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Galois conjugate representations are grouped into single lines.
Label Dimension Conductor Defining polynomial of Artin field $G$ Ind $\chi(c)$
12.144...376.18t218.a.a $12$ $ 2^{10} \cdot 269^{5}$ x9 - 4x7 - 2x6 + 2x5 - 24x4 - 8x3 + 80x2 + 68x + 4 $(((C_3 \times (C_3^2 : C_2)) : C_2) : C_3) : C_2$ $1$ $0$
12.731...449.18t218.a.a $12$ $ 1489^{5}$ x9 - 2x8 - x7 + 11x6 - 25x5 - 33x4 + 35x3 + 18x2 + 14x + 29 $(((C_3 \times (C_3^2 : C_2)) : C_2) : C_3) : C_2$ $1$ $0$
12.912...776.18t218.a.a $12$ $ 2^{10} \cdot 389^{5}$ x9 - 3x8 - 2x7 + 12x6 - 12x5 - 6x4 + 16x3 - 4x2 - 5x + 1 $(((C_3 \times (C_3^2 : C_2)) : C_2) : C_3) : C_2$ $1$ $0$
12.127...016.18t206.a.a $12$ $ 2^{6} \cdot 7^{10} \cdot 29^{4}$ x9 - 2x8 + x7 - 7x6 + 7x5 + 14x3 - x2 - 5x - 1 $S_3 \wr C_3 $ $1$ $0$
12.198...088.18t315.a.a $12$ $ 2^{10} \cdot 23^{4} \cdot 37^{5}$ x9 - 3x8 + 2x7 - 2x6 + 6x5 - 2x4 + 2x3 - 6x2 - 3x + 1 $S_3\wr S_3$ $1$ $0$
12.258...624.18t315.a.a $12$ $ 2^{10} \cdot 7^{4} \cdot 101^{5}$ x9 - x8 - 4x7 + 2x6 + 2x5 + 2x4 - 18x3 + 28x2 - 27x + 9 $S_3\wr S_3$ $1$ $0$
12.369...344.18t315.a.a $12$ $ 2^{6} \cdot 31^{5} \cdot 67^{4}$ x9 - 2x8 + 3x7 - 3x6 + x5 + 4x4 - 8x3 + 9x2 - 5x + 1 $S_3\wr S_3$ $1$ $2$
12.381...416.18t315.a.a $12$ $ 2^{6} \cdot 3^{6} \cdot 13^{4} \cdot 31^{5}$ x9 - x8 + 3x7 + 2x6 + 8x5 - 3x4 + 15x3 + 13x2 - 1 $S_3\wr S_3$ $1$ $2$
12.415...448.18t315.a.a $12$ $ 2^{10} \cdot 3^{15} \cdot 41^{4}$ x9 + 6x5 - 6x2 + 2 $S_3\wr S_3$ $1$ $2$
12.428...752.18t315.a.a $12$ $ 2^{6} \cdot 23^{5} \cdot 101^{4}$ x9 - 4x7 + 4x5 - 12x4 - 12x3 + 8x2 - 8 $S_3\wr S_3$ $1$ $2$
12.492...099.18t218.a.a $12$ $ 7^{6} \cdot 211^{5}$ x9 - 4x8 + 7x7 - 9x6 + 8x5 - 21x4 + 14x3 - 15x2 + 14x - 4 $(((C_3 \times (C_3^2 : C_2)) : C_2) : C_3) : C_2$ $1$ $2$
12.498...241.18t315.a.a $12$ $ 3^{5} \cdot 11^{4} \cdot 107^{5}$ x9 - 3x8 - 2x7 + 9x6 + 2x5 - 8x4 - x3 - 2x2 + 4x - 1 $S_3\wr S_3$ $1$ $0$
12.539...152.18t315.a.a $12$ $ 2^{6} \cdot 23^{5} \cdot 107^{4}$ x9 - 4x8 + 9x7 - 15x6 + 17x5 - 14x4 + 8x3 - x2 - x + 1 $S_3\wr S_3$ $1$ $2$
12.567...443.18t218.a.a $12$ $ 2243^{5}$ x9 - 2x8 + 6x7 - 18x6 + 41x5 - 51x4 + 106x3 - 116x2 + 72x + 16 $(((C_3 \times (C_3^2 : C_2)) : C_2) : C_3) : C_2$ $1$ $2$
12.632...019.18t315.a.a $12$ $ 59^{5} \cdot 97^{4}$ x9 + x7 - x6 + x5 + x4 + 2x3 + x2 - x - 1 $S_3\wr S_3$ $1$ $2$
12.655...328.18t315.a.a $12$ $ 2^{10} \cdot 31^{4} \cdot 37^{5}$ x9 - 3x8 + 4x7 - 2x6 + 2x5 - 2x4 - 2x3 + 8x2 - 3x - 1 $S_3\wr S_3$ $1$ $0$
