The representation theory of the restricted rational Cherednik algebra for G16

Computed by Ulrich Thiel using CHAMP (see LMS J. Comput. Math., 2015). Last update on Fri Mar 27 12:48:20 CET 2015.

Note: In the larger tables each cell has a mouseover tooltip providing information about the cell.

Quick navigation: Exceptional hyperplanes

For generic parameters

Non-singleton Calogero–Moser families

4,17,  ϕ4,12},   {ϕ4,8,  ϕ4,3},   {ϕ4,15,  ϕ4,20},   {ϕ4,14,  ϕ4,9},   {ϕ4,6,  ϕ4,11},   {ϕ5,12,  ϕ5,4,  ϕ5,16,  ϕ5,8,  ϕ5,10}

Dimensions, Poincaré series and diagonal Verma multiplicities of the simple modules

ϕ dim L(ϕ) [Δ(ϕ) : L(ϕ)] PL(ϕ)
ϕ1,060011 + 2t + 3t2 + 4t3 + 5t4 + 6t5 + 7t6 + 8t7 + 9t8 + 10t9 + 11t10 + 12t11 + 13t12 + 14t13 + 15t14 + 16t15 + 17t16 + 18t17 + 19t18 + 20t19 + 20t20 + 20t21 + 20t22 + 20t23 + 20t24 + 20t25 + 20t26 + 20t27 + 20t28 + 20t29 + 19t30 + 18t31 + 17t32 + 16t33 + 15t34 + 14t35 + 13t36 + 12t37 + 11t38 + 10t39 + 9t40 + 8t41 + 7t42 + 6t43 + 5t44 + 4t45 + 3t46 + 2t47 + t48
ϕ1,1260011 + 2t + 3t2 + 4t3 + 5t4 + 6t5 + 7t6 + 8t7 + 9t8 + 10t9 + 11t10 + 12t11 + 13t12 + 14t13 + 15t14 + 16t15 + 17t16 + 18t17 + 19t18 + 20t19 + 20t20 + 20t21 + 20t22 + 20t23 + 20t24 + 20t25 + 20t26 + 20t27 + 20t28 + 20t29 + 19t30 + 18t31 + 17t32 + 16t33 + 15t34 + 14t35 + 13t36 + 12t37 + 11t38 + 10t39 + 9t40 + 8t41 + 7t42 + 6t43 + 5t44 + 4t45 + 3t46 + 2t47 + t48
ϕ1,2460011 + 2t + 3t2 + 4t3 + 5t4 + 6t5 + 7t6 + 8t7 + 9t8 + 10t9 + 11t10 + 12t11 + 13t12 + 14t13 + 15t14 + 16t15 + 17t16 + 18t17 + 19t18 + 20t19 + 20t20 + 20t21 + 20t22 + 20t23 + 20t24 + 20t25 + 20t26 + 20t27 + 20t28 + 20t29 + 19t30 + 18t31 + 17t32 + 16t33 + 15t34 + 14t35 + 13t36 + 12t37 + 11t38 + 10t39 + 9t40 + 8t41 + 7t42 + 6t43 + 5t44 + 4t45 + 3t46 + 2t47 + t48
ϕ1,3660011 + 2t + 3t2 + 4t3 + 5t4 + 6t5 + 7t6 + 8t7 + 9t8 + 10t9 + 11t10 + 12t11 + 13t12 + 14t13 + 15t14 + 16t15 + 17t16 + 18t17 + 19t18 + 20t19 + 20t20 + 20t21 + 20t22 + 20t23 + 20t24 + 20t25 + 20t26 + 20t27 + 20t28 + 20t29 + 19t30 + 18t31 + 17t32 + 16t33 + 15t34 + 14t35 + 13t36 + 12t37 + 11t38 + 10t39 + 9t40 + 8t41 + 7t42 + 6t43 + 5t44 + 4t45 + 3t46 + 2t47 + t48
ϕ1,4860011 + 2t + 3t2 + 4t3 + 5t4 + 6t5 + 7t6 + 8t7 + 9t8 + 10t9 + 11t10 + 12t11 + 13t12 + 14t13 + 15t14 + 16t15 + 17t16 + 18t17 + 19t18 + 20t19 + 20t20 + 20t21 + 20t22 + 20t23 + 20t24 + 20t25 + 20t26 + 20t27 + 20t28 + 20t29 + 19t30 + 18t31 + 17t32 + 16t33 + 15t34 + 14t35 + 13t36 + 12t37 + 11t38 + 10t39 + 9t40 + 8t41 + 7t42 + 6t43 + 5t44 + 4t45 + 3t46 + 2t47 + t48
ϕ2,160022 + 4t + 6t2 + 8t3 + 10t4 + 12t5 + 14t6 + 16t7 + 18t8 + 20t9 + 20t10 + 20t11 + 20t12 + 20t13 + 20t14 + 20t15 + 20t16 + 20t17 + 20t18 + 20t19 + 20t20 + 20t21 + 20t22 + 20t23 + 20t24 + 20t25 + 20t26 + 20t27 + 20t28 + 20t29 + 18t30 + 16t31 + 14t32 + 12t33 + 10t34 + 8t35 + 6t36 + 4t37 + 2t38
ϕ2,760022 + 4t + 6t2 + 8t3 + 10t4 + 12t5 + 14t6 + 16t7 + 18t8 + 20t9 + 20t10 + 20t11 + 20t12 + 20t13 + 20t14 + 20t15 + 20t16 + 20t17 + 20t18 + 20t19 + 20t20 + 20t21 + 20t22 + 20t23 + 20t24 + 20t25 + 20t26 + 20t27 + 20t28 + 20t29 + 18t30 + 16t31 + 14t32 + 12t33 + 10t34 + 8t35 + 6t36 + 4t37 + 2t38
ϕ2,13'60022 + 4t + 6t2 + 8t3 + 10t4 + 12t5 + 14t6 + 16t7 + 18t8 + 20t9 + 20t10 + 20t11 + 20t12 + 20t13 + 20t14 + 20t15 + 20t16 + 20t17 + 20t18 + 20t19 + 20t20 + 20t21 + 20t22 + 20t23 + 20t24 + 20t25 + 20t26 + 20t27 + 20t28 + 20t29 + 18t30 + 16t31 + 14t32 + 12t33 + 10t34 + 8t35 + 6t36 + 4t37 + 2t38
ϕ2,19'60022 + 4t + 6t2 + 8t3 + 10t4 + 12t5 + 14t6 + 16t7 + 18t8 + 20t9 + 20t10 + 20t11 + 20t12 + 20t13 + 20t14 + 20t15 + 20t16 + 20t17 + 20t18 + 20t19 + 20t20 + 20t21 + 20t22 + 20t23 + 20t24 + 20t25 + 20t26 + 20t27 + 20t28 + 20t29 + 18t30 + 16t31 + 14t32 + 12t33 + 10t34 + 8t35 + 6t36 + 4t37 + 2t38
ϕ2,13''60022 + 4t + 6t2 + 8t3 + 10t4 + 12t5 + 14t6 + 16t7 + 18t8 + 20t9 + 20t10 + 20t11 + 20t12 + 20t13 + 20t14 + 20t15 + 20t16 + 20t17 + 20t18 + 20t19 + 20t20 + 20t21 + 20t22 + 20t23 + 20t24 + 20t25 + 20t26 + 20t27 + 20t28 + 20t29 + 18t30 + 16t31 + 14t32 + 12t33 + 10t34 + 8t35 + 6t36 + 4t37 + 2t38
ϕ2,19''60022 + 4t + 6t2 + 8t3 + 10t4 + 12t5 + 14t6 + 16t7 + 18t8 + 20t9 + 20t10 + 20t11 + 20t12 + 20t13 + 20t14 + 20t15 + 20t16 + 20t17 + 20t18 + 20t19 + 20t20 + 20t21 + 20t22 + 20t23 + 20t24 + 20t25 + 20t26 + 20t27 + 20t28 + 20t29 + 18t30 + 16t31 + 14t32 + 12t33 + 10t34 + 8t35 + 6t36 + 4t37 + 2t38
ϕ2,25'60022 + 4t + 6t2 + 8t3 + 10t4 + 12t5 + 14t6 + 16t7 + 18t8 + 20t9 + 20t10 + 20t11 + 20t12 + 20t13 + 20t14 + 20t15 + 20t16 + 20t17 + 20t18 + 20t19 + 20t20 + 20t21 + 20t22 + 20t23 + 20t24 + 20t25 + 20t26 + 20t27 + 20t28 + 20t29 + 18t30 + 16t31 + 14t32 + 12t33 + 10t34 + 8t35 + 6t36 + 4t37 + 2t38
