 37^{74} + \left(36 a^{2} + 31 a + 36\right)\cdot 37^{75} + \left(17 a^{2} + 4 a + 28\right)\cdot 37^{76} + \left(6 a^{2} + 20 a + 9\right)\cdot 37^{77} + \left(17 a^{2} + 11 a + 21\right)\cdot 37^{78} + \left(8 a^{2} + 12 a + 30\right)\cdot 37^{79} + \left(28 a^{2} + 11\right)\cdot 37^{80} + \left(5 a^{2} + 2 a + 10\right)\cdot 37^{81} + \left(9 a^{2} + 17 a + 25\right)\cdot 37^{82} + \left(12 a^{2} + 3 a + 20\right)\cdot 37^{83} + \left(24 a^{2} + 3 a + 36\right)\cdot 37^{84} + \left(19 a^{2} + 17 a + 3\right)\cdot 37^{85} + \left(14 a^{2} + 31 a + 12\right)\cdot 37^{86} + \left(11 a^{2} + 10 a + 26\right)\cdot 37^{87} + \left(33 a^{2} + 13 a + 7\right)\cdot 37^{88} + \left(32 a^{2} + 14 a + 24\right)\cdot 37^{89} + \left(28 a^{2} + 31 a + 3\right)\cdot 37^{90} + \left(29 a^{2} + 29 a + 4\right)\cdot 37^{91} + \left(21 a^{2} + 26 a + 4\right)\cdot 37^{92} + \left(2 a^{2} + 13 a + 11\right)\cdot 37^{93} + \left(10 a^{2} + 32 a + 8\right)\cdot 37^{94} + \left(25 a^{2} + 15 a + 25\right)\cdot 37^{95} + \left(30 a^{2} + 7 a + 30\right)\cdot 37^{96} + \left(35 a^{2} + 32 a + 27\right)\cdot 37^{97} + \left(13 a^{2} + 22 a + 36\right)\cdot 37^{98} + \left(7 a^{2} + 29 a + 27\right)\cdot 37^{99} + \left(32 a^{2} + 14 a + 9\right)\cdot 37^{100} + \left(17 a^{2} + 33 a + 1\right)\cdot 37^{101} + \left(33 a^{2} + 13 a + 34\right)\cdot 37^{102} + \left(13 a^{2} + 18 a + 30\right)\cdot 37^{103} + \left(a^{2} + 13 a + 29\right)\cdot 37^{104} + \left(29 a^{2} + 10 a + 19\right)\cdot 37^{105} + \left(27 a^{2} + 32 a + 32\right)\cdot 37^{106} + \left(20 a^{2} + 6 a + 21\right)\cdot 37^{107} + \left(16 a^{2} + 11 a + 18\right)\cdot 37^{108} + \left(6 a^{2} + 32 a + 4\right)\cdot 37^{109} + \left(21 a^{2} + 27 a + 32\right)\cdot 37^{110} + \left(34 a^{2} + 10 a + 2\right)\cdot 37^{111} + \left(7 a^{2} + 33 a + 28\right)\cdot 37^{112} + \left(5 a^{2} + 18 a + 35\right)\cdot 37^{113} + \left(32 a^{2} + 34 a + 11\right)\cdot 37^{114} + \left(2 a^{2} + 28 a + 34\right)\cdot 37^{115} + \left(25 a^{2} + a + 24\right)\cdot 37^{116} + \left(2 a^{2} + 18 a + 16\right)\cdot 37^{117} + \left(12 a^{2} + 31 a + 30\right)\cdot 37^{118} + \left(32 a^{2} + 15 a + 8\right)\cdot 37^{119} + \left(7 a^{2} + 34 a + 18\right)\cdot 37^{120} + \left(7 a^{2} + 33 a + 28\right)\cdot 37^{121} + \left(11 a^{2} + 6 a + 5\right)\cdot 37^{122} + \left(2 a^{2} + 17 a + 29\right)\cdot 37^{123} + \left(32 a^{2} + 16 a + 27\right)\cdot 37^{124} + \left(32 a^{2} + 21 a + 30\right)\cdot 37^{125} + \left(25 a^{2} + 28 a + 9\right)\cdot 37^{126} + \left(18 a^{2} + 19 a + 31\right)\cdot 37^{127} + \left(36 a^{2} + 12 a + 20\right)\cdot 37^{128} + \left(34 a^{2} + 14 a + 7\right)\cdot 37^{129} + \left(13 a^{2} + 5 a + 26\right)\cdot 37^{130} + \left(12 a^{2} + 30 a + 9\right)\cdot 37^{131} + \left(2 a^{2} + 22 a + 29\right)\cdot 37^{132} + \left(36 a^{2} + 16 a + 27\right)\cdot 37^{133} + \left(12 a^{2} + 14 a + 27\right)\cdot 37^{134} + \left(27 a^{2} + 6 a + 23\right)\cdot 37^{135} + \left(32 a^{2} + 2 a + 7\right)\cdot 37^{136} + \left(36 a^{2} + 18 a + 30\right)\cdot 37^{137} + \left(33 a^{2} + 12 a + 29\right)\cdot 37^{138} + \left(11 a^{2} + 16 a + 11\right)\cdot 37^{139} + \left(18 a^{2} + 19 a + 30\right)\cdot 37^{140} +O\left(37^{ 141 }\right)$ $r_{ 5 }$ $=$ $29 a^{2} + 5 a + 14 + \left(19 a^{2} + 4 a + 2\right)\cdot 37 + \left(35 a^{2} + 2 a + 32\right)\cdot 37^{2} + \left(13 a^{2} + 21 a + 13\right)\cdot 37^{3} + \left(20 a^{2} + 4 a + 9\right)\cdot 37^{4} + \left(12 a^{2} + 34 a + 24\right)\cdot 37^{5} + \left(3 a^{2} + 31 a + 24\right)\cdot 37^{6} + \left(33 a^{2} + 32 a + 28\right)\cdot 37^{7} + \left(19 a^{2} + 23 a + 13\right)\cdot 37^{8} + \left(9 a^{2} + 17 a + 26\right)\cdot 37^{9} + \left(27 a^{2} + 21 a + 28\right)\cdot 37^{10} + \left(31 a^{2} + 26\right)\cdot 37^{11} + \left(23 a^{2} + 25 a\right)\cdot 37^{12} + \left(15 a^{2} + 25 a + 25\right)\cdot 37^{13} + \left(16 a^{2} + 17 a + 14\right)\cdot 37^{14} + \left(30 a^{2} + 15 a\right)\cdot 37^{15} + \left(14 a^{2} + 35 a + 13\right)\cdot 37^{16} + \left(21 a^{2} + 9 a + 5\right)\cdot 37^{17} + \left(31 a^{2} + 34 a + 26\right)\cdot 37^{18} + \left(32 a^{2} + 11 a + 29\right)\cdot 37^{19} + \left(21 a^{2} + 8 a + 33\right)\cdot 37^{20} + \left(7 a^{2} + 3 a + 1\right)\cdot 37^{21} + \left(a^{2} + 6 a + 6\right)\cdot 37^{22} + \left(26 a^{2} + 31 a + 20\right)\cdot 37^{23} + \left(28 a^{2} + 3 a + 32\right)\cdot 37^{24} + \left(11 a^{2} + 35 a + 25\right)\cdot 37^{25} + \left(7 a^{2} + 3 a + 24\right)\cdot 37^{26} + \left(36 a^{2} + 32 a + 27\right)\cdot 37^{27} + \left(18 a^{2} + 16 a + 22\right)\cdot 37^{28} + \left(25 a^{2} + 16 a + 34\right)\cdot 37^{29} + \left(16 a^{2} + 24 a + 7\right)\cdot 37^{30} + \left(4 a^{2} + 19 a + 26\right)\cdot 37^{31} + \left(32 