/*
Generated by Allan Steel in Magma, 2010.

Field defining polynomial: x^2 + x + 1 [Q(zeta_3)].

Traces:    [ 111, 0 ]
Density:   [ 0.99996753, 1.0000000 ]
Numer max: [ 3239, 2826 ]
Numer av:  [ 102.23742, 123.08362 ]
Denom max: [ 20, 20 ], [ [ <2, 2>, <5, 1> ], [ <2, 2>, <5, 1> ] ]
Denom LCM: [ 20, 20 ], [ [ <2, 2>, <5, 1> ], [ <2, 2>, <5, 1> ] ]
*/

G := PermutationGroup(ATLASGroup("3F22"));
M :=
GModule(G,[
Matrix(K,351,351,
[[123/10,381/10],[53/10,277/10],[-66/5,-173/10],[81/5,
-157/5],[151/5,46/5],[177/5,184/5],[101/5,151/10],[-47/5,
8/5],[-151/5,-99/5],[-31/10,-333/10],[291/10,37/2],[
227/5,-61/5],[127/10,23/10],[9/10,-39/5],[46/5,221/10],[
-60,-12],[-139/10,-166/5],[-112/5,-78/5],[-623/10,-103/10
],[-217/5,-129/5],[-339/10,-227/10],[-83/10,281/10],[
-41/5,-679/10],[211/10,36],[-9,-109/10],[83/10,297/10],[
329/10,5],[-269/10,-73/2],[-106/5,-57/2],[-737/10,-213/5],
[-129/5,-216/5],[-207/5,-253/10],[-418/5,-377/10],[9/5,
-102/5],[-191/5,-333/10],[-25/2,-23/2],[-72/5,63/5],[
123/5,38],[45,322/5],[-3/10,-17/10],[47/10,-133/10],[
42/5,-43/10],[101/5,282/5],[113/5,44/5],[487/10,91/2],[
-699/10,-579/10],[-111/5,-48/5],[4,182/5],[-131/2,-14],[
39/5,33],[69/5,-181/10],[27/2,167/10],[293/10,131/10],[
-119/5,89/5],[19/10,-34/5],[8/5,-156/5],[-126/5,-179/5],[
-6,-11/5],[-271/10,17/5],[-3/2,-163/10],[43/5,429/10],[
-151/10,-73/2],[29/5,53/2],[17,-81/10],[199/10,257/10],[
389/10,74/5],[-169/10,15],[171/5,16/5],[102/5,71/10],[
25,351/10],[37/10,-221/10],[-17/10,23/2],[-121/10,181/5],
[-69/10,221/10],[-104/5,35/2],[61/5,176/5],[-73/10,21/10
],[-31/10,-174/5],[14,0],[51/5,-3/5],[63/10,-16/5],[
121/10,10],[-36/5,-6],[-76/5,21/2],[-87/10,13/10],[
-101/10,-57/5],[-9/5,3/5],[148/5,68/5],[-19/5,2/5],[
29/10,1],[22,-97/5],[-29/10,-7],[-2/5,1/5],[-2/5,11/10
],[111/10,87/10],[-29/10,17/5],[12/5,22/5],[1/10,-4/5],
[7/10,16/5],[-93/10,-33/10],[69/10,83/10],[-63/5,-8/5],[
16/5,111/10],[31/10,11/2],[10,111/10],[-71/10,-7],[
-43/10,-43/5],[3,43/5],[-29/5,-8],[31/5,33/5],[-23/10,
21/10],[18/5,38/5],[1,-11/10],[17/2,-11/5],[51/5,27/10
],[1,4/5],[-37/10,-39/10],[-93/10,-47/5],[27/5,8/5],[
15/2,15/2],[3/10,13/5],[-3/10,11/5],[2,-29/10],[44/5,4
],[-7/2,-7],[-33/10,-1/2],[17/10,-42/5],[32/5,6],[
53/10,21/5],[8/5,-14/5],[-13/5,-1],[31/5,-11/5],[6/5,-3
],[9/10,2/5],[31/10,-4],[-19/10,6/5],[-2/5,17/5],[
-19/5,-13/10],[-17/5,-37/5],[-41/10,-12/5],[9/10,-49/10],
[-16/5,-38/5],[-17/10,-41/10],[-3,6/5],[19/10,-3/5],[
-5,-17/10],[41/10,17/5],[9/2,43/10],[-26/5,-97/10],[
28/5,6],[-21/10,3/5],[24/5,1],[-3/10,-6],[41/5,12/5],
