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 926)

Galois conjugate representations are grouped into single lines.

Label	Dimension	Conductor	Defining polynomial of Artin field	$G$	Ind	$\chi(c)$
7.29e6.8t25.1c1	$7$	$ 29^{6}$	x^8 - 3x^7 + 9x^6 - 15x^5 + 23x^4 - 21x^3 + 18x^2 - 7x + 2	$C_2^3:C_7$	$1$	$-1$
7.2e6_73e4.8t36.1c1	$7$	$ 2^{6} \cdot 73^{4}$	x^8 - x^7 + 6x^6 - 2x^5 + 12x^4 + 4x^3 + 14x^2 + 2	$C_2^3:(C_7: C_3)$	$1$	$-1$
7.313e4.8t36.2c1	$7$	$ 313^{4}$	x^8 - x^7 + x^6 + 3x^5 + 5x^4 - 5x^3 + 7x + 9	$C_2^3:(C_7: C_3)$	$1$	$-1$
7.313e4.8t36.1c1	$7$	$ 313^{4}$	x^8 - x^7 - x^6 - 4x^5 + x^4 + 11x^3 + 16x^2 + 5x + 1	$C_2^3:(C_7: C_3)$	$1$	$-1$
7.2e6_7e10.8t36.1c1	$7$	$ 2^{6} \cdot 7^{10}$	x^8 - x^7 + 7x^6 + 7x^5 + 7x^4 + 7x^3 + 7x^2 + 5x + 2	$C_2^3:(C_7: C_3)$	$1$	$-1$
7.2e8_3e6_7e6.16t713.1c1	$7$	$ 2^{8} \cdot 3^{6} \cdot 7^{6}$	x^8 - 4x^7 + 21x^4 - 18x + 9	$\PGL(2,7)$	$1$	$-1$
7.2e10_73e4.8t36.1c1	$7$	$ 2^{10} \cdot 73^{4}$	x^8 - 2x^7 + 8x^6 - 2x^5 + 14x^4 + 10x^3 + 28x^2 + 10x + 1	$C_2^3:(C_7: C_3)$	$1$	$-1$
7.2e6_5e4_7e7.8t43.1c1	$7$	$ 2^{6} \cdot 5^{4} \cdot 7^{7}$	x^8 - 3x^7 + 14x^4 - 14x^2 - 10x + 2	$\PGL(2,7)$	$1$	$1$
7.3e8_7e8.8t37.1c1	$7$	$ 3^{8} \cdot 7^{8}$	x^7 - 7x^4 - 21x^3 + 21x^2 + 42x - 9	$\GL(3,2)$	$1$	$-1$
7.2e6_3e4_53e4.8t37.1c1	$7$	$ 2^{6} \cdot 3^{4} \cdot 53^{4}$	x^7 - 2x^6 - 4x^5 + 10x^3 + 4x^2 - 10x - 6	$\GL(3,2)$	$1$	$-1$
7.2e8_7e10.8t36.1c1	$7$	$ 2^{8} \cdot 7^{10}$	x^8 - 4x^7 + 14x^6 - 14x^5 + 14x^4 + 28x^3 + 14x^2 - 2x + 1	$C_2^3:(C_7: C_3)$	$1$	$-1$
7.2e8_7e10.56.1c1	$7$	$ 2^{8} \cdot 7^{10}$	x^9 - x^8 - 4x^7 + 28x^3 + 26x^2 + 9x + 1	$\mathrm{P}\Gamma\mathrm{L}(2,8)$	$1$	$-1$
7.2e6_3e6_11e6.8t37.1c1	$7$	$ 2^{6} \cdot 3^{6} \cdot 11^{6}$	x^7 - x^6 - 9x^5 - x^4 + 19x^3 + 21x^2 - 23x - 13	$\GL(3,2)$	$1$	$-1$
7.3e4_5e4_11e6.8t37.1c1	$7$	$ 3^{4} \cdot 5^{4} \cdot 11^{6}$	x^7 - x^6 - 9x^5 + 21x^4 - 3x^3 - 23x^2 + 10x + 9	$\GL(3,2)$	$1$	$-1$
7.2e6_199e4.8t36.1c1	$7$	$ 2^{6} \cdot 199^{4}$	x^8 - 3x^7 + 4x^6 - 16x^5 + 46x^4 - 70x^3 + 82x^2 - 48x + 22	$C_2^3:(C_7: C_3)$	$1$	$-1$
7.2e16_11e6.8t37.1c1	$7$	$ 2^{16} \cdot 11^{6}$	x^7 - x^6 + 2x^5 - 12x^4 - 14x^3 + 10x^2 + 10x - 2	$\GL(3,2)$	$1$	$-1$