a^{2} + 15 a + 26\right)\cdot 37^{32} + \left(16 a^{2} + 13 a + 11\right)\cdot 37^{33} + \left(32 a^{2} + 17 a + 4\right)\cdot 37^{34} + \left(23 a^{2} + 26 a + 5\right)\cdot 37^{35} + \left(11 a^{2} + 11 a + 28\right)\cdot 37^{36} + \left(5 a^{2} + 35 a + 17\right)\cdot 37^{37} + \left(10 a^{2} + 19 a + 20\right)\cdot 37^{38} + \left(19 a^{2} + 11 a + 1\right)\cdot 37^{39} + \left(29 a^{2} + 2 a + 6\right)\cdot 37^{40} + \left(27 a^{2} + 26 a + 36\right)\cdot 37^{41} + \left(22 a^{2} + 23 a + 19\right)\cdot 37^{42} + \left(29 a^{2} + 27 a + 12\right)\cdot 37^{43} + \left(29 a^{2} + 13 a + 36\right)\cdot 37^{44} + \left(10 a^{2} + 24 a + 14\right)\cdot 37^{45} + \left(19 a^{2} + 33 a + 26\right)\cdot 37^{46} + \left(36 a^{2} + 34 a + 19\right)\cdot 37^{47} + \left(14 a^{2} + 4 a + 10\right)\cdot 37^{48} + \left(36 a^{2} + 5 a + 18\right)\cdot 37^{49} + \left(23 a^{2} + 33 a + 25\right)\cdot 37^{50} + \left(18 a^{2} + 13 a + 35\right)\cdot 37^{51} + \left(5 a^{2} + 18 a + 21\right)\cdot 37^{52} + \left(20 a^{2} + 22 a + 12\right)\cdot 37^{53} + \left(30 a^{2} + 18 a + 30\right)\cdot 37^{54} + \left(4 a^{2} + 13 a + 14\right)\cdot 37^{55} + \left(7 a^{2} + 25 a + 25\right)\cdot 37^{56} + \left(7 a^{2} + 21 a + 11\right)\cdot 37^{57} + \left(a^{2} + 25 a + 16\right)\cdot 37^{58} + \left(6 a^{2} + 35 a + 31\right)\cdot 37^{59} + \left(14 a^{2} + 13 a + 6\right)\cdot 37^{60} + \left(5 a^{2} + 25 a + 17\right)\cdot 37^{61} + \left(12 a^{2} + 23 a + 14\right)\cdot 37^{62} + \left(11 a^{2} + 5 a + 20\right)\cdot 37^{63} + \left(5 a^{2} + 17 a + 2\right)\cdot 37^{64} + \left(5 a^{2} + 3 a + 21\right)\cdot 37^{65} + \left(15 a^{2} + 23 a + 17\right)\cdot 37^{66} + \left(35 a^{2} + 32 a + 24\right)\cdot 37^{67} + \left(22 a^{2} + 12 a + 26\right)\cdot 37^{68} + \left(25 a^{2} + 32 a\right)\cdot 37^{69} + \left(32 a^{2} + 4 a + 17\right)\cdot 37^{70} + \left(31 a^{2} + 28 a + 24\right)\cdot 37^{71} + \left(4 a^{2} + 21\right)\cdot 37^{72} + \left(36 a^{2} + 14 a + 14\right)\cdot 37^{73} + \left(6 a^{2} + 14 a + 6\right)\cdot 37^{74} + \left(10 a^{2} + 14 a + 10\right)\cdot 37^{75} + \left(22 a^{2} + 17 a\right)\cdot 37^{76} + \left(30 a^{2} + 30 a + 29\right)\cdot 37^{77} + \left(32 a^{2} + 9\right)\cdot 37^{78} + \left(24 a^{2} + 15 a + 10\right)\cdot 37^{79} + \left(28 a^{2} + 16 a + 28\right)\cdot 37^{80} + \left(11 a^{2} + 17 a + 13\right)\cdot 37^{81} + \left(3 a^{2} + 10 a + 7\right)\cdot 37^{82} + \left(23 a^{2} + 12 a + 32\right)\cdot 37^{83} + \left(19 a^{2} + 21 a + 36\right)\cdot 37^{84} + \left(13 a^{2} + 25 a + 26\right)\cdot 37^{85} + \left(17 a^{2} + 30 a + 17\right)\cdot 37^{86} + \left(29 a^{2} + 30 a + 15\right)\cdot 37^{87} + \left(16 a^{2} + 13\right)\cdot 37^{88} + \left(12 a^{2} + 19 a + 22\right)\cdot 37^{89} + \left(13 a^{2} + 24 a + 14\right)\cdot 37^{90} + \left(13 a^{2} + 19 a + 25\right)\cdot 37^{91} + \left(21 a^{2} + 28 a + 8\right)\cdot 37^{92} + \left(29 a^{2} + 34 a + 24\right)\cdot 37^{93} + \left(27 a^{2} + a + 5\right)\cdot 37^{94} + \left(18 a^{2} + 35 a + 22\right)\cdot 37^{95} + \left(8 a^{2} + 29 a\right)\cdot 37^{96} + \left(7 a^{2} + 11 a + 9\right)\cdot 37^{97} + \left(14 a^{2} + 19 a + 30\right)\cdot 37^{98} + \left(7 a^{2} + 10 a + 22\right)\cdot 37^{99} + \left(a^{2} + 6 a + 31\right)\cdot 37^{100} + \left(18 a^{2} + 18 a + 5\right)\cdot 37^{101} + \left(29 a^{2} + 24 a + 14\right)\cdot 37^{102} + \left(12 a^{2} + 17 a + 7\right)\cdot 37^{103} + \left(22 a^{2} + 9 a + 13\right)\cdot 37^{104} + \left(35 a^{2} + 2 a + 7\right)\cdot 37^{105} + \left(11 a^{2} + 25 a + 26\right)\cdot 37^{106} + \left(34 a^{2} + 27 a + 28\right)\cdot 37^{107} + \left(a^{2} + 31 a + 20\right)\cdot 37^{108} + \left(16 a^{2} + 2 a + 4\right)\cdot 37^{109} + \left(34 a^{2} + 20 a + 36\right)\cdot 37^{110} + \left(10 a^{2} + 30 a + 6\right)\cdot 37^{111} + \left(13 a^{2} + 13 a + 17\right)\cdot 37^{112} + \left(16 a^{2} + 30 a + 31\right)\cdot 37^{113} + \left(20 a^{2} + 5 a + 19\right)\cdot 37^{114} + \left(31 a^{2} + 33 a + 25\right)\cdot 37^{115} + \left(a + 32\right)\cdot 37^{116} + \left(20 a^{2} + 25 a + 26\right)\cdot 37^{117} + \left(34 a^{2} + 5 a + 12\right)\cdot 37^{118} + \left(20 a^{2} + 16 a + 8\right)\cdot 37^{119} + \left(28 a^{2} + 5 a + 27\right)\cdot 37^{120} + \left(14 a^{2} + 14 a + 16\right)\cdot 37^{121} + \left(5 a^{2} + 22 a + 27\right)\cdot 37^{122} + \left(19 a^{2} + 12 a + 28\right)\cdot 37^{123} + \left(2 a^{2} + 13 a + 19\right)\cdot 37^{124} + \left(23 a^{2} + 16 a + 22\right)\cdot 37^{125} + \left(14 a^{2} + 26 a + 36\right)\cdot 37^{126} + \left(34 a^{2} + 3 a + 7\right)\cdot 37^{127} + \left(8 a^{2} + 7 a + 31\right)\cdot 37^{128} + \left(5 a^{2} + 28 a + 23\right)\cdot 37^{129} + \left(26 a^{2} + 10 a + 5\right)\cdot 37^{130} + \left(4 