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Galois conjugate representations are grouped into single lines.
Label Dimension Conductor Defining polynomial of Artin field $G$ Ind $\chi(c)$
3.229.4t5.1c1 $3$ $ 229 $ x4 - x + 1 $S_4$ $1$ $-1$
3.257.4t5.1c1 $3$ $ 257 $ x4 + x2 - x + 1 $S_4$ $1$ $-1$
3.283.4t5.1c1 $3$ $ 283 $ x4 - x - 1 $S_4$ $1$ $1$
3.331.4t5.1c1 $3$ $ 331 $ x4 - x3 + x2 + x - 1 $S_4$ $1$ $1$
3.491.4t5.1c1 $3$ $ 491 $ x4 - x3 - x2 + 3x - 1 $S_4$ $1$ $1$
3.563.4t5.1c1 $3$ $ 563 $ x4 - x3 + x2 - x - 1 $S_4$ $1$ $1$
3.2e4_37.4t5.1c1 $3$ $ 2^{4} \cdot 37 $ x4 + 2x2 - 2x + 1 $S_4$ $1$ $-1$
3.643.4t5.1c1 $3$ $ 643 $ x4 - x3 - 2x + 1 $S_4$ $1$ $1$
3.2e4_43.4t5.1c1 $3$ $ 2^{4} \cdot 43 $ x4 - 2x - 1 $S_4$ $1$ $1$
3.17_41.4t5.1c1 $3$ $ 17 \cdot 41 $ x4 - x3 + 2x2 - x + 2 $S_4$ $1$ $-1$
3.17_43.4t5.1c1 $3$ $ 17 \cdot 43 $ x4 - x3 + 2x2 - 1 $S_4$ $1$ $1$
3.751.4t5.1c1 $3$ $ 751 $ x4 - 2x3 + x2 - x - 1 $S_4$ $1$ $1$
3.761.4t5.1c1 $3$ $ 761 $ x4 - x3 + x2 + 2x + 1 $S_4$ $1$ $-1$
3.2e2_197.4t5.1c1 $3$ $ 2^{2} \cdot 197 $ x4 - x3 + 2x2 - 2x + 2 $S_4$ $1$ $-1$
3.2e4_53.4t5.1c1 $3$ $ 2^{4} \cdot 53 $ x4 - x2 - 2x + 1 $S_4$ $1$ $1$
3.2e2_223.4t5.1c1 $3$ $ 2^{2} \cdot 223 $ x4 - x3 - x2 + 2 $S_4$ $1$ $-1$
3.2e4_61.4t5.1c1 $3$ $ 2^{4} \cdot 61 $ x4 - 2x3 + 3x2 - 1 $S_4$ $1$ $1$
3.5_197.4t5.1c1 $3$ $ 5 \cdot 197 $ x4 - x3 + 2x2 - 3x + 2 $S_4$ $1$ $-1$
3.2e3_127.4t5.1c1 $3$ $ 2^{3} \cdot 127 $ x4 - x3 + x2 - 2x + 2 $S_4$ $1$ $-1$
3.2e2_269.4t5.1c1 $3$ $ 2^{2} \cdot 269 $ x4 - x3 + 3x2 - 3x + 2 $S_4$ $1$ $-1$
3.7_157.4t5.1c1 $3$ $ 7 \cdot 157 $ x4 - x3 + x2 - 3x + 1 $S_4$ $1$ $1$
3.3e3_41.4t5.1c1 $3$ $ 3^{3} \cdot 41 $ x4 - x3 - 2x - 1 $S_4$ $1$ $1$
3.1129.4t5.1c1 $3$ $ 1129 $ x4 - x3 - x + 2 $S_4$ $1$ $-1$
3.2e3_149.4t5.1c1 $3$ $ 2^{3} \cdot 149 $ x4 - x3 + 2x2 + x - 1 $S_4$ $1$ $1$
3.1229.4t5.1c1 $3$ $ 1229 $ x4 - x3 + 3x2 - x + 3 $S_4$ $1$ $-1$
