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Label	Polynomial	Degree	Signature	Discriminant	Ram. prime count	Root discriminant	Galois root discriminant	CM field	Galois	Monogenic	Galois group	Class group	Unit group torsion	Unit group rank	Regulator
4.0.392.1	$x^{4} - x^{3} + x + 1$	$4$	[0,2]	$2^{3}\cdot 7^{2}$	$2$	$4.44960558625$	$7.483314773547883$			✓	$D_{4}$ (as 4T3)	trivial	$2$	$1$	$0.632974319201$
4.0.784.1	$x^{4} - 3 x^{2} + 4$	$4$	[0,2]	$2^{4}\cdot 7^{2}$	$2$	$5.29150262213$	$5.291502622129181$	✓	✓		$C_2^2$ (as 4T2)	trivial	$4$	$1$	$2.76865938331$
4.0.1225.1	$x^{4} - x^{3} + 5 x^{2} + 2 x + 4$	$4$	[0,2]	$5^{2}\cdot 7^{2}$	$2$	$5.9160797831$	$5.916079783099616$	✓	✓		$C_2^2$ (as 4T2)	trivial	$2$	$1$	$0.962423650119$
4.2.1323.1	$x^{4} - x^{3} - 3 x^{2} - x + 1$	$4$	[2,1]	$-\,3^{3}\cdot 7^{2}$	$2$	$6.03100878452$	$6.03100878451909$			✓	$D_{4}$ (as 4T3)	trivial	$2$	$2$	$1.35144993247$
4.0.1421.1	$x^{4} - 2 x^{3} + 2 x^{2} - x + 2$	$4$	[0,2]	$7^{2}\cdot 29$	$2$	$6.13971934619$	$14.247806848775006$			✓	$D_{4}$ (as 4T3)	trivial	$2$	$1$	$2.22757871637$
4.0.1813.1	$x^{4} - 2 x^{3} + x + 2$	$4$	[0,2]	$7^{2}\cdot 37$	$2$	$6.52528449281$	$16.09347693943108$			✓	$D_{4}$ (as 4T3)	trivial	$2$	$1$	$2.63987071546$
4.0.2156.2	$x^{4} - x^{3} - 2 x^{2} + 2 x + 4$	$4$	[0,2]	$2^{2}\cdot 7^{2}\cdot 11$	$3$	$6.81415783975$	$17.549928774784245$				$D_{4}$ (as 4T3)	trivial	$2$	$1$	$3.99846955784$
4.0.3136.2	$x^{4} - 2 x^{3} + 9 x^{2} - 8 x + 2$	$4$	[0,2]	$2^{6}\cdot 7^{2}$	$2$	$7.48331477355$	$7.483314773547883$	✓	✓	✓	$C_2^2$ (as 4T2)	trivial	$2$	$1$	$3.40008441411$
4.0.3528.1	$x^{4} - x^{3} + 5 x^{2} - 5 x + 4$	$4$	[0,2]	$2^{3}\cdot 3^{2}\cdot 7^{2}$	$3$	$7.70694294903$	$12.96148139681572$				$D_{4}$ (as 4T3)	$[2]$	$2$	$1$	$2.79876781094$
4.0.4312.1	$x^{4} - x^{3} - 3 x^{2} - x + 8$	$4$	[0,2]	$2^{3}\cdot 7^{2}\cdot 11$	$3$	$8.10344498578$	$24.819347291981714$				$D_{4}$ (as 4T3)	trivial	$2$	$1$	$6.40056462073$
4.0.4508.2	$x^{4} - x^{3} - 6 x + 8$	$4$	[0,2]	$2^{2}\cdot 7^{2}\cdot 23$	$3$	$8.19400032502$	$25.37715508089904$				$D_{4}$ (as 4T3)	trivial	$2$	$1$	$6.53567429615$
4.0.5341.1	$x^{4} - 2 x^{3} + 6 x^{2} - 5 x + 8$	$4$	[0,2]	$7^{2}\cdot 109$	$2$	$8.54880959914$	$27.622454633866266$			✓	$D_{4}$ (as 4T3)	trivial	$2$	$1$	$5.22551751307$