a^{2} + 29 a + 2\right)\cdot 37^{131} + \left(35 a^{2} + 23 a + 11\right)\cdot 37^{132} + \left(24 a^{2} + 21 a + 1\right)\cdot 37^{133} + \left(33 a^{2} + 30 a + 29\right)\cdot 37^{134} + \left(19 a^{2} + 26 a + 24\right)\cdot 37^{135} + \left(8 a^{2} + 15 a + 16\right)\cdot 37^{136} + \left(5 a^{2} + 27 a + 7\right)\cdot 37^{137} + \left(12 a^{2} + 4 a + 27\right)\cdot 37^{138} + \left(8 a^{2} + 8 a + 32\right)\cdot 37^{139} + \left(2 a^{2} + 27 a + 22\right)\cdot 37^{140} +O\left(37^{ 141 }\right)$ $r_{ 6 }$ $=$ $7 a^{2} + 17 a + 36 + \left(15 a^{2} + 23 a + 30\right)\cdot 37 + \left(2 a^{2} + 8 a + 10\right)\cdot 37^{2} + \left(22 a^{2} + 27 a + 21\right)\cdot 37^{3} + \left(19 a^{2} + a + 36\right)\cdot 37^{4} + \left(22 a^{2} + 16 a + 30\right)\cdot 37^{5} + \left(27 a^{2} + 28 a + 19\right)\cdot 37^{6} + \left(8 a^{2} + 28 a + 18\right)\cdot 37^{7} + \left(25 a^{2} + 15 a + 35\right)\cdot 37^{8} + \left(24 a^{2} + 14 a + 7\right)\cdot 37^{9} + \left(17 a^{2} + 35 a + 7\right)\cdot 37^{10} + \left(31 a^{2} + 29 a + 24\right)\cdot 37^{11} + \left(18 a^{2} + 21 a + 7\right)\cdot 37^{12} + \left(17 a^{2} + 23 a + 4\right)\cdot 37^{13} + \left(34 a^{2} + 13 a + 34\right)\cdot 37^{14} + \left(6 a^{2} + 13 a + 33\right)\cdot 37^{15} + \left(16 a^{2} + 22 a + 18\right)\cdot 37^{16} + \left(25 a^{2} + 24 a + 23\right)\cdot 37^{17} + \left(28 a^{2} + 25 a + 4\right)\cdot 37^{18} + \left(17 a^{2} + 20 a + 28\right)\cdot 37^{19} + \left(16 a^{2} + 15 a + 5\right)\cdot 37^{20} + \left(24 a^{2} + 28 a + 8\right)\cdot 37^{21} + \left(8 a^{2} + 34 a + 6\right)\cdot 37^{22} + \left(9 a^{2} + 23 a + 7\right)\cdot 37^{23} + \left(4 a^{2} + 27 a + 26\right)\cdot 37^{24} + \left(25 a^{2} + 19\right)\cdot 37^{25} + \left(34 a^{2} + a + 18\right)\cdot 37^{26} + \left(36 a^{2} + 2 a\right)\cdot 37^{27} + \left(18 a + 16\right)\cdot 37^{28} + \left(7 a^{2} + 35 a + 16\right)\cdot 37^{29} + \left(11 a^{2} + 28 a + 2\right)\cdot 37^{30} + \left(12 a^{2} + 24 a + 21\right)\cdot 37^{31} + \left(36 a^{2} + 27 a + 35\right)\cdot 37^{32} + \left(36 a^{2} + 19 a + 32\right)\cdot 37^{33} + \left(5 a^{2} + 36 a + 8\right)\cdot 37^{34} + \left(35 a^{2} + 23 a + 25\right)\cdot 37^{35} + \left(33 a^{2} + 21 a + 8\right)\cdot 37^{36} + \left(32 a^{2} + 9 a + 11\right)\cdot 37^{37} + \left(15 a^{2} + 4 a + 1\right)\cdot 37^{38} + \left(13 a^{2} + 21 a + 23\right)\cdot 37^{39} + \left(22 a^{2} + a + 28\right)\cdot 37^{40} + \left(25 a^{2} + 12 a + 11\right)\cdot 37^{41} + \left(9 a^{2} + 33 a + 33\right)\cdot 37^{42} + \left(35 a^{2} + 10 a + 17\right)\cdot 37^{43} + \left(22 a^{2} + 25 a + 9\right)\cdot 37^{44} + \left(31 a^{2} + 5 a + 4\right)\cdot 37^{45} + \left(5 a^{2} + 9 a + 21\right)\cdot 37^{46} + \left(20 a^{2} + 8 a + 10\right)\cdot 37^{47} + \left(13 a^{2} + 20 a + 26\right)\cdot 37^{48} + \left(8 a^{2} + 4 a + 2\right)\cdot 37^{49} + \left(30 a^{2} + 19 a + 26\right)\cdot 37^{50} + \left(16 a + 21\right)\cdot 37^{51} + \left(18 a^{2} + 2\right)\cdot 37^{52} + \left(30 a^{2} + 20 a + 11\right)\cdot 37^{53} + \left(14 a^{2} + 8 a + 1\right)\cdot 37^{54} + \left(29 a^{2} + 36 a + 3\right)\cdot 37^{55} + \left(14 a^{2} + 29 a + 3\right)\cdot 37^{56} + \left(22 a^{2} + 24 a + 21\right)\cdot 37^{57} + \left(31 a^{2} + 34 a + 24\right)\cdot 37^{58} + \left(13 a^{2} + 4 a\right)\cdot 37^{59} + \left(26 a^{2} + 30 a + 20\right)\cdot 37^{60} + \left(4 a^{2} + 29 a + 10\right)\cdot 37^{61} + 20 a\cdot 37^{62} + \left(23 a^{2} + 7 a + 36\right)\cdot 37^{63} + \left(10 a^{2} + 21 a + 20\right)\cdot 37^{64} + \left(23 a^{2} + 25 a + 8\right)\cdot 37^{65} + \left(13 a^{2} + 15 a + 10\right)\cdot 37^{66} + \left(34 a^{2} + 23 a + 17\right)\cdot 37^{67} + \left(6 a^{2} + 18 a + 23\right)\cdot 37^{68} + \left(18 a^{2} + 28 a + 6\right)\cdot 37^{69} + \left(15 a^{2} + 34 a + 3\right)\cdot 37^{70} + \left(25 a^{2} + 19 a + 28\right)\cdot 37^{71} + \left(32 a^{2} + 12 a + 27\right)\cdot 37^{72} + \left(13 a^{2} + 10 a + 19\right)\cdot 37^{73} + \left(15 a^{2} + 33 a + 21\right)\cdot 37^{74} + \left(25 a^{2} + 31 a + 27\right)\cdot 37^{75} + \left(15 a^{2} + 13 a + 15\right)\cdot 37^{76} + \left(7 a^{2} + 9\right)\cdot 37^{77} + \left(6 a^{2} + 12 a + 7\right)\cdot 37^{78} + \left(25 a^{2} + 21 a + 16\right)\cdot 37^{79} + \left(18 a^{2} + 3 a + 32\right)\cdot 37^{80} + \left(20 a^{2} + 6 a\right)\cdot 37^{81} + \left(a^{2} + 22 a + 27\right)\cdot 37^{82} + \left(30 a^{2} + 21 a + 18\right)\cdot 37^{83} + \left(4 a^{2} + 11 a + 2\right)\cdot 37^{84} + \left(30 a^{2} + 14 a + 29\right)\cdot 37^{85} + \left(25 a^{2} + 19 a + 11\right)\cdot 37^{86} + \left(15 a^{2} + 11 a + 34\right)\cdot 37^{87} + \left(13 a^{2} + 29 a + 1\right)\cdot 37^{88} + \left(27 a^{2} + 4 a + 30\right)\cdot 37^{89} + \left(21 a^{2} + 30 a + 5\right)\cdot 37^{90} + \left(10 a^{2} + 25 a + 13\right)\cdot 37^{91} + \left(6 a^{2} + 31 a + 29\right)\cdot 37^{92} + \left(8 a^{2} + 24 a + 13\right)\cdot 37^{93} + \left(19 a^{2} + 14 a + 26\right)\cdot 37^{94} + \left(31 a^{2} + 14 a + 21\right)\cdot 37^{95} + \left(12 a^{2} + 19 a + 2\right)\cdot 37^{96} + \left(13 a^{2} + 10 a + 31\right)\cdot 37^{97} + \left(7 a^{2} + 6 a + 34\right)\cdot 37^{98} + \left(32 a^{2} + 6 a + 35\right)\cdot 37^{99} + \left(20 a^{2} + 19 a + 20\right)\cdot 37^{100} + \left(21 a^{2} + 15 a + 16\right)\cdot 37^{101} + \left(23 a^{2} + 9 a + 7\right)\cdot 37^{102} + \left(3 a^{2} + 12 a\right)\cdot 37^{103} + \left(13 a^{2} + 13 a + 15\right)\cdot 37^{104} + \left(9 a^{2} + 6 a + 34\right)\cdot 37^{105} + \left(17 a^{2} + 34 a + 18\right)\cdot 37^{106} + \left(a^{2} + 33 a + 6\right)\cdot 37^{107} + \left(33 a^{2} + 19 a + 23\right)\cdot 37^{108} + \left(25 a^{2} + 14 a + 21\right)\cdot 37^{109} + \left(13 a^{2} + 19 a + 17\right)\cdot 37^{110} + \left(19 a^{2} + 23 a + 21\right)\cdot 37^{111} + \left(20 a^{2} + 20 a + 11\right)\cdot 37^{112} + \left(21 a^{2} + 3 a + 26\right)\cdot 37^{113} + \left(6 a^{2} + 6 a + 12\right)\cdot 37^{114} + \left(19 a^{2} + 34 a + 34\right)\cdot 37^{115} + \left(23 a + 30\right)\cdot 37^{116} + \left(3 a^{2} + 7 a + 5\right)\cdot 37^{117} + \left(6 a + 20\right)\cdot 37^{118} + \left(27 a^{2} + 20 a + 36\right)\cdot 37^{119} + \left(21 a^{2} + 29 a + 6\right)\cdot 37^{120} + \left(a^{2} + 18 a + 7\right)\cdot 37^{121} + \left(20 a^{2} + 24 a + 34\right)\cdot 37^{122} + \left(12 a^{2} + 12 a + 14\right)\cdot 37^{123} + \left(12 a^{2} + 32 a + 7\right)\cdot 37^{124} + \left(17 a^{2} + 4 a + 8\right)\cdot 37^{125} + \left(14 a^{2} + 12 a + 16\right)\cdot 37^{126} + \left(30 a^{2} + 35 a + 34\right)\cdot 37^{127} + \left(28 a^{2} + 23 a + 11\right)\cdot 37^{128} + \left(4 a^{2} + 28 a + 29\right)\cdot 37^{129} + \left(19 a^{2} + \frac{249}{8} a + 8\right)\cdot 37^{130} + \left(\frac{31}{2} a^{2} + 11 a + 15\right)\cdot 37^{131} + \left(3 a^{2} + 29 a + 12\right)\cdot 37^{132} + \left(18 a^{2} + 3 a + 28\right)\cdot 37^{133} + \left(16 a^{2} + 30 a + 10\right)\cdot 37^{134} + \left(12 a^{2} + 22 a + 5\right)\cdot 37^{135} + \left(14 a^{2} + 27 a + 13\right)\cdot 37^{136} + \left(4 a^{2} + 21 a\right)\cdot 37^{137} + \left(14 a^{2} + 18 a + 36\right)\cdot 37^{138} + \left(17 a^{2} + 8 a + 31\right)\cdot 37^{139} + \left(31 a^{2} + 6\right)\cdot 37^{140} +O\left(37^{ 141 }\right)$ $r_{ 7 }$ $=$ $15 a^{2} + 18 a + 32 + \left(19 a^{2} + 33 a + 31\right)\cdot 37 + \left(26 a^{2} + 11 a + 14\right)\cdot 37^{2} + \left(12 a^{2} + 36\right)\cdot 37^{3} + \left(35 a^{2} + 13 a + 3\right)\cdot 37^{4} + \left(35 a^{2} + 32 a + 22\right)\cdot 37^{5} + \left(11 a^{2} + 19 a + 20\right)\cdot 37^{6} + \left(10 a^{2} + 27 a + 13\right)\cdot 37^{7} + \left(14 a^{2} + 32 a + 8\right)\cdot 37^{8} + \left(25 a^{2} + 8 a + 36\right)\cdot 37^{9} + \left(15 a^{2} + 13 a\right)\cdot 37^{10} + \left(9 a^{2} + 26 a + 27\right)\cdot 37^{11} + \left(a^{2} + 10 a + 14\right)\cdot 37^{12} + \left(19 a^{2} + 30 a + 6\right)\cdot 37^{13} + \left(34 a^{2} + 8 a + 34\right)\cdot 37^{14} + \left(15 a^{2} + 14 a + 5\right)\cdot 37^{15} + \left(32 a^{2} + 10 a + 11\right)\cdot 37^{16} + \left(13 a^{2} + 17 a + 30\right)\cdot 37^{17} + \left(19 a^{2} + 14 a + 35\right)\cdot 37^{18} + \left(10 a^{2} + 28 a + 2\right)\cdot 37^{19} + \left(29 a^{2} + 26 a + 36\right)\cdot 37^{20} + \left(21 a^{2} + 13 a + 29\right)\cdot 37^{21} + \left(33 a^{2} + 10 a + 34\right)\cdot 37^{22} + \left(3 a^{2} + 28 a + 33\right)\cdot 37^{23} + \left(24 a^{2} + 10 a + 27\right)\cdot 37^{24} + \left(4 a^{2} + 34 a + 19\right)\cdot 37^{25} + \left(10 a^{2} + 31 a + 20\right)\cdot 37^{26} + \left(18 a^{2} + 2 a + 27\right)\cdot 37^{27} + \left(32 a^{2} + a + 26\right)\cdot 37^{28} + \left(4 a^{2} + 22 a + 3\right)\cdot 37^{29} + \left(18 a^{2} + 5 a + 21\right)\cdot 37^{30} + \left(21 a^{2} + 24 a + 29\right)\cdot 37^{31} + \left(10 a^{2} + 36\right)\cdot 37^{32} + \left(4 a^{2} + 16 a + 17\right)\cdot 37^{33} + \left(25 a^{2} + 12 a + 17\right)\cdot 37^{34} + \left(25 a^{2} + 20 a + 22\right)\cdot 37^{35} + \left(21 a^{2} + 16 a + 22\right)\cdot 37^{36} + \left(26 a^{2} + 22 a + 22\right)\cdot 37^{37} + \left(25 a^{2} + 10 a + 7\right)\cdot 37^{38} + \left(17 a^{2} + 20 a + 6\right)\cdot 37^{39} + \left(26 a^{2} + 7 a + 31\right)\cdot 37^{40} + \left(30 a^{2} + 8 a + 14\right)\cdot 37^{41} + \left(10 a^{2} + 11 a + 32\right)\cdot 37^{42} + \left(14 a^{2} + 31 a + 25\right)\cdot 37^{43} + \left(3 a^{2} + 33 a + 13\right)\cdot 37^{44} + \left(29 a^{2} + 35 a + 5\right)\cdot 37^{45} + \left(19 a^{2} + 24 a\right)\cdot 37^{46} + \left(19 a^{2} + 6 a + 27\right)\cdot 37^{47} + \left(32 