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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
7.1.184607.1	$x^{7} - x^{6} - x^{5} + x^{4} - x^{2} + x + 1$	$7$	[1,3]	$-\,184607$	$1$	$5.65354907534$	$429.65916724771506$	✓	$S_7$ (as 7T7)	trivial	$2$	$3$	$0.38044710632$
7.1.193327.1	$x^{7} - x^{6} + 2 x^{4} - 2 x^{3} + 2 x - 1$	$7$	[1,3]	$-\,193327$	$1$	$5.69094835632$	$439.68966328536766$	✓	$S_7$ (as 7T7)	trivial	$2$	$3$	$0.393017719366$
7.1.193607.1	$x^{7} - x^{4} - x^{3} + x^{2} + 1$	$7$	[1,3]	$-\,193607$	$1$	$5.69212510227$	$440.0079544735527$	✓	$S_7$ (as 7T7)	trivial	$2$	$3$	$0.393408738575$
7.1.196127.1	$x^{7} - 2 x^{6} + 2 x^{5} - x^{4} + 2 x^{2} - 2 x + 1$	$7$	[1,3]	$-\,29\cdot 6763$	$2$	$5.70265067941$	$442.86228107618285$	✓	$S_7$ (as 7T7)	trivial	$2$	$3$	$0.396915724261$
7.1.199559.1	$x^{7} - x^{6} + x^{3} - x + 1$	$7$	[1,3]	$-\,199559$	$1$	$5.71680061491$	$446.7202704153909$	✓	$S_7$ (as 7T7)	trivial	$2$	$3$	$0.401633777334$
7.1.201671.1	$x^{7} - x^{6} + 2 x^{5} - 2 x^{4} + 2 x^{3} - 2 x^{2} + 2 x - 1$	$7$	[1,3]	$-\,17\cdot 11863$	$2$	$5.72540492691$	$449.07794423685516$	✓	$S_7$ (as 7T7)	trivial	$2$	$3$	$0.404575486366$
7.1.202471.1	$x^{7} - x^{6} - x^{5} + 2 x^{4} - x^{2} + 1$	$7$	[1,3]	$-\,202471$	$1$	$5.72864397615$	$449.96777662406004$	✓	$S_7$ (as 7T7)	trivial	$2$	$3$	$0.406196645226$
7.1.207911.1	$x^{7} - x^{5} - x^{4} - x^{3} + x^{2} + x + 1$	$7$	[1,3]	$-\,11\cdot 41\cdot 461$	$3$	$5.75038312609$	$455.9725868953089$	✓	$S_7$ (as 7T7)	trivial	$2$	$3$	$0.413665504587$
7.1.211831.1	$x^{7} - x^{6} + 2 x^{5} - x^{4} + x^{2} - 2 x + 1$	$7$	[1,3]	$-\,19\cdot 11149$	$2$	$5.76574784303$	$460.2510184670969$	✓	$S_7$ (as 7T7)	trivial	$2$	$3$	$0.418943361216$
7.1.214607.1	$x^{7} - x^{6} + 2 x^{5} - 2 x^{4} + 2 x^{3} - 2 x^{2} - 1$	$7$	[1,3]	$-\,214607$	$1$	$5.77648183449$	$463.2569481400144$	✓	$S_7$ (as 7T7)	trivial	$2$	$3$	$0.422976590532$
7.1.224647.1	$x^{7} - 2 x^{5} - x^{4} + 2 x^{3} + 2 x^{2} - 1$	$7$	[1,3]	$-\,277\cdot 811$	$2$	$5.81433551514$	$473.96940829551437$	✓	$S_7$ (as 7T7)	trivial	$2$	$3$	$0.437537324447$
7.1.227287.1	$x^{7} - 2 x^{6} + 3 x^{5} - 3 x^{4} + 3 x^{3} - 2 x^{2} + 2 x - 1$	$7$	[1,3]	$-\,167\cdot 1361$	$2$	$5.82404795569$	$476.7462637504357$	✓	$S_7$ (as 7T7)	trivial	$2$	$3$	$0.440973429986$