12.886...081.18t206.a.a $12$ $ 3^{20} \cdot 71^{4}$ x9 - 3x8 + 6x7 - 9x6 + 6x5 - 3x4 - 3x3 + 6x2 - 3x - 1 $S_3 \wr C_3 $ $1$ $0$
12.118...757.18t218.a.a $12$ $ 7^{10} \cdot 53^{5}$ x9 - 7x7 - 7x6 - 7x5 + 84x4 + 35x3 - 280x2 + 28x + 280 $(((C_3 \times (C_3^2 : C_2)) : C_2) : C_3) : C_2$ $1$ $0$
12.118...000.24t2821.a.a $12$ $ 2^{16} \cdot 5^{6} \cdot 41^{5}$ x8 - 2x7 + 6x6 - 2x5 + 26x4 - 24x3 - 24x2 + 16x + 4 $S_4\wr C_2$ $1$ $0$
12.123...099.18t218.a.a $12$ $ 3^{15} \cdot 97^{5}$ x9 - 24x6 + 48x5 - 135x4 + 249x3 - 42x2 + 108x - 161 $(((C_3 \times (C_3^2 : C_2)) : C_2) : C_3) : C_2$ $1$ $2$
12.137...016.18t315.a.a $12$ $ 2^{16} \cdot 3^{4} \cdot 11^{10}$ x9 - x8 - 2x7 + 5x6 - 10x5 + 6x4 + 24x3 - 20x2 - 8x + 24 $S_3\wr S_3$ $1$ $2$
12.139...000.18t315.a.a $12$ $ 2^{18} \cdot 3^{4} \cdot 5^{8} \cdot 7^{5}$ x9 - 2x8 - x6 + 3x5 - x4 + 3x3 - 4x2 + 3x - 3 $S_3\wr S_3$ $1$ $2$
12.161...824.18t218.a.a $12$ $ 2^{10} \cdot 691^{5}$ x9 - 3x8 + 12x7 - 2x5 + 106x4 - 76x3 + 160x2 + 33x + 9 $(((C_3 \times (C_3^2 : C_2)) : C_2) : C_3) : C_2$ $1$ $2$
12.162...607.18t218.a.a $12$ $ 2767^{5}$ x9 - 4x8 + 6x7 - 31x6 + 14x5 + 156x4 + 117x3 + 14x2 + 9x - 1 $(((C_3 \times (C_3^2 : C_2)) : C_2) : C_3) : C_2$ $1$ $2$
12.164...000.18t206.a.a $12$ $ 2^{6} \cdot 5^{6} \cdot 7^{8} \cdot 13^{4}$ x9 + x7 - 3x6 - 23x5 + 68x4 - 124x3 + 93x2 + x - 1 $S_3 \wr C_3 $ $1$ $0$
12.165...456.18t315.a.a $12$ $ 2^{18} \cdot 229^{5}$ x9 - 3x8 + 9x7 - 7x6 + 2x5 + 14x4 - 9x3 - 11x2 - 3x - 1 $S_3\wr S_3$ $1$ $0$
12.171...241.18t206.a.a $12$ $ 11^{4} \cdot 43^{8}$ x9 - 3x7 - 4x6 + 3x5 + 8x4 - 10x3 - 4x2 + 9x + 4 $S_3 \wr C_3 $ $1$ $0$
12.192...584.18t315.a.a $12$ $ 2^{14} \cdot 3^{5} \cdot 137^{5}$ x9 - 4x8 + 3x7 + 3x6 + 2x5 - 4x4 - 5x3 + 2x2 + 3x + 3 $S_3\wr S_3$ $1$ $2$
12.201...875.18t218.a.a $12$ $ 5^{6} \cdot 419^{5}$ x9 + x7 - 8x6 - 5x5 - 2x4 + 20x3 + 5x2 + 23x + 5 $(((C_3 \times (C_3^2 : C_2)) : C_2) : C_3) : C_2$ $1$ $2$
12.203...752.18t315.a.a $12$ $ 2^{6} \cdot 23^{5} \cdot 149^{4}$ x9 - x8 - x7 - 4x6 + 7x4 + 7x3 + 5x2 + 4x - 1 $S_3\wr S_3$ $1$ $2$
12.212...409.18t206.a.a $12$ $ 3^{26} \cdot 17^{4}$ x9 - 3x6 - 9x5 + 9x4 + 9x3 - 9x2 + 1 $S_3 \wr C_3 $ $1$ $0$
12.218...359.18t315.a.a $12$ $ 23^{4} \cdot 239^{5}$ x9 + 5x7 - 6x6 + 7x5 - 18x4 + 9x3 - 11x2 + 3x + 1 $S_3\wr S_3$ $1$ $2$
12.218...641.18t206.a.a $12$ $ 3^{20} \cdot 89^{4}$ x9 - 3x8 + 3x7 - 6x5 + 6x4 - 3x3 - 3x2 + 3x + 1 $S_3 \wr C_3 $ $1$ $0$
