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Label	Polynomial	Degree	Signature	Discriminant	Ram. prime count	Root discriminant	Galois root discriminant	Monogenic	Galois group	Class group	Unit group torsion	Unit group rank	Regulator
9.1.7126573229.1	$x^{9} - x^{8} + 5 x^{7} - 6 x^{6} + 5 x^{5} - 14 x^{4} - 3 x^{3} - 10 x^{2} - 3 x - 1$	$9$	[1,4]	$31^{3}\cdot 139\cdot 1721$	$3$	$12.4384002594$	$2723.1946313108065$	?	$S_3\wr S_3$ (as 9T31)	$[2]$	$2$	$4$	$11.8851105087$
9.1.8008148501.1	$x^{9} - 3 x^{8} + 5 x^{7} - 6 x^{6} + 9 x^{5} - 11 x^{4} + 8 x^{3} + 5 x + 1$	$9$	[1,4]	$31^{3}\cdot 268811$	$2$	$12.6006357522$	$2886.7180326453777$	?	$S_3\wr S_3$ (as 9T31)	$[2]$	$2$	$4$	$12.8527700601$
9.1.8770691453.1	$x^{9} - 4 x^{8} + 13 x^{7} - 29 x^{6} + 54 x^{5} - 79 x^{4} + 93 x^{3} - 87 x^{2} + 58 x - 19$	$9$	[1,4]	$23^{3}\cdot 107\cdot 6737$	$3$	$12.7286263234$	$4071.824775208285$	?	$S_3\wr S_3$ (as 9T31)	$[2]$	$2$	$4$	$11.599521033$
9.1.9194881741.1	$x^{9} - x^{8} + 5 x^{7} - x^{6} + 4 x^{5} + 11 x^{4} - 9 x^{3} + 35 x^{2} - 9 x + 25$	$9$	[1,4]	$23^{3}\cdot 733\cdot 1031$	$3$	$12.7956008207$	$4169.128086302938$	?	$S_3\wr S_3$ (as 9T31)	$[2]$	$2$	$4$	$13.7006202034$
9.1.9455991101.1	$x^{9} - 2 x^{8} + 4 x^{7} - 3 x^{6} - 6 x^{5} + 20 x^{4} - 22 x^{3} + 4 x^{2} + 4 x + 1$	$9$	[1,4]	$31^{3}\cdot 317411$	$2$	$12.835473517$	$3136.8361449077956$	?	$S_3\wr S_3$ (as 9T31)	$[2]$	$2$	$4$	$14.5156526121$
9.1.9483875477.1	$x^{9} - x^{7} - x^{6} - 9 x^{5} + 10 x^{4} + 15 x^{3} - 21 x^{2} + 8 x - 1$	$9$	[1,4]	$31^{3}\cdot 318347$	$2$	$12.8396735698$	$3141.4577826225836$	?	$S_3\wr S_3$ (as 9T31)	$[2]$	$2$	$4$	$14.6662111482$
9.1.9501750077.1	$x^{9} - 2 x^{8} + 3 x^{7} - 3 x^{6} + 15 x^{4} - x^{3} - 7 x^{2} + 2 x + 1$	$9$	[1,4]	$31^{3}\cdot 313\cdot 1019$	$3$	$12.8423601416$	$3144.4167980724183$	?	$S_3\wr S_3$ (as 9T31)	$[2]$	$2$	$4$	$13.2860058748$
9.1.9613287581.1	$x^{9} - 3 x^{8} + 5 x^{7} - 6 x^{6} + 3 x^{5} - 6 x^{4} + x^{3} - 6 x^{2} - 5 x - 1$	$9$	[1,4]	$31^{3}\cdot 523\cdot 617$	$3$	$12.8590235803$	$3162.8185215089406$	?	$S_3\wr S_3$ (as 9T31)	$[2]$	$2$	$4$	$15.4913624732$
9.1.9653772313.1	$x^{9} - 4 x^{8} + 6 x^{7} - 3 x^{6} + x^{5} + 11 x^{4} - 5 x^{3} - 20 x^{2} + 15 x - 1$	$9$	[1,4]	$23^{3}\cdot 793439$	$2$	$12.8650294145$	$4271.8961831954675$		$S_3\wr S_3$ (as 9T31)	$[2]$	$2$	$4$	$13.3052232896$
