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 all 43 matches)

Label	Polynomial	Discriminant	Galois group	Class group
9.1.89526025681.1	x^9 - 3x^8 + x^6 + 15x^5 - 13x^4 - 3x^3 + 4x - 1	\( 547^{4} \)	$(C_3^2:Q_8):C_3$ (as 9T23)	$[3]$
9.1.817583065209.1	x^9 - 3x^8 + 6x^7 + 15x^5 + 15x^4 + 27x^3 + 21x^2 + 15x + 7	\( 3^{10}\cdot 61^{4} \)	$(C_3^2:Q_8):C_3$ (as 9T23)	Trivial
9.1.949470950464.1	x^9 - x^8 + 2x^7 + 28x^5 - 42x^4 + 2x^3 + 52x^2 - 33x + 7	\( 2^{6}\cdot 349^{4} \)	$(C_3^2:Q_8):C_3$ (as 9T23)	$[3]$
9.1.1616465588409.1	x^9 + 10x^7 - 7x^6 + 27x^5 - 35x^4 + 63x^3 - 42x^2 + 11x - 1	\( 3^{6}\cdot 7^{4}\cdot 31^{4} \)	$(C_3^2:Q_8):C_3$ (as 9T23)	$[3]$
9.1.3873527824384.1	x^9 - 3x^8 - 2x^7 + 10x^6 + 5x^5 - 11x^4 - 34x^3 + 42x^2 - x + 3	\( 2^{22}\cdot 31^{4} \)	$(C_3^2:Q_8):C_3$ (as 9T23)	$[3]$
9.1.3931920170649.1	x^9 - 2x^8 - x^7 + 4x^6 + 4x^5 - 4x^4 - 19x^3 - 22x^2 - 32x - 24	\( 3^{6}\cdot 271^{4} \)	$(C_3^2:Q_8):C_3$ (as 9T23)	$[3]$
9.1.10415381380369.1	x^9 - x^8 + 7x^7 - 20x^6 + 17x^5 - 54x^4 + 118x^3 - 6x^2 + 15x - 76	\( 7^{6}\cdot 97^{4} \)	$(C_3^2:Q_8):C_3$ (as 9T23)	$[9]$
9.1.37558352909169.1	x^9 - x^8 + x^7 + 17x^6 - 57x^5 + 150x^4 - 221x^3 + 242x^2 - 143x + 59	\( 3^{6}\cdot 61^{6} \)	$(C_3^2:Q_8):C_3$ (as 9T23)	$[3]$
9.1.115660367211601.1	x^9 - 15x^7 - 21x^6 + 39x^5 + 18x^4 - 110x^3 + 63x^2 + 49x - 263	\( 19^{4}\cdot 31^{6} \)	$(C_3^2:Q_8):C_3$ (as 9T23)	$[3]$
9.1.458566205677281.1	x^9 - x^8 + 6x^7 - 15x^6 + 35x^5 + 48x^4 + 52x^3 - 95x^2 + 114x - 209	\( 3^{6}\cdot 13^{6}\cdot 19^{4} \)	$(C_3^2:Q_8):C_3$ (as 9T23)	$[3]$
9.1.979540829878689.1	x^9 - 4x^8 + 14x^7 + 26x^6 - 197x^5 + 514x^4 - 721x^3 + 685x^2 - 443x + 132	\( 3^{6}\cdot 13^{4}\cdot 19^{6} \)	$(C_3^2:Q_8):C_3$ (as 9T23)	$[3]$ (GRH)
9.1.1806976738085401.1	x^9 - 3x^8 - 9x^7 + x^6 + 80x^5 + 106x^4 - 195x^3 - 746x^2 - 529x - 110	\( 349^{6} \)	$(C_3^2:Q_8):C_3$ (as 9T23)	$[3]$
9.1.1999965783834529.1	x^9 - 4x^8 + 9x^7 - 12x^6 + 13x^5 + 19x^4 - 12x^3 + 13x^2 - 22x - 47	\( 7^{4}\cdot 97^{6} \)	$(C_3^2:Q_8):C_3$ (as 9T23)	$[9]$
9.1.3722460239233024.1	x^9 - 16x^6 + 62x^5 - 80x^3 - 496x^2 + 868x + 32	\( 2^{22}\cdot 31^{6} \)	$(C_3^2:Q_8):C_3$ (as 9T23)	$[3]$
9.1.3722460239233024.2	x^9 - 2x^8 - 6x^7 + 28x^6 - 15x^5 - 94x^4 + 230x^3 - 232x^2 + 145x - 54	\( 2^{22}\cdot 31^{6} \)	$(C_3^2:Q_8):C_3$ (as 9T23)	$[9]$
