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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}$ x8 - 3x7 + 9x6 - 15x5 + 23x4 - 21x3 + 18x2 - 7x + 2 $C_2^3:C_7$ $1$ $-1$
7.2e6_73e4.8t36.1c1 $7$ $ 2^{6} \cdot 73^{4}$ x8 - x7 + 6x6 - 2x5 + 12x4 + 4x3 + 14x2 + 2 $C_2^3:(C_7: C_3)$ $1$ $-1$
7.313e4.8t36.1c1 $7$ $ 313^{4}$ x8 - x7 - x6 - 4x5 + x4 + 11x3 + 16x2 + 5x + 1 $C_2^3:(C_7: C_3)$ $1$ $-1$
7.313e4.8t36.2c1 $7$ $ 313^{4}$ x8 - x7 + x6 + 3x5 + 5x4 - 5x3 + 7x + 9 $C_2^3:(C_7: C_3)$ $1$ $-1$
7.2e6_7e10.8t36.1c1 $7$ $ 2^{6} \cdot 7^{10}$ x8 - x7 + 7x6 + 7x5 + 7x4 + 7x3 + 7x2 + 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}$ x8 - 4x7 + 21x4 - 18x + 9 $\PGL(2,7)$ $1$ $-1$
7.2e10_73e4.8t36.1c1 $7$ $ 2^{10} \cdot 73^{4}$ x8 - 2x7 + 8x6 - 2x5 + 14x4 + 10x3 + 28x2 + 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}$ x8 - 3x7 + 14x4 - 14x2 - 10x + 2 $\PGL(2,7)$ $1$ $1$
7.3e8_7e8.8t37.1c1 $7$ $ 3^{8} \cdot 7^{8}$ x7 - 7x4 - 21x3 + 21x2 + 42x - 9 $\GL(3,2)$ $1$ $-1$
7.2e6_3e4_53e4.8t37.1c1 $7$ $ 2^{6} \cdot 3^{4} \cdot 53^{4}$ x7 - 2x6 - 4x5 + 10x3 + 4x2 - 10x - 6 $\GL(3,2)$ $1$ $-1$
7.2e8_7e10.8t36.1c1 $7$ $ 2^{8} \cdot 7^{10}$ x8 - 4x7 + 14x6 - 14x5 + 14x4 + 28x3 + 14x2 - 2x + 1 $C_2^3:(C_7: C_3)$ $1$ $-1$
7.2e8_7e10.56.1c1 $7$ $ 2^{8} \cdot 7^{10}$ x9 - x8 - 4x7 + 28x3 + 26x2 + 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}$ x7 - x6 - 9x5 - x4 + 19x3 + 21x2 - 23x - 13 $\GL(3,2)$ $1$ $-1$
7.3e4_5e4_11e6.8t37.1c1 $7$ $ 3^{4} \cdot 5^{4} \cdot 11^{6}$ x7 - x6 - 9x5 + 21x4 - 3x3 - 23x2 + 10x + 9 $\GL(3,2)$ $1$ $-1$
7.2e6_199e4.8t36.1c1 $7$ $ 2^{6} \cdot 199^{4}$ x8 - 3x7 + 4x6 - 16x5 + 46x4 - 70x3 + 82x2 - 48x + 22 $C_2^3:(C_7: C_3)$ $1$ $-1$
7.2e16_11e6.8t37.1c1 $7$ $ 2^{16} \cdot 11^{6}$ x7 - x6 + 2x5 - 12x4 - 14x3 + 10x2 + 10x - 2 $\GL(3,2)$ $1$ $-1$
7.2e12_73e4.8t36.1c1 $7$ $ 2^{12} \cdot 73^{4}$ x8 - 2x7 - 4x6 - 8x5 + 56x4 - 54x3 + 20x2 - 4x + 1 $C_2^3:(C_7: C_3)$ $1$ $-1$