[16/5,-24/5],[13,11],[-21/10,-22/5],[-51/10,-79/10],[
-24/5,1/10],[7,119/10],[-37/5,-57/5],[-18/5,9/5],[
-21/10,5],[1/5,3/5],[-16/5,-13/2],[-7,-41/5],[33/5,
37/10],[23/5,-1/5],[3/5,-9/2],[-7/2,19/5],[-9/10,19/10
],[-1/2,23/5],[29/10,87/10],[5,4],[9/5,69/10],[11/10,
-17/5],[9/2,-1/5],[29/10,42/5],[-17/2,-59/10],[1/5,-6/5
],[9/10,-7/5],[-21/10,-71/10],[24/5,-8/5],[5/2,-79/10],
[4/5,26/5],[-7/5,-2/5],[-22/5,-28/5],[8,41/10],[-27/10,
6/5],[6,21/2],[-5,-81/10],[-3/5,28/5],[-13/2,-67/10],[
-33/10,24/5],[29/10,10],[29/5,-13/10],[73/10,12/5],[
-9/5,59/10],[18/5,8],[5/2,41/10],[-4/5,61/10],[47/10,
29/5],[-29/5,-1/5],[1/2,2/5],[-7/5,19/5],[-12/5,22/5],
[-9,-6/5],[-69/10,-8/5],[8/5,31/10],[8,33/5],[7/5,
-17/5],[-3,-17/5],[33/10,19/10],[41/10,1],[-3,13/10],[
21/10,-4],[39/10,-7/5],[-23/5,-21/2],[-5,-43/10],[
-63/10,-13/10],[-67/10,-48/5],[-33/10,-1/5],[-19/10,7/10],
[-49/10,-4],[-17/10,11/2],[-9/10,13/10],[19/5,-11/5],[
-13/5,9/2],[-12/5,-24/5],[-5,3],[8/5,-4/5],[-5,-17/5],
[19/5,4],[-103/10,-56/5],[19/5,-3/5],[-26/5,17/5],[
-7/5,13/10],[-7/2,8/5],[-13/10,21/5],[-49/10,-3/2],[
3/10,-22/5],[-57/10,-7],[1/5,18/5],[21/10,-18/5],[19/10,
9/5],[-27/10,47/10],[5/2,-11/5],[-1,1/5],[-29/10,-12/5
],[2/5,24/5],[17/5,-41/10],[53/10,17/10],[-6,-49/5],[
-39/5,-41/10],[19/5,-19/5],[13/10,-12/5],[18/5,-1/2],[1,
10],[-2/5,41/10],[-9/10,1/10],[-17/2,-9/2],[-39/10,1],
[3/2,-12/5],[23/5,21/10],[43/10,73/10],[33/5,27/10],[
39/5,9/10],[9/2,57/10],[4,16/5],[1/2,53/10],[49/10,
57/10],[-3,-2/5],[-19/10,-39/5],[-19/10,-23/5],[42/5,
63/10],[-43/10,-9/5],[-21/5,-11/10],[9/2,18/5],[-5,
-43/10],[-27/10,-4/5],[1,-16/5],[-9/10,-43/5],[27/5,
19/10],[31/10,2],[-38/5,-39/5],[18/5,-21/5],[1,14/5],[
53/10,-29/10],[3/5,-57/10],[-12/5,-83/10],[-44/5,-32/5],[
5,42/5],[-14/5,-9/5],[39/10,-4/5],[7/10,9/5],[-9/5,27/5
],[-11/5,-2/5],[-29/5,-53/5],[117/10,42/5],[-3,-18/5],[
-23/5,23/5],[57/10,93/10],[-18/5,37/10],[17/2,6],[-2,
-23/5],[4/5,-5/2],[-33/10,0],[3/2,8],[1/2,6/5],[
101/10,19/10],[11/10,3/5],[-39/5,-47/10],[-97/10,14/5],[
-1/10,17/5],[-1/5,17/5],[-11/5,33/10],[-17/10,-17/10],[
39/5,31/10],[53/5,63/10],[109/10,67/10],[-54/5,-19/10],[
23/10,9/10],[-7/10,-16/5],[1/2,-8/5],[-4/5,-11/5],[13/5,
7/2],[32/5,63/10],[-49/10,-33/10],[-1/10,0],[49/5,5/2],
[7/5,33/10],[49/10,33/10],[23/5,4/5],[46/5,78/5],[
-11/10,-41/5],[1/5,6],[-19/10,-3/2],[-4/5,-33/10],[
-16/5,13/5],[-14/5,23/5],[21/10,19/5],[-63/10,31/10],[
26/5,77/10],[7,83/10],[-14/5,-53/10],[19/5,1/5],[24/5,
21/5],[-28/5,-13/10],[3/10,44/5],[71/10,109/10],[19/10,