ϕ2,25''60022 + 4t + 6t2 + 8t3 + 10t4 + 12t5 + 14t6 + 16t7 + 18t8 + 20t9 + 20t10 + 20t11 + 20t12 + 20t13 + 20t14 + 20t15 + 20t16 + 20t17 + 20t18 + 20t19 + 20t20 + 20t21 + 20t22 + 20t23 + 20t24 + 20t25 + 20t26 + 20t27 + 20t28 + 20t29 + 18t30 + 16t31 + 14t32 + 12t33 + 10t34 + 8t35 + 6t36 + 4t37 + 2t38
ϕ2,3160022 + 4t + 6t2 + 8t3 + 10t4 + 12t5 + 14t6 + 16t7 + 18t8 + 20t9 + 20t10 + 20t11 + 20t12 + 20t13 + 20t14 + 20t15 + 20t16 + 20t17 + 20t18 + 20t19 + 20t20 + 20t21 + 20t22 + 20t23 + 20t24 + 20t25 + 20t26 + 20t27 + 20t28 + 20t29 + 18t30 + 16t31 + 14t32 + 12t33 + 10t34 + 8t35 + 6t36 + 4t37 + 2t38
ϕ2,3760022 + 4t + 6t2 + 8t3 + 10t4 + 12t5 + 14t6 + 16t7 + 18t8 + 20t9 + 20t10 + 20t11 + 20t12 + 20t13 + 20t14 + 20t15 + 20t16 + 20t17 + 20t18 + 20t19 + 20t20 + 20t21 + 20t22 + 20t23 + 20t24 + 20t25 + 20t26 + 20t27 + 20t28 + 20t29 + 18t30 + 16t31 + 14t32 + 12t33 + 10t34 + 8t35 + 6t36 + 4t37 + 2t38
ϕ3,260033 + 6t + 9t2 + 12t3 + 15t4 + 18t5 + 21t6 + 24t7 + 27t8 + 30t9 + 30t10 + 30t11 + 30t12 + 30t13 + 30t14 + 30t15 + 30t16 + 30t17 + 30t18 + 30t19 + 27t20 + 24t21 + 21t22 + 18t23 + 15t24 + 12t25 + 9t26 + 6t27 + 3t28
ϕ3,660033 + 6t + 9t2 + 12t3 + 15t4 + 18t5 + 21t6 + 24t7 + 27t8 + 30t9 + 30t10 + 30t11 + 30t12 + 30t13 + 30t14 + 30t15 + 30t16 + 30t17 + 30t18 + 30t19 + 27t20 + 24t21 + 21t22 + 18t23 + 15t24 + 12t25 + 9t26 + 6t27 + 3t28
ϕ3,10'60033 + 6t + 9t2 + 12t3 + 15t4 + 18t5 + 21t6 + 24t7 + 27t8 + 30t9 + 30t10 + 30t11 + 30t12 + 30t13 + 30t14 + 30t15 + 30t16 + 30t17 + 30t18 + 30t19 + 27t20 + 24t21 + 21t22 + 18t23 + 15t24 + 12t25 + 9t26 + 6t27 + 3t28
ϕ3,10''60033 + 6t + 9t2 + 12t3 + 15t4 + 18t5 + 21t6 + 24t7 + 27t8 + 30t9 + 30t10 + 30t11 + 30t12 + 30t13 + 30t14 + 30t15 + 30t16 + 30t17 + 30t18 + 30t19 + 27t20 + 24t21 + 21t22 + 18t23 + 15t24 + 12t25 + 9t26 + 6t27 + 3t28
ϕ3,14'60033 + 6t + 9t2 + 12t3 + 15t4 + 18t5 + 21t6 + 24t7 + 27t8 + 30t9 + 30t10 + 30t11 + 30t12 + 30t13 + 30t14 + 30t15 + 30t16 + 30t17 + 30t18 + 30t19 + 27t20 + 24t21 + 21t22 + 18t23 + 15t24 + 12t25 + 9t26 + 6t27 + 3t28
ϕ3,18'60033 + 6t + 9t2 + 12t3 + 15t4 + 18t5 + 21t6 + 24t7 + 27t8 + 30t9 + 30t10 + 30t11 + 30t12 + 30t13 + 30t14 + 30t15 + 30t16 + 30t17 + 30t18 + 30t19 + 27t20 + 24t21 + 21t22 + 18t23 + 15t24 + 12t25 + 9t26 + 6t27 + 3t28
ϕ3,14''60033 + 6t + 9t2 + 12t3 + 15t4 + 18t5 + 21t6 + 24t7 + 27t8 + 30t9 + 30t10 + 30t11 + 30t12 + 30t13 + 30t14 + 30t15 + 30t16 + 30t17 + 30t18 + 30t19 + 27t20 + 24t21 + 21t22 + 18t23 + 15t24 + 12t25 + 9t26 + 6t27 + 3t28
ϕ3,18''60033 + 6t + 9t2 + 12t3 + 15t4 + 18t5 + 21t6 + 24t7 + 27t8 + 30t9 + 30t10 + 30t11 + 30t12 + 30t13 + 30t14 + 30t15 + 30t16 + 30t17 + 30t18 + 30t19 + 27t20 + 24t21 + 21t22 + 18t23 + 15t24 + 12t25 + 9t26 + 6t27 + 3t28
ϕ3,2260033 + 6t + 9t2 + 12t3 + 15t4 + 18t5 + 21t6 + 24t7 + 27t8 + 30t9 + 30t10 + 30t11 + 30t12 + 30t13 + 30t14 + 30t15 + 30t16 + 30t17 + 30t18 + 30t19 + 27t20 + 24t21 + 21t22 + 18t23 + 15t24 + 12t25 + 9t26 + 6t27 + 3t28
ϕ3,2660033 + 6t + 9t2 + 12t3 + 15t4 + 18t5 + 21t6 + 24t7 + 27t8 + 30t9 + 30t10 + 30t11 + 30t12 + 30t13 + 30t14 + 30t15 + 30t16 + 30t17 + 30t18 + 30t19 + 27t20 + 24t21 + 21t22 + 18t23 + 15t24 + 12t25 + 9t26 + 6t27 + 3t28
ϕ4,1530044 + 8t + 12t2 + 16t3 + 20t4 + 20t5 + 20t6 + 20t7 + 20t8 + 20t9 + 20t10 + 20t11 + 20t12 + 20t13 + 20t14 + 16t15 + 12t16 + 8t17 + 4t18
ϕ4,1730044 + 8t + 12t2 + 16t3 + 20t4 + 20t5 + 20t6 + 20t7 + 20t8 + 20t9 + 20t10 + 20t11 + 20t12 + 20t13 + 20t14 + 16t15 + 12t16 + 8t17 + 4t18
ϕ4,930044 + 8t + 12t2 + 16t3 + 20t4 + 20t5 + 20t6 + 20t7 + 20t8 + 20t9 + 20t10 + 20t11 + 20t12 + 20t13 + 20t14 + 16t15 + 12t16 + 8t17 + 4t18
ϕ4,1130044 + 8t + 12t2 + 16t3 + 20t4 + 20t5 + 20t6 + 20t7 + 20t8 + 20t9 + 20t10 + 20t11 + 20t12 + 20t13 + 20t14 + 16t15 + 12t16 + 8t17 + 4t18
ϕ4,330044 + 8t + 12t2 + 16t3 + 20t4 + 20t5 + 20t6 + 20t7 + 20t8 + 20t9 + 20t10 + 20t11 + 20t12 + 20t13 + 20t14 + 16t15 + 12t16 + 8t17 + 4t18
ϕ4,2030044 + 8t + 12t2 + 16t3 + 20t4 + 20t5 + 20t6 + 20t7 + 20t8 + 20t9 + 20t10 + 20t11 + 20t12 + 20t13 + 20t14 + 16t15 + 12t16 + 8t17 + 4t18
ϕ4,1230044 + 8t + 12t2 + 16t3 + 20t4 + 20t5 + 20t6 + 20t7 + 20t8 + 20t9 + 20t10 + 20t11 + 20t12 + 20t13 + 20t14 + 16t15 + 12t16 + 8t17 + 4t18
ϕ4,1430044 + 8t + 12t2 + 16t3 + 20t4 + 20t5 + 20t6 + 20t7 + 20t8 + 20t9 + 20t10 + 20t11 + 20t12 + 20t13 + 20t14 + 16t15 + 12t16 + 8t17 + 4t18
ϕ4,630044 + 8t + 12t2 + 16t3 + 20t4 + 20t5 + 20t6 + 20t7 + 20t8 + 20t9 + 20t10 + 20t11 + 20t12 + 20t13 + 20t14 + 16t15 + 12t16 + 8t17 + 4t18
