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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 $S_4$ $1$ $1$
3.491.4t5.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 $S_4$ $1$ $-1$
3.643.4t5.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 $S_4$ $1$ $-1$
3.731.4t5.a.a $3$ $ 17 \cdot 43 $ x4 - x3 + 2x2 - 1 $S_4$ $1$ $1$
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 $S_4$ $1$ $-1$
3.848.4t5.b.a $3$ $ 2^{4} \cdot 53 $ x4 - x2 - 2x + 1 $S_4$ $1$ $1$
3.892.4t5.a.a $3$ $ 2^{2} \cdot 223 $ x4 - x3 - x2 + 2 $S_4$ $1$ $-1$
3.976.4t5.b.a $3$ $ 2^{4} \cdot 61 $ x4 - 2x3 + 3x2 - 1 $S_4$ $1$ $1$
3.985.4t5.a.a $3$ $ 5 \cdot 197 $ x4 - x3 + 2x2 - 3x + 2 $S_4$ $1$ $-1$
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 $S_4$ $1$ $1$
3.1107.4t5.a.a $3$ $ 3^{3} \cdot 41 $ x4 - x3 - 2x - 1 $S_4$ $1$ $1$
3.1129.4t5.a.a $3$ $ 1129 $ x4 - x3 - x + 2 $S_4$ $1$ $-1$
3.1192.4t5.a.a $3$ $ 2^{3} \cdot 149 $ x4 - x3 + 2x2 + x - 1 $S_4$ $1$ $1$
3.1229.4t5.a.a $3$ $ 1229 $ x4 - x3 + 3x2 - x + 3 $S_4$ $1$ $-1$
3.1255.4t5.a.a $3$ $ 5 \cdot 251 $ x4 - x2 - 3x - 1 $S_4$ $1$ $1$
3.1257.4t5.a.a $3$ $ 3 \cdot 419 $ x4 - x2 - x + 2 $S_4$ $1$ $-1$
3.1264.4t5.a.a $3$ $ 2^{4} \cdot 79 $ x4 + 3x2 - 2x + 1 $S_4$ $1$ $-1$
3.1328.4t5.b.a $3$ $ 2^{4} \cdot 83 $ x4 - 3x2 - 2x + 1 $S_4$ $1$ $1$
3.1371.4t5.a.a $3$ $ 3 \cdot 457 $ x4 + 2x2 - x - 1 $S_4$ $1$ $1$
3.1384.4t5.a.a $3$ $ 2^{3} \cdot 173 $ x4 - x3 - x2 + 2x + 2 $S_4$ $1$ $-1$
3.1396.4t5.a.a $3$ $ 2^{2} \cdot 349 $ x4 - x3 + x2 - x + 2 $S_4$ $1$ $-1$
3.1399.4t5.a.a $3$ $ 1399 $ x4 - x3 + x - 2 $S_4$ $1$ $1$
3.1423.4t5.a.a $3$ $ 1423 $ x4 - x3 + x2 - 2x - 1 $S_4$ $1$ $1$
3.1424.4t5.a.a $3$ $ 2^{4} \cdot 89 $ x4 + x2 - 2x - 1 $S_4$ $1$ $1$
3.1436.4t5.a.a $3$ $ 2^{2} \cdot 359 $ x4 - x3 + 3x2 + 2 $S_4$ $1$ $-1$
3.1444.6t8.a.a $3$ $ 2^{2} \cdot 19^{2}$ x4 - x3 - 2x2 - 6x - 2 $S_4$ $1$ $-1$
3.1456.4t5.b.a $3$ $ 2^{4} \cdot 7 \cdot 13 $ x4 - 2x2 - 2x + 1 $S_4$ $1$ $1$
3.1472.4t5.b.a $3$ $ 2^{6} \cdot 23 $ x4 - 2x3 + 2x2 - 2 $S_4$ $1$ $1$
3.1489.4t5.a.a $3$ $ 1489 $ x4 - x3 + 4x2 - x + 2 $S_4$ $1$ $-1$
3.1492.4t5.a.a $3$ $ 2^{2} \cdot 373 $ x4 - x3 + 2x2 + 2 $S_4$ $1$ $-1$
3.1509.4t5.a.a $3$ $ 3 \cdot 503 $ x4 - x3 + 2x2 + 2x + 1 $S_4$ $1$ $-1$
3.1556.4t5.a.a $3$ $ 2^{2} \cdot 389 $ x4 - x3 - x2 + x + 2 $S_4$ $1$ $-1$
3.1588.4t5.a.a $3$ $ 2^{2} \cdot 397 $ x4 - x3 - 3x2 + 2 $S_4$ $1$ $1$
3.1593.4t5.a.a $3$ $ 3^{3} \cdot 59 $ x4 - 2x3 + 3x2 - x + 2 $S_4$ $1$ $-1$
3.1616.4t5.a.a $3$ $ 2^{4} \cdot 101 $ x4 - 2x + 2 $S_4$ $1$ $-1$
3.1732.4t5.a.a $3$ $ 2^{2} \cdot 433 $ x4 - x3 + 3x - 1 $S_4$ $1$ $1$
3.1765.4t5.a.a $3$ $ 5 \cdot 353 $ x4 - x3 - x2 - x + 3 $S_4$ $1$ $-1$
3.1791.4t5.b.a $3$ $ 3^{2} \cdot 199 $ x4 - x3 - x2 - 2x + 1 $S_4$ $1$ $1$
3.1823.4t5.a.a $3$ $ 1823 $ x4 - x3 + 3x - 2 $S_4$ $1$ $1$
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