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Galois conjugate representations are grouped into single lines.
Label Dimension Conductor Defining polynomial of Artin field $G$ Ind $\chi(c)$
3.229.4t5.a.a $3$ $ 229 $ x4 - x + 1 $S_4$ $1$ $-1$
3.257.4t5.a.a $3$ $ 257 $ x4 + x2 - x + 1 $S_4$ $1$ $-1$
3.283.4t5.b.a $3$ $ 283 $ x4 - x - 1 $S_4$ $1$ $1$
3.331.4t5.a.a $3$ $ 331 $ x4 - x3 + x2 + x - 1 $S_4$ $1$ $1$
3.332.6t11.a.a $3$ $ 2^{2} \cdot 83 $ x6 - x5 + 2x3 - x + 1 $S_4\times C_2$ $1$ $-1$
3.341.6t11.c.a $3$ $ 11 \cdot 31 $ x6 - x5 - x4 + 2x3 - x + 1 $S_4\times C_2$ $1$ $-1$
3.437.6t11.b.a $3$ $ 19 \cdot 23 $ x6 - x5 + 2x4 - 2x3 + 2x2 - 2x + 1 $S_4\times C_2$ $1$ $-1$
3.472.6t11.a.a $3$ $ 2^{3} \cdot 59 $ x6 - x5 + 2x4 + 2x2 - x + 1 $S_4\times C_2$ $1$ $-1$
3.491.4t5.b.a $3$ $ 491 $ x4 - x3 - x2 + 3x - 1 $S_4$ $1$ $1$
3.563.4t5.b.a $3$ $ 563 $ x4 - x3 + x2 - x - 1 $S_4$ $1$ $1$
3.592.4t5.a.a $3$ $ 2^{4} \cdot 37 $ x4 + 2x2 - 2x + 1 $S_4$ $1$ $-1$
3.597.6t11.b.a $3$ $ 3 \cdot 199 $ x6 - 2x5 + 3x3 - 2x + 1 $S_4\times C_2$ $1$ $-1$
3.637.6t6.a.a $3$ $ 7^{2} \cdot 13 $ x6 - 2x5 + 2x4 - 3x3 + 2x2 - 2x + 1 $A_4\times C_2$ $1$ $-1$
3.643.4t5.a.a $3$ $ 643 $ x4 - x3 - 2x + 1 $S_4$ $1$ $1$
3.688.4t5.b.a $3$ $ 2^{4} \cdot 43 $ x4 - 2x - 1 $S_4$ $1$ $1$
3.697.4t5.a.a $3$ $ 17 \cdot 41 $ x4 - x3 + 2x2 - x + 2 $S_4$ $1$ $-1$
3.717.6t11.b.a $3$ $ 3 \cdot 239 $ x6 + 2x4 - 3x3 + 2x2 + 1 $S_4\times C_2$ $1$ $-1$
3.731.4t5.a.a $3$ $ 17 \cdot 43 $ x4 - x3 + 2x2 - 1 $S_4$ $1$ $1$
3.740.6t11.c.a $3$ $ 2^{2} \cdot 5 \cdot 37 $ x6 - x5 - x3 - x + 1 $S_4\times C_2$ $1$ $-1$
3.749.6t11.b.a $3$ $ 7 \cdot 107 $ x6 - 2x5 + x4 + x3 + x2 - 2x + 1 $S_4\times C_2$ $1$ $-1$
3.751.4t5.a.a $3$ $ 751 $ x4 - 2x3 + x2 - x - 1 $S_4$ $1$ $1$
3.761.4t5.a.a $3$ $ 761 $ x4 - x3 + x2 + 2x + 1 $S_4$ $1$ $-1$
3.788.4t5.a.a $3$ $ 2^{2} \cdot 197 $ x4 - x3 + 2x2 - 2x + 2 $S_4$ $1$ $-1$
3.804.6t11.a.a $3$ $ 2^{2} \cdot 3 \cdot 67 $ x6 - x5 + 3x3 - x + 1 $S_4\times C_2$ $1$ $-1$
3.805.6t11.a.a $3$ $ 5 \cdot 7 \cdot 23 $ x6 + 2x4 - x3 + 2x2 + 1 $S_4\times C_2$ $1$ $-1$
