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Galois conjugate representations are grouped into single lines.
Label Dimension Conductor Artin stem field $G$ Ind $\chi(c)$
$12$ $ 2^{22} \cdot 3^{24}$ 9.1.1190155742208.1 $S_3\wr S_3$ $1$ $-2$
$12$ $ 11^{9} \cdot 61^{5}$ 9.1.3323228821.1 $S_3\wr S_3$ $1$ $-2$
$12$ $ 2^{10} \cdot 3^{9} \cdot 7^{5} \cdot 23^{5}$ 9.1.86537154816.1 $S_3\wr S_3$ $1$ $-2$
$12$ $ 2^{19} \cdot 3^{9} \cdot 61^{5}$ 9.1.37653424128.1 $S_3\wr S_3$ $1$ $-2$
$12$ $ 2^{10} \cdot 3^{6} \cdot 13^{6} \cdot 19^{5}$ 9.1.8012189952.1 $S_3\wr S_3$ $1$ $-2$
$12$ $ 2^{22} \cdot 3^{17} \cdot 7^{5}$ 9.1.186659085312.1 $S_3\wr S_3$ $1$ $-2$
$12$ $ 2^{33} \cdot 3^{19}$ 9.1.13060694016.1 $S_3\wr S_3$ $1$ $-2$
$12$ $ 3^{23} \cdot 41^{5}$ 9.1.26701407522369.1 $S_3\wr S_3$ $1$ $-2$
$12$ $ 2^{16} \cdot 3^{8} \cdot 11^{10}$ 9.1.164627620608.1 $S_3\wr S_3$ $1$ $-2$
$12$ $ 2^{30} \cdot 3^{21}$ 9.1.58773123072.1 $S_3\wr S_3$ $1$ $-2$
$12$ $ 17^{9} \cdot 41^{5}$ 9.5.5756350841.1 $S_3\wr S_3$ $1$ $0$
$12$ $ 2^{18} \cdot 3^{9} \cdot 7^{5} \cdot 11^{5}$ 9.1.2366667072.1 $S_3\wr S_3$ $1$ $-2$
$12$ $ 2^{6} \cdot 3^{15} \cdot 109^{5}$ 9.1.60420873024.1 $S_3\wr S_3$ $1$ $-2$
$12$ $ 2^{33} \cdot 3^{6} \cdot 19^{5}$ 9.1.3034202112.1 $S_3\wr S_3$ $1$ $-2$
$12$ $ 2^{10} \cdot 5^{9} \cdot 97^{5}$ 9.5.146027680000.1 $S_3\wr S_3$ $1$ $0$
$12$ $ 2^{16} \cdot 3^{20} \cdot 7^{6}$ 9.1.179992689408.1 $S_3\wr S_3$ $1$ $-2$
$12$ $ 2^{10} \cdot 3^{6} \cdot 523^{5}$ 9.1.988800770304.1 $S_3\wr S_3$ $1$ $-2$
$12$ $ 2^{10} \cdot 3^{9} \cdot 271^{5}$ 9.3.412698468096.1 $S_3\wr S_3$ $1$ $0$
$12$ $ 2^{33} \cdot 3^{20}$ 9.1.1410554953728.1 $S_3\wr S_3$ $1$ $-2$
$12$ $ 3^{19} \cdot 11^{10}$ 9.1.31068844930233.1 $S_3\wr S_3$ $1$ $-2$
$12$ $ 2^{6} \cdot 3^{9} \cdot 5^{10} \cdot 19^{5}$ 9.7.13889475000000.1 $S_3\wr S_3$ $1$ $-4$
$12$ $ 2^{12} \cdot 3^{20} \cdot 19^{5}$ 9.1.1574706449808.1 $S_3\wr S_3$ $1$ $-2$
$12$ $ 3^{9} \cdot 7^{6} \cdot 109^{5}$ 9.1.12341068212501.1 $S_3\wr S_3$ $1$ $-2$
$12$ $ 2^{10} \cdot 3^{9} \cdot 5^{6} \cdot 41^{5}$ 9.1.35728646400.1 $S_3\wr S_3$ $1$ $-2$
$12$ $ 2^{10} \cdot 3^{8} \cdot 5^{5} \cdot 71^{5}$ 9.1.34359456000.1 $S_3\wr S_3$ $1$ $-2$