7.1.237751.1	$x^{7} - x^{6} + x^{5} - x^{4} + x^{3} + x^{2} - 2 x + 1$	$7$	[1,3]	$-\,23\cdot 10337$	$2$	$5.86161755087$	$487.597169803107$	✓	$S_7$ (as 7T7)	trivial	$2$	$3$	$0.455031505787$
7.1.242147.1	$x^{7} - 2 x^{6} + 2 x^{5} - x^{4} - x^{3} + 2 x^{2} - x + 1$	$7$	[1,3]	$-\,242147$	$1$	$5.87697923351$	$492.0843423641927$	✓	$S_7$ (as 7T7)	trivial	$2$	$3$	$0.462048944553$
7.1.242971.1	$x^{7} - x^{6} - x^{5} + 2 x^{4} - 2 x^{2} + x + 1$	$7$	[1,3]	$-\,242971$	$1$	$5.87983203622$	$492.92088614705705$	✓	$S_7$ (as 7T7)	trivial	$2$	$3$	$0.463179955519$
7.1.250367.1	$x^{7} - 2 x^{6} + 4 x^{5} - 4 x^{4} + 3 x^{3} - x^{2} - x + 1$	$7$	[1,3]	$-\,13\cdot 19259$	$2$	$5.90507336826$	$500.3668654097711$	✓	$S_7$ (as 7T7)	trivial	$2$	$3$	$0.47044808157$
7.1.252071.1	$x^{7} - x^{6} + 2 x^{4} - x^{3} - 2 x^{2} + x + 1$	$7$	[1,3]	$-\,83\cdot 3037$	$2$	$5.91079811742$	$502.06672863275855$	✓	$S_7$ (as 7T7)	trivial	$2$	$3$	$0.477737923503$
7.1.261871.1	$x^{7} - x^{6} - x^{5} + 2 x^{4} - x^{3} - x^{2} + x - 1$	$7$	[1,3]	$-\,307\cdot 853$	$2$	$5.94309245715$	$511.7333289907938$	✓	$S_7$ (as 7T7)	trivial	$2$	$3$	$0.486346206108$
7.1.267347.1	$x^{7} - x^{4} - 2 x^{3} + x^{2} + x - 1$	$7$	[1,3]	$-\,101\cdot 2647$	$2$	$5.96068914485$	$517.0560898007101$	?	$S_7$ (as 7T7)	trivial	$2$	$3$	$0.494190197375$
7.1.270607.1	$x^{7} - x^{6} + x^{5} - 3 x^{4} + 2 x^{3} - 2 x^{2} + 2 x - 1$	$7$	[1,3]	$-\,461\cdot 587$	$2$	$5.97101871474$	$520.199000383507$	✓	$S_7$ (as 7T7)	trivial	$2$	$3$	$0.501506225408$
7.1.272671.1	$x^{7} - 2 x^{6} + 3 x^{5} - 4 x^{4} + 4 x^{3} - 3 x^{2} + x - 1$	$7$	[1,3]	$-\,7\cdot 38953$	$2$	$5.97750365205$	$522.1790880531314$	✓	$S_7$ (as 7T7)	trivial	$2$	$3$	$0.503526635102$
7.1.283223.1	$x^{7} + x^{3} - 2 x - 1$	$7$	[1,3]	$-\,61\cdot 4643$	$2$	$6.01001426292$	$532.1869972105669$	✓	$S_7$ (as 7T7)	trivial	$2$	$3$	$0.51649446517$
7.1.286711.1	$x^{7} - x^{5} - 2 x^{4} + x^{3} + 2 x^{2} - x - 1$	$7$	[1,3]	$-\,286711$	$1$	$6.02053253858$	$535.4540129646989$	✓	$S_7$ (as 7T7)	trivial	$2$	$3$	$0.522130800433$
7.1.289831.1	$x^{7} + x^{5} - x^{4} + x^{3} - x^{2} + x - 1$	$7$	[1,3]	$-\,109\cdot 2659$	$2$	$6.02984856129$	$538.3595452854904$	✓	$S_7$ (as 7T7)	trivial	$2$	$3$	$0.525879627826$
7.1.289987.1	$x^{7} - x^{6} + 2 x^{5} - 2 x^{4} + 2 x^{3} - x^{2} + x - 1$	$7$	[1,3]	$-\,289987$	$1$	$6.0303121021$	$538.5044103811964$	✓	$S_7$ (as 7T7)	trivial	$2$	$3$	$0.522561592791$