ϕ4,830044 + 8t + 12t2 + 16t3 + 20t4 + 20t5 + 20t6 + 20t7 + 20t8 + 20t9 + 20t10 + 20t11 + 20t12 + 20t13 + 20t14 + 16t15 + 12t16 + 8t17 + 4t18
ϕ5,1212055 + 10t + 15t2 + 20t3 + 20t4 + 20t5 + 15t6 + 10t7 + 5t8
ϕ5,412055 + 10t + 15t2 + 20t3 + 20t4 + 20t5 + 15t6 + 10t7 + 5t8
ϕ5,1612055 + 10t + 15t2 + 20t3 + 20t4 + 20t5 + 15t6 + 10t7 + 5t8
ϕ5,812055 + 10t + 15t2 + 20t3 + 20t4 + 20t5 + 15t6 + 10t7 + 5t8
ϕ5,1012055 + 10t + 15t2 + 20t3 + 20t4 + 20t5 + 15t6 + 10t7 + 5t8
ϕ6,560066 + 12t + 18t2 + 24t3 + 30t4 + 36t5 + 42t6 + 48t7 + 54t8 + 60t9 + 54t10 + 48t11 + 42t12 + 36t13 + 30t14 + 24t15 + 18t16 + 12t17 + 6t18
ϕ6,760066 + 12t + 18t2 + 24t3 + 30t4 + 36t5 + 42t6 + 48t7 + 54t8 + 60t9 + 54t10 + 48t11 + 42t12 + 36t13 + 30t14 + 24t15 + 18t16 + 12t17 + 6t18
ϕ6,960066 + 12t + 18t2 + 24t3 + 30t4 + 36t5 + 42t6 + 48t7 + 54t8 + 60t9 + 54t10 + 48t11 + 42t12 + 36t13 + 30t14 + 24t15 + 18t16 + 12t17 + 6t18
ϕ6,1160066 + 12t + 18t2 + 24t3 + 30t4 + 36t5 + 42t6 + 48t7 + 54t8 + 60t9 + 54t10 + 48t11 + 42t12 + 36t13 + 30t14 + 24t15 + 18t16 + 12t17 + 6t18
ϕ6,1360066 + 12t + 18t2 + 24t3 + 30t4 + 36t5 + 42t6 + 48t7 + 54t8 + 60t9 + 54t10 + 48t11 + 42t12 + 36t13 + 30t14 + 24t15 + 18t16 + 12t17 + 6t18

Characters of the simple modules

ϕ L(ϕ1,0) L(ϕ1,12) L(ϕ1,24) L(ϕ1,36) L(ϕ1,48) L(ϕ2,1) L(ϕ2,7) L(ϕ2,13') L(ϕ2,19') L(ϕ2,13'') L(ϕ2,19'') L(ϕ2,25') L(ϕ2,25'') L(ϕ2,31) L(ϕ2,37) L(ϕ3,2) L(ϕ3,6) L(ϕ3,10') L(ϕ3,10'') L(ϕ3,14') L(ϕ3,18') L(ϕ3,14'') L(ϕ3,18'') L(ϕ3,22) L(ϕ3,26) L(ϕ4,15) L(ϕ4,17) L(ϕ4,9) L(ϕ4,11) L(ϕ4,3) L(ϕ4,20) L(ϕ4,12) L(ϕ4,14) L(ϕ4,6) L(ϕ4,8) L(ϕ5,12) L(ϕ5,4) L(ϕ5,16) L(ϕ5,8) L(ϕ5,10) L(ϕ6,5) L(ϕ6,7) L(ϕ6,9) L(ϕ6,11) L(ϕ6,13)
ϕ1,0 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 0 1 0 1 0 1 0 1 0 0 1 0 0 0 1 1 1 1 1
ϕ1,12 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 0 1 0 0 0 1 0 1 0 0 1 0 0 1 1 1 1 1
ϕ1,24 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 0 1 1 0 1 1 0 0 1 0 0 0 0 1 0 1 1 1 1 1
ϕ1,36 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 0 1 1 0 0 1 0 0 1 0 0 0 0 1 1 1 1 1 1
ϕ1,48 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 0 1 0 1 1 1 0 1 0 0 1 0 0 0 0 1 1 1 1 1
ϕ2,1 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 1 1 1 1 0 1 1 1 1 0 1 1 0 0 2 2 2 2 2
ϕ2,7 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 1 1 0 2 0 1 1 2 0 2 1 0 0 0 1 2 2 2 2 2
ϕ2,13' 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 0 2 0 1 1 2 0 2 1 1 0 0 1 1 0 2 2 2 2 2
ϕ2,19' 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 1 1 1 1 2 1 1 1 1 0 1 1 0 0 0 2 2 2 2 2
ϕ2,13'' 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 1 2 1 1 1 1 0 1 1 1 0 0 1 1 0 2 2 2 2 2
ϕ2,19'' 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 0 1 1 0 2 2 1 1 2 0 1 1 0 0 0 2 2 2 2 2
ϕ2,25' 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 1 0 2 0 1 1 2 0 2 1 0 0 0 1 1 2 2 2 2 2
ϕ2,25'' 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 1 1 2 1 1 1 1 0 1 1 0 0 0 1 1 2 2 2 2 2
ϕ2,31 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 0 1 1 0 0 2 1 1 2 0 1 1 0 0 2 2 2 2 2
ϕ2,37 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 1 1 1 2 1 1 1 1 0 1 1 0 0 0 1 2 2 2 2 2
ϕ3,2 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 2 2 2 1 2 1 1 1 2 1 0 1 1 1 0 3 3 3 3 3
ϕ3,6 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 1 1 2 2 1 2 2 1 1 2 1 0 0 1 1 3 3 3 3 3
ϕ3,10' 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 2 2 1 2 2 1 1 2 1 1 1 1 1 0 0 3 3 3 3 3
ϕ3,10'' 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 2 1 1 1 2 1 2 2 2 1 1 1 1 0 0 3 3 3 3 3
ϕ3,14' 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 1 2 2 1 1 2 1 1 2 2 0 0 1 1 1 3 3 3 3 3
ϕ3,18' 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 2 1 2 2 2 1 2 1 1 1 1 1 0 0 1 3 3 3 3 3
ϕ3,14'' 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 2 2 2 2 1 1 1 1 1 2 0 0 1 1 1 3 3 3 3 3
ϕ3,18'' 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 1 1 1 2 2 2 2 2 1 1 1 1 0 0 1 3 3 3 3 3
ϕ3,22 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 2 2 1 1 1 1 1 2 2 2 0 1 1 1 0 3 3 3 3 3
ϕ3,26 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 1 2 2 2 2 2 1 1 1 1 1 0 0 1 1 3 3 3 3 3
ϕ4,15 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 2 3 2 3 2 2 1 2 1 2 1 0 1 1 1 4 4 4 4 4
ϕ4,17 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 2 2 3 2 3 2 2 1 2 1 1 1 0 1 1 4 4 4 4 4
ϕ4,9 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 3 2 2 3 2 1 2 2 1 2 1 1 1 0 1 4 4 4 4 4
ϕ4,11 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 2 3 2 2 3 2 1 2 2 1 1 1 1 1 0 4 4 4 4 4