-26/5],[-253/20,-44/5],[57/20,-27/10],[44/5,9/2],[11/5,
-41/5],[-97/20,43/2],[26,5],[7,169/10],[-399/20,4/5],[
24,9/2],[-1/10,-81/10],[73/4,72/5],[-27/5,-19/2],[
-89/10,1/10],[543/20,183/10],[-16,37/5],[97/20,13/5],[
-27/2,-121/10],[-3,21/10],[-181/20,-151/10],[-1/20,7/2],[
39/10,94/5],[-47/4,-1/10],[677/20,3/2],[-67/5,-41/10],[
77/4,31/2],[-49/5,-299/10],[-134/5,12/5],[26/5,-171/10],[
187/20,-81/10],[943/20,223/10],[-43/20,13/10],[323/20,-37/5
],[207/10,-163/10],[-167/10,48/5],[159/4,128/5],[229/10,
47/2],[-4,-51/5],[17/2,-3/5],[-1/5,-79/10],[-33,-27/2],
[52/5,-12/5],[49/10,48/5],[-229/20,-32/5],[0,-161/10],[
-169/20,17/5],[239/20,-34/5],[44/5,-29/5],[-49/10,-29/10],
[337/10,66/5],[-43/10,-37/10],[-187/10,-7/2],[-147/20,
81/10],[58/5,-181/10],[-29/2,1/5],[-9/10,17/5],[13/20,
77/10],[81/10,181/10],[6,193/10],[67/10,-109/10],[-27/20,
6/5],[-63/20,-119/10],[223/20,203/10],[-31/5,-241/10],[
-157/10,-121/10],[53/5,133/10],[-259/20,-87/10],[389/20,
19/2],[-17/20,-9/5],[-269/20,-33/10],[-307/20,7/10],[
-69/10,-13/5],[99/20,-21/10],[-1,121/10],[31/5,17/10],[
19/20,41/10],[-117/20,-101/10],[8,3],[-19/4,17/10],[
-159/20,13/5],[-247/20,-77/5],[163/10,71/10],[541/20,117/10
],[-71/20,-17/10],[-15/4,-153/10],[-5/4,-83/10],[11/20,
3/5],[33/20,17/10],[-19/20,69/10],[217/20,37/10],[9/20,
9/10],[1/5,5],[3/20,1/5],[11/4,21/10],[-9/4,-9/10],[
-53/20,3],[57/20,-9/10],[-9/4,-1/10],[5/4,29/5],[21/20,
3/10],[-33/20,1/5],[-73/20,-13/5],[-113/20,-23/5],[-1/20,
-1],[-15/4,-3/10],[21/20,1/5],[93/20,21/10],[5/4,-4/5],
[-69/20,8/5],[-3/20,-17/10],[7/20,13/10],[61/20,21/5],[
-47/20,6/5],[-29/20,-19/10],[1/4,1/2],[21/20,1],[-7/4,
-21/5],[43/20,7/5],[87/20,22/5],[17/20,-8/5],[-5/4,-3/2
],[73/20,-2/5],[73/20,14/5],[-33/20,-1/5],[-19/20,2/5],
[61/20,-7/5],[-27/20,-19/10],[37/20,7/5],[-61/20,-5/2],[
-29/20,17/10],[11/20,1/2],[-11/20,-1/2],[69/20,4],[7/20,
-23/10],[-13/20,-21/10],[-53/20,-2],[7/4,-21/10],[-33/20,
3/2],[21/20,11/5],[-3/20,8/5],[-11/20,-13/10],[7/20,
-7/10],[11/20,29/10],[1/4,3/10],[-1/20,-5/2],[17/20,
-3/10],[-19/20,-9/10],[-47/20,7/10],[49/20,-3/10],[27/20,
-9/10],[-107/20,-24/5],[-9/20,9/10],[3/20,-21/10],[
-31/20,-2/5],[-53/20,-49/10],[-11/4,4/5],[-9/4,-8/5],[
17/20,19/10],[7/20,23/5],[41/20,13/5],[-121/20,-11/2],[
61/20,6/5],[-7/4,-23/10],[7/4,-1/10],[-15/4,-23/5],[
9/20,-3/5],[-71/20,-17/5],[33/20,11/10],[-11/20,-1/5],[
1/4,23/5],[-59/20,-33/10],[37/20,9/5],[7/20,5/2],[19/20,
8/5],[-3/4,-27/10],[23/20,-7/5],[-89/20,-7/10],[49/20,
41/10],[-7/20,0],[27/20,13/5],[11/20,7/5],[-19/4,-7/5],
