Global number field search results

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Degree	Signature	Galois group	Class number	Class group
Regulator	Num. ramified primes	Ramified primes		Unramified primes
CM field	Discriminant		Root discriminant

Results (displaying matches 1-50 of 1720)

Label	Polynomial	Discriminant	Galois group	Class group
9.9.36763077169.1	x^9 - 4x^8 - 2x^7 + 22x^6 - 14x^5 - 22x^4 + 20x^3 + 2x^2 - 5x + 1	\( 7^{6}\cdot 13^{2}\cdot 43^{2} \)	$C_3 \wr C_3 $ (as 9T17)	Trivial
9.9.53286643921.1	x^9 - 2x^8 - 8x^7 + 18x^6 + 10x^5 - 36x^4 + 10x^3 + 12x^2 - 7x + 1	\( 7^{6}\cdot 673^{2} \)	$C_3 \wr C_3 $ (as 9T17)	Trivial
9.9.69573030289.1	x^9 - x^8 - 10x^7 + 14x^6 + 20x^5 - 36x^4 + 18x^2 - 8x + 1	\( 7^{6}\cdot 769^{2} \)	$C_3 \wr C_3 $ (as 9T17)	Trivial
9.9.139858796529.1	x^9 - 18x^7 - 3x^6 + 45x^5 + 9x^4 - 36x^3 - 9x^2 + 9x + 3	\( 3^{18}\cdot 19^{2} \)	$C_3 \wr C_3 $ (as 9T17)	Trivial
9.9.187076145529.1	x^9 - 15x^7 - 10x^6 + 47x^5 + 23x^4 - 52x^3 - 5x^2 + 13x - 1	\( 7^{6}\cdot 13^{2}\cdot 97^{2} \)	$C_3 \wr C_3 $ (as 9T17)	Trivial
9.9.188860645561.1	x^9 - x^8 - 12x^7 + 42x^5 + 28x^4 - 28x^3 - 32x^2 - 10x - 1	\( 7^{8}\cdot 181^{2} \)	$C_3 \wr C_3 $ (as 9T17)	Trivial
9.9.229395976209.1	x^9 - 3x^8 - 6x^7 + 24x^6 - 6x^5 - 30x^4 + 18x^3 + 6x^2 - 6x + 1	\( 3^{16}\cdot 73^{2} \)	$C_3 \wr C_3 $ (as 9T17)	Trivial
9.9.262642925169.1	x^9 - 3x^8 - 6x^7 + 22x^6 - 36x^4 + 20x^3 + 6x^2 - 6x + 1	\( 3^{12}\cdot 19^{2}\cdot 37^{2} \)	$C_3 \wr C_3 $ (as 9T17)	Trivial
9.9.286677788929.1	x^9 - 14x^7 + 63x^5 - 105x^3 - 7x^2 + 56x + 7	\( 7^{8}\cdot 223^{2} \)	$C_3 \wr C_3 $ (as 9T17)	Trivial
9.9.320687761849.1	x^9 - 2x^8 - 12x^7 + 8x^6 + 48x^5 + 14x^4 - 48x^3 - 40x^2 - 11x - 1	\( 7^{6}\cdot 13^{2}\cdot 127^{2} \)	$C_3 \wr C_3 $ (as 9T17)	Trivial
9.9.371503659121.1	x^9 - 2x^8 - 12x^7 + 20x^6 + 53x^5 - 64x^4 - 103x^3 + 68x^2 + 76x - 8	\( 7^{6}\cdot 1777^{2} \)	$C_3 \wr C_3 $ (as 9T17)	Trivial