ϕ4,3 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 3 2 3 2 2 1 2 1 2 2 0 1 1 1 1 4 4 4 4 4
ϕ4,20 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 2 1 2 1 2 2 3 2 3 2 1 2 1 0 0 4 4 4 4 4
ϕ4,12 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 2 2 1 2 1 2 2 3 2 3 0 1 2 1 0 4 4 4 4 4
ϕ4,14 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 1 2 2 1 2 3 2 2 3 2 0 0 1 2 1 4 4 4 4 4
ϕ4,6 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 2 1 2 2 1 2 3 2 2 3 1 0 0 1 2 4 4 4 4 4
ϕ4,8 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 1 2 1 2 2 3 2 3 2 2 2 1 0 0 1 4 4 4 4 4
ϕ5,12 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 3 3 3 1 3 2 2 2 4 2 1 1 1 1 1 5 5 5 5 5
ϕ5,4 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 3 3 3 3 1 2 2 2 2 4 1 1 1 1 1 5 5 5 5 5
ϕ5,16 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 1 3 3 3 3 4 2 2 2 2 1 1 1 1 1 5 5 5 5 5
ϕ5,8 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 3 1 3 3 3 2 4 2 2 2 1 1 1 1 1 5 5 5 5 5
ϕ5,10 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 3 3 1 3 3 2 2 4 2 2 1 1 1 1 1 5 5 5 5 5
ϕ6,5 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 2 3 4 3 2 4 3 2 3 4 1 0 1 2 2 6 6 6 6 6
ϕ6,7 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 2 2 3 4 3 4 4 3 2 3 2 1 0 1 2 6 6 6 6 6
ϕ6,9 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 3 2 2 3 4 3 4 4 3 2 2 2 1 0 1 6 6 6 6 6
ϕ6,11 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 4 3 2 2 3 2 3 4 4 3 1 2 2 1 0 6 6 6 6 6
ϕ6,13 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 3 4 3 2 2 3 2 3 4 4 0 1 2 2 1 6 6 6 6 6

Graded characters of the simple modules

ϕ L(ϕ1,0) L(ϕ1,12) L(ϕ1,24) L(ϕ1,36) L(ϕ1,48) L(ϕ2,1) L(ϕ2,7) L(ϕ2,13') L(ϕ2,19') L(ϕ2,13'') L(ϕ2,19'') L(ϕ2,25') L(ϕ2,25'') L(ϕ2,31) L(ϕ2,37) L(ϕ3,2) L(ϕ3,6) L(ϕ3,10') L(ϕ3,10'') L(ϕ3,14') L(ϕ3,18') L(ϕ3,14'') L(ϕ3,18'') L(ϕ3,22) L(ϕ3,26) L(ϕ4,15) L(ϕ4,17) L(ϕ4,9) L(ϕ4,11) L(ϕ4,3) L(ϕ4,20) L(ϕ4,12) L(ϕ4,14) L(ϕ4,6) L(ϕ4,8) L(ϕ5,12) L(ϕ5,4) L(ϕ5,16) L(ϕ5,8) L(ϕ5,10) L(ϕ6,5) L(ϕ6,7) L(ϕ6,9) L(ϕ6,11) L(ϕ6,13)
ϕ1,0 1 t12 t24 t36 t48 t t7 t13 t19 t13 t19 t25 t25 t31 t37 t2 t6 t10 t10 t14 t18 t14 t18 t22 t26 t15 0 t9 0 t3 0 t12 0 t6 0 0 t4 0 0 0 t5 t7 t9 t11 t13
ϕ1,12 t48 1 t12 t24 t36 t19 t25 t31 t37 t t7 t13 t13 t19 t25 t10 t14 t18 t18 t22 t26 t2 t6 t10 t14 t3 t15 0 t9 0 0 0 t12 0 t6 0 0 t4 0 0 t13 t5 t7 t9 t11
ϕ1,24 t36 t48 1 t12 t24 t37 t13 t19 t25 t19 t25 t31 t t7 t13 t18 t22 t26 t6 t10 t14 t10 t14 t18 t2 0 t3 t15 0 t9 t6 0 0 t12 0 0 0 0 t4 0 t11 t13 t5 t7 t9
ϕ1,36 t24 t36 t48 1 t12 t25 t31 t7 t13 t37 t13 t19 t19 t25 t t26 t10 t14 t14 t18 t2 t18 t22 t6 t10 t9 0 t3 t15 0 0 t6 0 0 t12 0 0 0 0 t4 t9 t11 t13 t5 t7
ϕ1,48 t12 t24 t36 t48 1 t13 t19 t25 t t25 t31 t7 t37 t13 t19 t14 t18 t2 t22 t6 t10 t26 t10 t14 t18 0 t9 0 t3 t15 t12 0 t6 0 0 t4 0 0 0 0 t7 t9 t11 t13 t5
ϕ2,1 t19 + t29 t + t11 t13 + t23 t25 + t35 t37 + t47 1 + t20 t6 + t26 t12 + t32 t18 + t38 t2 + t12 t8 + t18 t14 + t24 t14 + t24 t20 + t30 t26 + t36 t + t11 t5 + t15 t9 + t19 t9 + t19 t13 + t23 t17 + t27 t3 + t13 t7 + t17 t11 + t21 t15 + t25 t4 + t14 t16 t8 t10 t2 0 t11 t13 t5 t7 0 t3 t5 0 0 t4 + t14 2t6 2t8 2t10 2t12
ϕ2,7 t13 + t23 t25 + t35 t7 + t17 t19 + t29 t31 + t41 t14 + t24 1 + t20 t6 + t26 t12 + t32 t6 + t26 t12 + t32 t18 + t38 t8 + t18 t14 + t24 t20 + t30 t5 + t15 t9 + t19 t13 + t23 t3 + t13 t7 + t17 t11 + t21 t7 + t17 t11 + t21 t15 + t25 t9 + t19 t8 t10 0 t4 + t14 0 t13 t5 t7 + t17 0 t + t11 t5 0 0 0 t3 2t8 2t10 t2 + t12 t4 + t14 t6 + t16
ϕ2,13' t7 + t17 t19 + t29 t31 + t41 t13 + t23 t25 + t35 t8 + t18 t14 + t24 1 + t20 t6 + t26 t20 + t30 t6 + t26 t12 + t32 t12 + t32 t18 + t38 t14 + t24 t9 + t19 t3 + t13 t7 + t17 t7 + t17 t11 + t21 t5 + t15 t11 + t21 t15 + t25 t9 + t19 t13 + t23 0 t4 + t14 0 t8 t10 t7 + t17 0 t + t11 t13 t5 0 0 t3 t5 0 t2 + t12 t4 + t14 t6 + t16 2t8 2t10
ϕ2,19' t + t11 t13 + t23 t25 + t35 t37 + t47 t19 + t29 t2 + t12 t8 + t18 t14 + t24 1 + t20 t14 + t24 t20 + t30 t6 + t26 t26 + t36 t12 + t32 t18 + t38 t3 + t13 t7 + t17 t + t11 t11 + t21 t5 + t15 t9 + t19 t15 + t25 t9 + t19 t13 + t23 t17 + t27 t16 t8 t10 t2 t4 + t14 t11 t13 t5 t7 0 t3 t5 0 0 0 2t6 2t8 2t10 2t12 t4 + t14
ϕ2,13'' t37 + t47 t19 + t29 t + t11 t13 + t23 t25 + t35 t18 + t38 t14 + t24 t20 + t30 t26 + t36 1 + t20 t6 + t26 t12 + t32 t2 + t12 t8 + t18 t14 + t24 t9 + t19 t13 + t23 t17 + t27 t7 + t17 t11 + t21 t15 + t25 t + t11 t5 + t15 t9 + t19 t3 + t13 t2 t4 + t14 t16 t8 t10 t7 0 t11 t13 t5 0 0 t3 t5 0 2t12 t4 + t14 2t6 2t8 2t10