4.0.5929.1	$x^{4} + 9 x^{2} + 1$	$4$	[0,2]	$7^{2}\cdot 11^{2}$	$2$	$8.77496438739$	$8.774964387392123$	✓	✓		$C_2^2$ (as 4T2)	trivial	$2$	$1$	$2.18464379161$
4.0.6713.1	$x^{4} - 2 x^{3} - x^{2} + 2 x + 8$	$4$	[0,2]	$7^{2}\cdot 137$	$2$	$9.05167936767$	$30.967725134404045$				$D_{4}$ (as 4T3)	trivial	$2$	$1$	$12.6646149521$
4.0.7056.1	$x^{4} + 11 x^{2} + 25$	$4$	[0,2]	$2^{4}\cdot 3^{2}\cdot 7^{2}$	$3$	$9.16515138991$	$9.16515138991168$	✓	✓		$C_2^2$ (as 4T2)	$[2]$	$4$	$1$	$3.13359847394$
4.4.7056.1	$x^{4} - 5 x^{2} + 1$	$4$	[4,0]	$2^{4}\cdot 3^{2}\cdot 7^{2}$	$3$	$9.16515138991$	$9.16515138991168$		✓	✓	$C_2^2$ (as 4T2)	trivial	$2$	$3$	$5.7128756596$
4.0.7056.2	$x^{4} - 2 x^{3} - x^{2} + 2 x + 22$	$4$	[0,2]	$2^{4}\cdot 3^{2}\cdot 7^{2}$	$3$	$9.16515138991$	$9.16515138991168$	✓	✓		$C_2^2$ (as 4T2)	$[2]$	$2$	$1$	$2.63391579385$
4.0.8281.2	$x^{4} - 3 x^{2} + 25$	$4$	[0,2]	$7^{2}\cdot 13^{2}$	$2$	$9.53939201417$	$9.539392014169456$	✓	✓		$C_2^2$ (as 4T2)	trivial	$2$	$1$	$2.38952643457$
4.0.8428.2	$x^{4} - x^{3} + 4 x^{2} + 6 x + 8$	$4$	[0,2]	$2^{2}\cdot 7^{2}\cdot 43$	$3$	$9.58144766412$	$34.698703145794944$				$D_{4}$ (as 4T3)	trivial	$2$	$1$	$9.73447587067$
4.0.9016.2	$x^{4} - x^{3} - 2 x^{2} + 9 x + 11$	$4$	[0,2]	$2^{3}\cdot 7^{2}\cdot 23$	$3$	$9.74436348684$	$35.888716889852724$				$D_{4}$ (as 4T3)	trivial	$2$	$1$	$4.02734075184$
4.2.9408.2	$x^{4} - 2 x^{3} - 6 x + 9$	$4$	[2,1]	$-\,2^{6}\cdot 3\cdot 7^{2}$	$3$	$9.84859610421$	$12.96148139681572$				$D_{4}$ (as 4T3)	trivial	$2$	$2$	$9.40204384113$
4.0.11025.1	$x^{4} - x^{3} + 4 x^{2} - 15 x + 15$	$4$	[0,2]	$3^{2}\cdot 5^{2}\cdot 7^{2}$	$3$	$10.246950766$	$10.246950765959598$	✓	✓		$C_2^2$ (as 4T2)	$[2]$	$2$	$1$	$3.13359847394$
4.4.11025.1	$x^{4} - 13 x^{2} + 16$	$4$	[4,0]	$3^{2}\cdot 5^{2}\cdot 7^{2}$	$3$	$10.246950766$	$10.246950765959598$		✓		$C_2^2$ (as 4T2)	trivial	$2$	$3$	$6.64477622728$
4.0.11025.2	$x^{4} + 11 x^{2} + 4$	$4$	[0,2]	$3^{2}\cdot 5^{2}\cdot 7^{2}$	$3$	$10.246950766$	$10.246950765959598$	✓	✓		$C_2^2$ (as 4T2)	$[2]$	$2$	$1$	$8.81314098615$
4.0.11417.2	$x^{4} - 2 x^{3} + 7 x^{2} - 6 x + 16$	$4$	[0,2]	$7^{2}\cdot 233$	$2$	$10.3368449083$	$40.38564101261734$				$D_{4}$ (as 4T3)	trivial	$2$	$1$	$18.0164890918$