a^{2} + 19 a + 33\right)\cdot 37^{48} + \left(29 a^{2} + 27 a + 29\right)\cdot 37^{49} + \left(6 a^{2} + 30 a + 24\right)\cdot 37^{50} + \left(28 a^{2} + 34 a + 1\right)\cdot 37^{51} + \left(6 a^{2} + 27 a + 13\right)\cdot 37^{52} + \left(12 a^{2} + 28 a + 6\right)\cdot 37^{53} + \left(31 a^{2} + 34 a + 35\right)\cdot 37^{54} + \left(4 a^{2} + 14 a + 20\right)\cdot 37^{55} + \left(28 a^{2} + a + 14\right)\cdot 37^{56} + \left(10 a^{2} + 18\right)\cdot 37^{57} + \left(13 a^{2} + 22 a + 22\right)\cdot 37^{58} + \left(23 a^{2} + 11 a + 35\right)\cdot 37^{59} + \left(11 a^{2} + 27 a + 14\right)\cdot 37^{60} + \left(7 a^{2} + 19 a + 23\right)\cdot 37^{61} + \left(10 a^{2} + 21 a + 35\right)\cdot 37^{62} + \left(6 a^{2} + 25 a + 6\right)\cdot 37^{63} + \left(20 a^{2} + 15 a + 27\right)\cdot 37^{64} + \left(5 a^{2} + 23 a + 9\right)\cdot 37^{65} + \left(9 a^{2} + 8 a + 33\right)\cdot 37^{66} + \left(8 a^{2} + 16 a + 36\right)\cdot 37^{67} + \left(16 a^{2} + 24 a + 3\right)\cdot 37^{68} + \left(11 a^{2} + 9 a + 16\right)\cdot 37^{69} + \left(33 a + 1\right)\cdot 37^{70} + \left(3 a^{2} + 30 a + 20\right)\cdot 37^{71} + \left(29 a^{2} + 18 a + 30\right)\cdot 37^{72} + \left(4 a^{2} + 28 a + 11\right)\cdot 37^{73} + \left(20 a^{2} + 21 a + 36\right)\cdot 37^{74} + \left(18 a^{2} + 5 a + 11\right)\cdot 37^{75} + \left(35 a^{2} + 33 a + 5\right)\cdot 37^{76} + \left(a^{2} + 15 a + 33\right)\cdot 37^{77} + \left(35 a^{2} + 10 a + 13\right)\cdot 37^{78} + \left(18 a^{2} + 33 a + 34\right)\cdot 37^{79} + \left(a^{2} + 5 a + 23\right)\cdot 37^{80} + \left(28 a^{2} + 26 a + 19\right)\cdot 37^{81} + \left(27 a^{2} + 31 a + 26\right)\cdot 37^{82} + \left(26 a^{2} + 30 a + 28\right)\cdot 37^{83} + \left(a^{2} + 4 a + 8\right)\cdot 37^{84} + \left(8 a + 34\right)\cdot 37^{85} + \left(14 a^{2} + 22 a + 31\right)\cdot 37^{86} + \left(24 a^{2} + 21 a + 33\right)\cdot 37^{87} + \left(2 a^{2} + 6 a + 20\right)\cdot 37^{88} + \left(31 a^{2} + 20 a + 7\right)\cdot 37^{89} + \left(5 a^{2} + a + 2\right)\cdot 37^{90} + \left(4 a^{2} + 32 a + 26\right)\cdot 37^{91} + \left(36 a^{2} + 27 a + 1\right)\cdot 37^{92} + \left(10 a^{2} + 18 a + 36\right)\cdot 37^{93} + \left(a^{2} + 29\right)\cdot 37^{94} + \left(18 a^{2} + 25 a + 8\right)\cdot 37^{95} + \left(12 a^{2} + 34 a + 17\right)\cdot 37^{96} + \left(32 a^{2} + 21 a + 16\right)\cdot 37^{97} + \left(10 a^{2} + 16 a + 25\right)\cdot 37^{98} + \left(30 a^{2} + 4 a + 28\right)\cdot 37^{99} + \left(21 a^{2} + 13 a + 29\right)\cdot 37^{100} + \left(33 a^{2} + 6 a + 34\right)\cdot 37^{101} + \left(17 a^{2} + 5 a + 19\right)\cdot 37^{102} + \left(5 a^{2} + 33 a + 26\right)\cdot 37^{103} + \left(22 a^{2} + 19 a + 33\right)\cdot 37^{104} + \left(5 a^{2} + 31 a + 29\right)\cdot 37^{105} + \left(25 a^{2} + 20 a + 22\right)\cdot 37^{106} + \left(36 a^{2} + 22 a + 12\right)\cdot 37^{107} + \left(29 a^{2} + 27 a + 7\right)\cdot 37^{108} + \left(29 a^{2} + 23 a + 20\right)\cdot 37^{109} + \left(32 a^{2} + 19 a + 31\right)\cdot 37^{110} + \left(9 a^{2} + 20 a + 21\right)\cdot 37^{111} + \left(7 a^{2} + 30 a + 12\right)\cdot 37^{112} + \left(25 a^{2} + 11 a + 9\right)\cdot 37^{113} + \left(7 a^{2} + 35\right)\cdot 37^{114} + \left(9 a^{2} + 11 a + 30\right)\cdot 37^{115} + \left(10 a^{2} + 22 a + 7\right)\cdot 37^{116} + \left(7 a^{2} + a + 11\right)\cdot 37^{117} + \left(25 a^{2} + 7 a + 26\right)\cdot 37^{118} + \left(5 a^{2} + 36 a + 11\right)\cdot 37^{119} + \left(13 a^{2} + 26 a + 26\right)\cdot 37^{120} + \left(29 a^{2} + 8\right)\cdot 37^{121} + \left(28 a^{2} + 36 a + 1\right)\cdot 37^{122} + \left(21 a^{2} + 5 a + 20\right)\cdot 37^{123} + \left(6 a^{2} + 34 a + 17\right)\cdot 37^{124} + \left(24 a^{2} + 32 a + 19\right)\cdot 37^{125} + \left(6 a^{2} + 10 a + 4\right)\cdot 37^{126} + \left(25 a^{2} + 24 a + 31\right)\cdot 37^{127} + \left(32 a^{2} + 18 a + 17\right)\cdot 37^{128} + \left(16 a^{2} + 18 a + 10\right)\cdot 37^{129} + \left(16 a^{2} + 3\right)\cdot 37^{130} + \left(3 a^{2} + 23 a + 36\right)\cdot 37^{131} + \left(35 a^{2} + 12 a + 10\right)\cdot 37^{132} + \left(31 a^{2} + 28 a + 29\right)\cdot 37^{133} + \left(19 a^{2} + 18 a + 10\right)\cdot 37^{134} + \left(17 a^{2} + 21 a + 15\right)\cdot 37^{135} + \left(13 a + 21\right)\cdot 37^{136} + \left(16 a^{2} + 2 a + 13\right)\cdot 37^{137} + \left(30 a^{2} + 27 a + 26\right)\cdot 37^{138} + \left(11 a^{2} + 9 a + 9\right)\cdot 37^{139} + \left(6 a^{2} + 27 a + 2\right)\cdot 37^{140} +O\left(37^{ 141 }\right)$ $r_{ 8 }$ $=$ $13 a^{2} + 19 a + 23 + \left(25 a^{2} + 24 a + 7\right)\cdot 37 + \left(32 a^{2} + 17 a + 23\right)\cdot 37^{2} + \left(8 a^{2} + 29 a + 8\right)\cdot 37^{3} + \left(23 a^{2} + 10 a + 7\right)\cdot 37^{4} + \left(25 a + 33\right)\cdot 37^{5} + \left(27 a^{2} + 16 a + 12\right)\cdot 