9.1.3722460239233024.3	x^9 - 4x^8 + 20x^7 - 72x^6 + 196x^5 - 336x^4 + 728x^3 - 704x^2 + 467x + 108	\( 2^{22}\cdot 31^{6} \)	$(C_3^2:Q_8):C_3$ (as 9T23)	$[9]$
9.1.3722460239233024.4	x^9 - 4x^8 - 4x^7 + 16x^6 + 26x^5 - 72x^4 + 116x^3 - 208x^2 + 377x - 836	\( 2^{22}\cdot 31^{6} \)	$(C_3^2:Q_8):C_3$ (as 9T23)	$[9]$
9.1.3915101633817529.1	x^9 - 4x^8 - x^7 + 29x^6 - 12x^5 - 81x^4 - 15x^3 + 445x^2 + 35x + 214	\( 397^{6} \)	$(C_3^2:Q_8):C_3$ (as 9T23)	$[3]$
9.1.4545340842854449.1	x^9 - 3x^8 + 5x^7 - 3x^6 - 87x^5 + 139x^4 + 62x^3 + 608x^2 - 513x + 199	\( 11^{6}\cdot 37^{6} \)	$(C_3^2:Q_8):C_3$ (as 9T23)	$[3]$
9.1.5364162490836249.1	x^9 - 9x^7 - 24x^6 + 18x^5 + 126x^4 + 156x^3 - 9x^2 - 486x - 773	\( 3^{18}\cdot 61^{4} \)	$(C_3^2:Q_8):C_3$ (as 9T23)	Trivial
9.1.11198680244449489.1	x^9 - x^8 - 3x^7 + 17x^5 - 350x^4 - 386x^3 + 1160x^2 + 651x - 1368	\( 11^{6}\cdot 43^{6} \)	$(C_3^2:Q_8):C_3$ (as 9T23)	$[9]$
9.1.11722105986255625.1	x^9 - x^8 + 9x^7 + 45x^6 - 28x^5 + 36x^4 + 697x^3 - 2172x^2 + 2895x - 2974	\( 5^{4}\cdot 163^{6} \)	$(C_3^2:Q_8):C_3$ (as 9T23)	$[9]$
9.1.14354071161059529.1	x^9 - x^8 - 5x^7 - 13x^6 + 16x^5 + 17x^4 + 103x^3 - 34x^2 - 71x - 258	\( 3^{10}\cdot 79^{6} \)	$(C_3^2:Q_8):C_3$ (as 9T23)	$[3]$ (GRH)
9.1.17804320388674561.1	x^9 - 4x^8 + 13x^7 - 73x^6 + 58x^5 - 121x^4 + 777x^3 + 474x^2 - 1970x - 2929	\( 7^{6}\cdot 73^{6} \)	$(C_3^2:Q_8):C_3$ (as 9T23)	$[9]$
9.9.20276944341002496.1	x^9 - 2x^8 - 43x^7 - 74x^6 + 100x^5 + 242x^4 - 43x^3 - 214x^2 - 14x + 48	\( 2^{8}\cdot 3^{6}\cdot 7^{6}\cdot 31^{4} \)	$(C_3^2:Q_8):C_3$ (as 9T23)	$[3]$
9.9.24009628939366464.1	x^9 - 3x^8 - 27x^7 + 63x^6 + 174x^5 - 288x^4 - 228x^3 + 384x^2 - 144x + 16	\( 2^{6}\cdot 3^{12}\cdot 163^{4} \)	$(C_3^2:Q_8):C_3$ (as 9T23)	Trivial (GRH)
9.9.26786992617986329.1	x^9 - 2x^8 - 36x^7 + 7x^6 + 403x^5 + 460x^4 - 947x^3 - 2210x^2 - 1457x - 290	\( 547^{6} \)	$(C_3^2:Q_8):C_3$ (as 9T23)	$[3]$
9.1.36590103105447609.1	x^9 - 3x^8 + 15x^7 - 16x^6 - 235x^5 + 1141x^4 - 2474x^3 + 3718x^2 - 3216x + 1689	\( 3^{4}\cdot 277^{6} \)	$(C_3^2:Q_8):C_3$ (as 9T23)	$[9]$
9.1.76821993791524864.1	x^9 - 4x^8 - 16x^7 + 26x^6 + 55x^5 + 594x^4 + 2255x^3 + 1760x^2 + 632x - 64	\( 2^{12}\cdot 163^{6} \)	$(C_3^2:Q_8):C_3$ (as 9T23)	$[3]$ (GRH)