[7/4,1],[-7/20,-7/2],[93/20,13/10],[15/4,-7/10],[3/20,
9/10],[23/20,-1],[-19/20,-11/10],[77/20,5/2],[-23/4,1/5
],[91/20,21/5],[-1/20,2],[-53/20,-16/5],[-23/20,-8/5],[
-73/20,3/10],[-61/20,-2/5],[-53/20,-43/10],[9/4,1/10],[
-11/4,-3/2],[-39/20,-7/5],[-23/20,-2],[-1/4,19/10],[
49/20,-1/2],[-13/20,3/2],[-21/20,-3/2],[-21/20,-13/10],[
13/20,22/5],[-31/20,-11/10],[11/4,-11/10],[7/20,17/10],[
-21/20,6/5],[-57/20,-7/10],[23/20,7/5],[3/20,3/2],[
31/20,13/10],[3/4,-2],[-121/20,-1/2],[-103/20,-13/5],[
39/20,29/10],[11/20,-1/5],[-17/20,-7/10],[-11/4,14/5],[
-11/20,-2/5],[-59/20,-11/5],[-33/20,1],[-5/4,1/5],[
-41/20,-4/5],[109/20,12/5],[69/20,-3/2],[27/20,6/5],[
-47/20,-17/5],[-51/20,-12/5],[-19/20,-13/10],[-29/20,9/5],
[19/20,2/5],[-1/20,-1/10],[-1/4,-43/10],[7/4,-11/10],[
1/4,9/10],[111/20,7/5],[-11/20,33/10],[43/20,12/5],[
-9/20,17/10],[53/20,7/2],[-13/20,-7/10],[1/20,8/5],[
-9/20,-7/5],[-19/20,1/2],[-15/4,-43/10],[-43/20,-1],[
49/20,1/2],[39/20,-7/10],[9/20,2],[59/20,21/5],[-69/20,
-21/5],[-67/20,-3/10],[-59/20,-14/5],[-57/20,-31/10],[
77/20,9/10],[-1/4,-27/10],[1/4,3/5],[-5/4,4/5],[-27/20,
-3/2],[23/20,-3/10],[9/20,-6/5],[-71/20,-23/5],[31/20,
4/5],[-89/20,-19/10],[-13/4,1/2],[51/20,19/10],[-13/4,
-43/5],[-3/4,-1/2],[-71/20,-2],[-23/20,-13/10],[-11/20,
-7/5],[1/4,8/5],[-19/20,-4/5],[37/20,6/5],[17/20,1],[
-9/20,6/5],[17/20,-1/5],[7/4,3/2],[-5/4,-3],[-1/5,51/10
],[-1/4,7/5],[17/10,-4/5],[-3/20,-23/10],[-13/10,-49/10
],[31/20,1/2],[-2/5,3/5],[17/20,-4/5],[57/20,21/10],[
-23/20,11/10],[-7/4,23/10],[-43/20,-2/5],[-1/20,-7/10],[
3/20,27/10],[63/20,-9/5],[-37/20,3/2],[13/20,-23/10],[
7/20,-2/5],[-117/20,-23/5],[-3/4,-9/2],[-31/20,-18/5],[
21/20,2],[39/20,29/10],[7/20,17/5],[-19/20,11/10],[
17/20,-4/5],[-83/20,-8/5],[23/20,-1/10],[73/20,-1],[1/4,
1/2],[27/20,3/10],[-37/20,-2/5],[3/20,6/5],[-107/20,
-17/10],[3/4,3/5],[-21/20,3/5],[41/20,12/5],[29/20,19/10
],[-37/20,-1/5],[53/20,-1/5],[19/20,7/10],[-31/20,-5/2],
[-7/20,4/5],[-1/4,-19/5],[11/20,-1],[-57/20,-18/5],[
7/20,-13/10],[-39/20,-9/10],[-13/20,0],[-51/20,9/10],[
-73/20,-3/2],[27/20,-27/10],[7/20,0],[-9/20,9/10],[
27/20,16/5],[-1/20,-19/10],[39/20,3/2],[5/4,-4/5],[
19/20,3/10],[-21/20,2/5],[-91/20,-23/10],[-5/4,23/10],[
5/4,4/5],[-23/20,3/2],[7/4,0],[-11/4,-31/10],[-11/4,
23/10],[-31/20,11/10],[137/4,-16],[559/20,373/10],[
-357/10,-194/5],[-77/5,101/5],[759/20,-6],[-247/5,-421/10
],[53/2,111/10],[119/20,-28/5],[273/10,57/10],[439/10,
169/10],[231/20,28/5],[53/5,-431/10],[-77/10,72/5],[
-77/4,269/10],[53/10,-133/10],[759/20,63/2],[-76,-689/10],