4.0.12397.2	$x^{4} - 2 x^{3} + 2 x^{2} - x + 16$	$4$	[0,2]	$7^{2}\cdot 11\cdot 23$	$3$	$10.5518631551$	$42.08325082500163$				$D_{4}$ (as 4T3)	trivial	$2$	$1$	$8.63060244424$
4.0.12544.1	$x^{4} + 8 x^{2} + 9$	$4$	[0,2]	$2^{8}\cdot 7^{2}$	$2$	$10.5830052443$	$10.583005244258363$	✓	✓		$C_2^2$ (as 4T2)	$[4]$	$2$	$1$	$2.76865938331$
4.0.12544.2	$x^{4} + 49$	$4$	[0,2]	$2^{8}\cdot 7^{2}$	$2$	$10.5830052443$	$10.583005244258363$	✓	✓		$C_2^2$ (as 4T2)	$[4]$	$4$	$1$	$3.40008441411$
4.0.12789.1	$x^{4} - 2 x^{3} + x + 16$	$4$	[0,2]	$3^{2}\cdot 7^{2}\cdot 29$	$3$	$10.6343058518$	$24.677925358506133$			✓	$D_{4}$ (as 4T3)	$[2]$	$2$	$1$	$4.16348864333$
4.0.13132.2	$x^{4} - x^{3} + 5 x^{2} - 12 x + 18$	$4$	[0,2]	$2^{2}\cdot 7^{2}\cdot 67$	$3$	$10.7049025594$	$43.31281565541543$				$D_{4}$ (as 4T3)	trivial	$2$	$1$	$5.20419011527$
4.0.13769.1	$x^{4} - 2 x^{3} - 5 x^{2} + 6 x + 16$	$4$	[0,2]	$7^{2}\cdot 281$	$2$	$10.8324227345$	$44.35087372307337$				$D_{4}$ (as 4T3)	trivial	$2$	$1$	$20.2451842028$
4.0.13916.2	$x^{4} - x^{3} - 3 x^{2} - 8 x + 22$	$4$	[0,2]	$2^{2}\cdot 7^{2}\cdot 71$	$3$	$10.861219859$	$44.58699361921591$				$D_{4}$ (as 4T3)	trivial	$2$	$1$	$4.7619559584$
4.0.14161.1	$x^{4} - 5 x^{2} + 36$	$4$	[0,2]	$7^{2}\cdot 17^{2}$	$2$	$10.9087121146$	$10.908712114635714$	✓	✓		$C_2^2$ (as 4T2)	$[5]$	$2$	$1$	$4.18942509452$
4.0.15484.1	$x^{4} - x^{3} - 7 x^{2} + 8 x + 22$	$4$	[0,2]	$2^{2}\cdot 7^{2}\cdot 79$	$3$	$11.1550312345$	$47.031904065219386$				$D_{4}$ (as 4T3)	trivial	$2$	$1$	$5.27691511571$
4.0.16317.2	$x^{4} - 2 x^{3} + 6 x^{2} - 5 x + 22$	$4$	[0,2]	$3^{2}\cdot 7^{2}\cdot 37$	$3$	$11.3021242754$	$27.874719729532707$				$D_{4}$ (as 4T3)	$[2]$	$2$	$1$	$4.96971749814$
4.0.16513.1	$x^{4} - 2 x^{3} + 9 x^{2} - 8 x + 23$	$4$	[0,2]	$7^{2}\cdot 337$	$2$	$11.3359127667$	$48.569537778323564$				$D_{4}$ (as 4T3)	trivial	$2$	$1$	$3.59264479079$
4.0.16856.1	$x^{4} - x^{3} + 7 x^{2} - 13 x + 22$	$4$	[0,2]	$2^{3}\cdot 7^{2}\cdot 43$	$3$	$11.3943257342$	$49.07137658554119$				$D_{4}$ (as 4T3)	trivial	$2$	$1$	$14.1943811486$
4.0.17248.3	$x^{4} - 5 x^{2} + 22$	$4$	[0,2]	$2^{5}\cdot 7^{2}\cdot 11$	$3$	$11.4600018008$	$35.09985754956849$				$D_{4}$ (as 4T3)	$[2]$	$2$	$1$	$4.29741767551$