7.2e12_73e4.8t36.2c1 $7$ $ 2^{12} \cdot 73^{4}$ x8 - 2x7 + 10x6 - 6x5 + 2x4 + 8x3 - 16x2 + 16x + 26 $C_2^3:(C_7: C_3)$ $1$ $-1$
7.2e8_3e4_7e8.8t37.1c1 $7$ $ 2^{8} \cdot 3^{4} \cdot 7^{8}$ x7 - 7x5 + 21x3 - 14x2 - 7x + 4 $\GL(3,2)$ $1$ $-1$
7.2e6_7e11.24t283.1c1 7.2e6_7e11.24t283.1c2 $7$ $ 2^{6} \cdot 7^{11}$ x8 - x7 + 7x6 + 7x5 + 7x4 + 7x3 + 7x2 + 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}$ x8 - x7 + 6x6 - 2x5 + 12x4 + 4x3 + 14x2 + 2 $C_2^3:(C_7: C_3)$ $0$ $-1$
7.2e16_1423e2.8t48.1c1 $7$ $ 2^{16} \cdot 1423^{2}$ x8 - 10x6 - 4x5 + 27x4 + 20x3 - 10x2 - 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}$ x8 - 4x7 + 21x4 - 18x + 9 $\PGL(2,7)$ $1$ $1$
7.2e4_5e6_7e7.8t43.1c1 $7$ $ 2^{4} \cdot 5^{6} \cdot 7^{7}$ x8 - 4x7 + 35x4 - 50x + 25 $\PGL(2,7)$ $1$ $1$
7.2e6_5e4_7e8.16t713.1c1 $7$ $ 2^{6} \cdot 5^{4} \cdot 7^{8}$ x8 - 3x7 + 14x4 - 14x2 - 10x + 2 $\PGL(2,7)$ $1$ $-1$
7.2e6_7e4_11e6.8t36.1c1 $7$ $ 2^{6} \cdot 7^{4} \cdot 11^{6}$ x8 - x7 - 9x6 - x5 + 41x4 + 21x3 - 67x2 - 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}$ x8 - 3x7 + 9x6 - 21x5 + 33x4 - 69x3 + 7x2 - 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}$ x7 - x6 - 9x5 - x4 + 8x3 - 12x2 - 12x - 2 $\GL(3,2)$ $1$ $-1$
7.2e6_3e8_7e7.8t43.1c1 $7$ $ 2^{6} \cdot 3^{8} \cdot 7^{7}$ x8 - 3x7 + 14x5 - 84x3 + 112x2 - 24x - 12 $\PGL(2,7)$ $1$ $1$
7.3e6_5e4_7e7.8t43.1c1 $7$ $ 3^{6} \cdot 5^{4} \cdot 7^{7}$ x8 - 4x7 - 21x4 - 21x2 - 15x - 3 $\PGL(2,7)$ $1$ $1$
7.2e16_7e8.8t37.1c1 $7$ $ 2^{16} \cdot 7^{8}$ x7 - 7x5 - 14x4 - 7x3 - 7x + 2 $\GL(3,2)$ $1$ $-1$
7.2e6_3e8_31e4.8t36.1c1 $7$ $ 2^{6} \cdot 3^{8} \cdot 31^{4}$ x8 + 4x6 - 14x5 + 6x4 + 16x3 + 32x2 + 18x + 8 $C_2^3:(C_7: C_3)$ $1$ $-1$
7.2e8_199e4.8t36.1c1 $7$ $ 2^{8} \cdot 199^{4}$ x8 - 2x7 + 4x6 - 4x5 - 8x4 + 4x3 + 16x2 - 14x + 6 $C_2^3:(C_7: C_3)$ $1$ $-1$