[27/2,-36/5],[31/4,437/10],[403/20,-22/5],[207/10,71/5],
[-9/4,583/10],[-21/4,277/10],[379/10,95/2],[709/20,438/5
],[93/10,-97/10],[-181/5,-168/5],[487/10,23/2],[-339/20,
-61/10],[289/20,-167/10],[1071/20,-23/5],[-155/4,17/2],[
227/5,547/10],[-39/10,36],[49/4,17/2],[-211/10,-52],[
291/10,44],[-17/10,49/5],[-3/10,21/10],[-297/5,-133/5],[
-7,-15],[-4,317/10],[-403/20,-91/10],[-119/10,329/10],[
153/20,-238/5],[1593/20,125/2],[-141/10,-81/5],[-99/2,
-103/5],[282/5,59/2],[9,349/10],[-297/10,109/10],[-43/4,
31/2],[-128/5,2/5],[78/5,-45],[-69/5,-59/10],[-71/20,
-203/10],[-71/5,-7/5],[239/10,-35/2],[191/5,18],[223/20,
14],[-191/20,29/5],[-209/20,77/10],[18,-5],[-47/5,82/5
],[-267/10,-471/10],[-69/4,-74/5],[21/20,43/10],[-9/20,
-159/10],[-51/4,1],[-277/20,-33/2],[9/2,271/10],[63/4,
17/5],[-97/5,-433/10],[4/5,111/10],[-531/20,-9/10],[
-477/20,58/5],[102/5,-54/5],[45/4,152/5],[-533/20,-23/2],
[-437/20,-73/5],[39/10,-337/10],[77/20,-25/2],[-81/20,
93/10],[901/20,0],[199/20,-117/10],[49/20,21/5],[47/20,
-31/10],[-291/20,197/10],[237/20,-8/5],[-51/20,9/10],[
-23,229/10],[129/20,37/5],[19/20,-1/2],[-57/20,-39/10],[
-133/20,-71/10],[-89/20,-33/10],[-163/20,-83/10],[-23/4,
-46/5],[-131/20,-11/10],[7/4,13/2],[-109/20,27/10],[
141/20,43/10],[-51/20,8],[-229/20,-73/10],[-3/20,12/5],[
-177/20,-2],[-47/20,3],[47/20,4/5],[9/20,17/10],[-71/20,
-5/2],[109/20,52/5],[-43/20,-41/10],[-9/4,11/10],[-7/4,
73/10],[13/4,-3/10],[233/20,69/10],[111/20,19/5],[107/20,
36/5],[-13/4,-8/5],[-121/20,2],[-79/20,49/10],[41/20,5/2
],[-37/20,-17/5],[73/20,-1/2],[19/20,-1/10],[183/20,39/10
],[141/20,9/5],[-89/20,-29/10],[-53/20,4/5],[-99/20,27/10
],[-1/20,-7/10],[11/4,9/10],[79/20,37/10],[99/20,-21/5],
[101/20,-19/10],[67/20,-17/10],[-19/20,-97/10],[-87/20,4/5
],[37/20,-15/2],[-91/20,29/10],[-33/20,59/10],[29/20,
11/10],[-19/4,-103/10],[33/20,3/2],[11/20,-5],[-61/20,
-43/10],[-71/20,-53/10],[31/20,-34/5],[-177/20,-9/10],[
109/20,31/10],[127/20,-53/10],[-53/20,-141/10],[3/20,6],[
79/20,-19/10],[223/20,12/5],[-33/20,21/5],[91/20,-11/10],
[-11/4,32/5],[107/20,69/10],[129/20,77/10],[-51/20,-63/10
],[11/4,-13/10],[37/20,5/2],[9/20,-4/5],[-59/20,-11/5],
[-13/4,-26/5],[77/20,-11/10],[223/20,36/5],[-7/20,-23/10
],[-29/20,23/5],[21/20,69/10],[217/20,-29/10],[-63/20,
3/10],[-49/20,11/10],[-23/4,-41/5],[257/20,101/10],[
-171/20,-13/10],[-13/4,27/5],[-139/20,71/10],[-37/4,-1],[
9/4,3],[31/20,11/5],[-21/20,-81/10],[101/20,2],[53/20,
-41/10],[33/4,39/10],[-19/20,-21/10],[189/20,29/10],[