ϕ2,19'' t31 + t41 t13 + t23 t25 + t35 t7 + t17 t19 + t29 t12 + t32 t18 + t38 t14 + t24 t20 + t30 t14 + t24 1 + t20 t6 + t26 t6 + t26 t12 + t32 t8 + t18 t13 + t23 t7 + t17 t11 + t21 t11 + t21 t15 + t25 t9 + t19 t5 + t15 t9 + t19 t3 + t13 t7 + t17 0 t8 t10 0 t4 + t14 t + t11 t13 t5 t7 + t17 0 t3 t5 0 0 0 t6 + t16 2t8 2t10 t2 + t12 t4 + t14
ϕ2,25' t25 + t35 t7 + t17 t19 + t29 t31 + t41 t13 + t23 t6 + t26 t12 + t32 t18 + t38 t14 + t24 t8 + t18 t14 + t24 1 + t20 t20 + t30 t6 + t26 t12 + t32 t7 + t17 t11 + t21 t5 + t15 t15 + t25 t9 + t19 t13 + t23 t9 + t19 t3 + t13 t7 + t17 t11 + t21 t10 0 t4 + t14 0 t8 t5 t7 + t17 0 t + t11 t13 0 0 0 t3 t5 2t10 t2 + t12 t4 + t14 t6 + t16 2t8
ϕ2,25'' t25 + t35 t37 + t47 t19 + t29 t + t11 t13 + t23 t26 + t36 t12 + t32 t8 + t18 t14 + t24 t18 + t38 t14 + t24 t20 + t30 1 + t20 t6 + t26 t2 + t12 t17 + t27 t11 + t21 t15 + t25 t5 + t15 t9 + t19 t3 + t13 t9 + t19 t13 + t23 t7 + t17 t + t11 t10 t2 t4 + t14 t16 t8 t5 t7 0 t11 t13 0 0 0 t3 t5 2t10 2t12 t4 + t14 2t6 2t8
ϕ2,31 t19 + t29 t31 + t41 t13 + t23 t25 + t35 t7 + t17 t20 + t30 t6 + t26 t12 + t32 t8 + t18 t12 + t32 t18 + t38 t14 + t24 t14 + t24 1 + t20 t6 + t26 t11 + t21 t15 + t25 t9 + t19 t9 + t19 t3 + t13 t7 + t17 t13 + t23 t7 + t17 t11 + t21 t5 + t15 t4 + t14 0 t8 t10 0 0 t + t11 t13 t5 t7 + t17 0 t3 t5 0 0 t4 + t14 t6 + t16 2t8 2t10 t2 + t12
ϕ2,37 t13 + t23 t25 + t35 t37 + t47 t19 + t29 t + t11 t14 + t24 t20 + t30 t6 + t26 t2 + t12 t26 + t36 t12 + t32 t8 + t18 t18 + t38 t14 + t24 1 + t20 t15 + t25 t9 + t19 t3 + t13 t13 + t23 t7 + t17 t + t11 t17 + t27 t11 + t21 t5 + t15 t9 + t19 t8 t10 t2 t4 + t14 t16 t13 t5 t7 0 t11 t5 0 0 0 t3 2t8 2t10 2t12 t4 + t14 2t6
ϕ3,2 t18 + t28 + t38 t10 + t20 + t30 t2 + t12 + t22 t14 + t24 + t34 t26 + t36 + t46 t9 + t19 + t29 t5 + t15 + t25 t11 + t21 + t31 t17 + t27 + t37 t + t11 + t21 t7 + t17 + t27 t13 + t23 + t33 t3 + t13 + t23 t9 + t19 + t29 t15 + t25 + t35 1 + t10 + t20 t4 + t14 + t24 t8 + t18 + t28 2t8 + t18 2t12 + t22 2t16 + t26 t2 + 2t12 t6 + 2t16 t10 + 2t20 t4 + t14 + t24 t3 + t13 t5 + t15 t7 + t17 t9 t + t11 t8 t10 t12 t4 + t14 t6 0 t2 t4 t6 0 t3 + 2t13 2t5 + t15 3t7 3t9 3t11
ϕ3,6 t14 + t24 + t34 t6 + t16 + t26 t18 + t28 + t38 t10 + t20 + t30 t22 + t32 + t42 t5 + t15 + t25 t11 + t21 + t31 t7 + t17 + t27 t13 + t23 + t33 t7 + t17 + t27 t3 + t13 + t23 t9 + t19 + t29 t9 + t19 + t29 t15 + t25 + t35 t11 + t21 + t31 t6 + 2t16 1 + t10 + t20 t4 + t14 + t24 t4 + t14 + t24 t8 + t18 + t28 2t12 + t22 2t8 + t18 2t12 + t22 t6 + 2t16 t10 + 2t20 t9 t11 t3 + t13 t5 + t15 t7 t4 + t14 t6 + t16 t8 t10 t2 + t12 t6 0 0 t2 t4 3t9 t + 2t11 t3 + 2t13 2t5 + t15 2t7 + t17
ϕ3,10' t10 + t20 + t30 t2 + t12 + t22 t14 + t24 + t34 t26 + t36 + t46 t18 + t28 + t38 t + t11 + t21 t7 + t17 + t27 t13 + t23 + t33 t9 + t19 + t29 t3 + t13 + t23 t9 + t19 + t29 t5 + t15 + t25 t15 + t25 + t35 t11 + t21 + t31 t17 + t27 + t37 t2 + 2t12 t6 + 2t16 1 + t10 + t20 t10 + 2t20 t4 + t14 + t24 t8 + t18 + t28 t4 + t14 + t24 2t8 + t18 2t12 + t22 2t16 + t26 t5 + t15 t7 + t17 t9 t + t11 t3 + t13 t10 t12 t4 + t14 t6 t8 t2 t4 t6 0 0 2t5 + t15 3t7 3t9 3t11 t3 + 2t13
ϕ3,10'' t10 + t20 + t30 t22 + t32 + t42 t14 + t24 + t34 t6 + t16 + t26 t18 + t28 + t38 t11 + t21 + t31 t7 + t17 + t27 t3 + t13 + t23 t9 + t19 + t29 t13 + t23 + t33 t9 + t19 + t29 t15 + t25 + t35 t5 + t15 + t25 t11 + t21 + t31 t7 + t17 + t27 2t12 + t22 t6 + 2t16 t10 + 2t20 1 + t10 + t20 t4 + t14 + t24 2t8 + t18 t4 + t14 + t24 t8 + t18 + t28 2t12 + t22 t6 + 2t16 t5 + t15 t7 t9 t11 t3 + t13 t10 t2 + t12 t4 + t14 t6 + t16 t8 t2 t4 t6 0 0 2t5 + t15 2t7 + t17 3t9 t + 2t11 t3 + 2t13
ϕ3,14' t6 + t16 + t26 t18 + t28 + t38 t10 + t20 + t30 t22 + t32 + t42 t14 + t24 + t34 t7 + t17 + t27 t3 + t13 + t23 t9 + t19 + t29 t5 + t15 + t25 t9 + t19 + t29 t15 + t25 + t35 t11 + t21 + t31 t11 + t21 + t31 t7 + t17 + t27 t13 + t23 + t33 2t8 + t18 2t12 + t22 t6 + 2t16 t6 + 2t16 1 + t10 + t20 t4 + t14 + t24 t10 + 2t20 t4 + t14 + t24 t8 + t18 + t28 2t12 + t22 t11 t3 + t13 t5 + t15 t7 t9 t6 + t16 t8 t10 t2 + t12 t4 + t14 0 0 t2 t4 t6 t + 2t11 t3 + 2t13 2t5 + t15 2t7 + t17 3t9
ϕ3,18' t2 + t12 + t22 t14 + t24 + t34 t26 + t36 + t46 t18 + t28 + t38 t10 + t20 + t30 t3 + t13 + t23 t9 + t19 + t29 t5 + t15 + t25 t + t11 + t21 t15 + t25 + t35 t11 + t21 + t31 t7 + t17 + t27 t17 + t27 + t37 t13 + t23 + t33 t9 + t19 + t29 t4 + t14 + t24 2t8 + t18 t2 + 2t12 2t12 + t22 t6 + 2t16 1 + t10 + t20 2t16 + t26 t10 + 2t20 t4 + t14 + t24 t8 + t18 + t28 t7 + t17 t9 t + t11 t3 + t13 t5 + t15 t12 t4 + t14 t6 t8 t10 t4 t6 0 0 t2 3t7 3t9 3t11 t3 + 2t13 2t5 + t15
