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Label	Polynomial	Degree	Signature	Discriminant	Ram. prime count	Root discriminant	Galois root discriminant	Galois	Monogenic	Galois group	Class group	Unit group torsion	Unit group rank	Regulator
9.9.9685993193.1	$x^{9} - 9 x^{7} + 24 x^{5} - 2 x^{4} - 20 x^{3} + 3 x^{2} + 5 x - 1$	$9$	[9,0]	$9685993193$	$1$	$12.8697933433$	$98417.44354025865$		✓	$S_9$ (as 9T34)	trivial	$2$	$8$	$62.3871578911$
9.9.11779563529.1	$x^{9} - 9 x^{7} - 2 x^{6} + 22 x^{5} + 5 x^{4} - 17 x^{3} - 4 x^{2} + 4 x + 1$	$9$	[9,0]	$11779563529$	$1$	$13.1526830709$	$108533.69766574803$		✓	$S_9$ (as 9T34)	trivial	$2$	$8$	$70.2532718066$
9.9.16240385609.1	$x^{9} - x^{8} - 9 x^{7} + 4 x^{6} + 26 x^{5} - 2 x^{4} - 25 x^{3} - x^{2} + 7 x + 1$	$9$	[9,0]	$7^{6}\cdot 138041$	$2$	$13.6304660092$	$1359.5736588385284$		✓	$S_3 \wr C_3 $ (as 9T28)	trivial	$2$	$8$	$86.0068912213$
9.9.16440305941.1	$x^{9} - 2 x^{8} - 9 x^{7} + 11 x^{6} + 28 x^{5} - 18 x^{4} - 34 x^{3} + 8 x^{2} + 13 x + 1$	$9$	[9,0]	$37^{2}\cdot 229^{3}$	$2$	$13.6490083503$	$168.0295085661925$		✓	$C_3 \wr S_3 $ (as 9T20)	trivial	$2$	$8$	$88.7274555605$
9.9.16898785417.1	$x^{9} - 2 x^{8} - 7 x^{7} + 11 x^{6} + 18 x^{5} - 17 x^{4} - 19 x^{3} + 6 x^{2} + 7 x + 1$	$9$	[9,0]	$17\cdot 994046201$	$2$	$13.6907861842$	$129995.32844298675$		✓	$S_9$ (as 9T34)	trivial	$2$	$8$	$86.8916845133$
9.9.16983563041.1	$x^{9} - x^{8} - 8 x^{7} + 7 x^{6} + 21 x^{5} - 15 x^{4} - 20 x^{3} + 10 x^{2} + 5 x - 1$	$9$	[9,0]	$19^{8}$	$1$	$13.698400752$	$13.69840075203899$	✓	✓	$C_9$ (as 9T1)	trivial	$2$	$8$	$87.132402653$
9.9.17515230173.1	$x^{9} - 4 x^{8} - 3 x^{7} + 29 x^{6} - 26 x^{5} - 24 x^{4} + 34 x^{3} - 2 x^{2} - 5 x + 1$	$9$	[9,0]	$7^{6}\cdot 53^{3}$	$2$	$13.7453979089$	$26.640147687438905$		✓	$S_3\times C_3$ (as 9T4)	trivial	$2$	$8$	$92.2723177847$
9.9.18625670317.1	$x^{9} - 9 x^{7} - x^{6} + 23 x^{5} + 4 x^{4} - 19 x^{3} - 3 x^{2} + 4 x + 1$	$9$	[9,0]	$18625670317$	$1$	$13.8396002436$	$136475.89646893696$		✓	$S_9$ (as 9T34)	trivial	$2$	$8$	$95.7516616162$
9.9.18756753353.1	$x^{9} - 3 x^{8} - 4 x^{7} + 15 x^{6} + 4 x^{5} - 22 x^{4} - x^{3} + 10 x^{2} - 1$	$9$	[9,0]	$13\cdot 11743\cdot 122867$	$3$	$13.8503887436$	$136955.29691472324$		✓	$S_9$ (as 9T34)	trivial	$2$	$8$	$94.1793807753$
