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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
4.2.507.1	$x^{4} - x^{3} - x^{2} - x + 1$	$4$	[2,1]	$-\,3\cdot 13^{2}$	$2$	$4.74517233601$	$6.244997998398398$			✓	$D_{4}$ (as 4T3)	trivial	$2$	$2$	$0.649395711926$
4.2.2704.1	$x^{4} - 3 x^{2} - 1$	$4$	[2,1]	$-\,2^{4}\cdot 13^{2}$	$2$	$7.21110255093$	$10.198039027185569$			✓	$D_{4}$ (as 4T3)	trivial	$2$	$2$	$2.55514700441$
4.0.2873.1	$x^{4} - x^{3} + x^{2} - 2 x + 4$	$4$	[0,2]	$13^{2}\cdot 17$	$2$	$7.32122757009$	$14.866068747318506$	✓			$D_{4}$ (as 4T3)	trivial	$2$	$1$	$2.38952643457$
4.4.4225.1	$x^{4} - 9 x^{2} + 4$	$4$	[4,0]	$5^{2}\cdot 13^{2}$	$2$	$8.0622577483$	$8.06225774829855$		✓		$C_2^2$ (as 4T2)	trivial	$2$	$3$	$3.19257767414$
4.2.8112.1	$x^{4} - x^{2} - 3$	$4$	[2,1]	$-\,2^{4}\cdot 3\cdot 13^{2}$	$3$	$9.49034467201$	$12.489995996796797$			✓	$D_{4}$ (as 4T3)	trivial	$2$	$2$	$6.15369517281$
4.0.8281.1	$x^{4} - x^{3} + 5 x^{2} - 4 x + 3$	$4$	[0,2]	$7^{2}\cdot 13^{2}$	$2$	$9.53939201417$	$13.193814370085985$			✓	$A_4$ (as 4T4)	$[2]$	$2$	$1$	$2.66193075$
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	$2$	$1$	$2.38952643457$
4.4.10816.1	$x^{4} - 2 x^{3} - 9 x^{2} + 10 x - 1$	$4$	[4,0]	$2^{6}\cdot 13^{2}$	$2$	$10.1980390272$	$10.198039027185569$		✓		$C_2^2$ (as 4T2)	trivial	$2$	$3$	$4.87014657656$
4.0.10816.2	$x^{4} - 2 x^{3} - x^{2} + 2 x + 27$	$4$	[0,2]	$2^{6}\cdot 13^{2}$	$2$	$10.1980390272$	$10.198039027185569$	✓	✓		$C_2^2$ (as 4T2)	$[3]$	$2$	$1$	$2.38952643457$
4.0.11661.1	$x^{4} - x^{3} + 3 x^{2} - 3 x + 9$	$4$	[0,2]	$3\cdot 13^{2}\cdot 23$	$3$	$10.3916365515$	$29.949958263743873$	✓			$D_{4}$ (as 4T3)	$[2]$	$2$	$1$	$2.38952643457$
4.4.11661.1	$x^{4} - 2 x^{3} - 4 x^{2} + 5 x + 3$	$4$	[4,0]	$3\cdot 13^{2}\cdot 23$	$3$	$10.3916365515$	$29.949958263743873$			✓	$D_{4}$ (as 4T3)	trivial	$2$	$3$	$8.58274234488$
4.2.13351.1	$x^{4} - x^{3} - 2 x^{2} - 7 x - 3$	$4$	[2,1]	$-\,13^{2}\cdot 79$	$2$	$10.7492570639$	$32.046840717924134$				$D_{4}$ (as 4T3)	trivial	$2$	$2$	$7.72158948671$
4.2.14703.2	$x^{4} - 2 x^{3} + 7 x^{2} - 6 x - 4$	$4$	[2,1]	$-\,3\cdot 13^{2}\cdot 29$	$3$	$11.011626932$	$33.63034344160047$				$D_{4}$ (as 4T3)	trivial	$2$	$2$	$6.32993857103$