7.1.300527.1	$x^{7} - 2 x^{6} + 2 x^{5} - 2 x^{3} + 4 x^{2} - 3 x + 1$	$7$	[1,3]	$-\,29\cdot 43\cdot 241$	$3$	$6.06114655535$	$548.2034293945999$	✓	$S_7$ (as 7T7)	trivial	$2$	$3$	$0.554319459602$
7.1.311071.1	$x^{7} - x^{6} + 3 x^{5} - 3 x^{4} + 4 x^{3} - 4 x^{2} + 2 x - 1$	$7$	[1,3]	$-\,277\cdot 1123$	$2$	$6.09107879886$	$557.7373934030244$	✓	$S_7$ (as 7T7)	trivial	$2$	$3$	$0.551167883255$
7.1.315631.1	$x^{7} - x^{5} - 2 x^{4} + x^{2} + x + 1$	$7$	[1,3]	$-\,315631$	$1$	$6.10375499982$	$561.810466260642$	✓	$S_7$ (as 7T7)	trivial	$2$	$3$	$0.572829060133$
7.1.317159.1	$x^{7} - 3 x^{6} + 4 x^{5} - 4 x^{4} + 4 x^{3} - 4 x^{2} + 2 x - 1$	$7$	[1,3]	$-\,317159$	$1$	$6.10796753424$	$563.1687136196399$	✓	$S_7$ (as 7T7)	trivial	$2$	$3$	$0.574674996244$
7.1.319831.1	$x^{7} - x^{6} + 2 x^{4} - 3 x^{3} + 4 x^{2} - 3 x + 1$	$7$	[1,3]	$-\,319831$	$1$	$6.11529232696$	$565.5360289141621$	✓	$S_7$ (as 7T7)	trivial	$2$	$3$	$0.556553782424$
7.1.320975.1	$x^{7} - x^{6} + x^{5} - x^{4} + 2 x^{2} - 2 x + 1$	$7$	[1,3]	$-\,5^{2}\cdot 37\cdot 347$	$3$	$6.11841236479$	$331.31843579389084$	✓	$S_7$ (as 7T7)	trivial	$2$	$3$	$0.579234073903$
7.1.330487.1	$x^{7} + x^{5} - x^{3} - x - 1$	$7$	[1,3]	$-\,23\cdot 14369$	$2$	$6.14399177779$	$574.879987475647$	✓	$S_7$ (as 7T7)	trivial	$2$	$3$	$0.576186901918$
7.1.332447.1	$x^{7} - x^{5} - x^{4} + x^{3} + x^{2} - x - 1$	$7$	[1,3]	$-\,332447$	$1$	$6.14918399759$	$576.5821710736467$	✓	$S_7$ (as 7T7)	trivial	$2$	$3$	$0.593670022855$
7.1.334727.1	$x^{7} - x^{5} - 2 x^{4} - x^{3} + 2 x^{2} + x + 1$	$7$	[1,3]	$-\,334727$	$1$	$6.15519101525$	$578.5559609925388$	✓	$S_7$ (as 7T7)	trivial	$2$	$3$	$0.574923274999$
7.1.338191.1	$x^{7} - x^{4} - 2 x^{3} + 2 x + 1$	$7$	[1,3]	$-\,7\cdot 48313$	$2$	$6.16425068742$	$581.5419159441561$	✓	$S_7$ (as 7T7)	trivial	$2$	$3$	$0.58504050247$
7.1.349847.1	$x^{7} - x^{6} + x^{5} - x^{4} + x^{2} - x + 1$	$7$	[1,3]	$-\,19\cdot 18413$	$2$	$6.1941624833$	$591.4786555743157$	✓	$S_7$ (as 7T7)	trivial	$2$	$3$	$0.59590218239$
7.1.351587.1	$x^{7} - 2 x^{5} - 2 x^{4} + 2 x^{3} + 3 x^{2} - 1$	$7$	[1,3]	$-\,351587$	$1$	$6.19855417442$	$592.9477211356833$	✓	$S_7$ (as 7T7)	trivial	$2$	$3$	$0.638803050262$
7.1.351655.1	$x^{7} - x^{6} - 2 x^{4} + x^{3} + x + 1$	$7$	[1,3]	$-\,5\cdot 53\cdot 1327$	$3$	$6.19872542517$	$593.0050590003427$	✓	$S_7$ (as 7T7)	trivial	$2$	$3$	$0.616197560931$
