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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 $S_4$ $1$ $1$
3.2e2_83.6t11.2c1 $3$ $ 2^{2} \cdot 83 $ x6 - x5 + 2x3 - x + 1 $S_4\times C_2$ $1$ $-1$
3.11_31.6t11.2c1 $3$ $ 11 \cdot 31 $ x6 - x5 - x4 + 2x3 - x + 1 $S_4\times C_2$ $1$ $-1$
3.19_23.6t11.2c1 $3$ $ 19 \cdot 23 $ x6 - x5 + 2x4 - 2x3 + 2x2 - 2x + 1 $S_4\times C_2$ $1$ $-1$
3.2e3_59.6t11.2c1 $3$ $ 2^{3} \cdot 59 $ x6 - x5 + 2x4 + 2x2 - x + 1 $S_4\times C_2$ $1$ $-1$
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 $S_4$ $1$ $-1$
3.3_199.6t11.2c1 $3$ $ 3 \cdot 199 $ x6 - 2x5 + 3x3 - 2x + 1 $S_4\times C_2$ $1$ $-1$
3.7e2_13.6t6.1c1 $3$ $ 7^{2} \cdot 13 $ x6 - 2x5 + 2x4 - 3x3 + 2x2 - 2x + 1 $A_4\times C_2$ $1$ $-1$
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 $S_4$ $1$ $-1$
3.3_239.6t11.2c1 $3$ $ 3 \cdot 239 $ x6 + 2x4 - 3x3 + 2x2 + 1 $S_4\times C_2$ $1$ $-1$
3.17_43.4t5.1c1 $3$ $ 17 \cdot 43 $ x4 - x3 + 2x2 - 1 $S_4$ $1$ $1$
3.2e2_5_37.6t11.2c1 $3$ $ 2^{2} \cdot 5 \cdot 37 $ x6 - x5 - x3 - x + 1 $S_4\times C_2$ $1$ $-1$
3.7_107.6t11.2c1 $3$ $ 7 \cdot 107 $ x6 - 2x5 + x4 + x3 + x2 - 2x + 1 $S_4\times C_2$ $1$ $-1$
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 $S_4$ $1$ $-1$
3.2e2_3_67.6t11.2c1 $3$ $ 2^{2} \cdot 3 \cdot 67 $ x6 - x5 + 3x3 - x + 1 $S_4\times C_2$ $1$ $-1$
3.5_7_23.6t11.2c1 $3$ $ 5 \cdot 7 \cdot 23 $ x6 + 2x4 - x3 + 2x2 + 1 $S_4\times C_2$ $1$ $-1$
3.2e2_211.6t11.2c1 $3$ $ 2^{2} \cdot 211 $ x6 - x5 - x4 + x3 + x2 - 2x + 3 $S_4\times C_2$ $1$ $-1$
3.5_13e2.6t6.1c1 $3$ $ 5 \cdot 13^{2}$ x6 - 2x5 + x3 - 2x + 1 $A_4\times C_2$ $1$ $-1$
3.2e4_53.4t5.1c1 $3$ $ 2^{4} \cdot 53 $ x4 - x2 - 2x + 1 $S_4$ $1$ $1$
3.2e3_107.6t11.1c1 $3$ $ 2^{3} \cdot 107 $ x6 - x5 - x - 1 $S_4\times C_2$ $1$ $1$
3.2e2_223.4t5.1c1 $3$ $ 2^{2} \cdot 223 $ x4 - x3 - x2 + 2 $S_4$ $1$ $-1$
3.2e4_3_19.6t11.2c1 $3$ $ 2^{4} \cdot 3 \cdot 19 $ x6 + x4 - 2x3 + x2 + 1 $S_4\times C_2$ $1$ $-1$
3.3_307.6t11.2c1 $3$ $ 3 \cdot 307 $ x6 - 3x5 + 2x4 + x3 + 2x2 - 3x + 2 $S_4\times C_2$ $1$ $-1$
3.2e4_59.6t11.2c1 $3$ $ 2^{4} \cdot 59 $ x6 + 2x2 + 1 $S_4\times C_2$ $1$ $-1$
3.3e2_107.6t11.1c1 $3$ $ 3^{2} \cdot 107 $ x6 - 2x5 - 2x4 + 5x3 - 2x2 - 2x + 1 $S_4\times C_2$ $1$ $1$
3.2e4_61.4t5.1c1 $3$ $ 2^{4} \cdot 61 $ x4 - 2x3 + 3x2 - 1 $S_4$ $1$ $1$
3.3e2_109.6t11.2c1 $3$ $ 3^{2} \cdot 109 $ x6 - 2x5 + 2x4 + x3 + 2x2 - 2x + 1 $S_4\times C_2$ $1$ $-1$
3.5_197.4t5.1c1 $3$ $ 5 \cdot 197 $ x4 - x3 + 2x2 - 3x + 2 $S_4$ $1$ $-1$
3.2e2_13_19.6t11.1c1 $3$ $ 2^{2} \cdot 13 \cdot 19 $ x6 - x5 + x3 - x - 1 $S_4\times C_2$ $1$ $1$
3.23_43.6t11.2c1 $3$ $ 23 \cdot 43 $ x6 - x5 - 2x3 + x2 + x + 1 $S_4\times C_2$ $1$ $-1$
3.17_59.6t11.1c1 $3$ $ 17 \cdot 59 $ x6 - x4 - x3 + x2 - 1 $S_4\times C_2$ $1$ $1$
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 $S_4$ $1$ $1$
3.3_367.6t11.1c1 $3$ $ 3 \cdot 367 $ x6 - x4 + 2x2 + 3 $S_4\times C_2$ $1$ $-1$
3.3e3_41.4t5.1c1 $3$ $ 3^{3} \cdot 41 $ x4 - x3 - 2x - 1 $S_4$ $1$ $1$
3.2e3_139.6t11.2c1 $3$ $ 2^{3} \cdot 139 $ x6 - x5 + 4x4 - 3x3 + 3x2 - 2x + 2 $S_4\times C_2$ $1$ $-1$
3.1129.4t5.1c1 $3$ $ 1129 $ x4 - x3 - x + 2 $S_4$ $1$ $-1$
3.3_379.6t11.2c1 $3$ $ 3 \cdot 379 $ x6 - 3x5 + 4x4 - 3x3 + 2x2 - x + 4 $S_4\times C_2$ $1$ $-1$
3.31_37.6t11.1c1 $3$ $ 31 \cdot 37 $ x6 - 2x4 - x3 + 2x2 - 1 $S_4\times C_2$ $1$ $1$
3.2e3_149.4t5.1c1 $3$ $ 2^{3} \cdot 149 $ x4 - x3 + 2x2 + x - 1 $S_4$ $1$ $1$
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