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	$\chi(c)$
8.5e2_7e4_131e2.12t213.1c1	$8$	$ 5^{2} \cdot 7^{4} \cdot 131^{2}$	x^9 - 4x^8 + 6x^7 - 2x^6 - 6x^5 + 8x^4 - 4x^2 + x - 1	$S_3\wr S_3$	$1$	$0$
8.3e4_7e2_11e2_47e2.12t213.1c1	$8$	$ 3^{4} \cdot 7^{2} \cdot 11^{2} \cdot 47^{2}$	x^9 + 9x^7 - 4x^6 + 27x^5 - 24x^4 + 31x^3 - 36x^2 + 12x + 11	$S_3\wr S_3$	$1$	$0$
8.2e10_1229e2.12t213.1c1	$8$	$ 2^{10} \cdot 1229^{2}$	x^9 - 2x^8 - x^7 - x^6 + 19x^5 - 41x^4 + 50x^3 - 35x^2 + 4x + 8	$S_3\wr S_3$	$1$	$0$
8.2e8_3e4_7e2_41e2.12t213.1c1	$8$	$ 2^{8} \cdot 3^{4} \cdot 7^{2} \cdot 41^{2}$	x^9 - x^8 + 6x^7 - 5x^6 + 7x^5 + 7x^4 + 16x^3 - 3x^2 - 6x + 2	$S_3\wr S_3$	$1$	$0$
8.7e4_19e2_53e2.12t213.1c1	$8$	$ 7^{4} \cdot 19^{2} \cdot 53^{2}$	x^9 - 3x^8 + 5x^7 - 2x^6 - 5x^5 + 8x^4 + 4x^3 - 4x^2 + 2x + 1	$S_3\wr S_3$	$1$	$0$
8.2e8_3e4_5e2_71e2.12t213.1c1	$8$	$ 2^{8} \cdot 3^{4} \cdot 5^{2} \cdot 71^{2}$	x^9 - x^8 + 4x^7 - 6x^6 + 8x^5 - 2x^4 + 4x^2 - x - 1	$S_3\wr S_3$	$1$	$0$
8.2e8_3e4_7e2_53e2.12t213.1c1	$8$	$ 2^{8} \cdot 3^{4} \cdot 7^{2} \cdot 53^{2}$	x^9 - 6x^7 + 20x^5 - 16x^4 - 4x^3 - 4x^2 + 20x - 12	$S_3\wr S_3$	$1$	$0$
8.2e14_499e2.12t213.1c1	$8$	$ 2^{14} \cdot 499^{2}$	x^9 - 2x^8 + 2x^7 + 3x^6 - 2x^5 - 10x^4 + 5x^3 + 14x^2 + 6x + 1	$S_3\wr S_3$	$1$	$0$
8.2e8_3e6_7e2_23e2.12t213.1c1	$8$	$ 2^{8} \cdot 3^{6} \cdot 7^{2} \cdot 23^{2}$	x^9 - 3x^8 + 4x^7 + 2x^5 - 2x^4 - 2x^3 + 4x^2 + x + 1	$S_3\wr S_3$	$1$	$0$
8.2e8_3e4_523e2.12t213.1c1	$8$	$ 2^{8} \cdot 3^{4} \cdot 523^{2}$	x^9 - 2x^8 + 6x^7 + 6x^6 - 14x^5 + 48x^4 - 6x^3 - 4x^2 + 4x + 42	$S_3\wr S_3$	$1$	$0$
8.11e6_61e2.12t213.1c1	$8$	$ 11^{6} \cdot 61^{2}$	x^9 - 3x^8 + 6x^7 - 4x^6 - x^5 + 7x^4 - 8x^3 - x^2 + 3x + 1	$S_3\wr S_3$	$1$	$0$
8.2e12_3e4_11e2_13e2.12t213.1c1	$8$	$ 2^{12} \cdot 3^{4} \cdot 11^{2} \cdot 13^{2}$	x^9 - x^8 + 3x^7 + x^6 - x^5 - x^4 - 4x^2 - 3x - 1	$S_3\wr S_3$	$1$	$0$