4.2.14703.3	$x^{4} - x^{3} + 3 x^{2} + 10 x - 4$	$4$	[2,1]	$-\,3\cdot 13^{2}\cdot 29$	$3$	$11.011626932$	$33.63034344160047$				$D_{4}$ (as 4T3)	trivial	$2$	$2$	$10.026984968$
4.2.16900.2	$x^{4} - x^{2} - 16$	$4$	[2,1]	$-\,2^{2}\cdot 5^{2}\cdot 13^{2}$	$3$	$11.401754251$	$16.1245154965971$				$D_{4}$ (as 4T3)	$[2]$	$2$	$2$	$9.63060791938$
4.4.17069.1	$x^{4} - x^{3} - 8 x^{2} - 4 x + 3$	$4$	[4,0]	$13^{2}\cdot 101$	$2$	$11.4301523645$	$36.235341863986875$			✓	$D_{4}$ (as 4T3)	trivial	$2$	$3$	$8.83283066561$
4.2.18083.1	$x^{4} - x^{3} + 5 x^{2} - 17 x + 3$	$4$	[2,1]	$-\,13^{2}\cdot 107$	$2$	$11.5962513609$	$37.296112397943034$				$D_{4}$ (as 4T3)	trivial	$2$	$2$	$10.996558893$
4.0.18252.1	$x^{4} - x^{3} + 6 x^{2} + 2 x + 4$	$4$	[0,2]	$2^{2}\cdot 3^{3}\cdot 13^{2}$	$3$	$11.6232509648$	$16.437759153264928$				$D_{4}$ (as 4T3)	$[4]$	$2$	$1$	$5.39746890278$
4.0.18252.2	$x^{4} - 3 x^{2} + 12$	$4$	[0,2]	$2^{2}\cdot 3^{3}\cdot 13^{2}$	$3$	$11.6232509648$	$16.437759153264928$				$D_{4}$ (as 4T3)	$[4]$	$2$	$1$	$2.47180204665$
4.0.20449.1	$x^{4} - x^{2} + 36$	$4$	[0,2]	$11^{2}\cdot 13^{2}$	$2$	$11.9582607431$	$11.958260743101398$	✓	✓		$C_2^2$ (as 4T2)	$[5]$	$2$	$1$	$2.38952643457$
4.0.21801.1	$x^{4} - x^{3} + 6 x^{2} - 11 x + 17$	$4$	[0,2]	$3\cdot 13^{2}\cdot 43$	$3$	$12.151198171$	$40.95119045888654$	✓			$D_{4}$ (as 4T3)	$[4]$	$2$	$1$	$2.38952643457$
4.4.21801.1	$x^{4} - x^{3} - 7 x^{2} + 2 x + 4$	$4$	[4,0]	$3\cdot 13^{2}\cdot 43$	$3$	$12.151198171$	$40.95119045888654$				$D_{4}$ (as 4T3)	trivial	$2$	$3$	$10.6046729554$
4.2.22139.1	$x^{4} - x^{3} - 7 x^{2} - 11 x - 9$	$4$	[2,1]	$-\,13^{2}\cdot 131$	$2$	$12.198024465$	$41.2674205639267$				$D_{4}$ (as 4T3)	trivial	$2$	$2$	$12.3706674547$
4.2.23491.1	$x^{4} - x^{3} + x^{2} + 11 x - 9$	$4$	[2,1]	$-\,13^{2}\cdot 139$	$2$	$12.3801348778$	$42.50882261366456$				$D_{4}$ (as 4T3)	trivial	$2$	$2$	$7.41171737731$
4.2.24336.2	$x^{4} - 9 x^{2} - 9$	$4$	[2,1]	$-\,2^{4}\cdot 3^{2}\cdot 13^{2}$	$3$	$12.4899959968$	$17.663521732655695$				$D_{4}$ (as 4T3)	$[2]$	$2$	$2$	$4.45446328808$