7.2e8_199e4.8t36.2c1 $7$ $ 2^{8} \cdot 199^{4}$ x8 - 2x7 - 4x6 + 4x5 + 12x4 - 16x3 + 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}$ x8 - 4x7 + 14x6 - 14x5 + 14x4 + 28x3 + 14x2 - 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}$ x9 - x8 - 4x7 + 28x3 + 26x2 + 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}$ x8 - 2x7 + 2x6 - 12x5 + 64x4 - 184x3 + 296x2 - 280x + 128 $C_2^3:(C_7: C_3)$ $1$ $-1$
7.2e6_7e4_43e4.8t36.1c1 $7$ $ 2^{6} \cdot 7^{4} \cdot 43^{4}$ x8 - 2x7 + 2x6 + 20x5 + 20x4 + 56x2 + 52x + 40 $C_2^3:(C_7: C_3)$ $1$ $-1$
7.2e6_7e4_43e4.8t36.3c1 $7$ $ 2^{6} \cdot 7^{4} \cdot 43^{4}$ x8 - 2x7 + 14x6 - 38x5 + 100x4 - 198x3 + 338x2 - 322x + 139 $C_2^3:(C_7: C_3)$ $1$ $-1$
7.877e4.8t36.2c1 $7$ $ 877^{4}$ x8 - 2x7 - 2x6 + 7x5 + 3x4 - 34x3 + 93x2 - 29x + 39 $C_2^3:(C_7: C_3)$ $1$ $-1$
7.877e4.8t36.1c1 $7$ $ 877^{4}$ x8 - x7 + 11x6 - 13x5 + 16x4 - 10x3 + 17x2 - 7x + 4 $C_2^3:(C_7: C_3)$ $1$ $-1$
7.2e6_317e4.8t37.1c1 $7$ $ 2^{6} \cdot 317^{4}$ x7 - 2x6 + 2x4 - 2x3 + 2x2 - 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}$ x9 - 12x6 - 18x5 + 36x2 - 27x - 128 $\PSL(2,8)$ $1$ $-1$
7.3e4_313e4.8t36.1c1 $7$ $ 3^{4} \cdot 313^{4}$ x8 - 9x6 - 4x5 + 24x4 + 21x3 + 22x2 - 3x + 3 $C_2^3:(C_7: C_3)$ $1$ $-1$
7.3e4_313e4.8t36.2c1 $7$ $ 3^{4} \cdot 313^{4}$ x8 - 3x7 + 9x6 - 19x5 + 35x4 - 39x3 + 19x2 - 4x + 4 $C_2^3:(C_7: C_3)$ $1$ $-1$
7.2e6_5e4_73e4.8t36.1c1 $7$ $ 2^{6} \cdot 5^{4} \cdot 73^{4}$ x8 - 2x7 + 16x6 - 20x5 + 56x4 - 56x3 + 80x2 - 80x + 64 $C_2^3:(C_7: C_3)$ $1$ $-1$
7.2e12_7e10.8t36.1c1 $7$ $ 2^{12} \cdot 7^{10}$ x8 - 4x7 + 14x6 - 14x5 + 14x4 + 28x3 + 14x2 - 18x + 23 $C_2^3:(C_7: C_3)$ $1$ $-1$
7.2e12_7e10.8t36.2c1 $7$ $ 2^{12} \cdot 7^{10}$ x8 - 2x7 + 28x4 - 14x3 - 56x2 + 40x + 53 $C_2^3:(C_7: C_3)$ $1$ $-1$
7.3e6_5e6_7e6.16t713.1c1 $7$ $ 3^{6} \cdot 5^{6} \cdot 7^{6}$ x8 - x7 + 7x6 - 28x5 + 70x4 - 112x3 + 112x2 - 64x + 1 $\PGL(2,7)$ $1$ $-1$
7.2e4_5e6_7e8.16t713.1c1 $7$ $ 2^{4} \cdot 5^{6} \cdot 7^{8}$ x8 - 4x7 + 35x4 - 50x + 25 $\PGL(2,7)$ $1$ $-1$
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