37^{6} + \left(6 a^{2} + 24 a\right)\cdot 37^{7} + \left(22 a^{2} + 28 a + 6\right)\cdot 37^{8} + \left(2 a^{2} + 8 a + 36\right)\cdot 37^{9} + \left(27 a^{2} + 21 a + 3\right)\cdot 37^{10} + \left(18 a^{2} + 5 a + 21\right)\cdot 37^{11} + \left(11 a^{2} + 24 a + 7\right)\cdot 37^{12} + \left(31 a^{2} + 36 a + 35\right)\cdot 37^{13} + \left(16 a^{2} + 20 a + 33\right)\cdot 37^{14} + \left(22 a^{2} + 11 a + 10\right)\cdot 37^{15} + \left(31 a^{2} + 18 a + 31\right)\cdot 37^{16} + \left(31 a^{2} + 28 a + 33\right)\cdot 37^{17} + \left(12 a^{2} + 25 a + 25\right)\cdot 37^{18} + \left(19 a^{2} + 33 a + 2\right)\cdot 37^{19} + \left(19 a^{2} + 29 a + 10\right)\cdot 37^{20} + \left(13 a^{2} + 7 a + 36\right)\cdot 37^{21} + \left(23 a^{2} + 17 a + 9\right)\cdot 37^{22} + \left(13 a^{2} + 11 a + 36\right)\cdot 37^{23} + \left(35 a^{2} + 24 a + 27\right)\cdot 37^{24} + \left(36 a^{2} + 5 a + 11\right)\cdot 37^{25} + \left(4 a^{2} + 16 a + 34\right)\cdot 37^{26} + \left(26 a^{2} + 8 a + 31\right)\cdot 37^{27} + \left(22 a^{2} + 25 a + 21\right)\cdot 37^{28} + \left(12 a^{2} + a + 31\right)\cdot 37^{29} + \left(33 a^{2} + 23 a + 3\right)\cdot 37^{30} + \left(27 a^{2} + 21 a + 16\right)\cdot 37^{31} + \left(8 a^{2} + 28 a + 27\right)\cdot 37^{32} + \left(23 a^{2} + 5 a + 36\right)\cdot 37^{33} + \left(17 a^{2} + 24 a + 14\right)\cdot 37^{34} + \left(16 a^{2} + a + 20\right)\cdot 37^{35} + \left(12 a^{2} + 22 a + 21\right)\cdot 37^{36} + \left(4 a^{2} + 6 a + 25\right)\cdot 37^{37} + \left(10 a^{2} + 7 a + 29\right)\cdot 37^{38} + \left(a^{2} + 23 a + 17\right)\cdot 37^{39} + \left(9 a^{2} + 19 a + 22\right)\cdot 37^{40} + \left(9 a^{2} + 17\right)\cdot 37^{41} + \left(2 a^{2} + 22 a + 36\right)\cdot 37^{42} + \left(6 a^{2} + 33 a + 23\right)\cdot 37^{43} + \left(33 a^{2} + 26 a + 10\right)\cdot 37^{44} + \left(7 a^{2} + 6 a + 34\right)\cdot 37^{45} + \left(21 a^{2} + 32 a + 33\right)\cdot 37^{46} + \left(8 a^{2} + a + 22\right)\cdot 37^{47} + \left(24 a^{2} + 29 a + 13\right)\cdot 37^{48} + \left(10 a^{2} + 21 a + 36\right)\cdot 37^{49} + \left(8 a^{2} + 13 a + 12\right)\cdot 37^{50} + \left(11 a^{2} + 15 a + 13\right)\cdot 37^{51} + \left(2 a^{2} + 23 a + 20\right)\cdot 37^{52} + \left(24 a^{2} + 34 a + 15\right)\cdot 37^{53} + \left(19 a^{2} + 27 a + 14\right)\cdot 37^{54} + \left(7 a^{2} + 34 a + 35\right)\cdot 37^{55} + \left(a^{2} + 8 a + 6\right)\cdot 37^{56} + \left(3 a^{2} + 32 a + 15\right)\cdot 37^{57} + \left(22 a^{2} + 25 a + 30\right)\cdot 37^{58} + \left(3 a^{2} + 14 a + 9\right)\cdot 37^{59} + \left(10 a^{2} + 34 a + 3\right)\cdot 37^{60} + \left(4 a^{2} + 3 a + 19\right)\cdot 37^{61} + \left(16 a^{2} + 20 a + 22\right)\cdot 37^{62} + \left(20 a^{2} + 16 a + 19\right)\cdot 37^{63} + \left(28 a^{2} + 13 a + 36\right)\cdot 37^{64} + \left(2 a^{2} + 32 a + 1\right)\cdot 37^{65} + \left(15 a^{2} + 31\right)\cdot 37^{66} + \left(32 a + 21\right)\cdot 37^{67} + \left(35 a^{2} + 5 a + 11\right)\cdot 37^{68} + \left(28 a^{2} + 5 a + 21\right)\cdot 37^{69} + \left(31 a^{2} + 27 a + 23\right)\cdot 37^{70} + \left(13 a^{2} + 7 a + 28\right)\cdot 37^{71} + \left(25 a^{2} + 12 a + 33\right)\cdot 37^{72} + \left(11 a^{2} + 31 a + 21\right)\cdot 37^{73} + \left(5 a^{2} + 32 a + 33\right)\cdot 37^{74} + \left(23 a^{2} + 15 a + 34\right)\cdot 37^{75} + \left(23 a^{2} + 26 a + 22\right)\cdot 37^{76} + \left(12 a^{2} + 24 a + 21\right)\cdot 37^{77} + \left(30 a^{2} + 19 a + 18\right)\cdot 37^{78} + \left(27 a^{2} + 5 a + 4\right)\cdot 37^{79} + \left(30 a^{2} + 14 a + 29\right)\cdot 37^{80} + \left(27 a^{2} + 33 a + 18\right)\cdot 37^{81} + \left(13 a^{2} + 6 a\right)\cdot 37^{82} + \left(30 a^{2} + 21 a + 32\right)\cdot 37^{83} + \left(15 a^{2} + 12 a + 23\right)\cdot 37^{84} + \left(28 a^{2} + 19 a + 11\right)\cdot 37^{85} + \left(22 a^{2} + 28 a + 16\right)\cdot 37^{86} + \left(32 a^{2} + 35 a + 3\right)\cdot 37^{87} + \left(28 a^{2} + 13 a + 1\right)\cdot 37^{88} + \left(14 a^{2} + 11 a + 18\right)\cdot 37^{89} + \left(19 a^{2} + 32 a + 8\right)\cdot 37^{90} + \left(7 a + 24\right)\cdot 37^{91} + \left(35 a^{2} + 12 a + 17\right)\cdot 37^{92} + \left(35 a^{2} + 14 a + 27\right)\cdot 37^{93} + \left(2 a^{2} + 3 a + 35\right)\cdot 37^{94} + \left(24 a^{2} + 5 a + 4\right)\cdot 37^{95} + \left(a^{2} + 24 a + 27\right)\cdot 37^{96} + \left(16 a^{2} + 11 a + 2\right)\cdot 37^{97} + \left(6 a^{2} + 10 a + 33\right)\cdot 37^{98} + \left(13 a^{2} + 12 a + 11\right)\cdot 37^{99} + \left(23 a^{2} + 16 a + 23\right)\cdot 37^{100} + \left(12 a^{2} + 16 a + 33\right)\cdot 37^{101} + \left(13 a^{2} + 7 a + 33\right)\cdot 37^{102} + \left(4 a^{2} + 23 a + 17\right)\cdot 37^{103} + \left(31 a^{2} + 26 a\right)\cdot 37^{104} + \left(28 a^{2} + 2 a + 13\right)\cdot 37^{105} + \left(21 a^{2} + 32 a + 