3.5_251.4t5.1c1 $3$ $ 5 \cdot 251 $ x4 - x2 - 3x - 1 $S_4$ $1$ $1$
3.3_419.4t5.1c1 $3$ $ 3 \cdot 419 $ x4 - x2 - x + 2 $S_4$ $1$ $-1$
3.2e4_79.4t5.1c1 $3$ $ 2^{4} \cdot 79 $ x4 + 3x2 - 2x + 1 $S_4$ $1$ $-1$
3.2e4_83.4t5.1c1 $3$ $ 2^{4} \cdot 83 $ x4 - 3x2 - 2x + 1 $S_4$ $1$ $1$
3.3_457.4t5.1c1 $3$ $ 3 \cdot 457 $ x4 + 2x2 - x - 1 $S_4$ $1$ $1$
3.2e3_173.4t5.1c1 $3$ $ 2^{3} \cdot 173 $ x4 - x3 - x2 + 2x + 2 $S_4$ $1$ $-1$
3.2e2_349.4t5.1c1 $3$ $ 2^{2} \cdot 349 $ x4 - x3 + x2 - x + 2 $S_4$ $1$ $-1$
3.1399.4t5.1c1 $3$ $ 1399 $ x4 - x3 + x - 2 $S_4$ $1$ $1$
3.1423.4t5.1c1 $3$ $ 1423 $ x4 - x3 + x2 - 2x - 1 $S_4$ $1$ $1$
3.2e4_89.4t5.1c1 $3$ $ 2^{4} \cdot 89 $ x4 + x2 - 2x - 1 $S_4$ $1$ $1$
3.2e2_359.4t5.1c1 $3$ $ 2^{2} \cdot 359 $ x4 - x3 + 3x2 + 2 $S_4$ $1$ $-1$
3.2e2_19e2.6t8.1c1 $3$ $ 2^{2} \cdot 19^{2}$ x4 - x3 - 2x2 - 6x - 2 $S_4$ $1$ $-1$
3.2e4_7_13.4t5.1c1 $3$ $ 2^{4} \cdot 7 \cdot 13 $ x4 - 2x2 - 2x + 1 $S_4$ $1$ $1$
3.2e6_23.4t5.1c1 $3$ $ 2^{6} \cdot 23 $ x4 - 2x3 + 2x2 - 2 $S_4$ $1$ $1$
3.1489.4t5.1c1 $3$ $ 1489 $ x4 - x3 + 4x2 - x + 2 $S_4$ $1$ $-1$
3.2e2_373.4t5.1c1 $3$ $ 2^{2} \cdot 373 $ x4 - x3 + 2x2 + 2 $S_4$ $1$ $-1$
3.3_503.4t5.1c1 $3$ $ 3 \cdot 503 $ x4 - x3 + 2x2 + 2x + 1 $S_4$ $1$ $-1$
3.2e2_389.4t5.1c1 $3$ $ 2^{2} \cdot 389 $ x4 - x3 - x2 + x + 2 $S_4$ $1$ $-1$
3.2e2_397.4t5.1c1 $3$ $ 2^{2} \cdot 397 $ x4 - x3 - 3x2 + 2 $S_4$ $1$ $1$
3.3e3_59.4t5.1c1 $3$ $ 3^{3} \cdot 59 $ x4 - 2x3 + 3x2 - x + 2 $S_4$ $1$ $-1$
3.2e4_101.4t5.1c1 $3$ $ 2^{4} \cdot 101 $ x4 - 2x + 2 $S_4$ $1$ $-1$
3.2e2_433.4t5.1c1 $3$ $ 2^{2} \cdot 433 $ x4 - x3 + 3x - 1 $S_4$ $1$ $1$
3.5_353.4t5.1c1 $3$ $ 5 \cdot 353 $ x4 - x3 - x2 - x + 3 $S_4$ $1$ $-1$
3.3e2_199.4t5.1c1 $3$ $ 3^{2} \cdot 199 $ x4 - x3 - x2 - 2x + 1 $S_4$ $1$ $1$
3.1823.4t5.1c1 $3$ $ 1823 $ x4 - x3 + 3x - 2 $S_4$ $1$ $1$
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