Artin Representation Search Results

Dimension	Conductor	Group	Root number	Parity
Smallest container	Ramified primes	Unramified primes	Frobenius-Schur indicator

Results (displaying matches 1-50 of )

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 $	x^4 - x + 1	$S_4$	$1$	$-1$
3.257.4t5.1c1	$3$	$ 257 $	x^4 + x^2 - x + 1	$S_4$	$1$	$-1$
3.283.4t5.1c1	$3$	$ 283 $	x^4 - x - 1	$S_4$	$1$	$1$
3.331.4t5.1c1	$3$	$ 331 $	x^4 - x^3 + x^2 + x - 1	$S_4$	$1$	$1$
3.2e2_83.6t11.2c1	$3$	$ 2^{2} \cdot 83 $	x^6 - x^5 + 2x^3 - x + 1	$S_4\times C_2$	$1$	$-1$
3.11_31.6t11.2c1	$3$	$ 11 \cdot 31 $	x^6 - x^5 - x^4 + 2x^3 - x + 1	$S_4\times C_2$	$1$	$-1$
3.19_23.6t11.2c1	$3$	$ 19 \cdot 23 $	x^6 - x^5 + 2x^4 - 2x^3 + 2x^2 - 2x + 1	$S_4\times C_2$	$1$	$-1$
3.2e3_59.6t11.2c1	$3$	$ 2^{3} \cdot 59 $	x^6 - x^5 + 2x^4 + 2x^2 - x + 1	$S_4\times C_2$	$1$	$-1$
3.491.4t5.1c1	$3$	$ 491 $	x^4 - x^3 - x^2 + 3x - 1	$S_4$	$1$	$1$
3.563.4t5.1c1	$3$	$ 563 $	x^4 - x^3 + x^2 - x - 1	$S_4$	$1$	$1$
3.2e4_37.4t5.1c1	$3$	$ 2^{4} \cdot 37 $	x^4 + 2x^2 - 2x + 1	$S_4$	$1$	$-1$
3.3_199.6t11.2c1	$3$	$ 3 \cdot 199 $	x^6 - 2x^5 + 3x^3 - 2x + 1	$S_4\times C_2$	$1$	$-1$
3.7e2_13.6t6.1c1	$3$	$ 7^{2} \cdot 13 $	x^6 - 2x^5 + 2x^4 - 3x^3 + 2x^2 - 2x + 1	$A_4\times C_2$	$1$	$-1$
3.643.4t5.1c1	$3$	$ 643 $	x^4 - x^3 - 2x + 1	$S_4$	$1$	$1$
3.2e4_43.4t5.1c1	$3$	$ 2^{4} \cdot 43 $	x^4 - 2x - 1	$S_4$	$1$	$1$
3.17_41.4t5.1c1	$3$	$ 17 \cdot 41 $	x^4 - x^3 + 2x^2 - x + 2	$S_4$	$1$	$-1$
3.3_239.6t11.2c1	$3$	$ 3 \cdot 239 $	x^6 + 2x^4 - 3x^3 + 2x^2 + 1	$S_4\times C_2$	$1$	$-1$
3.17_43.4t5.1c1	$3$	$ 17 \cdot 43 $	x^4 - x^3 + 2x^2 - 1	$S_4$	$1$	$1$
3.2e2_5_37.6t11.2c1	$3$	$ 2^{2} \cdot 5 \cdot 37 $	x^6 - x^5 - x^3 - x + 1	$S_4\times C_2$	$1$	$-1$
3.7_107.6t11.2c1	$3$	$ 7 \cdot 107 $	x^6 - 2x^5 + x^4 + x^3 + x^2 - 2x + 1	$S_4\times C_2$	$1$	$-1$
3.751.4t5.1c1	$3$	$ 751 $	x^4 - 2x^3 + x^2 - x - 1	$S_4$	$1$	$1$
3.761.4t5.1c1	$3$	$ 761 $	x^4 - x^3 + x^2 + 2x + 1	$S_4$	$1$	$-1$
3.2e2_197.4t5.1c1	$3$	$ 2^{2} \cdot 197 $	x^4 - x^3 + 2x^2 - 2x + 2	$S_4$	$1$	$-1$
3.2e2_3_67.6t11.2c1	$3$	$ 2^{2} \cdot 3 \cdot 67 $	x^6 - x^5 + 3x^3 - x + 1	$S_4\times C_2$	$1$	$-1$
3.5_7_23.6t11.2c1	$3$	$ 5 \cdot 7 \cdot 23 $	x^6 + 2x^4 - x^3 + 2x^2 + 1	$S_4\times C_2$	$1$	$-1$