11\right)\cdot 37^{106} + \left(13 a^{2} + 5 a + 2\right)\cdot 37^{107} + \left(14 a^{2} + 27 a\right)\cdot 37^{108} + \left(24 a^{2} + 3 a + 27\right)\cdot 37^{109} + \left(29 a^{2} + a + 16\right)\cdot 37^{110} + \left(a^{2} + 29 a + 3\right)\cdot 37^{111} + \left(28 a^{2} + 36 a + 7\right)\cdot 37^{112} + \left(4 a^{2} + 18 a + 34\right)\cdot 37^{113} + \left(27 a^{2} + a + 36\right)\cdot 37^{114} + \left(31 a^{2} + 32 a + 35\right)\cdot 37^{115} + \left(15 a^{2} + 21 a + 28\right)\cdot 37^{116} + \left(a^{2} + 29 a + 13\right)\cdot 37^{117} + \left(3 a^{2} + 12 a + 29\right)\cdot 37^{118} + \left(31 a^{2} + 36 a + 22\right)\cdot 37^{119} + \left(17 a^{2} + 24 a + 13\right)\cdot 37^{120} + \left(13 a^{2} + 6 a + 23\right)\cdot 37^{121} + \left(4 a^{2} + 20 a + 15\right)\cdot 37^{122} + \left(29 a^{2} + 23 a + 14\right)\cdot 37^{123} + \left(16 a^{2} + 19 a + 23\right)\cdot 37^{124} + \left(36 a^{2} + 9 a + 36\right)\cdot 37^{125} + \left(14 a^{2} + 23 a + 19\right)\cdot 37^{126} + \left(23 a^{2} + 3 a + 7\right)\cdot 37^{127} + \left(2 a^{2} + 35 a + 29\right)\cdot 37^{128} + \left(14 a^{2} + 16 a + 25\right)\cdot 37^{129} + \left(2 a^{2} + 34 a + 26\right)\cdot 37^{130} + \left(35 a^{2} + 35 a + 23\right)\cdot 37^{131} + \left(33 a^{2} + 5 a + 23\right)\cdot 37^{132} + \left(12 a^{2} + 4 a + 7\right)\cdot 37^{133} + \left(16 a^{2} + 3 a + 10\right)\cdot 37^{134} + \left(32 a^{2} + 5 a + 11\right)\cdot 37^{135} + \left(18 a^{2} + 25 a + 31\right)\cdot 37^{136} + \left(11 a^{2} + 35 a + 28\right)\cdot 37^{137} + \left(13 a^{2} + 20 a + 32\right)\cdot 37^{138} + \left(6 a^{2} + 17 a + 24\right)\cdot 37^{139} + \left(30 a^{2} + 9 a + 1\right)\cdot 37^{140} +O\left(37^{ 141 }\right)$ $r_{ 9 }$ $=$ $32 a^{2} + 13 a + 1 + \left(33 a^{2} + 29 a + 26\right)\cdot 37 + \left(35 a^{2} + 9 a + 3\right)\cdot 37^{2} + \left(32 a^{2} + 32 a + 35\right)\cdot 37^{3} + \left(a^{2} + 5 a + 8\right)\cdot 37^{4} + \left(30 a^{2} + 27\right)\cdot 37^{5} + \left(10 a^{2} + 16 a + 21\right)\cdot 37^{6} + \left(24 a^{2} + 14 a + 6\right)\cdot 37^{7} + \left(24 a^{2} + 32 a + 27\right)\cdot 37^{8} + \left(8 a^{2} + 18 a + 10\right)\cdot 37^{9} + \left(19 a^{2} + 2 a + 11\right)\cdot 37^{10} + \left(8 a^{2} + 9 a + 32\right)\cdot 37^{11} + \left(6 a^{2} + 7 a + 28\right)\cdot 37^{12} + \left(22 a^{2} + 8 a + 19\right)\cdot 37^{13} + \left(22 a^{2} + 31 a + 31\right)\cdot 37^{14} + \left(21 a^{2} + 21 a + 6\right)\cdot 37^{15} + \left(31 a^{2} + 5 a + 36\right)\cdot 37^{16} + \left(2 a^{2} + 35 a + 15\right)\cdot 37^{17} + \left(8 a^{2} + 24 a + 12\right)\cdot 37^{18} + \left(34 a^{2} + 32 a + 35\right)\cdot 37^{19} + \left(34 a^{2} + 10 a + 22\right)\cdot 37^{20} + \left(8 a^{2} + 32 a + 16\right)\cdot 37^{21} + \left(24 a + 14\right)\cdot 37^{22} + \left(31 a^{2} + 12 a + 14\right)\cdot 37^{23} + \left(8 a^{2} + 9 a + 13\right)\cdot 37^{24} + \left(17 a^{2} + 16 a + 35\right)\cdot 37^{25} + \left(34 a^{2} + 4 a + 19\right)\cdot 37^{26} + \left(23 a^{2} + 23\right)\cdot 37^{27} + \left(12 a^{2} + 25 a + 32\right)\cdot 37^{28} + \left(28 a^{2} + 34 a + 7\right)\cdot 37^{29} + \left(28 a^{2} + 15 a + 16\right)\cdot 37^{30} + \left(25 a^{2} + 31 a + 6\right)\cdot 37^{31} + \left(7 a^{2} + 18 a + 27\right)\cdot 37^{32} + \left(6 a^{2} + 33 a + 17\right)\cdot 37^{33} + \left(17 a^{2} + 6 a + 35\right)\cdot 37^{34} + \left(34 a^{2} + 32 a + 35\right)\cdot 37^{35} + \left(35 a^{2} + 23 a + 5\right)\cdot 37^{36} + \left(21 a^{2} + 7 a + 29\right)\cdot 37^{37} + \left(24 a + 14\right)\cdot 37^{38} + \left(6 a^{2} + 27 a + 31\right)\cdot 37^{39} + \left(6 a^{2} + 19 a + 12\right)\cdot 37^{40} + \left(36 a^{2} + 8 a + 3\right)\cdot 37^{41} + \left(23 a^{2} + 28 a + 36\right)\cdot 37^{42} + \left(23 a^{2} + 13 a + 12\right)\cdot 37^{43} + \left(21 a^{2} + 13 a + 18\right)\cdot 37^{44} + \left(10 a^{2} + 28 a + 36\right)\cdot 37^{45} + \left(6 a^{2} + 24 a + 6\right)\cdot 37^{46} + \left(8 a^{2} + 29 a + 1\right)\cdot 37^{47} + \left(31 a^{2} + 12 a + 32\right)\cdot 37^{48} + \left(27 a^{2} + 10 a + 20\right)\cdot 37^{49} + \left(35 a^{2} + 34 a + 36\right)\cdot 37^{50} + \left(22 a^{2} + 13 a + 17\right)\cdot 37^{51} + \left(2 a^{2} + 10 a + 17\right)\cdot 37^{52} + \left(a^{2} + 22 a + 10\right)\cdot 37^{53} + \left(32 a^{2} + 33 a + 2\right)\cdot 37^{54} + \left(8 a^{2} + 31 a + 27\right)\cdot 37^{55} + \left(18 a^{2} + 35 a + 22\right)\cdot 37^{56} + \left(8 a^{2} + 26 a + 33\right)\cdot 37^{57} + \left(17 a^{2} + 6 a + 14\right)\cdot 37^{58} + \left(29 a^{2} + 34 a + 10\right)\cdot 37^{59} + \left(14 a^{2} + 22 a + 26\right)\cdot 37^{60} + \left(10 a^{2} + 6 a + 30\right)\cdot 37^{61} + \left(9 a^{2} + 21 a + 5\right)\cdot 37^{62} + \left(30 a^{2} + 36 a + 21\right)\cdot 37^{63} + \left(15 a^{2} + 14\right)\cdot 