9.1.9750756928.1	$x^{9} + 2 x^{7} - 3 x^{6} + 2 x^{5} + 6 x^{4} + 7 x^{3} + 14 x^{2} - 8 x + 1$	$9$	[1,4]	$2^{6}\cdot 11^{3}\cdot 114467$	$3$	$12.8793263457$	$1781.242943004396$	?	$S_3\wr S_3$ (as 9T31)	$[2]$	$2$	$4$	$21.6658077629$
9.1.10154128021.1	$x^{9} - 4 x^{7} + 4 x^{5} - 8 x^{4} + 23 x^{3} - 16 x^{2} - 1$	$9$	[1,4]	$23^{3}\cdot 101\cdot 8263$	$3$	$12.9374648131$	$4381.204058247002$	✓	$S_3\wr S_3$ (as 9T31)	$[2]$	$2$	$4$	$14.1545205273$
9.1.10363595093.1	$x^{9} - 3 x^{8} + 7 x^{7} - 19 x^{6} + 26 x^{5} - 47 x^{4} + 43 x^{3} - 37 x^{2} + 15 x - 11$	$9$	[1,4]	$23^{3}\cdot 317\cdot 2687$	$3$	$12.966850179$	$4426.162785076934$	?	$S_3\wr S_3$ (as 9T31)	$[2]$	$2$	$4$	$13.3626466901$
9.1.10518099833.1	$x^{9} - x^{8} - 2 x^{7} + 4 x^{6} + 3 x^{5} - 7 x^{4} + 7 x^{3} - 5 x^{2} - x + 9$	$9$	[1,4]	$31^{3}\cdot 89\cdot 3967$	$3$	$12.9881886384$	$3308.315734629934$		$S_3\wr S_3$ (as 9T31)	$[2]$	$2$	$4$	$16.356958417$
9.1.10630233157.1	$x^{9} - 4 x^{8} + 10 x^{7} - 18 x^{6} + 17 x^{5} + 2 x^{4} - 16 x^{3} + 3 x^{2} + 5 x + 1$	$9$	[1,4]	$31^{3}\cdot 239\cdot 1493$	$3$	$13.0035014376$	$3325.9039372778043$	?	$S_3\wr S_3$ (as 9T31)	$[2]$	$2$	$4$	$14.6542414594$
9.1.10816986181.1	$x^{9} - x^{8} - 4 x^{7} + 3 x^{6} + 10 x^{5} - 5 x^{4} - 24 x^{3} + 15 x^{2} + 29 x - 25$	$9$	[1,4]	$23^{3}\cdot 889043$	$2$	$13.0286883936$	$4521.945267249484$	✓	$S_3\wr S_3$ (as 9T31)	$[2]$	$2$	$4$	$16.5850850171$
9.1.11015356949.1	$x^{9} - 2 x^{8} + 4 x^{6} - 3 x^{5} - 12 x^{4} + 10 x^{3} + 23 x^{2} + 13 x + 1$	$9$	[1,4]	$23^{3}\cdot 905347$	$2$	$13.055022343$	$4563.2204636637925$	?	$S_3\wr S_3$ (as 9T31)	$[2]$	$2$	$4$	$15.372072184$
9.1.11075668189.1	$x^{9} - 3 x^{8} + 7 x^{7} - 14 x^{6} + 22 x^{5} - 27 x^{4} + 28 x^{3} - 26 x^{2} + 12 x - 9$	$9$	[1,4]	$31^{3}\cdot 371779$	$2$	$13.0629451727$	$3394.8709842938065$		$S_3\wr S_3$ (as 9T31)	$[2]$	$2$	$4$	$16.5774448937$
9.1.11219329088.1	$x^{9} - x^{8} + 5 x^{6} - 2 x^{5} - 3 x^{4} + 5 x^{3} - 4 x^{2} - 4 x + 4$	$9$	[1,4]	$2^{6}\cdot 11^{3}\cdot 131707$	$3$	$13.081663918$	$1910.6777011853908$	?	$S_3\wr S_3$ (as 9T31)	$[2]$	$2$	$4$	$22.5818233186$
9.1.11296852661.1	$x^{9} + 6 x^{7} - 2 x^{6} + 15 x^{5} - 5 x^{4} + 14 x^{3} - 5 x^{2} - 6 x + 7$	$9$	[1,4]	$23^{3}\cdot 59\cdot 15737$	$3$	$13.0916767604$	$4621.158837348052$	?	$S_3\wr S_3$ (as 9T31)	$[2]$	$2$	$4$	$15.1607498334$
9.1.11373578189.1	$x^{9} - 3 x^{8} + 8 x^{6} - 5 x^{5} - 11 x^{4} + 14 x^{3} + 7 x^{2} - 23 x + 13$	$9$	[1,4]	$31^{3}\cdot 293\cdot 1303$	$3$	$13.1015265704$	$3440.2251379815248$	?	$S_3\wr S_3$ (as 9T31)	$[2]$	$2$	$4$	$15.9330320853$