9.9.384153279601.1	x^9 - x^8 - 14x^7 + 10x^6 + 67x^5 - 27x^4 - 131x^3 + 19x^2 + 85x - 1	\( 7^{6}\cdot 13^{2}\cdot 139^{2} \)	$C_3 \wr C_3 $ (as 9T17)	Trivial
9.9.521918108721.1	x^9 - 12x^7 - 10x^6 + 30x^5 + 36x^4 - 10x^3 - 24x^2 - 9x - 1	\( 3^{12}\cdot 991^{2} \)	$C_3 \wr C_3 $ (as 9T17)	Trivial
9.9.530378649441.1	x^9 - 18x^7 - 18x^6 + 72x^5 + 99x^4 - 66x^3 - 135x^2 - 45x + 1	\( 3^{18}\cdot 37^{2} \)	$C_3 \wr C_3 $ (as 9T17)	Trivial
9.9.589788672529.1	x^9 - x^8 - 15x^7 + 15x^6 + 63x^5 - 46x^4 - 78x^3 + 4x^2 + 15x + 1	\( 7^{6}\cdot 2239^{2} \)	$C_3 \wr C_3 $ (as 9T17)	Trivial
9.9.628330484929.1	x^9 - 16x^7 - 10x^6 + 62x^5 + 88x^4 + 18x^3 - 20x^2 - 9x - 1	\( 7^{6}\cdot 2311^{2} \)	$C_3 \wr C_3 $ (as 9T17)	Trivial
9.9.654702684769.1	x^9 - 4x^8 - 10x^7 + 49x^6 + 7x^5 - 175x^4 + 119x^3 + 138x^2 - 153x + 27	\( 7^{8}\cdot 337^{2} \)	$C_3 \wr C_3 $ (as 9T17)	Trivial
9.9.663073089849.1	x^9 - 12x^7 - 8x^6 + 36x^5 + 42x^4 - 8x^3 - 24x^2 - 9x - 1	\( 3^{12}\cdot 1117^{2} \)	$C_3 \wr C_3 $ (as 9T17)	Trivial
9.9.805741412161.1	x^9 - 17x^7 - 8x^6 + 87x^5 + 58x^4 - 136x^3 - 57x^2 + 72x - 13	\( 7^{6}\cdot 2617^{2} \)	$C_3 \wr C_3 $ (as 9T17)	Trivial
9.9.885196840801.1	x^9 - 4x^8 - 9x^7 + 42x^6 + 19x^5 - 134x^4 + 31x^3 + 129x^2 - 87x + 13	\( 7^{6}\cdot 13^{2}\cdot 211^{2} \)	$C_3 \wr C_3 $ (as 9T17)	Trivial
9.9.1021759094041.1	x^9 - 4x^8 - 10x^7 + 49x^6 + 14x^5 - 154x^4 + 7x^3 + 180x^2 - 13x - 71	\( 7^{8}\cdot 421^{2} \)	$C_3 \wr C_3 $ (as 9T17)	Trivial
9.9.1137181233769.1	x^9 - 2x^8 - 17x^7 + 31x^6 + 69x^5 - 139x^4 - 22x^3 + 125x^2 - 44x - 1	\( 7^{6}\cdot 3109^{2} \)	$C_3 \wr C_3 $ (as 9T17)	Trivial
9.9.1177027538281.1	x^9 - 2x^8 - 16x^7 + 27x^6 + 79x^5 - 119x^4 - 129x^3 + 184x^2 + 59x - 83	\( 7^{6}\cdot 3163^{2} \)	$C_3 \wr C_3 $ (as 9T17)	Trivial
9.9.1235794625569.1	x^9 - 4x^8 - 10x^7 + 28x^6 + 56x^5 - 28x^4 - 98x^3 - 58x^2 - 13x - 1	\( 7^{8}\cdot 463^{2} \)	$C_3 \wr C_3 $ (as 9T17)	Trivial