4.4.25857.1	$x^{4} - x^{3} - 8 x^{2} + 9 x + 3$	$4$	[4,0]	$3^{2}\cdot 13^{2}\cdot 17$	$3$	$12.6807381252$	$25.748786379167466$				$D_{4}$ (as 4T3)	trivial	$2$	$3$	$14.4793070433$
4.2.26871.1	$x^{4} - 2 x^{3} + 5 x^{2} - 4 x - 9$	$4$	[2,1]	$-\,3\cdot 13^{2}\cdot 53$	$3$	$12.803271565$	$45.46427168667722$				$D_{4}$ (as 4T3)	$[2]$	$2$	$2$	$7.24847935197$
4.2.26871.2	$x^{4} - x^{3} - x^{2} + 12 x - 12$	$4$	[2,1]	$-\,3\cdot 13^{2}\cdot 53$	$3$	$12.803271565$	$45.46427168667722$				$D_{4}$ (as 4T3)	$[2]$	$2$	$2$	$4.3460994676$
4.4.29237.1	$x^{4} - 2 x^{3} - 6 x^{2} + 7 x + 9$	$4$	[4,0]	$13^{2}\cdot 173$	$2$	$13.0762496035$	$47.4236228055175$			✓	$D_{4}$ (as 4T3)	trivial	$2$	$3$	$11.8867910971$
4.0.30589.1	$x^{4} - x^{3} + 6 x^{2} + 2 x + 17$	$4$	[0,2]	$13^{2}\cdot 181$	$2$	$13.2248672058$	$48.507731342539614$	✓			$D_{4}$ (as 4T3)	trivial	$2$	$1$	$2.38952643457$
4.2.30927.1	$x^{4} - 2 x^{3} - x^{2} + 2 x - 12$	$4$	[2,1]	$-\,3\cdot 13^{2}\cdot 61$	$3$	$13.2612495776$	$48.774993593028796$				$D_{4}$ (as 4T3)	$[2]$	$2$	$2$	$7.82312113144$
4.2.30927.2	$x^{4} - x^{3} + 6 x^{2} + 15 x - 9$	$4$	[2,1]	$-\,3\cdot 13^{2}\cdot 61$	$3$	$13.2612495776$	$48.774993593028796$				$D_{4}$ (as 4T3)	$[2]$	$2$	$2$	$7.93493201484$
4.2.32279.1	$x^{4} - x^{3} + 3 x^{2} - 16 x - 4$	$4$	[2,1]	$-\,13^{2}\cdot 191$	$2$	$13.4038641628$	$49.82971001320397$				$D_{4}$ (as 4T3)	trivial	$2$	$2$	$7.35197021222$
4.0.32448.1	$x^{4} + 10 x^{2} + 12$	$4$	[0,2]	$2^{6}\cdot 3\cdot 13^{2}$	$3$	$13.4213741468$	$24.979991993593593$	✓			$D_{4}$ (as 4T3)	$[2]$	$2$	$1$	$2.38952643457$
4.4.32448.1	$x^{4} - 10 x^{2} + 12$	$4$	[4,0]	$2^{6}\cdot 3\cdot 13^{2}$	$3$	$13.4213741468$	$24.979991993593593$				$D_{4}$ (as 4T3)	trivial	$2$	$3$	$18.2793947124$
4.2.35659.3	$x^{4} - x^{3} - 8 x^{2} + 22 x - 23$	$4$	[2,1]	$-\,13^{2}\cdot 211$	$2$	$13.7417578061$	$52.373657500693994$				$D_{4}$ (as 4T3)	trivial	$2$	$2$	$9.10263290773$
4.0.38025.1	$x^{4} - x^{3} - x^{2} + 25 x + 40$	$4$	[0,2]	$3^{2}\cdot 5^{2}\cdot 13^{2}$	$3$	$13.9642400438$	$13.96424004376894$	✓	✓		$C_2^2$ (as 4T2)	$[8]$	$2$	$1$	$5.55294456145$
4.0.38025.2	$x^{4} + x^{2} + 49$	$4$	[0,2]	$3^{2}\cdot 5^{2}\cdot 13^{2}$	$3$	$13.9642400438$	$13.96424004376894$	✓	✓		$C_2^2$ (as 4T2)	$[2, 2]$	$2$	$1$	$2.38952643457$