4.2.17444.1	$x^{4} - x^{3} - 2 x^{2} - 5 x - 3$	$4$	[2,1]	$-\,2^{2}\cdot 7^{2}\cdot 89$	$3$	$11.4924208002$	$49.91993589739474$			✓	$S_4$ (as 4T5)	trivial	$2$	$2$	$11.0177158457$
4.0.19061.1	$x^{4} - 2 x^{3} - 8 x^{2} + 9 x + 22$	$4$	[0,2]	$7^{2}\cdot 389$	$2$	$11.7499608707$	$52.182372502598994$			✓	$D_{4}$ (as 4T3)	trivial	$2$	$1$	$10.3854398565$
4.0.19404.1	$x^{4} - x^{3} + 11 x^{2} - 8 x + 22$	$4$	[0,2]	$2^{2}\cdot 3^{2}\cdot 7^{2}\cdot 11$	$4$	$11.8024675892$	$30.397368307141328$				$D_{4}$ (as 4T3)	$[2]$	$2$	$1$	$2.88446488466$
4.4.19600.1	$x^{4} - 2 x^{3} - 15 x^{2} + 16 x + 29$	$4$	[4,0]	$2^{4}\cdot 5^{2}\cdot 7^{2}$	$3$	$11.8321595662$	$11.832159566199232$		✓		$C_2^2$ (as 4T2)	trivial	$2$	$3$	$6.60263997027$
4.0.19600.2	$x^{4} - 17 x^{2} + 81$	$4$	[0,2]	$2^{4}\cdot 5^{2}\cdot 7^{2}$	$3$	$11.8321595662$	$11.832159566199232$	✓	✓		$C_2^2$ (as 4T2)	$[2]$	$4$	$1$	$4.95577746058$
4.0.19649.1	$x^{4} - 2 x^{3} - 7 x^{2} + 8 x + 23$	$4$	[0,2]	$7^{2}\cdot 401$	$2$	$11.8395477431$	$52.98112871579842$				$D_{4}$ (as 4T3)	trivial	$2$	$1$	$3.73769760687$
4.2.20727.2	$x^{4} - x^{3} - 2 x^{2} + 9 x - 3$	$4$	[2,1]	$-\,3^{2}\cdot 7^{2}\cdot 47$	$3$	$11.9986977047$	$31.416556144810016$				$D_{4}$ (as 4T3)	trivial	$2$	$2$	$11.7068873209$
4.2.20727.3	$x^{4} - 2 x^{3} - 7 x^{2} + 8 x - 5$	$4$	[2,1]	$-\,3^{2}\cdot 7^{2}\cdot 47$	$3$	$11.9986977047$	$31.416556144810016$				$D_{4}$ (as 4T3)	trivial	$2$	$2$	$7.33569336447$
4.0.20776.1	$x^{4} - x^{3} + 11 x^{2} - x + 22$	$4$	[0,2]	$2^{3}\cdot 7^{2}\cdot 53$	$3$	$12.0057828555$	$54.47935388750494$				$D_{4}$ (as 4T3)	$[2]$	$2$	$1$	$8.19589383834$
4.0.20776.2	$x^{4} - x^{3} + 4 x^{2} - 15 x + 29$	$4$	[0,2]	$2^{3}\cdot 7^{2}\cdot 53$	$3$	$12.0057828555$	$54.47935388750494$				$D_{4}$ (as 4T3)	$[2]$	$2$	$1$	$3.05628951175$
4.0.20972.1	$x^{4} - x^{3} + 7 x^{2} + 8 x + 22$	$4$	[0,2]	$2^{2}\cdot 7^{2}\cdot 107$	$3$	$12.033998756$	$54.735728733616035$			✓	$D_{4}$ (as 4T3)	trivial	$2$	$1$	$5.22084933116$
4.0.23177.2	$x^{4} - 2 x^{3} - x^{2} + 2 x + 29$	$4$	[0,2]	$7^{2}\cdot 11\cdot 43$	$3$	$12.3385551098$	$57.54128952326321$				$D_{4}$ (as 4T3)	trivial	$2$	$1$	$3.10590857455$

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