9.9.19936446593.1	$x^{9} - 3 x^{8} - 5 x^{7} + 17 x^{6} + 7 x^{5} - 30 x^{4} - x^{3} + 16 x^{2} - 2 x - 1$	$9$	[9,0]	$7^{6}\cdot 169457$	$2$	$13.9445757545$	$1506.358873599988$		✓	$S_3 \wr C_3 $ (as 9T28)	trivial	$2$	$8$	$96.5906109701$
9.9.20370652633.1	$x^{9} - x^{8} - 8 x^{7} + 8 x^{6} + 17 x^{5} - 15 x^{4} - 12 x^{3} + 8 x^{2} + 2 x - 1$	$9$	[9,0]	$20370652633$	$1$	$13.9779986334$	$142725.79526140325$		✓	$S_9$ (as 9T34)	trivial	$2$	$8$	$97.8358327625$
9.9.22211510281.1	$x^{9} - x^{8} - 9 x^{7} + 3 x^{6} + 22 x^{5} - x^{4} - 17 x^{3} - 2 x^{2} + 4 x + 1$	$9$	[9,0]	$22211510281$	$1$	$14.1130144999$	$149035.26522605313$		✓	$S_9$ (as 9T34)	trivial	$2$	$8$	$107.779777867$
9.9.22384826361.1	$x^{9} - 9 x^{7} - x^{6} + 24 x^{5} + 3 x^{4} - 22 x^{3} + 6 x - 1$	$9$	[9,0]	$3^{12}\cdot 73\cdot 577$	$3$	$14.1252082329$	$887.9960002144848$		✓	$S_3 \wr C_3 $ (as 9T28)	trivial	$2$	$8$	$103.558573046$
9.9.23041013113.1	$x^{9} - 9 x^{7} - x^{6} + 24 x^{5} + 3 x^{4} - 21 x^{3} - 4 x^{2} + 5 x + 1$	$9$	[9,0]	$23041013113$	$1$	$14.1706268953$	$151792.66488536264$		✓	$S_9$ (as 9T34)	trivial	$2$	$8$	$107.339716518$
9.9.25405254289.1	$x^{9} - x^{8} - 9 x^{7} + 5 x^{6} + 22 x^{5} - 8 x^{4} - 17 x^{3} + 5 x^{2} + 4 x - 1$	$9$	[9,0]	$25405254289$	$1$	$14.3252634041$	$159390.25782336885$		✓	$S_9$ (as 9T34)	trivial	$2$	$8$	$117.128921779$
9.9.29297320489.1	$x^{9} - 3 x^{8} - 5 x^{7} + 19 x^{6} + 4 x^{5} - 36 x^{4} + 9 x^{3} + 18 x^{2} - 9 x + 1$	$9$	[9,0]	$23\cdot 1273796543$	$2$	$14.5539499805$	$171164.6005720809$		✓	$S_9$ (as 9T34)	trivial	$2$	$8$	$127.371942561$
9.9.29397823793.1	$x^{9} - x^{8} - 9 x^{7} + 5 x^{6} + 22 x^{5} - 8 x^{4} - 16 x^{3} + 5 x^{2} + 3 x - 1$	$9$	[9,0]	$13\cdot 373\cdot 1229\cdot 4933$	$4$	$14.5594889578$	$171457.93592890358$		✓	$S_9$ (as 9T34)	trivial	$2$	$8$	$122.474102739$
9.9.29430250297.1	$x^{9} - x^{8} - 8 x^{7} + 6 x^{6} + 20 x^{5} - 11 x^{4} - 18 x^{3} + 7 x^{2} + 4 x - 1$	$9$	[9,0]	$7^{6}\cdot 250153$	$2$	$14.5612724687$	$1830.212643150634$		✓	$S_3 \wr C_3 $ (as 9T28)	trivial	$2$	$8$	$120.592925589$
9.9.30609108809.1	$x^{9} - 2 x^{8} - 7 x^{7} + 12 x^{6} + 17 x^{5} - 20 x^{4} - 18 x^{3} + 8 x^{2} + 7 x + 1$	$9$	[9,0]	$61\cdot 5171\cdot 97039$	$3$	$14.6249543978$	$174954.59070570284$		✓	$S_9$ (as 9T34)	trivial	$2$	$8$	$123.971330019$
9.9.31381059609.1	$x^{9} - 9 x^{7} + 27 x^{5} - 30 x^{3} + 9 x - 1$	$9$	[9,0]	$3^{22}$	$1$	$14.665484$	$14.665483999969616$	✓	✓	$C_9$ (as 9T1)	trivial	$2$	$8$	$159.898566189$