9.1.90177605334914769.1	x^9 - x^8 + 2x^7 - 52x^6 + 154x^5 - 194x^4 + 548x^3 - 965x^2 + 568x - 111	\( 3^{6}\cdot 7^{4}\cdot 61^{6} \)	$(C_3^2:Q_8):C_3$ (as 9T23)	$[3]$ (GRH)
9.1.97998323407891921.1	x^9 - 2x^8 + 20x^7 - 116x^6 + 212x^5 - 1410x^4 + 1735x^3 - 7284x^2 + 8477x - 6420	\( 7^{6}\cdot 97^{6} \)	$(C_3^2:Q_8):C_3$ (as 9T23)	$[3, 9]$
9.1.97998323407891921.2	x^9 - x^8 + 17x^7 - 34x^6 + 51x^5 - 536x^4 + 428x^3 - 1486x^2 + 7209x + 1336	\( 7^{6}\cdot 97^{6} \)	$(C_3^2:Q_8):C_3$ (as 9T23)	$[3, 9]$
9.1.106054873287491584.1	x^9 - 3x^8 + 4x^7 + 28x^6 - 204x^5 + 252x^4 - 108x^3 - 2916x^2 + 4617x - 8019	\( 2^{24}\cdot 43^{6} \)	$(C_3^2:Q_8):C_3$ (as 9T23)	$[9]$ (GRH)
9.1.115642794999933184.1	x^9 - 3x^8 + 26x^7 - 102x^6 + 217x^5 - 59x^4 - 796x^3 + 5300x^2 - 9228x + 7452	\( 2^{8}\cdot 277^{6} \)	$(C_3^2:Q_8):C_3$ (as 9T23)	$[3]$ (GRH)
9.1.115646511237465664.1	x^9 - 4x^8 - 25x^7 + 22x^6 + 257x^5 + 510x^4 + 1333x^3 + 3378x^2 + 4066x + 3454	\( 2^{6}\cdot 349^{6} \)	$(C_3^2:Q_8):C_3$ (as 9T23)	$[9]$
9.1.115646511237465664.2	x^9 - 4x^8 + 11x^7 - 8x^6 - 151x^5 + 768x^4 - 1761x^3 - 6346x^2 + 24024x + 46278	\( 2^{6}\cdot 349^{6} \)	$(C_3^2:Q_8):C_3$ (as 9T23)	$[9]$
9.1.127021550911887241.1	x^9 - 2x^8 + 21x^7 - 95x^6 + 299x^5 - 1236x^4 + 1742x^3 - 5425x^2 + 2793x - 9261	\( 709^{6} \)	$(C_3^2:Q_8):C_3$ (as 9T23)	$[3]$
9.1.153839013515956224.1	x^9 - 4x^8 + 7x^7 + 80x^6 + 45x^5 - 864x^4 + 928x^3 + 4316x^2 + 3247x + 638	\( 2^{12}\cdot 3^{6}\cdot 61^{6} \)	$(C_3^2:Q_8):C_3$ (as 9T23)	$[3]$ (GRH)
9.1.153839013515956224.2	x^9 - 2x^8 - 20x^7 - 14x^6 + 279x^5 + 96x^4 + 181x^3 + 4180x^2 + 1399x + 9142	\( 2^{12}\cdot 3^{6}\cdot 61^{6} \)	$(C_3^2:Q_8):C_3$ (as 9T23)	$[3]$ (GRH)
9.1.165542400249498441.1	x^9 - 3x^8 + 28x^7 - x^6 + 51x^5 + 181x^4 - 1626x^3 + 2337x^2 + 5435x - 9550	\( 3^{6}\cdot 13^{6}\cdot 19^{6} \)	$(C_3^2:Q_8):C_3$ (as 9T23)	$[3, 3]$
9.1.165542400249498441.2	x^9 - 2x^8 - 8x^7 + 46x^6 - 5x^5 + 214x^4 + 337x^3 + 295x^2 + 397x + 246	\( 3^{6}\cdot 13^{6}\cdot 19^{6} \)	$(C_3^2:Q_8):C_3$ (as 9T23)	$[3, 3]$
9.9.1944779944088683584.1	x^9 - 3x^8 - 57x^7 + 131x^6 + 1050x^5 - 2010x^4 - 6686x^3 + 11268x^2 + 6624x - 4020	\( 2^{6}\cdot 3^{16}\cdot 163^{4} \)	$(C_3^2:Q_8):C_3$ (as 9T23)	$[3]$
9.9.754169853931401428161.1	x^9 - 2x^8 - 66x^7 + 196x^6 + 1022x^5 - 3614x^4 - 2711x^3 + 14194x^2 - 4931x - 5714	\( 71^{6}\cdot 277^{4} \)	$(C_3^2:Q_8):C_3$ (as 9T23)	$[3]$ (GRH)