8.2e8_3e4_587e2.12t213.1c1	$8$	$ 2^{8} \cdot 3^{4} \cdot 587^{2}$	x^9 - 3x^8 - 4x^6 + 18x^5 + 6x^4 - 20x^3 - 8x^2 + x - 3	$S_3\wr S_3$	$1$	$0$
8.2e20_5e2_17e2.12t213.1c1	$8$	$ 2^{20} \cdot 5^{2} \cdot 17^{2}$	x^9 - 2x^8 + 5x^7 + 2x^6 + 2x^5 + 6x^4 + 2x^3 + 4x^2 + 8x + 4	$S_3\wr S_3$	$1$	$0$
8.3e10_367e2.12t213.1c1	$8$	$ 3^{10} \cdot 367^{2}$	x^9 - 2x^8 + x^7 - 2x^6 + 5x^5 + 5x^4 - 16x^3 + 7x^2 + 4x - 4	$S_3\wr S_3$	$1$	$0$
8.2e8_3e4_631e2.12t213.1c1	$8$	$ 2^{8} \cdot 3^{4} \cdot 631^{2}$	x^9 - 3x^8 + 2x^7 + 4x^6 - 22x^5 + 16x^4 + 26x^3 - 18x^2 - x + 1	$S_3\wr S_3$	$1$	$0$
8.2e20_3e2_31e2.12t213.1c1	$8$	$ 2^{20} \cdot 3^{2} \cdot 31^{2}$	x^9 + 4x^7 - 6x^6 + 13x^5 - 16x^4 + 18x^3 - 26x^2 + 16x - 8	$S_3\wr S_3$	$1$	$0$
8.3e12_131e2.12t213.1c1	$8$	$ 3^{12} \cdot 131^{2}$	x^9 - 3x^8 + 9x^7 + 21x^6 - 6x^5 + 72x^4 + 33x^3 + 60x^2 + 64	$S_3\wr S_3$	$1$	$0$
8.2e6_523e3.9t26.1c1	$8$	$ 2^{6} \cdot 523^{3}$	x^9 - x^7 - 5x^6 + x^5 + 2x^4 + 4x^3 - 3x^2 - x + 1	$((C_3^2:Q_8):C_3):C_2$	$1$	$2$
8.3e10_397e2.12t213.1c1	$8$	$ 3^{10} \cdot 397^{2}$	x^9 - 4x^8 + 7x^7 - 9x^6 + 8x^5 - 17x^4 + 3x^3 + 5x^2 - 2x - 1	$S_3\wr S_3$	$1$	$0$
8.2e18_3e2_5e2_13e2.12t213.1c1	$8$	$ 2^{18} \cdot 3^{2} \cdot 5^{2} \cdot 13^{2}$	x^9 - 2x^8 - x^7 + 15x^5 - 40x^4 + 47x^3 - 32x^2 + 12x - 2	$S_3\wr S_3$	$1$	$0$
8.2e12_3e6_61e2.12t213.1c1	$8$	$ 2^{12} \cdot 3^{6} \cdot 61^{2}$	x^9 - x^8 - 4x^7 + 5x^5 + x^4 + 7x^3 + 5x^2 + 3x + 1	$S_3\wr S_3$	$1$	$0$
8.2e18_211e2.12t213.1c1	$8$	$ 2^{18} \cdot 211^{2}$	x^9 - 2x^8 + 4x^7 - 2x^5 + 8x^4 - x^3 + 2x^2 + 4x + 2	$S_3\wr S_3$	$1$	$0$
8.2e8_3e6_251e2.12t213.1c1	$8$	$ 2^{8} \cdot 3^{6} \cdot 251^{2}$	x^9 - 4x^8 + 11x^7 - 34x^6 + 71x^5 - 104x^4 + 117x^3 - 82x^2 + 60x - 24	$S_3\wr S_3$	$1$	$0$