3.844.6t11.a.a $3$ $ 2^{2} \cdot 211 $ x6 - x5 - x4 + x3 + x2 - 2x + 3 $S_4\times C_2$ $1$ $-1$
3.845.6t6.a.a $3$ $ 5 \cdot 13^{2}$ x6 - 2x5 + x3 - 2x + 1 $A_4\times C_2$ $1$ $-1$
3.848.4t5.b.a $3$ $ 2^{4} \cdot 53 $ x4 - x2 - 2x + 1 $S_4$ $1$ $1$
3.856.6t11.a.a $3$ $ 2^{3} \cdot 107 $ x6 - x5 - x - 1 $S_4\times C_2$ $1$ $1$
3.892.4t5.a.a $3$ $ 2^{2} \cdot 223 $ x4 - x3 - x2 + 2 $S_4$ $1$ $-1$
3.912.6t11.b.a $3$ $ 2^{4} \cdot 3 \cdot 19 $ x6 + x4 - 2x3 + x2 + 1 $S_4\times C_2$ $1$ $-1$
3.921.6t11.a.a $3$ $ 3 \cdot 307 $ x6 - 3x5 + 2x4 + x3 + 2x2 - 3x + 2 $S_4\times C_2$ $1$ $-1$
3.944.6t11.a.a $3$ $ 2^{4} \cdot 59 $ x6 + 2x2 + 1 $S_4\times C_2$ $1$ $-1$
3.963.6t11.a.a $3$ $ 3^{2} \cdot 107 $ x6 - 2x5 - 2x4 + 5x3 - 2x2 - 2x + 1 $S_4\times C_2$ $1$ $1$
3.976.4t5.b.a $3$ $ 2^{4} \cdot 61 $ x4 - 2x3 + 3x2 - 1 $S_4$ $1$ $1$
3.981.6t11.b.a $3$ $ 3^{2} \cdot 109 $ x6 - 2x5 + 2x4 + x3 + 2x2 - 2x + 1 $S_4\times C_2$ $1$ $-1$
3.985.4t5.a.a $3$ $ 5 \cdot 197 $ x4 - x3 + 2x2 - 3x + 2 $S_4$ $1$ $-1$
3.988.6t11.a.a $3$ $ 2^{2} \cdot 13 \cdot 19 $ x6 - x5 + x3 - x - 1 $S_4\times C_2$ $1$ $1$
3.989.6t11.b.a $3$ $ 23 \cdot 43 $ x6 - x5 - 2x3 + x2 + x + 1 $S_4\times C_2$ $1$ $-1$
3.1003.6t11.b.a $3$ $ 17 \cdot 59 $ x6 - x4 - x3 + x2 - 1 $S_4\times C_2$ $1$ $1$
3.1016.4t5.a.a $3$ $ 2^{3} \cdot 127 $ x4 - x3 + x2 - 2x + 2 $S_4$ $1$ $-1$
3.1076.4t5.a.a $3$ $ 2^{2} \cdot 269 $ x4 - x3 + 3x2 - 3x + 2 $S_4$ $1$ $-1$
3.1099.4t5.a.a $3$ $ 7 \cdot 157 $ x4 - x3 + x2 - 3x + 1 $S_4$ $1$ $1$
3.1101.6t11.b.a $3$ $ 3 \cdot 367 $ x6 - x4 + 2x2 + 3 $S_4\times C_2$ $1$ $-1$
3.1107.4t5.a.a $3$ $ 3^{3} \cdot 41 $ x4 - x3 - 2x - 1 $S_4$ $1$ $1$
3.1112.6t11.b.a $3$ $ 2^{3} \cdot 139 $ x6 - x5 + 4x4 - 3x3 + 3x2 - 2x + 2 $S_4\times C_2$ $1$ $-1$
3.1129.4t5.a.a $3$ $ 1129 $ x4 - x3 - x + 2 $S_4$ $1$ $-1$
3.1137.6t11.b.a $3$ $ 3 \cdot 379 $ x6 - 3x5 + 4x4 - 3x3 + 2x2 - x + 4 $S_4\times C_2$ $1$ $-1$
3.1147.6t11.b.a $3$ $ 31 \cdot 37 $ x6 - 2x4 - x3 + 2x2 - 1 $S_4\times C_2$ $1$ $1$
3.1192.4t5.a.a $3$ $ 2^{3} \cdot 149 $ x4 - x3 + 2x2 + x - 1 $S_4$ $1$ $1$
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