37^{64} + \left(19 a^{2} + 18 a + 13\right)\cdot 37^{65} + \left(25 a^{2} + 20 a + 36\right)\cdot 37^{66} + \left(10 a^{2} + 29 a + 18\right)\cdot 37^{67} + \left(16 a^{2} + 24 a + 9\right)\cdot 37^{68} + \left(24 a^{2} + 25 a + 2\right)\cdot 37^{69} + \left(29 a^{2} + a + 31\right)\cdot 37^{70} + \left(27 a^{2} + 5 a + 26\right)\cdot 37^{71} + \left(15 a^{2} + 24 a + 23\right)\cdot 37^{72} + \left(10 a^{2} + 14 a + 28\right)\cdot 37^{73} + \left(12 a^{2} + 22 a + 26\right)\cdot 37^{74} + \left(25 a^{2} + 25 a + 12\right)\cdot 37^{75} + \left(28 a^{2} + 11 a + 6\right)\cdot 37^{76} + \left(23 a^{2} + 22 a + 2\right)\cdot 37^{77} + \left(27 a^{2} + 34 a + 21\right)\cdot 37^{78} + \left(28 a^{2} + 8 a + 32\right)\cdot 37^{79} + \left(31 a^{2} + 9 a + 26\right)\cdot 37^{80} + \left(25 a^{2} + 14 a + 21\right)\cdot 37^{81} + \left(4 a^{2} + 28 a + 14\right)\cdot 37^{82} + \left(12 a^{2} + 24 a + 19\right)\cdot 37^{83} + \left(18 a^{2} + 22 a + 27\right)\cdot 37^{84} + \left(22 a^{2} + 30 a + 14\right)\cdot 37^{85} + \left(a^{2} + 35 a + 4\right)\cdot 37^{86} + \left(2 a^{2} + 22 a + 13\right)\cdot 37^{87} + \left(32 a^{2} + 6 a + 24\right)\cdot 37^{88} + \left(32 a^{2} + 6 a + 5\right)\cdot 37^{89} + \left(29 a^{2} + 16 a + 12\right)\cdot 37^{90} + \left(a^{2} + 29 a + 33\right)\cdot 37^{91} + \left(21 a^{2} + 13 a + 1\right)\cdot 37^{92} + \left(8 a^{2} + 10 a + 32\right)\cdot 37^{93} + \left(5 a^{2} + 20 a + 4\right)\cdot 37^{94} + \left(10 a^{2} + 31 a + 5\right)\cdot 37^{95} + \left(13 a^{2} + 10 a + 17\right)\cdot 37^{96} + \left(10 a^{2} + 14 a + 12\right)\cdot 37^{97} + \left(35 a^{2} + 9 a + 14\right)\cdot 37^{98} + \left(16 a^{2} + 25 a + 21\right)\cdot 37^{99} + \left(36 a^{2} + 4 a + 25\right)\cdot 37^{100} + \left(32 a^{2} + 28 a + 24\right)\cdot 37^{101} + \left(4 a^{2} + 7 a + 19\right)\cdot 37^{102} + \left(35 a^{2} + 22 a + 12\right)\cdot 37^{103} + \left(10 a^{2} + 23 a + 9\right)\cdot 37^{104} + \left(23 a^{2} + 8 a + 22\right)\cdot 37^{105} + \left(36 a^{2} + 14 a + 21\right)\cdot 37^{106} + \left(13 a^{2} + 15 a + 23\right)\cdot 37^{107} + \left(14 a^{2} + 12\right)\cdot 37^{108} + \left(17 a^{2} + 29 a + 10\right)\cdot 37^{109} + \left(30 a^{2} + 5 a + 13\right)\cdot 37^{110} + \left(23 a^{2} + 4 a + 22\right)\cdot 37^{111} + \left(31 a^{2} + 12 a + 10\right)\cdot 37^{112} + \left(9 a^{2} + 4 a + 32\right)\cdot 37^{113} + \left(3 a^{2} + 18 a + 2\right)\cdot 37^{114} + \left(27 a^{2} + 17 a + 20\right)\cdot 37^{115} + \left(5 a^{2} + 29 a + 33\right)\cdot 37^{116} + \left(27 a^{2} + 34 a + 31\right)\cdot 37^{117} + \left(29 a^{2} + 22 a + 12\right)\cdot 37^{118} + \left(23 a^{2} + 31 a + 13\right)\cdot 37^{119} + \left(9 a^{2} + 24 a + 35\right)\cdot 37^{120} + \left(22 a^{2} + 20 a\right)\cdot 37^{121} + \left(35 a^{2} + 36 a + 3\right)\cdot 37^{122} + \left(22 a^{2} + 19 a + 19\right)\cdot 37^{123} + \left(2 a^{2} + 22 a + 27\right)\cdot 37^{124} + \left(29 a^{2} + 8 a + 15\right)\cdot 37^{125} + \left(36 a^{2} + 3 a + 10\right)\cdot 37^{126} + \left(18 a^{2} + 24 a + 8\right)\cdot 37^{127} + \left(9 a^{2} + 26 a + 6\right)\cdot 37^{128} + \left(10 a^{2} + 12 a + 19\right)\cdot 37^{129} + \left(27 a^{2} + 36 a + 34\right)\cdot 37^{130} + \left(31 a^{2} + 5 a + 10\right)\cdot 37^{131} + \left(4 a^{2} + 7 a + 2\right)\cdot 37^{132} + \left(36 a^{2} + 11 a + 28\right)\cdot 37^{133} + \left(23 a^{2} + 3 a + 34\right)\cdot 37^{134} + \left(21 a^{2} + 5 a\right)\cdot 37^{135} + \left(9 a^{2} + 33 a + 26\right)\cdot 37^{136} + \left(20 a^{2} + 10 a\right)\cdot 37^{137} + \left(11 a^{2} + 11 a + 14\right)\cdot 37^{138} + \left(22 a^{2} + 11 a + 16\right)\cdot 37^{139} + \left(4 a^{2} + 12\right)\cdot 37^{140} +O\left(37^{ 141 }\right)$

### Generators of the action on the roots $r_1, \ldots, r_{ 9 }$

 Cycle notation $(1,4,7)$ $(1,2)(3,4)(6,7)$ $(1,4)$ $(5,8,9)$ $(2,3,6)$ $(1,2,5)(3,8,4)(6,9,7)$

### Character values on conjugacy classes

 Size Order Action on $r_1, \ldots, r_{ 9 }$ Character value $1$ $1$ $()$ $8$ $9$ $2$ $(1,4)$ $0$ $18$ $2$ $(1,2)(3,4)(6,7)$ $4$ $27$ $2$ $(1,4)(2,3)(5,8)$ $0$ $27$ $2$ $(1,4)(2,3)$ $0$ $54$ $2$ $(1,4)(2,5)(3,8)(6,9)$ $0$ $6$ $3$ $(5,8,9)$ $-4$ $8$ $3$ $(1,4,7)(2,3,6)(5,8,9)$ $-1$ $12$ $3$ $(1,4,7)(5,8,9)$ $2$ $72$ $3$ $(1,2,5)(3,8,4)(6,9,7)$ $2$ $54$ $4$ $(1,3,4,2)(6,7)$ $0$ $162$ $4$ $(1,8,4,5)(3,6)(7,9)$ $0$ $36$ $6$ $(1,2)(3,4)(5,8,9)(6,7)$ $-2$ $36$ $6$ $(1,5,4,8,7,9)$ $-2$ $36$ $6$ $(1,4)(5,8,9)$ $0$ $36$ $6$ $(1,4)(2,3,6)(5,8,9)$ $0$ $54$ $6$ $(1,4)(2,3)(5,9,8)$ $0$ $72$ $6$ $(1,2,4,3,7,6)(5,8,9)$ $1$ $108$ $6$ $(1,4)(2,5,3,8,6,9)$ $0$ $216$ $6$ $(1,3,8,4,2,5)(6,9,7)$ $0$ $144$ $9$ $(1,2,5,4,3,8,7,6,9)$ $-1$ $108$ $12$ $(1,3,4,2)(5,8,9)(6,7)$ $0$
The blue line marks the conjugacy class containing complex conjugation.