4.0.38025.3	$x^{4} + 17 x^{2} + 121$	$4$	[0,2]	$3^{2}\cdot 5^{2}\cdot 13^{2}$	$3$	$13.9642400438$	$13.96424004376894$	✓	✓		$C_2^2$ (as 4T2)	$[8]$	$2$	$1$	$0.962423650119$
4.4.39377.1	$x^{4} - 2 x^{3} - 9 x^{2} + 10 x + 12$	$4$	[4,0]	$13^{2}\cdot 233$	$2$	$14.0867451099$	$55.036351623268054$				$D_{4}$ (as 4T3)	trivial	$2$	$3$	$19.1731032049$
4.0.43264.1	$x^{4} - 12 x^{2} + 49$	$4$	[0,2]	$2^{8}\cdot 13^{2}$	$2$	$14.4222051019$	$14.422205101855956$	✓	✓		$C_2^2$ (as 4T2)	$[2]$	$2$	$1$	$4.62487668255$
4.0.43264.2	$x^{4} + 12 x^{2} + 49$	$4$	[0,2]	$2^{8}\cdot 13^{2}$	$2$	$14.4222051019$	$14.422205101855956$	✓	✓		$C_2^2$ (as 4T2)	$[6]$	$2$	$1$	$1.76274717404$
4.4.43433.1	$x^{4} - x^{3} - 14 x^{2} + 25 x + 1$	$4$	[4,0]	$13^{2}\cdot 257$	$2$	$14.4362687023$	$57.8013840664737$				$D_{4}$ (as 4T3)	trivial	$2$	$3$	$20.2378324211$
4.2.44447.1	$x^{4} - x^{3} - x^{2} - 14 x - 12$	$4$	[2,1]	$-\,13^{2}\cdot 263$	$2$	$14.5197992969$	$58.47221562417487$				$D_{4}$ (as 4T3)	trivial	$2$	$2$	$24.6514243541$
4.4.45968.1	$x^{4} - 9 x^{2} + 17$	$4$	[4,0]	$2^{4}\cdot 13^{2}\cdot 17$	$3$	$14.6424551402$	$29.732137494637012$			✓	$D_{4}$ (as 4T3)	trivial	$2$	$3$	$18.0810087504$
4.4.46813.1	$x^{4} - x^{3} - 10 x^{2} + 10 x + 9$	$4$	[4,0]	$13^{2}\cdot 277$	$2$	$14.7092868863$	$60.00833275470999$				$D_{4}$ (as 4T3)	trivial	$2$	$3$	$25.1624107449$
4.0.52221.1	$x^{4} - x^{3} + 12 x^{2} + 12 x + 27$	$4$	[0,2]	$3\cdot 13^{2}\cdot 103$	$3$	$15.1168497315$	$63.3798075099633$	✓			$D_{4}$ (as 4T3)	$[4]$	$2$	$1$	$2.38952643457$
4.4.52221.1	$x^{4} - 2 x^{3} - 8 x^{2} + 9 x + 17$	$4$	[4,0]	$3\cdot 13^{2}\cdot 103$	$3$	$15.1168497315$	$63.3798075099633$			✓	$D_{4}$ (as 4T3)	trivial	$2$	$3$	$11.5995762707$
4.2.56615.1	$x^{4} - x^{3} - 2 x^{2} - 7 x - 16$	$4$	[2,1]	$-\,5\cdot 13^{2}\cdot 67$	$3$	$15.4252736712$	$65.99242380758567$			✓	$S_4$ (as 4T5)	$[2]$	$2$	$2$	$9.77772225919$
4.0.56953.1	$x^{4} - x^{3} + 11 x^{2} - 20 x + 36$	$4$	[0,2]	$13^{2}\cdot 337$	$2$	$15.4482451029$	$66.18912297349165$	✓			$D_{4}$ (as 4T3)	$[9]$	$2$	$1$	$2.38952643457$

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