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	$\chi(c)$
1.1.1t1.1c1	$1$	$1$	x	Trivial	$1$	$1$
1.3.2t1.1c1	$1$	$ 3 $	x^2 - x + 1	$C_2$	$1$	$-1$
1.2e2.2t1.1c1	$1$	$ 2^{2}$	x^2 + 1	$C_2$	$1$	$-1$
1.5.2t1.1c1	$1$	$ 5 $	x^2 - x - 1	$C_2$	$1$	$1$
1.5.4t1.1c1 1.5.4t1.1c2	$1$	$ 5 $	x^4 - x^3 + x^2 - x + 1	$C_4$	$0$	$-1$
1.7.2t1.1c1	$1$	$ 7 $	x^2 - x + 2	$C_2$	$1$	$-1$
1.7.3t1.1c1 1.7.3t1.1c2	$1$	$ 7 $	x^3 - x^2 - 2x + 1	$C_3$	$0$	$1$
1.7.6t1.1c1 1.7.6t1.1c2	$1$	$ 7 $	x^6 - x^5 + x^4 - x^3 + x^2 - x + 1	$C_6$	$0$	$-1$
1.2e3.2t1.2c1	$1$	$ 2^{3}$	x^2 + 2	$C_2$	$1$	$-1$
1.2e3.2t1.1c1	$1$	$ 2^{3}$	x^2 - 2	$C_2$	$1$	$1$
1.3e2.3t1.1c1 1.3e2.3t1.1c2	$1$	$ 3^{2}$	x^3 - 3x - 1	$C_3$	$0$	$1$
1.3e2.6t1.1c1 1.3e2.6t1.1c2	$1$	$ 3^{2}$	x^6 - x^3 + 1	$C_6$	$0$	$-1$
1.11.2t1.1c1	$1$	$ 11 $	x^2 - x + 3	$C_2$	$1$	$-1$
1.11.5t1.1c1 1.11.5t1.1c2 1.11.5t1.1c3 1.11.5t1.1c4	$1$	$ 11 $	x^5 - x^4 - 4x^3 + 3x^2 + 3x - 1	$C_5$	$0$	$1$
1.11.10t1.1c1 1.11.10t1.1c2 1.11.10t1.1c3 1.11.10t1.1c4	$1$	$ 11 $	x^10 - x^9 + x^8 - x^7 + x^6 - x^5 + x^4 - x^3 + x^2 - x + 1	$C_{10}$	$0$	$-1$
1.2e2_3.2t1.1c1	$1$	$ 2^{2} \cdot 3 $	x^2 - 3	$C_2$	$1$	$1$
1.13.2t1.1c1	$1$	$ 13 $	x^2 - x - 3	$C_2$	$1$	$1$
1.13.3t1.1c1 1.13.3t1.1c2	$1$	$ 13 $	x^3 - x^2 - 4x - 1	$C_3$	$0$	$1$
1.13.4t1.1c1 1.13.4t1.1c2	$1$	$ 13 $	x^4 - x^3 + 2x^2 + 4x + 3	$C_4$	$0$	$-1$
1.13.6t1.1c1 1.13.6t1.1c2	$1$	$ 13 $	x^6 - x^5 - 5x^4 + 4x^3 + 6x^2 - 3x - 1	$C_6$	$0$	$1$
1.3_5.2t1.1c1	$1$	$ 3 \cdot 5 $	x^2 - x + 4	$C_2$	$1$	$-1$
1.3_5.4t1.1c1 1.3_5.4t1.1c2	$1$	$ 3 \cdot 5 $	x^4 - x^3 - 4x^2 + 4x + 1	$C_4$	$0$	$1$
1.2e4.4t1.1c1 1.2e4.4t1.1c2	$1$	$ 2^{4}$	x^4 - 4x^2 + 2	$C_4$	$0$	$1$
1.2e4.4t1.2c1 1.2e4.4t1.2c2	$1$	$ 2^{4}$	x^4 + 4x^2 + 2	$C_4$	$0$	$-1$
1.17.2t1.1c1	$1$	$ 17 $	x^2 - x - 4	$C_2$	$1$	$1$
1.17.4t1.1c1 1.17.4t1.1c2	$1$	$ 17 $	x^4 - x^3 - 6x^2 + x + 1	$C_4$	$0$	$1$
1.17.8t1.1c1 1.17.8t1.1c2 1.17.8t1.1c3 1.17.8t1.1c4	$1$	$ 17 $	x^8 - x^7 - 7x^6 + 6x^5 + 15x^4 - 10x^3 - 10x^2 + 4x + 1	$C_8$	$0$	$1$
1.19.2t1.1c1	$1$	$ 19 $	x^2 - x + 5	$C_2$	$1$	$-1$
1.19.3t1.1c1 1.19.3t1.1c2	$1$	$ 19 $	x^3 - x^2 - 6x + 7	$C_3$	$0$	$1$
1.19.6t1.1c1 1.19.6t1.1c2	$1$	$ 19 $	x^6 - x^5 + 2x^4 + 8x^3 - x^2 - 5x + 7	$C_6$	$0$	$-1$