7.1.357911.1	$x^{7} - x^{6} - x^{5} + x^{4} - x^{3} - x^{2} + 2 x + 1$	$7$	[1,3]	$-\,71^{3}$	$1$	$6.21436038191$	$8.426149773176359$	✓	$D_{7}$ (as 7T2)	trivial	$2$	$3$	$0.604934372036$
7.1.364871.1	$x^{7} - x^{6} + 2 x^{4} + 2 x + 1$	$7$	[1,3]	$-\,13^{2}\cdot 17\cdot 127$	$3$	$6.23148186231$	$167.5320864789787$	✓	$S_7$ (as 7T7)	trivial	$2$	$3$	$0.631311355925$
7.1.371131.1	$x^{7} - x^{4} - 2 x^{2} - x - 1$	$7$	[1,3]	$-\,371131$	$1$	$6.24664387708$	$609.2052199382405$	?	$S_7$ (as 7T7)	trivial	$2$	$3$	$0.662365609841$
7.1.373607.1	$x^{7} - x^{6} + x^{5} - 2 x^{3} + 3 x^{2} - 2 x + 1$	$7$	[1,3]	$-\,13\cdot 29\cdot 991$	$3$	$6.25258042141$	$611.2339977455442$	✓	$S_7$ (as 7T7)	trivial	$2$	$3$	$0.641053178539$
7.1.376163.1	$x^{7} - x^{6} - x^{4} - x^{3} + x^{2} + x + 1$	$7$	[1,3]	$-\,389\cdot 967$	$2$	$6.25867350642$	$613.3212861135671$	✓	$S_7$ (as 7T7)	trivial	$2$	$3$	$0.668307729133$
7.1.380831.1	$x^{7} - x^{5} - x^{4} - x^{3} + 2 x + 1$	$7$	[1,3]	$-\,11\cdot 89\cdot 389$	$3$	$6.26971024638$	$617.1150622047724$	✓	$S_7$ (as 7T7)	trivial	$2$	$3$	$0.63105320574$
7.1.382631.1	$x^{7} - x^{5} + x^{3} - x - 1$	$7$	[1,3]	$-\,382631$	$1$	$6.2739350993$	$618.5717419992608$	✓	$S_7$ (as 7T7)	trivial	$2$	$3$	$0.633168351139$
7.1.383687.1	$x^{7} - x^{6} + 2 x^{5} - 2 x^{4} + x^{3} - x + 1$	$7$	[1,3]	$-\,31\cdot 12377$	$2$	$6.27640575735$	$619.4247331193678$	✓	$S_7$ (as 7T7)	trivial	$2$	$3$	$0.652352405095$
7.1.396259.1	$x^{7} - x^{4} - x^{3} + x + 1$	$7$	[1,3]	$-\,396259$	$1$	$6.30538059113$	$629.491064273354$	✓	$S_7$ (as 7T7)	trivial	$2$	$3$	$0.644452230084$
7.1.397703.1	$x^{7} + x^{5} + x^{3} - 2 x^{2} + x - 1$	$7$	[1,3]	$-\,499\cdot 797$	$2$	$6.30865795045$	$630.6369795690703$	✓	$S_7$ (as 7T7)	trivial	$2$	$3$	$0.658575476914$
7.1.397991.1	$x^{7} - 2 x^{5} + 3 x^{3} - x^{2} - x + 1$	$7$	[1,3]	$-\,11\cdot 97\cdot 373$	$3$	$6.3093103863$	$630.8652788036444$	✓	$S_7$ (as 7T7)	trivial	$2$	$3$	$0.649296920624$
7.1.402011.1	$x^{7} - x^{6} + 2 x^{5} - 4 x^{4} + 3 x^{3} - 3 x^{2} + 2 x - 1$	$7$	[1,3]	$-\,73\cdot 5507$	$2$	$6.31837531276$	$634.0433739106497$	✓	$S_7$ (as 7T7)	trivial	$2$	$3$	$0.698068206909$

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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.