ϕ3,14'' t26 + t36 + t46 t18 + t28 + t38 t10 + t20 + t30 t2 + t12 + t22 t14 + t24 + t34 t17 + t27 + t37 t13 + t23 + t33 t9 + t19 + t29 t15 + t25 + t35 t9 + t19 + t29 t5 + t15 + t25 t11 + t21 + t31 t + t11 + t21 t7 + t17 + t27 t3 + t13 + t23 t8 + t18 + t28 2t12 + t22 2t16 + t26 t6 + 2t16 t10 + 2t20 t4 + t14 + t24 1 + t10 + t20 t4 + t14 + t24 2t8 + t18 t2 + 2t12 t + t11 t3 + t13 t5 + t15 t7 + t17 t9 t6 t8 t10 t12 t4 + t14 0 0 t2 t4 t6 3t11 t3 + 2t13 2t5 + t15 3t7 3t9
ϕ3,18'' t22 + t32 + t42 t14 + t24 + t34 t6 + t16 + t26 t18 + t28 + t38 t10 + t20 + t30 t13 + t23 + t33 t9 + t19 + t29 t15 + t25 + t35 t11 + t21 + t31 t5 + t15 + t25 t11 + t21 + t31 t7 + t17 + t27 t7 + t17 + t27 t3 + t13 + t23 t9 + t19 + t29 t4 + t14 + t24 t8 + t18 + t28 2t12 + t22 2t12 + t22 t6 + 2t16 t10 + 2t20 t6 + 2t16 1 + t10 + t20 t4 + t14 + t24 2t8 + t18 t7 t9 t11 t3 + t13 t5 + t15 t2 + t12 t4 + t14 t6 + t16 t8 t10 t4 t6 0 0 t2 2t7 + t17 3t9 t + 2t11 t3 + 2t13 2t5 + t15
ϕ3,22 t18 + t28 + t38 t10 + t20 + t30 t22 + t32 + t42 t14 + t24 + t34 t6 + t16 + t26 t9 + t19 + t29 t15 + t25 + t35 t11 + t21 + t31 t7 + t17 + t27 t11 + t21 + t31 t7 + t17 + t27 t3 + t13 + t23 t13 + t23 + t33 t9 + t19 + t29 t5 + t15 + t25 t10 + 2t20 t4 + t14 + t24 2t8 + t18 t8 + t18 + t28 2t12 + t22 t6 + 2t16 2t12 + t22 t6 + 2t16 1 + t10 + t20 t4 + t14 + t24 t3 + t13 t5 + t15 t7 t9 t11 t8 t10 t2 + t12 t4 + t14 t6 + t16 0 t2 t4 t6 0 t3 + 2t13 2t5 + t15 2t7 + t17 3t9 t + 2t11
ϕ3,26 t14 + t24 + t34 t26 + t36 + t46 t18 + t28 + t38 t10 + t20 + t30 t2 + t12 + t22 t15 + t25 + t35 t11 + t21 + t31 t7 + t17 + t27 t3 + t13 + t23 t17 + t27 + t37 t13 + t23 + t33 t9 + t19 + t29 t9 + t19 + t29 t5 + t15 + t25 t + t11 + t21 2t16 + t26 t10 + 2t20 t4 + t14 + t24 t4 + t14 + t24 2t8 + t18 t2 + 2t12 t8 + t18 + t28 2t12 + t22 t6 + 2t16 1 + t10 + t20 t9 t + t11 t3 + t13 t5 + t15 t7 + t17 t4 + t14 t6 t8 t10 t12 t6 0 0 t2 t4 3t9 3t11 t3 + 2t13 2t5 + t15 3t7
ϕ4,15 t15 + t25 + t35 + t45 t17 + 2t27 + t37 t9 + t19 + t29 + t39 t11 + 2t21 + t31 t3 + t13 + t23 + t33 2t16 + t26 + t36 t12 + 2t22 + t32 t8 + t18 + 2t28 t4 + t14 + t24 + t34 t8 + t18 + 2t28 t4 + t14 + t24 + t34 2t10 + t20 + t30 2t10 + t20 + t30 t6 + 2t16 + t26 t2 + t12 + 2t22 t7 + 2t17 + t27 2t11 + 2t21 t5 + 2t15 + t25 t5 + 2t15 + t25 2t9 + 2t19 t3 + 2t13 + t23 2t9 + 2t19 t3 + 2t13 + t23 2t7 + 2t17 t + 2t11 + t21 1 + t10 t2 + 2t12 t4 + t14 2t6 + t16 t8 + t18 t5 + t15 t7 2t9 t11 t3 + t13 t7 0 t t3 t5 4t10 t2 + 3t12 2t4 + 2t14 3t6 + t16 4t8
ϕ4,17 t3 + t13 + t23 + t33 t15 + t25 + t35 + t45 t17 + 2t27 + t37 t9 + t19 + t29 + t39 t11 + 2t21 + t31 t4 + t14 + t24 + t34 2t10 + t20 + t30 t6 + 2t16 + t26 t2 + t12 + 2t22 2t16 + t26 + t36 t12 + 2t22 + t32 t8 + t18 + 2t28 t8 + t18 + 2t28 t4 + t14 + t24 + t34 2t10 + t20 + t30 t5 + 2t15 + t25 2t9 + 2t19 t3 + 2t13 + t23 t3 + 2t13 + t23 2t7 + 2t17 t + 2t11 + t21 t7 + 2t17 + t27 2t11 + 2t21 t5 + 2t15 + t25 2t9 + 2t19 t8 + t18 1 + t10 t2 + 2t12 t4 + t14 2t6 + t16 t3 + t13 t5 + t15 t7 2t9 t11 t5 t7 0 t t3 4t8 4t10 t2 + 3t12 2t4 + 2t14 3t6 + t16
ϕ4,9 t11 + 2t21 + t31 t3 + t13 + t23 + t33 t15 + t25 + t35 + t45 t17 + 2t27 + t37 t9 + t19 + t29 + t39 t2 + t12 + 2t22 t8 + t18 + 2t28 t4 + t14 + t24 + t34 2t10 + t20 + t30 t4 + t14 + t24 + t34 2t10 + t20 + t30 t6 + 2t16 + t26 2t16 + t26 + t36 t12 + 2t22 + t32 t8 + t18 + 2t28 t3 + 2t13 + t23 2t7 + 2t17 t + 2t11 + t21 2t11 + 2t21 t5 + 2t15 + t25 2t9 + 2t19 t5 + 2t15 + t25 2t9 + 2t19 t3 + 2t13 + t23 t7 + 2t17 + t27 2t6 + t16 t8 + t18 1 + t10 t2 + 2t12 t4 + t14 t11 t3 + t13 t5 + t15 t7 2t9 t3 t5 t7 0 t 3t6 + t16 4t8 4t10 t2 + 3t12 2t4 + 2t14
ϕ4,11 t9 + t19 + t29 + t39 t11 + 2t21 + t31 t3 + t13 + t23 + t33 t15 + t25 + t35 + t45 t17 + 2t27 + t37 2t10 + t20 + t30 t6 + 2t16 + t26 t12 + 2t22 + t32 t8 + t18 + 2t28 t2 + t12 + 2t22 t8 + t18 + 2t28 t4 + t14 + t24 + t34 t4 + t14 + t24 + t34 2t10 + t20 + t30 2t16 + t26 + t36 t + 2t11 + t21 t5 + 2t15 + t25 2t9 + 2t19 2t9 + 2t19 t3 + 2t13 + t23 t7 + 2t17 + t27 t3 + 2t13 + t23 2t7 + 2t17 2t11 + 2t21 t5 + 2t15 + t25 t4 + t14 2t6 + t16 t8 + t18 1 + t10 t2 + 2t12 2t9 t11 t3 + t13 t5 + t15 t7 t t3 t5 t7 0 2t4 + 2t14 3t6 + t16 4t8 4t10 t2 + 3t12
ϕ4,3 t17 + 2t27 + t37 t9 + t19 + t29 + t39 t11 + 2t21 + t31 t3 + t13 + t23 + t33 t15 + t25 + t35 + t45 t8 + t18 + 2t28 t4 + t14 + t24 + t34 2t10 + t20 + t30 2t16 + t26 + t36 2t10 + t20 + t30 t6 + 2t16 + t26 t12 + 2t22 + t32 t2 + t12 + 2t22 t8 + t18 + 2t28 t4 + t14 + t24 + t34 2t9 + 2t19 t3 + 2t13 + t23 t7 + 2t17 + t27 2t7 + 2t17 2t11 + 2t21 t5 + 2t15 + t25 t + 2t11 + t21 t5 + 2t15 + t25 2t9 + 2t19 t3 + 2t13 + t23 t2 + 2t12 t4 + t14 2t6 + t16 t8 + t18 1 + t10 t7 2t9 t11 t3 + t13 t5 + t15 0 t t3 t5 t7 t2 + 3t12 2t4 + 2t14 3t6 + t16 4t8 4t10