-43/20,-3/2],[-181/20,-9/10],[121/20,87/10],[-1/4,-4/5],[
-157/20,-83/10],[31/20,3/5],[63/20,16/5],[-47/20,9/10],[
103/20,-1/2],[111/20,-3/10],[-1/4,-13/10],[-23/20,-9/10],
[-43/20,-7],[-31/20,2],[-39/20,51/10],[-23/20,-37/10],[
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-11/20],[-69/20,-79/20],[-181/20,21/4],[-113/20,-3/20],[
-207/20,19/20],[-93/20,13/20],[-19/20,-181/20],[39/20,13/20
],[31/20,-13/20],[17/20,-33/20],[-29/20,-153/20],[41/20,
137/20],[9/20,37/4],[-41/20,-13/4],[151/20,-71/20],[13/4,
-93/20],[21/20,-73/20],[-37/20,-27/20],[177/20,-19/20],[
-1/20,143/20],[77/20,61/20],[33/20,-5/4],[-9/20,37/20],[
81/20,203/20],[-29/4,-83/20],[17/20,-107/20],[23/4,17/20],
[-11/4,-97/20],[111/20,29/4],[-167/20,-183/20],[117/20,
147/20],[59/20,117/20],[-31/20,-63/20],[-1/20,15/4],[
-73/20,3/20],[69/20,109/20],[-13/20,31/4],[97/20,11/20],[
31/4,107/20],[-11/20,91/20],[21/4,69/20],[-31/4,-123/20],
[61/20,3/20],[119/20,-21/20],[-113/20,-11/4],[-31/20,
-23/20],[111/20,137/20],[-111/20,-51/4],[-49/20,-19/4],[
9/4,-67/20],[-11/20,1/20],[-79/20,-133/20],[57/20,93/20],
[-15/4,-33/4],[157/20,143/20],[-113/20,1/4],[-127/20,
-111/20],[199/20,51/20],[-41/20,71/20],[-21/20,97/20],[
-107/20,31/4],[109/20,169/20],[203/20,87/20],[-151/20,
-147/20],[-141/20,89/20],[19/20,63/20],[-13/20,-113/20],[
-91/20,-17/20],[47/20,-7/4],[-13/4,-89/20],[-107/20,-139/20
],[117/20,-27/20],[29/20,167/20],[-47/20,37/20],[33/20,
7/4],[-11/20,5/4],[-91/20,-131/20],[9/4,51/20],[-1/4,
39/20],[87/5,-12/5],[-19/4,-219/20],[-59/5,-2],[-189/20,
-77/20],[-3/2,-119/10],[-3/4,-101/20],[3/10,-133/10],[
-17/4,-27/20],[97/20,197/20],[67/20,33/20],[25/4,-21/4],[
117/20,43/20],[33/20,-5/4],[79/20,63/20],[11/20,-139/20],
[111/20,1/4],[-57/20,-9/4],[-171/20,-121/20],[-39/20,
-53/20],[-83/20,-173/20],[137/20,27/20],[41/4,-9/20],[
41/20,147/20],[-71/20,17/20],[191/20,11/4],[-53/20,-57/20
],[-67/20,-17/20],[-21/4,97/20],[-207/20,-147/20],[127/20,
-63/20],[-43/20,-33/20],[-19/20,-121/20],[123/20,27/20],[
-19/20,35/4],[-7/4,-117/20],[-133/20,-53/20],[131/20,127/20
],[-13/20,-17/4],[-241/20,-193/20],[-3/4,29/20],[-13/20,
91/20],[21/20,1/4],[-9/4,-21/4],[157/20,243/20],[-129/20,
-181/20],[-37/20,9/4],[103/20,25/4],[-33/20,-41/20],[
167/20,19/4],[99/20,159/20],[-267/20,-289/20],[121/20,11/20
],[-13/20,-39/20],[219/20,13/20],[129/20,81/20],[117/20,
-139/20],[1/4,-101/20],[-43/20,-29/4],[5/4,27/20],[69/20,
161/20],[37/20,33/20],[111/20,61/20],[9/20,-57/20],[
-63/20,-137/20],[-181/20,-209/20],[11/20,13/20],[-181/20,
-3/20],[-11/20,-23/20],[96/5,-837/20],[51/5,-197/20],[