8.2e12_3e10_7e2.12t213.1c1	$8$	$ 2^{12} \cdot 3^{10} \cdot 7^{2}$	x^9 - 3x^8 + 3x^7 + 3x^6 - 3x^5 - 3x^4 + 15x^3 - 9x^2 + 12	$S_3\wr S_3$	$1$	$0$
8.2e10_59e4.12t178.1c1	$8$	$ 2^{10} \cdot 59^{4}$	x^9 - 3x^8 - 7x^7 + 21x^6 + 39x^5 - 25x^4 - 77x^3 - 25x^2 + 48x + 44	$(((C_3 \times (C_3^2 : C_2)) : C_2) : C_3) : C_2$	$1$	$0$
8.3e10_11e2_43e2.12t213.1c1	$8$	$ 3^{10} \cdot 11^{2} \cdot 43^{2}$	x^9 - 4x^8 + 4x^7 + 3x^6 - 2x^5 - 7x^4 + 11x^2 + 4x + 1	$S_3\wr S_3$	$1$	$0$
8.2e6_3e6_13e2_41e2.12t213.1c1	$8$	$ 2^{6} \cdot 3^{6} \cdot 13^{2} \cdot 41^{2}$	x^9 - 3x^8 + 11x^7 - 20x^6 + 18x^5 + x^4 - 25x^3 - 15x^2 + 26x - 13	$S_3\wr S_3$	$1$	$0$
8.2e8_3e6_271e2.12t213.1c1	$8$	$ 2^{8} \cdot 3^{6} \cdot 271^{2}$	x^9 - 3x^8 + 6x^7 - 6x^6 + 4x^5 - 10x^3 + 10x^2 - 9x - 3	$S_3\wr S_3$	$1$	$0$
8.2e8_3e6_5e4_11e2.12t213.1c1	$8$	$ 2^{8} \cdot 3^{6} \cdot 5^{4} \cdot 11^{2}$	x^9 - 3x^8 + 9x^7 - 18x^6 + 28x^5 - 37x^4 + 48x^3 - 40x^2 + 40x - 40	$S_3\wr S_3$	$1$	$0$
8.2e18_3e10.12t213.1c1	$8$	$ 2^{18} \cdot 3^{10}$	x^9 - 3x^6 + 3x^5 - 3x^4 - 6x^2 + 6x - 2	$S_3\wr S_3$	$1$	$0$
8.2e10_3e4_433e2.12t213.1c1	$8$	$ 2^{10} \cdot 3^{4} \cdot 433^{2}$	x^9 - 5x^7 - 2x^6 + 8x^5 + 2x^4 + 9x^3 - 4x^2 - 26x + 18	$S_3\wr S_3$	$1$	$0$
8.11e3_233e3.9t26.1c1	$8$	$ 11^{3} \cdot 233^{3}$	x^9 - 2x^8 + 2x^7 - x^6 + 3x^5 + 3x^4 - 14x^3 - 12x^2 + x + 2	$((C_3^2:Q_8):C_3):C_2$	$1$	$2$
8.2e20_127e2.12t213.1c1	$8$	$ 2^{20} \cdot 127^{2}$	x^9 - 4x^8 + 9x^7 - 6x^6 - 7x^5 + 12x^4 + 5x^3 - 2x^2 - 8x - 4	$S_3\wr S_3$	$1$	$0$
8.3e7_53e4.9t26.1c1	$8$	$ 3^{7} \cdot 53^{4}$	x^9 - x^8 - 3x^7 + 3x^6 - 3x^5 + 6x^4 + 9x^3 - 18x^2 - 9x + 18	$((C_3^2:Q_8):C_3):C_2$	$1$	$2$
8.3e7_53e4.18t157.1c1	$8$	$ 3^{7} \cdot 53^{4}$	x^9 - x^8 - 3x^7 + 3x^6 - 3x^5 + 6x^4 + 9x^3 - 18x^2 - 9x + 18	$((C_3^2:Q_8):C_3):C_2$	$1$	$-2$
8.2e12_3e6_7e2_11e2.12t213.1c1	$8$	$ 2^{12} \cdot 3^{6} \cdot 7^{2} \cdot 11^{2}$	x^9 - x^8 - 3x^6 + x^5 + 3x^4 + 3x^3 - 4x^2 + 1	$S_3\wr S_3$	$1$	$0$