ϕ4,20 t20 + 2t30 + t40 t12 + t22 + t32 + t42 t14 + 2t24 + t34 t6 + t16 + t26 + t36 t8 + 2t18 + t28 t11 + t21 + 2t31 t7 + t17 + t27 + t37 2t13 + t23 + t33 t9 + 2t19 + t29 2t13 + t23 + t33 t9 + 2t19 + t29 t5 + t15 + 2t25 t5 + t15 + 2t25 t + t11 + t21 + t31 2t7 + t17 + t27 2t12 + 2t22 t6 + 2t16 + t26 2t10 + 2t20 2t10 + 2t20 t4 + 2t14 + t24 2t8 + 2t18 t4 + 2t14 + t24 2t8 + 2t18 t2 + 2t12 + t22 2t6 + 2t16 t5 + t15 t7 2t9 t11 t3 + t13 1 + t10 t2 + 2t12 t4 + t14 2t6 + t16 t8 + t18 t2 2t4 t6 0 0 2t5 + 2t15 3t7 + t17 4t9 t + 3t11 2t3 + 2t13
ϕ4,12 t8 + 2t18 + t28 t20 + 2t30 + t40 t12 + t22 + t32 + t42 t14 + 2t24 + t34 t6 + t16 + t26 + t36 t9 + 2t19 + t29 t5 + t15 + 2t25 t + t11 + t21 + t31 2t7 + t17 + t27 t11 + t21 + 2t31 t7 + t17 + t27 + t37 2t13 + t23 + t33 2t13 + t23 + t33 t9 + 2t19 + t29 t5 + t15 + 2t25 2t10 + 2t20 t4 + 2t14 + t24 2t8 + 2t18 2t8 + 2t18 t2 + 2t12 + t22 2t6 + 2t16 2t12 + 2t22 t6 + 2t16 + t26 2t10 + 2t20 t4 + 2t14 + t24 t3 + t13 t5 + t15 t7 2t9 t11 t8 + t18 1 + t10 t2 + 2t12 t4 + t14 2t6 + t16 0 t2 2t4 t6 0 2t3 + 2t13 2t5 + 2t15 3t7 + t17 4t9 t + 3t11
ϕ4,14 t6 + t16 + t26 + t36 t8 + 2t18 + t28 t20 + 2t30 + t40 t12 + t22 + t32 + t42 t14 + 2t24 + t34 2t7 + t17 + t27 2t13 + t23 + t33 t9 + 2t19 + t29 t5 + t15 + 2t25 t9 + 2t19 + t29 t5 + t15 + 2t25 t + t11 + t21 + t31 t11 + t21 + 2t31 t7 + t17 + t27 + t37 2t13 + t23 + t33 2t8 + 2t18 t2 + 2t12 + t22 2t6 + 2t16 t6 + 2t16 + t26 2t10 + 2t20 t4 + 2t14 + t24 2t10 + 2t20 t4 + 2t14 + t24 2t8 + 2t18 2t12 + 2t22 t11 t3 + t13 t5 + t15 t7 2t9 2t6 + t16 t8 + t18 1 + t10 t2 + 2t12 t4 + t14 0 0 t2 2t4 t6 t + 3t11 2t3 + 2t13 2t5 + 2t15 3t7 + t17 4t9
ϕ4,6 t14 + 2t24 + t34 t6 + t16 + t26 + t36 t8 + 2t18 + t28 t20 + 2t30 + t40 t12 + t22 + t32 + t42 t5 + t15 + 2t25 t + t11 + t21 + t31 t7 + t17 + t27 + t37 2t13 + t23 + t33 2t7 + t17 + t27 2t13 + t23 + t33 t9 + 2t19 + t29 t9 + 2t19 + t29 t5 + t15 + 2t25 t11 + t21 + 2t31 2t6 + 2t16 2t10 + 2t20 t4 + 2t14 + t24 t4 + 2t14 + t24 2t8 + 2t18 2t12 + 2t22 2t8 + 2t18 t2 + 2t12 + t22 t6 + 2t16 + t26 2t10 + 2t20 2t9 t11 t3 + t13 t5 + t15 t7 t4 + t14 2t6 + t16 t8 + t18 1 + t10 t2 + 2t12 t6 0 0 t2 2t4 4t9 t + 3t11 2t3 + 2t13 2t5 + 2t15 3t7 + t17
ϕ4,8 t12 + t22 + t32 + t42 t14 + 2t24 + t34 t6 + t16 + t26 + t36 t8 + 2t18 + t28 t20 + 2t30 + t40 2t13 + t23 + t33 t9 + 2t19 + t29 t5 + t15 + 2t25 t11 + t21 + 2t31 t5 + t15 + 2t25 t + t11 + t21 + t31 t7 + t17 + t27 + t37 2t7 + t17 + t27 2t13 + t23 + t33 t9 + 2t19 + t29 t4 + 2t14 + t24 2t8 + 2t18 2t12 + 2t22 t2 + 2t12 + t22 t6 + 2t16 + t26 2t10 + 2t20 2t6 + 2t16 2t10 + 2t20 t4 + 2t14 + t24 2t8 + 2t18 t7 2t9 t11 t3 + t13 t5 + t15 t2 + 2t12 t4 + t14 2t6 + t16 t8 + t18 1 + t10 2t4 t6 0 0 t2 3t7 + t17 4t9 t + 3t11 2t3 + 2t13 2t5 + 2t15
ϕ5,12 t8 + t18 + 2t28 + t38 t10 + 2t20 + t30 + t40 t12 + 2t22 + 2t32 t4 + t14 + t24 + t34 + t44 2t16 + 2t26 + t36 2t9 + t19 + 2t29 t5 + 2t15 + t25 + t35 2t11 + 2t21 + t31 t7 + 2t17 + 2t27 2t11 + 2t21 + t31 t7 + 2t17 + 2t27 t3 + t13 + 2t23 + t33 t3 + t13 + 2t23 + t33 2t9 + t19 + 2t29 t5 + 2t15 + t25 + t35 3t10 + 2t20 t4 + 3t14 + t24 2t8 + 3t18 2t8 + 3t18 t2 + 2t12 + 2t22 2t6 + 2t16 + t26 t2 + 2t12 + 2t22 2t6 + 2t16 + t26 3t10 + 2t20 t4 + 3t14 + t24 t3 + 2t13 2t5 + t15 2t7 + t17 t9 t + 2t11 2t8 2t10 t2 + t12 2t4 + 2t14 t6 + t16 1 t2 t4 t6 t8 2t3 + 3t13 3t5 + 2t15 4t7 + t17 5t9 t + 4t11
ϕ5,4 2t16 + 2t26 + t36 t8 + t18 + 2t28 + t38 t10 + 2t20 + t30 + t40 t12 + 2t22 + 2t32 t4 + t14 + t24 + t34 + t44 t7 + 2t17 + 2t27 t3 + t13 + 2t23 + t33 2t9 + t19 + 2t29 t5 + 2t15 + t25 + t35 2t9 + t19 + 2t29 t5 + 2t15 + t25 + t35 2t11 + 2t21 + t31 2t11 + 2t21 + t31 t7 + 2t17 + 2t27 t3 + t13 + 2t23 + t33 2t8 + 3t18 t2 + 2t12 + 2t22 2t6 + 2t16 + t26 2t6 + 2t16 + t26 3t10 + 2t20 t4 + 3t14 + t24 3t10 + 2t20 t4 + 3t14 + t24 2t8 + 3t18 t2 + 2t12 + 2t22 t + 2t11 t3 + 2t13 2t5 + t15 2t7 + t17 t9 t6 + t16 2t8 2t10 t2 + t12 2t4 + 2t14 t8 1 t2 t4 t6 t + 4t11 2t3 + 3t13 3t5 + 2t15 4t7 + t17 5t9
ϕ5,16 t4 + t14 + t24 + t34 + t44 2t16 + 2t26 + t36 t8 + t18 + 2t28 + t38 t10 + 2t20 + t30 + t40 t12 + 2t22 + 2t32 t5 + 2t15 + t25 + t35 2t11 + 2t21 + t31 t7 + 2t17 + 2t27 t3 + t13 + 2t23 + t33 t7 + 2t17 + 2t27 t3 + t13 + 2t23 + t33 2t9 + t19 + 2t29 2t9 + t19 + 2t29 t5 + 2t15 + t25 + t35 2t11 + 2t21 + t31 2t6 + 2t16 + t26 3t10 + 2t20 t4 + 3t14 + t24 t4 + 3t14 + t24 2t8 + 3t18 t2 + 2t12 + 2t22 2t8 + 3t18 t2 + 2t12 + 2t22 2t6 + 2t16 + t26 3t10 + 2t20 t9 t + 2t11 t3 + 2t13 2t5 + t15 2t7 + t17 2t4 + 2t14 t6 + t16 2t8 2t10 t2 + t12 t6 t8 1 t2 t4 5t9 t + 4t11 2t3 + 3t13 3t5 + 2t15 4t7 + t17