9.1.11557323797.1	$x^{9} - 3 x^{8} + 10 x^{7} - 12 x^{6} + 19 x^{5} - 2 x^{4} + 6 x^{3} + 11 x^{2} + 6 x - 1$	$9$	[1,4]	$23^{3}\cdot 949891$	$2$	$13.1248773425$	$4674.130186462504$	?	$S_3\wr S_3$ (as 9T31)	$[2]$	$2$	$4$	$17.1659503283$
9.1.11669503537.3	$x^{9} - 5 x^{7} - 2 x^{6} + 10 x^{5} + 12 x^{4} - 17 x^{2} - 6 x - 1$	$9$	[1,4]	$23^{3}\cdot 661\cdot 1451$	$3$	$13.1389716498$	$4696.759840570944$		$S_3\wr S_3$ (as 9T31)	$[2]$	$2$	$4$	$15.0553377338$
9.1.11773611737.2	$x^{9} - x^{8} - 4 x^{7} + 5 x^{6} + 3 x^{5} - 11 x^{4} + 21 x^{3} - 18 x^{2} + 4 x - 1$	$9$	[1,4]	$31^{3}\cdot 227\cdot 1741$	$3$	$13.1519445073$	$3500.202422717863$		$S_3\wr S_3$ (as 9T31)	$[2]$	$2$	$4$	$17.4395289305$
9.1.11833855373.1	$x^{9} - 2 x^{8} + x^{7} + 2 x^{6} - 8 x^{5} - 9 x^{4} + 46 x^{3} - 40 x^{2} + 11 x - 1$	$9$	[1,4]	$23^{3}\cdot 37\cdot 97\cdot 271$	$4$	$13.1594049281$	$4729.718490565797$	?	$S_3\wr S_3$ (as 9T31)	$[2]$	$2$	$4$	$13.1929110155$
9.1.11877802577.1	$x^{9} - x^{8} - 3 x^{7} - 7 x^{6} + 7 x^{5} + 23 x^{4} + 7 x^{3} - 8 x^{2} - 12 x - 8$	$9$	[1,4]	$23^{3}\cdot 976231$	$2$	$13.164825973$	$4738.492692829651$		$S_3\wr S_3$ (as 9T31)	$[2]$	$2$	$4$	$15.0906798444$
9.1.12016930669.1	$x^{9} - 3 x^{8} + 7 x^{7} - 6 x^{6} + 3 x^{5} + 3 x^{4} - 4 x^{2} + 2 x + 1$	$9$	[1,4]	$59^{3}\cdot 58511$	$2$	$13.181871136$	$1857.995963397122$		$S_3\wr S_3$ (as 9T31)	$[2]$	$2$	$4$	$28.0291360515$
9.1.12039877412.1	$x^{9} - 2 x^{8} + x^{7} + 9 x^{6} - 12 x^{5} + 10 x^{4} + 8 x^{3} + 2 x + 1$	$9$	[1,4]	$2^{2}\cdot 83\cdot 331^{3}$	$3$	$13.1846655694$	$263.11142507980094$	?	$S_3\wr S_3$ (as 9T31)	$[2]$	$2$	$4$	$21.4599103268$
9.1.12230548241.1	$x^{9} - 2 x^{8} - x^{7} + 4 x^{5} - 8 x^{4} + 17 x^{3} + 6 x^{2} - 8 x - 8$	$9$	[1,4]	$23^{3}\cdot 1005223$	$2$	$13.2077039293$	$4808.339526281396$		$S_3\wr S_3$ (as 9T31)	$[2]$	$2$	$4$	$14.9678751321$
9.1.12307196541.1	$x^{9} - x^{7} - 2 x^{6} - x^{5} + x^{4} + 6 x^{3} + 2 x^{2} + 4 x - 1$	$9$	[1,4]	$3\cdot 181\cdot 283^{3}$	$3$	$13.2168753127$	$392.0063774991422$	?	$S_3\wr S_3$ (as 9T31)	$[2]$	$2$	$4$	$20.1881817097$
9.1.12326618873.1	$x^{9} - 2 x^{8} - 2 x^{7} + x^{5} + 2 x^{4} + 19 x^{3} + 42 x^{2} + 32 x + 8$	$9$	[1,4]	$23^{3}\cdot 907\cdot 1117$	$3$	$13.2191912357$	$4827.187276251047$		$S_3\wr S_3$ (as 9T31)	$[2]$	$2$	$4$	$15.4812288049$