9.9.32202550729.1	$x^{9} - x^{8} - 9 x^{7} + 5 x^{6} + 26 x^{5} - 5 x^{4} - 24 x^{3} + x^{2} + 6 x + 1$	$9$	[9,0]	$19\cdot 31\cdot 54673261$	$3$	$14.7076526185$	$179450.6916370065$		✓	$S_9$ (as 9T34)	trivial	$2$	$8$	$126.091252215$
9.9.33600968473.1	$x^{9} - x^{8} - 9 x^{7} + 11 x^{6} + 20 x^{5} - 27 x^{4} - 10 x^{3} + 17 x^{2} - 2 x - 1$	$9$	[9,0]	$33600968473$	$1$	$14.7772848143$	$183305.66950588298$		✓	$S_9$ (as 9T34)	trivial	$2$	$8$	$133.332255247$
9.9.34189107913.1	$x^{9} - x^{8} - 8 x^{7} + 8 x^{6} + 18 x^{5} - 17 x^{4} - 12 x^{3} + 10 x^{2} + x - 1$	$9$	[9,0]	$1019\cdot 33551627$	$2$	$14.8058032658$	$184902.96891342767$		✓	$S_9$ (as 9T34)	trivial	$2$	$8$	$138.987493305$
9.9.34651324493.1	$x^{9} - 4 x^{8} - 2 x^{7} + 22 x^{6} - 10 x^{5} - 34 x^{4} + 25 x^{3} + 10 x^{2} - 8 x + 1$	$9$	[9,0]	$34651324493$	$1$	$14.8279113933$	$186148.66234544906$		✓	$S_9$ (as 9T34)	trivial	$2$	$8$	$141.306893163$
9.9.34800272761.1	$x^{9} - 3 x^{8} - 5 x^{7} + 17 x^{6} + 9 x^{5} - 30 x^{4} - 8 x^{3} + 16 x^{2} + 3 x - 1$	$9$	[9,0]	$34800272761$	$1$	$14.834979854$	$186548.31213656155$		✓	$S_9$ (as 9T34)	trivial	$2$	$8$	$148.935801471$
9.9.35754308089.1	$x^{9} - 2 x^{8} - 7 x^{7} + 11 x^{6} + 14 x^{5} - 17 x^{4} - 10 x^{3} + 8 x^{2} + 2 x - 1$	$9$	[9,0]	$7283\cdot 4909283$	$2$	$14.8796269138$	$189088.09610602143$		✓	$S_9$ (as 9T34)	trivial	$2$	$8$	$137.599317923$
9.9.35896709933.1	$x^{9} - 2 x^{8} - 7 x^{7} + 11 x^{6} + 16 x^{5} - 19 x^{4} - 13 x^{3} + 11 x^{2} + 2 x - 1$	$9$	[9,0]	$7^{6}\cdot 463\cdot 659$	$3$	$14.8861999989$	$2021.3052134345623$		✓	$S_3 \wr C_3 $ (as 9T28)	trivial	$2$	$8$	$142.337918176$
9.9.36288414161.1	$x^{9} - 2 x^{8} - 7 x^{7} + 15 x^{6} + 11 x^{5} - 29 x^{4} + 13 x^{2} - 2 x - 1$	$9$	[9,0]	$409\cdot 88724729$	$2$	$14.9041617233$	$190495.181463994$		✓	$S_9$ (as 9T34)	trivial	$2$	$8$	$143.862687459$
9.9.36446755221.1	$x^{9} - 9 x^{7} - x^{6} + 24 x^{5} + 6 x^{4} - 18 x^{3} - 6 x^{2} + 3 x + 1$	$9$	[9,0]	$3^{12}\cdot 68581$	$2$	$14.9113736262$	$1133.0878421457462$		✓	$S_3 \wr C_3 $ (as 9T28)	trivial	$2$	$8$	$143.044860663$
9.9.36763077169.1	$x^{9} - 4 x^{8} - 2 x^{7} + 22 x^{6} - 14 x^{5} - 22 x^{4} + 20 x^{3} + 2 x^{2} - 5 x + 1$	$9$	[9,0]	$7^{6}\cdot 13^{2}\cdot 43^{2}$	$3$	$14.9256980207$	$248.31706433165067$		✓	$C_3 \wr C_3 $ (as 9T17)	trivial	$2$	$8$	$137.053104106$