7.2e12_73e4.8t36.2c1	$7$	$ 2^{12} \cdot 73^{4}$	x^8 - 2x^7 + 10x^6 - 6x^5 + 2x^4 + 8x^3 - 16x^2 + 16x + 26	$C_2^3:(C_7: C_3)$	$1$	$-1$
7.2e12_73e4.8t36.1c1	$7$	$ 2^{12} \cdot 73^{4}$	x^8 - 2x^7 - 4x^6 - 8x^5 + 56x^4 - 54x^3 + 20x^2 - 4x + 1	$C_2^3:(C_7: C_3)$	$1$	$-1$
7.2e8_3e4_7e8.8t37.1c1	$7$	$ 2^{8} \cdot 3^{4} \cdot 7^{8}$	x^7 - 7x^5 + 21x^3 - 14x^2 - 7x + 4	$\GL(3,2)$	$1$	$-1$
7.2e6_7e11.24t283.1c1 7.2e6_7e11.24t283.1c2	$7$	$ 2^{6} \cdot 7^{11}$	x^8 - x^7 + 7x^6 + 7x^5 + 7x^4 + 7x^3 + 7x^2 + 5x + 2	$C_2^3:(C_7: C_3)$	$0$	$-1$
7.2e6_73e5.24t283.1c1 7.2e6_73e5.24t283.1c2	$7$	$ 2^{6} \cdot 73^{5}$	x^8 - x^7 + 6x^6 - 2x^5 + 12x^4 + 4x^3 + 14x^2 + 2	$C_2^3:(C_7: C_3)$	$0$	$-1$
7.2e16_1423e2.8t48.1c1	$7$	$ 2^{16} \cdot 1423^{2}$	x^8 - 10x^6 - 4x^5 + 27x^4 + 20x^3 - 10x^2 - 8x - 1	$C_2^3:\GL(3,2)$	$1$	$7$
7.2e8_3e6_7e7.8t43.1c1	$7$	$ 2^{8} \cdot 3^{6} \cdot 7^{7}$	x^8 - 4x^7 + 21x^4 - 18x + 9	$\PGL(2,7)$	$1$	$1$
7.2e4_5e6_7e7.8t43.1c1	$7$	$ 2^{4} \cdot 5^{6} \cdot 7^{7}$	x^8 - 4x^7 + 35x^4 - 50x + 25	$\PGL(2,7)$	$1$	$1$
7.2e6_5e4_7e8.16t713.1c1	$7$	$ 2^{6} \cdot 5^{4} \cdot 7^{8}$	x^8 - 3x^7 + 14x^4 - 14x^2 - 10x + 2	$\PGL(2,7)$	$1$	$-1$
7.2e6_7e4_11e6.8t36.1c1	$7$	$ 2^{6} \cdot 7^{4} \cdot 11^{6}$	x^8 - x^7 - 9x^6 - x^5 + 41x^4 + 21x^3 - 67x^2 - 35x + 66	$C_2^3:(C_7: C_3)$	$1$	$-1$
7.2e6_7e4_11e6.8t36.2c1	$7$	$ 2^{6} \cdot 7^{4} \cdot 11^{6}$	x^8 - 3x^7 + 9x^6 - 21x^5 + 33x^4 - 69x^3 + 7x^2 - 7x + 238	$C_2^3:(C_7: C_3)$	$1$	$-1$
7.2e8_5e4_11e6.8t37.1c1	$7$	$ 2^{8} \cdot 5^{4} \cdot 11^{6}$	x^7 - x^6 - 9x^5 - x^4 + 8x^3 - 12x^2 - 12x - 2	$\GL(3,2)$	$1$	$-1$
7.2e6_3e8_7e7.8t43.1c1	$7$	$ 2^{6} \cdot 3^{8} \cdot 7^{7}$	x^8 - 3x^7 + 14x^5 - 84x^3 + 112x^2 - 24x - 12	$\PGL(2,7)$	$1$	$1$
7.3e6_5e4_7e7.8t43.1c1	$7$	$ 3^{6} \cdot 5^{4} \cdot 7^{7}$	x^8 - 4x^7 - 21x^4 - 21x^2 - 15x - 3	$\PGL(2,7)$	$1$	$1$
7.2e16_7e8.8t37.1c1	$7$	$ 2^{16} \cdot 7^{8}$	x^7 - 7x^5 - 14x^4 - 7x^3 - 7x + 2	$\GL(3,2)$	$1$	$-1$
7.2e6_3e8_31e4.8t36.1c1	$7$	$ 2^{6} \cdot 3^{8} \cdot 31^{4}$	x^8 + 4x^6 - 14x^5 + 6x^4 + 16x^3 + 32x^2 + 18x + 8	$C_2^3:(C_7: C_3)$	$1$	$-1$
7.2e8_199e4.8t36.1c1	$7$	$ 2^{8} \cdot 199^{4}$	x^8 - 2x^7 + 4x^6 - 4x^5 - 8x^4 + 4x^3 + 16x^2 - 14x + 6	$C_2^3:(C_7: C_3)$	$1$	$-1$
7.2e8_199e4.8t36.2c1	$7$	$ 2^{8} \cdot 199^{4}$	x^8 - 2x^7 - 4x^6 + 4x^5 + 12x^4 - 16x^3 + 68x + 52	$C_2^3:(C_7: C_3)$	$1$	$-1$