9.1.12326890189.1	$x^{9} - 3 x^{8} + 6 x^{7} - 10 x^{6} + 7 x^{5} - 8 x^{4} + 8 x^{3} + 9 x^{2} + 1$	$9$	[1,4]	$31^{3}\cdot 413779$	$2$	$13.2192235645$	$3581.50094234247$	?	$S_3\wr S_3$ (as 9T31)	$[2]$	$2$	$4$	$17.0039549136$
9.1.12503967893.2	$x^{9} - x^{8} - x^{7} + 7 x^{6} - x^{4} + 13 x^{3} + 9 x^{2} + 11 x + 9$	$9$	[1,4]	$31^{3}\cdot 43^{2}\cdot 227$	$3$	$13.240189639$	$550.082721052025$	?	$S_3\wr S_3$ (as 9T31)	$[2]$	$2$	$4$	$16.2223052101$
9.1.12592200149.1	$x^{9} - x^{8} + 2 x^{7} - 8 x^{6} + 9 x^{5} + 20 x^{4} - 56 x^{3} + 59 x^{2} - 36 x + 11$	$9$	[1,4]	$23^{3}\cdot 101\cdot 10247$	$3$	$13.2505380368$	$4878.911866389882$	?	$S_3\wr S_3$ (as 9T31)	$[2]$	$2$	$4$	$14.2768945003$
9.1.12702971773.1	$x^{9} - 2 x^{8} + 3 x^{7} - 3 x^{6} - 2 x^{5} + 10 x^{4} - 12 x^{3} + 12 x^{2} + x + 1$	$9$	[1,4]	$31^{3}\cdot 577\cdot 739$	$3$	$13.2634391147$	$3635.7245495224197$		$S_3\wr S_3$ (as 9T31)	$[2]$	$2$	$4$	$18.115829627$
9.1.12711339413.1	$x^{9} - 4 x^{8} + 7 x^{7} - 13 x^{6} + 20 x^{5} - 13 x^{4} + 17 x^{3} - 7 x^{2} - 6 x - 1$	$9$	[1,4]	$23^{3}\cdot 1044739$	$2$	$13.2644095893$	$4901.938086104312$	?	$S_3\wr S_3$ (as 9T31)	$[2]$	$2$	$4$	$14.9971213438$
9.1.12772403776.1	$x^{9} - 4 x^{7} - 3 x^{6} + 8 x^{5} + 8 x^{4} - x^{3} - 8 x^{2} - 4 x - 1$	$9$	[1,4]	$2^{6}\cdot 11^{3}\cdot 149939$	$3$	$13.2714746596$	$2038.6389210951806$	?	$S_3\wr S_3$ (as 9T31)	$[2]$	$2$	$4$	$24.6637925755$
9.1.12860995136.1	$x^{9} - 2 x^{8} + x^{6} + 8 x^{4} - 11 x^{3} - 8 x^{2} + 14 x + 1$	$9$	[1,4]	$2^{6}\cdot 11^{3}\cdot 150979$	$3$	$13.2816713763$	$2045.6968602961967$	?	$S_3\wr S_3$ (as 9T31)	$[2]$	$2$	$4$	$24.9762772026$
9.1.13121951329.1	$x^{9} - 3 x^{8} + 9 x^{7} - 11 x^{6} + 15 x^{5} - 5 x^{4} + 14 x^{3} - 6 x^{2} + 25 x + 1$	$9$	[1,4]	$23^{3}\cdot 937\cdot 1151$	$3$	$13.311348293$	$4980.482004786284$		$S_3\wr S_3$ (as 9T31)	$[2]$	$2$	$4$	$15.3775774244$
9.1.13307035733.1	$x^{9} - 2 x^{8} - 4 x^{7} + 15 x^{6} - 4 x^{5} - 32 x^{4} + 44 x^{3} + 6 x^{2} - 46 x + 23$	$9$	[1,4]	$23^{3}\cdot 1093699$	$2$	$13.332080423$	$5015.483725424698$	?	$S_3\wr S_3$ (as 9T31)	$[2]$	$2$	$4$	$14.2245294763$
9.1.13309141597.1	$x^{9} - 2 x^{8} + 2 x^{6} + 4 x^{5} - 14 x^{4} + 19 x^{3} - 14 x^{2} + 6 x - 1$	$9$	[1,4]	$331^{3}\cdot 367$	$2$	$13.3323148318$	$348.53550751680956$	✓	$S_3\wr S_3$ (as 9T31)	$[2]$	$2$	$4$	$13.1759200389$
9.1.13494816553.1	$x^{9} - 3 x^{8} + 7 x^{7} - 12 x^{6} + 13 x^{5} - 14 x^{4} + 20 x^{3} - 6 x^{2} + 4 x - 1$	$9$	[1,4]	$31^{3}\cdot 452983$	$2$	$13.352854277$	$3747.328781945881$		$S_3\wr S_3$ (as 9T31)	$[2]$	$2$	$4$	$18.213701791$