9.9.36911831833.1	$x^{9} - 2 x^{8} - 7 x^{7} + 11 x^{6} + 17 x^{5} - 17 x^{4} - 15 x^{3} + 8 x^{2} + 4 x - 1$	$9$	[9,0]	$139\cdot 265552747$	$2$	$14.9323964217$	$192124.52168580669$		✓	$S_9$ (as 9T34)	trivial	$2$	$8$	$141.500734421$
9.9.37161412073.1	$x^{9} - x^{8} - 8 x^{7} + 6 x^{6} + 19 x^{5} - 11 x^{4} - 15 x^{3} + 6 x^{2} + 3 x - 1$	$9$	[9,0]	$101\cdot 367934773$	$2$	$14.9435812693$	$192772.95472394463$		✓	$S_9$ (as 9T34)	trivial	$2$	$8$	$146.090962678$
9.9.53038958912.1	$x^{9} - x^{8} - 9 x^{7} + 6 x^{6} + 22 x^{5} - 9 x^{4} - 17 x^{3} + 5 x^{2} + 4 x - 1$	$9$	[9,0]	$2^{6}\cdot 37^{3}\cdot 16361$	$3$	$15.5461074699$	$1235.0724893715435$		✓	$S_3\wr S_3$ (as 9T31)	trivial	$2$	$8$	$177.201889286$
9.9.53286643921.1	$x^{9} - 2 x^{8} - 8 x^{7} + 18 x^{6} + 10 x^{5} - 36 x^{4} + 10 x^{3} + 12 x^{2} - 7 x + 1$	$9$	[9,0]	$7^{6}\cdot 673^{2}$	$2$	$15.5541572538$	$281.02313187907936$		✓	$C_3 \wr C_3 $ (as 9T17)	trivial	$2$	$8$	$176.828462779$
9.9.62523502209.1	$x^{9} - 15 x^{7} - 4 x^{6} + 54 x^{5} + 12 x^{4} - 38 x^{3} - 9 x^{2} + 6 x + 1$	$9$	[9,0]	$3^{12}\cdot 7^{6}$	$2$	$15.8328962637$	$15.83289626371223$	✓		$C_3^2$ (as 9T2)	trivial	$2$	$8$	$212.533159721$
9.9.63162460553.1	$x^{9} - x^{8} - 11 x^{7} + 9 x^{6} + 34 x^{5} - 10 x^{4} - 39 x^{3} - 12 x^{2} + 3 x + 1$	$9$	[9,0]	$61^{2}\cdot 257^{3}$	$2$	$15.8507933654$	$248.4199394965967$		?	$C_3 \wr S_3 $ (as 9T20)	trivial	$2$	$8$	$180.740325882$
9.9.69573030289.1	$x^{9} - x^{8} - 10 x^{7} + 14 x^{6} + 20 x^{5} - 36 x^{4} + 18 x^{2} - 8 x + 1$	$9$	[9,0]	$7^{6}\cdot 769^{2}$	$2$	$16.0219605382$	$307.149340067649$		✓	$C_3 \wr C_3 $ (as 9T17)	trivial	$2$	$8$	$234.89346257$
9.9.69775386569.1	$x^{9} - 10 x^{7} - 2 x^{6} + 31 x^{5} + 11 x^{4} - 30 x^{3} - 16 x^{2} + x + 1$	$9$	[9,0]	$7^{6}\cdot 593081$	$2$	$16.0271317006$	$2818.0954511280875$		✓	$S_3 \wr C_3 $ (as 9T28)	trivial	$2$	$8$	$211.18652949646722$
9.9.74724856128.1	$x^{9} - 3 x^{8} - 9 x^{7} + 14 x^{6} + 24 x^{5} - 15 x^{4} - 21 x^{3} + 3 x^{2} + 6 x + 1$	$9$	[9,0]	$2^{6}\cdot 3^{12}\cdot 13^{3}$	$3$	$16.1496378363$	$24.76395538367976$		✓	$S_3\times C_3$ (as 9T4)	trivial	$2$	$8$	$216.126778464$
9.9.80174499328.1	$x^{9} - 4 x^{8} - 6 x^{7} + 29 x^{6} + 19 x^{5} - 63 x^{4} - 41 x^{3} + 18 x^{2} + 5 x - 1$	$9$	[9,0]	$2^{9}\cdot 7^{6}\cdot 11^{3}$	$3$	$16.2764460888$	$34.32733034460722$		✓	$S_3\times C_3$ (as 9T4)	trivial	$2$	$8$	$234.388460085$