ϕ5,8 t12 + 2t22 + 2t32 t4 + t14 + t24 + t34 + t44 2t16 + 2t26 + t36 t8 + t18 + 2t28 + t38 t10 + 2t20 + t30 + t40 t3 + t13 + 2t23 + t33 2t9 + t19 + 2t29 t5 + 2t15 + t25 + t35 2t11 + 2t21 + t31 t5 + 2t15 + t25 + t35 2t11 + 2t21 + t31 t7 + 2t17 + 2t27 t7 + 2t17 + 2t27 t3 + t13 + 2t23 + t33 2t9 + t19 + 2t29 t4 + 3t14 + t24 2t8 + 3t18 t2 + 2t12 + 2t22 t2 + 2t12 + 2t22 2t6 + 2t16 + t26 3t10 + 2t20 2t6 + 2t16 + t26 3t10 + 2t20 t4 + 3t14 + t24 2t8 + 3t18 2t7 + t17 t9 t + 2t11 t3 + 2t13 2t5 + t15 t2 + t12 2t4 + 2t14 t6 + t16 2t8 2t10 t4 t6 t8 1 t2 4t7 + t17 5t9 t + 4t11 2t3 + 3t13 3t5 + 2t15
ϕ5,10 t10 + 2t20 + t30 + t40 t12 + 2t22 + 2t32 t4 + t14 + t24 + t34 + t44 2t16 + 2t26 + t36 t8 + t18 + 2t28 + t38 2t11 + 2t21 + t31 t7 + 2t17 + 2t27 t3 + t13 + 2t23 + t33 2t9 + t19 + 2t29 t3 + t13 + 2t23 + t33 2t9 + t19 + 2t29 t5 + 2t15 + t25 + t35 t5 + 2t15 + t25 + t35 2t11 + 2t21 + t31 t7 + 2t17 + 2t27 t2 + 2t12 + 2t22 2t6 + 2t16 + t26 3t10 + 2t20 3t10 + 2t20 t4 + 3t14 + t24 2t8 + 3t18 t4 + 3t14 + t24 2t8 + 3t18 t2 + 2t12 + 2t22 2t6 + 2t16 + t26 2t5 + t15 2t7 + t17 t9 t + 2t11 t3 + 2t13 2t10 t2 + t12 2t4 + 2t14 t6 + t16 2t8 t2 t4 t6 t8 1 3t5 + 2t15 4t7 + t17 5t9 t + 4t11 2t3 + 3t13
ϕ6,5 t5 + 2t15 + 2t25 + t35 t7 + 2t17 + 2t27 + t37 t9 + 2t19 + 2t29 + t39 t11 + 2t21 + 2t31 + t41 t13 + 2t23 + 2t33 + t43 2t6 + 2t16 + 2t26 t2 + 2t12 + 2t22 + t32 2t8 + 2t18 + 2t28 t4 + 2t14 + 2t24 + t34 2t8 + 2t18 + 2t28 t4 + 2t14 + 2t24 + t34 2t10 + 2t20 + 2t30 2t10 + 2t20 + 2t30 t6 + 2t16 + 2t26 + t36 2t12 + 2t22 + 2t32 3t7 + 3t17 t + 3t11 + 2t21 2t5 + 3t15 + t25 2t5 + 3t15 + t25 3t9 + 3t19 t3 + 3t13 + 2t23 3t9 + 3t19 t3 + 3t13 + 2t23 2t7 + 3t17 + t27 3t11 + 3t21 2t10 t2 + 2t12 2t4 + 2t14 2t6 + t16 2t8 2t5 + 2t15 2t7 + t17 2t9 t + 2t11 2t3 + 2t13 t7 0 t 2t3 2t5 1 + 5t10 2t2 + 4t12 3t4 + 3t14 4t6 + 2t16 5t8 + t18
ϕ6,7 t13 + 2t23 + 2t33 + t43 t5 + 2t15 + 2t25 + t35 t7 + 2t17 + 2t27 + t37 t9 + 2t19 + 2t29 + t39 t11 + 2t21 + 2t31 + t41 t4 + 2t14 + 2t24 + t34 2t10 + 2t20 + 2t30 t6 + 2t16 + 2t26 + t36 2t12 + 2t22 + 2t32 2t6 + 2t16 + 2t26 t2 + 2t12 + 2t22 + t32 2t8 + 2t18 + 2t28 2t8 + 2t18 + 2t28 t4 + 2t14 + 2t24 + t34 2t10 + 2t20 + 2t30 2t5 + 3t15 + t25 3t9 + 3t19 t3 + 3t13 + 2t23 t3 + 3t13 + 2t23 2t7 + 3t17 + t27 3t11 + 3t21 3t7 + 3t17 t + 3t11 + 2t21 2t5 + 3t15 + t25 3t9 + 3t19 2t8 2t10 t2 + 2t12 2t4 + 2t14 2t6 + t16 2t3 + 2t13 2t5 + 2t15 2t7 + t17 2t9 t + 2t11 2t5 t7 0 t 2t3 5t8 + t18 1 + 5t10 2t2 + 4t12 3t4 + 3t14 4t6 + 2t16
ϕ6,9 t11 + 2t21 + 2t31 + t41 t13 + 2t23 + 2t33 + t43 t5 + 2t15 + 2t25 + t35 t7 + 2t17 + 2t27 + t37 t9 + 2t19 + 2t29 + t39 2t12 + 2t22 + 2t32 2t8 + 2t18 + 2t28 t4 + 2t14 + 2t24 + t34 2t10 + 2t20 + 2t30 t4 + 2t14 + 2t24 + t34 2t10 + 2t20 + 2t30 t6 + 2t16 + 2t26 + t36 2t6 + 2t16 + 2t26 t2 + 2t12 + 2t22 + t32 2t8 + 2t18 + 2t28 t3 + 3t13 + 2t23 2t7 + 3t17 + t27 3t11 + 3t21 t + 3t11 + 2t21 2t5 + 3t15 + t25 3t9 + 3t19 2t5 + 3t15 + t25 3t9 + 3t19 t3 + 3t13 + 2t23 3t7 + 3t17 2t6 + t16 2t8 2t10 t2 + 2t12 2t4 + 2t14 t + 2t11 2t3 + 2t13 2t5 + 2t15 2t7 + t17 2t9 2t3 2t5 t7 0 t 4t6 + 2t16 5t8 + t18 1 + 5t10 2t2 + 4t12 3t4 + 3t14
ϕ6,11 t9 + 2t19 + 2t29 + t39 t11 + 2t21 + 2t31 + t41 t13 + 2t23 + 2t33 + t43 t5 + 2t15 + 2t25 + t35 t7 + 2t17 + 2t27 + t37 2t10 + 2t20 + 2t30 t6 + 2t16 + 2t26 + t36 t2 + 2t12 + 2t22 + t32 2t8 + 2t18 + 2t28 2t12 + 2t22 + 2t32 2t8 + 2t18 + 2t28 t4 + 2t14 + 2t24 + t34 t4 + 2t14 + 2t24 + t34 2t10 + 2t20 + 2t30 2t6 + 2t16 + 2t26 3t11 + 3t21 2t5 + 3t15 + t25 3t9 + 3t19 3t9 + 3t19 t3 + 3t13 + 2t23 3t7 + 3t17 t3 + 3t13 + 2t23 2t7 + 3t17 + t27 t + 3t11 + 2t21 2t5 + 3t15 + t25 2t4 + 2t14 2t6 + t16 2t8 2t10 t2 + 2t12 2t9 t + 2t11 2t3 + 2t13 2t5 + 2t15 2t7 + t17 t 2t3 2t5 t7 0 3t4 + 3t14 4t6 + 2t16 5t8 + t18 1 + 5t10 2t2 + 4t12
ϕ6,13 t7 + 2t17 + 2t27 + t37 t9 + 2t19 + 2t29 + t39 t11 + 2t21 + 2t31 + t41 t13 + 2t23 + 2t33 + t43 t5 + 2t15 + 2t25 + t35 2t8 + 2t18 + 2t28 t4 + 2t14 + 2t24 + t34 2t10 + 2t20 + 2t30 2t6 + 2t16 + 2t26 2t10 + 2t20 + 2t30 t6 + 2t16 + 2t26 + t36 t2 + 2t12 + 2t22 + t32 2t12 + 2t22 + 2t32 2t8 + 2t18 + 2t28 t4 + 2t14 + 2t24 + t34 3t9 + 3t19 t3 + 3t13 + 2t23 3t7 + 3t17 2t7 + 3t17 + t27 t + 3t11 + 2t21 2t5 + 3t15 + t25 3t11 + 3t21 2t5 + 3t15 + t25 3t9 + 3t19 t3 + 3t13 + 2t23 t2 + 2t12 2t4 + 2t14 2t6 + t16 2t8 2t10 2t7 + t17 2t9 t + 2t11 2t3 + 2t13 2t5 + 2t15 0 t 2t3 2t5 t7 2t2 + 4t12 3t4 + 3t14 4t6 + 2t16 5t8 + t18 1 + 5t10

Exceptional hyperplanes

Unknown