1.19.9t1.1c1 1.19.9t1.1c2 1.19.9t1.1c3 1.19.9t1.1c4 1.19.9t1.1c5 1.19.9t1.1c6	$1$	$ 19 $	x^9 - x^8 - 8x^7 + 7x^6 + 21x^5 - 15x^4 - 20x^3 + 10x^2 + 5x - 1	$C_9$	$0$	$1$
1.2e2_5.2t1.1c1	$1$	$ 2^{2} \cdot 5 $	x^2 + 5	$C_2$	$1$	$-1$
1.2e2_5.4t1.1c1 1.2e2_5.4t1.1c2	$1$	$ 2^{2} \cdot 5 $	x^4 - 5x^2 + 5	$C_4$	$0$	$1$
1.3_7.2t1.1c1	$1$	$ 3 \cdot 7 $	x^2 - x - 5	$C_2$	$1$	$1$
1.3_7.6t1.2c1 1.3_7.6t1.2c2	$1$	$ 3 \cdot 7 $	x^6 - x^5 + 3x^4 + 5x^2 - 2x + 1	$C_6$	$0$	$-1$
1.3_7.6t1.1c1 1.3_7.6t1.1c2	$1$	$ 3 \cdot 7 $	x^6 - x^5 - 6x^4 + 6x^3 + 8x^2 - 8x + 1	$C_6$	$0$	$1$
1.23.2t1.1c1	$1$	$ 23 $	x^2 - x + 6	$C_2$	$1$	$-1$
1.23.11t1.1c1 1.23.11t1.1c2 1.23.11t1.1c3 1.23.11t1.1c4 1.23.11t1.1c5 1.23.11t1.1c6 1.23.11t1.1c7 1.23.11t1.1c8 1.23.11t1.1c9 1.23.11t1.1c10	$1$	$ 23 $	x^11 - x^10 - 10x^9 + 9x^8 + 36x^7 - 28x^6 - 56x^5 + 35x^4 + 35x^3 - 15x^2 - 6x + 1	$C_{11}$	$0$	$1$
1.23.22t1.1c1 1.23.22t1.1c2 1.23.22t1.1c3 1.23.22t1.1c4 1.23.22t1.1c5 1.23.22t1.1c6 1.23.22t1.1c7 1.23.22t1.1c8 1.23.22t1.1c9 1.23.22t1.1c10	$1$	$ 23 $	x^22 - x^21 + x^20 - x^19 + x^18 - x^17 + x^16 - x^15 + x^14 - x^13 + x^12 - x^11 + x^10 - x^9 + x^8 - x^7 + x^6 - x^5 + x^4 - x^3 + x^2 - x + 1	22T1	$0$	$-1$
1.2e3_3.2t1.2c1	$1$	$ 2^{3} \cdot 3 $	x^2 + 6	$C_2$	$1$	$-1$
1.2e3_3.2t1.1c1	$1$	$ 2^{3} \cdot 3 $	x^2 - 6	$C_2$	$1$	$1$
1.5e2.5t1.1c1 1.5e2.5t1.1c2 1.5e2.5t1.1c3 1.5e2.5t1.1c4	$1$	$ 5^{2}$	x^5 - 10x^3 - 5x^2 + 10x - 1	$C_5$	$0$	$1$
1.3e3.9t1.1c1 1.3e3.9t1.1c2 1.3e3.9t1.1c3 1.3e3.9t1.1c4 1.3e3.9t1.1c5 1.3e3.9t1.1c6	$1$	$ 3^{3}$	x^9 - 9x^7 + 27x^5 - 30x^3 + 9x - 1	$C_9$	$0$	$1$
1.3e3.18t1.1c1 1.3e3.18t1.1c2 1.3e3.18t1.1c3 1.3e3.18t1.1c4 1.3e3.18t1.1c5 1.3e3.18t1.1c6	$1$	$ 3^{3}$	x^18 - x^9 + 1	$C_{18}$	$0$	$-1$
1.2e2_7.2t1.1c1	$1$	$ 2^{2} \cdot 7 $	x^2 - 7	$C_2$	$1$	$1$
1.2e2_7.6t1.2c1 1.2e2_7.6t1.2c2	$1$	$ 2^{2} \cdot 7 $	x^6 + 5x^4 + 6x^2 + 1	$C_6$	$0$	$-1$
1.2e2_7.6t1.1c1 1.2e2_7.6t1.1c2	$1$	$ 2^{2} \cdot 7 $	x^6 - 7x^4 + 14x^2 - 7	$C_6$	$0$	$1$
1.29.2t1.1c1	$1$	$ 29 $	x^2 - x - 7	$C_2$	$1$	$1$
1.29.4t1.1c1 1.29.4t1.1c2	$1$	$ 29 $	x^4 - x^3 + 4x^2 - 20x + 23	$C_4$	$0$	$-1$
1.29.7t1.1c1 1.29.7t1.1c2 1.29.7t1.1c3 1.29.7t1.1c4 1.29.7t1.1c5 1.29.7t1.1c6	$1$	$ 29 $	x^7 - x^6 - 12x^5 + 7x^4 + 28x^3 - 14x^2 - 9x - 1	$C_7$	$0$	$1$