301/10,49/5],[152/5,231/5],[146/5,91/4],[783/10,589/10],[
-8,-46/5],[-821/10,-1321/20],[153/10,-131/5],[27/5,-237/10
],[-113/5,-103/20],[-56/5,219/10],[-383/10,-37/10],[
-227/10,153/4],[853/10,-17],[-118/5,-37/4],[268/5,593/10],
[-336/5,-314/5],[-24,-81/4],[-154/5,-193/20],[-231/2,
-353/5],[61/5,63/4],[-39/5,817/20],[-47/2,-499/10],[
-271/5,-231/20],[109/10,257/10],[-603/10,-229/10],[11/5,
151/10],[289/10,-213/20],[-256/5,-323/4],[-69/2,-1389/20],
[-157/5,653/20],[59/10,51/2],[25/2,93/10],[-282/5,-513/20
],[-39/2,-123/10],[13,-9/2],[87,273/5],[849/10,254/5],[
222/5,521/10],[128/5,-55/2],[399/10,188/5],[28,363/20],[
213/10,-34/5],[10,-213/4],[10,761/20],[107/5,393/10],[
239/10,569/10],[-207/5,-166/5],[79/10,273/5],[38/5,167/10
],[192/5,391/20],[272/5,543/10],[303/5,-112/5],[143/10,
29/2],[69/10,243/20],[-517/10,-231/10],[-158/5,-459/10],[
-25/2,-3],[131/10,59/20],[7/5,397/20],[164/5,49/4],[
-199/5,-294/5],[-169/10,-20],[36,17/2],[-44/5,59/4],[
-99/5,-131/4],[-303/10,-1193/20],[-3/10,-61/4],[107/5,
241/20],[-117/10,-109/5],[-41/10,57/20],[-41/2,-19/2],[
-4/5,-138/5],[-49/10,149/20],[109/5,79/4],[317/10,134/5],
[9/5,-713/20],[217/5,19/4],[3,11/20],[-189/10,31/5],[
97/10,549/20],[5,127/20],[203/10,-3/4],[-81/10,-383/20],[
-17/10,5/4],[7/10,69/20],[51/10,-653/20],[29/10,149/20],[
17/10,3/20],[119/10,69/5],[29/5,17/4],[36/5,-27/20],[
13/10,81/20],[-36/5,123/20],[32/5,1/4],[203/10,163/20],[
26/5,9/4],[39/5,-41/20],[-5,31/20],[-7/5,1/20],[11/2,
49/20],[-3/5,3/4],[9,31/4],[2,-151/20],[-2/5,71/20],[
-21/2,-55/4],[2/5,33/4],[141/10,-79/20],[63/10,27/20],[
-1/5,-133/20],[27/5,41/20],[-2/5,11/20],[-15/2,111/20],[
63/10,13/4],[9/10,27/20],[-6,11/20],[-54/5,-73/20],[
-16/5,67/20],[27/10,57/20],[-13/10,241/20],[29/10,35/4],[
-13/5,-77/20],[93/10,21/20],[-3,49/20],[11/10,27/20],[
-9/5,163/20],[91/5,179/20],[71/5,137/20],[-14/5,-11/4],[
31/5,27/4],[-5/2,-11/20],[-56/5,-143/20],[-7/10,-27/4],[
0,33/20],[64/5,31/4],[-6/5,-31/20],[-2,19/20],[-46/5,
3/4],[-17/10,-93/20],[-21/2,-19/20],[31/5,177/20],[31/10,
109/20],[-9/5,117/20],[19/10,-239/20],[41/5,169/20],[
-47/5,-263/20],[9/10,-89/20],[-28/5,-169/20],[9/10,39/20],
[8/5,-243/20],[-9/2,33/20],[-31/10,-159/20],[22/5,-87/20
],[-69/10,-121/20],[-11/2,-113/20],[9/2,-17/20],[-2/5,
97/20],[4/5,-9/20],[-31/10,-55/4],[-74/5,139/20],[-11,
-7/20],[-8/5,-73/20],[-17/10,-31/20],[-10,37/20],[-1/5,
57/20],[-1/2,33/20],[-67/10,-39/20],[13/2,187/20],[43/10,
97/20],[71/5,27/4],[42/5,217/20],[-8,-87/20],[-19/5,
-11/20],[13/10,61/20],[-1/5,-33/20],[-19/5,7/20],[51/5,