12.219...929.18t206.a.a $12$ $ 7^{10} \cdot 167^{4}$ x9 - x8 + 2x7 - 4x2 + 4x - 1 $S_3 \wr C_3 $ $1$ $0$
12.220...943.18t218.a.a $12$ $ 3^{15} \cdot 109^{5}$ x9 - 2x8 + 3x6 - 10x5 + 18x4 - 15x3 + 10x2 - 3x + 1 $(((C_3 \times (C_3^2 : C_2)) : C_2) : C_3) : C_2$ $1$ $2$
12.223...504.18t206.a.a $12$ $ 2^{18} \cdot 31^{8}$ x9 - 3x8 + 5x7 - 8x6 - x5 + 2x4 + 5x3 + 6x2 + 2x - 1 $S_3 \wr C_3 $ $1$ $0$
12.224...656.18t315.a.a $12$ $ 2^{10} \cdot 19^{5} \cdot 97^{4}$ x9 - 3x8 + 6x7 - 8x6 + 8x5 - 6x4 + 6x3 - 4x2 + 3x - 1 $S_3\wr S_3$ $1$ $2$
12.250...352.18t315.a.a $12$ $ 2^{6} \cdot 23^{5} \cdot 157^{4}$ x9 - 4x8 + 7x7 - 3x6 - 3x5 + 4x4 + 2x3 - x2 - 9x + 7 $S_3\wr S_3$ $1$ $2$
12.253...019.18t315.a.a $12$ $ 47^{4} \cdot 139^{5}$ x9 - 2x8 - 5x7 + 10x6 + 9x5 - 19x4 - 6x3 + 17x2 + 2x - 4 $S_3\wr S_3$ $1$ $2$
12.270...625.18t206.a.a $12$ $ 3^{12} \cdot 5^{4} \cdot 13^{8}$ x9 - 3x7 - 17x6 - 36x5 + 21x4 + 39x3 + 9x2 + 90x + 53 $S_3 \wr C_3 $ $1$ $0$
12.289...375.18t315.a.a $12$ $ 5^{5} \cdot 7^{4} \cdot 131^{5}$ x9 - 4x8 + 6x7 - 2x6 - 6x5 + 8x4 - 4x2 + x - 1 $S_3\wr S_3$ $1$ $2$
12.317...384.18t315.a.a $12$ $ 2^{24} \cdot 7^{6} \cdot 11^{5}$ x9 - x8 + 3x7 - 9x6 + 10x5 - 6x4 + 8x3 - 4x2 - 2x + 2 $S_3\wr S_3$ $1$ $2$
12.331...609.18t206.a.a $12$ $ 3^{26} \cdot 19^{4}$ x9 - 9x7 + 27x5 - 36x3 + 27x - 9 $S_3 \wr C_3 $ $1$ $0$
12.332...976.18t315.a.a $12$ $ 2^{10} \cdot 19^{5} \cdot 107^{4}$ x9 - x8 - 2x7 + 2x5 + 2x3 + x + 1 $S_3\wr S_3$ $1$ $2$
12.332...856.18t315.a.a $12$ $ 2^{15} \cdot 3^{15} \cdot 29^{4}$ x9 - 6x6 - 9x5 - 18x4 - 15x3 - 18x2 - 9x - 8 $S_3\wr S_3$ $1$ $2$
12.335...000.36t1123.a.a $12$ $ 2^{35} \cdot 5^{10}$ x9 - 2x8 + 4x7 - 8x6 + 21x5 - 38x4 + 46x3 - 32x2 + 24x - 8 $(((C_3 \times (C_3^2 : C_2)) : C_2) : C_3) : C_2$ $1$ $-2$
12.335...000.18t218.a.a $12$ $ 2^{35} \cdot 5^{10}$ x9 - 2x8 + 4x7 - 8x6 + 21x5 - 38x4 + 46x3 - 32x2 + 24x - 8 $(((C_3 \times (C_3^2 : C_2)) : C_2) : C_3) : C_2$ $1$ $2$
12.372...107.18t218.a.a $12$ $ 3^{15} \cdot 11^{10}$ x9 - 3x8 + 15x7 - 30x6 + 15x5 - 27x4 - 93x3 + 51x2 + 48x - 25 $(((C_3 \times (C_3^2 : C_2)) : C_2) : C_3) : C_2$ $1$ $2$
12.373...032.36t2216.a.a $12$ $ 2^{10} \cdot 3^{17} \cdot 41^{4}$ x9 + 6x5 - 6x2 + 2 $S_3\wr S_3$ $1$ $-2$
12.385...144.18t315.a.a $12$ $ 2^{8} \cdot 19^{5} \cdot 157^{4}$ x9 - x8 + x7 + 2x5 - 5x4 + 5x3 - x2 - 2x + 1 $S_3\wr S_3$ $1$ $2$
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