3.2e2_211.6t11.2c1	$3$	$ 2^{2} \cdot 211 $	x^6 - x^5 - x^4 + x^3 + x^2 - 2x + 3	$S_4\times C_2$	$1$	$-1$
3.5_13e2.6t6.1c1	$3$	$ 5 \cdot 13^{2}$	x^6 - 2x^5 + x^3 - 2x + 1	$A_4\times C_2$	$1$	$-1$
3.2e4_53.4t5.1c1	$3$	$ 2^{4} \cdot 53 $	x^4 - x^2 - 2x + 1	$S_4$	$1$	$1$
3.2e3_107.6t11.1c1	$3$	$ 2^{3} \cdot 107 $	x^6 - x^5 - x - 1	$S_4\times C_2$	$1$	$1$
3.2e2_223.4t5.1c1	$3$	$ 2^{2} \cdot 223 $	x^4 - x^3 - x^2 + 2	$S_4$	$1$	$-1$
3.2e4_3_19.6t11.2c1	$3$	$ 2^{4} \cdot 3 \cdot 19 $	x^6 + x^4 - 2x^3 + x^2 + 1	$S_4\times C_2$	$1$	$-1$
3.3_307.6t11.2c1	$3$	$ 3 \cdot 307 $	x^6 - 3x^5 + 2x^4 + x^3 + 2x^2 - 3x + 2	$S_4\times C_2$	$1$	$-1$
3.2e4_59.6t11.2c1	$3$	$ 2^{4} \cdot 59 $	x^6 + 2x^2 + 1	$S_4\times C_2$	$1$	$-1$
3.3e2_107.6t11.1c1	$3$	$ 3^{2} \cdot 107 $	x^6 - 2x^5 - 2x^4 + 5x^3 - 2x^2 - 2x + 1	$S_4\times C_2$	$1$	$1$
3.2e4_61.4t5.1c1	$3$	$ 2^{4} \cdot 61 $	x^4 - 2x^3 + 3x^2 - 1	$S_4$	$1$	$1$
3.3e2_109.6t11.2c1	$3$	$ 3^{2} \cdot 109 $	x^6 - 2x^5 + 2x^4 + x^3 + 2x^2 - 2x + 1	$S_4\times C_2$	$1$	$-1$
3.5_197.4t5.1c1	$3$	$ 5 \cdot 197 $	x^4 - x^3 + 2x^2 - 3x + 2	$S_4$	$1$	$-1$
3.2e2_13_19.6t11.1c1	$3$	$ 2^{2} \cdot 13 \cdot 19 $	x^6 - x^5 + x^3 - x - 1	$S_4\times C_2$	$1$	$1$
3.23_43.6t11.2c1	$3$	$ 23 \cdot 43 $	x^6 - x^5 - 2x^3 + x^2 + x + 1	$S_4\times C_2$	$1$	$-1$
3.17_59.6t11.1c1	$3$	$ 17 \cdot 59 $	x^6 - x^4 - x^3 + x^2 - 1	$S_4\times C_2$	$1$	$1$
3.2e3_127.4t5.1c1	$3$	$ 2^{3} \cdot 127 $	x^4 - x^3 + x^2 - 2x + 2	$S_4$	$1$	$-1$
3.2e2_269.4t5.1c1	$3$	$ 2^{2} \cdot 269 $	x^4 - x^3 + 3x^2 - 3x + 2	$S_4$	$1$	$-1$
3.7_157.4t5.1c1	$3$	$ 7 \cdot 157 $	x^4 - x^3 + x^2 - 3x + 1	$S_4$	$1$	$1$
3.3_367.6t11.1c1	$3$	$ 3 \cdot 367 $	x^6 - x^4 + 2x^2 + 3	$S_4\times C_2$	$1$	$-1$
3.3e3_41.4t5.1c1	$3$	$ 3^{3} \cdot 41 $	x^4 - x^3 - 2x - 1	$S_4$	$1$	$1$
3.2e3_139.6t11.2c1	$3$	$ 2^{3} \cdot 139 $	x^6 - x^5 + 4x^4 - 3x^3 + 3x^2 - 2x + 2	$S_4\times C_2$	$1$	$-1$
3.1129.4t5.1c1	$3$	$ 1129 $	x^4 - x^3 - x + 2	$S_4$	$1$	$-1$
3.3_379.6t11.2c1	$3$	$ 3 \cdot 379 $	x^6 - 3x^5 + 4x^4 - 3x^3 + 2x^2 - x + 4	$S_4\times C_2$	$1$	$-1$
3.31_37.6t11.1c1	$3$	$ 31 \cdot 37 $	x^6 - 2x^4 - x^3 + 2x^2 - 1	$S_4\times C_2$	$1$	$1$
3.2e3_149.4t5.1c1	$3$	$ 2^{3} \cdot 149 $	x^4 - x^3 + 2x^2 + x - 1	$S_4$	$1$	$1$