63/20],[14/5,-13/4],[-21/5,-123/20],[-24/5,49/20],[
-59/10,-177/20],[-14/5,23/20],[73/10,87/20],[14/5,-17/4],
[-13/5,-3/4],[33/5,-3/4],[36/5,11/4],[-9/10,-47/20],[
1/10,81/20],[61/5,-3/20],[26/5,91/20],[34/5,9/4],[-24/5,
-163/20],[0,-121/20],[-37/10,-25/4],[-17/5,-187/20],[
137/10,123/20],[-4/5,41/20],[1/2,-109/20],[-1,-47/4],[
-12/5,131/20],[-57/10,-71/20],[-27/2,-313/20],[-23/5,33/20
],[117/10,3/4],[43/5,-17/20],[-12/5,93/20],[24/5,247/20
],[34/5,25/4],[-19/10,43/20],[-41/10,1/20],[19/5,133/20
],[28/5,117/20],[23/10,67/20],[31/5,59/20],[0,-93/20],[
9/2,-59/20],[-101/10,-23/4],[2/5,91/20],[-34/5,249/20],[
4/5,-21/20],[-44/5,-113/20],[4/5,-119/20],[0,-71/20],[
7/5,1/4],[16/5,-41/20],[42/5,177/20],[48/5,-21/20],[
111/10,113/20],[-36/5,23/20],[27/5,69/20],[-7/2,3/4],[
-21/10,197/20],[6/5,123/20],[2/5,37/20],[1/2,-31/20],[6,
-87/20],[21/5,-149/20],[-14/5,-67/20],[3,89/20],[49/10,
73/20],[-44/5,37/20],[13/5,-63/20],[1/10,-133/20],[2/5,
13/20],[43/10,-3/20],[1,149/20],[9,203/20],[-11/2,
-123/20],[51/10,-33/20],[21/10,61/20],[4/5,21/20],[17/5,
29/20],[-19/10,-187/20],[-13/5,61/20],[19/5,73/20],[-5/2,
-37/20],[-51/10,7/20],[-23/10,-29/4],[53/5,9/20],[-7/2,
-33/20],[-18/5,-283/20],[77/10,-59/20],[51/5,3/20],[
-19/2,-167/20],[-42/5,9/4],[12/5,161/20],[7/2,-39/20],[
27/5,67/20],[47/5,55/4],[-31/10,-7/20],[29/10,41/20],[
-27/10,-91/20],[11,17/20],[-4,37/20],[9,73/20],[121/10,
-69/20],[-5,-177/20],[-3/5,1/4],[6,109/20],[13/10,7/20
],[-3/5,-103/20],[-123/10,-19/10],[-47/10,93/20],[91/5,
11/10],[3/2,-9/20],[24/5,71/10],[-9/10,11/4],[-161/10,
-4/5],[12/5,41/20],[17/5,-47/20],[-49/10,-79/20],[-19/5,
-25/4],[-17/10,223/20],[-31/10,13/4],[-21/5,-113/20],[
-13/10,79/20],[19/10,-31/20],[3,203/20],[51/10,9/4],[
7/10,67/20],[-19/10,79/20],[-2,-13/20],[6,-1/4],[-14/5,
-263/20],[-19/5,-127/20],[-91/5,-323/20],[5/2,-21/20],[
79/10,57/4],[59/5,17/20],[10,17/20],[-7/2,133/20],[
-67/10,-61/20],[-71/10,41/20],[5,21/20],[-82/5,-307/20],[
-63/10,153/20],[9/2,169/20],[-34/5,-11/4],[39/5,159/20],[
71/10,97/20],[0,-93/20],[-1/2,259/20],[19/10,-1/4],[
19/5,63/20],[11/5,21/20],[49/10,181/20],[-13/5,-51/20],[
41/5,1/20],[-7/5,9/20],[-4/5,-1/4],[43/10,-7/4],[81/10,
31/4],[-11/10,63/20],[-4,9/20],[-13/10,109/20],[2/5,
-211/20],[-83/5,-179/20],[9/10,-1/20],[-32/5,-7/20],[
-83/10,13/4],[123/10,5/4],[23/2,53/20],[67/10,-1/20],[
-12/5,163/20],[71/10,121/20],[159/10,197/20],[41/10,-143/20
],[1,-99/20],[44/5,13/4]])
]:Check:=false)where w:=K.1 where K:=CyclotomicField(3);
K<w>:=BaseRing(M);
K;
M;