9.1.13526820421.1	$x^{9} - 3 x^{8} + 8 x^{7} - 4 x^{6} + 7 x^{5} - 9 x^{4} + 34 x^{3} - 3 x^{2} + 11 x + 1$	$9$	[1,4]	$23^{3}\cdot 337\cdot 3299$	$3$	$13.356369151$	$5056.733036259676$	?	$S_3\wr S_3$ (as 9T31)	$[2]$	$2$	$4$	$14.6036660399$
9.1.13600990453.1	$x^{9} + 6 x^{7} - 4 x^{6} + 18 x^{5} - 14 x^{4} + 23 x^{3} - 30 x^{2} + 18 x - 1$	$9$	[1,4]	$23^{3}\cdot 103\cdot 10853$	$3$	$13.3644866575$	$5070.577580512894$	?	$S_3\wr S_3$ (as 9T31)	$[2]$	$2$	$4$	$14.1380659559$
9.1.13647419725.1	$x^{9} - 2 x^{8} + 9 x^{7} - 13 x^{6} + 30 x^{5} - 28 x^{4} + 48 x^{3} - 20 x^{2} + 32 x - 1$	$9$	[1,4]	$5^{2}\cdot 23^{3}\cdot 44867$	$3$	$13.3695480861$	$2271.4984041376742$	?	$S_3\wr S_3$ (as 9T31)	$[2]$	$2$	$4$	$14.5199638261$
9.1.13954904149.2	$x^{9} - 2 x^{8} + x^{7} - 4 x^{6} + 3 x^{5} + 9 x^{4} + 12 x^{3} - 28 x^{2} + 10 x - 1$	$9$	[1,4]	$23^{3}\cdot 1146947$	$2$	$13.4026869287$	$5136.125095828566$	?	$S_3\wr S_3$ (as 9T31)	$[2]$	$2$	$4$	$14.417102519$
9.1.14387952013.1	$x^{9} - x^{8} + 9 x^{7} - 10 x^{6} + 32 x^{5} - 35 x^{4} + 54 x^{3} - 44 x^{2} + 36 x - 7$	$9$	[1,4]	$23^{3}\cdot 1182539$	$2$	$13.4482741367$	$5215.2082412881655$	?	$S_3\wr S_3$ (as 9T31)	$[2]$	$2$	$4$	$17.7292406226$
9.1.14472439661.1	$x^{9} - x^{8} - x^{7} - 3 x^{6} + 10 x^{5} + 7 x^{4} - 11 x^{3} + 9 x^{2} + 15 x + 1$	$9$	[1,4]	$23^{3}\cdot 1189483$	$2$	$13.4570257386$	$5230.497968645051$	?	$S_3\wr S_3$ (as 9T31)	$[2]$	$2$	$4$	$14.8374320736$
9.1.14483054493.1	$x^{9} - 3 x^{8} + 2 x^{7} + 5 x^{6} - 14 x^{5} + 17 x^{4} - 12 x^{3} + 7 x^{2} - 3 x + 1$	$9$	[1,4]	$3^{2}\cdot 71\cdot 283^{3}$	$3$	$13.4581220563$	$245.5178201271753$	✓	$S_3\wr S_3$ (as 9T31)	$[2]$	$2$	$4$	$13.5662529616$
9.1.14488208093.1	$x^{9} - x^{8} - 2 x^{7} + x^{6} - 4 x^{5} + 11 x^{4} + 28 x^{3} + 5 x^{2} - 5 x + 1$	$9$	[1,4]	$23^{5}\cdot 2251$	$2$	$13.4586540712$	$647.0844212535872$	?	$S_3\wr S_3$ (as 9T31)	$[2]$	$2$	$4$	$14.3865421013$
9.1.14610438208.1	$x^{9} - 2 x^{8} + 11 x^{6} - 14 x^{5} - 4 x^{4} + 27 x^{3} - 20 x^{2} + 8 x - 1$	$9$	[1,4]	$2^{6}\cdot 19^{3}\cdot 83\cdot 401$	$4$	$13.471223045$	$1262.3352120331351$	?	$S_3\wr S_3$ (as 9T31)	$[2]$	$2$	$4$	$34.4562617912$

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This project is supported by grants from the US National Science Foundation, the UK Engineering and Physical Sciences Research Council, and the Simons Foundation.