9.9.100602531136.1	$x^{9} - 3 x^{8} - 5 x^{7} + 20 x^{6} - 31 x^{4} + 7 x^{3} + 15 x^{2} - 2 x - 1$	$9$	[9,0]	$2^{6}\cdot 37^{3}\cdot 31033$	$3$	$16.6921431626$	$1700.9807805094924$		✓	$S_3\wr S_3$ (as 9T31)	trivial	$2$	$8$	$257.146391902$
9.9.114864601117.1	$x^{9} - 4 x^{8} - 4 x^{7} + 24 x^{6} + 4 x^{5} - 40 x^{4} - x^{3} + 20 x^{2} - 1$	$9$	[9,0]	$7^{6}\cdot 41\cdot 23813$	$3$	$16.9398507161$	$3615.744029005373$		?	$S_3 \wr C_3 $ (as 9T28)	trivial	$2$	$8$	$287.55792881488884$
9.9.139858796529.1	$x^{9} - 18 x^{7} - 3 x^{6} + 45 x^{5} + 9 x^{4} - 36 x^{3} - 9 x^{2} + 9 x + 3$	$9$	[9,0]	$3^{18}\cdot 19^{2}$	$2$	$17.3145008613$	$75.41010411601474$		✓	$C_3 \wr C_3 $ (as 9T17)	trivial	$2$	$8$	$389.602926161$
9.9.144872805473.1	$x^{9} - 4 x^{8} - 4 x^{7} + 28 x^{6} - 14 x^{5} - 29 x^{4} + 15 x^{3} + 10 x^{2} - 3 x - 1$	$9$	[9,0]	$11^{3}\cdot 37^{2}\cdot 43^{3}$	$3$	$17.3823965046$	$241.48957456928824$		?	$C_3 \wr S_3 $ (as 9T20)	trivial	$2$	$8$	$335.764904866$
9.9.164648481361.1	$x^{9} - 14 x^{7} + 63 x^{5} - 98 x^{3} + 42 x - 7$	$9$	[9,0]	$7^{8}\cdot 13^{4}$	$2$	$17.6312941965$	$31.176485742782422$		?	$C_9:C_3$ (as 9T6)	trivial	$2$	$8$	$349.786286149$
9.9.174583151469.1	$x^{9} - 12 x^{7} - 3 x^{6} + 36 x^{5} + 6 x^{4} - 30 x^{3} + 6 x - 1$	$9$	[9,0]	$3^{15}\cdot 23^{3}$	$2$	$17.7464450991$	$31.810664815402767$		?	$S_3\times C_3$ (as 9T4)	trivial	$2$	$8$	$464.326538723$
9.9.177559431424.1	$x^{9} - 4 x^{8} - 4 x^{7} + 22 x^{6} + 10 x^{5} - 36 x^{4} - 18 x^{3} + 16 x^{2} + 12 x + 2$	$9$	[9,0]	$2^{8}\cdot 37^{3}\cdot 13693$	$3$	$17.7798086566$	$1318.051514496552$		✓	$S_3\wr S_3$ (as 9T31)	trivial	$2$	$8$	$572.355821352$
9.9.183637853504.1	$x^{9} - 14 x^{7} - 8 x^{6} + 56 x^{5} + 56 x^{4} - 44 x^{3} - 56 x^{2} + 8$	$9$	[9,0]	$2^{6}\cdot 7^{6}\cdot 29^{3}$	$3$	$17.846430146$	$31.281268504572243$		?	$S_3\times C_3$ (as 9T4)	trivial	$2$	$8$	$349.512616311$
9.9.187076145529.1	$x^{9} - 15 x^{7} - 10 x^{6} + 47 x^{5} + 23 x^{4} - 52 x^{3} - 5 x^{2} + 13 x - 1$	$9$	[9,0]	$7^{6}\cdot 13^{2}\cdot 97^{2}$	$3$	$17.8832517509$	$427.1123058534058$		?	$C_3 \wr C_3 $ (as 9T17)	trivial	$2$	$8$	$335.060700671$
9.9.188860645561.1	$x^{9} - x^{8} - 12 x^{7} + 42 x^{5} + 28 x^{4} - 28 x^{3} - 32 x^{2} - 10 x - 1$	$9$	[9,0]	$7^{8}\cdot 181^{2}$	$2$	$17.9021259289$	$180.43355574409867$		✓	$C_3 \wr C_3 $ (as 9T17)	trivial	$2$	$8$	$389.835362791$

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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.