8.3e9_97e3.9t26.1c1	$8$	$ 3^{9} \cdot 97^{3}$	x^9 - 3x^8 + 7x^6 - 3x^5 - 12x^4 + 8x^3 + 3x - 2	$((C_3^2:Q_8):C_3):C_2$	$1$	$2$
8.3e12_229e2.12t213.1c1	$8$	$ 3^{12} \cdot 229^{2}$	x^9 - 9x^7 + 27x^5 - 31x^3 + 12x - 1	$S_3\wr S_3$	$1$	$0$
8.2e8_3e6_409e2.12t213.1c1	$8$	$ 2^{8} \cdot 3^{6} \cdot 409^{2}$	x^9 - 3x^8 + 10x^6 - 10x^5 - 8x^4 + 28x^3 - 14x^2 - 19x + 21	$S_3\wr S_3$	$1$	$0$
8.2e10_5e4_223e2.12t213.1c1	$8$	$ 2^{10} \cdot 5^{4} \cdot 223^{2}$	x^9 - 3x^8 + 4x^7 - 6x^6 - x^5 + 9x^4 - 21x^3 + 7x^2 + 25x + 5	$S_3\wr S_3$	$1$	$0$
8.2e6_3e6_5e2_167e2.12t213.1c1	$8$	$ 2^{6} \cdot 3^{6} \cdot 5^{2} \cdot 167^{2}$	x^9 - 2x^8 - 3x^7 + 5x^6 + 15x^5 + 10x^4 - 12x^3 - 15x^2 - 9x + 9	$S_3\wr S_3$	$1$	$0$
8.3e12_257e2.12t213.1c1	$8$	$ 3^{12} \cdot 257^{2}$	x^9 - 9x^7 - x^6 + 27x^5 + 6x^4 - 31x^3 - 9x^2 + 12x + 3	$S_3\wr S_3$	$1$	$0$
8.3e9_37e4.9t26.1c1	$8$	$ 3^{9} \cdot 37^{4}$	x^9 + 3x^7 - 3x^6 + 6x^3 + 3x^2 - 9x - 5	$((C_3^2:Q_8):C_3):C_2$	$1$	$2$
8.3e9_37e4.18t157.1c1	$8$	$ 3^{9} \cdot 37^{4}$	x^9 + 3x^7 - 3x^6 + 6x^3 + 3x^2 - 9x - 5	$((C_3^2:Q_8):C_3):C_2$	$1$	$-2$
8.2e8_5e6_97e2.12t213.1c1	$8$	$ 2^{8} \cdot 5^{6} \cdot 97^{2}$	x^9 - 3x^8 + 8x^6 - 6x^5 - 6x^4 + 8x^2 + 5x - 5	$S_3\wr S_3$	$1$	$0$
8.17e6_41e2.12t213.1c1	$8$	$ 17^{6} \cdot 41^{2}$	x^9 - 2x^8 - 4x^7 + 11x^6 + 2x^5 - 19x^4 + 7x^3 + 11x^2 - 5x - 1	$S_3\wr S_3$	$1$	$0$
8.2e22_101e2.12t213.1c1	$8$	$ 2^{22} \cdot 101^{2}$	x^9 - 4x^8 + 8x^7 - 11x^6 + 15x^5 - 29x^4 + 44x^3 - 38x^2 + 14x + 2	$S_3\wr S_3$	$1$	$0$
8.2e6_3e10_109e2.12t213.1c1	$8$	$ 2^{6} \cdot 3^{10} \cdot 109^{2}$	x^9 - 4x^8 + 5x^7 + 5x^6 - 17x^5 + 10x^4 + 10x^3 - 13x^2 + 5x - 3	$S_3\wr S_3$	$1$	$0$
8.3571e3.9t26.1c1	$8$	$ 3571^{3}$	x^9 - 3x^8 - 2x^7 + 8x^6 + 9x^5 - 10x^4 - 6x^3 + 9x^2 - x - 1	$((C_3^2:Q_8):C_3):C_2$	$1$	$2$