$12$ $ 2^{33} \cdot 5^{5} \cdot 17^{5}$ 9.1.20123648000.1 $S_3\wr S_3$ $1$ $-2$
$12$ $ 2^{14} \cdot 3^{9} \cdot 17^{9}$ 9.1.8508782723328.1 $S_3\wr S_3$ $1$ $-2$
$12$ $ 2^{20} \cdot 3^{12} \cdot 37^{5}$ 9.5.1020931070976.1 $S_3\wr S_3$ $1$ $0$
$12$ $ 2^{10} \cdot 7^{6} \cdot 19^{9}$ 9.3.11443226368.1 $S_3\wr S_3$ $1$ $2$
$12$ $ 2^{14} \cdot 3^{6} \cdot 37^{8}$ 9.1.17734300939008.1 $S_3\wr S_3$ $1$ $-2$
$12$ $ 2^{23} \cdot 3^{9} \cdot 7^{10}$ 9.1.3825245233152.1 $S_3\wr S_3$ $1$ $-2$
$12$ $ 2^{10} \cdot 3^{8} \cdot 7^{5} \cdot 53^{5}$ 9.1.39217774848.1 $S_3\wr S_3$ $1$ $-2$
$12$ $ 2^{20} \cdot 3^{17} \cdot 5^{8}$ 9.1.314928000000.1 $S_3\wr S_3$ $1$ $-2$
$12$ $ 2^{6} \cdot 3^{9} \cdot 13^{5} \cdot 41^{5}$ 9.1.784958361408.1 $S_3\wr S_3$ $1$ $-2$
$12$ $ 2^{8} \cdot 7^{6} \cdot 283^{5}$ 9.1.31096636564.1 $S_3\wr S_3$ $1$ $-2$
$12$ $ 2^{16} \cdot 3^{24} \cdot 5^{5}$ 9.1.37192366944000.1 $S_3\wr S_3$ $1$ $-2$
$12$ $ 2^{10} \cdot 3^{16} \cdot 67^{5}$ 9.1.2078873856.1 $S_3\wr S_3$ $1$ $-2$
$12$ $ 2^{33} \cdot 3^{5} \cdot 31^{5}$ 9.1.26357170176.1 $S_3\wr S_3$ $1$ $-2$
$12$ $ 2^{35} \cdot 71^{5}$ 9.3.23456055296.1 $S_3\wr S_3$ $1$ $0$
$12$ $ 2^{14} \cdot 5^{9} \cdot 7^{11}$ 9.1.94119200000.1 $S_3\wr S_3$ $1$ $-2$
$12$ $ 2^{18} \cdot 3^{17} \cdot 5^{9}$ 9.1.106288200000.1 $S_3\wr S_3$ $1$ $-2$
$12$ $ 2^{8} \cdot 3^{5} \cdot 47^{9}$ 9.3.8432088768.1 $S_3\wr S_3$ $1$ $0$
$12$ $ 2^{18} \cdot 3^{20} \cdot 5^{7}$ 9.1.9183300480000.1 $S_3\wr S_3$ $1$ $-2$
$12$ $ 2^{10} \cdot 3^{6} \cdot 7^{6} \cdot 13^{8}$ 9.1.408695571648.1 $S_3\wr S_3$ $1$ $-2$
$12$ $ 2^{20} \cdot 3^{29}$ 9.1.10711401679872.1 $S_3\wr S_3$ $1$ $-2$
$12$ $ 2^{18} \cdot 3^{23} \cdot 5^{5}$ 9.1.3099363912000.4 $S_3\wr S_3$ $1$ $-2$
$12$ $ 2^{18} \cdot 3^{15} \cdot 29^{5}$ 9.1.1137893184.1 $S_3\wr S_3$ $1$ $-2$
$12$ $ 2^{14} \cdot 5^{6} \cdot 7^{7} \cdot 13^{5}$ 9.1.21099988000000.1 $S_3\wr S_3$ $1$ $-2$
$12$ $ 3^{8} \cdot 5^{6} \cdot 239^{5}$ 9.1.639933703125.1 $S_3\wr S_3$ $1$ $-2$
$12$ $ 2^{16} \cdot 3^{9} \cdot 5^{8} \cdot 11^{5}$ 9.1.431244000000.1 $S_3\wr S_3$ $1$ $-2$
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