9.9.1275140066841.1	x^9 - 3x^8 - 12x^7 + 50x^6 - 36x^5 - 30x^4 + 34x^3 - 6x + 1	\( 3^{12}\cdot 1549^{2} \)	$C_3 \wr C_3 $ (as 9T17)	Trivial
9.9.1618459762969.1	x^9 - 20x^7 - 8x^6 + 117x^5 + 74x^4 - 234x^3 - 186x^2 + 88x + 71	\( 7^{6}\cdot 3709^{2} \)	$C_3 \wr C_3 $ (as 9T17)	Trivial
9.9.1768397295721.1	x^9 - x^8 - 18x^7 + 22x^6 + 93x^5 - 109x^4 - 167x^3 + 138x^2 + 111x - 29	\( 7^{6}\cdot 3877^{2} \)	$C_3 \wr C_3 $ (as 9T17)	Trivial
9.9.1801390781281.1	x^9 - x^8 - 19x^7 + 7x^6 + 105x^5 - 21x^4 - 217x^3 + 52x^2 + 144x - 64	\( 7^{8}\cdot 13^{2}\cdot 43^{2} \)	$C_3 \wr C_3 $ (as 9T17)	Trivial
9.9.1801390781281.2	x^9 - 4x^8 - 10x^7 + 49x^6 + 21x^5 - 168x^4 - 21x^3 + 187x^2 + 43x - 1	\( 7^{8}\cdot 13^{2}\cdot 43^{2} \)	$C_3 \wr C_3 $ (as 9T17)	Trivial
9.9.1873922801569.1	x^9 - 4x^8 - 11x^7 + 46x^6 + 34x^5 - 116x^4 - 74x^3 + 31x^2 + 21x + 1	\( 7^{6}\cdot 13^{2}\cdot 307^{2} \)	$C_3 \wr C_3 $ (as 9T17)	Trivial
9.9.2005755565009.1	x^9 - 2x^8 - 16x^7 + 27x^6 + 86x^5 - 119x^4 - 171x^3 + 170x^2 + 80x + 8	\( 7^{6}\cdot 4129^{2} \)	$C_3 \wr C_3 $ (as 9T17)	Trivial
9.9.2046768006409.1	x^9 - x^8 - 18x^7 + 8x^6 + 107x^5 - 11x^4 - 230x^3 - 2x^2 + 146x + 13	\( 7^{6}\cdot 43^{2}\cdot 97^{2} \)	$C_3 \wr C_3 $ (as 9T17)	Trivial
9.9.2215343490409.1	x^9 - 2x^8 - 12x^7 + 24x^6 + 24x^5 - 70x^4 + 32x^3 + 8x^2 - 7x + 1	\( 7^{2}\cdot 19^{6}\cdot 31^{2} \)	$C_3 \wr C_3 $ (as 9T17)	Trivial
9.9.2279372238081.1	x^9 - 3x^8 - 12x^7 + 32x^6 + 18x^5 - 84x^4 + 52x^3 - 6x + 1	\( 3^{12}\cdot 19^{2}\cdot 109^{2} \)	$C_3 \wr C_3 $ (as 9T17)	Trivial
9.9.2421730428481.1	x^9 - 4x^8 - 12x^7 + 74x^6 - 42x^5 - 264x^4 + 426x^3 + 12x^2 - 387x + 197	\( 7^{6}\cdot 13^{2}\cdot 349^{2} \)	$C_3 \wr C_3 $ (as 9T17)	Trivial
9.9.2692812078441.1	x^9 - 3x^8 - 12x^7 + 34x^6 + 51x^5 - 123x^4 - 99x^3 + 147x^2 + 87x - 19	\( 3^{12}\cdot 2251^{2} \)	$C_3 \wr C_3 $ (as 9T17)	Trivial
9.9.2736050118201.1	x^9 - 3x^8 - 12x^7 + 16x^6 + 54x^5 - 68x^3 - 48x^2 - 12x - 1	\( 3^{12}\cdot 2269^{2} \)	$C_3 \wr C_3 $ (as 9T17)	Trivial