7.2e8_7e11.24t283.1c1 7.2e8_7e11.24t283.1c2	$7$	$ 2^{8} \cdot 7^{11}$	x^8 - 4x^7 + 14x^6 - 14x^5 + 14x^4 + 28x^3 + 14x^2 - 2x + 1	$C_2^3:(C_7: C_3)$	$0$	$-1$
7.2e8_7e11.168.1c1 7.2e8_7e11.168.1c2	$7$	$ 2^{8} \cdot 7^{11}$	x^9 - x^8 - 4x^7 + 28x^3 + 26x^2 + 9x + 1	$\mathrm{P}\Gamma\mathrm{L}(2,8)$	$0$	$-1$
7.2e6_7e4_43e4.8t36.2c1	$7$	$ 2^{6} \cdot 7^{4} \cdot 43^{4}$	x^8 - 2x^7 + 2x^6 - 12x^5 + 64x^4 - 184x^3 + 296x^2 - 280x + 128	$C_2^3:(C_7: C_3)$	$1$	$-1$
7.2e6_7e4_43e4.8t36.3c1	$7$	$ 2^{6} \cdot 7^{4} \cdot 43^{4}$	x^8 - 2x^7 + 14x^6 - 38x^5 + 100x^4 - 198x^3 + 338x^2 - 322x + 139	$C_2^3:(C_7: C_3)$	$1$	$-1$
7.2e6_7e4_43e4.8t36.1c1	$7$	$ 2^{6} \cdot 7^{4} \cdot 43^{4}$	x^8 - 2x^7 + 2x^6 + 20x^5 + 20x^4 + 56x^2 + 52x + 40	$C_2^3:(C_7: C_3)$	$1$	$-1$
7.877e4.8t36.2c1	$7$	$ 877^{4}$	x^8 - 2x^7 - 2x^6 + 7x^5 + 3x^4 - 34x^3 + 93x^2 - 29x + 39	$C_2^3:(C_7: C_3)$	$1$	$-1$
7.877e4.8t36.1c1	$7$	$ 877^{4}$	x^8 - x^7 + 11x^6 - 13x^5 + 16x^4 - 10x^3 + 17x^2 - 7x + 4	$C_2^3:(C_7: C_3)$	$1$	$-1$
7.2e6_317e4.8t37.1c1	$7$	$ 2^{6} \cdot 317^{4}$	x^7 - 2x^6 + 2x^4 - 2x^3 + 2x^2 - 2	$\GL(3,2)$	$1$	$-1$
7.2e14_3e16.56.1c1 7.2e14_3e16.56.1c2 7.2e14_3e16.56.1c3	$7$	$ 2^{14} \cdot 3^{16}$	x^9 - 12x^6 - 18x^5 + 36x^2 - 27x - 128	$\PSL(2,8)$	$1$	$-1$
7.3e4_313e4.8t36.2c1	$7$	$ 3^{4} \cdot 313^{4}$	x^8 - 3x^7 + 9x^6 - 19x^5 + 35x^4 - 39x^3 + 19x^2 - 4x + 4	$C_2^3:(C_7: C_3)$	$1$	$-1$
7.3e4_313e4.8t36.1c1	$7$	$ 3^{4} \cdot 313^{4}$	x^8 - 9x^6 - 4x^5 + 24x^4 + 21x^3 + 22x^2 - 3x + 3	$C_2^3:(C_7: C_3)$	$1$	$-1$
7.2e6_5e4_73e4.8t36.1c1	$7$	$ 2^{6} \cdot 5^{4} \cdot 73^{4}$	x^8 - 2x^7 + 16x^6 - 20x^5 + 56x^4 - 56x^3 + 80x^2 - 80x + 64	$C_2^3:(C_7: C_3)$	$1$	$-1$
7.2e12_7e10.8t36.2c1	$7$	$ 2^{12} \cdot 7^{10}$	x^8 - 2x^7 + 28x^4 - 14x^3 - 56x^2 + 40x + 53	$C_2^3:(C_7: C_3)$	$1$	$-1$
7.2e12_7e10.8t36.1c1	$7$	$ 2^{12} \cdot 7^{10}$	x^8 - 4x^7 + 14x^6 - 14x^5 + 14x^4 + 28x^3 + 14x^2 - 18x + 23	$C_2^3:(C_7: C_3)$	$1$	$-1$
7.3e6_5e6_7e6.16t713.1c1	$7$	$ 3^{6} \cdot 5^{6} \cdot 7^{6}$	x^8 - x^7 + 7x^6 - 28x^5 + 70x^4 - 112x^3 + 112x^2 - 64x + 1	$\PGL(2,7)$	$1$	$-1$
7.2e4_5e6_7e8.16t713.1c1	$7$	$ 2^{4} \cdot 5^{6} \cdot 7^{8}$	x^8 - 4x^7 + 35x^4 - 50x + 25	$\PGL(2,7)$	$1$	$-1$