9.9.2855968181521.1	x^9 - x^8 - 18x^7 + 21x^6 + 103x^5 - 121x^4 - 209x^3 + 196x^2 + 112x + 7	\( 7^{6}\cdot 13^{2}\cdot 379^{2} \)	$C_3 \wr C_3 $ (as 9T17)	Trivial
9.9.2912446014921.1	x^9 - 18x^7 - 2x^6 + 99x^5 + 18x^4 - 201x^3 - 42x^2 + 120x + 8	\( 3^{12}\cdot 2341^{2} \)	$C_3 \wr C_3 $ (as 9T17)	Trivial
9.9.3094351891929.1	x^9 - 18x^7 - 7x^6 + 90x^5 + 63x^4 - 85x^3 - 27x^2 + 21x - 1	\( 3^{12}\cdot 19^{2}\cdot 127^{2} \)	$C_3 \wr C_3 $ (as 9T17)	Trivial
9.9.3155884743361.1	x^9 - 2x^8 - 16x^7 - 2x^6 + 50x^5 + 36x^4 - 30x^3 - 36x^2 - 11x - 1	\( 7^{2}\cdot 19^{6}\cdot 37^{2} \)	$C_3 \wr C_3 $ (as 9T17)	Trivial
9.9.3161394236961.1	x^9 - 3x^8 - 12x^7 + 18x^6 + 60x^5 + 6x^4 - 66x^3 - 48x^2 - 12x - 1	\( 3^{16}\cdot 271^{2} \)	$C_3 \wr C_3 $ (as 9T17)	Trivial
9.9.3454828886089.1	x^9 - 22x^7 - 3x^6 + 159x^5 + 37x^4 - 451x^3 - 152x^2 + 419x + 181	\( 7^{6}\cdot 5419^{2} \)	$C_3 \wr C_3 $ (as 9T17)	Trivial
9.9.3508589773129.1	x^9 - 22x^7 - 11x^6 + 152x^5 + 103x^4 - 423x^3 - 324x^2 + 412x + 344	\( 7^{6}\cdot 43^{2}\cdot 127^{2} \)	$C_3 \wr C_3 $ (as 9T17)	Trivial
9.9.3512029669681.1	x^9 - 2x^8 - 10x^7 + 26x^6 + 2x^5 - 38x^4 + 16x^3 + 10x^2 - 7x + 1	\( 13^{6}\cdot 853^{2} \)	$C_3 \wr C_3 $ (as 9T17)	Trivial
9.9.3561610651729.1	x^9 - 4x^8 - 4x^7 + 26x^6 - 10x^5 - 36x^4 + 30x^3 - 5x + 1	\( 13^{6}\cdot 859^{2} \)	$C_3 \wr C_3 $ (as 9T17)	Trivial
9.9.3727783978009.1	x^9 - x^8 - 20x^7 + 3x^6 + 129x^5 + 72x^4 - 253x^3 - 298x^2 - 67x + 13	\( 7^{6}\cdot 13^{2}\cdot 433^{2} \)	$C_3 \wr C_3 $ (as 9T17)	Trivial
9.9.3743694828769.1	x^9 - 2x^8 - 19x^7 + 28x^6 + 103x^5 - 95x^4 - 126x^3 + x^2 + 17x + 1	\( 7^{6}\cdot 5641^{2} \)	$C_3 \wr C_3 $ (as 9T17)	Trivial
9.9.3791630678521.1	x^9 - 3x^8 - 17x^7 + 42x^6 + 91x^5 - 168x^4 - 196x^3 + 198x^2 + 162x - 27	\( 7^{8}\cdot 811^{2} \)	$C_3 \wr C_3 $ (as 9T17)	Trivial
9.9.4011115711729.1	x^9 - 4x^8 - 12x^7 + 52x^6 + 47x^5 - 206x^4 - 85x^3 + 243x^2 + 90x - 43	\( 7^{6}\cdot 5839^{2} \)	$C_3 \wr C_3 $ (as 9T17)	Trivial